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  24 <a name="special_function_error_rates_rep"></a>Special Function Error Rates Report</h2></div>
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  26 <a name="special_function_error_rates_rep.legal"></a><p>
  27         Distributed under the Boost Software License, Version 1.0. (See accompanying
  28         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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  34 <div class="toc">
  35 <p><b>Table of Contents</b></p>
  36 <dl>
  37 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta">beta</a></span></dt>
  38 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta_incomplete_">beta
  39     (incomplete)</a></span></dt>
  40 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_betac">betac</a></span></dt>
  41 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_binomial_coefficient">binomial_coefficient</a></span></dt>
  42 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_boost_math_powm1">boost::math::powm1</a></span></dt>
  43 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cbrt">cbrt</a></span></dt>
  44 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cos_pi">cos_pi</a></span></dt>
  45 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i">cyl_bessel_i</a></span></dt>
  46 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_">cyl_bessel_i
  47     (integer orders)</a></span></dt>
  48 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime">cyl_bessel_i_prime</a></span></dt>
  49 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_">cyl_bessel_i_prime
  50     (integer orders)</a></span></dt>
  51 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j">cyl_bessel_j</a></span></dt>
  52 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_">cyl_bessel_j
  53     (integer orders)</a></span></dt>
  54 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime">cyl_bessel_j_prime</a></span></dt>
  55 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_">cyl_bessel_j_prime
  56     (integer orders)</a></span></dt>
  57 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k">cyl_bessel_k</a></span></dt>
  58 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_">cyl_bessel_k
  59     (integer orders)</a></span></dt>
  60 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime">cyl_bessel_k_prime</a></span></dt>
  61 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_">cyl_bessel_k_prime
  62     (integer orders)</a></span></dt>
  63 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann">cyl_neumann</a></span></dt>
  64 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_">cyl_neumann
  65     (integer orders)</a></span></dt>
  66 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime">cyl_neumann_prime</a></span></dt>
  67 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_">cyl_neumann_prime
  68     (integer orders)</a></span></dt>
  69 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_digamma">digamma</a></span></dt>
  70 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1">ellint_1</a></span></dt>
  71 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1_complete_">ellint_1
  72     (complete)</a></span></dt>
  73 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2">ellint_2</a></span></dt>
  74 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2_complete_">ellint_2
  75     (complete)</a></span></dt>
  76 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3">ellint_3</a></span></dt>
  77 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3_complete_">ellint_3
  78     (complete)</a></span></dt>
  79 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d">ellint_d</a></span></dt>
  80 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d_complete_">ellint_d
  81     (complete)</a></span></dt>
  82 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rc">ellint_rc</a></span></dt>
  83 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rd">ellint_rd</a></span></dt>
  84 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rf">ellint_rf</a></span></dt>
  85 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rg">ellint_rg</a></span></dt>
  86 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rj">ellint_rj</a></span></dt>
  87 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf">erf</a></span></dt>
  88 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf_inv">erf_inv</a></span></dt>
  89 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc">erfc</a></span></dt>
  90 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc_inv">erfc_inv</a></span></dt>
  91 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_Ei_">expint
  92     (Ei)</a></span></dt>
  93 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_En_">expint
  94     (En)</a></span></dt>
  95 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expm1">expm1</a></span></dt>
  96 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p">gamma_p</a></span></dt>
  97 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inv">gamma_p_inv</a></span></dt>
  98 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inva">gamma_p_inva</a></span></dt>
  99 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q">gamma_q</a></span></dt>
 100 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inv">gamma_q_inv</a></span></dt>
 101 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inva">gamma_q_inva</a></span></dt>
 102 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_hermite">hermite</a></span></dt>
 103 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_heuman_lambda">heuman_lambda</a></span></dt>
 104 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta">ibeta</a></span></dt>
 105 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inv">ibeta_inv</a></span></dt>
 106 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inva">ibeta_inva</a></span></dt>
 107 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_invb">ibeta_invb</a></span></dt>
 108 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac">ibetac</a></span></dt>
 109 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inv">ibetac_inv</a></span></dt>
 110 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inva">ibetac_inva</a></span></dt>
 111 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_invb">ibetac_invb</a></span></dt>
 112 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_cn">jacobi_cn</a></span></dt>
 113 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_dn">jacobi_dn</a></span></dt>
 114 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_sn">jacobi_sn</a></span></dt>
 115 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_zeta">jacobi_zeta</a></span></dt>
 116 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_">laguerre(n,
 117     m, x)</a></span></dt>
 118 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_x_">laguerre(n,
 119     x)</a></span></dt>
 120 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p">legendre_p</a></span></dt>
 121 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p_associated_">legendre_p
 122     (associated)</a></span></dt>
 123 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_q">legendre_q</a></span></dt>
 124 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_lgamma">lgamma</a></span></dt>
 125 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_log1p">log1p</a></span></dt>
 126 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF">non
 127     central beta CDF</a></span></dt>
 128 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement">non
 129     central beta CDF complement</a></span></dt>
 130 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF">non
 131     central chi squared CDF</a></span></dt>
 132 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement">non
 133     central chi squared CDF complement</a></span></dt>
 134 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF">non
 135     central t CDF</a></span></dt>
 136 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement">non
 137     central t CDF complement</a></span></dt>
 138 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_owens_t">owens_t</a></span></dt>
 139 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_polygamma">polygamma</a></span></dt>
 140 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_powm1">powm1</a></span></dt>
 141 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sin_pi">sin_pi</a></span></dt>
 142 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel">sph_bessel</a></span></dt>
 143 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel_prime">sph_bessel_prime</a></span></dt>
 144 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann">sph_neumann</a></span></dt>
 145 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann_prime">sph_neumann_prime</a></span></dt>
 146 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i">spherical_harmonic_i</a></span></dt>
 147 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r">spherical_harmonic_r</a></span></dt>
 148 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sqrt1pm1">sqrt1pm1</a></span></dt>
 149 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma">tgamma</a></span></dt>
 150 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma1pm1">tgamma1pm1</a></span></dt>
 151 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio">tgamma_delta_ratio</a></span></dt>
 152 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_">tgamma
 153     (incomplete)</a></span></dt>
 154 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_lower">tgamma_lower</a></span></dt>
 155 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_ratio">tgamma_ratio</a></span></dt>
 156 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_trigamma">trigamma</a></span></dt>
 157 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_zeta">zeta</a></span></dt>
 158 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.error_logs">Error Logs</a></span></dt>
 159 <dt><span class="section"><a href="index.html#special_function_error_rates_rep.all_the_tables">Tables</a></span></dt>
 160 </dl>
 161 </div>
 162 <div class="section">
 163 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 164 <a name="special_function_error_rates_rep.section_beta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta" title="beta">beta</a>
 165 </h2></div></div></div>
 166 <div class="table">
 167 <a name="special_function_error_rates_rep.section_beta.table_beta"></a><p class="title"><b>Table&#160;1.&#160;Error rates for beta</b></p>
 168 <div class="table-contents"><table class="table" summary="Error rates for beta">
 169 <colgroup>
 170 <col>
 171 <col>
 172 <col>
 173 <col>
 174 <col>
 175 </colgroup>
 176 <thead><tr>
 177 <th>
 178             </th>
 179 <th>
 180               <p>
 181                 GNU C++ version 7.1.0<br> linux<br> double
 182               </p>
 183             </th>
 184 <th>
 185               <p>
 186                 GNU C++ version 7.1.0<br> linux<br> long double
 187               </p>
 188             </th>
 189 <th>
 190               <p>
 191                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
 192               </p>
 193             </th>
 194 <th>
 195               <p>
 196                 Microsoft Visual C++ version 14.1<br> Win32<br> double
 197               </p>
 198             </th>
 199 </tr></thead>
 200 <tbody>
 201 <tr>
 202 <td>
 203               <p>
 204                 Beta Function: Small Values
 205               </p>
 206             </td>
 207 <td>
 208               <p>
 209                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 210                 2.1:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And
 211                 other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 212                 Max = 1.14&#949; (Mean = 0.574&#949;))
 213               </p>
 214             </td>
 215 <td>
 216               <p>
 217                 <span class="blue">Max = 2.86&#949; (Mean = 1.22&#949;)</span><br> <br>
 218                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 364&#949; (Mean = 76.2&#949;))
 219               </p>
 220             </td>
 221 <td>
 222               <p>
 223                 <span class="blue">Max = 2.86&#949; (Mean = 1.22&#949;)</span>
 224               </p>
 225             </td>
 226 <td>
 227               <p>
 228                 <span class="blue">Max = 2.23&#949; (Mean = 1.14&#949;)</span>
 229               </p>
 230             </td>
 231 </tr>
 232 <tr>
 233 <td>
 234               <p>
 235                 Beta Function: Medium Values
 236               </p>
 237             </td>
 238 <td>
 239               <p>
 240                 <span class="blue">Max = 0.978&#949; (Mean = 0.0595&#949;)</span><br> <br>
 241                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03&#949; (Mean = 238&#949;))<br>
 242                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03&#949; (Mean = 265&#949;))
 243               </p>
 244             </td>
 245 <td>
 246               <p>
 247                 <span class="blue">Max = 61.4&#949; (Mean = 19.4&#949;)</span><br> <br>
 248                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.07e+03&#949; (Mean = 264&#949;))
 249               </p>
 250             </td>
 251 <td>
 252               <p>
 253                 <span class="blue">Max = 107&#949; (Mean = 24.5&#949;)</span>
 254               </p>
 255             </td>
 256 <td>
 257               <p>
 258                 <span class="blue">Max = 96.5&#949; (Mean = 22.4&#949;)</span>
 259               </p>
 260             </td>
 261 </tr>
 262 <tr>
 263 <td>
 264               <p>
 265                 Beta Function: Divergent Values
 266               </p>
 267             </td>
 268 <td>
 269               <p>
 270                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 271                 2.1:</em></span> Max = 12.1&#949; (Mean = 1.99&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 272                 Max = 176&#949; (Mean = 28&#949;))
 273               </p>
 274             </td>
 275 <td>
 276               <p>
 277                 <span class="blue">Max = 8.99&#949; (Mean = 2.44&#949;)</span><br> <br>
 278                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 128&#949; (Mean = 23.8&#949;))
 279               </p>
 280             </td>
 281 <td>
 282               <p>
 283                 <span class="blue">Max = 18.8&#949; (Mean = 2.71&#949;)</span>
 284               </p>
 285             </td>
 286 <td>
 287               <p>
 288                 <span class="blue">Max = 11.4&#949; (Mean = 2.19&#949;)</span>
 289               </p>
 290             </td>
 291 </tr>
 292 </tbody>
 293 </table></div>
 294 </div>
 295 <br class="table-break">
 296 </div>
 297 <div class="section">
 298 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 299 <a name="special_function_error_rates_rep.section_beta_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta_incomplete_" title="beta (incomplete)">beta
 300     (incomplete)</a>
 301 </h2></div></div></div>
 302 <div class="table">
 303 <a name="special_function_error_rates_rep.section_beta_incomplete_.table_beta_incomplete_"></a><p class="title"><b>Table&#160;2.&#160;Error rates for beta (incomplete)</b></p>
 304 <div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
 305 <colgroup>
 306 <col>
 307 <col>
 308 <col>
 309 <col>
 310 <col>
 311 </colgroup>
 312 <thead><tr>
 313 <th>
 314             </th>
 315 <th>
 316               <p>
 317                 GNU C++ version 7.1.0<br> linux<br> double
 318               </p>
 319             </th>
 320 <th>
 321               <p>
 322                 GNU C++ version 7.1.0<br> linux<br> long double
 323               </p>
 324             </th>
 325 <th>
 326               <p>
 327                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
 328               </p>
 329             </th>
 330 <th>
 331               <p>
 332                 Microsoft Visual C++ version 14.1<br> Win32<br> double
 333               </p>
 334             </th>
 335 </tr></thead>
 336 <tbody>
 337 <tr>
 338 <td>
 339               <p>
 340                 Incomplete Beta Function: Small Values
 341               </p>
 342             </td>
 343 <td>
 344               <p>
 345                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 346               </p>
 347             </td>
 348 <td>
 349               <p>
 350                 <span class="blue">Max = 11.1&#949; (Mean = 2.32&#949;)</span>
 351               </p>
 352             </td>
 353 <td>
 354               <p>
 355                 <span class="blue">Max = 18.7&#949; (Mean = 3.19&#949;)</span>
 356               </p>
 357             </td>
 358 <td>
 359               <p>
 360                 <span class="blue">Max = 9.94&#949; (Mean = 2.17&#949;)</span>
 361               </p>
 362             </td>
 363 </tr>
 364 <tr>
 365 <td>
 366               <p>
 367                 Incomplete Beta Function: Medium Values
 368               </p>
 369             </td>
 370 <td>
 371               <p>
 372                 <span class="blue">Max = 0.568&#949; (Mean = 0.0254&#949;)</span>
 373               </p>
 374             </td>
 375 <td>
 376               <p>
 377                 <span class="blue">Max = 69.2&#949; (Mean = 13.4&#949;)</span>
 378               </p>
 379             </td>
 380 <td>
 381               <p>
 382                 <span class="blue">Max = 174&#949; (Mean = 25&#949;)</span>
 383               </p>
 384             </td>
 385 <td>
 386               <p>
 387                 <span class="blue">Max = 90&#949; (Mean = 12.7&#949;)</span>
 388               </p>
 389             </td>
 390 </tr>
 391 <tr>
 392 <td>
 393               <p>
 394                 Incomplete Beta Function: Large and Diverse Values
 395               </p>
 396             </td>
 397 <td>
 398               <p>
 399                 <span class="blue">Max = 0.999&#949; (Mean = 0.0325&#949;)</span>
 400               </p>
 401             </td>
 402 <td>
 403               <p>
 404                 <span class="blue">Max = 6.84e+04&#949; (Mean = 2.76e+03&#949;)</span>
 405               </p>
 406             </td>
 407 <td>
 408               <p>
 409                 <span class="blue">Max = 6.86e+04&#949; (Mean = 2.79e+03&#949;)</span>
 410               </p>
 411             </td>
 412 <td>
 413               <p>
 414                 <span class="blue">Max = 633&#949; (Mean = 29.7&#949;)</span>
 415               </p>
 416             </td>
 417 </tr>
 418 <tr>
 419 <td>
 420               <p>
 421                 Incomplete Beta Function: Small Integer Values
 422               </p>
 423             </td>
 424 <td>
 425               <p>
 426                 <span class="blue">Max = 0.786&#949; (Mean = 0.0323&#949;)</span>
 427               </p>
 428             </td>
 429 <td>
 430               <p>
 431                 <span class="blue">Max = 11.6&#949; (Mean = 3.6&#949;)</span>
 432               </p>
 433             </td>
 434 <td>
 435               <p>
 436                 <span class="blue">Max = 51.8&#949; (Mean = 11&#949;)</span>
 437               </p>
 438             </td>
 439 <td>
 440               <p>
 441                 <span class="blue">Max = 26&#949; (Mean = 6.28&#949;)</span>
 442               </p>
 443             </td>
 444 </tr>
 445 </tbody>
 446 </table></div>
 447 </div>
 448 <br class="table-break">
 449 </div>
 450 <div class="section">
 451 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 452 <a name="special_function_error_rates_rep.section_betac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_betac" title="betac">betac</a>
 453 </h2></div></div></div>
 454 <div class="table">
 455 <a name="special_function_error_rates_rep.section_betac.table_betac"></a><p class="title"><b>Table&#160;3.&#160;Error rates for betac</b></p>
 456 <div class="table-contents"><table class="table" summary="Error rates for betac">
 457 <colgroup>
 458 <col>
 459 <col>
 460 <col>
 461 <col>
 462 <col>
 463 </colgroup>
 464 <thead><tr>
 465 <th>
 466             </th>
 467 <th>
 468               <p>
 469                 GNU C++ version 7.1.0<br> linux<br> double
 470               </p>
 471             </th>
 472 <th>
 473               <p>
 474                 GNU C++ version 7.1.0<br> linux<br> long double
 475               </p>
 476             </th>
 477 <th>
 478               <p>
 479                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
 480               </p>
 481             </th>
 482 <th>
 483               <p>
 484                 Microsoft Visual C++ version 14.1<br> Win32<br> double
 485               </p>
 486             </th>
 487 </tr></thead>
 488 <tbody>
 489 <tr>
 490 <td>
 491               <p>
 492                 Incomplete Beta Function: Small Values
 493               </p>
 494             </td>
 495 <td>
 496               <p>
 497                 <span class="blue">Max = 0.676&#949; (Mean = 0.0302&#949;)</span>
 498               </p>
 499             </td>
 500 <td>
 501               <p>
 502                 <span class="blue">Max = 9.92&#949; (Mean = 2.3&#949;)</span>
 503               </p>
 504             </td>
 505 <td>
 506               <p>
 507                 <span class="blue">Max = 11.2&#949; (Mean = 2.94&#949;)</span>
 508               </p>
 509             </td>
 510 <td>
 511               <p>
 512                 <span class="blue">Max = 8.94&#949; (Mean = 2.06&#949;)</span>
 513               </p>
 514             </td>
 515 </tr>
 516 <tr>
 517 <td>
 518               <p>
 519                 Incomplete Beta Function: Medium Values
 520               </p>
 521             </td>
 522 <td>
 523               <p>
 524                 <span class="blue">Max = 0.949&#949; (Mean = 0.098&#949;)</span>
 525               </p>
 526             </td>
 527 <td>
 528               <p>
 529                 <span class="blue">Max = 63.5&#949; (Mean = 13.5&#949;)</span>
 530               </p>
 531             </td>
 532 <td>
 533               <p>
 534                 <span class="blue">Max = 97.6&#949; (Mean = 24.3&#949;)</span>
 535               </p>
 536             </td>
 537 <td>
 538               <p>
 539                 <span class="blue">Max = 90.6&#949; (Mean = 14.8&#949;)</span>
 540               </p>
 541             </td>
 542 </tr>
 543 <tr>
 544 <td>
 545               <p>
 546                 Incomplete Beta Function: Large and Diverse Values
 547               </p>
 548             </td>
 549 <td>
 550               <p>
 551                 <span class="blue">Max = 1.12&#949; (Mean = 0.0458&#949;)</span>
 552               </p>
 553             </td>
 554 <td>
 555               <p>
 556                 <span class="blue">Max = 1.05e+05&#949; (Mean = 5.45e+03&#949;)</span>
 557               </p>
 558             </td>
 559 <td>
 560               <p>
 561                 <span class="blue">Max = 1.04e+05&#949; (Mean = 5.46e+03&#949;)</span>
 562               </p>
 563             </td>
 564 <td>
 565               <p>
 566                 <span class="blue">Max = 3.72e+03&#949; (Mean = 113&#949;)</span>
 567               </p>
 568             </td>
 569 </tr>
 570 <tr>
 571 <td>
 572               <p>
 573                 Incomplete Beta Function: Small Integer Values
 574               </p>
 575             </td>
 576 <td>
 577               <p>
 578                 <span class="blue">Max = 0.586&#949; (Mean = 0.0314&#949;)</span>
 579               </p>
 580             </td>
 581 <td>
 582               <p>
 583                 <span class="blue">Max = 11.1&#949; (Mean = 3.65&#949;)</span>
 584               </p>
 585             </td>
 586 <td>
 587               <p>
 588                 <span class="blue">Max = 103&#949; (Mean = 17.4&#949;)</span>
 589               </p>
 590             </td>
 591 <td>
 592               <p>
 593                 <span class="blue">Max = 26.2&#949; (Mean = 6.36&#949;)</span>
 594               </p>
 595             </td>
 596 </tr>
 597 </tbody>
 598 </table></div>
 599 </div>
 600 <br class="table-break">
 601 </div>
 602 <div class="section">
 603 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 604 <a name="special_function_error_rates_rep.section_binomial_coefficient"></a><a class="link" href="index.html#special_function_error_rates_rep.section_binomial_coefficient" title="binomial_coefficient">binomial_coefficient</a>
 605 </h2></div></div></div>
 606 <div class="table">
 607 <a name="special_function_error_rates_rep.section_binomial_coefficient.table_binomial_coefficient"></a><p class="title"><b>Table&#160;4.&#160;Error rates for binomial_coefficient</b></p>
 608 <div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
 609 <colgroup>
 610 <col>
 611 <col>
 612 <col>
 613 <col>
 614 <col>
 615 </colgroup>
 616 <thead><tr>
 617 <th>
 618             </th>
 619 <th>
 620               <p>
 621                 GNU C++ version 7.1.0<br> linux<br> double
 622               </p>
 623             </th>
 624 <th>
 625               <p>
 626                 GNU C++ version 7.1.0<br> linux<br> long double
 627               </p>
 628             </th>
 629 <th>
 630               <p>
 631                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
 632               </p>
 633             </th>
 634 <th>
 635               <p>
 636                 Microsoft Visual C++ version 14.1<br> Win32<br> double
 637               </p>
 638             </th>
 639 </tr></thead>
 640 <tbody>
 641 <tr>
 642 <td>
 643               <p>
 644                 Binomials: small arguments
 645               </p>
 646             </td>
 647 <td>
 648               <p>
 649                 <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
 650               </p>
 651             </td>
 652 <td>
 653               <p>
 654                 <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
 655               </p>
 656             </td>
 657 <td>
 658               <p>
 659                 <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
 660               </p>
 661             </td>
 662 <td>
 663               <p>
 664                 <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
 665               </p>
 666             </td>
 667 </tr>
 668 <tr>
 669 <td>
 670               <p>
 671                 Binomials: large arguments
 672               </p>
 673             </td>
 674 <td>
 675               <p>
 676                 <span class="blue">Max = 0.939&#949; (Mean = 0.314&#949;)</span>
 677               </p>
 678             </td>
 679 <td>
 680               <p>
 681                 <span class="blue">Max = 26.6&#949; (Mean = 6.13&#949;)</span>
 682               </p>
 683             </td>
 684 <td>
 685               <p>
 686                 <span class="blue">Max = 53.2&#949; (Mean = 10.8&#949;)</span>
 687               </p>
 688             </td>
 689 <td>
 690               <p>
 691                 <span class="blue">Max = 37.2&#949; (Mean = 7.4&#949;)</span>
 692               </p>
 693             </td>
 694 </tr>
 695 </tbody>
 696 </table></div>
 697 </div>
 698 <br class="table-break">
 699 </div>
 700 <div class="section">
 701 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 702 <a name="special_function_error_rates_rep.section_boost_math_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_boost_math_powm1" title="boost::math::powm1">boost::math::powm1</a>
 703 </h2></div></div></div>
 704 <div class="table">
 705 <a name="special_function_error_rates_rep.section_boost_math_powm1.table_boost_math_powm1"></a><p class="title"><b>Table&#160;5.&#160;Error rates for boost::math::powm1</b></p>
 706 <div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1">
 707 <colgroup>
 708 <col>
 709 <col>
 710 <col>
 711 <col>
 712 <col>
 713 </colgroup>
 714 <thead><tr>
 715 <th>
 716             </th>
 717 <th>
 718               <p>
 719                 GNU C++ version 7.1.0<br> linux<br> long double
 720               </p>
 721             </th>
 722 <th>
 723               <p>
 724                 GNU C++ version 7.1.0<br> linux<br> double
 725               </p>
 726             </th>
 727 <th>
 728               <p>
 729                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
 730               </p>
 731             </th>
 732 <th>
 733               <p>
 734                 Microsoft Visual C++ version 14.1<br> Win32<br> double
 735               </p>
 736             </th>
 737 </tr></thead>
 738 <tbody><tr>
 739 <td>
 740               <p>
 741                 powm1
 742               </p>
 743             </td>
 744 <td>
 745               <p>
 746                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.04&#949; (Mean = 0.493&#949;))<br>
 747                 <br> <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span><br>
 748                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.04&#949; (Mean = 0.493&#949;))
 749               </p>
 750             </td>
 751 <td>
 752               <p>
 753                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06&#949; (Mean = 0.425&#949;))<br>
 754                 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06&#949; (Mean = 0.425&#949;))<br>
 755                 <br> <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
 756               </p>
 757             </td>
 758 <td>
 759               <p>
 760                 <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span><br> <br>
 761                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.88&#949; (Mean = 0.49&#949;))
 762               </p>
 763             </td>
 764 <td>
 765               <p>
 766                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.486&#949;))<br>
 767                 <br> <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
 768               </p>
 769             </td>
 770 </tr></tbody>
 771 </table></div>
 772 </div>
 773 <br class="table-break">
 774 </div>
 775 <div class="section">
 776 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 777 <a name="special_function_error_rates_rep.section_cbrt"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cbrt" title="cbrt">cbrt</a>
 778 </h2></div></div></div>
 779 <div class="table">
 780 <a name="special_function_error_rates_rep.section_cbrt.table_cbrt"></a><p class="title"><b>Table&#160;6.&#160;Error rates for cbrt</b></p>
 781 <div class="table-contents"><table class="table" summary="Error rates for cbrt">
 782 <colgroup>
 783 <col>
 784 <col>
 785 <col>
 786 <col>
 787 <col>
 788 </colgroup>
 789 <thead><tr>
 790 <th>
 791             </th>
 792 <th>
 793               <p>
 794                 GNU C++ version 7.1.0<br> linux<br> double
 795               </p>
 796             </th>
 797 <th>
 798               <p>
 799                 GNU C++ version 7.1.0<br> linux<br> long double
 800               </p>
 801             </th>
 802 <th>
 803               <p>
 804                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
 805               </p>
 806             </th>
 807 <th>
 808               <p>
 809                 Microsoft Visual C++ version 14.1<br> Win32<br> double
 810               </p>
 811             </th>
 812 </tr></thead>
 813 <tbody><tr>
 814 <td>
 815               <p>
 816                 cbrt Function
 817               </p>
 818             </td>
 819 <td>
 820               <p>
 821                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 822               </p>
 823             </td>
 824 <td>
 825               <p>
 826                 <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
 827                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))<br>
 828                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
 829               </p>
 830             </td>
 831 <td>
 832               <p>
 833                 <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
 834                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
 835               </p>
 836             </td>
 837 <td>
 838               <p>
 839                 <span class="blue">Max = 1.7&#949; (Mean = 0.565&#949;)</span><br> <br>
 840                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.7&#949; (Mean = 0.565&#949;))
 841               </p>
 842             </td>
 843 </tr></tbody>
 844 </table></div>
 845 </div>
 846 <br class="table-break">
 847 </div>
 848 <div class="section">
 849 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 850 <a name="special_function_error_rates_rep.section_cos_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cos_pi" title="cos_pi">cos_pi</a>
 851 </h2></div></div></div>
 852 <div class="table">
 853 <a name="special_function_error_rates_rep.section_cos_pi.table_cos_pi"></a><p class="title"><b>Table&#160;7.&#160;Error rates for cos_pi</b></p>
 854 <div class="table-contents"><table class="table" summary="Error rates for cos_pi">
 855 <colgroup>
 856 <col>
 857 <col>
 858 <col>
 859 <col>
 860 <col>
 861 </colgroup>
 862 <thead><tr>
 863 <th>
 864             </th>
 865 <th>
 866               <p>
 867                 GNU C++ version 7.1.0<br> linux<br> double
 868               </p>
 869             </th>
 870 <th>
 871               <p>
 872                 GNU C++ version 7.1.0<br> linux<br> long double
 873               </p>
 874             </th>
 875 <th>
 876               <p>
 877                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
 878               </p>
 879             </th>
 880 <th>
 881               <p>
 882                 Microsoft Visual C++ version 14.1<br> Win32<br> double
 883               </p>
 884             </th>
 885 </tr></thead>
 886 <tbody>
 887 <tr>
 888 <td>
 889               <p>
 890                 sin_pi and cos_pi
 891               </p>
 892             </td>
 893 <td>
 894               <p>
 895                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 896               </p>
 897             </td>
 898 <td>
 899               <p>
 900                 <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
 901               </p>
 902             </td>
 903 <td>
 904               <p>
 905                 <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
 906               </p>
 907             </td>
 908 <td>
 909               <p>
 910                 <span class="blue">Max = 0.996&#949; (Mean = 0.284&#949;)</span>
 911               </p>
 912             </td>
 913 </tr>
 914 <tr>
 915 <td>
 916               <p>
 917                 sin_pi and cos_pi near integers and half integers
 918               </p>
 919             </td>
 920 <td>
 921               <p>
 922                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 923               </p>
 924             </td>
 925 <td>
 926               <p>
 927                 <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
 928               </p>
 929             </td>
 930 <td>
 931               <p>
 932                 <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
 933               </p>
 934             </td>
 935 <td>
 936               <p>
 937                 <span class="blue">Max = 0.996&#949; (Mean = 0.298&#949;)</span>
 938               </p>
 939             </td>
 940 </tr>
 941 </tbody>
 942 </table></div>
 943 </div>
 944 <br class="table-break">
 945 </div>
 946 <div class="section">
 947 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
 948 <a name="special_function_error_rates_rep.section_cyl_bessel_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i" title="cyl_bessel_i">cyl_bessel_i</a>
 949 </h2></div></div></div>
 950 <div class="table">
 951 <a name="special_function_error_rates_rep.section_cyl_bessel_i.table_cyl_bessel_i"></a><p class="title"><b>Table&#160;8.&#160;Error rates for cyl_bessel_i</b></p>
 952 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
 953 <colgroup>
 954 <col>
 955 <col>
 956 <col>
 957 <col>
 958 <col>
 959 </colgroup>
 960 <thead><tr>
 961 <th>
 962             </th>
 963 <th>
 964               <p>
 965                 GNU C++ version 7.1.0<br> linux<br> double
 966               </p>
 967             </th>
 968 <th>
 969               <p>
 970                 GNU C++ version 7.1.0<br> linux<br> long double
 971               </p>
 972             </th>
 973 <th>
 974               <p>
 975                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
 976               </p>
 977             </th>
 978 <th>
 979               <p>
 980                 Microsoft Visual C++ version 14.1<br> Win32<br> double
 981               </p>
 982             </th>
 983 </tr></thead>
 984 <tbody>
 985 <tr>
 986 <td>
 987               <p>
 988                 Bessel I0: Mathworld Data
 989               </p>
 990             </td>
 991 <td>
 992               <p>
 993                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 994                 2.1:</em></span> Max = 270&#949; (Mean = 91.6&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And
 995                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
 996                 Max = 1.52&#949; (Mean = 0.622&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And
 997                 other failures.</a>)
 998               </p>
 999             </td>
1000 <td>
1001               <p>
1002                 <span class="blue">Max = 1.95&#949; (Mean = 0.738&#949;)</span><br> <br>
1003                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And
1004                 other failures.</a>)
1005               </p>
1006             </td>
1007 <td>
1008               <p>
1009                 <span class="blue">Max = 1.95&#949; (Mean = 0.661&#949;)</span>
1010               </p>
1011             </td>
1012 <td>
1013               <p>
1014                 <span class="blue">Max = 0.762&#949; (Mean = 0.329&#949;)</span>
1015               </p>
1016             </td>
1017 </tr>
1018 <tr>
1019 <td>
1020               <p>
1021                 Bessel I1: Mathworld Data
1022               </p>
1023             </td>
1024 <td>
1025               <p>
1026                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1027                 2.1:</em></span> Max = 128&#949; (Mean = 41&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And
1028                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1029                 Max = 1.53&#949; (Mean = 0.483&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And
1030                 other failures.</a>)
1031               </p>
1032             </td>
1033 <td>
1034               <p>
1035                 <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span><br> <br>
1036                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And
1037                 other failures.</a>)
1038               </p>
1039             </td>
1040 <td>
1041               <p>
1042                 <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span>
1043               </p>
1044             </td>
1045 <td>
1046               <p>
1047                 <span class="blue">Max = 0.767&#949; (Mean = 0.398&#949;)</span>
1048               </p>
1049             </td>
1050 </tr>
1051 <tr>
1052 <td>
1053               <p>
1054                 Bessel In: Mathworld Data
1055               </p>
1056             </td>
1057 <td>
1058               <p>
1059                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1060                 2.1:</em></span> Max = 2.31&#949; (Mean = 0.838&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And
1061                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1062                 Max = 1.73&#949; (Mean = 0.601&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And
1063                 other failures.</a>)
1064               </p>
1065             </td>
1066 <td>
1067               <p>
1068                 <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
1069                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And
1070                 other failures.</a>)
1071               </p>
1072             </td>
1073 <td>
1074               <p>
1075                 <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
1076               </p>
1077             </td>
1078 <td>
1079               <p>
1080                 <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
1081               </p>
1082             </td>
1083 </tr>
1084 <tr>
1085 <td>
1086               <p>
1087                 Bessel Iv: Mathworld Data
1088               </p>
1089             </td>
1090 <td>
1091               <p>
1092                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1093                 2.1:</em></span> Max = 5.95&#949; (Mean = 2.08&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And
1094                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1095                 Max = 3.53&#949; (Mean = 1.39&#949;))
1096               </p>
1097             </td>
1098 <td>
1099               <p>
1100                 <span class="blue">Max = 4.12&#949; (Mean = 1.85&#949;)</span><br> <br>
1101                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 616&#949; (Mean = 221&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And
1102                 other failures.</a>)
1103               </p>
1104             </td>
1105 <td>
1106               <p>
1107                 <span class="blue">Max = 4.12&#949; (Mean = 1.95&#949;)</span>
1108               </p>
1109             </td>
1110 <td>
1111               <p>
1112                 <span class="blue">Max = 2.97&#949; (Mean = 1.24&#949;)</span>
1113               </p>
1114             </td>
1115 </tr>
1116 <tr>
1117 <td>
1118               <p>
1119                 Bessel In: Random Data
1120               </p>
1121             </td>
1122 <td>
1123               <p>
1124                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1125                 2.1:</em></span> Max = 261&#949; (Mean = 53.2&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And
1126                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1127                 Max = 7.37&#949; (Mean = 2.4&#949;))
1128               </p>
1129             </td>
1130 <td>
1131               <p>
1132                 <span class="blue">Max = 4.62&#949; (Mean = 1.06&#949;)</span><br> <br>
1133                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 645&#949; (Mean = 132&#949;))
1134               </p>
1135             </td>
1136 <td>
1137               <p>
1138                 <span class="blue">Max = 176&#949; (Mean = 39.1&#949;)</span>
1139               </p>
1140             </td>
1141 <td>
1142               <p>
1143                 <span class="blue">Max = 9.67&#949; (Mean = 1.88&#949;)</span>
1144               </p>
1145             </td>
1146 </tr>
1147 <tr>
1148 <td>
1149               <p>
1150                 Bessel Iv: Random Data
1151               </p>
1152             </td>
1153 <td>
1154               <p>
1155                 <span class="blue">Max = 0.661&#949; (Mean = 0.0441&#949;)</span><br> <br>
1156                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03&#949; (Mean = 1.55e+03&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And
1157                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1158                 <span class="red">Max = 4.28e+08&#949; (Mean = 2.85e+07&#949;))</span>
1159               </p>
1160             </td>
1161 <td>
1162               <p>
1163                 <span class="blue">Max = 8.35&#949; (Mean = 1.62&#949;)</span><br> <br>
1164                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.05e+03&#949; (Mean = 224&#949;)
1165                 <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And
1166                 other failures.</a>)
1167               </p>
1168             </td>
1169 <td>
1170               <p>
1171                 <span class="blue">Max = 283&#949; (Mean = 88.4&#949;)</span>
1172               </p>
1173             </td>
1174 <td>
1175               <p>
1176                 <span class="blue">Max = 7.46&#949; (Mean = 1.71&#949;)</span>
1177               </p>
1178             </td>
1179 </tr>
1180 <tr>
1181 <td>
1182               <p>
1183                 Bessel Iv: Mathworld Data (large values)
1184               </p>
1185             </td>
1186 <td>
1187               <p>
1188                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1189                 2.1:</em></span> Max = 37&#949; (Mean = 18&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And
1190                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1191                 <span class="red">Max = 3.77e+168&#949; (Mean = 2.39e+168&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And
1192                 other failures.</a>)</span>
1193               </p>
1194             </td>
1195 <td>
1196               <p>
1197                 <span class="blue">Max = 14.7&#949; (Mean = 6.66&#949;)</span><br> <br>
1198                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 118&#949; (Mean = 57.2&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And
1199                 other failures.</a>)
1200               </p>
1201             </td>
1202 <td>
1203               <p>
1204                 <span class="blue">Max = 14.7&#949; (Mean = 6.59&#949;)</span>
1205               </p>
1206             </td>
1207 <td>
1208               <p>
1209                 <span class="blue">Max = 3.67&#949; (Mean = 1.64&#949;)</span>
1210               </p>
1211             </td>
1212 </tr>
1213 </tbody>
1214 </table></div>
1215 </div>
1216 <br class="table-break">
1217 </div>
1218 <div class="section">
1219 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
1220 <a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_" title="cyl_bessel_i (integer orders)">cyl_bessel_i
1221     (integer orders)</a>
1222 </h2></div></div></div>
1223 <div class="table">
1224 <a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table&#160;9.&#160;Error rates for cyl_bessel_i (integer orders)</b></p>
1225 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
1226 <colgroup>
1227 <col>
1228 <col>
1229 <col>
1230 <col>
1231 <col>
1232 </colgroup>
1233 <thead><tr>
1234 <th>
1235             </th>
1236 <th>
1237               <p>
1238                 GNU C++ version 7.1.0<br> linux<br> double
1239               </p>
1240             </th>
1241 <th>
1242               <p>
1243                 GNU C++ version 7.1.0<br> linux<br> long double
1244               </p>
1245             </th>
1246 <th>
1247               <p>
1248                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
1249               </p>
1250             </th>
1251 <th>
1252               <p>
1253                 Microsoft Visual C++ version 14.1<br> Win32<br> double
1254               </p>
1255             </th>
1256 </tr></thead>
1257 <tbody>
1258 <tr>
1259 <td>
1260               <p>
1261                 Bessel I0: Mathworld Data (Integer Version)
1262               </p>
1263             </td>
1264 <td>
1265               <p>
1266                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1267                 2.1:</em></span> Max = 0.79&#949; (Mean = 0.482&#949;))<br> (<span class="emphasis"><em>Rmath
1268                 3.2.3:</em></span> Max = 1.52&#949; (Mean = 0.622&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And
1269                 other failures.</a>)
1270               </p>
1271             </td>
1272 <td>
1273               <p>
1274                 <span class="blue">Max = 1.95&#949; (Mean = 0.738&#949;)</span><br> <br>
1275                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
1276                 other failures.</a>)
1277               </p>
1278             </td>
1279 <td>
1280               <p>
1281                 <span class="blue">Max = 1.95&#949; (Mean = 0.661&#949;)</span>
1282               </p>
1283             </td>
1284 <td>
1285               <p>
1286                 <span class="blue">Max = 0.762&#949; (Mean = 0.329&#949;)</span>
1287               </p>
1288             </td>
1289 </tr>
1290 <tr>
1291 <td>
1292               <p>
1293                 Bessel I1: Mathworld Data (Integer Version)
1294               </p>
1295             </td>
1296 <td>
1297               <p>
1298                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1299                 2.1:</em></span> Max = 0.82&#949; (Mean = 0.456&#949;))<br> (<span class="emphasis"><em>Rmath
1300                 3.2.3:</em></span> Max = 1.53&#949; (Mean = 0.483&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And
1301                 other failures.</a>)
1302               </p>
1303             </td>
1304 <td>
1305               <p>
1306                 <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span><br> <br>
1307                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
1308                 other failures.</a>)
1309               </p>
1310             </td>
1311 <td>
1312               <p>
1313                 <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span>
1314               </p>
1315             </td>
1316 <td>
1317               <p>
1318                 <span class="blue">Max = 0.767&#949; (Mean = 0.398&#949;)</span>
1319               </p>
1320             </td>
1321 </tr>
1322 <tr>
1323 <td>
1324               <p>
1325                 Bessel In: Mathworld Data (Integer Version)
1326               </p>
1327             </td>
1328 <td>
1329               <p>
1330                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1331                 2.1:</em></span> Max = 5.15&#949; (Mean = 2.13&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And
1332                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1333                 Max = 1.73&#949; (Mean = 0.601&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And
1334                 other failures.</a>)
1335               </p>
1336             </td>
1337 <td>
1338               <p>
1339                 <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
1340                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
1341                 other failures.</a>)
1342               </p>
1343             </td>
1344 <td>
1345               <p>
1346                 <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
1347               </p>
1348             </td>
1349 <td>
1350               <p>
1351                 <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
1352               </p>
1353             </td>
1354 </tr>
1355 </tbody>
1356 </table></div>
1357 </div>
1358 <br class="table-break">
1359 </div>
1360 <div class="section">
1361 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
1362 <a name="special_function_error_rates_rep.section_cyl_bessel_i_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime" title="cyl_bessel_i_prime">cyl_bessel_i_prime</a>
1363 </h2></div></div></div>
1364 <div class="table">
1365 <a name="special_function_error_rates_rep.section_cyl_bessel_i_prime.table_cyl_bessel_i_prime"></a><p class="title"><b>Table&#160;10.&#160;Error rates for cyl_bessel_i_prime</b></p>
1366 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
1367 <colgroup>
1368 <col>
1369 <col>
1370 <col>
1371 <col>
1372 <col>
1373 </colgroup>
1374 <thead><tr>
1375 <th>
1376             </th>
1377 <th>
1378               <p>
1379                 GNU C++ version 7.1.0<br> linux<br> double
1380               </p>
1381             </th>
1382 <th>
1383               <p>
1384                 GNU C++ version 7.1.0<br> linux<br> long double
1385               </p>
1386             </th>
1387 <th>
1388               <p>
1389                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
1390               </p>
1391             </th>
1392 <th>
1393               <p>
1394                 Microsoft Visual C++ version 14.1<br> Win32<br> double
1395               </p>
1396             </th>
1397 </tr></thead>
1398 <tbody>
1399 <tr>
1400 <td>
1401               <p>
1402                 Bessel I'0: Mathworld Data
1403               </p>
1404             </td>
1405 <td>
1406               <p>
1407                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1408               </p>
1409             </td>
1410 <td>
1411               <p>
1412                 <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
1413               </p>
1414             </td>
1415 <td>
1416               <p>
1417                 <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
1418               </p>
1419             </td>
1420 <td>
1421               <p>
1422                 <span class="blue">Max = 0.82&#949; (Mean = 0.354&#949;)</span>
1423               </p>
1424             </td>
1425 </tr>
1426 <tr>
1427 <td>
1428               <p>
1429                 Bessel I'1: Mathworld Data
1430               </p>
1431             </td>
1432 <td>
1433               <p>
1434                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1435               </p>
1436             </td>
1437 <td>
1438               <p>
1439                 <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
1440               </p>
1441             </td>
1442 <td>
1443               <p>
1444                 <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
1445               </p>
1446             </td>
1447 <td>
1448               <p>
1449                 <span class="blue">Max = 1.36&#949; (Mean = 0.782&#949;)</span>
1450               </p>
1451             </td>
1452 </tr>
1453 <tr>
1454 <td>
1455               <p>
1456                 Bessel I'n: Mathworld Data
1457               </p>
1458             </td>
1459 <td>
1460               <p>
1461                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1462               </p>
1463             </td>
1464 <td>
1465               <p>
1466                 <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
1467               </p>
1468             </td>
1469 <td>
1470               <p>
1471                 <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
1472               </p>
1473             </td>
1474 <td>
1475               <p>
1476                 <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
1477               </p>
1478             </td>
1479 </tr>
1480 <tr>
1481 <td>
1482               <p>
1483                 Bessel I'v: Mathworld Data
1484               </p>
1485             </td>
1486 <td>
1487               <p>
1488                 <span class="blue">Max = 1.62&#949; (Mean = 0.512&#949;)</span>
1489               </p>
1490             </td>
1491 <td>
1492               <p>
1493                 <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
1494               </p>
1495             </td>
1496 <td>
1497               <p>
1498                 <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
1499               </p>
1500             </td>
1501 <td>
1502               <p>
1503                 <span class="blue">Max = 3.76e+03&#949; (Mean = 1.19e+03&#949;)</span>
1504               </p>
1505             </td>
1506 </tr>
1507 <tr>
1508 <td>
1509               <p>
1510                 Bessel I'n: Random Data
1511               </p>
1512             </td>
1513 <td>
1514               <p>
1515                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1516               </p>
1517             </td>
1518 <td>
1519               <p>
1520                 <span class="blue">Max = 3.95&#949; (Mean = 1.06&#949;)</span>
1521               </p>
1522             </td>
1523 <td>
1524               <p>
1525                 <span class="blue">Max = 195&#949; (Mean = 37.1&#949;)</span>
1526               </p>
1527             </td>
1528 <td>
1529               <p>
1530                 <span class="blue">Max = 9.85&#949; (Mean = 1.82&#949;)</span>
1531               </p>
1532             </td>
1533 </tr>
1534 <tr>
1535 <td>
1536               <p>
1537                 Bessel I'v: Random Data
1538               </p>
1539             </td>
1540 <td>
1541               <p>
1542                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1543               </p>
1544             </td>
1545 <td>
1546               <p>
1547                 <span class="blue">Max = 14.1&#949; (Mean = 2.93&#949;)</span>
1548               </p>
1549             </td>
1550 <td>
1551               <p>
1552                 <span class="blue">Max = 336&#949; (Mean = 68.5&#949;)</span>
1553               </p>
1554             </td>
1555 <td>
1556               <p>
1557                 <span class="blue">Max = 14&#949; (Mean = 2.5&#949;)</span>
1558               </p>
1559             </td>
1560 </tr>
1561 <tr>
1562 <td>
1563               <p>
1564                 Bessel I'v: Mathworld Data (large values)
1565               </p>
1566             </td>
1567 <td>
1568               <p>
1569                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1570               </p>
1571             </td>
1572 <td>
1573               <p>
1574                 <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
1575               </p>
1576             </td>
1577 <td>
1578               <p>
1579                 <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
1580               </p>
1581             </td>
1582 <td>
1583               <p>
1584                 <span class="blue">Max = 59.5&#949; (Mean = 26.6&#949;)</span>
1585               </p>
1586             </td>
1587 </tr>
1588 </tbody>
1589 </table></div>
1590 </div>
1591 <br class="table-break">
1592 </div>
1593 <div class="section">
1594 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
1595 <a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_" title="cyl_bessel_i_prime (integer orders)">cyl_bessel_i_prime
1596     (integer orders)</a>
1597 </h2></div></div></div>
1598 <div class="table">
1599 <a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table&#160;11.&#160;Error rates for cyl_bessel_i_prime (integer orders)</b></p>
1600 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
1601 <colgroup>
1602 <col>
1603 <col>
1604 <col>
1605 <col>
1606 <col>
1607 </colgroup>
1608 <thead><tr>
1609 <th>
1610             </th>
1611 <th>
1612               <p>
1613                 GNU C++ version 7.1.0<br> linux<br> double
1614               </p>
1615             </th>
1616 <th>
1617               <p>
1618                 GNU C++ version 7.1.0<br> linux<br> long double
1619               </p>
1620             </th>
1621 <th>
1622               <p>
1623                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
1624               </p>
1625             </th>
1626 <th>
1627               <p>
1628                 Microsoft Visual C++ version 14.1<br> Win32<br> double
1629               </p>
1630             </th>
1631 </tr></thead>
1632 <tbody>
1633 <tr>
1634 <td>
1635               <p>
1636                 Bessel I'0: Mathworld Data (Integer Version)
1637               </p>
1638             </td>
1639 <td>
1640               <p>
1641                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1642               </p>
1643             </td>
1644 <td>
1645               <p>
1646                 <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
1647               </p>
1648             </td>
1649 <td>
1650               <p>
1651                 <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
1652               </p>
1653             </td>
1654 <td>
1655               <p>
1656                 <span class="blue">Max = 0.82&#949; (Mean = 0.354&#949;)</span>
1657               </p>
1658             </td>
1659 </tr>
1660 <tr>
1661 <td>
1662               <p>
1663                 Bessel I'1: Mathworld Data (Integer Version)
1664               </p>
1665             </td>
1666 <td>
1667               <p>
1668                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1669               </p>
1670             </td>
1671 <td>
1672               <p>
1673                 <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
1674               </p>
1675             </td>
1676 <td>
1677               <p>
1678                 <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
1679               </p>
1680             </td>
1681 <td>
1682               <p>
1683                 <span class="blue">Max = 1.36&#949; (Mean = 0.782&#949;)</span>
1684               </p>
1685             </td>
1686 </tr>
1687 <tr>
1688 <td>
1689               <p>
1690                 Bessel I'n: Mathworld Data (Integer Version)
1691               </p>
1692             </td>
1693 <td>
1694               <p>
1695                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1696               </p>
1697             </td>
1698 <td>
1699               <p>
1700                 <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
1701               </p>
1702             </td>
1703 <td>
1704               <p>
1705                 <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
1706               </p>
1707             </td>
1708 <td>
1709               <p>
1710                 <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
1711               </p>
1712             </td>
1713 </tr>
1714 </tbody>
1715 </table></div>
1716 </div>
1717 <br class="table-break">
1718 </div>
1719 <div class="section">
1720 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
1721 <a name="special_function_error_rates_rep.section_cyl_bessel_j"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j" title="cyl_bessel_j">cyl_bessel_j</a>
1722 </h2></div></div></div>
1723 <div class="table">
1724 <a name="special_function_error_rates_rep.section_cyl_bessel_j.table_cyl_bessel_j"></a><p class="title"><b>Table&#160;12.&#160;Error rates for cyl_bessel_j</b></p>
1725 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
1726 <colgroup>
1727 <col>
1728 <col>
1729 <col>
1730 <col>
1731 <col>
1732 </colgroup>
1733 <thead><tr>
1734 <th>
1735             </th>
1736 <th>
1737               <p>
1738                 GNU C++ version 7.1.0<br> linux<br> long double
1739               </p>
1740             </th>
1741 <th>
1742               <p>
1743                 GNU C++ version 7.1.0<br> linux<br> double
1744               </p>
1745             </th>
1746 <th>
1747               <p>
1748                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
1749               </p>
1750             </th>
1751 <th>
1752               <p>
1753                 Microsoft Visual C++ version 14.1<br> Win32<br> double
1754               </p>
1755             </th>
1756 </tr></thead>
1757 <tbody>
1758 <tr>
1759 <td>
1760               <p>
1761                 Bessel J0: Mathworld Data
1762               </p>
1763             </td>
1764 <td>
1765               <p>
1766                 <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span><br> <br>
1767                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And
1768                 other failures.</a>)
1769               </p>
1770             </td>
1771 <td>
1772               <p>
1773                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1774                 2.1:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And
1775                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1776                 Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And
1777                 other failures.</a>)
1778               </p>
1779             </td>
1780 <td>
1781               <p>
1782                 <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
1783               </p>
1784             </td>
1785 <td>
1786               <p>
1787                 <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span>
1788               </p>
1789             </td>
1790 </tr>
1791 <tr>
1792 <td>
1793               <p>
1794                 Bessel J0: Mathworld Data (Tricky cases)
1795               </p>
1796             </td>
1797 <td>
1798               <p>
1799                 <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span><br>
1800                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean =
1801                 1.96e+08&#949;))
1802               </p>
1803             </td>
1804 <td>
1805               <p>
1806                 <span class="blue">Max = 8e+04&#949; (Mean = 3.27e+04&#949;)</span><br>
1807                 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07&#949; (Mean = 2.66e+07&#949;))<br>
1808                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))
1809               </p>
1810             </td>
1811 <td>
1812               <p>
1813                 <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
1814               </p>
1815             </td>
1816 <td>
1817               <p>
1818                 <span class="blue">Max = 1e+07&#949; (Mean = 4.09e+06&#949;)</span>
1819               </p>
1820             </td>
1821 </tr>
1822 <tr>
1823 <td>
1824               <p>
1825                 Bessel J1: Mathworld Data
1826               </p>
1827             </td>
1828 <td>
1829               <p>
1830                 <span class="blue">Max = 3.59&#949; (Mean = 1.33&#949;)</span><br> <br>
1831                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And
1832                 other failures.</a>)
1833               </p>
1834             </td>
1835 <td>
1836               <p>
1837                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1838                 2.1:</em></span> Max = 6.62&#949; (Mean = 2.35&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And
1839                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1840                 Max = 0.946&#949; (Mean = 0.39&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And
1841                 other failures.</a>)
1842               </p>
1843             </td>
1844 <td>
1845               <p>
1846                 <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
1847               </p>
1848             </td>
1849 <td>
1850               <p>
1851                 <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span>
1852               </p>
1853             </td>
1854 </tr>
1855 <tr>
1856 <td>
1857               <p>
1858                 Bessel J1: Mathworld Data (tricky cases)
1859               </p>
1860             </td>
1861 <td>
1862               <p>
1863                 <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
1864                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean =
1865                 1.58e+06&#949;))
1866               </p>
1867             </td>
1868 <td>
1869               <p>
1870                 <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
1871                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05&#949; (Mean = 5.32e+05&#949;))<br>
1872                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))
1873               </p>
1874             </td>
1875 <td>
1876               <p>
1877                 <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
1878               </p>
1879             </td>
1880 <td>
1881               <p>
1882                 <span class="blue">Max = 3.23e+04&#949; (Mean = 1.45e+04&#949;)</span>
1883               </p>
1884             </td>
1885 </tr>
1886 <tr>
1887 <td>
1888               <p>
1889                 Bessel JN: Mathworld Data
1890               </p>
1891             </td>
1892 <td>
1893               <p>
1894                 <span class="blue">Max = 6.85&#949; (Mean = 3.35&#949;)</span><br> <br>
1895                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.13e+19&#949; (Mean
1896                 = 5.16e+18&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And
1897                 other failures.</a>)</span>
1898               </p>
1899             </td>
1900 <td>
1901               <p>
1902                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1903                 2.1:</em></span> Max = 6.9e+05&#949; (Mean = 2.15e+05&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And
1904                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1905                 <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And
1906                 other failures.</a>)</span>
1907               </p>
1908             </td>
1909 <td>
1910               <p>
1911                 <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
1912               </p>
1913             </td>
1914 <td>
1915               <p>
1916                 <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span>
1917               </p>
1918             </td>
1919 </tr>
1920 <tr>
1921 <td>
1922               <p>
1923                 Bessel J: Mathworld Data
1924               </p>
1925             </td>
1926 <td>
1927               <p>
1928                 <span class="blue">Max = 14.7&#949; (Mean = 4.11&#949;)</span><br> <br>
1929                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.49e+05&#949; (Mean = 8.09e+04&#949;)
1930                 <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And
1931                 other failures.</a>)
1932               </p>
1933             </td>
1934 <td>
1935               <p>
1936                 <span class="blue">Max = 10&#949; (Mean = 2.24&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1937                 2.1:</em></span> Max = 2.39e+05&#949; (Mean = 5.37e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And
1938                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1939                 <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And
1940                 other failures.</a>)</span>
1941               </p>
1942             </td>
1943 <td>
1944               <p>
1945                 <span class="blue">Max = 14.7&#949; (Mean = 4.22&#949;)</span>
1946               </p>
1947             </td>
1948 <td>
1949               <p>
1950                 <span class="blue">Max = 14.9&#949; (Mean = 3.89&#949;)</span>
1951               </p>
1952             </td>
1953 </tr>
1954 <tr>
1955 <td>
1956               <p>
1957                 Bessel J: Mathworld Data (large values)
1958               </p>
1959             </td>
1960 <td>
1961               <p>
1962                 <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
1963                 Max = 34.9&#949; (Mean = 17.4&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And
1964                 other failures.</a>)
1965               </p>
1966             </td>
1967 <td>
1968               <p>
1969                 <span class="blue">Max = 0.536&#949; (Mean = 0.268&#949;)</span><br> <br>
1970                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03&#949; (Mean = 2.46e+03&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And
1971                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
1972                 Max = 5.9&#949; (Mean = 3.76&#949;))
1973               </p>
1974             </td>
1975 <td>
1976               <p>
1977                 <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span>
1978               </p>
1979             </td>
1980 <td>
1981               <p>
1982                 <span class="blue">Max = 9.31&#949; (Mean = 5.52&#949;)</span>
1983               </p>
1984             </td>
1985 </tr>
1986 <tr>
1987 <td>
1988               <p>
1989                 Bessel JN: Random Data
1990               </p>
1991             </td>
1992 <td>
1993               <p>
1994                 <span class="blue">Max = 50.8&#949; (Mean = 3.69&#949;)</span><br> <br>
1995                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.12e+03&#949; (Mean = 88.7&#949;))
1996               </p>
1997             </td>
1998 <td>
1999               <p>
2000                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2001                 2.1:</em></span> Max = 75.7&#949; (Mean = 5.36&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2002                 Max = 3.93&#949; (Mean = 1.22&#949;))
2003               </p>
2004             </td>
2005 <td>
2006               <p>
2007                 <span class="blue">Max = 99.6&#949; (Mean = 22&#949;)</span>
2008               </p>
2009             </td>
2010 <td>
2011               <p>
2012                 <span class="blue">Max = 17.5&#949; (Mean = 1.46&#949;)</span>
2013               </p>
2014             </td>
2015 </tr>
2016 <tr>
2017 <td>
2018               <p>
2019                 Bessel J: Random Data
2020               </p>
2021             </td>
2022 <td>
2023               <p>
2024                 <span class="blue">Max = 11.4&#949; (Mean = 1.68&#949;)</span><br> <br>
2025                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 501&#949; (Mean = 52.3&#949;))
2026               </p>
2027             </td>
2028 <td>
2029               <p>
2030                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2031                 2.1:</em></span> Max = 15.5&#949; (Mean = 3.33&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And
2032                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2033                 Max = 6.74&#949; (Mean = 1.3&#949;))
2034               </p>
2035             </td>
2036 <td>
2037               <p>
2038                 <span class="blue">Max = 260&#949; (Mean = 34&#949;)</span>
2039               </p>
2040             </td>
2041 <td>
2042               <p>
2043                 <span class="blue">Max = 9.24&#949; (Mean = 1.17&#949;)</span>
2044               </p>
2045             </td>
2046 </tr>
2047 <tr>
2048 <td>
2049               <p>
2050                 Bessel J: Random Data (Tricky large values)
2051               </p>
2052             </td>
2053 <td>
2054               <p>
2055                 <span class="blue">Max = 785&#949; (Mean = 94.2&#949;)</span><br> <br>
2056                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 5.01e+17&#949; (Mean
2057                 = 6.23e+16&#949;))</span>
2058               </p>
2059             </td>
2060 <td>
2061               <p>
2062                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2063                 2.1:</em></span> Max = 2.48e+05&#949; (Mean = 5.11e+04&#949;))<br> (<span class="emphasis"><em>Rmath
2064                 3.2.3:</em></span> Max = 71.6&#949; (Mean = 11.7&#949;))
2065               </p>
2066             </td>
2067 <td>
2068               <p>
2069                 <span class="blue">Max = 785&#949; (Mean = 97.4&#949;)</span>
2070               </p>
2071             </td>
2072 <td>
2073               <p>
2074                 <span class="blue">Max = 59.2&#949; (Mean = 8.67&#949;)</span>
2075               </p>
2076             </td>
2077 </tr>
2078 </tbody>
2079 </table></div>
2080 </div>
2081 <br class="table-break">
2082 </div>
2083 <div class="section">
2084 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
2085 <a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_" title="cyl_bessel_j (integer orders)">cyl_bessel_j
2086     (integer orders)</a>
2087 </h2></div></div></div>
2088 <div class="table">
2089 <a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table&#160;13.&#160;Error rates for cyl_bessel_j (integer orders)</b></p>
2090 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
2091 <colgroup>
2092 <col>
2093 <col>
2094 <col>
2095 <col>
2096 <col>
2097 </colgroup>
2098 <thead><tr>
2099 <th>
2100             </th>
2101 <th>
2102               <p>
2103                 GNU C++ version 7.1.0<br> linux<br> long double
2104               </p>
2105             </th>
2106 <th>
2107               <p>
2108                 GNU C++ version 7.1.0<br> linux<br> double
2109               </p>
2110             </th>
2111 <th>
2112               <p>
2113                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
2114               </p>
2115             </th>
2116 <th>
2117               <p>
2118                 Microsoft Visual C++ version 14.1<br> Win32<br> double
2119               </p>
2120             </th>
2121 </tr></thead>
2122 <tbody>
2123 <tr>
2124 <td>
2125               <p>
2126                 Bessel J0: Mathworld Data (Integer Version)
2127               </p>
2128             </td>
2129 <td>
2130               <p>
2131                 <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span><br> <br>
2132                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
2133                 other failures.</a>)
2134               </p>
2135             </td>
2136 <td>
2137               <p>
2138                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2139                 2.1:</em></span> Max = 1.12&#949; (Mean = 0.488&#949;))<br> (<span class="emphasis"><em>Rmath
2140                 3.2.3:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And
2141                 other failures.</a>)
2142               </p>
2143             </td>
2144 <td>
2145               <p>
2146                 <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
2147               </p>
2148             </td>
2149 <td>
2150               <p>
2151                 <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span><br> <br>
2152                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.89&#949; (Mean = 0.988&#949;))
2153               </p>
2154             </td>
2155 </tr>
2156 <tr>
2157 <td>
2158               <p>
2159                 Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
2160               </p>
2161             </td>
2162 <td>
2163               <p>
2164                 <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span><br>
2165                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean =
2166                 1.96e+08&#949;))
2167               </p>
2168             </td>
2169 <td>
2170               <p>
2171                 <span class="blue">Max = 8e+04&#949; (Mean = 3.27e+04&#949;)</span><br>
2172                 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07&#949; (Mean = 4.11e+06&#949;))<br>
2173                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))
2174               </p>
2175             </td>
2176 <td>
2177               <p>
2178                 <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
2179               </p>
2180             </td>
2181 <td>
2182               <p>
2183                 <span class="blue">Max = 1e+07&#949; (Mean = 4.09e+06&#949;)</span><br>
2184                 <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max
2185                 = 2.54e+08&#949; (Mean = 1.04e+08&#949;))</span>
2186               </p>
2187             </td>
2188 </tr>
2189 <tr>
2190 <td>
2191               <p>
2192                 Bessel J1: Mathworld Data (Integer Version)
2193               </p>
2194             </td>
2195 <td>
2196               <p>
2197                 <span class="blue">Max = 3.59&#949; (Mean = 1.33&#949;)</span><br> <br>
2198                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
2199                 other failures.</a>)
2200               </p>
2201             </td>
2202 <td>
2203               <p>
2204                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2205                 2.1:</em></span> Max = 1.89&#949; (Mean = 0.721&#949;))<br> (<span class="emphasis"><em>Rmath
2206                 3.2.3:</em></span> Max = 0.946&#949; (Mean = 0.39&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And
2207                 other failures.</a>)
2208               </p>
2209             </td>
2210 <td>
2211               <p>
2212                 <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
2213               </p>
2214             </td>
2215 <td>
2216               <p>
2217                 <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span><br> <br>
2218                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 11.4&#949; (Mean = 4.15&#949;))
2219               </p>
2220             </td>
2221 </tr>
2222 <tr>
2223 <td>
2224               <p>
2225                 Bessel J1: Mathworld Data (tricky cases) (Integer Version)
2226               </p>
2227             </td>
2228 <td>
2229               <p>
2230                 <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
2231                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean =
2232                 1.58e+06&#949;))
2233               </p>
2234             </td>
2235 <td>
2236               <p>
2237                 <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
2238                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06&#949; (Mean = 6.28e+05&#949;))<br>
2239                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))
2240               </p>
2241             </td>
2242 <td>
2243               <p>
2244                 <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
2245               </p>
2246             </td>
2247 <td>
2248               <p>
2249                 <span class="blue">Max = 3.23e+04&#949; (Mean = 1.45e+04&#949;)</span><br>
2250                 <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.44e+07&#949; (Mean
2251                 = 6.5e+06&#949;))
2252               </p>
2253             </td>
2254 </tr>
2255 <tr>
2256 <td>
2257               <p>
2258                 Bessel JN: Mathworld Data (Integer Version)
2259               </p>
2260             </td>
2261 <td>
2262               <p>
2263                 <span class="blue">Max = 6.85&#949; (Mean = 3.35&#949;)</span><br> <br>
2264                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.13e+19&#949; (Mean
2265                 = 5.16e+18&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
2266                 other failures.</a>)</span>
2267               </p>
2268             </td>
2269 <td>
2270               <p>
2271                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2272                 2.1:</em></span> Max = 6.9e+05&#949; (Mean = 2.53e+05&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And
2273                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2274                 <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And
2275                 other failures.</a>)</span>
2276               </p>
2277             </td>
2278 <td>
2279               <p>
2280                 <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
2281               </p>
2282             </td>
2283 <td>
2284               <p>
2285                 <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span><br> <br>
2286                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
2287                 = +INF&#949;) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
2288                 other failures.</a>)</span>
2289               </p>
2290             </td>
2291 </tr>
2292 </tbody>
2293 </table></div>
2294 </div>
2295 <br class="table-break">
2296 </div>
2297 <div class="section">
2298 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
2299 <a name="special_function_error_rates_rep.section_cyl_bessel_j_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime" title="cyl_bessel_j_prime">cyl_bessel_j_prime</a>
2300 </h2></div></div></div>
2301 <div class="table">
2302 <a name="special_function_error_rates_rep.section_cyl_bessel_j_prime.table_cyl_bessel_j_prime"></a><p class="title"><b>Table&#160;14.&#160;Error rates for cyl_bessel_j_prime</b></p>
2303 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
2304 <colgroup>
2305 <col>
2306 <col>
2307 <col>
2308 <col>
2309 <col>
2310 </colgroup>
2311 <thead><tr>
2312 <th>
2313             </th>
2314 <th>
2315               <p>
2316                 GNU C++ version 7.1.0<br> linux<br> double
2317               </p>
2318             </th>
2319 <th>
2320               <p>
2321                 GNU C++ version 7.1.0<br> linux<br> long double
2322               </p>
2323             </th>
2324 <th>
2325               <p>
2326                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
2327               </p>
2328             </th>
2329 <th>
2330               <p>
2331                 Microsoft Visual C++ version 14.1<br> Win32<br> double
2332               </p>
2333             </th>
2334 </tr></thead>
2335 <tbody>
2336 <tr>
2337 <td>
2338               <p>
2339                 Bessel J0': Mathworld Data
2340               </p>
2341             </td>
2342 <td>
2343               <p>
2344                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2345               </p>
2346             </td>
2347 <td>
2348               <p>
2349                 <span class="blue">Max = 18.9&#949; (Mean = 6.82&#949;)</span>
2350               </p>
2351             </td>
2352 <td>
2353               <p>
2354                 <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
2355               </p>
2356             </td>
2357 <td>
2358               <p>
2359                 <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
2360               </p>
2361             </td>
2362 </tr>
2363 <tr>
2364 <td>
2365               <p>
2366                 Bessel J0': Mathworld Data (Tricky cases)
2367               </p>
2368             </td>
2369 <td>
2370               <p>
2371                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2372               </p>
2373             </td>
2374 <td>
2375               <p>
2376                 <span class="blue">Max = 7.44&#949; (Mean = 3.34&#949;)</span>
2377               </p>
2378             </td>
2379 <td>
2380               <p>
2381                 <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
2382               </p>
2383             </td>
2384 <td>
2385               <p>
2386                 <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
2387               </p>
2388             </td>
2389 </tr>
2390 <tr>
2391 <td>
2392               <p>
2393                 Bessel J1': Mathworld Data
2394               </p>
2395             </td>
2396 <td>
2397               <p>
2398                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2399               </p>
2400             </td>
2401 <td>
2402               <p>
2403                 <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2404               </p>
2405             </td>
2406 <td>
2407               <p>
2408                 <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2409               </p>
2410             </td>
2411 <td>
2412               <p>
2413                 <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
2414               </p>
2415             </td>
2416 </tr>
2417 <tr>
2418 <td>
2419               <p>
2420                 Bessel J1': Mathworld Data (tricky cases)
2421               </p>
2422             </td>
2423 <td>
2424               <p>
2425                 <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
2426               </p>
2427             </td>
2428 <td>
2429               <p>
2430                 <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2431               </p>
2432             </td>
2433 <td>
2434               <p>
2435                 <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2436               </p>
2437             </td>
2438 <td>
2439               <p>
2440                 <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
2441               </p>
2442             </td>
2443 </tr>
2444 <tr>
2445 <td>
2446               <p>
2447                 Bessel JN': Mathworld Data
2448               </p>
2449             </td>
2450 <td>
2451               <p>
2452                 <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
2453               </p>
2454             </td>
2455 <td>
2456               <p>
2457                 <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
2458               </p>
2459             </td>
2460 <td>
2461               <p>
2462                 <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
2463               </p>
2464             </td>
2465 <td>
2466               <p>
2467                 <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
2468               </p>
2469             </td>
2470 </tr>
2471 <tr>
2472 <td>
2473               <p>
2474                 Bessel J': Mathworld Data
2475               </p>
2476             </td>
2477 <td>
2478               <p>
2479                 <span class="blue">Max = 21.5&#949; (Mean = 4.7&#949;)</span>
2480               </p>
2481             </td>
2482 <td>
2483               <p>
2484                 <span class="blue">Max = 42.5&#949; (Mean = 9.31&#949;)</span>
2485               </p>
2486             </td>
2487 <td>
2488               <p>
2489                 <span class="blue">Max = 42.5&#949; (Mean = 9.32&#949;)</span>
2490               </p>
2491             </td>
2492 <td>
2493               <p>
2494                 <span class="blue">Max = 23.7&#949; (Mean = 8&#949;)</span>
2495               </p>
2496             </td>
2497 </tr>
2498 <tr>
2499 <td>
2500               <p>
2501                 Bessel J': Mathworld Data (large values)
2502               </p>
2503             </td>
2504 <td>
2505               <p>
2506                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2507               </p>
2508             </td>
2509 <td>
2510               <p>
2511                 <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
2512               </p>
2513             </td>
2514 <td>
2515               <p>
2516                 <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
2517               </p>
2518             </td>
2519 <td>
2520               <p>
2521                 <span class="blue">Max = 2.9&#949; (Mean = 1.61&#949;)</span>
2522               </p>
2523             </td>
2524 </tr>
2525 <tr>
2526 <td>
2527               <p>
2528                 Bessel JN': Random Data
2529               </p>
2530             </td>
2531 <td>
2532               <p>
2533                 <span class="blue">Max = 0.593&#949; (Mean = 0.0396&#949;)</span>
2534               </p>
2535             </td>
2536 <td>
2537               <p>
2538                 <span class="blue">Max = 11.3&#949; (Mean = 1.85&#949;)</span>
2539               </p>
2540             </td>
2541 <td>
2542               <p>
2543                 <span class="blue">Max = 79.4&#949; (Mean = 16.2&#949;)</span>
2544               </p>
2545             </td>
2546 <td>
2547               <p>
2548                 <span class="blue">Max = 6.34&#949; (Mean = 0.999&#949;)</span>
2549               </p>
2550             </td>
2551 </tr>
2552 <tr>
2553 <td>
2554               <p>
2555                 Bessel J': Random Data
2556               </p>
2557             </td>
2558 <td>
2559               <p>
2560                 <span class="blue">Max = 0.885&#949; (Mean = 0.033&#949;)</span>
2561               </p>
2562             </td>
2563 <td>
2564               <p>
2565                 <span class="blue">Max = 139&#949; (Mean = 6.47&#949;)</span>
2566               </p>
2567             </td>
2568 <td>
2569               <p>
2570                 <span class="blue">Max = 279&#949; (Mean = 27.2&#949;)</span>
2571               </p>
2572             </td>
2573 <td>
2574               <p>
2575                 <span class="blue">Max = 176&#949; (Mean = 9.75&#949;)</span>
2576               </p>
2577             </td>
2578 </tr>
2579 <tr>
2580 <td>
2581               <p>
2582                 Bessel J': Random Data (Tricky large values)
2583               </p>
2584             </td>
2585 <td>
2586               <p>
2587                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2588               </p>
2589             </td>
2590 <td>
2591               <p>
2592                 <span class="blue">Max = 474&#949; (Mean = 62.2&#949;)</span>
2593               </p>
2594             </td>
2595 <td>
2596               <p>
2597                 <span class="blue">Max = 474&#949; (Mean = 64.5&#949;)</span>
2598               </p>
2599             </td>
2600 <td>
2601               <p>
2602                 <span class="blue">Max = 379&#949; (Mean = 45.4&#949;)</span>
2603               </p>
2604             </td>
2605 </tr>
2606 </tbody>
2607 </table></div>
2608 </div>
2609 <br class="table-break">
2610 </div>
2611 <div class="section">
2612 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
2613 <a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_" title="cyl_bessel_j_prime (integer orders)">cyl_bessel_j_prime
2614     (integer orders)</a>
2615 </h2></div></div></div>
2616 <div class="table">
2617 <a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table&#160;15.&#160;Error rates for cyl_bessel_j_prime (integer orders)</b></p>
2618 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
2619 <colgroup>
2620 <col>
2621 <col>
2622 <col>
2623 <col>
2624 <col>
2625 </colgroup>
2626 <thead><tr>
2627 <th>
2628             </th>
2629 <th>
2630               <p>
2631                 GNU C++ version 7.1.0<br> linux<br> double
2632               </p>
2633             </th>
2634 <th>
2635               <p>
2636                 GNU C++ version 7.1.0<br> linux<br> long double
2637               </p>
2638             </th>
2639 <th>
2640               <p>
2641                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
2642               </p>
2643             </th>
2644 <th>
2645               <p>
2646                 Microsoft Visual C++ version 14.1<br> Win32<br> double
2647               </p>
2648             </th>
2649 </tr></thead>
2650 <tbody>
2651 <tr>
2652 <td>
2653               <p>
2654                 Bessel J0': Mathworld Data (Integer Version)
2655               </p>
2656             </td>
2657 <td>
2658               <p>
2659                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2660               </p>
2661             </td>
2662 <td>
2663               <p>
2664                 <span class="blue">Max = 18.9&#949; (Mean = 6.82&#949;)</span>
2665               </p>
2666             </td>
2667 <td>
2668               <p>
2669                 <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
2670               </p>
2671             </td>
2672 <td>
2673               <p>
2674                 <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
2675               </p>
2676             </td>
2677 </tr>
2678 <tr>
2679 <td>
2680               <p>
2681                 Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
2682               </p>
2683             </td>
2684 <td>
2685               <p>
2686                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2687               </p>
2688             </td>
2689 <td>
2690               <p>
2691                 <span class="blue">Max = 7.44&#949; (Mean = 3.34&#949;)</span>
2692               </p>
2693             </td>
2694 <td>
2695               <p>
2696                 <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
2697               </p>
2698             </td>
2699 <td>
2700               <p>
2701                 <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
2702               </p>
2703             </td>
2704 </tr>
2705 <tr>
2706 <td>
2707               <p>
2708                 Bessel J1': Mathworld Data (Integer Version)
2709               </p>
2710             </td>
2711 <td>
2712               <p>
2713                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2714               </p>
2715             </td>
2716 <td>
2717               <p>
2718                 <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2719               </p>
2720             </td>
2721 <td>
2722               <p>
2723                 <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2724               </p>
2725             </td>
2726 <td>
2727               <p>
2728                 <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
2729               </p>
2730             </td>
2731 </tr>
2732 <tr>
2733 <td>
2734               <p>
2735                 Bessel J1': Mathworld Data (tricky cases) (Integer Version)
2736               </p>
2737             </td>
2738 <td>
2739               <p>
2740                 <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
2741               </p>
2742             </td>
2743 <td>
2744               <p>
2745                 <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2746               </p>
2747             </td>
2748 <td>
2749               <p>
2750                 <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2751               </p>
2752             </td>
2753 <td>
2754               <p>
2755                 <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
2756               </p>
2757             </td>
2758 </tr>
2759 <tr>
2760 <td>
2761               <p>
2762                 Bessel JN': Mathworld Data (Integer Version)
2763               </p>
2764             </td>
2765 <td>
2766               <p>
2767                 <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
2768               </p>
2769             </td>
2770 <td>
2771               <p>
2772                 <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
2773               </p>
2774             </td>
2775 <td>
2776               <p>
2777                 <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
2778               </p>
2779             </td>
2780 <td>
2781               <p>
2782                 <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
2783               </p>
2784             </td>
2785 </tr>
2786 </tbody>
2787 </table></div>
2788 </div>
2789 <br class="table-break">
2790 </div>
2791 <div class="section">
2792 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
2793 <a name="special_function_error_rates_rep.section_cyl_bessel_k"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k" title="cyl_bessel_k">cyl_bessel_k</a>
2794 </h2></div></div></div>
2795 <div class="table">
2796 <a name="special_function_error_rates_rep.section_cyl_bessel_k.table_cyl_bessel_k"></a><p class="title"><b>Table&#160;16.&#160;Error rates for cyl_bessel_k</b></p>
2797 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
2798 <colgroup>
2799 <col>
2800 <col>
2801 <col>
2802 <col>
2803 <col>
2804 </colgroup>
2805 <thead><tr>
2806 <th>
2807             </th>
2808 <th>
2809               <p>
2810                 GNU C++ version 7.1.0<br> linux<br> long double
2811               </p>
2812             </th>
2813 <th>
2814               <p>
2815                 GNU C++ version 7.1.0<br> linux<br> double
2816               </p>
2817             </th>
2818 <th>
2819               <p>
2820                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
2821               </p>
2822             </th>
2823 <th>
2824               <p>
2825                 Microsoft Visual C++ version 14.1<br> Win32<br> double
2826               </p>
2827             </th>
2828 </tr></thead>
2829 <tbody>
2830 <tr>
2831 <td>
2832               <p>
2833                 Bessel K0: Mathworld Data
2834               </p>
2835             </td>
2836 <td>
2837               <p>
2838                 <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span><br> <br>
2839                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
2840               </p>
2841             </td>
2842 <td>
2843               <p>
2844                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2845                 2.1:</em></span> Max = 6.04&#949; (Mean = 2.16&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2846                 Max = 0.833&#949; (Mean = 0.601&#949;))
2847               </p>
2848             </td>
2849 <td>
2850               <p>
2851                 <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span>
2852               </p>
2853             </td>
2854 <td>
2855               <p>
2856                 <span class="blue">Max = 0.833&#949; (Mean = 0.552&#949;)</span>
2857               </p>
2858             </td>
2859 </tr>
2860 <tr>
2861 <td>
2862               <p>
2863                 Bessel K1: Mathworld Data
2864               </p>
2865             </td>
2866 <td>
2867               <p>
2868                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span><br> <br>
2869                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
2870               </p>
2871             </td>
2872 <td>
2873               <p>
2874                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2875                 2.1:</em></span> Max = 6.26&#949; (Mean = 2.21&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2876                 Max = 0.894&#949; (Mean = 0.516&#949;))
2877               </p>
2878             </td>
2879 <td>
2880               <p>
2881                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
2882               </p>
2883             </td>
2884 <td>
2885               <p>
2886                 <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
2887               </p>
2888             </td>
2889 </tr>
2890 <tr>
2891 <td>
2892               <p>
2893                 Bessel Kn: Mathworld Data
2894               </p>
2895             </td>
2896 <td>
2897               <p>
2898                 <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span><br> <br>
2899                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And
2900                 other failures.</a>)
2901               </p>
2902             </td>
2903 <td>
2904               <p>
2905                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2906                 2.1:</em></span> Max = 3.36&#949; (Mean = 1.43&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And
2907                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2908                 Max = 8.48&#949; (Mean = 2.98&#949;))
2909               </p>
2910             </td>
2911 <td>
2912               <p>
2913                 <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span>
2914               </p>
2915             </td>
2916 <td>
2917               <p>
2918                 <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
2919               </p>
2920             </td>
2921 </tr>
2922 <tr>
2923 <td>
2924               <p>
2925                 Bessel Kv: Mathworld Data
2926               </p>
2927             </td>
2928 <td>
2929               <p>
2930                 <span class="blue">Max = 3.58&#949; (Mean = 2.39&#949;)</span><br> <br>
2931                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13&#949; (Mean = 4.81&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And
2932                 other failures.</a>)
2933               </p>
2934             </td>
2935 <td>
2936               <p>
2937                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2938                 2.1:</em></span> Max = 5.47&#949; (Mean = 2.04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And
2939                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2940                 Max = 3.15&#949; (Mean = 1.35&#949;))
2941               </p>
2942             </td>
2943 <td>
2944               <p>
2945                 <span class="blue">Max = 5.21&#949; (Mean = 2.53&#949;)</span>
2946               </p>
2947             </td>
2948 <td>
2949               <p>
2950                 <span class="blue">Max = 4.78&#949; (Mean = 2.19&#949;)</span>
2951               </p>
2952             </td>
2953 </tr>
2954 <tr>
2955 <td>
2956               <p>
2957                 Bessel Kv: Mathworld Data (large values)
2958               </p>
2959             </td>
2960 <td>
2961               <p>
2962                 <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
2963                 Max = 42.3&#949; (Mean = 19.8&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And
2964                 other failures.</a>)
2965               </p>
2966             </td>
2967 <td>
2968               <p>
2969                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2970                 2.1:</em></span> Max = 308&#949; (Mean = 142&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And
2971                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
2972                 Max = 84.6&#949; (Mean = 37.8&#949;))
2973               </p>
2974             </td>
2975 <td>
2976               <p>
2977                 <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span>
2978               </p>
2979             </td>
2980 <td>
2981               <p>
2982                 <span class="blue">Max = 59.8&#949; (Mean = 26.9&#949;)</span>
2983               </p>
2984             </td>
2985 </tr>
2986 <tr>
2987 <td>
2988               <p>
2989                 Bessel Kn: Random Data
2990               </p>
2991             </td>
2992 <td>
2993               <p>
2994                 <span class="blue">Max = 4.55&#949; (Mean = 1.12&#949;)</span><br> <br>
2995                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13.9&#949; (Mean = 2.91&#949;))
2996               </p>
2997             </td>
2998 <td>
2999               <p>
3000                 <span class="blue">Max = 0.764&#949; (Mean = 0.0348&#949;)</span><br> <br>
3001                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71&#949; (Mean = 1.76&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And
3002                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3003                 Max = 7.47&#949; (Mean = 1.34&#949;))
3004               </p>
3005             </td>
3006 <td>
3007               <p>
3008                 <span class="blue">Max = 4.55&#949; (Mean = 1.12&#949;)</span>
3009               </p>
3010             </td>
3011 <td>
3012               <p>
3013                 <span class="blue">Max = 9.34&#949; (Mean = 1.7&#949;)</span>
3014               </p>
3015             </td>
3016 </tr>
3017 <tr>
3018 <td>
3019               <p>
3020                 Bessel Kv: Random Data
3021               </p>
3022             </td>
3023 <td>
3024               <p>
3025                 <span class="blue">Max = 7.88&#949; (Mean = 1.48&#949;)</span><br> <br>
3026                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13.6&#949; (Mean = 2.68&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And
3027                 other failures.</a>)
3028               </p>
3029             </td>
3030 <td>
3031               <p>
3032                 <span class="blue">Max = 0.507&#949; (Mean = 0.0313&#949;)</span><br> <br>
3033                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71&#949; (Mean = 1.47&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And
3034                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3035                 Max = 7.37&#949; (Mean = 1.49&#949;))
3036               </p>
3037             </td>
3038 <td>
3039               <p>
3040                 <span class="blue">Max = 7.88&#949; (Mean = 1.47&#949;)</span>
3041               </p>
3042             </td>
3043 <td>
3044               <p>
3045                 <span class="blue">Max = 8.33&#949; (Mean = 1.62&#949;)</span>
3046               </p>
3047             </td>
3048 </tr>
3049 </tbody>
3050 </table></div>
3051 </div>
3052 <br class="table-break">
3053 </div>
3054 <div class="section">
3055 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
3056 <a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_" title="cyl_bessel_k (integer orders)">cyl_bessel_k
3057     (integer orders)</a>
3058 </h2></div></div></div>
3059 <div class="table">
3060 <a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table&#160;17.&#160;Error rates for cyl_bessel_k (integer orders)</b></p>
3061 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
3062 <colgroup>
3063 <col>
3064 <col>
3065 <col>
3066 <col>
3067 <col>
3068 </colgroup>
3069 <thead><tr>
3070 <th>
3071             </th>
3072 <th>
3073               <p>
3074                 GNU C++ version 7.1.0<br> linux<br> long double
3075               </p>
3076             </th>
3077 <th>
3078               <p>
3079                 GNU C++ version 7.1.0<br> linux<br> double
3080               </p>
3081             </th>
3082 <th>
3083               <p>
3084                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
3085               </p>
3086             </th>
3087 <th>
3088               <p>
3089                 Microsoft Visual C++ version 14.1<br> Win32<br> double
3090               </p>
3091             </th>
3092 </tr></thead>
3093 <tbody>
3094 <tr>
3095 <td>
3096               <p>
3097                 Bessel K0: Mathworld Data (Integer Version)
3098               </p>
3099             </td>
3100 <td>
3101               <p>
3102                 <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span><br> <br>
3103                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
3104               </p>
3105             </td>
3106 <td>
3107               <p>
3108                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3109                 2.1:</em></span> Max = 1.2&#949; (Mean = 0.733&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3110                 Max = 0.833&#949; (Mean = 0.601&#949;))
3111               </p>
3112             </td>
3113 <td>
3114               <p>
3115                 <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span>
3116               </p>
3117             </td>
3118 <td>
3119               <p>
3120                 <span class="blue">Max = 0.833&#949; (Mean = 0.552&#949;)</span>
3121               </p>
3122             </td>
3123 </tr>
3124 <tr>
3125 <td>
3126               <p>
3127                 Bessel K1: Mathworld Data (Integer Version)
3128               </p>
3129             </td>
3130 <td>
3131               <p>
3132                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span><br> <br>
3133                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
3134               </p>
3135             </td>
3136 <td>
3137               <p>
3138                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3139                 2.1:</em></span> Max = 0.626&#949; (Mean = 0.333&#949;))<br> (<span class="emphasis"><em>Rmath
3140                 3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.516&#949;))
3141               </p>
3142             </td>
3143 <td>
3144               <p>
3145                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3146               </p>
3147             </td>
3148 <td>
3149               <p>
3150                 <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
3151               </p>
3152             </td>
3153 </tr>
3154 <tr>
3155 <td>
3156               <p>
3157                 Bessel Kn: Mathworld Data (Integer Version)
3158               </p>
3159             </td>
3160 <td>
3161               <p>
3162                 <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span><br> <br>
3163                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
3164                 other failures.</a>)
3165               </p>
3166             </td>
3167 <td>
3168               <p>
3169                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3170                 2.1:</em></span> Max = 168&#949; (Mean = 59.5&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3171                 Max = 8.48&#949; (Mean = 2.98&#949;))
3172               </p>
3173             </td>
3174 <td>
3175               <p>
3176                 <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span>
3177               </p>
3178             </td>
3179 <td>
3180               <p>
3181                 <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
3182               </p>
3183             </td>
3184 </tr>
3185 </tbody>
3186 </table></div>
3187 </div>
3188 <br class="table-break">
3189 </div>
3190 <div class="section">
3191 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
3192 <a name="special_function_error_rates_rep.section_cyl_bessel_k_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime" title="cyl_bessel_k_prime">cyl_bessel_k_prime</a>
3193 </h2></div></div></div>
3194 <div class="table">
3195 <a name="special_function_error_rates_rep.section_cyl_bessel_k_prime.table_cyl_bessel_k_prime"></a><p class="title"><b>Table&#160;18.&#160;Error rates for cyl_bessel_k_prime</b></p>
3196 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
3197 <colgroup>
3198 <col>
3199 <col>
3200 <col>
3201 <col>
3202 <col>
3203 </colgroup>
3204 <thead><tr>
3205 <th>
3206             </th>
3207 <th>
3208               <p>
3209                 GNU C++ version 7.1.0<br> linux<br> double
3210               </p>
3211             </th>
3212 <th>
3213               <p>
3214                 GNU C++ version 7.1.0<br> linux<br> long double
3215               </p>
3216             </th>
3217 <th>
3218               <p>
3219                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
3220               </p>
3221             </th>
3222 <th>
3223               <p>
3224                 Microsoft Visual C++ version 14.1<br> Win32<br> double
3225               </p>
3226             </th>
3227 </tr></thead>
3228 <tbody>
3229 <tr>
3230 <td>
3231               <p>
3232                 Bessel K'0: Mathworld Data
3233               </p>
3234             </td>
3235 <td>
3236               <p>
3237                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3238               </p>
3239             </td>
3240 <td>
3241               <p>
3242                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3243               </p>
3244             </td>
3245 <td>
3246               <p>
3247                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3248               </p>
3249             </td>
3250 <td>
3251               <p>
3252                 <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
3253               </p>
3254             </td>
3255 </tr>
3256 <tr>
3257 <td>
3258               <p>
3259                 Bessel K'1: Mathworld Data
3260               </p>
3261             </td>
3262 <td>
3263               <p>
3264                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3265               </p>
3266             </td>
3267 <td>
3268               <p>
3269                 <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
3270               </p>
3271             </td>
3272 <td>
3273               <p>
3274                 <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
3275               </p>
3276             </td>
3277 <td>
3278               <p>
3279                 <span class="blue">Max = 0.761&#949; (Mean = 0.444&#949;)</span>
3280               </p>
3281             </td>
3282 </tr>
3283 <tr>
3284 <td>
3285               <p>
3286                 Bessel K'n: Mathworld Data
3287               </p>
3288             </td>
3289 <td>
3290               <p>
3291                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3292               </p>
3293             </td>
3294 <td>
3295               <p>
3296                 <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
3297               </p>
3298             </td>
3299 <td>
3300               <p>
3301                 <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
3302               </p>
3303             </td>
3304 <td>
3305               <p>
3306                 <span class="blue">Max = 4.17&#949; (Mean = 1.75&#949;)</span>
3307               </p>
3308             </td>
3309 </tr>
3310 <tr>
3311 <td>
3312               <p>
3313                 Bessel K'v: Mathworld Data
3314               </p>
3315             </td>
3316 <td>
3317               <p>
3318                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3319               </p>
3320             </td>
3321 <td>
3322               <p>
3323                 <span class="blue">Max = 3.94&#949; (Mean = 2.44&#949;)</span>
3324               </p>
3325             </td>
3326 <td>
3327               <p>
3328                 <span class="blue">Max = 3.94&#949; (Mean = 2.34&#949;)</span>
3329               </p>
3330             </td>
3331 <td>
3332               <p>
3333                 <span class="blue">Max = 3.94&#949; (Mean = 1.47&#949;)</span>
3334               </p>
3335             </td>
3336 </tr>
3337 <tr>
3338 <td>
3339               <p>
3340                 Bessel K'v: Mathworld Data (large values)
3341               </p>
3342             </td>
3343 <td>
3344               <p>
3345                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3346               </p>
3347             </td>
3348 <td>
3349               <p>
3350                 <span class="blue">Max = 59.2&#949; (Mean = 42.9&#949;)</span>
3351               </p>
3352             </td>
3353 <td>
3354               <p>
3355                 <span class="blue">Max = 58.7&#949; (Mean = 42.6&#949;)</span>
3356               </p>
3357             </td>
3358 <td>
3359               <p>
3360                 <span class="blue">Max = 18.6&#949; (Mean = 11.8&#949;)</span>
3361               </p>
3362             </td>
3363 </tr>
3364 <tr>
3365 <td>
3366               <p>
3367                 Bessel K'n: Random Data
3368               </p>
3369             </td>
3370 <td>
3371               <p>
3372                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3373               </p>
3374             </td>
3375 <td>
3376               <p>
3377                 <span class="blue">Max = 4.45&#949; (Mean = 1.19&#949;)</span>
3378               </p>
3379             </td>
3380 <td>
3381               <p>
3382                 <span class="blue">Max = 4.45&#949; (Mean = 1.19&#949;)</span>
3383               </p>
3384             </td>
3385 <td>
3386               <p>
3387                 <span class="blue">Max = 9.67&#949; (Mean = 1.73&#949;)</span>
3388               </p>
3389             </td>
3390 </tr>
3391 <tr>
3392 <td>
3393               <p>
3394                 Bessel K'v: Random Data
3395               </p>
3396             </td>
3397 <td>
3398               <p>
3399                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3400               </p>
3401             </td>
3402 <td>
3403               <p>
3404                 <span class="blue">Max = 7.95&#949; (Mean = 1.53&#949;)</span>
3405               </p>
3406             </td>
3407 <td>
3408               <p>
3409                 <span class="blue">Max = 7.95&#949; (Mean = 1.52&#949;)</span>
3410               </p>
3411             </td>
3412 <td>
3413               <p>
3414                 <span class="blue">Max = 8.32&#949; (Mean = 1.65&#949;)</span>
3415               </p>
3416             </td>
3417 </tr>
3418 </tbody>
3419 </table></div>
3420 </div>
3421 <br class="table-break">
3422 </div>
3423 <div class="section">
3424 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
3425 <a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_" title="cyl_bessel_k_prime (integer orders)">cyl_bessel_k_prime
3426     (integer orders)</a>
3427 </h2></div></div></div>
3428 <div class="table">
3429 <a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table&#160;19.&#160;Error rates for cyl_bessel_k_prime (integer orders)</b></p>
3430 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
3431 <colgroup>
3432 <col>
3433 <col>
3434 <col>
3435 <col>
3436 <col>
3437 </colgroup>
3438 <thead><tr>
3439 <th>
3440             </th>
3441 <th>
3442               <p>
3443                 GNU C++ version 7.1.0<br> linux<br> double
3444               </p>
3445             </th>
3446 <th>
3447               <p>
3448                 GNU C++ version 7.1.0<br> linux<br> long double
3449               </p>
3450             </th>
3451 <th>
3452               <p>
3453                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
3454               </p>
3455             </th>
3456 <th>
3457               <p>
3458                 Microsoft Visual C++ version 14.1<br> Win32<br> double
3459               </p>
3460             </th>
3461 </tr></thead>
3462 <tbody>
3463 <tr>
3464 <td>
3465               <p>
3466                 Bessel K'0: Mathworld Data (Integer Version)
3467               </p>
3468             </td>
3469 <td>
3470               <p>
3471                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3472               </p>
3473             </td>
3474 <td>
3475               <p>
3476                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3477               </p>
3478             </td>
3479 <td>
3480               <p>
3481                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
3482               </p>
3483             </td>
3484 <td>
3485               <p>
3486                 <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
3487               </p>
3488             </td>
3489 </tr>
3490 <tr>
3491 <td>
3492               <p>
3493                 Bessel K'1: Mathworld Data (Integer Version)
3494               </p>
3495             </td>
3496 <td>
3497               <p>
3498                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3499               </p>
3500             </td>
3501 <td>
3502               <p>
3503                 <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
3504               </p>
3505             </td>
3506 <td>
3507               <p>
3508                 <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
3509               </p>
3510             </td>
3511 <td>
3512               <p>
3513                 <span class="blue">Max = 0.761&#949; (Mean = 0.444&#949;)</span>
3514               </p>
3515             </td>
3516 </tr>
3517 <tr>
3518 <td>
3519               <p>
3520                 Bessel K'n: Mathworld Data (Integer Version)
3521               </p>
3522             </td>
3523 <td>
3524               <p>
3525                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3526               </p>
3527             </td>
3528 <td>
3529               <p>
3530                 <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
3531               </p>
3532             </td>
3533 <td>
3534               <p>
3535                 <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
3536               </p>
3537             </td>
3538 <td>
3539               <p>
3540                 <span class="blue">Max = 4.17&#949; (Mean = 1.75&#949;)</span>
3541               </p>
3542             </td>
3543 </tr>
3544 </tbody>
3545 </table></div>
3546 </div>
3547 <br class="table-break">
3548 </div>
3549 <div class="section">
3550 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
3551 <a name="special_function_error_rates_rep.section_cyl_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann" title="cyl_neumann">cyl_neumann</a>
3552 </h2></div></div></div>
3553 <div class="table">
3554 <a name="special_function_error_rates_rep.section_cyl_neumann.table_cyl_neumann"></a><p class="title"><b>Table&#160;20.&#160;Error rates for cyl_neumann</b></p>
3555 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
3556 <colgroup>
3557 <col>
3558 <col>
3559 <col>
3560 <col>
3561 <col>
3562 </colgroup>
3563 <thead><tr>
3564 <th>
3565             </th>
3566 <th>
3567               <p>
3568                 GNU C++ version 7.1.0<br> linux<br> long double
3569               </p>
3570             </th>
3571 <th>
3572               <p>
3573                 GNU C++ version 7.1.0<br> linux<br> double
3574               </p>
3575             </th>
3576 <th>
3577               <p>
3578                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
3579               </p>
3580             </th>
3581 <th>
3582               <p>
3583                 Microsoft Visual C++ version 14.1<br> Win32<br> double
3584               </p>
3585             </th>
3586 </tr></thead>
3587 <tbody>
3588 <tr>
3589 <td>
3590               <p>
3591                 Y0: Mathworld Data
3592               </p>
3593             </td>
3594 <td>
3595               <p>
3596                 <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span><br> <br>
3597                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean = 6.87e+04&#949;))
3598               </p>
3599             </td>
3600 <td>
3601               <p>
3602                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3603                 2.1:</em></span> Max = 60.9&#949; (Mean = 20.4&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3604                 Max = 167&#949; (Mean = 56.5&#949;))
3605               </p>
3606             </td>
3607 <td>
3608               <p>
3609                 <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
3610               </p>
3611             </td>
3612 <td>
3613               <p>
3614                 <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span>
3615               </p>
3616             </td>
3617 </tr>
3618 <tr>
3619 <td>
3620               <p>
3621                 Y1: Mathworld Data
3622               </p>
3623             </td>
3624 <td>
3625               <p>
3626                 <span class="blue">Max = 6.33&#949; (Mean = 2.25&#949;)</span><br> <br>
3627                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean = 4.08e+03&#949;))
3628               </p>
3629             </td>
3630 <td>
3631               <p>
3632                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3633                 2.1:</em></span> Max = 23.4&#949; (Mean = 8.1&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3634                 Max = 193&#949; (Mean = 64.4&#949;))
3635               </p>
3636             </td>
3637 <td>
3638               <p>
3639                 <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
3640               </p>
3641             </td>
3642 <td>
3643               <p>
3644                 <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span>
3645               </p>
3646             </td>
3647 </tr>
3648 <tr>
3649 <td>
3650               <p>
3651                 Yn: Mathworld Data
3652               </p>
3653             </td>
3654 <td>
3655               <p>
3656                 <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span><br> <br>
3657                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.2e+20&#949; (Mean
3658                 = 6.97e+19&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And
3659                 other failures.</a>)</span>
3660               </p>
3661             </td>
3662 <td>
3663               <p>
3664                 <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
3665                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And
3666                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3667                 Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
3668               </p>
3669             </td>
3670 <td>
3671               <p>
3672                 <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
3673               </p>
3674             </td>
3675 <td>
3676               <p>
3677                 <span class="blue">Max = 35&#949; (Mean = 11.9&#949;)</span>
3678               </p>
3679             </td>
3680 </tr>
3681 <tr>
3682 <td>
3683               <p>
3684                 Yv: Mathworld Data
3685               </p>
3686             </td>
3687 <td>
3688               <p>
3689                 <span class="blue">Max = 10.7&#949; (Mean = 4.93&#949;)</span><br> <br>
3690                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 3.49e+15&#949; (Mean
3691                 = 1.05e+15&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And
3692                 other failures.</a>)</span>
3693               </p>
3694             </td>
3695 <td>
3696               <p>
3697                 <span class="blue">Max = 10&#949; (Mean = 3.02&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3698                 2.1:</em></span> Max = 1.07e+05&#949; (Mean = 3.22e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And
3699                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3700                 Max = 243&#949; (Mean = 73.9&#949;))
3701               </p>
3702             </td>
3703 <td>
3704               <p>
3705                 <span class="blue">Max = 10.7&#949; (Mean = 5.1&#949;)</span>
3706               </p>
3707             </td>
3708 <td>
3709               <p>
3710                 <span class="blue">Max = 7.89&#949; (Mean = 3.27&#949;)</span>
3711               </p>
3712             </td>
3713 </tr>
3714 <tr>
3715 <td>
3716               <p>
3717                 Yv: Mathworld Data (large values)
3718               </p>
3719             </td>
3720 <td>
3721               <p>
3722                 <span class="blue">Max = 1.7&#949; (Mean = 1.33&#949;)</span><br> <br>
3723                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 43.2&#949; (Mean = 16.3&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And
3724                 other failures.</a>)
3725               </p>
3726             </td>
3727 <td>
3728               <p>
3729                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3730                 2.1:</em></span> Max = 60.8&#949; (Mean = 23&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And
3731                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3732                 Max = 0.682&#949; (Mean = 0.335&#949;))
3733               </p>
3734             </td>
3735 <td>
3736               <p>
3737                 <span class="blue">Max = 1.7&#949; (Mean = 1.33&#949;)</span>
3738               </p>
3739             </td>
3740 <td>
3741               <p>
3742                 <span class="blue">Max = 0.682&#949; (Mean = 0.423&#949;)</span>
3743               </p>
3744             </td>
3745 </tr>
3746 <tr>
3747 <td>
3748               <p>
3749                 Y0 and Y1: Random Data
3750               </p>
3751             </td>
3752 <td>
3753               <p>
3754                 <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span><br> <br>
3755                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.59e+03&#949; (Mean = 500&#949;))
3756               </p>
3757             </td>
3758 <td>
3759               <p>
3760                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3761                 2.1:</em></span> Max = 34.4&#949; (Mean = 8.9&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3762                 Max = 83&#949; (Mean = 14.2&#949;))
3763               </p>
3764             </td>
3765 <td>
3766               <p>
3767                 <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span>
3768               </p>
3769             </td>
3770 <td>
3771               <p>
3772                 <span class="blue">Max = 4.17&#949; (Mean = 1.24&#949;)</span>
3773               </p>
3774             </td>
3775 </tr>
3776 <tr>
3777 <td>
3778               <p>
3779                 Yn: Random Data
3780               </p>
3781             </td>
3782 <td>
3783               <p>
3784                 <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span><br> <br>
3785                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.01e+03&#949; (Mean = 348&#949;))
3786               </p>
3787             </td>
3788 <td>
3789               <p>
3790                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3791                 2.1:</em></span> Max = 500&#949; (Mean = 47.8&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3792                 Max = 691&#949; (Mean = 67.9&#949;))
3793               </p>
3794             </td>
3795 <td>
3796               <p>
3797                 <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span>
3798               </p>
3799             </td>
3800 <td>
3801               <p>
3802                 <span class="blue">Max = 117&#949; (Mean = 10.2&#949;)</span>
3803               </p>
3804             </td>
3805 </tr>
3806 <tr>
3807 <td>
3808               <p>
3809                 Yv: Random Data
3810               </p>
3811             </td>
3812 <td>
3813               <p>
3814                 <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span><br> <br>
3815                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
3816                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And
3817                 other failures.</a>)</span>
3818               </p>
3819             </td>
3820 <td>
3821               <p>
3822                 <span class="blue">Max = 1.53&#949; (Mean = 0.102&#949;)</span><br> <br>
3823                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06&#949; (Mean = 7.67e+04&#949;))<br>
3824                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05&#949; (Mean = 9.64e+03&#949;))
3825               </p>
3826             </td>
3827 <td>
3828               <p>
3829                 <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span>
3830               </p>
3831             </td>
3832 <td>
3833               <p>
3834                 <span class="blue">Max = 1.23e+03&#949; (Mean = 69.9&#949;)</span>
3835               </p>
3836             </td>
3837 </tr>
3838 </tbody>
3839 </table></div>
3840 </div>
3841 <br class="table-break">
3842 </div>
3843 <div class="section">
3844 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
3845 <a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_" title="cyl_neumann (integer orders)">cyl_neumann
3846     (integer orders)</a>
3847 </h2></div></div></div>
3848 <div class="table">
3849 <a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table&#160;21.&#160;Error rates for cyl_neumann (integer orders)</b></p>
3850 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
3851 <colgroup>
3852 <col>
3853 <col>
3854 <col>
3855 <col>
3856 <col>
3857 </colgroup>
3858 <thead><tr>
3859 <th>
3860             </th>
3861 <th>
3862               <p>
3863                 GNU C++ version 7.1.0<br> linux<br> long double
3864               </p>
3865             </th>
3866 <th>
3867               <p>
3868                 GNU C++ version 7.1.0<br> linux<br> double
3869               </p>
3870             </th>
3871 <th>
3872               <p>
3873                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
3874               </p>
3875             </th>
3876 <th>
3877               <p>
3878                 Microsoft Visual C++ version 14.1<br> Win32<br> double
3879               </p>
3880             </th>
3881 </tr></thead>
3882 <tbody>
3883 <tr>
3884 <td>
3885               <p>
3886                 Y0: Mathworld Data (Integer Version)
3887               </p>
3888             </td>
3889 <td>
3890               <p>
3891                 <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span><br> <br>
3892                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean = 6.87e+04&#949;))
3893               </p>
3894             </td>
3895 <td>
3896               <p>
3897                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3898                 2.1:</em></span> Max = 6.46&#949; (Mean = 2.38&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
3899                 Max = 167&#949; (Mean = 56.5&#949;))
3900               </p>
3901             </td>
3902 <td>
3903               <p>
3904                 <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
3905               </p>
3906             </td>
3907 <td>
3908               <p>
3909                 <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span><br> <br>
3910                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 5.37e+03&#949; (Mean = 1.81e+03&#949;))
3911               </p>
3912             </td>
3913 </tr>
3914 <tr>
3915 <td>
3916               <p>
3917                 Y1: Mathworld Data (Integer Version)
3918               </p>
3919             </td>
3920 <td>
3921               <p>
3922                 <span class="blue">Max = 6.33&#949; (Mean = 2.25&#949;)</span><br> <br>
3923                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean = 4.08e+03&#949;))
3924               </p>
3925             </td>
3926 <td>
3927               <p>
3928                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3929                 2.1:</em></span> Max = 1.51&#949; (Mean = 0.839&#949;))<br> (<span class="emphasis"><em>Rmath
3930                 3.2.3:</em></span> Max = 193&#949; (Mean = 64.4&#949;))
3931               </p>
3932             </td>
3933 <td>
3934               <p>
3935                 <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
3936               </p>
3937             </td>
3938 <td>
3939               <p>
3940                 <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span><br> <br>
3941                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.86e+04&#949; (Mean = 6.2e+03&#949;))
3942               </p>
3943             </td>
3944 </tr>
3945 <tr>
3946 <td>
3947               <p>
3948                 Yn: Mathworld Data (Integer Version)
3949               </p>
3950             </td>
3951 <td>
3952               <p>
3953                 <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span><br> <br>
3954                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.2e+20&#949; (Mean
3955                 = 6.97e+19&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And
3956                 other failures.</a>)</span>
3957               </p>
3958             </td>
3959 <td>
3960               <p>
3961                 <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
3962                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;))<br>
3963                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
3964               </p>
3965             </td>
3966 <td>
3967               <p>
3968                 <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
3969               </p>
3970             </td>
3971 <td>
3972               <p>
3973                 <span class="blue">Max = 35&#949; (Mean = 11.9&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
3974                 Max = 2.49e+05&#949; (Mean = 8.14e+04&#949;))
3975               </p>
3976             </td>
3977 </tr>
3978 </tbody>
3979 </table></div>
3980 </div>
3981 <br class="table-break">
3982 </div>
3983 <div class="section">
3984 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
3985 <a name="special_function_error_rates_rep.section_cyl_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime" title="cyl_neumann_prime">cyl_neumann_prime</a>
3986 </h2></div></div></div>
3987 <div class="table">
3988 <a name="special_function_error_rates_rep.section_cyl_neumann_prime.table_cyl_neumann_prime"></a><p class="title"><b>Table&#160;22.&#160;Error rates for cyl_neumann_prime</b></p>
3989 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
3990 <colgroup>
3991 <col>
3992 <col>
3993 <col>
3994 <col>
3995 <col>
3996 </colgroup>
3997 <thead><tr>
3998 <th>
3999             </th>
4000 <th>
4001               <p>
4002                 GNU C++ version 7.1.0<br> linux<br> double
4003               </p>
4004             </th>
4005 <th>
4006               <p>
4007                 GNU C++ version 7.1.0<br> linux<br> long double
4008               </p>
4009             </th>
4010 <th>
4011               <p>
4012                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
4013               </p>
4014             </th>
4015 <th>
4016               <p>
4017                 Microsoft Visual C++ version 14.1<br> Win32<br> double
4018               </p>
4019             </th>
4020 </tr></thead>
4021 <tbody>
4022 <tr>
4023 <td>
4024               <p>
4025                 Y'0: Mathworld Data
4026               </p>
4027             </td>
4028 <td>
4029               <p>
4030                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4031               </p>
4032             </td>
4033 <td>
4034               <p>
4035                 <span class="blue">Max = 6.33&#949; (Mean = 3.12&#949;)</span>
4036               </p>
4037             </td>
4038 <td>
4039               <p>
4040                 <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
4041               </p>
4042             </td>
4043 <td>
4044               <p>
4045                 <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
4046               </p>
4047             </td>
4048 </tr>
4049 <tr>
4050 <td>
4051               <p>
4052                 Y'1: Mathworld Data
4053               </p>
4054             </td>
4055 <td>
4056               <p>
4057                 <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
4058               </p>
4059             </td>
4060 <td>
4061               <p>
4062                 <span class="blue">Max = 37.1&#949; (Mean = 12.8&#949;)</span>
4063               </p>
4064             </td>
4065 <td>
4066               <p>
4067                 <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
4068               </p>
4069             </td>
4070 <td>
4071               <p>
4072                 <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
4073               </p>
4074             </td>
4075 </tr>
4076 <tr>
4077 <td>
4078               <p>
4079                 Y'n: Mathworld Data
4080               </p>
4081             </td>
4082 <td>
4083               <p>
4084                 <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
4085               </p>
4086             </td>
4087 <td>
4088               <p>
4089                 <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
4090               </p>
4091             </td>
4092 <td>
4093               <p>
4094                 <span class="blue">Max = 56&#949; (Mean = 21.3&#949;)</span>
4095               </p>
4096             </td>
4097 <td>
4098               <p>
4099                 <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
4100               </p>
4101             </td>
4102 </tr>
4103 <tr>
4104 <td>
4105               <p>
4106                 Y'v: Mathworld Data
4107               </p>
4108             </td>
4109 <td>
4110               <p>
4111                 <span class="blue">Max = 21.5&#949; (Mean = 6.49&#949;)</span>
4112               </p>
4113             </td>
4114 <td>
4115               <p>
4116                 <span class="blue">Max = 42.5&#949; (Mean = 13.4&#949;)</span>
4117               </p>
4118             </td>
4119 <td>
4120               <p>
4121                 <span class="blue">Max = 42.5&#949; (Mean = 13.6&#949;)</span>
4122               </p>
4123             </td>
4124 <td>
4125               <p>
4126                 <span class="blue">Max = 23.7&#949; (Mean = 10.1&#949;)</span>
4127               </p>
4128             </td>
4129 </tr>
4130 <tr>
4131 <td>
4132               <p>
4133                 Y'v: Mathworld Data (large values)
4134               </p>
4135             </td>
4136 <td>
4137               <p>
4138                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4139               </p>
4140             </td>
4141 <td>
4142               <p>
4143                 <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
4144               </p>
4145             </td>
4146 <td>
4147               <p>
4148                 <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
4149               </p>
4150             </td>
4151 <td>
4152               <p>
4153                 <span class="blue">Max = 0.627&#949; (Mean = 0.237&#949;)</span>
4154               </p>
4155             </td>
4156 </tr>
4157 <tr>
4158 <td>
4159               <p>
4160                 Y'0 and Y'1: Random Data
4161               </p>
4162             </td>
4163 <td>
4164               <p>
4165                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4166               </p>
4167             </td>
4168 <td>
4169               <p>
4170                 <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
4171               </p>
4172             </td>
4173 <td>
4174               <p>
4175                 <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
4176               </p>
4177             </td>
4178 <td>
4179               <p>
4180                 <span class="blue">Max = 5.95&#949; (Mean = 1.36&#949;)</span>
4181               </p>
4182             </td>
4183 </tr>
4184 <tr>
4185 <td>
4186               <p>
4187                 Y'n: Random Data
4188               </p>
4189             </td>
4190 <td>
4191               <p>
4192                 <span class="blue">Max = 1.53&#949; (Mean = 0.0885&#949;)</span>
4193               </p>
4194             </td>
4195 <td>
4196               <p>
4197                 <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
4198               </p>
4199             </td>
4200 <td>
4201               <p>
4202                 <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
4203               </p>
4204             </td>
4205 <td>
4206               <p>
4207                 <span class="blue">Max = 621&#949; (Mean = 36&#949;)</span>
4208               </p>
4209             </td>
4210 </tr>
4211 <tr>
4212 <td>
4213               <p>
4214                 Y'v: Random Data
4215               </p>
4216             </td>
4217 <td>
4218               <p>
4219                 <span class="blue">Max = 56.8&#949; (Mean = 2.59&#949;)</span>
4220               </p>
4221             </td>
4222 <td>
4223               <p>
4224                 <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
4225               </p>
4226             </td>
4227 <td>
4228               <p>
4229                 <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
4230               </p>
4231             </td>
4232 <td>
4233               <p>
4234                 <span class="blue">Max = 3.23e+04&#949; (Mean = 1.13e+03&#949;)</span>
4235               </p>
4236             </td>
4237 </tr>
4238 </tbody>
4239 </table></div>
4240 </div>
4241 <br class="table-break">
4242 </div>
4243 <div class="section">
4244 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
4245 <a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_" title="cyl_neumann_prime (integer orders)">cyl_neumann_prime
4246     (integer orders)</a>
4247 </h2></div></div></div>
4248 <div class="table">
4249 <a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table&#160;23.&#160;Error rates for cyl_neumann_prime (integer orders)</b></p>
4250 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
4251 <colgroup>
4252 <col>
4253 <col>
4254 <col>
4255 <col>
4256 <col>
4257 </colgroup>
4258 <thead><tr>
4259 <th>
4260             </th>
4261 <th>
4262               <p>
4263                 GNU C++ version 7.1.0<br> linux<br> double
4264               </p>
4265             </th>
4266 <th>
4267               <p>
4268                 GNU C++ version 7.1.0<br> linux<br> long double
4269               </p>
4270             </th>
4271 <th>
4272               <p>
4273                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
4274               </p>
4275             </th>
4276 <th>
4277               <p>
4278                 Microsoft Visual C++ version 14.1<br> Win32<br> double
4279               </p>
4280             </th>
4281 </tr></thead>
4282 <tbody>
4283 <tr>
4284 <td>
4285               <p>
4286                 Y'0: Mathworld Data (Integer Version)
4287               </p>
4288             </td>
4289 <td>
4290               <p>
4291                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4292               </p>
4293             </td>
4294 <td>
4295               <p>
4296                 <span class="blue">Max = 6.33&#949; (Mean = 3.12&#949;)</span>
4297               </p>
4298             </td>
4299 <td>
4300               <p>
4301                 <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
4302               </p>
4303             </td>
4304 <td>
4305               <p>
4306                 <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
4307               </p>
4308             </td>
4309 </tr>
4310 <tr>
4311 <td>
4312               <p>
4313                 Y'1: Mathworld Data (Integer Version)
4314               </p>
4315             </td>
4316 <td>
4317               <p>
4318                 <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
4319               </p>
4320             </td>
4321 <td>
4322               <p>
4323                 <span class="blue">Max = 37.1&#949; (Mean = 12.8&#949;)</span>
4324               </p>
4325             </td>
4326 <td>
4327               <p>
4328                 <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
4329               </p>
4330             </td>
4331 <td>
4332               <p>
4333                 <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
4334               </p>
4335             </td>
4336 </tr>
4337 <tr>
4338 <td>
4339               <p>
4340                 Y'n: Mathworld Data (Integer Version)
4341               </p>
4342             </td>
4343 <td>
4344               <p>
4345                 <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
4346               </p>
4347             </td>
4348 <td>
4349               <p>
4350                 <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
4351               </p>
4352             </td>
4353 <td>
4354               <p>
4355                 <span class="blue">Max = 56&#949; (Mean = 21.3&#949;)</span>
4356               </p>
4357             </td>
4358 <td>
4359               <p>
4360                 <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
4361               </p>
4362             </td>
4363 </tr>
4364 </tbody>
4365 </table></div>
4366 </div>
4367 <br class="table-break">
4368 </div>
4369 <div class="section">
4370 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
4371 <a name="special_function_error_rates_rep.section_digamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_digamma" title="digamma">digamma</a>
4372 </h2></div></div></div>
4373 <div class="table">
4374 <a name="special_function_error_rates_rep.section_digamma.table_digamma"></a><p class="title"><b>Table&#160;24.&#160;Error rates for digamma</b></p>
4375 <div class="table-contents"><table class="table" summary="Error rates for digamma">
4376 <colgroup>
4377 <col>
4378 <col>
4379 <col>
4380 <col>
4381 <col>
4382 </colgroup>
4383 <thead><tr>
4384 <th>
4385             </th>
4386 <th>
4387               <p>
4388                 GNU C++ version 7.1.0<br> linux<br> double
4389               </p>
4390             </th>
4391 <th>
4392               <p>
4393                 GNU C++ version 7.1.0<br> linux<br> long double
4394               </p>
4395             </th>
4396 <th>
4397               <p>
4398                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
4399               </p>
4400             </th>
4401 <th>
4402               <p>
4403                 Microsoft Visual C++ version 14.1<br> Win32<br> double
4404               </p>
4405             </th>
4406 </tr></thead>
4407 <tbody>
4408 <tr>
4409 <td>
4410               <p>
4411                 Digamma Function: Large Values
4412               </p>
4413             </td>
4414 <td>
4415               <p>
4416                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4417                 2.1:</em></span> Max = 1.84&#949; (Mean = 0.71&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
4418                 Max = 1.18&#949; (Mean = 0.331&#949;))
4419               </p>
4420             </td>
4421 <td>
4422               <p>
4423                 <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
4424               </p>
4425             </td>
4426 <td>
4427               <p>
4428                 <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
4429               </p>
4430             </td>
4431 <td>
4432               <p>
4433                 <span class="blue">Max = 0.98&#949; (Mean = 0.369&#949;)</span>
4434               </p>
4435             </td>
4436 </tr>
4437 <tr>
4438 <td>
4439               <p>
4440                 Digamma Function: Near the Positive Root
4441               </p>
4442             </td>
4443 <td>
4444               <p>
4445                 <span class="blue">Max = 0.891&#949; (Mean = 0.0995&#949;)</span><br> <br>
4446                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135&#949; (Mean = 11.9&#949;))<br> (<span class="emphasis"><em>Rmath
4447                 3.2.3:</em></span> Max = 2.02e+03&#949; (Mean = 256&#949;))
4448               </p>
4449             </td>
4450 <td>
4451               <p>
4452                 <span class="blue">Max = 1.37&#949; (Mean = 0.477&#949;)</span>
4453               </p>
4454             </td>
4455 <td>
4456               <p>
4457                 <span class="blue">Max = 1.31&#949; (Mean = 0.471&#949;)</span>
4458               </p>
4459             </td>
4460 <td>
4461               <p>
4462                 <span class="blue">Max = 0.997&#949; (Mean = 0.527&#949;)</span>
4463               </p>
4464             </td>
4465 </tr>
4466 <tr>
4467 <td>
4468               <p>
4469                 Digamma Function: Near Zero
4470               </p>
4471             </td>
4472 <td>
4473               <p>
4474                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4475                 2.1:</em></span> Max = 0.953&#949; (Mean = 0.348&#949;))<br> (<span class="emphasis"><em>Rmath
4476                 3.2.3:</em></span> Max = 1.17&#949; (Mean = 0.564&#949;))
4477               </p>
4478             </td>
4479 <td>
4480               <p>
4481                 <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
4482               </p>
4483             </td>
4484 <td>
4485               <p>
4486                 <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
4487               </p>
4488             </td>
4489 <td>
4490               <p>
4491                 <span class="blue">Max = 0.953&#949; (Mean = 0.337&#949;)</span>
4492               </p>
4493             </td>
4494 </tr>
4495 <tr>
4496 <td>
4497               <p>
4498                 Digamma Function: Negative Values
4499               </p>
4500             </td>
4501 <td>
4502               <p>
4503                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4504                 2.1:</em></span> Max = 4.56e+04&#949; (Mean = 3.91e+03&#949;))<br> (<span class="emphasis"><em>Rmath
4505                 3.2.3:</em></span> Max = 4.6e+04&#949; (Mean = 3.94e+03&#949;))
4506               </p>
4507             </td>
4508 <td>
4509               <p>
4510                 <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
4511               </p>
4512             </td>
4513 <td>
4514               <p>
4515                 <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
4516               </p>
4517             </td>
4518 <td>
4519               <p>
4520                 <span class="blue">Max = 214&#949; (Mean = 16.1&#949;)</span>
4521               </p>
4522             </td>
4523 </tr>
4524 <tr>
4525 <td>
4526               <p>
4527                 Digamma Function: Values near 0
4528               </p>
4529             </td>
4530 <td>
4531               <p>
4532                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4533                 2.1:</em></span> Max = 0.866&#949; (Mean = 0.387&#949;))<br> (<span class="emphasis"><em>Rmath
4534                 3.2.3:</em></span> Max = 3.58e+05&#949; (Mean = 1.6e+05&#949;))
4535               </p>
4536             </td>
4537 <td>
4538               <p>
4539                 <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
4540               </p>
4541             </td>
4542 <td>
4543               <p>
4544                 <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
4545               </p>
4546             </td>
4547 <td>
4548               <p>
4549                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4550               </p>
4551             </td>
4552 </tr>
4553 <tr>
4554 <td>
4555               <p>
4556                 Digamma Function: Integer arguments
4557               </p>
4558             </td>
4559 <td>
4560               <p>
4561                 <span class="blue">Max = 0.992&#949; (Mean = 0.215&#949;)</span><br> <br>
4562                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18&#949; (Mean = 0.607&#949;))<br> (<span class="emphasis"><em>Rmath
4563                 3.2.3:</em></span> Max = 4.33&#949; (Mean = 0.982&#949;))
4564               </p>
4565             </td>
4566 <td>
4567               <p>
4568                 <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
4569               </p>
4570             </td>
4571 <td>
4572               <p>
4573                 <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
4574               </p>
4575             </td>
4576 <td>
4577               <p>
4578                 <span class="blue">Max = 0.992&#949; (Mean = 0.452&#949;)</span>
4579               </p>
4580             </td>
4581 </tr>
4582 <tr>
4583 <td>
4584               <p>
4585                 Digamma Function: Half integer arguments
4586               </p>
4587             </td>
4588 <td>
4589               <p>
4590                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4591                 2.1:</em></span> Max = 1.09&#949; (Mean = 0.531&#949;))<br> (<span class="emphasis"><em>Rmath
4592                 3.2.3:</em></span> Max = 46.2&#949; (Mean = 7.24&#949;))
4593               </p>
4594             </td>
4595 <td>
4596               <p>
4597                 <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
4598               </p>
4599             </td>
4600 <td>
4601               <p>
4602                 <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
4603               </p>
4604             </td>
4605 <td>
4606               <p>
4607                 <span class="blue">Max = 0.78&#949; (Mean = 0.314&#949;)</span>
4608               </p>
4609             </td>
4610 </tr>
4611 </tbody>
4612 </table></div>
4613 </div>
4614 <br class="table-break">
4615 </div>
4616 <div class="section">
4617 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
4618 <a name="special_function_error_rates_rep.section_ellint_1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1" title="ellint_1">ellint_1</a>
4619 </h2></div></div></div>
4620 <div class="table">
4621 <a name="special_function_error_rates_rep.section_ellint_1.table_ellint_1"></a><p class="title"><b>Table&#160;25.&#160;Error rates for ellint_1</b></p>
4622 <div class="table-contents"><table class="table" summary="Error rates for ellint_1">
4623 <colgroup>
4624 <col>
4625 <col>
4626 <col>
4627 <col>
4628 <col>
4629 </colgroup>
4630 <thead><tr>
4631 <th>
4632             </th>
4633 <th>
4634               <p>
4635                 GNU C++ version 7.1.0<br> linux<br> long double
4636               </p>
4637             </th>
4638 <th>
4639               <p>
4640                 GNU C++ version 7.1.0<br> linux<br> double
4641               </p>
4642             </th>
4643 <th>
4644               <p>
4645                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
4646               </p>
4647             </th>
4648 <th>
4649               <p>
4650                 Microsoft Visual C++ version 14.1<br> Win32<br> double
4651               </p>
4652             </th>
4653 </tr></thead>
4654 <tbody>
4655 <tr>
4656 <td>
4657               <p>
4658                 Elliptic Integral F: Mathworld Data
4659               </p>
4660             </td>
4661 <td>
4662               <p>
4663                 <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span><br> <br>
4664                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
4665                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And
4666                 other failures.</a>)</span>
4667               </p>
4668             </td>
4669 <td>
4670               <p>
4671                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4672                 2.1:</em></span> Max = 0.919&#949; (Mean = 0.544&#949;))
4673               </p>
4674             </td>
4675 <td>
4676               <p>
4677                 <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span>
4678               </p>
4679             </td>
4680 <td>
4681               <p>
4682                 <span class="blue">Max = 0.919&#949; (Mean = 0.542&#949;)</span>
4683               </p>
4684             </td>
4685 </tr>
4686 <tr>
4687 <td>
4688               <p>
4689                 Elliptic Integral F: Random Data
4690               </p>
4691             </td>
4692 <td>
4693               <p>
4694                 <span class="blue">Max = 1.57&#949; (Mean = 0.56&#949;)</span><br> <br>
4695                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.56&#949; (Mean = 0.816&#949;))
4696               </p>
4697             </td>
4698 <td>
4699               <p>
4700                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4701                 2.1:</em></span> Max = 2.99&#949; (Mean = 0.797&#949;))
4702               </p>
4703             </td>
4704 <td>
4705               <p>
4706                 <span class="blue">Max = 1.57&#949; (Mean = 0.561&#949;)</span>
4707               </p>
4708             </td>
4709 <td>
4710               <p>
4711                 <span class="blue">Max = 2.26&#949; (Mean = 0.631&#949;)</span>
4712               </p>
4713             </td>
4714 </tr>
4715 </tbody>
4716 </table></div>
4717 </div>
4718 <br class="table-break">
4719 </div>
4720 <div class="section">
4721 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
4722 <a name="special_function_error_rates_rep.section_ellint_1_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1_complete_" title="ellint_1 (complete)">ellint_1
4723     (complete)</a>
4724 </h2></div></div></div>
4725 <div class="table">
4726 <a name="special_function_error_rates_rep.section_ellint_1_complete_.table_ellint_1_complete_"></a><p class="title"><b>Table&#160;26.&#160;Error rates for ellint_1 (complete)</b></p>
4727 <div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
4728 <colgroup>
4729 <col>
4730 <col>
4731 <col>
4732 <col>
4733 <col>
4734 </colgroup>
4735 <thead><tr>
4736 <th>
4737             </th>
4738 <th>
4739               <p>
4740                 GNU C++ version 7.1.0<br> linux<br> long double
4741               </p>
4742             </th>
4743 <th>
4744               <p>
4745                 GNU C++ version 7.1.0<br> linux<br> double
4746               </p>
4747             </th>
4748 <th>
4749               <p>
4750                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
4751               </p>
4752             </th>
4753 <th>
4754               <p>
4755                 Microsoft Visual C++ version 14.1<br> Win32<br> double
4756               </p>
4757             </th>
4758 </tr></thead>
4759 <tbody>
4760 <tr>
4761 <td>
4762               <p>
4763                 Elliptic Integral K: Mathworld Data
4764               </p>
4765             </td>
4766 <td>
4767               <p>
4768                 <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span><br> <br>
4769                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.19&#949; (Mean = 0.765&#949;))
4770               </p>
4771             </td>
4772 <td>
4773               <p>
4774                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4775                 2.1:</em></span> Max = 0.623&#949; (Mean = 0.393&#949;))
4776               </p>
4777             </td>
4778 <td>
4779               <p>
4780                 <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span>
4781               </p>
4782             </td>
4783 <td>
4784               <p>
4785                 <span class="blue">Max = 0.915&#949; (Mean = 0.547&#949;)</span>
4786               </p>
4787             </td>
4788 </tr>
4789 <tr>
4790 <td>
4791               <p>
4792                 Elliptic Integral K: Random Data
4793               </p>
4794             </td>
4795 <td>
4796               <p>
4797                 <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span><br> <br>
4798                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.19&#949; (Mean = 0.694&#949;))
4799               </p>
4800             </td>
4801 <td>
4802               <p>
4803                 <span class="blue">Max = 0.851&#949; (Mean = 0.0851&#949;)</span><br> <br>
4804                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32&#949; (Mean = 0.688&#949;))
4805               </p>
4806             </td>
4807 <td>
4808               <p>
4809                 <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span>
4810               </p>
4811             </td>
4812 <td>
4813               <p>
4814                 <span class="blue">Max = 0.958&#949; (Mean = 0.408&#949;)</span>
4815               </p>
4816             </td>
4817 </tr>
4818 </tbody>
4819 </table></div>
4820 </div>
4821 <br class="table-break">
4822 </div>
4823 <div class="section">
4824 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
4825 <a name="special_function_error_rates_rep.section_ellint_2"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2" title="ellint_2">ellint_2</a>
4826 </h2></div></div></div>
4827 <div class="table">
4828 <a name="special_function_error_rates_rep.section_ellint_2.table_ellint_2"></a><p class="title"><b>Table&#160;27.&#160;Error rates for ellint_2</b></p>
4829 <div class="table-contents"><table class="table" summary="Error rates for ellint_2">
4830 <colgroup>
4831 <col>
4832 <col>
4833 <col>
4834 <col>
4835 <col>
4836 </colgroup>
4837 <thead><tr>
4838 <th>
4839             </th>
4840 <th>
4841               <p>
4842                 GNU C++ version 7.1.0<br> linux<br> double
4843               </p>
4844             </th>
4845 <th>
4846               <p>
4847                 GNU C++ version 7.1.0<br> linux<br> long double
4848               </p>
4849             </th>
4850 <th>
4851               <p>
4852                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
4853               </p>
4854             </th>
4855 <th>
4856               <p>
4857                 Microsoft Visual C++ version 14.1<br> Win32<br> double
4858               </p>
4859             </th>
4860 </tr></thead>
4861 <tbody>
4862 <tr>
4863 <td>
4864               <p>
4865                 Elliptic Integral E: Mathworld Data
4866               </p>
4867             </td>
4868 <td>
4869               <p>
4870                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4871                 2.1:</em></span> Max = 0.63&#949; (Mean = 0.325&#949;))
4872               </p>
4873             </td>
4874 <td>
4875               <p>
4876                 <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span><br> <br>
4877                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
4878                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And
4879                 other failures.</a>)</span>
4880               </p>
4881             </td>
4882 <td>
4883               <p>
4884                 <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span>
4885               </p>
4886             </td>
4887 <td>
4888               <p>
4889                 <span class="blue">Max = 1.31&#949; (Mean = 0.727&#949;)</span>
4890               </p>
4891             </td>
4892 </tr>
4893 <tr>
4894 <td>
4895               <p>
4896                 Elliptic Integral E: Random Data
4897               </p>
4898             </td>
4899 <td>
4900               <p>
4901                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4902                 2.1:</em></span> Max = 4.4&#949; (Mean = 1.16&#949;))
4903               </p>
4904             </td>
4905 <td>
4906               <p>
4907                 <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span><br> <br>
4908                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.08e+04&#949; (Mean = 3.84e+03&#949;))
4909               </p>
4910             </td>
4911 <td>
4912               <p>
4913                 <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span>
4914               </p>
4915             </td>
4916 <td>
4917               <p>
4918                 <span class="blue">Max = 2.23&#949; (Mean = 0.639&#949;)</span>
4919               </p>
4920             </td>
4921 </tr>
4922 <tr>
4923 <td>
4924               <p>
4925                 Elliptic Integral E: Small Angles
4926               </p>
4927             </td>
4928 <td>
4929               <p>
4930                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4931                 2.1:</em></span> Max = 0.5&#949; (Mean = 0.118&#949;))
4932               </p>
4933             </td>
4934 <td>
4935               <p>
4936                 <span class="blue">Max = 1&#949; (Mean = 0.283&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
4937                 Max = 2&#949; (Mean = 0.333&#949;))
4938               </p>
4939             </td>
4940 <td>
4941               <p>
4942                 <span class="blue">Max = 1&#949; (Mean = 0.283&#949;)</span>
4943               </p>
4944             </td>
4945 <td>
4946               <p>
4947                 <span class="blue">Max = 1&#949; (Mean = 0.421&#949;)</span>
4948               </p>
4949             </td>
4950 </tr>
4951 </tbody>
4952 </table></div>
4953 </div>
4954 <br class="table-break">
4955 </div>
4956 <div class="section">
4957 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
4958 <a name="special_function_error_rates_rep.section_ellint_2_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2_complete_" title="ellint_2 (complete)">ellint_2
4959     (complete)</a>
4960 </h2></div></div></div>
4961 <div class="table">
4962 <a name="special_function_error_rates_rep.section_ellint_2_complete_.table_ellint_2_complete_"></a><p class="title"><b>Table&#160;28.&#160;Error rates for ellint_2 (complete)</b></p>
4963 <div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
4964 <colgroup>
4965 <col>
4966 <col>
4967 <col>
4968 <col>
4969 <col>
4970 </colgroup>
4971 <thead><tr>
4972 <th>
4973             </th>
4974 <th>
4975               <p>
4976                 GNU C++ version 7.1.0<br> linux<br> double
4977               </p>
4978             </th>
4979 <th>
4980               <p>
4981                 GNU C++ version 7.1.0<br> linux<br> long double
4982               </p>
4983             </th>
4984 <th>
4985               <p>
4986                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
4987               </p>
4988             </th>
4989 <th>
4990               <p>
4991                 Microsoft Visual C++ version 14.1<br> Win32<br> double
4992               </p>
4993             </th>
4994 </tr></thead>
4995 <tbody>
4996 <tr>
4997 <td>
4998               <p>
4999                 Elliptic Integral E: Mathworld Data
5000               </p>
5001             </td>
5002 <td>
5003               <p>
5004                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5005                 2.1:</em></span> Max = 3.09&#949; (Mean = 1.04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And
5006                 other failures.</a>)
5007               </p>
5008             </td>
5009 <td>
5010               <p>
5011                 <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span><br> <br>
5012                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 170&#949; (Mean = 55.1&#949;))
5013               </p>
5014             </td>
5015 <td>
5016               <p>
5017                 <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span>
5018               </p>
5019             </td>
5020 <td>
5021               <p>
5022                 <span class="blue">Max = 1.3&#949; (Mean = 0.615&#949;)</span>
5023               </p>
5024             </td>
5025 </tr>
5026 <tr>
5027 <td>
5028               <p>
5029                 Elliptic Integral E: Random Data
5030               </p>
5031             </td>
5032 <td>
5033               <p>
5034                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5035                 2.1:</em></span> Max = 4.34&#949; (Mean = 1.18&#949;))
5036               </p>
5037             </td>
5038 <td>
5039               <p>
5040                 <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span><br> <br>
5041                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.49e+04&#949; (Mean = 3.39e+03&#949;))
5042               </p>
5043             </td>
5044 <td>
5045               <p>
5046                 <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span>
5047               </p>
5048             </td>
5049 <td>
5050               <p>
5051                 <span class="blue">Max = 1.71&#949; (Mean = 0.553&#949;)</span>
5052               </p>
5053             </td>
5054 </tr>
5055 </tbody>
5056 </table></div>
5057 </div>
5058 <br class="table-break">
5059 </div>
5060 <div class="section">
5061 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
5062 <a name="special_function_error_rates_rep.section_ellint_3"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3" title="ellint_3">ellint_3</a>
5063 </h2></div></div></div>
5064 <div class="table">
5065 <a name="special_function_error_rates_rep.section_ellint_3.table_ellint_3"></a><p class="title"><b>Table&#160;29.&#160;Error rates for ellint_3</b></p>
5066 <div class="table-contents"><table class="table" summary="Error rates for ellint_3">
5067 <colgroup>
5068 <col>
5069 <col>
5070 <col>
5071 <col>
5072 <col>
5073 </colgroup>
5074 <thead><tr>
5075 <th>
5076             </th>
5077 <th>
5078               <p>
5079                 GNU C++ version 7.1.0<br> linux<br> long double
5080               </p>
5081             </th>
5082 <th>
5083               <p>
5084                 GNU C++ version 7.1.0<br> linux<br> double
5085               </p>
5086             </th>
5087 <th>
5088               <p>
5089                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
5090               </p>
5091             </th>
5092 <th>
5093               <p>
5094                 Microsoft Visual C++ version 14.1<br> Win32<br> double
5095               </p>
5096             </th>
5097 </tr></thead>
5098 <tbody>
5099 <tr>
5100 <td>
5101               <p>
5102                 Elliptic Integral PI: Mathworld Data
5103               </p>
5104             </td>
5105 <td>
5106               <p>
5107                 <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span><br> <br>
5108                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
5109                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And
5110                 other failures.</a>)</span>
5111               </p>
5112             </td>
5113 <td>
5114               <p>
5115                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5116                 2.1:</em></span> Max = 1.48e+05&#949; (Mean = 2.54e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And
5117                 other failures.</a>)
5118               </p>
5119             </td>
5120 <td>
5121               <p>
5122                 <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span>
5123               </p>
5124             </td>
5125 <td>
5126               <p>
5127                 <span class="blue">Max = 565&#949; (Mean = 102&#949;)</span>
5128               </p>
5129             </td>
5130 </tr>
5131 <tr>
5132 <td>
5133               <p>
5134                 Elliptic Integral PI: Random Data
5135               </p>
5136             </td>
5137 <td>
5138               <p>
5139                 <span class="blue">Max = 4.54&#949; (Mean = 0.895&#949;)</span><br> <br>
5140                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 3.37e+20&#949; (Mean
5141                 = 3.47e+19&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And
5142                 other failures.</a>)</span>
5143               </p>
5144             </td>
5145 <td>
5146               <p>
5147                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5148                 2.1:</em></span> Max = 633&#949; (Mean = 50.1&#949;))
5149               </p>
5150             </td>
5151 <td>
5152               <p>
5153                 <span class="blue">Max = 4.49&#949; (Mean = 0.885&#949;)</span>
5154               </p>
5155             </td>
5156 <td>
5157               <p>
5158                 <span class="blue">Max = 8.33&#949; (Mean = 0.971&#949;)</span>
5159               </p>
5160             </td>
5161 </tr>
5162 <tr>
5163 <td>
5164               <p>
5165                 Elliptic Integral PI: Large Random Data
5166               </p>
5167             </td>
5168 <td>
5169               <p>
5170                 <span class="blue">Max = 3.7&#949; (Mean = 0.893&#949;)</span><br> <br>
5171                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.52e+18&#949; (Mean
5172                 = 4.83e+17&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And
5173                 other failures.</a>)</span>
5174               </p>
5175             </td>
5176 <td>
5177               <p>
5178                 <span class="blue">Max = 0.557&#949; (Mean = 0.0389&#949;)</span><br> <br>
5179                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1&#949; (Mean = 7.77&#949;))
5180               </p>
5181             </td>
5182 <td>
5183               <p>
5184                 <span class="blue">Max = 3.7&#949; (Mean = 0.892&#949;)</span>
5185               </p>
5186             </td>
5187 <td>
5188               <p>
5189                 <span class="blue">Max = 2.86&#949; (Mean = 0.944&#949;)</span>
5190               </p>
5191             </td>
5192 </tr>
5193 </tbody>
5194 </table></div>
5195 </div>
5196 <br class="table-break">
5197 </div>
5198 <div class="section">
5199 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
5200 <a name="special_function_error_rates_rep.section_ellint_3_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3_complete_" title="ellint_3 (complete)">ellint_3
5201     (complete)</a>
5202 </h2></div></div></div>
5203 <div class="table">
5204 <a name="special_function_error_rates_rep.section_ellint_3_complete_.table_ellint_3_complete_"></a><p class="title"><b>Table&#160;30.&#160;Error rates for ellint_3 (complete)</b></p>
5205 <div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
5206 <colgroup>
5207 <col>
5208 <col>
5209 <col>
5210 <col>
5211 <col>
5212 </colgroup>
5213 <thead><tr>
5214 <th>
5215             </th>
5216 <th>
5217               <p>
5218                 GNU C++ version 7.1.0<br> linux<br> long double
5219               </p>
5220             </th>
5221 <th>
5222               <p>
5223                 GNU C++ version 7.1.0<br> linux<br> double
5224               </p>
5225             </th>
5226 <th>
5227               <p>
5228                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
5229               </p>
5230             </th>
5231 <th>
5232               <p>
5233                 Microsoft Visual C++ version 14.1<br> Win32<br> double
5234               </p>
5235             </th>
5236 </tr></thead>
5237 <tbody>
5238 <tr>
5239 <td>
5240               <p>
5241                 Complete Elliptic Integral PI: Mathworld Data
5242               </p>
5243             </td>
5244 <td>
5245               <p>
5246                 <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span><br> <br>
5247                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 6.31e+20&#949; (Mean
5248                 = 1.53e+20&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
5249                 other failures.</a>)</span>
5250               </p>
5251             </td>
5252 <td>
5253               <p>
5254                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5255                 2.1:</em></span> Max = 6.33e+04&#949; (Mean = 1.54e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And
5256                 other failures.</a>)
5257               </p>
5258             </td>
5259 <td>
5260               <p>
5261                 <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span>
5262               </p>
5263             </td>
5264 <td>
5265               <p>
5266                 <span class="blue">Max = 0.971&#949; (Mean = 0.464&#949;)</span>
5267               </p>
5268             </td>
5269 </tr>
5270 <tr>
5271 <td>
5272               <p>
5273                 Complete Elliptic Integral PI: Random Data
5274               </p>
5275             </td>
5276 <td>
5277               <p>
5278                 <span class="blue">Max = 2.45&#949; (Mean = 0.696&#949;)</span><br> <br>
5279                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 8.78e+20&#949; (Mean
5280                 = 1.02e+20&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And
5281                 other failures.</a>)</span>
5282               </p>
5283             </td>
5284 <td>
5285               <p>
5286                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5287                 2.1:</em></span> Max = 24&#949; (Mean = 2.99&#949;))
5288               </p>
5289             </td>
5290 <td>
5291               <p>
5292                 <span class="blue">Max = 2.4&#949; (Mean = 0.677&#949;)</span>
5293               </p>
5294             </td>
5295 <td>
5296               <p>
5297                 <span class="blue">Max = 2.46&#949; (Mean = 0.657&#949;)</span>
5298               </p>
5299             </td>
5300 </tr>
5301 </tbody>
5302 </table></div>
5303 </div>
5304 <br class="table-break">
5305 </div>
5306 <div class="section">
5307 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
5308 <a name="special_function_error_rates_rep.section_ellint_d"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d" title="ellint_d">ellint_d</a>
5309 </h2></div></div></div>
5310 <div class="table">
5311 <a name="special_function_error_rates_rep.section_ellint_d.table_ellint_d"></a><p class="title"><b>Table&#160;31.&#160;Error rates for ellint_d</b></p>
5312 <div class="table-contents"><table class="table" summary="Error rates for ellint_d">
5313 <colgroup>
5314 <col>
5315 <col>
5316 <col>
5317 <col>
5318 <col>
5319 </colgroup>
5320 <thead><tr>
5321 <th>
5322             </th>
5323 <th>
5324               <p>
5325                 GNU C++ version 7.1.0<br> linux<br> double
5326               </p>
5327             </th>
5328 <th>
5329               <p>
5330                 GNU C++ version 7.1.0<br> linux<br> long double
5331               </p>
5332             </th>
5333 <th>
5334               <p>
5335                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
5336               </p>
5337             </th>
5338 <th>
5339               <p>
5340                 Microsoft Visual C++ version 14.1<br> Win32<br> double
5341               </p>
5342             </th>
5343 </tr></thead>
5344 <tbody>
5345 <tr>
5346 <td>
5347               <p>
5348                 Elliptic Integral E: Mathworld Data
5349               </p>
5350             </td>
5351 <td>
5352               <p>
5353                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5354                 2.1:</em></span> Max = 0.862&#949; (Mean = 0.568&#949;))
5355               </p>
5356             </td>
5357 <td>
5358               <p>
5359                 <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
5360               </p>
5361             </td>
5362 <td>
5363               <p>
5364                 <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
5365               </p>
5366             </td>
5367 <td>
5368               <p>
5369                 <span class="blue">Max = 0.862&#949; (Mean = 0.457&#949;)</span>
5370               </p>
5371             </td>
5372 </tr>
5373 <tr>
5374 <td>
5375               <p>
5376                 Elliptic Integral D: Random Data
5377               </p>
5378             </td>
5379 <td>
5380               <p>
5381                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5382                 2.1:</em></span> Max = 3.01&#949; (Mean = 0.928&#949;))
5383               </p>
5384             </td>
5385 <td>
5386               <p>
5387                 <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
5388               </p>
5389             </td>
5390 <td>
5391               <p>
5392                 <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
5393               </p>
5394             </td>
5395 <td>
5396               <p>
5397                 <span class="blue">Max = 2.87&#949; (Mean = 0.805&#949;)</span>
5398               </p>
5399             </td>
5400 </tr>
5401 </tbody>
5402 </table></div>
5403 </div>
5404 <br class="table-break">
5405 </div>
5406 <div class="section">
5407 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
5408 <a name="special_function_error_rates_rep.section_ellint_d_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d_complete_" title="ellint_d (complete)">ellint_d
5409     (complete)</a>
5410 </h2></div></div></div>
5411 <div class="table">
5412 <a name="special_function_error_rates_rep.section_ellint_d_complete_.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;32.&#160;Error rates for ellint_d (complete)</b></p>
5413 <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
5414 <colgroup>
5415 <col>
5416 <col>
5417 <col>
5418 <col>
5419 <col>
5420 </colgroup>
5421 <thead><tr>
5422 <th>
5423             </th>
5424 <th>
5425               <p>
5426                 GNU C++ version 7.1.0<br> linux<br> double
5427               </p>
5428             </th>
5429 <th>
5430               <p>
5431                 GNU C++ version 7.1.0<br> linux<br> long double
5432               </p>
5433             </th>
5434 <th>
5435               <p>
5436                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
5437               </p>
5438             </th>
5439 <th>
5440               <p>
5441                 Microsoft Visual C++ version 14.1<br> Win32<br> double
5442               </p>
5443             </th>
5444 </tr></thead>
5445 <tbody>
5446 <tr>
5447 <td>
5448               <p>
5449                 Elliptic Integral E: Mathworld Data
5450               </p>
5451             </td>
5452 <td>
5453               <p>
5454                 <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
5455               </p>
5456             </td>
5457 <td>
5458               <p>
5459                 <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
5460               </p>
5461             </td>
5462 <td>
5463               <p>
5464                 <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
5465               </p>
5466             </td>
5467 <td>
5468               <p>
5469                 <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
5470               </p>
5471             </td>
5472 </tr>
5473 <tr>
5474 <td>
5475               <p>
5476                 Elliptic Integral D: Random Data
5477               </p>
5478             </td>
5479 <td>
5480               <p>
5481                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5482               </p>
5483             </td>
5484 <td>
5485               <p>
5486                 <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
5487               </p>
5488             </td>
5489 <td>
5490               <p>
5491                 <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
5492               </p>
5493             </td>
5494 <td>
5495               <p>
5496                 <span class="blue">Max = 1.27&#949; (Mean = 0.355&#949;)</span>
5497               </p>
5498             </td>
5499 </tr>
5500 </tbody>
5501 </table></div>
5502 </div>
5503 <br class="table-break">
5504 </div>
5505 <div class="section">
5506 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
5507 <a name="special_function_error_rates_rep.section_ellint_rc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rc" title="ellint_rc">ellint_rc</a>
5508 </h2></div></div></div>
5509 <div class="table">
5510 <a name="special_function_error_rates_rep.section_ellint_rc.table_ellint_rc"></a><p class="title"><b>Table&#160;33.&#160;Error rates for ellint_rc</b></p>
5511 <div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
5512 <colgroup>
5513 <col>
5514 <col>
5515 <col>
5516 <col>
5517 </colgroup>
5518 <thead><tr>
5519 <th>
5520             </th>
5521 <th>
5522               <p>
5523                 GNU C++ version 7.1.0<br> linux<br> double
5524               </p>
5525             </th>
5526 <th>
5527               <p>
5528                 GNU C++ version 7.1.0<br> linux<br> long double
5529               </p>
5530             </th>
5531 <th>
5532               <p>
5533                 Microsoft Visual C++ version 14.1<br> Win32<br> double
5534               </p>
5535             </th>
5536 </tr></thead>
5537 <tbody><tr>
5538 <td>
5539               <p>
5540                 RC: Random data
5541               </p>
5542             </td>
5543 <td>
5544               <p>
5545                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5546                 2.1:</em></span> Max = 2.4&#949; (Mean = 0.624&#949;))
5547               </p>
5548             </td>
5549 <td>
5550               <p>
5551                 <span class="blue">Max = 0.995&#949; (Mean = 0.433&#949;)</span>
5552               </p>
5553             </td>
5554 <td>
5555               <p>
5556                 <span class="blue">Max = 0.962&#949; (Mean = 0.407&#949;)</span>
5557               </p>
5558             </td>
5559 </tr></tbody>
5560 </table></div>
5561 </div>
5562 <br class="table-break">
5563 </div>
5564 <div class="section">
5565 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
5566 <a name="special_function_error_rates_rep.section_ellint_rd"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rd" title="ellint_rd">ellint_rd</a>
5567 </h2></div></div></div>
5568 <div class="table">
5569 <a name="special_function_error_rates_rep.section_ellint_rd.table_ellint_rd"></a><p class="title"><b>Table&#160;34.&#160;Error rates for ellint_rd</b></p>
5570 <div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
5571 <colgroup>
5572 <col>
5573 <col>
5574 <col>
5575 <col>
5576 </colgroup>
5577 <thead><tr>
5578 <th>
5579             </th>
5580 <th>
5581               <p>
5582                 GNU C++ version 7.1.0<br> linux<br> double
5583               </p>
5584             </th>
5585 <th>
5586               <p>
5587                 GNU C++ version 7.1.0<br> linux<br> long double
5588               </p>
5589             </th>
5590 <th>
5591               <p>
5592                 Microsoft Visual C++ version 14.1<br> Win32<br> double
5593               </p>
5594             </th>
5595 </tr></thead>
5596 <tbody>
5597 <tr>
5598 <td>
5599               <p>
5600                 RD: Random data
5601               </p>
5602             </td>
5603 <td>
5604               <p>
5605                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5606                 2.1:</em></span> Max = 2.59&#949; (Mean = 0.878&#949;))
5607               </p>
5608             </td>
5609 <td>
5610               <p>
5611                 <span class="blue">Max = 2.73&#949; (Mean = 0.831&#949;)</span>
5612               </p>
5613             </td>
5614 <td>
5615               <p>
5616                 <span class="blue">Max = 2.16&#949; (Mean = 0.803&#949;)</span>
5617               </p>
5618             </td>
5619 </tr>
5620 <tr>
5621 <td>
5622               <p>
5623                 RD: y = z
5624               </p>
5625             </td>
5626 <td>
5627               <p>
5628                 <span class="blue">Max = 0.896&#949; (Mean = 0.022&#949;)</span><br> <br>
5629                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88&#949; (Mean = 0.839&#949;))
5630               </p>
5631             </td>
5632 <td>
5633               <p>
5634                 <span class="blue">Max = 2.65&#949; (Mean = 0.82&#949;)</span>
5635               </p>
5636             </td>
5637 <td>
5638               <p>
5639                 <span class="blue">Max = 16.5&#949; (Mean = 0.843&#949;)</span>
5640               </p>
5641             </td>
5642 </tr>
5643 <tr>
5644 <td>
5645               <p>
5646                 RD: x = y
5647               </p>
5648             </td>
5649 <td>
5650               <p>
5651                 <span class="blue">Max = 0.824&#949; (Mean = 0.0272&#949;)</span><br> <br>
5652                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74&#949; (Mean = 0.84&#949;))
5653               </p>
5654             </td>
5655 <td>
5656               <p>
5657                 <span class="blue">Max = 2.85&#949; (Mean = 0.865&#949;)</span>
5658               </p>
5659             </td>
5660 <td>
5661               <p>
5662                 <span class="blue">Max = 3.51&#949; (Mean = 0.816&#949;)</span>
5663               </p>
5664             </td>
5665 </tr>
5666 <tr>
5667 <td>
5668               <p>
5669                 RD: x = 0, y = z
5670               </p>
5671             </td>
5672 <td>
5673               <p>
5674                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5675                 2.1:</em></span> Max = 2&#949; (Mean = 0.656&#949;))
5676               </p>
5677             </td>
5678 <td>
5679               <p>
5680                 <span class="blue">Max = 1.19&#949; (Mean = 0.522&#949;)</span>
5681               </p>
5682             </td>
5683 <td>
5684               <p>
5685                 <span class="blue">Max = 1.16&#949; (Mean = 0.497&#949;)</span>
5686               </p>
5687             </td>
5688 </tr>
5689 <tr>
5690 <td>
5691               <p>
5692                 RD: x = y = z
5693               </p>
5694             </td>
5695 <td>
5696               <p>
5697                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5698                 2.1:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
5699               </p>
5700             </td>
5701 <td>
5702               <p>
5703                 <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
5704               </p>
5705             </td>
5706 <td>
5707               <p>
5708                 <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
5709               </p>
5710             </td>
5711 </tr>
5712 <tr>
5713 <td>
5714               <p>
5715                 RD: x = 0
5716               </p>
5717             </td>
5718 <td>
5719               <p>
5720                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5721                 2.1:</em></span> Max = 2.85&#949; (Mean = 0.781&#949;))
5722               </p>
5723             </td>
5724 <td>
5725               <p>
5726                 <span class="blue">Max = 2.79&#949; (Mean = 0.883&#949;)</span>
5727               </p>
5728             </td>
5729 <td>
5730               <p>
5731                 <span class="blue">Max = 2.64&#949; (Mean = 0.894&#949;)</span>
5732               </p>
5733             </td>
5734 </tr>
5735 </tbody>
5736 </table></div>
5737 </div>
5738 <br class="table-break">
5739 </div>
5740 <div class="section">
5741 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
5742 <a name="special_function_error_rates_rep.section_ellint_rf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rf" title="ellint_rf">ellint_rf</a>
5743 </h2></div></div></div>
5744 <div class="table">
5745 <a name="special_function_error_rates_rep.section_ellint_rf.table_ellint_rf"></a><p class="title"><b>Table&#160;35.&#160;Error rates for ellint_rf</b></p>
5746 <div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
5747 <colgroup>
5748 <col>
5749 <col>
5750 <col>
5751 <col>
5752 </colgroup>
5753 <thead><tr>
5754 <th>
5755             </th>
5756 <th>
5757               <p>
5758                 GNU C++ version 7.1.0<br> linux<br> double
5759               </p>
5760             </th>
5761 <th>
5762               <p>
5763                 GNU C++ version 7.1.0<br> linux<br> long double
5764               </p>
5765             </th>
5766 <th>
5767               <p>
5768                 Microsoft Visual C++ version 14.1<br> Win32<br> double
5769               </p>
5770             </th>
5771 </tr></thead>
5772 <tbody>
5773 <tr>
5774 <td>
5775               <p>
5776                 RF: Random data
5777               </p>
5778             </td>
5779 <td>
5780               <p>
5781                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5782                 2.1:</em></span> Max = 2.73&#949; (Mean = 0.804&#949;))
5783               </p>
5784             </td>
5785 <td>
5786               <p>
5787                 <span class="blue">Max = 2.54&#949; (Mean = 0.674&#949;)</span>
5788               </p>
5789             </td>
5790 <td>
5791               <p>
5792                 <span class="blue">Max = 2.02&#949; (Mean = 0.677&#949;)</span>
5793               </p>
5794             </td>
5795 </tr>
5796 <tr>
5797 <td>
5798               <p>
5799                 RF: x = y = z
5800               </p>
5801             </td>
5802 <td>
5803               <p>
5804                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5805                 2.1:</em></span> Max = 0.999&#949; (Mean = 0.34&#949;))
5806               </p>
5807             </td>
5808 <td>
5809               <p>
5810                 <span class="blue">Max = 0.991&#949; (Mean = 0.345&#949;)</span>
5811               </p>
5812             </td>
5813 <td>
5814               <p>
5815                 <span class="blue">Max = 0.999&#949; (Mean = 0.34&#949;)</span>
5816               </p>
5817             </td>
5818 </tr>
5819 <tr>
5820 <td>
5821               <p>
5822                 RF: x = y or y = z or x = z
5823               </p>
5824             </td>
5825 <td>
5826               <p>
5827                 <span class="blue">Max = 0.536&#949; (Mean = 0.00658&#949;)</span><br> <br>
5828                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89&#949; (Mean = 0.749&#949;))
5829               </p>
5830             </td>
5831 <td>
5832               <p>
5833                 <span class="blue">Max = 1.95&#949; (Mean = 0.418&#949;)</span>
5834               </p>
5835             </td>
5836 <td>
5837               <p>
5838                 <span class="blue">Max = 1.21&#949; (Mean = 0.394&#949;)</span>
5839               </p>
5840             </td>
5841 </tr>
5842 <tr>
5843 <td>
5844               <p>
5845                 RF: x = 0, y = z
5846               </p>
5847             </td>
5848 <td>
5849               <p>
5850                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5851                 2.1:</em></span> Max = 1.29&#949; (Mean = 0.527&#949;))
5852               </p>
5853             </td>
5854 <td>
5855               <p>
5856                 <span class="blue">Max = 0.894&#949; (Mean = 0.338&#949;)</span>
5857               </p>
5858             </td>
5859 <td>
5860               <p>
5861                 <span class="blue">Max = 0.999&#949; (Mean = 0.407&#949;)</span>
5862               </p>
5863             </td>
5864 </tr>
5865 <tr>
5866 <td>
5867               <p>
5868                 RF: z = 0
5869               </p>
5870             </td>
5871 <td>
5872               <p>
5873                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5874                 2.1:</em></span> Max = 2.54&#949; (Mean = 0.781&#949;))
5875               </p>
5876             </td>
5877 <td>
5878               <p>
5879                 <span class="blue">Max = 1.7&#949; (Mean = 0.539&#949;)</span>
5880               </p>
5881             </td>
5882 <td>
5883               <p>
5884                 <span class="blue">Max = 1.89&#949; (Mean = 0.587&#949;)</span>
5885               </p>
5886             </td>
5887 </tr>
5888 </tbody>
5889 </table></div>
5890 </div>
5891 <br class="table-break">
5892 </div>
5893 <div class="section">
5894 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
5895 <a name="special_function_error_rates_rep.section_ellint_rg"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rg" title="ellint_rg">ellint_rg</a>
5896 </h2></div></div></div>
5897 <div class="table">
5898 <a name="special_function_error_rates_rep.section_ellint_rg.table_ellint_rg"></a><p class="title"><b>Table&#160;36.&#160;Error rates for ellint_rg</b></p>
5899 <div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
5900 <colgroup>
5901 <col>
5902 <col>
5903 <col>
5904 <col>
5905 </colgroup>
5906 <thead><tr>
5907 <th>
5908             </th>
5909 <th>
5910               <p>
5911                 GNU C++ version 7.1.0<br> linux<br> double
5912               </p>
5913             </th>
5914 <th>
5915               <p>
5916                 GNU C++ version 7.1.0<br> linux<br> long double
5917               </p>
5918             </th>
5919 <th>
5920               <p>
5921                 Microsoft Visual C++ version 14.1<br> Win32<br> double
5922               </p>
5923             </th>
5924 </tr></thead>
5925 <tbody>
5926 <tr>
5927 <td>
5928               <p>
5929                 RG: Random Data
5930               </p>
5931             </td>
5932 <td>
5933               <p>
5934                 <span class="blue">Max = 0.983&#949; (Mean = 0.0172&#949;)</span><br> <br>
5935                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983&#949; (Mean = 0.0172&#949;))
5936               </p>
5937             </td>
5938 <td>
5939               <p>
5940                 <span class="blue">Max = 3.95&#949; (Mean = 0.951&#949;)</span>
5941               </p>
5942             </td>
5943 <td>
5944               <p>
5945                 <span class="blue">Max = 3.65&#949; (Mean = 0.929&#949;)</span>
5946               </p>
5947             </td>
5948 </tr>
5949 <tr>
5950 <td>
5951               <p>
5952                 RG: two values 0
5953               </p>
5954             </td>
5955 <td>
5956               <p>
5957                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5958                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
5959               </p>
5960             </td>
5961 <td>
5962               <p>
5963                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5964               </p>
5965             </td>
5966 <td>
5967               <p>
5968                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5969               </p>
5970             </td>
5971 </tr>
5972 <tr>
5973 <td>
5974               <p>
5975                 RG: All values the same or zero
5976               </p>
5977             </td>
5978 <td>
5979               <p>
5980                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5981                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
5982               </p>
5983             </td>
5984 <td>
5985               <p>
5986                 <span class="blue">Max = 0.992&#949; (Mean = 0.288&#949;)</span>
5987               </p>
5988             </td>
5989 <td>
5990               <p>
5991                 <span class="blue">Max = 1.06&#949; (Mean = 0.348&#949;)</span>
5992               </p>
5993             </td>
5994 </tr>
5995 <tr>
5996 <td>
5997               <p>
5998                 RG: two values the same
5999               </p>
6000             </td>
6001 <td>
6002               <p>
6003                 <span class="blue">Max = 0.594&#949; (Mean = 0.0103&#949;)</span><br> <br>
6004                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594&#949; (Mean = 0.0103&#949;))
6005               </p>
6006             </td>
6007 <td>
6008               <p>
6009                 <span class="blue">Max = 1.51&#949; (Mean = 0.404&#949;)</span>
6010               </p>
6011             </td>
6012 <td>
6013               <p>
6014                 <span class="blue">Max = 1.96&#949; (Mean = 0.374&#949;)</span>
6015               </p>
6016             </td>
6017 </tr>
6018 <tr>
6019 <td>
6020               <p>
6021                 RG: one value zero
6022               </p>
6023             </td>
6024 <td>
6025               <p>
6026                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6027                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
6028               </p>
6029             </td>
6030 <td>
6031               <p>
6032                 <span class="blue">Max = 2.14&#949; (Mean = 0.722&#949;)</span>
6033               </p>
6034             </td>
6035 <td>
6036               <p>
6037                 <span class="blue">Max = 1.96&#949; (Mean = 0.674&#949;)</span>
6038               </p>
6039             </td>
6040 </tr>
6041 </tbody>
6042 </table></div>
6043 </div>
6044 <br class="table-break">
6045 </div>
6046 <div class="section">
6047 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6048 <a name="special_function_error_rates_rep.section_ellint_rj"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rj" title="ellint_rj">ellint_rj</a>
6049 </h2></div></div></div>
6050 <div class="table">
6051 <a name="special_function_error_rates_rep.section_ellint_rj.table_ellint_rj"></a><p class="title"><b>Table&#160;37.&#160;Error rates for ellint_rj</b></p>
6052 <div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
6053 <colgroup>
6054 <col>
6055 <col>
6056 <col>
6057 <col>
6058 </colgroup>
6059 <thead><tr>
6060 <th>
6061             </th>
6062 <th>
6063               <p>
6064                 GNU C++ version 7.1.0<br> linux<br> double
6065               </p>
6066             </th>
6067 <th>
6068               <p>
6069                 GNU C++ version 7.1.0<br> linux<br> long double
6070               </p>
6071             </th>
6072 <th>
6073               <p>
6074                 Microsoft Visual C++ version 14.1<br> Win32<br> double
6075               </p>
6076             </th>
6077 </tr></thead>
6078 <tbody>
6079 <tr>
6080 <td>
6081               <p>
6082                 RJ: Random data
6083               </p>
6084             </td>
6085 <td>
6086               <p>
6087                 <span class="blue">Max = 0.52&#949; (Mean = 0.0184&#949;)</span><br> <br>
6088                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57&#949; (Mean = 0.704&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And
6089                 other failures.</a>)
6090               </p>
6091             </td>
6092 <td>
6093               <p>
6094                 <span class="blue">Max = 186&#949; (Mean = 6.67&#949;)</span>
6095               </p>
6096             </td>
6097 <td>
6098               <p>
6099                 <span class="blue">Max = 215&#949; (Mean = 7.66&#949;)</span>
6100               </p>
6101             </td>
6102 </tr>
6103 <tr>
6104 <td>
6105               <p>
6106                 RJ: 4 Equal Values
6107               </p>
6108             </td>
6109 <td>
6110               <p>
6111                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6112                 2.1:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
6113               </p>
6114             </td>
6115 <td>
6116               <p>
6117                 <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
6118               </p>
6119             </td>
6120 <td>
6121               <p>
6122                 <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
6123               </p>
6124             </td>
6125 </tr>
6126 <tr>
6127 <td>
6128               <p>
6129                 RJ: 3 Equal Values
6130               </p>
6131             </td>
6132 <td>
6133               <p>
6134                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6135                 2.1:</em></span> Max = 3.96&#949; (Mean = 1.06&#949;))
6136               </p>
6137             </td>
6138 <td>
6139               <p>
6140                 <span class="blue">Max = 20.8&#949; (Mean = 0.986&#949;)</span>
6141               </p>
6142             </td>
6143 <td>
6144               <p>
6145                 <span class="blue">Max = 39.9&#949; (Mean = 1.17&#949;)</span>
6146               </p>
6147             </td>
6148 </tr>
6149 <tr>
6150 <td>
6151               <p>
6152                 RJ: 2 Equal Values
6153               </p>
6154             </td>
6155 <td>
6156               <p>
6157                 <span class="blue">Max = 0.6&#949; (Mean = 0.0228&#949;)</span><br> <br>
6158                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57&#949; (Mean = 0.754&#949;))
6159               </p>
6160             </td>
6161 <td>
6162               <p>
6163                 <span class="blue">Max = 220&#949; (Mean = 6.64&#949;)</span>
6164               </p>
6165             </td>
6166 <td>
6167               <p>
6168                 <span class="blue">Max = 214&#949; (Mean = 5.28&#949;)</span>
6169               </p>
6170             </td>
6171 </tr>
6172 <tr>
6173 <td>
6174               <p>
6175                 RJ: Equal z and p
6176               </p>
6177             </td>
6178 <td>
6179               <p>
6180                 <span class="blue">Max = 0.742&#949; (Mean = 0.0166&#949;)</span><br> <br>
6181                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62&#949; (Mean = 0.699&#949;))
6182               </p>
6183             </td>
6184 <td>
6185               <p>
6186                 <span class="blue">Max = 17.2&#949; (Mean = 1.16&#949;)</span>
6187               </p>
6188             </td>
6189 <td>
6190               <p>
6191                 <span class="blue">Max = 16.1&#949; (Mean = 1.14&#949;)</span>
6192               </p>
6193             </td>
6194 </tr>
6195 </tbody>
6196 </table></div>
6197 </div>
6198 <br class="table-break">
6199 </div>
6200 <div class="section">
6201 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6202 <a name="special_function_error_rates_rep.section_erf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf" title="erf">erf</a>
6203 </h2></div></div></div>
6204 <div class="table">
6205 <a name="special_function_error_rates_rep.section_erf.table_erf"></a><p class="title"><b>Table&#160;38.&#160;Error rates for erf</b></p>
6206 <div class="table-contents"><table class="table" summary="Error rates for erf">
6207 <colgroup>
6208 <col>
6209 <col>
6210 <col>
6211 <col>
6212 <col>
6213 </colgroup>
6214 <thead><tr>
6215 <th>
6216             </th>
6217 <th>
6218               <p>
6219                 GNU C++ version 7.1.0<br> linux<br> long double
6220               </p>
6221             </th>
6222 <th>
6223               <p>
6224                 GNU C++ version 7.1.0<br> linux<br> double
6225               </p>
6226             </th>
6227 <th>
6228               <p>
6229                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
6230               </p>
6231             </th>
6232 <th>
6233               <p>
6234                 Microsoft Visual C++ version 14.1<br> Win32<br> double
6235               </p>
6236             </th>
6237 </tr></thead>
6238 <tbody>
6239 <tr>
6240 <td>
6241               <p>
6242                 Erf Function: Small Values
6243               </p>
6244             </td>
6245 <td>
6246               <p>
6247                 <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
6248                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))<br>
6249                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))
6250               </p>
6251             </td>
6252 <td>
6253               <p>
6254                 <span class="blue">Max = 0.841&#949; (Mean = 0.0687&#949;)</span><br> <br>
6255                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06&#949; (Mean = 0.319&#949;))
6256               </p>
6257             </td>
6258 <td>
6259               <p>
6260                 <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
6261                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.194&#949;))
6262               </p>
6263             </td>
6264 <td>
6265               <p>
6266                 <span class="blue">Max = 0.996&#949; (Mean = 0.182&#949;)</span><br> <br>
6267                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.57&#949; (Mean = 0.317&#949;))
6268               </p>
6269             </td>
6270 </tr>
6271 <tr>
6272 <td>
6273               <p>
6274                 Erf Function: Medium Values
6275               </p>
6276             </td>
6277 <td>
6278               <p>
6279                 <span class="blue">Max = 1.5&#949; (Mean = 0.193&#949;)</span><br> <br>
6280                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))<br>
6281                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))
6282               </p>
6283             </td>
6284 <td>
6285               <p>
6286                 <span class="blue">Max = 1&#949; (Mean = 0.119&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6287                 2.1:</em></span> Max = 2.31&#949; (Mean = 0.368&#949;))
6288               </p>
6289             </td>
6290 <td>
6291               <p>
6292                 <span class="blue">Max = 1.5&#949; (Mean = 0.197&#949;)</span><br> <br>
6293                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.071&#949;))
6294               </p>
6295             </td>
6296 <td>
6297               <p>
6298                 <span class="blue">Max = 1&#949; (Mean = 0.171&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6299                 Max = 1.19&#949; (Mean = 0.244&#949;))
6300               </p>
6301             </td>
6302 </tr>
6303 <tr>
6304 <td>
6305               <p>
6306                 Erf Function: Large Values
6307               </p>
6308             </td>
6309 <td>
6310               <p>
6311                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
6312                 Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max
6313                 = 0&#949; (Mean = 0&#949;))
6314               </p>
6315             </td>
6316 <td>
6317               <p>
6318                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6319                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
6320               </p>
6321             </td>
6322 <td>
6323               <p>
6324                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6325                 Max = 0&#949; (Mean = 0&#949;))
6326               </p>
6327             </td>
6328 <td>
6329               <p>
6330                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6331                 Max = 0&#949; (Mean = 0&#949;))
6332               </p>
6333             </td>
6334 </tr>
6335 </tbody>
6336 </table></div>
6337 </div>
6338 <br class="table-break">
6339 </div>
6340 <div class="section">
6341 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6342 <a name="special_function_error_rates_rep.section_erf_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf_inv" title="erf_inv">erf_inv</a>
6343 </h2></div></div></div>
6344 <div class="table">
6345 <a name="special_function_error_rates_rep.section_erf_inv.table_erf_inv"></a><p class="title"><b>Table&#160;39.&#160;Error rates for erf_inv</b></p>
6346 <div class="table-contents"><table class="table" summary="Error rates for erf_inv">
6347 <colgroup>
6348 <col>
6349 <col>
6350 <col>
6351 <col>
6352 <col>
6353 </colgroup>
6354 <thead><tr>
6355 <th>
6356             </th>
6357 <th>
6358               <p>
6359                 GNU C++ version 7.1.0<br> linux<br> double
6360               </p>
6361             </th>
6362 <th>
6363               <p>
6364                 GNU C++ version 7.1.0<br> linux<br> long double
6365               </p>
6366             </th>
6367 <th>
6368               <p>
6369                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
6370               </p>
6371             </th>
6372 <th>
6373               <p>
6374                 Microsoft Visual C++ version 14.1<br> Win32<br> double
6375               </p>
6376             </th>
6377 </tr></thead>
6378 <tbody><tr>
6379 <td>
6380               <p>
6381                 Inverse Erf Function
6382               </p>
6383             </td>
6384 <td>
6385               <p>
6386                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
6387               </p>
6388             </td>
6389 <td>
6390               <p>
6391                 <span class="blue">Max = 0.996&#949; (Mean = 0.389&#949;)</span>
6392               </p>
6393             </td>
6394 <td>
6395               <p>
6396                 <span class="blue">Max = 1.08&#949; (Mean = 0.395&#949;)</span>
6397               </p>
6398             </td>
6399 <td>
6400               <p>
6401                 <span class="blue">Max = 1.09&#949; (Mean = 0.502&#949;)</span>
6402               </p>
6403             </td>
6404 </tr></tbody>
6405 </table></div>
6406 </div>
6407 <br class="table-break">
6408 </div>
6409 <div class="section">
6410 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6411 <a name="special_function_error_rates_rep.section_erfc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc" title="erfc">erfc</a>
6412 </h2></div></div></div>
6413 <div class="table">
6414 <a name="special_function_error_rates_rep.section_erfc.table_erfc"></a><p class="title"><b>Table&#160;40.&#160;Error rates for erfc</b></p>
6415 <div class="table-contents"><table class="table" summary="Error rates for erfc">
6416 <colgroup>
6417 <col>
6418 <col>
6419 <col>
6420 <col>
6421 <col>
6422 </colgroup>
6423 <thead><tr>
6424 <th>
6425             </th>
6426 <th>
6427               <p>
6428                 GNU C++ version 7.1.0<br> linux<br> long double
6429               </p>
6430             </th>
6431 <th>
6432               <p>
6433                 GNU C++ version 7.1.0<br> linux<br> double
6434               </p>
6435             </th>
6436 <th>
6437               <p>
6438                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
6439               </p>
6440             </th>
6441 <th>
6442               <p>
6443                 Microsoft Visual C++ version 14.1<br> Win32<br> double
6444               </p>
6445             </th>
6446 </tr></thead>
6447 <tbody>
6448 <tr>
6449 <td>
6450               <p>
6451                 Erf Function: Small Values
6452               </p>
6453             </td>
6454 <td>
6455               <p>
6456                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
6457                 Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max
6458                 = 0&#949; (Mean = 0&#949;))
6459               </p>
6460             </td>
6461 <td>
6462               <p>
6463                 <span class="blue">Max = 0.658&#949; (Mean = 0.0537&#949;)</span><br> <br>
6464                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01&#949; (Mean = 0.485&#949;))
6465               </p>
6466             </td>
6467 <td>
6468               <p>
6469                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6470                 Max = 0&#949; (Mean = 0&#949;))
6471               </p>
6472             </td>
6473 <td>
6474               <p>
6475                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6476                 Max = 0&#949; (Mean = 0&#949;))
6477               </p>
6478             </td>
6479 </tr>
6480 <tr>
6481 <td>
6482               <p>
6483                 Erf Function: Medium Values
6484               </p>
6485             </td>
6486 <td>
6487               <p>
6488                 <span class="blue">Max = 1.76&#949; (Mean = 0.365&#949;)</span><br> <br>
6489                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))<br>
6490                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))
6491               </p>
6492             </td>
6493 <td>
6494               <p>
6495                 <span class="blue">Max = 0.983&#949; (Mean = 0.213&#949;)</span><br> <br>
6496                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64&#949; (Mean = 0.662&#949;))
6497               </p>
6498             </td>
6499 <td>
6500               <p>
6501                 <span class="blue">Max = 1.76&#949; (Mean = 0.38&#949;)</span><br> <br>
6502                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.81&#949; (Mean = 0.739&#949;))
6503               </p>
6504             </td>
6505 <td>
6506               <p>
6507                 <span class="blue">Max = 1.65&#949; (Mean = 0.373&#949;)</span><br> <br>
6508                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.36&#949; (Mean = 0.539&#949;))
6509               </p>
6510             </td>
6511 </tr>
6512 <tr>
6513 <td>
6514               <p>
6515                 Erf Function: Large Values
6516               </p>
6517             </td>
6518 <td>
6519               <p>
6520                 <span class="blue">Max = 1.57&#949; (Mean = 0.542&#949;)</span><br> <br>
6521                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))<br>
6522                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))
6523               </p>
6524             </td>
6525 <td>
6526               <p>
6527                 <span class="blue">Max = 0.868&#949; (Mean = 0.147&#949;)</span><br> <br>
6528                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9&#949; (Mean = 0.472&#949;))
6529               </p>
6530             </td>
6531 <td>
6532               <p>
6533                 <span class="blue">Max = 1.57&#949; (Mean = 0.564&#949;)</span><br> <br>
6534                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 4.91&#949; (Mean = 1.54&#949;))
6535               </p>
6536             </td>
6537 <td>
6538               <p>
6539                 <span class="blue">Max = 1.14&#949; (Mean = 0.248&#949;)</span><br> <br>
6540                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.331&#949;))
6541               </p>
6542             </td>
6543 </tr>
6544 </tbody>
6545 </table></div>
6546 </div>
6547 <br class="table-break">
6548 </div>
6549 <div class="section">
6550 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6551 <a name="special_function_error_rates_rep.section_erfc_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc_inv" title="erfc_inv">erfc_inv</a>
6552 </h2></div></div></div>
6553 <div class="table">
6554 <a name="special_function_error_rates_rep.section_erfc_inv.table_erfc_inv"></a><p class="title"><b>Table&#160;41.&#160;Error rates for erfc_inv</b></p>
6555 <div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
6556 <colgroup>
6557 <col>
6558 <col>
6559 <col>
6560 <col>
6561 <col>
6562 </colgroup>
6563 <thead><tr>
6564 <th>
6565             </th>
6566 <th>
6567               <p>
6568                 GNU C++ version 7.1.0<br> linux<br> double
6569               </p>
6570             </th>
6571 <th>
6572               <p>
6573                 GNU C++ version 7.1.0<br> linux<br> long double
6574               </p>
6575             </th>
6576 <th>
6577               <p>
6578                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
6579               </p>
6580             </th>
6581 <th>
6582               <p>
6583                 Microsoft Visual C++ version 14.1<br> Win32<br> double
6584               </p>
6585             </th>
6586 </tr></thead>
6587 <tbody>
6588 <tr>
6589 <td>
6590               <p>
6591                 Inverse Erfc Function
6592               </p>
6593             </td>
6594 <td>
6595               <p>
6596                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
6597               </p>
6598             </td>
6599 <td>
6600               <p>
6601                 <span class="blue">Max = 0.996&#949; (Mean = 0.397&#949;)</span>
6602               </p>
6603             </td>
6604 <td>
6605               <p>
6606                 <span class="blue">Max = 1.08&#949; (Mean = 0.403&#949;)</span>
6607               </p>
6608             </td>
6609 <td>
6610               <p>
6611                 <span class="blue">Max = 1&#949; (Mean = 0.491&#949;)</span>
6612               </p>
6613             </td>
6614 </tr>
6615 <tr>
6616 <td>
6617               <p>
6618                 Inverse Erfc Function: extreme values
6619               </p>
6620             </td>
6621 <td>
6622             </td>
6623 <td>
6624               <p>
6625                 <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
6626               </p>
6627             </td>
6628 <td>
6629               <p>
6630                 <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
6631               </p>
6632             </td>
6633 <td>
6634             </td>
6635 </tr>
6636 </tbody>
6637 </table></div>
6638 </div>
6639 <br class="table-break">
6640 </div>
6641 <div class="section">
6642 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6643 <a name="special_function_error_rates_rep.section_expint_Ei_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_Ei_" title="expint (Ei)">expint
6644     (Ei)</a>
6645 </h2></div></div></div>
6646 <div class="table">
6647 <a name="special_function_error_rates_rep.section_expint_Ei_.table_expint_Ei_"></a><p class="title"><b>Table&#160;42.&#160;Error rates for expint (Ei)</b></p>
6648 <div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
6649 <colgroup>
6650 <col>
6651 <col>
6652 <col>
6653 <col>
6654 <col>
6655 </colgroup>
6656 <thead><tr>
6657 <th>
6658             </th>
6659 <th>
6660               <p>
6661                 GNU C++ version 7.1.0<br> linux<br> long double
6662               </p>
6663             </th>
6664 <th>
6665               <p>
6666                 GNU C++ version 7.1.0<br> linux<br> double
6667               </p>
6668             </th>
6669 <th>
6670               <p>
6671                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
6672               </p>
6673             </th>
6674 <th>
6675               <p>
6676                 Microsoft Visual C++ version 14.1<br> Win32<br> double
6677               </p>
6678             </th>
6679 </tr></thead>
6680 <tbody>
6681 <tr>
6682 <td>
6683               <p>
6684                 Exponential Integral Ei
6685               </p>
6686             </td>
6687 <td>
6688               <p>
6689                 <span class="blue">Max = 5.05&#949; (Mean = 0.821&#949;)</span><br> <br>
6690                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 14.1&#949; (Mean = 2.43&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And
6691                 other failures.</a>)
6692               </p>
6693             </td>
6694 <td>
6695               <p>
6696                 <span class="blue">Max = 0.994&#949; (Mean = 0.142&#949;)</span><br> <br>
6697                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96&#949; (Mean = 0.703&#949;))
6698               </p>
6699             </td>
6700 <td>
6701               <p>
6702                 <span class="blue">Max = 5.05&#949; (Mean = 0.835&#949;)</span>
6703               </p>
6704             </td>
6705 <td>
6706               <p>
6707                 <span class="blue">Max = 1.43&#949; (Mean = 0.54&#949;)</span>
6708               </p>
6709             </td>
6710 </tr>
6711 <tr>
6712 <td>
6713               <p>
6714                 Exponential Integral Ei: double exponent range
6715               </p>
6716             </td>
6717 <td>
6718               <p>
6719                 <span class="blue">Max = 1.72&#949; (Mean = 0.593&#949;)</span><br> <br>
6720                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.11&#949; (Mean = 1.13&#949;))
6721               </p>
6722             </td>
6723 <td>
6724               <p>
6725                 <span class="blue">Max = 0.998&#949; (Mean = 0.156&#949;)</span><br> <br>
6726                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5&#949; (Mean = 0.612&#949;))
6727               </p>
6728             </td>
6729 <td>
6730               <p>
6731                 <span class="blue">Max = 1.72&#949; (Mean = 0.607&#949;)</span>
6732               </p>
6733             </td>
6734 <td>
6735               <p>
6736                 <span class="blue">Max = 1.7&#949; (Mean = 0.66&#949;)</span>
6737               </p>
6738             </td>
6739 </tr>
6740 <tr>
6741 <td>
6742               <p>
6743                 Exponential Integral Ei: long exponent range
6744               </p>
6745             </td>
6746 <td>
6747               <p>
6748                 <span class="blue">Max = 1.98&#949; (Mean = 0.595&#949;)</span><br> <br>
6749                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.93&#949; (Mean = 0.855&#949;))
6750               </p>
6751             </td>
6752 <td>
6753             </td>
6754 <td>
6755               <p>
6756                 <span class="blue">Max = 1.98&#949; (Mean = 0.575&#949;)</span>
6757               </p>
6758             </td>
6759 <td>
6760             </td>
6761 </tr>
6762 </tbody>
6763 </table></div>
6764 </div>
6765 <br class="table-break">
6766 </div>
6767 <div class="section">
6768 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6769 <a name="special_function_error_rates_rep.section_expint_En_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_En_" title="expint (En)">expint
6770     (En)</a>
6771 </h2></div></div></div>
6772 <div class="table">
6773 <a name="special_function_error_rates_rep.section_expint_En_.table_expint_En_"></a><p class="title"><b>Table&#160;43.&#160;Error rates for expint (En)</b></p>
6774 <div class="table-contents"><table class="table" summary="Error rates for expint (En)">
6775 <colgroup>
6776 <col>
6777 <col>
6778 <col>
6779 <col>
6780 <col>
6781 </colgroup>
6782 <thead><tr>
6783 <th>
6784             </th>
6785 <th>
6786               <p>
6787                 GNU C++ version 7.1.0<br> linux<br> double
6788               </p>
6789             </th>
6790 <th>
6791               <p>
6792                 GNU C++ version 7.1.0<br> linux<br> long double
6793               </p>
6794             </th>
6795 <th>
6796               <p>
6797                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
6798               </p>
6799             </th>
6800 <th>
6801               <p>
6802                 Microsoft Visual C++ version 14.1<br> Win32<br> double
6803               </p>
6804             </th>
6805 </tr></thead>
6806 <tbody>
6807 <tr>
6808 <td>
6809               <p>
6810                 Exponential Integral En
6811               </p>
6812             </td>
6813 <td>
6814               <p>
6815                 <span class="blue">Max = 0.589&#949; (Mean = 0.0331&#949;)</span><br> <br>
6816                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5&#949; (Mean = 17.1&#949;))
6817               </p>
6818             </td>
6819 <td>
6820               <p>
6821                 <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
6822               </p>
6823             </td>
6824 <td>
6825               <p>
6826                 <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
6827               </p>
6828             </td>
6829 <td>
6830               <p>
6831                 <span class="blue">Max = 7.16&#949; (Mean = 1.85&#949;)</span>
6832               </p>
6833             </td>
6834 </tr>
6835 <tr>
6836 <td>
6837               <p>
6838                 Exponential Integral En: small z values
6839               </p>
6840             </td>
6841 <td>
6842               <p>
6843                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6844                 2.1:</em></span> Max = 115&#949; (Mean = 23.6&#949;))
6845               </p>
6846             </td>
6847 <td>
6848               <p>
6849                 <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
6850               </p>
6851             </td>
6852 <td>
6853               <p>
6854                 <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
6855               </p>
6856             </td>
6857 <td>
6858               <p>
6859                 <span class="blue">Max = 2.62&#949; (Mean = 0.531&#949;)</span>
6860               </p>
6861             </td>
6862 </tr>
6863 <tr>
6864 <td>
6865               <p>
6866                 Exponential Integral E1
6867               </p>
6868             </td>
6869 <td>
6870               <p>
6871                 <span class="blue">Max = 0.556&#949; (Mean = 0.0625&#949;)</span><br> <br>
6872                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988&#949; (Mean = 0.469&#949;))
6873               </p>
6874             </td>
6875 <td>
6876               <p>
6877                 <span class="blue">Max = 0.965&#949; (Mean = 0.414&#949;)</span>
6878               </p>
6879             </td>
6880 <td>
6881               <p>
6882                 <span class="blue">Max = 0.965&#949; (Mean = 0.408&#949;)</span>
6883               </p>
6884             </td>
6885 <td>
6886               <p>
6887                 <span class="blue">Max = 0.988&#949; (Mean = 0.486&#949;)</span>
6888               </p>
6889             </td>
6890 </tr>
6891 </tbody>
6892 </table></div>
6893 </div>
6894 <br class="table-break">
6895 </div>
6896 <div class="section">
6897 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6898 <a name="special_function_error_rates_rep.section_expm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expm1" title="expm1">expm1</a>
6899 </h2></div></div></div>
6900 <div class="table">
6901 <a name="special_function_error_rates_rep.section_expm1.table_expm1"></a><p class="title"><b>Table&#160;44.&#160;Error rates for expm1</b></p>
6902 <div class="table-contents"><table class="table" summary="Error rates for expm1">
6903 <colgroup>
6904 <col>
6905 <col>
6906 <col>
6907 <col>
6908 <col>
6909 </colgroup>
6910 <thead><tr>
6911 <th>
6912             </th>
6913 <th>
6914               <p>
6915                 GNU C++ version 7.1.0<br> linux<br> long double
6916               </p>
6917             </th>
6918 <th>
6919               <p>
6920                 GNU C++ version 7.1.0<br> linux<br> double
6921               </p>
6922             </th>
6923 <th>
6924               <p>
6925                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
6926               </p>
6927             </th>
6928 <th>
6929               <p>
6930                 Microsoft Visual C++ version 14.1<br> Win32<br> double
6931               </p>
6932             </th>
6933 </tr></thead>
6934 <tbody><tr>
6935 <td>
6936               <p>
6937                 Random test data
6938               </p>
6939             </td>
6940 <td>
6941               <p>
6942                 <span class="blue">Max = 0.992&#949; (Mean = 0.402&#949;)</span><br> <br>
6943                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.992&#949; (Mean = 0.402&#949;))<br>
6944                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.992&#949; (Mean = 0.402&#949;))
6945               </p>
6946             </td>
6947 <td>
6948               <p>
6949                 <span class="blue">Max = 0.793&#949; (Mean = 0.126&#949;)</span><br> <br>
6950                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793&#949; (Mean = 0.126&#949;))
6951               </p>
6952             </td>
6953 <td>
6954               <p>
6955                 <span class="blue">Max = 1.31&#949; (Mean = 0.428&#949;)</span><br> <br>
6956                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.996&#949; (Mean = 0.426&#949;))
6957               </p>
6958             </td>
6959 <td>
6960               <p>
6961                 <span class="blue">Max = 1.31&#949; (Mean = 0.496&#949;)</span><br> <br>
6962                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.31&#949; (Mean = 0.496&#949;))
6963               </p>
6964             </td>
6965 </tr></tbody>
6966 </table></div>
6967 </div>
6968 <br class="table-break">
6969 </div>
6970 <div class="section">
6971 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
6972 <a name="special_function_error_rates_rep.section_gamma_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p" title="gamma_p">gamma_p</a>
6973 </h2></div></div></div>
6974 <div class="table">
6975 <a name="special_function_error_rates_rep.section_gamma_p.table_gamma_p"></a><p class="title"><b>Table&#160;45.&#160;Error rates for gamma_p</b></p>
6976 <div class="table-contents"><table class="table" summary="Error rates for gamma_p">
6977 <colgroup>
6978 <col>
6979 <col>
6980 <col>
6981 <col>
6982 <col>
6983 </colgroup>
6984 <thead><tr>
6985 <th>
6986             </th>
6987 <th>
6988               <p>
6989                 GNU C++ version 7.1.0<br> linux<br> double
6990               </p>
6991             </th>
6992 <th>
6993               <p>
6994                 GNU C++ version 7.1.0<br> linux<br> long double
6995               </p>
6996             </th>
6997 <th>
6998               <p>
6999                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7000               </p>
7001             </th>
7002 <th>
7003               <p>
7004                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7005               </p>
7006             </th>
7007 </tr></thead>
7008 <tbody>
7009 <tr>
7010 <td>
7011               <p>
7012                 tgamma(a, z) medium values
7013               </p>
7014             </td>
7015 <td>
7016               <p>
7017                 <span class="blue">Max = 0.955&#949; (Mean = 0.05&#949;)</span><br> <br>
7018                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342&#949; (Mean = 45.8&#949;))<br> (<span class="emphasis"><em>Rmath
7019                 3.2.3:</em></span> Max = 389&#949; (Mean = 44&#949;))
7020               </p>
7021             </td>
7022 <td>
7023               <p>
7024                 <span class="blue">Max = 41.6&#949; (Mean = 8.09&#949;)</span>
7025               </p>
7026             </td>
7027 <td>
7028               <p>
7029                 <span class="blue">Max = 239&#949; (Mean = 30.2&#949;)</span>
7030               </p>
7031             </td>
7032 <td>
7033               <p>
7034                 <span class="blue">Max = 35.1&#949; (Mean = 6.98&#949;)</span>
7035               </p>
7036             </td>
7037 </tr>
7038 <tr>
7039 <td>
7040               <p>
7041                 tgamma(a, z) small values
7042               </p>
7043             </td>
7044 <td>
7045               <p>
7046                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7047                 2.1:</em></span> Max = 4.82&#949; (Mean = 0.758&#949;))<br> (<span class="emphasis"><em>Rmath
7048                 3.2.3:</em></span> Max = 1.01&#949; (Mean = 0.306&#949;))
7049               </p>
7050             </td>
7051 <td>
7052               <p>
7053                 <span class="blue">Max = 2&#949; (Mean = 0.464&#949;)</span>
7054               </p>
7055             </td>
7056 <td>
7057               <p>
7058                 <span class="blue">Max = 2&#949; (Mean = 0.461&#949;)</span>
7059               </p>
7060             </td>
7061 <td>
7062               <p>
7063                 <span class="blue">Max = 1.54&#949; (Mean = 0.439&#949;)</span>
7064               </p>
7065             </td>
7066 </tr>
7067 <tr>
7068 <td>
7069               <p>
7070                 tgamma(a, z) large values
7071               </p>
7072             </td>
7073 <td>
7074               <p>
7075                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7076                 2.1:</em></span> Max = 1.02e+03&#949; (Mean = 105&#949;))<br> (<span class="emphasis"><em>Rmath
7077                 3.2.3:</em></span> Max = 1.11e+03&#949; (Mean = 67.5&#949;))
7078               </p>
7079             </td>
7080 <td>
7081               <p>
7082                 <span class="blue">Max = 3.08e+04&#949; (Mean = 1.86e+03&#949;)</span>
7083               </p>
7084             </td>
7085 <td>
7086               <p>
7087                 <span class="blue">Max = 3.02e+04&#949; (Mean = 1.91e+03&#949;)</span>
7088               </p>
7089             </td>
7090 <td>
7091               <p>
7092                 <span class="blue">Max = 243&#949; (Mean = 20.2&#949;)</span>
7093               </p>
7094             </td>
7095 </tr>
7096 <tr>
7097 <td>
7098               <p>
7099                 tgamma(a, z) integer and half integer values
7100               </p>
7101             </td>
7102 <td>
7103               <p>
7104                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7105                 2.1:</em></span> Max = 128&#949; (Mean = 22.6&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
7106                 Max = 66.2&#949; (Mean = 12.2&#949;))
7107               </p>
7108             </td>
7109 <td>
7110               <p>
7111                 <span class="blue">Max = 11.8&#949; (Mean = 2.66&#949;)</span>
7112               </p>
7113             </td>
7114 <td>
7115               <p>
7116                 <span class="blue">Max = 71.6&#949; (Mean = 9.47&#949;)</span>
7117               </p>
7118             </td>
7119 <td>
7120               <p>
7121                 <span class="blue">Max = 13&#949; (Mean = 2.97&#949;)</span>
7122               </p>
7123             </td>
7124 </tr>
7125 </tbody>
7126 </table></div>
7127 </div>
7128 <br class="table-break">
7129 </div>
7130 <div class="section">
7131 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
7132 <a name="special_function_error_rates_rep.section_gamma_p_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inv" title="gamma_p_inv">gamma_p_inv</a>
7133 </h2></div></div></div>
7134 <div class="table">
7135 <a name="special_function_error_rates_rep.section_gamma_p_inv.table_gamma_p_inv"></a><p class="title"><b>Table&#160;46.&#160;Error rates for gamma_p_inv</b></p>
7136 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
7137 <colgroup>
7138 <col>
7139 <col>
7140 <col>
7141 <col>
7142 <col>
7143 </colgroup>
7144 <thead><tr>
7145 <th>
7146             </th>
7147 <th>
7148               <p>
7149                 GNU C++ version 7.1.0<br> linux<br> double
7150               </p>
7151             </th>
7152 <th>
7153               <p>
7154                 GNU C++ version 7.1.0<br> linux<br> long double
7155               </p>
7156             </th>
7157 <th>
7158               <p>
7159                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7160               </p>
7161             </th>
7162 <th>
7163               <p>
7164                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7165               </p>
7166             </th>
7167 </tr></thead>
7168 <tbody>
7169 <tr>
7170 <td>
7171               <p>
7172                 incomplete gamma inverse(a, z) medium values
7173               </p>
7174             </td>
7175 <td>
7176               <p>
7177                 <span class="blue">Max = 0.993&#949; (Mean = 0.15&#949;)</span><br> <br>
7178                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88&#949; (Mean = 0.868&#949;))
7179               </p>
7180             </td>
7181 <td>
7182               <p>
7183                 <span class="blue">Max = 1.8&#949; (Mean = 0.406&#949;)</span>
7184               </p>
7185             </td>
7186 <td>
7187               <p>
7188                 <span class="blue">Max = 1.89&#949; (Mean = 0.466&#949;)</span>
7189               </p>
7190             </td>
7191 <td>
7192               <p>
7193                 <span class="blue">Max = 1.71&#949; (Mean = 0.34&#949;)</span>
7194               </p>
7195             </td>
7196 </tr>
7197 <tr>
7198 <td>
7199               <p>
7200                 incomplete gamma inverse(a, z) large values
7201               </p>
7202             </td>
7203 <td>
7204               <p>
7205                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
7206                 3.2.3:</em></span> Max = 0.816&#949; (Mean = 0.0874&#949;))
7207               </p>
7208             </td>
7209 <td>
7210               <p>
7211                 <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
7212               </p>
7213             </td>
7214 <td>
7215               <p>
7216                 <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
7217               </p>
7218             </td>
7219 <td>
7220               <p>
7221                 <span class="blue">Max = 0.924&#949; (Mean = 0.108&#949;)</span>
7222               </p>
7223             </td>
7224 </tr>
7225 <tr>
7226 <td>
7227               <p>
7228                 incomplete gamma inverse(a, z) small values
7229               </p>
7230             </td>
7231 <td>
7232               <p>
7233                 <span class="blue">Max = 441&#949; (Mean = 53.9&#949;)</span><br> <br>
7234                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547&#949; (Mean = 61.6&#949;))
7235               </p>
7236             </td>
7237 <td>
7238               <p>
7239                 <span class="blue">Max = 9.17e+03&#949; (Mean = 1.45e+03&#949;)</span>
7240               </p>
7241             </td>
7242 <td>
7243               <p>
7244                 <span class="blue">Max = 1.09e+04&#949; (Mean = 1.3e+03&#949;)</span>
7245               </p>
7246             </td>
7247 <td>
7248               <p>
7249                 <span class="blue">Max = 1.1e+03&#949; (Mean = 131&#949;)</span>
7250               </p>
7251             </td>
7252 </tr>
7253 </tbody>
7254 </table></div>
7255 </div>
7256 <br class="table-break">
7257 </div>
7258 <div class="section">
7259 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
7260 <a name="special_function_error_rates_rep.section_gamma_p_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inva" title="gamma_p_inva">gamma_p_inva</a>
7261 </h2></div></div></div>
7262 <div class="table">
7263 <a name="special_function_error_rates_rep.section_gamma_p_inva.table_gamma_p_inva"></a><p class="title"><b>Table&#160;47.&#160;Error rates for gamma_p_inva</b></p>
7264 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
7265 <colgroup>
7266 <col>
7267 <col>
7268 <col>
7269 <col>
7270 <col>
7271 </colgroup>
7272 <thead><tr>
7273 <th>
7274             </th>
7275 <th>
7276               <p>
7277                 GNU C++ version 7.1.0<br> linux<br> double
7278               </p>
7279             </th>
7280 <th>
7281               <p>
7282                 GNU C++ version 7.1.0<br> linux<br> long double
7283               </p>
7284             </th>
7285 <th>
7286               <p>
7287                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7288               </p>
7289             </th>
7290 <th>
7291               <p>
7292                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7293               </p>
7294             </th>
7295 </tr></thead>
7296 <tbody><tr>
7297 <td>
7298               <p>
7299                 Incomplete gamma inverses.
7300               </p>
7301             </td>
7302 <td>
7303               <p>
7304                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7305               </p>
7306             </td>
7307 <td>
7308               <p>
7309                 <span class="blue">Max = 7.87&#949; (Mean = 1.15&#949;)</span>
7310               </p>
7311             </td>
7312 <td>
7313               <p>
7314                 <span class="blue">Max = 4.08&#949; (Mean = 1.12&#949;)</span>
7315               </p>
7316             </td>
7317 <td>
7318               <p>
7319                 <span class="blue">Max = 4.92&#949; (Mean = 1.03&#949;)</span>
7320               </p>
7321             </td>
7322 </tr></tbody>
7323 </table></div>
7324 </div>
7325 <br class="table-break">
7326 </div>
7327 <div class="section">
7328 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
7329 <a name="special_function_error_rates_rep.section_gamma_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q" title="gamma_q">gamma_q</a>
7330 </h2></div></div></div>
7331 <div class="table">
7332 <a name="special_function_error_rates_rep.section_gamma_q.table_gamma_q"></a><p class="title"><b>Table&#160;48.&#160;Error rates for gamma_q</b></p>
7333 <div class="table-contents"><table class="table" summary="Error rates for gamma_q">
7334 <colgroup>
7335 <col>
7336 <col>
7337 <col>
7338 <col>
7339 <col>
7340 </colgroup>
7341 <thead><tr>
7342 <th>
7343             </th>
7344 <th>
7345               <p>
7346                 GNU C++ version 7.1.0<br> linux<br> double
7347               </p>
7348             </th>
7349 <th>
7350               <p>
7351                 GNU C++ version 7.1.0<br> linux<br> long double
7352               </p>
7353             </th>
7354 <th>
7355               <p>
7356                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7357               </p>
7358             </th>
7359 <th>
7360               <p>
7361                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7362               </p>
7363             </th>
7364 </tr></thead>
7365 <tbody>
7366 <tr>
7367 <td>
7368               <p>
7369                 tgamma(a, z) medium values
7370               </p>
7371             </td>
7372 <td>
7373               <p>
7374                 <span class="blue">Max = 0.927&#949; (Mean = 0.035&#949;)</span><br> <br>
7375                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201&#949; (Mean = 13.5&#949;))<br> (<span class="emphasis"><em>Rmath
7376                 3.2.3:</em></span> Max = 131&#949; (Mean = 12.7&#949;))
7377               </p>
7378             </td>
7379 <td>
7380               <p>
7381                 <span class="blue">Max = 32.3&#949; (Mean = 6.61&#949;)</span>
7382               </p>
7383             </td>
7384 <td>
7385               <p>
7386                 <span class="blue">Max = 199&#949; (Mean = 26.6&#949;)</span>
7387               </p>
7388             </td>
7389 <td>
7390               <p>
7391                 <span class="blue">Max = 23.7&#949; (Mean = 4&#949;)</span>
7392               </p>
7393             </td>
7394 </tr>
7395 <tr>
7396 <td>
7397               <p>
7398                 tgamma(a, z) small values
7399               </p>
7400             </td>
7401 <td>
7402               <p>
7403                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7404                 2.1:</em></span> <span class="red">Max = 1.38e+10&#949; (Mean = 1.05e+09&#949;))</span><br>
7405                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6&#949; (Mean = 11&#949;))
7406               </p>
7407             </td>
7408 <td>
7409               <p>
7410                 <span class="blue">Max = 2.45&#949; (Mean = 0.885&#949;)</span>
7411               </p>
7412             </td>
7413 <td>
7414               <p>
7415                 <span class="blue">Max = 2.45&#949; (Mean = 0.819&#949;)</span>
7416               </p>
7417             </td>
7418 <td>
7419               <p>
7420                 <span class="blue">Max = 2.26&#949; (Mean = 0.74&#949;)</span>
7421               </p>
7422             </td>
7423 </tr>
7424 <tr>
7425 <td>
7426               <p>
7427                 tgamma(a, z) large values
7428               </p>
7429             </td>
7430 <td>
7431               <p>
7432                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7433                 2.1:</em></span> Max = 2.71e+04&#949; (Mean = 2.16e+03&#949;))<br> (<span class="emphasis"><em>Rmath
7434                 3.2.3:</em></span> Max = 1.02e+03&#949; (Mean = 62.7&#949;))
7435               </p>
7436             </td>
7437 <td>
7438               <p>
7439                 <span class="blue">Max = 6.82e+03&#949; (Mean = 414&#949;)</span>
7440               </p>
7441             </td>
7442 <td>
7443               <p>
7444                 <span class="blue">Max = 1.15e+04&#949; (Mean = 733&#949;)</span>
7445               </p>
7446             </td>
7447 <td>
7448               <p>
7449                 <span class="blue">Max = 469&#949; (Mean = 31.5&#949;)</span>
7450               </p>
7451             </td>
7452 </tr>
7453 <tr>
7454 <td>
7455               <p>
7456                 tgamma(a, z) integer and half integer values
7457               </p>
7458             </td>
7459 <td>
7460               <p>
7461                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7462                 2.1:</em></span> Max = 118&#949; (Mean = 12.5&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
7463                 Max = 138&#949; (Mean = 16.9&#949;))
7464               </p>
7465             </td>
7466 <td>
7467               <p>
7468                 <span class="blue">Max = 11.1&#949; (Mean = 2.07&#949;)</span>
7469               </p>
7470             </td>
7471 <td>
7472               <p>
7473                 <span class="blue">Max = 54.7&#949; (Mean = 6.16&#949;)</span>
7474               </p>
7475             </td>
7476 <td>
7477               <p>
7478                 <span class="blue">Max = 8.72&#949; (Mean = 1.48&#949;)</span>
7479               </p>
7480             </td>
7481 </tr>
7482 </tbody>
7483 </table></div>
7484 </div>
7485 <br class="table-break">
7486 </div>
7487 <div class="section">
7488 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
7489 <a name="special_function_error_rates_rep.section_gamma_q_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inv" title="gamma_q_inv">gamma_q_inv</a>
7490 </h2></div></div></div>
7491 <div class="table">
7492 <a name="special_function_error_rates_rep.section_gamma_q_inv.table_gamma_q_inv"></a><p class="title"><b>Table&#160;49.&#160;Error rates for gamma_q_inv</b></p>
7493 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
7494 <colgroup>
7495 <col>
7496 <col>
7497 <col>
7498 <col>
7499 <col>
7500 </colgroup>
7501 <thead><tr>
7502 <th>
7503             </th>
7504 <th>
7505               <p>
7506                 GNU C++ version 7.1.0<br> linux<br> double
7507               </p>
7508             </th>
7509 <th>
7510               <p>
7511                 GNU C++ version 7.1.0<br> linux<br> long double
7512               </p>
7513             </th>
7514 <th>
7515               <p>
7516                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7517               </p>
7518             </th>
7519 <th>
7520               <p>
7521                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7522               </p>
7523             </th>
7524 </tr></thead>
7525 <tbody>
7526 <tr>
7527 <td>
7528               <p>
7529                 incomplete gamma inverse(a, z) medium values
7530               </p>
7531             </td>
7532 <td>
7533               <p>
7534                 <span class="blue">Max = 0.912&#949; (Mean = 0.154&#949;)</span><br> <br>
7535                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66&#949; (Mean = 0.792&#949;))
7536               </p>
7537             </td>
7538 <td>
7539               <p>
7540                 <span class="blue">Max = 6.2&#949; (Mean = 0.627&#949;)</span>
7541               </p>
7542             </td>
7543 <td>
7544               <p>
7545                 <span class="blue">Max = 6.2&#949; (Mean = 0.683&#949;)</span>
7546               </p>
7547             </td>
7548 <td>
7549               <p>
7550                 <span class="blue">Max = 2.88&#949; (Mean = 0.469&#949;)</span>
7551               </p>
7552             </td>
7553 </tr>
7554 <tr>
7555 <td>
7556               <p>
7557                 incomplete gamma inverse(a, z) large values
7558               </p>
7559             </td>
7560 <td>
7561               <p>
7562                 <span class="blue">Max = 0.894&#949; (Mean = 0.0915&#949;)</span><br> <br>
7563                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.106&#949;))
7564               </p>
7565             </td>
7566 <td>
7567               <p>
7568                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7569               </p>
7570             </td>
7571 <td>
7572               <p>
7573                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7574               </p>
7575             </td>
7576 <td>
7577               <p>
7578                 <span class="blue">Max = 0.814&#949; (Mean = 0.0856&#949;)</span>
7579               </p>
7580             </td>
7581 </tr>
7582 <tr>
7583 <td>
7584               <p>
7585                 incomplete gamma inverse(a, z) small values
7586               </p>
7587             </td>
7588 <td>
7589               <p>
7590                 <span class="blue">Max = 292&#949; (Mean = 36.4&#949;)</span><br> <br>
7591                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415&#949; (Mean = 48.7&#949;))
7592               </p>
7593             </td>
7594 <td>
7595               <p>
7596                 <span class="blue">Max = 8.28e+03&#949; (Mean = 1.09e+03&#949;)</span>
7597               </p>
7598             </td>
7599 <td>
7600               <p>
7601                 <span class="blue">Max = 8.98e+03&#949; (Mean = 877&#949;)</span>
7602               </p>
7603             </td>
7604 <td>
7605               <p>
7606                 <span class="blue">Max = 451&#949; (Mean = 64.7&#949;)</span>
7607               </p>
7608             </td>
7609 </tr>
7610 </tbody>
7611 </table></div>
7612 </div>
7613 <br class="table-break">
7614 </div>
7615 <div class="section">
7616 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
7617 <a name="special_function_error_rates_rep.section_gamma_q_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inva" title="gamma_q_inva">gamma_q_inva</a>
7618 </h2></div></div></div>
7619 <div class="table">
7620 <a name="special_function_error_rates_rep.section_gamma_q_inva.table_gamma_q_inva"></a><p class="title"><b>Table&#160;50.&#160;Error rates for gamma_q_inva</b></p>
7621 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
7622 <colgroup>
7623 <col>
7624 <col>
7625 <col>
7626 <col>
7627 <col>
7628 </colgroup>
7629 <thead><tr>
7630 <th>
7631             </th>
7632 <th>
7633               <p>
7634                 GNU C++ version 7.1.0<br> linux<br> double
7635               </p>
7636             </th>
7637 <th>
7638               <p>
7639                 GNU C++ version 7.1.0<br> linux<br> long double
7640               </p>
7641             </th>
7642 <th>
7643               <p>
7644                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7645               </p>
7646             </th>
7647 <th>
7648               <p>
7649                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7650               </p>
7651             </th>
7652 </tr></thead>
7653 <tbody><tr>
7654 <td>
7655               <p>
7656                 Incomplete gamma inverses.
7657               </p>
7658             </td>
7659 <td>
7660               <p>
7661                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7662               </p>
7663             </td>
7664 <td>
7665               <p>
7666                 <span class="blue">Max = 8.42&#949; (Mean = 1.3&#949;)</span>
7667               </p>
7668             </td>
7669 <td>
7670               <p>
7671                 <span class="blue">Max = 7.86&#949; (Mean = 1.24&#949;)</span>
7672               </p>
7673             </td>
7674 <td>
7675               <p>
7676                 <span class="blue">Max = 5.05&#949; (Mean = 1.08&#949;)</span>
7677               </p>
7678             </td>
7679 </tr></tbody>
7680 </table></div>
7681 </div>
7682 <br class="table-break">
7683 </div>
7684 <div class="section">
7685 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
7686 <a name="special_function_error_rates_rep.section_hermite"></a><a class="link" href="index.html#special_function_error_rates_rep.section_hermite" title="hermite">hermite</a>
7687 </h2></div></div></div>
7688 <div class="table">
7689 <a name="special_function_error_rates_rep.section_hermite.table_hermite"></a><p class="title"><b>Table&#160;51.&#160;Error rates for hermite</b></p>
7690 <div class="table-contents"><table class="table" summary="Error rates for hermite">
7691 <colgroup>
7692 <col>
7693 <col>
7694 <col>
7695 <col>
7696 <col>
7697 </colgroup>
7698 <thead><tr>
7699 <th>
7700             </th>
7701 <th>
7702               <p>
7703                 GNU C++ version 7.1.0<br> linux<br> double
7704               </p>
7705             </th>
7706 <th>
7707               <p>
7708                 GNU C++ version 7.1.0<br> linux<br> long double
7709               </p>
7710             </th>
7711 <th>
7712               <p>
7713                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7714               </p>
7715             </th>
7716 <th>
7717               <p>
7718                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7719               </p>
7720             </th>
7721 </tr></thead>
7722 <tbody><tr>
7723 <td>
7724               <p>
7725                 Hermite Polynomials
7726               </p>
7727             </td>
7728 <td>
7729               <p>
7730                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7731               </p>
7732             </td>
7733 <td>
7734               <p>
7735                 <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
7736               </p>
7737             </td>
7738 <td>
7739               <p>
7740                 <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
7741               </p>
7742             </td>
7743 <td>
7744               <p>
7745                 <span class="blue">Max = 4.46&#949; (Mean = 1.41&#949;)</span>
7746               </p>
7747             </td>
7748 </tr></tbody>
7749 </table></div>
7750 </div>
7751 <br class="table-break">
7752 </div>
7753 <div class="section">
7754 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
7755 <a name="special_function_error_rates_rep.section_heuman_lambda"></a><a class="link" href="index.html#special_function_error_rates_rep.section_heuman_lambda" title="heuman_lambda">heuman_lambda</a>
7756 </h2></div></div></div>
7757 <div class="table">
7758 <a name="special_function_error_rates_rep.section_heuman_lambda.table_heuman_lambda"></a><p class="title"><b>Table&#160;52.&#160;Error rates for heuman_lambda</b></p>
7759 <div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
7760 <colgroup>
7761 <col>
7762 <col>
7763 <col>
7764 <col>
7765 <col>
7766 </colgroup>
7767 <thead><tr>
7768 <th>
7769             </th>
7770 <th>
7771               <p>
7772                 GNU C++ version 7.1.0<br> linux<br> double
7773               </p>
7774             </th>
7775 <th>
7776               <p>
7777                 GNU C++ version 7.1.0<br> linux<br> long double
7778               </p>
7779             </th>
7780 <th>
7781               <p>
7782                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7783               </p>
7784             </th>
7785 <th>
7786               <p>
7787                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7788               </p>
7789             </th>
7790 </tr></thead>
7791 <tbody>
7792 <tr>
7793 <td>
7794               <p>
7795                 Elliptic Integral Jacobi Zeta: Mathworld Data
7796               </p>
7797             </td>
7798 <td>
7799               <p>
7800                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7801               </p>
7802             </td>
7803 <td>
7804               <p>
7805                 <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
7806               </p>
7807             </td>
7808 <td>
7809               <p>
7810                 <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
7811               </p>
7812             </td>
7813 <td>
7814               <p>
7815                 <span class="blue">Max = 1.08&#949; (Mean = 0.734&#949;)</span>
7816               </p>
7817             </td>
7818 </tr>
7819 <tr>
7820 <td>
7821               <p>
7822                 Elliptic Integral Heuman Lambda: Random Data
7823               </p>
7824             </td>
7825 <td>
7826               <p>
7827                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7828               </p>
7829             </td>
7830 <td>
7831               <p>
7832                 <span class="blue">Max = 3.82&#949; (Mean = 0.609&#949;)</span>
7833               </p>
7834             </td>
7835 <td>
7836               <p>
7837                 <span class="blue">Max = 3.82&#949; (Mean = 0.608&#949;)</span>
7838               </p>
7839             </td>
7840 <td>
7841               <p>
7842                 <span class="blue">Max = 2.12&#949; (Mean = 0.588&#949;)</span>
7843               </p>
7844             </td>
7845 </tr>
7846 </tbody>
7847 </table></div>
7848 </div>
7849 <br class="table-break">
7850 </div>
7851 <div class="section">
7852 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
7853 <a name="special_function_error_rates_rep.section_ibeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta" title="ibeta">ibeta</a>
7854 </h2></div></div></div>
7855 <div class="table">
7856 <a name="special_function_error_rates_rep.section_ibeta.table_ibeta"></a><p class="title"><b>Table&#160;53.&#160;Error rates for ibeta</b></p>
7857 <div class="table-contents"><table class="table" summary="Error rates for ibeta">
7858 <colgroup>
7859 <col>
7860 <col>
7861 <col>
7862 <col>
7863 <col>
7864 </colgroup>
7865 <thead><tr>
7866 <th>
7867             </th>
7868 <th>
7869               <p>
7870                 GNU C++ version 7.1.0<br> linux<br> double
7871               </p>
7872             </th>
7873 <th>
7874               <p>
7875                 GNU C++ version 7.1.0<br> linux<br> long double
7876               </p>
7877             </th>
7878 <th>
7879               <p>
7880                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
7881               </p>
7882             </th>
7883 <th>
7884               <p>
7885                 Microsoft Visual C++ version 14.1<br> Win32<br> double
7886               </p>
7887             </th>
7888 </tr></thead>
7889 <tbody>
7890 <tr>
7891 <td>
7892               <p>
7893                 Incomplete Beta Function: Small Values
7894               </p>
7895             </td>
7896 <td>
7897               <p>
7898                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7899                 2.1:</em></span> Max = 682&#949; (Mean = 32.6&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
7900                 Max = 22.9&#949; (Mean = 3.35&#949;))
7901               </p>
7902             </td>
7903 <td>
7904               <p>
7905                 <span class="blue">Max = 8.97&#949; (Mean = 2.09&#949;)</span>
7906               </p>
7907             </td>
7908 <td>
7909               <p>
7910                 <span class="blue">Max = 21.3&#949; (Mean = 2.75&#949;)</span>
7911               </p>
7912             </td>
7913 <td>
7914               <p>
7915                 <span class="blue">Max = 8.4&#949; (Mean = 1.93&#949;)</span>
7916               </p>
7917             </td>
7918 </tr>
7919 <tr>
7920 <td>
7921               <p>
7922                 Incomplete Beta Function: Medium Values
7923               </p>
7924             </td>
7925 <td>
7926               <p>
7927                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7928                 2.1:</em></span> Max = 690&#949; (Mean = 151&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
7929                 Max = 232&#949; (Mean = 27.9&#949;))
7930               </p>
7931             </td>
7932 <td>
7933               <p>
7934                 <span class="blue">Max = 50&#949; (Mean = 12.1&#949;)</span>
7935               </p>
7936             </td>
7937 <td>
7938               <p>
7939                 <span class="blue">Max = 124&#949; (Mean = 18.4&#949;)</span>
7940               </p>
7941             </td>
7942 <td>
7943               <p>
7944                 <span class="blue">Max = 106&#949; (Mean = 16.3&#949;)</span>
7945               </p>
7946             </td>
7947 </tr>
7948 <tr>
7949 <td>
7950               <p>
7951                 Incomplete Beta Function: Large and Diverse Values
7952               </p>
7953             </td>
7954 <td>
7955               <p>
7956                 <span class="blue">Max = 1.26&#949; (Mean = 0.063&#949;)</span><br> <br>
7957                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05&#949; (Mean = 1.82e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And
7958                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
7959                 Max = 574&#949; (Mean = 49.4&#949;))
7960               </p>
7961             </td>
7962 <td>
7963               <p>
7964                 <span class="blue">Max = 1.96e+04&#949; (Mean = 997&#949;)</span>
7965               </p>
7966             </td>
7967 <td>
7968               <p>
7969                 <span class="blue">Max = 4.98e+04&#949; (Mean = 2.07e+03&#949;)</span>
7970               </p>
7971             </td>
7972 <td>
7973               <p>
7974                 <span class="blue">Max = 1.32e+03&#949; (Mean = 68.5&#949;)</span>
7975               </p>
7976             </td>
7977 </tr>
7978 <tr>
7979 <td>
7980               <p>
7981                 Incomplete Beta Function: Small Integer Values
7982               </p>
7983             </td>
7984 <td>
7985               <p>
7986                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7987                 2.1:</em></span> Max = 254&#949; (Mean = 50.9&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
7988                 Max = 62.2&#949; (Mean = 8.95&#949;))
7989               </p>
7990             </td>
7991 <td>
7992               <p>
7993                 <span class="blue">Max = 4.45&#949; (Mean = 0.814&#949;)</span>
7994               </p>
7995             </td>
7996 <td>
7997               <p>
7998                 <span class="blue">Max = 44.5&#949; (Mean = 10.1&#949;)</span>
7999               </p>
8000             </td>
8001 <td>
8002               <p>
8003                 <span class="blue">Max = 3.85&#949; (Mean = 0.791&#949;)</span>
8004               </p>
8005             </td>
8006 </tr>
8007 </tbody>
8008 </table></div>
8009 </div>
8010 <br class="table-break">
8011 </div>
8012 <div class="section">
8013 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8014 <a name="special_function_error_rates_rep.section_ibeta_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inv" title="ibeta_inv">ibeta_inv</a>
8015 </h2></div></div></div>
8016 <div class="table">
8017 <a name="special_function_error_rates_rep.section_ibeta_inv.table_ibeta_inv"></a><p class="title"><b>Table&#160;54.&#160;Error rates for ibeta_inv</b></p>
8018 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
8019 <colgroup>
8020 <col>
8021 <col>
8022 <col>
8023 <col>
8024 <col>
8025 </colgroup>
8026 <thead><tr>
8027 <th>
8028             </th>
8029 <th>
8030               <p>
8031                 GNU C++ version 7.1.0<br> linux<br> double
8032               </p>
8033             </th>
8034 <th>
8035               <p>
8036                 GNU C++ version 7.1.0<br> linux<br> long double
8037               </p>
8038             </th>
8039 <th>
8040               <p>
8041                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8042               </p>
8043             </th>
8044 <th>
8045               <p>
8046                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8047               </p>
8048             </th>
8049 </tr></thead>
8050 <tbody><tr>
8051 <td>
8052               <p>
8053                 Inverse incomplete beta
8054               </p>
8055             </td>
8056 <td>
8057               <p>
8058                 <span class="blue">Max = 11&#949; (Mean = 0.345&#949;)</span><br> <br>
8059                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121&#949; (Mean
8060                 = 3.28e+119&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
8061                 other failures.</a>)</span>
8062               </p>
8063             </td>
8064 <td>
8065               <p>
8066                 <span class="blue">Max = 3.8e+04&#949; (Mean = 2.66e+03&#949;)</span>
8067               </p>
8068             </td>
8069 <td>
8070               <p>
8071                 <span class="blue">Max = 4.07e+04&#949; (Mean = 2.86e+03&#949;)</span>
8072               </p>
8073             </td>
8074 <td>
8075               <p>
8076                 <span class="blue">Max = 8.59e+03&#949; (Mean = 277&#949;)</span>
8077               </p>
8078             </td>
8079 </tr></tbody>
8080 </table></div>
8081 </div>
8082 <br class="table-break">
8083 </div>
8084 <div class="section">
8085 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8086 <a name="special_function_error_rates_rep.section_ibeta_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inva" title="ibeta_inva">ibeta_inva</a>
8087 </h2></div></div></div>
8088 <div class="table">
8089 <a name="special_function_error_rates_rep.section_ibeta_inva.table_ibeta_inva"></a><p class="title"><b>Table&#160;55.&#160;Error rates for ibeta_inva</b></p>
8090 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
8091 <colgroup>
8092 <col>
8093 <col>
8094 <col>
8095 <col>
8096 <col>
8097 </colgroup>
8098 <thead><tr>
8099 <th>
8100             </th>
8101 <th>
8102               <p>
8103                 GNU C++ version 7.1.0<br> linux<br> double
8104               </p>
8105             </th>
8106 <th>
8107               <p>
8108                 GNU C++ version 7.1.0<br> linux<br> long double
8109               </p>
8110             </th>
8111 <th>
8112               <p>
8113                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8114               </p>
8115             </th>
8116 <th>
8117               <p>
8118                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8119               </p>
8120             </th>
8121 </tr></thead>
8122 <tbody><tr>
8123 <td>
8124               <p>
8125                 Inverse incomplete beta
8126               </p>
8127             </td>
8128 <td>
8129               <p>
8130                 <span class="blue">Max = 0.602&#949; (Mean = 0.0239&#949;)</span>
8131               </p>
8132             </td>
8133 <td>
8134               <p>
8135                 <span class="blue">Max = 377&#949; (Mean = 24.4&#949;)</span>
8136               </p>
8137             </td>
8138 <td>
8139               <p>
8140                 <span class="blue">Max = 438&#949; (Mean = 31.3&#949;)</span>
8141               </p>
8142             </td>
8143 <td>
8144               <p>
8145                 <span class="blue">Max = 242&#949; (Mean = 22.9&#949;)</span>
8146               </p>
8147             </td>
8148 </tr></tbody>
8149 </table></div>
8150 </div>
8151 <br class="table-break">
8152 </div>
8153 <div class="section">
8154 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8155 <a name="special_function_error_rates_rep.section_ibeta_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_invb" title="ibeta_invb">ibeta_invb</a>
8156 </h2></div></div></div>
8157 <div class="table">
8158 <a name="special_function_error_rates_rep.section_ibeta_invb.table_ibeta_invb"></a><p class="title"><b>Table&#160;56.&#160;Error rates for ibeta_invb</b></p>
8159 <div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
8160 <colgroup>
8161 <col>
8162 <col>
8163 <col>
8164 <col>
8165 <col>
8166 </colgroup>
8167 <thead><tr>
8168 <th>
8169             </th>
8170 <th>
8171               <p>
8172                 GNU C++ version 7.1.0<br> linux<br> double
8173               </p>
8174             </th>
8175 <th>
8176               <p>
8177                 GNU C++ version 7.1.0<br> linux<br> long double
8178               </p>
8179             </th>
8180 <th>
8181               <p>
8182                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8183               </p>
8184             </th>
8185 <th>
8186               <p>
8187                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8188               </p>
8189             </th>
8190 </tr></thead>
8191 <tbody><tr>
8192 <td>
8193               <p>
8194                 Inverse incomplete beta
8195               </p>
8196             </td>
8197 <td>
8198               <p>
8199                 <span class="blue">Max = 0.765&#949; (Mean = 0.0422&#949;)</span>
8200               </p>
8201             </td>
8202 <td>
8203               <p>
8204                 <span class="blue">Max = 407&#949; (Mean = 27.2&#949;)</span>
8205               </p>
8206             </td>
8207 <td>
8208               <p>
8209                 <span class="blue">Max = 407&#949; (Mean = 24.4&#949;)</span>
8210               </p>
8211             </td>
8212 <td>
8213               <p>
8214                 <span class="blue">Max = 409&#949; (Mean = 19.3&#949;)</span>
8215               </p>
8216             </td>
8217 </tr></tbody>
8218 </table></div>
8219 </div>
8220 <br class="table-break">
8221 </div>
8222 <div class="section">
8223 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8224 <a name="special_function_error_rates_rep.section_ibetac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac" title="ibetac">ibetac</a>
8225 </h2></div></div></div>
8226 <div class="table">
8227 <a name="special_function_error_rates_rep.section_ibetac.table_ibetac"></a><p class="title"><b>Table&#160;57.&#160;Error rates for ibetac</b></p>
8228 <div class="table-contents"><table class="table" summary="Error rates for ibetac">
8229 <colgroup>
8230 <col>
8231 <col>
8232 <col>
8233 <col>
8234 <col>
8235 </colgroup>
8236 <thead><tr>
8237 <th>
8238             </th>
8239 <th>
8240               <p>
8241                 GNU C++ version 7.1.0<br> linux<br> double
8242               </p>
8243             </th>
8244 <th>
8245               <p>
8246                 GNU C++ version 7.1.0<br> linux<br> long double
8247               </p>
8248             </th>
8249 <th>
8250               <p>
8251                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8252               </p>
8253             </th>
8254 <th>
8255               <p>
8256                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8257               </p>
8258             </th>
8259 </tr></thead>
8260 <tbody>
8261 <tr>
8262 <td>
8263               <p>
8264                 Incomplete Beta Function: Small Values
8265               </p>
8266             </td>
8267 <td>
8268               <p>
8269                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
8270                 3.2.3:</em></span> Max = 22.4&#949; (Mean = 3.67&#949;))
8271               </p>
8272             </td>
8273 <td>
8274               <p>
8275                 <span class="blue">Max = 10.6&#949; (Mean = 2.22&#949;)</span>
8276               </p>
8277             </td>
8278 <td>
8279               <p>
8280                 <span class="blue">Max = 13.8&#949; (Mean = 2.68&#949;)</span>
8281               </p>
8282             </td>
8283 <td>
8284               <p>
8285                 <span class="blue">Max = 6.94&#949; (Mean = 1.71&#949;)</span>
8286               </p>
8287             </td>
8288 </tr>
8289 <tr>
8290 <td>
8291               <p>
8292                 Incomplete Beta Function: Medium Values
8293               </p>
8294             </td>
8295 <td>
8296               <p>
8297                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
8298                 3.2.3:</em></span> Max = 204&#949; (Mean = 25.8&#949;))
8299               </p>
8300             </td>
8301 <td>
8302               <p>
8303                 <span class="blue">Max = 73.9&#949; (Mean = 11.2&#949;)</span>
8304               </p>
8305             </td>
8306 <td>
8307               <p>
8308                 <span class="blue">Max = 132&#949; (Mean = 19.8&#949;)</span>
8309               </p>
8310             </td>
8311 <td>
8312               <p>
8313                 <span class="blue">Max = 56.7&#949; (Mean = 14.3&#949;)</span>
8314               </p>
8315             </td>
8316 </tr>
8317 <tr>
8318 <td>
8319               <p>
8320                 Incomplete Beta Function: Large and Diverse Values
8321               </p>
8322             </td>
8323 <td>
8324               <p>
8325                 <span class="blue">Max = 0.981&#949; (Mean = 0.0573&#949;)</span><br> <br>
8326                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889&#949; (Mean = 68.4&#949;))
8327               </p>
8328             </td>
8329 <td>
8330               <p>
8331                 <span class="blue">Max = 3.45e+04&#949; (Mean = 1.32e+03&#949;)</span>
8332               </p>
8333             </td>
8334 <td>
8335               <p>
8336                 <span class="blue">Max = 6.31e+04&#949; (Mean = 2.04e+03&#949;)</span>
8337               </p>
8338             </td>
8339 <td>
8340               <p>
8341                 <span class="blue">Max = 1.88e+03&#949; (Mean = 82.7&#949;)</span>
8342               </p>
8343             </td>
8344 </tr>
8345 <tr>
8346 <td>
8347               <p>
8348                 Incomplete Beta Function: Small Integer Values
8349               </p>
8350             </td>
8351 <td>
8352               <p>
8353                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
8354                 3.2.3:</em></span> Max = 84.6&#949; (Mean = 18&#949;))
8355               </p>
8356             </td>
8357 <td>
8358               <p>
8359                 <span class="blue">Max = 5.34&#949; (Mean = 1.11&#949;)</span>
8360               </p>
8361             </td>
8362 <td>
8363               <p>
8364                 <span class="blue">Max = 107&#949; (Mean = 17.1&#949;)</span>
8365               </p>
8366             </td>
8367 <td>
8368               <p>
8369                 <span class="blue">Max = 6.37&#949; (Mean = 1.03&#949;)</span>
8370               </p>
8371             </td>
8372 </tr>
8373 </tbody>
8374 </table></div>
8375 </div>
8376 <br class="table-break">
8377 </div>
8378 <div class="section">
8379 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8380 <a name="special_function_error_rates_rep.section_ibetac_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inv" title="ibetac_inv">ibetac_inv</a>
8381 </h2></div></div></div>
8382 <div class="table">
8383 <a name="special_function_error_rates_rep.section_ibetac_inv.table_ibetac_inv"></a><p class="title"><b>Table&#160;58.&#160;Error rates for ibetac_inv</b></p>
8384 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
8385 <colgroup>
8386 <col>
8387 <col>
8388 <col>
8389 <col>
8390 <col>
8391 </colgroup>
8392 <thead><tr>
8393 <th>
8394             </th>
8395 <th>
8396               <p>
8397                 GNU C++ version 7.1.0<br> linux<br> double
8398               </p>
8399             </th>
8400 <th>
8401               <p>
8402                 GNU C++ version 7.1.0<br> linux<br> long double
8403               </p>
8404             </th>
8405 <th>
8406               <p>
8407                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8408               </p>
8409             </th>
8410 <th>
8411               <p>
8412                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8413               </p>
8414             </th>
8415 </tr></thead>
8416 <tbody><tr>
8417 <td>
8418               <p>
8419                 Inverse incomplete beta
8420               </p>
8421             </td>
8422 <td>
8423               <p>
8424                 <span class="blue">Max = 0.977&#949; (Mean = 0.0976&#949;)</span><br> <br>
8425                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132&#949; (Mean
8426                 = 8.65e+130&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
8427                 other failures.</a>)</span>
8428               </p>
8429             </td>
8430 <td>
8431               <p>
8432                 <span class="blue">Max = 4.88e+04&#949; (Mean = 3.16e+03&#949;)</span>
8433               </p>
8434             </td>
8435 <td>
8436               <p>
8437                 <span class="blue">Max = 5.05e+04&#949; (Mean = 3.33e+03&#949;)</span>
8438               </p>
8439             </td>
8440 <td>
8441               <p>
8442                 <span class="blue">Max = 2.93e+03&#949; (Mean = 198&#949;)</span>
8443               </p>
8444             </td>
8445 </tr></tbody>
8446 </table></div>
8447 </div>
8448 <br class="table-break">
8449 </div>
8450 <div class="section">
8451 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8452 <a name="special_function_error_rates_rep.section_ibetac_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inva" title="ibetac_inva">ibetac_inva</a>
8453 </h2></div></div></div>
8454 <div class="table">
8455 <a name="special_function_error_rates_rep.section_ibetac_inva.table_ibetac_inva"></a><p class="title"><b>Table&#160;59.&#160;Error rates for ibetac_inva</b></p>
8456 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
8457 <colgroup>
8458 <col>
8459 <col>
8460 <col>
8461 <col>
8462 <col>
8463 </colgroup>
8464 <thead><tr>
8465 <th>
8466             </th>
8467 <th>
8468               <p>
8469                 GNU C++ version 7.1.0<br> linux<br> double
8470               </p>
8471             </th>
8472 <th>
8473               <p>
8474                 GNU C++ version 7.1.0<br> linux<br> long double
8475               </p>
8476             </th>
8477 <th>
8478               <p>
8479                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8480               </p>
8481             </th>
8482 <th>
8483               <p>
8484                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8485               </p>
8486             </th>
8487 </tr></thead>
8488 <tbody><tr>
8489 <td>
8490               <p>
8491                 Inverse incomplete beta
8492               </p>
8493             </td>
8494 <td>
8495               <p>
8496                 <span class="blue">Max = 0.683&#949; (Mean = 0.0314&#949;)</span>
8497               </p>
8498             </td>
8499 <td>
8500               <p>
8501                 <span class="blue">Max = 382&#949; (Mean = 22.2&#949;)</span>
8502               </p>
8503             </td>
8504 <td>
8505               <p>
8506                 <span class="blue">Max = 315&#949; (Mean = 23.7&#949;)</span>
8507               </p>
8508             </td>
8509 <td>
8510               <p>
8511                 <span class="blue">Max = 408&#949; (Mean = 26.7&#949;)</span>
8512               </p>
8513             </td>
8514 </tr></tbody>
8515 </table></div>
8516 </div>
8517 <br class="table-break">
8518 </div>
8519 <div class="section">
8520 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8521 <a name="special_function_error_rates_rep.section_ibetac_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_invb" title="ibetac_invb">ibetac_invb</a>
8522 </h2></div></div></div>
8523 <div class="table">
8524 <a name="special_function_error_rates_rep.section_ibetac_invb.table_ibetac_invb"></a><p class="title"><b>Table&#160;60.&#160;Error rates for ibetac_invb</b></p>
8525 <div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
8526 <colgroup>
8527 <col>
8528 <col>
8529 <col>
8530 <col>
8531 <col>
8532 </colgroup>
8533 <thead><tr>
8534 <th>
8535             </th>
8536 <th>
8537               <p>
8538                 GNU C++ version 7.1.0<br> linux<br> double
8539               </p>
8540             </th>
8541 <th>
8542               <p>
8543                 GNU C++ version 7.1.0<br> linux<br> long double
8544               </p>
8545             </th>
8546 <th>
8547               <p>
8548                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8549               </p>
8550             </th>
8551 <th>
8552               <p>
8553                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8554               </p>
8555             </th>
8556 </tr></thead>
8557 <tbody><tr>
8558 <td>
8559               <p>
8560                 Inverse incomplete beta
8561               </p>
8562             </td>
8563 <td>
8564               <p>
8565                 <span class="blue">Max = 0.724&#949; (Mean = 0.0303&#949;)</span>
8566               </p>
8567             </td>
8568 <td>
8569               <p>
8570                 <span class="blue">Max = 317&#949; (Mean = 19.8&#949;)</span>
8571               </p>
8572             </td>
8573 <td>
8574               <p>
8575                 <span class="blue">Max = 369&#949; (Mean = 22.6&#949;)</span>
8576               </p>
8577             </td>
8578 <td>
8579               <p>
8580                 <span class="blue">Max = 271&#949; (Mean = 16.4&#949;)</span>
8581               </p>
8582             </td>
8583 </tr></tbody>
8584 </table></div>
8585 </div>
8586 <br class="table-break">
8587 </div>
8588 <div class="section">
8589 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8590 <a name="special_function_error_rates_rep.section_jacobi_cn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_cn" title="jacobi_cn">jacobi_cn</a>
8591 </h2></div></div></div>
8592 <div class="table">
8593 <a name="special_function_error_rates_rep.section_jacobi_cn.table_jacobi_cn"></a><p class="title"><b>Table&#160;61.&#160;Error rates for jacobi_cn</b></p>
8594 <div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
8595 <colgroup>
8596 <col>
8597 <col>
8598 <col>
8599 <col>
8600 <col>
8601 </colgroup>
8602 <thead><tr>
8603 <th>
8604             </th>
8605 <th>
8606               <p>
8607                 GNU C++ version 7.1.0<br> linux<br> double
8608               </p>
8609             </th>
8610 <th>
8611               <p>
8612                 GNU C++ version 7.1.0<br> linux<br> long double
8613               </p>
8614             </th>
8615 <th>
8616               <p>
8617                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8618               </p>
8619             </th>
8620 <th>
8621               <p>
8622                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8623               </p>
8624             </th>
8625 </tr></thead>
8626 <tbody>
8627 <tr>
8628 <td>
8629               <p>
8630                 Jacobi Elliptic: Mathworld Data
8631               </p>
8632             </td>
8633 <td>
8634               <p>
8635                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8636                 2.1:</em></span> Max = 17.3&#949; (Mean = 4.29&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
8637                 other failures.</a>)
8638               </p>
8639             </td>
8640 <td>
8641               <p>
8642                 <span class="blue">Max = 71.6&#949; (Mean = 19.3&#949;)</span>
8643               </p>
8644             </td>
8645 <td>
8646               <p>
8647                 <span class="blue">Max = 71.6&#949; (Mean = 19.4&#949;)</span>
8648               </p>
8649             </td>
8650 <td>
8651               <p>
8652                 <span class="blue">Max = 45.8&#949; (Mean = 11.4&#949;)</span>
8653               </p>
8654             </td>
8655 </tr>
8656 <tr>
8657 <td>
8658               <p>
8659                 Jacobi Elliptic: Random Data
8660               </p>
8661             </td>
8662 <td>
8663               <p>
8664                 <span class="blue">Max = 0.816&#949; (Mean = 0.0563&#949;)</span><br> <br>
8665                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43&#949; (Mean = 0.803&#949;))
8666               </p>
8667             </td>
8668 <td>
8669               <p>
8670                 <span class="blue">Max = 1.68&#949; (Mean = 0.443&#949;)</span>
8671               </p>
8672             </td>
8673 <td>
8674               <p>
8675                 <span class="blue">Max = 1.68&#949; (Mean = 0.454&#949;)</span>
8676               </p>
8677             </td>
8678 <td>
8679               <p>
8680                 <span class="blue">Max = 1.83&#949; (Mean = 0.455&#949;)</span>
8681               </p>
8682             </td>
8683 </tr>
8684 <tr>
8685 <td>
8686               <p>
8687                 Jacobi Elliptic: Random Small Values
8688               </p>
8689             </td>
8690 <td>
8691               <p>
8692                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8693                 2.1:</em></span> Max = 55.2&#949; (Mean = 1.64&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
8694                 other failures.</a>)
8695               </p>
8696             </td>
8697 <td>
8698               <p>
8699                 <span class="blue">Max = 10.4&#949; (Mean = 0.594&#949;)</span>
8700               </p>
8701             </td>
8702 <td>
8703               <p>
8704                 <span class="blue">Max = 10.4&#949; (Mean = 0.602&#949;)</span>
8705               </p>
8706             </td>
8707 <td>
8708               <p>
8709                 <span class="blue">Max = 26.2&#949; (Mean = 1.17&#949;)</span>
8710               </p>
8711             </td>
8712 </tr>
8713 <tr>
8714 <td>
8715               <p>
8716                 Jacobi Elliptic: Modulus near 1
8717               </p>
8718             </td>
8719 <td>
8720               <p>
8721                 <span class="blue">Max = 0.919&#949; (Mean = 0.127&#949;)</span><br> <br>
8722                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
8723                 other failures.</a>)
8724               </p>
8725             </td>
8726 <td>
8727               <p>
8728                 <span class="blue">Max = 675&#949; (Mean = 87.1&#949;)</span>
8729               </p>
8730             </td>
8731 <td>
8732               <p>
8733                 <span class="blue">Max = 675&#949; (Mean = 86.8&#949;)</span>
8734               </p>
8735             </td>
8736 <td>
8737               <p>
8738                 <span class="blue">Max = 513&#949; (Mean = 126&#949;)</span>
8739               </p>
8740             </td>
8741 </tr>
8742 <tr>
8743 <td>
8744               <p>
8745                 Jacobi Elliptic: Large Phi
8746               </p>
8747             </td>
8748 <td>
8749               <p>
8750                 <span class="blue">Max = 14.2&#949; (Mean = 0.927&#949;)</span><br> <br>
8751                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03&#949; (Mean = 477&#949;))
8752               </p>
8753             </td>
8754 <td>
8755               <p>
8756                 <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
8757               </p>
8758             </td>
8759 <td>
8760               <p>
8761                 <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
8762               </p>
8763             </td>
8764 <td>
8765               <p>
8766                 <span class="blue">Max = 3.27e+04&#949; (Mean = 1.93e+03&#949;)</span>
8767               </p>
8768             </td>
8769 </tr>
8770 </tbody>
8771 </table></div>
8772 </div>
8773 <br class="table-break">
8774 </div>
8775 <div class="section">
8776 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8777 <a name="special_function_error_rates_rep.section_jacobi_dn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_dn" title="jacobi_dn">jacobi_dn</a>
8778 </h2></div></div></div>
8779 <div class="table">
8780 <a name="special_function_error_rates_rep.section_jacobi_dn.table_jacobi_dn"></a><p class="title"><b>Table&#160;62.&#160;Error rates for jacobi_dn</b></p>
8781 <div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
8782 <colgroup>
8783 <col>
8784 <col>
8785 <col>
8786 <col>
8787 <col>
8788 </colgroup>
8789 <thead><tr>
8790 <th>
8791             </th>
8792 <th>
8793               <p>
8794                 GNU C++ version 7.1.0<br> linux<br> double
8795               </p>
8796             </th>
8797 <th>
8798               <p>
8799                 GNU C++ version 7.1.0<br> linux<br> long double
8800               </p>
8801             </th>
8802 <th>
8803               <p>
8804                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8805               </p>
8806             </th>
8807 <th>
8808               <p>
8809                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8810               </p>
8811             </th>
8812 </tr></thead>
8813 <tbody>
8814 <tr>
8815 <td>
8816               <p>
8817                 Jacobi Elliptic: Mathworld Data
8818               </p>
8819             </td>
8820 <td>
8821               <p>
8822                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8823                 2.1:</em></span> Max = 2.82&#949; (Mean = 1.18&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
8824                 other failures.</a>)
8825               </p>
8826             </td>
8827 <td>
8828               <p>
8829                 <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
8830               </p>
8831             </td>
8832 <td>
8833               <p>
8834                 <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
8835               </p>
8836             </td>
8837 <td>
8838               <p>
8839                 <span class="blue">Max = 34.3&#949; (Mean = 8.71&#949;)</span>
8840               </p>
8841             </td>
8842 </tr>
8843 <tr>
8844 <td>
8845               <p>
8846                 Jacobi Elliptic: Random Data
8847               </p>
8848             </td>
8849 <td>
8850               <p>
8851                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8852                 2.1:</em></span> Max = 3&#949; (Mean = 0.61&#949;))
8853               </p>
8854             </td>
8855 <td>
8856               <p>
8857                 <span class="blue">Max = 1.53&#949; (Mean = 0.473&#949;)</span>
8858               </p>
8859             </td>
8860 <td>
8861               <p>
8862                 <span class="blue">Max = 1.53&#949; (Mean = 0.481&#949;)</span>
8863               </p>
8864             </td>
8865 <td>
8866               <p>
8867                 <span class="blue">Max = 1.52&#949; (Mean = 0.466&#949;)</span>
8868               </p>
8869             </td>
8870 </tr>
8871 <tr>
8872 <td>
8873               <p>
8874                 Jacobi Elliptic: Random Small Values
8875               </p>
8876             </td>
8877 <td>
8878               <p>
8879                 <span class="blue">Max = 0.5&#949; (Mean = 0.0122&#949;)</span><br> <br>
8880                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5&#949; (Mean = 0.391&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
8881                 other failures.</a>)
8882               </p>
8883             </td>
8884 <td>
8885               <p>
8886                 <span class="blue">Max = 22.4&#949; (Mean = 0.777&#949;)</span>
8887               </p>
8888             </td>
8889 <td>
8890               <p>
8891                 <span class="blue">Max = 22.4&#949; (Mean = 0.763&#949;)</span>
8892               </p>
8893             </td>
8894 <td>
8895               <p>
8896                 <span class="blue">Max = 16.1&#949; (Mean = 0.685&#949;)</span>
8897               </p>
8898             </td>
8899 </tr>
8900 <tr>
8901 <td>
8902               <p>
8903                 Jacobi Elliptic: Modulus near 1
8904               </p>
8905             </td>
8906 <td>
8907               <p>
8908                 <span class="blue">Max = 2.28&#949; (Mean = 0.194&#949;)</span><br> <br>
8909                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
8910                 other failures.</a>)
8911               </p>
8912             </td>
8913 <td>
8914               <p>
8915                 <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
8916               </p>
8917             </td>
8918 <td>
8919               <p>
8920                 <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
8921               </p>
8922             </td>
8923 <td>
8924               <p>
8925                 <span class="blue">Max = 6.24e+03&#949; (Mean = 482&#949;)</span>
8926               </p>
8927             </td>
8928 </tr>
8929 <tr>
8930 <td>
8931               <p>
8932                 Jacobi Elliptic: Large Phi
8933               </p>
8934             </td>
8935 <td>
8936               <p>
8937                 <span class="blue">Max = 14.1&#949; (Mean = 0.897&#949;)</span><br> <br>
8938                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121&#949; (Mean = 22&#949;))
8939               </p>
8940             </td>
8941 <td>
8942               <p>
8943                 <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
8944               </p>
8945             </td>
8946 <td>
8947               <p>
8948                 <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
8949               </p>
8950             </td>
8951 <td>
8952               <p>
8953                 <span class="blue">Max = 1.67e+04&#949; (Mean = 1e+03&#949;)</span>
8954               </p>
8955             </td>
8956 </tr>
8957 </tbody>
8958 </table></div>
8959 </div>
8960 <br class="table-break">
8961 </div>
8962 <div class="section">
8963 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
8964 <a name="special_function_error_rates_rep.section_jacobi_sn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_sn" title="jacobi_sn">jacobi_sn</a>
8965 </h2></div></div></div>
8966 <div class="table">
8967 <a name="special_function_error_rates_rep.section_jacobi_sn.table_jacobi_sn"></a><p class="title"><b>Table&#160;63.&#160;Error rates for jacobi_sn</b></p>
8968 <div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
8969 <colgroup>
8970 <col>
8971 <col>
8972 <col>
8973 <col>
8974 <col>
8975 </colgroup>
8976 <thead><tr>
8977 <th>
8978             </th>
8979 <th>
8980               <p>
8981                 GNU C++ version 7.1.0<br> linux<br> double
8982               </p>
8983             </th>
8984 <th>
8985               <p>
8986                 GNU C++ version 7.1.0<br> linux<br> long double
8987               </p>
8988             </th>
8989 <th>
8990               <p>
8991                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
8992               </p>
8993             </th>
8994 <th>
8995               <p>
8996                 Microsoft Visual C++ version 14.1<br> Win32<br> double
8997               </p>
8998             </th>
8999 </tr></thead>
9000 <tbody>
9001 <tr>
9002 <td>
9003               <p>
9004                 Jacobi Elliptic: Mathworld Data
9005               </p>
9006             </td>
9007 <td>
9008               <p>
9009                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9010                 2.1:</em></span> Max = 588&#949; (Mean = 146&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
9011                 other failures.</a>)
9012               </p>
9013             </td>
9014 <td>
9015               <p>
9016                 <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
9017               </p>
9018             </td>
9019 <td>
9020               <p>
9021                 <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
9022               </p>
9023             </td>
9024 <td>
9025               <p>
9026                 <span class="blue">Max = 481&#949; (Mean = 113&#949;)</span>
9027               </p>
9028             </td>
9029 </tr>
9030 <tr>
9031 <td>
9032               <p>
9033                 Jacobi Elliptic: Random Data
9034               </p>
9035             </td>
9036 <td>
9037               <p>
9038                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9039                 2.1:</em></span> Max = 4.02&#949; (Mean = 1.07&#949;))
9040               </p>
9041             </td>
9042 <td>
9043               <p>
9044                 <span class="blue">Max = 2.01&#949; (Mean = 0.584&#949;)</span>
9045               </p>
9046             </td>
9047 <td>
9048               <p>
9049                 <span class="blue">Max = 2.01&#949; (Mean = 0.593&#949;)</span>
9050               </p>
9051             </td>
9052 <td>
9053               <p>
9054                 <span class="blue">Max = 1.92&#949; (Mean = 0.567&#949;)</span>
9055               </p>
9056             </td>
9057 </tr>
9058 <tr>
9059 <td>
9060               <p>
9061                 Jacobi Elliptic: Random Small Values
9062               </p>
9063             </td>
9064 <td>
9065               <p>
9066                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9067                 2.1:</em></span> Max = 11.7&#949; (Mean = 1.65&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
9068                 other failures.</a>)
9069               </p>
9070             </td>
9071 <td>
9072               <p>
9073                 <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
9074               </p>
9075             </td>
9076 <td>
9077               <p>
9078                 <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
9079               </p>
9080             </td>
9081 <td>
9082               <p>
9083                 <span class="blue">Max = 2.11&#949; (Mean = 0.385&#949;)</span>
9084               </p>
9085             </td>
9086 </tr>
9087 <tr>
9088 <td>
9089               <p>
9090                 Jacobi Elliptic: Modulus near 1
9091               </p>
9092             </td>
9093 <td>
9094               <p>
9095                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9096                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
9097                 other failures.</a>)
9098               </p>
9099             </td>
9100 <td>
9101               <p>
9102                 <span class="blue">Max = 109&#949; (Mean = 7.35&#949;)</span>
9103               </p>
9104             </td>
9105 <td>
9106               <p>
9107                 <span class="blue">Max = 109&#949; (Mean = 7.38&#949;)</span>
9108               </p>
9109             </td>
9110 <td>
9111               <p>
9112                 <span class="blue">Max = 23.2&#949; (Mean = 1.85&#949;)</span>
9113               </p>
9114             </td>
9115 </tr>
9116 <tr>
9117 <td>
9118               <p>
9119                 Jacobi Elliptic: Large Phi
9120               </p>
9121             </td>
9122 <td>
9123               <p>
9124                 <span class="blue">Max = 12&#949; (Mean = 0.771&#949;)</span><br> <br>
9125                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04&#949; (Mean = 2.63e+03&#949;))
9126               </p>
9127             </td>
9128 <td>
9129               <p>
9130                 <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
9131               </p>
9132             </td>
9133 <td>
9134               <p>
9135                 <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
9136               </p>
9137             </td>
9138 <td>
9139               <p>
9140                 <span class="blue">Max = 4.36e+04&#949; (Mean = 2.54e+03&#949;)</span>
9141               </p>
9142             </td>
9143 </tr>
9144 </tbody>
9145 </table></div>
9146 </div>
9147 <br class="table-break">
9148 </div>
9149 <div class="section">
9150 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
9151 <a name="special_function_error_rates_rep.section_jacobi_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_zeta" title="jacobi_zeta">jacobi_zeta</a>
9152 </h2></div></div></div>
9153 <div class="table">
9154 <a name="special_function_error_rates_rep.section_jacobi_zeta.table_jacobi_zeta"></a><p class="title"><b>Table&#160;64.&#160;Error rates for jacobi_zeta</b></p>
9155 <div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
9156 <colgroup>
9157 <col>
9158 <col>
9159 <col>
9160 <col>
9161 <col>
9162 </colgroup>
9163 <thead><tr>
9164 <th>
9165             </th>
9166 <th>
9167               <p>
9168                 GNU C++ version 7.1.0<br> linux<br> double
9169               </p>
9170             </th>
9171 <th>
9172               <p>
9173                 GNU C++ version 7.1.0<br> linux<br> long double
9174               </p>
9175             </th>
9176 <th>
9177               <p>
9178                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
9179               </p>
9180             </th>
9181 <th>
9182               <p>
9183                 Microsoft Visual C++ version 14.1<br> Win32<br> double
9184               </p>
9185             </th>
9186 </tr></thead>
9187 <tbody>
9188 <tr>
9189 <td>
9190               <p>
9191                 Elliptic Integral Jacobi Zeta: Mathworld Data
9192               </p>
9193             </td>
9194 <td>
9195               <p>
9196                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
9197               </p>
9198             </td>
9199 <td>
9200               <p>
9201                 <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
9202               </p>
9203             </td>
9204 <td>
9205               <p>
9206                 <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
9207               </p>
9208             </td>
9209 <td>
9210               <p>
9211                 <span class="blue">Max = 1.52&#949; (Mean = 0.357&#949;)</span>
9212               </p>
9213             </td>
9214 </tr>
9215 <tr>
9216 <td>
9217               <p>
9218                 Elliptic Integral Jacobi Zeta: Random Data
9219               </p>
9220             </td>
9221 <td>
9222               <p>
9223                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
9224               </p>
9225             </td>
9226 <td>
9227               <p>
9228                 <span class="blue">Max = 2.99&#949; (Mean = 0.824&#949;)</span>
9229               </p>
9230             </td>
9231 <td>
9232               <p>
9233                 <span class="blue">Max = 3.96&#949; (Mean = 1.06&#949;)</span>
9234               </p>
9235             </td>
9236 <td>
9237               <p>
9238                 <span class="blue">Max = 3.89&#949; (Mean = 0.824&#949;)</span>
9239               </p>
9240             </td>
9241 </tr>
9242 <tr>
9243 <td>
9244               <p>
9245                 Elliptic Integral Jacobi Zeta: Large Phi Values
9246               </p>
9247             </td>
9248 <td>
9249               <p>
9250                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
9251               </p>
9252             </td>
9253 <td>
9254               <p>
9255                 <span class="blue">Max = 2.92&#949; (Mean = 0.951&#949;)</span>
9256               </p>
9257             </td>
9258 <td>
9259               <p>
9260                 <span class="blue">Max = 3.05&#949; (Mean = 1.13&#949;)</span>
9261               </p>
9262             </td>
9263 <td>
9264               <p>
9265                 <span class="blue">Max = 2.52&#949; (Mean = 0.977&#949;)</span>
9266               </p>
9267             </td>
9268 </tr>
9269 </tbody>
9270 </table></div>
9271 </div>
9272 <br class="table-break">
9273 </div>
9274 <div class="section">
9275 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
9276 <a name="special_function_error_rates_rep.section_laguerre_n_m_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_" title="laguerre(n, m, x)">laguerre(n,
9277     m, x)</a>
9278 </h2></div></div></div>
9279 <div class="table">
9280 <a name="special_function_error_rates_rep.section_laguerre_n_m_x_.table_laguerre_n_m_x_"></a><p class="title"><b>Table&#160;65.&#160;Error rates for laguerre(n, m, x)</b></p>
9281 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
9282 <colgroup>
9283 <col>
9284 <col>
9285 <col>
9286 <col>
9287 <col>
9288 </colgroup>
9289 <thead><tr>
9290 <th>
9291             </th>
9292 <th>
9293               <p>
9294                 GNU C++ version 7.1.0<br> linux<br> double
9295               </p>
9296             </th>
9297 <th>
9298               <p>
9299                 GNU C++ version 7.1.0<br> linux<br> long double
9300               </p>
9301             </th>
9302 <th>
9303               <p>
9304                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
9305               </p>
9306             </th>
9307 <th>
9308               <p>
9309                 Microsoft Visual C++ version 14.1<br> Win32<br> double
9310               </p>
9311             </th>
9312 </tr></thead>
9313 <tbody><tr>
9314 <td>
9315               <p>
9316                 Associated Laguerre Polynomials
9317               </p>
9318             </td>
9319 <td>
9320               <p>
9321                 <span class="blue">Max = 0.84&#949; (Mean = 0.0358&#949;)</span><br> <br>
9322                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434&#949; (Mean = 10.7&#949;))
9323               </p>
9324             </td>
9325 <td>
9326               <p>
9327                 <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span><br> <br>
9328                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 206&#949; (Mean = 6.86&#949;))
9329               </p>
9330             </td>
9331 <td>
9332               <p>
9333                 <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span>
9334               </p>
9335             </td>
9336 <td>
9337               <p>
9338                 <span class="blue">Max = 434&#949; (Mean = 11.1&#949;)</span>
9339               </p>
9340             </td>
9341 </tr></tbody>
9342 </table></div>
9343 </div>
9344 <br class="table-break">
9345 </div>
9346 <div class="section">
9347 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
9348 <a name="special_function_error_rates_rep.section_laguerre_n_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_x_" title="laguerre(n, x)">laguerre(n,
9349     x)</a>
9350 </h2></div></div></div>
9351 <div class="table">
9352 <a name="special_function_error_rates_rep.section_laguerre_n_x_.table_laguerre_n_x_"></a><p class="title"><b>Table&#160;66.&#160;Error rates for laguerre(n, x)</b></p>
9353 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
9354 <colgroup>
9355 <col>
9356 <col>
9357 <col>
9358 <col>
9359 <col>
9360 </colgroup>
9361 <thead><tr>
9362 <th>
9363             </th>
9364 <th>
9365               <p>
9366                 GNU C++ version 7.1.0<br> linux<br> double
9367               </p>
9368             </th>
9369 <th>
9370               <p>
9371                 GNU C++ version 7.1.0<br> linux<br> long double
9372               </p>
9373             </th>
9374 <th>
9375               <p>
9376                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
9377               </p>
9378             </th>
9379 <th>
9380               <p>
9381                 Microsoft Visual C++ version 14.1<br> Win32<br> double
9382               </p>
9383             </th>
9384 </tr></thead>
9385 <tbody><tr>
9386 <td>
9387               <p>
9388                 Laguerre Polynomials
9389               </p>
9390             </td>
9391 <td>
9392               <p>
9393                 <span class="blue">Max = 6.82&#949; (Mean = 0.408&#949;)</span><br> <br>
9394                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03&#949; (Mean = 185&#949;))
9395               </p>
9396             </td>
9397 <td>
9398               <p>
9399                 <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span><br> <br>
9400                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.2e+03&#949; (Mean = 251&#949;))
9401               </p>
9402             </td>
9403 <td>
9404               <p>
9405                 <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span>
9406               </p>
9407             </td>
9408 <td>
9409               <p>
9410                 <span class="blue">Max = 3.1e+03&#949; (Mean = 185&#949;)</span>
9411               </p>
9412             </td>
9413 </tr></tbody>
9414 </table></div>
9415 </div>
9416 <br class="table-break">
9417 </div>
9418 <div class="section">
9419 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
9420 <a name="special_function_error_rates_rep.section_legendre_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p" title="legendre_p">legendre_p</a>
9421 </h2></div></div></div>
9422 <div class="table">
9423 <a name="special_function_error_rates_rep.section_legendre_p.table_legendre_p"></a><p class="title"><b>Table&#160;67.&#160;Error rates for legendre_p</b></p>
9424 <div class="table-contents"><table class="table" summary="Error rates for legendre_p">
9425 <colgroup>
9426 <col>
9427 <col>
9428 <col>
9429 <col>
9430 <col>
9431 </colgroup>
9432 <thead><tr>
9433 <th>
9434             </th>
9435 <th>
9436               <p>
9437                 GNU C++ version 7.1.0<br> linux<br> double
9438               </p>
9439             </th>
9440 <th>
9441               <p>
9442                 GNU C++ version 7.1.0<br> linux<br> long double
9443               </p>
9444             </th>
9445 <th>
9446               <p>
9447                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
9448               </p>
9449             </th>
9450 <th>
9451               <p>
9452                 Microsoft Visual C++ version 14.1<br> Win32<br> double
9453               </p>
9454             </th>
9455 </tr></thead>
9456 <tbody>
9457 <tr>
9458 <td>
9459               <p>
9460                 Legendre Polynomials: Small Values
9461               </p>
9462             </td>
9463 <td>
9464               <p>
9465                 <span class="blue">Max = 0.732&#949; (Mean = 0.0619&#949;)</span><br> <br>
9466                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211&#949; (Mean = 20.4&#949;))
9467               </p>
9468             </td>
9469 <td>
9470               <p>
9471                 <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span><br> <br>
9472                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 124&#949; (Mean = 13.2&#949;))
9473               </p>
9474             </td>
9475 <td>
9476               <p>
9477                 <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span>
9478               </p>
9479             </td>
9480 <td>
9481               <p>
9482                 <span class="blue">Max = 211&#949; (Mean = 20.4&#949;)</span>
9483               </p>
9484             </td>
9485 </tr>
9486 <tr>
9487 <td>
9488               <p>
9489                 Legendre Polynomials: Large Values
9490               </p>
9491             </td>
9492 <td>
9493               <p>
9494                 <span class="blue">Max = 0.632&#949; (Mean = 0.0693&#949;)</span><br> <br>
9495                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300&#949; (Mean = 33.2&#949;))
9496               </p>
9497             </td>
9498 <td>
9499               <p>
9500                 <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span><br> <br>
9501                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 343&#949; (Mean = 32.1&#949;))
9502               </p>
9503             </td>
9504 <td>
9505               <p>
9506                 <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span>
9507               </p>
9508             </td>
9509 <td>
9510               <p>
9511                 <span class="blue">Max = 300&#949; (Mean = 33.2&#949;)</span>
9512               </p>
9513             </td>
9514 </tr>
9515 </tbody>
9516 </table></div>
9517 </div>
9518 <br class="table-break">
9519 </div>
9520 <div class="section">
9521 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
9522 <a name="special_function_error_rates_rep.section_legendre_p_associated_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p_associated_" title="legendre_p (associated)">legendre_p
9523     (associated)</a>
9524 </h2></div></div></div>
9525 <div class="table">
9526 <a name="special_function_error_rates_rep.section_legendre_p_associated_.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;68.&#160;Error rates for legendre_p (associated)</b></p>
9527 <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
9528 <colgroup>
9529 <col>
9530 <col>
9531 <col>
9532 <col>
9533 <col>
9534 </colgroup>
9535 <thead><tr>
9536 <th>
9537             </th>
9538 <th>
9539               <p>
9540                 GNU C++ version 7.1.0<br> linux<br> double
9541               </p>
9542             </th>
9543 <th>
9544               <p>
9545                 GNU C++ version 7.1.0<br> linux<br> long double
9546               </p>
9547             </th>
9548 <th>
9549               <p>
9550                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
9551               </p>
9552             </th>
9553 <th>
9554               <p>
9555                 Microsoft Visual C++ version 14.1<br> Win32<br> double
9556               </p>
9557             </th>
9558 </tr></thead>
9559 <tbody><tr>
9560 <td>
9561               <p>
9562                 Associated Legendre Polynomials: Small Values
9563               </p>
9564             </td>
9565 <td>
9566               <p>
9567                 <span class="blue">Max = 0.999&#949; (Mean = 0.05&#949;)</span><br> <br>
9568                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121&#949; (Mean = 6.75&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And
9569                 other failures.</a>)
9570               </p>
9571             </td>
9572 <td>
9573               <p>
9574                 <span class="blue">Max = 175&#949; (Mean = 9.88&#949;)</span><br> <br>
9575                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 175&#949; (Mean = 9.36&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And
9576                 other failures.</a>)
9577               </p>
9578             </td>
9579 <td>
9580               <p>
9581                 <span class="blue">Max = 77.7&#949; (Mean = 5.59&#949;)</span>
9582               </p>
9583             </td>
9584 <td>
9585               <p>
9586                 <span class="blue">Max = 121&#949; (Mean = 7.14&#949;)</span>
9587               </p>
9588             </td>
9589 </tr></tbody>
9590 </table></div>
9591 </div>
9592 <br class="table-break">
9593 </div>
9594 <div class="section">
9595 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
9596 <a name="special_function_error_rates_rep.section_legendre_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_q" title="legendre_q">legendre_q</a>
9597 </h2></div></div></div>
9598 <div class="table">
9599 <a name="special_function_error_rates_rep.section_legendre_q.table_legendre_q"></a><p class="title"><b>Table&#160;69.&#160;Error rates for legendre_q</b></p>
9600 <div class="table-contents"><table class="table" summary="Error rates for legendre_q">
9601 <colgroup>
9602 <col>
9603 <col>
9604 <col>
9605 <col>
9606 <col>
9607 </colgroup>
9608 <thead><tr>
9609 <th>
9610             </th>
9611 <th>
9612               <p>
9613                 GNU C++ version 7.1.0<br> linux<br> double
9614               </p>
9615             </th>
9616 <th>
9617               <p>
9618                 GNU C++ version 7.1.0<br> linux<br> long double
9619               </p>
9620             </th>
9621 <th>
9622               <p>
9623                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
9624               </p>
9625             </th>
9626 <th>
9627               <p>
9628                 Microsoft Visual C++ version 14.1<br> Win32<br> double
9629               </p>
9630             </th>
9631 </tr></thead>
9632 <tbody>
9633 <tr>
9634 <td>
9635               <p>
9636                 Legendre Polynomials: Small Values
9637               </p>
9638             </td>
9639 <td>
9640               <p>
9641                 <span class="blue">Max = 0.612&#949; (Mean = 0.0517&#949;)</span><br> <br>
9642                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4&#949; (Mean = 7.46&#949;))
9643               </p>
9644             </td>
9645 <td>
9646               <p>
9647                 <span class="blue">Max = 50.9&#949; (Mean = 9&#949;)</span>
9648               </p>
9649             </td>
9650 <td>
9651               <p>
9652                 <span class="blue">Max = 50.9&#949; (Mean = 8.98&#949;)</span>
9653               </p>
9654             </td>
9655 <td>
9656               <p>
9657                 <span class="blue">Max = 46.4&#949; (Mean = 7.32&#949;)</span>
9658               </p>
9659             </td>
9660 </tr>
9661 <tr>
9662 <td>
9663               <p>
9664                 Legendre Polynomials: Large Values
9665               </p>
9666             </td>
9667 <td>
9668               <p>
9669                 <span class="blue">Max = 2.49&#949; (Mean = 0.202&#949;)</span><br> <br>
9670                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03&#949; (Mean = 366&#949;))
9671               </p>
9672             </td>
9673 <td>
9674               <p>
9675                 <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
9676               </p>
9677             </td>
9678 <td>
9679               <p>
9680                 <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
9681               </p>
9682             </td>
9683 <td>
9684               <p>
9685                 <span class="blue">Max = 4.6e+03&#949; (Mean = 366&#949;)</span>
9686               </p>
9687             </td>
9688 </tr>
9689 </tbody>
9690 </table></div>
9691 </div>
9692 <br class="table-break">
9693 </div>
9694 <div class="section">
9695 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
9696 <a name="special_function_error_rates_rep.section_lgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_lgamma" title="lgamma">lgamma</a>
9697 </h2></div></div></div>
9698 <div class="table">
9699 <a name="special_function_error_rates_rep.section_lgamma.table_lgamma"></a><p class="title"><b>Table&#160;70.&#160;Error rates for lgamma</b></p>
9700 <div class="table-contents"><table class="table" summary="Error rates for lgamma">
9701 <colgroup>
9702 <col>
9703 <col>
9704 <col>
9705 <col>
9706 <col>
9707 </colgroup>
9708 <thead><tr>
9709 <th>
9710             </th>
9711 <th>
9712               <p>
9713                 GNU C++ version 7.1.0<br> linux<br> double
9714               </p>
9715             </th>
9716 <th>
9717               <p>
9718                 GNU C++ version 7.1.0<br> linux<br> long double
9719               </p>
9720             </th>
9721 <th>
9722               <p>
9723                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
9724               </p>
9725             </th>
9726 <th>
9727               <p>
9728                 Microsoft Visual C++ version 14.1<br> Win32<br> double
9729               </p>
9730             </th>
9731 </tr></thead>
9732 <tbody>
9733 <tr>
9734 <td>
9735               <p>
9736                 factorials
9737               </p>
9738             </td>
9739 <td>
9740               <p>
9741                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9742                 2.1:</em></span> Max = 33.6&#949; (Mean = 2.78&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
9743                 Max = 1.55&#949; (Mean = 0.592&#949;))
9744               </p>
9745             </td>
9746 <td>
9747               <p>
9748                 <span class="blue">Max = 0.991&#949; (Mean = 0.308&#949;)</span><br> <br>
9749                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))<br>
9750                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))
9751               </p>
9752             </td>
9753 <td>
9754               <p>
9755                 <span class="blue">Max = 0.991&#949; (Mean = 0.383&#949;)</span><br> <br>
9756                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.36&#949; (Mean = 0.476&#949;))
9757               </p>
9758             </td>
9759 <td>
9760               <p>
9761                 <span class="blue">Max = 0.914&#949; (Mean = 0.175&#949;)</span><br> <br>
9762                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.958&#949; (Mean = 0.38&#949;))
9763               </p>
9764             </td>
9765 </tr>
9766 <tr>
9767 <td>
9768               <p>
9769                 near 0
9770               </p>
9771             </td>
9772 <td>
9773               <p>
9774                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9775                 2.1:</em></span> Max = 5.21&#949; (Mean = 1.57&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
9776                 Max = 0&#949; (Mean = 0&#949;))
9777               </p>
9778             </td>
9779 <td>
9780               <p>
9781                 <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
9782                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))<br>
9783                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
9784               </p>
9785             </td>
9786 <td>
9787               <p>
9788                 <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
9789                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
9790               </p>
9791             </td>
9792 <td>
9793               <p>
9794                 <span class="blue">Max = 0.964&#949; (Mean = 0.462&#949;)</span><br> <br>
9795                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.962&#949; (Mean = 0.372&#949;))
9796               </p>
9797             </td>
9798 </tr>
9799 <tr>
9800 <td>
9801               <p>
9802                 near 1
9803               </p>
9804             </td>
9805 <td>
9806               <p>
9807                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9808                 2.1:</em></span> Max = 442&#949; (Mean = 88.8&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
9809                 Max = 7.99e+04&#949; (Mean = 1.68e+04&#949;))
9810               </p>
9811             </td>
9812 <td>
9813               <p>
9814                 <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
9815                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))<br>
9816                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))
9817               </p>
9818             </td>
9819 <td>
9820               <p>
9821                 <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
9822                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.71&#949; (Mean = 0.581&#949;))
9823               </p>
9824             </td>
9825 <td>
9826               <p>
9827                 <span class="blue">Max = 0.867&#949; (Mean = 0.468&#949;)</span><br> <br>
9828                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.906&#949; (Mean = 0.565&#949;))
9829               </p>
9830             </td>
9831 </tr>
9832 <tr>
9833 <td>
9834               <p>
9835                 near 2
9836               </p>
9837             </td>
9838 <td>
9839               <p>
9840                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9841                 2.1:</em></span> Max = 1.17e+03&#949; (Mean = 274&#949;))<br> (<span class="emphasis"><em>Rmath
9842                 3.2.3:</em></span> Max = 2.63e+05&#949; (Mean = 5.84e+04&#949;))
9843               </p>
9844             </td>
9845 <td>
9846               <p>
9847                 <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
9848                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))<br>
9849                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))
9850               </p>
9851             </td>
9852 <td>
9853               <p>
9854                 <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
9855                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.598&#949; (Mean = 0.235&#949;))
9856               </p>
9857             </td>
9858 <td>
9859               <p>
9860                 <span class="blue">Max = 0.591&#949; (Mean = 0.159&#949;)</span><br> <br>
9861                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.473&#949;))
9862               </p>
9863             </td>
9864 </tr>
9865 <tr>
9866 <td>
9867               <p>
9868                 near -10
9869               </p>
9870             </td>
9871 <td>
9872               <p>
9873                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9874                 2.1:</em></span> Max = 24.9&#949; (Mean = 4.6&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
9875                 Max = 4.22&#949; (Mean = 1.26&#949;))
9876               </p>
9877             </td>
9878 <td>
9879               <p>
9880                 <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
9881                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.997&#949; (Mean = 0.412&#949;))<br>
9882                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.412&#949;))
9883               </p>
9884             </td>
9885 <td>
9886               <p>
9887                 <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
9888                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.04&#949; (Mean = 1.01&#949;))
9889               </p>
9890             </td>
9891 <td>
9892               <p>
9893                 <span class="blue">Max = 4.22&#949; (Mean = 1.33&#949;)</span><br> <br>
9894                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.444&#949;))
9895               </p>
9896             </td>
9897 </tr>
9898 <tr>
9899 <td>
9900               <p>
9901                 near -55
9902               </p>
9903             </td>
9904 <td>
9905               <p>
9906                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9907                 2.1:</em></span> Max = 7.02&#949; (Mean = 1.47&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
9908                 Max = 250&#949; (Mean = 60.9&#949;))
9909               </p>
9910             </td>
9911 <td>
9912               <p>
9913                 <span class="blue">Max = 0.821&#949; (Mean = 0.513&#949;)</span><br> <br>
9914                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))<br>
9915                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))
9916               </p>
9917             </td>
9918 <td>
9919               <p>
9920                 <span class="blue">Max = 1.59&#949; (Mean = 0.587&#949;)</span><br> <br>
9921                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.821&#949; (Mean = 0.674&#949;))
9922               </p>
9923             </td>
9924 <td>
9925               <p>
9926                 <span class="blue">Max = 0.821&#949; (Mean = 0.419&#949;)</span><br> <br>
9927                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 249&#949; (Mean = 43.1&#949;))
9928               </p>
9929             </td>
9930 </tr>
9931 </tbody>
9932 </table></div>
9933 </div>
9934 <br class="table-break">
9935 </div>
9936 <div class="section">
9937 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
9938 <a name="special_function_error_rates_rep.section_log1p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_log1p" title="log1p">log1p</a>
9939 </h2></div></div></div>
9940 <div class="table">
9941 <a name="special_function_error_rates_rep.section_log1p.table_log1p"></a><p class="title"><b>Table&#160;71.&#160;Error rates for log1p</b></p>
9942 <div class="table-contents"><table class="table" summary="Error rates for log1p">
9943 <colgroup>
9944 <col>
9945 <col>
9946 <col>
9947 <col>
9948 <col>
9949 </colgroup>
9950 <thead><tr>
9951 <th>
9952             </th>
9953 <th>
9954               <p>
9955                 GNU C++ version 7.1.0<br> linux<br> long double
9956               </p>
9957             </th>
9958 <th>
9959               <p>
9960                 GNU C++ version 7.1.0<br> linux<br> double
9961               </p>
9962             </th>
9963 <th>
9964               <p>
9965                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
9966               </p>
9967             </th>
9968 <th>
9969               <p>
9970                 Microsoft Visual C++ version 14.1<br> Win32<br> double
9971               </p>
9972             </th>
9973 </tr></thead>
9974 <tbody><tr>
9975 <td>
9976               <p>
9977                 Random test data
9978               </p>
9979             </td>
9980 <td>
9981               <p>
9982                 <span class="blue">Max = 0.818&#949; (Mean = 0.227&#949;)</span><br> <br>
9983                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))<br>
9984                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))
9985               </p>
9986             </td>
9987 <td>
9988               <p>
9989                 <span class="blue">Max = 0.846&#949; (Mean = 0.153&#949;)</span><br> <br>
9990                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846&#949; (Mean = 0.153&#949;))
9991               </p>
9992             </td>
9993 <td>
9994               <p>
9995                 <span class="blue">Max = 2.3&#949; (Mean = 0.66&#949;)</span><br> <br>
9996                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.249&#949;))
9997               </p>
9998             </td>
9999 <td>
10000               <p>
10001                 <span class="blue">Max = 0.509&#949; (Mean = 0.057&#949;)</span><br> <br>
10002                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.509&#949; (Mean = 0.057&#949;))
10003               </p>
10004             </td>
10005 </tr></tbody>
10006 </table></div>
10007 </div>
10008 <br class="table-break">
10009 </div>
10010 <div class="section">
10011 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
10012 <a name="special_function_error_rates_rep.section_non_central_beta_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF" title="non central beta CDF">non
10013     central beta CDF</a>
10014 </h2></div></div></div>
10015 <div class="table">
10016 <a name="special_function_error_rates_rep.section_non_central_beta_CDF.table_non_central_beta_CDF"></a><p class="title"><b>Table&#160;72.&#160;Error rates for non central beta CDF</b></p>
10017 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
10018 <colgroup>
10019 <col>
10020 <col>
10021 <col>
10022 <col>
10023 <col>
10024 </colgroup>
10025 <thead><tr>
10026 <th>
10027             </th>
10028 <th>
10029               <p>
10030                 GNU C++ version 7.1.0<br> linux<br> double
10031               </p>
10032             </th>
10033 <th>
10034               <p>
10035                 GNU C++ version 7.1.0<br> linux<br> long double
10036               </p>
10037             </th>
10038 <th>
10039               <p>
10040                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
10041               </p>
10042             </th>
10043 <th>
10044               <p>
10045                 Microsoft Visual C++ version 14.1<br> Win32<br> double
10046               </p>
10047             </th>
10048 </tr></thead>
10049 <tbody>
10050 <tr>
10051 <td>
10052               <p>
10053                 Non Central Beta, medium parameters
10054               </p>
10055             </td>
10056 <td>
10057               <p>
10058                 <span class="blue">Max = 0.998&#949; (Mean = 0.0649&#949;)</span><br> <br>
10059                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26&#949; (Mean
10060                 = 3.5e+24&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
10061                 other failures.</a>)</span>
10062               </p>
10063             </td>
10064 <td>
10065               <p>
10066                 <span class="blue">Max = 824&#949; (Mean = 27.4&#949;)</span>
10067               </p>
10068             </td>
10069 <td>
10070               <p>
10071                 <span class="blue">Max = 832&#949; (Mean = 38.1&#949;)</span>
10072               </p>
10073             </td>
10074 <td>
10075               <p>
10076                 <span class="blue">Max = 242&#949; (Mean = 31&#949;)</span>
10077               </p>
10078             </td>
10079 </tr>
10080 <tr>
10081 <td>
10082               <p>
10083                 Non Central Beta, large parameters
10084               </p>
10085             </td>
10086 <td>
10087               <p>
10088                 <span class="blue">Max = 1.18&#949; (Mean = 0.175&#949;)</span><br> <br>
10089                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36&#949; (Mean
10090                 = 1.19e+35&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
10091                 other failures.</a>)</span>
10092               </p>
10093             </td>
10094 <td>
10095               <p>
10096                 <span class="blue">Max = 2.5e+04&#949; (Mean = 3.78e+03&#949;)</span>
10097               </p>
10098             </td>
10099 <td>
10100               <p>
10101                 <span class="blue">Max = 2.57e+04&#949; (Mean = 4.45e+03&#949;)</span>
10102               </p>
10103             </td>
10104 <td>
10105               <p>
10106                 <span class="blue">Max = 3.66e+03&#949; (Mean = 500&#949;)</span>
10107               </p>
10108             </td>
10109 </tr>
10110 </tbody>
10111 </table></div>
10112 </div>
10113 <br class="table-break">
10114 </div>
10115 <div class="section">
10116 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
10117 <a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement" title="non central beta CDF complement">non
10118     central beta CDF complement</a>
10119 </h2></div></div></div>
10120 <div class="table">
10121 <a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table&#160;73.&#160;Error rates for non central beta CDF complement</b></p>
10122 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
10123 <colgroup>
10124 <col>
10125 <col>
10126 <col>
10127 <col>
10128 <col>
10129 </colgroup>
10130 <thead><tr>
10131 <th>
10132             </th>
10133 <th>
10134               <p>
10135                 GNU C++ version 7.1.0<br> linux<br> double
10136               </p>
10137             </th>
10138 <th>
10139               <p>
10140                 GNU C++ version 7.1.0<br> linux<br> long double
10141               </p>
10142             </th>
10143 <th>
10144               <p>
10145                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
10146               </p>
10147             </th>
10148 <th>
10149               <p>
10150                 Microsoft Visual C++ version 14.1<br> Win32<br> double
10151               </p>
10152             </th>
10153 </tr></thead>
10154 <tbody>
10155 <tr>
10156 <td>
10157               <p>
10158                 Non Central Beta, medium parameters
10159               </p>
10160             </td>
10161 <td>
10162               <p>
10163                 <span class="blue">Max = 0.998&#949; (Mean = 0.0936&#949;)</span><br> <br>
10164                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97&#949; (Mean
10165                 = 1.37e+96&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
10166                 other failures.</a>)</span>
10167               </p>
10168             </td>
10169 <td>
10170               <p>
10171                 <span class="blue">Max = 396&#949; (Mean = 50.7&#949;)</span>
10172               </p>
10173             </td>
10174 <td>
10175               <p>
10176                 <span class="blue">Max = 554&#949; (Mean = 57.2&#949;)</span>
10177               </p>
10178             </td>
10179 <td>
10180               <p>
10181                 <span class="blue">Max = 624&#949; (Mean = 62.7&#949;)</span>
10182               </p>
10183             </td>
10184 </tr>
10185 <tr>
10186 <td>
10187               <p>
10188                 Non Central Beta, large parameters
10189               </p>
10190             </td>
10191 <td>
10192               <p>
10193                 <span class="blue">Max = 0.986&#949; (Mean = 0.188&#949;)</span><br> <br>
10194                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
10195                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
10196                 other failures.</a>)</span>
10197               </p>
10198             </td>
10199 <td>
10200               <p>
10201                 <span class="blue">Max = 6.83e+03&#949; (Mean = 993&#949;)</span>
10202               </p>
10203             </td>
10204 <td>
10205               <p>
10206                 <span class="blue">Max = 3.56e+03&#949; (Mean = 707&#949;)</span>
10207               </p>
10208             </td>
10209 <td>
10210               <p>
10211                 <span class="blue">Max = 1.25e+04&#949; (Mean = 1.49e+03&#949;)</span>
10212               </p>
10213             </td>
10214 </tr>
10215 </tbody>
10216 </table></div>
10217 </div>
10218 <br class="table-break">
10219 </div>
10220 <div class="section">
10221 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
10222 <a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF" title="non central chi squared CDF">non
10223     central chi squared CDF</a>
10224 </h2></div></div></div>
10225 <div class="table">
10226 <a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table&#160;74.&#160;Error rates for non central chi squared CDF</b></p>
10227 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
10228 <colgroup>
10229 <col>
10230 <col>
10231 <col>
10232 <col>
10233 <col>
10234 </colgroup>
10235 <thead><tr>
10236 <th>
10237             </th>
10238 <th>
10239               <p>
10240                 GNU C++ version 7.1.0<br> linux<br> double
10241               </p>
10242             </th>
10243 <th>
10244               <p>
10245                 GNU C++ version 7.1.0<br> linux<br> long double
10246               </p>
10247             </th>
10248 <th>
10249               <p>
10250                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
10251               </p>
10252             </th>
10253 <th>
10254               <p>
10255                 Microsoft Visual C++ version 14.1<br> Win32<br> double
10256               </p>
10257             </th>
10258 </tr></thead>
10259 <tbody>
10260 <tr>
10261 <td>
10262               <p>
10263                 Non Central Chi Squared, medium parameters
10264               </p>
10265             </td>
10266 <td>
10267               <p>
10268                 <span class="blue">Max = 0.99&#949; (Mean = 0.0544&#949;)</span><br> <br>
10269                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727&#949; (Mean = 121&#949;))
10270               </p>
10271             </td>
10272 <td>
10273               <p>
10274                 <span class="blue">Max = 46.5&#949; (Mean = 10.3&#949;)</span>
10275               </p>
10276             </td>
10277 <td>
10278               <p>
10279                 <span class="blue">Max = 115&#949; (Mean = 13.9&#949;)</span>
10280               </p>
10281             </td>
10282 <td>
10283               <p>
10284                 <span class="blue">Max = 48.9&#949; (Mean = 10&#949;)</span>
10285               </p>
10286             </td>
10287 </tr>
10288 <tr>
10289 <td>
10290               <p>
10291                 Non Central Chi Squared, large parameters
10292               </p>
10293             </td>
10294 <td>
10295               <p>
10296                 <span class="blue">Max = 1.07&#949; (Mean = 0.102&#949;)</span><br> <br>
10297                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08&#949; (Mean
10298                 = 2.23e+07&#949;))</span>
10299               </p>
10300             </td>
10301 <td>
10302               <p>
10303                 <span class="blue">Max = 3.07e+03&#949; (Mean = 336&#949;)</span>
10304               </p>
10305             </td>
10306 <td>
10307               <p>
10308                 <span class="blue">Max = 6.17e+03&#949; (Mean = 677&#949;)</span>
10309               </p>
10310             </td>
10311 <td>
10312               <p>
10313                 <span class="blue">Max = 9.79e+03&#949; (Mean = 723&#949;)</span>
10314               </p>
10315             </td>
10316 </tr>
10317 </tbody>
10318 </table></div>
10319 </div>
10320 <br class="table-break">
10321 </div>
10322 <div class="section">
10323 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
10324 <a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement" title="non central chi squared CDF complement">non
10325     central chi squared CDF complement</a>
10326 </h2></div></div></div>
10327 <div class="table">
10328 <a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table&#160;75.&#160;Error rates for non central chi squared CDF complement</b></p>
10329 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
10330 <colgroup>
10331 <col>
10332 <col>
10333 <col>
10334 <col>
10335 <col>
10336 </colgroup>
10337 <thead><tr>
10338 <th>
10339             </th>
10340 <th>
10341               <p>
10342                 GNU C++ version 7.1.0<br> linux<br> double
10343               </p>
10344             </th>
10345 <th>
10346               <p>
10347                 GNU C++ version 7.1.0<br> linux<br> long double
10348               </p>
10349             </th>
10350 <th>
10351               <p>
10352                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
10353               </p>
10354             </th>
10355 <th>
10356               <p>
10357                 Microsoft Visual C++ version 14.1<br> Win32<br> double
10358               </p>
10359             </th>
10360 </tr></thead>
10361 <tbody>
10362 <tr>
10363 <td>
10364               <p>
10365                 Non Central Chi Squared, medium parameters
10366               </p>
10367             </td>
10368 <td>
10369               <p>
10370                 <span class="blue">Max = 0.96&#949; (Mean = 0.0635&#949;)</span><br> <br>
10371                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
10372                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And
10373                 other failures.</a>)</span>
10374               </p>
10375             </td>
10376 <td>
10377               <p>
10378                 <span class="blue">Max = 107&#949; (Mean = 17.2&#949;)</span>
10379               </p>
10380             </td>
10381 <td>
10382               <p>
10383                 <span class="blue">Max = 171&#949; (Mean = 22.8&#949;)</span>
10384               </p>
10385             </td>
10386 <td>
10387               <p>
10388                 <span class="blue">Max = 98.6&#949; (Mean = 15.8&#949;)</span>
10389               </p>
10390             </td>
10391 </tr>
10392 <tr>
10393 <td>
10394               <p>
10395                 Non Central Chi Squared, large parameters
10396               </p>
10397             </td>
10398 <td>
10399               <p>
10400                 <span class="blue">Max = 2.11&#949; (Mean = 0.278&#949;)</span><br> <br>
10401                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
10402                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And
10403                 other failures.</a>)</span>
10404               </p>
10405             </td>
10406 <td>
10407               <p>
10408                 <span class="blue">Max = 5.02e+03&#949; (Mean = 630&#949;)</span>
10409               </p>
10410             </td>
10411 <td>
10412               <p>
10413                 <span class="blue">Max = 5.1e+03&#949; (Mean = 577&#949;)</span>
10414               </p>
10415             </td>
10416 <td>
10417               <p>
10418                 <span class="blue">Max = 5.43e+03&#949; (Mean = 705&#949;)</span>
10419               </p>
10420             </td>
10421 </tr>
10422 </tbody>
10423 </table></div>
10424 </div>
10425 <br class="table-break">
10426 </div>
10427 <div class="section">
10428 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
10429 <a name="special_function_error_rates_rep.section_non_central_t_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF" title="non central t CDF">non
10430     central t CDF</a>
10431 </h2></div></div></div>
10432 <div class="table">
10433 <a name="special_function_error_rates_rep.section_non_central_t_CDF.table_non_central_t_CDF"></a><p class="title"><b>Table&#160;76.&#160;Error rates for non central t CDF</b></p>
10434 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
10435 <colgroup>
10436 <col>
10437 <col>
10438 <col>
10439 <col>
10440 <col>
10441 </colgroup>
10442 <thead><tr>
10443 <th>
10444             </th>
10445 <th>
10446               <p>
10447                 GNU C++ version 7.1.0<br> linux<br> double
10448               </p>
10449             </th>
10450 <th>
10451               <p>
10452                 GNU C++ version 7.1.0<br> linux<br> long double
10453               </p>
10454             </th>
10455 <th>
10456               <p>
10457                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
10458               </p>
10459             </th>
10460 <th>
10461               <p>
10462                 Microsoft Visual C++ version 14.1<br> Win32<br> double
10463               </p>
10464             </th>
10465 </tr></thead>
10466 <tbody>
10467 <tr>
10468 <td>
10469               <p>
10470                 Non Central T
10471               </p>
10472             </td>
10473 <td>
10474               <p>
10475                 <span class="blue">Max = 0.796&#949; (Mean = 0.0691&#949;)</span><br> <br>
10476                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15&#949; (Mean
10477                 = 8.49e+14&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And
10478                 other failures.</a>)</span>
10479               </p>
10480             </td>
10481 <td>
10482               <p>
10483                 <span class="blue">Max = 139&#949; (Mean = 31&#949;)</span>
10484               </p>
10485             </td>
10486 <td>
10487               <p>
10488                 <span class="blue">Max = 145&#949; (Mean = 30.9&#949;)</span>
10489               </p>
10490             </td>
10491 <td>
10492               <p>
10493                 <span class="blue">Max = 135&#949; (Mean = 32.1&#949;)</span>
10494               </p>
10495             </td>
10496 </tr>
10497 <tr>
10498 <td>
10499               <p>
10500                 Non Central T (small non-centrality)
10501               </p>
10502             </td>
10503 <td>
10504               <p>
10505                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
10506                 3.2.3:</em></span> Max = 2.09e+03&#949; (Mean = 244&#949;))
10507               </p>
10508             </td>
10509 <td>
10510               <p>
10511                 <span class="blue">Max = 3.86&#949; (Mean = 1.4&#949;)</span>
10512               </p>
10513             </td>
10514 <td>
10515               <p>
10516                 <span class="blue">Max = 9.15&#949; (Mean = 2.13&#949;)</span>
10517               </p>
10518             </td>
10519 <td>
10520               <p>
10521                 <span class="blue">Max = 6.17&#949; (Mean = 1.45&#949;)</span>
10522               </p>
10523             </td>
10524 </tr>
10525 <tr>
10526 <td>
10527               <p>
10528                 Non Central T (large parameters)
10529               </p>
10530             </td>
10531 <td>
10532               <p>
10533                 <span class="blue">Max = 257&#949; (Mean = 72.1&#949;)</span><br> <br>
10534                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46&#949; (Mean = 0.657&#949;))
10535               </p>
10536             </td>
10537 <td>
10538               <p>
10539                 <span class="blue">Max = 5.26e+05&#949; (Mean = 1.48e+05&#949;)</span>
10540               </p>
10541             </td>
10542 <td>
10543               <p>
10544                 <span class="blue">Max = 5.24e+05&#949; (Mean = 1.47e+05&#949;)</span>
10545               </p>
10546             </td>
10547 <td>
10548               <p>
10549                 <span class="blue">Max = 286&#949; (Mean = 62.8&#949;)</span>
10550               </p>
10551             </td>
10552 </tr>
10553 </tbody>
10554 </table></div>
10555 </div>
10556 <br class="table-break">
10557 </div>
10558 <div class="section">
10559 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
10560 <a name="special_function_error_rates_rep.section_non_central_t_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement" title="non central t CDF complement">non
10561     central t CDF complement</a>
10562 </h2></div></div></div>
10563 <div class="table">
10564 <a name="special_function_error_rates_rep.section_non_central_t_CDF_complement.table_non_central_t_CDF_complement"></a><p class="title"><b>Table&#160;77.&#160;Error rates for non central t CDF complement</b></p>
10565 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
10566 <colgroup>
10567 <col>
10568 <col>
10569 <col>
10570 <col>
10571 <col>
10572 </colgroup>
10573 <thead><tr>
10574 <th>
10575             </th>
10576 <th>
10577               <p>
10578                 GNU C++ version 7.1.0<br> linux<br> double
10579               </p>
10580             </th>
10581 <th>
10582               <p>
10583                 GNU C++ version 7.1.0<br> linux<br> long double
10584               </p>
10585             </th>
10586 <th>
10587               <p>
10588                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
10589               </p>
10590             </th>
10591 <th>
10592               <p>
10593                 Microsoft Visual C++ version 14.1<br> Win32<br> double
10594               </p>
10595             </th>
10596 </tr></thead>
10597 <tbody>
10598 <tr>
10599 <td>
10600               <p>
10601                 Non Central T
10602               </p>
10603             </td>
10604 <td>
10605               <p>
10606                 <span class="blue">Max = 0.707&#949; (Mean = 0.0497&#949;)</span><br> <br>
10607                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15&#949; (Mean
10608                 = 6.72e+14&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And
10609                 other failures.</a>)</span>
10610               </p>
10611             </td>
10612 <td>
10613               <p>
10614                 <span class="blue">Max = 201&#949; (Mean = 31.7&#949;)</span>
10615               </p>
10616             </td>
10617 <td>
10618               <p>
10619                 <span class="blue">Max = 340&#949; (Mean = 43.2&#949;)</span>
10620               </p>
10621             </td>
10622 <td>
10623               <p>
10624                 <span class="blue">Max = 154&#949; (Mean = 32.1&#949;)</span>
10625               </p>
10626             </td>
10627 </tr>
10628 <tr>
10629 <td>
10630               <p>
10631                 Non Central T (small non-centrality)
10632               </p>
10633             </td>
10634 <td>
10635               <p>
10636                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
10637                 3.2.3:</em></span> Max = 1.87e+03&#949; (Mean = 263&#949;))
10638               </p>
10639             </td>
10640 <td>
10641               <p>
10642                 <span class="blue">Max = 10.5&#949; (Mean = 2.13&#949;)</span>
10643               </p>
10644             </td>
10645 <td>
10646               <p>
10647                 <span class="blue">Max = 10.5&#949; (Mean = 2.39&#949;)</span>
10648               </p>
10649             </td>
10650 <td>
10651               <p>
10652                 <span class="blue">Max = 4.6&#949; (Mean = 1.63&#949;)</span>
10653               </p>
10654             </td>
10655 </tr>
10656 <tr>
10657 <td>
10658               <p>
10659                 Non Central T (large parameters)
10660               </p>
10661             </td>
10662 <td>
10663               <p>
10664                 <span class="blue">Max = 478&#949; (Mean = 96.3&#949;)</span><br> <br>
10665                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24&#949; (Mean = 0.945&#949;))
10666               </p>
10667             </td>
10668 <td>
10669               <p>
10670                 <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
10671               </p>
10672             </td>
10673 <td>
10674               <p>
10675                 <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
10676               </p>
10677             </td>
10678 <td>
10679               <p>
10680                 <span class="blue">Max = 227&#949; (Mean = 50.4&#949;)</span>
10681               </p>
10682             </td>
10683 </tr>
10684 </tbody>
10685 </table></div>
10686 </div>
10687 <br class="table-break">
10688 </div>
10689 <div class="section">
10690 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
10691 <a name="special_function_error_rates_rep.section_owens_t"></a><a class="link" href="index.html#special_function_error_rates_rep.section_owens_t" title="owens_t">owens_t</a>
10692 </h2></div></div></div>
10693 <div class="table">
10694 <a name="special_function_error_rates_rep.section_owens_t.table_owens_t"></a><p class="title"><b>Table&#160;78.&#160;Error rates for owens_t</b></p>
10695 <div class="table-contents"><table class="table" summary="Error rates for owens_t">
10696 <colgroup>
10697 <col>
10698 <col>
10699 <col>
10700 <col>
10701 <col>
10702 </colgroup>
10703 <thead><tr>
10704 <th>
10705             </th>
10706 <th>
10707               <p>
10708                 GNU C++ version 7.1.0<br> linux<br> double
10709               </p>
10710             </th>
10711 <th>
10712               <p>
10713                 GNU C++ version 7.1.0<br> linux<br> long double
10714               </p>
10715             </th>
10716 <th>
10717               <p>
10718                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
10719               </p>
10720             </th>
10721 <th>
10722               <p>
10723                 Microsoft Visual C++ version 14.1<br> Win32<br> double
10724               </p>
10725             </th>
10726 </tr></thead>
10727 <tbody>
10728 <tr>
10729 <td>
10730               <p>
10731                 Owens T (medium small values)
10732               </p>
10733             </td>
10734 <td>
10735               <p>
10736                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10737               </p>
10738             </td>
10739 <td>
10740               <p>
10741                 <span class="blue">Max = 3.34&#949; (Mean = 0.944&#949;)</span>
10742               </p>
10743             </td>
10744 <td>
10745               <p>
10746                 <span class="blue">Max = 3.34&#949; (Mean = 0.911&#949;)</span>
10747               </p>
10748             </td>
10749 <td>
10750               <p>
10751                 <span class="blue">Max = 4.37&#949; (Mean = 0.98&#949;)</span>
10752               </p>
10753             </td>
10754 </tr>
10755 <tr>
10756 <td>
10757               <p>
10758                 Owens T (large and diverse values)
10759               </p>
10760             </td>
10761 <td>
10762               <p>
10763                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10764               </p>
10765             </td>
10766 <td>
10767               <p>
10768                 <span class="blue">Max = 49&#949; (Mean = 2.16&#949;)</span>
10769               </p>
10770             </td>
10771 <td>
10772               <p>
10773                 <span class="blue">Max = 24.5&#949; (Mean = 1.39&#949;)</span>
10774               </p>
10775             </td>
10776 <td>
10777               <p>
10778                 <span class="blue">Max = 3.78&#949; (Mean = 0.621&#949;)</span>
10779               </p>
10780             </td>
10781 </tr>
10782 </tbody>
10783 </table></div>
10784 </div>
10785 <br class="table-break">
10786 </div>
10787 <div class="section">
10788 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
10789 <a name="special_function_error_rates_rep.section_polygamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_polygamma" title="polygamma">polygamma</a>
10790 </h2></div></div></div>
10791 <div class="table">
10792 <a name="special_function_error_rates_rep.section_polygamma.table_polygamma"></a><p class="title"><b>Table&#160;79.&#160;Error rates for polygamma</b></p>
10793 <div class="table-contents"><table class="table" summary="Error rates for polygamma">
10794 <colgroup>
10795 <col>
10796 <col>
10797 <col>
10798 <col>
10799 <col>
10800 </colgroup>
10801 <thead><tr>
10802 <th>
10803             </th>
10804 <th>
10805               <p>
10806                 GNU C++ version 7.1.0<br> linux<br> double
10807               </p>
10808             </th>
10809 <th>
10810               <p>
10811                 GNU C++ version 7.1.0<br> linux<br> long double
10812               </p>
10813             </th>
10814 <th>
10815               <p>
10816                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
10817               </p>
10818             </th>
10819 <th>
10820               <p>
10821                 Microsoft Visual C++ version 14.1<br> Win32<br> double
10822               </p>
10823             </th>
10824 </tr></thead>
10825 <tbody>
10826 <tr>
10827 <td>
10828               <p>
10829                 Mathematica Data
10830               </p>
10831             </td>
10832 <td>
10833               <p>
10834                 <span class="blue">Max = 0.824&#949; (Mean = 0.0574&#949;)</span><br> <br>
10835                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9&#949; (Mean = 12.8&#949;))<br> (<span class="emphasis"><em>Rmath
10836                 3.2.3:</em></span> Max = 108&#949; (Mean = 15.2&#949;))
10837               </p>
10838             </td>
10839 <td>
10840               <p>
10841                 <span class="blue">Max = 7.38&#949; (Mean = 1.84&#949;)</span>
10842               </p>
10843             </td>
10844 <td>
10845               <p>
10846                 <span class="blue">Max = 34.3&#949; (Mean = 7.65&#949;)</span>
10847               </p>
10848             </td>
10849 <td>
10850               <p>
10851                 <span class="blue">Max = 9.32&#949; (Mean = 1.95&#949;)</span>
10852               </p>
10853             </td>
10854 </tr>
10855 <tr>
10856 <td>
10857               <p>
10858                 Mathematica Data - large arguments
10859               </p>
10860             </td>
10861 <td>
10862               <p>
10863                 <span class="blue">Max = 0.998&#949; (Mean = 0.0592&#949;)</span><br> <br>
10864                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244&#949; (Mean = 32.8&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And
10865                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10866                 <span class="red">Max = 1.71e+56&#949; (Mean = 1.01e+55&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And
10867                 other failures.</a>)</span>
10868               </p>
10869             </td>
10870 <td>
10871               <p>
10872                 <span class="blue">Max = 2.23&#949; (Mean = 0.323&#949;)</span>
10873               </p>
10874             </td>
10875 <td>
10876               <p>
10877                 <span class="blue">Max = 11.1&#949; (Mean = 0.848&#949;)</span>
10878               </p>
10879             </td>
10880 <td>
10881               <p>
10882                 <span class="blue">Max = 150&#949; (Mean = 13.9&#949;)</span>
10883               </p>
10884             </td>
10885 </tr>
10886 <tr>
10887 <td>
10888               <p>
10889                 Mathematica Data - negative arguments
10890               </p>
10891             </td>
10892 <td>
10893               <p>
10894                 <span class="blue">Max = 0.516&#949; (Mean = 0.022&#949;)</span><br> <br>
10895                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6&#949; (Mean = 3.04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And
10896                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10897                 Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And
10898                 other failures.</a>)
10899               </p>
10900             </td>
10901 <td>
10902               <p>
10903                 <span class="blue">Max = 269&#949; (Mean = 87.7&#949;)</span>
10904               </p>
10905             </td>
10906 <td>
10907               <p>
10908                 <span class="blue">Max = 269&#949; (Mean = 88.4&#949;)</span>
10909               </p>
10910             </td>
10911 <td>
10912               <p>
10913                 <span class="blue">Max = 497&#949; (Mean = 129&#949;)</span>
10914               </p>
10915             </td>
10916 </tr>
10917 <tr>
10918 <td>
10919               <p>
10920                 Mathematica Data - large negative arguments
10921               </p>
10922             </td>
10923 <td>
10924               <p>
10925                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
10926                 2.1:</em></span> Max = 1.79&#949; (Mean = 0.197&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And
10927                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10928                 Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And
10929                 other failures.</a>)
10930               </p>
10931             </td>
10932 <td>
10933               <p>
10934                 <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
10935               </p>
10936             </td>
10937 <td>
10938               <p>
10939                 <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
10940               </p>
10941             </td>
10942 <td>
10943               <p>
10944                 <span class="blue">Max = 162&#949; (Mean = 101&#949;)</span>
10945               </p>
10946             </td>
10947 </tr>
10948 <tr>
10949 <td>
10950               <p>
10951                 Mathematica Data - small arguments
10952               </p>
10953             </td>
10954 <td>
10955               <p>
10956                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
10957                 2.1:</em></span> Max = 15.2&#949; (Mean = 5.03&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10958                 Max = 106&#949; (Mean = 20&#949;))
10959               </p>
10960             </td>
10961 <td>
10962               <p>
10963                 <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
10964               </p>
10965             </td>
10966 <td>
10967               <p>
10968                 <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
10969               </p>
10970             </td>
10971 <td>
10972               <p>
10973                 <span class="blue">Max = 3&#949; (Mean = 0.496&#949;)</span>
10974               </p>
10975             </td>
10976 </tr>
10977 <tr>
10978 <td>
10979               <p>
10980                 Mathematica Data - Large orders and other bug cases
10981               </p>
10982             </td>
10983 <td>
10984               <p>
10985                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
10986                 2.1:</em></span> Max = 151&#949; (Mean = 39.3&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And
10987                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
10988                 <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And
10989                 other failures.</a>)</span>
10990               </p>
10991             </td>
10992 <td>
10993               <p>
10994                 <span class="blue">Max = 54.5&#949; (Mean = 13.3&#949;)</span>
10995               </p>
10996             </td>
10997 <td>
10998               <p>
10999                 <span class="blue">Max = 145&#949; (Mean = 55.9&#949;)</span>
11000               </p>
11001             </td>
11002 <td>
11003               <p>
11004                 <span class="blue">Max = 200&#949; (Mean = 57.2&#949;)</span>
11005               </p>
11006             </td>
11007 </tr>
11008 </tbody>
11009 </table></div>
11010 </div>
11011 <br class="table-break">
11012 </div>
11013 <div class="section">
11014 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11015 <a name="special_function_error_rates_rep.section_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_powm1" title="powm1">powm1</a>
11016 </h2></div></div></div>
11017 <div class="table">
11018 <a name="special_function_error_rates_rep.section_powm1.table_powm1"></a><p class="title"><b>Table&#160;80.&#160;Error rates for powm1</b></p>
11019 <div class="table-contents"><table class="table" summary="Error rates for powm1">
11020 <colgroup>
11021 <col>
11022 <col>
11023 <col>
11024 <col>
11025 <col>
11026 </colgroup>
11027 <thead><tr>
11028 <th>
11029             </th>
11030 <th>
11031               <p>
11032                 GNU C++ version 7.1.0<br> linux<br> double
11033               </p>
11034             </th>
11035 <th>
11036               <p>
11037                 GNU C++ version 7.1.0<br> linux<br> long double
11038               </p>
11039             </th>
11040 <th>
11041               <p>
11042                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11043               </p>
11044             </th>
11045 <th>
11046               <p>
11047                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11048               </p>
11049             </th>
11050 </tr></thead>
11051 <tbody><tr>
11052 <td>
11053               <p>
11054                 powm1
11055               </p>
11056             </td>
11057 <td>
11058               <p>
11059                 <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
11060               </p>
11061             </td>
11062 <td>
11063               <p>
11064                 <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span>
11065               </p>
11066             </td>
11067 <td>
11068               <p>
11069                 <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span>
11070               </p>
11071             </td>
11072 <td>
11073               <p>
11074                 <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
11075               </p>
11076             </td>
11077 </tr></tbody>
11078 </table></div>
11079 </div>
11080 <br class="table-break">
11081 </div>
11082 <div class="section">
11083 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11084 <a name="special_function_error_rates_rep.section_sin_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sin_pi" title="sin_pi">sin_pi</a>
11085 </h2></div></div></div>
11086 <div class="table">
11087 <a name="special_function_error_rates_rep.section_sin_pi.table_sin_pi"></a><p class="title"><b>Table&#160;81.&#160;Error rates for sin_pi</b></p>
11088 <div class="table-contents"><table class="table" summary="Error rates for sin_pi">
11089 <colgroup>
11090 <col>
11091 <col>
11092 <col>
11093 <col>
11094 <col>
11095 </colgroup>
11096 <thead><tr>
11097 <th>
11098             </th>
11099 <th>
11100               <p>
11101                 GNU C++ version 7.1.0<br> linux<br> double
11102               </p>
11103             </th>
11104 <th>
11105               <p>
11106                 GNU C++ version 7.1.0<br> linux<br> long double
11107               </p>
11108             </th>
11109 <th>
11110               <p>
11111                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11112               </p>
11113             </th>
11114 <th>
11115               <p>
11116                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11117               </p>
11118             </th>
11119 </tr></thead>
11120 <tbody>
11121 <tr>
11122 <td>
11123               <p>
11124                 sin_pi and cos_pi
11125               </p>
11126             </td>
11127 <td>
11128               <p>
11129                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11130               </p>
11131             </td>
11132 <td>
11133               <p>
11134                 <span class="blue">Max = 0.996&#949; (Mean = 0.335&#949;)</span>
11135               </p>
11136             </td>
11137 <td>
11138               <p>
11139                 <span class="blue">Max = 0.996&#949; (Mean = 0.336&#949;)</span>
11140               </p>
11141             </td>
11142 <td>
11143               <p>
11144                 <span class="blue">Max = 0.99&#949; (Mean = 0.328&#949;)</span>
11145               </p>
11146             </td>
11147 </tr>
11148 <tr>
11149 <td>
11150               <p>
11151                 sin_pi and cos_pi near integers and half integers
11152               </p>
11153             </td>
11154 <td>
11155               <p>
11156                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11157               </p>
11158             </td>
11159 <td>
11160               <p>
11161                 <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
11162               </p>
11163             </td>
11164 <td>
11165               <p>
11166                 <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
11167               </p>
11168             </td>
11169 <td>
11170               <p>
11171                 <span class="blue">Max = 0.996&#949; (Mean = 0.343&#949;)</span>
11172               </p>
11173             </td>
11174 </tr>
11175 </tbody>
11176 </table></div>
11177 </div>
11178 <br class="table-break">
11179 </div>
11180 <div class="section">
11181 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11182 <a name="special_function_error_rates_rep.section_sph_bessel"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel" title="sph_bessel">sph_bessel</a>
11183 </h2></div></div></div>
11184 <div class="table">
11185 <a name="special_function_error_rates_rep.section_sph_bessel.table_sph_bessel"></a><p class="title"><b>Table&#160;82.&#160;Error rates for sph_bessel</b></p>
11186 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
11187 <colgroup>
11188 <col>
11189 <col>
11190 <col>
11191 <col>
11192 <col>
11193 </colgroup>
11194 <thead><tr>
11195 <th>
11196             </th>
11197 <th>
11198               <p>
11199                 GNU C++ version 7.1.0<br> linux<br> long double
11200               </p>
11201             </th>
11202 <th>
11203               <p>
11204                 GNU C++ version 7.1.0<br> linux<br> double
11205               </p>
11206             </th>
11207 <th>
11208               <p>
11209                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11210               </p>
11211             </th>
11212 <th>
11213               <p>
11214                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11215               </p>
11216             </th>
11217 </tr></thead>
11218 <tbody><tr>
11219 <td>
11220               <p>
11221                 Bessel j: Random Data
11222               </p>
11223             </td>
11224 <td>
11225               <p>
11226                 <span class="blue">Max = 243&#949; (Mean = 13.3&#949;)</span><br> <br>
11227                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.91e+06&#949; (Mean = 1.09e+05&#949;))
11228               </p>
11229             </td>
11230 <td>
11231               <p>
11232                 <span class="blue">Max = 0.978&#949; (Mean = 0.0445&#949;)</span><br> <br>
11233                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03&#949; (Mean = 107&#949;))
11234               </p>
11235             </td>
11236 <td>
11237               <p>
11238                 <span class="blue">Max = 243&#949; (Mean = 33.7&#949;)</span>
11239               </p>
11240             </td>
11241 <td>
11242               <p>
11243                 <span class="blue">Max = 245&#949; (Mean = 16.3&#949;)</span>
11244               </p>
11245             </td>
11246 </tr></tbody>
11247 </table></div>
11248 </div>
11249 <br class="table-break">
11250 </div>
11251 <div class="section">
11252 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11253 <a name="special_function_error_rates_rep.section_sph_bessel_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel_prime" title="sph_bessel_prime">sph_bessel_prime</a>
11254 </h2></div></div></div>
11255 <div class="table">
11256 <a name="special_function_error_rates_rep.section_sph_bessel_prime.table_sph_bessel_prime"></a><p class="title"><b>Table&#160;83.&#160;Error rates for sph_bessel_prime</b></p>
11257 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
11258 <colgroup>
11259 <col>
11260 <col>
11261 <col>
11262 <col>
11263 <col>
11264 </colgroup>
11265 <thead><tr>
11266 <th>
11267             </th>
11268 <th>
11269               <p>
11270                 GNU C++ version 7.1.0<br> linux<br> double
11271               </p>
11272             </th>
11273 <th>
11274               <p>
11275                 GNU C++ version 7.1.0<br> linux<br> long double
11276               </p>
11277             </th>
11278 <th>
11279               <p>
11280                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11281               </p>
11282             </th>
11283 <th>
11284               <p>
11285                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11286               </p>
11287             </th>
11288 </tr></thead>
11289 <tbody><tr>
11290 <td>
11291               <p>
11292                 Bessel j': Random Data
11293               </p>
11294             </td>
11295 <td>
11296               <p>
11297                 <span class="blue">Max = 0.753&#949; (Mean = 0.0343&#949;)</span>
11298               </p>
11299             </td>
11300 <td>
11301               <p>
11302                 <span class="blue">Max = 167&#949; (Mean = 12&#949;)</span>
11303               </p>
11304             </td>
11305 <td>
11306               <p>
11307                 <span class="blue">Max = 167&#949; (Mean = 33.2&#949;)</span>
11308               </p>
11309             </td>
11310 <td>
11311               <p>
11312                 <span class="blue">Max = 307&#949; (Mean = 25.2&#949;)</span>
11313               </p>
11314             </td>
11315 </tr></tbody>
11316 </table></div>
11317 </div>
11318 <br class="table-break">
11319 </div>
11320 <div class="section">
11321 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11322 <a name="special_function_error_rates_rep.section_sph_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann" title="sph_neumann">sph_neumann</a>
11323 </h2></div></div></div>
11324 <div class="table">
11325 <a name="special_function_error_rates_rep.section_sph_neumann.table_sph_neumann"></a><p class="title"><b>Table&#160;84.&#160;Error rates for sph_neumann</b></p>
11326 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
11327 <colgroup>
11328 <col>
11329 <col>
11330 <col>
11331 <col>
11332 <col>
11333 </colgroup>
11334 <thead><tr>
11335 <th>
11336             </th>
11337 <th>
11338               <p>
11339                 GNU C++ version 7.1.0<br> linux<br> long double
11340               </p>
11341             </th>
11342 <th>
11343               <p>
11344                 GNU C++ version 7.1.0<br> linux<br> double
11345               </p>
11346             </th>
11347 <th>
11348               <p>
11349                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11350               </p>
11351             </th>
11352 <th>
11353               <p>
11354                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11355               </p>
11356             </th>
11357 </tr></thead>
11358 <tbody><tr>
11359 <td>
11360               <p>
11361                 y: Random Data
11362               </p>
11363             </td>
11364 <td>
11365               <p>
11366                 <span class="blue">Max = 234&#949; (Mean = 19.5&#949;)</span><br> <br>
11367                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.6e+06&#949; (Mean = 1.4e+05&#949;))
11368               </p>
11369             </td>
11370 <td>
11371               <p>
11372                 <span class="blue">Max = 0.995&#949; (Mean = 0.0665&#949;)</span><br> <br>
11373                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04&#949; (Mean = 5.33e+03&#949;))
11374               </p>
11375             </td>
11376 <td>
11377               <p>
11378                 <span class="blue">Max = 234&#949; (Mean = 19.8&#949;)</span>
11379               </p>
11380             </td>
11381 <td>
11382               <p>
11383                 <span class="blue">Max = 281&#949; (Mean = 31.1&#949;)</span>
11384               </p>
11385             </td>
11386 </tr></tbody>
11387 </table></div>
11388 </div>
11389 <br class="table-break">
11390 </div>
11391 <div class="section">
11392 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11393 <a name="special_function_error_rates_rep.section_sph_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann_prime" title="sph_neumann_prime">sph_neumann_prime</a>
11394 </h2></div></div></div>
11395 <div class="table">
11396 <a name="special_function_error_rates_rep.section_sph_neumann_prime.table_sph_neumann_prime"></a><p class="title"><b>Table&#160;85.&#160;Error rates for sph_neumann_prime</b></p>
11397 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
11398 <colgroup>
11399 <col>
11400 <col>
11401 <col>
11402 <col>
11403 <col>
11404 </colgroup>
11405 <thead><tr>
11406 <th>
11407             </th>
11408 <th>
11409               <p>
11410                 GNU C++ version 7.1.0<br> linux<br> double
11411               </p>
11412             </th>
11413 <th>
11414               <p>
11415                 GNU C++ version 7.1.0<br> linux<br> long double
11416               </p>
11417             </th>
11418 <th>
11419               <p>
11420                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11421               </p>
11422             </th>
11423 <th>
11424               <p>
11425                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11426               </p>
11427             </th>
11428 </tr></thead>
11429 <tbody><tr>
11430 <td>
11431               <p>
11432                 y': Random Data
11433               </p>
11434             </td>
11435 <td>
11436               <p>
11437                 <span class="blue">Max = 0.988&#949; (Mean = 0.0869&#949;)</span>
11438               </p>
11439             </td>
11440 <td>
11441               <p>
11442                 <span class="blue">Max = 158&#949; (Mean = 18.8&#949;)</span>
11443               </p>
11444             </td>
11445 <td>
11446               <p>
11447                 <span class="blue">Max = 158&#949; (Mean = 20.2&#949;)</span>
11448               </p>
11449             </td>
11450 <td>
11451               <p>
11452                 <span class="blue">Max = 296&#949; (Mean = 25.6&#949;)</span>
11453               </p>
11454             </td>
11455 </tr></tbody>
11456 </table></div>
11457 </div>
11458 <br class="table-break">
11459 </div>
11460 <div class="section">
11461 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11462 <a name="special_function_error_rates_rep.section_spherical_harmonic_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i" title="spherical_harmonic_i">spherical_harmonic_i</a>
11463 </h2></div></div></div>
11464 <div class="table">
11465 <a name="special_function_error_rates_rep.section_spherical_harmonic_i.table_spherical_harmonic_i"></a><p class="title"><b>Table&#160;86.&#160;Error rates for spherical_harmonic_i</b></p>
11466 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
11467 <colgroup>
11468 <col>
11469 <col>
11470 <col>
11471 <col>
11472 <col>
11473 </colgroup>
11474 <thead><tr>
11475 <th>
11476             </th>
11477 <th>
11478               <p>
11479                 GNU C++ version 7.1.0<br> linux<br> double
11480               </p>
11481             </th>
11482 <th>
11483               <p>
11484                 GNU C++ version 7.1.0<br> linux<br> long double
11485               </p>
11486             </th>
11487 <th>
11488               <p>
11489                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11490               </p>
11491             </th>
11492 <th>
11493               <p>
11494                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11495               </p>
11496             </th>
11497 </tr></thead>
11498 <tbody><tr>
11499 <td>
11500               <p>
11501                 Spherical Harmonics
11502               </p>
11503             </td>
11504 <td>
11505               <p>
11506                 <span class="blue">Max = 1.36&#949; (Mean = 0.0765&#949;)</span>
11507               </p>
11508             </td>
11509 <td>
11510               <p>
11511                 <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
11512               </p>
11513             </td>
11514 <td>
11515               <p>
11516                 <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
11517               </p>
11518             </td>
11519 <td>
11520               <p>
11521                 <span class="blue">Max = 2.27e+04&#949; (Mean = 725&#949;)</span>
11522               </p>
11523             </td>
11524 </tr></tbody>
11525 </table></div>
11526 </div>
11527 <br class="table-break">
11528 </div>
11529 <div class="section">
11530 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11531 <a name="special_function_error_rates_rep.section_spherical_harmonic_r"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r" title="spherical_harmonic_r">spherical_harmonic_r</a>
11532 </h2></div></div></div>
11533 <div class="table">
11534 <a name="special_function_error_rates_rep.section_spherical_harmonic_r.table_spherical_harmonic_r"></a><p class="title"><b>Table&#160;87.&#160;Error rates for spherical_harmonic_r</b></p>
11535 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
11536 <colgroup>
11537 <col>
11538 <col>
11539 <col>
11540 <col>
11541 <col>
11542 </colgroup>
11543 <thead><tr>
11544 <th>
11545             </th>
11546 <th>
11547               <p>
11548                 GNU C++ version 7.1.0<br> linux<br> double
11549               </p>
11550             </th>
11551 <th>
11552               <p>
11553                 GNU C++ version 7.1.0<br> linux<br> long double
11554               </p>
11555             </th>
11556 <th>
11557               <p>
11558                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11559               </p>
11560             </th>
11561 <th>
11562               <p>
11563                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11564               </p>
11565             </th>
11566 </tr></thead>
11567 <tbody><tr>
11568 <td>
11569               <p>
11570                 Spherical Harmonics
11571               </p>
11572             </td>
11573 <td>
11574               <p>
11575                 <span class="blue">Max = 1.58&#949; (Mean = 0.0707&#949;)</span>
11576               </p>
11577             </td>
11578 <td>
11579               <p>
11580                 <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
11581               </p>
11582             </td>
11583 <td>
11584               <p>
11585                 <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
11586               </p>
11587             </td>
11588 <td>
11589               <p>
11590                 <span class="blue">Max = 2.27e+04&#949; (Mean = 725&#949;)</span>
11591               </p>
11592             </td>
11593 </tr></tbody>
11594 </table></div>
11595 </div>
11596 <br class="table-break">
11597 </div>
11598 <div class="section">
11599 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11600 <a name="special_function_error_rates_rep.section_sqrt1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sqrt1pm1" title="sqrt1pm1">sqrt1pm1</a>
11601 </h2></div></div></div>
11602 <div class="table">
11603 <a name="special_function_error_rates_rep.section_sqrt1pm1.table_sqrt1pm1"></a><p class="title"><b>Table&#160;88.&#160;Error rates for sqrt1pm1</b></p>
11604 <div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
11605 <colgroup>
11606 <col>
11607 <col>
11608 <col>
11609 <col>
11610 <col>
11611 </colgroup>
11612 <thead><tr>
11613 <th>
11614             </th>
11615 <th>
11616               <p>
11617                 GNU C++ version 7.1.0<br> linux<br> double
11618               </p>
11619             </th>
11620 <th>
11621               <p>
11622                 GNU C++ version 7.1.0<br> linux<br> long double
11623               </p>
11624             </th>
11625 <th>
11626               <p>
11627                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11628               </p>
11629             </th>
11630 <th>
11631               <p>
11632                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11633               </p>
11634             </th>
11635 </tr></thead>
11636 <tbody><tr>
11637 <td>
11638               <p>
11639                 sqrt1pm1
11640               </p>
11641             </td>
11642 <td>
11643               <p>
11644                 <span class="blue">Max = 1.3&#949; (Mean = 0.404&#949;)</span>
11645               </p>
11646             </td>
11647 <td>
11648               <p>
11649                 <span class="blue">Max = 1.33&#949; (Mean = 0.404&#949;)</span>
11650               </p>
11651             </td>
11652 <td>
11653               <p>
11654                 <span class="blue">Max = 1.54&#949; (Mean = 0.563&#949;)</span>
11655               </p>
11656             </td>
11657 <td>
11658               <p>
11659                 <span class="blue">Max = 1.35&#949; (Mean = 0.497&#949;)</span>
11660               </p>
11661             </td>
11662 </tr></tbody>
11663 </table></div>
11664 </div>
11665 <br class="table-break">
11666 </div>
11667 <div class="section">
11668 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11669 <a name="special_function_error_rates_rep.section_tgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma" title="tgamma">tgamma</a>
11670 </h2></div></div></div>
11671 <div class="table">
11672 <a name="special_function_error_rates_rep.section_tgamma.table_tgamma"></a><p class="title"><b>Table&#160;89.&#160;Error rates for tgamma</b></p>
11673 <div class="table-contents"><table class="table" summary="Error rates for tgamma">
11674 <colgroup>
11675 <col>
11676 <col>
11677 <col>
11678 <col>
11679 <col>
11680 </colgroup>
11681 <thead><tr>
11682 <th>
11683             </th>
11684 <th>
11685               <p>
11686                 GNU C++ version 7.1.0<br> linux<br> double
11687               </p>
11688             </th>
11689 <th>
11690               <p>
11691                 GNU C++ version 7.1.0<br> linux<br> long double
11692               </p>
11693             </th>
11694 <th>
11695               <p>
11696                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11697               </p>
11698             </th>
11699 <th>
11700               <p>
11701                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11702               </p>
11703             </th>
11704 </tr></thead>
11705 <tbody>
11706 <tr>
11707 <td>
11708               <p>
11709                 factorials
11710               </p>
11711             </td>
11712 <td>
11713               <p>
11714                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11715                 2.1:</em></span> Max = 3.95&#949; (Mean = 0.783&#949;))<br> (<span class="emphasis"><em>Rmath
11716                 3.2.3:</em></span> Max = 314&#949; (Mean = 93.4&#949;))
11717               </p>
11718             </td>
11719 <td>
11720               <p>
11721                 <span class="blue">Max = 2.67&#949; (Mean = 0.617&#949;)</span><br> <br>
11722                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))<br>
11723                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))
11724               </p>
11725             </td>
11726 <td>
11727               <p>
11728                 <span class="blue">Max = 172&#949; (Mean = 41&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
11729                 Max = 0&#949; (Mean = 0&#949;))
11730               </p>
11731             </td>
11732 <td>
11733               <p>
11734                 <span class="blue">Max = 1.85&#949; (Mean = 0.566&#949;)</span><br> <br>
11735                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.17&#949; (Mean = 0.928&#949;))
11736               </p>
11737             </td>
11738 </tr>
11739 <tr>
11740 <td>
11741               <p>
11742                 near 0
11743               </p>
11744             </td>
11745 <td>
11746               <p>
11747                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11748                 2.1:</em></span> Max = 4.51&#949; (Mean = 1.92&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
11749                 Max = 1&#949; (Mean = 0.335&#949;))
11750               </p>
11751             </td>
11752 <td>
11753               <p>
11754                 <span class="blue">Max = 2&#949; (Mean = 0.608&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
11755                 Max = 1&#949; (Mean = 0.376&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
11756                 Max = 1&#949; (Mean = 0.376&#949;))
11757               </p>
11758             </td>
11759 <td>
11760               <p>
11761                 <span class="blue">Max = 2&#949; (Mean = 0.647&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
11762                 Max = 0.5&#949; (Mean = 0.0791&#949;))
11763               </p>
11764             </td>
11765 <td>
11766               <p>
11767                 <span class="blue">Max = 1.5&#949; (Mean = 0.635&#949;)</span><br> <br>
11768                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.405&#949;))
11769               </p>
11770             </td>
11771 </tr>
11772 <tr>
11773 <td>
11774               <p>
11775                 near 1
11776               </p>
11777             </td>
11778 <td>
11779               <p>
11780                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11781                 2.1:</em></span> Max = 4.41&#949; (Mean = 1.81&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
11782                 Max = 1&#949; (Mean = 0.32&#949;))
11783               </p>
11784             </td>
11785 <td>
11786               <p>
11787                 <span class="blue">Max = 2.51&#949; (Mean = 1.02&#949;)</span><br> <br>
11788                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))<br>
11789                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))
11790               </p>
11791             </td>
11792 <td>
11793               <p>
11794                 <span class="blue">Max = 3.01&#949; (Mean = 1.06&#949;)</span><br> <br>
11795                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.175&#949;))
11796               </p>
11797             </td>
11798 <td>
11799               <p>
11800                 <span class="blue">Max = 1.1&#949; (Mean = 0.59&#949;)</span><br> <br>
11801                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.4&#949;))
11802               </p>
11803             </td>
11804 </tr>
11805 <tr>
11806 <td>
11807               <p>
11808                 near 2
11809               </p>
11810             </td>
11811 <td>
11812               <p>
11813                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11814                 2.1:</em></span> Max = 7.95&#949; (Mean = 3.12&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
11815                 Max = 1&#949; (Mean = 0.191&#949;))
11816               </p>
11817             </td>
11818 <td>
11819               <p>
11820                 <span class="blue">Max = 4.1&#949; (Mean = 1.55&#949;)</span><br> <br>
11821                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))<br>
11822                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))
11823               </p>
11824             </td>
11825 <td>
11826               <p>
11827                 <span class="blue">Max = 5.01&#949; (Mean = 1.89&#949;)</span><br> <br>
11828                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11829               </p>
11830             </td>
11831 <td>
11832               <p>
11833                 <span class="blue">Max = 2&#949; (Mean = 0.733&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
11834                 Max = 0&#949; (Mean = 0&#949;))
11835               </p>
11836             </td>
11837 </tr>
11838 <tr>
11839 <td>
11840               <p>
11841                 near -10
11842               </p>
11843             </td>
11844 <td>
11845               <p>
11846                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11847                 2.1:</em></span> Max = 2.6&#949; (Mean = 1.05&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
11848                 Max = 34.9&#949; (Mean = 9.2&#949;))
11849               </p>
11850             </td>
11851 <td>
11852               <p>
11853                 <span class="blue">Max = 1.75&#949; (Mean = 0.895&#949;)</span><br> <br>
11854                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))<br>
11855                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))
11856               </p>
11857             </td>
11858 <td>
11859               <p>
11860                 <span class="blue">Max = 1.75&#949; (Mean = 0.819&#949;)</span><br> <br>
11861                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11862               </p>
11863             </td>
11864 <td>
11865               <p>
11866                 <span class="blue">Max = 1.86&#949; (Mean = 0.881&#949;)</span><br> <br>
11867                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.866&#949; (Mean = 0.445&#949;))
11868               </p>
11869             </td>
11870 </tr>
11871 <tr>
11872 <td>
11873               <p>
11874                 near -55
11875               </p>
11876             </td>
11877 <td>
11878               <p>
11879                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11880                 2.1:</em></span> Max = 1.8&#949; (Mean = 0.782&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
11881                 Max = 3.89e+04&#949; (Mean = 9.52e+03&#949;))
11882               </p>
11883             </td>
11884 <td>
11885               <p>
11886                 <span class="blue">Max = 2.69&#949; (Mean = 1.09&#949;)</span><br> <br>
11887                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))<br>
11888                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))
11889               </p>
11890             </td>
11891 <td>
11892               <p>
11893                 <span class="blue">Max = 98.5&#949; (Mean = 53.4&#949;)</span><br> <br>
11894                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11895               </p>
11896             </td>
11897 <td>
11898               <p>
11899                 <span class="blue">Max = 2.7&#949; (Mean = 1.35&#949;)</span><br> <br>
11900                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.87e+04&#949; (Mean = 6.71e+03&#949;))
11901               </p>
11902             </td>
11903 </tr>
11904 </tbody>
11905 </table></div>
11906 </div>
11907 <br class="table-break">
11908 </div>
11909 <div class="section">
11910 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11911 <a name="special_function_error_rates_rep.section_tgamma1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma1pm1" title="tgamma1pm1">tgamma1pm1</a>
11912 </h2></div></div></div>
11913 <div class="table">
11914 <a name="special_function_error_rates_rep.section_tgamma1pm1.table_tgamma1pm1"></a><p class="title"><b>Table&#160;90.&#160;Error rates for tgamma1pm1</b></p>
11915 <div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
11916 <colgroup>
11917 <col>
11918 <col>
11919 <col>
11920 <col>
11921 <col>
11922 </colgroup>
11923 <thead><tr>
11924 <th>
11925             </th>
11926 <th>
11927               <p>
11928                 GNU C++ version 7.1.0<br> linux<br> double
11929               </p>
11930             </th>
11931 <th>
11932               <p>
11933                 GNU C++ version 7.1.0<br> linux<br> long double
11934               </p>
11935             </th>
11936 <th>
11937               <p>
11938                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
11939               </p>
11940             </th>
11941 <th>
11942               <p>
11943                 Microsoft Visual C++ version 14.1<br> Win32<br> double
11944               </p>
11945             </th>
11946 </tr></thead>
11947 <tbody><tr>
11948 <td>
11949               <p>
11950                 tgamma1pm1(dz)
11951               </p>
11952             </td>
11953 <td>
11954               <p>
11955                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11956               </p>
11957             </td>
11958 <td>
11959               <p>
11960                 <span class="blue">Max = 1.12&#949; (Mean = 0.49&#949;)</span>
11961               </p>
11962             </td>
11963 <td>
11964               <p>
11965                 <span class="blue">Max = 6.61&#949; (Mean = 0.84&#949;)</span>
11966               </p>
11967             </td>
11968 <td>
11969               <p>
11970                 <span class="blue">Max = 3.31&#949; (Mean = 0.517&#949;)</span>
11971               </p>
11972             </td>
11973 </tr></tbody>
11974 </table></div>
11975 </div>
11976 <br class="table-break">
11977 </div>
11978 <div class="section">
11979 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
11980 <a name="special_function_error_rates_rep.section_tgamma_delta_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio" title="tgamma_delta_ratio">tgamma_delta_ratio</a>
11981 </h2></div></div></div>
11982 <div class="table">
11983 <a name="special_function_error_rates_rep.section_tgamma_delta_ratio.table_tgamma_delta_ratio"></a><p class="title"><b>Table&#160;91.&#160;Error rates for tgamma_delta_ratio</b></p>
11984 <div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
11985 <colgroup>
11986 <col>
11987 <col>
11988 <col>
11989 <col>
11990 <col>
11991 </colgroup>
11992 <thead><tr>
11993 <th>
11994             </th>
11995 <th>
11996               <p>
11997                 GNU C++ version 7.1.0<br> linux<br> double
11998               </p>
11999             </th>
12000 <th>
12001               <p>
12002                 GNU C++ version 7.1.0<br> linux<br> long double
12003               </p>
12004             </th>
12005 <th>
12006               <p>
12007                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
12008               </p>
12009             </th>
12010 <th>
12011               <p>
12012                 Microsoft Visual C++ version 14.1<br> Win32<br> double
12013               </p>
12014             </th>
12015 </tr></thead>
12016 <tbody>
12017 <tr>
12018 <td>
12019               <p>
12020                 tgamma + small delta ratios
12021               </p>
12022             </td>
12023 <td>
12024               <p>
12025                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
12026               </p>
12027             </td>
12028 <td>
12029               <p>
12030                 <span class="blue">Max = 5.83&#949; (Mean = 1.3&#949;)</span>
12031               </p>
12032             </td>
12033 <td>
12034               <p>
12035                 <span class="blue">Max = 15.4&#949; (Mean = 2.09&#949;)</span>
12036               </p>
12037             </td>
12038 <td>
12039               <p>
12040                 <span class="blue">Max = 7.56&#949; (Mean = 1.31&#949;)</span>
12041               </p>
12042             </td>
12043 </tr>
12044 <tr>
12045 <td>
12046               <p>
12047                 tgamma + small delta ratios (negative delta)
12048               </p>
12049             </td>
12050 <td>
12051               <p>
12052                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
12053               </p>
12054             </td>
12055 <td>
12056               <p>
12057                 <span class="blue">Max = 7.94&#949; (Mean = 1.4&#949;)</span>
12058               </p>
12059             </td>
12060 <td>
12061               <p>
12062                 <span class="blue">Max = 18.3&#949; (Mean = 2.03&#949;)</span>
12063               </p>
12064             </td>
12065 <td>
12066               <p>
12067                 <span class="blue">Max = 7.43&#949; (Mean = 1.42&#949;)</span>
12068               </p>
12069             </td>
12070 </tr>
12071 <tr>
12072 <td>
12073               <p>
12074                 tgamma + small integer ratios
12075               </p>
12076             </td>
12077 <td>
12078               <p>
12079                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
12080               </p>
12081             </td>
12082 <td>
12083               <p>
12084                 <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
12085               </p>
12086             </td>
12087 <td>
12088               <p>
12089                 <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
12090               </p>
12091             </td>
12092 <td>
12093               <p>
12094                 <span class="blue">Max = 2.74&#949; (Mean = 0.736&#949;)</span>
12095               </p>
12096             </td>
12097 </tr>
12098 <tr>
12099 <td>
12100               <p>
12101                 tgamma + small integer ratios (negative delta)
12102               </p>
12103             </td>
12104 <td>
12105               <p>
12106                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
12107               </p>
12108             </td>
12109 <td>
12110               <p>
12111                 <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
12112               </p>
12113             </td>
12114 <td>
12115               <p>
12116                 <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
12117               </p>
12118             </td>
12119 <td>
12120               <p>
12121                 <span class="blue">Max = 2.15&#949; (Mean = 0.685&#949;)</span>
12122               </p>
12123             </td>
12124 </tr>
12125 <tr>
12126 <td>
12127               <p>
12128                 integer tgamma ratios
12129               </p>
12130             </td>
12131 <td>
12132               <p>
12133                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
12134               </p>
12135             </td>
12136 <td>
12137               <p>
12138                 <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
12139               </p>
12140             </td>
12141 <td>
12142               <p>
12143                 <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
12144               </p>
12145             </td>
12146 <td>
12147               <p>
12148                 <span class="blue">Max = 0.968&#949; (Mean = 0.386&#949;)</span>
12149               </p>
12150             </td>
12151 </tr>
12152 <tr>
12153 <td>
12154               <p>
12155                 integer tgamma ratios (negative delta)
12156               </p>
12157             </td>
12158 <td>
12159               <p>
12160                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
12161               </p>
12162             </td>
12163 <td>
12164               <p>
12165                 <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
12166               </p>
12167             </td>
12168 <td>
12169               <p>
12170                 <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
12171               </p>
12172             </td>
12173 <td>
12174               <p>
12175                 <span class="blue">Max = 0.974&#949; (Mean = 0.175&#949;)</span>
12176               </p>
12177             </td>
12178 </tr>
12179 </tbody>
12180 </table></div>
12181 </div>
12182 <br class="table-break">
12183 </div>
12184 <div class="section">
12185 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
12186 <a name="special_function_error_rates_rep.section_tgamma_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_" title="tgamma (incomplete)">tgamma
12187     (incomplete)</a>
12188 </h2></div></div></div>
12189 <div class="table">
12190 <a name="special_function_error_rates_rep.section_tgamma_incomplete_.table_tgamma_incomplete_"></a><p class="title"><b>Table&#160;92.&#160;Error rates for tgamma (incomplete)</b></p>
12191 <div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
12192 <colgroup>
12193 <col>
12194 <col>
12195 <col>
12196 <col>
12197 <col>
12198 </colgroup>
12199 <thead><tr>
12200 <th>
12201             </th>
12202 <th>
12203               <p>
12204                 GNU C++ version 7.1.0<br> linux<br> double
12205               </p>
12206             </th>
12207 <th>
12208               <p>
12209                 GNU C++ version 7.1.0<br> linux<br> long double
12210               </p>
12211             </th>
12212 <th>
12213               <p>
12214                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
12215               </p>
12216             </th>
12217 <th>
12218               <p>
12219                 Microsoft Visual C++ version 14.1<br> Win32<br> double
12220               </p>
12221             </th>
12222 </tr></thead>
12223 <tbody>
12224 <tr>
12225 <td>
12226               <p>
12227                 tgamma(a, z) medium values
12228               </p>
12229             </td>
12230 <td>
12231               <p>
12232                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12233                 2.1:</em></span> Max = 200&#949; (Mean = 13.3&#949;))
12234               </p>
12235             </td>
12236 <td>
12237               <p>
12238                 <span class="blue">Max = 8.47&#949; (Mean = 1.9&#949;)</span>
12239               </p>
12240             </td>
12241 <td>
12242               <p>
12243                 <span class="blue">Max = 412&#949; (Mean = 95.5&#949;)</span>
12244               </p>
12245             </td>
12246 <td>
12247               <p>
12248                 <span class="blue">Max = 8.14&#949; (Mean = 1.76&#949;)</span>
12249               </p>
12250             </td>
12251 </tr>
12252 <tr>
12253 <td>
12254               <p>
12255                 tgamma(a, z) small values
12256               </p>
12257             </td>
12258 <td>
12259               <p>
12260                 <span class="blue">Max = 0.753&#949; (Mean = 0.0474&#949;)</span><br> <br>
12261                 (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10&#949; (Mean
12262                 = 1.05e+09&#949;))</span>
12263               </p>
12264             </td>
12265 <td>
12266               <p>
12267                 <span class="blue">Max = 2.31&#949; (Mean = 0.775&#949;)</span>
12268               </p>
12269             </td>
12270 <td>
12271               <p>
12272                 <span class="blue">Max = 2.13&#949; (Mean = 0.717&#949;)</span>
12273               </p>
12274             </td>
12275 <td>
12276               <p>
12277                 <span class="blue">Max = 2.53&#949; (Mean = 0.66&#949;)</span>
12278               </p>
12279             </td>
12280 </tr>
12281 <tr>
12282 <td>
12283               <p>
12284                 tgamma(a, z) integer and half integer values
12285               </p>
12286             </td>
12287 <td>
12288               <p>
12289                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12290                 2.1:</em></span> Max = 117&#949; (Mean = 12.5&#949;))
12291               </p>
12292             </td>
12293 <td>
12294               <p>
12295                 <span class="blue">Max = 5.52&#949; (Mean = 1.48&#949;)</span>
12296               </p>
12297             </td>
12298 <td>
12299               <p>
12300                 <span class="blue">Max = 79.6&#949; (Mean = 20.9&#949;)</span>
12301               </p>
12302             </td>
12303 <td>
12304               <p>
12305                 <span class="blue">Max = 5.16&#949; (Mean = 1.33&#949;)</span>
12306               </p>
12307             </td>
12308 </tr>
12309 </tbody>
12310 </table></div>
12311 </div>
12312 <br class="table-break">
12313 </div>
12314 <div class="section">
12315 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
12316 <a name="special_function_error_rates_rep.section_tgamma_lower"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_lower" title="tgamma_lower">tgamma_lower</a>
12317 </h2></div></div></div>
12318 <div class="table">
12319 <a name="special_function_error_rates_rep.section_tgamma_lower.table_tgamma_lower"></a><p class="title"><b>Table&#160;93.&#160;Error rates for tgamma_lower</b></p>
12320 <div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
12321 <colgroup>
12322 <col>
12323 <col>
12324 <col>
12325 <col>
12326 <col>
12327 </colgroup>
12328 <thead><tr>
12329 <th>
12330             </th>
12331 <th>
12332               <p>
12333                 GNU C++ version 7.1.0<br> linux<br> double
12334               </p>
12335             </th>
12336 <th>
12337               <p>
12338                 GNU C++ version 7.1.0<br> linux<br> long double
12339               </p>
12340             </th>
12341 <th>
12342               <p>
12343                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
12344               </p>
12345             </th>
12346 <th>
12347               <p>
12348                 Microsoft Visual C++ version 14.1<br> Win32<br> double
12349               </p>
12350             </th>
12351 </tr></thead>
12352 <tbody>
12353 <tr>
12354 <td>
12355               <p>
12356                 tgamma(a, z) medium values
12357               </p>
12358             </td>
12359 <td>
12360               <p>
12361                 <span class="blue">Max = 0.833&#949; (Mean = 0.0315&#949;)</span><br> <br>
12362                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833&#949; (Mean = 0.0315&#949;))
12363               </p>
12364             </td>
12365 <td>
12366               <p>
12367                 <span class="blue">Max = 6.79&#949; (Mean = 1.46&#949;)</span>
12368               </p>
12369             </td>
12370 <td>
12371               <p>
12372                 <span class="blue">Max = 363&#949; (Mean = 63.8&#949;)</span>
12373               </p>
12374             </td>
12375 <td>
12376               <p>
12377                 <span class="blue">Max = 5.62&#949; (Mean = 1.49&#949;)</span>
12378               </p>
12379             </td>
12380 </tr>
12381 <tr>
12382 <td>
12383               <p>
12384                 tgamma(a, z) small values
12385               </p>
12386             </td>
12387 <td>
12388               <p>
12389                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12390                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
12391               </p>
12392             </td>
12393 <td>
12394               <p>
12395                 <span class="blue">Max = 1.97&#949; (Mean = 0.555&#949;)</span>
12396               </p>
12397             </td>
12398 <td>
12399               <p>
12400                 <span class="blue">Max = 1.97&#949; (Mean = 0.558&#949;)</span>
12401               </p>
12402             </td>
12403 <td>
12404               <p>
12405                 <span class="blue">Max = 1.57&#949; (Mean = 0.525&#949;)</span>
12406               </p>
12407             </td>
12408 </tr>
12409 <tr>
12410 <td>
12411               <p>
12412                 tgamma(a, z) integer and half integer values
12413               </p>
12414             </td>
12415 <td>
12416               <p>
12417                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12418                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
12419               </p>
12420             </td>
12421 <td>
12422               <p>
12423                 <span class="blue">Max = 4.83&#949; (Mean = 1.15&#949;)</span>
12424               </p>
12425             </td>
12426 <td>
12427               <p>
12428                 <span class="blue">Max = 84.7&#949; (Mean = 17.5&#949;)</span>
12429               </p>
12430             </td>
12431 <td>
12432               <p>
12433                 <span class="blue">Max = 2.69&#949; (Mean = 0.849&#949;)</span>
12434               </p>
12435             </td>
12436 </tr>
12437 </tbody>
12438 </table></div>
12439 </div>
12440 <br class="table-break">
12441 </div>
12442 <div class="section">
12443 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
12444 <a name="special_function_error_rates_rep.section_tgamma_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_ratio" title="tgamma_ratio">tgamma_ratio</a>
12445 </h2></div></div></div>
12446 <div class="table">
12447 <a name="special_function_error_rates_rep.section_tgamma_ratio.table_tgamma_ratio"></a><p class="title"><b>Table&#160;94.&#160;Error rates for tgamma_ratio</b></p>
12448 <div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
12449 <colgroup>
12450 <col>
12451 <col>
12452 <col>
12453 <col>
12454 <col>
12455 </colgroup>
12456 <thead><tr>
12457 <th>
12458             </th>
12459 <th>
12460               <p>
12461                 GNU C++ version 7.1.0<br> linux<br> double
12462               </p>
12463             </th>
12464 <th>
12465               <p>
12466                 GNU C++ version 7.1.0<br> linux<br> long double
12467               </p>
12468             </th>
12469 <th>
12470               <p>
12471                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
12472               </p>
12473             </th>
12474 <th>
12475               <p>
12476                 Microsoft Visual C++ version 14.1<br> Win32<br> double
12477               </p>
12478             </th>
12479 </tr></thead>
12480 <tbody><tr>
12481 <td>
12482               <p>
12483                 tgamma ratios
12484               </p>
12485             </td>
12486 <td>
12487               <p>
12488                 <span class="blue">Max = 0.694&#949; (Mean = 0.0347&#949;)</span>
12489               </p>
12490             </td>
12491 <td>
12492               <p>
12493                 <span class="blue">Max = 2.99&#949; (Mean = 1.15&#949;)</span>
12494               </p>
12495             </td>
12496 <td>
12497               <p>
12498                 <span class="blue">Max = 174&#949; (Mean = 61.2&#949;)</span>
12499               </p>
12500             </td>
12501 <td>
12502               <p>
12503                 <span class="blue">Max = 3.28&#949; (Mean = 1.12&#949;)</span>
12504               </p>
12505             </td>
12506 </tr></tbody>
12507 </table></div>
12508 </div>
12509 <br class="table-break">
12510 </div>
12511 <div class="section">
12512 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
12513 <a name="special_function_error_rates_rep.section_trigamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_trigamma" title="trigamma">trigamma</a>
12514 </h2></div></div></div>
12515 <div class="table">
12516 <a name="special_function_error_rates_rep.section_trigamma.table_trigamma"></a><p class="title"><b>Table&#160;95.&#160;Error rates for trigamma</b></p>
12517 <div class="table-contents"><table class="table" summary="Error rates for trigamma">
12518 <colgroup>
12519 <col>
12520 <col>
12521 <col>
12522 <col>
12523 <col>
12524 </colgroup>
12525 <thead><tr>
12526 <th>
12527             </th>
12528 <th>
12529               <p>
12530                 GNU C++ version 7.1.0<br> linux<br> double
12531               </p>
12532             </th>
12533 <th>
12534               <p>
12535                 GNU C++ version 7.1.0<br> linux<br> long double
12536               </p>
12537             </th>
12538 <th>
12539               <p>
12540                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
12541               </p>
12542             </th>
12543 <th>
12544               <p>
12545                 Microsoft Visual C++ version 14.1<br> Win32<br> double
12546               </p>
12547             </th>
12548 </tr></thead>
12549 <tbody><tr>
12550 <td>
12551               <p>
12552                 Mathematica Data
12553               </p>
12554             </td>
12555 <td>
12556               <p>
12557                 <span class="blue">Max = 0.998&#949; (Mean = 0.105&#949;)</span><br> <br>
12558                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04&#949; (Mean = 1.49e+03&#949;))<br>
12559                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04&#949; (Mean = 1.51e+03&#949;))
12560               </p>
12561             </td>
12562 <td>
12563               <p>
12564                 <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
12565               </p>
12566             </td>
12567 <td>
12568               <p>
12569                 <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
12570               </p>
12571             </td>
12572 <td>
12573               <p>
12574                 <span class="blue">Max = 1&#949; (Mean = 0.382&#949;)</span>
12575               </p>
12576             </td>
12577 </tr></tbody>
12578 </table></div>
12579 </div>
12580 <br class="table-break">
12581 </div>
12582 <div class="section">
12583 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
12584 <a name="special_function_error_rates_rep.section_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_zeta" title="zeta">zeta</a>
12585 </h2></div></div></div>
12586 <div class="table">
12587 <a name="special_function_error_rates_rep.section_zeta.table_zeta"></a><p class="title"><b>Table&#160;96.&#160;Error rates for zeta</b></p>
12588 <div class="table-contents"><table class="table" summary="Error rates for zeta">
12589 <colgroup>
12590 <col>
12591 <col>
12592 <col>
12593 <col>
12594 <col>
12595 </colgroup>
12596 <thead><tr>
12597 <th>
12598             </th>
12599 <th>
12600               <p>
12601                 GNU C++ version 7.1.0<br> linux<br> long double
12602               </p>
12603             </th>
12604 <th>
12605               <p>
12606                 GNU C++ version 7.1.0<br> linux<br> double
12607               </p>
12608             </th>
12609 <th>
12610               <p>
12611                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
12612               </p>
12613             </th>
12614 <th>
12615               <p>
12616                 Microsoft Visual C++ version 14.1<br> Win32<br> double
12617               </p>
12618             </th>
12619 </tr></thead>
12620 <tbody>
12621 <tr>
12622 <td>
12623               <p>
12624                 Zeta: Random values greater than 1
12625               </p>
12626             </td>
12627 <td>
12628               <p>
12629                 <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span><br> <br>
12630                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.45&#949; (Mean = 1&#949;))
12631               </p>
12632             </td>
12633 <td>
12634               <p>
12635                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12636                 2.1:</em></span> Max = 8.69&#949; (Mean = 1.03&#949;))
12637               </p>
12638             </td>
12639 <td>
12640               <p>
12641                 <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span>
12642               </p>
12643             </td>
12644 <td>
12645               <p>
12646                 <span class="blue">Max = 0.836&#949; (Mean = 0.093&#949;)</span>
12647               </p>
12648             </td>
12649 </tr>
12650 <tr>
12651 <td>
12652               <p>
12653                 Zeta: Random values less than 1
12654               </p>
12655             </td>
12656 <td>
12657               <p>
12658                 <span class="blue">Max = 7.03&#949; (Mean = 2.93&#949;)</span><br> <br>
12659                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 538&#949; (Mean = 59.3&#949;))
12660               </p>
12661             </td>
12662 <td>
12663               <p>
12664                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12665                 2.1:</em></span> Max = 137&#949; (Mean = 13.8&#949;))
12666               </p>
12667             </td>
12668 <td>
12669               <p>
12670                 <span class="blue">Max = 70.1&#949; (Mean = 17.1&#949;)</span>
12671               </p>
12672             </td>
12673 <td>
12674               <p>
12675                 <span class="blue">Max = 6.84&#949; (Mean = 3.12&#949;)</span>
12676               </p>
12677             </td>
12678 </tr>
12679 <tr>
12680 <td>
12681               <p>
12682                 Zeta: Values close to and greater than 1
12683               </p>
12684             </td>
12685 <td>
12686               <p>
12687                 <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span><br> <br>
12688                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.9e+06&#949; (Mean = 5.11e+05&#949;))
12689               </p>
12690             </td>
12691 <td>
12692               <p>
12693                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12694                 2.1:</em></span> Max = 7.73&#949; (Mean = 4.07&#949;))
12695               </p>
12696             </td>
12697 <td>
12698               <p>
12699                 <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span>
12700               </p>
12701             </td>
12702 <td>
12703               <p>
12704                 <span class="blue">Max = 0.994&#949; (Mean = 0.421&#949;)</span>
12705               </p>
12706             </td>
12707 </tr>
12708 <tr>
12709 <td>
12710               <p>
12711                 Zeta: Values close to and less than 1
12712               </p>
12713             </td>
12714 <td>
12715               <p>
12716                 <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span><br> <br>
12717                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.53e+06&#949; (Mean = 1.87e+06&#949;))
12718               </p>
12719             </td>
12720 <td>
12721               <p>
12722                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12723                 2.1:</em></span> Max = 0.991&#949; (Mean = 0.28&#949;))
12724               </p>
12725             </td>
12726 <td>
12727               <p>
12728                 <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span>
12729               </p>
12730             </td>
12731 <td>
12732               <p>
12733                 <span class="blue">Max = 0.991&#949; (Mean = 0.375&#949;)</span>
12734               </p>
12735             </td>
12736 </tr>
12737 <tr>
12738 <td>
12739               <p>
12740                 Zeta: Integer arguments
12741               </p>
12742             </td>
12743 <td>
12744               <p>
12745                 <span class="blue">Max = 9&#949; (Mean = 3.06&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
12746                 Max = 70.3&#949; (Mean = 17.4&#949;))
12747               </p>
12748             </td>
12749 <td>
12750               <p>
12751                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12752                 2.1:</em></span> Max = 3.75&#949; (Mean = 1.1&#949;))
12753               </p>
12754             </td>
12755 <td>
12756               <p>
12757                 <span class="blue">Max = 28&#949; (Mean = 5.62&#949;)</span>
12758               </p>
12759             </td>
12760 <td>
12761               <p>
12762                 <span class="blue">Max = 9&#949; (Mean = 3&#949;)</span>
12763               </p>
12764             </td>
12765 </tr>
12766 </tbody>
12767 </table></div>
12768 </div>
12769 <br class="table-break">
12770 </div>
12771 <div class="section">
12772 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
12773 <a name="special_function_error_rates_rep.error_logs"></a><a class="link" href="index.html#special_function_error_rates_rep.error_logs" title="Error Logs">Error Logs</a>
12774 </h2></div></div></div>
12775 <h5>
12776 <a name="special_function_error_rates_rep.error_logs.h0"></a>
12777       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in">Error
12778       Output For cyl_bessel_j (integer orders) with compiler Microsoft Visual C++
12779       version 14.1 and library &lt;math.h&gt; and test data Bessel JN: Mathworld
12780       Data (Integer Version)</a>
12781     </h5>
12782 <p>
12783       <a name="errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_"></a>CAUTION:
12784       Found non-finite result, when a finite value was expected at entry 16<br>
12785       Found: -nan(ind) Expected 0 Error: 1.79769e+308<br> 10, 1e-100, 0<br> CAUTION:
12786       Gross error found at entry 16.<br> Found: -nan(ind) Expected 0 Error: 1.79769e+308<br>
12787       10, 1e-100, 0<br>
12788     </p>
12789 <h5>
12790 <a name="special_function_error_rates_rep.error_logs.h1"></a>
12791       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso">Error
12792       Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and
12793       library GSL 2.1 and test data Associated Legendre Polynomials: Small Values</a>
12794     </h5>
12795 <p>
12796       <a name="errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values"></a>domain
12797       error<br> 3.75573, -3, 0.264719, 0.0186823<br> domain error<br> 3.75573,
12798       -3, 0.670017, 0.0085227<br> domain error<br> 3.75573, -3, 0.915014, 0.00136786<br>
12799       domain error<br> 3.75573, -3, 0.93539, 0.000921218<br> domain error<br>
12800       3.75573, -2, -0.804919, -0.035427<br> domain error<br> 3.75573, -2, -0.623236,
12801       -0.0476446<br> domain error<br> 3.75573, -2, 0.629447, 0.0475072<br>
12802       domain error<br> 3.75573, -2, 0.929777, 0.0157498<br> domain error<br>
12803       3.75573, -2, 0.985763, 0.0034837<br> domain error<br> 3.75573, -1, 0.093763,
12804       -0.118979<br> domain error<br> 4.28576, -4, 0.0944412, 0.00255792<br>
12805       domain error<br> 4.28576, -4, 0.670017, 0.000790849<br> domain error<br>
12806       4.28576, -3, -0.746026, -0.00458957<br> domain error<br> 4.28576, -2, -0.623236,
12807       0.0219016<br> domain error<br> 4.28576, -2, 0.629447, 0.0223081<br> domain
12808       error<br> 4.28576, -2, 0.93539, 0.0133504<br> domain error<br> 4.28576,
12809       -1, 0.915014, 0.132001<br> domain error<br> 4.28576, -1, 0.985763, 0.0787743<br>
12810       domain error<br> 4.43859, -4, 0.093763, 0.00255858<br> domain error<br>
12811       4.43859, -4, 0.811584, 0.000303404<br> domain error<br> 4.43859, -4, 0.826752,
12812       0.000260835<br> domain error<br> 4.43859, -4, 0.929777, 4.78235e-05<br>
12813       domain error<br> 4.43859, -3, -0.804919, -0.00350364<br> domain error<br>
12814       4.43859, -3, -0.729046, -0.00487043<br> domain error<br> 4.43859, -3, -0.623236,
12815       -0.00620995<br> domain error<br> 4.43859, -3, 0.93539, 0.000861698<br>
12816       domain error<br> 4.43859, -2, -0.557932, 0.0169167<br> domain error<br>
12817       4.43859, -2, -0.443004, 0.0062586<br> domain error<br> 4.43859, -2, 0.915014,
12818       0.016481<br> domain error<br> 4.43859, -1, 0.629447, -0.0138523<br> domain
12819       error<br> 5.39088, -5, 0.0944412, 0.000254649<br> domain error<br> 5.39088,
12820       -5, 0.264719, 0.000217164<br> domain error<br> 5.39088, -5, 0.670017, 5.87083e-05<br>
12821       domain error<br> 5.39088, -5, 0.915014, 2.78273e-06<br> domain error<br>
12822       5.39088, -3, 0.929777, 0.000880849<br> domain error<br> 5.39088, -2, 0.629447,
12823       0.00448021<br> domain error<br> 5.39088, -2, 0.826752, 0.01718<br> domain
12824       error<br> 5.39088, -2, 0.937736, 0.011583<br> domain error<br> 5.39088,
12825       -1, -0.804919, 0.0276144<br> domain error<br> 5.39088, -1, -0.746026, -0.0119425<br>
12826       domain error<br> 5.39088, -1, -0.443004, -0.0525987<br> domain error<br>
12827       5.39088, -1, 0.811584, 0.032475<br> domain error<br> 5.39088, -1, 0.985763,
12828       0.0759289<br> domain error<br> 5.97861, -5, -0.729046, 3.91223e-05<br>
12829       domain error<br> 5.97861, -5, -0.383666, 0.000174899<br> domain error<br>
12830       5.97861, -5, 0.93539, 1.43993e-06<br> domain error<br> 5.97861, -4, -0.623236,
12831       -0.000607048<br> domain error<br> 5.97861, -4, 0.264719, 0.00059614<br>
12832       domain error<br> 5.97861, -3, 0.629447, 0.00313497<br> domain error<br>
12833       5.97861, -3, 0.670017, 0.00323895<br> domain error<br> 5.97861, -2, 0.915014,
12834       0.0140705<br> domain error<br> 5.97861, -2, 0.992923, 0.00171356<br>
12835       domain error<br> 5.97861, -1, -0.746026, -0.0119425<br> domain error<br>
12836       5.97861, -1, 0.937736, 0.106972<br> domain error<br> 7.01297, -6, -0.443004,
12837       -4.99177e-06<br> domain error<br> 7.01297, -6, 0.629447, 3.00689e-06<br>
12838       domain error<br> 7.01297, -6, 0.811584, 7.00407e-07<br> domain error<br>
12839       7.01297, -6, 0.985763, 4.83431e-10<br> domain error<br> 7.01297, -3, 0.670017,
12840       0.000233323<br> domain error<br> 7.01297, -2, -0.804919, -0.0027739<br>
12841       domain error<br> 7.01297, -1, -0.383666, 0.0397866<br> domain error<br>
12842       7.01297, -1, 0.929777, 0.0544549<br> domain error<br> 7.54701, -7, 0.929777,
12843       1.42008e-09<br> domain error<br> 7.54701, -6, 0.992923, 6.04622e-11<br>
12844       domain error<br> 7.54701, -5, -0.804919, 1.18502e-05<br> domain error<br>
12845       7.54701, -5, -0.623236, 2.57049e-05<br> domain error<br> 7.54701, -5, -0.557932,
12846       2.60266e-05<br> domain error<br> 7.54701, -5, 0.826752, 9.64276e-06<br>
12847       domain error<br> 7.54701, -4, -0.746026, -0.0001618<br> domain error<br>
12848       7.54701, -3, 0.0944412, 0.000622493<br> domain error<br> 7.54701, -3, 0.985763,
12849       9.14782e-05<br> domain error<br> 7.54701, -1, 0.811584, -0.0376184<br>
12850       domain error<br> 11.8439, -10, -0.557932, -2.32652e-11<br> domain error<br>
12851       11.8439, -10, 0.811584, 1.01194e-12<br> domain error<br> 11.8439, -8, -0.746026,
12852       -1.34891e-09<br> domain error<br> 11.8439, -8, -0.729046, -1.5428e-09<br>
12853       domain error<br> 11.8439, -8, 0.985763, 5.90035e-14<br> domain error<br>
12854       11.8439, -4, 0.629447, -1.44723e-05<br> domain error<br> 11.8439, -4, 0.929777,
12855       1.98812e-05<br> domain error<br> 11.8439, -3, 0.670017, -4.58296e-05<br>
12856       domain error<br> 11.8439, -2, 0.826752, -0.00244759<br> domain error<br>
12857       11.8439, -2, 0.992923, 0.00151458<br> domain error<br> 11.8439, -1, -0.383666,
12858       0.00419108<br> domain error<br> 11.85, -11, 0.093763, 1.16526e-11<br>
12859       domain error<br> 11.85, -11, 0.929777, 2.05797e-16<br> domain error<br>
12860       11.85, -11, 0.93539, 1.32249e-16<br> domain error<br> *** FURTHER CONTENT
12861       HAS BEEN TRUNCATED FOR BREVITY ***<br>
12862     </p>
12863 <h5>
12864 <a name="special_function_error_rates_rep.error_logs.h2"></a>
12865       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0">Error
12866       Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and
12867       library &lt;cmath&gt; and test data Associated Legendre Polynomials: Small
12868       Values</a>
12869     </h5>
12870 <p>
12871       <a name="errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values"></a>order
12872       parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.264719, 0.0186823<br>
12873       order parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.670017,
12874       0.0085227<br> order parameters less than 0 not supported in TR1<br> 3.75573,
12875       -3, 0.915014, 0.00136786<br> order parameters less than 0 not supported in
12876       TR1<br> 3.75573, -3, 0.93539, 0.000921218<br> order parameters less than
12877       0 not supported in TR1<br> 3.75573, -2, -0.804919, -0.035427<br> order
12878       parameters less than 0 not supported in TR1<br> 3.75573, -2, -0.623236, -0.0476446<br>
12879       order parameters less than 0 not supported in TR1<br> 3.75573, -2, 0.629447,
12880       0.0475072<br> order parameters less than 0 not supported in TR1<br> 3.75573,
12881       -2, 0.929777, 0.0157498<br> order parameters less than 0 not supported in
12882       TR1<br> 3.75573, -2, 0.985763, 0.0034837<br> order parameters less than
12883       0 not supported in TR1<br> 3.75573, -1, 0.093763, -0.118979<br> order parameters
12884       less than 0 not supported in TR1<br> 4.28576, -4, 0.0944412, 0.00255792<br>
12885       order parameters less than 0 not supported in TR1<br> 4.28576, -4, 0.670017,
12886       0.000790849<br> order parameters less than 0 not supported in TR1<br> 4.28576,
12887       -3, -0.746026, -0.00458957<br> order parameters less than 0 not supported
12888       in TR1<br> 4.28576, -2, -0.623236, 0.0219016<br> order parameters less
12889       than 0 not supported in TR1<br> 4.28576, -2, 0.629447, 0.0223081<br> order
12890       parameters less than 0 not supported in TR1<br> 4.28576, -2, 0.93539, 0.0133504<br>
12891       order parameters less than 0 not supported in TR1<br> 4.28576, -1, 0.915014,
12892       0.132001<br> order parameters less than 0 not supported in TR1<br> 4.28576,
12893       -1, 0.985763, 0.0787743<br> order parameters less than 0 not supported in
12894       TR1<br> 4.43859, -4, 0.093763, 0.00255858<br> order parameters less than
12895       0 not supported in TR1<br> 4.43859, -4, 0.811584, 0.000303404<br> order
12896       parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.826752, 0.000260835<br>
12897       order parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.929777,
12898       4.78235e-05<br> order parameters less than 0 not supported in TR1<br> 4.43859,
12899       -3, -0.804919, -0.00350364<br> order parameters less than 0 not supported
12900       in TR1<br> 4.43859, -3, -0.729046, -0.00487043<br> order parameters less
12901       than 0 not supported in TR1<br> 4.43859, -3, -0.623236, -0.00620995<br>
12902       order parameters less than 0 not supported in TR1<br> 4.43859, -3, 0.93539,
12903       0.000861698<br> order parameters less than 0 not supported in TR1<br> 4.43859,
12904       -2, -0.557932, 0.0169167<br> order parameters less than 0 not supported in
12905       TR1<br> 4.43859, -2, -0.443004, 0.0062586<br> order parameters less than
12906       0 not supported in TR1<br> 4.43859, -2, 0.915014, 0.016481<br> order parameters
12907       less than 0 not supported in TR1<br> 4.43859, -1, 0.629447, -0.0138523<br>
12908       order parameters less than 0 not supported in TR1<br> 5.39088, -5, 0.0944412,
12909       0.000254649<br> order parameters less than 0 not supported in TR1<br> 5.39088,
12910       -5, 0.264719, 0.000217164<br> order parameters less than 0 not supported
12911       in TR1<br> 5.39088, -5, 0.670017, 5.87083e-05<br> order parameters less
12912       than 0 not supported in TR1<br> 5.39088, -5, 0.915014, 2.78273e-06<br>
12913       order parameters less than 0 not supported in TR1<br> 5.39088, -3, 0.929777,
12914       0.000880849<br> order parameters less than 0 not supported in TR1<br> 5.39088,
12915       -2, 0.629447, 0.00448021<br> order parameters less than 0 not supported in
12916       TR1<br> 5.39088, -2, 0.826752, 0.01718<br> order parameters less than 0
12917       not supported in TR1<br> 5.39088, -2, 0.937736, 0.011583<br> order parameters
12918       less than 0 not supported in TR1<br> 5.39088, -1, -0.804919, 0.0276144<br>
12919       order parameters less than 0 not supported in TR1<br> 5.39088, -1, -0.746026,
12920       -0.0119425<br> order parameters less than 0 not supported in TR1<br> 5.39088,
12921       -1, -0.443004, -0.0525987<br> order parameters less than 0 not supported
12922       in TR1<br> 5.39088, -1, 0.811584, 0.032475<br> order parameters less than
12923       0 not supported in TR1<br> 5.39088, -1, 0.985763, 0.0759289<br> order parameters
12924       less than 0 not supported in TR1<br> 5.97861, -5, -0.729046, 3.91223e-05<br>
12925       order parameters less than 0 not supported in TR1<br> 5.97861, -5, -0.383666,
12926       0.000174899<br> order parameters less than 0 not supported in TR1<br> 5.97861,
12927       -5, 0.93539, 1.43993e-06<br> order parameters less than 0 not supported in
12928       TR1<br> 5.97861, -4, -0.623236, -0.000607048<br> order parameters less
12929       than 0 not supported in TR1<br> 5.97861, -4, 0.264719, 0.00059614<br> order
12930       parameters less than 0 not supported in TR1<br> 5.97861, -3, 0.629447, 0.00313497<br>
12931       *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
12932     </p>
12933 <h5>
12934 <a name="special_function_error_rates_rep.error_logs.h3"></a>
12935       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi">Error
12936       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
12937       3.2.3 and test data Bessel Iv: Mathworld Data (large values)</a>
12938     </h5>
12939 <p>
12940       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_"></a>CAUTION:
12941       Gross error found at entry 0.<br> Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br>
12942       -1, 3.72917e-155, 1.86459e-155<br> CAUTION: Gross error found at entry 1.<br>
12943       Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br> 1, 3.72917e-155, 1.86459e-155<br>
12944       CAUTION: Gross error found at entry 3.<br> Found: 0 Expected 8.02269e-175
12945       Error: 3.60559e+133<br> 1.125, 3.72917e-155, 8.02269e-175<br>
12946     </p>
12947 <h5>
12948 <a name="special_function_error_rates_rep.error_logs.h4"></a>
12949       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in">Error
12950       Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
12951       and library Rmath 3.2.3 and test data Bessel In: Mathworld Data (Integer Version)</a>
12952     </h5>
12953 <p>
12954       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_"></a>Unsupported
12955       domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br>
12956       Unsupported domain<br> -100, -200, 4.35275e+74<br>
12957     </p>
12958 <h5>
12959 <a name="special_function_error_rates_rep.error_logs.h5"></a>
12960       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0">Error
12961       Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
12962       and library Rmath 3.2.3 and test data Bessel I1: Mathworld Data (Integer Version)</a>
12963     </h5>
12964 <p>
12965       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_"></a>Unsupported
12966       domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br>
12967       Unsupported domain<br> 1, -10, -2670.99<br>
12968     </p>
12969 <h5>
12970 <a name="special_function_error_rates_rep.error_logs.h6"></a>
12971       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1">Error
12972       Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
12973       and library Rmath 3.2.3 and test data Bessel I0: Mathworld Data (Integer Version)</a>
12974     </h5>
12975 <p>
12976       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_"></a>Unsupported
12977       domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br>
12978       Unsupported domain<br> 0, -1, 1.26607<br>
12979     </p>
12980 <h5>
12981 <a name="special_function_error_rates_rep.error_logs.h7"></a>
12982       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0">Error
12983       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
12984       3.2.3 and test data Bessel In: Mathworld Data</a>
12985     </h5>
12986 <p>
12987       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data"></a>Unsupported
12988       domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br>
12989       Unsupported domain<br> -100, -200, 4.35275e+74<br>
12990     </p>
12991 <h5>
12992 <a name="special_function_error_rates_rep.error_logs.h8"></a>
12993       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1">Error
12994       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
12995       3.2.3 and test data Bessel I1: Mathworld Data</a>
12996     </h5>
12997 <p>
12998       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data"></a>Unsupported
12999       domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br>
13000       Unsupported domain<br> 1, -10, -2670.99<br>
13001     </p>
13002 <h5>
13003 <a name="special_function_error_rates_rep.error_logs.h9"></a>
13004       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2">Error
13005       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
13006       3.2.3 and test data Bessel I0: Mathworld Data</a>
13007     </h5>
13008 <p>
13009       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data"></a>Unsupported
13010       domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br>
13011       Unsupported domain<br> 0, -1, 1.26607<br>
13012     </p>
13013 <h5>
13014 <a name="special_function_error_rates_rep.error_logs.h10"></a>
13015       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi">Error
13016       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
13017       3.2.3 and test data Bessel J: Mathworld Data</a>
13018     </h5>
13019 <p>
13020       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data"></a>CAUTION:
13021       Gross error found at entry 6.<br> Found: 0 Expected -0.000747424 Error: 3.3591e+304<br>
13022       5.5, 1e+06, -0.000747424<br> CAUTION: Gross error found at entry 7.<br>
13023       Found: 0 Expected -0.0007766 Error: 3.49022e+304<br> 5.125, 1e+06, -0.0007766<br>
13024       CAUTION: Gross error found at entry 8.<br> Found: 0 Expected -0.000466323
13025       Error: 2.09576e+304<br> 5.875, 1e+06, -0.000466323<br>
13026     </p>
13027 <h5>
13028 <a name="special_function_error_rates_rep.error_logs.h11"></a>
13029       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0">Error
13030       Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
13031       and library Rmath 3.2.3 and test data Bessel JN: Mathworld Data (Integer Version)</a>
13032     </h5>
13033 <p>
13034       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_"></a>Unsupported
13035       domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br>
13036       Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br>
13037       CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964
13038       Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br>
13039       -5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br>
13040       Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found
13041       at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br>
13042       -10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br>
13043       Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br>
13044     </p>
13045 <h5>
13046 <a name="special_function_error_rates_rep.error_logs.h12"></a>
13047       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1">Error
13048       Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
13049       and library Rmath 3.2.3 and test data Bessel J1: Mathworld Data (Integer Version)</a>
13050     </h5>
13051 <p>
13052       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_"></a>Unsupported
13053       domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br>
13054       Unsupported domain<br> 1, -10, -0.0434727<br>
13055     </p>
13056 <h5>
13057 <a name="special_function_error_rates_rep.error_logs.h13"></a>
13058       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2">Error
13059       Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
13060       and library Rmath 3.2.3 and test data Bessel J0: Mathworld Data (Integer Version)</a>
13061     </h5>
13062 <p>
13063       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_"></a>Unsupported
13064       domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br>
13065       Unsupported domain<br> 0, -10, -0.245936<br>
13066     </p>
13067 <h5>
13068 <a name="special_function_error_rates_rep.error_logs.h14"></a>
13069       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0">Error
13070       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
13071       3.2.3 and test data Bessel JN: Mathworld Data</a>
13072     </h5>
13073 <p>
13074       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data"></a>Unsupported
13075       domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br>
13076       Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br>
13077       CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964
13078       Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br>
13079       -5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br>
13080       Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found
13081       at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br>
13082       -10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br>
13083       Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br>
13084     </p>
13085 <h5>
13086 <a name="special_function_error_rates_rep.error_logs.h15"></a>
13087       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1">Error
13088       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
13089       3.2.3 and test data Bessel J1: Mathworld Data</a>
13090     </h5>
13091 <p>
13092       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data"></a>Unsupported
13093       domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br>
13094       Unsupported domain<br> 1, -10, -0.0434727<br>
13095     </p>
13096 <h5>
13097 <a name="special_function_error_rates_rep.error_logs.h16"></a>
13098       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2">Error
13099       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
13100       3.2.3 and test data Bessel J0: Mathworld Data</a>
13101     </h5>
13102 <p>
13103       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data"></a>Unsupported
13104       domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br>
13105       Unsupported domain<br> 0, -10, -0.245936<br>
13106     </p>
13107 <h5>
13108 <a name="special_function_error_rates_rep.error_logs.h17"></a>
13109       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with">Error
13110       Output For ibetac_inv with compiler GNU C++ version 7.1.0 and library Rmath
13111       3.2.3 and test data Inverse incomplete beta</a>
13112     </h5>
13113 <p>
13114       <a name="errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION:
13115       Gross error found at entry 7.<br> Found: 3.8247e-302 Expected 0 Error: 1.71891e+06<br>
13116       1.38853e-05, 0.0497627, 0.632396, 0, 0<br> CAUTION: Gross error found at
13117       entry 71.<br> Found: 1.38362e-204 Expected 0 Error: 6.21832e+103<br> 3.77931e-05,
13118       0.0150073, 0.835025, 0, 0<br> CAUTION: Gross error found at entry 90.<br>
13119       Found: 1.09275e-303 Expected 0 Error: 49109.6<br> 4.29383e-05, 0.0428761,
13120       0.814742, 0, 0<br> CAUTION: Gross error found at entry 102.<br> Found:
13121       3.8625e-304 Expected 0 Error: 17358<br> 4.80089e-05, 0.0296236, 0.913384,
13122       0, 0<br> CAUTION: Gross error found at entry 115.<br> Found: 1.51774e-303
13123       Expected 0 Error: 68209.8<br> 0.000130387, 0.0404969, 0.814742, 0, 0<br>
13124       CAUTION: Gross error found at entry 123.<br> Found: 1.28036e-303 Expected
13125       0 Error: 57541.4<br> 0.000149328, 0.0201182, 0.905801, 5.70765e-267, 0<br>
13126       CAUTION: Gross error found at entry 133.<br> Found: 1.96732e-302 Expected
13127       0 Error: 884160<br> 0.000173563, 0.0301908, 0.913384, 4.21662e-213, 0<br>
13128       CAUTION: Gross error found at entry 159.<br> Found: 1.48697e-191 Expected
13129       0 Error: 6.68279e+116<br> 0.000260723, 0.0252933, 0.632396, 0, 0<br> CAUTION:
13130       Gross error found at entry 256.<br> Found: 9.24166e-245 Expected 0 Error:
13131       4.15342e+63<br> 0.00246975, 0.016063, 0.913384, 1, 0<br>
13132     </p>
13133 <h5>
13134 <a name="special_function_error_rates_rep.error_logs.h18"></a>
13135       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_">Error
13136       Output For ibeta_inv with compiler GNU C++ version 7.1.0 and library Rmath
13137       3.2.3 and test data Inverse incomplete beta</a>
13138     </h5>
13139 <p>
13140       <a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION:
13141       Gross error found at entry 1.<br> Found: 1.90197e-247 Expected 0 Error: 8.54789e+60<br>
13142       1.12733e-05, 0.022662, 0.135563, 0, 0<br> CAUTION: Gross error found at entry
13143       30.<br> Found: 1.36217e-301 Expected 0 Error: 6.12191e+06<br> 2.10769e-05,
13144       0.0448972, 0.221112, 0, 0<br> CAUTION: Gross error found at entry 152.<br>
13145       Found: 2.92621e-285 Expected 0 Error: 1.31511e+23<br> 0.000240381, 0.017982,
13146       0.221112, 0, 0<br> CAUTION: Gross error found at entry 184.<br> Found:
13147       5.63355e-203 Expected 0 Error: 2.53185e+105<br> 0.000348822, 0.0275467, 0.135563,
13148       0, 1.88165e-166<br> CAUTION: Gross error found at entry 205.<br> Found:
13149       5.52731e-303 Expected 0 Error: 248409<br> 0.000441212, 0.0313573, 0.127074,
13150       0, 9.07221e-121<br>
13151     </p>
13152 <h5>
13153 <a name="special_function_error_rates_rep.error_logs.h19"></a>
13154       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_bet"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_bet">Error
13155       Output For non central beta CDF complement with compiler GNU C++ version 7.1.0
13156       and library Rmath 3.2.3 and test data Non Central Beta, large parameters</a>
13157     </h5>
13158 <p>
13159       <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION:
13160       Gross error found at entry 10.<br> Found: 9.76918e-10 Expected 1.61248e-15
13161       Error: 605846<br> 290.682, 72.6705, 20005.4, 0.997663, 1, 1.61248e-15<br>
13162       CAUTION: Gross error found at entry 11.<br> Found: 9.94184e-10 Expected 3.0108e-42
13163       Error: 3.30205e+32<br> 290.682, 145.341, 53489.1, 0.998663, 1, 3.0108e-42<br>
13164       CAUTION: Gross error found at entry 16.<br> Found: 8.45406e-10 Expected 4.46652e-22
13165       Error: 1.89276e+12<br> 290.682, 1162.73, 2308.07, 0.656921, 1, 4.46652e-22<br>
13166       CAUTION: Gross error found at entry 17.<br> Found: 9.41971e-10 Expected 1.7241e-50
13167       Error: 5.46356e+40<br> 290.682, 1453.41, 8064.48, 0.832237, 1, 1.7241e-50<br>
13168       CAUTION: Gross error found at entry 18.<br> Found: 9.30663e-10 Expected 2.09803e-305
13169       Error: 4.43589e+295<br> 975.766, 731.824, 232.285, 0.919742, 1, 2.09803e-305<br>
13170       CAUTION: Gross error found at entry 27.<br> Found: 9.76918e-10 Expected 9.3474e-18
13171       Error: 1.04512e+08<br> 1879.05, 187.905, 20005.4, 0.992215, 1, 9.3474e-18<br>
13172       CAUTION: Gross error found at entry 28.<br> Found: 9.94184e-10 Expected 1.8122e-90
13173       Error: 5.48607e+80<br> 1879.05, 469.762, 53489.1, 0.994618, 1, 1.8122e-90<br>
13174       CAUTION: Gross error found at entry 32.<br> Found: 9.27224e-10 Expected 3.18255e-15
13175       Error: 291345<br> 1879.05, 3758.1, 1879.05, 0.480508, 1, 3.18255e-15<br>
13176       CAUTION: Gross error found at entry 33.<br> Found: 8.45406e-10 Expected 1.10218e-77
13177       Error: 7.67029e+67<br> 1879.05, 5637.15, 2308.07, 0.458181, 1, 1.10218e-77<br>
13178       CAUTION: Gross error found at entry 34.<br> Found: 9.30663e-10 Expected 0
13179       Error: 4.18262e+298<br> 2308.07, 1154.03, 232.285, 0.919371, 1, 0<br> CAUTION:
13180       Gross error found at entry 35.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
13181       2308.07, 1731.05, 290.682, 0.917262, 1, 0<br> CAUTION: Gross error found
13182       at entry 43.<br> Found: 9.94184e-10 Expected 3.57283e-70 Error: 2.78262e+60<br>
13183       8064.48, 806.448, 53489.1, 0.988678, 1, 3.57283e-70<br> CAUTION: Gross error
13184       found at entry 48.<br> Found: 8.45406e-10 Expected 8.78057e-74 Error: 9.62814e+63<br>
13185       8064.48, 16129, 2308.07, 0.421531, 1, 8.78057e-74<br> CAUTION: Gross error
13186       found at entry 49.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br>
13187       15674.4, 3918.59, 232.285, 0.933726, 1, 0<br> CAUTION: Gross error found
13188       at entry 50.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
13189       15674.4, 7837.19, 290.682, 0.917179, 1, 0<br> CAUTION: Gross error found
13190       at entry 51.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 15674.4,
13191       11755.8, 975.766, 0.915784, 1, 0<br> CAUTION: Gross error found at entry
13192       63.<br> Found: 9.41971e-10 Expected 2.31296e-171 Error: 4.07258e+161<br>
13193       20005.4, 40010.8, 8064.48, 0.432094, 1, 2.31296e-171<br> CAUTION: Gross error
13194       found at entry 64.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br>
13195       53489.1, 5348.92, 232.285, 0.954635, 1, 0<br> CAUTION: Gross error found
13196       at entry 65.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
13197       53489.1, 13372.3, 290.682, 0.933478, 1, 0<br> CAUTION: Gross error found
13198       at entry 66.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 53489.1,
13199       26744.6, 975.766, 0.91717, 1, 0<br>
13200     </p>
13201 <h5>
13202 <a name="special_function_error_rates_rep.error_logs.h20"></a>
13203       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be0">Error
13204       Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library
13205       Rmath 3.2.3 and test data Non Central Beta, large parameters</a>
13206     </h5>
13207 <p>
13208       <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION:
13209       Gross error found at entry 0.<br> Found: 9.1136e-209 Expected 5.82279e-200
13210       Error: 6.38913e+08<br> 232.285, 209.056, 232.285, 0.062486, 5.82279e-200,
13211       1<br> CAUTION: Gross error found at entry 1.<br> Found: 4.08108e-115 Expected
13212       2.37643e-112 Error: 581.304<br> 232.285, 229.962, 290.682, 0.155342, 2.37643e-112,
13213       1<br> CAUTION: Gross error found at entry 2.<br> Found: 1.07549e-93 Expected
13214       9.53431e-89 Error: 88650<br> 232.285, 232.052, 975.766, 0.378086, 9.53431e-89,
13215       1<br> CAUTION: Gross error found at entry 3.<br> Found: 2.58402e-54 Expected
13216       8.27353e-53 Error: 31.0181<br> 232.285, 232.285, 1879.05, 0.625865, 8.27353e-53,
13217       1<br> CAUTION: Gross error found at entry 4.<br> Found: 1.93718e-19 Expected
13218       6.64275e-16 Error: 3428.08<br> 232.285, 232.308, 2308.07, 0.770774, 6.64275e-16,
13219       1<br> CAUTION: Gross error found at entry 21.<br> Found: 8.12962e-240 Expected
13220       1.82294e-219 Error: 2.24234e+20<br> 975.766, 974.79, 1879.05, 0.331337, 1.82294e-219,
13221       1<br> CAUTION: Gross error found at entry 22.<br> Found: 3.47274e-69 Expected
13222       1.42183e-67 Error: 39.9426<br> 975.766, 975.766, 2308.07, 0.514323, 1.42183e-67,
13223       1<br> CAUTION: Gross error found at entry 23.<br> Found: 5.86885e-50 Expected
13224       1.27896e-47 Error: 216.923<br> 975.766, 975.863, 8064.48, 0.753209, 1.27896e-47,
13225       1<br> CAUTION: Gross error found at entry 39.<br> Found: 4.82785e-230 Expected
13226       1.25446e-213 Error: 2.59838e+16<br> 2308.07, 2308.07, 8064.48, 0.54983, 1.25446e-213,
13227       1<br> CAUTION: Gross error found at entry 40.<br> Found: 1.22971e-87 Expected
13228       1.82618e-85 Error: 147.505<br> 2308.07, 2308.3, 15674.4, 0.733174, 1.82618e-85,
13229       1<br> CAUTION: Gross error found at entry 56.<br> Found: 2.97337e-127 Expected
13230       2.56068e-124 Error: 860.205<br> 15674.4, 15675.9, 20005.4, 0.55883, 2.56068e-124,
13231       1<br>
13232     </p>
13233 <h5>
13234 <a name="special_function_error_rates_rep.error_logs.h21"></a>
13235       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be1">Error
13236       Output For non central beta CDF complement with compiler GNU C++ version 7.1.0
13237       and library Rmath 3.2.3 and test data Non Central Beta, medium parameters</a>
13238     </h5>
13239 <p>
13240       <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION:
13241       Gross error found at entry 296.<br> Found: 9.44166e-10 Expected 6.22975e-10
13242       Error: 0.515577<br> 22.9367, 114.683, 19.5081, 0.480981, 1, 6.22975e-10<br>
13243       CAUTION: Gross error found at entry 369.<br> Found: 2.52234e-10 Expected
13244       1.40246e-10 Error: 0.79851<br> 27.5277, 20.6457, 0.956697, 0.915111, 1, 1.40246e-10<br>
13245       CAUTION: Gross error found at entry 429.<br> Found: 1.18105e-09 Expected
13246       7.45745e-10 Error: 0.58372<br> 28.8063, 21.6047, 60.3826, 0.946143, 1, 7.45745e-10<br>
13247       CAUTION: Gross error found at entry 430.<br> Found: 2.44435e-09 Expected
13248       1.60695e-09 Error: 0.521115<br> 28.8063, 21.6047, 148.129, 0.965121, 1, 1.60695e-09<br>
13249       CAUTION: Gross error found at entry 477.<br> Found: 7.57435e-10 Expected
13250       7.14133e-11 Error: 9.60635<br> 28.8063, 144.032, 42.3849, 0.504845, 1, 7.14133e-11<br>
13251       CAUTION: Gross error found at entry 489.<br> Found: 4.8561e-10 Expected 5.62991e-11
13252       Error: 7.62553<br> 31.9438, 23.9579, 44.2068, 0.93835, 1, 5.62991e-11<br>
13253       CAUTION: Gross error found at entry 490.<br> Found: 8.35187e-10 Expected
13254       1.87483e-10 Error: 3.45473<br> 31.9438, 23.9579, 135.747, 0.961117, 1, 1.87483e-10<br>
13255       CAUTION: Gross error found at entry 491.<br> Found: 1.00174e-09 Expected
13256       2.38491e-10 Error: 3.20032<br> 31.9438, 23.9579, 191.501, 0.968273, 1, 2.38491e-10<br>
13257       CAUTION: Gross error found at entry 537.<br> Found: 7.29746e-10 Expected
13258       1.31223e-12 Error: 555.111<br> 31.9438, 159.719, 34.2373, 0.489796, 1, 1.31223e-12<br>
13259       CAUTION: Gross error found at entry 538.<br> Found: 2.49663e-09 Expected
13260       1.54239e-09 Error: 0.618681<br> 31.9438, 159.719, 126.472, 0.581861, 1, 1.54239e-09<br>
13261       CAUTION: Gross error found at entry 549.<br> Found: 4.16125e-10 Expected
13262       4.8536e-13 Error: 856.353<br> 38.0822, 28.5617, 34.773, 0.931853, 1, 4.8536e-13<br>
13263       CAUTION: Gross error found at entry 550.<br> Found: 9.69907e-10 Expected
13264       2.87054e-12 Error: 336.883<br> 38.0822, 28.5617, 127.953, 0.956104, 1, 2.87054e-12<br>
13265       CAUTION: Gross error found at entry 551.<br> Found: 5.90132e-10 Expected
13266       4.08361e-12 Error: 143.512<br> 38.0822, 28.5617, 183.147, 0.963764, 1, 4.08361e-12<br>
13267       CAUTION: Gross error found at entry 597.<br> Found: 4.67033e-10 Expected
13268       9.82939e-16 Error: 475139<br> 38.0822, 190.411, 27.0954, 0.475419, 1, 9.82939e-16<br>
13269       CAUTION: Gross error found at entry 598.<br> Found: 9.33207e-10 Expected
13270       4.03465e-12 Error: 230.298<br> 38.0822, 190.411, 100.733, 0.544491, 1, 4.03465e-12<br>
13271       CAUTION: Gross error found at entry 599.<br> Found: 7.4092e-10 Expected 9.53942e-11
13272       Error: 6.76693<br> 38.0822, 190.411, 169.826, 0.594614, 1, 9.53942e-11<br>
13273       CAUTION: Gross error found at entry 609.<br> Found: 5.71813e-10 Expected
13274       1.17207e-14 Error: 48785.7<br> 42.7789, 32.0842, 28.3773, 0.927814, 1, 1.17207e-14<br>
13275       CAUTION: Gross error found at entry 610.<br> Found: 5.16834e-10 Expected
13276       9.62679e-14 Error: 5367.71<br> 42.7789, 32.0842, 109.376, 0.950307, 1, 9.62679e-14<br>
13277       CAUTION: Gross error found at entry 611.<br> Found: 6.08012e-10 Expected
13278       1.7454e-13 Error: 3482.51<br> 42.7789, 32.0842, 175.686, 0.960431, 1, 1.7454e-13<br>
13279       CAUTION: Gross error found at entry 657.<br> Found: 5.59489e-10 Expected
13280       2.86344e-18 Error: 1.95391e+08<br> 42.7789, 213.895, 21.9724, 0.467166, 1,
13281       2.86344e-18<br> CAUTION: Gross error found at entry 658.<br> Found: 5.14798e-10
13282       Expected 2.50972e-14 Error: 20511.2<br> 42.7789, 213.895, 84.4175, 0.522676,
13283       1, 2.50972e-14<br> CAUTION: Gross error found at entry 659.<br> Found:
13284       8.49991e-10 Expected 2.38005e-12 Error: 356.131<br> 42.7789, 213.895, 160.056,
13285       0.576191, 1, 2.38005e-12<br> CAUTION: Gross error found at entry 671.<br>
13286       Found: 3.03281e-10 Expected 2.22036e-15 Error: 136590<br> 44.5963, 33.4472,
13287       22.4929, 0.924976, 1, 2.22036e-15<br> CAUTION: Gross error found at entry
13288       672.<br> Found: 8.40636e-10 Expected 2.22384e-14 Error: 37800.1<br> 44.5963,
13289       33.4472, 94.9517, 0.946545, 1, 2.22384e-14<br> CAUTION: Gross error found
13290       at entry 673.<br> Found: 8.15021e-10 Expected 4.75974e-14 Error: 17122.2<br>
13291       44.5963, 33.4472, 162.945, 0.95793, 1, 4.75974e-14<br> CAUTION: Gross error
13292       found at entry 716.<br> Found: 1.11988e-10 Expected 2.84965e-22 Error: 3.92989e+11<br>
13293       44.5963, 222.981, 0.956697, 0.445432, 1, 2.84965e-22<br> CAUTION: Gross error
13294       found at entry 717.<br> Found: 7.99524e-10 Expected 3.04552e-15 Error: 262523<br>
13295       44.5963, 222.981, 78.4454, 0.515267, 1, 3.04552e-15<br> CAUTION: Gross error
13296       found at entry 718.<br> Found: 8.0958e-10 Expected 5.89458e-13 Error: 1372.43<br>
13297       44.5963, 222.981, 158.441, 0.57107, 1, 5.89458e-13<br> *** FURTHER CONTENT
13298       HAS BEEN TRUNCATED FOR BREVITY ***<br>
13299     </p>
13300 <h5>
13301 <a name="special_function_error_rates_rep.error_logs.h22"></a>
13302       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be2">Error
13303       Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library
13304       Rmath 3.2.3 and test data Non Central Beta, medium parameters</a>
13305     </h5>
13306 <p>
13307       <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION:
13308       Gross error found at entry 14.<br> Found: 4.64669e-35 Expected 7.14875e-33
13309       Error: 152.846<br> 1.45431, 1.30887, 158.441, 0.0983847, 7.14875e-33, 1<br>
13310       CAUTION: Gross error found at entry 15.<br> Found: 4.66674e-46 Expected 3.13332e-40
13311       Error: 671416<br> 1.45431, 1.30887, 196.222, 0.09869, 3.13332e-40, 1<br>
13312       CAUTION: Gross error found at entry 18.<br> Found: 5.84342e-28 Expected 3.61559e-27
13313       Error: 5.18745<br> 1.45431, 1.43976, 159.586, 0.245596, 3.61559e-27, 1<br>
13314       CAUTION: Gross error found at entry 19.<br> Found: 1.72833e-34 Expected 1.76943e-33
13315       Error: 9.2378<br> 1.45431, 1.43976, 198.576, 0.246444, 1.76943e-33, 1<br>
13316       CAUTION: Gross error found at entry 22.<br> Found: 1.76915e-19 Expected 3.69506e-18
13317       Error: 19.8861<br> 1.45431, 1.45285, 159.621, 0.491116, 3.69506e-18, 1<br>
13318       CAUTION: Gross error found at entry 23.<br> Found: 2.52007e-25 Expected 2.00482e-22
13319       Error: 794.544<br> 1.45431, 1.45285, 199.292, 0.492849, 2.00482e-22, 1<br>
13320       CAUTION: Gross error found at entry 73.<br> Found: 2.04477e-34 Expected 2.45287e-33
13321       Error: 10.9958<br> 7.62448, 6.86203, 148.129, 0.0921776, 2.45287e-33, 1<br>
13322       CAUTION: Gross error found at entry 74.<br> Found: 2.36587e-46 Expected 7.32638e-42
13323       Error: 30966<br> 7.62448, 6.86203, 193.539, 0.093784, 7.32638e-42, 1<br>
13324       CAUTION: Gross error found at entry 76.<br> Found: 3.29122e-26 Expected 7.418e-25
13325       Error: 21.5387<br> 7.62448, 7.54824, 148.626, 0.228717, 7.418e-25, 1<br>
13326       CAUTION: Gross error found at entry 77.<br> Found: 1.70126e-32 Expected 1.07666e-31
13327       Error: 5.32864<br> 7.62448, 7.54824, 193.774, 0.23303, 1.07666e-31, 1<br>
13328       CAUTION: Gross error found at entry 79.<br> Found: 1.3478e-15 Expected 4.21836e-15
13329       Error: 2.12982<br> 7.62448, 7.61686, 151.548, 0.457773, 4.21836e-15, 1<br>
13330       CAUTION: Gross error found at entry 80.<br> Found: 8.78487e-21 Expected 3.41238e-19
13331       Error: 37.8438<br> 7.62448, 7.61686, 194.119, 0.465826, 3.41238e-19, 1<br>
13332       CAUTION: Gross error found at entry 132.<br> Found: 3.85783e-23 Expected
13333       1.54142e-22 Error: 2.99555<br> 19.9593, 17.9634, 44.2068, 0.0698905, 1.54142e-22,
13334       1<br> CAUTION: Gross error found at entry 133.<br> Found: 8.6122e-39 Expected
13335       3.94361e-38 Error: 3.5791<br> 19.9593, 17.9634, 135.747, 0.0829178, 3.94361e-38,
13336       1<br> CAUTION: Gross error found at entry 134.<br> Found: 3.61781e-52 Expected
13337       3.98669e-48 Error: 11018.6<br> 19.9593, 17.9634, 191.501, 0.0864897, 3.98669e-48,
13338       1<br> CAUTION: Gross error found at entry 135.<br> Found: 2.07122e-15 Expected
13339       7.08614e-15 Error: 2.42124<br> 19.9593, 19.7597, 55.6996, 0.176444, 7.08614e-15,
13340       1<br> CAUTION: Gross error found at entry 136.<br> Found: 2.28223e-27 Expected
13341       2.16759e-25 Error: 93.977<br> 19.9593, 19.7597, 136.272, 0.20393, 2.16759e-25,
13342       1<br> CAUTION: Gross error found at entry 137.<br> Found: 6.4251e-34 Expected
13343       4.0064e-33 Error: 5.23554<br> 19.9593, 19.7597, 191.898, 0.213398, 4.0064e-33,
13344       1<br> CAUTION: Gross error found at entry 139.<br> Found: 2.1734e-14 Expected
13345       4.65637e-14 Error: 1.14243<br> 19.9593, 19.9394, 145.168, 0.410858, 4.65637e-14,
13346       1<br> CAUTION: Gross error found at entry 140.<br> Found: 2.18388e-19 Expected
13347       5.1677e-18 Error: 22.663<br> 19.9593, 19.9394, 192.978, 0.426523, 5.1677e-18,
13348       1<br> CAUTION: Gross error found at entry 192.<br> Found: 3.29537e-23 Expected
13349       8.29996e-23 Error: 1.51867<br> 22.4174, 20.1757, 34.773, 0.0661999, 8.29996e-23,
13350       1<br> CAUTION: Gross error found at entry 193.<br> Found: 7.86091e-39 Expected
13351       2.77686e-38 Error: 2.5325<br> 22.4174, 20.1757, 127.953, 0.0809614, 2.77686e-38,
13352       1<br> CAUTION: Gross error found at entry 194.<br> Found: 3.0161e-51 Expected
13353       4.5396e-48 Error: 1504.12<br> 22.4174, 20.1757, 183.147, 0.0848857, 4.5396e-48,
13354       1<br> CAUTION: Gross error found at entry 195.<br> Found: 3.08022e-14 Expected
13355       1.42713e-13 Error: 3.6332<br> 22.4174, 22.1932, 37.6764, 0.162145, 1.42713e-13,
13356       1<br> CAUTION: Gross error found at entry 196.<br> Found: 8.89935e-28 Expected
13357       2.56187e-25 Error: 286.871<br> 22.4174, 22.1932, 131.096, 0.199361, 2.56187e-25,
13358       1<br> CAUTION: Gross error found at entry 197.<br> Found: 9.34392e-34 Expected
13359       6.14831e-33 Error: 5.58001<br> 22.4174, 22.1932, 186.799, 0.209601, 6.14831e-33,
13360       1<br> CAUTION: Gross error found at entry 199.<br> Found: 2.79341e-13 Expected
13361       4.79277e-13 Error: 0.71574<br> 22.4174, 22.395, 131.148, 0.398015, 4.79277e-13,
13362       1<br> CAUTION: Gross error found at entry 200.<br> Found: 3.13989e-19 Expected
13363       7.01608e-18 Error: 21.345<br> 22.4174, 22.395, 191.433, 0.419933, 7.01608e-18,
13364       1<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
13365     </p>
13366 <h5>
13367 <a name="special_function_error_rates_rep.error_logs.h23"></a>
13368       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_chi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_chi">Error
13369       Output For non central chi squared CDF complement with compiler GNU C++ version
13370       7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, large
13371       parameters</a>
13372     </h5>
13373 <p>
13374       <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters"></a>CAUTION:
13375       Gross error found at entry 12.<br> Found: 0 Expected 1.17655e-12 Error: 5.28771e+295<br>
13376       101.815, 5236.73, 6406.25, 1, 1.17655e-12<br> CAUTION: Gross error found
13377       at entry 13.<br> Found: 0 Expected 1.79374e-44 Error: 8.06149e+263<br>
13378       101.815, 9735.22, 12788.2, 1, 1.79374e-44<br> CAUTION: Gross error found
13379       at entry 35.<br> Found: 2.58682e-14 Expected 1.84404e-61 Error: 1.4028e+47<br>
13380       107.623, 122.456, 920.317, 1, 1.84404e-61<br> CAUTION: Gross error found
13381       at entry 36.<br> Found: 0 Expected 2.30757e-102 Error: 1.03707e+206<br>
13382       107.623, 156.292, 1319.58, 1, 2.30757e-102<br> CAUTION: Gross error found
13383       at entry 52.<br> Found: 0 Expected 6.40952e-24 Error: 2.88059e+284<br>
13384       114.68, 417.884, 1065.13, 1, 6.40952e-24<br> CAUTION: Gross error found at
13385       entry 53.<br> Found: 0 Expected 1.02366e-98 Error: 4.60058e+209<br> 114.68,
13386       669.781, 2353.38, 1, 1.02366e-98<br> CAUTION: Gross error found at entry
13387       69.<br> Found: 0 Expected 6.55726e-39 Error: 2.94699e+269<br> 118.032,
13388       3168.71, 4930.11, 1, 6.55726e-39<br> CAUTION: Gross error found at entry
13389       85.<br> Found: 0 Expected 7.30688e-22 Error: 3.28388e+286<br> 163.004,
13390       9735.22, 11877.9, 1, 7.30688e-22<br> CAUTION: Gross error found at entry
13391       86.<br> Found: 0 Expected 1.17171e-111 Error: 5.26596e+196<br> 163.004,
13392       25344.1, 33159.2, 1, 1.17171e-111<br> CAUTION: Gross error found at entry
13393       108.<br> Found: 1.12355e-13 Expected 2.67349e-61 Error: 4.20255e+47<br>
13394       256.292, 122.456, 1136.25, 1, 2.67349e-61<br> CAUTION: Gross error found
13395       at entry 109.<br> Found: 1.16462e-13 Expected 8.30595e-116 Error: 1.40216e+102<br>
13396       256.292, 156.292, 1650.34, 1, 8.30595e-116<br> CAUTION: Gross error found
13397       at entry 124.<br> Found: 1.05804e-13 Expected 1.01672e-15 Error: 103.064<br>
13398       517.884, 417.884, 1403.65, 1, 1.01672e-15<br> CAUTION: Gross error found
13399       at entry 125.<br> Found: 2.00728e-13 Expected 3.50192e-56 Error: 5.73194e+42<br>
13400       517.884, 669.781, 2375.33, 1, 3.50192e-56<br> CAUTION: Gross error found
13401       at entry 141.<br> Found: 0 Expected 1.36924e-20 Error: 6.15368e+287<br>
13402       769.781, 3168.71, 5120.04, 1, 1.36924e-20<br> CAUTION: Gross error found
13403       at entry 142.<br> Found: 0 Expected 3.19215e-72 Error: 1.43463e+236<br>
13404       769.781, 5236.73, 9009.76, 1, 3.19215e-72<br> CAUTION: Gross error found
13405       at entry 157.<br> Found: 0 Expected 7.26231e-08 Error: 3.26385e+300<br>
13406       1223.88, 9735.22, 12055, 1, 7.26231e-08<br> CAUTION: Gross error found at
13407       entry 158.<br> Found: 0 Expected 4.5906e-56 Error: 2.06312e+252<br> 1223.88,
13408       25344.1, 31881.6, 1, 4.5906e-56<br> CAUTION: Gross error found at entry 194.<br>
13409       Found: 0 Expected 5.34714e-12 Error: 2.40313e+296<br> 9835.22, 122.456, 10953.4,
13410       1, 5.34714e-12<br> CAUTION: Gross error found at entry 195.<br> Found:
13411       0 Expected 4.84412e-40 Error: 2.17706e+268<br> 9835.22, 156.292, 11989.8,
13412       1, 4.84412e-40<br> CAUTION: Gross error found at entry 196.<br> Found:
13413       0 Expected 5.50199e-83 Error: 2.47272e+225<br> 9835.22, 417.884, 13329, 1,
13414       5.50199e-83<br> CAUTION: Gross error found at entry 197.<br> Found: 0 Expected
13415       1.28192e-205 Error: 5.76124e+102<br> 9835.22, 669.781, 15757.5, 1, 1.28192e-205<br>
13416       CAUTION: Gross error found at entry 211.<br> Found: 0 Expected 3.83272e-28
13417       Error: 1.72251e+280<br> 25444.1, 1123.88, 29224.8, 1, 3.83272e-28<br> CAUTION:
13418       Gross error found at entry 212.<br> Found: 0 Expected 1.69815e-101 Error:
13419       7.63188e+206<br> 25444.1, 3168.71, 34335.4, 1, 1.69815e-101<br> CAUTION:
13420       Gross error found at entry 213.<br> Found: 0 Expected 1.09245e-217 Error:
13421       4.90974e+90<br> 25444.1, 5236.73, 39885.1, 1, 1.09245e-217<br>
13422     </p>
13423 <h5>
13424 <a name="special_function_error_rates_rep.error_logs.h24"></a>
13425       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0">Error
13426       Output For non central chi squared CDF complement with compiler GNU C++ version
13427       7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, medium
13428       parameters</a>
13429     </h5>
13430 <p>
13431       <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters"></a>CAUTION:
13432       Gross error found at entry 36.<br> Found: 1.11022e-14 Expected 1.30043e-26
13433       Error: 8.53738e+11<br> 1.95191, 109.376, 445.313, 1, 1.30043e-26<br> CAUTION:
13434       Gross error found at entry 37.<br> Found: 0 Expected 1.45478e-39 Error: 6.53812e+268<br>
13435       1.95191, 109.444, 556.98, 1, 1.45478e-39<br> CAUTION: Gross error found at
13436       entry 54.<br> Found: 2.91989e-14 Expected 4.25949e-21 Error: 6.85501e+06<br>
13437       1.95191, 159.586, 484.613, 1, 4.25949e-21<br> CAUTION: Gross error found
13438       at entry 55.<br> Found: 0 Expected 1.33424e-37 Error: 5.99639e+270<br>
13439       1.95191, 159.621, 646.292, 1, 1.33424e-37<br> CAUTION: Gross error found
13440       at entry 56.<br> Found: 1.25455e-14 Expected 1.95903e-56 Error: 6.40393e+41<br>
13441       1.95191, 160.056, 810.04, 1, 1.95903e-56<br> CAUTION: Gross error found at
13442       entry 73.<br> Found: 0 Expected 4.34735e-25 Error: 1.9538e+283<br> 1.95191,
13443       193.539, 586.473, 1, 4.34735e-25<br> CAUTION: Gross error found at entry
13444       74.<br> Found: 0 Expected 4.66119e-45 Error: 2.09485e+263<br> 1.95191,
13445       193.774, 782.902, 1, 4.66119e-45<br> CAUTION: Gross error found at entry
13446       75.<br> Found: 4.77396e-15 Expected 8.92248e-68 Error: 5.35048e+52<br>
13447       1.95191, 194.119, 980.352, 1, 8.92248e-68<br> CAUTION: Gross error found
13448       at entry 111.<br> Found: 0 Expected 3.1064e-15 Error: 1.39609e+293<br>
13449       20.4105, 84.4175, 314.484, 1, 3.1064e-15<br> CAUTION: Gross error found at
13450       entry 112.<br> Found: 0 Expected 7.50903e-29 Error: 3.37473e+279<br> 20.4105,
13451       94.9517, 461.449, 1, 7.50903e-29<br> CAUTION: Gross error found at entry
13452       113.<br> Found: 3.77476e-15 Expected 1.74225e-43 Error: 2.1666e+28<br>
13453       20.4105, 97.0751, 587.428, 1, 1.74225e-43<br> CAUTION: Gross error found
13454       at entry 130.<br> Found: 8.88178e-16 Expected 4.13277e-23 Error: 2.14911e+07<br>
13455       20.4105, 151.548, 515.876, 1, 4.13277e-23<br> CAUTION: Gross error found
13456       at entry 131.<br> Found: 1.75415e-14 Expected 1.92146e-41 Error: 9.12928e+26<br>
13457       20.4105, 152.75, 692.642, 1, 1.92146e-41<br> CAUTION: Gross error found at
13458       entry 132.<br> Found: 1.38778e-14 Expected 7.09864e-64 Error: 1.95499e+49<br>
13459       20.4105, 158.441, 894.26, 1, 7.09864e-64<br> CAUTION: Gross error found at
13460       entry 149.<br> Found: 2.22045e-16 Expected 8.74501e-28 Error: 2.5391e+11<br>
13461       20.4105, 191.433, 635.532, 1, 8.74501e-28<br> CAUTION: Gross error found
13462       at entry 150.<br> Found: 0 Expected 6.94227e-50 Error: 3.12002e+258<br>
13463       20.4105, 191.501, 847.648, 1, 6.94227e-50<br> CAUTION: Gross error found
13464       at entry 151.<br> Found: 3.40838e-14 Expected 5.3889e-75 Error: 6.32482e+60<br>
13465       20.4105, 191.898, 1061.55, 1, 5.3889e-75<br> CAUTION: Gross error found at
13466       entry 206.<br> Found: 5.88418e-15 Expected 2.69136e-22 Error: 2.18632e+07<br>
13467       22.8625, 141.209, 492.215, 1, 2.69136e-22<br> CAUTION: Gross error found
13468       at entry 207.<br> Found: 3.60822e-14 Expected 1.64941e-40 Error: 2.18759e+26<br>
13469       22.8625, 145.168, 672.121, 1, 1.64941e-40<br> CAUTION: Gross error found
13470       at entry 208.<br> Found: 3.73035e-14 Expected 1.6094e-61 Error: 2.31784e+47<br>
13471       22.8625, 148.129, 854.96, 1, 1.6094e-61<br> CAUTION: Gross error found at
13472       entry 225.<br> Found: 0 Expected 3.73672e-27 Error: 1.67937e+281<br> 22.8625,
13473       182.675, 616.613, 1, 3.73672e-27<br> CAUTION: Gross error found at entry
13474       226.<br> Found: 0 Expected 8.85688e-49 Error: 3.98049e+259<br> 22.8625,
13475       183.147, 824.038, 1, 8.85688e-49<br> CAUTION: Gross error found at entry
13476       227.<br> Found: 0 Expected 2.29176e-74 Error: 1.02997e+234<br> 22.8625,
13477       186.799, 1048.31, 1, 2.29176e-74<br> CAUTION: Gross error found at entry
13478       282.<br> Found: 0 Expected 2.18831e-21 Error: 9.8348e+286<br> 23.3804,
13479       132.721, 468.305, 1, 2.18831e-21<br> CAUTION: Gross error found at entry
13480       283.<br> Found: 0 Expected 1.3071e-38 Error: 5.87439e+269<br> 23.3804,
13481       135.747, 636.51, 1, 1.3071e-38<br> CAUTION: Gross error found at entry 284.<br>
13482       Found: 1.84297e-14 Expected 8.27843e-58 Error: 2.22623e+43<br> 23.3804, 136.272,
13483       798.262, 1, 8.27843e-58<br> CAUTION: Gross error found at entry 301.<br>
13484       Found: 0 Expected 9.85282e-26 Error: 4.42808e+282<br> 23.3804, 169.826, 579.619,
13485       1, 9.85282e-26<br> CAUTION: Gross error found at entry 302.<br> Found:
13486       0 Expected 4.8094e-47 Error: 2.16145e+261<br> 23.3804, 174.486, 791.465,
13487       1, 4.8094e-47<br> CAUTION: Gross error found at entry 303.<br> Found: 1.11022e-16
13488       Expected 6.70476e-71 Error: 1.65587e+54<br> 23.3804, 175.686, 995.333, 1,
13489       6.70476e-71<br> CAUTION: Gross error found at entry 358.<br> Found: 0 Expected
13490       3.9702e-21 Error: 1.7843e+287<br> 26.2704, 126.472, 458.227, 1, 3.9702e-21<br>
13491       CAUTION: Gross error found at entry 359.<br> *** FURTHER CONTENT HAS BEEN
13492       TRUNCATED FOR BREVITY ***<br>
13493     </p>
13494 <h5>
13495 <a name="special_function_error_rates_rep.error_logs.h25"></a>
13496       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c">Error
13497       Output For non central t CDF complement with compiler GNU C++ version 7.1.0
13498       and library Rmath 3.2.3 and test data Non Central T</a>
13499     </h5>
13500 <p>
13501       <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T"></a>CAUTION:
13502       Gross error found at entry 56.<br> Found: 0.000186411 Expected 7.85192e-05
13503       Error: 1.37408<br> 61.6335, 46.2251, 68.8608, 0.999921, 7.85192e-05<br>
13504       CAUTION: Gross error found at entry 75.<br> Found: 0.00011439 Expected 5.05344e-05
13505       Error: 1.26361<br> 80.8418, 60.6313, 86.1278, 0.999949, 5.05344e-05<br>
13506       CAUTION: Gross error found at entry 93.<br> Found: 0.000655162 Expected 0.000423927
13507       Error: 0.545458<br> 100.733, 50.3663, 65.7619, 0.999576, 0.000423927<br>
13508       CAUTION: Gross error found at entry 112.<br> Found: 0.000518249 Expected
13509       0.00034473 Error: 0.503348<br> 127.953, 63.9764, 81.0824, 0.999655, 0.00034473<br>
13510     </p>
13511 <h5>
13512 <a name="special_function_error_rates_rep.error_logs.h26"></a>
13513       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0">Error
13514       Output For non central t CDF with compiler GNU C++ version 7.1.0 and library
13515       Rmath 3.2.3 and test data Non Central T</a>
13516     </h5>
13517 <p>
13518       <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T"></a>CAUTION:
13519       Gross error found at entry 74.<br> Found: 0.000830062 Expected 0.000522858
13520       Error: 0.587549<br> 79.7478, -39.8739, -53.8066, 0.000522858, 0.999477<br>
13521       CAUTION: Gross error found at entry 94.<br> Found: 7.69292e-05 Expected 3.54024e-05
13522       Error: 1.17299<br> 101.191, -75.8936, -104.104, 3.54024e-05, 0.999965<br>
13523       CAUTION: Gross error found at entry 113.<br> Found: 5.07713e-05 Expected
13524       2.4439e-05 Error: 1.07747<br> 128.792, -96.5942, -128.112, 2.4439e-05, 0.999976<br>
13525       CAUTION: Gross error found at entry 132.<br> Found: 4.08612e-05 Expected
13526       2.01542e-05 Error: 1.02743<br> 146.56, -109.92, -143.392, 2.01542e-05, 0.99998<br>
13527       CAUTION: Gross error found at entry 151.<br> Found: 3.55146e-05 Expected
13528       1.7803e-05 Error: 0.994869<br> 159.586, -119.689, -154.522, 1.7803e-05, 0.999982<br>
13529       CAUTION: Gross error found at entry 170.<br> Found: 3.03671e-05 Expected
13530       1.55023e-05 Error: 0.958873<br> 175.686, -131.765, -168.211, 1.55023e-05,
13531       0.999984<br> CAUTION: Gross error found at entry 189.<br> Found: 2.61339e-05
13532       Expected 1.3581e-05 Error: 0.924298<br> 192.978, -144.733, -182.834, 1.3581e-05,
13533       0.999986<br>
13534     </p>
13535 <h5>
13536 <a name="special_function_error_rates_rep.error_logs.h27"></a>
13537       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_">Error
13538       Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
13539       3.2.3 and test data Mathematica Data - Large orders and other bug cases</a>
13540     </h5>
13541 <p>
13542       <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases"></a>CAUTION:
13543       Found non-finite result, when a finite value was expected at entry 0<br>
13544       Found: -nan Expected 2.07309e+257 Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br>
13545       CAUTION: Gross error found at entry 0.<br> Found: -nan Expected 2.07309e+257
13546       Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br> CAUTION: Found non-finite
13547       result, when a finite value was expected at entry 1<br> Found: -nan Expected
13548       7.42912e+188 Error: 1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION:
13549       Gross error found at entry 1.<br> Found: -nan Expected 7.42912e+188 Error:
13550       1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION: Found non-finite result,
13551       when a finite value was expected at entry 2<br> Found: -nan Expected -4.81295e+247
13552       Error: 1.79769e+308<br> 166, 2, -4.81295e+247<br> CAUTION: Gross error
13553       found at entry 2.<br> Found: -nan Expected -4.81295e+247 Error: 1.79769e+308<br>
13554       166, 2, -4.81295e+247<br> CAUTION: Found non-finite result, when a finite
13555       value was expected at entry 3<br> Found: -nan Expected -1.88439e+218 Error:
13556       1.79769e+308<br> 166, 3, -1.88439e+218<br> CAUTION: Gross error found at
13557       entry 3.<br> Found: -nan Expected -1.88439e+218 Error: 1.79769e+308<br>
13558       166, 3, -1.88439e+218<br> CAUTION: Found non-finite result, when a finite
13559       value was expected at entry 4<br> Found: -nan Expected 7.53144e+74 Error:
13560       1.79769e+308<br> 171, 23, 7.53144e+74<br> CAUTION: Gross error found at
13561       entry 4.<br> Found: -nan Expected 7.53144e+74 Error: 1.79769e+308<br> 171,
13562       23, 7.53144e+74<br> CAUTION: Found non-finite result, when a finite value
13563       was expected at entry 5<br> Found: -nan Expected -6.52661e-66 Error: 1.79769e+308<br>
13564       168, 150, -6.52661e-66<br> CAUTION: Gross error found at entry 5.<br> Found:
13565       -nan Expected -6.52661e-66 Error: 1.79769e+308<br> 168, 150, -6.52661e-66<br>
13566       CAUTION: Found non-finite result, when a finite value was expected at entry
13567       6<br> Found: -nan Expected 9.2734e-88 Error: 1.79769e+308<br> 169, 202,
13568       9.2734e-88<br> CAUTION: Gross error found at entry 6.<br> Found: -nan Expected
13569       9.2734e-88 Error: 1.79769e+308<br> 169, 202, 9.2734e-88<br> Outside supported
13570       domain<br> 20, -9.5, -0.00103076<br> Outside supported domain<br> 21,
13571       -9.5, 4.28582e+26<br> Outside supported domain<br> 22, -9.5, -0.00419144<br>
13572       Outside supported domain<br> 23, -9.5, 8.6745e+29<br> Outside supported
13573       domain<br> 24, -9.5, -0.0204825<br> Outside supported domain<br> 25,
13574       -9.5, 2.08188e+33<br> Outside supported domain<br> 26, -9.5, -0.118403<br>
13575       Outside supported domain<br> 27, -9.5, 5.84592e+36<br> Outside supported
13576       domain<br> 28, -9.5, -0.798969<br> Outside supported domain<br> 29, -9.5,
13577       1.89875e+40<br> Outside supported domain<br> 30, -9.5, -6.22245<br>
13578     </p>
13579 <h5>
13580 <a name="special_function_error_rates_rep.error_logs.h28"></a>
13581       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0">Error
13582       Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
13583       3.2.3 and test data Mathematica Data - large negative arguments</a>
13584     </h5>
13585 <p>
13586       <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments"></a>Outside
13587       supported domain<br> 124, -1.5, 7.63705e+240<br> Outside supported domain<br>
13588       124, -2.5, 7.63705e+240<br> Outside supported domain<br> 124, -3.5, 7.63705e+240<br>
13589       Outside supported domain<br> 124, -4.5, 7.63705e+240<br> Outside supported
13590       domain<br> 124, -5.5, 7.63705e+240<br> Outside supported domain<br> 124,
13591       -6.5, 7.63705e+240<br> Outside supported domain<br> 124, -7.5, 7.63705e+240<br>
13592       Outside supported domain<br> 124, -8.5, 7.63705e+240<br> Outside supported
13593       domain<br> 124, -9.5, 7.63705e+240<br> Outside supported domain<br> 124,
13594       -10.5, 7.63705e+240<br> Outside supported domain<br> 124, -11.5, 7.63705e+240<br>
13595       Outside supported domain<br> 124, -12.5, 7.63705e+240<br> Outside supported
13596       domain<br> 124, -13.5, 7.63705e+240<br> Outside supported domain<br>
13597       124, -14.5, 7.63705e+240<br> Outside supported domain<br> 124, -15.5, 7.63705e+240<br>
13598       Outside supported domain<br> 124, -16.5, 7.63705e+240<br> Outside supported
13599       domain<br> 124, -17.5, 7.63705e+240<br> Outside supported domain<br>
13600       124, -18.5, 7.63705e+240<br> Outside supported domain<br> 124, -19.5, 7.63705e+240<br>
13601       Outside supported domain<br> 124, -20.5, 7.63705e+240<br> Outside supported
13602       domain<br> 124, -1.5, -7.63705e+240<br> Outside supported domain<br>
13603       124, -2.5, -7.63705e+240<br> Outside supported domain<br> 124, -3.5, -7.63705e+240<br>
13604       Outside supported domain<br> 124, -4.5, -7.63705e+240<br> Outside supported
13605       domain<br> 124, -5.5, -7.63705e+240<br> Outside supported domain<br>
13606       124, -6.5, -7.63705e+240<br> Outside supported domain<br> 124, -7.5, -7.63705e+240<br>
13607       Outside supported domain<br> 124, -8.5, -7.63705e+240<br> Outside supported
13608       domain<br> 124, -9.5, -7.63705e+240<br> Outside supported domain<br>
13609       124, -10.5, -7.63705e+240<br> Outside supported domain<br> 124, -11.5,
13610       -7.63705e+240<br> Outside supported domain<br> 124, -12.5, -7.63705e+240<br>
13611       Outside supported domain<br> 124, -13.5, -7.63705e+240<br> Outside supported
13612       domain<br> 124, -14.5, -7.63705e+240<br> Outside supported domain<br>
13613       124, -15.5, -7.63705e+240<br> Outside supported domain<br> 124, -16.5,
13614       -7.63705e+240<br> Outside supported domain<br> 124, -17.5, -7.63705e+240<br>
13615       Outside supported domain<br> 124, -18.5, -7.63705e+240<br> Outside supported
13616       domain<br> 124, -19.5, -7.63705e+240<br> Outside supported domain<br>
13617       124, -20.5, -7.63705e+240<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
13618       Outside supported domain<br> 2, -0.5, -0.828797<br> Outside supported domain<br>
13619       3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47425<br>
13620       Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br>
13621       6, -0.5, -43.4579<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br>
13622       Outside supported domain<br> 8, -0.5, -1059.96<br> Outside supported domain<br>
13623       9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -42108.9<br>
13624       Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported
13625       domain<br> 12, -0.5, -2.46448e+06<br> Outside supported domain<br> 13,
13626       -0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -1.9918e+08<br>
13627       Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported
13628       domain<br> 16, -0.5, -2.12394e+10<br> Outside supported domain<br> 17,
13629       -0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -2.88824e+12<br>
13630       Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported
13631       domain<br> 20, -0.5, -4.87773e+14<br> Outside supported domain<br> 21,
13632       -0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
13633       Outside supported domain<br> 2, -0.5, -0.828843<br> Outside supported domain<br>
13634       3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47791<br>
13635       Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br>
13636       6, -0.5, -44.0732<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br>
13637       Outside supported domain<br> 8, -0.5, -1237.15<br> Outside supported domain<br>
13638       9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -120071<br>
13639       Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported
13640       domain<br> 12, -0.5, -5.11131e+07<br> Outside supported domain<br> 13,
13641       -0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -4.1064e+10<br>
13642       Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported
13643       domain<br> 16, -0.5, -4.44822e+13<br> Outside supported domain<br> 17,
13644       -0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -6.08254e+16<br>
13645       Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported
13646       domain<br> 20, -0.5, -1.02182e+20<br> Outside supported domain<br> 21,
13647       -0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
13648       Outside supported domain<br> 2, -0.5, -0.828751<br> Outside supported domain<br>
13649       3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47059<br>
13650       Outside supported domain<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY
13651       ***<br>
13652     </p>
13653 <h5>
13654 <a name="special_function_error_rates_rep.error_logs.h29"></a>
13655       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1">Error
13656       Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
13657       3.2.3 and test data Mathematica Data - negative arguments</a>
13658     </h5>
13659 <p>
13660       <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments"></a>Outside
13661       supported domain<br> 1, -12.75, 19.6638<br> Outside supported domain<br>
13662       1, -12.25, 19.6608<br> Outside supported domain<br> 1, -11.75, 19.6576<br>
13663       Outside supported domain<br> 1, -11.25, 19.6542<br> Outside supported domain<br>
13664       1, -10.75, 19.6504<br> Outside supported domain<br> 1, -10.25, 19.6463<br>
13665       Outside supported domain<br> 1, -9.75, 19.6417<br> Outside supported domain<br>
13666       1, -9.25, 19.6367<br> Outside supported domain<br> 1, -8.75, 19.6312<br>
13667       Outside supported domain<br> 1, -8.25, 19.625<br> Outside supported domain<br>
13668       1, -7.75, 19.6181<br> Outside supported domain<br> 1, -7.25, 19.6104<br>
13669       Outside supported domain<br> 1, -6.75, 19.6015<br> Outside supported domain<br>
13670       1, -6.25, 19.5913<br> Outside supported domain<br> 1, -5.75, 19.5795<br>
13671       Outside supported domain<br> 1, -5.25, 19.5657<br> Outside supported domain<br>
13672       1, -4.75, 19.5493<br> Outside supported domain<br> 1, -4.25, 19.5294<br>
13673       Outside supported domain<br> 1, -3.75, 19.505<br> Outside supported domain<br>
13674       1, -3.25, 19.4741<br> Outside supported domain<br> 1, -2.75, 19.4339<br>
13675       Outside supported domain<br> 1, -2.25, 19.3794<br> Outside supported domain<br>
13676       1, -1.75, 19.3016<br> Outside supported domain<br> 1, -1.25, 19.1819<br>
13677       Outside supported domain<br> 1, -0.75, 18.9751<br> Outside supported domain<br>
13678       1, -0.25, 18.5419<br> Outside supported domain<br> 2, -12.75, -124.031<br>
13679       Outside supported domain<br> 2, -12.25, 124.019<br> Outside supported domain<br>
13680       2, -11.75, -124.032<br> Outside supported domain<br> 2, -11.25, 124.018<br>
13681       Outside supported domain<br> 2, -10.75, -124.033<br> Outside supported
13682       domain<br> 2, -10.25, 124.016<br> Outside supported domain<br> 2, -9.75,
13683       -124.035<br> Outside supported domain<br> 2, -9.25, 124.015<br> Outside
13684       supported domain<br> 2, -8.75, -124.037<br> Outside supported domain<br>
13685       2, -8.25, 124.012<br> Outside supported domain<br> 2, -7.75, -124.04<br>
13686       Outside supported domain<br> 2, -7.25, 124.009<br> Outside supported domain<br>
13687       2, -6.75, -124.044<br> Outside supported domain<br> 2, -6.25, 124.003<br>
13688       Outside supported domain<br> 2, -5.75, -124.051<br> Outside supported domain<br>
13689       2, -5.25, 123.995<br> Outside supported domain<br> 2, -4.75, -124.061<br>
13690       Outside supported domain<br> 2, -4.25, 123.981<br> Outside supported domain<br>
13691       2, -3.75, -124.08<br> Outside supported domain<br> 2, -3.25, 123.955<br>
13692       Outside supported domain<br> 2, -2.75, -124.118<br> Outside supported domain<br>
13693       2, -2.25, 123.897<br> Outside supported domain<br> 2, -1.75, -124.214<br>
13694       Outside supported domain<br> 2, -1.25, 123.721<br> Outside supported domain<br>
13695       2, -0.75, -124.587<br> Outside supported domain<br> 2, -0.25, 122.697<br>
13696       Outside supported domain<br> 3, -12.75, 1558.54<br> Outside supported domain<br>
13697       3, -12.25, 1558.54<br> Outside supported domain<br> 3, -11.75, 1558.54<br>
13698       Outside supported domain<br> 3, -11.25, 1558.54<br> Outside supported domain<br>
13699       3, -10.75, 1558.54<br> Outside supported domain<br> 3, -10.25, 1558.54<br>
13700       Outside supported domain<br> 3, -9.75, 1558.54<br> Outside supported domain<br>
13701       3, -9.25, 1558.54<br> Outside supported domain<br> 3, -8.75, 1558.54<br>
13702       Outside supported domain<br> 3, -8.25, 1558.54<br> Outside supported domain<br>
13703       3, -7.75, 1558.54<br> Outside supported domain<br> 3, -7.25, 1558.54<br>
13704       Outside supported domain<br> 3, -6.75, 1558.54<br> Outside supported domain<br>
13705       3, -6.25, 1558.54<br> Outside supported domain<br> 3, -5.75, 1558.54<br>
13706       Outside supported domain<br> 3, -5.25, 1558.54<br> Outside supported domain<br>
13707       3, -4.75, 1558.53<br> Outside supported domain<br> 3, -4.25, 1558.53<br>
13708       Outside supported domain<br> 3, -3.75, 1558.52<br> Outside supported domain<br>
13709       3, -3.25, 1558.51<br> Outside supported domain<br> 3, -2.75, 1558.49<br>
13710       Outside supported domain<br> 3, -2.25, 1558.46<br> Outside supported domain<br>
13711       3, -1.75, 1558.38<br> Outside supported domain<br> 3, -1.25, 1558.22<br>
13712       Outside supported domain<br> 3, -0.75, 1557.75<br> Outside supported domain<br>
13713       3, -0.25, 1555.76<br> Outside supported domain<br> 4, -12.75, -24481.6<br>
13714       Outside supported domain<br> 4, -12.25, 24481.6<br> Outside supported domain<br>
13715       4, -11.75, -24481.6<br> Outside supported domain<br> 4, -11.25, 24481.6<br>
13716       Outside supported domain<br> 4, -10.75, -24481.6<br> Outside supported
13717       domain<br> 4, -10.25, 24481.6<br> Outside supported domain<br> 4, -9.75,
13718       -24481.6<br> Outside supported domain<br> 4, -9.25, 24481.6<br> Outside
13719       supported domain<br> 4, -8.75, -24481.6<br> Outside supported domain<br>
13720       4, -8.25, 24481.6<br> Outside supported domain<br> 4, -7.75, -24481.6<br>
13721       Outside supported domain<br> 4, -7.25, 24481.6<br> Outside supported domain<br>
13722       4, -6.75, -24481.6<br> Outside supported domain<br> 4, -6.25, 24481.6<br>
13723       Outside supported domain<br> 4, -5.75, -24481.6<br> Outside supported domain<br>
13724       4, -5.25, 24481.6<br> Outside supported domain<br> *** FURTHER CONTENT
13725       HAS BEEN TRUNCATED FOR BREVITY ***<br>
13726     </p>
13727 <h5>
13728 <a name="special_function_error_rates_rep.error_logs.h30"></a>
13729       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2">Error
13730       Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
13731       3.2.3 and test data Mathematica Data - large arguments</a>
13732     </h5>
13733 <p>
13734       <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments"></a>CAUTION:
13735       Gross error found at entry 211.<br> Found: -0 Expected -8.44974e-268 Error:
13736       3.79751e+40<br> 30, 8.58993e+09, -8.44974e-268<br> CAUTION: Gross error
13737       found at entry 212.<br> Found: -0 Expected -7.86943e-277 Error: 3.5367e+31<br>
13738       30, 1.71799e+10, -7.86943e-277<br> CAUTION: Gross error found at entry 213.<br>
13739       Found: -0 Expected -7.32898e-286 Error: 3.29381e+22<br> 30, 3.43597e+10,
13740       -7.32898e-286<br> CAUTION: Gross error found at entry 214.<br> Found: -0
13741       Expected -6.82564e-295 Error: 3.0676e+13<br> 30, 6.87195e+10, -6.82564e-295<br>
13742       CAUTION: Gross error found at entry 215.<br> Found: -0 Expected -6.35687e-304
13743       Error: 28568.3<br> 30, 1.37439e+11, -6.35687e-304<br>
13744     </p>
13745 <h5>
13746 <a name="special_function_error_rates_rep.error_logs.h31"></a>
13747       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3">Error
13748       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
13749       2.1 and test data Bessel Iv: Mathworld Data (large values)</a>
13750     </h5>
13751 <p>
13752       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_"></a>domain
13753       error<br> -1, 3.72917e-155, 1.86459e-155<br> domain error<br> -1.125,
13754       3.72917e-155, -1.34964e+173<br>
13755     </p>
13756 <h5>
13757 <a name="special_function_error_rates_rep.error_logs.h32"></a>
13758       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4">Error
13759       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
13760       2.1 and test data Bessel Iv: Random Data</a>
13761     </h5>
13762 <p>
13763       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data"></a>domain
13764       error<br> -80.4919, 24.7501, 4.18698e+28<br> domain error<br> -80.4919,
13765       63.7722, 2.03248e+06<br> domain error<br> -74.6026, 24.7501, 7.20977e+23<br>
13766       domain error<br> -74.6026, 63.7722, 8.7549e+08<br> domain error<br> -72.9046,
13767       24.7501, 1.04535e+22<br> domain error<br> -72.9046, 63.7722, 4.7162e+09<br>
13768       domain error<br> -62.3236, 24.7501, 3.65147e+14<br> domain error<br>
13769       -62.3236, 63.7722, 8.56683e+13<br> domain error<br> -55.7932, 24.7501,
13770       -7.70364e+09<br> domain error<br> -55.7932, 63.7722, 1.95969e+16<br>
13771       domain error<br> -44.3004, 9.50706, 2.93478e+22<br> domain error<br>
13772       -44.3004, 24.7501, 640.568<br> domain error<br> -44.3004, 63.7722, 8.05557e+19<br>
13773       domain error<br> -38.3666, 5.11399, 2.89105e+27<br> domain error<br>
13774       -38.3666, 9.50706, 8.80632e+16<br> domain error<br> -38.3666, 24.7501,
13775       0.389004<br> domain error<br> -38.3666, 63.7722, 3.06303e+21<br> underflow<br>
13776       81.1584, 0.00177219, 0<br> underflow<br> 81.1584, 0.00221773, 0<br> underflow<br>
13777       81.1584, 0.0074445, 6.08857e-319<br> underflow<br> 82.6752, 0.00177219,
13778       0<br> underflow<br> 82.6752, 0.00221773, 0<br> underflow<br> 82.6752,
13779       0.0074445, 0<br> underflow<br> 91.5014, 0.00177219, 0<br> underflow<br>
13780       91.5014, 0.00221773, 0<br> underflow<br> 91.5014, 0.0074445, 0<br> underflow<br>
13781       91.5014, 0.014336, 0<br> underflow<br> 91.5014, 0.0176092, 0<br> underflow<br>
13782       92.9777, 0.00177219, 0<br> underflow<br> 92.9777, 0.00221773, 0<br> underflow<br>
13783       92.9777, 0.0074445, 0<br> underflow<br> 92.9777, 0.014336, 0<br> underflow<br>
13784       92.9777, 0.0176092, 0<br> underflow<br> 93.539, 0.00177219, 0<br> underflow<br>
13785       93.539, 0.00221773, 0<br> underflow<br> 93.539, 0.0074445, 0<br> underflow<br>
13786       93.539, 0.014336, 0<br> underflow<br> 93.539, 0.0176092, 0<br> underflow<br>
13787       93.7736, 0.00177219, 0<br> underflow<br> 93.7736, 0.00221773, 0<br> underflow<br>
13788       93.7736, 0.0074445, 0<br> underflow<br> 93.7736, 0.014336, 0<br> underflow<br>
13789       93.7736, 0.0176092, 0<br> underflow<br> 98.5763, 0.00177219, 0<br> underflow<br>
13790       98.5763, 0.00221773, 0<br> underflow<br> 98.5763, 0.0074445, 0<br> underflow<br>
13791       98.5763, 0.014336, 0<br> underflow<br> 98.5763, 0.0176092, 0<br> underflow<br>
13792       99.2923, 0.00177219, 0<br> underflow<br> 99.2923, 0.00221773, 0<br> underflow<br>
13793       99.2923, 0.0074445, 0<br> underflow<br> 99.2923, 0.014336, 0<br> underflow<br>
13794       99.2923, 0.0176092, 0<br>
13795     </p>
13796 <h5>
13797 <a name="special_function_error_rates_rep.error_logs.h33"></a>
13798       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5">Error
13799       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
13800       2.1 and test data Bessel In: Random Data</a>
13801     </h5>
13802 <p>
13803       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data"></a>underflow<br>
13804       70, 0.00177219, 1.75887e-314<br> underflow<br> 73, 0.00177219, 0<br>
13805       underflow<br> 73, 0.00221773, 4.24896e-322<br> underflow<br> 76, 0.00177219,
13806       0<br> underflow<br> 76, 0.00221773, 0<br> underflow<br> 79, 0.00177219,
13807       0<br> underflow<br> 79, 0.00221773, 0<br> underflow<br> 79, 0.0074445,
13808       1.38676e-309<br> underflow<br> 82, 0.00177219, 0<br> underflow<br>
13809       82, 0.00221773, 0<br> underflow<br> 82, 0.0074445, 1.33398e-322<br> underflow<br>
13810       85, 0.00177219, 0<br> underflow<br> 85, 0.00221773, 0<br> underflow<br>
13811       85, 0.0074445, 0<br> underflow<br> 85, 0.014336, 1.81568e-311<br> underflow<br>
13812       88, 0.00177219, 0<br> underflow<br> 88, 0.00221773, 0<br> underflow<br>
13813       88, 0.0074445, 0<br> underflow<br> 88, 0.014336, 9.88131e-324<br> underflow<br>
13814       88, 0.0176092, 7.34647e-316<br>
13815     </p>
13816 <h5>
13817 <a name="special_function_error_rates_rep.error_logs.h34"></a>
13818       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6">Error
13819       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
13820       2.1 and test data Bessel Iv: Mathworld Data</a>
13821     </h5>
13822 <p>
13823       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data"></a>domain
13824       error<br> -4.99902, 2.125, 0.0267921<br> domain error<br> -5.5, 10, 597.578<br>
13825       domain error<br> -5.5, 100, 9.22363e+41<br> domain error<br> -10.0003,
13826       0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 50, 1.07153e+20<br>
13827       domain error<br> -141.4, 100, 2066.28<br>
13828     </p>
13829 <h5>
13830 <a name="special_function_error_rates_rep.error_logs.h35"></a>
13831       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2">Error
13832       Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
13833       and library GSL 2.1 and test data Bessel In: Mathworld Data (Integer Version)</a>
13834     </h5>
13835 <p>
13836       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_"></a>underflow<br>
13837       10, 1e-100, 0<br>
13838     </p>
13839 <h5>
13840 <a name="special_function_error_rates_rep.error_logs.h36"></a>
13841       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7">Error
13842       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
13843       2.1 and test data Bessel In: Mathworld Data</a>
13844     </h5>
13845 <p>
13846       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data"></a>domain
13847       error<br> -2, 0, 0<br> domain error<br> -5, 100, 9.47009e+41<br> domain
13848       error<br> -5, -1, -0.000271463<br> domain error<br> 10, -5, 0.00458004<br>
13849       domain error<br> -100, -200, 4.35275e+74<br> underflow<br> 10, 1e-100,
13850       0<br>
13851     </p>
13852 <h5>
13853 <a name="special_function_error_rates_rep.error_logs.h37"></a>
13854       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8">Error
13855       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
13856       2.1 and test data Bessel I1: Mathworld Data</a>
13857     </h5>
13858 <p>
13859       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data"></a>domain
13860       error<br> 1, -2, -1.59064<br> domain error<br> 1, -8, -399.873<br>
13861       domain error<br> 1, -10, -2670.99<br>
13862     </p>
13863 <h5>
13864 <a name="special_function_error_rates_rep.error_logs.h38"></a>
13865       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9">Error
13866       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
13867       2.1 and test data Bessel I0: Mathworld Data</a>
13868     </h5>
13869 <p>
13870       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data"></a>domain
13871       error<br> 0, -2, 2.27959<br> domain error<br> 0, -7, 168.594<br> domain
13872       error<br> 0, -1, 1.26607<br>
13873     </p>
13874 <h5>
13875 <a name="special_function_error_rates_rep.error_logs.h39"></a>
13876       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0">Error
13877       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
13878       and test data Bessel Iv: Mathworld Data (large values)</a>
13879     </h5>
13880 <p>
13881       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_"></a>Bad
13882       argument in __cyl_bessel_i.<br> -1, 3.72917e-155, 1.86459e-155<br> Bad
13883       argument in __cyl_bessel_i.<br> -1.125, 3.72917e-155, -1.34964e+173<br>
13884     </p>
13885 <h5>
13886 <a name="special_function_error_rates_rep.error_logs.h40"></a>
13887       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1">Error
13888       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
13889       and test data Bessel Iv: Random Data</a>
13890     </h5>
13891 <p>
13892       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data"></a>Bad
13893       argument in __cyl_bessel_i.<br> -80.4919, 24.7501, 4.18698e+28<br> Bad
13894       argument in __cyl_bessel_i.<br> -80.4919, 63.7722, 2.03248e+06<br> Bad
13895       argument in __cyl_bessel_i.<br> -74.6026, 24.7501, 7.20977e+23<br> Bad
13896       argument in __cyl_bessel_i.<br> -74.6026, 63.7722, 8.7549e+08<br> Bad argument
13897       in __cyl_bessel_i.<br> -72.9046, 24.7501, 1.04535e+22<br> Bad argument
13898       in __cyl_bessel_i.<br> -72.9046, 63.7722, 4.7162e+09<br> Bad argument in
13899       __cyl_bessel_i.<br> -62.3236, 24.7501, 3.65147e+14<br> Bad argument in
13900       __cyl_bessel_i.<br> -62.3236, 63.7722, 8.56683e+13<br> Bad argument in
13901       __cyl_bessel_i.<br> -55.7932, 24.7501, -7.70364e+09<br> Bad argument in
13902       __cyl_bessel_i.<br> -55.7932, 63.7722, 1.95969e+16<br> Bad argument in
13903       __cyl_bessel_i.<br> -44.3004, 9.50706, 2.93478e+22<br> Bad argument in
13904       __cyl_bessel_i.<br> -44.3004, 24.7501, 640.568<br> Bad argument in __cyl_bessel_i.<br>
13905       -44.3004, 63.7722, 8.05557e+19<br> Bad argument in __cyl_bessel_i.<br>
13906       -38.3666, 5.11399, 2.89105e+27<br> Bad argument in __cyl_bessel_i.<br>
13907       -38.3666, 9.50706, 8.80632e+16<br> Bad argument in __cyl_bessel_i.<br>
13908       -38.3666, 24.7501, 0.389004<br> Bad argument in __cyl_bessel_i.<br> -38.3666,
13909       63.7722, 3.06303e+21<br>
13910     </p>
13911 <h5>
13912 <a name="special_function_error_rates_rep.error_logs.h41"></a>
13913       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2">Error
13914       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
13915       and test data Bessel Iv: Mathworld Data</a>
13916     </h5>
13917 <p>
13918       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data"></a>Bad
13919       argument in __cyl_bessel_i.<br> -4.99902, 2.125, 0.0267921<br> Bad argument
13920       in __cyl_bessel_i.<br> -5.5, 10, 597.578<br> Bad argument in __cyl_bessel_i.<br>
13921       -5.5, 100, 9.22363e+41<br> Bad argument in __cyl_bessel_i.<br> -10.0003,
13922       0.000976562, 1.41474e+35<br> Bad argument in __cyl_bessel_i.<br> -10.0003,
13923       50, 1.07153e+20<br> Bad argument in __cyl_bessel_i.<br> -141.4, 100, 2066.28<br>
13924     </p>
13925 <h5>
13926 <a name="special_function_error_rates_rep.error_logs.h42"></a>
13927       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3">Error
13928       Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
13929       and library &lt;cmath&gt; and test data Bessel In: Mathworld Data (Integer
13930       Version)</a>
13931     </h5>
13932 <p>
13933       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_"></a>Bad
13934       argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br>
13935       -5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br>
13936       Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument
13937       in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br>
13938     </p>
13939 <h5>
13940 <a name="special_function_error_rates_rep.error_logs.h43"></a>
13941       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4">Error
13942       Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
13943       and library &lt;cmath&gt; and test data Bessel I1: Mathworld Data (Integer
13944       Version)</a>
13945     </h5>
13946 <p>
13947       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_"></a>Bad
13948       argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br>
13949       1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br>
13950     </p>
13951 <h5>
13952 <a name="special_function_error_rates_rep.error_logs.h44"></a>
13953       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5">Error
13954       Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
13955       and library &lt;cmath&gt; and test data Bessel I0: Mathworld Data (Integer
13956       Version)</a>
13957     </h5>
13958 <p>
13959       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_"></a>Bad
13960       argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br>
13961       0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br>
13962     </p>
13963 <h5>
13964 <a name="special_function_error_rates_rep.error_logs.h45"></a>
13965       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3">Error
13966       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
13967       and test data Bessel In: Mathworld Data</a>
13968     </h5>
13969 <p>
13970       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data"></a>Bad
13971       argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br>
13972       -5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br>
13973       Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument
13974       in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br>
13975     </p>
13976 <h5>
13977 <a name="special_function_error_rates_rep.error_logs.h46"></a>
13978       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4">Error
13979       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
13980       and test data Bessel I1: Mathworld Data</a>
13981     </h5>
13982 <p>
13983       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data"></a>Bad
13984       argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br>
13985       1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br>
13986     </p>
13987 <h5>
13988 <a name="special_function_error_rates_rep.error_logs.h47"></a>
13989       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5">Error
13990       Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
13991       and test data Bessel I0: Mathworld Data</a>
13992     </h5>
13993 <p>
13994       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data"></a>Bad
13995       argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br>
13996       0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br>
13997     </p>
13998 <h5>
13999 <a name="special_function_error_rates_rep.error_logs.h48"></a>
14000       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3">Error
14001       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
14002       2.1 and test data Bessel J: Random Data</a>
14003     </h5>
14004 <p>
14005       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data"></a>underflow<br>
14006       63.8868, 5.5381e-05, 0<br> underflow<br> 63.8868, 6.9304e-05, 0<br> underflow<br>
14007       63.8868, 0.000232641, 0<br> underflow<br> 63.8868, 0.000448, 8.39912e-323<br>
14008       underflow<br> 63.8868, 0.000550287, 4.32897e-317<br>
14009     </p>
14010 <h5>
14011 <a name="special_function_error_rates_rep.error_logs.h49"></a>
14012       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4">Error
14013       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
14014       2.1 and test data Bessel J: Mathworld Data (large values)</a>
14015     </h5>
14016 <p>
14017       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_"></a>domain
14018       error<br> -0.5, 1.2459e-206, 7.14823e+102<br> domain error<br> -256,
14019       8, 0<br> domain error<br> -2.5, 4, -0.0145679<br>
14020     </p>
14021 <h5>
14022 <a name="special_function_error_rates_rep.error_logs.h50"></a>
14023       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5">Error
14024       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
14025       2.1 and test data Bessel J: Mathworld Data</a>
14026     </h5>
14027 <p>
14028       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data"></a>domain
14029       error<br> -5.5, 3.1416, -2.5582<br> domain error<br> -5.5, 10000, 0.00244984<br>
14030       domain error<br> -5.5, 10000, 0.00244984<br> domain error<br> -5.5, 1e+06,
14031       0.000279243<br> domain error<br> -0.5, 101, 0.0708185<br> domain error<br>
14032       -10.0003, 0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 15, -0.0902239<br>
14033       domain error<br> -10.0003, 100, -0.0547614<br> domain error<br> -10.0003,
14034       20000, -0.00556869<br> domain error<br> -8.5, 12.5664, -0.257087<br>
14035     </p>
14036 <h5>
14037 <a name="special_function_error_rates_rep.error_logs.h51"></a>
14038       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3">Error
14039       Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
14040       and library GSL 2.1 and test data Bessel JN: Mathworld Data (Integer Version)</a>
14041     </h5>
14042 <p>
14043       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_"></a>underflow<br>
14044       10, 1e-100, 0<br>
14045     </p>
14046 <h5>
14047 <a name="special_function_error_rates_rep.error_logs.h52"></a>
14048       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6">Error
14049       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
14050       2.1 and test data Bessel JN: Mathworld Data</a>
14051     </h5>
14052 <p>
14053       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data"></a>domain
14054       error<br> -1, 1.25, -0.510623<br> domain error<br> -2, 0, 0<br> domain
14055       error<br> 5, -10, 0.234062<br> domain error<br> -5, 1e+06, 0.000725964<br>
14056       domain error<br> -5, -1, 0.000249758<br> domain error<br> 10, -10, 0.207486<br>
14057       domain error<br> 10, -5, 0.0014678<br> domain error<br> -10, 1e+06, -0.000331079<br>
14058       underflow<br> 10, 1e-100, 0<br>
14059     </p>
14060 <h5>
14061 <a name="special_function_error_rates_rep.error_logs.h53"></a>
14062       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7">Error
14063       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
14064       2.1 and test data Bessel J1: Mathworld Data</a>
14065     </h5>
14066 <p>
14067       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data"></a>domain
14068       error<br> 1, -2, -0.576725<br> domain error<br> 1, -8, -0.234636<br>
14069       domain error<br> 1, -10, -0.0434727<br>
14070     </p>
14071 <h5>
14072 <a name="special_function_error_rates_rep.error_logs.h54"></a>
14073       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8">Error
14074       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
14075       2.1 and test data Bessel J0: Mathworld Data</a>
14076     </h5>
14077 <p>
14078       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data"></a>domain
14079       error<br> 0, -2, 0.223891<br> domain error<br> 0, -8, 0.171651<br>
14080       domain error<br> 0, -10, -0.245936<br>
14081     </p>
14082 <h5>
14083 <a name="special_function_error_rates_rep.error_logs.h55"></a>
14084       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9">Error
14085       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14086       and test data Bessel J: Mathworld Data (large values)</a>
14087     </h5>
14088 <p>
14089       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_"></a>Bad
14090       argument in __cyl_bessel_j.<br> -0.5, 1.2459e-206, 7.14823e+102<br> Bad
14091       argument in __cyl_bessel_j.<br> -256, 8, 1.46866e-353<br> Bad argument
14092       in __cyl_bessel_j.<br> -2.5, 4, -0.0145679<br>
14093     </p>
14094 <h5>
14095 <a name="special_function_error_rates_rep.error_logs.h56"></a>
14096       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0">Error
14097       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14098       and test data Bessel J: Mathworld Data</a>
14099     </h5>
14100 <p>
14101       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data"></a>Bad
14102       argument in __cyl_bessel_j.<br> -5.5, 3.1416, -2.5582<br> Bad argument
14103       in __cyl_bessel_j.<br> -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br>
14104       -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br> -5.5, 1e+06,
14105       0.000279243<br> Bad argument in __cyl_bessel_j.<br> -0.5, 101, 0.0708185<br>
14106       Bad argument in __cyl_bessel_j.<br> -10.0003, 0.000976562, 1.41474e+35<br>
14107       Bad argument in __cyl_bessel_j.<br> -10.0003, 15, -0.0902239<br> Bad argument
14108       in __cyl_bessel_j.<br> -10.0003, 100, -0.0547614<br> Bad argument in __cyl_bessel_j.<br>
14109       -10.0003, 20000, -0.00556869<br> Bad argument in __cyl_bessel_j.<br> -8.5,
14110       12.5664, -0.257087<br>
14111     </p>
14112 <h5>
14113 <a name="special_function_error_rates_rep.error_logs.h57"></a>
14114       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4">Error
14115       Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
14116       and library &lt;cmath&gt; and test data Bessel JN: Mathworld Data (Integer
14117       Version)</a>
14118     </h5>
14119 <p>
14120       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_"></a>Bad
14121       argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in
14122       __cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br>
14123       5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br>
14124       Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument
14125       in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br>
14126       10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br>
14127       CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318
14128       Error: 2.305<br> 1000, 100000, 0.00128318<br>
14129     </p>
14130 <h5>
14131 <a name="special_function_error_rates_rep.error_logs.h58"></a>
14132       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5">Error
14133       Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
14134       and library &lt;cmath&gt; and test data Bessel J1: Mathworld Data (Integer
14135       Version)</a>
14136     </h5>
14137 <p>
14138       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_"></a>Bad
14139       argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br>
14140       1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br>
14141     </p>
14142 <h5>
14143 <a name="special_function_error_rates_rep.error_logs.h59"></a>
14144       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6">Error
14145       Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
14146       and library &lt;cmath&gt; and test data Bessel J0: Mathworld Data (Integer
14147       Version)</a>
14148     </h5>
14149 <p>
14150       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_"></a>Bad
14151       argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br>
14152       0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br>
14153     </p>
14154 <h5>
14155 <a name="special_function_error_rates_rep.error_logs.h60"></a>
14156       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1">Error
14157       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14158       and test data Bessel JN: Mathworld Data</a>
14159     </h5>
14160 <p>
14161       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data"></a>Bad
14162       argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in
14163       __cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br>
14164       5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br>
14165       Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument
14166       in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br>
14167       10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br>
14168       CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318
14169       Error: 2.305<br> 1000, 100000, 0.00128318<br>
14170     </p>
14171 <h5>
14172 <a name="special_function_error_rates_rep.error_logs.h61"></a>
14173       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2">Error
14174       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14175       and test data Bessel J1: Mathworld Data</a>
14176     </h5>
14177 <p>
14178       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data"></a>Bad
14179       argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br>
14180       1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br>
14181     </p>
14182 <h5>
14183 <a name="special_function_error_rates_rep.error_logs.h62"></a>
14184       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3">Error
14185       Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14186       and test data Bessel J0: Mathworld Data</a>
14187     </h5>
14188 <p>
14189       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data"></a>Bad
14190       argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br>
14191       0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br>
14192     </p>
14193 <h5>
14194 <a name="special_function_error_rates_rep.error_logs.h63"></a>
14195       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi">Error
14196       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
14197       2.1 and test data Bessel Kv: Random Data</a>
14198     </h5>
14199 <p>
14200       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data"></a>domain
14201       error<br> -80.4919, 24.7501, 6.57902e+28<br> domain error<br> -80.4919,
14202       63.7722, 2.39552e-09<br> domain error<br> -80.4919, 125.28, 3.06904e-45<br>
14203       domain error<br> -80.4919, 255.547, 2.30343e-107<br> domain error<br>
14204       -80.4919, 503.011, 1.20315e-217<br> domain error<br> -80.4919, 1007.46,
14205       0<br> domain error<br> -80.4919, 1185.4, 0<br> domain error<br> -80.4919,
14206       3534.52, 0<br> domain error<br> -80.4919, 8071.55, 0<br> domain error<br>
14207       -80.4919, 16229.2, 0<br> domain error<br> -80.4919, 32066.2, 0<br> domain
14208       error<br> -80.4919, 36367.9, 0<br> domain error<br> -74.6026, 24.7501,
14209       1.19405e+24<br> domain error<br> -74.6026, 63.7722, 5.81897e-12<br> domain
14210       error<br> -74.6026, 125.28, 9.89214e-47<br> domain error<br> -74.6026,
14211       255.547, 3.9726e-108<br> domain error<br> -74.6026, 503.011, 4.87462e-218<br>
14212       domain error<br> -74.6026, 1007.46, 0<br> domain error<br> -74.6026,
14213       1185.4, 0<br> domain error<br> -74.6026, 3534.52, 0<br> domain error<br>
14214       -74.6026, 8071.55, 0<br> domain error<br> -74.6026, 16229.2, 0<br> domain
14215       error<br> -74.6026, 32066.2, 0<br> domain error<br> -74.6026, 36367.9,
14216       0<br> domain error<br> -72.9046, 24.7501, 5.5618e+22<br> domain error<br>
14217       -72.9046, 63.7722, 1.09452e-12<br> domain error<br> -72.9046, 125.28, 3.8393e-47<br>
14218       domain error<br> -72.9046, 255.547, 2.45173e-108<br> domain error<br>
14219       -72.9046, 503.011, 3.80454e-218<br> domain error<br> -72.9046, 1007.46,
14220       0<br> domain error<br> -72.9046, 1185.4, 0<br> domain error<br> -72.9046,
14221       3534.52, 0<br> domain error<br> -72.9046, 8071.55, 0<br> domain error<br>
14222       -72.9046, 16229.2, 0<br> domain error<br> -72.9046, 32066.2, 0<br> domain
14223       error<br> -72.9046, 36367.9, 0<br> domain error<br> -62.3236, 24.7501,
14224       6.74518e+14<br> domain error<br> -62.3236, 63.7722, 6.54531e-17<br> domain
14225       error<br> -62.3236, 125.28, 1.65653e-49<br> domain error<br> -62.3236,
14226       255.547, 1.54767e-109<br> domain error<br> -62.3236, 503.011, 9.22721e-219<br>
14227       domain error<br> -62.3236, 1007.46, 0<br> domain error<br> -62.3236,
14228       1185.4, 0<br> domain error<br> -62.3236, 3534.52, 0<br> domain error<br>
14229       -62.3236, 8071.55, 0<br> domain error<br> -62.3236, 16229.2, 0<br> domain
14230       error<br> -62.3236, 32066.2, 0<br> domain error<br> -62.3236, 36367.9,
14231       0<br> domain error<br> -55.7932, 24.7501, 2.00028e+10<br> domain error<br>
14232       -55.7932, 63.7722, 3.01107e-19<br> domain error<br> -55.7932, 125.28, 8.54693e-51<br>
14233       domain error<br> -55.7932, 255.547, 3.47666e-110<br> domain error<br>
14234       -55.7932, 503.011, 4.29705e-219<br> domain error<br> -55.7932, 1007.46,
14235       0<br> domain error<br> -55.7932, 1185.4, 0<br> domain error<br> -55.7932,
14236       3534.52, 0<br> domain error<br> -55.7932, 8071.55, 0<br> domain error<br>
14237       -55.7932, 16229.2, 0<br> domain error<br> -55.7932, 32066.2, 0<br> domain
14238       error<br> -55.7932, 36367.9, 0<br> domain error<br> -44.3004, 9.50706,
14239       5.6936e+22<br> domain error<br> -44.3004, 24.7501, 1242.73<br> domain
14240       error<br> -44.3004, 63.7722, 7.99341e-23<br> domain error<br> -44.3004,
14241       125.28, 9.88149e-53<br> domain error<br> -44.3004, 255.547, 3.73007e-111<br>
14242       domain error<br> -44.3004, 503.011, 1.37367e-219<br> domain error<br>
14243       -44.3004, 1007.46, 0<br> domain error<br> -44.3004, 1185.4, 0<br> domain
14244       error<br> -44.3004, 3534.52, 0<br> domain error<br> -44.3004, 8071.55,
14245       0<br> domain error<br> -44.3004, 16229.2, 0<br> domain error<br> -44.3004,
14246       32066.2, 0<br> domain error<br> -44.3004, 36367.9, 0<br> domain error<br>
14247       -38.3666, 5.11399, 4.97154e+27<br> domain error<br> -38.3666, 9.50706,
14248       1.51436e+17<br> domain error<br> -38.3666, 24.7501, 0.639495<br> domain
14249       error<br> -38.3666, 63.7722, 2.19334e-24<br> domain error<br> -38.3666,
14250       125.28, 1.45351e-53<br> domain error<br> -38.3666, 255.547, 1.43713e-111<br>
14251       domain error<br> -38.3666, 503.011, 8.44445e-220<br> domain error<br>
14252       -38.3666, 1007.46, 0<br> domain error<br> -38.3666, 1185.4, 0<br> domain
14253       error<br> -38.3666, 3534.52, 0<br> domain error<br> -38.3666, 8071.55,
14254       0<br> domain error<br> -38.3666, 16229.2, 0<br> domain error<br> -38.3666,
14255       32066.2, 0<br> domain error<br> -38.3666, 36367.9, 0<br> underflow<br>
14256       9.3763, 1007.46, 0<br> underflow<br> 9.3763, 1185.4, 0<br> underflow<br>
14257       9.3763, 3534.52, 0<br> underflow<br> 9.3763, 8071.55, 0<br> underflow<br>
14258       9.3763, 16229.2, 0<br> underflow<br> 9.3763, 32066.2, 0<br> underflow<br>
14259       9.3763, 36367.9, 0<br> underflow<br> 9.44412, 1007.46, 0<br> underflow<br>
14260       9.44412, 1185.4, 0<br> underflow<br> 9.44412, 3534.52, 0<br> underflow<br>
14261       9.44412, 8071.55, 0<br> underflow<br> 9.44412, 16229.2, 0<br> underflow<br>
14262       9.44412, 32066.2, 0<br> underflow<br> 9.44412, 36367.9, 0<br> underflow<br>
14263       26.4719, 1007.46, 0<br> underflow<br> 26.4719, 1185.4, 0<br> underflow<br>
14264       26.4719, 3534.52, 0<br> underflow<br> 26.4719, 8071.55, 0<br> underflow<br>
14265       26.4719, 16229.2, 0<br> underflow<br> 26.4719, 32066.2, 0<br> underflow<br>
14266       26.4719, 36367.9, 0<br> underflow<br> 62.9447, 1007.46, 0<br> underflow<br>
14267       62.9447, 1185.4, 0<br> underflow<br> 62.9447, 3534.52, 0<br> underflow<br>
14268       62.9447, 8071.55, 0<br> underflow<br> 62.9447, 16229.2, 0<br> underflow<br>
14269       *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
14270     </p>
14271 <h5>
14272 <a name="special_function_error_rates_rep.error_logs.h64"></a>
14273       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0">Error
14274       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
14275       2.1 and test data Bessel Kn: Random Data</a>
14276     </h5>
14277 <p>
14278       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data"></a>underflow<br>
14279       0, 1007.46, 0<br> underflow<br> 0, 1185.4, 0<br> underflow<br> 0, 3534.52,
14280       0<br> underflow<br> 0, 8071.55, 0<br> underflow<br> 0, 16229.2, 0<br>
14281       underflow<br> 0, 32066.2, 0<br> underflow<br> 0, 36367.9, 0<br> underflow<br>
14282       1, 1007.46, 0<br> underflow<br> 1, 1185.4, 0<br> underflow<br> 1, 3534.52,
14283       0<br> underflow<br> 1, 8071.55, 0<br> underflow<br> 1, 16229.2, 0<br>
14284       underflow<br> 1, 32066.2, 0<br> underflow<br> 1, 36367.9, 0<br> underflow<br>
14285       4, 1007.46, 0<br> underflow<br> 4, 1185.4, 0<br> underflow<br> 4, 3534.52,
14286       0<br> underflow<br> 4, 8071.55, 0<br> underflow<br> 4, 16229.2, 0<br>
14287       underflow<br> 4, 32066.2, 0<br> underflow<br> 4, 36367.9, 0<br> underflow<br>
14288       7, 1007.46, 0<br> underflow<br> 7, 1185.4, 0<br> underflow<br> 7, 3534.52,
14289       0<br> underflow<br> 7, 8071.55, 0<br> underflow<br> 7, 16229.2, 0<br>
14290       underflow<br> 7, 32066.2, 0<br> underflow<br> 7, 36367.9, 0<br> underflow<br>
14291       10, 1007.46, 0<br> underflow<br> 10, 1185.4, 0<br> underflow<br> 10,
14292       3534.52, 0<br> underflow<br> 10, 8071.55, 0<br> underflow<br> 10, 16229.2,
14293       0<br> underflow<br> 10, 32066.2, 0<br> underflow<br> 10, 36367.9, 0<br>
14294       underflow<br> 13, 1007.46, 0<br> underflow<br> 13, 1185.4, 0<br> underflow<br>
14295       13, 3534.52, 0<br> underflow<br> 13, 8071.55, 0<br> underflow<br> 13,
14296       16229.2, 0<br> underflow<br> 13, 32066.2, 0<br> underflow<br> 13, 36367.9,
14297       0<br> underflow<br> 16, 1007.46, 0<br> underflow<br> 16, 1185.4, 0<br>
14298       underflow<br> 16, 3534.52, 0<br> underflow<br> 16, 8071.55, 0<br> underflow<br>
14299       16, 16229.2, 0<br> underflow<br> 16, 32066.2, 0<br> underflow<br> 16,
14300       36367.9, 0<br> underflow<br> 19, 1007.46, 0<br> underflow<br> 19, 1185.4,
14301       0<br> underflow<br> 19, 3534.52, 0<br> underflow<br> 19, 8071.55, 0<br>
14302       underflow<br> 19, 16229.2, 0<br> underflow<br> 19, 32066.2, 0<br> underflow<br>
14303       19, 36367.9, 0<br> underflow<br> 22, 1007.46, 0<br> underflow<br> 22,
14304       1185.4, 0<br> underflow<br> 22, 3534.52, 0<br> underflow<br> 22, 8071.55,
14305       0<br> underflow<br> 22, 16229.2, 0<br> underflow<br> 22, 32066.2, 0<br>
14306       underflow<br> 22, 36367.9, 0<br> underflow<br> 25, 1007.46, 0<br> underflow<br>
14307       25, 1185.4, 0<br> underflow<br> 25, 3534.52, 0<br> underflow<br> 25,
14308       8071.55, 0<br> underflow<br> 25, 16229.2, 0<br> underflow<br> 25, 32066.2,
14309       0<br> underflow<br> 25, 36367.9, 0<br> underflow<br> 28, 1007.46, 0<br>
14310       underflow<br> 28, 1185.4, 0<br> underflow<br> 28, 3534.52, 0<br> underflow<br>
14311       28, 8071.55, 0<br> underflow<br> 28, 16229.2, 0<br> underflow<br> 28,
14312       32066.2, 0<br> underflow<br> 28, 36367.9, 0<br> underflow<br> 31, 1007.46,
14313       0<br> underflow<br> 31, 1185.4, 0<br> underflow<br> 31, 3534.52, 0<br>
14314       underflow<br> 31, 8071.55, 0<br> underflow<br> 31, 16229.2, 0<br> underflow<br>
14315       31, 32066.2, 0<br> underflow<br> 31, 36367.9, 0<br> underflow<br> 34,
14316       1007.46, 0<br> underflow<br> 34, 1185.4, 0<br> underflow<br> 34, 3534.52,
14317       0<br> underflow<br> 34, 8071.55, 0<br> underflow<br> 34, 16229.2, 0<br>
14318       underflow<br> 34, 32066.2, 0<br> underflow<br> 34, 36367.9, 0<br> underflow<br>
14319       37, 1007.46, 0<br> underflow<br> 37, 1185.4, 0<br> underflow<br> 37,
14320       3534.52, 0<br> underflow<br> 37, 8071.55, 0<br> underflow<br> 37, 16229.2,
14321       0<br> underflow<br> 37, 32066.2, 0<br> underflow<br> 37, 36367.9, 0<br>
14322       underflow<br> 40, 1007.46, 0<br> underflow<br> 40, 1185.4, 0<br> underflow<br>
14323       40, 3534.52, 0<br> underflow<br> 40, 8071.55, 0<br> underflow<br> 40,
14324       16229.2, 0<br> underflow<br> 40, 32066.2, 0<br> underflow<br> 40, 36367.9,
14325       0<br> underflow<br> 43, 1007.46, 0<br> underflow<br> 43, 1185.4, 0<br>
14326       underflow<br> 43, 3534.52, 0<br> underflow<br> 43, 8071.55, 0<br> underflow<br>
14327       43, 16229.2, 0<br> underflow<br> 43, 32066.2, 0<br> underflow<br> 43,
14328       36367.9, 0<br> underflow<br> 46, 1007.46, 0<br> underflow<br> 46, 1185.4,
14329       0<br> underflow<br> 46, 3534.52, 0<br> underflow<br> 46, 8071.55, 0<br>
14330       underflow<br> 46, 16229.2, 0<br> underflow<br> 46, 32066.2, 0<br> underflow<br>
14331       46, 36367.9, 0<br> underflow<br> 49, 1007.46, 0<br> underflow<br> 49,
14332       1185.4, 0<br> underflow<br> 49, 3534.52, 0<br> underflow<br> 49, 8071.55,
14333       0<br> underflow<br> 49, 16229.2, 0<br> underflow<br> 49, 32066.2, 0<br>
14334       underflow<br> 49, 36367.9, 0<br> underflow<br> 52, 1007.46, 0<br> underflow<br>
14335       52, 1185.4, 0<br> underflow<br> 52, 3534.52, 0<br> underflow<br> 52,
14336       8071.55, 0<br> underflow<br> 52, 16229.2, 0<br> underflow<br> 52, 32066.2,
14337       0<br> underflow<br> 52, 36367.9, 0<br> underflow<br> 55, 1007.46, 0<br>
14338       underflow<br> 55, 1185.4, 0<br> underflow<br> 55, 3534.52, 0<br> underflow<br>
14339       55, 8071.55, 0<br> underflow<br> 55, 16229.2, 0<br> underflow<br> 55,
14340       32066.2, 0<br> underflow<br> 55, 36367.9, 0<br> underflow<br> 58, 1007.46,
14341       0<br> underflow<br> 58, 1185.4, 0<br> underflow<br> 58, 3534.52, 0<br>
14342       underflow<br> 58, 8071.55, 0<br> underflow<br> 58, 16229.2, 0<br> underflow<br>
14343       58, 32066.2, 0<br> underflow<br> 58, 36367.9, 0<br> underflow<br> 61,
14344       1007.46, 0<br> underflow<br> 61, 1185.4, 0<br> underflow<br> 61, 3534.52,
14345       0<br> underflow<br> 61, 8071.55, 0<br> underflow<br> 61, 16229.2, 0<br>
14346       underflow<br> 61, 32066.2, 0<br> underflow<br> 61, 36367.9, 0<br> underflow<br>
14347       64, 1007.46, 0<br> underflow<br> 64, 1185.4, 0<br> underflow<br> 64,
14348       3534.52, 0<br> underflow<br> 64, 8071.55, 0<br> underflow<br> 64, 16229.2,
14349       0<br> underflow<br> 64, 32066.2, 0<br> underflow<br> 64, 36367.9, 0<br>
14350       underflow<br> 67, 1007.46, 0<br> underflow<br> 67, 1185.4, 0<br> underflow<br>
14351       67, 3534.52, 0<br> underflow<br> 67, 8071.55, 0<br> underflow<br> 67,
14352       16229.2, 0<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
14353     </p>
14354 <h5>
14355 <a name="special_function_error_rates_rep.error_logs.h65"></a>
14356       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1">Error
14357       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
14358       2.1 and test data Bessel Kv: Mathworld Data (large values)</a>
14359     </h5>
14360 <p>
14361       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_"></a>domain
14362       error<br> -1, 3.72917e-155, 2.68156e+154<br> domain error<br> -1.125,
14363       3.72917e-155, 5.53984e+173<br>
14364     </p>
14365 <h5>
14366 <a name="special_function_error_rates_rep.error_logs.h66"></a>
14367       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2">Error
14368       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
14369       2.1 and test data Bessel Kv: Mathworld Data</a>
14370     </h5>
14371 <p>
14372       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data"></a>domain
14373       error<br> -5.5, 10, 7.33045e-05<br> domain error<br> -5.5, 100, 5.41275e-45<br>
14374       domain error<br> -141.399, 50, 1.30185e+42<br>
14375     </p>
14376 <h5>
14377 <a name="special_function_error_rates_rep.error_logs.h67"></a>
14378       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3">Error
14379       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
14380       2.1 and test data Bessel Kn: Mathworld Data</a>
14381     </h5>
14382 <p>
14383       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data"></a>domain
14384       error<br> -5, 100, 5.27326e-45<br> domain error<br> -10, 1, 1.80713e+08<br>
14385       domain error<br> -1000, 700, 6.51562e-31<br>
14386     </p>
14387 <h5>
14388 <a name="special_function_error_rates_rep.error_logs.h68"></a>
14389       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4">Error
14390       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14391       and test data Bessel Kv: Random Data</a>
14392     </h5>
14393 <p>
14394       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data"></a>Bad
14395       argument in __cyl_bessel_k.<br> -80.4919, 24.7501, 6.57902e+28<br> Bad
14396       argument in __cyl_bessel_k.<br> -80.4919, 63.7722, 2.39552e-09<br> Bad
14397       argument in __cyl_bessel_k.<br> -80.4919, 125.28, 3.06904e-45<br> Bad argument
14398       in __cyl_bessel_k.<br> -80.4919, 255.547, 2.30343e-107<br> Bad argument
14399       in __cyl_bessel_k.<br> -80.4919, 503.011, 1.20315e-217<br> Bad argument
14400       in __cyl_bessel_k.<br> -80.4919, 1007.46, 2.86537e-438<br> Bad argument
14401       in __cyl_bessel_k.<br> -80.4919, 1185.4, 8.63263e-516<br> Bad argument
14402       in __cyl_bessel_k.<br> -80.4919, 3534.52, 5.01367e-1537<br> Bad argument
14403       in __cyl_bessel_k.<br> -80.4919, 8071.55, 7.76555e-3508<br> Bad argument
14404       in __cyl_bessel_k.<br> -80.4919, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br>
14405       -80.4919, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -80.4919,
14406       36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -74.6026, 24.7501, 1.19405e+24<br>
14407       Bad argument in __cyl_bessel_k.<br> -74.6026, 63.7722, 5.81897e-12<br>
14408       Bad argument in __cyl_bessel_k.<br> -74.6026, 125.28, 9.89214e-47<br> Bad
14409       argument in __cyl_bessel_k.<br> -74.6026, 255.547, 3.9726e-108<br> Bad
14410       argument in __cyl_bessel_k.<br> -74.6026, 503.011, 4.87462e-218<br> Bad
14411       argument in __cyl_bessel_k.<br> -74.6026, 1007.46, 1.82221e-438<br> Bad
14412       argument in __cyl_bessel_k.<br> -74.6026, 1185.4, 5.87506e-516<br> Bad
14413       argument in __cyl_bessel_k.<br> -74.6026, 3534.52, 4.40608e-1537<br> Bad
14414       argument in __cyl_bessel_k.<br> -74.6026, 8071.55, 7.3384e-3508<br> Bad
14415       argument in __cyl_bessel_k.<br> -74.6026, 16229.2, 0<br> Bad argument in
14416       __cyl_bessel_k.<br> -74.6026, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br>
14417       -74.6026, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -72.9046,
14418       24.7501, 5.5618e+22<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 63.7722,
14419       1.09452e-12<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 125.28, 3.8393e-47<br>
14420       Bad argument in __cyl_bessel_k.<br> -72.9046, 255.547, 2.45173e-108<br>
14421       Bad argument in __cyl_bessel_k.<br> -72.9046, 503.011, 3.80454e-218<br>
14422       Bad argument in __cyl_bessel_k.<br> -72.9046, 1007.46, 1.60949e-438<br>
14423       Bad argument in __cyl_bessel_k.<br> -72.9046, 1185.4, 5.28662e-516<br>
14424       Bad argument in __cyl_bessel_k.<br> -72.9046, 3534.52, 4.25273e-1537<br>
14425       Bad argument in __cyl_bessel_k.<br> -72.9046, 8071.55, 7.22542e-3508<br>
14426       Bad argument in __cyl_bessel_k.<br> -72.9046, 16229.2, 0<br> Bad argument
14427       in __cyl_bessel_k.<br> -72.9046, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br>
14428       -72.9046, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
14429       24.7501, 6.74518e+14<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
14430       63.7722, 6.54531e-17<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
14431       125.28, 1.65653e-49<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 255.547,
14432       1.54767e-109<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 503.011,
14433       9.22721e-219<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1007.46,
14434       7.91894e-439<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1185.4,
14435       2.89281e-516<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 3534.52,
14436       3.4736e-1537<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 8071.55,
14437       6.6126e-3508<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 16229.2,
14438       0<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 32066.2, 0<br> Bad
14439       argument in __cyl_bessel_k.<br> -62.3236, 36367.9, 0<br> Bad argument in
14440       __cyl_bessel_k.<br> -55.7932, 24.7501, 2.00028e+10<br> Bad argument in
14441       __cyl_bessel_k.<br> -55.7932, 63.7722, 3.01107e-19<br> Bad argument in
14442       __cyl_bessel_k.<br> -55.7932, 125.28, 8.54693e-51<br> Bad argument in __cyl_bessel_k.<br>
14443       -55.7932, 255.547, 3.47666e-110<br> Bad argument in __cyl_bessel_k.<br>
14444       -55.7932, 503.011, 4.29705e-219<br> Bad argument in __cyl_bessel_k.<br>
14445       -55.7932, 1007.46, 5.40242e-439<br> Bad argument in __cyl_bessel_k.<br>
14446       -55.7932, 1185.4, 2.08996e-516<br> Bad argument in __cyl_bessel_k.<br>
14447       -55.7932, 3534.52, 3.11458e-1537<br> Bad argument in __cyl_bessel_k.<br>
14448       -55.7932, 8071.55, 6.30409e-3508<br> Bad argument in __cyl_bessel_k.<br>
14449       -55.7932, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932,
14450       32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932, 36367.9, 0<br>
14451       Bad argument in __cyl_bessel_k.<br> -44.3004, 9.50706, 5.6936e+22<br> Bad
14452       argument in __cyl_bessel_k.<br> -44.3004, 24.7501, 1242.73<br> Bad argument
14453       in __cyl_bessel_k.<br> -44.3004, 63.7722, 7.99341e-23<br> Bad argument
14454       in __cyl_bessel_k.<br> -44.3004, 125.28, 9.88149e-53<br> Bad argument in
14455       __cyl_bessel_k.<br> -44.3004, 255.547, 3.73007e-111<br> Bad argument in
14456       __cyl_bessel_k.<br> -44.3004, 503.011, 1.37367e-219<br> Bad argument in
14457       __cyl_bessel_k.<br> -44.3004, 1007.46, 3.05398e-439<br> Bad argument in
14458       __cyl_bessel_k.<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
14459     </p>
14460 <h5>
14461 <a name="special_function_error_rates_rep.error_logs.h69"></a>
14462       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5">Error
14463       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14464       and test data Bessel Kv: Mathworld Data (large values)</a>
14465     </h5>
14466 <p>
14467       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_"></a>Bad
14468       argument in __cyl_bessel_k.<br> -1, 3.72917e-155, 2.68156e+154<br> Bad
14469       argument in __cyl_bessel_k.<br> -1.125, 3.72917e-155, 5.53984e+173<br>
14470     </p>
14471 <h5>
14472 <a name="special_function_error_rates_rep.error_logs.h70"></a>
14473       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6">Error
14474       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14475       and test data Bessel Kv: Mathworld Data</a>
14476     </h5>
14477 <p>
14478       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data"></a>Bad
14479       argument in __cyl_bessel_k.<br> -5.5, 10, 7.33045e-05<br> Bad argument
14480       in __cyl_bessel_k.<br> -5.5, 100, 5.41275e-45<br> Bad argument in __cyl_bessel_k.<br>
14481       -141.399, 50, 1.30185e+42<br>
14482     </p>
14483 <h5>
14484 <a name="special_function_error_rates_rep.error_logs.h71"></a>
14485       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in">Error
14486       Output For cyl_bessel_k (integer orders) with compiler GNU C++ version 7.1.0
14487       and library &lt;cmath&gt; and test data Bessel Kn: Mathworld Data (Integer
14488       Version)</a>
14489     </h5>
14490 <p>
14491       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_"></a>Bad
14492       argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in
14493       __cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br>
14494       -1000, 700, 6.51562e-31<br>
14495     </p>
14496 <h5>
14497 <a name="special_function_error_rates_rep.error_logs.h72"></a>
14498       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7">Error
14499       Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14500       and test data Bessel Kn: Mathworld Data</a>
14501     </h5>
14502 <p>
14503       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data"></a>Bad
14504       argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in
14505       __cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br>
14506       -1000, 700, 6.51562e-31<br>
14507     </p>
14508 <h5>
14509 <a name="special_function_error_rates_rep.error_logs.h73"></a>
14510       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit">Error
14511       Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
14512       2.1 and test data Yv: Mathworld Data (large values)</a>
14513     </h5>
14514 <p>
14515       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_"></a>domain
14516       error<br> -0.5, 1.2459e-206, 8.90598e-104<br>
14517     </p>
14518 <h5>
14519 <a name="special_function_error_rates_rep.error_logs.h74"></a>
14520       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0">Error
14521       Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
14522       2.1 and test data Yv: Mathworld Data</a>
14523     </h5>
14524 <p>
14525       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data"></a>domain
14526       error<br> -5.5, 3.125, -0.0274994<br> domain error<br> -5.5, 10000, -0.00759344<br>
14527       domain error<br> -10.0003, 0.000976562, -1.50382e+38<br> domain error<br>
14528       -10.0003, 100, 0.0583042<br> domain error<br> -141.75, 100, -3.8101e+09<br>
14529       domain error<br> -8.5, 12.5664, 0.0436808<br>
14530     </p>
14531 <h5>
14532 <a name="special_function_error_rates_rep.error_logs.h75"></a>
14533       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1">Error
14534       Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
14535       2.1 and test data Yn: Mathworld Data</a>
14536     </h5>
14537 <p>
14538       <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data"></a>domain
14539       error<br> -5, 1e+06, 0.000331052<br> domain error<br> -10, 1e+06, 0.000725952<br>
14540       domain error<br> -1000, 700, -1.88753e+77<br> domain error<br> -25, 8,
14541       3.45114e+08<br>
14542     </p>
14543 <h5>
14544 <a name="special_function_error_rates_rep.error_logs.h76"></a>
14545       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2">Error
14546       Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14547       and test data Yv: Random Data</a>
14548     </h5>
14549 <p>
14550       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data"></a>CAUTION:
14551       Gross error found at entry 394.<br> Found: -3.29903 Expected 0.0192842 Error:
14552       1.18973e+4932<br> 125.28, 1007.46, 0.0192842<br> CAUTION: Gross error found
14553       at entry 395.<br> Found: 1.13543 Expected 0.0230358 Error: 48.2897<br>
14554       125.28, 1185.4, 0.0230358<br> CAUTION: Gross error found at entry 396.<br>
14555       Found: 0.00119445 Expected 0.00460223 Error: 2.85302<br> 125.28, 3534.52,
14556       0.00460223<br> CAUTION: Gross error found at entry 403.<br> Found: 1068
14557       Expected -0.00270959 Error: 1.18973e+4932<br> 255.547, 1007.46, -0.00270959<br>
14558       CAUTION: Gross error found at entry 404.<br> Found: -395.006 Expected 0.00738845
14559       Error: 1.18973e+4932<br> 255.547, 1185.4, 0.00738845<br> CAUTION: Gross
14560       error found at entry 405.<br> Found: 1.08701 Expected -0.000407036 Error:
14561       1.18973e+4932<br> 255.547, 3534.52, -0.000407036<br> CAUTION: Gross error
14562       found at entry 406.<br> Found: 0.0232211 Expected 0.00886946 Error: 1.61809<br>
14563       255.547, 8071.55, 0.00886946<br> CAUTION: Gross error found at entry 411.<br>
14564       Found: 65895.7 Expected -0.0158467 Error: 1.18973e+4932<br> 503.011, 1007.46,
14565       -0.0158467<br> CAUTION: Gross error found at entry 412.<br> Found: -123316
14566       Expected 0.00594357 Error: 1.18973e+4932<br> 503.011, 1185.4, 0.00594357<br>
14567       CAUTION: Gross error found at entry 413.<br> Found: -706.209 Expected 0.010151
14568       Error: 1.18973e+4932<br> 503.011, 3534.52, 0.010151<br> CAUTION: Gross
14569       error found at entry 414.<br> Found: -21.2081 Expected 0.00888375 Error:
14570       1.18973e+4932<br> 503.011, 8071.55, 0.00888375<br> CAUTION: Gross error
14571       found at entry 415.<br> Found: 0.0272835 Expected 0.00552287 Error: 3.94008<br>
14572       503.011, 16229.2, 0.00552287<br> CAUTION: Gross error found at entry 416.<br>
14573       Found: 0.0103324 Expected 0.00445559 Error: 1.31898<br> 503.011, 32066.2,
14574       0.00445559<br> CAUTION: Gross error found at entry 417.<br> Found: 0.00540788
14575       Expected -0.00384344 Error: 1.18973e+4932<br> 503.011, 36367.9, -0.00384344<br>
14576       CAUTION: Gross error found at entry 418.<br> Found: 5.43091e+07 Expected
14577       -0.0772843 Error: 1.18973e+4932<br> 1007.46, 1007.46, -0.0772843<br> CAUTION:
14578       Gross error found at entry 419.<br> Found: -2.84383e+07 Expected 0.0304312
14579       Error: 1.18973e+4932<br> 1007.46, 1185.4, 0.0304312<br> CAUTION: Gross
14580       error found at entry 420.<br> Found: -61440.2 Expected -0.00474217 Error:
14581       1.29562e+07<br> 1007.46, 3534.52, -0.00474217<br> CAUTION: Gross error
14582       found at entry 421.<br> Found: -4126.89 Expected -0.0074205 Error: 556146<br>
14583       1007.46, 8071.55, -0.0074205<br> CAUTION: Gross error found at entry 422.<br>
14584       Found: -69.2831 Expected -0.00179572 Error: 38581.4<br> 1007.46, 16229.2,
14585       -0.00179572<br> CAUTION: Gross error found at entry 423.<br> Found: 2.32048
14586       Expected 0.000750053 Error: 3092.76<br> 1007.46, 32066.2, 0.000750053<br>
14587       CAUTION: Gross error found at entry 424.<br> Found: 3.90724 Expected 0.00305125
14588       Error: 1279.54<br> 1007.46, 36367.9, 0.00305125<br> CAUTION: Gross error
14589       found at entry 425.<br> Found: -1.83374e+08 Expected -7.25176e+28 Error:
14590       3.95463e+20<br> 1185.4, 1007.46, -7.25176e+28<br> CAUTION: Gross error
14591       found at entry 426.<br> Found: 1.09822e+08 Expected -0.0732059 Error: 1.18973e+4932<br>
14592       1185.4, 1185.4, -0.0732059<br> CAUTION: Gross error found at entry 427.<br>
14593       Found: 315632 Expected 0.000479585 Error: 6.58136e+08<br> 1185.4, 3534.52,
14594       0.000479585<br> CAUTION: Gross error found at entry 428.<br> Found: 16815.6
14595       Expected 0.00174909 Error: 9.61391e+06<br> 1185.4, 8071.55, 0.00174909<br>
14596       CAUTION: Gross error found at entry 429.<br> Found: 133.356 Expected 0.00416288
14597       Error: 32033.6<br> 1185.4, 16229.2, 0.00416288<br> CAUTION: Gross error
14598       found at entry 430.<br> Found: -1.38401 Expected -0.000320056 Error: 4323.27<br>
14599       1185.4, 32066.2, -0.000320056<br> CAUTION: Gross error found at entry 431.<br>
14600       Found: -17.7085 Expected -0.00417656 Error: 4238.96<br> 1185.4, 36367.9,
14601       -0.00417656<br>
14602     </p>
14603 <h5>
14604 <a name="special_function_error_rates_rep.error_logs.h77"></a>
14605       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3">Error
14606       Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14607       and test data Yv: Mathworld Data (large values)</a>
14608     </h5>
14609 <p>
14610       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_"></a>Bad
14611       argument in __cyl_neumann_n.<br> -0.5, 1.2459e-206, 8.90598e-104<br>
14612     </p>
14613 <h5>
14614 <a name="special_function_error_rates_rep.error_logs.h78"></a>
14615       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4">Error
14616       Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14617       and test data Yv: Mathworld Data</a>
14618     </h5>
14619 <p>
14620       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data"></a>Bad
14621       argument in __cyl_neumann_n.<br> -5.5, 3.125, -0.0274994<br> Bad argument
14622       in __cyl_neumann_n.<br> -5.5, 10000, -0.00759344<br> Bad argument in __cyl_neumann_n.<br>
14623       -10.0003, 0.000976562, -1.50382e+38<br> Bad argument in __cyl_neumann_n.<br>
14624       -10.0003, 100, 0.0583042<br> Bad argument in __cyl_neumann_n.<br> -141.75,
14625       100, -3.8101e+09<br> Bad argument in __cyl_neumann_n.<br> -8.5, 12.5664,
14626       0.0436808<br>
14627     </p>
14628 <h5>
14629 <a name="special_function_error_rates_rep.error_logs.h79"></a>
14630       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int">Error
14631       Output For cyl_neumann (integer orders) with compiler GNU C++ version 7.1.0
14632       and library &lt;cmath&gt; and test data Yn: Mathworld Data (Integer Version)</a>
14633     </h5>
14634 <p>
14635       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_"></a>Bad
14636       argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument
14637       in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error
14638       found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br>
14639       1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000,
14640       700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br>
14641     </p>
14642 <h5>
14643 <a name="special_function_error_rates_rep.error_logs.h80"></a>
14644       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5">Error
14645       Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14646       and test data Yn: Mathworld Data</a>
14647     </h5>
14648 <p>
14649       <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data"></a>Bad
14650       argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument
14651       in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error
14652       found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br>
14653       1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000,
14654       700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br>
14655     </p>
14656 <h5>
14657 <a name="special_function_error_rates_rep.error_logs.h81"></a>
14658       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi">Error
14659       Output For beta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and
14660       test data Beta Function: Small Values</a>
14661     </h5>
14662 <p>
14663       <a name="errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values"></a>CAUTION:
14664       Found non-finite result, when a finite value was expected at entry 22<br>
14665       Found: inf Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155,
14666       5.69832e+154<br> CAUTION: Gross error found at entry 22.<br> Found: inf
14667       Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155,
14668       5.69832e+154<br>
14669     </p>
14670 <h5>
14671 <a name="special_function_error_rates_rep.error_logs.h82"></a>
14672       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_">Error
14673       Output For ellint_rj with compiler GNU C++ version 7.1.0 and library GSL 2.1
14674       and test data RJ: Random data</a>
14675     </h5>
14676 <p>
14677       <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data"></a>domain
14678       error<br> 1.77787e-31, 1.40657e+18, 10.046, -4.8298e-10, -2.51795e-10<br>
14679       domain error<br> 3.37448e-31, 4.65772e+22, 0.469831, -4.33756e-09, -2.95865e-11<br>
14680       domain error<br> 5.25297e-31, 5.85483e+25, 2.02482e-15, -1.87347e-28, 3.36445e+07<br>
14681       domain error<br> 6.22216e-31, 3.43401e+23, 0.673005, -2.7626e-13, -7.58898e-12<br>
14682       domain error<br> 6.26875e-31, 2.62568e-13, 1.06394e+24, -1.36451e+14, -6.70372e-25<br>
14683       domain error<br> 6.84599e-31, 3.57666e-29, 1.82191e+11, -3.63292e+08, -8.35235e-13<br>
14684       domain error<br> 8.90482e-31, 1.97093e-28, 1.14939e-31, -1.26424e-12, -6.39454e+26<br>
14685       domain error<br> 1.07374e-30, 1.70005e-12, 1.88773e-25, -1.16558e-29, 4.31668e+32<br>
14686       domain error<br> 1.17141e-30, 24.2523, 3.67522e+21, -4.79065e-22, 2.2702e-05<br>
14687       domain error<br> 1.64143e-30, 2.01978e-22, 2.58942e+12, -8.52649e-12, -2.82629e+06<br>
14688       domain error<br> 1.85141e-30, 0.0386712, 2.37846e-13, -1.57357e+15, -1.38574e-13<br>
14689       domain error<br> 2.70034e-30, 4.43896e-24, 7.54576e+16, -1.1436e-14, -1.10082e+07<br>
14690       domain error<br> 4.01162e-30, 2.73343e+23, 1.32333e+13, -1.86032e-07, -4.16626e-25<br>
14691       domain error<br> 4.13665e-30, 1.08034e-30, 3.13547e-16, -5.58099e-08, -5.14643e+16<br>
14692       domain error<br> 4.3728e-30, 7.79812e+12, 8.58894e+21, -4.58312e-24, 5.28901e-09<br>
14693       domain error<br> 5.6397e-30, 1.64768e+23, 9.64423e-15, -1.82207e+20, -1.62886e-30<br>
14694       domain error<br> 9.89841e-30, 9.69731e+10, 1.03263e+21, -0.00343967, -9.62714e-22<br>
14695       domain error<br> 1.3797e-29, 6.03357e+08, 5.62497e-15, -5.87235e+16, -5.80287e-20<br>
14696       domain error<br> 1.96963e-29, 3.22384e-25, 2.92187e+23, -3.80643e+27, -8.2513e-38<br>
14697       domain error<br> 2.00927e-29, 5.6976e-05, 1.16219e+25, -1.64129e-22, 0.00318397<br>
14698       domain error<br> 7.29506e-29, 5904.94, 9.93922e+10, -19.528, -1.60795e-09<br>
14699       domain error<br> 1.19698e-28, 1.66816e-22, 28472, -1.21137e-19, -5.84699e+17<br>
14700       domain error<br> 1.64095e-28, 2.13421e-21, 7.8914e-15, -1.77584e-07, -1.70156e+15<br>
14701       domain error<br> 2.03475e-28, 4.40987e+15, 28739.1, -9624.5, -1.29418e-12<br>
14702       domain error<br> 2.73113e-28, 1.08457e+19, 4.00674e+08, -5.70043e-11, 1.092e-17<br>
14703       domain error<br> 5.52633e-28, 1.45707e-17, 1.29411e-27, -1.67255e-15, -5.84881e+24<br>
14704       domain error<br> 5.61278e-28, 9.22881e-12, 8.64222e-13, -5.6282e+23, -4.57782e-18<br>
14705       domain error<br> 6.08465e-28, 1.32249e+26, 1.25536e-30, -1.89097e-14, -223.246<br>
14706       domain error<br> 9.50943e-28, 2.49682e-18, 0.000904584, -3.1419e-12, -2.44954e+14<br>
14707       domain error<br> 1.20779e-27, 35383.2, 1.35533e-15, -4.67834e-24, 3.20581e+15<br>
14708       domain error<br> 2.29822e-27, 3.35258e-16, 2.60689e+08, -9.99161e-20, -5.4924e+11<br>
14709       domain error<br> 3.0926e-27, 3.11839e-13, 3.37883e-23, -1.94349e+26, -3.55191e-19<br>
14710       domain error<br> 3.12803e-27, 1.15118e+16, 1.52495e+10, -4.2399e+13, -3.07515e-21<br>
14711       domain error<br> 4.49747e-27, 716.685, 1.69018e-23, -1.32558e-14, -9.2291e+13<br>
14712       domain error<br> 4.84575e-27, 3.44028e-27, 3.42665e+09, -812.399, -2.12767e-06<br>
14713       domain error<br> 5.81424e-27, 3.70845e-15, 3.69338e+11, -4.15794e+06, -2.95944e-11<br>
14714       domain error<br> 6.08654e-27, 1.23742e+08, 1.09124e-26, -2.19946e+16, -4.90896e-19<br>
14715       domain error<br> 7.71967e-27, 9.46115e-26, 1.24324e+25, -522800, -5.83203e-17<br>
14716       domain error<br> 9.20037e-27, 207550, 2.45782e-17, -6.06901e+29, -2.88945e-31<br>
14717       domain error<br> 1.75502e-26, 5.81507e+16, 8.83063e+21, -1.11214e-21, 1.57697e-11<br>
14718       domain error<br> 2.29965e-26, 2.9716e-21, 1.81059e-25, -5.23972e-08, -6.23302e+18<br>
14719       domain error<br> 2.32628e-26, 0.0655133, 1.62901e-21, -7.15441e-17, -9.88586e+17<br>
14720       domain error<br> 3.49194e-26, 2.53343e+14, 756.217, -1.3359e+10, -1.275e-16<br>
14721       domain error<br> 1.009e-25, 0.0694304, 1.20267e-14, -1.55746e-22, 2.10701e+17<br>
14722       domain error<br> 3.54771e-25, 1.67999e-27, 2.3917e+24, -9.98754e+25, -1.11704e-36<br>
14723       domain error<br> 6.31714e-25, 3.4594e-28, 6.37951e-24, -1.25529e-24, -9.56292e+35<br>
14724       domain error<br> 6.74086e-25, 2.47169e+12, 1.32962e+23, -6.78845e+06, -3.32861e-24<br>
14725       domain error<br> 1.8099e-24, 4.5215e-06, 8.66937e-11, -3.70795e-08, -1.41893e+11<br>
14726       domain error<br> 2.29798e-24, 9.30454e-30, 6.56584e-17, -9890.38, -373149<br>
14727       domain error<br> 2.88161e-24, 8.82377e-05, 1.57747e+21, -4.25068e-24, 2260.61<br>
14728       domain error<br> 3.25991e-24, 1.92923e+29, 3.09752e-05, -1.00986e+11, -1.25485e-24<br>
14729       domain error<br> 6.36705e-24, 2.8074e+22, 1.75569e-13, -1.53152e+24, -4.89823e-34<br>
14730       domain error<br> 7.90772e-24, 2.11611e-30, 1.42682e-07, -0.00296297, -5.38814e+07<br>
14731       domain error<br> 1.05302e-23, 4.83473e+26, 4.43149e-30, -1.56818e+13, -3.6836e-25<br>
14732       *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
14733     </p>
14734 <h5>
14735 <a name="special_function_error_rates_rep.error_logs.h83"></a>
14736       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c">Error
14737       Output For ellint_1 with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14738       and test data Elliptic Integral F: Mathworld Data</a>
14739     </h5>
14740 <p>
14741       <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data"></a>CAUTION:
14742       Gross error found at entry 9.<br> Found: -7.02862e+09 Expected 1.04181e+20
14743       Error: 1.18973e+4932<br> 1e+20, 0.390625, 1.04181e+20<br> CAUTION: Gross
14744       error found at entry 10.<br> Found: -9.3866e+09 Expected 1.39133e+50 Error:
14745       1.18973e+4932<br> 1e+50, 0.875, 1.39133e+50<br>
14746     </p>
14747 <h5>
14748 <a name="special_function_error_rates_rep.error_logs.h84"></a>
14749       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple">Error
14750       Output For ellint_2 (complete) with compiler GNU C++ version 7.1.0 and library
14751       GSL 2.1 and test data Elliptic Integral E: Mathworld Data</a>
14752     </h5>
14753 <p>
14754       <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data"></a>domain
14755       error<br> -1, 1<br>
14756     </p>
14757 <h5>
14758 <a name="special_function_error_rates_rep.error_logs.h85"></a>
14759       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c">Error
14760       Output For ellint_2 with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14761       and test data Elliptic Integral E: Mathworld Data</a>
14762     </h5>
14763 <p>
14764       <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data"></a>CAUTION:
14765       Gross error found at entry 7.<br> Found: -6.3027e+09 Expected 9.34215e+09
14766       Error: 1.18973e+4932<br> 1e+10, -0.5, 9.34215e+09<br> CAUTION: Gross error
14767       found at entry 8.<br> Found: -6.48129e+09 Expected 7.08861e+19 Error: 1.18973e+4932<br>
14768       7.3787e+19, 0.390625, 7.08861e+19<br> CAUTION: Gross error found at entry
14769       9.<br> Found: -5.13973e+09 Expected 7.1259e+49 Error: 1.18973e+4932<br>
14770       9.35361e+49, 0.878906, 7.1259e+49<br>
14771     </p>
14772 <h5>
14773 <a name="special_function_error_rates_rep.error_logs.h86"></a>
14774       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple">Error
14775       Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
14776       GSL 2.1 and test data Complete Elliptic Integral PI: Mathworld Data</a>
14777     </h5>
14778 <p>
14779       <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data"></a>domain
14780       error<br> -4.14952e+180, 0.5, 7.71119e-91<br>
14781     </p>
14782 <h5>
14783 <a name="special_function_error_rates_rep.error_logs.h87"></a>
14784       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c">Error
14785       Output For ellint_3 with compiler GNU C++ version 7.1.0 and library GSL 2.1
14786       and test data Elliptic Integral PI: Mathworld Data</a>
14787     </h5>
14788 <p>
14789       <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data"></a>domain
14790       error<br> 1.125, 10, 0.25, 0.662468<br> domain error<br> 1.125, 3, 0.25,
14791       -0.142697<br> domain error<br> 1.00391, 21.5, 0.125, -0.535406<br> domain
14792       error<br> 1, 2, 0.5, -2.87535<br> domain error<br> 1, -2, 0.5, 2.87535<br>
14793       domain error<br> 1, 2, 6.22302e-61, -2.18504<br> domain error<br> 1,
14794       -2, 6.22302e-61, 2.18504<br> domain error<br> 20, 3.14257, 0.5, 0.000975941<br>
14795       domain error<br> 20, -3.14257, 0.5, -0.000975941<br> domain error<br>
14796       1.01562, 1.6958, 0.5, -27.1647<br> domain error<br> 1.01562, -1.6958, 0.5,
14797       27.1647<br>
14798     </p>
14799 <h5>
14800 <a name="special_function_error_rates_rep.error_logs.h88"></a>
14801       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0">Error
14802       Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
14803       &lt;cmath&gt; and test data Complete Elliptic Integral PI: Random Data</a>
14804     </h5>
14805 <p>
14806       <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data"></a>Argument
14807       too small in __ellint_rj<br> -87.1743, 0.126987, 0.167413<br> Argument
14808       too small in __ellint_rj<br> -87.1743, 0.135477, 0.167431<br> Argument
14809       too small in __ellint_rj<br> -87.1743, 0.221034, 0.167683<br> Argument
14810       too small in __ellint_rj<br> -87.1743, 0.308167, 0.168078<br> Argument
14811       too small in __ellint_rj<br> -87.1743, 0.632359, 0.17122<br> Argument too
14812       small in __ellint_rj<br> -87.1743, 0.814724, 0.175341<br> Argument too
14813       small in __ellint_rj<br> -87.1743, 0.835009, 0.176056<br> Argument too
14814       small in __ellint_rj<br> -87.1743, 0.905792, 0.179501<br> Argument too
14815       small in __ellint_rj<br> -87.1743, 0.913376, 0.180014<br> Argument too
14816       small in __ellint_rj<br> -87.1743, 0.968868, 0.186162<br> Argument too
14817       small in __ellint_rj<br> -86.3168, 0.126987, 0.168233<br> Argument too
14818       small in __ellint_rj<br> -86.3168, 0.135477, 0.168252<br> Argument too
14819       small in __ellint_rj<br> -86.3168, 0.221034, 0.168506<br> Argument too
14820       small in __ellint_rj<br> -86.3168, 0.308167, 0.168905<br> Argument too
14821       small in __ellint_rj<br> -86.3168, 0.632359, 0.172077<br> Argument too
14822       small in __ellint_rj<br> -86.3168, 0.814724, 0.176237<br> Argument too
14823       small in __ellint_rj<br> -86.3168, 0.835009, 0.176958<br> Argument too
14824       small in __ellint_rj<br> -86.3168, 0.905792, 0.180437<br> Argument too
14825       small in __ellint_rj<br> -86.3168, 0.913376, 0.180955<br> Argument too
14826       small in __ellint_rj<br> -86.3168, 0.968868, 0.187163<br> Argument too
14827       small in __ellint_rj<br> -77.6756, 0.126987, 0.177238<br> Argument too
14828       small in __ellint_rj<br> -77.6756, 0.135477, 0.177258<br> Argument too
14829       small in __ellint_rj<br> -77.6756, 0.221034, 0.17754<br> Argument too small
14830       in __ellint_rj<br> -77.6756, 0.308167, 0.17798<br> Argument too small in
14831       __ellint_rj<br> -77.6756, 0.632359, 0.181485<br> Argument too small in
14832       __ellint_rj<br> -77.6756, 0.814724, 0.186089<br> Argument too small in
14833       __ellint_rj<br> -77.6756, 0.835009, 0.186888<br> Argument too small in
14834       __ellint_rj<br> -77.6756, 0.905792, 0.190742<br> Argument too small in
14835       __ellint_rj<br> -77.6756, 0.913376, 0.191315<br> Argument too small in
14836       __ellint_rj<br> -77.6756, 0.968868, 0.1982<br> Argument too small in __ellint_rj<br>
14837       -68.8751, 0.126987, 0.188077<br> Argument too small in __ellint_rj<br>
14838       -68.8751, 0.135477, 0.188099<br> Argument too small in __ellint_rj<br>
14839       -68.8751, 0.221034, 0.188414<br> Argument too small in __ellint_rj<br>
14840       -68.8751, 0.308167, 0.188907<br> Argument too small in __ellint_rj<br>
14841       -68.8751, 0.632359, 0.192834<br> Argument too small in __ellint_rj<br>
14842       -68.8751, 0.814724, 0.198<br> Argument too small in __ellint_rj<br> -68.8751,
14843       0.835009, 0.198896<br> Argument too small in __ellint_rj<br> -68.8751,
14844       0.905792, 0.203226<br> Argument too small in __ellint_rj<br> -68.8751,
14845       0.913376, 0.203871<br> Argument too small in __ellint_rj<br> -68.8751,
14846       0.968868, 0.211615<br> Argument too small in __ellint_rj<br> -36.1317,
14847       0.126987, 0.258074<br> Argument too small in __ellint_rj<br> -36.1317,
14848       0.135477, 0.258115<br> Argument too small in __ellint_rj<br> -36.1317,
14849       0.221034, 0.258686<br> Argument too small in __ellint_rj<br> -36.1317,
14850       0.308167, 0.259579<br> Argument too small in __ellint_rj<br> -36.1317,
14851       0.632359, 0.266738<br> Argument too small in __ellint_rj<br> -36.1317,
14852       0.814724, 0.276242<br> Argument too small in __ellint_rj<br> -36.1317,
14853       0.835009, 0.2779<br> Argument too small in __ellint_rj<br> -36.1317, 0.905792,
14854       0.285938<br> Argument too small in __ellint_rj<br> -36.1317, 0.913376,
14855       0.287139<br> Argument too small in __ellint_rj<br> -36.1317, 0.968868,
14856       0.301608<br> Argument too small in __ellint_rj<br> -17.7129, 0.126987,
14857       0.363673<br> Argument too small in __ellint_rj<br> -17.7129, 0.135477,
14858       0.36375<br> Argument too small in __ellint_rj<br> -17.7129, 0.221034, 0.364822<br>
14859       Argument too small in __ellint_rj<br> -17.7129, 0.308167, 0.366503<br>
14860       Argument too small in __ellint_rj<br> -17.7129, 0.632359, 0.380066<br>
14861       Argument too small in __ellint_rj<br> -17.7129, 0.814724, 0.398311<br>
14862       Argument too small in __ellint_rj<br> -17.7129, 0.835009, 0.401518<br>
14863       Argument too small in __ellint_rj<br> -17.7129, 0.905792, 0.417145<br>
14864       Argument too small in __ellint_rj<br> -17.7129, 0.913376, 0.41949<br> Argument
14865       too small in __ellint_rj<br> -17.7129, 0.968868, 0.447893<br> Argument
14866       too small in __ellint_rj<br> -15.6641, 0.126987, 0.385409<br> Argument
14867       too small in __ellint_rj<br> -15.6641, 0.135477, 0.385495<br> Argument
14868       too small in __ellint_rj<br> -15.6641, 0.221034, 0.386686<br> Argument
14869       too small in __ellint_rj<br> -15.6641, 0.308167, 0.388553<br> Argument
14870       too small in __ellint_rj<br> -15.6641, 0.632359, 0.403643<br> Argument
14871       too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY
14872       ***<br>
14873     </p>
14874 <h5>
14875 <a name="special_function_error_rates_rep.error_logs.h89"></a>
14876       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1">Error
14877       Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
14878       &lt;cmath&gt; and test data Complete Elliptic Integral PI: Mathworld Data</a>
14879     </h5>
14880 <p>
14881       <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION:
14882       Gross error found at entry 3.<br> Found: 1.28255 Expected 2.22144 Error:
14883       0.732051<br> 0.5, 0, 2.22144<br> Argument too small in __ellint_rj<br>
14884       -4, 0.3, 0.712709<br> Argument too small in __ellint_rj<br> -100000, -0.5,
14885       0.00496945<br> Argument too small in __ellint_rj<br> -1e+10, -0.75, 1.5708e-05<br>
14886       CAUTION: Gross error found at entry 8.<br> Found: 1.45615 Expected 101.045
14887       Error: 68.3919<br> 0.999023, -0.875, 101.045<br> Argument too small in
14888       __ellint_rj<br> -4.14952e+180, 0.5, 7.71119e-91<br>
14889     </p>
14890 <h5>
14891 <a name="special_function_error_rates_rep.error_logs.h90"></a>
14892       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0">Error
14893       Output For ellint_3 with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14894       and test data Elliptic Integral PI: Large Random Data</a>
14895     </h5>
14896 <p>
14897       <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data"></a>Argument
14898       too small in __ellint_rj<br> -88.2952, -8.04919, 0.814724, -0.874724<br>
14899       Argument too small in __ellint_rj<br> -88.2952, -7.46026, 0.135477, -0.827189<br>
14900       Argument too small in __ellint_rj<br> -88.2952, -7.29046, 0.905792, -0.877476<br>
14901       Argument too small in __ellint_rj<br> -88.2952, -6.23236, 0.835009, -0.652152<br>
14902       Argument too small in __ellint_rj<br> -88.2952, -5.57932, 0.126987, -0.512276<br>
14903       Argument too small in __ellint_rj<br> -88.2952, -4.43004, 0.968868, -0.543324<br>
14904       Argument too small in __ellint_rj<br> -88.2952, -3.83666, 0.913376, -0.513389<br>
14905       Argument too small in __ellint_rj<br> -88.2952, 0.93763, 0.221034, 0.158243<br>
14906       Argument too small in __ellint_rj<br> -88.2952, 0.944412, 0.632359, 0.160101<br>
14907       Argument too small in __ellint_rj<br> -88.2952, 2.64719, 0.308167, 0.188127<br>
14908       Argument too small in __ellint_rj<br> -88.2952, 6.29447, 0.0975404, 0.676465<br>
14909       Argument too small in __ellint_rj<br> -88.2952, 6.70017, 0.547221, 0.817785<br>
14910       Argument too small in __ellint_rj<br> -88.2952, 8.11584, 0.278498, 0.837452<br>
14911       Argument too small in __ellint_rj<br> -88.2952, 8.26752, 0.188382, 0.837571<br>
14912       Argument too small in __ellint_rj<br> -88.2952, 9.15014, 0.546881, 0.885365<br>
14913       Argument too small in __ellint_rj<br> -88.2952, 9.29777, 0.992881, 1.06701<br>
14914       Argument too small in __ellint_rj<br> -88.2952, 9.3539, 0.957507, 1.03573<br>
14915       Argument too small in __ellint_rj<br> -88.2952, 9.37736, 0.996461, 1.13933<br>
14916       Argument too small in __ellint_rj<br> -88.2952, 9.85763, 0.964889, 1.24906<br>
14917       Argument too small in __ellint_rj<br> -88.2952, 9.92923, 0.967695, 1.25621<br>
14918       Argument too small in __ellint_rj<br> -86.8166, -8.04919, 0.157613, -0.841405<br>
14919       Argument too small in __ellint_rj<br> -86.8166, -7.46026, 0.725839, -0.859877<br>
14920       Argument too small in __ellint_rj<br> -86.8166, -7.29046, 0.970593, -0.914439<br>
14921       Argument too small in __ellint_rj<br> -86.8166, -6.23236, 0.98111, -0.710627<br>
14922       Argument too small in __ellint_rj<br> -86.8166, -5.57932, 0.957167, -0.58106<br>
14923       Argument too small in __ellint_rj<br> -86.8166, -4.43004, 0.109862, -0.499839<br>
14924       Argument too small in __ellint_rj<br> -86.8166, -3.83666, 0.485376, -0.494286<br>
14925       Argument too small in __ellint_rj<br> -86.8166, 0.93763, 0.798106, 0.162644<br>
14926       Argument too small in __ellint_rj<br> -86.8166, 0.944412, 0.80028, 0.16282<br>
14927       Argument too small in __ellint_rj<br> -86.8166, 2.64719, 0.297029, 0.18978<br>
14928       Argument too small in __ellint_rj<br> -86.8166, 6.29447, 0.141886, 0.682392<br>
14929       Argument too small in __ellint_rj<br> -86.8166, 6.70017, 0.00478348, 0.812885<br>
14930       Argument too small in __ellint_rj<br> -86.8166, 8.11584, 0.421761, 0.849249<br>
14931       Argument too small in __ellint_rj<br> -86.8166, 8.26752, 0.112465, 0.843648<br>
14932       Argument too small in __ellint_rj<br> -86.8166, 9.15014, 0.915736, 0.953733<br>
14933       Argument too small in __ellint_rj<br> -86.8166, 9.29777, 0.639763, 0.936743<br>
14934       Argument too small in __ellint_rj<br> -86.8166, 9.3539, 0.792207, 0.987359<br>
14935       Argument too small in __ellint_rj<br> -86.8166, 9.37736, 0.878431, 1.02525<br>
14936       Argument too small in __ellint_rj<br> -86.8166, 9.85763, 0.959492, 1.25508<br>
14937       Argument too small in __ellint_rj<br> -86.8166, 9.92923, 0.503663, 1.16735<br>
14938       Argument too small in __ellint_rj<br> -84.7616, -8.04919, 0.655741, -0.873305<br>
14939       Argument too small in __ellint_rj<br> -84.7616, -7.46026, 0.797929, -0.879044<br>
14940       Argument too small in __ellint_rj<br> -84.7616, -7.29046, 0.0357117, -0.840785<br>
14941       Argument too small in __ellint_rj<br> -84.7616, -6.23236, 0.361294, -0.635502<br>
14942       Argument too small in __ellint_rj<br> -84.7616, -5.57932, 0.849129, -0.558231<br>
14943       Argument too small in __ellint_rj<br> -84.7616, -4.43004, 0.211924, -0.506533<br>
14944       Argument too small in __ellint_rj<br> -84.7616, -3.83666, 0.933993, -0.527681<br>
14945       Argument too small in __ellint_rj<br> -84.7616, 0.93763, 0.68136, 0.163458<br>
14946       Argument too small in __ellint_rj<br> -84.7616, 0.944412, 0.678735, 0.163582<br>
14947       Argument too small in __ellint_rj<br> -84.7616, 2.64719, 0.398739, 0.193458<br>
14948       Argument too small in __ellint_rj<br> -84.7616, 6.29447, 0.75774, 0.716086<br>
14949       Argument too small in __ellint_rj<br> -84.7616, 6.70017, 0.740647, 0.847849<br>
14950       Argument too small in __ellint_rj<br> -84.7616, 8.11584, 0.743132, 0.883827<br>
14951       Argument too small in __ellint_rj<br> -84.7616, 8.26752, 0.474759, 0.864181<br>
14952       Argument too small in __ellint_rj<br> -84.7616, 9.15014, 0.392227, 0.895646<br>
14953       Argument too small in __ellint_rj<br> -84.7616, 9.29777, 0.422088, 0.933423<br>
14954       Argument too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED
14955       FOR BREVITY ***<br>
14956     </p>
14957 <h5>
14958 <a name="special_function_error_rates_rep.error_logs.h91"></a>
14959       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1">Error
14960       Output For ellint_3 with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
14961       and test data Elliptic Integral PI: Random Data</a>
14962     </h5>
14963 <p>
14964       <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data"></a>CAUTION:
14965       Gross error found at entry 150.<br> Found: 1.09748 Expected 1.76311 Error:
14966       0.606506<br> 0.546881, 1.27977, 0.349984, 1.76311<br> CAUTION: Gross error
14967       found at entry 151.<br> Found: 1.39529 Expected 2.4686 Error: 0.769232<br>
14968       0.546881, 1.31163, 0.907365, 2.4686<br> CAUTION: Gross error found at entry
14969       152.<br> Found: 1.17627 Expected 2.03097 Error: 0.726615<br> 0.546881,
14970       1.42281, 0.196595, 2.03097<br> CAUTION: Gross error found at entry 153.<br>
14971       Found: 1.47192 Expected 2.76894 Error: 0.881179<br> 0.546881, 1.43473, 0.848468,
14972       2.76894<br> CAUTION: Gross error found at entry 154.<br> Found: 1.23674
14973       Expected 2.22733 Error: 0.800966<br> 0.546881, 1.50405, 0.251084, 2.22733<br>
14974       CAUTION: Gross error found at entry 155.<br> Found: 1.87704 Expected 3.98415
14975       Error: 1.12257<br> 0.546881, 1.51564, 0.955018, 3.98415<br> CAUTION: Gross
14976       error found at entry 156.<br> Found: 1.35817 Expected 2.53989 Error: 0.870091<br>
14977       0.546881, 1.52005, 0.616045, 2.53989<br> CAUTION: Gross error found at entry
14978       157.<br> Found: 1.48427 Expected 2.87082 Error: 0.934166<br> 0.546881,
14979       1.52189, 0.778898, 2.87082<br> CAUTION: Gross error found at entry 158.<br>
14980       Found: 1.32687 Expected 2.48679 Error: 0.874176<br> 0.546881, 1.55961, 0.473289,
14981       2.48679<br> CAUTION: Gross error found at entry 159.<br> Found: 2.37485
14982       Expected 5.58805 Error: 1.35301<br> 0.546881, 1.56524, 0.98746, 5.58805<br>
14983       CAUTION: Gross error found at entry 170.<br> Found: 1.08889 Expected 1.74565
14984       Error: 0.603142<br> 0.547221, 1.27977, 0.285839, 1.74565<br> CAUTION: Gross
14985       error found at entry 171.<br> Found: 1.21346 Expected 2.03956 Error: 0.680778<br>
14986       0.547221, 1.31163, 0.67982, 2.03956<br> CAUTION: Gross error found at entry
14987       172.<br> Found: 1.36407 Expected 2.48392 Error: 0.820965<br> 0.547221,
14988       1.42281, 0.7572, 2.48392<br> CAUTION: Gross error found at entry 173.<br>
14989       Found: 1.21442 Expected 2.12881 Error: 0.752947<br> 0.547221, 1.43473, 0.39232,
14990       2.12881<br> CAUTION: Gross error found at entry 174.<br> Found: 1.4409
14991       Expected 2.74399 Error: 0.904352<br> 0.547221, 1.50405, 0.753729, 2.74399<br>
14992       CAUTION: Gross error found at entry 175.<br> Found: 1.32796 Expected 2.46156
14993       Error: 0.853642<br> 0.547221, 1.51564, 0.561557, 2.46156<br> CAUTION: Gross
14994       error found at entry 176.<br> Found: 1.27163 Expected 2.32413 Error: 0.82767<br>
14995       0.547221, 1.52005, 0.380446, 2.32413<br> CAUTION: Gross error found at entry
14996       177.<br> Found: 1.24298 Expected 2.25511 Error: 0.814274<br> 0.547221,
14997       1.52189, 0.208068, 2.25511<br> CAUTION: Gross error found at entry 178.<br>
14998       Found: 1.36528 Expected 2.58635 Error: 0.894379<br> 0.547221, 1.55961, 0.567822,
14999       2.58635<br> CAUTION: Gross error found at entry 179.<br> Found: 1.35151
15000       Expected 2.55463 Error: 0.890206<br> 0.547221, 1.56524, 0.527371, 2.55463<br>
15001       CAUTION: Gross error found at entry 189.<br> Found: 1.01047 Expected 1.52344
15002       Error: 0.507658<br> 0.632359, 0.993308, 0.964966, 1.52344<br> CAUTION:
15003       Gross error found at entry 190.<br> Found: 1.05231 Expected 1.84135 Error:
15004       0.749817<br> 0.632359, 1.27977, 0.129906, 1.84135<br> CAUTION: Gross error
15005       found at entry 191.<br> Found: 1.07393 Expected 1.92224 Error: 0.789918<br>
15006       0.632359, 1.31163, 0.154438, 1.92224<br> CAUTION: Gross error found at entry
15007       192.<br> Found: 1.22616 Expected 2.43657 Error: 0.987156<br> 0.632359,
15008       1.42281, 0.568824, 2.43657<br> CAUTION: Gross error found at entry 193.<br>
15009       Found: 1.18462 Expected 2.33142 Error: 0.968083<br> 0.632359, 1.43473, 0.394908,
15010       2.33142<br> CAUTION: Gross error found at entry 194.<br> Found: 1.25094
15011       Expected 2.59169 Error: 1.0718<br> 0.632359, 1.50405, 0.469391, 2.59169<br>
15012       CAUTION: Gross error found at entry 195.<br> Found: 1.23693 Expected 2.56158
15013       Error: 1.07091<br> 0.632359, 1.51564, 0.387296, 2.56158<br> CAUTION: Gross
15014       error found at entry 196.<br> Found: 1.19839 Expected 2.45293 Error: 1.04685<br>
15015       0.632359, 1.52005, 0.0119021, 2.45293<br> CAUTION: Gross error found at entry
15016       197.<br> Found: 1.39415 Expected 3.05228 Error: 1.18935<br> 0.632359, 1.52189,
15017       0.726955, 3.05228<br> CAUTION: Gross error found at entry 198.<br> Found:
15018       1.25489 Expected 2.6569 Error: 1.11723<br> 0.632359, 1.55961, 0.337123, 2.6569<br>
15019       CAUTION: Gross error found at entry 199.<br> Found: 1.27021 Expected 2.70857
15020       Error: 1.13237<br> 0.632359, 1.56524, 0.38857, 2.70857<br> CAUTION: Gross
15021       error found at entry 209.<br> Found: 0.83304 Expected 1.35947 Error: 0.631944<br>
15022       0.814724, 0.993308, 0.119547, 1.35947<br> CAUTION: Gross error found at entry
15023       210.<br> Found: 1.07764 Expected 2.50291 Error: 1.32258<br> *** FURTHER
15024       CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
15025     </p>
15026 <h5>
15027 <a name="special_function_error_rates_rep.error_logs.h92"></a>
15028       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2">Error
15029       Output For ellint_3 with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
15030       and test data Elliptic Integral PI: Mathworld Data</a>
15031     </h5>
15032 <p>
15033       <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION:
15034       Gross error found at entry 0.<br> Found: -0.809353 Expected -1.55741 Error:
15035       0.924263<br> 1, -1, 0, -1.55741<br> CAUTION: Gross error found at entry
15036       11.<br> Found: 1.07555 Expected 13.2822 Error: 11.3492<br> 0.999023, 1.5,
15037       0, 13.2822<br> CAUTION: Gross error found at entry 13.<br> Found: -5.86896e+09
15038       Expected 1.53659e+10 Error: 1.18973e+4932<br> 0.5, 1e+10, 0.5, 1.53659e+10<br>
15039       Argument too small in __ellint_rj<br> -100000, 10, 0.75, 0.0347926<br>
15040       Argument too small in __ellint_rj<br> -1e+10, 10, 0.875, 0.000109956<br>
15041       Argument too small in __ellint_rj<br> -1e+10, 1e+20, 0.875, 1.00001e+15<br>
15042       Argument too small in __ellint_rj<br> -1e+10, 1.57031, 0.875, 1.57081e-05<br>
15043       CAUTION: Gross error found at entry 18.<br> Found: -6.25413e+09 Expected
15044       6.43274e+21 Error: 1.18973e+4932<br> 0.999023, 1e+20, 0.875, 6.43274e+21<br>
15045       CAUTION: Gross error found at entry 19.<br> Found: 0.102424 Expected 0.196321
15046       Error: 0.916748<br> 50, 0.125, 0.25, 0.196321<br> CAUTION: Gross error
15047       found at entry 20.<br> Found: 0.798807 Expected 1.773 Error: 1.21956<br>
15048       1.125, 1, 0.25, 1.773<br> CAUTION: Gross error found at entry 21.<br> Found:
15049       7.07138 Expected 0.662468 Error: 9.6743<br> 1.125, 10, 0.25, 0.662468<br>
15050       CAUTION: Gross error found at entry 22.<br> Found: 2.04288 Expected -0.142697
15051       Error: 1.18973e+4932<br> 1.125, 3, 0.25, -0.142697<br> CAUTION: Gross error
15052       found at entry 23.<br> Found: 1.07762 Expected 22.2699 Error: 19.6659<br>
15053       1.00391, 1.5, 0.125, 22.2699<br> CAUTION: Gross error found at entry 24.<br>
15054       Found: 15.1275 Expected -0.535406 Error: 1.18973e+4932<br> 1.00391, 21.5,
15055       0.125, -0.535406<br> CAUTION: Gross error found at entry 41.<br> Found:
15056       1.57454 Expected 3.0338 Error: 0.926787<br> 0.5, 2, 0, 3.0338<br> CAUTION:
15057       Gross error found at entry 42.<br> Found: 3.0338 Expected 1.57454 Error:
15058       0.926787<br> -0.5, 2, 0, 1.57454<br> CAUTION: Gross error found at entry
15059       43.<br> Found: -1.57454 Expected -3.0338 Error: 0.926787<br> 0.5, -2, 0,
15060       -3.0338<br> CAUTION: Gross error found at entry 44.<br> Found: -3.0338
15061       Expected -1.57454 Error: 0.926787<br> -0.5, -2, 0, -1.57454<br> CAUTION:
15062       Found non-finite result, when a finite value was expected at entry 51<br>
15063       Found: inf Expected -2.87535 Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br>
15064       CAUTION: Gross error found at entry 51.<br> Found: inf Expected -2.87535
15065       Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br> CAUTION: Found non-finite
15066       result, when a finite value was expected at entry 52<br> Found: -inf Expected
15067       2.87535 Error: 1.18973e+4932<br> 1, -2, 0.5, 2.87535<br> CAUTION: Gross
15068       error found at entry 52.<br> Found: -inf Expected 2.87535 Error: 1.18973e+4932<br>
15069       1, -2, 0.5, 2.87535<br> CAUTION: Found non-finite result, when a finite value
15070       was expected at entry 53<br> Found: inf Expected -2.18504 Error: 1.18973e+4932<br>
15071       1, 2, 6.22302e-61, -2.18504<br> CAUTION: Gross error found at entry 53.<br>
15072       Found: inf Expected -2.18504 Error: 1.18973e+4932<br> 1, 2, 6.22302e-61,
15073       -2.18504<br> CAUTION: Found non-finite result, when a finite value was expected
15074       at entry 54<br> Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1,
15075       -2, 6.22302e-61, 2.18504<br> CAUTION: Gross error found at entry 54.<br>
15076       Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1, -2, 6.22302e-61,
15077       2.18504<br> CAUTION: Gross error found at entry 57.<br> Found: 0.703907
15078       Expected 0.000975941 Error: 720.259<br> 20, 3.14257, 0.5, 0.000975941<br>
15079       CAUTION: Gross error found at entry 58.<br> Found: -0.703907 Expected -0.000975941
15080       Error: 720.259<br> 20, -3.14257, 0.5, -0.000975941<br> CAUTION: Gross error
15081       found at entry 59.<br> Found: 1.24445 Expected -27.1647 Error: 1.18973e+4932<br>
15082       1.01562, 1.6958, 0.5, -27.1647<br> CAUTION: Gross error found at entry 60.<br>
15083       Found: -1.24445 Expected 27.1647 Error: 1.18973e+4932<br> 1.01562, -1.6958,
15084       0.5, 27.1647<br>
15085     </p>
15086 <h5>
15087 <a name="special_function_error_rates_rep.error_logs.h93"></a>
15088       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_">Error
15089       Output For expint (Ei) with compiler GNU C++ version 7.1.0 and library &lt;cmath&gt;
15090       and test data Exponential Integral Ei</a>
15091     </h5>
15092 <p>
15093       <a name="errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei"></a>Continued
15094       fraction failed in __expint_En_cont_frac.<br> -1.30539, -0.134326<br>
15095     </p>
15096 <h5>
15097 <a name="special_function_error_rates_rep.error_logs.h94"></a>
15098       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp">Error
15099       Output For ibeta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and
15100       test data Incomplete Beta Function: Large and Diverse Values</a>
15101     </h5>
15102 <p>
15103       <a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values"></a>underflow<br>
15104       1.04761e-05, 39078.2, 0.913384, 95444.4, 0, 1, 0<br> underflow<br> 1.2158e-05,
15105       24110.5, 0.135563, 82239.7, 0, 1, 0<br> underflow<br> 1.30342e-05, 26168.3,
15106       0.127074, 76710.7, 0, 1, 0<br> underflow<br> 1.51962e-05, 16177.5, 0.814742,
15107       65795.4, 0, 1, 0<br> underflow<br> 1.64873e-05, 470997, 0.127074, 60639.1,
15108       0, 1, 0<br> underflow<br> 1.66259e-05, 147819, 0.632396, 60134.5, 0, 1,
15109       0<br> underflow<br> 1.78638e-05, 439.387, 0.835025, 55972.4, 0, 1, 0<br>
15110       underflow<br> 2.00434e-05, 482.007, 0.905801, 49885.1, 0, 1, 0<br> underflow<br>
15111       2.05189e-05, 236088, 0.835025, 48722.7, 0, 1, 0<br> underflow<br> 2.14336e-05,
15112       3719.28, 0.814742, 46647, 0, 1, 0<br> underflow<br> 2.24486e-05, 445071,
15113       0.221112, 44532.6, 0, 1, 0<br> underflow<br> 2.34849e-05, 25542.8, 0.968871,
15114       42569.8, 0, 1, 0<br> underflow<br> 2.39993e-05, 462.946, 0.814742, 41661.1,
15115       0, 1, 0<br> underflow<br> 2.52178e-05, 1832.27, 0.913384, 39646.4, 0, 1,
15116       0<br> underflow<br> 2.87756e-05, 25491.8, 0.905801, 34740.9, 0, 1, 0<br>
15117       underflow<br> 2.89316e-05, 494.984, 0.968871, 34557.6, 0, 1, 0<br> underflow<br>
15118       3.11413e-05, 348144, 0.308236, 32098.3, 0, 1, 0<br> underflow<br> 3.12319e-05,
15119       33713, 0.221112, 32007.5, 0, 1, 0<br> underflow<br> 3.19889e-05, 3931.19,
15120       0.308236, 31251.9, 0, 1, 0<br> underflow<br> 3.27129e-05, 3109.49, 0.968871,
15121       30560.4, 0, 1, 0<br> underflow<br> 3.27529e-05, 25796.3, 0.835025, 30520.9,
15122       0, 1, 0<br> underflow<br> 3.34106e-05, 3378.01, 0.221112, 29922, 0, 1,
15123       0<br> underflow<br> 3.40793e-05, 288783, 0.814742, 29330.2, 0, 1, 0<br>
15124       underflow<br> 3.46418e-05, 411.559, 0.913384, 28860.3, 0, 1, 0<br> underflow<br>
15125       3.61632e-05, 311937, 0.905801, 27639.2, 0, 1, 0<br> underflow<br> 3.75686e-05,
15126       386440, 0.913384, 26604.5, 0, 1, 0<br> underflow<br> 3.99261e-05, 495352,
15127       0.968871, 25032.6, 0, 1, 0<br> underflow<br> 4.01492e-05, 3246.23, 0.905801,
15128       24898.5, 0, 1, 0<br> underflow<br> 4.0288e-05, 2569.28, 0.835025, 24812.9,
15129       0, 1, 0<br> underflow<br> 4.11667e-05, 24253.8, 0.308236, 24280.8, 0, 1,
15130       0<br> underflow<br> 4.17714e-05, 274447, 0.135563, 23926.7, 0, 1, 0<br>
15131       underflow<br> 4.66877e-05, 3780.93, 0.632396, 21410.1, 0, 1, 0<br> underflow<br>
15132       4.73604e-05, 48598.7, 0.632396, 21103.3, 0, 1, 0<br> underflow<br> 0.00013245,
15133       251.768, 0.968871, 7543.9, 0, 1, 0<br> underflow<br> 0.000168283, 195801,
15134       0.905801, 5929.61, 0, 1, 0<br> underflow<br> 0.000177906, 276489, 0.814742,
15135       5607.86, 0, 1, 0<br> underflow<br> 0.000183097, 316055, 0.127074, 5448.36,
15136       0, 1, 0<br> underflow<br> 0.000190369, 159132, 0.835025, 5240.42, 0, 1,
15137       0<br> underflow<br> 0.000191066, 419861, 0.913384, 5220.29, 0, 1, 0<br>
15138       underflow<br> 0.000192195, 177798, 0.308236, 5190.39, 0, 1, 0<br> underflow<br>
15139       0.000220499, 107380, 0.135563, 4523.03, 0, 1, 0<br> underflow<br> 0.00022254,
15140       1432.25, 0.814742, 4485.74, 0, 1, 0<br> underflow<br> 0.000240291, 49604.4,
15141       0.632396, 4150.25, 0, 1, 0<br> underflow<br> 0.000251444, 15605.8, 0.135563,
15142       3966.81, 0, 1, 0<br> underflow<br> 0.000274279, 289206, 0.968871, 3632.79,
15143       0, 1, 0<br> underflow<br> 0.000274343, 2954.47, 0.308236, 3636.51, 0, 1,
15144       0<br> underflow<br> 0.000278714, 4023.16, 0.632396, 3579.05, 0, 1, 0<br>
15145       underflow<br> 0.000288369, 460073, 0.221112, 3454.19, 0, 1, 0<br> underflow<br>
15146       0.000294717, 4642.26, 0.221112, 3384.08, 0, 1, 0<br> underflow<br> 0.000303403,
15147       2574.36, 0.835025, 3287.52, 0, 1, 0<br> underflow<br> 0.000304309, 4480.75,
15148       0.905801, 3277.17, 0, 1, 0<br> underflow<br> 0.00031313, 47957, 0.308236,
15149       3182.22, 0, 1, 0<br> underflow<br> 0.000320063, 25544.6, 0.905801, 3113.68,
15150       0, 1, 0<br> underflow<br> 0.000334818, 29065.5, 0.968871, 2975.86, 0, 1,
15151       0<br> underflow<br> 0.00034899, 41187.6, 0.913384, 2854.23, 0, 1, 0<br>
15152       underflow<br> 0.000350247, 426.308, 0.905801, 2848.5, 0, 1, 0<br> underflow<br>
15153       0.000357727, 31752.2, 0.127074, 2784.5, 0, 1, 0<br> underflow<br> 0.000412091,
15154       367.714, 0.913384, 2420.17, 0, 1, 0<br> underflow<br> 0.000417933, 4668.47,
15155       0.968871, 2383.72, 0, 1, 0<br> underflow<br> 0.000424632, 17994.9, 0.221112,
15156       2344.63, 0, 1, 0<br> underflow<br> 0.000427051, 2443.44, 0.913384, 2333.28,
15157       0, 1, 0<br> underflow<br> 0.000437724, 454399, 0.632396, 2270.98, 0, 1,
15158       0<br> underflow<br> 0.000450377, 10660.8, 0.835025, 2210.53, 0, 1, 0<br>
15159       underflow<br> 0.000475601, 19603, 0.814742, 2092.17, 0, 1, 0<br> underflow<br>
15160       0.00116972, 4487.22, 0.221112, 845.964, 0, 1, 0<br> underflow<br> 0.00124188,
15161       211066, 0.632396, 792.493, 0, 1, 0<br> underflow<br> 0.00128578, 4738.41,
15162       0.308236, 768.75, 0, 1, 0<br> underflow<br> 0.00133388, 46277.8, 0.913384,
15163       738.46, 0, 1, 0<br> underflow<br> 0.00138692, 2158.76, 0.814742, 712.816,
15164       0, 1, 0<br> underflow<br> 0.00153268, 13060.2, 0.968871, 642.474, 0, 1,
15165       0<br> underflow<br> 0.00159946, 1780.43, 0.968871, 617.202, 0, 1, 0<br>
15166       *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
15167     </p>
15168 <h5>
15169 <a name="special_function_error_rates_rep.error_logs.h95"></a>
15170       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_">Error
15171       Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15172       and test data Jacobi Elliptic: Modulus near 1</a>
15173     </h5>
15174 <p>
15175       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
15176       &gt; 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| &gt; 1.0<br>
15177       -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| &gt; 1.0<br> -4.0246,
15178       1, -0.99936, 0.0357762, 0.0356829<br> |m| &gt; 1.0<br> -4.0246, 1, -0.999359,
15179       0.0357895, 0.0356695<br> |m| &gt; 1.0<br> -4.0246, 1.00001, -0.999354,
15180       0.0359354, 0.0355222<br> |m| &gt; 1.0<br> -4.0246, 1.00003, -0.999347,
15181       0.0361343, 0.0353212<br> |m| &gt; 1.0<br> -4.0246, 1.00004, -0.999343,
15182       0.036247, 0.0352073<br> |m| &gt; 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
15183       0.0343296<br> |m| &gt; 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
15184       |m| &gt; 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
15185       |m| &gt; 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
15186       &gt; 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
15187       &gt; 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| &gt;
15188       1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| &gt; 1.0<br>
15189       -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| &gt; 1.0<br> -4.0246,
15190       1.03059, -0.890373, 0.455232, -0.397492<br> |m| &gt; 1.0<br> -4.0246, 1.06239,
15191       -0.607191, 0.794556, -0.76412<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998849,
15192       0.0479567, 0.0479467<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
15193       0.0479367<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
15194       |m| &gt; 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| &gt;
15195       1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| &gt;
15196       1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| &gt;
15197       1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| &gt;
15198       1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| &gt; 1.0<br>
15199       -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| &gt; 1.0<br>
15200       -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| &gt; 1.0<br>
15201       -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| &gt; 1.0<br>
15202       -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| &gt; 1.0<br>
15203       -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| &gt; 1.0<br>
15204       -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| &gt; 1.0<br>
15205       -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| &gt; 1.0<br>
15206       -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| &gt; 1.0<br>
15207       -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| &gt; 1.0<br>
15208       -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| &gt; 1.0<br> -3.64523,
15209       1, -0.998636, 0.0522087, 0.0521814<br> |m| &gt; 1.0<br> -3.64523, 1, -0.998635,
15210       0.0522268, 0.052163<br> |m| &gt; 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
15211       0.0521538<br> |m| &gt; 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
15212       |m| &gt; 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
15213       |m| &gt; 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
15214       |m| &gt; 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
15215       |m| &gt; 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
15216       |m| &gt; 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
15217       |m| &gt; 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
15218       |m| &gt; 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
15219       |m| &gt; 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
15220       |m| &gt; 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
15221       |m| &gt; 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
15222       |m| &gt; 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
15223       |m| &gt; 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
15224       |m| &gt; 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| &gt;
15225       1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| &gt; 1.0<br>
15226       -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| &gt; 1.0<br> -3.11618,
15227       1, -0.996076, 0.0885019, 0.0884538<br> |m| &gt; 1.0<br> -3.11618, 1.00001,
15228       -0.996071, 0.0885593, 0.0883936<br> |m| &gt; 1.0<br> -3.11618, 1.00003,
15229       -0.996064, 0.0886376, 0.0883114<br> |m| &gt; 1.0<br> -3.11618, 1.00004,
15230       -0.99606, 0.0886819, 0.0882648<br> |m| &gt; 1.0<br> -3.11618, 1.0001, -0.99603,
15231       0.0890236, 0.0879059<br> |m| &gt; 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
15232       0.0875607<br> |m| &gt; 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
15233       0.0869386<br> |m| &gt; 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
15234       0.0841353<br> |m| &gt; 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
15235       0.0812953<br> |m| &gt; 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
15236       0.0751049<br> |m| &gt; 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
15237       0.0534858<br> |m| &gt; 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
15238       -0.00273723<br> |m| &gt; 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
15239       -0.0934336<br> |m| &gt; 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
15240       -0.289151<br> |m| &gt; 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
15241       |m| &gt; 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
15242       CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
15243     </p>
15244 <h5>
15245 <a name="special_function_error_rates_rep.error_logs.h96"></a>
15246       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_">Error
15247       Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15248       and test data Jacobi Elliptic: Modulus near 1</a>
15249     </h5>
15250 <p>
15251       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
15252       &gt; 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| &gt; 1.0<br>
15253       -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| &gt; 1.0<br> -4.0246,
15254       1, -0.99936, 0.0357762, 0.0356829<br> |m| &gt; 1.0<br> -4.0246, 1, -0.999359,
15255       0.0357895, 0.0356695<br> |m| &gt; 1.0<br> -4.0246, 1.00001, -0.999354,
15256       0.0359354, 0.0355222<br> |m| &gt; 1.0<br> -4.0246, 1.00003, -0.999347,
15257       0.0361343, 0.0353212<br> |m| &gt; 1.0<br> -4.0246, 1.00004, -0.999343,
15258       0.036247, 0.0352073<br> |m| &gt; 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
15259       0.0343296<br> |m| &gt; 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
15260       |m| &gt; 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
15261       |m| &gt; 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
15262       &gt; 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
15263       &gt; 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| &gt;
15264       1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| &gt; 1.0<br>
15265       -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| &gt; 1.0<br> -4.0246,
15266       1.03059, -0.890373, 0.455232, -0.397492<br> |m| &gt; 1.0<br> -4.0246, 1.06239,
15267       -0.607191, 0.794556, -0.76412<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998849,
15268       0.0479567, 0.0479467<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
15269       0.0479367<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
15270       |m| &gt; 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| &gt;
15271       1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| &gt;
15272       1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| &gt;
15273       1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| &gt;
15274       1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| &gt; 1.0<br>
15275       -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| &gt; 1.0<br>
15276       -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| &gt; 1.0<br>
15277       -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| &gt; 1.0<br>
15278       -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| &gt; 1.0<br>
15279       -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| &gt; 1.0<br>
15280       -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| &gt; 1.0<br>
15281       -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| &gt; 1.0<br>
15282       -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| &gt; 1.0<br>
15283       -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| &gt; 1.0<br>
15284       -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| &gt; 1.0<br> -3.64523,
15285       1, -0.998636, 0.0522087, 0.0521814<br> |m| &gt; 1.0<br> -3.64523, 1, -0.998635,
15286       0.0522268, 0.052163<br> |m| &gt; 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
15287       0.0521538<br> |m| &gt; 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
15288       |m| &gt; 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
15289       |m| &gt; 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
15290       |m| &gt; 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
15291       |m| &gt; 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
15292       |m| &gt; 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
15293       |m| &gt; 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
15294       |m| &gt; 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
15295       |m| &gt; 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
15296       |m| &gt; 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
15297       |m| &gt; 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
15298       |m| &gt; 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
15299       |m| &gt; 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
15300       |m| &gt; 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| &gt;
15301       1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| &gt; 1.0<br>
15302       -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| &gt; 1.0<br> -3.11618,
15303       1, -0.996076, 0.0885019, 0.0884538<br> |m| &gt; 1.0<br> -3.11618, 1.00001,
15304       -0.996071, 0.0885593, 0.0883936<br> |m| &gt; 1.0<br> -3.11618, 1.00003,
15305       -0.996064, 0.0886376, 0.0883114<br> |m| &gt; 1.0<br> -3.11618, 1.00004,
15306       -0.99606, 0.0886819, 0.0882648<br> |m| &gt; 1.0<br> -3.11618, 1.0001, -0.99603,
15307       0.0890236, 0.0879059<br> |m| &gt; 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
15308       0.0875607<br> |m| &gt; 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
15309       0.0869386<br> |m| &gt; 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
15310       0.0841353<br> |m| &gt; 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
15311       0.0812953<br> |m| &gt; 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
15312       0.0751049<br> |m| &gt; 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
15313       0.0534858<br> |m| &gt; 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
15314       -0.00273723<br> |m| &gt; 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
15315       -0.0934336<br> |m| &gt; 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
15316       -0.289151<br> |m| &gt; 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
15317       |m| &gt; 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
15318       CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
15319     </p>
15320 <h5>
15321 <a name="special_function_error_rates_rep.error_logs.h97"></a>
15322       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_">Error
15323       Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15324       and test data Jacobi Elliptic: Modulus near 1</a>
15325     </h5>
15326 <p>
15327       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
15328       &gt; 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| &gt; 1.0<br>
15329       -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| &gt; 1.0<br> -4.0246,
15330       1, -0.99936, 0.0357762, 0.0356829<br> |m| &gt; 1.0<br> -4.0246, 1, -0.999359,
15331       0.0357895, 0.0356695<br> |m| &gt; 1.0<br> -4.0246, 1.00001, -0.999354,
15332       0.0359354, 0.0355222<br> |m| &gt; 1.0<br> -4.0246, 1.00003, -0.999347,
15333       0.0361343, 0.0353212<br> |m| &gt; 1.0<br> -4.0246, 1.00004, -0.999343,
15334       0.036247, 0.0352073<br> |m| &gt; 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
15335       0.0343296<br> |m| &gt; 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
15336       |m| &gt; 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
15337       |m| &gt; 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
15338       &gt; 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
15339       &gt; 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| &gt;
15340       1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| &gt; 1.0<br>
15341       -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| &gt; 1.0<br> -4.0246,
15342       1.03059, -0.890373, 0.455232, -0.397492<br> |m| &gt; 1.0<br> -4.0246, 1.06239,
15343       -0.607191, 0.794556, -0.76412<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998849,
15344       0.0479567, 0.0479467<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
15345       0.0479367<br> |m| &gt; 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
15346       |m| &gt; 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| &gt;
15347       1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| &gt;
15348       1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| &gt;
15349       1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| &gt;
15350       1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| &gt; 1.0<br>
15351       -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| &gt; 1.0<br>
15352       -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| &gt; 1.0<br>
15353       -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| &gt; 1.0<br>
15354       -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| &gt; 1.0<br>
15355       -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| &gt; 1.0<br>
15356       -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| &gt; 1.0<br>
15357       -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| &gt; 1.0<br>
15358       -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| &gt; 1.0<br>
15359       -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| &gt; 1.0<br>
15360       -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| &gt; 1.0<br> -3.64523,
15361       1, -0.998636, 0.0522087, 0.0521814<br> |m| &gt; 1.0<br> -3.64523, 1, -0.998635,
15362       0.0522268, 0.052163<br> |m| &gt; 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
15363       0.0521538<br> |m| &gt; 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
15364       |m| &gt; 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
15365       |m| &gt; 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
15366       |m| &gt; 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
15367       |m| &gt; 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
15368       |m| &gt; 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
15369       |m| &gt; 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
15370       |m| &gt; 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
15371       |m| &gt; 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
15372       |m| &gt; 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
15373       |m| &gt; 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
15374       |m| &gt; 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
15375       |m| &gt; 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
15376       |m| &gt; 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| &gt;
15377       1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| &gt; 1.0<br>
15378       -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| &gt; 1.0<br> -3.11618,
15379       1, -0.996076, 0.0885019, 0.0884538<br> |m| &gt; 1.0<br> -3.11618, 1.00001,
15380       -0.996071, 0.0885593, 0.0883936<br> |m| &gt; 1.0<br> -3.11618, 1.00003,
15381       -0.996064, 0.0886376, 0.0883114<br> |m| &gt; 1.0<br> -3.11618, 1.00004,
15382       -0.99606, 0.0886819, 0.0882648<br> |m| &gt; 1.0<br> -3.11618, 1.0001, -0.99603,
15383       0.0890236, 0.0879059<br> |m| &gt; 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
15384       0.0875607<br> |m| &gt; 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
15385       0.0869386<br> |m| &gt; 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
15386       0.0841353<br> |m| &gt; 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
15387       0.0812953<br> |m| &gt; 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
15388       0.0751049<br> |m| &gt; 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
15389       0.0534858<br> |m| &gt; 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
15390       -0.00273723<br> |m| &gt; 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
15391       -0.0934336<br> |m| &gt; 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
15392       -0.289151<br> |m| &gt; 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
15393       |m| &gt; 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
15394       CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
15395     </p>
15396 <h5>
15397 <a name="special_function_error_rates_rep.error_logs.h98"></a>
15398       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0">Error
15399       Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15400       and test data Jacobi Elliptic: Random Small Values</a>
15401     </h5>
15402 <p>
15403       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
15404       &gt; 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| &gt; 1.0<br>
15405       2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| &gt; 1.0<br> 6.93323e-12,
15406       1.65574, 6.93323e-12, 1, 1<br> |m| &gt; 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
15407       1, 1<br> |m| &gt; 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
15408       |m| &gt; 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| &gt; 1.0<br>
15409       1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| &gt; 1.0<br> 1.42147e-10,
15410       1.65574, 1.42147e-10, 1, 1<br> |m| &gt; 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
15411       1, 1<br> |m| &gt; 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
15412       |m| &gt; 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| &gt; 1.0<br>
15413       2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| &gt; 1.0<br> 4.76278e-09,
15414       1.65574, 4.76278e-09, 1, 1<br> |m| &gt; 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
15415       1, 1<br> |m| &gt; 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
15416       |m| &gt; 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| &gt; 1.0<br>
15417       1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| &gt; 1.0<br> 2.37997e-07,
15418       1.65574, 2.37997e-07, 1, 1<br> |m| &gt; 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
15419       1, 1<br> |m| &gt; 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
15420       &gt; 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| &gt; 1.0<br>
15421       3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| &gt; 1.0<br> 7.51721e-06,
15422       1.65574, 7.51721e-06, 1, 1<br> |m| &gt; 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
15423       1, 1<br> |m| &gt; 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
15424       &gt; 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| &gt; 1.0<br>
15425       9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| &gt; 1.0<br> 0.000219495,
15426       1.65574, 0.000219495, 1, 1<br> |m| &gt; 1.0<br> 0.000439522, 1.65574, 0.000439521,
15427       1, 1<br> |m| &gt; 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
15428       |m| &gt; 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
15429       |m| &gt; 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
15430       |m| &gt; 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
15431       |m| &gt; 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
15432       |m| &gt; 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
15433       |m| &gt; 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
15434       |m| &gt; 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
15435       &gt; 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| &gt;
15436       1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| &gt; 1.0<br>
15437       0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| &gt; 1.0<br> 1.65574,
15438       1.65574, 0.408154, 0.912913, -0.737088<br>
15439     </p>
15440 <h5>
15441 <a name="special_function_error_rates_rep.error_logs.h99"></a>
15442       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0">Error
15443       Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15444       and test data Jacobi Elliptic: Random Small Values</a>
15445     </h5>
15446 <p>
15447       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
15448       &gt; 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| &gt; 1.0<br>
15449       2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| &gt; 1.0<br> 6.93323e-12,
15450       1.65574, 6.93323e-12, 1, 1<br> |m| &gt; 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
15451       1, 1<br> |m| &gt; 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
15452       |m| &gt; 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| &gt; 1.0<br>
15453       1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| &gt; 1.0<br> 1.42147e-10,
15454       1.65574, 1.42147e-10, 1, 1<br> |m| &gt; 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
15455       1, 1<br> |m| &gt; 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
15456       |m| &gt; 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| &gt; 1.0<br>
15457       2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| &gt; 1.0<br> 4.76278e-09,
15458       1.65574, 4.76278e-09, 1, 1<br> |m| &gt; 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
15459       1, 1<br> |m| &gt; 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
15460       |m| &gt; 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| &gt; 1.0<br>
15461       1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| &gt; 1.0<br> 2.37997e-07,
15462       1.65574, 2.37997e-07, 1, 1<br> |m| &gt; 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
15463       1, 1<br> |m| &gt; 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
15464       &gt; 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| &gt; 1.0<br>
15465       3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| &gt; 1.0<br> 7.51721e-06,
15466       1.65574, 7.51721e-06, 1, 1<br> |m| &gt; 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
15467       1, 1<br> |m| &gt; 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
15468       &gt; 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| &gt; 1.0<br>
15469       9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| &gt; 1.0<br> 0.000219495,
15470       1.65574, 0.000219495, 1, 1<br> |m| &gt; 1.0<br> 0.000439522, 1.65574, 0.000439521,
15471       1, 1<br> |m| &gt; 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
15472       |m| &gt; 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
15473       |m| &gt; 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
15474       |m| &gt; 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
15475       |m| &gt; 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
15476       |m| &gt; 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
15477       |m| &gt; 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
15478       |m| &gt; 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
15479       &gt; 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| &gt;
15480       1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| &gt; 1.0<br>
15481       0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| &gt; 1.0<br> 1.65574,
15482       1.65574, 0.408154, 0.912913, -0.737088<br>
15483     </p>
15484 <h5>
15485 <a name="special_function_error_rates_rep.error_logs.h100"></a>
15486       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0">Error
15487       Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15488       and test data Jacobi Elliptic: Random Small Values</a>
15489     </h5>
15490 <p>
15491       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
15492       &gt; 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| &gt; 1.0<br>
15493       2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| &gt; 1.0<br> 6.93323e-12,
15494       1.65574, 6.93323e-12, 1, 1<br> |m| &gt; 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
15495       1, 1<br> |m| &gt; 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
15496       |m| &gt; 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| &gt; 1.0<br>
15497       1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| &gt; 1.0<br> 1.42147e-10,
15498       1.65574, 1.42147e-10, 1, 1<br> |m| &gt; 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
15499       1, 1<br> |m| &gt; 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
15500       |m| &gt; 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| &gt; 1.0<br>
15501       2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| &gt; 1.0<br> 4.76278e-09,
15502       1.65574, 4.76278e-09, 1, 1<br> |m| &gt; 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
15503       1, 1<br> |m| &gt; 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
15504       |m| &gt; 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| &gt; 1.0<br>
15505       1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| &gt; 1.0<br> 2.37997e-07,
15506       1.65574, 2.37997e-07, 1, 1<br> |m| &gt; 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
15507       1, 1<br> |m| &gt; 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
15508       &gt; 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| &gt; 1.0<br>
15509       3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| &gt; 1.0<br> 7.51721e-06,
15510       1.65574, 7.51721e-06, 1, 1<br> |m| &gt; 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
15511       1, 1<br> |m| &gt; 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
15512       &gt; 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| &gt; 1.0<br>
15513       9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| &gt; 1.0<br> 0.000219495,
15514       1.65574, 0.000219495, 1, 1<br> |m| &gt; 1.0<br> 0.000439522, 1.65574, 0.000439521,
15515       1, 1<br> |m| &gt; 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
15516       |m| &gt; 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
15517       |m| &gt; 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
15518       |m| &gt; 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
15519       |m| &gt; 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
15520       |m| &gt; 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
15521       |m| &gt; 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
15522       |m| &gt; 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
15523       &gt; 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| &gt;
15524       1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| &gt; 1.0<br>
15525       0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| &gt; 1.0<br> 1.65574,
15526       1.65574, 0.408154, 0.912913, -0.737088<br>
15527     </p>
15528 <h5>
15529 <a name="special_function_error_rates_rep.error_logs.h101"></a>
15530       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1">Error
15531       Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15532       and test data Jacobi Elliptic: Mathworld Data</a>
15533     </h5>
15534 <p>
15535       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
15536       &gt; 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| &gt; 1.0<br>
15537       -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| &gt; 1.0<br> 0.25, 1.5, 0.24183,
15538       0.970319, 0.931888<br> |m| &gt; 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
15539       0.931888<br> |m| &gt; 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
15540       |m| &gt; 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| &gt;
15541       1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| &gt; 1.0<br> -25,
15542       1.5, -0.618665, 0.785655, 0.372585<br>
15543     </p>
15544 <h5>
15545 <a name="special_function_error_rates_rep.error_logs.h102"></a>
15546       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1">Error
15547       Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15548       and test data Jacobi Elliptic: Mathworld Data</a>
15549     </h5>
15550 <p>
15551       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
15552       &gt; 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| &gt; 1.0<br>
15553       -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| &gt; 1.0<br> 0.25, 1.5, 0.24183,
15554       0.970319, 0.931888<br> |m| &gt; 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
15555       0.931888<br> |m| &gt; 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
15556       |m| &gt; 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| &gt;
15557       1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| &gt; 1.0<br> -25,
15558       1.5, -0.618665, 0.785655, 0.372585<br>
15559     </p>
15560 <h5>
15561 <a name="special_function_error_rates_rep.error_logs.h103"></a>
15562       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1">Error
15563       Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
15564       and test data Jacobi Elliptic: Mathworld Data</a>
15565     </h5>
15566 <p>
15567       <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
15568       &gt; 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| &gt; 1.0<br>
15569       -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| &gt; 1.0<br> 0.25, 1.5, 0.24183,
15570       0.970319, 0.931888<br> |m| &gt; 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
15571       0.931888<br> |m| &gt; 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
15572       |m| &gt; 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| &gt;
15573       1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| &gt; 1.0<br> -25,
15574       1.5, -0.618665, 0.785655, 0.372585<br>
15575     </p>
15576 <h5>
15577 <a name="special_function_error_rates_rep.error_logs.h104"></a>
15578       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3">Error
15579       Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
15580       and test data Mathematica Data - Large orders and other bug cases</a>
15581     </h5>
15582 <p>
15583       <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases"></a>underflow<br>
15584       168, 150, -6.52661e-66<br> underflow<br> 169, 202, 9.2734e-88<br> domain
15585       error<br> 20, -9.5, -0.00103076<br> domain error<br> 21, -9.5, 4.28582e+26<br>
15586       domain error<br> 22, -9.5, -0.00419144<br> domain error<br> 23, -9.5,
15587       8.6745e+29<br> domain error<br> 24, -9.5, -0.0204825<br> domain error<br>
15588       25, -9.5, 2.08188e+33<br> domain error<br> 26, -9.5, -0.118403<br> domain
15589       error<br> 27, -9.5, 5.84592e+36<br> domain error<br> 28, -9.5, -0.798969<br>
15590       domain error<br> 29, -9.5, 1.89875e+40<br> domain error<br> 30, -9.5,
15591       -6.22245<br> underflow<br> 10, 1.32923e+36, -0<br> underflow<br> 15,
15592       1.32923e+36, 0<br>
15593     </p>
15594 <h5>
15595 <a name="special_function_error_rates_rep.error_logs.h105"></a>
15596       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4">Error
15597       Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
15598       and test data Mathematica Data - large negative arguments</a>
15599     </h5>
15600 <p>
15601       <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments"></a>domain
15602       error<br> 124, -1.5, 7.63705e+240<br> domain error<br> 124, -2.5, 7.63705e+240<br>
15603       domain error<br> 124, -3.5, 7.63705e+240<br> domain error<br> 124, -4.5,
15604       7.63705e+240<br> domain error<br> 124, -5.5, 7.63705e+240<br> domain
15605       error<br> 124, -6.5, 7.63705e+240<br> domain error<br> 124, -7.5, 7.63705e+240<br>
15606       domain error<br> 124, -8.5, 7.63705e+240<br> domain error<br> 124, -9.5,
15607       7.63705e+240<br> domain error<br> 124, -10.5, 7.63705e+240<br> domain
15608       error<br> 124, -11.5, 7.63705e+240<br> domain error<br> 124, -12.5, 7.63705e+240<br>
15609       domain error<br> 124, -13.5, 7.63705e+240<br> domain error<br> 124, -14.5,
15610       7.63705e+240<br> domain error<br> 124, -15.5, 7.63705e+240<br> domain
15611       error<br> 124, -16.5, 7.63705e+240<br> domain error<br> 124, -17.5, 7.63705e+240<br>
15612       domain error<br> 124, -18.5, 7.63705e+240<br> domain error<br> 124, -19.5,
15613       7.63705e+240<br> domain error<br> 124, -20.5, 7.63705e+240<br> domain
15614       error<br> 124, -1.5, -7.63705e+240<br> domain error<br> 124, -2.5, -7.63705e+240<br>
15615       domain error<br> 124, -3.5, -7.63705e+240<br> domain error<br> 124, -4.5,
15616       -7.63705e+240<br> domain error<br> 124, -5.5, -7.63705e+240<br> domain
15617       error<br> 124, -6.5, -7.63705e+240<br> domain error<br> 124, -7.5, -7.63705e+240<br>
15618       domain error<br> 124, -8.5, -7.63705e+240<br> domain error<br> 124, -9.5,
15619       -7.63705e+240<br> domain error<br> 124, -10.5, -7.63705e+240<br> domain
15620       error<br> 124, -11.5, -7.63705e+240<br> domain error<br> 124, -12.5,
15621       -7.63705e+240<br> domain error<br> 124, -13.5, -7.63705e+240<br> domain
15622       error<br> 124, -14.5, -7.63705e+240<br> domain error<br> 124, -15.5,
15623       -7.63705e+240<br> domain error<br> 124, -16.5, -7.63705e+240<br> domain
15624       error<br> 124, -17.5, -7.63705e+240<br> domain error<br> 124, -18.5,
15625       -7.63705e+240<br> domain error<br> 124, -19.5, -7.63705e+240<br> domain
15626       error<br> 124, -20.5, -7.63705e+240<br> domain error<br> 2, -0.5, -0.828797<br>
15627       domain error<br> 3, -0.5, 193.409<br> domain error<br> 4, -0.5, -3.47425<br>
15628       domain error<br> 5, -0.5, 15371.1<br> domain error<br> 6, -0.5, -43.4579<br>
15629       domain error<br> 7, -0.5, 2.58068e+06<br> domain error<br> 8, -0.5, -1059.96<br>
15630       domain error<br> 9, -0.5, 7.43185e+08<br> domain error<br> 10, -0.5,
15631       -42108.9<br> domain error<br> 11, -0.5, 3.26999e+11<br> domain error<br>
15632       12, -0.5, -2.46448e+06<br> domain error<br> 13, -0.5, 2.04047e+14<br>
15633       domain error<br> 14, -0.5, -1.9918e+08<br> domain error<br> 15, -0.5,
15634       1.71399e+17<br> domain error<br> 16, -0.5, -2.12394e+10<br> domain error<br>
15635       17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, -2.88824e+12<br>
15636       domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> 20, -0.5,
15637       -4.87773e+14<br> domain error<br> 21, -0.5, 4.28582e+26<br> domain error<br>
15638       2, -0.5, -0.828843<br> domain error<br> 3, -0.5, 193.409<br> domain error<br>
15639       4, -0.5, -3.47791<br> domain error<br> 5, -0.5, 15371.1<br> domain error<br>
15640       6, -0.5, -44.0732<br> domain error<br> 7, -0.5, 2.58068e+06<br> domain
15641       error<br> 8, -0.5, -1237.15<br> domain error<br> 9, -0.5, 7.43185e+08<br>
15642       domain error<br> 10, -0.5, -120071<br> domain error<br> 11, -0.5, 3.26999e+11<br>
15643       domain error<br> 12, -0.5, -5.11131e+07<br> domain error<br> 13, -0.5,
15644       2.04047e+14<br> domain error<br> 14, -0.5, -4.1064e+10<br> domain error<br>
15645       15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, -4.44822e+13<br>
15646       domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5,
15647       -6.08254e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br>
15648       20, -0.5, -1.02182e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br>
15649       domain error<br> 2, -0.5, -0.828751<br> domain error<br> 3, -0.5, 193.409<br>
15650       domain error<br> 4, -0.5, -3.47059<br> domain error<br> 5, -0.5, 15371.1<br>
15651       domain error<br> 6, -0.5, -42.8426<br> domain error<br> 7, -0.5, 2.58068e+06<br>
15652       domain error<br> 8, -0.5, -882.773<br> domain error<br> 9, -0.5, 7.43185e+08<br>
15653       domain error<br> 10, -0.5, 35853.7<br> domain error<br> 11, -0.5, 3.26999e+11<br>
15654       domain error<br> 12, -0.5, 4.61841e+07<br> domain error<br> 13, -0.5,
15655       2.04047e+14<br> domain error<br> 14, -0.5, 4.06656e+10<br> domain error<br>
15656       15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, 4.44397e+13<br>
15657       domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5,
15658       6.08197e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br>
15659       20, -0.5, 1.02181e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br>
15660     </p>
15661 <h5>
15662 <a name="special_function_error_rates_rep.error_logs.h106"></a>
15663       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5">Error
15664       Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
15665       and test data Mathematica Data - negative arguments</a>
15666     </h5>
15667 <p>
15668       <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments"></a>domain
15669       error<br> 2, -12.75, -124.031<br> domain error<br> 2, -12.25, 124.019<br>
15670       domain error<br> 2, -11.75, -124.032<br> domain error<br> 2, -11.25,
15671       124.018<br> domain error<br> 2, -10.75, -124.033<br> domain error<br>
15672       2, -10.25, 124.016<br> domain error<br> 2, -9.75, -124.035<br> domain
15673       error<br> 2, -9.25, 124.015<br> domain error<br> 2, -8.75, -124.037<br>
15674       domain error<br> 2, -8.25, 124.012<br> domain error<br> 2, -7.75, -124.04<br>
15675       domain error<br> 2, -7.25, 124.009<br> domain error<br> 2, -6.75, -124.044<br>
15676       domain error<br> 2, -6.25, 124.003<br> domain error<br> 2, -5.75, -124.051<br>
15677       domain error<br> 2, -5.25, 123.995<br> domain error<br> 2, -4.75, -124.061<br>
15678       domain error<br> 2, -4.25, 123.981<br> domain error<br> 2, -3.75, -124.08<br>
15679       domain error<br> 2, -3.25, 123.955<br> domain error<br> 2, -2.75, -124.118<br>
15680       domain error<br> 2, -2.25, 123.897<br> domain error<br> 2, -1.75, -124.214<br>
15681       domain error<br> 2, -1.25, 123.721<br> domain error<br> 2, -0.75, -124.587<br>
15682       domain error<br> 2, -0.25, 122.697<br> domain error<br> 3, -12.75, 1558.54<br>
15683       domain error<br> 3, -12.25, 1558.54<br> domain error<br> 3, -11.75, 1558.54<br>
15684       domain error<br> 3, -11.25, 1558.54<br> domain error<br> 3, -10.75, 1558.54<br>
15685       domain error<br> 3, -10.25, 1558.54<br> domain error<br> 3, -9.75, 1558.54<br>
15686       domain error<br> 3, -9.25, 1558.54<br> domain error<br> 3, -8.75, 1558.54<br>
15687       domain error<br> 3, -8.25, 1558.54<br> domain error<br> 3, -7.75, 1558.54<br>
15688       domain error<br> 3, -7.25, 1558.54<br> domain error<br> 3, -6.75, 1558.54<br>
15689       domain error<br> 3, -6.25, 1558.54<br> domain error<br> 3, -5.75, 1558.54<br>
15690       domain error<br> 3, -5.25, 1558.54<br> domain error<br> 3, -4.75, 1558.53<br>
15691       domain error<br> 3, -4.25, 1558.53<br> domain error<br> 3, -3.75, 1558.52<br>
15692       domain error<br> 3, -3.25, 1558.51<br> domain error<br> 3, -2.75, 1558.49<br>
15693       domain error<br> 3, -2.25, 1558.46<br> domain error<br> 3, -1.75, 1558.38<br>
15694       domain error<br> 3, -1.25, 1558.22<br> domain error<br> 3, -0.75, 1557.75<br>
15695       domain error<br> 3, -0.25, 1555.76<br> domain error<br> 4, -12.75, -24481.6<br>
15696       domain error<br> 4, -12.25, 24481.6<br> domain error<br> 4, -11.75, -24481.6<br>
15697       domain error<br> 4, -11.25, 24481.6<br> domain error<br> 4, -10.75, -24481.6<br>
15698       domain error<br> 4, -10.25, 24481.6<br> domain error<br> 4, -9.75, -24481.6<br>
15699       domain error<br> 4, -9.25, 24481.6<br> domain error<br> 4, -8.75, -24481.6<br>
15700       domain error<br> 4, -8.25, 24481.6<br> domain error<br> 4, -7.75, -24481.6<br>
15701       domain error<br> 4, -7.25, 24481.6<br> domain error<br> 4, -6.75, -24481.6<br>
15702       domain error<br> 4, -6.25, 24481.6<br> domain error<br> 4, -5.75, -24481.6<br>
15703       domain error<br> 4, -5.25, 24481.6<br> domain error<br> 4, -4.75, -24481.6<br>
15704       domain error<br> 4, -4.25, 24481.6<br> domain error<br> 4, -3.75, -24481.6<br>
15705       domain error<br> 4, -3.25, 24481.5<br> domain error<br> 4, -2.75, -24481.6<br>
15706       domain error<br> 4, -2.25, 24481.5<br> domain error<br> 4, -1.75, -24481.8<br>
15707       domain error<br> 4, -1.25, 24481.1<br> domain error<br> 4, -0.75, -24483.2<br>
15708       domain error<br> 4, -0.25, 24473.2<br> domain error<br> 5, -12.75, 492231<br>
15709       domain error<br> 5, -12.25, 492231<br> domain error<br> 5, -11.75, 492231<br>
15710       domain error<br> 5, -11.25, 492231<br> domain error<br> 5, -10.75, 492231<br>
15711       domain error<br> 5, -10.25, 492231<br> domain error<br> 5, -9.75, 492231<br>
15712       domain error<br> 5, -9.25, 492231<br> domain error<br> 5, -8.75, 492231<br>
15713       domain error<br> 5, -8.25, 492231<br> domain error<br> 5, -7.75, 492231<br>
15714       domain error<br> 5, -7.25, 492231<br> domain error<br> 5, -6.75, 492231<br>
15715       domain error<br> 5, -6.25, 492231<br> domain error<br> 5, -5.75, 492231<br>
15716       domain error<br> 5, -5.25, 492231<br> domain error<br> 5, -4.75, 492231<br>
15717       domain error<br> 5, -4.25, 492231<br> domain error<br> 5, -3.75, 492231<br>
15718       domain error<br> 5, -3.25, 492231<br> domain error<br> 5, -2.75, 492231<br>
15719       domain error<br> 5, -2.25, 492231<br> domain error<br> 5, -1.75, 492231<br>
15720       domain error<br> 5, -1.25, 492230<br> domain error<br> 5, -0.75, 492227<br>
15721       domain error<br> 5, -0.25, 492199<br> domain error<br> 6, -12.75, -1.17912e+07<br>
15722       domain error<br> 6, -12.25, 1.17912e+07<br> domain error<br> 6, -11.75,
15723       -1.17912e+07<br> domain error<br> 6, -11.25, 1.17912e+07<br> domain error<br>
15724       6, -10.75, -1.17912e+07<br> domain error<br> 6, -10.25, 1.17912e+07<br>
15725       domain error<br> 6, -9.75, -1.17912e+07<br> domain error<br> 6, -9.25,
15726       1.17912e+07<br> domain error<br> 6, -8.75, -1.17912e+07<br> domain error<br>
15727       6, -8.25, 1.17912e+07<br> domain error<br> 6, -7.75, -1.17912e+07<br>
15728       domain error<br> 6, -7.25, 1.17912e+07<br> domain error<br> 6, -6.75,
15729       -1.17912e+07<br> domain error<br> 6, -6.25, 1.17912e+07<br> domain error<br>
15730       6, -5.75, -1.17912e+07<br> domain error<br> 6, -5.25, 1.17912e+07<br>
15731       domain error<br> 6, -4.75, -1.17912e+07<br> domain error<br> 6, -4.25,
15732       1.17912e+07<br> domain error<br> 6, -3.75, -1.17912e+07<br> domain error<br>
15733       6, -3.25, 1.17912e+07<br> domain error<br> 6, -2.75, -1.17912e+07<br>
15734       domain error<br> 6, -2.25, 1.17912e+07<br> domain error<br> 6, -1.75,
15735       -1.17912e+07<br> domain error<br> 6, -1.25, 1.17912e+07<br> *** FURTHER
15736       CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
15737     </p>
15738 <h5>
15739 <a name="special_function_error_rates_rep.error_logs.h107"></a>
15740       <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6">Error
15741       Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
15742       and test data Mathematica Data - large arguments</a>
15743     </h5>
15744 <p>
15745       <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments"></a>underflow<br>
15746       30, 8.58993e+09, -8.44974e-268<br> underflow<br> 30, 1.71799e+10, -7.86943e-277<br>
15747       underflow<br> 30, 3.43597e+10, -7.32898e-286<br> underflow<br> 30, 6.87195e+10,
15748       -6.82564e-295<br> underflow<br> 30, 1.37439e+11, -6.35687e-304<br> underflow<br>
15749       30, 2.74878e+11, -5.9203e-313<br> underflow<br> 30, 5.49756e+11, -5.53354e-322<br>
15750       underflow<br> 30, 1.09951e+12, -0<br> underflow<br> 30, 2.19902e+12,
15751       -0<br> underflow<br> 30, 4.39805e+12, -0<br> underflow<br> 30, 8.79609e+12,
15752       -0<br> underflow<br> 30, 1.75922e+13, -0<br> underflow<br> 30, 3.51844e+13,
15753       -0<br> underflow<br> 30, 7.03687e+13, -0<br> underflow<br> 30, 1.40737e+14,
15754       -0<br> underflow<br> 30, 2.81475e+14, -0<br> underflow<br> 30, 5.6295e+14,
15755       -0<br> underflow<br> 30, 1.1259e+15, -0<br> underflow<br> 30, 2.2518e+15,
15756       -0<br> underflow<br> 30, 4.5036e+15, -0<br> underflow<br> 30, 9.0072e+15,
15757       -0<br> underflow<br> 30, 1.80144e+16, -0<br> underflow<br> 30, 3.60288e+16,
15758       -0<br> underflow<br> 30, 7.20576e+16, -0<br> underflow<br> 30, 1.44115e+17,
15759       -0<br> underflow<br> 30, 2.8823e+17, -0<br> underflow<br> 30, 5.76461e+17,
15760       -0<br> underflow<br> 30, 1.15292e+18, -0<br> underflow<br> 30, 2.30584e+18,
15761       -0<br> underflow<br> 30, 4.61169e+18, -0<br> underflow<br> 30, 9.22337e+18,
15762       -0<br> underflow<br> 30, 1.84467e+19, -0<br> underflow<br> 30, 3.68935e+19,
15763       -0<br> underflow<br> 30, 7.3787e+19, -0<br> underflow<br> 30, 1.47574e+20,
15764       -0<br> underflow<br> 30, 2.95148e+20, -0<br> underflow<br> 30, 5.90296e+20,
15765       -0<br> underflow<br> 30, 1.18059e+21, -0<br> underflow<br> 30, 2.36118e+21,
15766       -0<br> underflow<br> 30, 4.72237e+21, -0<br> underflow<br> 30, 9.44473e+21,
15767       -0<br> underflow<br> 30, 1.88895e+22, -0<br> underflow<br> 30, 3.77789e+22,
15768       -0<br> underflow<br> 30, 7.55579e+22, -0<br> underflow<br> 30, 1.51116e+23,
15769       -0<br> underflow<br> 30, 3.02231e+23, -0<br> underflow<br> 30, 6.04463e+23,
15770       -0<br> underflow<br> 30, 1.20893e+24, -0<br> underflow<br> 30, 2.41785e+24,
15771       -0<br> underflow<br> 30, 4.8357e+24, -0<br> underflow<br> 30, 9.67141e+24,
15772       -0<br> underflow<br> 30, 1.93428e+25, -0<br> underflow<br> 30, 3.86856e+25,
15773       -0<br> underflow<br> 30, 7.73713e+25, -0<br> underflow<br> 30, 1.54743e+26,
15774       -0<br> underflow<br> 30, 3.09485e+26, -0<br> underflow<br> 30, 6.1897e+26,
15775       -0<br> underflow<br> 30, 1.23794e+27, -0<br> underflow<br> 30, 2.47588e+27,
15776       -0<br> underflow<br> 30, 4.95176e+27, -0<br> underflow<br> 30, 9.90352e+27,
15777       -0<br> underflow<br> 30, 1.9807e+28, -0<br> underflow<br> 30, 3.96141e+28,
15778       -0<br> underflow<br> 30, 7.92282e+28, -0<br> underflow<br> 30, 1.58456e+29,
15779       -0<br> underflow<br> 30, 3.16913e+29, -0<br> underflow<br> 30, 6.33825e+29,
15780       -0<br> underflow<br> 30, 1.26765e+30, -0<br>
15781     </p>
15782 </div>
15783 <div class="section">
15784 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
15785 <a name="special_function_error_rates_rep.all_the_tables"></a><a class="link" href="index.html#special_function_error_rates_rep.all_the_tables" title="Tables">Tables</a>
15786 </h2></div></div></div>
15787 <div class="table">
15788 <a name="special_function_error_rates_rep.all_the_tables.table_beta"></a><p class="title"><b>Table&#160;97.&#160;Error rates for beta</b></p>
15789 <div class="table-contents"><table class="table" summary="Error rates for beta">
15790 <colgroup>
15791 <col>
15792 <col>
15793 <col>
15794 <col>
15795 <col>
15796 </colgroup>
15797 <thead><tr>
15798 <th>
15799             </th>
15800 <th>
15801               <p>
15802                 GNU C++ version 7.1.0<br> linux<br> double
15803               </p>
15804             </th>
15805 <th>
15806               <p>
15807                 GNU C++ version 7.1.0<br> linux<br> long double
15808               </p>
15809             </th>
15810 <th>
15811               <p>
15812                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
15813               </p>
15814             </th>
15815 <th>
15816               <p>
15817                 Microsoft Visual C++ version 14.1<br> Win32<br> double
15818               </p>
15819             </th>
15820 </tr></thead>
15821 <tbody>
15822 <tr>
15823 <td>
15824               <p>
15825                 Beta Function: Small Values
15826               </p>
15827             </td>
15828 <td>
15829               <p>
15830                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
15831                 2.1:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And
15832                 other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
15833                 Max = 1.14&#949; (Mean = 0.574&#949;))
15834               </p>
15835             </td>
15836 <td>
15837               <p>
15838                 <span class="blue">Max = 2.86&#949; (Mean = 1.22&#949;)</span><br> <br>
15839                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 364&#949; (Mean = 76.2&#949;))
15840               </p>
15841             </td>
15842 <td>
15843               <p>
15844                 <span class="blue">Max = 2.86&#949; (Mean = 1.22&#949;)</span>
15845               </p>
15846             </td>
15847 <td>
15848               <p>
15849                 <span class="blue">Max = 2.23&#949; (Mean = 1.14&#949;)</span>
15850               </p>
15851             </td>
15852 </tr>
15853 <tr>
15854 <td>
15855               <p>
15856                 Beta Function: Medium Values
15857               </p>
15858             </td>
15859 <td>
15860               <p>
15861                 <span class="blue">Max = 0.978&#949; (Mean = 0.0595&#949;)</span><br> <br>
15862                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03&#949; (Mean = 238&#949;))<br>
15863                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03&#949; (Mean = 265&#949;))
15864               </p>
15865             </td>
15866 <td>
15867               <p>
15868                 <span class="blue">Max = 61.4&#949; (Mean = 19.4&#949;)</span><br> <br>
15869                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.07e+03&#949; (Mean = 264&#949;))
15870               </p>
15871             </td>
15872 <td>
15873               <p>
15874                 <span class="blue">Max = 107&#949; (Mean = 24.5&#949;)</span>
15875               </p>
15876             </td>
15877 <td>
15878               <p>
15879                 <span class="blue">Max = 96.5&#949; (Mean = 22.4&#949;)</span>
15880               </p>
15881             </td>
15882 </tr>
15883 <tr>
15884 <td>
15885               <p>
15886                 Beta Function: Divergent Values
15887               </p>
15888             </td>
15889 <td>
15890               <p>
15891                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
15892                 2.1:</em></span> Max = 12.1&#949; (Mean = 1.99&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
15893                 Max = 176&#949; (Mean = 28&#949;))
15894               </p>
15895             </td>
15896 <td>
15897               <p>
15898                 <span class="blue">Max = 8.99&#949; (Mean = 2.44&#949;)</span><br> <br>
15899                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 128&#949; (Mean = 23.8&#949;))
15900               </p>
15901             </td>
15902 <td>
15903               <p>
15904                 <span class="blue">Max = 18.8&#949; (Mean = 2.71&#949;)</span>
15905               </p>
15906             </td>
15907 <td>
15908               <p>
15909                 <span class="blue">Max = 11.4&#949; (Mean = 2.19&#949;)</span>
15910               </p>
15911             </td>
15912 </tr>
15913 </tbody>
15914 </table></div>
15915 </div>
15916 <br class="table-break"><div class="table">
15917 <a name="special_function_error_rates_rep.all_the_tables.table_beta_incomplete_"></a><p class="title"><b>Table&#160;98.&#160;Error rates for beta (incomplete)</b></p>
15918 <div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
15919 <colgroup>
15920 <col>
15921 <col>
15922 <col>
15923 <col>
15924 <col>
15925 </colgroup>
15926 <thead><tr>
15927 <th>
15928             </th>
15929 <th>
15930               <p>
15931                 GNU C++ version 7.1.0<br> linux<br> double
15932               </p>
15933             </th>
15934 <th>
15935               <p>
15936                 GNU C++ version 7.1.0<br> linux<br> long double
15937               </p>
15938             </th>
15939 <th>
15940               <p>
15941                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
15942               </p>
15943             </th>
15944 <th>
15945               <p>
15946                 Microsoft Visual C++ version 14.1<br> Win32<br> double
15947               </p>
15948             </th>
15949 </tr></thead>
15950 <tbody>
15951 <tr>
15952 <td>
15953               <p>
15954                 Incomplete Beta Function: Small Values
15955               </p>
15956             </td>
15957 <td>
15958               <p>
15959                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
15960               </p>
15961             </td>
15962 <td>
15963               <p>
15964                 <span class="blue">Max = 11.1&#949; (Mean = 2.32&#949;)</span>
15965               </p>
15966             </td>
15967 <td>
15968               <p>
15969                 <span class="blue">Max = 18.7&#949; (Mean = 3.19&#949;)</span>
15970               </p>
15971             </td>
15972 <td>
15973               <p>
15974                 <span class="blue">Max = 9.94&#949; (Mean = 2.17&#949;)</span>
15975               </p>
15976             </td>
15977 </tr>
15978 <tr>
15979 <td>
15980               <p>
15981                 Incomplete Beta Function: Medium Values
15982               </p>
15983             </td>
15984 <td>
15985               <p>
15986                 <span class="blue">Max = 0.568&#949; (Mean = 0.0254&#949;)</span>
15987               </p>
15988             </td>
15989 <td>
15990               <p>
15991                 <span class="blue">Max = 69.2&#949; (Mean = 13.4&#949;)</span>
15992               </p>
15993             </td>
15994 <td>
15995               <p>
15996                 <span class="blue">Max = 174&#949; (Mean = 25&#949;)</span>
15997               </p>
15998             </td>
15999 <td>
16000               <p>
16001                 <span class="blue">Max = 90&#949; (Mean = 12.7&#949;)</span>
16002               </p>
16003             </td>
16004 </tr>
16005 <tr>
16006 <td>
16007               <p>
16008                 Incomplete Beta Function: Large and Diverse Values
16009               </p>
16010             </td>
16011 <td>
16012               <p>
16013                 <span class="blue">Max = 0.999&#949; (Mean = 0.0325&#949;)</span>
16014               </p>
16015             </td>
16016 <td>
16017               <p>
16018                 <span class="blue">Max = 6.84e+04&#949; (Mean = 2.76e+03&#949;)</span>
16019               </p>
16020             </td>
16021 <td>
16022               <p>
16023                 <span class="blue">Max = 6.86e+04&#949; (Mean = 2.79e+03&#949;)</span>
16024               </p>
16025             </td>
16026 <td>
16027               <p>
16028                 <span class="blue">Max = 633&#949; (Mean = 29.7&#949;)</span>
16029               </p>
16030             </td>
16031 </tr>
16032 <tr>
16033 <td>
16034               <p>
16035                 Incomplete Beta Function: Small Integer Values
16036               </p>
16037             </td>
16038 <td>
16039               <p>
16040                 <span class="blue">Max = 0.786&#949; (Mean = 0.0323&#949;)</span>
16041               </p>
16042             </td>
16043 <td>
16044               <p>
16045                 <span class="blue">Max = 11.6&#949; (Mean = 3.6&#949;)</span>
16046               </p>
16047             </td>
16048 <td>
16049               <p>
16050                 <span class="blue">Max = 51.8&#949; (Mean = 11&#949;)</span>
16051               </p>
16052             </td>
16053 <td>
16054               <p>
16055                 <span class="blue">Max = 26&#949; (Mean = 6.28&#949;)</span>
16056               </p>
16057             </td>
16058 </tr>
16059 </tbody>
16060 </table></div>
16061 </div>
16062 <br class="table-break"><div class="table">
16063 <a name="special_function_error_rates_rep.all_the_tables.table_betac"></a><p class="title"><b>Table&#160;99.&#160;Error rates for betac</b></p>
16064 <div class="table-contents"><table class="table" summary="Error rates for betac">
16065 <colgroup>
16066 <col>
16067 <col>
16068 <col>
16069 <col>
16070 <col>
16071 </colgroup>
16072 <thead><tr>
16073 <th>
16074             </th>
16075 <th>
16076               <p>
16077                 GNU C++ version 7.1.0<br> linux<br> double
16078               </p>
16079             </th>
16080 <th>
16081               <p>
16082                 GNU C++ version 7.1.0<br> linux<br> long double
16083               </p>
16084             </th>
16085 <th>
16086               <p>
16087                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
16088               </p>
16089             </th>
16090 <th>
16091               <p>
16092                 Microsoft Visual C++ version 14.1<br> Win32<br> double
16093               </p>
16094             </th>
16095 </tr></thead>
16096 <tbody>
16097 <tr>
16098 <td>
16099               <p>
16100                 Incomplete Beta Function: Small Values
16101               </p>
16102             </td>
16103 <td>
16104               <p>
16105                 <span class="blue">Max = 0.676&#949; (Mean = 0.0302&#949;)</span>
16106               </p>
16107             </td>
16108 <td>
16109               <p>
16110                 <span class="blue">Max = 9.92&#949; (Mean = 2.3&#949;)</span>
16111               </p>
16112             </td>
16113 <td>
16114               <p>
16115                 <span class="blue">Max = 11.2&#949; (Mean = 2.94&#949;)</span>
16116               </p>
16117             </td>
16118 <td>
16119               <p>
16120                 <span class="blue">Max = 8.94&#949; (Mean = 2.06&#949;)</span>
16121               </p>
16122             </td>
16123 </tr>
16124 <tr>
16125 <td>
16126               <p>
16127                 Incomplete Beta Function: Medium Values
16128               </p>
16129             </td>
16130 <td>
16131               <p>
16132                 <span class="blue">Max = 0.949&#949; (Mean = 0.098&#949;)</span>
16133               </p>
16134             </td>
16135 <td>
16136               <p>
16137                 <span class="blue">Max = 63.5&#949; (Mean = 13.5&#949;)</span>
16138               </p>
16139             </td>
16140 <td>
16141               <p>
16142                 <span class="blue">Max = 97.6&#949; (Mean = 24.3&#949;)</span>
16143               </p>
16144             </td>
16145 <td>
16146               <p>
16147                 <span class="blue">Max = 90.6&#949; (Mean = 14.8&#949;)</span>
16148               </p>
16149             </td>
16150 </tr>
16151 <tr>
16152 <td>
16153               <p>
16154                 Incomplete Beta Function: Large and Diverse Values
16155               </p>
16156             </td>
16157 <td>
16158               <p>
16159                 <span class="blue">Max = 1.12&#949; (Mean = 0.0458&#949;)</span>
16160               </p>
16161             </td>
16162 <td>
16163               <p>
16164                 <span class="blue">Max = 1.05e+05&#949; (Mean = 5.45e+03&#949;)</span>
16165               </p>
16166             </td>
16167 <td>
16168               <p>
16169                 <span class="blue">Max = 1.04e+05&#949; (Mean = 5.46e+03&#949;)</span>
16170               </p>
16171             </td>
16172 <td>
16173               <p>
16174                 <span class="blue">Max = 3.72e+03&#949; (Mean = 113&#949;)</span>
16175               </p>
16176             </td>
16177 </tr>
16178 <tr>
16179 <td>
16180               <p>
16181                 Incomplete Beta Function: Small Integer Values
16182               </p>
16183             </td>
16184 <td>
16185               <p>
16186                 <span class="blue">Max = 0.586&#949; (Mean = 0.0314&#949;)</span>
16187               </p>
16188             </td>
16189 <td>
16190               <p>
16191                 <span class="blue">Max = 11.1&#949; (Mean = 3.65&#949;)</span>
16192               </p>
16193             </td>
16194 <td>
16195               <p>
16196                 <span class="blue">Max = 103&#949; (Mean = 17.4&#949;)</span>
16197               </p>
16198             </td>
16199 <td>
16200               <p>
16201                 <span class="blue">Max = 26.2&#949; (Mean = 6.36&#949;)</span>
16202               </p>
16203             </td>
16204 </tr>
16205 </tbody>
16206 </table></div>
16207 </div>
16208 <br class="table-break"><div class="table">
16209 <a name="special_function_error_rates_rep.all_the_tables.table_binomial_coefficient"></a><p class="title"><b>Table&#160;100.&#160;Error rates for binomial_coefficient</b></p>
16210 <div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
16211 <colgroup>
16212 <col>
16213 <col>
16214 <col>
16215 <col>
16216 <col>
16217 </colgroup>
16218 <thead><tr>
16219 <th>
16220             </th>
16221 <th>
16222               <p>
16223                 GNU C++ version 7.1.0<br> linux<br> double
16224               </p>
16225             </th>
16226 <th>
16227               <p>
16228                 GNU C++ version 7.1.0<br> linux<br> long double
16229               </p>
16230             </th>
16231 <th>
16232               <p>
16233                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
16234               </p>
16235             </th>
16236 <th>
16237               <p>
16238                 Microsoft Visual C++ version 14.1<br> Win32<br> double
16239               </p>
16240             </th>
16241 </tr></thead>
16242 <tbody>
16243 <tr>
16244 <td>
16245               <p>
16246                 Binomials: small arguments
16247               </p>
16248             </td>
16249 <td>
16250               <p>
16251                 <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
16252               </p>
16253             </td>
16254 <td>
16255               <p>
16256                 <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
16257               </p>
16258             </td>
16259 <td>
16260               <p>
16261                 <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
16262               </p>
16263             </td>
16264 <td>
16265               <p>
16266                 <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
16267               </p>
16268             </td>
16269 </tr>
16270 <tr>
16271 <td>
16272               <p>
16273                 Binomials: large arguments
16274               </p>
16275             </td>
16276 <td>
16277               <p>
16278                 <span class="blue">Max = 0.939&#949; (Mean = 0.314&#949;)</span>
16279               </p>
16280             </td>
16281 <td>
16282               <p>
16283                 <span class="blue">Max = 26.6&#949; (Mean = 6.13&#949;)</span>
16284               </p>
16285             </td>
16286 <td>
16287               <p>
16288                 <span class="blue">Max = 53.2&#949; (Mean = 10.8&#949;)</span>
16289               </p>
16290             </td>
16291 <td>
16292               <p>
16293                 <span class="blue">Max = 37.2&#949; (Mean = 7.4&#949;)</span>
16294               </p>
16295             </td>
16296 </tr>
16297 </tbody>
16298 </table></div>
16299 </div>
16300 <br class="table-break"><div class="table">
16301 <a name="special_function_error_rates_rep.all_the_tables.table_boost_math_powm1"></a><p class="title"><b>Table&#160;101.&#160;Error rates for boost::math::powm1</b></p>
16302 <div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1">
16303 <colgroup>
16304 <col>
16305 <col>
16306 <col>
16307 <col>
16308 <col>
16309 </colgroup>
16310 <thead><tr>
16311 <th>
16312             </th>
16313 <th>
16314               <p>
16315                 GNU C++ version 7.1.0<br> linux<br> long double
16316               </p>
16317             </th>
16318 <th>
16319               <p>
16320                 GNU C++ version 7.1.0<br> linux<br> double
16321               </p>
16322             </th>
16323 <th>
16324               <p>
16325                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
16326               </p>
16327             </th>
16328 <th>
16329               <p>
16330                 Microsoft Visual C++ version 14.1<br> Win32<br> double
16331               </p>
16332             </th>
16333 </tr></thead>
16334 <tbody><tr>
16335 <td>
16336               <p>
16337                 powm1
16338               </p>
16339             </td>
16340 <td>
16341               <p>
16342                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.04&#949; (Mean = 0.493&#949;))<br>
16343                 <br> <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span><br>
16344                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.04&#949; (Mean = 0.493&#949;))
16345               </p>
16346             </td>
16347 <td>
16348               <p>
16349                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06&#949; (Mean = 0.425&#949;))<br>
16350                 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06&#949; (Mean = 0.425&#949;))<br>
16351                 <br> <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
16352               </p>
16353             </td>
16354 <td>
16355               <p>
16356                 <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span><br> <br>
16357                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.88&#949; (Mean = 0.49&#949;))
16358               </p>
16359             </td>
16360 <td>
16361               <p>
16362                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.486&#949;))<br>
16363                 <br> <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
16364               </p>
16365             </td>
16366 </tr></tbody>
16367 </table></div>
16368 </div>
16369 <br class="table-break"><div class="table">
16370 <a name="special_function_error_rates_rep.all_the_tables.table_cbrt"></a><p class="title"><b>Table&#160;102.&#160;Error rates for cbrt</b></p>
16371 <div class="table-contents"><table class="table" summary="Error rates for cbrt">
16372 <colgroup>
16373 <col>
16374 <col>
16375 <col>
16376 <col>
16377 <col>
16378 </colgroup>
16379 <thead><tr>
16380 <th>
16381             </th>
16382 <th>
16383               <p>
16384                 GNU C++ version 7.1.0<br> linux<br> double
16385               </p>
16386             </th>
16387 <th>
16388               <p>
16389                 GNU C++ version 7.1.0<br> linux<br> long double
16390               </p>
16391             </th>
16392 <th>
16393               <p>
16394                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
16395               </p>
16396             </th>
16397 <th>
16398               <p>
16399                 Microsoft Visual C++ version 14.1<br> Win32<br> double
16400               </p>
16401             </th>
16402 </tr></thead>
16403 <tbody><tr>
16404 <td>
16405               <p>
16406                 cbrt Function
16407               </p>
16408             </td>
16409 <td>
16410               <p>
16411                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
16412               </p>
16413             </td>
16414 <td>
16415               <p>
16416                 <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
16417                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))<br>
16418                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
16419               </p>
16420             </td>
16421 <td>
16422               <p>
16423                 <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
16424                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
16425               </p>
16426             </td>
16427 <td>
16428               <p>
16429                 <span class="blue">Max = 1.7&#949; (Mean = 0.565&#949;)</span><br> <br>
16430                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.7&#949; (Mean = 0.565&#949;))
16431               </p>
16432             </td>
16433 </tr></tbody>
16434 </table></div>
16435 </div>
16436 <br class="table-break"><div class="table">
16437 <a name="special_function_error_rates_rep.all_the_tables.table_cos_pi"></a><p class="title"><b>Table&#160;103.&#160;Error rates for cos_pi</b></p>
16438 <div class="table-contents"><table class="table" summary="Error rates for cos_pi">
16439 <colgroup>
16440 <col>
16441 <col>
16442 <col>
16443 <col>
16444 <col>
16445 </colgroup>
16446 <thead><tr>
16447 <th>
16448             </th>
16449 <th>
16450               <p>
16451                 GNU C++ version 7.1.0<br> linux<br> double
16452               </p>
16453             </th>
16454 <th>
16455               <p>
16456                 GNU C++ version 7.1.0<br> linux<br> long double
16457               </p>
16458             </th>
16459 <th>
16460               <p>
16461                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
16462               </p>
16463             </th>
16464 <th>
16465               <p>
16466                 Microsoft Visual C++ version 14.1<br> Win32<br> double
16467               </p>
16468             </th>
16469 </tr></thead>
16470 <tbody>
16471 <tr>
16472 <td>
16473               <p>
16474                 sin_pi and cos_pi
16475               </p>
16476             </td>
16477 <td>
16478               <p>
16479                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
16480               </p>
16481             </td>
16482 <td>
16483               <p>
16484                 <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
16485               </p>
16486             </td>
16487 <td>
16488               <p>
16489                 <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
16490               </p>
16491             </td>
16492 <td>
16493               <p>
16494                 <span class="blue">Max = 0.996&#949; (Mean = 0.284&#949;)</span>
16495               </p>
16496             </td>
16497 </tr>
16498 <tr>
16499 <td>
16500               <p>
16501                 sin_pi and cos_pi near integers and half integers
16502               </p>
16503             </td>
16504 <td>
16505               <p>
16506                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
16507               </p>
16508             </td>
16509 <td>
16510               <p>
16511                 <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
16512               </p>
16513             </td>
16514 <td>
16515               <p>
16516                 <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
16517               </p>
16518             </td>
16519 <td>
16520               <p>
16521                 <span class="blue">Max = 0.996&#949; (Mean = 0.298&#949;)</span>
16522               </p>
16523             </td>
16524 </tr>
16525 </tbody>
16526 </table></div>
16527 </div>
16528 <br class="table-break"><div class="table">
16529 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i"></a><p class="title"><b>Table&#160;104.&#160;Error rates for cyl_bessel_i</b></p>
16530 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
16531 <colgroup>
16532 <col>
16533 <col>
16534 <col>
16535 <col>
16536 <col>
16537 </colgroup>
16538 <thead><tr>
16539 <th>
16540             </th>
16541 <th>
16542               <p>
16543                 GNU C++ version 7.1.0<br> linux<br> double
16544               </p>
16545             </th>
16546 <th>
16547               <p>
16548                 GNU C++ version 7.1.0<br> linux<br> long double
16549               </p>
16550             </th>
16551 <th>
16552               <p>
16553                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
16554               </p>
16555             </th>
16556 <th>
16557               <p>
16558                 Microsoft Visual C++ version 14.1<br> Win32<br> double
16559               </p>
16560             </th>
16561 </tr></thead>
16562 <tbody>
16563 <tr>
16564 <td>
16565               <p>
16566                 Bessel I0: Mathworld Data
16567               </p>
16568             </td>
16569 <td>
16570               <p>
16571                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16572                 2.1:</em></span> Max = 270&#949; (Mean = 91.6&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And
16573                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
16574                 Max = 1.52&#949; (Mean = 0.622&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And
16575                 other failures.</a>)
16576               </p>
16577             </td>
16578 <td>
16579               <p>
16580                 <span class="blue">Max = 1.95&#949; (Mean = 0.738&#949;)</span><br> <br>
16581                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And
16582                 other failures.</a>)
16583               </p>
16584             </td>
16585 <td>
16586               <p>
16587                 <span class="blue">Max = 1.95&#949; (Mean = 0.661&#949;)</span>
16588               </p>
16589             </td>
16590 <td>
16591               <p>
16592                 <span class="blue">Max = 0.762&#949; (Mean = 0.329&#949;)</span>
16593               </p>
16594             </td>
16595 </tr>
16596 <tr>
16597 <td>
16598               <p>
16599                 Bessel I1: Mathworld Data
16600               </p>
16601             </td>
16602 <td>
16603               <p>
16604                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16605                 2.1:</em></span> Max = 128&#949; (Mean = 41&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And
16606                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
16607                 Max = 1.53&#949; (Mean = 0.483&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And
16608                 other failures.</a>)
16609               </p>
16610             </td>
16611 <td>
16612               <p>
16613                 <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span><br> <br>
16614                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And
16615                 other failures.</a>)
16616               </p>
16617             </td>
16618 <td>
16619               <p>
16620                 <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span>
16621               </p>
16622             </td>
16623 <td>
16624               <p>
16625                 <span class="blue">Max = 0.767&#949; (Mean = 0.398&#949;)</span>
16626               </p>
16627             </td>
16628 </tr>
16629 <tr>
16630 <td>
16631               <p>
16632                 Bessel In: Mathworld Data
16633               </p>
16634             </td>
16635 <td>
16636               <p>
16637                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16638                 2.1:</em></span> Max = 2.31&#949; (Mean = 0.838&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And
16639                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
16640                 Max = 1.73&#949; (Mean = 0.601&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And
16641                 other failures.</a>)
16642               </p>
16643             </td>
16644 <td>
16645               <p>
16646                 <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
16647                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And
16648                 other failures.</a>)
16649               </p>
16650             </td>
16651 <td>
16652               <p>
16653                 <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
16654               </p>
16655             </td>
16656 <td>
16657               <p>
16658                 <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
16659               </p>
16660             </td>
16661 </tr>
16662 <tr>
16663 <td>
16664               <p>
16665                 Bessel Iv: Mathworld Data
16666               </p>
16667             </td>
16668 <td>
16669               <p>
16670                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16671                 2.1:</em></span> Max = 5.95&#949; (Mean = 2.08&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And
16672                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
16673                 Max = 3.53&#949; (Mean = 1.39&#949;))
16674               </p>
16675             </td>
16676 <td>
16677               <p>
16678                 <span class="blue">Max = 4.12&#949; (Mean = 1.85&#949;)</span><br> <br>
16679                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 616&#949; (Mean = 221&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And
16680                 other failures.</a>)
16681               </p>
16682             </td>
16683 <td>
16684               <p>
16685                 <span class="blue">Max = 4.12&#949; (Mean = 1.95&#949;)</span>
16686               </p>
16687             </td>
16688 <td>
16689               <p>
16690                 <span class="blue">Max = 2.97&#949; (Mean = 1.24&#949;)</span>
16691               </p>
16692             </td>
16693 </tr>
16694 <tr>
16695 <td>
16696               <p>
16697                 Bessel In: Random Data
16698               </p>
16699             </td>
16700 <td>
16701               <p>
16702                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16703                 2.1:</em></span> Max = 261&#949; (Mean = 53.2&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And
16704                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
16705                 Max = 7.37&#949; (Mean = 2.4&#949;))
16706               </p>
16707             </td>
16708 <td>
16709               <p>
16710                 <span class="blue">Max = 4.62&#949; (Mean = 1.06&#949;)</span><br> <br>
16711                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 645&#949; (Mean = 132&#949;))
16712               </p>
16713             </td>
16714 <td>
16715               <p>
16716                 <span class="blue">Max = 176&#949; (Mean = 39.1&#949;)</span>
16717               </p>
16718             </td>
16719 <td>
16720               <p>
16721                 <span class="blue">Max = 9.67&#949; (Mean = 1.88&#949;)</span>
16722               </p>
16723             </td>
16724 </tr>
16725 <tr>
16726 <td>
16727               <p>
16728                 Bessel Iv: Random Data
16729               </p>
16730             </td>
16731 <td>
16732               <p>
16733                 <span class="blue">Max = 0.661&#949; (Mean = 0.0441&#949;)</span><br> <br>
16734                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03&#949; (Mean = 1.55e+03&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And
16735                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
16736                 <span class="red">Max = 4.28e+08&#949; (Mean = 2.85e+07&#949;))</span>
16737               </p>
16738             </td>
16739 <td>
16740               <p>
16741                 <span class="blue">Max = 8.35&#949; (Mean = 1.62&#949;)</span><br> <br>
16742                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.05e+03&#949; (Mean = 224&#949;)
16743                 <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And
16744                 other failures.</a>)
16745               </p>
16746             </td>
16747 <td>
16748               <p>
16749                 <span class="blue">Max = 283&#949; (Mean = 88.4&#949;)</span>
16750               </p>
16751             </td>
16752 <td>
16753               <p>
16754                 <span class="blue">Max = 7.46&#949; (Mean = 1.71&#949;)</span>
16755               </p>
16756             </td>
16757 </tr>
16758 <tr>
16759 <td>
16760               <p>
16761                 Bessel Iv: Mathworld Data (large values)
16762               </p>
16763             </td>
16764 <td>
16765               <p>
16766                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16767                 2.1:</em></span> Max = 37&#949; (Mean = 18&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And
16768                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
16769                 <span class="red">Max = 3.77e+168&#949; (Mean = 2.39e+168&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And
16770                 other failures.</a>)</span>
16771               </p>
16772             </td>
16773 <td>
16774               <p>
16775                 <span class="blue">Max = 14.7&#949; (Mean = 6.66&#949;)</span><br> <br>
16776                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 118&#949; (Mean = 57.2&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And
16777                 other failures.</a>)
16778               </p>
16779             </td>
16780 <td>
16781               <p>
16782                 <span class="blue">Max = 14.7&#949; (Mean = 6.59&#949;)</span>
16783               </p>
16784             </td>
16785 <td>
16786               <p>
16787                 <span class="blue">Max = 3.67&#949; (Mean = 1.64&#949;)</span>
16788               </p>
16789             </td>
16790 </tr>
16791 </tbody>
16792 </table></div>
16793 </div>
16794 <br class="table-break"><div class="table">
16795 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table&#160;105.&#160;Error rates for cyl_bessel_i (integer orders)</b></p>
16796 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
16797 <colgroup>
16798 <col>
16799 <col>
16800 <col>
16801 <col>
16802 <col>
16803 </colgroup>
16804 <thead><tr>
16805 <th>
16806             </th>
16807 <th>
16808               <p>
16809                 GNU C++ version 7.1.0<br> linux<br> double
16810               </p>
16811             </th>
16812 <th>
16813               <p>
16814                 GNU C++ version 7.1.0<br> linux<br> long double
16815               </p>
16816             </th>
16817 <th>
16818               <p>
16819                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
16820               </p>
16821             </th>
16822 <th>
16823               <p>
16824                 Microsoft Visual C++ version 14.1<br> Win32<br> double
16825               </p>
16826             </th>
16827 </tr></thead>
16828 <tbody>
16829 <tr>
16830 <td>
16831               <p>
16832                 Bessel I0: Mathworld Data (Integer Version)
16833               </p>
16834             </td>
16835 <td>
16836               <p>
16837                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16838                 2.1:</em></span> Max = 0.79&#949; (Mean = 0.482&#949;))<br> (<span class="emphasis"><em>Rmath
16839                 3.2.3:</em></span> Max = 1.52&#949; (Mean = 0.622&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And
16840                 other failures.</a>)
16841               </p>
16842             </td>
16843 <td>
16844               <p>
16845                 <span class="blue">Max = 1.95&#949; (Mean = 0.738&#949;)</span><br> <br>
16846                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
16847                 other failures.</a>)
16848               </p>
16849             </td>
16850 <td>
16851               <p>
16852                 <span class="blue">Max = 1.95&#949; (Mean = 0.661&#949;)</span>
16853               </p>
16854             </td>
16855 <td>
16856               <p>
16857                 <span class="blue">Max = 0.762&#949; (Mean = 0.329&#949;)</span>
16858               </p>
16859             </td>
16860 </tr>
16861 <tr>
16862 <td>
16863               <p>
16864                 Bessel I1: Mathworld Data (Integer Version)
16865               </p>
16866             </td>
16867 <td>
16868               <p>
16869                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16870                 2.1:</em></span> Max = 0.82&#949; (Mean = 0.456&#949;))<br> (<span class="emphasis"><em>Rmath
16871                 3.2.3:</em></span> Max = 1.53&#949; (Mean = 0.483&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And
16872                 other failures.</a>)
16873               </p>
16874             </td>
16875 <td>
16876               <p>
16877                 <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span><br> <br>
16878                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
16879                 other failures.</a>)
16880               </p>
16881             </td>
16882 <td>
16883               <p>
16884                 <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span>
16885               </p>
16886             </td>
16887 <td>
16888               <p>
16889                 <span class="blue">Max = 0.767&#949; (Mean = 0.398&#949;)</span>
16890               </p>
16891             </td>
16892 </tr>
16893 <tr>
16894 <td>
16895               <p>
16896                 Bessel In: Mathworld Data (Integer Version)
16897               </p>
16898             </td>
16899 <td>
16900               <p>
16901                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
16902                 2.1:</em></span> Max = 5.15&#949; (Mean = 2.13&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And
16903                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
16904                 Max = 1.73&#949; (Mean = 0.601&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And
16905                 other failures.</a>)
16906               </p>
16907             </td>
16908 <td>
16909               <p>
16910                 <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
16911                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
16912                 other failures.</a>)
16913               </p>
16914             </td>
16915 <td>
16916               <p>
16917                 <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
16918               </p>
16919             </td>
16920 <td>
16921               <p>
16922                 <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
16923               </p>
16924             </td>
16925 </tr>
16926 </tbody>
16927 </table></div>
16928 </div>
16929 <br class="table-break"><div class="table">
16930 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime"></a><p class="title"><b>Table&#160;106.&#160;Error rates for cyl_bessel_i_prime</b></p>
16931 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
16932 <colgroup>
16933 <col>
16934 <col>
16935 <col>
16936 <col>
16937 <col>
16938 </colgroup>
16939 <thead><tr>
16940 <th>
16941             </th>
16942 <th>
16943               <p>
16944                 GNU C++ version 7.1.0<br> linux<br> double
16945               </p>
16946             </th>
16947 <th>
16948               <p>
16949                 GNU C++ version 7.1.0<br> linux<br> long double
16950               </p>
16951             </th>
16952 <th>
16953               <p>
16954                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
16955               </p>
16956             </th>
16957 <th>
16958               <p>
16959                 Microsoft Visual C++ version 14.1<br> Win32<br> double
16960               </p>
16961             </th>
16962 </tr></thead>
16963 <tbody>
16964 <tr>
16965 <td>
16966               <p>
16967                 Bessel I'0: Mathworld Data
16968               </p>
16969             </td>
16970 <td>
16971               <p>
16972                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
16973               </p>
16974             </td>
16975 <td>
16976               <p>
16977                 <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
16978               </p>
16979             </td>
16980 <td>
16981               <p>
16982                 <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
16983               </p>
16984             </td>
16985 <td>
16986               <p>
16987                 <span class="blue">Max = 0.82&#949; (Mean = 0.354&#949;)</span>
16988               </p>
16989             </td>
16990 </tr>
16991 <tr>
16992 <td>
16993               <p>
16994                 Bessel I'1: Mathworld Data
16995               </p>
16996             </td>
16997 <td>
16998               <p>
16999                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17000               </p>
17001             </td>
17002 <td>
17003               <p>
17004                 <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
17005               </p>
17006             </td>
17007 <td>
17008               <p>
17009                 <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
17010               </p>
17011             </td>
17012 <td>
17013               <p>
17014                 <span class="blue">Max = 1.36&#949; (Mean = 0.782&#949;)</span>
17015               </p>
17016             </td>
17017 </tr>
17018 <tr>
17019 <td>
17020               <p>
17021                 Bessel I'n: Mathworld Data
17022               </p>
17023             </td>
17024 <td>
17025               <p>
17026                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17027               </p>
17028             </td>
17029 <td>
17030               <p>
17031                 <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
17032               </p>
17033             </td>
17034 <td>
17035               <p>
17036                 <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
17037               </p>
17038             </td>
17039 <td>
17040               <p>
17041                 <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
17042               </p>
17043             </td>
17044 </tr>
17045 <tr>
17046 <td>
17047               <p>
17048                 Bessel I'v: Mathworld Data
17049               </p>
17050             </td>
17051 <td>
17052               <p>
17053                 <span class="blue">Max = 1.62&#949; (Mean = 0.512&#949;)</span>
17054               </p>
17055             </td>
17056 <td>
17057               <p>
17058                 <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
17059               </p>
17060             </td>
17061 <td>
17062               <p>
17063                 <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
17064               </p>
17065             </td>
17066 <td>
17067               <p>
17068                 <span class="blue">Max = 3.76e+03&#949; (Mean = 1.19e+03&#949;)</span>
17069               </p>
17070             </td>
17071 </tr>
17072 <tr>
17073 <td>
17074               <p>
17075                 Bessel I'n: Random Data
17076               </p>
17077             </td>
17078 <td>
17079               <p>
17080                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17081               </p>
17082             </td>
17083 <td>
17084               <p>
17085                 <span class="blue">Max = 3.95&#949; (Mean = 1.06&#949;)</span>
17086               </p>
17087             </td>
17088 <td>
17089               <p>
17090                 <span class="blue">Max = 195&#949; (Mean = 37.1&#949;)</span>
17091               </p>
17092             </td>
17093 <td>
17094               <p>
17095                 <span class="blue">Max = 9.85&#949; (Mean = 1.82&#949;)</span>
17096               </p>
17097             </td>
17098 </tr>
17099 <tr>
17100 <td>
17101               <p>
17102                 Bessel I'v: Random Data
17103               </p>
17104             </td>
17105 <td>
17106               <p>
17107                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17108               </p>
17109             </td>
17110 <td>
17111               <p>
17112                 <span class="blue">Max = 14.1&#949; (Mean = 2.93&#949;)</span>
17113               </p>
17114             </td>
17115 <td>
17116               <p>
17117                 <span class="blue">Max = 336&#949; (Mean = 68.5&#949;)</span>
17118               </p>
17119             </td>
17120 <td>
17121               <p>
17122                 <span class="blue">Max = 14&#949; (Mean = 2.5&#949;)</span>
17123               </p>
17124             </td>
17125 </tr>
17126 <tr>
17127 <td>
17128               <p>
17129                 Bessel I'v: Mathworld Data (large values)
17130               </p>
17131             </td>
17132 <td>
17133               <p>
17134                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17135               </p>
17136             </td>
17137 <td>
17138               <p>
17139                 <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
17140               </p>
17141             </td>
17142 <td>
17143               <p>
17144                 <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
17145               </p>
17146             </td>
17147 <td>
17148               <p>
17149                 <span class="blue">Max = 59.5&#949; (Mean = 26.6&#949;)</span>
17150               </p>
17151             </td>
17152 </tr>
17153 </tbody>
17154 </table></div>
17155 </div>
17156 <br class="table-break"><div class="table">
17157 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table&#160;107.&#160;Error rates for cyl_bessel_i_prime (integer orders)</b></p>
17158 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
17159 <colgroup>
17160 <col>
17161 <col>
17162 <col>
17163 <col>
17164 <col>
17165 </colgroup>
17166 <thead><tr>
17167 <th>
17168             </th>
17169 <th>
17170               <p>
17171                 GNU C++ version 7.1.0<br> linux<br> double
17172               </p>
17173             </th>
17174 <th>
17175               <p>
17176                 GNU C++ version 7.1.0<br> linux<br> long double
17177               </p>
17178             </th>
17179 <th>
17180               <p>
17181                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
17182               </p>
17183             </th>
17184 <th>
17185               <p>
17186                 Microsoft Visual C++ version 14.1<br> Win32<br> double
17187               </p>
17188             </th>
17189 </tr></thead>
17190 <tbody>
17191 <tr>
17192 <td>
17193               <p>
17194                 Bessel I'0: Mathworld Data (Integer Version)
17195               </p>
17196             </td>
17197 <td>
17198               <p>
17199                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17200               </p>
17201             </td>
17202 <td>
17203               <p>
17204                 <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
17205               </p>
17206             </td>
17207 <td>
17208               <p>
17209                 <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
17210               </p>
17211             </td>
17212 <td>
17213               <p>
17214                 <span class="blue">Max = 0.82&#949; (Mean = 0.354&#949;)</span>
17215               </p>
17216             </td>
17217 </tr>
17218 <tr>
17219 <td>
17220               <p>
17221                 Bessel I'1: Mathworld Data (Integer Version)
17222               </p>
17223             </td>
17224 <td>
17225               <p>
17226                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17227               </p>
17228             </td>
17229 <td>
17230               <p>
17231                 <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
17232               </p>
17233             </td>
17234 <td>
17235               <p>
17236                 <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
17237               </p>
17238             </td>
17239 <td>
17240               <p>
17241                 <span class="blue">Max = 1.36&#949; (Mean = 0.782&#949;)</span>
17242               </p>
17243             </td>
17244 </tr>
17245 <tr>
17246 <td>
17247               <p>
17248                 Bessel I'n: Mathworld Data (Integer Version)
17249               </p>
17250             </td>
17251 <td>
17252               <p>
17253                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17254               </p>
17255             </td>
17256 <td>
17257               <p>
17258                 <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
17259               </p>
17260             </td>
17261 <td>
17262               <p>
17263                 <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
17264               </p>
17265             </td>
17266 <td>
17267               <p>
17268                 <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
17269               </p>
17270             </td>
17271 </tr>
17272 </tbody>
17273 </table></div>
17274 </div>
17275 <br class="table-break"><div class="table">
17276 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j"></a><p class="title"><b>Table&#160;108.&#160;Error rates for cyl_bessel_j</b></p>
17277 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
17278 <colgroup>
17279 <col>
17280 <col>
17281 <col>
17282 <col>
17283 <col>
17284 </colgroup>
17285 <thead><tr>
17286 <th>
17287             </th>
17288 <th>
17289               <p>
17290                 GNU C++ version 7.1.0<br> linux<br> long double
17291               </p>
17292             </th>
17293 <th>
17294               <p>
17295                 GNU C++ version 7.1.0<br> linux<br> double
17296               </p>
17297             </th>
17298 <th>
17299               <p>
17300                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
17301               </p>
17302             </th>
17303 <th>
17304               <p>
17305                 Microsoft Visual C++ version 14.1<br> Win32<br> double
17306               </p>
17307             </th>
17308 </tr></thead>
17309 <tbody>
17310 <tr>
17311 <td>
17312               <p>
17313                 Bessel J0: Mathworld Data
17314               </p>
17315             </td>
17316 <td>
17317               <p>
17318                 <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span><br> <br>
17319                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And
17320                 other failures.</a>)
17321               </p>
17322             </td>
17323 <td>
17324               <p>
17325                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17326                 2.1:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And
17327                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
17328                 Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And
17329                 other failures.</a>)
17330               </p>
17331             </td>
17332 <td>
17333               <p>
17334                 <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
17335               </p>
17336             </td>
17337 <td>
17338               <p>
17339                 <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span>
17340               </p>
17341             </td>
17342 </tr>
17343 <tr>
17344 <td>
17345               <p>
17346                 Bessel J0: Mathworld Data (Tricky cases)
17347               </p>
17348             </td>
17349 <td>
17350               <p>
17351                 <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span><br>
17352                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean =
17353                 1.96e+08&#949;))
17354               </p>
17355             </td>
17356 <td>
17357               <p>
17358                 <span class="blue">Max = 8e+04&#949; (Mean = 3.27e+04&#949;)</span><br>
17359                 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07&#949; (Mean = 2.66e+07&#949;))<br>
17360                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))
17361               </p>
17362             </td>
17363 <td>
17364               <p>
17365                 <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
17366               </p>
17367             </td>
17368 <td>
17369               <p>
17370                 <span class="blue">Max = 1e+07&#949; (Mean = 4.09e+06&#949;)</span>
17371               </p>
17372             </td>
17373 </tr>
17374 <tr>
17375 <td>
17376               <p>
17377                 Bessel J1: Mathworld Data
17378               </p>
17379             </td>
17380 <td>
17381               <p>
17382                 <span class="blue">Max = 3.59&#949; (Mean = 1.33&#949;)</span><br> <br>
17383                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And
17384                 other failures.</a>)
17385               </p>
17386             </td>
17387 <td>
17388               <p>
17389                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17390                 2.1:</em></span> Max = 6.62&#949; (Mean = 2.35&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And
17391                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
17392                 Max = 0.946&#949; (Mean = 0.39&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And
17393                 other failures.</a>)
17394               </p>
17395             </td>
17396 <td>
17397               <p>
17398                 <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
17399               </p>
17400             </td>
17401 <td>
17402               <p>
17403                 <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span>
17404               </p>
17405             </td>
17406 </tr>
17407 <tr>
17408 <td>
17409               <p>
17410                 Bessel J1: Mathworld Data (tricky cases)
17411               </p>
17412             </td>
17413 <td>
17414               <p>
17415                 <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
17416                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean =
17417                 1.58e+06&#949;))
17418               </p>
17419             </td>
17420 <td>
17421               <p>
17422                 <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
17423                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05&#949; (Mean = 5.32e+05&#949;))<br>
17424                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))
17425               </p>
17426             </td>
17427 <td>
17428               <p>
17429                 <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
17430               </p>
17431             </td>
17432 <td>
17433               <p>
17434                 <span class="blue">Max = 3.23e+04&#949; (Mean = 1.45e+04&#949;)</span>
17435               </p>
17436             </td>
17437 </tr>
17438 <tr>
17439 <td>
17440               <p>
17441                 Bessel JN: Mathworld Data
17442               </p>
17443             </td>
17444 <td>
17445               <p>
17446                 <span class="blue">Max = 6.85&#949; (Mean = 3.35&#949;)</span><br> <br>
17447                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.13e+19&#949; (Mean
17448                 = 5.16e+18&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And
17449                 other failures.</a>)</span>
17450               </p>
17451             </td>
17452 <td>
17453               <p>
17454                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17455                 2.1:</em></span> Max = 6.9e+05&#949; (Mean = 2.15e+05&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And
17456                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
17457                 <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And
17458                 other failures.</a>)</span>
17459               </p>
17460             </td>
17461 <td>
17462               <p>
17463                 <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
17464               </p>
17465             </td>
17466 <td>
17467               <p>
17468                 <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span>
17469               </p>
17470             </td>
17471 </tr>
17472 <tr>
17473 <td>
17474               <p>
17475                 Bessel J: Mathworld Data
17476               </p>
17477             </td>
17478 <td>
17479               <p>
17480                 <span class="blue">Max = 14.7&#949; (Mean = 4.11&#949;)</span><br> <br>
17481                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.49e+05&#949; (Mean = 8.09e+04&#949;)
17482                 <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And
17483                 other failures.</a>)
17484               </p>
17485             </td>
17486 <td>
17487               <p>
17488                 <span class="blue">Max = 10&#949; (Mean = 2.24&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17489                 2.1:</em></span> Max = 2.39e+05&#949; (Mean = 5.37e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And
17490                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
17491                 <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And
17492                 other failures.</a>)</span>
17493               </p>
17494             </td>
17495 <td>
17496               <p>
17497                 <span class="blue">Max = 14.7&#949; (Mean = 4.22&#949;)</span>
17498               </p>
17499             </td>
17500 <td>
17501               <p>
17502                 <span class="blue">Max = 14.9&#949; (Mean = 3.89&#949;)</span>
17503               </p>
17504             </td>
17505 </tr>
17506 <tr>
17507 <td>
17508               <p>
17509                 Bessel J: Mathworld Data (large values)
17510               </p>
17511             </td>
17512 <td>
17513               <p>
17514                 <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
17515                 Max = 34.9&#949; (Mean = 17.4&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And
17516                 other failures.</a>)
17517               </p>
17518             </td>
17519 <td>
17520               <p>
17521                 <span class="blue">Max = 0.536&#949; (Mean = 0.268&#949;)</span><br> <br>
17522                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03&#949; (Mean = 2.46e+03&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And
17523                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
17524                 Max = 5.9&#949; (Mean = 3.76&#949;))
17525               </p>
17526             </td>
17527 <td>
17528               <p>
17529                 <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span>
17530               </p>
17531             </td>
17532 <td>
17533               <p>
17534                 <span class="blue">Max = 9.31&#949; (Mean = 5.52&#949;)</span>
17535               </p>
17536             </td>
17537 </tr>
17538 <tr>
17539 <td>
17540               <p>
17541                 Bessel JN: Random Data
17542               </p>
17543             </td>
17544 <td>
17545               <p>
17546                 <span class="blue">Max = 50.8&#949; (Mean = 3.69&#949;)</span><br> <br>
17547                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.12e+03&#949; (Mean = 88.7&#949;))
17548               </p>
17549             </td>
17550 <td>
17551               <p>
17552                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17553                 2.1:</em></span> Max = 75.7&#949; (Mean = 5.36&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
17554                 Max = 3.93&#949; (Mean = 1.22&#949;))
17555               </p>
17556             </td>
17557 <td>
17558               <p>
17559                 <span class="blue">Max = 99.6&#949; (Mean = 22&#949;)</span>
17560               </p>
17561             </td>
17562 <td>
17563               <p>
17564                 <span class="blue">Max = 17.5&#949; (Mean = 1.46&#949;)</span>
17565               </p>
17566             </td>
17567 </tr>
17568 <tr>
17569 <td>
17570               <p>
17571                 Bessel J: Random Data
17572               </p>
17573             </td>
17574 <td>
17575               <p>
17576                 <span class="blue">Max = 11.4&#949; (Mean = 1.68&#949;)</span><br> <br>
17577                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 501&#949; (Mean = 52.3&#949;))
17578               </p>
17579             </td>
17580 <td>
17581               <p>
17582                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17583                 2.1:</em></span> Max = 15.5&#949; (Mean = 3.33&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And
17584                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
17585                 Max = 6.74&#949; (Mean = 1.3&#949;))
17586               </p>
17587             </td>
17588 <td>
17589               <p>
17590                 <span class="blue">Max = 260&#949; (Mean = 34&#949;)</span>
17591               </p>
17592             </td>
17593 <td>
17594               <p>
17595                 <span class="blue">Max = 9.24&#949; (Mean = 1.17&#949;)</span>
17596               </p>
17597             </td>
17598 </tr>
17599 <tr>
17600 <td>
17601               <p>
17602                 Bessel J: Random Data (Tricky large values)
17603               </p>
17604             </td>
17605 <td>
17606               <p>
17607                 <span class="blue">Max = 785&#949; (Mean = 94.2&#949;)</span><br> <br>
17608                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 5.01e+17&#949; (Mean
17609                 = 6.23e+16&#949;))</span>
17610               </p>
17611             </td>
17612 <td>
17613               <p>
17614                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17615                 2.1:</em></span> Max = 2.48e+05&#949; (Mean = 5.11e+04&#949;))<br> (<span class="emphasis"><em>Rmath
17616                 3.2.3:</em></span> Max = 71.6&#949; (Mean = 11.7&#949;))
17617               </p>
17618             </td>
17619 <td>
17620               <p>
17621                 <span class="blue">Max = 785&#949; (Mean = 97.4&#949;)</span>
17622               </p>
17623             </td>
17624 <td>
17625               <p>
17626                 <span class="blue">Max = 59.2&#949; (Mean = 8.67&#949;)</span>
17627               </p>
17628             </td>
17629 </tr>
17630 </tbody>
17631 </table></div>
17632 </div>
17633 <br class="table-break"><div class="table">
17634 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table&#160;109.&#160;Error rates for cyl_bessel_j (integer orders)</b></p>
17635 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
17636 <colgroup>
17637 <col>
17638 <col>
17639 <col>
17640 <col>
17641 <col>
17642 </colgroup>
17643 <thead><tr>
17644 <th>
17645             </th>
17646 <th>
17647               <p>
17648                 GNU C++ version 7.1.0<br> linux<br> long double
17649               </p>
17650             </th>
17651 <th>
17652               <p>
17653                 GNU C++ version 7.1.0<br> linux<br> double
17654               </p>
17655             </th>
17656 <th>
17657               <p>
17658                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
17659               </p>
17660             </th>
17661 <th>
17662               <p>
17663                 Microsoft Visual C++ version 14.1<br> Win32<br> double
17664               </p>
17665             </th>
17666 </tr></thead>
17667 <tbody>
17668 <tr>
17669 <td>
17670               <p>
17671                 Bessel J0: Mathworld Data (Integer Version)
17672               </p>
17673             </td>
17674 <td>
17675               <p>
17676                 <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span><br> <br>
17677                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
17678                 other failures.</a>)
17679               </p>
17680             </td>
17681 <td>
17682               <p>
17683                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17684                 2.1:</em></span> Max = 1.12&#949; (Mean = 0.488&#949;))<br> (<span class="emphasis"><em>Rmath
17685                 3.2.3:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And
17686                 other failures.</a>)
17687               </p>
17688             </td>
17689 <td>
17690               <p>
17691                 <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
17692               </p>
17693             </td>
17694 <td>
17695               <p>
17696                 <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span><br> <br>
17697                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.89&#949; (Mean = 0.988&#949;))
17698               </p>
17699             </td>
17700 </tr>
17701 <tr>
17702 <td>
17703               <p>
17704                 Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
17705               </p>
17706             </td>
17707 <td>
17708               <p>
17709                 <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span><br>
17710                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean =
17711                 1.96e+08&#949;))
17712               </p>
17713             </td>
17714 <td>
17715               <p>
17716                 <span class="blue">Max = 8e+04&#949; (Mean = 3.27e+04&#949;)</span><br>
17717                 <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07&#949; (Mean = 4.11e+06&#949;))<br>
17718                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))
17719               </p>
17720             </td>
17721 <td>
17722               <p>
17723                 <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
17724               </p>
17725             </td>
17726 <td>
17727               <p>
17728                 <span class="blue">Max = 1e+07&#949; (Mean = 4.09e+06&#949;)</span><br>
17729                 <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max
17730                 = 2.54e+08&#949; (Mean = 1.04e+08&#949;))</span>
17731               </p>
17732             </td>
17733 </tr>
17734 <tr>
17735 <td>
17736               <p>
17737                 Bessel J1: Mathworld Data (Integer Version)
17738               </p>
17739             </td>
17740 <td>
17741               <p>
17742                 <span class="blue">Max = 3.59&#949; (Mean = 1.33&#949;)</span><br> <br>
17743                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
17744                 other failures.</a>)
17745               </p>
17746             </td>
17747 <td>
17748               <p>
17749                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17750                 2.1:</em></span> Max = 1.89&#949; (Mean = 0.721&#949;))<br> (<span class="emphasis"><em>Rmath
17751                 3.2.3:</em></span> Max = 0.946&#949; (Mean = 0.39&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And
17752                 other failures.</a>)
17753               </p>
17754             </td>
17755 <td>
17756               <p>
17757                 <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
17758               </p>
17759             </td>
17760 <td>
17761               <p>
17762                 <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span><br> <br>
17763                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 11.4&#949; (Mean = 4.15&#949;))
17764               </p>
17765             </td>
17766 </tr>
17767 <tr>
17768 <td>
17769               <p>
17770                 Bessel J1: Mathworld Data (tricky cases) (Integer Version)
17771               </p>
17772             </td>
17773 <td>
17774               <p>
17775                 <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
17776                 <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean =
17777                 1.58e+06&#949;))
17778               </p>
17779             </td>
17780 <td>
17781               <p>
17782                 <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
17783                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06&#949; (Mean = 6.28e+05&#949;))<br>
17784                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))
17785               </p>
17786             </td>
17787 <td>
17788               <p>
17789                 <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
17790               </p>
17791             </td>
17792 <td>
17793               <p>
17794                 <span class="blue">Max = 3.23e+04&#949; (Mean = 1.45e+04&#949;)</span><br>
17795                 <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.44e+07&#949; (Mean
17796                 = 6.5e+06&#949;))
17797               </p>
17798             </td>
17799 </tr>
17800 <tr>
17801 <td>
17802               <p>
17803                 Bessel JN: Mathworld Data (Integer Version)
17804               </p>
17805             </td>
17806 <td>
17807               <p>
17808                 <span class="blue">Max = 6.85&#949; (Mean = 3.35&#949;)</span><br> <br>
17809                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.13e+19&#949; (Mean
17810                 = 5.16e+18&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
17811                 other failures.</a>)</span>
17812               </p>
17813             </td>
17814 <td>
17815               <p>
17816                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
17817                 2.1:</em></span> Max = 6.9e+05&#949; (Mean = 2.53e+05&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And
17818                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
17819                 <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And
17820                 other failures.</a>)</span>
17821               </p>
17822             </td>
17823 <td>
17824               <p>
17825                 <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
17826               </p>
17827             </td>
17828 <td>
17829               <p>
17830                 <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span><br> <br>
17831                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
17832                 = +INF&#949;) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
17833                 other failures.</a>)</span>
17834               </p>
17835             </td>
17836 </tr>
17837 </tbody>
17838 </table></div>
17839 </div>
17840 <br class="table-break"><div class="table">
17841 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime"></a><p class="title"><b>Table&#160;110.&#160;Error rates for cyl_bessel_j_prime</b></p>
17842 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
17843 <colgroup>
17844 <col>
17845 <col>
17846 <col>
17847 <col>
17848 <col>
17849 </colgroup>
17850 <thead><tr>
17851 <th>
17852             </th>
17853 <th>
17854               <p>
17855                 GNU C++ version 7.1.0<br> linux<br> double
17856               </p>
17857             </th>
17858 <th>
17859               <p>
17860                 GNU C++ version 7.1.0<br> linux<br> long double
17861               </p>
17862             </th>
17863 <th>
17864               <p>
17865                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
17866               </p>
17867             </th>
17868 <th>
17869               <p>
17870                 Microsoft Visual C++ version 14.1<br> Win32<br> double
17871               </p>
17872             </th>
17873 </tr></thead>
17874 <tbody>
17875 <tr>
17876 <td>
17877               <p>
17878                 Bessel J0': Mathworld Data
17879               </p>
17880             </td>
17881 <td>
17882               <p>
17883                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17884               </p>
17885             </td>
17886 <td>
17887               <p>
17888                 <span class="blue">Max = 18.9&#949; (Mean = 6.82&#949;)</span>
17889               </p>
17890             </td>
17891 <td>
17892               <p>
17893                 <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
17894               </p>
17895             </td>
17896 <td>
17897               <p>
17898                 <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
17899               </p>
17900             </td>
17901 </tr>
17902 <tr>
17903 <td>
17904               <p>
17905                 Bessel J0': Mathworld Data (Tricky cases)
17906               </p>
17907             </td>
17908 <td>
17909               <p>
17910                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17911               </p>
17912             </td>
17913 <td>
17914               <p>
17915                 <span class="blue">Max = 7.44&#949; (Mean = 3.34&#949;)</span>
17916               </p>
17917             </td>
17918 <td>
17919               <p>
17920                 <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
17921               </p>
17922             </td>
17923 <td>
17924               <p>
17925                 <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
17926               </p>
17927             </td>
17928 </tr>
17929 <tr>
17930 <td>
17931               <p>
17932                 Bessel J1': Mathworld Data
17933               </p>
17934             </td>
17935 <td>
17936               <p>
17937                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
17938               </p>
17939             </td>
17940 <td>
17941               <p>
17942                 <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
17943               </p>
17944             </td>
17945 <td>
17946               <p>
17947                 <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
17948               </p>
17949             </td>
17950 <td>
17951               <p>
17952                 <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
17953               </p>
17954             </td>
17955 </tr>
17956 <tr>
17957 <td>
17958               <p>
17959                 Bessel J1': Mathworld Data (tricky cases)
17960               </p>
17961             </td>
17962 <td>
17963               <p>
17964                 <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
17965               </p>
17966             </td>
17967 <td>
17968               <p>
17969                 <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
17970               </p>
17971             </td>
17972 <td>
17973               <p>
17974                 <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
17975               </p>
17976             </td>
17977 <td>
17978               <p>
17979                 <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
17980               </p>
17981             </td>
17982 </tr>
17983 <tr>
17984 <td>
17985               <p>
17986                 Bessel JN': Mathworld Data
17987               </p>
17988             </td>
17989 <td>
17990               <p>
17991                 <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
17992               </p>
17993             </td>
17994 <td>
17995               <p>
17996                 <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
17997               </p>
17998             </td>
17999 <td>
18000               <p>
18001                 <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
18002               </p>
18003             </td>
18004 <td>
18005               <p>
18006                 <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
18007               </p>
18008             </td>
18009 </tr>
18010 <tr>
18011 <td>
18012               <p>
18013                 Bessel J': Mathworld Data
18014               </p>
18015             </td>
18016 <td>
18017               <p>
18018                 <span class="blue">Max = 21.5&#949; (Mean = 4.7&#949;)</span>
18019               </p>
18020             </td>
18021 <td>
18022               <p>
18023                 <span class="blue">Max = 42.5&#949; (Mean = 9.31&#949;)</span>
18024               </p>
18025             </td>
18026 <td>
18027               <p>
18028                 <span class="blue">Max = 42.5&#949; (Mean = 9.32&#949;)</span>
18029               </p>
18030             </td>
18031 <td>
18032               <p>
18033                 <span class="blue">Max = 23.7&#949; (Mean = 8&#949;)</span>
18034               </p>
18035             </td>
18036 </tr>
18037 <tr>
18038 <td>
18039               <p>
18040                 Bessel J': Mathworld Data (large values)
18041               </p>
18042             </td>
18043 <td>
18044               <p>
18045                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18046               </p>
18047             </td>
18048 <td>
18049               <p>
18050                 <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
18051               </p>
18052             </td>
18053 <td>
18054               <p>
18055                 <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
18056               </p>
18057             </td>
18058 <td>
18059               <p>
18060                 <span class="blue">Max = 2.9&#949; (Mean = 1.61&#949;)</span>
18061               </p>
18062             </td>
18063 </tr>
18064 <tr>
18065 <td>
18066               <p>
18067                 Bessel JN': Random Data
18068               </p>
18069             </td>
18070 <td>
18071               <p>
18072                 <span class="blue">Max = 0.593&#949; (Mean = 0.0396&#949;)</span>
18073               </p>
18074             </td>
18075 <td>
18076               <p>
18077                 <span class="blue">Max = 11.3&#949; (Mean = 1.85&#949;)</span>
18078               </p>
18079             </td>
18080 <td>
18081               <p>
18082                 <span class="blue">Max = 79.4&#949; (Mean = 16.2&#949;)</span>
18083               </p>
18084             </td>
18085 <td>
18086               <p>
18087                 <span class="blue">Max = 6.34&#949; (Mean = 0.999&#949;)</span>
18088               </p>
18089             </td>
18090 </tr>
18091 <tr>
18092 <td>
18093               <p>
18094                 Bessel J': Random Data
18095               </p>
18096             </td>
18097 <td>
18098               <p>
18099                 <span class="blue">Max = 0.885&#949; (Mean = 0.033&#949;)</span>
18100               </p>
18101             </td>
18102 <td>
18103               <p>
18104                 <span class="blue">Max = 139&#949; (Mean = 6.47&#949;)</span>
18105               </p>
18106             </td>
18107 <td>
18108               <p>
18109                 <span class="blue">Max = 279&#949; (Mean = 27.2&#949;)</span>
18110               </p>
18111             </td>
18112 <td>
18113               <p>
18114                 <span class="blue">Max = 176&#949; (Mean = 9.75&#949;)</span>
18115               </p>
18116             </td>
18117 </tr>
18118 <tr>
18119 <td>
18120               <p>
18121                 Bessel J': Random Data (Tricky large values)
18122               </p>
18123             </td>
18124 <td>
18125               <p>
18126                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18127               </p>
18128             </td>
18129 <td>
18130               <p>
18131                 <span class="blue">Max = 474&#949; (Mean = 62.2&#949;)</span>
18132               </p>
18133             </td>
18134 <td>
18135               <p>
18136                 <span class="blue">Max = 474&#949; (Mean = 64.5&#949;)</span>
18137               </p>
18138             </td>
18139 <td>
18140               <p>
18141                 <span class="blue">Max = 379&#949; (Mean = 45.4&#949;)</span>
18142               </p>
18143             </td>
18144 </tr>
18145 </tbody>
18146 </table></div>
18147 </div>
18148 <br class="table-break"><div class="table">
18149 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table&#160;111.&#160;Error rates for cyl_bessel_j_prime (integer orders)</b></p>
18150 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
18151 <colgroup>
18152 <col>
18153 <col>
18154 <col>
18155 <col>
18156 <col>
18157 </colgroup>
18158 <thead><tr>
18159 <th>
18160             </th>
18161 <th>
18162               <p>
18163                 GNU C++ version 7.1.0<br> linux<br> double
18164               </p>
18165             </th>
18166 <th>
18167               <p>
18168                 GNU C++ version 7.1.0<br> linux<br> long double
18169               </p>
18170             </th>
18171 <th>
18172               <p>
18173                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
18174               </p>
18175             </th>
18176 <th>
18177               <p>
18178                 Microsoft Visual C++ version 14.1<br> Win32<br> double
18179               </p>
18180             </th>
18181 </tr></thead>
18182 <tbody>
18183 <tr>
18184 <td>
18185               <p>
18186                 Bessel J0': Mathworld Data (Integer Version)
18187               </p>
18188             </td>
18189 <td>
18190               <p>
18191                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18192               </p>
18193             </td>
18194 <td>
18195               <p>
18196                 <span class="blue">Max = 18.9&#949; (Mean = 6.82&#949;)</span>
18197               </p>
18198             </td>
18199 <td>
18200               <p>
18201                 <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
18202               </p>
18203             </td>
18204 <td>
18205               <p>
18206                 <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
18207               </p>
18208             </td>
18209 </tr>
18210 <tr>
18211 <td>
18212               <p>
18213                 Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
18214               </p>
18215             </td>
18216 <td>
18217               <p>
18218                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18219               </p>
18220             </td>
18221 <td>
18222               <p>
18223                 <span class="blue">Max = 7.44&#949; (Mean = 3.34&#949;)</span>
18224               </p>
18225             </td>
18226 <td>
18227               <p>
18228                 <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
18229               </p>
18230             </td>
18231 <td>
18232               <p>
18233                 <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
18234               </p>
18235             </td>
18236 </tr>
18237 <tr>
18238 <td>
18239               <p>
18240                 Bessel J1': Mathworld Data (Integer Version)
18241               </p>
18242             </td>
18243 <td>
18244               <p>
18245                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18246               </p>
18247             </td>
18248 <td>
18249               <p>
18250                 <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
18251               </p>
18252             </td>
18253 <td>
18254               <p>
18255                 <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
18256               </p>
18257             </td>
18258 <td>
18259               <p>
18260                 <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
18261               </p>
18262             </td>
18263 </tr>
18264 <tr>
18265 <td>
18266               <p>
18267                 Bessel J1': Mathworld Data (tricky cases) (Integer Version)
18268               </p>
18269             </td>
18270 <td>
18271               <p>
18272                 <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
18273               </p>
18274             </td>
18275 <td>
18276               <p>
18277                 <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
18278               </p>
18279             </td>
18280 <td>
18281               <p>
18282                 <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
18283               </p>
18284             </td>
18285 <td>
18286               <p>
18287                 <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
18288               </p>
18289             </td>
18290 </tr>
18291 <tr>
18292 <td>
18293               <p>
18294                 Bessel JN': Mathworld Data (Integer Version)
18295               </p>
18296             </td>
18297 <td>
18298               <p>
18299                 <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
18300               </p>
18301             </td>
18302 <td>
18303               <p>
18304                 <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
18305               </p>
18306             </td>
18307 <td>
18308               <p>
18309                 <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
18310               </p>
18311             </td>
18312 <td>
18313               <p>
18314                 <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
18315               </p>
18316             </td>
18317 </tr>
18318 </tbody>
18319 </table></div>
18320 </div>
18321 <br class="table-break"><div class="table">
18322 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k"></a><p class="title"><b>Table&#160;112.&#160;Error rates for cyl_bessel_k</b></p>
18323 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
18324 <colgroup>
18325 <col>
18326 <col>
18327 <col>
18328 <col>
18329 <col>
18330 </colgroup>
18331 <thead><tr>
18332 <th>
18333             </th>
18334 <th>
18335               <p>
18336                 GNU C++ version 7.1.0<br> linux<br> long double
18337               </p>
18338             </th>
18339 <th>
18340               <p>
18341                 GNU C++ version 7.1.0<br> linux<br> double
18342               </p>
18343             </th>
18344 <th>
18345               <p>
18346                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
18347               </p>
18348             </th>
18349 <th>
18350               <p>
18351                 Microsoft Visual C++ version 14.1<br> Win32<br> double
18352               </p>
18353             </th>
18354 </tr></thead>
18355 <tbody>
18356 <tr>
18357 <td>
18358               <p>
18359                 Bessel K0: Mathworld Data
18360               </p>
18361             </td>
18362 <td>
18363               <p>
18364                 <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span><br> <br>
18365                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
18366               </p>
18367             </td>
18368 <td>
18369               <p>
18370                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
18371                 2.1:</em></span> Max = 6.04&#949; (Mean = 2.16&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18372                 Max = 0.833&#949; (Mean = 0.601&#949;))
18373               </p>
18374             </td>
18375 <td>
18376               <p>
18377                 <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span>
18378               </p>
18379             </td>
18380 <td>
18381               <p>
18382                 <span class="blue">Max = 0.833&#949; (Mean = 0.552&#949;)</span>
18383               </p>
18384             </td>
18385 </tr>
18386 <tr>
18387 <td>
18388               <p>
18389                 Bessel K1: Mathworld Data
18390               </p>
18391             </td>
18392 <td>
18393               <p>
18394                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span><br> <br>
18395                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
18396               </p>
18397             </td>
18398 <td>
18399               <p>
18400                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
18401                 2.1:</em></span> Max = 6.26&#949; (Mean = 2.21&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18402                 Max = 0.894&#949; (Mean = 0.516&#949;))
18403               </p>
18404             </td>
18405 <td>
18406               <p>
18407                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
18408               </p>
18409             </td>
18410 <td>
18411               <p>
18412                 <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
18413               </p>
18414             </td>
18415 </tr>
18416 <tr>
18417 <td>
18418               <p>
18419                 Bessel Kn: Mathworld Data
18420               </p>
18421             </td>
18422 <td>
18423               <p>
18424                 <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span><br> <br>
18425                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And
18426                 other failures.</a>)
18427               </p>
18428             </td>
18429 <td>
18430               <p>
18431                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
18432                 2.1:</em></span> Max = 3.36&#949; (Mean = 1.43&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And
18433                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18434                 Max = 8.48&#949; (Mean = 2.98&#949;))
18435               </p>
18436             </td>
18437 <td>
18438               <p>
18439                 <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span>
18440               </p>
18441             </td>
18442 <td>
18443               <p>
18444                 <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
18445               </p>
18446             </td>
18447 </tr>
18448 <tr>
18449 <td>
18450               <p>
18451                 Bessel Kv: Mathworld Data
18452               </p>
18453             </td>
18454 <td>
18455               <p>
18456                 <span class="blue">Max = 3.58&#949; (Mean = 2.39&#949;)</span><br> <br>
18457                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13&#949; (Mean = 4.81&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And
18458                 other failures.</a>)
18459               </p>
18460             </td>
18461 <td>
18462               <p>
18463                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
18464                 2.1:</em></span> Max = 5.47&#949; (Mean = 2.04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And
18465                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18466                 Max = 3.15&#949; (Mean = 1.35&#949;))
18467               </p>
18468             </td>
18469 <td>
18470               <p>
18471                 <span class="blue">Max = 5.21&#949; (Mean = 2.53&#949;)</span>
18472               </p>
18473             </td>
18474 <td>
18475               <p>
18476                 <span class="blue">Max = 4.78&#949; (Mean = 2.19&#949;)</span>
18477               </p>
18478             </td>
18479 </tr>
18480 <tr>
18481 <td>
18482               <p>
18483                 Bessel Kv: Mathworld Data (large values)
18484               </p>
18485             </td>
18486 <td>
18487               <p>
18488                 <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
18489                 Max = 42.3&#949; (Mean = 19.8&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And
18490                 other failures.</a>)
18491               </p>
18492             </td>
18493 <td>
18494               <p>
18495                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
18496                 2.1:</em></span> Max = 308&#949; (Mean = 142&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And
18497                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18498                 Max = 84.6&#949; (Mean = 37.8&#949;))
18499               </p>
18500             </td>
18501 <td>
18502               <p>
18503                 <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span>
18504               </p>
18505             </td>
18506 <td>
18507               <p>
18508                 <span class="blue">Max = 59.8&#949; (Mean = 26.9&#949;)</span>
18509               </p>
18510             </td>
18511 </tr>
18512 <tr>
18513 <td>
18514               <p>
18515                 Bessel Kn: Random Data
18516               </p>
18517             </td>
18518 <td>
18519               <p>
18520                 <span class="blue">Max = 4.55&#949; (Mean = 1.12&#949;)</span><br> <br>
18521                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13.9&#949; (Mean = 2.91&#949;))
18522               </p>
18523             </td>
18524 <td>
18525               <p>
18526                 <span class="blue">Max = 0.764&#949; (Mean = 0.0348&#949;)</span><br> <br>
18527                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71&#949; (Mean = 1.76&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And
18528                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18529                 Max = 7.47&#949; (Mean = 1.34&#949;))
18530               </p>
18531             </td>
18532 <td>
18533               <p>
18534                 <span class="blue">Max = 4.55&#949; (Mean = 1.12&#949;)</span>
18535               </p>
18536             </td>
18537 <td>
18538               <p>
18539                 <span class="blue">Max = 9.34&#949; (Mean = 1.7&#949;)</span>
18540               </p>
18541             </td>
18542 </tr>
18543 <tr>
18544 <td>
18545               <p>
18546                 Bessel Kv: Random Data
18547               </p>
18548             </td>
18549 <td>
18550               <p>
18551                 <span class="blue">Max = 7.88&#949; (Mean = 1.48&#949;)</span><br> <br>
18552                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13.6&#949; (Mean = 2.68&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And
18553                 other failures.</a>)
18554               </p>
18555             </td>
18556 <td>
18557               <p>
18558                 <span class="blue">Max = 0.507&#949; (Mean = 0.0313&#949;)</span><br> <br>
18559                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71&#949; (Mean = 1.47&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And
18560                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18561                 Max = 7.37&#949; (Mean = 1.49&#949;))
18562               </p>
18563             </td>
18564 <td>
18565               <p>
18566                 <span class="blue">Max = 7.88&#949; (Mean = 1.47&#949;)</span>
18567               </p>
18568             </td>
18569 <td>
18570               <p>
18571                 <span class="blue">Max = 8.33&#949; (Mean = 1.62&#949;)</span>
18572               </p>
18573             </td>
18574 </tr>
18575 </tbody>
18576 </table></div>
18577 </div>
18578 <br class="table-break"><div class="table">
18579 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table&#160;113.&#160;Error rates for cyl_bessel_k (integer orders)</b></p>
18580 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
18581 <colgroup>
18582 <col>
18583 <col>
18584 <col>
18585 <col>
18586 <col>
18587 </colgroup>
18588 <thead><tr>
18589 <th>
18590             </th>
18591 <th>
18592               <p>
18593                 GNU C++ version 7.1.0<br> linux<br> long double
18594               </p>
18595             </th>
18596 <th>
18597               <p>
18598                 GNU C++ version 7.1.0<br> linux<br> double
18599               </p>
18600             </th>
18601 <th>
18602               <p>
18603                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
18604               </p>
18605             </th>
18606 <th>
18607               <p>
18608                 Microsoft Visual C++ version 14.1<br> Win32<br> double
18609               </p>
18610             </th>
18611 </tr></thead>
18612 <tbody>
18613 <tr>
18614 <td>
18615               <p>
18616                 Bessel K0: Mathworld Data (Integer Version)
18617               </p>
18618             </td>
18619 <td>
18620               <p>
18621                 <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span><br> <br>
18622                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
18623               </p>
18624             </td>
18625 <td>
18626               <p>
18627                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
18628                 2.1:</em></span> Max = 1.2&#949; (Mean = 0.733&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18629                 Max = 0.833&#949; (Mean = 0.601&#949;))
18630               </p>
18631             </td>
18632 <td>
18633               <p>
18634                 <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span>
18635               </p>
18636             </td>
18637 <td>
18638               <p>
18639                 <span class="blue">Max = 0.833&#949; (Mean = 0.552&#949;)</span>
18640               </p>
18641             </td>
18642 </tr>
18643 <tr>
18644 <td>
18645               <p>
18646                 Bessel K1: Mathworld Data (Integer Version)
18647               </p>
18648             </td>
18649 <td>
18650               <p>
18651                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span><br> <br>
18652                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
18653               </p>
18654             </td>
18655 <td>
18656               <p>
18657                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
18658                 2.1:</em></span> Max = 0.626&#949; (Mean = 0.333&#949;))<br> (<span class="emphasis"><em>Rmath
18659                 3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.516&#949;))
18660               </p>
18661             </td>
18662 <td>
18663               <p>
18664                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
18665               </p>
18666             </td>
18667 <td>
18668               <p>
18669                 <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
18670               </p>
18671             </td>
18672 </tr>
18673 <tr>
18674 <td>
18675               <p>
18676                 Bessel Kn: Mathworld Data (Integer Version)
18677               </p>
18678             </td>
18679 <td>
18680               <p>
18681                 <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span><br> <br>
18682                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
18683                 other failures.</a>)
18684               </p>
18685             </td>
18686 <td>
18687               <p>
18688                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
18689                 2.1:</em></span> Max = 168&#949; (Mean = 59.5&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
18690                 Max = 8.48&#949; (Mean = 2.98&#949;))
18691               </p>
18692             </td>
18693 <td>
18694               <p>
18695                 <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span>
18696               </p>
18697             </td>
18698 <td>
18699               <p>
18700                 <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
18701               </p>
18702             </td>
18703 </tr>
18704 </tbody>
18705 </table></div>
18706 </div>
18707 <br class="table-break"><div class="table">
18708 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime"></a><p class="title"><b>Table&#160;114.&#160;Error rates for cyl_bessel_k_prime</b></p>
18709 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
18710 <colgroup>
18711 <col>
18712 <col>
18713 <col>
18714 <col>
18715 <col>
18716 </colgroup>
18717 <thead><tr>
18718 <th>
18719             </th>
18720 <th>
18721               <p>
18722                 GNU C++ version 7.1.0<br> linux<br> double
18723               </p>
18724             </th>
18725 <th>
18726               <p>
18727                 GNU C++ version 7.1.0<br> linux<br> long double
18728               </p>
18729             </th>
18730 <th>
18731               <p>
18732                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
18733               </p>
18734             </th>
18735 <th>
18736               <p>
18737                 Microsoft Visual C++ version 14.1<br> Win32<br> double
18738               </p>
18739             </th>
18740 </tr></thead>
18741 <tbody>
18742 <tr>
18743 <td>
18744               <p>
18745                 Bessel K'0: Mathworld Data
18746               </p>
18747             </td>
18748 <td>
18749               <p>
18750                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18751               </p>
18752             </td>
18753 <td>
18754               <p>
18755                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
18756               </p>
18757             </td>
18758 <td>
18759               <p>
18760                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
18761               </p>
18762             </td>
18763 <td>
18764               <p>
18765                 <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
18766               </p>
18767             </td>
18768 </tr>
18769 <tr>
18770 <td>
18771               <p>
18772                 Bessel K'1: Mathworld Data
18773               </p>
18774             </td>
18775 <td>
18776               <p>
18777                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18778               </p>
18779             </td>
18780 <td>
18781               <p>
18782                 <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
18783               </p>
18784             </td>
18785 <td>
18786               <p>
18787                 <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
18788               </p>
18789             </td>
18790 <td>
18791               <p>
18792                 <span class="blue">Max = 0.761&#949; (Mean = 0.444&#949;)</span>
18793               </p>
18794             </td>
18795 </tr>
18796 <tr>
18797 <td>
18798               <p>
18799                 Bessel K'n: Mathworld Data
18800               </p>
18801             </td>
18802 <td>
18803               <p>
18804                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18805               </p>
18806             </td>
18807 <td>
18808               <p>
18809                 <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
18810               </p>
18811             </td>
18812 <td>
18813               <p>
18814                 <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
18815               </p>
18816             </td>
18817 <td>
18818               <p>
18819                 <span class="blue">Max = 4.17&#949; (Mean = 1.75&#949;)</span>
18820               </p>
18821             </td>
18822 </tr>
18823 <tr>
18824 <td>
18825               <p>
18826                 Bessel K'v: Mathworld Data
18827               </p>
18828             </td>
18829 <td>
18830               <p>
18831                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18832               </p>
18833             </td>
18834 <td>
18835               <p>
18836                 <span class="blue">Max = 3.94&#949; (Mean = 2.44&#949;)</span>
18837               </p>
18838             </td>
18839 <td>
18840               <p>
18841                 <span class="blue">Max = 3.94&#949; (Mean = 2.34&#949;)</span>
18842               </p>
18843             </td>
18844 <td>
18845               <p>
18846                 <span class="blue">Max = 3.94&#949; (Mean = 1.47&#949;)</span>
18847               </p>
18848             </td>
18849 </tr>
18850 <tr>
18851 <td>
18852               <p>
18853                 Bessel K'v: Mathworld Data (large values)
18854               </p>
18855             </td>
18856 <td>
18857               <p>
18858                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18859               </p>
18860             </td>
18861 <td>
18862               <p>
18863                 <span class="blue">Max = 59.2&#949; (Mean = 42.9&#949;)</span>
18864               </p>
18865             </td>
18866 <td>
18867               <p>
18868                 <span class="blue">Max = 58.7&#949; (Mean = 42.6&#949;)</span>
18869               </p>
18870             </td>
18871 <td>
18872               <p>
18873                 <span class="blue">Max = 18.6&#949; (Mean = 11.8&#949;)</span>
18874               </p>
18875             </td>
18876 </tr>
18877 <tr>
18878 <td>
18879               <p>
18880                 Bessel K'n: Random Data
18881               </p>
18882             </td>
18883 <td>
18884               <p>
18885                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18886               </p>
18887             </td>
18888 <td>
18889               <p>
18890                 <span class="blue">Max = 4.45&#949; (Mean = 1.19&#949;)</span>
18891               </p>
18892             </td>
18893 <td>
18894               <p>
18895                 <span class="blue">Max = 4.45&#949; (Mean = 1.19&#949;)</span>
18896               </p>
18897             </td>
18898 <td>
18899               <p>
18900                 <span class="blue">Max = 9.67&#949; (Mean = 1.73&#949;)</span>
18901               </p>
18902             </td>
18903 </tr>
18904 <tr>
18905 <td>
18906               <p>
18907                 Bessel K'v: Random Data
18908               </p>
18909             </td>
18910 <td>
18911               <p>
18912                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18913               </p>
18914             </td>
18915 <td>
18916               <p>
18917                 <span class="blue">Max = 7.95&#949; (Mean = 1.53&#949;)</span>
18918               </p>
18919             </td>
18920 <td>
18921               <p>
18922                 <span class="blue">Max = 7.95&#949; (Mean = 1.52&#949;)</span>
18923               </p>
18924             </td>
18925 <td>
18926               <p>
18927                 <span class="blue">Max = 8.32&#949; (Mean = 1.65&#949;)</span>
18928               </p>
18929             </td>
18930 </tr>
18931 </tbody>
18932 </table></div>
18933 </div>
18934 <br class="table-break"><div class="table">
18935 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table&#160;115.&#160;Error rates for cyl_bessel_k_prime (integer orders)</b></p>
18936 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
18937 <colgroup>
18938 <col>
18939 <col>
18940 <col>
18941 <col>
18942 <col>
18943 </colgroup>
18944 <thead><tr>
18945 <th>
18946             </th>
18947 <th>
18948               <p>
18949                 GNU C++ version 7.1.0<br> linux<br> double
18950               </p>
18951             </th>
18952 <th>
18953               <p>
18954                 GNU C++ version 7.1.0<br> linux<br> long double
18955               </p>
18956             </th>
18957 <th>
18958               <p>
18959                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
18960               </p>
18961             </th>
18962 <th>
18963               <p>
18964                 Microsoft Visual C++ version 14.1<br> Win32<br> double
18965               </p>
18966             </th>
18967 </tr></thead>
18968 <tbody>
18969 <tr>
18970 <td>
18971               <p>
18972                 Bessel K'0: Mathworld Data (Integer Version)
18973               </p>
18974             </td>
18975 <td>
18976               <p>
18977                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
18978               </p>
18979             </td>
18980 <td>
18981               <p>
18982                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
18983               </p>
18984             </td>
18985 <td>
18986               <p>
18987                 <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
18988               </p>
18989             </td>
18990 <td>
18991               <p>
18992                 <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
18993               </p>
18994             </td>
18995 </tr>
18996 <tr>
18997 <td>
18998               <p>
18999                 Bessel K'1: Mathworld Data (Integer Version)
19000               </p>
19001             </td>
19002 <td>
19003               <p>
19004                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
19005               </p>
19006             </td>
19007 <td>
19008               <p>
19009                 <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
19010               </p>
19011             </td>
19012 <td>
19013               <p>
19014                 <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
19015               </p>
19016             </td>
19017 <td>
19018               <p>
19019                 <span class="blue">Max = 0.761&#949; (Mean = 0.444&#949;)</span>
19020               </p>
19021             </td>
19022 </tr>
19023 <tr>
19024 <td>
19025               <p>
19026                 Bessel K'n: Mathworld Data (Integer Version)
19027               </p>
19028             </td>
19029 <td>
19030               <p>
19031                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
19032               </p>
19033             </td>
19034 <td>
19035               <p>
19036                 <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
19037               </p>
19038             </td>
19039 <td>
19040               <p>
19041                 <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
19042               </p>
19043             </td>
19044 <td>
19045               <p>
19046                 <span class="blue">Max = 4.17&#949; (Mean = 1.75&#949;)</span>
19047               </p>
19048             </td>
19049 </tr>
19050 </tbody>
19051 </table></div>
19052 </div>
19053 <br class="table-break"><div class="table">
19054 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann"></a><p class="title"><b>Table&#160;116.&#160;Error rates for cyl_neumann</b></p>
19055 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
19056 <colgroup>
19057 <col>
19058 <col>
19059 <col>
19060 <col>
19061 <col>
19062 </colgroup>
19063 <thead><tr>
19064 <th>
19065             </th>
19066 <th>
19067               <p>
19068                 GNU C++ version 7.1.0<br> linux<br> long double
19069               </p>
19070             </th>
19071 <th>
19072               <p>
19073                 GNU C++ version 7.1.0<br> linux<br> double
19074               </p>
19075             </th>
19076 <th>
19077               <p>
19078                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
19079               </p>
19080             </th>
19081 <th>
19082               <p>
19083                 Microsoft Visual C++ version 14.1<br> Win32<br> double
19084               </p>
19085             </th>
19086 </tr></thead>
19087 <tbody>
19088 <tr>
19089 <td>
19090               <p>
19091                 Y0: Mathworld Data
19092               </p>
19093             </td>
19094 <td>
19095               <p>
19096                 <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span><br> <br>
19097                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean = 6.87e+04&#949;))
19098               </p>
19099             </td>
19100 <td>
19101               <p>
19102                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19103                 2.1:</em></span> Max = 60.9&#949; (Mean = 20.4&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19104                 Max = 167&#949; (Mean = 56.5&#949;))
19105               </p>
19106             </td>
19107 <td>
19108               <p>
19109                 <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
19110               </p>
19111             </td>
19112 <td>
19113               <p>
19114                 <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span>
19115               </p>
19116             </td>
19117 </tr>
19118 <tr>
19119 <td>
19120               <p>
19121                 Y1: Mathworld Data
19122               </p>
19123             </td>
19124 <td>
19125               <p>
19126                 <span class="blue">Max = 6.33&#949; (Mean = 2.25&#949;)</span><br> <br>
19127                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean = 4.08e+03&#949;))
19128               </p>
19129             </td>
19130 <td>
19131               <p>
19132                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19133                 2.1:</em></span> Max = 23.4&#949; (Mean = 8.1&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19134                 Max = 193&#949; (Mean = 64.4&#949;))
19135               </p>
19136             </td>
19137 <td>
19138               <p>
19139                 <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
19140               </p>
19141             </td>
19142 <td>
19143               <p>
19144                 <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span>
19145               </p>
19146             </td>
19147 </tr>
19148 <tr>
19149 <td>
19150               <p>
19151                 Yn: Mathworld Data
19152               </p>
19153             </td>
19154 <td>
19155               <p>
19156                 <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span><br> <br>
19157                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.2e+20&#949; (Mean
19158                 = 6.97e+19&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And
19159                 other failures.</a>)</span>
19160               </p>
19161             </td>
19162 <td>
19163               <p>
19164                 <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
19165                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And
19166                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19167                 Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
19168               </p>
19169             </td>
19170 <td>
19171               <p>
19172                 <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
19173               </p>
19174             </td>
19175 <td>
19176               <p>
19177                 <span class="blue">Max = 35&#949; (Mean = 11.9&#949;)</span>
19178               </p>
19179             </td>
19180 </tr>
19181 <tr>
19182 <td>
19183               <p>
19184                 Yv: Mathworld Data
19185               </p>
19186             </td>
19187 <td>
19188               <p>
19189                 <span class="blue">Max = 10.7&#949; (Mean = 4.93&#949;)</span><br> <br>
19190                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 3.49e+15&#949; (Mean
19191                 = 1.05e+15&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And
19192                 other failures.</a>)</span>
19193               </p>
19194             </td>
19195 <td>
19196               <p>
19197                 <span class="blue">Max = 10&#949; (Mean = 3.02&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19198                 2.1:</em></span> Max = 1.07e+05&#949; (Mean = 3.22e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And
19199                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19200                 Max = 243&#949; (Mean = 73.9&#949;))
19201               </p>
19202             </td>
19203 <td>
19204               <p>
19205                 <span class="blue">Max = 10.7&#949; (Mean = 5.1&#949;)</span>
19206               </p>
19207             </td>
19208 <td>
19209               <p>
19210                 <span class="blue">Max = 7.89&#949; (Mean = 3.27&#949;)</span>
19211               </p>
19212             </td>
19213 </tr>
19214 <tr>
19215 <td>
19216               <p>
19217                 Yv: Mathworld Data (large values)
19218               </p>
19219             </td>
19220 <td>
19221               <p>
19222                 <span class="blue">Max = 1.7&#949; (Mean = 1.33&#949;)</span><br> <br>
19223                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 43.2&#949; (Mean = 16.3&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And
19224                 other failures.</a>)
19225               </p>
19226             </td>
19227 <td>
19228               <p>
19229                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19230                 2.1:</em></span> Max = 60.8&#949; (Mean = 23&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And
19231                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19232                 Max = 0.682&#949; (Mean = 0.335&#949;))
19233               </p>
19234             </td>
19235 <td>
19236               <p>
19237                 <span class="blue">Max = 1.7&#949; (Mean = 1.33&#949;)</span>
19238               </p>
19239             </td>
19240 <td>
19241               <p>
19242                 <span class="blue">Max = 0.682&#949; (Mean = 0.423&#949;)</span>
19243               </p>
19244             </td>
19245 </tr>
19246 <tr>
19247 <td>
19248               <p>
19249                 Y0 and Y1: Random Data
19250               </p>
19251             </td>
19252 <td>
19253               <p>
19254                 <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span><br> <br>
19255                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.59e+03&#949; (Mean = 500&#949;))
19256               </p>
19257             </td>
19258 <td>
19259               <p>
19260                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19261                 2.1:</em></span> Max = 34.4&#949; (Mean = 8.9&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19262                 Max = 83&#949; (Mean = 14.2&#949;))
19263               </p>
19264             </td>
19265 <td>
19266               <p>
19267                 <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span>
19268               </p>
19269             </td>
19270 <td>
19271               <p>
19272                 <span class="blue">Max = 4.17&#949; (Mean = 1.24&#949;)</span>
19273               </p>
19274             </td>
19275 </tr>
19276 <tr>
19277 <td>
19278               <p>
19279                 Yn: Random Data
19280               </p>
19281             </td>
19282 <td>
19283               <p>
19284                 <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span><br> <br>
19285                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.01e+03&#949; (Mean = 348&#949;))
19286               </p>
19287             </td>
19288 <td>
19289               <p>
19290                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19291                 2.1:</em></span> Max = 500&#949; (Mean = 47.8&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19292                 Max = 691&#949; (Mean = 67.9&#949;))
19293               </p>
19294             </td>
19295 <td>
19296               <p>
19297                 <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span>
19298               </p>
19299             </td>
19300 <td>
19301               <p>
19302                 <span class="blue">Max = 117&#949; (Mean = 10.2&#949;)</span>
19303               </p>
19304             </td>
19305 </tr>
19306 <tr>
19307 <td>
19308               <p>
19309                 Yv: Random Data
19310               </p>
19311             </td>
19312 <td>
19313               <p>
19314                 <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span><br> <br>
19315                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
19316                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And
19317                 other failures.</a>)</span>
19318               </p>
19319             </td>
19320 <td>
19321               <p>
19322                 <span class="blue">Max = 1.53&#949; (Mean = 0.102&#949;)</span><br> <br>
19323                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06&#949; (Mean = 7.67e+04&#949;))<br>
19324                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05&#949; (Mean = 9.64e+03&#949;))
19325               </p>
19326             </td>
19327 <td>
19328               <p>
19329                 <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span>
19330               </p>
19331             </td>
19332 <td>
19333               <p>
19334                 <span class="blue">Max = 1.23e+03&#949; (Mean = 69.9&#949;)</span>
19335               </p>
19336             </td>
19337 </tr>
19338 </tbody>
19339 </table></div>
19340 </div>
19341 <br class="table-break"><div class="table">
19342 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table&#160;117.&#160;Error rates for cyl_neumann (integer orders)</b></p>
19343 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
19344 <colgroup>
19345 <col>
19346 <col>
19347 <col>
19348 <col>
19349 <col>
19350 </colgroup>
19351 <thead><tr>
19352 <th>
19353             </th>
19354 <th>
19355               <p>
19356                 GNU C++ version 7.1.0<br> linux<br> long double
19357               </p>
19358             </th>
19359 <th>
19360               <p>
19361                 GNU C++ version 7.1.0<br> linux<br> double
19362               </p>
19363             </th>
19364 <th>
19365               <p>
19366                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
19367               </p>
19368             </th>
19369 <th>
19370               <p>
19371                 Microsoft Visual C++ version 14.1<br> Win32<br> double
19372               </p>
19373             </th>
19374 </tr></thead>
19375 <tbody>
19376 <tr>
19377 <td>
19378               <p>
19379                 Y0: Mathworld Data (Integer Version)
19380               </p>
19381             </td>
19382 <td>
19383               <p>
19384                 <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span><br> <br>
19385                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean = 6.87e+04&#949;))
19386               </p>
19387             </td>
19388 <td>
19389               <p>
19390                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19391                 2.1:</em></span> Max = 6.46&#949; (Mean = 2.38&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19392                 Max = 167&#949; (Mean = 56.5&#949;))
19393               </p>
19394             </td>
19395 <td>
19396               <p>
19397                 <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
19398               </p>
19399             </td>
19400 <td>
19401               <p>
19402                 <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span><br> <br>
19403                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 5.37e+03&#949; (Mean = 1.81e+03&#949;))
19404               </p>
19405             </td>
19406 </tr>
19407 <tr>
19408 <td>
19409               <p>
19410                 Y1: Mathworld Data (Integer Version)
19411               </p>
19412             </td>
19413 <td>
19414               <p>
19415                 <span class="blue">Max = 6.33&#949; (Mean = 2.25&#949;)</span><br> <br>
19416                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean = 4.08e+03&#949;))
19417               </p>
19418             </td>
19419 <td>
19420               <p>
19421                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19422                 2.1:</em></span> Max = 1.51&#949; (Mean = 0.839&#949;))<br> (<span class="emphasis"><em>Rmath
19423                 3.2.3:</em></span> Max = 193&#949; (Mean = 64.4&#949;))
19424               </p>
19425             </td>
19426 <td>
19427               <p>
19428                 <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
19429               </p>
19430             </td>
19431 <td>
19432               <p>
19433                 <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span><br> <br>
19434                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.86e+04&#949; (Mean = 6.2e+03&#949;))
19435               </p>
19436             </td>
19437 </tr>
19438 <tr>
19439 <td>
19440               <p>
19441                 Yn: Mathworld Data (Integer Version)
19442               </p>
19443             </td>
19444 <td>
19445               <p>
19446                 <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span><br> <br>
19447                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.2e+20&#949; (Mean
19448                 = 6.97e+19&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And
19449                 other failures.</a>)</span>
19450               </p>
19451             </td>
19452 <td>
19453               <p>
19454                 <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
19455                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;))<br>
19456                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
19457               </p>
19458             </td>
19459 <td>
19460               <p>
19461                 <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
19462               </p>
19463             </td>
19464 <td>
19465               <p>
19466                 <span class="blue">Max = 35&#949; (Mean = 11.9&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
19467                 Max = 2.49e+05&#949; (Mean = 8.14e+04&#949;))
19468               </p>
19469             </td>
19470 </tr>
19471 </tbody>
19472 </table></div>
19473 </div>
19474 <br class="table-break"><div class="table">
19475 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime"></a><p class="title"><b>Table&#160;118.&#160;Error rates for cyl_neumann_prime</b></p>
19476 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
19477 <colgroup>
19478 <col>
19479 <col>
19480 <col>
19481 <col>
19482 <col>
19483 </colgroup>
19484 <thead><tr>
19485 <th>
19486             </th>
19487 <th>
19488               <p>
19489                 GNU C++ version 7.1.0<br> linux<br> double
19490               </p>
19491             </th>
19492 <th>
19493               <p>
19494                 GNU C++ version 7.1.0<br> linux<br> long double
19495               </p>
19496             </th>
19497 <th>
19498               <p>
19499                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
19500               </p>
19501             </th>
19502 <th>
19503               <p>
19504                 Microsoft Visual C++ version 14.1<br> Win32<br> double
19505               </p>
19506             </th>
19507 </tr></thead>
19508 <tbody>
19509 <tr>
19510 <td>
19511               <p>
19512                 Y'0: Mathworld Data
19513               </p>
19514             </td>
19515 <td>
19516               <p>
19517                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
19518               </p>
19519             </td>
19520 <td>
19521               <p>
19522                 <span class="blue">Max = 6.33&#949; (Mean = 3.12&#949;)</span>
19523               </p>
19524             </td>
19525 <td>
19526               <p>
19527                 <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
19528               </p>
19529             </td>
19530 <td>
19531               <p>
19532                 <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
19533               </p>
19534             </td>
19535 </tr>
19536 <tr>
19537 <td>
19538               <p>
19539                 Y'1: Mathworld Data
19540               </p>
19541             </td>
19542 <td>
19543               <p>
19544                 <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
19545               </p>
19546             </td>
19547 <td>
19548               <p>
19549                 <span class="blue">Max = 37.1&#949; (Mean = 12.8&#949;)</span>
19550               </p>
19551             </td>
19552 <td>
19553               <p>
19554                 <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
19555               </p>
19556             </td>
19557 <td>
19558               <p>
19559                 <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
19560               </p>
19561             </td>
19562 </tr>
19563 <tr>
19564 <td>
19565               <p>
19566                 Y'n: Mathworld Data
19567               </p>
19568             </td>
19569 <td>
19570               <p>
19571                 <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
19572               </p>
19573             </td>
19574 <td>
19575               <p>
19576                 <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
19577               </p>
19578             </td>
19579 <td>
19580               <p>
19581                 <span class="blue">Max = 56&#949; (Mean = 21.3&#949;)</span>
19582               </p>
19583             </td>
19584 <td>
19585               <p>
19586                 <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
19587               </p>
19588             </td>
19589 </tr>
19590 <tr>
19591 <td>
19592               <p>
19593                 Y'v: Mathworld Data
19594               </p>
19595             </td>
19596 <td>
19597               <p>
19598                 <span class="blue">Max = 21.5&#949; (Mean = 6.49&#949;)</span>
19599               </p>
19600             </td>
19601 <td>
19602               <p>
19603                 <span class="blue">Max = 42.5&#949; (Mean = 13.4&#949;)</span>
19604               </p>
19605             </td>
19606 <td>
19607               <p>
19608                 <span class="blue">Max = 42.5&#949; (Mean = 13.6&#949;)</span>
19609               </p>
19610             </td>
19611 <td>
19612               <p>
19613                 <span class="blue">Max = 23.7&#949; (Mean = 10.1&#949;)</span>
19614               </p>
19615             </td>
19616 </tr>
19617 <tr>
19618 <td>
19619               <p>
19620                 Y'v: Mathworld Data (large values)
19621               </p>
19622             </td>
19623 <td>
19624               <p>
19625                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
19626               </p>
19627             </td>
19628 <td>
19629               <p>
19630                 <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
19631               </p>
19632             </td>
19633 <td>
19634               <p>
19635                 <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
19636               </p>
19637             </td>
19638 <td>
19639               <p>
19640                 <span class="blue">Max = 0.627&#949; (Mean = 0.237&#949;)</span>
19641               </p>
19642             </td>
19643 </tr>
19644 <tr>
19645 <td>
19646               <p>
19647                 Y'0 and Y'1: Random Data
19648               </p>
19649             </td>
19650 <td>
19651               <p>
19652                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
19653               </p>
19654             </td>
19655 <td>
19656               <p>
19657                 <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
19658               </p>
19659             </td>
19660 <td>
19661               <p>
19662                 <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
19663               </p>
19664             </td>
19665 <td>
19666               <p>
19667                 <span class="blue">Max = 5.95&#949; (Mean = 1.36&#949;)</span>
19668               </p>
19669             </td>
19670 </tr>
19671 <tr>
19672 <td>
19673               <p>
19674                 Y'n: Random Data
19675               </p>
19676             </td>
19677 <td>
19678               <p>
19679                 <span class="blue">Max = 1.53&#949; (Mean = 0.0885&#949;)</span>
19680               </p>
19681             </td>
19682 <td>
19683               <p>
19684                 <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
19685               </p>
19686             </td>
19687 <td>
19688               <p>
19689                 <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
19690               </p>
19691             </td>
19692 <td>
19693               <p>
19694                 <span class="blue">Max = 621&#949; (Mean = 36&#949;)</span>
19695               </p>
19696             </td>
19697 </tr>
19698 <tr>
19699 <td>
19700               <p>
19701                 Y'v: Random Data
19702               </p>
19703             </td>
19704 <td>
19705               <p>
19706                 <span class="blue">Max = 56.8&#949; (Mean = 2.59&#949;)</span>
19707               </p>
19708             </td>
19709 <td>
19710               <p>
19711                 <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
19712               </p>
19713             </td>
19714 <td>
19715               <p>
19716                 <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
19717               </p>
19718             </td>
19719 <td>
19720               <p>
19721                 <span class="blue">Max = 3.23e+04&#949; (Mean = 1.13e+03&#949;)</span>
19722               </p>
19723             </td>
19724 </tr>
19725 </tbody>
19726 </table></div>
19727 </div>
19728 <br class="table-break"><div class="table">
19729 <a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table&#160;119.&#160;Error rates for cyl_neumann_prime (integer orders)</b></p>
19730 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
19731 <colgroup>
19732 <col>
19733 <col>
19734 <col>
19735 <col>
19736 <col>
19737 </colgroup>
19738 <thead><tr>
19739 <th>
19740             </th>
19741 <th>
19742               <p>
19743                 GNU C++ version 7.1.0<br> linux<br> double
19744               </p>
19745             </th>
19746 <th>
19747               <p>
19748                 GNU C++ version 7.1.0<br> linux<br> long double
19749               </p>
19750             </th>
19751 <th>
19752               <p>
19753                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
19754               </p>
19755             </th>
19756 <th>
19757               <p>
19758                 Microsoft Visual C++ version 14.1<br> Win32<br> double
19759               </p>
19760             </th>
19761 </tr></thead>
19762 <tbody>
19763 <tr>
19764 <td>
19765               <p>
19766                 Y'0: Mathworld Data (Integer Version)
19767               </p>
19768             </td>
19769 <td>
19770               <p>
19771                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
19772               </p>
19773             </td>
19774 <td>
19775               <p>
19776                 <span class="blue">Max = 6.33&#949; (Mean = 3.12&#949;)</span>
19777               </p>
19778             </td>
19779 <td>
19780               <p>
19781                 <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
19782               </p>
19783             </td>
19784 <td>
19785               <p>
19786                 <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
19787               </p>
19788             </td>
19789 </tr>
19790 <tr>
19791 <td>
19792               <p>
19793                 Y'1: Mathworld Data (Integer Version)
19794               </p>
19795             </td>
19796 <td>
19797               <p>
19798                 <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
19799               </p>
19800             </td>
19801 <td>
19802               <p>
19803                 <span class="blue">Max = 37.1&#949; (Mean = 12.8&#949;)</span>
19804               </p>
19805             </td>
19806 <td>
19807               <p>
19808                 <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
19809               </p>
19810             </td>
19811 <td>
19812               <p>
19813                 <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
19814               </p>
19815             </td>
19816 </tr>
19817 <tr>
19818 <td>
19819               <p>
19820                 Y'n: Mathworld Data (Integer Version)
19821               </p>
19822             </td>
19823 <td>
19824               <p>
19825                 <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
19826               </p>
19827             </td>
19828 <td>
19829               <p>
19830                 <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
19831               </p>
19832             </td>
19833 <td>
19834               <p>
19835                 <span class="blue">Max = 56&#949; (Mean = 21.3&#949;)</span>
19836               </p>
19837             </td>
19838 <td>
19839               <p>
19840                 <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
19841               </p>
19842             </td>
19843 </tr>
19844 </tbody>
19845 </table></div>
19846 </div>
19847 <br class="table-break"><div class="table">
19848 <a name="special_function_error_rates_rep.all_the_tables.table_digamma"></a><p class="title"><b>Table&#160;120.&#160;Error rates for digamma</b></p>
19849 <div class="table-contents"><table class="table" summary="Error rates for digamma">
19850 <colgroup>
19851 <col>
19852 <col>
19853 <col>
19854 <col>
19855 <col>
19856 </colgroup>
19857 <thead><tr>
19858 <th>
19859             </th>
19860 <th>
19861               <p>
19862                 GNU C++ version 7.1.0<br> linux<br> double
19863               </p>
19864             </th>
19865 <th>
19866               <p>
19867                 GNU C++ version 7.1.0<br> linux<br> long double
19868               </p>
19869             </th>
19870 <th>
19871               <p>
19872                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
19873               </p>
19874             </th>
19875 <th>
19876               <p>
19877                 Microsoft Visual C++ version 14.1<br> Win32<br> double
19878               </p>
19879             </th>
19880 </tr></thead>
19881 <tbody>
19882 <tr>
19883 <td>
19884               <p>
19885                 Digamma Function: Large Values
19886               </p>
19887             </td>
19888 <td>
19889               <p>
19890                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19891                 2.1:</em></span> Max = 1.84&#949; (Mean = 0.71&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
19892                 Max = 1.18&#949; (Mean = 0.331&#949;))
19893               </p>
19894             </td>
19895 <td>
19896               <p>
19897                 <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
19898               </p>
19899             </td>
19900 <td>
19901               <p>
19902                 <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
19903               </p>
19904             </td>
19905 <td>
19906               <p>
19907                 <span class="blue">Max = 0.98&#949; (Mean = 0.369&#949;)</span>
19908               </p>
19909             </td>
19910 </tr>
19911 <tr>
19912 <td>
19913               <p>
19914                 Digamma Function: Near the Positive Root
19915               </p>
19916             </td>
19917 <td>
19918               <p>
19919                 <span class="blue">Max = 0.891&#949; (Mean = 0.0995&#949;)</span><br> <br>
19920                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135&#949; (Mean = 11.9&#949;))<br> (<span class="emphasis"><em>Rmath
19921                 3.2.3:</em></span> Max = 2.02e+03&#949; (Mean = 256&#949;))
19922               </p>
19923             </td>
19924 <td>
19925               <p>
19926                 <span class="blue">Max = 1.37&#949; (Mean = 0.477&#949;)</span>
19927               </p>
19928             </td>
19929 <td>
19930               <p>
19931                 <span class="blue">Max = 1.31&#949; (Mean = 0.471&#949;)</span>
19932               </p>
19933             </td>
19934 <td>
19935               <p>
19936                 <span class="blue">Max = 0.997&#949; (Mean = 0.527&#949;)</span>
19937               </p>
19938             </td>
19939 </tr>
19940 <tr>
19941 <td>
19942               <p>
19943                 Digamma Function: Near Zero
19944               </p>
19945             </td>
19946 <td>
19947               <p>
19948                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19949                 2.1:</em></span> Max = 0.953&#949; (Mean = 0.348&#949;))<br> (<span class="emphasis"><em>Rmath
19950                 3.2.3:</em></span> Max = 1.17&#949; (Mean = 0.564&#949;))
19951               </p>
19952             </td>
19953 <td>
19954               <p>
19955                 <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
19956               </p>
19957             </td>
19958 <td>
19959               <p>
19960                 <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
19961               </p>
19962             </td>
19963 <td>
19964               <p>
19965                 <span class="blue">Max = 0.953&#949; (Mean = 0.337&#949;)</span>
19966               </p>
19967             </td>
19968 </tr>
19969 <tr>
19970 <td>
19971               <p>
19972                 Digamma Function: Negative Values
19973               </p>
19974             </td>
19975 <td>
19976               <p>
19977                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
19978                 2.1:</em></span> Max = 4.56e+04&#949; (Mean = 3.91e+03&#949;))<br> (<span class="emphasis"><em>Rmath
19979                 3.2.3:</em></span> Max = 4.6e+04&#949; (Mean = 3.94e+03&#949;))
19980               </p>
19981             </td>
19982 <td>
19983               <p>
19984                 <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
19985               </p>
19986             </td>
19987 <td>
19988               <p>
19989                 <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
19990               </p>
19991             </td>
19992 <td>
19993               <p>
19994                 <span class="blue">Max = 214&#949; (Mean = 16.1&#949;)</span>
19995               </p>
19996             </td>
19997 </tr>
19998 <tr>
19999 <td>
20000               <p>
20001                 Digamma Function: Values near 0
20002               </p>
20003             </td>
20004 <td>
20005               <p>
20006                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20007                 2.1:</em></span> Max = 0.866&#949; (Mean = 0.387&#949;))<br> (<span class="emphasis"><em>Rmath
20008                 3.2.3:</em></span> Max = 3.58e+05&#949; (Mean = 1.6e+05&#949;))
20009               </p>
20010             </td>
20011 <td>
20012               <p>
20013                 <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
20014               </p>
20015             </td>
20016 <td>
20017               <p>
20018                 <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
20019               </p>
20020             </td>
20021 <td>
20022               <p>
20023                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
20024               </p>
20025             </td>
20026 </tr>
20027 <tr>
20028 <td>
20029               <p>
20030                 Digamma Function: Integer arguments
20031               </p>
20032             </td>
20033 <td>
20034               <p>
20035                 <span class="blue">Max = 0.992&#949; (Mean = 0.215&#949;)</span><br> <br>
20036                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18&#949; (Mean = 0.607&#949;))<br> (<span class="emphasis"><em>Rmath
20037                 3.2.3:</em></span> Max = 4.33&#949; (Mean = 0.982&#949;))
20038               </p>
20039             </td>
20040 <td>
20041               <p>
20042                 <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
20043               </p>
20044             </td>
20045 <td>
20046               <p>
20047                 <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
20048               </p>
20049             </td>
20050 <td>
20051               <p>
20052                 <span class="blue">Max = 0.992&#949; (Mean = 0.452&#949;)</span>
20053               </p>
20054             </td>
20055 </tr>
20056 <tr>
20057 <td>
20058               <p>
20059                 Digamma Function: Half integer arguments
20060               </p>
20061             </td>
20062 <td>
20063               <p>
20064                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20065                 2.1:</em></span> Max = 1.09&#949; (Mean = 0.531&#949;))<br> (<span class="emphasis"><em>Rmath
20066                 3.2.3:</em></span> Max = 46.2&#949; (Mean = 7.24&#949;))
20067               </p>
20068             </td>
20069 <td>
20070               <p>
20071                 <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
20072               </p>
20073             </td>
20074 <td>
20075               <p>
20076                 <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
20077               </p>
20078             </td>
20079 <td>
20080               <p>
20081                 <span class="blue">Max = 0.78&#949; (Mean = 0.314&#949;)</span>
20082               </p>
20083             </td>
20084 </tr>
20085 </tbody>
20086 </table></div>
20087 </div>
20088 <br class="table-break"><div class="table">
20089 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_1"></a><p class="title"><b>Table&#160;121.&#160;Error rates for ellint_1</b></p>
20090 <div class="table-contents"><table class="table" summary="Error rates for ellint_1">
20091 <colgroup>
20092 <col>
20093 <col>
20094 <col>
20095 <col>
20096 <col>
20097 </colgroup>
20098 <thead><tr>
20099 <th>
20100             </th>
20101 <th>
20102               <p>
20103                 GNU C++ version 7.1.0<br> linux<br> long double
20104               </p>
20105             </th>
20106 <th>
20107               <p>
20108                 GNU C++ version 7.1.0<br> linux<br> double
20109               </p>
20110             </th>
20111 <th>
20112               <p>
20113                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
20114               </p>
20115             </th>
20116 <th>
20117               <p>
20118                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20119               </p>
20120             </th>
20121 </tr></thead>
20122 <tbody>
20123 <tr>
20124 <td>
20125               <p>
20126                 Elliptic Integral F: Mathworld Data
20127               </p>
20128             </td>
20129 <td>
20130               <p>
20131                 <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span><br> <br>
20132                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
20133                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And
20134                 other failures.</a>)</span>
20135               </p>
20136             </td>
20137 <td>
20138               <p>
20139                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20140                 2.1:</em></span> Max = 0.919&#949; (Mean = 0.544&#949;))
20141               </p>
20142             </td>
20143 <td>
20144               <p>
20145                 <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span>
20146               </p>
20147             </td>
20148 <td>
20149               <p>
20150                 <span class="blue">Max = 0.919&#949; (Mean = 0.542&#949;)</span>
20151               </p>
20152             </td>
20153 </tr>
20154 <tr>
20155 <td>
20156               <p>
20157                 Elliptic Integral F: Random Data
20158               </p>
20159             </td>
20160 <td>
20161               <p>
20162                 <span class="blue">Max = 1.57&#949; (Mean = 0.56&#949;)</span><br> <br>
20163                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.56&#949; (Mean = 0.816&#949;))
20164               </p>
20165             </td>
20166 <td>
20167               <p>
20168                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20169                 2.1:</em></span> Max = 2.99&#949; (Mean = 0.797&#949;))
20170               </p>
20171             </td>
20172 <td>
20173               <p>
20174                 <span class="blue">Max = 1.57&#949; (Mean = 0.561&#949;)</span>
20175               </p>
20176             </td>
20177 <td>
20178               <p>
20179                 <span class="blue">Max = 2.26&#949; (Mean = 0.631&#949;)</span>
20180               </p>
20181             </td>
20182 </tr>
20183 </tbody>
20184 </table></div>
20185 </div>
20186 <br class="table-break"><div class="table">
20187 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_1_complete_"></a><p class="title"><b>Table&#160;122.&#160;Error rates for ellint_1 (complete)</b></p>
20188 <div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
20189 <colgroup>
20190 <col>
20191 <col>
20192 <col>
20193 <col>
20194 <col>
20195 </colgroup>
20196 <thead><tr>
20197 <th>
20198             </th>
20199 <th>
20200               <p>
20201                 GNU C++ version 7.1.0<br> linux<br> long double
20202               </p>
20203             </th>
20204 <th>
20205               <p>
20206                 GNU C++ version 7.1.0<br> linux<br> double
20207               </p>
20208             </th>
20209 <th>
20210               <p>
20211                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
20212               </p>
20213             </th>
20214 <th>
20215               <p>
20216                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20217               </p>
20218             </th>
20219 </tr></thead>
20220 <tbody>
20221 <tr>
20222 <td>
20223               <p>
20224                 Elliptic Integral K: Mathworld Data
20225               </p>
20226             </td>
20227 <td>
20228               <p>
20229                 <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span><br> <br>
20230                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.19&#949; (Mean = 0.765&#949;))
20231               </p>
20232             </td>
20233 <td>
20234               <p>
20235                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20236                 2.1:</em></span> Max = 0.623&#949; (Mean = 0.393&#949;))
20237               </p>
20238             </td>
20239 <td>
20240               <p>
20241                 <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span>
20242               </p>
20243             </td>
20244 <td>
20245               <p>
20246                 <span class="blue">Max = 0.915&#949; (Mean = 0.547&#949;)</span>
20247               </p>
20248             </td>
20249 </tr>
20250 <tr>
20251 <td>
20252               <p>
20253                 Elliptic Integral K: Random Data
20254               </p>
20255             </td>
20256 <td>
20257               <p>
20258                 <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span><br> <br>
20259                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.19&#949; (Mean = 0.694&#949;))
20260               </p>
20261             </td>
20262 <td>
20263               <p>
20264                 <span class="blue">Max = 0.851&#949; (Mean = 0.0851&#949;)</span><br> <br>
20265                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32&#949; (Mean = 0.688&#949;))
20266               </p>
20267             </td>
20268 <td>
20269               <p>
20270                 <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span>
20271               </p>
20272             </td>
20273 <td>
20274               <p>
20275                 <span class="blue">Max = 0.958&#949; (Mean = 0.408&#949;)</span>
20276               </p>
20277             </td>
20278 </tr>
20279 </tbody>
20280 </table></div>
20281 </div>
20282 <br class="table-break"><div class="table">
20283 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_2"></a><p class="title"><b>Table&#160;123.&#160;Error rates for ellint_2</b></p>
20284 <div class="table-contents"><table class="table" summary="Error rates for ellint_2">
20285 <colgroup>
20286 <col>
20287 <col>
20288 <col>
20289 <col>
20290 <col>
20291 </colgroup>
20292 <thead><tr>
20293 <th>
20294             </th>
20295 <th>
20296               <p>
20297                 GNU C++ version 7.1.0<br> linux<br> double
20298               </p>
20299             </th>
20300 <th>
20301               <p>
20302                 GNU C++ version 7.1.0<br> linux<br> long double
20303               </p>
20304             </th>
20305 <th>
20306               <p>
20307                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
20308               </p>
20309             </th>
20310 <th>
20311               <p>
20312                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20313               </p>
20314             </th>
20315 </tr></thead>
20316 <tbody>
20317 <tr>
20318 <td>
20319               <p>
20320                 Elliptic Integral E: Mathworld Data
20321               </p>
20322             </td>
20323 <td>
20324               <p>
20325                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20326                 2.1:</em></span> Max = 0.63&#949; (Mean = 0.325&#949;))
20327               </p>
20328             </td>
20329 <td>
20330               <p>
20331                 <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span><br> <br>
20332                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
20333                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And
20334                 other failures.</a>)</span>
20335               </p>
20336             </td>
20337 <td>
20338               <p>
20339                 <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span>
20340               </p>
20341             </td>
20342 <td>
20343               <p>
20344                 <span class="blue">Max = 1.31&#949; (Mean = 0.727&#949;)</span>
20345               </p>
20346             </td>
20347 </tr>
20348 <tr>
20349 <td>
20350               <p>
20351                 Elliptic Integral E: Random Data
20352               </p>
20353             </td>
20354 <td>
20355               <p>
20356                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20357                 2.1:</em></span> Max = 4.4&#949; (Mean = 1.16&#949;))
20358               </p>
20359             </td>
20360 <td>
20361               <p>
20362                 <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span><br> <br>
20363                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.08e+04&#949; (Mean = 3.84e+03&#949;))
20364               </p>
20365             </td>
20366 <td>
20367               <p>
20368                 <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span>
20369               </p>
20370             </td>
20371 <td>
20372               <p>
20373                 <span class="blue">Max = 2.23&#949; (Mean = 0.639&#949;)</span>
20374               </p>
20375             </td>
20376 </tr>
20377 <tr>
20378 <td>
20379               <p>
20380                 Elliptic Integral E: Small Angles
20381               </p>
20382             </td>
20383 <td>
20384               <p>
20385                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20386                 2.1:</em></span> Max = 0.5&#949; (Mean = 0.118&#949;))
20387               </p>
20388             </td>
20389 <td>
20390               <p>
20391                 <span class="blue">Max = 1&#949; (Mean = 0.283&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
20392                 Max = 2&#949; (Mean = 0.333&#949;))
20393               </p>
20394             </td>
20395 <td>
20396               <p>
20397                 <span class="blue">Max = 1&#949; (Mean = 0.283&#949;)</span>
20398               </p>
20399             </td>
20400 <td>
20401               <p>
20402                 <span class="blue">Max = 1&#949; (Mean = 0.421&#949;)</span>
20403               </p>
20404             </td>
20405 </tr>
20406 </tbody>
20407 </table></div>
20408 </div>
20409 <br class="table-break"><div class="table">
20410 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_2_complete_"></a><p class="title"><b>Table&#160;124.&#160;Error rates for ellint_2 (complete)</b></p>
20411 <div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
20412 <colgroup>
20413 <col>
20414 <col>
20415 <col>
20416 <col>
20417 <col>
20418 </colgroup>
20419 <thead><tr>
20420 <th>
20421             </th>
20422 <th>
20423               <p>
20424                 GNU C++ version 7.1.0<br> linux<br> double
20425               </p>
20426             </th>
20427 <th>
20428               <p>
20429                 GNU C++ version 7.1.0<br> linux<br> long double
20430               </p>
20431             </th>
20432 <th>
20433               <p>
20434                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
20435               </p>
20436             </th>
20437 <th>
20438               <p>
20439                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20440               </p>
20441             </th>
20442 </tr></thead>
20443 <tbody>
20444 <tr>
20445 <td>
20446               <p>
20447                 Elliptic Integral E: Mathworld Data
20448               </p>
20449             </td>
20450 <td>
20451               <p>
20452                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20453                 2.1:</em></span> Max = 3.09&#949; (Mean = 1.04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And
20454                 other failures.</a>)
20455               </p>
20456             </td>
20457 <td>
20458               <p>
20459                 <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span><br> <br>
20460                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 170&#949; (Mean = 55.1&#949;))
20461               </p>
20462             </td>
20463 <td>
20464               <p>
20465                 <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span>
20466               </p>
20467             </td>
20468 <td>
20469               <p>
20470                 <span class="blue">Max = 1.3&#949; (Mean = 0.615&#949;)</span>
20471               </p>
20472             </td>
20473 </tr>
20474 <tr>
20475 <td>
20476               <p>
20477                 Elliptic Integral E: Random Data
20478               </p>
20479             </td>
20480 <td>
20481               <p>
20482                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20483                 2.1:</em></span> Max = 4.34&#949; (Mean = 1.18&#949;))
20484               </p>
20485             </td>
20486 <td>
20487               <p>
20488                 <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span><br> <br>
20489                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.49e+04&#949; (Mean = 3.39e+03&#949;))
20490               </p>
20491             </td>
20492 <td>
20493               <p>
20494                 <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span>
20495               </p>
20496             </td>
20497 <td>
20498               <p>
20499                 <span class="blue">Max = 1.71&#949; (Mean = 0.553&#949;)</span>
20500               </p>
20501             </td>
20502 </tr>
20503 </tbody>
20504 </table></div>
20505 </div>
20506 <br class="table-break"><div class="table">
20507 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_3"></a><p class="title"><b>Table&#160;125.&#160;Error rates for ellint_3</b></p>
20508 <div class="table-contents"><table class="table" summary="Error rates for ellint_3">
20509 <colgroup>
20510 <col>
20511 <col>
20512 <col>
20513 <col>
20514 <col>
20515 </colgroup>
20516 <thead><tr>
20517 <th>
20518             </th>
20519 <th>
20520               <p>
20521                 GNU C++ version 7.1.0<br> linux<br> long double
20522               </p>
20523             </th>
20524 <th>
20525               <p>
20526                 GNU C++ version 7.1.0<br> linux<br> double
20527               </p>
20528             </th>
20529 <th>
20530               <p>
20531                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
20532               </p>
20533             </th>
20534 <th>
20535               <p>
20536                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20537               </p>
20538             </th>
20539 </tr></thead>
20540 <tbody>
20541 <tr>
20542 <td>
20543               <p>
20544                 Elliptic Integral PI: Mathworld Data
20545               </p>
20546             </td>
20547 <td>
20548               <p>
20549                 <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span><br> <br>
20550                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
20551                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And
20552                 other failures.</a>)</span>
20553               </p>
20554             </td>
20555 <td>
20556               <p>
20557                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20558                 2.1:</em></span> Max = 1.48e+05&#949; (Mean = 2.54e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And
20559                 other failures.</a>)
20560               </p>
20561             </td>
20562 <td>
20563               <p>
20564                 <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span>
20565               </p>
20566             </td>
20567 <td>
20568               <p>
20569                 <span class="blue">Max = 565&#949; (Mean = 102&#949;)</span>
20570               </p>
20571             </td>
20572 </tr>
20573 <tr>
20574 <td>
20575               <p>
20576                 Elliptic Integral PI: Random Data
20577               </p>
20578             </td>
20579 <td>
20580               <p>
20581                 <span class="blue">Max = 4.54&#949; (Mean = 0.895&#949;)</span><br> <br>
20582                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 3.37e+20&#949; (Mean
20583                 = 3.47e+19&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And
20584                 other failures.</a>)</span>
20585               </p>
20586             </td>
20587 <td>
20588               <p>
20589                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20590                 2.1:</em></span> Max = 633&#949; (Mean = 50.1&#949;))
20591               </p>
20592             </td>
20593 <td>
20594               <p>
20595                 <span class="blue">Max = 4.49&#949; (Mean = 0.885&#949;)</span>
20596               </p>
20597             </td>
20598 <td>
20599               <p>
20600                 <span class="blue">Max = 8.33&#949; (Mean = 0.971&#949;)</span>
20601               </p>
20602             </td>
20603 </tr>
20604 <tr>
20605 <td>
20606               <p>
20607                 Elliptic Integral PI: Large Random Data
20608               </p>
20609             </td>
20610 <td>
20611               <p>
20612                 <span class="blue">Max = 3.7&#949; (Mean = 0.893&#949;)</span><br> <br>
20613                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.52e+18&#949; (Mean
20614                 = 4.83e+17&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And
20615                 other failures.</a>)</span>
20616               </p>
20617             </td>
20618 <td>
20619               <p>
20620                 <span class="blue">Max = 0.557&#949; (Mean = 0.0389&#949;)</span><br> <br>
20621                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1&#949; (Mean = 7.77&#949;))
20622               </p>
20623             </td>
20624 <td>
20625               <p>
20626                 <span class="blue">Max = 3.7&#949; (Mean = 0.892&#949;)</span>
20627               </p>
20628             </td>
20629 <td>
20630               <p>
20631                 <span class="blue">Max = 2.86&#949; (Mean = 0.944&#949;)</span>
20632               </p>
20633             </td>
20634 </tr>
20635 </tbody>
20636 </table></div>
20637 </div>
20638 <br class="table-break"><div class="table">
20639 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_3_complete_"></a><p class="title"><b>Table&#160;126.&#160;Error rates for ellint_3 (complete)</b></p>
20640 <div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
20641 <colgroup>
20642 <col>
20643 <col>
20644 <col>
20645 <col>
20646 <col>
20647 </colgroup>
20648 <thead><tr>
20649 <th>
20650             </th>
20651 <th>
20652               <p>
20653                 GNU C++ version 7.1.0<br> linux<br> long double
20654               </p>
20655             </th>
20656 <th>
20657               <p>
20658                 GNU C++ version 7.1.0<br> linux<br> double
20659               </p>
20660             </th>
20661 <th>
20662               <p>
20663                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
20664               </p>
20665             </th>
20666 <th>
20667               <p>
20668                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20669               </p>
20670             </th>
20671 </tr></thead>
20672 <tbody>
20673 <tr>
20674 <td>
20675               <p>
20676                 Complete Elliptic Integral PI: Mathworld Data
20677               </p>
20678             </td>
20679 <td>
20680               <p>
20681                 <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span><br> <br>
20682                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 6.31e+20&#949; (Mean
20683                 = 1.53e+20&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
20684                 other failures.</a>)</span>
20685               </p>
20686             </td>
20687 <td>
20688               <p>
20689                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20690                 2.1:</em></span> Max = 6.33e+04&#949; (Mean = 1.54e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And
20691                 other failures.</a>)
20692               </p>
20693             </td>
20694 <td>
20695               <p>
20696                 <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span>
20697               </p>
20698             </td>
20699 <td>
20700               <p>
20701                 <span class="blue">Max = 0.971&#949; (Mean = 0.464&#949;)</span>
20702               </p>
20703             </td>
20704 </tr>
20705 <tr>
20706 <td>
20707               <p>
20708                 Complete Elliptic Integral PI: Random Data
20709               </p>
20710             </td>
20711 <td>
20712               <p>
20713                 <span class="blue">Max = 2.45&#949; (Mean = 0.696&#949;)</span><br> <br>
20714                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 8.78e+20&#949; (Mean
20715                 = 1.02e+20&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And
20716                 other failures.</a>)</span>
20717               </p>
20718             </td>
20719 <td>
20720               <p>
20721                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20722                 2.1:</em></span> Max = 24&#949; (Mean = 2.99&#949;))
20723               </p>
20724             </td>
20725 <td>
20726               <p>
20727                 <span class="blue">Max = 2.4&#949; (Mean = 0.677&#949;)</span>
20728               </p>
20729             </td>
20730 <td>
20731               <p>
20732                 <span class="blue">Max = 2.46&#949; (Mean = 0.657&#949;)</span>
20733               </p>
20734             </td>
20735 </tr>
20736 </tbody>
20737 </table></div>
20738 </div>
20739 <br class="table-break"><div class="table">
20740 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_d"></a><p class="title"><b>Table&#160;127.&#160;Error rates for ellint_d</b></p>
20741 <div class="table-contents"><table class="table" summary="Error rates for ellint_d">
20742 <colgroup>
20743 <col>
20744 <col>
20745 <col>
20746 <col>
20747 <col>
20748 </colgroup>
20749 <thead><tr>
20750 <th>
20751             </th>
20752 <th>
20753               <p>
20754                 GNU C++ version 7.1.0<br> linux<br> double
20755               </p>
20756             </th>
20757 <th>
20758               <p>
20759                 GNU C++ version 7.1.0<br> linux<br> long double
20760               </p>
20761             </th>
20762 <th>
20763               <p>
20764                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
20765               </p>
20766             </th>
20767 <th>
20768               <p>
20769                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20770               </p>
20771             </th>
20772 </tr></thead>
20773 <tbody>
20774 <tr>
20775 <td>
20776               <p>
20777                 Elliptic Integral E: Mathworld Data
20778               </p>
20779             </td>
20780 <td>
20781               <p>
20782                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20783                 2.1:</em></span> Max = 0.862&#949; (Mean = 0.568&#949;))
20784               </p>
20785             </td>
20786 <td>
20787               <p>
20788                 <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
20789               </p>
20790             </td>
20791 <td>
20792               <p>
20793                 <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
20794               </p>
20795             </td>
20796 <td>
20797               <p>
20798                 <span class="blue">Max = 0.862&#949; (Mean = 0.457&#949;)</span>
20799               </p>
20800             </td>
20801 </tr>
20802 <tr>
20803 <td>
20804               <p>
20805                 Elliptic Integral D: Random Data
20806               </p>
20807             </td>
20808 <td>
20809               <p>
20810                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20811                 2.1:</em></span> Max = 3.01&#949; (Mean = 0.928&#949;))
20812               </p>
20813             </td>
20814 <td>
20815               <p>
20816                 <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
20817               </p>
20818             </td>
20819 <td>
20820               <p>
20821                 <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
20822               </p>
20823             </td>
20824 <td>
20825               <p>
20826                 <span class="blue">Max = 2.87&#949; (Mean = 0.805&#949;)</span>
20827               </p>
20828             </td>
20829 </tr>
20830 </tbody>
20831 </table></div>
20832 </div>
20833 <br class="table-break"><div class="table">
20834 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;128.&#160;Error rates for ellint_d (complete)</b></p>
20835 <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
20836 <colgroup>
20837 <col>
20838 <col>
20839 <col>
20840 <col>
20841 <col>
20842 </colgroup>
20843 <thead><tr>
20844 <th>
20845             </th>
20846 <th>
20847               <p>
20848                 GNU C++ version 7.1.0<br> linux<br> double
20849               </p>
20850             </th>
20851 <th>
20852               <p>
20853                 GNU C++ version 7.1.0<br> linux<br> long double
20854               </p>
20855             </th>
20856 <th>
20857               <p>
20858                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
20859               </p>
20860             </th>
20861 <th>
20862               <p>
20863                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20864               </p>
20865             </th>
20866 </tr></thead>
20867 <tbody>
20868 <tr>
20869 <td>
20870               <p>
20871                 Elliptic Integral E: Mathworld Data
20872               </p>
20873             </td>
20874 <td>
20875               <p>
20876                 <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
20877               </p>
20878             </td>
20879 <td>
20880               <p>
20881                 <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
20882               </p>
20883             </td>
20884 <td>
20885               <p>
20886                 <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
20887               </p>
20888             </td>
20889 <td>
20890               <p>
20891                 <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
20892               </p>
20893             </td>
20894 </tr>
20895 <tr>
20896 <td>
20897               <p>
20898                 Elliptic Integral D: Random Data
20899               </p>
20900             </td>
20901 <td>
20902               <p>
20903                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
20904               </p>
20905             </td>
20906 <td>
20907               <p>
20908                 <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
20909               </p>
20910             </td>
20911 <td>
20912               <p>
20913                 <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
20914               </p>
20915             </td>
20916 <td>
20917               <p>
20918                 <span class="blue">Max = 1.27&#949; (Mean = 0.355&#949;)</span>
20919               </p>
20920             </td>
20921 </tr>
20922 </tbody>
20923 </table></div>
20924 </div>
20925 <br class="table-break"><div class="table">
20926 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rc"></a><p class="title"><b>Table&#160;129.&#160;Error rates for ellint_rc</b></p>
20927 <div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
20928 <colgroup>
20929 <col>
20930 <col>
20931 <col>
20932 <col>
20933 </colgroup>
20934 <thead><tr>
20935 <th>
20936             </th>
20937 <th>
20938               <p>
20939                 GNU C++ version 7.1.0<br> linux<br> double
20940               </p>
20941             </th>
20942 <th>
20943               <p>
20944                 GNU C++ version 7.1.0<br> linux<br> long double
20945               </p>
20946             </th>
20947 <th>
20948               <p>
20949                 Microsoft Visual C++ version 14.1<br> Win32<br> double
20950               </p>
20951             </th>
20952 </tr></thead>
20953 <tbody><tr>
20954 <td>
20955               <p>
20956                 RC: Random data
20957               </p>
20958             </td>
20959 <td>
20960               <p>
20961                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
20962                 2.1:</em></span> Max = 2.4&#949; (Mean = 0.624&#949;))
20963               </p>
20964             </td>
20965 <td>
20966               <p>
20967                 <span class="blue">Max = 0.995&#949; (Mean = 0.433&#949;)</span>
20968               </p>
20969             </td>
20970 <td>
20971               <p>
20972                 <span class="blue">Max = 0.962&#949; (Mean = 0.407&#949;)</span>
20973               </p>
20974             </td>
20975 </tr></tbody>
20976 </table></div>
20977 </div>
20978 <br class="table-break"><div class="table">
20979 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rd"></a><p class="title"><b>Table&#160;130.&#160;Error rates for ellint_rd</b></p>
20980 <div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
20981 <colgroup>
20982 <col>
20983 <col>
20984 <col>
20985 <col>
20986 </colgroup>
20987 <thead><tr>
20988 <th>
20989             </th>
20990 <th>
20991               <p>
20992                 GNU C++ version 7.1.0<br> linux<br> double
20993               </p>
20994             </th>
20995 <th>
20996               <p>
20997                 GNU C++ version 7.1.0<br> linux<br> long double
20998               </p>
20999             </th>
21000 <th>
21001               <p>
21002                 Microsoft Visual C++ version 14.1<br> Win32<br> double
21003               </p>
21004             </th>
21005 </tr></thead>
21006 <tbody>
21007 <tr>
21008 <td>
21009               <p>
21010                 RD: Random data
21011               </p>
21012             </td>
21013 <td>
21014               <p>
21015                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21016                 2.1:</em></span> Max = 2.59&#949; (Mean = 0.878&#949;))
21017               </p>
21018             </td>
21019 <td>
21020               <p>
21021                 <span class="blue">Max = 2.73&#949; (Mean = 0.831&#949;)</span>
21022               </p>
21023             </td>
21024 <td>
21025               <p>
21026                 <span class="blue">Max = 2.16&#949; (Mean = 0.803&#949;)</span>
21027               </p>
21028             </td>
21029 </tr>
21030 <tr>
21031 <td>
21032               <p>
21033                 RD: y = z
21034               </p>
21035             </td>
21036 <td>
21037               <p>
21038                 <span class="blue">Max = 0.896&#949; (Mean = 0.022&#949;)</span><br> <br>
21039                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88&#949; (Mean = 0.839&#949;))
21040               </p>
21041             </td>
21042 <td>
21043               <p>
21044                 <span class="blue">Max = 2.65&#949; (Mean = 0.82&#949;)</span>
21045               </p>
21046             </td>
21047 <td>
21048               <p>
21049                 <span class="blue">Max = 16.5&#949; (Mean = 0.843&#949;)</span>
21050               </p>
21051             </td>
21052 </tr>
21053 <tr>
21054 <td>
21055               <p>
21056                 RD: x = y
21057               </p>
21058             </td>
21059 <td>
21060               <p>
21061                 <span class="blue">Max = 0.824&#949; (Mean = 0.0272&#949;)</span><br> <br>
21062                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74&#949; (Mean = 0.84&#949;))
21063               </p>
21064             </td>
21065 <td>
21066               <p>
21067                 <span class="blue">Max = 2.85&#949; (Mean = 0.865&#949;)</span>
21068               </p>
21069             </td>
21070 <td>
21071               <p>
21072                 <span class="blue">Max = 3.51&#949; (Mean = 0.816&#949;)</span>
21073               </p>
21074             </td>
21075 </tr>
21076 <tr>
21077 <td>
21078               <p>
21079                 RD: x = 0, y = z
21080               </p>
21081             </td>
21082 <td>
21083               <p>
21084                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21085                 2.1:</em></span> Max = 2&#949; (Mean = 0.656&#949;))
21086               </p>
21087             </td>
21088 <td>
21089               <p>
21090                 <span class="blue">Max = 1.19&#949; (Mean = 0.522&#949;)</span>
21091               </p>
21092             </td>
21093 <td>
21094               <p>
21095                 <span class="blue">Max = 1.16&#949; (Mean = 0.497&#949;)</span>
21096               </p>
21097             </td>
21098 </tr>
21099 <tr>
21100 <td>
21101               <p>
21102                 RD: x = y = z
21103               </p>
21104             </td>
21105 <td>
21106               <p>
21107                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21108                 2.1:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
21109               </p>
21110             </td>
21111 <td>
21112               <p>
21113                 <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
21114               </p>
21115             </td>
21116 <td>
21117               <p>
21118                 <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
21119               </p>
21120             </td>
21121 </tr>
21122 <tr>
21123 <td>
21124               <p>
21125                 RD: x = 0
21126               </p>
21127             </td>
21128 <td>
21129               <p>
21130                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21131                 2.1:</em></span> Max = 2.85&#949; (Mean = 0.781&#949;))
21132               </p>
21133             </td>
21134 <td>
21135               <p>
21136                 <span class="blue">Max = 2.79&#949; (Mean = 0.883&#949;)</span>
21137               </p>
21138             </td>
21139 <td>
21140               <p>
21141                 <span class="blue">Max = 2.64&#949; (Mean = 0.894&#949;)</span>
21142               </p>
21143             </td>
21144 </tr>
21145 </tbody>
21146 </table></div>
21147 </div>
21148 <br class="table-break"><div class="table">
21149 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rf"></a><p class="title"><b>Table&#160;131.&#160;Error rates for ellint_rf</b></p>
21150 <div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
21151 <colgroup>
21152 <col>
21153 <col>
21154 <col>
21155 <col>
21156 </colgroup>
21157 <thead><tr>
21158 <th>
21159             </th>
21160 <th>
21161               <p>
21162                 GNU C++ version 7.1.0<br> linux<br> double
21163               </p>
21164             </th>
21165 <th>
21166               <p>
21167                 GNU C++ version 7.1.0<br> linux<br> long double
21168               </p>
21169             </th>
21170 <th>
21171               <p>
21172                 Microsoft Visual C++ version 14.1<br> Win32<br> double
21173               </p>
21174             </th>
21175 </tr></thead>
21176 <tbody>
21177 <tr>
21178 <td>
21179               <p>
21180                 RF: Random data
21181               </p>
21182             </td>
21183 <td>
21184               <p>
21185                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21186                 2.1:</em></span> Max = 2.73&#949; (Mean = 0.804&#949;))
21187               </p>
21188             </td>
21189 <td>
21190               <p>
21191                 <span class="blue">Max = 2.54&#949; (Mean = 0.674&#949;)</span>
21192               </p>
21193             </td>
21194 <td>
21195               <p>
21196                 <span class="blue">Max = 2.02&#949; (Mean = 0.677&#949;)</span>
21197               </p>
21198             </td>
21199 </tr>
21200 <tr>
21201 <td>
21202               <p>
21203                 RF: x = y = z
21204               </p>
21205             </td>
21206 <td>
21207               <p>
21208                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21209                 2.1:</em></span> Max = 0.999&#949; (Mean = 0.34&#949;))
21210               </p>
21211             </td>
21212 <td>
21213               <p>
21214                 <span class="blue">Max = 0.991&#949; (Mean = 0.345&#949;)</span>
21215               </p>
21216             </td>
21217 <td>
21218               <p>
21219                 <span class="blue">Max = 0.999&#949; (Mean = 0.34&#949;)</span>
21220               </p>
21221             </td>
21222 </tr>
21223 <tr>
21224 <td>
21225               <p>
21226                 RF: x = y or y = z or x = z
21227               </p>
21228             </td>
21229 <td>
21230               <p>
21231                 <span class="blue">Max = 0.536&#949; (Mean = 0.00658&#949;)</span><br> <br>
21232                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89&#949; (Mean = 0.749&#949;))
21233               </p>
21234             </td>
21235 <td>
21236               <p>
21237                 <span class="blue">Max = 1.95&#949; (Mean = 0.418&#949;)</span>
21238               </p>
21239             </td>
21240 <td>
21241               <p>
21242                 <span class="blue">Max = 1.21&#949; (Mean = 0.394&#949;)</span>
21243               </p>
21244             </td>
21245 </tr>
21246 <tr>
21247 <td>
21248               <p>
21249                 RF: x = 0, y = z
21250               </p>
21251             </td>
21252 <td>
21253               <p>
21254                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21255                 2.1:</em></span> Max = 1.29&#949; (Mean = 0.527&#949;))
21256               </p>
21257             </td>
21258 <td>
21259               <p>
21260                 <span class="blue">Max = 0.894&#949; (Mean = 0.338&#949;)</span>
21261               </p>
21262             </td>
21263 <td>
21264               <p>
21265                 <span class="blue">Max = 0.999&#949; (Mean = 0.407&#949;)</span>
21266               </p>
21267             </td>
21268 </tr>
21269 <tr>
21270 <td>
21271               <p>
21272                 RF: z = 0
21273               </p>
21274             </td>
21275 <td>
21276               <p>
21277                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21278                 2.1:</em></span> Max = 2.54&#949; (Mean = 0.781&#949;))
21279               </p>
21280             </td>
21281 <td>
21282               <p>
21283                 <span class="blue">Max = 1.7&#949; (Mean = 0.539&#949;)</span>
21284               </p>
21285             </td>
21286 <td>
21287               <p>
21288                 <span class="blue">Max = 1.89&#949; (Mean = 0.587&#949;)</span>
21289               </p>
21290             </td>
21291 </tr>
21292 </tbody>
21293 </table></div>
21294 </div>
21295 <br class="table-break"><div class="table">
21296 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rg"></a><p class="title"><b>Table&#160;132.&#160;Error rates for ellint_rg</b></p>
21297 <div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
21298 <colgroup>
21299 <col>
21300 <col>
21301 <col>
21302 <col>
21303 </colgroup>
21304 <thead><tr>
21305 <th>
21306             </th>
21307 <th>
21308               <p>
21309                 GNU C++ version 7.1.0<br> linux<br> double
21310               </p>
21311             </th>
21312 <th>
21313               <p>
21314                 GNU C++ version 7.1.0<br> linux<br> long double
21315               </p>
21316             </th>
21317 <th>
21318               <p>
21319                 Microsoft Visual C++ version 14.1<br> Win32<br> double
21320               </p>
21321             </th>
21322 </tr></thead>
21323 <tbody>
21324 <tr>
21325 <td>
21326               <p>
21327                 RG: Random Data
21328               </p>
21329             </td>
21330 <td>
21331               <p>
21332                 <span class="blue">Max = 0.983&#949; (Mean = 0.0172&#949;)</span><br> <br>
21333                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983&#949; (Mean = 0.0172&#949;))
21334               </p>
21335             </td>
21336 <td>
21337               <p>
21338                 <span class="blue">Max = 3.95&#949; (Mean = 0.951&#949;)</span>
21339               </p>
21340             </td>
21341 <td>
21342               <p>
21343                 <span class="blue">Max = 3.65&#949; (Mean = 0.929&#949;)</span>
21344               </p>
21345             </td>
21346 </tr>
21347 <tr>
21348 <td>
21349               <p>
21350                 RG: two values 0
21351               </p>
21352             </td>
21353 <td>
21354               <p>
21355                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21356                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
21357               </p>
21358             </td>
21359 <td>
21360               <p>
21361                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
21362               </p>
21363             </td>
21364 <td>
21365               <p>
21366                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
21367               </p>
21368             </td>
21369 </tr>
21370 <tr>
21371 <td>
21372               <p>
21373                 RG: All values the same or zero
21374               </p>
21375             </td>
21376 <td>
21377               <p>
21378                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21379                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
21380               </p>
21381             </td>
21382 <td>
21383               <p>
21384                 <span class="blue">Max = 0.992&#949; (Mean = 0.288&#949;)</span>
21385               </p>
21386             </td>
21387 <td>
21388               <p>
21389                 <span class="blue">Max = 1.06&#949; (Mean = 0.348&#949;)</span>
21390               </p>
21391             </td>
21392 </tr>
21393 <tr>
21394 <td>
21395               <p>
21396                 RG: two values the same
21397               </p>
21398             </td>
21399 <td>
21400               <p>
21401                 <span class="blue">Max = 0.594&#949; (Mean = 0.0103&#949;)</span><br> <br>
21402                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594&#949; (Mean = 0.0103&#949;))
21403               </p>
21404             </td>
21405 <td>
21406               <p>
21407                 <span class="blue">Max = 1.51&#949; (Mean = 0.404&#949;)</span>
21408               </p>
21409             </td>
21410 <td>
21411               <p>
21412                 <span class="blue">Max = 1.96&#949; (Mean = 0.374&#949;)</span>
21413               </p>
21414             </td>
21415 </tr>
21416 <tr>
21417 <td>
21418               <p>
21419                 RG: one value zero
21420               </p>
21421             </td>
21422 <td>
21423               <p>
21424                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21425                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
21426               </p>
21427             </td>
21428 <td>
21429               <p>
21430                 <span class="blue">Max = 2.14&#949; (Mean = 0.722&#949;)</span>
21431               </p>
21432             </td>
21433 <td>
21434               <p>
21435                 <span class="blue">Max = 1.96&#949; (Mean = 0.674&#949;)</span>
21436               </p>
21437             </td>
21438 </tr>
21439 </tbody>
21440 </table></div>
21441 </div>
21442 <br class="table-break"><div class="table">
21443 <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rj"></a><p class="title"><b>Table&#160;133.&#160;Error rates for ellint_rj</b></p>
21444 <div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
21445 <colgroup>
21446 <col>
21447 <col>
21448 <col>
21449 <col>
21450 </colgroup>
21451 <thead><tr>
21452 <th>
21453             </th>
21454 <th>
21455               <p>
21456                 GNU C++ version 7.1.0<br> linux<br> double
21457               </p>
21458             </th>
21459 <th>
21460               <p>
21461                 GNU C++ version 7.1.0<br> linux<br> long double
21462               </p>
21463             </th>
21464 <th>
21465               <p>
21466                 Microsoft Visual C++ version 14.1<br> Win32<br> double
21467               </p>
21468             </th>
21469 </tr></thead>
21470 <tbody>
21471 <tr>
21472 <td>
21473               <p>
21474                 RJ: Random data
21475               </p>
21476             </td>
21477 <td>
21478               <p>
21479                 <span class="blue">Max = 0.52&#949; (Mean = 0.0184&#949;)</span><br> <br>
21480                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57&#949; (Mean = 0.704&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And
21481                 other failures.</a>)
21482               </p>
21483             </td>
21484 <td>
21485               <p>
21486                 <span class="blue">Max = 186&#949; (Mean = 6.67&#949;)</span>
21487               </p>
21488             </td>
21489 <td>
21490               <p>
21491                 <span class="blue">Max = 215&#949; (Mean = 7.66&#949;)</span>
21492               </p>
21493             </td>
21494 </tr>
21495 <tr>
21496 <td>
21497               <p>
21498                 RJ: 4 Equal Values
21499               </p>
21500             </td>
21501 <td>
21502               <p>
21503                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21504                 2.1:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
21505               </p>
21506             </td>
21507 <td>
21508               <p>
21509                 <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
21510               </p>
21511             </td>
21512 <td>
21513               <p>
21514                 <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
21515               </p>
21516             </td>
21517 </tr>
21518 <tr>
21519 <td>
21520               <p>
21521                 RJ: 3 Equal Values
21522               </p>
21523             </td>
21524 <td>
21525               <p>
21526                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21527                 2.1:</em></span> Max = 3.96&#949; (Mean = 1.06&#949;))
21528               </p>
21529             </td>
21530 <td>
21531               <p>
21532                 <span class="blue">Max = 20.8&#949; (Mean = 0.986&#949;)</span>
21533               </p>
21534             </td>
21535 <td>
21536               <p>
21537                 <span class="blue">Max = 39.9&#949; (Mean = 1.17&#949;)</span>
21538               </p>
21539             </td>
21540 </tr>
21541 <tr>
21542 <td>
21543               <p>
21544                 RJ: 2 Equal Values
21545               </p>
21546             </td>
21547 <td>
21548               <p>
21549                 <span class="blue">Max = 0.6&#949; (Mean = 0.0228&#949;)</span><br> <br>
21550                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57&#949; (Mean = 0.754&#949;))
21551               </p>
21552             </td>
21553 <td>
21554               <p>
21555                 <span class="blue">Max = 220&#949; (Mean = 6.64&#949;)</span>
21556               </p>
21557             </td>
21558 <td>
21559               <p>
21560                 <span class="blue">Max = 214&#949; (Mean = 5.28&#949;)</span>
21561               </p>
21562             </td>
21563 </tr>
21564 <tr>
21565 <td>
21566               <p>
21567                 RJ: Equal z and p
21568               </p>
21569             </td>
21570 <td>
21571               <p>
21572                 <span class="blue">Max = 0.742&#949; (Mean = 0.0166&#949;)</span><br> <br>
21573                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62&#949; (Mean = 0.699&#949;))
21574               </p>
21575             </td>
21576 <td>
21577               <p>
21578                 <span class="blue">Max = 17.2&#949; (Mean = 1.16&#949;)</span>
21579               </p>
21580             </td>
21581 <td>
21582               <p>
21583                 <span class="blue">Max = 16.1&#949; (Mean = 1.14&#949;)</span>
21584               </p>
21585             </td>
21586 </tr>
21587 </tbody>
21588 </table></div>
21589 </div>
21590 <br class="table-break"><div class="table">
21591 <a name="special_function_error_rates_rep.all_the_tables.table_erf"></a><p class="title"><b>Table&#160;134.&#160;Error rates for erf</b></p>
21592 <div class="table-contents"><table class="table" summary="Error rates for erf">
21593 <colgroup>
21594 <col>
21595 <col>
21596 <col>
21597 <col>
21598 <col>
21599 </colgroup>
21600 <thead><tr>
21601 <th>
21602             </th>
21603 <th>
21604               <p>
21605                 GNU C++ version 7.1.0<br> linux<br> long double
21606               </p>
21607             </th>
21608 <th>
21609               <p>
21610                 GNU C++ version 7.1.0<br> linux<br> double
21611               </p>
21612             </th>
21613 <th>
21614               <p>
21615                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
21616               </p>
21617             </th>
21618 <th>
21619               <p>
21620                 Microsoft Visual C++ version 14.1<br> Win32<br> double
21621               </p>
21622             </th>
21623 </tr></thead>
21624 <tbody>
21625 <tr>
21626 <td>
21627               <p>
21628                 Erf Function: Small Values
21629               </p>
21630             </td>
21631 <td>
21632               <p>
21633                 <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
21634                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))<br>
21635                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))
21636               </p>
21637             </td>
21638 <td>
21639               <p>
21640                 <span class="blue">Max = 0.841&#949; (Mean = 0.0687&#949;)</span><br> <br>
21641                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06&#949; (Mean = 0.319&#949;))
21642               </p>
21643             </td>
21644 <td>
21645               <p>
21646                 <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
21647                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.194&#949;))
21648               </p>
21649             </td>
21650 <td>
21651               <p>
21652                 <span class="blue">Max = 0.996&#949; (Mean = 0.182&#949;)</span><br> <br>
21653                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.57&#949; (Mean = 0.317&#949;))
21654               </p>
21655             </td>
21656 </tr>
21657 <tr>
21658 <td>
21659               <p>
21660                 Erf Function: Medium Values
21661               </p>
21662             </td>
21663 <td>
21664               <p>
21665                 <span class="blue">Max = 1.5&#949; (Mean = 0.193&#949;)</span><br> <br>
21666                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))<br>
21667                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))
21668               </p>
21669             </td>
21670 <td>
21671               <p>
21672                 <span class="blue">Max = 1&#949; (Mean = 0.119&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21673                 2.1:</em></span> Max = 2.31&#949; (Mean = 0.368&#949;))
21674               </p>
21675             </td>
21676 <td>
21677               <p>
21678                 <span class="blue">Max = 1.5&#949; (Mean = 0.197&#949;)</span><br> <br>
21679                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.071&#949;))
21680               </p>
21681             </td>
21682 <td>
21683               <p>
21684                 <span class="blue">Max = 1&#949; (Mean = 0.171&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
21685                 Max = 1.19&#949; (Mean = 0.244&#949;))
21686               </p>
21687             </td>
21688 </tr>
21689 <tr>
21690 <td>
21691               <p>
21692                 Erf Function: Large Values
21693               </p>
21694             </td>
21695 <td>
21696               <p>
21697                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
21698                 Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max
21699                 = 0&#949; (Mean = 0&#949;))
21700               </p>
21701             </td>
21702 <td>
21703               <p>
21704                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
21705                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
21706               </p>
21707             </td>
21708 <td>
21709               <p>
21710                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
21711                 Max = 0&#949; (Mean = 0&#949;))
21712               </p>
21713             </td>
21714 <td>
21715               <p>
21716                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
21717                 Max = 0&#949; (Mean = 0&#949;))
21718               </p>
21719             </td>
21720 </tr>
21721 </tbody>
21722 </table></div>
21723 </div>
21724 <br class="table-break"><div class="table">
21725 <a name="special_function_error_rates_rep.all_the_tables.table_erf_inv"></a><p class="title"><b>Table&#160;135.&#160;Error rates for erf_inv</b></p>
21726 <div class="table-contents"><table class="table" summary="Error rates for erf_inv">
21727 <colgroup>
21728 <col>
21729 <col>
21730 <col>
21731 <col>
21732 <col>
21733 </colgroup>
21734 <thead><tr>
21735 <th>
21736             </th>
21737 <th>
21738               <p>
21739                 GNU C++ version 7.1.0<br> linux<br> double
21740               </p>
21741             </th>
21742 <th>
21743               <p>
21744                 GNU C++ version 7.1.0<br> linux<br> long double
21745               </p>
21746             </th>
21747 <th>
21748               <p>
21749                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
21750               </p>
21751             </th>
21752 <th>
21753               <p>
21754                 Microsoft Visual C++ version 14.1<br> Win32<br> double
21755               </p>
21756             </th>
21757 </tr></thead>
21758 <tbody><tr>
21759 <td>
21760               <p>
21761                 Inverse Erf Function
21762               </p>
21763             </td>
21764 <td>
21765               <p>
21766                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
21767               </p>
21768             </td>
21769 <td>
21770               <p>
21771                 <span class="blue">Max = 0.996&#949; (Mean = 0.389&#949;)</span>
21772               </p>
21773             </td>
21774 <td>
21775               <p>
21776                 <span class="blue">Max = 1.08&#949; (Mean = 0.395&#949;)</span>
21777               </p>
21778             </td>
21779 <td>
21780               <p>
21781                 <span class="blue">Max = 1.09&#949; (Mean = 0.502&#949;)</span>
21782               </p>
21783             </td>
21784 </tr></tbody>
21785 </table></div>
21786 </div>
21787 <br class="table-break"><div class="table">
21788 <a name="special_function_error_rates_rep.all_the_tables.table_erfc"></a><p class="title"><b>Table&#160;136.&#160;Error rates for erfc</b></p>
21789 <div class="table-contents"><table class="table" summary="Error rates for erfc">
21790 <colgroup>
21791 <col>
21792 <col>
21793 <col>
21794 <col>
21795 <col>
21796 </colgroup>
21797 <thead><tr>
21798 <th>
21799             </th>
21800 <th>
21801               <p>
21802                 GNU C++ version 7.1.0<br> linux<br> long double
21803               </p>
21804             </th>
21805 <th>
21806               <p>
21807                 GNU C++ version 7.1.0<br> linux<br> double
21808               </p>
21809             </th>
21810 <th>
21811               <p>
21812                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
21813               </p>
21814             </th>
21815 <th>
21816               <p>
21817                 Microsoft Visual C++ version 14.1<br> Win32<br> double
21818               </p>
21819             </th>
21820 </tr></thead>
21821 <tbody>
21822 <tr>
21823 <td>
21824               <p>
21825                 Erf Function: Small Values
21826               </p>
21827             </td>
21828 <td>
21829               <p>
21830                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
21831                 Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max
21832                 = 0&#949; (Mean = 0&#949;))
21833               </p>
21834             </td>
21835 <td>
21836               <p>
21837                 <span class="blue">Max = 0.658&#949; (Mean = 0.0537&#949;)</span><br> <br>
21838                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01&#949; (Mean = 0.485&#949;))
21839               </p>
21840             </td>
21841 <td>
21842               <p>
21843                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
21844                 Max = 0&#949; (Mean = 0&#949;))
21845               </p>
21846             </td>
21847 <td>
21848               <p>
21849                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
21850                 Max = 0&#949; (Mean = 0&#949;))
21851               </p>
21852             </td>
21853 </tr>
21854 <tr>
21855 <td>
21856               <p>
21857                 Erf Function: Medium Values
21858               </p>
21859             </td>
21860 <td>
21861               <p>
21862                 <span class="blue">Max = 1.76&#949; (Mean = 0.365&#949;)</span><br> <br>
21863                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))<br>
21864                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))
21865               </p>
21866             </td>
21867 <td>
21868               <p>
21869                 <span class="blue">Max = 0.983&#949; (Mean = 0.213&#949;)</span><br> <br>
21870                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64&#949; (Mean = 0.662&#949;))
21871               </p>
21872             </td>
21873 <td>
21874               <p>
21875                 <span class="blue">Max = 1.76&#949; (Mean = 0.38&#949;)</span><br> <br>
21876                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.81&#949; (Mean = 0.739&#949;))
21877               </p>
21878             </td>
21879 <td>
21880               <p>
21881                 <span class="blue">Max = 1.65&#949; (Mean = 0.373&#949;)</span><br> <br>
21882                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.36&#949; (Mean = 0.539&#949;))
21883               </p>
21884             </td>
21885 </tr>
21886 <tr>
21887 <td>
21888               <p>
21889                 Erf Function: Large Values
21890               </p>
21891             </td>
21892 <td>
21893               <p>
21894                 <span class="blue">Max = 1.57&#949; (Mean = 0.542&#949;)</span><br> <br>
21895                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))<br>
21896                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))
21897               </p>
21898             </td>
21899 <td>
21900               <p>
21901                 <span class="blue">Max = 0.868&#949; (Mean = 0.147&#949;)</span><br> <br>
21902                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9&#949; (Mean = 0.472&#949;))
21903               </p>
21904             </td>
21905 <td>
21906               <p>
21907                 <span class="blue">Max = 1.57&#949; (Mean = 0.564&#949;)</span><br> <br>
21908                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 4.91&#949; (Mean = 1.54&#949;))
21909               </p>
21910             </td>
21911 <td>
21912               <p>
21913                 <span class="blue">Max = 1.14&#949; (Mean = 0.248&#949;)</span><br> <br>
21914                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.331&#949;))
21915               </p>
21916             </td>
21917 </tr>
21918 </tbody>
21919 </table></div>
21920 </div>
21921 <br class="table-break"><div class="table">
21922 <a name="special_function_error_rates_rep.all_the_tables.table_erfc_inv"></a><p class="title"><b>Table&#160;137.&#160;Error rates for erfc_inv</b></p>
21923 <div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
21924 <colgroup>
21925 <col>
21926 <col>
21927 <col>
21928 <col>
21929 <col>
21930 </colgroup>
21931 <thead><tr>
21932 <th>
21933             </th>
21934 <th>
21935               <p>
21936                 GNU C++ version 7.1.0<br> linux<br> double
21937               </p>
21938             </th>
21939 <th>
21940               <p>
21941                 GNU C++ version 7.1.0<br> linux<br> long double
21942               </p>
21943             </th>
21944 <th>
21945               <p>
21946                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
21947               </p>
21948             </th>
21949 <th>
21950               <p>
21951                 Microsoft Visual C++ version 14.1<br> Win32<br> double
21952               </p>
21953             </th>
21954 </tr></thead>
21955 <tbody>
21956 <tr>
21957 <td>
21958               <p>
21959                 Inverse Erfc Function
21960               </p>
21961             </td>
21962 <td>
21963               <p>
21964                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
21965               </p>
21966             </td>
21967 <td>
21968               <p>
21969                 <span class="blue">Max = 0.996&#949; (Mean = 0.397&#949;)</span>
21970               </p>
21971             </td>
21972 <td>
21973               <p>
21974                 <span class="blue">Max = 1.08&#949; (Mean = 0.403&#949;)</span>
21975               </p>
21976             </td>
21977 <td>
21978               <p>
21979                 <span class="blue">Max = 1&#949; (Mean = 0.491&#949;)</span>
21980               </p>
21981             </td>
21982 </tr>
21983 <tr>
21984 <td>
21985               <p>
21986                 Inverse Erfc Function: extreme values
21987               </p>
21988             </td>
21989 <td>
21990             </td>
21991 <td>
21992               <p>
21993                 <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
21994               </p>
21995             </td>
21996 <td>
21997               <p>
21998                 <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
21999               </p>
22000             </td>
22001 <td>
22002             </td>
22003 </tr>
22004 </tbody>
22005 </table></div>
22006 </div>
22007 <br class="table-break"><div class="table">
22008 <a name="special_function_error_rates_rep.all_the_tables.table_expint_Ei_"></a><p class="title"><b>Table&#160;138.&#160;Error rates for expint (Ei)</b></p>
22009 <div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
22010 <colgroup>
22011 <col>
22012 <col>
22013 <col>
22014 <col>
22015 <col>
22016 </colgroup>
22017 <thead><tr>
22018 <th>
22019             </th>
22020 <th>
22021               <p>
22022                 GNU C++ version 7.1.0<br> linux<br> long double
22023               </p>
22024             </th>
22025 <th>
22026               <p>
22027                 GNU C++ version 7.1.0<br> linux<br> double
22028               </p>
22029             </th>
22030 <th>
22031               <p>
22032                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22033               </p>
22034             </th>
22035 <th>
22036               <p>
22037                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22038               </p>
22039             </th>
22040 </tr></thead>
22041 <tbody>
22042 <tr>
22043 <td>
22044               <p>
22045                 Exponential Integral Ei
22046               </p>
22047             </td>
22048 <td>
22049               <p>
22050                 <span class="blue">Max = 5.05&#949; (Mean = 0.821&#949;)</span><br> <br>
22051                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 14.1&#949; (Mean = 2.43&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And
22052                 other failures.</a>)
22053               </p>
22054             </td>
22055 <td>
22056               <p>
22057                 <span class="blue">Max = 0.994&#949; (Mean = 0.142&#949;)</span><br> <br>
22058                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96&#949; (Mean = 0.703&#949;))
22059               </p>
22060             </td>
22061 <td>
22062               <p>
22063                 <span class="blue">Max = 5.05&#949; (Mean = 0.835&#949;)</span>
22064               </p>
22065             </td>
22066 <td>
22067               <p>
22068                 <span class="blue">Max = 1.43&#949; (Mean = 0.54&#949;)</span>
22069               </p>
22070             </td>
22071 </tr>
22072 <tr>
22073 <td>
22074               <p>
22075                 Exponential Integral Ei: double exponent range
22076               </p>
22077             </td>
22078 <td>
22079               <p>
22080                 <span class="blue">Max = 1.72&#949; (Mean = 0.593&#949;)</span><br> <br>
22081                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.11&#949; (Mean = 1.13&#949;))
22082               </p>
22083             </td>
22084 <td>
22085               <p>
22086                 <span class="blue">Max = 0.998&#949; (Mean = 0.156&#949;)</span><br> <br>
22087                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5&#949; (Mean = 0.612&#949;))
22088               </p>
22089             </td>
22090 <td>
22091               <p>
22092                 <span class="blue">Max = 1.72&#949; (Mean = 0.607&#949;)</span>
22093               </p>
22094             </td>
22095 <td>
22096               <p>
22097                 <span class="blue">Max = 1.7&#949; (Mean = 0.66&#949;)</span>
22098               </p>
22099             </td>
22100 </tr>
22101 <tr>
22102 <td>
22103               <p>
22104                 Exponential Integral Ei: long exponent range
22105               </p>
22106             </td>
22107 <td>
22108               <p>
22109                 <span class="blue">Max = 1.98&#949; (Mean = 0.595&#949;)</span><br> <br>
22110                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.93&#949; (Mean = 0.855&#949;))
22111               </p>
22112             </td>
22113 <td>
22114             </td>
22115 <td>
22116               <p>
22117                 <span class="blue">Max = 1.98&#949; (Mean = 0.575&#949;)</span>
22118               </p>
22119             </td>
22120 <td>
22121             </td>
22122 </tr>
22123 </tbody>
22124 </table></div>
22125 </div>
22126 <br class="table-break"><div class="table">
22127 <a name="special_function_error_rates_rep.all_the_tables.table_expint_En_"></a><p class="title"><b>Table&#160;139.&#160;Error rates for expint (En)</b></p>
22128 <div class="table-contents"><table class="table" summary="Error rates for expint (En)">
22129 <colgroup>
22130 <col>
22131 <col>
22132 <col>
22133 <col>
22134 <col>
22135 </colgroup>
22136 <thead><tr>
22137 <th>
22138             </th>
22139 <th>
22140               <p>
22141                 GNU C++ version 7.1.0<br> linux<br> double
22142               </p>
22143             </th>
22144 <th>
22145               <p>
22146                 GNU C++ version 7.1.0<br> linux<br> long double
22147               </p>
22148             </th>
22149 <th>
22150               <p>
22151                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22152               </p>
22153             </th>
22154 <th>
22155               <p>
22156                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22157               </p>
22158             </th>
22159 </tr></thead>
22160 <tbody>
22161 <tr>
22162 <td>
22163               <p>
22164                 Exponential Integral En
22165               </p>
22166             </td>
22167 <td>
22168               <p>
22169                 <span class="blue">Max = 0.589&#949; (Mean = 0.0331&#949;)</span><br> <br>
22170                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5&#949; (Mean = 17.1&#949;))
22171               </p>
22172             </td>
22173 <td>
22174               <p>
22175                 <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
22176               </p>
22177             </td>
22178 <td>
22179               <p>
22180                 <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
22181               </p>
22182             </td>
22183 <td>
22184               <p>
22185                 <span class="blue">Max = 7.16&#949; (Mean = 1.85&#949;)</span>
22186               </p>
22187             </td>
22188 </tr>
22189 <tr>
22190 <td>
22191               <p>
22192                 Exponential Integral En: small z values
22193               </p>
22194             </td>
22195 <td>
22196               <p>
22197                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
22198                 2.1:</em></span> Max = 115&#949; (Mean = 23.6&#949;))
22199               </p>
22200             </td>
22201 <td>
22202               <p>
22203                 <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
22204               </p>
22205             </td>
22206 <td>
22207               <p>
22208                 <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
22209               </p>
22210             </td>
22211 <td>
22212               <p>
22213                 <span class="blue">Max = 2.62&#949; (Mean = 0.531&#949;)</span>
22214               </p>
22215             </td>
22216 </tr>
22217 <tr>
22218 <td>
22219               <p>
22220                 Exponential Integral E1
22221               </p>
22222             </td>
22223 <td>
22224               <p>
22225                 <span class="blue">Max = 0.556&#949; (Mean = 0.0625&#949;)</span><br> <br>
22226                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988&#949; (Mean = 0.469&#949;))
22227               </p>
22228             </td>
22229 <td>
22230               <p>
22231                 <span class="blue">Max = 0.965&#949; (Mean = 0.414&#949;)</span>
22232               </p>
22233             </td>
22234 <td>
22235               <p>
22236                 <span class="blue">Max = 0.965&#949; (Mean = 0.408&#949;)</span>
22237               </p>
22238             </td>
22239 <td>
22240               <p>
22241                 <span class="blue">Max = 0.988&#949; (Mean = 0.486&#949;)</span>
22242               </p>
22243             </td>
22244 </tr>
22245 </tbody>
22246 </table></div>
22247 </div>
22248 <br class="table-break"><div class="table">
22249 <a name="special_function_error_rates_rep.all_the_tables.table_expm1"></a><p class="title"><b>Table&#160;140.&#160;Error rates for expm1</b></p>
22250 <div class="table-contents"><table class="table" summary="Error rates for expm1">
22251 <colgroup>
22252 <col>
22253 <col>
22254 <col>
22255 <col>
22256 <col>
22257 </colgroup>
22258 <thead><tr>
22259 <th>
22260             </th>
22261 <th>
22262               <p>
22263                 GNU C++ version 7.1.0<br> linux<br> long double
22264               </p>
22265             </th>
22266 <th>
22267               <p>
22268                 GNU C++ version 7.1.0<br> linux<br> double
22269               </p>
22270             </th>
22271 <th>
22272               <p>
22273                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22274               </p>
22275             </th>
22276 <th>
22277               <p>
22278                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22279               </p>
22280             </th>
22281 </tr></thead>
22282 <tbody><tr>
22283 <td>
22284               <p>
22285                 Random test data
22286               </p>
22287             </td>
22288 <td>
22289               <p>
22290                 <span class="blue">Max = 0.992&#949; (Mean = 0.402&#949;)</span><br> <br>
22291                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.992&#949; (Mean = 0.402&#949;))<br>
22292                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.992&#949; (Mean = 0.402&#949;))
22293               </p>
22294             </td>
22295 <td>
22296               <p>
22297                 <span class="blue">Max = 0.793&#949; (Mean = 0.126&#949;)</span><br> <br>
22298                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793&#949; (Mean = 0.126&#949;))
22299               </p>
22300             </td>
22301 <td>
22302               <p>
22303                 <span class="blue">Max = 1.31&#949; (Mean = 0.428&#949;)</span><br> <br>
22304                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.996&#949; (Mean = 0.426&#949;))
22305               </p>
22306             </td>
22307 <td>
22308               <p>
22309                 <span class="blue">Max = 1.31&#949; (Mean = 0.496&#949;)</span><br> <br>
22310                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.31&#949; (Mean = 0.496&#949;))
22311               </p>
22312             </td>
22313 </tr></tbody>
22314 </table></div>
22315 </div>
22316 <br class="table-break"><div class="table">
22317 <a name="special_function_error_rates_rep.all_the_tables.table_gamma_p"></a><p class="title"><b>Table&#160;141.&#160;Error rates for gamma_p</b></p>
22318 <div class="table-contents"><table class="table" summary="Error rates for gamma_p">
22319 <colgroup>
22320 <col>
22321 <col>
22322 <col>
22323 <col>
22324 <col>
22325 </colgroup>
22326 <thead><tr>
22327 <th>
22328             </th>
22329 <th>
22330               <p>
22331                 GNU C++ version 7.1.0<br> linux<br> double
22332               </p>
22333             </th>
22334 <th>
22335               <p>
22336                 GNU C++ version 7.1.0<br> linux<br> long double
22337               </p>
22338             </th>
22339 <th>
22340               <p>
22341                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22342               </p>
22343             </th>
22344 <th>
22345               <p>
22346                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22347               </p>
22348             </th>
22349 </tr></thead>
22350 <tbody>
22351 <tr>
22352 <td>
22353               <p>
22354                 tgamma(a, z) medium values
22355               </p>
22356             </td>
22357 <td>
22358               <p>
22359                 <span class="blue">Max = 0.955&#949; (Mean = 0.05&#949;)</span><br> <br>
22360                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342&#949; (Mean = 45.8&#949;))<br> (<span class="emphasis"><em>Rmath
22361                 3.2.3:</em></span> Max = 389&#949; (Mean = 44&#949;))
22362               </p>
22363             </td>
22364 <td>
22365               <p>
22366                 <span class="blue">Max = 41.6&#949; (Mean = 8.09&#949;)</span>
22367               </p>
22368             </td>
22369 <td>
22370               <p>
22371                 <span class="blue">Max = 239&#949; (Mean = 30.2&#949;)</span>
22372               </p>
22373             </td>
22374 <td>
22375               <p>
22376                 <span class="blue">Max = 35.1&#949; (Mean = 6.98&#949;)</span>
22377               </p>
22378             </td>
22379 </tr>
22380 <tr>
22381 <td>
22382               <p>
22383                 tgamma(a, z) small values
22384               </p>
22385             </td>
22386 <td>
22387               <p>
22388                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
22389                 2.1:</em></span> Max = 4.82&#949; (Mean = 0.758&#949;))<br> (<span class="emphasis"><em>Rmath
22390                 3.2.3:</em></span> Max = 1.01&#949; (Mean = 0.306&#949;))
22391               </p>
22392             </td>
22393 <td>
22394               <p>
22395                 <span class="blue">Max = 2&#949; (Mean = 0.464&#949;)</span>
22396               </p>
22397             </td>
22398 <td>
22399               <p>
22400                 <span class="blue">Max = 2&#949; (Mean = 0.461&#949;)</span>
22401               </p>
22402             </td>
22403 <td>
22404               <p>
22405                 <span class="blue">Max = 1.54&#949; (Mean = 0.439&#949;)</span>
22406               </p>
22407             </td>
22408 </tr>
22409 <tr>
22410 <td>
22411               <p>
22412                 tgamma(a, z) large values
22413               </p>
22414             </td>
22415 <td>
22416               <p>
22417                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
22418                 2.1:</em></span> Max = 1.02e+03&#949; (Mean = 105&#949;))<br> (<span class="emphasis"><em>Rmath
22419                 3.2.3:</em></span> Max = 1.11e+03&#949; (Mean = 67.5&#949;))
22420               </p>
22421             </td>
22422 <td>
22423               <p>
22424                 <span class="blue">Max = 3.08e+04&#949; (Mean = 1.86e+03&#949;)</span>
22425               </p>
22426             </td>
22427 <td>
22428               <p>
22429                 <span class="blue">Max = 3.02e+04&#949; (Mean = 1.91e+03&#949;)</span>
22430               </p>
22431             </td>
22432 <td>
22433               <p>
22434                 <span class="blue">Max = 243&#949; (Mean = 20.2&#949;)</span>
22435               </p>
22436             </td>
22437 </tr>
22438 <tr>
22439 <td>
22440               <p>
22441                 tgamma(a, z) integer and half integer values
22442               </p>
22443             </td>
22444 <td>
22445               <p>
22446                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
22447                 2.1:</em></span> Max = 128&#949; (Mean = 22.6&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
22448                 Max = 66.2&#949; (Mean = 12.2&#949;))
22449               </p>
22450             </td>
22451 <td>
22452               <p>
22453                 <span class="blue">Max = 11.8&#949; (Mean = 2.66&#949;)</span>
22454               </p>
22455             </td>
22456 <td>
22457               <p>
22458                 <span class="blue">Max = 71.6&#949; (Mean = 9.47&#949;)</span>
22459               </p>
22460             </td>
22461 <td>
22462               <p>
22463                 <span class="blue">Max = 13&#949; (Mean = 2.97&#949;)</span>
22464               </p>
22465             </td>
22466 </tr>
22467 </tbody>
22468 </table></div>
22469 </div>
22470 <br class="table-break"><div class="table">
22471 <a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inv"></a><p class="title"><b>Table&#160;142.&#160;Error rates for gamma_p_inv</b></p>
22472 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
22473 <colgroup>
22474 <col>
22475 <col>
22476 <col>
22477 <col>
22478 <col>
22479 </colgroup>
22480 <thead><tr>
22481 <th>
22482             </th>
22483 <th>
22484               <p>
22485                 GNU C++ version 7.1.0<br> linux<br> double
22486               </p>
22487             </th>
22488 <th>
22489               <p>
22490                 GNU C++ version 7.1.0<br> linux<br> long double
22491               </p>
22492             </th>
22493 <th>
22494               <p>
22495                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22496               </p>
22497             </th>
22498 <th>
22499               <p>
22500                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22501               </p>
22502             </th>
22503 </tr></thead>
22504 <tbody>
22505 <tr>
22506 <td>
22507               <p>
22508                 incomplete gamma inverse(a, z) medium values
22509               </p>
22510             </td>
22511 <td>
22512               <p>
22513                 <span class="blue">Max = 0.993&#949; (Mean = 0.15&#949;)</span><br> <br>
22514                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88&#949; (Mean = 0.868&#949;))
22515               </p>
22516             </td>
22517 <td>
22518               <p>
22519                 <span class="blue">Max = 1.8&#949; (Mean = 0.406&#949;)</span>
22520               </p>
22521             </td>
22522 <td>
22523               <p>
22524                 <span class="blue">Max = 1.89&#949; (Mean = 0.466&#949;)</span>
22525               </p>
22526             </td>
22527 <td>
22528               <p>
22529                 <span class="blue">Max = 1.71&#949; (Mean = 0.34&#949;)</span>
22530               </p>
22531             </td>
22532 </tr>
22533 <tr>
22534 <td>
22535               <p>
22536                 incomplete gamma inverse(a, z) large values
22537               </p>
22538             </td>
22539 <td>
22540               <p>
22541                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
22542                 3.2.3:</em></span> Max = 0.816&#949; (Mean = 0.0874&#949;))
22543               </p>
22544             </td>
22545 <td>
22546               <p>
22547                 <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
22548               </p>
22549             </td>
22550 <td>
22551               <p>
22552                 <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
22553               </p>
22554             </td>
22555 <td>
22556               <p>
22557                 <span class="blue">Max = 0.924&#949; (Mean = 0.108&#949;)</span>
22558               </p>
22559             </td>
22560 </tr>
22561 <tr>
22562 <td>
22563               <p>
22564                 incomplete gamma inverse(a, z) small values
22565               </p>
22566             </td>
22567 <td>
22568               <p>
22569                 <span class="blue">Max = 441&#949; (Mean = 53.9&#949;)</span><br> <br>
22570                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547&#949; (Mean = 61.6&#949;))
22571               </p>
22572             </td>
22573 <td>
22574               <p>
22575                 <span class="blue">Max = 9.17e+03&#949; (Mean = 1.45e+03&#949;)</span>
22576               </p>
22577             </td>
22578 <td>
22579               <p>
22580                 <span class="blue">Max = 1.09e+04&#949; (Mean = 1.3e+03&#949;)</span>
22581               </p>
22582             </td>
22583 <td>
22584               <p>
22585                 <span class="blue">Max = 1.1e+03&#949; (Mean = 131&#949;)</span>
22586               </p>
22587             </td>
22588 </tr>
22589 </tbody>
22590 </table></div>
22591 </div>
22592 <br class="table-break"><div class="table">
22593 <a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inva"></a><p class="title"><b>Table&#160;143.&#160;Error rates for gamma_p_inva</b></p>
22594 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
22595 <colgroup>
22596 <col>
22597 <col>
22598 <col>
22599 <col>
22600 <col>
22601 </colgroup>
22602 <thead><tr>
22603 <th>
22604             </th>
22605 <th>
22606               <p>
22607                 GNU C++ version 7.1.0<br> linux<br> double
22608               </p>
22609             </th>
22610 <th>
22611               <p>
22612                 GNU C++ version 7.1.0<br> linux<br> long double
22613               </p>
22614             </th>
22615 <th>
22616               <p>
22617                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22618               </p>
22619             </th>
22620 <th>
22621               <p>
22622                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22623               </p>
22624             </th>
22625 </tr></thead>
22626 <tbody><tr>
22627 <td>
22628               <p>
22629                 Incomplete gamma inverses.
22630               </p>
22631             </td>
22632 <td>
22633               <p>
22634                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
22635               </p>
22636             </td>
22637 <td>
22638               <p>
22639                 <span class="blue">Max = 7.87&#949; (Mean = 1.15&#949;)</span>
22640               </p>
22641             </td>
22642 <td>
22643               <p>
22644                 <span class="blue">Max = 4.08&#949; (Mean = 1.12&#949;)</span>
22645               </p>
22646             </td>
22647 <td>
22648               <p>
22649                 <span class="blue">Max = 4.92&#949; (Mean = 1.03&#949;)</span>
22650               </p>
22651             </td>
22652 </tr></tbody>
22653 </table></div>
22654 </div>
22655 <br class="table-break"><div class="table">
22656 <a name="special_function_error_rates_rep.all_the_tables.table_gamma_q"></a><p class="title"><b>Table&#160;144.&#160;Error rates for gamma_q</b></p>
22657 <div class="table-contents"><table class="table" summary="Error rates for gamma_q">
22658 <colgroup>
22659 <col>
22660 <col>
22661 <col>
22662 <col>
22663 <col>
22664 </colgroup>
22665 <thead><tr>
22666 <th>
22667             </th>
22668 <th>
22669               <p>
22670                 GNU C++ version 7.1.0<br> linux<br> double
22671               </p>
22672             </th>
22673 <th>
22674               <p>
22675                 GNU C++ version 7.1.0<br> linux<br> long double
22676               </p>
22677             </th>
22678 <th>
22679               <p>
22680                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22681               </p>
22682             </th>
22683 <th>
22684               <p>
22685                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22686               </p>
22687             </th>
22688 </tr></thead>
22689 <tbody>
22690 <tr>
22691 <td>
22692               <p>
22693                 tgamma(a, z) medium values
22694               </p>
22695             </td>
22696 <td>
22697               <p>
22698                 <span class="blue">Max = 0.927&#949; (Mean = 0.035&#949;)</span><br> <br>
22699                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201&#949; (Mean = 13.5&#949;))<br> (<span class="emphasis"><em>Rmath
22700                 3.2.3:</em></span> Max = 131&#949; (Mean = 12.7&#949;))
22701               </p>
22702             </td>
22703 <td>
22704               <p>
22705                 <span class="blue">Max = 32.3&#949; (Mean = 6.61&#949;)</span>
22706               </p>
22707             </td>
22708 <td>
22709               <p>
22710                 <span class="blue">Max = 199&#949; (Mean = 26.6&#949;)</span>
22711               </p>
22712             </td>
22713 <td>
22714               <p>
22715                 <span class="blue">Max = 23.7&#949; (Mean = 4&#949;)</span>
22716               </p>
22717             </td>
22718 </tr>
22719 <tr>
22720 <td>
22721               <p>
22722                 tgamma(a, z) small values
22723               </p>
22724             </td>
22725 <td>
22726               <p>
22727                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
22728                 2.1:</em></span> <span class="red">Max = 1.38e+10&#949; (Mean = 1.05e+09&#949;))</span><br>
22729                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6&#949; (Mean = 11&#949;))
22730               </p>
22731             </td>
22732 <td>
22733               <p>
22734                 <span class="blue">Max = 2.45&#949; (Mean = 0.885&#949;)</span>
22735               </p>
22736             </td>
22737 <td>
22738               <p>
22739                 <span class="blue">Max = 2.45&#949; (Mean = 0.819&#949;)</span>
22740               </p>
22741             </td>
22742 <td>
22743               <p>
22744                 <span class="blue">Max = 2.26&#949; (Mean = 0.74&#949;)</span>
22745               </p>
22746             </td>
22747 </tr>
22748 <tr>
22749 <td>
22750               <p>
22751                 tgamma(a, z) large values
22752               </p>
22753             </td>
22754 <td>
22755               <p>
22756                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
22757                 2.1:</em></span> Max = 2.71e+04&#949; (Mean = 2.16e+03&#949;))<br> (<span class="emphasis"><em>Rmath
22758                 3.2.3:</em></span> Max = 1.02e+03&#949; (Mean = 62.7&#949;))
22759               </p>
22760             </td>
22761 <td>
22762               <p>
22763                 <span class="blue">Max = 6.82e+03&#949; (Mean = 414&#949;)</span>
22764               </p>
22765             </td>
22766 <td>
22767               <p>
22768                 <span class="blue">Max = 1.15e+04&#949; (Mean = 733&#949;)</span>
22769               </p>
22770             </td>
22771 <td>
22772               <p>
22773                 <span class="blue">Max = 469&#949; (Mean = 31.5&#949;)</span>
22774               </p>
22775             </td>
22776 </tr>
22777 <tr>
22778 <td>
22779               <p>
22780                 tgamma(a, z) integer and half integer values
22781               </p>
22782             </td>
22783 <td>
22784               <p>
22785                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
22786                 2.1:</em></span> Max = 118&#949; (Mean = 12.5&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
22787                 Max = 138&#949; (Mean = 16.9&#949;))
22788               </p>
22789             </td>
22790 <td>
22791               <p>
22792                 <span class="blue">Max = 11.1&#949; (Mean = 2.07&#949;)</span>
22793               </p>
22794             </td>
22795 <td>
22796               <p>
22797                 <span class="blue">Max = 54.7&#949; (Mean = 6.16&#949;)</span>
22798               </p>
22799             </td>
22800 <td>
22801               <p>
22802                 <span class="blue">Max = 8.72&#949; (Mean = 1.48&#949;)</span>
22803               </p>
22804             </td>
22805 </tr>
22806 </tbody>
22807 </table></div>
22808 </div>
22809 <br class="table-break"><div class="table">
22810 <a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inv"></a><p class="title"><b>Table&#160;145.&#160;Error rates for gamma_q_inv</b></p>
22811 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
22812 <colgroup>
22813 <col>
22814 <col>
22815 <col>
22816 <col>
22817 <col>
22818 </colgroup>
22819 <thead><tr>
22820 <th>
22821             </th>
22822 <th>
22823               <p>
22824                 GNU C++ version 7.1.0<br> linux<br> double
22825               </p>
22826             </th>
22827 <th>
22828               <p>
22829                 GNU C++ version 7.1.0<br> linux<br> long double
22830               </p>
22831             </th>
22832 <th>
22833               <p>
22834                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22835               </p>
22836             </th>
22837 <th>
22838               <p>
22839                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22840               </p>
22841             </th>
22842 </tr></thead>
22843 <tbody>
22844 <tr>
22845 <td>
22846               <p>
22847                 incomplete gamma inverse(a, z) medium values
22848               </p>
22849             </td>
22850 <td>
22851               <p>
22852                 <span class="blue">Max = 0.912&#949; (Mean = 0.154&#949;)</span><br> <br>
22853                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66&#949; (Mean = 0.792&#949;))
22854               </p>
22855             </td>
22856 <td>
22857               <p>
22858                 <span class="blue">Max = 6.2&#949; (Mean = 0.627&#949;)</span>
22859               </p>
22860             </td>
22861 <td>
22862               <p>
22863                 <span class="blue">Max = 6.2&#949; (Mean = 0.683&#949;)</span>
22864               </p>
22865             </td>
22866 <td>
22867               <p>
22868                 <span class="blue">Max = 2.88&#949; (Mean = 0.469&#949;)</span>
22869               </p>
22870             </td>
22871 </tr>
22872 <tr>
22873 <td>
22874               <p>
22875                 incomplete gamma inverse(a, z) large values
22876               </p>
22877             </td>
22878 <td>
22879               <p>
22880                 <span class="blue">Max = 0.894&#949; (Mean = 0.0915&#949;)</span><br> <br>
22881                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.106&#949;))
22882               </p>
22883             </td>
22884 <td>
22885               <p>
22886                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
22887               </p>
22888             </td>
22889 <td>
22890               <p>
22891                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
22892               </p>
22893             </td>
22894 <td>
22895               <p>
22896                 <span class="blue">Max = 0.814&#949; (Mean = 0.0856&#949;)</span>
22897               </p>
22898             </td>
22899 </tr>
22900 <tr>
22901 <td>
22902               <p>
22903                 incomplete gamma inverse(a, z) small values
22904               </p>
22905             </td>
22906 <td>
22907               <p>
22908                 <span class="blue">Max = 292&#949; (Mean = 36.4&#949;)</span><br> <br>
22909                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415&#949; (Mean = 48.7&#949;))
22910               </p>
22911             </td>
22912 <td>
22913               <p>
22914                 <span class="blue">Max = 8.28e+03&#949; (Mean = 1.09e+03&#949;)</span>
22915               </p>
22916             </td>
22917 <td>
22918               <p>
22919                 <span class="blue">Max = 8.98e+03&#949; (Mean = 877&#949;)</span>
22920               </p>
22921             </td>
22922 <td>
22923               <p>
22924                 <span class="blue">Max = 451&#949; (Mean = 64.7&#949;)</span>
22925               </p>
22926             </td>
22927 </tr>
22928 </tbody>
22929 </table></div>
22930 </div>
22931 <br class="table-break"><div class="table">
22932 <a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inva"></a><p class="title"><b>Table&#160;146.&#160;Error rates for gamma_q_inva</b></p>
22933 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
22934 <colgroup>
22935 <col>
22936 <col>
22937 <col>
22938 <col>
22939 <col>
22940 </colgroup>
22941 <thead><tr>
22942 <th>
22943             </th>
22944 <th>
22945               <p>
22946                 GNU C++ version 7.1.0<br> linux<br> double
22947               </p>
22948             </th>
22949 <th>
22950               <p>
22951                 GNU C++ version 7.1.0<br> linux<br> long double
22952               </p>
22953             </th>
22954 <th>
22955               <p>
22956                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
22957               </p>
22958             </th>
22959 <th>
22960               <p>
22961                 Microsoft Visual C++ version 14.1<br> Win32<br> double
22962               </p>
22963             </th>
22964 </tr></thead>
22965 <tbody><tr>
22966 <td>
22967               <p>
22968                 Incomplete gamma inverses.
22969               </p>
22970             </td>
22971 <td>
22972               <p>
22973                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
22974               </p>
22975             </td>
22976 <td>
22977               <p>
22978                 <span class="blue">Max = 8.42&#949; (Mean = 1.3&#949;)</span>
22979               </p>
22980             </td>
22981 <td>
22982               <p>
22983                 <span class="blue">Max = 7.86&#949; (Mean = 1.24&#949;)</span>
22984               </p>
22985             </td>
22986 <td>
22987               <p>
22988                 <span class="blue">Max = 5.05&#949; (Mean = 1.08&#949;)</span>
22989               </p>
22990             </td>
22991 </tr></tbody>
22992 </table></div>
22993 </div>
22994 <br class="table-break"><div class="table">
22995 <a name="special_function_error_rates_rep.all_the_tables.table_hermite"></a><p class="title"><b>Table&#160;147.&#160;Error rates for hermite</b></p>
22996 <div class="table-contents"><table class="table" summary="Error rates for hermite">
22997 <colgroup>
22998 <col>
22999 <col>
23000 <col>
23001 <col>
23002 <col>
23003 </colgroup>
23004 <thead><tr>
23005 <th>
23006             </th>
23007 <th>
23008               <p>
23009                 GNU C++ version 7.1.0<br> linux<br> double
23010               </p>
23011             </th>
23012 <th>
23013               <p>
23014                 GNU C++ version 7.1.0<br> linux<br> long double
23015               </p>
23016             </th>
23017 <th>
23018               <p>
23019                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23020               </p>
23021             </th>
23022 <th>
23023               <p>
23024                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23025               </p>
23026             </th>
23027 </tr></thead>
23028 <tbody><tr>
23029 <td>
23030               <p>
23031                 Hermite Polynomials
23032               </p>
23033             </td>
23034 <td>
23035               <p>
23036                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
23037               </p>
23038             </td>
23039 <td>
23040               <p>
23041                 <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
23042               </p>
23043             </td>
23044 <td>
23045               <p>
23046                 <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
23047               </p>
23048             </td>
23049 <td>
23050               <p>
23051                 <span class="blue">Max = 4.46&#949; (Mean = 1.41&#949;)</span>
23052               </p>
23053             </td>
23054 </tr></tbody>
23055 </table></div>
23056 </div>
23057 <br class="table-break"><div class="table">
23058 <a name="special_function_error_rates_rep.all_the_tables.table_heuman_lambda"></a><p class="title"><b>Table&#160;148.&#160;Error rates for heuman_lambda</b></p>
23059 <div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
23060 <colgroup>
23061 <col>
23062 <col>
23063 <col>
23064 <col>
23065 <col>
23066 </colgroup>
23067 <thead><tr>
23068 <th>
23069             </th>
23070 <th>
23071               <p>
23072                 GNU C++ version 7.1.0<br> linux<br> double
23073               </p>
23074             </th>
23075 <th>
23076               <p>
23077                 GNU C++ version 7.1.0<br> linux<br> long double
23078               </p>
23079             </th>
23080 <th>
23081               <p>
23082                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23083               </p>
23084             </th>
23085 <th>
23086               <p>
23087                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23088               </p>
23089             </th>
23090 </tr></thead>
23091 <tbody>
23092 <tr>
23093 <td>
23094               <p>
23095                 Elliptic Integral Jacobi Zeta: Mathworld Data
23096               </p>
23097             </td>
23098 <td>
23099               <p>
23100                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
23101               </p>
23102             </td>
23103 <td>
23104               <p>
23105                 <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
23106               </p>
23107             </td>
23108 <td>
23109               <p>
23110                 <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
23111               </p>
23112             </td>
23113 <td>
23114               <p>
23115                 <span class="blue">Max = 1.08&#949; (Mean = 0.734&#949;)</span>
23116               </p>
23117             </td>
23118 </tr>
23119 <tr>
23120 <td>
23121               <p>
23122                 Elliptic Integral Heuman Lambda: Random Data
23123               </p>
23124             </td>
23125 <td>
23126               <p>
23127                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
23128               </p>
23129             </td>
23130 <td>
23131               <p>
23132                 <span class="blue">Max = 3.82&#949; (Mean = 0.609&#949;)</span>
23133               </p>
23134             </td>
23135 <td>
23136               <p>
23137                 <span class="blue">Max = 3.82&#949; (Mean = 0.608&#949;)</span>
23138               </p>
23139             </td>
23140 <td>
23141               <p>
23142                 <span class="blue">Max = 2.12&#949; (Mean = 0.588&#949;)</span>
23143               </p>
23144             </td>
23145 </tr>
23146 </tbody>
23147 </table></div>
23148 </div>
23149 <br class="table-break"><div class="table">
23150 <a name="special_function_error_rates_rep.all_the_tables.table_ibeta"></a><p class="title"><b>Table&#160;149.&#160;Error rates for ibeta</b></p>
23151 <div class="table-contents"><table class="table" summary="Error rates for ibeta">
23152 <colgroup>
23153 <col>
23154 <col>
23155 <col>
23156 <col>
23157 <col>
23158 </colgroup>
23159 <thead><tr>
23160 <th>
23161             </th>
23162 <th>
23163               <p>
23164                 GNU C++ version 7.1.0<br> linux<br> double
23165               </p>
23166             </th>
23167 <th>
23168               <p>
23169                 GNU C++ version 7.1.0<br> linux<br> long double
23170               </p>
23171             </th>
23172 <th>
23173               <p>
23174                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23175               </p>
23176             </th>
23177 <th>
23178               <p>
23179                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23180               </p>
23181             </th>
23182 </tr></thead>
23183 <tbody>
23184 <tr>
23185 <td>
23186               <p>
23187                 Incomplete Beta Function: Small Values
23188               </p>
23189             </td>
23190 <td>
23191               <p>
23192                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
23193                 2.1:</em></span> Max = 682&#949; (Mean = 32.6&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
23194                 Max = 22.9&#949; (Mean = 3.35&#949;))
23195               </p>
23196             </td>
23197 <td>
23198               <p>
23199                 <span class="blue">Max = 8.97&#949; (Mean = 2.09&#949;)</span>
23200               </p>
23201             </td>
23202 <td>
23203               <p>
23204                 <span class="blue">Max = 21.3&#949; (Mean = 2.75&#949;)</span>
23205               </p>
23206             </td>
23207 <td>
23208               <p>
23209                 <span class="blue">Max = 8.4&#949; (Mean = 1.93&#949;)</span>
23210               </p>
23211             </td>
23212 </tr>
23213 <tr>
23214 <td>
23215               <p>
23216                 Incomplete Beta Function: Medium Values
23217               </p>
23218             </td>
23219 <td>
23220               <p>
23221                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
23222                 2.1:</em></span> Max = 690&#949; (Mean = 151&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
23223                 Max = 232&#949; (Mean = 27.9&#949;))
23224               </p>
23225             </td>
23226 <td>
23227               <p>
23228                 <span class="blue">Max = 50&#949; (Mean = 12.1&#949;)</span>
23229               </p>
23230             </td>
23231 <td>
23232               <p>
23233                 <span class="blue">Max = 124&#949; (Mean = 18.4&#949;)</span>
23234               </p>
23235             </td>
23236 <td>
23237               <p>
23238                 <span class="blue">Max = 106&#949; (Mean = 16.3&#949;)</span>
23239               </p>
23240             </td>
23241 </tr>
23242 <tr>
23243 <td>
23244               <p>
23245                 Incomplete Beta Function: Large and Diverse Values
23246               </p>
23247             </td>
23248 <td>
23249               <p>
23250                 <span class="blue">Max = 1.26&#949; (Mean = 0.063&#949;)</span><br> <br>
23251                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05&#949; (Mean = 1.82e+04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And
23252                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
23253                 Max = 574&#949; (Mean = 49.4&#949;))
23254               </p>
23255             </td>
23256 <td>
23257               <p>
23258                 <span class="blue">Max = 1.96e+04&#949; (Mean = 997&#949;)</span>
23259               </p>
23260             </td>
23261 <td>
23262               <p>
23263                 <span class="blue">Max = 4.98e+04&#949; (Mean = 2.07e+03&#949;)</span>
23264               </p>
23265             </td>
23266 <td>
23267               <p>
23268                 <span class="blue">Max = 1.32e+03&#949; (Mean = 68.5&#949;)</span>
23269               </p>
23270             </td>
23271 </tr>
23272 <tr>
23273 <td>
23274               <p>
23275                 Incomplete Beta Function: Small Integer Values
23276               </p>
23277             </td>
23278 <td>
23279               <p>
23280                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
23281                 2.1:</em></span> Max = 254&#949; (Mean = 50.9&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
23282                 Max = 62.2&#949; (Mean = 8.95&#949;))
23283               </p>
23284             </td>
23285 <td>
23286               <p>
23287                 <span class="blue">Max = 4.45&#949; (Mean = 0.814&#949;)</span>
23288               </p>
23289             </td>
23290 <td>
23291               <p>
23292                 <span class="blue">Max = 44.5&#949; (Mean = 10.1&#949;)</span>
23293               </p>
23294             </td>
23295 <td>
23296               <p>
23297                 <span class="blue">Max = 3.85&#949; (Mean = 0.791&#949;)</span>
23298               </p>
23299             </td>
23300 </tr>
23301 </tbody>
23302 </table></div>
23303 </div>
23304 <br class="table-break"><div class="table">
23305 <a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inv"></a><p class="title"><b>Table&#160;150.&#160;Error rates for ibeta_inv</b></p>
23306 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
23307 <colgroup>
23308 <col>
23309 <col>
23310 <col>
23311 <col>
23312 <col>
23313 </colgroup>
23314 <thead><tr>
23315 <th>
23316             </th>
23317 <th>
23318               <p>
23319                 GNU C++ version 7.1.0<br> linux<br> double
23320               </p>
23321             </th>
23322 <th>
23323               <p>
23324                 GNU C++ version 7.1.0<br> linux<br> long double
23325               </p>
23326             </th>
23327 <th>
23328               <p>
23329                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23330               </p>
23331             </th>
23332 <th>
23333               <p>
23334                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23335               </p>
23336             </th>
23337 </tr></thead>
23338 <tbody><tr>
23339 <td>
23340               <p>
23341                 Inverse incomplete beta
23342               </p>
23343             </td>
23344 <td>
23345               <p>
23346                 <span class="blue">Max = 11&#949; (Mean = 0.345&#949;)</span><br> <br>
23347                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121&#949; (Mean
23348                 = 3.28e+119&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
23349                 other failures.</a>)</span>
23350               </p>
23351             </td>
23352 <td>
23353               <p>
23354                 <span class="blue">Max = 3.8e+04&#949; (Mean = 2.66e+03&#949;)</span>
23355               </p>
23356             </td>
23357 <td>
23358               <p>
23359                 <span class="blue">Max = 4.07e+04&#949; (Mean = 2.86e+03&#949;)</span>
23360               </p>
23361             </td>
23362 <td>
23363               <p>
23364                 <span class="blue">Max = 8.59e+03&#949; (Mean = 277&#949;)</span>
23365               </p>
23366             </td>
23367 </tr></tbody>
23368 </table></div>
23369 </div>
23370 <br class="table-break"><div class="table">
23371 <a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inva"></a><p class="title"><b>Table&#160;151.&#160;Error rates for ibeta_inva</b></p>
23372 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
23373 <colgroup>
23374 <col>
23375 <col>
23376 <col>
23377 <col>
23378 <col>
23379 </colgroup>
23380 <thead><tr>
23381 <th>
23382             </th>
23383 <th>
23384               <p>
23385                 GNU C++ version 7.1.0<br> linux<br> double
23386               </p>
23387             </th>
23388 <th>
23389               <p>
23390                 GNU C++ version 7.1.0<br> linux<br> long double
23391               </p>
23392             </th>
23393 <th>
23394               <p>
23395                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23396               </p>
23397             </th>
23398 <th>
23399               <p>
23400                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23401               </p>
23402             </th>
23403 </tr></thead>
23404 <tbody><tr>
23405 <td>
23406               <p>
23407                 Inverse incomplete beta
23408               </p>
23409             </td>
23410 <td>
23411               <p>
23412                 <span class="blue">Max = 0.602&#949; (Mean = 0.0239&#949;)</span>
23413               </p>
23414             </td>
23415 <td>
23416               <p>
23417                 <span class="blue">Max = 377&#949; (Mean = 24.4&#949;)</span>
23418               </p>
23419             </td>
23420 <td>
23421               <p>
23422                 <span class="blue">Max = 438&#949; (Mean = 31.3&#949;)</span>
23423               </p>
23424             </td>
23425 <td>
23426               <p>
23427                 <span class="blue">Max = 242&#949; (Mean = 22.9&#949;)</span>
23428               </p>
23429             </td>
23430 </tr></tbody>
23431 </table></div>
23432 </div>
23433 <br class="table-break"><div class="table">
23434 <a name="special_function_error_rates_rep.all_the_tables.table_ibeta_invb"></a><p class="title"><b>Table&#160;152.&#160;Error rates for ibeta_invb</b></p>
23435 <div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
23436 <colgroup>
23437 <col>
23438 <col>
23439 <col>
23440 <col>
23441 <col>
23442 </colgroup>
23443 <thead><tr>
23444 <th>
23445             </th>
23446 <th>
23447               <p>
23448                 GNU C++ version 7.1.0<br> linux<br> double
23449               </p>
23450             </th>
23451 <th>
23452               <p>
23453                 GNU C++ version 7.1.0<br> linux<br> long double
23454               </p>
23455             </th>
23456 <th>
23457               <p>
23458                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23459               </p>
23460             </th>
23461 <th>
23462               <p>
23463                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23464               </p>
23465             </th>
23466 </tr></thead>
23467 <tbody><tr>
23468 <td>
23469               <p>
23470                 Inverse incomplete beta
23471               </p>
23472             </td>
23473 <td>
23474               <p>
23475                 <span class="blue">Max = 0.765&#949; (Mean = 0.0422&#949;)</span>
23476               </p>
23477             </td>
23478 <td>
23479               <p>
23480                 <span class="blue">Max = 407&#949; (Mean = 27.2&#949;)</span>
23481               </p>
23482             </td>
23483 <td>
23484               <p>
23485                 <span class="blue">Max = 407&#949; (Mean = 24.4&#949;)</span>
23486               </p>
23487             </td>
23488 <td>
23489               <p>
23490                 <span class="blue">Max = 409&#949; (Mean = 19.3&#949;)</span>
23491               </p>
23492             </td>
23493 </tr></tbody>
23494 </table></div>
23495 </div>
23496 <br class="table-break"><div class="table">
23497 <a name="special_function_error_rates_rep.all_the_tables.table_ibetac"></a><p class="title"><b>Table&#160;153.&#160;Error rates for ibetac</b></p>
23498 <div class="table-contents"><table class="table" summary="Error rates for ibetac">
23499 <colgroup>
23500 <col>
23501 <col>
23502 <col>
23503 <col>
23504 <col>
23505 </colgroup>
23506 <thead><tr>
23507 <th>
23508             </th>
23509 <th>
23510               <p>
23511                 GNU C++ version 7.1.0<br> linux<br> double
23512               </p>
23513             </th>
23514 <th>
23515               <p>
23516                 GNU C++ version 7.1.0<br> linux<br> long double
23517               </p>
23518             </th>
23519 <th>
23520               <p>
23521                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23522               </p>
23523             </th>
23524 <th>
23525               <p>
23526                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23527               </p>
23528             </th>
23529 </tr></thead>
23530 <tbody>
23531 <tr>
23532 <td>
23533               <p>
23534                 Incomplete Beta Function: Small Values
23535               </p>
23536             </td>
23537 <td>
23538               <p>
23539                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
23540                 3.2.3:</em></span> Max = 22.4&#949; (Mean = 3.67&#949;))
23541               </p>
23542             </td>
23543 <td>
23544               <p>
23545                 <span class="blue">Max = 10.6&#949; (Mean = 2.22&#949;)</span>
23546               </p>
23547             </td>
23548 <td>
23549               <p>
23550                 <span class="blue">Max = 13.8&#949; (Mean = 2.68&#949;)</span>
23551               </p>
23552             </td>
23553 <td>
23554               <p>
23555                 <span class="blue">Max = 6.94&#949; (Mean = 1.71&#949;)</span>
23556               </p>
23557             </td>
23558 </tr>
23559 <tr>
23560 <td>
23561               <p>
23562                 Incomplete Beta Function: Medium Values
23563               </p>
23564             </td>
23565 <td>
23566               <p>
23567                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
23568                 3.2.3:</em></span> Max = 204&#949; (Mean = 25.8&#949;))
23569               </p>
23570             </td>
23571 <td>
23572               <p>
23573                 <span class="blue">Max = 73.9&#949; (Mean = 11.2&#949;)</span>
23574               </p>
23575             </td>
23576 <td>
23577               <p>
23578                 <span class="blue">Max = 132&#949; (Mean = 19.8&#949;)</span>
23579               </p>
23580             </td>
23581 <td>
23582               <p>
23583                 <span class="blue">Max = 56.7&#949; (Mean = 14.3&#949;)</span>
23584               </p>
23585             </td>
23586 </tr>
23587 <tr>
23588 <td>
23589               <p>
23590                 Incomplete Beta Function: Large and Diverse Values
23591               </p>
23592             </td>
23593 <td>
23594               <p>
23595                 <span class="blue">Max = 0.981&#949; (Mean = 0.0573&#949;)</span><br> <br>
23596                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889&#949; (Mean = 68.4&#949;))
23597               </p>
23598             </td>
23599 <td>
23600               <p>
23601                 <span class="blue">Max = 3.45e+04&#949; (Mean = 1.32e+03&#949;)</span>
23602               </p>
23603             </td>
23604 <td>
23605               <p>
23606                 <span class="blue">Max = 6.31e+04&#949; (Mean = 2.04e+03&#949;)</span>
23607               </p>
23608             </td>
23609 <td>
23610               <p>
23611                 <span class="blue">Max = 1.88e+03&#949; (Mean = 82.7&#949;)</span>
23612               </p>
23613             </td>
23614 </tr>
23615 <tr>
23616 <td>
23617               <p>
23618                 Incomplete Beta Function: Small Integer Values
23619               </p>
23620             </td>
23621 <td>
23622               <p>
23623                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
23624                 3.2.3:</em></span> Max = 84.6&#949; (Mean = 18&#949;))
23625               </p>
23626             </td>
23627 <td>
23628               <p>
23629                 <span class="blue">Max = 5.34&#949; (Mean = 1.11&#949;)</span>
23630               </p>
23631             </td>
23632 <td>
23633               <p>
23634                 <span class="blue">Max = 107&#949; (Mean = 17.1&#949;)</span>
23635               </p>
23636             </td>
23637 <td>
23638               <p>
23639                 <span class="blue">Max = 6.37&#949; (Mean = 1.03&#949;)</span>
23640               </p>
23641             </td>
23642 </tr>
23643 </tbody>
23644 </table></div>
23645 </div>
23646 <br class="table-break"><div class="table">
23647 <a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inv"></a><p class="title"><b>Table&#160;154.&#160;Error rates for ibetac_inv</b></p>
23648 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
23649 <colgroup>
23650 <col>
23651 <col>
23652 <col>
23653 <col>
23654 <col>
23655 </colgroup>
23656 <thead><tr>
23657 <th>
23658             </th>
23659 <th>
23660               <p>
23661                 GNU C++ version 7.1.0<br> linux<br> double
23662               </p>
23663             </th>
23664 <th>
23665               <p>
23666                 GNU C++ version 7.1.0<br> linux<br> long double
23667               </p>
23668             </th>
23669 <th>
23670               <p>
23671                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23672               </p>
23673             </th>
23674 <th>
23675               <p>
23676                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23677               </p>
23678             </th>
23679 </tr></thead>
23680 <tbody><tr>
23681 <td>
23682               <p>
23683                 Inverse incomplete beta
23684               </p>
23685             </td>
23686 <td>
23687               <p>
23688                 <span class="blue">Max = 0.977&#949; (Mean = 0.0976&#949;)</span><br> <br>
23689                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132&#949; (Mean
23690                 = 8.65e+130&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
23691                 other failures.</a>)</span>
23692               </p>
23693             </td>
23694 <td>
23695               <p>
23696                 <span class="blue">Max = 4.88e+04&#949; (Mean = 3.16e+03&#949;)</span>
23697               </p>
23698             </td>
23699 <td>
23700               <p>
23701                 <span class="blue">Max = 5.05e+04&#949; (Mean = 3.33e+03&#949;)</span>
23702               </p>
23703             </td>
23704 <td>
23705               <p>
23706                 <span class="blue">Max = 2.93e+03&#949; (Mean = 198&#949;)</span>
23707               </p>
23708             </td>
23709 </tr></tbody>
23710 </table></div>
23711 </div>
23712 <br class="table-break"><div class="table">
23713 <a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inva"></a><p class="title"><b>Table&#160;155.&#160;Error rates for ibetac_inva</b></p>
23714 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
23715 <colgroup>
23716 <col>
23717 <col>
23718 <col>
23719 <col>
23720 <col>
23721 </colgroup>
23722 <thead><tr>
23723 <th>
23724             </th>
23725 <th>
23726               <p>
23727                 GNU C++ version 7.1.0<br> linux<br> double
23728               </p>
23729             </th>
23730 <th>
23731               <p>
23732                 GNU C++ version 7.1.0<br> linux<br> long double
23733               </p>
23734             </th>
23735 <th>
23736               <p>
23737                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23738               </p>
23739             </th>
23740 <th>
23741               <p>
23742                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23743               </p>
23744             </th>
23745 </tr></thead>
23746 <tbody><tr>
23747 <td>
23748               <p>
23749                 Inverse incomplete beta
23750               </p>
23751             </td>
23752 <td>
23753               <p>
23754                 <span class="blue">Max = 0.683&#949; (Mean = 0.0314&#949;)</span>
23755               </p>
23756             </td>
23757 <td>
23758               <p>
23759                 <span class="blue">Max = 382&#949; (Mean = 22.2&#949;)</span>
23760               </p>
23761             </td>
23762 <td>
23763               <p>
23764                 <span class="blue">Max = 315&#949; (Mean = 23.7&#949;)</span>
23765               </p>
23766             </td>
23767 <td>
23768               <p>
23769                 <span class="blue">Max = 408&#949; (Mean = 26.7&#949;)</span>
23770               </p>
23771             </td>
23772 </tr></tbody>
23773 </table></div>
23774 </div>
23775 <br class="table-break"><div class="table">
23776 <a name="special_function_error_rates_rep.all_the_tables.table_ibetac_invb"></a><p class="title"><b>Table&#160;156.&#160;Error rates for ibetac_invb</b></p>
23777 <div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
23778 <colgroup>
23779 <col>
23780 <col>
23781 <col>
23782 <col>
23783 <col>
23784 </colgroup>
23785 <thead><tr>
23786 <th>
23787             </th>
23788 <th>
23789               <p>
23790                 GNU C++ version 7.1.0<br> linux<br> double
23791               </p>
23792             </th>
23793 <th>
23794               <p>
23795                 GNU C++ version 7.1.0<br> linux<br> long double
23796               </p>
23797             </th>
23798 <th>
23799               <p>
23800                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23801               </p>
23802             </th>
23803 <th>
23804               <p>
23805                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23806               </p>
23807             </th>
23808 </tr></thead>
23809 <tbody><tr>
23810 <td>
23811               <p>
23812                 Inverse incomplete beta
23813               </p>
23814             </td>
23815 <td>
23816               <p>
23817                 <span class="blue">Max = 0.724&#949; (Mean = 0.0303&#949;)</span>
23818               </p>
23819             </td>
23820 <td>
23821               <p>
23822                 <span class="blue">Max = 317&#949; (Mean = 19.8&#949;)</span>
23823               </p>
23824             </td>
23825 <td>
23826               <p>
23827                 <span class="blue">Max = 369&#949; (Mean = 22.6&#949;)</span>
23828               </p>
23829             </td>
23830 <td>
23831               <p>
23832                 <span class="blue">Max = 271&#949; (Mean = 16.4&#949;)</span>
23833               </p>
23834             </td>
23835 </tr></tbody>
23836 </table></div>
23837 </div>
23838 <br class="table-break"><div class="table">
23839 <a name="special_function_error_rates_rep.all_the_tables.table_jacobi_cn"></a><p class="title"><b>Table&#160;157.&#160;Error rates for jacobi_cn</b></p>
23840 <div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
23841 <colgroup>
23842 <col>
23843 <col>
23844 <col>
23845 <col>
23846 <col>
23847 </colgroup>
23848 <thead><tr>
23849 <th>
23850             </th>
23851 <th>
23852               <p>
23853                 GNU C++ version 7.1.0<br> linux<br> double
23854               </p>
23855             </th>
23856 <th>
23857               <p>
23858                 GNU C++ version 7.1.0<br> linux<br> long double
23859               </p>
23860             </th>
23861 <th>
23862               <p>
23863                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
23864               </p>
23865             </th>
23866 <th>
23867               <p>
23868                 Microsoft Visual C++ version 14.1<br> Win32<br> double
23869               </p>
23870             </th>
23871 </tr></thead>
23872 <tbody>
23873 <tr>
23874 <td>
23875               <p>
23876                 Jacobi Elliptic: Mathworld Data
23877               </p>
23878             </td>
23879 <td>
23880               <p>
23881                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
23882                 2.1:</em></span> Max = 17.3&#949; (Mean = 4.29&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
23883                 other failures.</a>)
23884               </p>
23885             </td>
23886 <td>
23887               <p>
23888                 <span class="blue">Max = 71.6&#949; (Mean = 19.3&#949;)</span>
23889               </p>
23890             </td>
23891 <td>
23892               <p>
23893                 <span class="blue">Max = 71.6&#949; (Mean = 19.4&#949;)</span>
23894               </p>
23895             </td>
23896 <td>
23897               <p>
23898                 <span class="blue">Max = 45.8&#949; (Mean = 11.4&#949;)</span>
23899               </p>
23900             </td>
23901 </tr>
23902 <tr>
23903 <td>
23904               <p>
23905                 Jacobi Elliptic: Random Data
23906               </p>
23907             </td>
23908 <td>
23909               <p>
23910                 <span class="blue">Max = 0.816&#949; (Mean = 0.0563&#949;)</span><br> <br>
23911                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43&#949; (Mean = 0.803&#949;))
23912               </p>
23913             </td>
23914 <td>
23915               <p>
23916                 <span class="blue">Max = 1.68&#949; (Mean = 0.443&#949;)</span>
23917               </p>
23918             </td>
23919 <td>
23920               <p>
23921                 <span class="blue">Max = 1.68&#949; (Mean = 0.454&#949;)</span>
23922               </p>
23923             </td>
23924 <td>
23925               <p>
23926                 <span class="blue">Max = 1.83&#949; (Mean = 0.455&#949;)</span>
23927               </p>
23928             </td>
23929 </tr>
23930 <tr>
23931 <td>
23932               <p>
23933                 Jacobi Elliptic: Random Small Values
23934               </p>
23935             </td>
23936 <td>
23937               <p>
23938                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
23939                 2.1:</em></span> Max = 55.2&#949; (Mean = 1.64&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
23940                 other failures.</a>)
23941               </p>
23942             </td>
23943 <td>
23944               <p>
23945                 <span class="blue">Max = 10.4&#949; (Mean = 0.594&#949;)</span>
23946               </p>
23947             </td>
23948 <td>
23949               <p>
23950                 <span class="blue">Max = 10.4&#949; (Mean = 0.602&#949;)</span>
23951               </p>
23952             </td>
23953 <td>
23954               <p>
23955                 <span class="blue">Max = 26.2&#949; (Mean = 1.17&#949;)</span>
23956               </p>
23957             </td>
23958 </tr>
23959 <tr>
23960 <td>
23961               <p>
23962                 Jacobi Elliptic: Modulus near 1
23963               </p>
23964             </td>
23965 <td>
23966               <p>
23967                 <span class="blue">Max = 0.919&#949; (Mean = 0.127&#949;)</span><br> <br>
23968                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
23969                 other failures.</a>)
23970               </p>
23971             </td>
23972 <td>
23973               <p>
23974                 <span class="blue">Max = 675&#949; (Mean = 87.1&#949;)</span>
23975               </p>
23976             </td>
23977 <td>
23978               <p>
23979                 <span class="blue">Max = 675&#949; (Mean = 86.8&#949;)</span>
23980               </p>
23981             </td>
23982 <td>
23983               <p>
23984                 <span class="blue">Max = 513&#949; (Mean = 126&#949;)</span>
23985               </p>
23986             </td>
23987 </tr>
23988 <tr>
23989 <td>
23990               <p>
23991                 Jacobi Elliptic: Large Phi
23992               </p>
23993             </td>
23994 <td>
23995               <p>
23996                 <span class="blue">Max = 14.2&#949; (Mean = 0.927&#949;)</span><br> <br>
23997                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03&#949; (Mean = 477&#949;))
23998               </p>
23999             </td>
24000 <td>
24001               <p>
24002                 <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
24003               </p>
24004             </td>
24005 <td>
24006               <p>
24007                 <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
24008               </p>
24009             </td>
24010 <td>
24011               <p>
24012                 <span class="blue">Max = 3.27e+04&#949; (Mean = 1.93e+03&#949;)</span>
24013               </p>
24014             </td>
24015 </tr>
24016 </tbody>
24017 </table></div>
24018 </div>
24019 <br class="table-break"><div class="table">
24020 <a name="special_function_error_rates_rep.all_the_tables.table_jacobi_dn"></a><p class="title"><b>Table&#160;158.&#160;Error rates for jacobi_dn</b></p>
24021 <div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
24022 <colgroup>
24023 <col>
24024 <col>
24025 <col>
24026 <col>
24027 <col>
24028 </colgroup>
24029 <thead><tr>
24030 <th>
24031             </th>
24032 <th>
24033               <p>
24034                 GNU C++ version 7.1.0<br> linux<br> double
24035               </p>
24036             </th>
24037 <th>
24038               <p>
24039                 GNU C++ version 7.1.0<br> linux<br> long double
24040               </p>
24041             </th>
24042 <th>
24043               <p>
24044                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24045               </p>
24046             </th>
24047 <th>
24048               <p>
24049                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24050               </p>
24051             </th>
24052 </tr></thead>
24053 <tbody>
24054 <tr>
24055 <td>
24056               <p>
24057                 Jacobi Elliptic: Mathworld Data
24058               </p>
24059             </td>
24060 <td>
24061               <p>
24062                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24063                 2.1:</em></span> Max = 2.82&#949; (Mean = 1.18&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
24064                 other failures.</a>)
24065               </p>
24066             </td>
24067 <td>
24068               <p>
24069                 <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
24070               </p>
24071             </td>
24072 <td>
24073               <p>
24074                 <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
24075               </p>
24076             </td>
24077 <td>
24078               <p>
24079                 <span class="blue">Max = 34.3&#949; (Mean = 8.71&#949;)</span>
24080               </p>
24081             </td>
24082 </tr>
24083 <tr>
24084 <td>
24085               <p>
24086                 Jacobi Elliptic: Random Data
24087               </p>
24088             </td>
24089 <td>
24090               <p>
24091                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24092                 2.1:</em></span> Max = 3&#949; (Mean = 0.61&#949;))
24093               </p>
24094             </td>
24095 <td>
24096               <p>
24097                 <span class="blue">Max = 1.53&#949; (Mean = 0.473&#949;)</span>
24098               </p>
24099             </td>
24100 <td>
24101               <p>
24102                 <span class="blue">Max = 1.53&#949; (Mean = 0.481&#949;)</span>
24103               </p>
24104             </td>
24105 <td>
24106               <p>
24107                 <span class="blue">Max = 1.52&#949; (Mean = 0.466&#949;)</span>
24108               </p>
24109             </td>
24110 </tr>
24111 <tr>
24112 <td>
24113               <p>
24114                 Jacobi Elliptic: Random Small Values
24115               </p>
24116             </td>
24117 <td>
24118               <p>
24119                 <span class="blue">Max = 0.5&#949; (Mean = 0.0122&#949;)</span><br> <br>
24120                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5&#949; (Mean = 0.391&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
24121                 other failures.</a>)
24122               </p>
24123             </td>
24124 <td>
24125               <p>
24126                 <span class="blue">Max = 22.4&#949; (Mean = 0.777&#949;)</span>
24127               </p>
24128             </td>
24129 <td>
24130               <p>
24131                 <span class="blue">Max = 22.4&#949; (Mean = 0.763&#949;)</span>
24132               </p>
24133             </td>
24134 <td>
24135               <p>
24136                 <span class="blue">Max = 16.1&#949; (Mean = 0.685&#949;)</span>
24137               </p>
24138             </td>
24139 </tr>
24140 <tr>
24141 <td>
24142               <p>
24143                 Jacobi Elliptic: Modulus near 1
24144               </p>
24145             </td>
24146 <td>
24147               <p>
24148                 <span class="blue">Max = 2.28&#949; (Mean = 0.194&#949;)</span><br> <br>
24149                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
24150                 other failures.</a>)
24151               </p>
24152             </td>
24153 <td>
24154               <p>
24155                 <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
24156               </p>
24157             </td>
24158 <td>
24159               <p>
24160                 <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
24161               </p>
24162             </td>
24163 <td>
24164               <p>
24165                 <span class="blue">Max = 6.24e+03&#949; (Mean = 482&#949;)</span>
24166               </p>
24167             </td>
24168 </tr>
24169 <tr>
24170 <td>
24171               <p>
24172                 Jacobi Elliptic: Large Phi
24173               </p>
24174             </td>
24175 <td>
24176               <p>
24177                 <span class="blue">Max = 14.1&#949; (Mean = 0.897&#949;)</span><br> <br>
24178                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121&#949; (Mean = 22&#949;))
24179               </p>
24180             </td>
24181 <td>
24182               <p>
24183                 <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
24184               </p>
24185             </td>
24186 <td>
24187               <p>
24188                 <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
24189               </p>
24190             </td>
24191 <td>
24192               <p>
24193                 <span class="blue">Max = 1.67e+04&#949; (Mean = 1e+03&#949;)</span>
24194               </p>
24195             </td>
24196 </tr>
24197 </tbody>
24198 </table></div>
24199 </div>
24200 <br class="table-break"><div class="table">
24201 <a name="special_function_error_rates_rep.all_the_tables.table_jacobi_sn"></a><p class="title"><b>Table&#160;159.&#160;Error rates for jacobi_sn</b></p>
24202 <div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
24203 <colgroup>
24204 <col>
24205 <col>
24206 <col>
24207 <col>
24208 <col>
24209 </colgroup>
24210 <thead><tr>
24211 <th>
24212             </th>
24213 <th>
24214               <p>
24215                 GNU C++ version 7.1.0<br> linux<br> double
24216               </p>
24217             </th>
24218 <th>
24219               <p>
24220                 GNU C++ version 7.1.0<br> linux<br> long double
24221               </p>
24222             </th>
24223 <th>
24224               <p>
24225                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24226               </p>
24227             </th>
24228 <th>
24229               <p>
24230                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24231               </p>
24232             </th>
24233 </tr></thead>
24234 <tbody>
24235 <tr>
24236 <td>
24237               <p>
24238                 Jacobi Elliptic: Mathworld Data
24239               </p>
24240             </td>
24241 <td>
24242               <p>
24243                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24244                 2.1:</em></span> Max = 588&#949; (Mean = 146&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
24245                 other failures.</a>)
24246               </p>
24247             </td>
24248 <td>
24249               <p>
24250                 <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
24251               </p>
24252             </td>
24253 <td>
24254               <p>
24255                 <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
24256               </p>
24257             </td>
24258 <td>
24259               <p>
24260                 <span class="blue">Max = 481&#949; (Mean = 113&#949;)</span>
24261               </p>
24262             </td>
24263 </tr>
24264 <tr>
24265 <td>
24266               <p>
24267                 Jacobi Elliptic: Random Data
24268               </p>
24269             </td>
24270 <td>
24271               <p>
24272                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24273                 2.1:</em></span> Max = 4.02&#949; (Mean = 1.07&#949;))
24274               </p>
24275             </td>
24276 <td>
24277               <p>
24278                 <span class="blue">Max = 2.01&#949; (Mean = 0.584&#949;)</span>
24279               </p>
24280             </td>
24281 <td>
24282               <p>
24283                 <span class="blue">Max = 2.01&#949; (Mean = 0.593&#949;)</span>
24284               </p>
24285             </td>
24286 <td>
24287               <p>
24288                 <span class="blue">Max = 1.92&#949; (Mean = 0.567&#949;)</span>
24289               </p>
24290             </td>
24291 </tr>
24292 <tr>
24293 <td>
24294               <p>
24295                 Jacobi Elliptic: Random Small Values
24296               </p>
24297             </td>
24298 <td>
24299               <p>
24300                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24301                 2.1:</em></span> Max = 11.7&#949; (Mean = 1.65&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
24302                 other failures.</a>)
24303               </p>
24304             </td>
24305 <td>
24306               <p>
24307                 <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
24308               </p>
24309             </td>
24310 <td>
24311               <p>
24312                 <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
24313               </p>
24314             </td>
24315 <td>
24316               <p>
24317                 <span class="blue">Max = 2.11&#949; (Mean = 0.385&#949;)</span>
24318               </p>
24319             </td>
24320 </tr>
24321 <tr>
24322 <td>
24323               <p>
24324                 Jacobi Elliptic: Modulus near 1
24325               </p>
24326             </td>
24327 <td>
24328               <p>
24329                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24330                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
24331                 other failures.</a>)
24332               </p>
24333             </td>
24334 <td>
24335               <p>
24336                 <span class="blue">Max = 109&#949; (Mean = 7.35&#949;)</span>
24337               </p>
24338             </td>
24339 <td>
24340               <p>
24341                 <span class="blue">Max = 109&#949; (Mean = 7.38&#949;)</span>
24342               </p>
24343             </td>
24344 <td>
24345               <p>
24346                 <span class="blue">Max = 23.2&#949; (Mean = 1.85&#949;)</span>
24347               </p>
24348             </td>
24349 </tr>
24350 <tr>
24351 <td>
24352               <p>
24353                 Jacobi Elliptic: Large Phi
24354               </p>
24355             </td>
24356 <td>
24357               <p>
24358                 <span class="blue">Max = 12&#949; (Mean = 0.771&#949;)</span><br> <br>
24359                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04&#949; (Mean = 2.63e+03&#949;))
24360               </p>
24361             </td>
24362 <td>
24363               <p>
24364                 <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
24365               </p>
24366             </td>
24367 <td>
24368               <p>
24369                 <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
24370               </p>
24371             </td>
24372 <td>
24373               <p>
24374                 <span class="blue">Max = 4.36e+04&#949; (Mean = 2.54e+03&#949;)</span>
24375               </p>
24376             </td>
24377 </tr>
24378 </tbody>
24379 </table></div>
24380 </div>
24381 <br class="table-break"><div class="table">
24382 <a name="special_function_error_rates_rep.all_the_tables.table_jacobi_zeta"></a><p class="title"><b>Table&#160;160.&#160;Error rates for jacobi_zeta</b></p>
24383 <div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
24384 <colgroup>
24385 <col>
24386 <col>
24387 <col>
24388 <col>
24389 <col>
24390 </colgroup>
24391 <thead><tr>
24392 <th>
24393             </th>
24394 <th>
24395               <p>
24396                 GNU C++ version 7.1.0<br> linux<br> double
24397               </p>
24398             </th>
24399 <th>
24400               <p>
24401                 GNU C++ version 7.1.0<br> linux<br> long double
24402               </p>
24403             </th>
24404 <th>
24405               <p>
24406                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24407               </p>
24408             </th>
24409 <th>
24410               <p>
24411                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24412               </p>
24413             </th>
24414 </tr></thead>
24415 <tbody>
24416 <tr>
24417 <td>
24418               <p>
24419                 Elliptic Integral Jacobi Zeta: Mathworld Data
24420               </p>
24421             </td>
24422 <td>
24423               <p>
24424                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
24425               </p>
24426             </td>
24427 <td>
24428               <p>
24429                 <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
24430               </p>
24431             </td>
24432 <td>
24433               <p>
24434                 <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
24435               </p>
24436             </td>
24437 <td>
24438               <p>
24439                 <span class="blue">Max = 1.52&#949; (Mean = 0.357&#949;)</span>
24440               </p>
24441             </td>
24442 </tr>
24443 <tr>
24444 <td>
24445               <p>
24446                 Elliptic Integral Jacobi Zeta: Random Data
24447               </p>
24448             </td>
24449 <td>
24450               <p>
24451                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
24452               </p>
24453             </td>
24454 <td>
24455               <p>
24456                 <span class="blue">Max = 2.99&#949; (Mean = 0.824&#949;)</span>
24457               </p>
24458             </td>
24459 <td>
24460               <p>
24461                 <span class="blue">Max = 3.96&#949; (Mean = 1.06&#949;)</span>
24462               </p>
24463             </td>
24464 <td>
24465               <p>
24466                 <span class="blue">Max = 3.89&#949; (Mean = 0.824&#949;)</span>
24467               </p>
24468             </td>
24469 </tr>
24470 <tr>
24471 <td>
24472               <p>
24473                 Elliptic Integral Jacobi Zeta: Large Phi Values
24474               </p>
24475             </td>
24476 <td>
24477               <p>
24478                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
24479               </p>
24480             </td>
24481 <td>
24482               <p>
24483                 <span class="blue">Max = 2.92&#949; (Mean = 0.951&#949;)</span>
24484               </p>
24485             </td>
24486 <td>
24487               <p>
24488                 <span class="blue">Max = 3.05&#949; (Mean = 1.13&#949;)</span>
24489               </p>
24490             </td>
24491 <td>
24492               <p>
24493                 <span class="blue">Max = 2.52&#949; (Mean = 0.977&#949;)</span>
24494               </p>
24495             </td>
24496 </tr>
24497 </tbody>
24498 </table></div>
24499 </div>
24500 <br class="table-break"><div class="table">
24501 <a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_m_x_"></a><p class="title"><b>Table&#160;161.&#160;Error rates for laguerre(n, m, x)</b></p>
24502 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
24503 <colgroup>
24504 <col>
24505 <col>
24506 <col>
24507 <col>
24508 <col>
24509 </colgroup>
24510 <thead><tr>
24511 <th>
24512             </th>
24513 <th>
24514               <p>
24515                 GNU C++ version 7.1.0<br> linux<br> double
24516               </p>
24517             </th>
24518 <th>
24519               <p>
24520                 GNU C++ version 7.1.0<br> linux<br> long double
24521               </p>
24522             </th>
24523 <th>
24524               <p>
24525                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24526               </p>
24527             </th>
24528 <th>
24529               <p>
24530                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24531               </p>
24532             </th>
24533 </tr></thead>
24534 <tbody><tr>
24535 <td>
24536               <p>
24537                 Associated Laguerre Polynomials
24538               </p>
24539             </td>
24540 <td>
24541               <p>
24542                 <span class="blue">Max = 0.84&#949; (Mean = 0.0358&#949;)</span><br> <br>
24543                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434&#949; (Mean = 10.7&#949;))
24544               </p>
24545             </td>
24546 <td>
24547               <p>
24548                 <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span><br> <br>
24549                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 206&#949; (Mean = 6.86&#949;))
24550               </p>
24551             </td>
24552 <td>
24553               <p>
24554                 <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span>
24555               </p>
24556             </td>
24557 <td>
24558               <p>
24559                 <span class="blue">Max = 434&#949; (Mean = 11.1&#949;)</span>
24560               </p>
24561             </td>
24562 </tr></tbody>
24563 </table></div>
24564 </div>
24565 <br class="table-break"><div class="table">
24566 <a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_x_"></a><p class="title"><b>Table&#160;162.&#160;Error rates for laguerre(n, x)</b></p>
24567 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
24568 <colgroup>
24569 <col>
24570 <col>
24571 <col>
24572 <col>
24573 <col>
24574 </colgroup>
24575 <thead><tr>
24576 <th>
24577             </th>
24578 <th>
24579               <p>
24580                 GNU C++ version 7.1.0<br> linux<br> double
24581               </p>
24582             </th>
24583 <th>
24584               <p>
24585                 GNU C++ version 7.1.0<br> linux<br> long double
24586               </p>
24587             </th>
24588 <th>
24589               <p>
24590                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24591               </p>
24592             </th>
24593 <th>
24594               <p>
24595                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24596               </p>
24597             </th>
24598 </tr></thead>
24599 <tbody><tr>
24600 <td>
24601               <p>
24602                 Laguerre Polynomials
24603               </p>
24604             </td>
24605 <td>
24606               <p>
24607                 <span class="blue">Max = 6.82&#949; (Mean = 0.408&#949;)</span><br> <br>
24608                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03&#949; (Mean = 185&#949;))
24609               </p>
24610             </td>
24611 <td>
24612               <p>
24613                 <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span><br> <br>
24614                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.2e+03&#949; (Mean = 251&#949;))
24615               </p>
24616             </td>
24617 <td>
24618               <p>
24619                 <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span>
24620               </p>
24621             </td>
24622 <td>
24623               <p>
24624                 <span class="blue">Max = 3.1e+03&#949; (Mean = 185&#949;)</span>
24625               </p>
24626             </td>
24627 </tr></tbody>
24628 </table></div>
24629 </div>
24630 <br class="table-break"><div class="table">
24631 <a name="special_function_error_rates_rep.all_the_tables.table_legendre_p"></a><p class="title"><b>Table&#160;163.&#160;Error rates for legendre_p</b></p>
24632 <div class="table-contents"><table class="table" summary="Error rates for legendre_p">
24633 <colgroup>
24634 <col>
24635 <col>
24636 <col>
24637 <col>
24638 <col>
24639 </colgroup>
24640 <thead><tr>
24641 <th>
24642             </th>
24643 <th>
24644               <p>
24645                 GNU C++ version 7.1.0<br> linux<br> double
24646               </p>
24647             </th>
24648 <th>
24649               <p>
24650                 GNU C++ version 7.1.0<br> linux<br> long double
24651               </p>
24652             </th>
24653 <th>
24654               <p>
24655                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24656               </p>
24657             </th>
24658 <th>
24659               <p>
24660                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24661               </p>
24662             </th>
24663 </tr></thead>
24664 <tbody>
24665 <tr>
24666 <td>
24667               <p>
24668                 Legendre Polynomials: Small Values
24669               </p>
24670             </td>
24671 <td>
24672               <p>
24673                 <span class="blue">Max = 0.732&#949; (Mean = 0.0619&#949;)</span><br> <br>
24674                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211&#949; (Mean = 20.4&#949;))
24675               </p>
24676             </td>
24677 <td>
24678               <p>
24679                 <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span><br> <br>
24680                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 124&#949; (Mean = 13.2&#949;))
24681               </p>
24682             </td>
24683 <td>
24684               <p>
24685                 <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span>
24686               </p>
24687             </td>
24688 <td>
24689               <p>
24690                 <span class="blue">Max = 211&#949; (Mean = 20.4&#949;)</span>
24691               </p>
24692             </td>
24693 </tr>
24694 <tr>
24695 <td>
24696               <p>
24697                 Legendre Polynomials: Large Values
24698               </p>
24699             </td>
24700 <td>
24701               <p>
24702                 <span class="blue">Max = 0.632&#949; (Mean = 0.0693&#949;)</span><br> <br>
24703                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300&#949; (Mean = 33.2&#949;))
24704               </p>
24705             </td>
24706 <td>
24707               <p>
24708                 <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span><br> <br>
24709                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 343&#949; (Mean = 32.1&#949;))
24710               </p>
24711             </td>
24712 <td>
24713               <p>
24714                 <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span>
24715               </p>
24716             </td>
24717 <td>
24718               <p>
24719                 <span class="blue">Max = 300&#949; (Mean = 33.2&#949;)</span>
24720               </p>
24721             </td>
24722 </tr>
24723 </tbody>
24724 </table></div>
24725 </div>
24726 <br class="table-break"><div class="table">
24727 <a name="special_function_error_rates_rep.all_the_tables.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;164.&#160;Error rates for legendre_p (associated)</b></p>
24728 <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
24729 <colgroup>
24730 <col>
24731 <col>
24732 <col>
24733 <col>
24734 <col>
24735 </colgroup>
24736 <thead><tr>
24737 <th>
24738             </th>
24739 <th>
24740               <p>
24741                 GNU C++ version 7.1.0<br> linux<br> double
24742               </p>
24743             </th>
24744 <th>
24745               <p>
24746                 GNU C++ version 7.1.0<br> linux<br> long double
24747               </p>
24748             </th>
24749 <th>
24750               <p>
24751                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24752               </p>
24753             </th>
24754 <th>
24755               <p>
24756                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24757               </p>
24758             </th>
24759 </tr></thead>
24760 <tbody><tr>
24761 <td>
24762               <p>
24763                 Associated Legendre Polynomials: Small Values
24764               </p>
24765             </td>
24766 <td>
24767               <p>
24768                 <span class="blue">Max = 0.999&#949; (Mean = 0.05&#949;)</span><br> <br>
24769                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121&#949; (Mean = 6.75&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And
24770                 other failures.</a>)
24771               </p>
24772             </td>
24773 <td>
24774               <p>
24775                 <span class="blue">Max = 175&#949; (Mean = 9.88&#949;)</span><br> <br>
24776                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 175&#949; (Mean = 9.36&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And
24777                 other failures.</a>)
24778               </p>
24779             </td>
24780 <td>
24781               <p>
24782                 <span class="blue">Max = 77.7&#949; (Mean = 5.59&#949;)</span>
24783               </p>
24784             </td>
24785 <td>
24786               <p>
24787                 <span class="blue">Max = 121&#949; (Mean = 7.14&#949;)</span>
24788               </p>
24789             </td>
24790 </tr></tbody>
24791 </table></div>
24792 </div>
24793 <br class="table-break"><div class="table">
24794 <a name="special_function_error_rates_rep.all_the_tables.table_legendre_q"></a><p class="title"><b>Table&#160;165.&#160;Error rates for legendre_q</b></p>
24795 <div class="table-contents"><table class="table" summary="Error rates for legendre_q">
24796 <colgroup>
24797 <col>
24798 <col>
24799 <col>
24800 <col>
24801 <col>
24802 </colgroup>
24803 <thead><tr>
24804 <th>
24805             </th>
24806 <th>
24807               <p>
24808                 GNU C++ version 7.1.0<br> linux<br> double
24809               </p>
24810             </th>
24811 <th>
24812               <p>
24813                 GNU C++ version 7.1.0<br> linux<br> long double
24814               </p>
24815             </th>
24816 <th>
24817               <p>
24818                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24819               </p>
24820             </th>
24821 <th>
24822               <p>
24823                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24824               </p>
24825             </th>
24826 </tr></thead>
24827 <tbody>
24828 <tr>
24829 <td>
24830               <p>
24831                 Legendre Polynomials: Small Values
24832               </p>
24833             </td>
24834 <td>
24835               <p>
24836                 <span class="blue">Max = 0.612&#949; (Mean = 0.0517&#949;)</span><br> <br>
24837                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4&#949; (Mean = 7.46&#949;))
24838               </p>
24839             </td>
24840 <td>
24841               <p>
24842                 <span class="blue">Max = 50.9&#949; (Mean = 9&#949;)</span>
24843               </p>
24844             </td>
24845 <td>
24846               <p>
24847                 <span class="blue">Max = 50.9&#949; (Mean = 8.98&#949;)</span>
24848               </p>
24849             </td>
24850 <td>
24851               <p>
24852                 <span class="blue">Max = 46.4&#949; (Mean = 7.32&#949;)</span>
24853               </p>
24854             </td>
24855 </tr>
24856 <tr>
24857 <td>
24858               <p>
24859                 Legendre Polynomials: Large Values
24860               </p>
24861             </td>
24862 <td>
24863               <p>
24864                 <span class="blue">Max = 2.49&#949; (Mean = 0.202&#949;)</span><br> <br>
24865                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03&#949; (Mean = 366&#949;))
24866               </p>
24867             </td>
24868 <td>
24869               <p>
24870                 <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
24871               </p>
24872             </td>
24873 <td>
24874               <p>
24875                 <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
24876               </p>
24877             </td>
24878 <td>
24879               <p>
24880                 <span class="blue">Max = 4.6e+03&#949; (Mean = 366&#949;)</span>
24881               </p>
24882             </td>
24883 </tr>
24884 </tbody>
24885 </table></div>
24886 </div>
24887 <br class="table-break"><div class="table">
24888 <a name="special_function_error_rates_rep.all_the_tables.table_lgamma"></a><p class="title"><b>Table&#160;166.&#160;Error rates for lgamma</b></p>
24889 <div class="table-contents"><table class="table" summary="Error rates for lgamma">
24890 <colgroup>
24891 <col>
24892 <col>
24893 <col>
24894 <col>
24895 <col>
24896 </colgroup>
24897 <thead><tr>
24898 <th>
24899             </th>
24900 <th>
24901               <p>
24902                 GNU C++ version 7.1.0<br> linux<br> double
24903               </p>
24904             </th>
24905 <th>
24906               <p>
24907                 GNU C++ version 7.1.0<br> linux<br> long double
24908               </p>
24909             </th>
24910 <th>
24911               <p>
24912                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
24913               </p>
24914             </th>
24915 <th>
24916               <p>
24917                 Microsoft Visual C++ version 14.1<br> Win32<br> double
24918               </p>
24919             </th>
24920 </tr></thead>
24921 <tbody>
24922 <tr>
24923 <td>
24924               <p>
24925                 factorials
24926               </p>
24927             </td>
24928 <td>
24929               <p>
24930                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24931                 2.1:</em></span> Max = 33.6&#949; (Mean = 2.78&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
24932                 Max = 1.55&#949; (Mean = 0.592&#949;))
24933               </p>
24934             </td>
24935 <td>
24936               <p>
24937                 <span class="blue">Max = 0.991&#949; (Mean = 0.308&#949;)</span><br> <br>
24938                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))<br>
24939                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))
24940               </p>
24941             </td>
24942 <td>
24943               <p>
24944                 <span class="blue">Max = 0.991&#949; (Mean = 0.383&#949;)</span><br> <br>
24945                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.36&#949; (Mean = 0.476&#949;))
24946               </p>
24947             </td>
24948 <td>
24949               <p>
24950                 <span class="blue">Max = 0.914&#949; (Mean = 0.175&#949;)</span><br> <br>
24951                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.958&#949; (Mean = 0.38&#949;))
24952               </p>
24953             </td>
24954 </tr>
24955 <tr>
24956 <td>
24957               <p>
24958                 near 0
24959               </p>
24960             </td>
24961 <td>
24962               <p>
24963                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24964                 2.1:</em></span> Max = 5.21&#949; (Mean = 1.57&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
24965                 Max = 0&#949; (Mean = 0&#949;))
24966               </p>
24967             </td>
24968 <td>
24969               <p>
24970                 <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
24971                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))<br>
24972                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
24973               </p>
24974             </td>
24975 <td>
24976               <p>
24977                 <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
24978                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
24979               </p>
24980             </td>
24981 <td>
24982               <p>
24983                 <span class="blue">Max = 0.964&#949; (Mean = 0.462&#949;)</span><br> <br>
24984                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.962&#949; (Mean = 0.372&#949;))
24985               </p>
24986             </td>
24987 </tr>
24988 <tr>
24989 <td>
24990               <p>
24991                 near 1
24992               </p>
24993             </td>
24994 <td>
24995               <p>
24996                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
24997                 2.1:</em></span> Max = 442&#949; (Mean = 88.8&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
24998                 Max = 7.99e+04&#949; (Mean = 1.68e+04&#949;))
24999               </p>
25000             </td>
25001 <td>
25002               <p>
25003                 <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
25004                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))<br>
25005                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))
25006               </p>
25007             </td>
25008 <td>
25009               <p>
25010                 <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
25011                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.71&#949; (Mean = 0.581&#949;))
25012               </p>
25013             </td>
25014 <td>
25015               <p>
25016                 <span class="blue">Max = 0.867&#949; (Mean = 0.468&#949;)</span><br> <br>
25017                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.906&#949; (Mean = 0.565&#949;))
25018               </p>
25019             </td>
25020 </tr>
25021 <tr>
25022 <td>
25023               <p>
25024                 near 2
25025               </p>
25026             </td>
25027 <td>
25028               <p>
25029                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
25030                 2.1:</em></span> Max = 1.17e+03&#949; (Mean = 274&#949;))<br> (<span class="emphasis"><em>Rmath
25031                 3.2.3:</em></span> Max = 2.63e+05&#949; (Mean = 5.84e+04&#949;))
25032               </p>
25033             </td>
25034 <td>
25035               <p>
25036                 <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
25037                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))<br>
25038                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))
25039               </p>
25040             </td>
25041 <td>
25042               <p>
25043                 <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
25044                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.598&#949; (Mean = 0.235&#949;))
25045               </p>
25046             </td>
25047 <td>
25048               <p>
25049                 <span class="blue">Max = 0.591&#949; (Mean = 0.159&#949;)</span><br> <br>
25050                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.473&#949;))
25051               </p>
25052             </td>
25053 </tr>
25054 <tr>
25055 <td>
25056               <p>
25057                 near -10
25058               </p>
25059             </td>
25060 <td>
25061               <p>
25062                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
25063                 2.1:</em></span> Max = 24.9&#949; (Mean = 4.6&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
25064                 Max = 4.22&#949; (Mean = 1.26&#949;))
25065               </p>
25066             </td>
25067 <td>
25068               <p>
25069                 <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
25070                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.997&#949; (Mean = 0.412&#949;))<br>
25071                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.412&#949;))
25072               </p>
25073             </td>
25074 <td>
25075               <p>
25076                 <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
25077                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.04&#949; (Mean = 1.01&#949;))
25078               </p>
25079             </td>
25080 <td>
25081               <p>
25082                 <span class="blue">Max = 4.22&#949; (Mean = 1.33&#949;)</span><br> <br>
25083                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.444&#949;))
25084               </p>
25085             </td>
25086 </tr>
25087 <tr>
25088 <td>
25089               <p>
25090                 near -55
25091               </p>
25092             </td>
25093 <td>
25094               <p>
25095                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
25096                 2.1:</em></span> Max = 7.02&#949; (Mean = 1.47&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
25097                 Max = 250&#949; (Mean = 60.9&#949;))
25098               </p>
25099             </td>
25100 <td>
25101               <p>
25102                 <span class="blue">Max = 0.821&#949; (Mean = 0.513&#949;)</span><br> <br>
25103                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))<br>
25104                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))
25105               </p>
25106             </td>
25107 <td>
25108               <p>
25109                 <span class="blue">Max = 1.59&#949; (Mean = 0.587&#949;)</span><br> <br>
25110                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.821&#949; (Mean = 0.674&#949;))
25111               </p>
25112             </td>
25113 <td>
25114               <p>
25115                 <span class="blue">Max = 0.821&#949; (Mean = 0.419&#949;)</span><br> <br>
25116                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 249&#949; (Mean = 43.1&#949;))
25117               </p>
25118             </td>
25119 </tr>
25120 </tbody>
25121 </table></div>
25122 </div>
25123 <br class="table-break"><div class="table">
25124 <a name="special_function_error_rates_rep.all_the_tables.table_log1p"></a><p class="title"><b>Table&#160;167.&#160;Error rates for log1p</b></p>
25125 <div class="table-contents"><table class="table" summary="Error rates for log1p">
25126 <colgroup>
25127 <col>
25128 <col>
25129 <col>
25130 <col>
25131 <col>
25132 </colgroup>
25133 <thead><tr>
25134 <th>
25135             </th>
25136 <th>
25137               <p>
25138                 GNU C++ version 7.1.0<br> linux<br> long double
25139               </p>
25140             </th>
25141 <th>
25142               <p>
25143                 GNU C++ version 7.1.0<br> linux<br> double
25144               </p>
25145             </th>
25146 <th>
25147               <p>
25148                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25149               </p>
25150             </th>
25151 <th>
25152               <p>
25153                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25154               </p>
25155             </th>
25156 </tr></thead>
25157 <tbody><tr>
25158 <td>
25159               <p>
25160                 Random test data
25161               </p>
25162             </td>
25163 <td>
25164               <p>
25165                 <span class="blue">Max = 0.818&#949; (Mean = 0.227&#949;)</span><br> <br>
25166                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))<br>
25167                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))
25168               </p>
25169             </td>
25170 <td>
25171               <p>
25172                 <span class="blue">Max = 0.846&#949; (Mean = 0.153&#949;)</span><br> <br>
25173                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846&#949; (Mean = 0.153&#949;))
25174               </p>
25175             </td>
25176 <td>
25177               <p>
25178                 <span class="blue">Max = 2.3&#949; (Mean = 0.66&#949;)</span><br> <br>
25179                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.249&#949;))
25180               </p>
25181             </td>
25182 <td>
25183               <p>
25184                 <span class="blue">Max = 0.509&#949; (Mean = 0.057&#949;)</span><br> <br>
25185                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.509&#949; (Mean = 0.057&#949;))
25186               </p>
25187             </td>
25188 </tr></tbody>
25189 </table></div>
25190 </div>
25191 <br class="table-break"><div class="table">
25192 <a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF"></a><p class="title"><b>Table&#160;168.&#160;Error rates for non central beta CDF</b></p>
25193 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
25194 <colgroup>
25195 <col>
25196 <col>
25197 <col>
25198 <col>
25199 <col>
25200 </colgroup>
25201 <thead><tr>
25202 <th>
25203             </th>
25204 <th>
25205               <p>
25206                 GNU C++ version 7.1.0<br> linux<br> double
25207               </p>
25208             </th>
25209 <th>
25210               <p>
25211                 GNU C++ version 7.1.0<br> linux<br> long double
25212               </p>
25213             </th>
25214 <th>
25215               <p>
25216                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25217               </p>
25218             </th>
25219 <th>
25220               <p>
25221                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25222               </p>
25223             </th>
25224 </tr></thead>
25225 <tbody>
25226 <tr>
25227 <td>
25228               <p>
25229                 Non Central Beta, medium parameters
25230               </p>
25231             </td>
25232 <td>
25233               <p>
25234                 <span class="blue">Max = 0.998&#949; (Mean = 0.0649&#949;)</span><br> <br>
25235                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26&#949; (Mean
25236                 = 3.5e+24&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
25237                 other failures.</a>)</span>
25238               </p>
25239             </td>
25240 <td>
25241               <p>
25242                 <span class="blue">Max = 824&#949; (Mean = 27.4&#949;)</span>
25243               </p>
25244             </td>
25245 <td>
25246               <p>
25247                 <span class="blue">Max = 832&#949; (Mean = 38.1&#949;)</span>
25248               </p>
25249             </td>
25250 <td>
25251               <p>
25252                 <span class="blue">Max = 242&#949; (Mean = 31&#949;)</span>
25253               </p>
25254             </td>
25255 </tr>
25256 <tr>
25257 <td>
25258               <p>
25259                 Non Central Beta, large parameters
25260               </p>
25261             </td>
25262 <td>
25263               <p>
25264                 <span class="blue">Max = 1.18&#949; (Mean = 0.175&#949;)</span><br> <br>
25265                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36&#949; (Mean
25266                 = 1.19e+35&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
25267                 other failures.</a>)</span>
25268               </p>
25269             </td>
25270 <td>
25271               <p>
25272                 <span class="blue">Max = 2.5e+04&#949; (Mean = 3.78e+03&#949;)</span>
25273               </p>
25274             </td>
25275 <td>
25276               <p>
25277                 <span class="blue">Max = 2.57e+04&#949; (Mean = 4.45e+03&#949;)</span>
25278               </p>
25279             </td>
25280 <td>
25281               <p>
25282                 <span class="blue">Max = 3.66e+03&#949; (Mean = 500&#949;)</span>
25283               </p>
25284             </td>
25285 </tr>
25286 </tbody>
25287 </table></div>
25288 </div>
25289 <br class="table-break"><div class="table">
25290 <a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table&#160;169.&#160;Error rates for non central beta CDF complement</b></p>
25291 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
25292 <colgroup>
25293 <col>
25294 <col>
25295 <col>
25296 <col>
25297 <col>
25298 </colgroup>
25299 <thead><tr>
25300 <th>
25301             </th>
25302 <th>
25303               <p>
25304                 GNU C++ version 7.1.0<br> linux<br> double
25305               </p>
25306             </th>
25307 <th>
25308               <p>
25309                 GNU C++ version 7.1.0<br> linux<br> long double
25310               </p>
25311             </th>
25312 <th>
25313               <p>
25314                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25315               </p>
25316             </th>
25317 <th>
25318               <p>
25319                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25320               </p>
25321             </th>
25322 </tr></thead>
25323 <tbody>
25324 <tr>
25325 <td>
25326               <p>
25327                 Non Central Beta, medium parameters
25328               </p>
25329             </td>
25330 <td>
25331               <p>
25332                 <span class="blue">Max = 0.998&#949; (Mean = 0.0936&#949;)</span><br> <br>
25333                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97&#949; (Mean
25334                 = 1.37e+96&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
25335                 other failures.</a>)</span>
25336               </p>
25337             </td>
25338 <td>
25339               <p>
25340                 <span class="blue">Max = 396&#949; (Mean = 50.7&#949;)</span>
25341               </p>
25342             </td>
25343 <td>
25344               <p>
25345                 <span class="blue">Max = 554&#949; (Mean = 57.2&#949;)</span>
25346               </p>
25347             </td>
25348 <td>
25349               <p>
25350                 <span class="blue">Max = 624&#949; (Mean = 62.7&#949;)</span>
25351               </p>
25352             </td>
25353 </tr>
25354 <tr>
25355 <td>
25356               <p>
25357                 Non Central Beta, large parameters
25358               </p>
25359             </td>
25360 <td>
25361               <p>
25362                 <span class="blue">Max = 0.986&#949; (Mean = 0.188&#949;)</span><br> <br>
25363                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
25364                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
25365                 other failures.</a>)</span>
25366               </p>
25367             </td>
25368 <td>
25369               <p>
25370                 <span class="blue">Max = 6.83e+03&#949; (Mean = 993&#949;)</span>
25371               </p>
25372             </td>
25373 <td>
25374               <p>
25375                 <span class="blue">Max = 3.56e+03&#949; (Mean = 707&#949;)</span>
25376               </p>
25377             </td>
25378 <td>
25379               <p>
25380                 <span class="blue">Max = 1.25e+04&#949; (Mean = 1.49e+03&#949;)</span>
25381               </p>
25382             </td>
25383 </tr>
25384 </tbody>
25385 </table></div>
25386 </div>
25387 <br class="table-break"><div class="table">
25388 <a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table&#160;170.&#160;Error rates for non central chi squared CDF</b></p>
25389 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
25390 <colgroup>
25391 <col>
25392 <col>
25393 <col>
25394 <col>
25395 <col>
25396 </colgroup>
25397 <thead><tr>
25398 <th>
25399             </th>
25400 <th>
25401               <p>
25402                 GNU C++ version 7.1.0<br> linux<br> double
25403               </p>
25404             </th>
25405 <th>
25406               <p>
25407                 GNU C++ version 7.1.0<br> linux<br> long double
25408               </p>
25409             </th>
25410 <th>
25411               <p>
25412                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25413               </p>
25414             </th>
25415 <th>
25416               <p>
25417                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25418               </p>
25419             </th>
25420 </tr></thead>
25421 <tbody>
25422 <tr>
25423 <td>
25424               <p>
25425                 Non Central Chi Squared, medium parameters
25426               </p>
25427             </td>
25428 <td>
25429               <p>
25430                 <span class="blue">Max = 0.99&#949; (Mean = 0.0544&#949;)</span><br> <br>
25431                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727&#949; (Mean = 121&#949;))
25432               </p>
25433             </td>
25434 <td>
25435               <p>
25436                 <span class="blue">Max = 46.5&#949; (Mean = 10.3&#949;)</span>
25437               </p>
25438             </td>
25439 <td>
25440               <p>
25441                 <span class="blue">Max = 115&#949; (Mean = 13.9&#949;)</span>
25442               </p>
25443             </td>
25444 <td>
25445               <p>
25446                 <span class="blue">Max = 48.9&#949; (Mean = 10&#949;)</span>
25447               </p>
25448             </td>
25449 </tr>
25450 <tr>
25451 <td>
25452               <p>
25453                 Non Central Chi Squared, large parameters
25454               </p>
25455             </td>
25456 <td>
25457               <p>
25458                 <span class="blue">Max = 1.07&#949; (Mean = 0.102&#949;)</span><br> <br>
25459                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08&#949; (Mean
25460                 = 2.23e+07&#949;))</span>
25461               </p>
25462             </td>
25463 <td>
25464               <p>
25465                 <span class="blue">Max = 3.07e+03&#949; (Mean = 336&#949;)</span>
25466               </p>
25467             </td>
25468 <td>
25469               <p>
25470                 <span class="blue">Max = 6.17e+03&#949; (Mean = 677&#949;)</span>
25471               </p>
25472             </td>
25473 <td>
25474               <p>
25475                 <span class="blue">Max = 9.79e+03&#949; (Mean = 723&#949;)</span>
25476               </p>
25477             </td>
25478 </tr>
25479 </tbody>
25480 </table></div>
25481 </div>
25482 <br class="table-break"><div class="table">
25483 <a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table&#160;171.&#160;Error rates for non central chi squared CDF complement</b></p>
25484 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
25485 <colgroup>
25486 <col>
25487 <col>
25488 <col>
25489 <col>
25490 <col>
25491 </colgroup>
25492 <thead><tr>
25493 <th>
25494             </th>
25495 <th>
25496               <p>
25497                 GNU C++ version 7.1.0<br> linux<br> double
25498               </p>
25499             </th>
25500 <th>
25501               <p>
25502                 GNU C++ version 7.1.0<br> linux<br> long double
25503               </p>
25504             </th>
25505 <th>
25506               <p>
25507                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25508               </p>
25509             </th>
25510 <th>
25511               <p>
25512                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25513               </p>
25514             </th>
25515 </tr></thead>
25516 <tbody>
25517 <tr>
25518 <td>
25519               <p>
25520                 Non Central Chi Squared, medium parameters
25521               </p>
25522             </td>
25523 <td>
25524               <p>
25525                 <span class="blue">Max = 0.96&#949; (Mean = 0.0635&#949;)</span><br> <br>
25526                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
25527                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And
25528                 other failures.</a>)</span>
25529               </p>
25530             </td>
25531 <td>
25532               <p>
25533                 <span class="blue">Max = 107&#949; (Mean = 17.2&#949;)</span>
25534               </p>
25535             </td>
25536 <td>
25537               <p>
25538                 <span class="blue">Max = 171&#949; (Mean = 22.8&#949;)</span>
25539               </p>
25540             </td>
25541 <td>
25542               <p>
25543                 <span class="blue">Max = 98.6&#949; (Mean = 15.8&#949;)</span>
25544               </p>
25545             </td>
25546 </tr>
25547 <tr>
25548 <td>
25549               <p>
25550                 Non Central Chi Squared, large parameters
25551               </p>
25552             </td>
25553 <td>
25554               <p>
25555                 <span class="blue">Max = 2.11&#949; (Mean = 0.278&#949;)</span><br> <br>
25556                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
25557                 = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And
25558                 other failures.</a>)</span>
25559               </p>
25560             </td>
25561 <td>
25562               <p>
25563                 <span class="blue">Max = 5.02e+03&#949; (Mean = 630&#949;)</span>
25564               </p>
25565             </td>
25566 <td>
25567               <p>
25568                 <span class="blue">Max = 5.1e+03&#949; (Mean = 577&#949;)</span>
25569               </p>
25570             </td>
25571 <td>
25572               <p>
25573                 <span class="blue">Max = 5.43e+03&#949; (Mean = 705&#949;)</span>
25574               </p>
25575             </td>
25576 </tr>
25577 </tbody>
25578 </table></div>
25579 </div>
25580 <br class="table-break"><div class="table">
25581 <a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF"></a><p class="title"><b>Table&#160;172.&#160;Error rates for non central t CDF</b></p>
25582 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
25583 <colgroup>
25584 <col>
25585 <col>
25586 <col>
25587 <col>
25588 <col>
25589 </colgroup>
25590 <thead><tr>
25591 <th>
25592             </th>
25593 <th>
25594               <p>
25595                 GNU C++ version 7.1.0<br> linux<br> double
25596               </p>
25597             </th>
25598 <th>
25599               <p>
25600                 GNU C++ version 7.1.0<br> linux<br> long double
25601               </p>
25602             </th>
25603 <th>
25604               <p>
25605                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25606               </p>
25607             </th>
25608 <th>
25609               <p>
25610                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25611               </p>
25612             </th>
25613 </tr></thead>
25614 <tbody>
25615 <tr>
25616 <td>
25617               <p>
25618                 Non Central T
25619               </p>
25620             </td>
25621 <td>
25622               <p>
25623                 <span class="blue">Max = 0.796&#949; (Mean = 0.0691&#949;)</span><br> <br>
25624                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15&#949; (Mean
25625                 = 8.49e+14&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And
25626                 other failures.</a>)</span>
25627               </p>
25628             </td>
25629 <td>
25630               <p>
25631                 <span class="blue">Max = 139&#949; (Mean = 31&#949;)</span>
25632               </p>
25633             </td>
25634 <td>
25635               <p>
25636                 <span class="blue">Max = 145&#949; (Mean = 30.9&#949;)</span>
25637               </p>
25638             </td>
25639 <td>
25640               <p>
25641                 <span class="blue">Max = 135&#949; (Mean = 32.1&#949;)</span>
25642               </p>
25643             </td>
25644 </tr>
25645 <tr>
25646 <td>
25647               <p>
25648                 Non Central T (small non-centrality)
25649               </p>
25650             </td>
25651 <td>
25652               <p>
25653                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
25654                 3.2.3:</em></span> Max = 2.09e+03&#949; (Mean = 244&#949;))
25655               </p>
25656             </td>
25657 <td>
25658               <p>
25659                 <span class="blue">Max = 3.86&#949; (Mean = 1.4&#949;)</span>
25660               </p>
25661             </td>
25662 <td>
25663               <p>
25664                 <span class="blue">Max = 9.15&#949; (Mean = 2.13&#949;)</span>
25665               </p>
25666             </td>
25667 <td>
25668               <p>
25669                 <span class="blue">Max = 6.17&#949; (Mean = 1.45&#949;)</span>
25670               </p>
25671             </td>
25672 </tr>
25673 <tr>
25674 <td>
25675               <p>
25676                 Non Central T (large parameters)
25677               </p>
25678             </td>
25679 <td>
25680               <p>
25681                 <span class="blue">Max = 257&#949; (Mean = 72.1&#949;)</span><br> <br>
25682                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46&#949; (Mean = 0.657&#949;))
25683               </p>
25684             </td>
25685 <td>
25686               <p>
25687                 <span class="blue">Max = 5.26e+05&#949; (Mean = 1.48e+05&#949;)</span>
25688               </p>
25689             </td>
25690 <td>
25691               <p>
25692                 <span class="blue">Max = 5.24e+05&#949; (Mean = 1.47e+05&#949;)</span>
25693               </p>
25694             </td>
25695 <td>
25696               <p>
25697                 <span class="blue">Max = 286&#949; (Mean = 62.8&#949;)</span>
25698               </p>
25699             </td>
25700 </tr>
25701 </tbody>
25702 </table></div>
25703 </div>
25704 <br class="table-break"><div class="table">
25705 <a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF_complement"></a><p class="title"><b>Table&#160;173.&#160;Error rates for non central t CDF complement</b></p>
25706 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
25707 <colgroup>
25708 <col>
25709 <col>
25710 <col>
25711 <col>
25712 <col>
25713 </colgroup>
25714 <thead><tr>
25715 <th>
25716             </th>
25717 <th>
25718               <p>
25719                 GNU C++ version 7.1.0<br> linux<br> double
25720               </p>
25721             </th>
25722 <th>
25723               <p>
25724                 GNU C++ version 7.1.0<br> linux<br> long double
25725               </p>
25726             </th>
25727 <th>
25728               <p>
25729                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25730               </p>
25731             </th>
25732 <th>
25733               <p>
25734                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25735               </p>
25736             </th>
25737 </tr></thead>
25738 <tbody>
25739 <tr>
25740 <td>
25741               <p>
25742                 Non Central T
25743               </p>
25744             </td>
25745 <td>
25746               <p>
25747                 <span class="blue">Max = 0.707&#949; (Mean = 0.0497&#949;)</span><br> <br>
25748                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15&#949; (Mean
25749                 = 6.72e+14&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And
25750                 other failures.</a>)</span>
25751               </p>
25752             </td>
25753 <td>
25754               <p>
25755                 <span class="blue">Max = 201&#949; (Mean = 31.7&#949;)</span>
25756               </p>
25757             </td>
25758 <td>
25759               <p>
25760                 <span class="blue">Max = 340&#949; (Mean = 43.2&#949;)</span>
25761               </p>
25762             </td>
25763 <td>
25764               <p>
25765                 <span class="blue">Max = 154&#949; (Mean = 32.1&#949;)</span>
25766               </p>
25767             </td>
25768 </tr>
25769 <tr>
25770 <td>
25771               <p>
25772                 Non Central T (small non-centrality)
25773               </p>
25774             </td>
25775 <td>
25776               <p>
25777                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
25778                 3.2.3:</em></span> Max = 1.87e+03&#949; (Mean = 263&#949;))
25779               </p>
25780             </td>
25781 <td>
25782               <p>
25783                 <span class="blue">Max = 10.5&#949; (Mean = 2.13&#949;)</span>
25784               </p>
25785             </td>
25786 <td>
25787               <p>
25788                 <span class="blue">Max = 10.5&#949; (Mean = 2.39&#949;)</span>
25789               </p>
25790             </td>
25791 <td>
25792               <p>
25793                 <span class="blue">Max = 4.6&#949; (Mean = 1.63&#949;)</span>
25794               </p>
25795             </td>
25796 </tr>
25797 <tr>
25798 <td>
25799               <p>
25800                 Non Central T (large parameters)
25801               </p>
25802             </td>
25803 <td>
25804               <p>
25805                 <span class="blue">Max = 478&#949; (Mean = 96.3&#949;)</span><br> <br>
25806                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24&#949; (Mean = 0.945&#949;))
25807               </p>
25808             </td>
25809 <td>
25810               <p>
25811                 <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
25812               </p>
25813             </td>
25814 <td>
25815               <p>
25816                 <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
25817               </p>
25818             </td>
25819 <td>
25820               <p>
25821                 <span class="blue">Max = 227&#949; (Mean = 50.4&#949;)</span>
25822               </p>
25823             </td>
25824 </tr>
25825 </tbody>
25826 </table></div>
25827 </div>
25828 <br class="table-break"><div class="table">
25829 <a name="special_function_error_rates_rep.all_the_tables.table_owens_t"></a><p class="title"><b>Table&#160;174.&#160;Error rates for owens_t</b></p>
25830 <div class="table-contents"><table class="table" summary="Error rates for owens_t">
25831 <colgroup>
25832 <col>
25833 <col>
25834 <col>
25835 <col>
25836 <col>
25837 </colgroup>
25838 <thead><tr>
25839 <th>
25840             </th>
25841 <th>
25842               <p>
25843                 GNU C++ version 7.1.0<br> linux<br> double
25844               </p>
25845             </th>
25846 <th>
25847               <p>
25848                 GNU C++ version 7.1.0<br> linux<br> long double
25849               </p>
25850             </th>
25851 <th>
25852               <p>
25853                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25854               </p>
25855             </th>
25856 <th>
25857               <p>
25858                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25859               </p>
25860             </th>
25861 </tr></thead>
25862 <tbody>
25863 <tr>
25864 <td>
25865               <p>
25866                 Owens T (medium small values)
25867               </p>
25868             </td>
25869 <td>
25870               <p>
25871                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
25872               </p>
25873             </td>
25874 <td>
25875               <p>
25876                 <span class="blue">Max = 3.34&#949; (Mean = 0.944&#949;)</span>
25877               </p>
25878             </td>
25879 <td>
25880               <p>
25881                 <span class="blue">Max = 3.34&#949; (Mean = 0.911&#949;)</span>
25882               </p>
25883             </td>
25884 <td>
25885               <p>
25886                 <span class="blue">Max = 4.37&#949; (Mean = 0.98&#949;)</span>
25887               </p>
25888             </td>
25889 </tr>
25890 <tr>
25891 <td>
25892               <p>
25893                 Owens T (large and diverse values)
25894               </p>
25895             </td>
25896 <td>
25897               <p>
25898                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
25899               </p>
25900             </td>
25901 <td>
25902               <p>
25903                 <span class="blue">Max = 49&#949; (Mean = 2.16&#949;)</span>
25904               </p>
25905             </td>
25906 <td>
25907               <p>
25908                 <span class="blue">Max = 24.5&#949; (Mean = 1.39&#949;)</span>
25909               </p>
25910             </td>
25911 <td>
25912               <p>
25913                 <span class="blue">Max = 3.78&#949; (Mean = 0.621&#949;)</span>
25914               </p>
25915             </td>
25916 </tr>
25917 </tbody>
25918 </table></div>
25919 </div>
25920 <br class="table-break"><div class="table">
25921 <a name="special_function_error_rates_rep.all_the_tables.table_polygamma"></a><p class="title"><b>Table&#160;175.&#160;Error rates for polygamma</b></p>
25922 <div class="table-contents"><table class="table" summary="Error rates for polygamma">
25923 <colgroup>
25924 <col>
25925 <col>
25926 <col>
25927 <col>
25928 <col>
25929 </colgroup>
25930 <thead><tr>
25931 <th>
25932             </th>
25933 <th>
25934               <p>
25935                 GNU C++ version 7.1.0<br> linux<br> double
25936               </p>
25937             </th>
25938 <th>
25939               <p>
25940                 GNU C++ version 7.1.0<br> linux<br> long double
25941               </p>
25942             </th>
25943 <th>
25944               <p>
25945                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
25946               </p>
25947             </th>
25948 <th>
25949               <p>
25950                 Microsoft Visual C++ version 14.1<br> Win32<br> double
25951               </p>
25952             </th>
25953 </tr></thead>
25954 <tbody>
25955 <tr>
25956 <td>
25957               <p>
25958                 Mathematica Data
25959               </p>
25960             </td>
25961 <td>
25962               <p>
25963                 <span class="blue">Max = 0.824&#949; (Mean = 0.0574&#949;)</span><br> <br>
25964                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9&#949; (Mean = 12.8&#949;))<br> (<span class="emphasis"><em>Rmath
25965                 3.2.3:</em></span> Max = 108&#949; (Mean = 15.2&#949;))
25966               </p>
25967             </td>
25968 <td>
25969               <p>
25970                 <span class="blue">Max = 7.38&#949; (Mean = 1.84&#949;)</span>
25971               </p>
25972             </td>
25973 <td>
25974               <p>
25975                 <span class="blue">Max = 34.3&#949; (Mean = 7.65&#949;)</span>
25976               </p>
25977             </td>
25978 <td>
25979               <p>
25980                 <span class="blue">Max = 9.32&#949; (Mean = 1.95&#949;)</span>
25981               </p>
25982             </td>
25983 </tr>
25984 <tr>
25985 <td>
25986               <p>
25987                 Mathematica Data - large arguments
25988               </p>
25989             </td>
25990 <td>
25991               <p>
25992                 <span class="blue">Max = 0.998&#949; (Mean = 0.0592&#949;)</span><br> <br>
25993                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244&#949; (Mean = 32.8&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And
25994                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
25995                 <span class="red">Max = 1.71e+56&#949; (Mean = 1.01e+55&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And
25996                 other failures.</a>)</span>
25997               </p>
25998             </td>
25999 <td>
26000               <p>
26001                 <span class="blue">Max = 2.23&#949; (Mean = 0.323&#949;)</span>
26002               </p>
26003             </td>
26004 <td>
26005               <p>
26006                 <span class="blue">Max = 11.1&#949; (Mean = 0.848&#949;)</span>
26007               </p>
26008             </td>
26009 <td>
26010               <p>
26011                 <span class="blue">Max = 150&#949; (Mean = 13.9&#949;)</span>
26012               </p>
26013             </td>
26014 </tr>
26015 <tr>
26016 <td>
26017               <p>
26018                 Mathematica Data - negative arguments
26019               </p>
26020             </td>
26021 <td>
26022               <p>
26023                 <span class="blue">Max = 0.516&#949; (Mean = 0.022&#949;)</span><br> <br>
26024                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6&#949; (Mean = 3.04&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And
26025                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26026                 Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And
26027                 other failures.</a>)
26028               </p>
26029             </td>
26030 <td>
26031               <p>
26032                 <span class="blue">Max = 269&#949; (Mean = 87.7&#949;)</span>
26033               </p>
26034             </td>
26035 <td>
26036               <p>
26037                 <span class="blue">Max = 269&#949; (Mean = 88.4&#949;)</span>
26038               </p>
26039             </td>
26040 <td>
26041               <p>
26042                 <span class="blue">Max = 497&#949; (Mean = 129&#949;)</span>
26043               </p>
26044             </td>
26045 </tr>
26046 <tr>
26047 <td>
26048               <p>
26049                 Mathematica Data - large negative arguments
26050               </p>
26051             </td>
26052 <td>
26053               <p>
26054                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26055                 2.1:</em></span> Max = 1.79&#949; (Mean = 0.197&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And
26056                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26057                 Max = 0&#949; (Mean = 0&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And
26058                 other failures.</a>)
26059               </p>
26060             </td>
26061 <td>
26062               <p>
26063                 <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
26064               </p>
26065             </td>
26066 <td>
26067               <p>
26068                 <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
26069               </p>
26070             </td>
26071 <td>
26072               <p>
26073                 <span class="blue">Max = 162&#949; (Mean = 101&#949;)</span>
26074               </p>
26075             </td>
26076 </tr>
26077 <tr>
26078 <td>
26079               <p>
26080                 Mathematica Data - small arguments
26081               </p>
26082             </td>
26083 <td>
26084               <p>
26085                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26086                 2.1:</em></span> Max = 15.2&#949; (Mean = 5.03&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26087                 Max = 106&#949; (Mean = 20&#949;))
26088               </p>
26089             </td>
26090 <td>
26091               <p>
26092                 <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
26093               </p>
26094             </td>
26095 <td>
26096               <p>
26097                 <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
26098               </p>
26099             </td>
26100 <td>
26101               <p>
26102                 <span class="blue">Max = 3&#949; (Mean = 0.496&#949;)</span>
26103               </p>
26104             </td>
26105 </tr>
26106 <tr>
26107 <td>
26108               <p>
26109                 Mathematica Data - Large orders and other bug cases
26110               </p>
26111             </td>
26112 <td>
26113               <p>
26114                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26115                 2.1:</em></span> Max = 151&#949; (Mean = 39.3&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And
26116                 other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26117                 <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And
26118                 other failures.</a>)</span>
26119               </p>
26120             </td>
26121 <td>
26122               <p>
26123                 <span class="blue">Max = 54.5&#949; (Mean = 13.3&#949;)</span>
26124               </p>
26125             </td>
26126 <td>
26127               <p>
26128                 <span class="blue">Max = 145&#949; (Mean = 55.9&#949;)</span>
26129               </p>
26130             </td>
26131 <td>
26132               <p>
26133                 <span class="blue">Max = 200&#949; (Mean = 57.2&#949;)</span>
26134               </p>
26135             </td>
26136 </tr>
26137 </tbody>
26138 </table></div>
26139 </div>
26140 <br class="table-break"><div class="table">
26141 <a name="special_function_error_rates_rep.all_the_tables.table_powm1"></a><p class="title"><b>Table&#160;176.&#160;Error rates for powm1</b></p>
26142 <div class="table-contents"><table class="table" summary="Error rates for powm1">
26143 <colgroup>
26144 <col>
26145 <col>
26146 <col>
26147 <col>
26148 <col>
26149 </colgroup>
26150 <thead><tr>
26151 <th>
26152             </th>
26153 <th>
26154               <p>
26155                 GNU C++ version 7.1.0<br> linux<br> double
26156               </p>
26157             </th>
26158 <th>
26159               <p>
26160                 GNU C++ version 7.1.0<br> linux<br> long double
26161               </p>
26162             </th>
26163 <th>
26164               <p>
26165                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26166               </p>
26167             </th>
26168 <th>
26169               <p>
26170                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26171               </p>
26172             </th>
26173 </tr></thead>
26174 <tbody><tr>
26175 <td>
26176               <p>
26177                 powm1
26178               </p>
26179             </td>
26180 <td>
26181               <p>
26182                 <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
26183               </p>
26184             </td>
26185 <td>
26186               <p>
26187                 <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span>
26188               </p>
26189             </td>
26190 <td>
26191               <p>
26192                 <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span>
26193               </p>
26194             </td>
26195 <td>
26196               <p>
26197                 <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
26198               </p>
26199             </td>
26200 </tr></tbody>
26201 </table></div>
26202 </div>
26203 <br class="table-break"><div class="table">
26204 <a name="special_function_error_rates_rep.all_the_tables.table_sin_pi"></a><p class="title"><b>Table&#160;177.&#160;Error rates for sin_pi</b></p>
26205 <div class="table-contents"><table class="table" summary="Error rates for sin_pi">
26206 <colgroup>
26207 <col>
26208 <col>
26209 <col>
26210 <col>
26211 <col>
26212 </colgroup>
26213 <thead><tr>
26214 <th>
26215             </th>
26216 <th>
26217               <p>
26218                 GNU C++ version 7.1.0<br> linux<br> double
26219               </p>
26220             </th>
26221 <th>
26222               <p>
26223                 GNU C++ version 7.1.0<br> linux<br> long double
26224               </p>
26225             </th>
26226 <th>
26227               <p>
26228                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26229               </p>
26230             </th>
26231 <th>
26232               <p>
26233                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26234               </p>
26235             </th>
26236 </tr></thead>
26237 <tbody>
26238 <tr>
26239 <td>
26240               <p>
26241                 sin_pi and cos_pi
26242               </p>
26243             </td>
26244 <td>
26245               <p>
26246                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
26247               </p>
26248             </td>
26249 <td>
26250               <p>
26251                 <span class="blue">Max = 0.996&#949; (Mean = 0.335&#949;)</span>
26252               </p>
26253             </td>
26254 <td>
26255               <p>
26256                 <span class="blue">Max = 0.996&#949; (Mean = 0.336&#949;)</span>
26257               </p>
26258             </td>
26259 <td>
26260               <p>
26261                 <span class="blue">Max = 0.99&#949; (Mean = 0.328&#949;)</span>
26262               </p>
26263             </td>
26264 </tr>
26265 <tr>
26266 <td>
26267               <p>
26268                 sin_pi and cos_pi near integers and half integers
26269               </p>
26270             </td>
26271 <td>
26272               <p>
26273                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
26274               </p>
26275             </td>
26276 <td>
26277               <p>
26278                 <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
26279               </p>
26280             </td>
26281 <td>
26282               <p>
26283                 <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
26284               </p>
26285             </td>
26286 <td>
26287               <p>
26288                 <span class="blue">Max = 0.996&#949; (Mean = 0.343&#949;)</span>
26289               </p>
26290             </td>
26291 </tr>
26292 </tbody>
26293 </table></div>
26294 </div>
26295 <br class="table-break"><div class="table">
26296 <a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel"></a><p class="title"><b>Table&#160;178.&#160;Error rates for sph_bessel</b></p>
26297 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
26298 <colgroup>
26299 <col>
26300 <col>
26301 <col>
26302 <col>
26303 <col>
26304 </colgroup>
26305 <thead><tr>
26306 <th>
26307             </th>
26308 <th>
26309               <p>
26310                 GNU C++ version 7.1.0<br> linux<br> long double
26311               </p>
26312             </th>
26313 <th>
26314               <p>
26315                 GNU C++ version 7.1.0<br> linux<br> double
26316               </p>
26317             </th>
26318 <th>
26319               <p>
26320                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26321               </p>
26322             </th>
26323 <th>
26324               <p>
26325                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26326               </p>
26327             </th>
26328 </tr></thead>
26329 <tbody><tr>
26330 <td>
26331               <p>
26332                 Bessel j: Random Data
26333               </p>
26334             </td>
26335 <td>
26336               <p>
26337                 <span class="blue">Max = 243&#949; (Mean = 13.3&#949;)</span><br> <br>
26338                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.91e+06&#949; (Mean = 1.09e+05&#949;))
26339               </p>
26340             </td>
26341 <td>
26342               <p>
26343                 <span class="blue">Max = 0.978&#949; (Mean = 0.0445&#949;)</span><br> <br>
26344                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03&#949; (Mean = 107&#949;))
26345               </p>
26346             </td>
26347 <td>
26348               <p>
26349                 <span class="blue">Max = 243&#949; (Mean = 33.7&#949;)</span>
26350               </p>
26351             </td>
26352 <td>
26353               <p>
26354                 <span class="blue">Max = 245&#949; (Mean = 16.3&#949;)</span>
26355               </p>
26356             </td>
26357 </tr></tbody>
26358 </table></div>
26359 </div>
26360 <br class="table-break"><div class="table">
26361 <a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel_prime"></a><p class="title"><b>Table&#160;179.&#160;Error rates for sph_bessel_prime</b></p>
26362 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
26363 <colgroup>
26364 <col>
26365 <col>
26366 <col>
26367 <col>
26368 <col>
26369 </colgroup>
26370 <thead><tr>
26371 <th>
26372             </th>
26373 <th>
26374               <p>
26375                 GNU C++ version 7.1.0<br> linux<br> double
26376               </p>
26377             </th>
26378 <th>
26379               <p>
26380                 GNU C++ version 7.1.0<br> linux<br> long double
26381               </p>
26382             </th>
26383 <th>
26384               <p>
26385                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26386               </p>
26387             </th>
26388 <th>
26389               <p>
26390                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26391               </p>
26392             </th>
26393 </tr></thead>
26394 <tbody><tr>
26395 <td>
26396               <p>
26397                 Bessel j': Random Data
26398               </p>
26399             </td>
26400 <td>
26401               <p>
26402                 <span class="blue">Max = 0.753&#949; (Mean = 0.0343&#949;)</span>
26403               </p>
26404             </td>
26405 <td>
26406               <p>
26407                 <span class="blue">Max = 167&#949; (Mean = 12&#949;)</span>
26408               </p>
26409             </td>
26410 <td>
26411               <p>
26412                 <span class="blue">Max = 167&#949; (Mean = 33.2&#949;)</span>
26413               </p>
26414             </td>
26415 <td>
26416               <p>
26417                 <span class="blue">Max = 307&#949; (Mean = 25.2&#949;)</span>
26418               </p>
26419             </td>
26420 </tr></tbody>
26421 </table></div>
26422 </div>
26423 <br class="table-break"><div class="table">
26424 <a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann"></a><p class="title"><b>Table&#160;180.&#160;Error rates for sph_neumann</b></p>
26425 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
26426 <colgroup>
26427 <col>
26428 <col>
26429 <col>
26430 <col>
26431 <col>
26432 </colgroup>
26433 <thead><tr>
26434 <th>
26435             </th>
26436 <th>
26437               <p>
26438                 GNU C++ version 7.1.0<br> linux<br> long double
26439               </p>
26440             </th>
26441 <th>
26442               <p>
26443                 GNU C++ version 7.1.0<br> linux<br> double
26444               </p>
26445             </th>
26446 <th>
26447               <p>
26448                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26449               </p>
26450             </th>
26451 <th>
26452               <p>
26453                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26454               </p>
26455             </th>
26456 </tr></thead>
26457 <tbody><tr>
26458 <td>
26459               <p>
26460                 y: Random Data
26461               </p>
26462             </td>
26463 <td>
26464               <p>
26465                 <span class="blue">Max = 234&#949; (Mean = 19.5&#949;)</span><br> <br>
26466                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.6e+06&#949; (Mean = 1.4e+05&#949;))
26467               </p>
26468             </td>
26469 <td>
26470               <p>
26471                 <span class="blue">Max = 0.995&#949; (Mean = 0.0665&#949;)</span><br> <br>
26472                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04&#949; (Mean = 5.33e+03&#949;))
26473               </p>
26474             </td>
26475 <td>
26476               <p>
26477                 <span class="blue">Max = 234&#949; (Mean = 19.8&#949;)</span>
26478               </p>
26479             </td>
26480 <td>
26481               <p>
26482                 <span class="blue">Max = 281&#949; (Mean = 31.1&#949;)</span>
26483               </p>
26484             </td>
26485 </tr></tbody>
26486 </table></div>
26487 </div>
26488 <br class="table-break"><div class="table">
26489 <a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann_prime"></a><p class="title"><b>Table&#160;181.&#160;Error rates for sph_neumann_prime</b></p>
26490 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
26491 <colgroup>
26492 <col>
26493 <col>
26494 <col>
26495 <col>
26496 <col>
26497 </colgroup>
26498 <thead><tr>
26499 <th>
26500             </th>
26501 <th>
26502               <p>
26503                 GNU C++ version 7.1.0<br> linux<br> double
26504               </p>
26505             </th>
26506 <th>
26507               <p>
26508                 GNU C++ version 7.1.0<br> linux<br> long double
26509               </p>
26510             </th>
26511 <th>
26512               <p>
26513                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26514               </p>
26515             </th>
26516 <th>
26517               <p>
26518                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26519               </p>
26520             </th>
26521 </tr></thead>
26522 <tbody><tr>
26523 <td>
26524               <p>
26525                 y': Random Data
26526               </p>
26527             </td>
26528 <td>
26529               <p>
26530                 <span class="blue">Max = 0.988&#949; (Mean = 0.0869&#949;)</span>
26531               </p>
26532             </td>
26533 <td>
26534               <p>
26535                 <span class="blue">Max = 158&#949; (Mean = 18.8&#949;)</span>
26536               </p>
26537             </td>
26538 <td>
26539               <p>
26540                 <span class="blue">Max = 158&#949; (Mean = 20.2&#949;)</span>
26541               </p>
26542             </td>
26543 <td>
26544               <p>
26545                 <span class="blue">Max = 296&#949; (Mean = 25.6&#949;)</span>
26546               </p>
26547             </td>
26548 </tr></tbody>
26549 </table></div>
26550 </div>
26551 <br class="table-break"><div class="table">
26552 <a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_i"></a><p class="title"><b>Table&#160;182.&#160;Error rates for spherical_harmonic_i</b></p>
26553 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
26554 <colgroup>
26555 <col>
26556 <col>
26557 <col>
26558 <col>
26559 <col>
26560 </colgroup>
26561 <thead><tr>
26562 <th>
26563             </th>
26564 <th>
26565               <p>
26566                 GNU C++ version 7.1.0<br> linux<br> double
26567               </p>
26568             </th>
26569 <th>
26570               <p>
26571                 GNU C++ version 7.1.0<br> linux<br> long double
26572               </p>
26573             </th>
26574 <th>
26575               <p>
26576                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26577               </p>
26578             </th>
26579 <th>
26580               <p>
26581                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26582               </p>
26583             </th>
26584 </tr></thead>
26585 <tbody><tr>
26586 <td>
26587               <p>
26588                 Spherical Harmonics
26589               </p>
26590             </td>
26591 <td>
26592               <p>
26593                 <span class="blue">Max = 1.36&#949; (Mean = 0.0765&#949;)</span>
26594               </p>
26595             </td>
26596 <td>
26597               <p>
26598                 <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
26599               </p>
26600             </td>
26601 <td>
26602               <p>
26603                 <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
26604               </p>
26605             </td>
26606 <td>
26607               <p>
26608                 <span class="blue">Max = 2.27e+04&#949; (Mean = 725&#949;)</span>
26609               </p>
26610             </td>
26611 </tr></tbody>
26612 </table></div>
26613 </div>
26614 <br class="table-break"><div class="table">
26615 <a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_r"></a><p class="title"><b>Table&#160;183.&#160;Error rates for spherical_harmonic_r</b></p>
26616 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
26617 <colgroup>
26618 <col>
26619 <col>
26620 <col>
26621 <col>
26622 <col>
26623 </colgroup>
26624 <thead><tr>
26625 <th>
26626             </th>
26627 <th>
26628               <p>
26629                 GNU C++ version 7.1.0<br> linux<br> double
26630               </p>
26631             </th>
26632 <th>
26633               <p>
26634                 GNU C++ version 7.1.0<br> linux<br> long double
26635               </p>
26636             </th>
26637 <th>
26638               <p>
26639                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26640               </p>
26641             </th>
26642 <th>
26643               <p>
26644                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26645               </p>
26646             </th>
26647 </tr></thead>
26648 <tbody><tr>
26649 <td>
26650               <p>
26651                 Spherical Harmonics
26652               </p>
26653             </td>
26654 <td>
26655               <p>
26656                 <span class="blue">Max = 1.58&#949; (Mean = 0.0707&#949;)</span>
26657               </p>
26658             </td>
26659 <td>
26660               <p>
26661                 <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
26662               </p>
26663             </td>
26664 <td>
26665               <p>
26666                 <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
26667               </p>
26668             </td>
26669 <td>
26670               <p>
26671                 <span class="blue">Max = 2.27e+04&#949; (Mean = 725&#949;)</span>
26672               </p>
26673             </td>
26674 </tr></tbody>
26675 </table></div>
26676 </div>
26677 <br class="table-break"><div class="table">
26678 <a name="special_function_error_rates_rep.all_the_tables.table_sqrt1pm1"></a><p class="title"><b>Table&#160;184.&#160;Error rates for sqrt1pm1</b></p>
26679 <div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
26680 <colgroup>
26681 <col>
26682 <col>
26683 <col>
26684 <col>
26685 <col>
26686 </colgroup>
26687 <thead><tr>
26688 <th>
26689             </th>
26690 <th>
26691               <p>
26692                 GNU C++ version 7.1.0<br> linux<br> double
26693               </p>
26694             </th>
26695 <th>
26696               <p>
26697                 GNU C++ version 7.1.0<br> linux<br> long double
26698               </p>
26699             </th>
26700 <th>
26701               <p>
26702                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26703               </p>
26704             </th>
26705 <th>
26706               <p>
26707                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26708               </p>
26709             </th>
26710 </tr></thead>
26711 <tbody><tr>
26712 <td>
26713               <p>
26714                 sqrt1pm1
26715               </p>
26716             </td>
26717 <td>
26718               <p>
26719                 <span class="blue">Max = 1.3&#949; (Mean = 0.404&#949;)</span>
26720               </p>
26721             </td>
26722 <td>
26723               <p>
26724                 <span class="blue">Max = 1.33&#949; (Mean = 0.404&#949;)</span>
26725               </p>
26726             </td>
26727 <td>
26728               <p>
26729                 <span class="blue">Max = 1.54&#949; (Mean = 0.563&#949;)</span>
26730               </p>
26731             </td>
26732 <td>
26733               <p>
26734                 <span class="blue">Max = 1.35&#949; (Mean = 0.497&#949;)</span>
26735               </p>
26736             </td>
26737 </tr></tbody>
26738 </table></div>
26739 </div>
26740 <br class="table-break"><div class="table">
26741 <a name="special_function_error_rates_rep.all_the_tables.table_tgamma"></a><p class="title"><b>Table&#160;185.&#160;Error rates for tgamma</b></p>
26742 <div class="table-contents"><table class="table" summary="Error rates for tgamma">
26743 <colgroup>
26744 <col>
26745 <col>
26746 <col>
26747 <col>
26748 <col>
26749 </colgroup>
26750 <thead><tr>
26751 <th>
26752             </th>
26753 <th>
26754               <p>
26755                 GNU C++ version 7.1.0<br> linux<br> double
26756               </p>
26757             </th>
26758 <th>
26759               <p>
26760                 GNU C++ version 7.1.0<br> linux<br> long double
26761               </p>
26762             </th>
26763 <th>
26764               <p>
26765                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
26766               </p>
26767             </th>
26768 <th>
26769               <p>
26770                 Microsoft Visual C++ version 14.1<br> Win32<br> double
26771               </p>
26772             </th>
26773 </tr></thead>
26774 <tbody>
26775 <tr>
26776 <td>
26777               <p>
26778                 factorials
26779               </p>
26780             </td>
26781 <td>
26782               <p>
26783                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26784                 2.1:</em></span> Max = 3.95&#949; (Mean = 0.783&#949;))<br> (<span class="emphasis"><em>Rmath
26785                 3.2.3:</em></span> Max = 314&#949; (Mean = 93.4&#949;))
26786               </p>
26787             </td>
26788 <td>
26789               <p>
26790                 <span class="blue">Max = 2.67&#949; (Mean = 0.617&#949;)</span><br> <br>
26791                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))<br>
26792                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))
26793               </p>
26794             </td>
26795 <td>
26796               <p>
26797                 <span class="blue">Max = 172&#949; (Mean = 41&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
26798                 Max = 0&#949; (Mean = 0&#949;))
26799               </p>
26800             </td>
26801 <td>
26802               <p>
26803                 <span class="blue">Max = 1.85&#949; (Mean = 0.566&#949;)</span><br> <br>
26804                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.17&#949; (Mean = 0.928&#949;))
26805               </p>
26806             </td>
26807 </tr>
26808 <tr>
26809 <td>
26810               <p>
26811                 near 0
26812               </p>
26813             </td>
26814 <td>
26815               <p>
26816                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26817                 2.1:</em></span> Max = 4.51&#949; (Mean = 1.92&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26818                 Max = 1&#949; (Mean = 0.335&#949;))
26819               </p>
26820             </td>
26821 <td>
26822               <p>
26823                 <span class="blue">Max = 2&#949; (Mean = 0.608&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
26824                 Max = 1&#949; (Mean = 0.376&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
26825                 Max = 1&#949; (Mean = 0.376&#949;))
26826               </p>
26827             </td>
26828 <td>
26829               <p>
26830                 <span class="blue">Max = 2&#949; (Mean = 0.647&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
26831                 Max = 0.5&#949; (Mean = 0.0791&#949;))
26832               </p>
26833             </td>
26834 <td>
26835               <p>
26836                 <span class="blue">Max = 1.5&#949; (Mean = 0.635&#949;)</span><br> <br>
26837                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.405&#949;))
26838               </p>
26839             </td>
26840 </tr>
26841 <tr>
26842 <td>
26843               <p>
26844                 near 1
26845               </p>
26846             </td>
26847 <td>
26848               <p>
26849                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26850                 2.1:</em></span> Max = 4.41&#949; (Mean = 1.81&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26851                 Max = 1&#949; (Mean = 0.32&#949;))
26852               </p>
26853             </td>
26854 <td>
26855               <p>
26856                 <span class="blue">Max = 2.51&#949; (Mean = 1.02&#949;)</span><br> <br>
26857                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))<br>
26858                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))
26859               </p>
26860             </td>
26861 <td>
26862               <p>
26863                 <span class="blue">Max = 3.01&#949; (Mean = 1.06&#949;)</span><br> <br>
26864                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.175&#949;))
26865               </p>
26866             </td>
26867 <td>
26868               <p>
26869                 <span class="blue">Max = 1.1&#949; (Mean = 0.59&#949;)</span><br> <br>
26870                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.4&#949;))
26871               </p>
26872             </td>
26873 </tr>
26874 <tr>
26875 <td>
26876               <p>
26877                 near 2
26878               </p>
26879             </td>
26880 <td>
26881               <p>
26882                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26883                 2.1:</em></span> Max = 7.95&#949; (Mean = 3.12&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26884                 Max = 1&#949; (Mean = 0.191&#949;))
26885               </p>
26886             </td>
26887 <td>
26888               <p>
26889                 <span class="blue">Max = 4.1&#949; (Mean = 1.55&#949;)</span><br> <br>
26890                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))<br>
26891                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))
26892               </p>
26893             </td>
26894 <td>
26895               <p>
26896                 <span class="blue">Max = 5.01&#949; (Mean = 1.89&#949;)</span><br> <br>
26897                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
26898               </p>
26899             </td>
26900 <td>
26901               <p>
26902                 <span class="blue">Max = 2&#949; (Mean = 0.733&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
26903                 Max = 0&#949; (Mean = 0&#949;))
26904               </p>
26905             </td>
26906 </tr>
26907 <tr>
26908 <td>
26909               <p>
26910                 near -10
26911               </p>
26912             </td>
26913 <td>
26914               <p>
26915                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26916                 2.1:</em></span> Max = 2.6&#949; (Mean = 1.05&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26917                 Max = 34.9&#949; (Mean = 9.2&#949;))
26918               </p>
26919             </td>
26920 <td>
26921               <p>
26922                 <span class="blue">Max = 1.75&#949; (Mean = 0.895&#949;)</span><br> <br>
26923                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))<br>
26924                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))
26925               </p>
26926             </td>
26927 <td>
26928               <p>
26929                 <span class="blue">Max = 1.75&#949; (Mean = 0.819&#949;)</span><br> <br>
26930                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
26931               </p>
26932             </td>
26933 <td>
26934               <p>
26935                 <span class="blue">Max = 1.86&#949; (Mean = 0.881&#949;)</span><br> <br>
26936                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.866&#949; (Mean = 0.445&#949;))
26937               </p>
26938             </td>
26939 </tr>
26940 <tr>
26941 <td>
26942               <p>
26943                 near -55
26944               </p>
26945             </td>
26946 <td>
26947               <p>
26948                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
26949                 2.1:</em></span> Max = 1.8&#949; (Mean = 0.782&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
26950                 Max = 3.89e+04&#949; (Mean = 9.52e+03&#949;))
26951               </p>
26952             </td>
26953 <td>
26954               <p>
26955                 <span class="blue">Max = 2.69&#949; (Mean = 1.09&#949;)</span><br> <br>
26956                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))<br>
26957                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))
26958               </p>
26959             </td>
26960 <td>
26961               <p>
26962                 <span class="blue">Max = 98.5&#949; (Mean = 53.4&#949;)</span><br> <br>
26963                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
26964               </p>
26965             </td>
26966 <td>
26967               <p>
26968                 <span class="blue">Max = 2.7&#949; (Mean = 1.35&#949;)</span><br> <br>
26969                 (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.87e+04&#949; (Mean = 6.71e+03&#949;))
26970               </p>
26971             </td>
26972 </tr>
26973 </tbody>
26974 </table></div>
26975 </div>
26976 <br class="table-break"><div class="table">
26977 <a name="special_function_error_rates_rep.all_the_tables.table_tgamma1pm1"></a><p class="title"><b>Table&#160;186.&#160;Error rates for tgamma1pm1</b></p>
26978 <div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
26979 <colgroup>
26980 <col>
26981 <col>
26982 <col>
26983 <col>
26984 <col>
26985 </colgroup>
26986 <thead><tr>
26987 <th>
26988             </th>
26989 <th>
26990               <p>
26991                 GNU C++ version 7.1.0<br> linux<br> double
26992               </p>
26993             </th>
26994 <th>
26995               <p>
26996                 GNU C++ version 7.1.0<br> linux<br> long double
26997               </p>
26998             </th>
26999 <th>
27000               <p>
27001                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
27002               </p>
27003             </th>
27004 <th>
27005               <p>
27006                 Microsoft Visual C++ version 14.1<br> Win32<br> double
27007               </p>
27008             </th>
27009 </tr></thead>
27010 <tbody><tr>
27011 <td>
27012               <p>
27013                 tgamma1pm1(dz)
27014               </p>
27015             </td>
27016 <td>
27017               <p>
27018                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
27019               </p>
27020             </td>
27021 <td>
27022               <p>
27023                 <span class="blue">Max = 1.12&#949; (Mean = 0.49&#949;)</span>
27024               </p>
27025             </td>
27026 <td>
27027               <p>
27028                 <span class="blue">Max = 6.61&#949; (Mean = 0.84&#949;)</span>
27029               </p>
27030             </td>
27031 <td>
27032               <p>
27033                 <span class="blue">Max = 3.31&#949; (Mean = 0.517&#949;)</span>
27034               </p>
27035             </td>
27036 </tr></tbody>
27037 </table></div>
27038 </div>
27039 <br class="table-break"><div class="table">
27040 <a name="special_function_error_rates_rep.all_the_tables.table_tgamma_delta_ratio"></a><p class="title"><b>Table&#160;187.&#160;Error rates for tgamma_delta_ratio</b></p>
27041 <div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
27042 <colgroup>
27043 <col>
27044 <col>
27045 <col>
27046 <col>
27047 <col>
27048 </colgroup>
27049 <thead><tr>
27050 <th>
27051             </th>
27052 <th>
27053               <p>
27054                 GNU C++ version 7.1.0<br> linux<br> double
27055               </p>
27056             </th>
27057 <th>
27058               <p>
27059                 GNU C++ version 7.1.0<br> linux<br> long double
27060               </p>
27061             </th>
27062 <th>
27063               <p>
27064                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
27065               </p>
27066             </th>
27067 <th>
27068               <p>
27069                 Microsoft Visual C++ version 14.1<br> Win32<br> double
27070               </p>
27071             </th>
27072 </tr></thead>
27073 <tbody>
27074 <tr>
27075 <td>
27076               <p>
27077                 tgamma + small delta ratios
27078               </p>
27079             </td>
27080 <td>
27081               <p>
27082                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
27083               </p>
27084             </td>
27085 <td>
27086               <p>
27087                 <span class="blue">Max = 5.83&#949; (Mean = 1.3&#949;)</span>
27088               </p>
27089             </td>
27090 <td>
27091               <p>
27092                 <span class="blue">Max = 15.4&#949; (Mean = 2.09&#949;)</span>
27093               </p>
27094             </td>
27095 <td>
27096               <p>
27097                 <span class="blue">Max = 7.56&#949; (Mean = 1.31&#949;)</span>
27098               </p>
27099             </td>
27100 </tr>
27101 <tr>
27102 <td>
27103               <p>
27104                 tgamma + small delta ratios (negative delta)
27105               </p>
27106             </td>
27107 <td>
27108               <p>
27109                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
27110               </p>
27111             </td>
27112 <td>
27113               <p>
27114                 <span class="blue">Max = 7.94&#949; (Mean = 1.4&#949;)</span>
27115               </p>
27116             </td>
27117 <td>
27118               <p>
27119                 <span class="blue">Max = 18.3&#949; (Mean = 2.03&#949;)</span>
27120               </p>
27121             </td>
27122 <td>
27123               <p>
27124                 <span class="blue">Max = 7.43&#949; (Mean = 1.42&#949;)</span>
27125               </p>
27126             </td>
27127 </tr>
27128 <tr>
27129 <td>
27130               <p>
27131                 tgamma + small integer ratios
27132               </p>
27133             </td>
27134 <td>
27135               <p>
27136                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
27137               </p>
27138             </td>
27139 <td>
27140               <p>
27141                 <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
27142               </p>
27143             </td>
27144 <td>
27145               <p>
27146                 <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
27147               </p>
27148             </td>
27149 <td>
27150               <p>
27151                 <span class="blue">Max = 2.74&#949; (Mean = 0.736&#949;)</span>
27152               </p>
27153             </td>
27154 </tr>
27155 <tr>
27156 <td>
27157               <p>
27158                 tgamma + small integer ratios (negative delta)
27159               </p>
27160             </td>
27161 <td>
27162               <p>
27163                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
27164               </p>
27165             </td>
27166 <td>
27167               <p>
27168                 <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
27169               </p>
27170             </td>
27171 <td>
27172               <p>
27173                 <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
27174               </p>
27175             </td>
27176 <td>
27177               <p>
27178                 <span class="blue">Max = 2.15&#949; (Mean = 0.685&#949;)</span>
27179               </p>
27180             </td>
27181 </tr>
27182 <tr>
27183 <td>
27184               <p>
27185                 integer tgamma ratios
27186               </p>
27187             </td>
27188 <td>
27189               <p>
27190                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
27191               </p>
27192             </td>
27193 <td>
27194               <p>
27195                 <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
27196               </p>
27197             </td>
27198 <td>
27199               <p>
27200                 <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
27201               </p>
27202             </td>
27203 <td>
27204               <p>
27205                 <span class="blue">Max = 0.968&#949; (Mean = 0.386&#949;)</span>
27206               </p>
27207             </td>
27208 </tr>
27209 <tr>
27210 <td>
27211               <p>
27212                 integer tgamma ratios (negative delta)
27213               </p>
27214             </td>
27215 <td>
27216               <p>
27217                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
27218               </p>
27219             </td>
27220 <td>
27221               <p>
27222                 <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
27223               </p>
27224             </td>
27225 <td>
27226               <p>
27227                 <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
27228               </p>
27229             </td>
27230 <td>
27231               <p>
27232                 <span class="blue">Max = 0.974&#949; (Mean = 0.175&#949;)</span>
27233               </p>
27234             </td>
27235 </tr>
27236 </tbody>
27237 </table></div>
27238 </div>
27239 <br class="table-break"><div class="table">
27240 <a name="special_function_error_rates_rep.all_the_tables.table_tgamma_incomplete_"></a><p class="title"><b>Table&#160;188.&#160;Error rates for tgamma (incomplete)</b></p>
27241 <div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
27242 <colgroup>
27243 <col>
27244 <col>
27245 <col>
27246 <col>
27247 <col>
27248 </colgroup>
27249 <thead><tr>
27250 <th>
27251             </th>
27252 <th>
27253               <p>
27254                 GNU C++ version 7.1.0<br> linux<br> double
27255               </p>
27256             </th>
27257 <th>
27258               <p>
27259                 GNU C++ version 7.1.0<br> linux<br> long double
27260               </p>
27261             </th>
27262 <th>
27263               <p>
27264                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
27265               </p>
27266             </th>
27267 <th>
27268               <p>
27269                 Microsoft Visual C++ version 14.1<br> Win32<br> double
27270               </p>
27271             </th>
27272 </tr></thead>
27273 <tbody>
27274 <tr>
27275 <td>
27276               <p>
27277                 tgamma(a, z) medium values
27278               </p>
27279             </td>
27280 <td>
27281               <p>
27282                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27283                 2.1:</em></span> Max = 200&#949; (Mean = 13.3&#949;))
27284               </p>
27285             </td>
27286 <td>
27287               <p>
27288                 <span class="blue">Max = 8.47&#949; (Mean = 1.9&#949;)</span>
27289               </p>
27290             </td>
27291 <td>
27292               <p>
27293                 <span class="blue">Max = 412&#949; (Mean = 95.5&#949;)</span>
27294               </p>
27295             </td>
27296 <td>
27297               <p>
27298                 <span class="blue">Max = 8.14&#949; (Mean = 1.76&#949;)</span>
27299               </p>
27300             </td>
27301 </tr>
27302 <tr>
27303 <td>
27304               <p>
27305                 tgamma(a, z) small values
27306               </p>
27307             </td>
27308 <td>
27309               <p>
27310                 <span class="blue">Max = 0.753&#949; (Mean = 0.0474&#949;)</span><br> <br>
27311                 (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10&#949; (Mean
27312                 = 1.05e+09&#949;))</span>
27313               </p>
27314             </td>
27315 <td>
27316               <p>
27317                 <span class="blue">Max = 2.31&#949; (Mean = 0.775&#949;)</span>
27318               </p>
27319             </td>
27320 <td>
27321               <p>
27322                 <span class="blue">Max = 2.13&#949; (Mean = 0.717&#949;)</span>
27323               </p>
27324             </td>
27325 <td>
27326               <p>
27327                 <span class="blue">Max = 2.53&#949; (Mean = 0.66&#949;)</span>
27328               </p>
27329             </td>
27330 </tr>
27331 <tr>
27332 <td>
27333               <p>
27334                 tgamma(a, z) integer and half integer values
27335               </p>
27336             </td>
27337 <td>
27338               <p>
27339                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27340                 2.1:</em></span> Max = 117&#949; (Mean = 12.5&#949;))
27341               </p>
27342             </td>
27343 <td>
27344               <p>
27345                 <span class="blue">Max = 5.52&#949; (Mean = 1.48&#949;)</span>
27346               </p>
27347             </td>
27348 <td>
27349               <p>
27350                 <span class="blue">Max = 79.6&#949; (Mean = 20.9&#949;)</span>
27351               </p>
27352             </td>
27353 <td>
27354               <p>
27355                 <span class="blue">Max = 5.16&#949; (Mean = 1.33&#949;)</span>
27356               </p>
27357             </td>
27358 </tr>
27359 </tbody>
27360 </table></div>
27361 </div>
27362 <br class="table-break"><div class="table">
27363 <a name="special_function_error_rates_rep.all_the_tables.table_tgamma_lower"></a><p class="title"><b>Table&#160;189.&#160;Error rates for tgamma_lower</b></p>
27364 <div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
27365 <colgroup>
27366 <col>
27367 <col>
27368 <col>
27369 <col>
27370 <col>
27371 </colgroup>
27372 <thead><tr>
27373 <th>
27374             </th>
27375 <th>
27376               <p>
27377                 GNU C++ version 7.1.0<br> linux<br> double
27378               </p>
27379             </th>
27380 <th>
27381               <p>
27382                 GNU C++ version 7.1.0<br> linux<br> long double
27383               </p>
27384             </th>
27385 <th>
27386               <p>
27387                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
27388               </p>
27389             </th>
27390 <th>
27391               <p>
27392                 Microsoft Visual C++ version 14.1<br> Win32<br> double
27393               </p>
27394             </th>
27395 </tr></thead>
27396 <tbody>
27397 <tr>
27398 <td>
27399               <p>
27400                 tgamma(a, z) medium values
27401               </p>
27402             </td>
27403 <td>
27404               <p>
27405                 <span class="blue">Max = 0.833&#949; (Mean = 0.0315&#949;)</span><br> <br>
27406                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833&#949; (Mean = 0.0315&#949;))
27407               </p>
27408             </td>
27409 <td>
27410               <p>
27411                 <span class="blue">Max = 6.79&#949; (Mean = 1.46&#949;)</span>
27412               </p>
27413             </td>
27414 <td>
27415               <p>
27416                 <span class="blue">Max = 363&#949; (Mean = 63.8&#949;)</span>
27417               </p>
27418             </td>
27419 <td>
27420               <p>
27421                 <span class="blue">Max = 5.62&#949; (Mean = 1.49&#949;)</span>
27422               </p>
27423             </td>
27424 </tr>
27425 <tr>
27426 <td>
27427               <p>
27428                 tgamma(a, z) small values
27429               </p>
27430             </td>
27431 <td>
27432               <p>
27433                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27434                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
27435               </p>
27436             </td>
27437 <td>
27438               <p>
27439                 <span class="blue">Max = 1.97&#949; (Mean = 0.555&#949;)</span>
27440               </p>
27441             </td>
27442 <td>
27443               <p>
27444                 <span class="blue">Max = 1.97&#949; (Mean = 0.558&#949;)</span>
27445               </p>
27446             </td>
27447 <td>
27448               <p>
27449                 <span class="blue">Max = 1.57&#949; (Mean = 0.525&#949;)</span>
27450               </p>
27451             </td>
27452 </tr>
27453 <tr>
27454 <td>
27455               <p>
27456                 tgamma(a, z) integer and half integer values
27457               </p>
27458             </td>
27459 <td>
27460               <p>
27461                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27462                 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
27463               </p>
27464             </td>
27465 <td>
27466               <p>
27467                 <span class="blue">Max = 4.83&#949; (Mean = 1.15&#949;)</span>
27468               </p>
27469             </td>
27470 <td>
27471               <p>
27472                 <span class="blue">Max = 84.7&#949; (Mean = 17.5&#949;)</span>
27473               </p>
27474             </td>
27475 <td>
27476               <p>
27477                 <span class="blue">Max = 2.69&#949; (Mean = 0.849&#949;)</span>
27478               </p>
27479             </td>
27480 </tr>
27481 </tbody>
27482 </table></div>
27483 </div>
27484 <br class="table-break"><div class="table">
27485 <a name="special_function_error_rates_rep.all_the_tables.table_tgamma_ratio"></a><p class="title"><b>Table&#160;190.&#160;Error rates for tgamma_ratio</b></p>
27486 <div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
27487 <colgroup>
27488 <col>
27489 <col>
27490 <col>
27491 <col>
27492 <col>
27493 </colgroup>
27494 <thead><tr>
27495 <th>
27496             </th>
27497 <th>
27498               <p>
27499                 GNU C++ version 7.1.0<br> linux<br> double
27500               </p>
27501             </th>
27502 <th>
27503               <p>
27504                 GNU C++ version 7.1.0<br> linux<br> long double
27505               </p>
27506             </th>
27507 <th>
27508               <p>
27509                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
27510               </p>
27511             </th>
27512 <th>
27513               <p>
27514                 Microsoft Visual C++ version 14.1<br> Win32<br> double
27515               </p>
27516             </th>
27517 </tr></thead>
27518 <tbody><tr>
27519 <td>
27520               <p>
27521                 tgamma ratios
27522               </p>
27523             </td>
27524 <td>
27525               <p>
27526                 <span class="blue">Max = 0.694&#949; (Mean = 0.0347&#949;)</span>
27527               </p>
27528             </td>
27529 <td>
27530               <p>
27531                 <span class="blue">Max = 2.99&#949; (Mean = 1.15&#949;)</span>
27532               </p>
27533             </td>
27534 <td>
27535               <p>
27536                 <span class="blue">Max = 174&#949; (Mean = 61.2&#949;)</span>
27537               </p>
27538             </td>
27539 <td>
27540               <p>
27541                 <span class="blue">Max = 3.28&#949; (Mean = 1.12&#949;)</span>
27542               </p>
27543             </td>
27544 </tr></tbody>
27545 </table></div>
27546 </div>
27547 <br class="table-break"><div class="table">
27548 <a name="special_function_error_rates_rep.all_the_tables.table_trigamma"></a><p class="title"><b>Table&#160;191.&#160;Error rates for trigamma</b></p>
27549 <div class="table-contents"><table class="table" summary="Error rates for trigamma">
27550 <colgroup>
27551 <col>
27552 <col>
27553 <col>
27554 <col>
27555 <col>
27556 </colgroup>
27557 <thead><tr>
27558 <th>
27559             </th>
27560 <th>
27561               <p>
27562                 GNU C++ version 7.1.0<br> linux<br> double
27563               </p>
27564             </th>
27565 <th>
27566               <p>
27567                 GNU C++ version 7.1.0<br> linux<br> long double
27568               </p>
27569             </th>
27570 <th>
27571               <p>
27572                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
27573               </p>
27574             </th>
27575 <th>
27576               <p>
27577                 Microsoft Visual C++ version 14.1<br> Win32<br> double
27578               </p>
27579             </th>
27580 </tr></thead>
27581 <tbody><tr>
27582 <td>
27583               <p>
27584                 Mathematica Data
27585               </p>
27586             </td>
27587 <td>
27588               <p>
27589                 <span class="blue">Max = 0.998&#949; (Mean = 0.105&#949;)</span><br> <br>
27590                 (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04&#949; (Mean = 1.49e+03&#949;))<br>
27591                 (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04&#949; (Mean = 1.51e+03&#949;))
27592               </p>
27593             </td>
27594 <td>
27595               <p>
27596                 <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
27597               </p>
27598             </td>
27599 <td>
27600               <p>
27601                 <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
27602               </p>
27603             </td>
27604 <td>
27605               <p>
27606                 <span class="blue">Max = 1&#949; (Mean = 0.382&#949;)</span>
27607               </p>
27608             </td>
27609 </tr></tbody>
27610 </table></div>
27611 </div>
27612 <br class="table-break"><div class="table">
27613 <a name="special_function_error_rates_rep.all_the_tables.table_zeta"></a><p class="title"><b>Table&#160;192.&#160;Error rates for zeta</b></p>
27614 <div class="table-contents"><table class="table" summary="Error rates for zeta">
27615 <colgroup>
27616 <col>
27617 <col>
27618 <col>
27619 <col>
27620 <col>
27621 </colgroup>
27622 <thead><tr>
27623 <th>
27624             </th>
27625 <th>
27626               <p>
27627                 GNU C++ version 7.1.0<br> linux<br> long double
27628               </p>
27629             </th>
27630 <th>
27631               <p>
27632                 GNU C++ version 7.1.0<br> linux<br> double
27633               </p>
27634             </th>
27635 <th>
27636               <p>
27637                 Sun compiler version 0x5150<br> Sun Solaris<br> long double
27638               </p>
27639             </th>
27640 <th>
27641               <p>
27642                 Microsoft Visual C++ version 14.1<br> Win32<br> double
27643               </p>
27644             </th>
27645 </tr></thead>
27646 <tbody>
27647 <tr>
27648 <td>
27649               <p>
27650                 Zeta: Random values greater than 1
27651               </p>
27652             </td>
27653 <td>
27654               <p>
27655                 <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span><br> <br>
27656                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.45&#949; (Mean = 1&#949;))
27657               </p>
27658             </td>
27659 <td>
27660               <p>
27661                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27662                 2.1:</em></span> Max = 8.69&#949; (Mean = 1.03&#949;))
27663               </p>
27664             </td>
27665 <td>
27666               <p>
27667                 <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span>
27668               </p>
27669             </td>
27670 <td>
27671               <p>
27672                 <span class="blue">Max = 0.836&#949; (Mean = 0.093&#949;)</span>
27673               </p>
27674             </td>
27675 </tr>
27676 <tr>
27677 <td>
27678               <p>
27679                 Zeta: Random values less than 1
27680               </p>
27681             </td>
27682 <td>
27683               <p>
27684                 <span class="blue">Max = 7.03&#949; (Mean = 2.93&#949;)</span><br> <br>
27685                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 538&#949; (Mean = 59.3&#949;))
27686               </p>
27687             </td>
27688 <td>
27689               <p>
27690                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27691                 2.1:</em></span> Max = 137&#949; (Mean = 13.8&#949;))
27692               </p>
27693             </td>
27694 <td>
27695               <p>
27696                 <span class="blue">Max = 70.1&#949; (Mean = 17.1&#949;)</span>
27697               </p>
27698             </td>
27699 <td>
27700               <p>
27701                 <span class="blue">Max = 6.84&#949; (Mean = 3.12&#949;)</span>
27702               </p>
27703             </td>
27704 </tr>
27705 <tr>
27706 <td>
27707               <p>
27708                 Zeta: Values close to and greater than 1
27709               </p>
27710             </td>
27711 <td>
27712               <p>
27713                 <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span><br> <br>
27714                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.9e+06&#949; (Mean = 5.11e+05&#949;))
27715               </p>
27716             </td>
27717 <td>
27718               <p>
27719                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27720                 2.1:</em></span> Max = 7.73&#949; (Mean = 4.07&#949;))
27721               </p>
27722             </td>
27723 <td>
27724               <p>
27725                 <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span>
27726               </p>
27727             </td>
27728 <td>
27729               <p>
27730                 <span class="blue">Max = 0.994&#949; (Mean = 0.421&#949;)</span>
27731               </p>
27732             </td>
27733 </tr>
27734 <tr>
27735 <td>
27736               <p>
27737                 Zeta: Values close to and less than 1
27738               </p>
27739             </td>
27740 <td>
27741               <p>
27742                 <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span><br> <br>
27743                 (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.53e+06&#949; (Mean = 1.87e+06&#949;))
27744               </p>
27745             </td>
27746 <td>
27747               <p>
27748                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27749                 2.1:</em></span> Max = 0.991&#949; (Mean = 0.28&#949;))
27750               </p>
27751             </td>
27752 <td>
27753               <p>
27754                 <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span>
27755               </p>
27756             </td>
27757 <td>
27758               <p>
27759                 <span class="blue">Max = 0.991&#949; (Mean = 0.375&#949;)</span>
27760               </p>
27761             </td>
27762 </tr>
27763 <tr>
27764 <td>
27765               <p>
27766                 Zeta: Integer arguments
27767               </p>
27768             </td>
27769 <td>
27770               <p>
27771                 <span class="blue">Max = 9&#949; (Mean = 3.06&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
27772                 Max = 70.3&#949; (Mean = 17.4&#949;))
27773               </p>
27774             </td>
27775 <td>
27776               <p>
27777                 <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
27778                 2.1:</em></span> Max = 3.75&#949; (Mean = 1.1&#949;))
27779               </p>
27780             </td>
27781 <td>
27782               <p>
27783                 <span class="blue">Max = 28&#949; (Mean = 5.62&#949;)</span>
27784               </p>
27785             </td>
27786 <td>
27787               <p>
27788                 <span class="blue">Max = 9&#949; (Mean = 3&#949;)</span>
27789               </p>
27790             </td>
27791 </tr>
27792 </tbody>
27793 </table></div>
27794 </div>
27795 <br class="table-break">
27796 </div>
27797 </div>
27798 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
27799 <td align="left"><p><small>Last revised: March 09, 2018 at 13:43:44 GMT</small></p></td>
27800 <td align="right"><div class="copyright-footer"></div></td>
27801 </tr></table>
27802 <hr>
27803 <div class="spirit-nav"></div>
27804 </body>
27805 </html>