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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.logs_and_tables.all_table"></a><a class="link" href="all_table.html" title="Tables of Error Rates for all Functions">Tables of Error
  28       Rates for all Functions</a>
  29 </h3></div></div></div>
  30 <div class="table">
  31 <a name="math_toolkit.logs_and_tables.all_table.table_beta"></a><p class="title"><b>Table&#160;17.3.&#160;Error rates for beta</b></p>
  32 <div class="table-contents"><table class="table" summary="Error rates for beta">
  33 <colgroup>
  34 <col>
  35 <col>
  36 <col>
  37 <col>
  38 <col>
  39 </colgroup>
  40 <thead><tr>
  41 <th>
  42               </th>
  43 <th>
  44                 <p>
  45                   Microsoft Visual C++ version 12.0<br> Win32<br> double
  46                 </p>
  47               </th>
  48 <th>
  49                 <p>
  50                   GNU C++ version 5.1.0<br> linux<br> long double
  51                 </p>
  52               </th>
  53 <th>
  54                 <p>
  55                   GNU C++ version 5.1.0<br> linux<br> double
  56                 </p>
  57               </th>
  58 <th>
  59                 <p>
  60                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
  61                 </p>
  62               </th>
  63 </tr></thead>
  64 <tbody>
  65 <tr>
  66 <td>
  67                 <p>
  68                   Beta Function: Small Values
  69                 </p>
  70               </td>
  71 <td>
  72                 <p>
  73                   <span class="blue">Max = 1.75&#949; (Mean = 0.828&#949;)</span>
  74                 </p>
  75               </td>
  76 <td>
  77                 <p>
  78                   <span class="blue">Max = 2.65&#949; (Mean = 1.22&#949;)</span><br> <br>
  79                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 11.9&#949; (Mean = 7.03&#949;))
  80                 </p>
  81               </td>
  82 <td>
  83                 <p>
  84                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
  85                   1.16:</em></span> Max = 3.94&#949; (Mean = 1.44&#949;))<br> (<span class="emphasis"><em>Rmath
  86                   3.0.2:</em></span> Max = 1.14&#949; (Mean = 0.601&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
  87                   Max = 1.97&#949; (Mean = 0.934&#949;))
  88                 </p>
  89               </td>
  90 <td>
  91                 <p>
  92                   <span class="blue">Max = 2.86&#949; (Mean = 1.31&#949;)</span>
  93                 </p>
  94               </td>
  95 </tr>
  96 <tr>
  97 <td>
  98                 <p>
  99                   Beta Function: Medium Values
 100                 </p>
 101               </td>
 102 <td>
 103                 <p>
 104                   <span class="blue">Max = 99.1&#949; (Mean = 22.4&#949;)</span>
 105                 </p>
 106               </td>
 107 <td>
 108                 <p>
 109                   <span class="blue">Max = 60.4&#949; (Mean = 19.4&#949;)</span><br> <br>
 110                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.07e+03&#949; (Mean =
 111                   264&#949;))
 112                 </p>
 113               </td>
 114 <td>
 115                 <p>
 116                   <span class="blue">Max = 0.978&#949; (Mean = 0.0578&#949;)</span><br>
 117                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.18e+03&#949; (Mean = 238&#949;))<br>
 118                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.09e+03&#949; (Mean = 265&#949;))<br>
 119                   (<span class="emphasis"><em>Cephes:</em></span> Max = 1.5e+03&#949; (Mean = 329&#949;))
 120                 </p>
 121               </td>
 122 <td>
 123                 <p>
 124                   <span class="blue">Max = 107&#949; (Mean = 24.5&#949;)</span>
 125                 </p>
 126               </td>
 127 </tr>
 128 <tr>
 129 <td>
 130                 <p>
 131                   Beta Function: Divergent Values
 132                 </p>
 133               </td>
 134 <td>
 135                 <p>
 136                   <span class="blue">Max = 10.7&#949; (Mean = 2.22&#949;)</span>
 137                 </p>
 138               </td>
 139 <td>
 140                 <p>
 141                   <span class="blue">Max = 10.3&#949; (Mean = 2.41&#949;)</span><br> <br>
 142                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 128&#949; (Mean = 23.8&#949;))
 143                 </p>
 144               </td>
 145 <td>
 146                 <p>
 147                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 148                   1.16:</em></span> Max = 12.1&#949; (Mean = 1.99&#949;))<br> (<span class="emphasis"><em>Rmath
 149                   3.0.2:</em></span> Max = 176&#949; (Mean = 28&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
 150                   Max = 175&#949; (Mean = 22&#949;))
 151                 </p>
 152               </td>
 153 <td>
 154                 <p>
 155                   <span class="blue">Max = 19.7&#949; (Mean = 2.75&#949;)</span>
 156                 </p>
 157               </td>
 158 </tr>
 159 </tbody>
 160 </table></div>
 161 </div>
 162 <br class="table-break"><div class="table">
 163 <a name="math_toolkit.logs_and_tables.all_table.table_beta_incomplete_"></a><p class="title"><b>Table&#160;17.4.&#160;Error rates for beta (incomplete)</b></p>
 164 <div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
 165 <colgroup>
 166 <col>
 167 <col>
 168 <col>
 169 <col>
 170 <col>
 171 </colgroup>
 172 <thead><tr>
 173 <th>
 174               </th>
 175 <th>
 176                 <p>
 177                   Microsoft Visual C++ version 12.0<br> Win32<br> double
 178                 </p>
 179               </th>
 180 <th>
 181                 <p>
 182                   GNU C++ version 5.1.0<br> linux<br> double
 183                 </p>
 184               </th>
 185 <th>
 186                 <p>
 187                   GNU C++ version 5.1.0<br> linux<br> long double
 188                 </p>
 189               </th>
 190 <th>
 191                 <p>
 192                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
 193                 </p>
 194               </th>
 195 </tr></thead>
 196 <tbody>
 197 <tr>
 198 <td>
 199                 <p>
 200                   Incomplete Beta Function: Small Values
 201                 </p>
 202               </td>
 203 <td>
 204                 <p>
 205                   <span class="blue">Max = 11.1&#949; (Mean = 2.28&#949;)</span>
 206                 </p>
 207               </td>
 208 <td>
 209                 <p>
 210                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 211                 </p>
 212               </td>
 213 <td>
 214                 <p>
 215                   <span class="blue">Max = 12.5&#949; (Mean = 2.01&#949;)</span>
 216                 </p>
 217               </td>
 218 <td>
 219                 <p>
 220                   <span class="blue">Max = 18.7&#949; (Mean = 3.19&#949;)</span>
 221                 </p>
 222               </td>
 223 </tr>
 224 <tr>
 225 <td>
 226                 <p>
 227                   Incomplete Beta Function: Medium Values
 228                 </p>
 229               </td>
 230 <td>
 231                 <p>
 232                   <span class="blue">Max = 91.1&#949; (Mean = 12.7&#949;)</span>
 233                 </p>
 234               </td>
 235 <td>
 236                 <p>
 237                   <span class="blue">Max = 0.568&#949; (Mean = 0.0342&#949;)</span>
 238                 </p>
 239               </td>
 240 <td>
 241                 <p>
 242                   <span class="blue">Max = 67.1&#949; (Mean = 13.3&#949;)</span>
 243                 </p>
 244               </td>
 245 <td>
 246                 <p>
 247                   <span class="blue">Max = 174&#949; (Mean = 25&#949;)</span>
 248                 </p>
 249               </td>
 250 </tr>
 251 <tr>
 252 <td>
 253                 <p>
 254                   Incomplete Beta Function: Large and Diverse Values
 255                 </p>
 256               </td>
 257 <td>
 258                 <p>
 259                   <span class="blue">Max = 635&#949; (Mean = 29.5&#949;)</span>
 260                 </p>
 261               </td>
 262 <td>
 263                 <p>
 264                   <span class="blue">Max = 0.999&#949; (Mean = 0.0399&#949;)</span>
 265                 </p>
 266               </td>
 267 <td>
 268                 <p>
 269                   <span class="blue">Max = 6.84e+04&#949; (Mean = 2.76e+03&#949;)</span>
 270                 </p>
 271               </td>
 272 <td>
 273                 <p>
 274                   <span class="blue">Max = 6.86e+04&#949; (Mean = 2.79e+03&#949;)</span>
 275                 </p>
 276               </td>
 277 </tr>
 278 <tr>
 279 <td>
 280                 <p>
 281                   Incomplete Beta Function: Small Integer Values
 282                 </p>
 283               </td>
 284 <td>
 285                 <p>
 286                   <span class="blue">Max = 26.8&#949; (Mean = 6.61&#949;)</span>
 287                 </p>
 288               </td>
 289 <td>
 290                 <p>
 291                   <span class="blue">Max = 0.786&#949; (Mean = 0.0248&#949;)</span>
 292                 </p>
 293               </td>
 294 <td>
 295                 <p>
 296                   <span class="blue">Max = 10.2&#949; (Mean = 3.49&#949;)</span>
 297                 </p>
 298               </td>
 299 <td>
 300                 <p>
 301                   <span class="blue">Max = 51.8&#949; (Mean = 11&#949;)</span>
 302                 </p>
 303               </td>
 304 </tr>
 305 </tbody>
 306 </table></div>
 307 </div>
 308 <br class="table-break"><div class="table">
 309 <a name="math_toolkit.logs_and_tables.all_table.table_betac"></a><p class="title"><b>Table&#160;17.5.&#160;Error rates for betac</b></p>
 310 <div class="table-contents"><table class="table" summary="Error rates for betac">
 311 <colgroup>
 312 <col>
 313 <col>
 314 <col>
 315 <col>
 316 <col>
 317 </colgroup>
 318 <thead><tr>
 319 <th>
 320               </th>
 321 <th>
 322                 <p>
 323                   Microsoft Visual C++ version 12.0<br> Win32<br> double
 324                 </p>
 325               </th>
 326 <th>
 327                 <p>
 328                   GNU C++ version 5.1.0<br> linux<br> double
 329                 </p>
 330               </th>
 331 <th>
 332                 <p>
 333                   GNU C++ version 5.1.0<br> linux<br> long double
 334                 </p>
 335               </th>
 336 <th>
 337                 <p>
 338                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
 339                 </p>
 340               </th>
 341 </tr></thead>
 342 <tbody>
 343 <tr>
 344 <td>
 345                 <p>
 346                   Incomplete Beta Function: Small Values
 347                 </p>
 348               </td>
 349 <td>
 350                 <p>
 351                   <span class="blue">Max = 12&#949; (Mean = 2.43&#949;)</span>
 352                 </p>
 353               </td>
 354 <td>
 355                 <p>
 356                   <span class="blue">Max = 0.676&#949; (Mean = 0.0302&#949;)</span>
 357                 </p>
 358               </td>
 359 <td>
 360                 <p>
 361                   <span class="blue">Max = 7.75&#949; (Mean = 1.91&#949;)</span>
 362                 </p>
 363               </td>
 364 <td>
 365                 <p>
 366                   <span class="blue">Max = 12.6&#949; (Mean = 3.02&#949;)</span>
 367                 </p>
 368               </td>
 369 </tr>
 370 <tr>
 371 <td>
 372                 <p>
 373                   Incomplete Beta Function: Medium Values
 374                 </p>
 375               </td>
 376 <td>
 377                 <p>
 378                   <span class="blue">Max = 91.3&#949; (Mean = 14.8&#949;)</span>
 379                 </p>
 380               </td>
 381 <td>
 382                 <p>
 383                   <span class="blue">Max = 0.949&#949; (Mean = 0.0944&#949;)</span>
 384                 </p>
 385               </td>
 386 <td>
 387                 <p>
 388                   <span class="blue">Max = 63.5&#949; (Mean = 13.4&#949;)</span>
 389                 </p>
 390               </td>
 391 <td>
 392                 <p>
 393                   <span class="blue">Max = 97.6&#949; (Mean = 24.3&#949;)</span>
 394                 </p>
 395               </td>
 396 </tr>
 397 <tr>
 398 <td>
 399                 <p>
 400                   Incomplete Beta Function: Large and Diverse Values
 401                 </p>
 402               </td>
 403 <td>
 404                 <p>
 405                   <span class="blue">Max = 3.72e+003&#949; (Mean = 113&#949;)</span>
 406                 </p>
 407               </td>
 408 <td>
 409                 <p>
 410                   <span class="blue">Max = 1.12&#949; (Mean = 0.0458&#949;)</span>
 411                 </p>
 412               </td>
 413 <td>
 414                 <p>
 415                   <span class="blue">Max = 1.05e+05&#949; (Mean = 5.45e+03&#949;)</span>
 416                 </p>
 417               </td>
 418 <td>
 419                 <p>
 420                   <span class="blue">Max = 1.04e+05&#949; (Mean = 5.46e+03&#949;)</span>
 421                 </p>
 422               </td>
 423 </tr>
 424 <tr>
 425 <td>
 426                 <p>
 427                   Incomplete Beta Function: Small Integer Values
 428                 </p>
 429               </td>
 430 <td>
 431                 <p>
 432                   <span class="blue">Max = 26.7&#949; (Mean = 6.67&#949;)</span>
 433                 </p>
 434               </td>
 435 <td>
 436                 <p>
 437                   <span class="blue">Max = 0.586&#949; (Mean = 0.0314&#949;)</span>
 438                 </p>
 439               </td>
 440 <td>
 441                 <p>
 442                   <span class="blue">Max = 10.4&#949; (Mean = 3.54&#949;)</span>
 443                 </p>
 444               </td>
 445 <td>
 446                 <p>
 447                   <span class="blue">Max = 103&#949; (Mean = 17.4&#949;)</span>
 448                 </p>
 449               </td>
 450 </tr>
 451 </tbody>
 452 </table></div>
 453 </div>
 454 <br class="table-break"><div class="table">
 455 <a name="math_toolkit.logs_and_tables.all_table.table_binomial_coefficient"></a><p class="title"><b>Table&#160;17.6.&#160;Error rates for binomial_coefficient</b></p>
 456 <div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
 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                   Microsoft Visual C++ version 12.0<br> Win32<br> double
 470                 </p>
 471               </th>
 472 <th>
 473                 <p>
 474                   GNU C++ version 5.1.0<br> linux<br> double
 475                 </p>
 476               </th>
 477 <th>
 478                 <p>
 479                   GNU C++ version 5.1.0<br> linux<br> long double
 480                 </p>
 481               </th>
 482 <th>
 483                 <p>
 484                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
 485                 </p>
 486               </th>
 487 </tr></thead>
 488 <tbody>
 489 <tr>
 490 <td>
 491                 <p>
 492                   Binomials: small arguments
 493                 </p>
 494               </td>
 495 <td>
 496                 <p>
 497                   <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
 498                 </p>
 499               </td>
 500 <td>
 501                 <p>
 502                   <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
 503                 </p>
 504               </td>
 505 <td>
 506                 <p>
 507                   <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
 508                 </p>
 509               </td>
 510 <td>
 511                 <p>
 512                   <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
 513                 </p>
 514               </td>
 515 </tr>
 516 <tr>
 517 <td>
 518                 <p>
 519                   Binomials: large arguments
 520                 </p>
 521               </td>
 522 <td>
 523                 <p>
 524                   <span class="blue">Max = 24.3&#949; (Mean = 6.3&#949;)</span>
 525                 </p>
 526               </td>
 527 <td>
 528                 <p>
 529                   <span class="blue">Max = 0.939&#949; (Mean = 0.314&#949;)</span>
 530                 </p>
 531               </td>
 532 <td>
 533                 <p>
 534                   <span class="blue">Max = 26&#949; (Mean = 6.09&#949;)</span>
 535                 </p>
 536               </td>
 537 <td>
 538                 <p>
 539                   <span class="blue">Max = 54.1&#949; (Mean = 10.9&#949;)</span>
 540                 </p>
 541               </td>
 542 </tr>
 543 </tbody>
 544 </table></div>
 545 </div>
 546 <br class="table-break"><div class="table">
 547 <a name="math_toolkit.logs_and_tables.all_table.table_cbrt"></a><p class="title"><b>Table&#160;17.7.&#160;Error rates for cbrt</b></p>
 548 <div class="table-contents"><table class="table" summary="Error rates for cbrt">
 549 <colgroup>
 550 <col>
 551 <col>
 552 <col>
 553 <col>
 554 <col>
 555 </colgroup>
 556 <thead><tr>
 557 <th>
 558               </th>
 559 <th>
 560                 <p>
 561                   Microsoft Visual C++ version 12.0<br> Win32<br> double
 562                 </p>
 563               </th>
 564 <th>
 565                 <p>
 566                   GNU C++ version 5.1.0<br> linux<br> double
 567                 </p>
 568               </th>
 569 <th>
 570                 <p>
 571                   GNU C++ version 5.1.0<br> linux<br> long double
 572                 </p>
 573               </th>
 574 <th>
 575                 <p>
 576                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
 577                 </p>
 578               </th>
 579 </tr></thead>
 580 <tbody><tr>
 581 <td>
 582                 <p>
 583                   cbrt Function
 584                 </p>
 585               </td>
 586 <td>
 587                 <p>
 588                   <span class="blue">Max = 1.7&#949; (Mean = 0.565&#949;)</span><br> <br>
 589                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.7&#949; (Mean = 0.565&#949;))
 590                 </p>
 591               </td>
 592 <td>
 593                 <p>
 594                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Cephes:</em></span>
 595                   Max = 0&#949; (Mean = 0&#949;))
 596                 </p>
 597               </td>
 598 <td>
 599                 <p>
 600                   <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
 601                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))<br>
 602                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
 603                 </p>
 604               </td>
 605 <td>
 606                 <p>
 607                   <span class="blue">Max = 1.11&#949; (Mean = 0.424&#949;)</span><br> <br>
 608                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.11&#949; (Mean = 0.424&#949;))
 609                 </p>
 610               </td>
 611 </tr></tbody>
 612 </table></div>
 613 </div>
 614 <br class="table-break"><div class="table">
 615 <a name="math_toolkit.logs_and_tables.all_table.table_cos_pi"></a><p class="title"><b>Table&#160;17.8.&#160;Error rates for cos_pi</b></p>
 616 <div class="table-contents"><table class="table" summary="Error rates for cos_pi">
 617 <colgroup>
 618 <col>
 619 <col>
 620 <col>
 621 <col>
 622 <col>
 623 </colgroup>
 624 <thead><tr>
 625 <th>
 626               </th>
 627 <th>
 628                 <p>
 629                   Microsoft Visual C++ version 12.0<br> Win32<br> double
 630                 </p>
 631               </th>
 632 <th>
 633                 <p>
 634                   GNU C++ version 5.1.0<br> linux<br> double
 635                 </p>
 636               </th>
 637 <th>
 638                 <p>
 639                   GNU C++ version 5.1.0<br> linux<br> long double
 640                 </p>
 641               </th>
 642 <th>
 643                 <p>
 644                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
 645                 </p>
 646               </th>
 647 </tr></thead>
 648 <tbody>
 649 <tr>
 650 <td>
 651                 <p>
 652                   sin_pi and cos_pi
 653                 </p>
 654               </td>
 655 <td>
 656                 <p>
 657                   <span class="blue">Max = 0.996&#949; (Mean = 0.281&#949;)</span>
 658                 </p>
 659               </td>
 660 <td>
 661                 <p>
 662                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 663                 </p>
 664               </td>
 665 <td>
 666                 <p>
 667                   <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
 668                 </p>
 669               </td>
 670 <td>
 671                 <p>
 672                   <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
 673                 </p>
 674               </td>
 675 </tr>
 676 <tr>
 677 <td>
 678                 <p>
 679                   sin_pi and cos_pi near integers and half integers
 680                 </p>
 681               </td>
 682 <td>
 683                 <p>
 684                   <span class="blue">Max = 0.996&#949; (Mean = 0.298&#949;)</span>
 685                 </p>
 686               </td>
 687 <td>
 688                 <p>
 689                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
 690                 </p>
 691               </td>
 692 <td>
 693                 <p>
 694                   <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
 695                 </p>
 696               </td>
 697 <td>
 698                 <p>
 699                   <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
 700                 </p>
 701               </td>
 702 </tr>
 703 </tbody>
 704 </table></div>
 705 </div>
 706 <br class="table-break"><div class="table">
 707 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i"></a><p class="title"><b>Table&#160;17.9.&#160;Error rates for cyl_bessel_i</b></p>
 708 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
 709 <colgroup>
 710 <col>
 711 <col>
 712 <col>
 713 <col>
 714 <col>
 715 </colgroup>
 716 <thead><tr>
 717 <th>
 718               </th>
 719 <th>
 720                 <p>
 721                   Microsoft Visual C++ version 12.0<br> Win32<br> double
 722                 </p>
 723               </th>
 724 <th>
 725                 <p>
 726                   GNU C++ version 5.1.0<br> linux<br> long double
 727                 </p>
 728               </th>
 729 <th>
 730                 <p>
 731                   GNU C++ version 5.1.0<br> linux<br> double
 732                 </p>
 733               </th>
 734 <th>
 735                 <p>
 736                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
 737                 </p>
 738               </th>
 739 </tr></thead>
 740 <tbody>
 741 <tr>
 742 <td>
 743                 <p>
 744                   Bessel I0: Mathworld Data
 745                 </p>
 746               </td>
 747 <td>
 748                 <p>
 749                   <span class="blue">Max = 0.877&#949; (Mean = 0.549&#949;)</span>
 750                 </p>
 751               </td>
 752 <td>
 753                 <p>
 754                   <span class="blue">Max = 4.57&#949; (Mean = 2.1&#949;)</span><br> <br>
 755                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;)
 756                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_I0_Mathworld_Data">And
 757                   other failures.</a>)
 758                 </p>
 759               </td>
 760 <td>
 761                 <p>
 762                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 763                   1.16:</em></span> Max = 270&#949; (Mean = 91.6&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_I0_Mathworld_Data">And
 764                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
 765                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_I0_Mathworld_Data">And
 766                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
 767                   <span class="red">Max = 2.55e+43&#949; (Mean = 8.06e+42&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_I0_Mathworld_Data">And
 768                   other failures.</a>)</span>
 769                 </p>
 770               </td>
 771 <td>
 772                 <p>
 773                   <span class="blue">Max = 4.54&#949; (Mean = 2.11&#949;)</span>
 774                 </p>
 775               </td>
 776 </tr>
 777 <tr>
 778 <td>
 779                 <p>
 780                   Bessel I1: Mathworld Data
 781                 </p>
 782               </td>
 783 <td>
 784                 <p>
 785                   <span class="blue">Max = 0.885&#949; (Mean = 0.55&#949;)</span>
 786                 </p>
 787               </td>
 788 <td>
 789                 <p>
 790                   <span class="blue">Max = 7.83&#949; (Mean = 2.79&#949;)</span><br> <br>
 791                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;)
 792                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_I1_Mathworld_Data">And
 793                   other failures.</a>)
 794                 </p>
 795               </td>
 796 <td>
 797                 <p>
 798                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 799                   1.16:</em></span> Max = 128&#949; (Mean = 41&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_I1_Mathworld_Data">And
 800                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
 801                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_I1_Mathworld_Data">And
 802                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
 803                   <span class="red">Max = 1.28e+43&#949; (Mean = 4.05e+42&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_I1_Mathworld_Data">And
 804                   other failures.</a>)</span>
 805                 </p>
 806               </td>
 807 <td>
 808                 <p>
 809                   <span class="blue">Max = 6.52&#949; (Mean = 2.25&#949;)</span>
 810                 </p>
 811               </td>
 812 </tr>
 813 <tr>
 814 <td>
 815                 <p>
 816                   Bessel In: Mathworld Data
 817                 </p>
 818               </td>
 819 <td>
 820                 <p>
 821                   <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
 822                 </p>
 823               </td>
 824 <td>
 825                 <p>
 826                   <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
 827                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;)
 828                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_In_Mathworld_Data">And
 829                   other failures.</a>)
 830                 </p>
 831               </td>
 832 <td>
 833                 <p>
 834                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 835                   1.16:</em></span> Max = 2.31&#949; (Mean = 0.838&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_In_Mathworld_Data">And
 836                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
 837                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_In_Mathworld_Data">And
 838                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
 839                   <span class="red">Max = 3.67e+177&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_In_Mathworld_Data">And
 840                   other failures.</a>)</span>
 841                 </p>
 842               </td>
 843 <td>
 844                 <p>
 845                   <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
 846                 </p>
 847               </td>
 848 </tr>
 849 <tr>
 850 <td>
 851                 <p>
 852                   Bessel Iv: Mathworld Data
 853                 </p>
 854               </td>
 855 <td>
 856                 <p>
 857                   <span class="blue">Max = 2.97&#949; (Mean = 1.33&#949;)</span>
 858                 </p>
 859               </td>
 860 <td>
 861                 <p>
 862                   <span class="blue">Max = 4.12&#949; (Mean = 1.85&#949;)</span><br> <br>
 863                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 616&#949; (Mean = 221&#949;)
 864                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Mathworld_Data">And
 865                   other failures.</a>)
 866                 </p>
 867               </td>
 868 <td>
 869                 <p>
 870                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 871                   1.16:</em></span> Max = 5.95&#949; (Mean = 2.08&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Mathworld_Data">And
 872                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
 873                   Max = 1e+04&#949; (Mean = 3.18e+03&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
 874                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_Iv_Mathworld_Data">And
 875                   other failures.</a>)</span>
 876                 </p>
 877               </td>
 878 <td>
 879                 <p>
 880                   <span class="blue">Max = 4.12&#949; (Mean = 1.95&#949;)</span>
 881                 </p>
 882               </td>
 883 </tr>
 884 <tr>
 885 <td>
 886                 <p>
 887                   Bessel In: Random Data
 888                 </p>
 889               </td>
 890 <td>
 891                 <p>
 892                   <span class="blue">Max = 9.67&#949; (Mean = 1.89&#949;)</span>
 893                 </p>
 894               </td>
 895 <td>
 896                 <p>
 897                   <span class="blue">Max = 6.79&#949; (Mean = 1.15&#949;)</span><br> <br>
 898                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 645&#949; (Mean = 132&#949;))
 899                 </p>
 900               </td>
 901 <td>
 902                 <p>
 903                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 904                   1.16:</em></span> Max = 261&#949; (Mean = 53.2&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_In_Random_Data">And
 905                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
 906                   Max = 7.37&#949; (Mean = 2.4&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
 907                   = 4.22e+06&#949; (Mean = 2.26e+05&#949;))
 908                 </p>
 909               </td>
 910 <td>
 911                 <p>
 912                   <span class="blue">Max = 176&#949; (Mean = 39.2&#949;)</span>
 913                 </p>
 914               </td>
 915 </tr>
 916 <tr>
 917 <td>
 918                 <p>
 919                   Bessel Iv: Random Data
 920                 </p>
 921               </td>
 922 <td>
 923                 <p>
 924                   <span class="blue">Max = 7.46&#949; (Mean = 1.54&#949;)</span>
 925                 </p>
 926               </td>
 927 <td>
 928                 <p>
 929                   <span class="blue">Max = 8.35&#949; (Mean = 1.49&#949;)</span><br> <br>
 930                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.05e+03&#949; (Mean =
 931                   224&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Random_Data">And
 932                   other failures.</a>)
 933                 </p>
 934               </td>
 935 <td>
 936                 <p>
 937                   <span class="blue">Max = 0.661&#949; (Mean = 0.0441&#949;)</span><br>
 938                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 6.18e+03&#949; (Mean = 1.55e+03&#949;)
 939                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Random_Data">And
 940                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
 941                   <span class="red">Max = 4.28e+08&#949; (Mean = 2.85e+07&#949;))</span><br>
 942                   (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 6e+30&#949; (Mean
 943                   = 4e+29&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Cephes_Bessel_Iv_Random_Data">And
 944                   other failures.</a>)</span>
 945                 </p>
 946               </td>
 947 <td>
 948                 <p>
 949                   <span class="blue">Max = 283&#949; (Mean = 88.4&#949;)</span>
 950                 </p>
 951               </td>
 952 </tr>
 953 <tr>
 954 <td>
 955                 <p>
 956                   Bessel Iv: Mathworld Data (large values)
 957                 </p>
 958               </td>
 959 <td>
 960                 <p>
 961                   <span class="blue">Max = 3.67&#949; (Mean = 1.64&#949;)</span>
 962                 </p>
 963               </td>
 964 <td>
 965                 <p>
 966                   <span class="blue">Max = 14.7&#949; (Mean = 6.57&#949;)</span><br> <br>
 967                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 118&#949; (Mean = 57.2&#949;)
 968                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i__tr1_cmath__Bessel_Iv_Mathworld_Data_large_values_">And
 969                   other failures.</a>)
 970                 </p>
 971               </td>
 972 <td>
 973                 <p>
 974                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
 975                   1.16:</em></span> Max = 37&#949; (Mean = 18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_GSL_1_16_Bessel_Iv_Mathworld_Data_large_values_">And
 976                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
 977                   <span class="red">Max = 3.77e+168&#949; (Mean = 2.39e+168&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_Rmath_3_0_2_Bessel_Iv_Mathworld_Data_large_values_">And
 978                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
 979                   Max = 73.7&#949; (Mean = 58.5&#949;))
 980                 </p>
 981               </td>
 982 <td>
 983                 <p>
 984                   <span class="blue">Max = 14.7&#949; (Mean = 6.59&#949;)</span>
 985                 </p>
 986               </td>
 987 </tr>
 988 </tbody>
 989 </table></div>
 990 </div>
 991 <br class="table-break"><div class="table">
 992 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table&#160;17.10.&#160;Error rates for cyl_bessel_i (integer orders)</b></p>
 993 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
 994 <colgroup>
 995 <col>
 996 <col>
 997 <col>
 998 <col>
 999 <col>
1000 </colgroup>
1001 <thead><tr>
1002 <th>
1003               </th>
1004 <th>
1005                 <p>
1006                   Microsoft Visual C++ version 12.0<br> Win32<br> double
1007                 </p>
1008               </th>
1009 <th>
1010                 <p>
1011                   GNU C++ version 5.1.0<br> linux<br> long double
1012                 </p>
1013               </th>
1014 <th>
1015                 <p>
1016                   GNU C++ version 5.1.0<br> linux<br> double
1017                 </p>
1018               </th>
1019 <th>
1020                 <p>
1021                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
1022                 </p>
1023               </th>
1024 </tr></thead>
1025 <tbody>
1026 <tr>
1027 <td>
1028                 <p>
1029                   Bessel I0: Mathworld Data (Integer Version)
1030                 </p>
1031               </td>
1032 <td>
1033                 <p>
1034                   <span class="blue">Max = 0.877&#949; (Mean = 0.549&#949;)</span>
1035                 </p>
1036               </td>
1037 <td>
1038                 <p>
1039                   <span class="blue">Max = 4.57&#949; (Mean = 2.1&#949;)</span><br> <br>
1040                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;)
1041                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
1042                   other failures.</a>)
1043                 </p>
1044               </td>
1045 <td>
1046                 <p>
1047                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1048                   1.16:</em></span> Max = 0.79&#949; (Mean = 0.482&#949;))<br> (<span class="emphasis"><em>Rmath
1049                   3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_I0_Mathworld_Data_Integer_Version_">And
1050                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1051                   <span class="red">Max = 2.55e+43&#949; (Mean = 8.06e+42&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_I0_Mathworld_Data_Integer_Version_">And
1052                   other failures.</a>)</span>
1053                 </p>
1054               </td>
1055 <td>
1056                 <p>
1057                   <span class="blue">Max = 4.54&#949; (Mean = 2.11&#949;)</span>
1058                 </p>
1059               </td>
1060 </tr>
1061 <tr>
1062 <td>
1063                 <p>
1064                   Bessel I1: Mathworld Data (Integer Version)
1065                 </p>
1066               </td>
1067 <td>
1068                 <p>
1069                   <span class="blue">Max = 0.885&#949; (Mean = 0.55&#949;)</span>
1070                 </p>
1071               </td>
1072 <td>
1073                 <p>
1074                   <span class="blue">Max = 7.83&#949; (Mean = 2.79&#949;)</span><br> <br>
1075                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;)
1076                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
1077                   other failures.</a>)
1078                 </p>
1079               </td>
1080 <td>
1081                 <p>
1082                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1083                   1.16:</em></span> Max = 0.82&#949; (Mean = 0.456&#949;))<br> (<span class="emphasis"><em>Rmath
1084                   3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_I1_Mathworld_Data_Integer_Version_">And
1085                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1086                   <span class="red">Max = 1.28e+43&#949; (Mean = 4.05e+42&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_I1_Mathworld_Data_Integer_Version_">And
1087                   other failures.</a>)</span>
1088                 </p>
1089               </td>
1090 <td>
1091                 <p>
1092                   <span class="blue">Max = 6.52&#949; (Mean = 2.25&#949;)</span>
1093                 </p>
1094               </td>
1095 </tr>
1096 <tr>
1097 <td>
1098                 <p>
1099                   Bessel In: Mathworld Data (Integer Version)
1100                 </p>
1101               </td>
1102 <td>
1103                 <p>
1104                   <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
1105                 </p>
1106               </td>
1107 <td>
1108                 <p>
1109                   <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
1110                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;)
1111                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_i_integer_orders___tr1_cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
1112                   other failures.</a>)
1113                 </p>
1114               </td>
1115 <td>
1116                 <p>
1117                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1118                   1.16:</em></span> Max = 5.15&#949; (Mean = 2.13&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_1_16_Bessel_In_Mathworld_Data_Integer_Version_">And
1119                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1120                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_0_2_Bessel_In_Mathworld_Data_Integer_Version_">And
1121                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1122                   <span class="red">Max = 3.67e+177&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_i_integer_orders__Cephes_Bessel_In_Mathworld_Data_Integer_Version_">And
1123                   other failures.</a>)</span>
1124                 </p>
1125               </td>
1126 <td>
1127                 <p>
1128                   <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
1129                 </p>
1130               </td>
1131 </tr>
1132 </tbody>
1133 </table></div>
1134 </div>
1135 <br class="table-break"><div class="table">
1136 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime"></a><p class="title"><b>Table&#160;17.11.&#160;Error rates for cyl_bessel_i_prime</b></p>
1137 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
1138 <colgroup>
1139 <col>
1140 <col>
1141 <col>
1142 <col>
1143 <col>
1144 </colgroup>
1145 <thead><tr>
1146 <th>
1147               </th>
1148 <th>
1149                 <p>
1150                   Microsoft Visual C++ version 12.0<br> Win32<br> double
1151                 </p>
1152               </th>
1153 <th>
1154                 <p>
1155                   GNU C++ version 5.1.0<br> linux<br> double
1156                 </p>
1157               </th>
1158 <th>
1159                 <p>
1160                   GNU C++ version 5.1.0<br> linux<br> long double
1161                 </p>
1162               </th>
1163 <th>
1164                 <p>
1165                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
1166                 </p>
1167               </th>
1168 </tr></thead>
1169 <tbody>
1170 <tr>
1171 <td>
1172                 <p>
1173                   Bessel I'0: Mathworld Data
1174                 </p>
1175               </td>
1176 <td>
1177                 <p>
1178                   <span class="blue">Max = 0.885&#949; (Mean = 0.567&#949;)</span>
1179                 </p>
1180               </td>
1181 <td>
1182                 <p>
1183                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1184                 </p>
1185               </td>
1186 <td>
1187                 <p>
1188                   <span class="blue">Max = 7.83&#949; (Mean = 2.84&#949;)</span>
1189                 </p>
1190               </td>
1191 <td>
1192                 <p>
1193                   <span class="blue">Max = 6.52&#949; (Mean = 2.26&#949;)</span>
1194                 </p>
1195               </td>
1196 </tr>
1197 <tr>
1198 <td>
1199                 <p>
1200                   Bessel I'1: Mathworld Data
1201                 </p>
1202               </td>
1203 <td>
1204                 <p>
1205                   <span class="blue">Max = 1.61&#949; (Mean = 0.786&#949;)</span>
1206                 </p>
1207               </td>
1208 <td>
1209                 <p>
1210                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1211                 </p>
1212               </td>
1213 <td>
1214                 <p>
1215                   <span class="blue">Max = 2.3&#949; (Mean = 1.28&#949;)</span>
1216                 </p>
1217               </td>
1218 <td>
1219                 <p>
1220                   <span class="blue">Max = 2.3&#949; (Mean = 1.29&#949;)</span>
1221                 </p>
1222               </td>
1223 </tr>
1224 <tr>
1225 <td>
1226                 <p>
1227                   Bessel I'n: Mathworld Data
1228                 </p>
1229               </td>
1230 <td>
1231                 <p>
1232                   <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
1233                 </p>
1234               </td>
1235 <td>
1236                 <p>
1237                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1238                 </p>
1239               </td>
1240 <td>
1241                 <p>
1242                   <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
1243                 </p>
1244               </td>
1245 <td>
1246                 <p>
1247                   <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
1248                 </p>
1249               </td>
1250 </tr>
1251 <tr>
1252 <td>
1253                 <p>
1254                   Bessel I'v: Mathworld Data
1255                 </p>
1256               </td>
1257 <td>
1258                 <p>
1259                   <span class="blue">Max = 3.76e+003&#949; (Mean = 1.19e+003&#949;)</span>
1260                 </p>
1261               </td>
1262 <td>
1263                 <p>
1264                   <span class="blue">Max = 1.62&#949; (Mean = 0.512&#949;)</span>
1265                 </p>
1266               </td>
1267 <td>
1268                 <p>
1269                   <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
1270                 </p>
1271               </td>
1272 <td>
1273                 <p>
1274                   <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
1275                 </p>
1276               </td>
1277 </tr>
1278 <tr>
1279 <td>
1280                 <p>
1281                   Bessel I'n: Random Data
1282                 </p>
1283               </td>
1284 <td>
1285                 <p>
1286                   <span class="blue">Max = 9.85&#949; (Mean = 1.83&#949;)</span>
1287                 </p>
1288               </td>
1289 <td>
1290                 <p>
1291                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1292                 </p>
1293               </td>
1294 <td>
1295                 <p>
1296                   <span class="blue">Max = 6.79&#949; (Mean = 1.13&#949;)</span>
1297                 </p>
1298               </td>
1299 <td>
1300                 <p>
1301                   <span class="blue">Max = 195&#949; (Mean = 37.1&#949;)</span>
1302                 </p>
1303               </td>
1304 </tr>
1305 <tr>
1306 <td>
1307                 <p>
1308                   Bessel I'v: Random Data
1309                 </p>
1310               </td>
1311 <td>
1312                 <p>
1313                   <span class="blue">Max = 14&#949; (Mean = 2.46&#949;)</span>
1314                 </p>
1315               </td>
1316 <td>
1317                 <p>
1318                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1319                 </p>
1320               </td>
1321 <td>
1322                 <p>
1323                   <span class="blue">Max = 14.1&#949; (Mean = 2.93&#949;)</span>
1324                 </p>
1325               </td>
1326 <td>
1327                 <p>
1328                   <span class="blue">Max = 336&#949; (Mean = 68.5&#949;)</span>
1329                 </p>
1330               </td>
1331 </tr>
1332 <tr>
1333 <td>
1334                 <p>
1335                   Bessel I'v: Mathworld Data (large values)
1336                 </p>
1337               </td>
1338 <td>
1339                 <p>
1340                   <span class="blue">Max = 59.5&#949; (Mean = 26.8&#949;)</span>
1341                 </p>
1342               </td>
1343 <td>
1344                 <p>
1345                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1346                 </p>
1347               </td>
1348 <td>
1349                 <p>
1350                   <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
1351                 </p>
1352               </td>
1353 <td>
1354                 <p>
1355                   <span class="blue">Max = 43.9&#949; (Mean = 20.7&#949;)</span>
1356                 </p>
1357               </td>
1358 </tr>
1359 </tbody>
1360 </table></div>
1361 </div>
1362 <br class="table-break"><div class="table">
1363 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table&#160;17.12.&#160;Error rates for cyl_bessel_i_prime (integer orders)</b></p>
1364 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
1365 <colgroup>
1366 <col>
1367 <col>
1368 <col>
1369 <col>
1370 <col>
1371 </colgroup>
1372 <thead><tr>
1373 <th>
1374               </th>
1375 <th>
1376                 <p>
1377                   Microsoft Visual C++ version 12.0<br> Win32<br> double
1378                 </p>
1379               </th>
1380 <th>
1381                 <p>
1382                   GNU C++ version 5.1.0<br> linux<br> double
1383                 </p>
1384               </th>
1385 <th>
1386                 <p>
1387                   GNU C++ version 5.1.0<br> linux<br> long double
1388                 </p>
1389               </th>
1390 <th>
1391                 <p>
1392                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
1393                 </p>
1394               </th>
1395 </tr></thead>
1396 <tbody>
1397 <tr>
1398 <td>
1399                 <p>
1400                   Bessel I'0: Mathworld Data (Integer Version)
1401                 </p>
1402               </td>
1403 <td>
1404                 <p>
1405                   <span class="blue">Max = 0.885&#949; (Mean = 0.567&#949;)</span>
1406                 </p>
1407               </td>
1408 <td>
1409                 <p>
1410                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1411                 </p>
1412               </td>
1413 <td>
1414                 <p>
1415                   <span class="blue">Max = 7.83&#949; (Mean = 2.84&#949;)</span>
1416                 </p>
1417               </td>
1418 <td>
1419                 <p>
1420                   <span class="blue">Max = 6.52&#949; (Mean = 2.26&#949;)</span>
1421                 </p>
1422               </td>
1423 </tr>
1424 <tr>
1425 <td>
1426                 <p>
1427                   Bessel I'1: Mathworld Data (Integer Version)
1428                 </p>
1429               </td>
1430 <td>
1431                 <p>
1432                   <span class="blue">Max = 1.61&#949; (Mean = 0.786&#949;)</span>
1433                 </p>
1434               </td>
1435 <td>
1436                 <p>
1437                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1438                 </p>
1439               </td>
1440 <td>
1441                 <p>
1442                   <span class="blue">Max = 2.3&#949; (Mean = 1.28&#949;)</span>
1443                 </p>
1444               </td>
1445 <td>
1446                 <p>
1447                   <span class="blue">Max = 2.3&#949; (Mean = 1.29&#949;)</span>
1448                 </p>
1449               </td>
1450 </tr>
1451 <tr>
1452 <td>
1453                 <p>
1454                   Bessel I'n: Mathworld Data (Integer Version)
1455                 </p>
1456               </td>
1457 <td>
1458                 <p>
1459                   <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
1460                 </p>
1461               </td>
1462 <td>
1463                 <p>
1464                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
1465                 </p>
1466               </td>
1467 <td>
1468                 <p>
1469                   <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
1470                 </p>
1471               </td>
1472 <td>
1473                 <p>
1474                   <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
1475                 </p>
1476               </td>
1477 </tr>
1478 </tbody>
1479 </table></div>
1480 </div>
1481 <br class="table-break"><div class="table">
1482 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j"></a><p class="title"><b>Table&#160;17.13.&#160;Error rates for cyl_bessel_j</b></p>
1483 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
1484 <colgroup>
1485 <col>
1486 <col>
1487 <col>
1488 <col>
1489 <col>
1490 </colgroup>
1491 <thead><tr>
1492 <th>
1493               </th>
1494 <th>
1495                 <p>
1496                   Microsoft Visual C++ version 12.0<br> Win32<br> double
1497                 </p>
1498               </th>
1499 <th>
1500                 <p>
1501                   GNU C++ version 5.1.0<br> linux<br> long double
1502                 </p>
1503               </th>
1504 <th>
1505                 <p>
1506                   GNU C++ version 5.1.0<br> linux<br> double
1507                 </p>
1508               </th>
1509 <th>
1510                 <p>
1511                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
1512                 </p>
1513               </th>
1514 </tr></thead>
1515 <tbody>
1516 <tr>
1517 <td>
1518                 <p>
1519                   Bessel J0: Mathworld Data
1520                 </p>
1521               </td>
1522 <td>
1523                 <p>
1524                   <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span>
1525                 </p>
1526               </td>
1527 <td>
1528                 <p>
1529                   <span class="blue">Max = 6.55&#949; (Mean = 2.89&#949;)</span><br> <br>
1530                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;)
1531                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J0_Mathworld_Data">And
1532                   other failures.</a>)
1533                 </p>
1534               </td>
1535 <td>
1536                 <p>
1537                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1538                   1.16:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J0_Mathworld_Data">And
1539                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1540                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J0_Mathworld_Data">And
1541                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1542                   Max = 1.12&#949; (Mean = 0.568&#949;))
1543                 </p>
1544               </td>
1545 <td>
1546                 <p>
1547                   <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
1548                 </p>
1549               </td>
1550 </tr>
1551 <tr>
1552 <td>
1553                 <p>
1554                   Bessel J0: Mathworld Data (Tricky cases)
1555                 </p>
1556               </td>
1557 <td>
1558                 <p>
1559                   <span class="blue">Max = 1e+007&#949; (Mean = 4.09e+006&#949;)</span>
1560                 </p>
1561               </td>
1562 <td>
1563                 <p>
1564                   <span class="blue">Max = 1.63e+08&#949; (Mean = 6.67e+07&#949;)</span><br>
1565                   <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean
1566                   = 1.96e+08&#949;))
1567                 </p>
1568               </td>
1569 <td>
1570                 <p>
1571                   <span class="blue">Max = 7.98e+04&#949; (Mean = 3.26e+04&#949;)</span><br>
1572                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 6.5e+07&#949; (Mean = 2.66e+07&#949;))<br>
1573                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))<br>
1574                   (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 2.54e+08&#949; (Mean
1575                   = 1.04e+08&#949;))</span>
1576                 </p>
1577               </td>
1578 <td>
1579                 <p>
1580                   <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
1581                 </p>
1582               </td>
1583 </tr>
1584 <tr>
1585 <td>
1586                 <p>
1587                   Bessel J1: Mathworld Data
1588                 </p>
1589               </td>
1590 <td>
1591                 <p>
1592                   <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span>
1593                 </p>
1594               </td>
1595 <td>
1596                 <p>
1597                   <span class="blue">Max = 2.66&#949; (Mean = 1.38&#949;)</span><br> <br>
1598                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;)
1599                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J1_Mathworld_Data">And
1600                   other failures.</a>)
1601                 </p>
1602               </td>
1603 <td>
1604                 <p>
1605                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1606                   1.16:</em></span> Max = 6.62&#949; (Mean = 2.35&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J1_Mathworld_Data">And
1607                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1608                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J1_Mathworld_Data">And
1609                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1610                   Max = 2.88&#949; (Mean = 1.12&#949;))
1611                 </p>
1612               </td>
1613 <td>
1614                 <p>
1615                   <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
1616                 </p>
1617               </td>
1618 </tr>
1619 <tr>
1620 <td>
1621                 <p>
1622                   Bessel J1: Mathworld Data (tricky cases)
1623                 </p>
1624               </td>
1625 <td>
1626                 <p>
1627                   <span class="blue">Max = 3.23e+004&#949; (Mean = 1.45e+004&#949;)</span>
1628                 </p>
1629               </td>
1630 <td>
1631                 <p>
1632                   <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
1633                   <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean
1634                   = 1.58e+06&#949;))
1635                 </p>
1636               </td>
1637 <td>
1638                 <p>
1639                   <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
1640                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.75e+05&#949; (Mean = 5.32e+05&#949;))<br>
1641                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))<br>
1642                   (<span class="emphasis"><em>Cephes:</em></span> Max = 9.56e+05&#949; (Mean = 4.99e+05&#949;))
1643                 </p>
1644               </td>
1645 <td>
1646                 <p>
1647                   <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
1648                 </p>
1649               </td>
1650 </tr>
1651 <tr>
1652 <td>
1653                 <p>
1654                   Bessel JN: Mathworld Data
1655                 </p>
1656               </td>
1657 <td>
1658                 <p>
1659                   <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span>
1660                 </p>
1661               </td>
1662 <td>
1663                 <p>
1664                   <span class="blue">Max = 6.85&#949; (Mean = 3.41&#949;)</span><br> <br>
1665                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
1666                   = 2.13e+19&#949; (Mean = 5.16e+18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_JN_Mathworld_Data">And
1667                   other failures.</a>)</span>
1668                 </p>
1669               </td>
1670 <td>
1671                 <p>
1672                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1673                   1.16:</em></span> Max = 6.9e+05&#949; (Mean = 2.15e+05&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_JN_Mathworld_Data">And
1674                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1675                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_JN_Mathworld_Data">And
1676                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1677                   Max = 5.53e+05&#949; (Mean = 1.9e+05&#949;))
1678                 </p>
1679               </td>
1680 <td>
1681                 <p>
1682                   <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
1683                 </p>
1684               </td>
1685 </tr>
1686 <tr>
1687 <td>
1688                 <p>
1689                   Bessel J: Mathworld Data
1690                 </p>
1691               </td>
1692 <td>
1693                 <p>
1694                   <span class="blue">Max = 14.9&#949; (Mean = 3.82&#949;)</span>
1695                 </p>
1696               </td>
1697 <td>
1698                 <p>
1699                   <span class="blue">Max = 14.7&#949; (Mean = 4.05&#949;)</span><br> <br>
1700                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 3.49e+05&#949; (Mean =
1701                   7.89e+04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J_Mathworld_Data">And
1702                   other failures.</a>)
1703                 </p>
1704               </td>
1705 <td>
1706                 <p>
1707                   <span class="blue">Max = 10&#949; (Mean = 2.19&#949;)</span><br> <br>
1708                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.39e+05&#949; (Mean = 5.24e+04&#949;)
1709                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Mathworld_Data">And
1710                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1711                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Rmath_3_0_2_Bessel_J_Mathworld_Data">And
1712                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1713                   Max = 5.47e+05&#949; (Mean = 1.3e+05&#949;))
1714                 </p>
1715               </td>
1716 <td>
1717                 <p>
1718                   <span class="blue">Max = 14.7&#949; (Mean = 4.12&#949;)</span>
1719                 </p>
1720               </td>
1721 </tr>
1722 <tr>
1723 <td>
1724                 <p>
1725                   Bessel J: Mathworld Data (large values)
1726                 </p>
1727               </td>
1728 <td>
1729                 <p>
1730                   <span class="blue">Max = 9.31&#949; (Mean = 5.52&#949;)</span>
1731                 </p>
1732               </td>
1733 <td>
1734                 <p>
1735                   <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span><br> <br>
1736                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 34.9&#949; (Mean = 17.4&#949;)
1737                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j__tr1_cmath__Bessel_J_Mathworld_Data_large_values_">And
1738                   other failures.</a>)
1739                 </p>
1740               </td>
1741 <td>
1742                 <p>
1743                   <span class="blue">Max = 0.536&#949; (Mean = 0.268&#949;)</span><br> <br>
1744                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.91e+03&#949; (Mean = 2.46e+03&#949;)
1745                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Mathworld_Data_large_values_">And
1746                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1747                   Max = 35.9&#949; (Mean = 18.1&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_Cephes_Bessel_J_Mathworld_Data_large_values_">And
1748                   other failures.</a>)</span>
1749                 </p>
1750               </td>
1751 <td>
1752                 <p>
1753                   <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span>
1754                 </p>
1755               </td>
1756 </tr>
1757 <tr>
1758 <td>
1759                 <p>
1760                   Bessel JN: Random Data
1761                 </p>
1762               </td>
1763 <td>
1764                 <p>
1765                   <span class="blue">Max = 17.5&#949; (Mean = 1.46&#949;)</span>
1766                 </p>
1767               </td>
1768 <td>
1769                 <p>
1770                   <span class="blue">Max = 50.8&#949; (Mean = 4.15&#949;)</span><br> <br>
1771                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.12e+03&#949; (Mean =
1772                   88.7&#949;))
1773                 </p>
1774               </td>
1775 <td>
1776                 <p>
1777                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1778                   1.16:</em></span> Max = 75.7&#949; (Mean = 5.36&#949;))<br> (<span class="emphasis"><em>Rmath
1779                   3.0.2:</em></span> Max = 3.93&#949; (Mean = 1.22&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
1780                   Max = 91.4&#949; (Mean = 6.47&#949;))
1781                 </p>
1782               </td>
1783 <td>
1784                 <p>
1785                   <span class="blue">Max = 99.6&#949; (Mean = 22&#949;)</span>
1786                 </p>
1787               </td>
1788 </tr>
1789 <tr>
1790 <td>
1791                 <p>
1792                   Bessel J: Random Data
1793                 </p>
1794               </td>
1795 <td>
1796                 <p>
1797                   <span class="blue">Max = 9.24&#949; (Mean = 1.36&#949;)</span>
1798                 </p>
1799               </td>
1800 <td>
1801                 <p>
1802                   <span class="blue">Max = 9.81&#949; (Mean = 1.59&#949;)</span><br> <br>
1803                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 501&#949; (Mean = 52.3&#949;))
1804                 </p>
1805               </td>
1806 <td>
1807                 <p>
1808                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1809                   1.16:</em></span> Max = 15.5&#949; (Mean = 3.33&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_GSL_1_16_Bessel_J_Random_Data">And
1810                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
1811                   Max = 6.74&#949; (Mean = 1.3&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
1812                   = 16.7&#949; (Mean = 2.5&#949;))
1813                 </p>
1814               </td>
1815 <td>
1816                 <p>
1817                   <span class="blue">Max = 260&#949; (Mean = 34&#949;)</span>
1818                 </p>
1819               </td>
1820 </tr>
1821 <tr>
1822 <td>
1823                 <p>
1824                   Bessel J: Random Data (Tricky large values)
1825                 </p>
1826               </td>
1827 <td>
1828                 <p>
1829                   <span class="blue">Max = 59.2&#949; (Mean = 8.67&#949;)</span>
1830                 </p>
1831               </td>
1832 <td>
1833                 <p>
1834                   <span class="blue">Max = 785&#949; (Mean = 94.2&#949;)</span><br> <br>
1835                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
1836                   = 5.01e+17&#949; (Mean = 6.23e+16&#949;))</span>
1837                 </p>
1838               </td>
1839 <td>
1840                 <p>
1841                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1842                   1.16:</em></span> Max = 2.48e+05&#949; (Mean = 5.11e+04&#949;))<br> (<span class="emphasis"><em>Rmath
1843                   3.0.2:</em></span> Max = 71.6&#949; (Mean = 11.7&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
1844                   Max = 2.48e+05&#949; (Mean = 3.02e+04&#949;))
1845                 </p>
1846               </td>
1847 <td>
1848                 <p>
1849                   <span class="blue">Max = 785&#949; (Mean = 97.4&#949;)</span>
1850                 </p>
1851               </td>
1852 </tr>
1853 </tbody>
1854 </table></div>
1855 </div>
1856 <br class="table-break"><div class="table">
1857 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table&#160;17.14.&#160;Error rates for cyl_bessel_j (integer orders)</b></p>
1858 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
1859 <colgroup>
1860 <col>
1861 <col>
1862 <col>
1863 <col>
1864 <col>
1865 </colgroup>
1866 <thead><tr>
1867 <th>
1868               </th>
1869 <th>
1870                 <p>
1871                   Microsoft Visual C++ version 12.0<br> Win32<br> double
1872                 </p>
1873               </th>
1874 <th>
1875                 <p>
1876                   GNU C++ version 5.1.0<br> linux<br> long double
1877                 </p>
1878               </th>
1879 <th>
1880                 <p>
1881                   GNU C++ version 5.1.0<br> linux<br> double
1882                 </p>
1883               </th>
1884 <th>
1885                 <p>
1886                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
1887                 </p>
1888               </th>
1889 </tr></thead>
1890 <tbody>
1891 <tr>
1892 <td>
1893                 <p>
1894                   Bessel J0: Mathworld Data (Integer Version)
1895                 </p>
1896               </td>
1897 <td>
1898                 <p>
1899                   <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span><br> <br>
1900                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.89&#949; (Mean = 0.988&#949;))
1901                 </p>
1902               </td>
1903 <td>
1904                 <p>
1905                   <span class="blue">Max = 6.55&#949; (Mean = 2.89&#949;)</span><br> <br>
1906                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;)
1907                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
1908                   other failures.</a>)
1909                 </p>
1910               </td>
1911 <td>
1912                 <p>
1913                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1914                   1.16:</em></span> Max = 1.12&#949; (Mean = 0.488&#949;))<br> (<span class="emphasis"><em>Rmath
1915                   3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_J0_Mathworld_Data_Integer_Version_">And
1916                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1917                   Max = 1.12&#949; (Mean = 0.568&#949;))
1918                 </p>
1919               </td>
1920 <td>
1921                 <p>
1922                   <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
1923                 </p>
1924               </td>
1925 </tr>
1926 <tr>
1927 <td>
1928                 <p>
1929                   Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
1930                 </p>
1931               </td>
1932 <td>
1933                 <p>
1934                   <span class="blue">Max = 1e+007&#949; (Mean = 4.09e+006&#949;)</span><br>
1935                   <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max
1936                   = 2.54e+008&#949; (Mean = 1.04e+008&#949;))</span>
1937                 </p>
1938               </td>
1939 <td>
1940                 <p>
1941                   <span class="blue">Max = 1.63e+08&#949; (Mean = 6.67e+07&#949;)</span><br>
1942                   <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean
1943                   = 1.96e+08&#949;))
1944                 </p>
1945               </td>
1946 <td>
1947                 <p>
1948                   <span class="blue">Max = 7.98e+04&#949; (Mean = 3.26e+04&#949;)</span><br>
1949                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1e+07&#949; (Mean = 4.11e+06&#949;))<br>
1950                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))<br>
1951                   (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 2.54e+08&#949; (Mean
1952                   = 1.04e+08&#949;))</span>
1953                 </p>
1954               </td>
1955 <td>
1956                 <p>
1957                   <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
1958                 </p>
1959               </td>
1960 </tr>
1961 <tr>
1962 <td>
1963                 <p>
1964                   Bessel J1: Mathworld Data (Integer Version)
1965                 </p>
1966               </td>
1967 <td>
1968                 <p>
1969                   <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span><br> <br>
1970                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 11.4&#949; (Mean = 4.15&#949;))
1971                 </p>
1972               </td>
1973 <td>
1974                 <p>
1975                   <span class="blue">Max = 2.66&#949; (Mean = 1.38&#949;)</span><br> <br>
1976                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;)
1977                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
1978                   other failures.</a>)
1979                 </p>
1980               </td>
1981 <td>
1982                 <p>
1983                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
1984                   1.16:</em></span> Max = 1.89&#949; (Mean = 0.721&#949;))<br> (<span class="emphasis"><em>Rmath
1985                   3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_J1_Mathworld_Data_Integer_Version_">And
1986                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
1987                   Max = 2.88&#949; (Mean = 1.12&#949;))
1988                 </p>
1989               </td>
1990 <td>
1991                 <p>
1992                   <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
1993                 </p>
1994               </td>
1995 </tr>
1996 <tr>
1997 <td>
1998                 <p>
1999                   Bessel J1: Mathworld Data (tricky cases) (Integer Version)
2000                 </p>
2001               </td>
2002 <td>
2003                 <p>
2004                   <span class="blue">Max = 3.23e+004&#949; (Mean = 1.45e+004&#949;)</span><br>
2005                   <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.44e+007&#949; (Mean
2006                   = 6.5e+006&#949;))
2007                 </p>
2008               </td>
2009 <td>
2010                 <p>
2011                   <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
2012                   <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean
2013                   = 1.58e+06&#949;))
2014                 </p>
2015               </td>
2016 <td>
2017                 <p>
2018                   <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
2019                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.26e+06&#949; (Mean = 6.28e+05&#949;))<br>
2020                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))<br>
2021                   (<span class="emphasis"><em>Cephes:</em></span> Max = 9.56e+05&#949; (Mean = 4.99e+05&#949;))
2022                 </p>
2023               </td>
2024 <td>
2025                 <p>
2026                   <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
2027                 </p>
2028               </td>
2029 </tr>
2030 <tr>
2031 <td>
2032                 <p>
2033                   Bessel JN: Mathworld Data (Integer Version)
2034                 </p>
2035               </td>
2036 <td>
2037                 <p>
2038                   <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span><br> <br>
2039                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max =
2040                   +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_Microsoft_Visual_C_version_12_0_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
2041                   other failures.</a>)</span>
2042                 </p>
2043               </td>
2044 <td>
2045                 <p>
2046                   <span class="blue">Max = 6.85&#949; (Mean = 3.41&#949;)</span><br> <br>
2047                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
2048                   = 2.13e+19&#949; (Mean = 5.16e+18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_j_integer_orders___tr1_cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
2049                   other failures.</a>)</span>
2050                 </p>
2051               </td>
2052 <td>
2053                 <p>
2054                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2055                   1.16:</em></span> Max = 6.9e+05&#949; (Mean = 2.53e+05&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_1_16_Bessel_JN_Mathworld_Data_Integer_Version_">And
2056                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2057                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_0_2_Bessel_JN_Mathworld_Data_Integer_Version_">And
2058                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
2059                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_j_integer_orders__Cephes_Bessel_JN_Mathworld_Data_Integer_Version_">And
2060                   other failures.</a>)</span>
2061                 </p>
2062               </td>
2063 <td>
2064                 <p>
2065                   <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
2066                 </p>
2067               </td>
2068 </tr>
2069 </tbody>
2070 </table></div>
2071 </div>
2072 <br class="table-break"><div class="table">
2073 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime"></a><p class="title"><b>Table&#160;17.15.&#160;Error rates for cyl_bessel_j_prime</b></p>
2074 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
2075 <colgroup>
2076 <col>
2077 <col>
2078 <col>
2079 <col>
2080 <col>
2081 </colgroup>
2082 <thead><tr>
2083 <th>
2084               </th>
2085 <th>
2086                 <p>
2087                   Microsoft Visual C++ version 12.0<br> Win32<br> double
2088                 </p>
2089               </th>
2090 <th>
2091                 <p>
2092                   GNU C++ version 5.1.0<br> linux<br> double
2093                 </p>
2094               </th>
2095 <th>
2096                 <p>
2097                   GNU C++ version 5.1.0<br> linux<br> long double
2098                 </p>
2099               </th>
2100 <th>
2101                 <p>
2102                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
2103                 </p>
2104               </th>
2105 </tr></thead>
2106 <tbody>
2107 <tr>
2108 <td>
2109                 <p>
2110                   Bessel J0': Mathworld Data
2111                 </p>
2112               </td>
2113 <td>
2114                 <p>
2115                   <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
2116                 </p>
2117               </td>
2118 <td>
2119                 <p>
2120                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2121                 </p>
2122               </td>
2123 <td>
2124                 <p>
2125                   <span class="blue">Max = 18.9&#949; (Mean = 6.81&#949;)</span>
2126                 </p>
2127               </td>
2128 <td>
2129                 <p>
2130                   <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
2131                 </p>
2132               </td>
2133 </tr>
2134 <tr>
2135 <td>
2136                 <p>
2137                   Bessel J0': Mathworld Data (Tricky cases)
2138                 </p>
2139               </td>
2140 <td>
2141                 <p>
2142                   <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
2143                 </p>
2144               </td>
2145 <td>
2146                 <p>
2147                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2148                 </p>
2149               </td>
2150 <td>
2151                 <p>
2152                   <span class="blue">Max = 8.08&#949; (Mean = 4.57&#949;)</span>
2153                 </p>
2154               </td>
2155 <td>
2156                 <p>
2157                   <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
2158                 </p>
2159               </td>
2160 </tr>
2161 <tr>
2162 <td>
2163                 <p>
2164                   Bessel J1': Mathworld Data
2165                 </p>
2166               </td>
2167 <td>
2168                 <p>
2169                   <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
2170                 </p>
2171               </td>
2172 <td>
2173                 <p>
2174                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2175                 </p>
2176               </td>
2177 <td>
2178                 <p>
2179                   <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2180                 </p>
2181               </td>
2182 <td>
2183                 <p>
2184                   <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2185                 </p>
2186               </td>
2187 </tr>
2188 <tr>
2189 <td>
2190                 <p>
2191                   Bessel J1': Mathworld Data (tricky cases)
2192                 </p>
2193               </td>
2194 <td>
2195                 <p>
2196                   <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
2197                 </p>
2198               </td>
2199 <td>
2200                 <p>
2201                   <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
2202                 </p>
2203               </td>
2204 <td>
2205                 <p>
2206                   <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2207                 </p>
2208               </td>
2209 <td>
2210                 <p>
2211                   <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2212                 </p>
2213               </td>
2214 </tr>
2215 <tr>
2216 <td>
2217                 <p>
2218                   Bessel JN': Mathworld Data
2219                 </p>
2220               </td>
2221 <td>
2222                 <p>
2223                   <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
2224                 </p>
2225               </td>
2226 <td>
2227                 <p>
2228                   <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
2229                 </p>
2230               </td>
2231 <td>
2232                 <p>
2233                   <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
2234                 </p>
2235               </td>
2236 <td>
2237                 <p>
2238                   <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
2239                 </p>
2240               </td>
2241 </tr>
2242 <tr>
2243 <td>
2244                 <p>
2245                   Bessel J': Mathworld Data
2246                 </p>
2247               </td>
2248 <td>
2249                 <p>
2250                   <span class="blue">Max = 23.7&#949; (Mean = 8.01&#949;)</span>
2251                 </p>
2252               </td>
2253 <td>
2254                 <p>
2255                   <span class="blue">Max = 21.5&#949; (Mean = 4.7&#949;)</span>
2256                 </p>
2257               </td>
2258 <td>
2259                 <p>
2260                   <span class="blue">Max = 42.5&#949; (Mean = 9.31&#949;)</span>
2261                 </p>
2262               </td>
2263 <td>
2264                 <p>
2265                   <span class="blue">Max = 42.5&#949; (Mean = 9.32&#949;)</span>
2266                 </p>
2267               </td>
2268 </tr>
2269 <tr>
2270 <td>
2271                 <p>
2272                   Bessel J': Mathworld Data (large values)
2273                 </p>
2274               </td>
2275 <td>
2276                 <p>
2277                   <span class="blue">Max = 2.9&#949; (Mean = 1.61&#949;)</span>
2278                 </p>
2279               </td>
2280 <td>
2281                 <p>
2282                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2283                 </p>
2284               </td>
2285 <td>
2286                 <p>
2287                   <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
2288                 </p>
2289               </td>
2290 <td>
2291                 <p>
2292                   <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
2293                 </p>
2294               </td>
2295 </tr>
2296 <tr>
2297 <td>
2298                 <p>
2299                   Bessel JN': Random Data
2300                 </p>
2301               </td>
2302 <td>
2303                 <p>
2304                   <span class="blue">Max = 6.34&#949; (Mean = 0.997&#949;)</span>
2305                 </p>
2306               </td>
2307 <td>
2308                 <p>
2309                   <span class="blue">Max = 0.593&#949; (Mean = 0.0396&#949;)</span>
2310                 </p>
2311               </td>
2312 <td>
2313                 <p>
2314                   <span class="blue">Max = 17.3&#949; (Mean = 2.47&#949;)</span>
2315                 </p>
2316               </td>
2317 <td>
2318                 <p>
2319                   <span class="blue">Max = 79.4&#949; (Mean = 16.2&#949;)</span>
2320                 </p>
2321               </td>
2322 </tr>
2323 <tr>
2324 <td>
2325                 <p>
2326                   Bessel J': Random Data
2327                 </p>
2328               </td>
2329 <td>
2330                 <p>
2331                   <span class="blue">Max = 176&#949; (Mean = 9.76&#949;)</span>
2332                 </p>
2333               </td>
2334 <td>
2335                 <p>
2336                   <span class="blue">Max = 0.885&#949; (Mean = 0.0457&#949;)</span>
2337                 </p>
2338               </td>
2339 <td>
2340                 <p>
2341                   <span class="blue">Max = 139&#949; (Mean = 6.47&#949;)</span>
2342                 </p>
2343               </td>
2344 <td>
2345                 <p>
2346                   <span class="blue">Max = 279&#949; (Mean = 27.2&#949;)</span>
2347                 </p>
2348               </td>
2349 </tr>
2350 <tr>
2351 <td>
2352                 <p>
2353                   Bessel J': Random Data (Tricky large values)
2354                 </p>
2355               </td>
2356 <td>
2357                 <p>
2358                   <span class="blue">Max = 379&#949; (Mean = 45.4&#949;)</span>
2359                 </p>
2360               </td>
2361 <td>
2362                 <p>
2363                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2364                 </p>
2365               </td>
2366 <td>
2367                 <p>
2368                   <span class="blue">Max = 474&#949; (Mean = 62.2&#949;)</span>
2369                 </p>
2370               </td>
2371 <td>
2372                 <p>
2373                   <span class="blue">Max = 474&#949; (Mean = 64.5&#949;)</span>
2374                 </p>
2375               </td>
2376 </tr>
2377 </tbody>
2378 </table></div>
2379 </div>
2380 <br class="table-break"><div class="table">
2381 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table&#160;17.16.&#160;Error rates for cyl_bessel_j_prime (integer orders)</b></p>
2382 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
2383 <colgroup>
2384 <col>
2385 <col>
2386 <col>
2387 <col>
2388 <col>
2389 </colgroup>
2390 <thead><tr>
2391 <th>
2392               </th>
2393 <th>
2394                 <p>
2395                   Microsoft Visual C++ version 12.0<br> Win32<br> double
2396                 </p>
2397               </th>
2398 <th>
2399                 <p>
2400                   GNU C++ version 5.1.0<br> linux<br> double
2401                 </p>
2402               </th>
2403 <th>
2404                 <p>
2405                   GNU C++ version 5.1.0<br> linux<br> long double
2406                 </p>
2407               </th>
2408 <th>
2409                 <p>
2410                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
2411                 </p>
2412               </th>
2413 </tr></thead>
2414 <tbody>
2415 <tr>
2416 <td>
2417                 <p>
2418                   Bessel J0': Mathworld Data (Integer Version)
2419                 </p>
2420               </td>
2421 <td>
2422                 <p>
2423                   <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
2424                 </p>
2425               </td>
2426 <td>
2427                 <p>
2428                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2429                 </p>
2430               </td>
2431 <td>
2432                 <p>
2433                   <span class="blue">Max = 18.9&#949; (Mean = 6.81&#949;)</span>
2434                 </p>
2435               </td>
2436 <td>
2437                 <p>
2438                   <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
2439                 </p>
2440               </td>
2441 </tr>
2442 <tr>
2443 <td>
2444                 <p>
2445                   Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
2446                 </p>
2447               </td>
2448 <td>
2449                 <p>
2450                   <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
2451                 </p>
2452               </td>
2453 <td>
2454                 <p>
2455                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2456                 </p>
2457               </td>
2458 <td>
2459                 <p>
2460                   <span class="blue">Max = 8.08&#949; (Mean = 4.57&#949;)</span>
2461                 </p>
2462               </td>
2463 <td>
2464                 <p>
2465                   <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
2466                 </p>
2467               </td>
2468 </tr>
2469 <tr>
2470 <td>
2471                 <p>
2472                   Bessel J1': Mathworld Data (Integer Version)
2473                 </p>
2474               </td>
2475 <td>
2476                 <p>
2477                   <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
2478                 </p>
2479               </td>
2480 <td>
2481                 <p>
2482                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2483                 </p>
2484               </td>
2485 <td>
2486                 <p>
2487                   <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2488                 </p>
2489               </td>
2490 <td>
2491                 <p>
2492                   <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
2493                 </p>
2494               </td>
2495 </tr>
2496 <tr>
2497 <td>
2498                 <p>
2499                   Bessel J1': Mathworld Data (tricky cases) (Integer Version)
2500                 </p>
2501               </td>
2502 <td>
2503                 <p>
2504                   <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
2505                 </p>
2506               </td>
2507 <td>
2508                 <p>
2509                   <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
2510                 </p>
2511               </td>
2512 <td>
2513                 <p>
2514                   <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2515                 </p>
2516               </td>
2517 <td>
2518                 <p>
2519                   <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
2520                 </p>
2521               </td>
2522 </tr>
2523 <tr>
2524 <td>
2525                 <p>
2526                   Bessel JN': Mathworld Data (Integer Version)
2527                 </p>
2528               </td>
2529 <td>
2530                 <p>
2531                   <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
2532                 </p>
2533               </td>
2534 <td>
2535                 <p>
2536                   <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
2537                 </p>
2538               </td>
2539 <td>
2540                 <p>
2541                   <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
2542                 </p>
2543               </td>
2544 <td>
2545                 <p>
2546                   <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
2547                 </p>
2548               </td>
2549 </tr>
2550 </tbody>
2551 </table></div>
2552 </div>
2553 <br class="table-break"><div class="table">
2554 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k"></a><p class="title"><b>Table&#160;17.17.&#160;Error rates for cyl_bessel_k</b></p>
2555 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
2556 <colgroup>
2557 <col>
2558 <col>
2559 <col>
2560 <col>
2561 <col>
2562 </colgroup>
2563 <thead><tr>
2564 <th>
2565               </th>
2566 <th>
2567                 <p>
2568                   Microsoft Visual C++ version 12.0<br> Win32<br> double
2569                 </p>
2570               </th>
2571 <th>
2572                 <p>
2573                   GNU C++ version 5.1.0<br> linux<br> long double
2574                 </p>
2575               </th>
2576 <th>
2577                 <p>
2578                   GNU C++ version 5.1.0<br> linux<br> double
2579                 </p>
2580               </th>
2581 <th>
2582                 <p>
2583                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
2584                 </p>
2585               </th>
2586 </tr></thead>
2587 <tbody>
2588 <tr>
2589 <td>
2590                 <p>
2591                   Bessel K0: Mathworld Data
2592                 </p>
2593               </td>
2594 <td>
2595                 <p>
2596                   <span class="blue">Max = 1.55&#949; (Mean = 0.837&#949;)</span>
2597                 </p>
2598               </td>
2599 <td>
2600                 <p>
2601                   <span class="blue">Max = 4.16&#949; (Mean = 1.46&#949;)</span><br> <br>
2602                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
2603                 </p>
2604               </td>
2605 <td>
2606                 <p>
2607                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2608                   1.16:</em></span> Max = 6.04&#949; (Mean = 2.16&#949;))<br> (<span class="emphasis"><em>Rmath
2609                   3.0.2:</em></span> Max = 0.833&#949; (Mean = 0.601&#949;))
2610                 </p>
2611               </td>
2612 <td>
2613                 <p>
2614                   <span class="blue">Max = 4.16&#949; (Mean = 1.49&#949;)</span>
2615                 </p>
2616               </td>
2617 </tr>
2618 <tr>
2619 <td>
2620                 <p>
2621                   Bessel K1: Mathworld Data
2622                 </p>
2623               </td>
2624 <td>
2625                 <p>
2626                   <span class="blue">Max = 1&#949; (Mean = 0.573&#949;)</span>
2627                 </p>
2628               </td>
2629 <td>
2630                 <p>
2631                   <span class="blue">Max = 1.8&#949; (Mean = 1.02&#949;)</span><br> <br>
2632                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
2633                 </p>
2634               </td>
2635 <td>
2636                 <p>
2637                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2638                   1.16:</em></span> Max = 6.26&#949; (Mean = 2.21&#949;))<br> (<span class="emphasis"><em>Rmath
2639                   3.0.2:</em></span> Max = 0.894&#949; (Mean = 0.516&#949;))
2640                 </p>
2641               </td>
2642 <td>
2643                 <p>
2644                   <span class="blue">Max = 1.8&#949; (Mean = 1.02&#949;)</span>
2645                 </p>
2646               </td>
2647 </tr>
2648 <tr>
2649 <td>
2650                 <p>
2651                   Bessel Kn: Mathworld Data
2652                 </p>
2653               </td>
2654 <td>
2655                 <p>
2656                   <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
2657                 </p>
2658               </td>
2659 <td>
2660                 <p>
2661                   <span class="blue">Max = 4.48&#949; (Mean = 2.14&#949;)</span><br> <br>
2662                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;)
2663                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kn_Mathworld_Data">And
2664                   other failures.</a>)
2665                 </p>
2666               </td>
2667 <td>
2668                 <p>
2669                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2670                   1.16:</em></span> Max = 3.36&#949; (Mean = 1.43&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kn_Mathworld_Data">And
2671                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2672                   Max = 8.48&#949; (Mean = 2.98&#949;))
2673                 </p>
2674               </td>
2675 <td>
2676                 <p>
2677                   <span class="blue">Max = 4.48&#949; (Mean = 1.98&#949;)</span>
2678                 </p>
2679               </td>
2680 </tr>
2681 <tr>
2682 <td>
2683                 <p>
2684                   Bessel Kv: Mathworld Data
2685                 </p>
2686               </td>
2687 <td>
2688                 <p>
2689                   <span class="blue">Max = 4.78&#949; (Mean = 2.2&#949;)</span>
2690                 </p>
2691               </td>
2692 <td>
2693                 <p>
2694                   <span class="blue">Max = 3.58&#949; (Mean = 2.44&#949;)</span><br> <br>
2695                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 13&#949; (Mean = 4.81&#949;)
2696                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Mathworld_Data">And
2697                   other failures.</a>)
2698                 </p>
2699               </td>
2700 <td>
2701                 <p>
2702                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2703                   1.16:</em></span> Max = 5.47&#949; (Mean = 2.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Mathworld_Data">And
2704                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2705                   Max = 3.15&#949; (Mean = 1.35&#949;))
2706                 </p>
2707               </td>
2708 <td>
2709                 <p>
2710                   <span class="blue">Max = 3.58&#949; (Mean = 2.29&#949;)</span>
2711                 </p>
2712               </td>
2713 </tr>
2714 <tr>
2715 <td>
2716                 <p>
2717                   Bessel Kv: Mathworld Data (large values)
2718                 </p>
2719               </td>
2720 <td>
2721                 <p>
2722                   <span class="blue">Max = 59.8&#949; (Mean = 26.9&#949;)</span>
2723                 </p>
2724               </td>
2725 <td>
2726                 <p>
2727                   <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span><br> <br>
2728                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 42.3&#949; (Mean = 19.8&#949;)
2729                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Mathworld_Data_large_values_">And
2730                   other failures.</a>)
2731                 </p>
2732               </td>
2733 <td>
2734                 <p>
2735                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2736                   1.16:</em></span> Max = 308&#949; (Mean = 142&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Mathworld_Data_large_values_">And
2737                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2738                   Max = 84.6&#949; (Mean = 37.8&#949;))
2739                 </p>
2740               </td>
2741 <td>
2742                 <p>
2743                   <span class="blue">Max = 43.1&#949; (Mean = 21.3&#949;)</span>
2744                 </p>
2745               </td>
2746 </tr>
2747 <tr>
2748 <td>
2749                 <p>
2750                   Bessel Kn: Random Data
2751                 </p>
2752               </td>
2753 <td>
2754                 <p>
2755                   <span class="blue">Max = 7.47&#949; (Mean = 1.4&#949;)</span>
2756                 </p>
2757               </td>
2758 <td>
2759                 <p>
2760                   <span class="blue">Max = 4.55&#949; (Mean = 1.09&#949;)</span><br> <br>
2761                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 13.9&#949; (Mean = 2.91&#949;))
2762                 </p>
2763               </td>
2764 <td>
2765                 <p>
2766                   <span class="blue">Max = 0.764&#949; (Mean = 0.0348&#949;)</span><br>
2767                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.71&#949; (Mean = 1.76&#949;)
2768                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kn_Random_Data">And
2769                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2770                   Max = 7.47&#949; (Mean = 1.34&#949;))
2771                 </p>
2772               </td>
2773 <td>
2774                 <p>
2775                   <span class="blue">Max = 4.55&#949; (Mean = 1.21&#949;)</span>
2776                 </p>
2777               </td>
2778 </tr>
2779 <tr>
2780 <td>
2781                 <p>
2782                   Bessel Kv: Random Data
2783                 </p>
2784               </td>
2785 <td>
2786                 <p>
2787                   <span class="blue">Max = 8.33&#949; (Mean = 1.62&#949;)</span>
2788                 </p>
2789               </td>
2790 <td>
2791                 <p>
2792                   <span class="blue">Max = 7.88&#949; (Mean = 1.48&#949;)</span><br> <br>
2793                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 13.6&#949; (Mean = 2.68&#949;)
2794                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k__tr1_cmath__Bessel_Kv_Random_Data">And
2795                   other failures.</a>)
2796                 </p>
2797               </td>
2798 <td>
2799                 <p>
2800                   <span class="blue">Max = 0.507&#949; (Mean = 0.0313&#949;)</span><br>
2801                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 9.71&#949; (Mean = 1.47&#949;)
2802                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_GSL_1_16_Bessel_Kv_Random_Data">And
2803                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
2804                   Max = 7.37&#949; (Mean = 1.49&#949;))
2805                 </p>
2806               </td>
2807 <td>
2808                 <p>
2809                   <span class="blue">Max = 7.88&#949; (Mean = 1.49&#949;)</span>
2810                 </p>
2811               </td>
2812 </tr>
2813 </tbody>
2814 </table></div>
2815 </div>
2816 <br class="table-break"><div class="table">
2817 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table&#160;17.18.&#160;Error rates for cyl_bessel_k (integer orders)</b></p>
2818 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
2819 <colgroup>
2820 <col>
2821 <col>
2822 <col>
2823 <col>
2824 <col>
2825 </colgroup>
2826 <thead><tr>
2827 <th>
2828               </th>
2829 <th>
2830                 <p>
2831                   Microsoft Visual C++ version 12.0<br> Win32<br> double
2832                 </p>
2833               </th>
2834 <th>
2835                 <p>
2836                   GNU C++ version 5.1.0<br> linux<br> long double
2837                 </p>
2838               </th>
2839 <th>
2840                 <p>
2841                   GNU C++ version 5.1.0<br> linux<br> double
2842                 </p>
2843               </th>
2844 <th>
2845                 <p>
2846                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
2847                 </p>
2848               </th>
2849 </tr></thead>
2850 <tbody>
2851 <tr>
2852 <td>
2853                 <p>
2854                   Bessel K0: Mathworld Data (Integer Version)
2855                 </p>
2856               </td>
2857 <td>
2858                 <p>
2859                   <span class="blue">Max = 1.55&#949; (Mean = 0.837&#949;)</span>
2860                 </p>
2861               </td>
2862 <td>
2863                 <p>
2864                   <span class="blue">Max = 4.16&#949; (Mean = 1.46&#949;)</span><br> <br>
2865                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
2866                 </p>
2867               </td>
2868 <td>
2869                 <p>
2870                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2871                   1.16:</em></span> Max = 1.2&#949; (Mean = 0.733&#949;))<br> (<span class="emphasis"><em>Rmath
2872                   3.0.2:</em></span> Max = 0.833&#949; (Mean = 0.601&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
2873                   Max = 1.1e+06&#949; (Mean = 3.68e+05&#949;))
2874                 </p>
2875               </td>
2876 <td>
2877                 <p>
2878                   <span class="blue">Max = 4.16&#949; (Mean = 1.49&#949;)</span>
2879                 </p>
2880               </td>
2881 </tr>
2882 <tr>
2883 <td>
2884                 <p>
2885                   Bessel K1: Mathworld Data (Integer Version)
2886                 </p>
2887               </td>
2888 <td>
2889                 <p>
2890                   <span class="blue">Max = 1&#949; (Mean = 0.573&#949;)</span>
2891                 </p>
2892               </td>
2893 <td>
2894                 <p>
2895                   <span class="blue">Max = 1.8&#949; (Mean = 1.02&#949;)</span><br> <br>
2896                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
2897                 </p>
2898               </td>
2899 <td>
2900                 <p>
2901                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2902                   1.16:</em></span> Max = 0.626&#949; (Mean = 0.333&#949;))<br> (<span class="emphasis"><em>Rmath
2903                   3.0.2:</em></span> Max = 0.894&#949; (Mean = 0.516&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
2904                   Max = 5.38e+05&#949; (Mean = 1.79e+05&#949;))
2905                 </p>
2906               </td>
2907 <td>
2908                 <p>
2909                   <span class="blue">Max = 1.8&#949; (Mean = 1.02&#949;)</span>
2910                 </p>
2911               </td>
2912 </tr>
2913 <tr>
2914 <td>
2915                 <p>
2916                   Bessel Kn: Mathworld Data (Integer Version)
2917                 </p>
2918               </td>
2919 <td>
2920                 <p>
2921                   <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
2922                 </p>
2923               </td>
2924 <td>
2925                 <p>
2926                   <span class="blue">Max = 4.48&#949; (Mean = 2.14&#949;)</span><br> <br>
2927                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;)
2928                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_bessel_k_integer_orders___tr1_cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
2929                   other failures.</a>)
2930                 </p>
2931               </td>
2932 <td>
2933                 <p>
2934                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
2935                   1.16:</em></span> Max = 168&#949; (Mean = 59.5&#949;))<br> (<span class="emphasis"><em>Rmath
2936                   3.0.2:</em></span> Max = 8.48&#949; (Mean = 2.98&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
2937                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_bessel_k_integer_orders__Cephes_Bessel_Kn_Mathworld_Data_Integer_Version_">And
2938                   other failures.</a>)</span>
2939                 </p>
2940               </td>
2941 <td>
2942                 <p>
2943                   <span class="blue">Max = 4.48&#949; (Mean = 1.98&#949;)</span>
2944                 </p>
2945               </td>
2946 </tr>
2947 </tbody>
2948 </table></div>
2949 </div>
2950 <br class="table-break"><div class="table">
2951 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime"></a><p class="title"><b>Table&#160;17.19.&#160;Error rates for cyl_bessel_k_prime</b></p>
2952 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
2953 <colgroup>
2954 <col>
2955 <col>
2956 <col>
2957 <col>
2958 <col>
2959 </colgroup>
2960 <thead><tr>
2961 <th>
2962               </th>
2963 <th>
2964                 <p>
2965                   Microsoft Visual C++ version 12.0<br> Win32<br> double
2966                 </p>
2967               </th>
2968 <th>
2969                 <p>
2970                   GNU C++ version 5.1.0<br> linux<br> double
2971                 </p>
2972               </th>
2973 <th>
2974                 <p>
2975                   GNU C++ version 5.1.0<br> linux<br> long double
2976                 </p>
2977               </th>
2978 <th>
2979                 <p>
2980                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
2981                 </p>
2982               </th>
2983 </tr></thead>
2984 <tbody>
2985 <tr>
2986 <td>
2987                 <p>
2988                   Bessel K'0: Mathworld Data
2989                 </p>
2990               </td>
2991 <td>
2992                 <p>
2993                   <span class="blue">Max = 1&#949; (Mean = 0.573&#949;)</span>
2994                 </p>
2995               </td>
2996 <td>
2997                 <p>
2998                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
2999                 </p>
3000               </td>
3001 <td>
3002                 <p>
3003                   <span class="blue">Max = 1.8&#949; (Mean = 1.02&#949;)</span>
3004                 </p>
3005               </td>
3006 <td>
3007                 <p>
3008                   <span class="blue">Max = 1.8&#949; (Mean = 1.02&#949;)</span>
3009                 </p>
3010               </td>
3011 </tr>
3012 <tr>
3013 <td>
3014                 <p>
3015                   Bessel K'1: Mathworld Data
3016                 </p>
3017               </td>
3018 <td>
3019                 <p>
3020                   <span class="blue">Max = 1.09&#949; (Mean = 0.607&#949;)</span>
3021                 </p>
3022               </td>
3023 <td>
3024                 <p>
3025                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3026                 </p>
3027               </td>
3028 <td>
3029                 <p>
3030                   <span class="blue">Max = 1.96&#949; (Mean = 1&#949;)</span>
3031                 </p>
3032               </td>
3033 <td>
3034                 <p>
3035                   <span class="blue">Max = 1.96&#949; (Mean = 1.04&#949;)</span>
3036                 </p>
3037               </td>
3038 </tr>
3039 <tr>
3040 <td>
3041                 <p>
3042                   Bessel K'n: Mathworld Data
3043                 </p>
3044               </td>
3045 <td>
3046                 <p>
3047                   <span class="blue">Max = 4.17&#949; (Mean = 1.74&#949;)</span>
3048                 </p>
3049               </td>
3050 <td>
3051                 <p>
3052                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3053                 </p>
3054               </td>
3055 <td>
3056                 <p>
3057                   <span class="blue">Max = 4.47&#949; (Mean = 2.05&#949;)</span>
3058                 </p>
3059               </td>
3060 <td>
3061                 <p>
3062                   <span class="blue">Max = 4.47&#949; (Mean = 1.93&#949;)</span>
3063                 </p>
3064               </td>
3065 </tr>
3066 <tr>
3067 <td>
3068                 <p>
3069                   Bessel K'v: Mathworld Data
3070                 </p>
3071               </td>
3072 <td>
3073                 <p>
3074                   <span class="blue">Max = 3.94&#949; (Mean = 1.43&#949;)</span>
3075                 </p>
3076               </td>
3077 <td>
3078                 <p>
3079                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3080                 </p>
3081               </td>
3082 <td>
3083                 <p>
3084                   <span class="blue">Max = 3.94&#949; (Mean = 2.49&#949;)</span>
3085                 </p>
3086               </td>
3087 <td>
3088                 <p>
3089                   <span class="blue">Max = 3.94&#949; (Mean = 2.35&#949;)</span>
3090                 </p>
3091               </td>
3092 </tr>
3093 <tr>
3094 <td>
3095                 <p>
3096                   Bessel K'v: Mathworld Data (large values)
3097                 </p>
3098               </td>
3099 <td>
3100                 <p>
3101                   <span class="blue">Max = 18.6&#949; (Mean = 12.1&#949;)</span>
3102                 </p>
3103               </td>
3104 <td>
3105                 <p>
3106                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3107                 </p>
3108               </td>
3109 <td>
3110                 <p>
3111                   <span class="blue">Max = 59.2&#949; (Mean = 42.9&#949;)</span>
3112                 </p>
3113               </td>
3114 <td>
3115                 <p>
3116                   <span class="blue">Max = 59.8&#949; (Mean = 43.4&#949;)</span>
3117                 </p>
3118               </td>
3119 </tr>
3120 <tr>
3121 <td>
3122                 <p>
3123                   Bessel K'n: Random Data
3124                 </p>
3125               </td>
3126 <td>
3127                 <p>
3128                   <span class="blue">Max = 8.18&#949; (Mean = 1.45&#949;)</span>
3129                 </p>
3130               </td>
3131 <td>
3132                 <p>
3133                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3134                 </p>
3135               </td>
3136 <td>
3137                 <p>
3138                   <span class="blue">Max = 4.53&#949; (Mean = 1.12&#949;)</span>
3139                 </p>
3140               </td>
3141 <td>
3142                 <p>
3143                   <span class="blue">Max = 4.45&#949; (Mean = 1.23&#949;)</span>
3144                 </p>
3145               </td>
3146 </tr>
3147 <tr>
3148 <td>
3149                 <p>
3150                   Bessel K'v: Random Data
3151                 </p>
3152               </td>
3153 <td>
3154                 <p>
3155                   <span class="blue">Max = 8.32&#949; (Mean = 1.65&#949;)</span>
3156                 </p>
3157               </td>
3158 <td>
3159                 <p>
3160                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3161                 </p>
3162               </td>
3163 <td>
3164                 <p>
3165                   <span class="blue">Max = 7.95&#949; (Mean = 1.53&#949;)</span>
3166                 </p>
3167               </td>
3168 <td>
3169                 <p>
3170                   <span class="blue">Max = 7.95&#949; (Mean = 1.55&#949;)</span>
3171                 </p>
3172               </td>
3173 </tr>
3174 </tbody>
3175 </table></div>
3176 </div>
3177 <br class="table-break"><div class="table">
3178 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table&#160;17.20.&#160;Error rates for cyl_bessel_k_prime (integer orders)</b></p>
3179 <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
3180 <colgroup>
3181 <col>
3182 <col>
3183 <col>
3184 <col>
3185 <col>
3186 </colgroup>
3187 <thead><tr>
3188 <th>
3189               </th>
3190 <th>
3191                 <p>
3192                   Microsoft Visual C++ version 12.0<br> Win32<br> double
3193                 </p>
3194               </th>
3195 <th>
3196                 <p>
3197                   GNU C++ version 5.1.0<br> linux<br> double
3198                 </p>
3199               </th>
3200 <th>
3201                 <p>
3202                   GNU C++ version 5.1.0<br> linux<br> long double
3203                 </p>
3204               </th>
3205 <th>
3206                 <p>
3207                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
3208                 </p>
3209               </th>
3210 </tr></thead>
3211 <tbody>
3212 <tr>
3213 <td>
3214                 <p>
3215                   Bessel K'0: Mathworld Data (Integer Version)
3216                 </p>
3217               </td>
3218 <td>
3219                 <p>
3220                   <span class="blue">Max = 1&#949; (Mean = 0.573&#949;)</span>
3221                 </p>
3222               </td>
3223 <td>
3224                 <p>
3225                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3226                 </p>
3227               </td>
3228 <td>
3229                 <p>
3230                   <span class="blue">Max = 1.8&#949; (Mean = 1.02&#949;)</span>
3231                 </p>
3232               </td>
3233 <td>
3234                 <p>
3235                   <span class="blue">Max = 1.8&#949; (Mean = 1.02&#949;)</span>
3236                 </p>
3237               </td>
3238 </tr>
3239 <tr>
3240 <td>
3241                 <p>
3242                   Bessel K'1: Mathworld Data (Integer Version)
3243                 </p>
3244               </td>
3245 <td>
3246                 <p>
3247                   <span class="blue">Max = 1.09&#949; (Mean = 0.607&#949;)</span>
3248                 </p>
3249               </td>
3250 <td>
3251                 <p>
3252                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3253                 </p>
3254               </td>
3255 <td>
3256                 <p>
3257                   <span class="blue">Max = 1.96&#949; (Mean = 1&#949;)</span>
3258                 </p>
3259               </td>
3260 <td>
3261                 <p>
3262                   <span class="blue">Max = 1.96&#949; (Mean = 1.04&#949;)</span>
3263                 </p>
3264               </td>
3265 </tr>
3266 <tr>
3267 <td>
3268                 <p>
3269                   Bessel K'n: Mathworld Data (Integer Version)
3270                 </p>
3271               </td>
3272 <td>
3273                 <p>
3274                   <span class="blue">Max = 4.17&#949; (Mean = 1.74&#949;)</span>
3275                 </p>
3276               </td>
3277 <td>
3278                 <p>
3279                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3280                 </p>
3281               </td>
3282 <td>
3283                 <p>
3284                   <span class="blue">Max = 4.47&#949; (Mean = 2.05&#949;)</span>
3285                 </p>
3286               </td>
3287 <td>
3288                 <p>
3289                   <span class="blue">Max = 4.47&#949; (Mean = 1.93&#949;)</span>
3290                 </p>
3291               </td>
3292 </tr>
3293 </tbody>
3294 </table></div>
3295 </div>
3296 <br class="table-break"><div class="table">
3297 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann"></a><p class="title"><b>Table&#160;17.21.&#160;Error rates for cyl_neumann</b></p>
3298 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
3299 <colgroup>
3300 <col>
3301 <col>
3302 <col>
3303 <col>
3304 <col>
3305 </colgroup>
3306 <thead><tr>
3307 <th>
3308               </th>
3309 <th>
3310                 <p>
3311                   Microsoft Visual C++ version 12.0<br> Win32<br> double
3312                 </p>
3313               </th>
3314 <th>
3315                 <p>
3316                   GNU C++ version 5.1.0<br> linux<br> double
3317                 </p>
3318               </th>
3319 <th>
3320                 <p>
3321                   GNU C++ version 5.1.0<br> linux<br> long double
3322                 </p>
3323               </th>
3324 <th>
3325                 <p>
3326                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
3327                 </p>
3328               </th>
3329 </tr></thead>
3330 <tbody>
3331 <tr>
3332 <td>
3333                 <p>
3334                   Y0: Mathworld Data
3335                 </p>
3336               </td>
3337 <td>
3338                 <p>
3339                   <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span>
3340                 </p>
3341               </td>
3342 <td>
3343                 <p>
3344                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3345                   1.16:</em></span> Max = 60.9&#949; (Mean = 20.4&#949;))<br> (<span class="emphasis"><em>Rmath
3346                   3.0.2:</em></span> Max = 167&#949; (Mean = 56.5&#949;))
3347                 </p>
3348               </td>
3349 <td>
3350                 <p>
3351                   <span class="blue">Max = 5.59&#949; (Mean = 2.54&#949;)</span><br> <br>
3352                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean =
3353                   6.87e+04&#949;))
3354                 </p>
3355               </td>
3356 <td>
3357                 <p>
3358                   <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
3359                 </p>
3360               </td>
3361 </tr>
3362 <tr>
3363 <td>
3364                 <p>
3365                   Y1: Mathworld Data
3366                 </p>
3367               </td>
3368 <td>
3369                 <p>
3370                   <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span>
3371                 </p>
3372               </td>
3373 <td>
3374                 <p>
3375                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3376                   1.16:</em></span> Max = 23.4&#949; (Mean = 8.1&#949;))<br> (<span class="emphasis"><em>Rmath
3377                   3.0.2:</em></span> Max = 193&#949; (Mean = 64.4&#949;))
3378                 </p>
3379               </td>
3380 <td>
3381                 <p>
3382                   <span class="blue">Max = 12.7&#949; (Mean = 4.34&#949;)</span><br> <br>
3383                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean =
3384                   4.08e+03&#949;))
3385                 </p>
3386               </td>
3387 <td>
3388                 <p>
3389                   <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
3390                 </p>
3391               </td>
3392 </tr>
3393 <tr>
3394 <td>
3395                 <p>
3396                   Yn: Mathworld Data
3397                 </p>
3398               </td>
3399 <td>
3400                 <p>
3401                   <span class="blue">Max = 35&#949; (Mean = 11.8&#949;)</span>
3402                 </p>
3403               </td>
3404 <td>
3405                 <p>
3406                   <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
3407                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;)
3408                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yn_Mathworld_Data">And
3409                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
3410                   Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
3411                 </p>
3412               </td>
3413 <td>
3414                 <p>
3415                   <span class="blue">Max = 55.2&#949; (Mean = 17.7&#949;)</span><br> <br>
3416                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
3417                   = 2.2e+20&#949; (Mean = 6.97e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yn_Mathworld_Data">And
3418                   other failures.</a>)</span>
3419                 </p>
3420               </td>
3421 <td>
3422                 <p>
3423                   <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
3424                 </p>
3425               </td>
3426 </tr>
3427 <tr>
3428 <td>
3429                 <p>
3430                   Yv: Mathworld Data
3431                 </p>
3432               </td>
3433 <td>
3434                 <p>
3435                   <span class="blue">Max = 7.89&#949; (Mean = 3.27&#949;)</span>
3436                 </p>
3437               </td>
3438 <td>
3439                 <p>
3440                   <span class="blue">Max = 10&#949; (Mean = 3.02&#949;)</span><br> <br>
3441                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.07e+05&#949; (Mean = 3.22e+04&#949;)
3442                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yv_Mathworld_Data">And
3443                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
3444                   Max = 1.05e+03&#949; (Mean = 326&#949;))
3445                 </p>
3446               </td>
3447 <td>
3448                 <p>
3449                   <span class="blue">Max = 10.7&#949; (Mean = 4.92&#949;)</span><br> <br>
3450                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
3451                   = 3.49e+15&#949; (Mean = 1.05e+15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Mathworld_Data">And
3452                   other failures.</a>)</span>
3453                 </p>
3454               </td>
3455 <td>
3456                 <p>
3457                   <span class="blue">Max = 10.7&#949; (Mean = 5.1&#949;)</span>
3458                 </p>
3459               </td>
3460 </tr>
3461 <tr>
3462 <td>
3463                 <p>
3464                   Yv: Mathworld Data (large values)
3465                 </p>
3466               </td>
3467 <td>
3468                 <p>
3469                   <span class="blue">Max = 0.682&#949; (Mean = 0.35&#949;)</span>
3470                 </p>
3471               </td>
3472 <td>
3473                 <p>
3474                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3475                   1.16:</em></span> Max = 60.8&#949; (Mean = 23&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_GSL_1_16_Yv_Mathworld_Data_large_values_">And
3476                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
3477                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_cyl_neumann_Rmath_3_0_2_Yv_Mathworld_Data_large_values_">And
3478                   other failures.</a>)</span>
3479                 </p>
3480               </td>
3481 <td>
3482                 <p>
3483                   <span class="blue">Max = 1.57&#949; (Mean = 1.17&#949;)</span><br> <br>
3484                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 43.2&#949; (Mean = 16.3&#949;)
3485                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Mathworld_Data_large_values_">And
3486                   other failures.</a>)
3487                 </p>
3488               </td>
3489 <td>
3490                 <p>
3491                   <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
3492                 </p>
3493               </td>
3494 </tr>
3495 <tr>
3496 <td>
3497                 <p>
3498                   Y0 and Y1: Random Data
3499                 </p>
3500               </td>
3501 <td>
3502                 <p>
3503                   <span class="blue">Max = 4.17&#949; (Mean = 1.24&#949;)</span>
3504                 </p>
3505               </td>
3506 <td>
3507                 <p>
3508                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3509                   1.16:</em></span> Max = 34.4&#949; (Mean = 8.9&#949;))<br> (<span class="emphasis"><em>Rmath
3510                   3.0.2:</em></span> Max = 83&#949; (Mean = 14.2&#949;))
3511                 </p>
3512               </td>
3513 <td>
3514                 <p>
3515                   <span class="blue">Max = 11.8&#949; (Mean = 3.28&#949;)</span><br> <br>
3516                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.59e+03&#949; (Mean =
3517                   500&#949;))
3518                 </p>
3519               </td>
3520 <td>
3521                 <p>
3522                   <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span>
3523                 </p>
3524               </td>
3525 </tr>
3526 <tr>
3527 <td>
3528                 <p>
3529                   Yn: Random Data
3530                 </p>
3531               </td>
3532 <td>
3533                 <p>
3534                   <span class="blue">Max = 117&#949; (Mean = 10.2&#949;)</span>
3535                 </p>
3536               </td>
3537 <td>
3538                 <p>
3539                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3540                   1.16:</em></span> Max = 500&#949; (Mean = 47.8&#949;))<br> (<span class="emphasis"><em>Rmath
3541                   3.0.2:</em></span> Max = 691&#949; (Mean = 67.9&#949;))
3542                 </p>
3543               </td>
3544 <td>
3545                 <p>
3546                   <span class="blue">Max = 338&#949; (Mean = 28.2&#949;)</span><br> <br>
3547                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 4.01e+03&#949; (Mean =
3548                   348&#949;))
3549                 </p>
3550               </td>
3551 <td>
3552                 <p>
3553                   <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span>
3554                 </p>
3555               </td>
3556 </tr>
3557 <tr>
3558 <td>
3559                 <p>
3560                   Yv: Random Data
3561                 </p>
3562               </td>
3563 <td>
3564                 <p>
3565                   <span class="blue">Max = 1.23e+003&#949; (Mean = 69.9&#949;)</span>
3566                 </p>
3567               </td>
3568 <td>
3569                 <p>
3570                   <span class="blue">Max = 1.53&#949; (Mean = 0.102&#949;)</span><br> <br>
3571                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.41e+06&#949; (Mean = 7.67e+04&#949;))<br>
3572                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.79e+05&#949; (Mean = 9.64e+03&#949;))
3573                 </p>
3574               </td>
3575 <td>
3576                 <p>
3577                   <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span><br>
3578                   <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
3579                   = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann__tr1_cmath__Yv_Random_Data">And
3580                   other failures.</a>)</span>
3581                 </p>
3582               </td>
3583 <td>
3584                 <p>
3585                   <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span>
3586                 </p>
3587               </td>
3588 </tr>
3589 </tbody>
3590 </table></div>
3591 </div>
3592 <br class="table-break"><div class="table">
3593 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table&#160;17.22.&#160;Error rates for cyl_neumann (integer orders)</b></p>
3594 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
3595 <colgroup>
3596 <col>
3597 <col>
3598 <col>
3599 <col>
3600 <col>
3601 </colgroup>
3602 <thead><tr>
3603 <th>
3604               </th>
3605 <th>
3606                 <p>
3607                   Microsoft Visual C++ version 12.0<br> Win32<br> double
3608                 </p>
3609               </th>
3610 <th>
3611                 <p>
3612                   GNU C++ version 5.1.0<br> linux<br> double
3613                 </p>
3614               </th>
3615 <th>
3616                 <p>
3617                   GNU C++ version 5.1.0<br> linux<br> long double
3618                 </p>
3619               </th>
3620 <th>
3621                 <p>
3622                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
3623                 </p>
3624               </th>
3625 </tr></thead>
3626 <tbody>
3627 <tr>
3628 <td>
3629                 <p>
3630                   Y0: Mathworld Data (Integer Version)
3631                 </p>
3632               </td>
3633 <td>
3634                 <p>
3635                   <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span><br> <br>
3636                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 5.37e+003&#949; (Mean = 1.81e+003&#949;))
3637                 </p>
3638               </td>
3639 <td>
3640                 <p>
3641                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3642                   1.16:</em></span> Max = 6.46&#949; (Mean = 2.38&#949;))<br> (<span class="emphasis"><em>Rmath
3643                   3.0.2:</em></span> Max = 167&#949; (Mean = 56.5&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
3644                   Max = 5.37e+03&#949; (Mean = 1.81e+03&#949;))
3645                 </p>
3646               </td>
3647 <td>
3648                 <p>
3649                   <span class="blue">Max = 5.59&#949; (Mean = 2.54&#949;)</span><br> <br>
3650                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean =
3651                   6.87e+04&#949;))
3652                 </p>
3653               </td>
3654 <td>
3655                 <p>
3656                   <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
3657                 </p>
3658               </td>
3659 </tr>
3660 <tr>
3661 <td>
3662                 <p>
3663                   Y1: Mathworld Data (Integer Version)
3664                 </p>
3665               </td>
3666 <td>
3667                 <p>
3668                   <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span><br> <br>
3669                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.86e+004&#949; (Mean = 6.2e+003&#949;))
3670                 </p>
3671               </td>
3672 <td>
3673                 <p>
3674                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
3675                   1.16:</em></span> Max = 1.51&#949; (Mean = 0.839&#949;))<br> (<span class="emphasis"><em>Rmath
3676                   3.0.2:</em></span> Max = 193&#949; (Mean = 64.4&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
3677                   Max = 1.86e+04&#949; (Mean = 6.2e+03&#949;))
3678                 </p>
3679               </td>
3680 <td>
3681                 <p>
3682                   <span class="blue">Max = 12.7&#949; (Mean = 4.34&#949;)</span><br> <br>
3683                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean =
3684                   4.08e+03&#949;))
3685                 </p>
3686               </td>
3687 <td>
3688                 <p>
3689                   <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
3690                 </p>
3691               </td>
3692 </tr>
3693 <tr>
3694 <td>
3695                 <p>
3696                   Yn: Mathworld Data (Integer Version)
3697                 </p>
3698               </td>
3699 <td>
3700                 <p>
3701                   <span class="blue">Max = 35&#949; (Mean = 11.8&#949;)</span><br> <br>
3702                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.49e+005&#949; (Mean = 8.14e+004&#949;))
3703                 </p>
3704               </td>
3705 <td>
3706                 <p>
3707                   <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
3708                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;))<br>
3709                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.24e+04&#949; (Mean = 4e+03&#949;))<br>
3710                   (<span class="emphasis"><em>Cephes:</em></span> Max = 2.49e+05&#949; (Mean = 8.14e+04&#949;))
3711                 </p>
3712               </td>
3713 <td>
3714                 <p>
3715                   <span class="blue">Max = 55.2&#949; (Mean = 17.7&#949;)</span><br> <br>
3716                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
3717                   = 2.2e+20&#949; (Mean = 6.97e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_cyl_neumann_integer_orders___tr1_cmath__Yn_Mathworld_Data_Integer_Version_">And
3718                   other failures.</a>)</span>
3719                 </p>
3720               </td>
3721 <td>
3722                 <p>
3723                   <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
3724                 </p>
3725               </td>
3726 </tr>
3727 </tbody>
3728 </table></div>
3729 </div>
3730 <br class="table-break"><div class="table">
3731 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime"></a><p class="title"><b>Table&#160;17.23.&#160;Error rates for cyl_neumann_prime</b></p>
3732 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
3733 <colgroup>
3734 <col>
3735 <col>
3736 <col>
3737 <col>
3738 <col>
3739 </colgroup>
3740 <thead><tr>
3741 <th>
3742               </th>
3743 <th>
3744                 <p>
3745                   Microsoft Visual C++ version 12.0<br> Win32<br> double
3746                 </p>
3747               </th>
3748 <th>
3749                 <p>
3750                   GNU C++ version 5.1.0<br> linux<br> double
3751                 </p>
3752               </th>
3753 <th>
3754                 <p>
3755                   GNU C++ version 5.1.0<br> linux<br> long double
3756                 </p>
3757               </th>
3758 <th>
3759                 <p>
3760                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
3761                 </p>
3762               </th>
3763 </tr></thead>
3764 <tbody>
3765 <tr>
3766 <td>
3767                 <p>
3768                   Y'0: Mathworld Data
3769                 </p>
3770               </td>
3771 <td>
3772                 <p>
3773                   <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
3774                 </p>
3775               </td>
3776 <td>
3777                 <p>
3778                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3779                 </p>
3780               </td>
3781 <td>
3782                 <p>
3783                   <span class="blue">Max = 12.7&#949; (Mean = 4.85&#949;)</span>
3784                 </p>
3785               </td>
3786 <td>
3787                 <p>
3788                   <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
3789                 </p>
3790               </td>
3791 </tr>
3792 <tr>
3793 <td>
3794                 <p>
3795                   Y'1: Mathworld Data
3796                 </p>
3797               </td>
3798 <td>
3799                 <p>
3800                   <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
3801                 </p>
3802               </td>
3803 <td>
3804                 <p>
3805                   <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
3806                 </p>
3807               </td>
3808 <td>
3809                 <p>
3810                   <span class="blue">Max = 36.6&#949; (Mean = 12.7&#949;)</span>
3811                 </p>
3812               </td>
3813 <td>
3814                 <p>
3815                   <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
3816                 </p>
3817               </td>
3818 </tr>
3819 <tr>
3820 <td>
3821                 <p>
3822                   Y'n: Mathworld Data
3823                 </p>
3824               </td>
3825 <td>
3826                 <p>
3827                   <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
3828                 </p>
3829               </td>
3830 <td>
3831                 <p>
3832                   <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
3833                 </p>
3834               </td>
3835 <td>
3836                 <p>
3837                   <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
3838                 </p>
3839               </td>
3840 <td>
3841                 <p>
3842                   <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
3843                 </p>
3844               </td>
3845 </tr>
3846 <tr>
3847 <td>
3848                 <p>
3849                   Y'v: Mathworld Data
3850                 </p>
3851               </td>
3852 <td>
3853                 <p>
3854                   <span class="blue">Max = 23.7&#949; (Mean = 10.1&#949;)</span>
3855                 </p>
3856               </td>
3857 <td>
3858                 <p>
3859                   <span class="blue">Max = 21.5&#949; (Mean = 6.49&#949;)</span>
3860                 </p>
3861               </td>
3862 <td>
3863                 <p>
3864                   <span class="blue">Max = 42.5&#949; (Mean = 13.4&#949;)</span>
3865                 </p>
3866               </td>
3867 <td>
3868                 <p>
3869                   <span class="blue">Max = 42.5&#949; (Mean = 13.6&#949;)</span>
3870                 </p>
3871               </td>
3872 </tr>
3873 <tr>
3874 <td>
3875                 <p>
3876                   Y'v: Mathworld Data (large values)
3877                 </p>
3878               </td>
3879 <td>
3880                 <p>
3881                   <span class="blue">Max = 0.627&#949; (Mean = 0.237&#949;)</span>
3882                 </p>
3883               </td>
3884 <td>
3885                 <p>
3886                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3887                 </p>
3888               </td>
3889 <td>
3890                 <p>
3891                   <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
3892                 </p>
3893               </td>
3894 <td>
3895                 <p>
3896                   <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
3897                 </p>
3898               </td>
3899 </tr>
3900 <tr>
3901 <td>
3902                 <p>
3903                   Y'0 and Y'1: Random Data
3904                 </p>
3905               </td>
3906 <td>
3907                 <p>
3908                   <span class="blue">Max = 5.95&#949; (Mean = 1.36&#949;)</span>
3909                 </p>
3910               </td>
3911 <td>
3912                 <p>
3913                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
3914                 </p>
3915               </td>
3916 <td>
3917                 <p>
3918                   <span class="blue">Max = 23.8&#949; (Mean = 3.84&#949;)</span>
3919                 </p>
3920               </td>
3921 <td>
3922                 <p>
3923                   <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
3924                 </p>
3925               </td>
3926 </tr>
3927 <tr>
3928 <td>
3929                 <p>
3930                   Y'n: Random Data
3931                 </p>
3932               </td>
3933 <td>
3934                 <p>
3935                   <span class="blue">Max = 621&#949; (Mean = 36&#949;)</span>
3936                 </p>
3937               </td>
3938 <td>
3939                 <p>
3940                   <span class="blue">Max = 1.53&#949; (Mean = 0.0885&#949;)</span>
3941                 </p>
3942               </td>
3943 <td>
3944                 <p>
3945                   <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
3946                 </p>
3947               </td>
3948 <td>
3949                 <p>
3950                   <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
3951                 </p>
3952               </td>
3953 </tr>
3954 <tr>
3955 <td>
3956                 <p>
3957                   Y'v: Random Data
3958                 </p>
3959               </td>
3960 <td>
3961                 <p>
3962                   <span class="blue">Max = 3.23e+004&#949; (Mean = 1.13e+003&#949;)</span>
3963                 </p>
3964               </td>
3965 <td>
3966                 <p>
3967                   <span class="blue">Max = 56.8&#949; (Mean = 2.59&#949;)</span>
3968                 </p>
3969               </td>
3970 <td>
3971                 <p>
3972                   <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
3973                 </p>
3974               </td>
3975 <td>
3976                 <p>
3977                   <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
3978                 </p>
3979               </td>
3980 </tr>
3981 </tbody>
3982 </table></div>
3983 </div>
3984 <br class="table-break"><div class="table">
3985 <a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table&#160;17.24.&#160;Error rates for cyl_neumann_prime (integer orders)</b></p>
3986 <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
3987 <colgroup>
3988 <col>
3989 <col>
3990 <col>
3991 <col>
3992 <col>
3993 </colgroup>
3994 <thead><tr>
3995 <th>
3996               </th>
3997 <th>
3998                 <p>
3999                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4000                 </p>
4001               </th>
4002 <th>
4003                 <p>
4004                   GNU C++ version 5.1.0<br> linux<br> double
4005                 </p>
4006               </th>
4007 <th>
4008                 <p>
4009                   GNU C++ version 5.1.0<br> linux<br> long double
4010                 </p>
4011               </th>
4012 <th>
4013                 <p>
4014                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
4015                 </p>
4016               </th>
4017 </tr></thead>
4018 <tbody>
4019 <tr>
4020 <td>
4021                 <p>
4022                   Y'0: Mathworld Data (Integer Version)
4023                 </p>
4024               </td>
4025 <td>
4026                 <p>
4027                   <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
4028                 </p>
4029               </td>
4030 <td>
4031                 <p>
4032                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4033                 </p>
4034               </td>
4035 <td>
4036                 <p>
4037                   <span class="blue">Max = 12.7&#949; (Mean = 4.85&#949;)</span>
4038                 </p>
4039               </td>
4040 <td>
4041                 <p>
4042                   <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
4043                 </p>
4044               </td>
4045 </tr>
4046 <tr>
4047 <td>
4048                 <p>
4049                   Y'1: Mathworld Data (Integer Version)
4050                 </p>
4051               </td>
4052 <td>
4053                 <p>
4054                   <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
4055                 </p>
4056               </td>
4057 <td>
4058                 <p>
4059                   <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
4060                 </p>
4061               </td>
4062 <td>
4063                 <p>
4064                   <span class="blue">Max = 36.6&#949; (Mean = 12.7&#949;)</span>
4065                 </p>
4066               </td>
4067 <td>
4068                 <p>
4069                   <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
4070                 </p>
4071               </td>
4072 </tr>
4073 <tr>
4074 <td>
4075                 <p>
4076                   Y'n: Mathworld Data (Integer Version)
4077                 </p>
4078               </td>
4079 <td>
4080                 <p>
4081                   <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
4082                 </p>
4083               </td>
4084 <td>
4085                 <p>
4086                   <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
4087                 </p>
4088               </td>
4089 <td>
4090                 <p>
4091                   <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
4092                 </p>
4093               </td>
4094 <td>
4095                 <p>
4096                   <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
4097                 </p>
4098               </td>
4099 </tr>
4100 </tbody>
4101 </table></div>
4102 </div>
4103 <br class="table-break"><div class="table">
4104 <a name="math_toolkit.logs_and_tables.all_table.table_digamma"></a><p class="title"><b>Table&#160;17.25.&#160;Error rates for digamma</b></p>
4105 <div class="table-contents"><table class="table" summary="Error rates for digamma">
4106 <colgroup>
4107 <col>
4108 <col>
4109 <col>
4110 <col>
4111 <col>
4112 </colgroup>
4113 <thead><tr>
4114 <th>
4115               </th>
4116 <th>
4117                 <p>
4118                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4119                 </p>
4120               </th>
4121 <th>
4122                 <p>
4123                   GNU C++ version 5.1.0<br> linux<br> double
4124                 </p>
4125               </th>
4126 <th>
4127                 <p>
4128                   GNU C++ version 5.1.0<br> linux<br> long double
4129                 </p>
4130               </th>
4131 <th>
4132                 <p>
4133                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
4134                 </p>
4135               </th>
4136 </tr></thead>
4137 <tbody>
4138 <tr>
4139 <td>
4140                 <p>
4141                   Digamma Function: Large Values
4142                 </p>
4143               </td>
4144 <td>
4145                 <p>
4146                   <span class="blue">Max = 0.98&#949; (Mean = 0.369&#949;)</span>
4147                 </p>
4148               </td>
4149 <td>
4150                 <p>
4151                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4152                   1.16:</em></span> Max = 1.84&#949; (Mean = 0.71&#949;))<br> (<span class="emphasis"><em>Rmath
4153                   3.0.2:</em></span> Max = 1.18&#949; (Mean = 0.331&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4154                   Max = 0.919&#949; (Mean = 0.394&#949;))
4155                 </p>
4156               </td>
4157 <td>
4158                 <p>
4159                   <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
4160                 </p>
4161               </td>
4162 <td>
4163                 <p>
4164                   <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
4165                 </p>
4166               </td>
4167 </tr>
4168 <tr>
4169 <td>
4170                 <p>
4171                   Digamma Function: Near the Positive Root
4172                 </p>
4173               </td>
4174 <td>
4175                 <p>
4176                   <span class="blue">Max = 0.997&#949; (Mean = 0.527&#949;)</span>
4177                 </p>
4178               </td>
4179 <td>
4180                 <p>
4181                   <span class="blue">Max = 0.891&#949; (Mean = 0.0995&#949;)</span><br>
4182                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 135&#949; (Mean = 11.9&#949;))<br>
4183                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.02e+03&#949; (Mean = 256&#949;))<br>
4184                   (<span class="emphasis"><em>Cephes:</em></span> Max = 1.42e+04&#949; (Mean = 1.14e+03&#949;))
4185                 </p>
4186               </td>
4187 <td>
4188                 <p>
4189                   <span class="blue">Max = 1.37&#949; (Mean = 0.477&#949;)</span>
4190                 </p>
4191               </td>
4192 <td>
4193                 <p>
4194                   <span class="blue">Max = 1.31&#949; (Mean = 0.451&#949;)</span>
4195                 </p>
4196               </td>
4197 </tr>
4198 <tr>
4199 <td>
4200                 <p>
4201                   Digamma Function: Near Zero
4202                 </p>
4203               </td>
4204 <td>
4205                 <p>
4206                   <span class="blue">Max = 0.953&#949; (Mean = 0.337&#949;)</span>
4207                 </p>
4208               </td>
4209 <td>
4210                 <p>
4211                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4212                   1.16:</em></span> Max = 0.953&#949; (Mean = 0.348&#949;))<br> (<span class="emphasis"><em>Rmath
4213                   3.0.2:</em></span> Max = 1.17&#949; (Mean = 0.564&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4214                   Max = 3.5&#949; (Mean = 1.04&#949;))
4215                 </p>
4216               </td>
4217 <td>
4218                 <p>
4219                   <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
4220                 </p>
4221               </td>
4222 <td>
4223                 <p>
4224                   <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
4225                 </p>
4226               </td>
4227 </tr>
4228 <tr>
4229 <td>
4230                 <p>
4231                   Digamma Function: Negative Values
4232                 </p>
4233               </td>
4234 <td>
4235                 <p>
4236                   <span class="blue">Max = 214&#949; (Mean = 16.1&#949;)</span>
4237                 </p>
4238               </td>
4239 <td>
4240                 <p>
4241                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4242                   1.16:</em></span> Max = 4.56e+04&#949; (Mean = 3.91e+03&#949;))<br> (<span class="emphasis"><em>Rmath
4243                   3.0.2:</em></span> Max = 4.6e+04&#949; (Mean = 3.94e+03&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4244                   Max = 214&#949; (Mean = 16.4&#949;))
4245                 </p>
4246               </td>
4247 <td>
4248                 <p>
4249                   <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
4250                 </p>
4251               </td>
4252 <td>
4253                 <p>
4254                   <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
4255                 </p>
4256               </td>
4257 </tr>
4258 <tr>
4259 <td>
4260                 <p>
4261                   Digamma Function: Values near 0
4262                 </p>
4263               </td>
4264 <td>
4265                 <p>
4266                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
4267                 </p>
4268               </td>
4269 <td>
4270                 <p>
4271                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4272                   1.16:</em></span> Max = 0.866&#949; (Mean = 0.387&#949;))<br> (<span class="emphasis"><em>Rmath
4273                   3.0.2:</em></span> Max = 3.58e+05&#949; (Mean = 1.6e+05&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4274                   Max = 0.5&#949; (Mean = 0.224&#949;))
4275                 </p>
4276               </td>
4277 <td>
4278                 <p>
4279                   <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
4280                 </p>
4281               </td>
4282 <td>
4283                 <p>
4284                   <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
4285                 </p>
4286               </td>
4287 </tr>
4288 <tr>
4289 <td>
4290                 <p>
4291                   Digamma Function: Integer arguments
4292                 </p>
4293               </td>
4294 <td>
4295                 <p>
4296                   <span class="blue">Max = 0.992&#949; (Mean = 0.452&#949;)</span>
4297                 </p>
4298               </td>
4299 <td>
4300                 <p>
4301                   <span class="blue">Max = 0.992&#949; (Mean = 0.215&#949;)</span><br> <br>
4302                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.18&#949; (Mean = 0.607&#949;))<br>
4303                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.33&#949; (Mean = 0.982&#949;))<br>
4304                   (<span class="emphasis"><em>Cephes:</em></span> Max = 0.992&#949; (Mean = 0.383&#949;))
4305                 </p>
4306               </td>
4307 <td>
4308                 <p>
4309                   <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
4310                 </p>
4311               </td>
4312 <td>
4313                 <p>
4314                   <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
4315                 </p>
4316               </td>
4317 </tr>
4318 <tr>
4319 <td>
4320                 <p>
4321                   Digamma Function: Half integer arguments
4322                 </p>
4323               </td>
4324 <td>
4325                 <p>
4326                   <span class="blue">Max = 0.78&#949; (Mean = 0.314&#949;)</span>
4327                 </p>
4328               </td>
4329 <td>
4330                 <p>
4331                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4332                   1.16:</em></span> Max = 1.09&#949; (Mean = 0.531&#949;))<br> (<span class="emphasis"><em>Rmath
4333                   3.0.2:</em></span> Max = 46.2&#949; (Mean = 7.24&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4334                   Max = 8.56&#949; (Mean = 1.44&#949;))
4335                 </p>
4336               </td>
4337 <td>
4338                 <p>
4339                   <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
4340                 </p>
4341               </td>
4342 <td>
4343                 <p>
4344                   <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
4345                 </p>
4346               </td>
4347 </tr>
4348 </tbody>
4349 </table></div>
4350 </div>
4351 <br class="table-break"><div class="table">
4352 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_1"></a><p class="title"><b>Table&#160;17.26.&#160;Error rates for ellint_1</b></p>
4353 <div class="table-contents"><table class="table" summary="Error rates for ellint_1">
4354 <colgroup>
4355 <col>
4356 <col>
4357 <col>
4358 <col>
4359 <col>
4360 </colgroup>
4361 <thead><tr>
4362 <th>
4363               </th>
4364 <th>
4365                 <p>
4366                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4367                 </p>
4368               </th>
4369 <th>
4370                 <p>
4371                   GNU C++ version 5.1.0<br> linux<br> long double
4372                 </p>
4373               </th>
4374 <th>
4375                 <p>
4376                   GNU C++ version 5.1.0<br> linux<br> double
4377                 </p>
4378               </th>
4379 <th>
4380                 <p>
4381                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
4382                 </p>
4383               </th>
4384 </tr></thead>
4385 <tbody>
4386 <tr>
4387 <td>
4388                 <p>
4389                   Elliptic Integral F: Mathworld Data
4390                 </p>
4391               </td>
4392 <td>
4393                 <p>
4394                   <span class="blue">Max = 0.919&#949; (Mean = 0.542&#949;)</span>
4395                 </p>
4396               </td>
4397 <td>
4398                 <p>
4399                   <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span><br> <br>
4400                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
4401                   = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_1__tr1_cmath__Elliptic_Integral_F_Mathworld_Data">And
4402                   other failures.</a>)</span>
4403                 </p>
4404               </td>
4405 <td>
4406                 <p>
4407                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4408                   1.16:</em></span> Max = 0.919&#949; (Mean = 0.544&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4409                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_1_Cephes_Elliptic_Integral_F_Mathworld_Data">And
4410                   other failures.</a>)</span>
4411                 </p>
4412               </td>
4413 <td>
4414                 <p>
4415                   <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span>
4416                 </p>
4417               </td>
4418 </tr>
4419 <tr>
4420 <td>
4421                 <p>
4422                   Elliptic Integral F: Random Data
4423                 </p>
4424               </td>
4425 <td>
4426                 <p>
4427                   <span class="blue">Max = 2.26&#949; (Mean = 0.631&#949;)</span>
4428                 </p>
4429               </td>
4430 <td>
4431                 <p>
4432                   <span class="blue">Max = 1.57&#949; (Mean = 0.56&#949;)</span><br> <br>
4433                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.56&#949; (Mean = 0.816&#949;))
4434                 </p>
4435               </td>
4436 <td>
4437                 <p>
4438                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4439                   1.16:</em></span> Max = 2.99&#949; (Mean = 0.797&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4440                   Max = 2.18&#949; (Mean = 0.535&#949;))
4441                 </p>
4442               </td>
4443 <td>
4444                 <p>
4445                   <span class="blue">Max = 1.57&#949; (Mean = 0.561&#949;)</span>
4446                 </p>
4447               </td>
4448 </tr>
4449 </tbody>
4450 </table></div>
4451 </div>
4452 <br class="table-break"><div class="table">
4453 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_1_complete_"></a><p class="title"><b>Table&#160;17.27.&#160;Error rates for ellint_1 (complete)</b></p>
4454 <div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
4455 <colgroup>
4456 <col>
4457 <col>
4458 <col>
4459 <col>
4460 <col>
4461 </colgroup>
4462 <thead><tr>
4463 <th>
4464               </th>
4465 <th>
4466                 <p>
4467                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4468                 </p>
4469               </th>
4470 <th>
4471                 <p>
4472                   GNU C++ version 5.1.0<br> linux<br> long double
4473                 </p>
4474               </th>
4475 <th>
4476                 <p>
4477                   GNU C++ version 5.1.0<br> linux<br> double
4478                 </p>
4479               </th>
4480 <th>
4481                 <p>
4482                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
4483                 </p>
4484               </th>
4485 </tr></thead>
4486 <tbody>
4487 <tr>
4488 <td>
4489                 <p>
4490                   Elliptic Integral K: Mathworld Data
4491                 </p>
4492               </td>
4493 <td>
4494                 <p>
4495                   <span class="blue">Max = 0.915&#949; (Mean = 0.547&#949;)</span>
4496                 </p>
4497               </td>
4498 <td>
4499                 <p>
4500                   <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span><br> <br>
4501                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.19&#949; (Mean = 0.765&#949;))
4502                 </p>
4503               </td>
4504 <td>
4505                 <p>
4506                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4507                   1.16:</em></span> Max = 0.623&#949; (Mean = 0.393&#949;))
4508                 </p>
4509               </td>
4510 <td>
4511                 <p>
4512                   <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span>
4513                 </p>
4514               </td>
4515 </tr>
4516 <tr>
4517 <td>
4518                 <p>
4519                   Elliptic Integral K: Random Data
4520                 </p>
4521               </td>
4522 <td>
4523                 <p>
4524                   <span class="blue">Max = 0.958&#949; (Mean = 0.408&#949;)</span>
4525                 </p>
4526               </td>
4527 <td>
4528                 <p>
4529                   <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span><br> <br>
4530                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.19&#949; (Mean = 0.694&#949;))
4531                 </p>
4532               </td>
4533 <td>
4534                 <p>
4535                   <span class="blue">Max = 0.851&#949; (Mean = 0.0851&#949;)</span><br>
4536                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.32&#949; (Mean = 0.688&#949;))
4537                 </p>
4538               </td>
4539 <td>
4540                 <p>
4541                   <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span>
4542                 </p>
4543               </td>
4544 </tr>
4545 </tbody>
4546 </table></div>
4547 </div>
4548 <br class="table-break"><div class="table">
4549 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_2"></a><p class="title"><b>Table&#160;17.28.&#160;Error rates for ellint_2</b></p>
4550 <div class="table-contents"><table class="table" summary="Error rates for ellint_2">
4551 <colgroup>
4552 <col>
4553 <col>
4554 <col>
4555 <col>
4556 <col>
4557 </colgroup>
4558 <thead><tr>
4559 <th>
4560               </th>
4561 <th>
4562                 <p>
4563                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4564                 </p>
4565               </th>
4566 <th>
4567                 <p>
4568                   GNU C++ version 5.1.0<br> linux<br> long double
4569                 </p>
4570               </th>
4571 <th>
4572                 <p>
4573                   GNU C++ version 5.1.0<br> linux<br> double
4574                 </p>
4575               </th>
4576 <th>
4577                 <p>
4578                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
4579                 </p>
4580               </th>
4581 </tr></thead>
4582 <tbody>
4583 <tr>
4584 <td>
4585                 <p>
4586                   Elliptic Integral E: Mathworld Data
4587                 </p>
4588               </td>
4589 <td>
4590                 <p>
4591                   <span class="blue">Max = 1.31&#949; (Mean = 0.727&#949;)</span>
4592                 </p>
4593               </td>
4594 <td>
4595                 <p>
4596                   <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span><br> <br>
4597                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
4598                   = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_2__tr1_cmath__Elliptic_Integral_E_Mathworld_Data">And
4599                   other failures.</a>)</span>
4600                 </p>
4601               </td>
4602 <td>
4603                 <p>
4604                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4605                   1.16:</em></span> Max = 0.63&#949; (Mean = 0.325&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4606                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_2_Cephes_Elliptic_Integral_E_Mathworld_Data">And
4607                   other failures.</a>)</span>
4608                 </p>
4609               </td>
4610 <td>
4611                 <p>
4612                   <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span>
4613                 </p>
4614               </td>
4615 </tr>
4616 <tr>
4617 <td>
4618                 <p>
4619                   Elliptic Integral E: Random Data
4620                 </p>
4621               </td>
4622 <td>
4623                 <p>
4624                   <span class="blue">Max = 2.23&#949; (Mean = 0.639&#949;)</span>
4625                 </p>
4626               </td>
4627 <td>
4628                 <p>
4629                   <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span><br> <br>
4630                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 3.08e+04&#949; (Mean =
4631                   3.84e+03&#949;))
4632                 </p>
4633               </td>
4634 <td>
4635                 <p>
4636                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4637                   1.16:</em></span> Max = 4.4&#949; (Mean = 1.16&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
4638                   Max = 8.92&#949; (Mean = 1.48&#949;))
4639                 </p>
4640               </td>
4641 <td>
4642                 <p>
4643                   <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span>
4644                 </p>
4645               </td>
4646 </tr>
4647 </tbody>
4648 </table></div>
4649 </div>
4650 <br class="table-break"><div class="table">
4651 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_2_complete_"></a><p class="title"><b>Table&#160;17.29.&#160;Error rates for ellint_2 (complete)</b></p>
4652 <div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
4653 <colgroup>
4654 <col>
4655 <col>
4656 <col>
4657 <col>
4658 <col>
4659 </colgroup>
4660 <thead><tr>
4661 <th>
4662               </th>
4663 <th>
4664                 <p>
4665                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4666                 </p>
4667               </th>
4668 <th>
4669                 <p>
4670                   GNU C++ version 5.1.0<br> linux<br> long double
4671                 </p>
4672               </th>
4673 <th>
4674                 <p>
4675                   GNU C++ version 5.1.0<br> linux<br> double
4676                 </p>
4677               </th>
4678 <th>
4679                 <p>
4680                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
4681                 </p>
4682               </th>
4683 </tr></thead>
4684 <tbody>
4685 <tr>
4686 <td>
4687                 <p>
4688                   Elliptic Integral E: Mathworld Data
4689                 </p>
4690               </td>
4691 <td>
4692                 <p>
4693                   <span class="blue">Max = 1.3&#949; (Mean = 0.615&#949;)</span>
4694                 </p>
4695               </td>
4696 <td>
4697                 <p>
4698                   <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span><br> <br>
4699                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 170&#949; (Mean = 55.1&#949;))
4700                 </p>
4701               </td>
4702 <td>
4703                 <p>
4704                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4705                   1.16:</em></span> Max = 3.09&#949; (Mean = 1.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_2_complete__GSL_1_16_Elliptic_Integral_E_Mathworld_Data">And
4706                   other failures.</a>)
4707                 </p>
4708               </td>
4709 <td>
4710                 <p>
4711                   <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span>
4712                 </p>
4713               </td>
4714 </tr>
4715 <tr>
4716 <td>
4717                 <p>
4718                   Elliptic Integral E: Random Data
4719                 </p>
4720               </td>
4721 <td>
4722                 <p>
4723                   <span class="blue">Max = 1.71&#949; (Mean = 0.553&#949;)</span>
4724                 </p>
4725               </td>
4726 <td>
4727                 <p>
4728                   <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span><br> <br>
4729                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.49e+04&#949; (Mean =
4730                   3.39e+03&#949;))
4731                 </p>
4732               </td>
4733 <td>
4734                 <p>
4735                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4736                   1.16:</em></span> Max = 4.34&#949; (Mean = 1.18&#949;))
4737                 </p>
4738               </td>
4739 <td>
4740                 <p>
4741                   <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span>
4742                 </p>
4743               </td>
4744 </tr>
4745 </tbody>
4746 </table></div>
4747 </div>
4748 <br class="table-break"><div class="table">
4749 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_3"></a><p class="title"><b>Table&#160;17.30.&#160;Error rates for ellint_3</b></p>
4750 <div class="table-contents"><table class="table" summary="Error rates for ellint_3">
4751 <colgroup>
4752 <col>
4753 <col>
4754 <col>
4755 <col>
4756 <col>
4757 </colgroup>
4758 <thead><tr>
4759 <th>
4760               </th>
4761 <th>
4762                 <p>
4763                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4764                 </p>
4765               </th>
4766 <th>
4767                 <p>
4768                   GNU C++ version 5.1.0<br> linux<br> long double
4769                 </p>
4770               </th>
4771 <th>
4772                 <p>
4773                   GNU C++ version 5.1.0<br> linux<br> double
4774                 </p>
4775               </th>
4776 <th>
4777                 <p>
4778                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
4779                 </p>
4780               </th>
4781 </tr></thead>
4782 <tbody>
4783 <tr>
4784 <td>
4785                 <p>
4786                   Elliptic Integral PI: Mathworld Data
4787                 </p>
4788               </td>
4789 <td>
4790                 <p>
4791                   <span class="blue">Max = 565&#949; (Mean = 102&#949;)</span>
4792                 </p>
4793               </td>
4794 <td>
4795                 <p>
4796                   <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span><br> <br>
4797                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
4798                   = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Mathworld_Data">And
4799                   other failures.</a>)</span>
4800                 </p>
4801               </td>
4802 <td>
4803                 <p>
4804                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4805                   1.16:</em></span> Max = 1.48e+05&#949; (Mean = 2.54e+04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_3_GSL_1_16_Elliptic_Integral_PI_Mathworld_Data">And
4806                   other failures.</a>)
4807                 </p>
4808               </td>
4809 <td>
4810                 <p>
4811                   <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span>
4812                 </p>
4813               </td>
4814 </tr>
4815 <tr>
4816 <td>
4817                 <p>
4818                   Elliptic Integral PI: Random Data
4819                 </p>
4820               </td>
4821 <td>
4822                 <p>
4823                   <span class="blue">Max = 9.08&#949; (Mean = 0.99&#949;)</span>
4824                 </p>
4825               </td>
4826 <td>
4827                 <p>
4828                   <span class="blue">Max = 4.54&#949; (Mean = 0.895&#949;)</span><br> <br>
4829                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
4830                   = 3.37e+20&#949; (Mean = 3.47e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Random_Data">And
4831                   other failures.</a>)</span>
4832                 </p>
4833               </td>
4834 <td>
4835                 <p>
4836                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4837                   1.16:</em></span> Max = 633&#949; (Mean = 50.1&#949;))
4838                 </p>
4839               </td>
4840 <td>
4841                 <p>
4842                   <span class="blue">Max = 4.49&#949; (Mean = 0.891&#949;)</span>
4843                 </p>
4844               </td>
4845 </tr>
4846 <tr>
4847 <td>
4848                 <p>
4849                   Elliptic Integral PI: Large Random Data
4850                 </p>
4851               </td>
4852 <td>
4853                 <p>
4854                   <span class="blue">Max = 2.86&#949; (Mean = 0.944&#949;)</span>
4855                 </p>
4856               </td>
4857 <td>
4858                 <p>
4859                   <span class="blue">Max = 3.7&#949; (Mean = 0.893&#949;)</span><br> <br>
4860                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
4861                   = 2.52e+18&#949; (Mean = 4.83e+17&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3__tr1_cmath__Elliptic_Integral_PI_Large_Random_Data">And
4862                   other failures.</a>)</span>
4863                 </p>
4864               </td>
4865 <td>
4866                 <p>
4867                   <span class="blue">Max = 0.557&#949; (Mean = 0.0389&#949;)</span><br>
4868                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 40.1&#949; (Mean = 7.77&#949;))
4869                 </p>
4870               </td>
4871 <td>
4872                 <p>
4873                   <span class="blue">Max = 3.7&#949; (Mean = 0.892&#949;)</span>
4874                 </p>
4875               </td>
4876 </tr>
4877 </tbody>
4878 </table></div>
4879 </div>
4880 <br class="table-break"><div class="table">
4881 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_3_complete_"></a><p class="title"><b>Table&#160;17.31.&#160;Error rates for ellint_3 (complete)</b></p>
4882 <div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
4883 <colgroup>
4884 <col>
4885 <col>
4886 <col>
4887 <col>
4888 <col>
4889 </colgroup>
4890 <thead><tr>
4891 <th>
4892               </th>
4893 <th>
4894                 <p>
4895                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4896                 </p>
4897               </th>
4898 <th>
4899                 <p>
4900                   GNU C++ version 5.1.0<br> linux<br> long double
4901                 </p>
4902               </th>
4903 <th>
4904                 <p>
4905                   GNU C++ version 5.1.0<br> linux<br> double
4906                 </p>
4907               </th>
4908 <th>
4909                 <p>
4910                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
4911                 </p>
4912               </th>
4913 </tr></thead>
4914 <tbody>
4915 <tr>
4916 <td>
4917                 <p>
4918                   Complete Elliptic Integral PI: Mathworld Data
4919                 </p>
4920               </td>
4921 <td>
4922                 <p>
4923                   <span class="blue">Max = 0.971&#949; (Mean = 0.464&#949;)</span>
4924                 </p>
4925               </td>
4926 <td>
4927                 <p>
4928                   <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span><br> <br>
4929                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
4930                   = 6.31e+20&#949; (Mean = 1.53e+20&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3_complete___tr1_cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
4931                   other failures.</a>)</span>
4932                 </p>
4933               </td>
4934 <td>
4935                 <p>
4936                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4937                   1.16:</em></span> Max = 6.33e+04&#949; (Mean = 1.54e+04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_3_complete__GSL_1_16_Complete_Elliptic_Integral_PI_Mathworld_Data">And
4938                   other failures.</a>)
4939                 </p>
4940               </td>
4941 <td>
4942                 <p>
4943                   <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span>
4944                 </p>
4945               </td>
4946 </tr>
4947 <tr>
4948 <td>
4949                 <p>
4950                   Complete Elliptic Integral PI: Random Data
4951                 </p>
4952               </td>
4953 <td>
4954                 <p>
4955                   <span class="blue">Max = 2.46&#949; (Mean = 0.654&#949;)</span>
4956                 </p>
4957               </td>
4958 <td>
4959                 <p>
4960                   <span class="blue">Max = 2.45&#949; (Mean = 0.696&#949;)</span><br> <br>
4961                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
4962                   = 8.78e+20&#949; (Mean = 1.02e+20&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_ellint_3_complete___tr1_cmath__Complete_Elliptic_Integral_PI_Random_Data">And
4963                   other failures.</a>)</span>
4964                 </p>
4965               </td>
4966 <td>
4967                 <p>
4968                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
4969                   1.16:</em></span> Max = 24&#949; (Mean = 2.99&#949;))
4970                 </p>
4971               </td>
4972 <td>
4973                 <p>
4974                   <span class="blue">Max = 2.4&#949; (Mean = 0.681&#949;)</span>
4975                 </p>
4976               </td>
4977 </tr>
4978 </tbody>
4979 </table></div>
4980 </div>
4981 <br class="table-break"><div class="table">
4982 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_d"></a><p class="title"><b>Table&#160;17.32.&#160;Error rates for ellint_d</b></p>
4983 <div class="table-contents"><table class="table" summary="Error rates for ellint_d">
4984 <colgroup>
4985 <col>
4986 <col>
4987 <col>
4988 <col>
4989 <col>
4990 </colgroup>
4991 <thead><tr>
4992 <th>
4993               </th>
4994 <th>
4995                 <p>
4996                   Microsoft Visual C++ version 12.0<br> Win32<br> double
4997                 </p>
4998               </th>
4999 <th>
5000                 <p>
5001                   GNU C++ version 5.1.0<br> linux<br> double
5002                 </p>
5003               </th>
5004 <th>
5005                 <p>
5006                   GNU C++ version 5.1.0<br> linux<br> long double
5007                 </p>
5008               </th>
5009 <th>
5010                 <p>
5011                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
5012                 </p>
5013               </th>
5014 </tr></thead>
5015 <tbody>
5016 <tr>
5017 <td>
5018                 <p>
5019                   Elliptic Integral E: Mathworld Data
5020                 </p>
5021               </td>
5022 <td>
5023                 <p>
5024                   <span class="blue">Max = 0.862&#949; (Mean = 0.457&#949;)</span>
5025                 </p>
5026               </td>
5027 <td>
5028                 <p>
5029                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5030                   1.16:</em></span> Max = 0.862&#949; (Mean = 0.568&#949;))
5031                 </p>
5032               </td>
5033 <td>
5034                 <p>
5035                   <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
5036                 </p>
5037               </td>
5038 <td>
5039                 <p>
5040                   <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
5041                 </p>
5042               </td>
5043 </tr>
5044 <tr>
5045 <td>
5046                 <p>
5047                   Elliptic Integral D: Random Data
5048                 </p>
5049               </td>
5050 <td>
5051                 <p>
5052                   <span class="blue">Max = 2.87&#949; (Mean = 0.805&#949;)</span>
5053                 </p>
5054               </td>
5055 <td>
5056                 <p>
5057                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5058                   1.16:</em></span> Max = 3.01&#949; (Mean = 0.928&#949;))
5059                 </p>
5060               </td>
5061 <td>
5062                 <p>
5063                   <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
5064                 </p>
5065               </td>
5066 <td>
5067                 <p>
5068                   <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
5069                 </p>
5070               </td>
5071 </tr>
5072 </tbody>
5073 </table></div>
5074 </div>
5075 <br class="table-break"><div class="table">
5076 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;17.33.&#160;Error rates for ellint_d (complete)</b></p>
5077 <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
5078 <colgroup>
5079 <col>
5080 <col>
5081 <col>
5082 <col>
5083 <col>
5084 </colgroup>
5085 <thead><tr>
5086 <th>
5087               </th>
5088 <th>
5089                 <p>
5090                   Microsoft Visual C++ version 12.0<br> Win32<br> double
5091                 </p>
5092               </th>
5093 <th>
5094                 <p>
5095                   GNU C++ version 5.1.0<br> linux<br> double
5096                 </p>
5097               </th>
5098 <th>
5099                 <p>
5100                   GNU C++ version 5.1.0<br> linux<br> long double
5101                 </p>
5102               </th>
5103 <th>
5104                 <p>
5105                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
5106                 </p>
5107               </th>
5108 </tr></thead>
5109 <tbody>
5110 <tr>
5111 <td>
5112                 <p>
5113                   Elliptic Integral E: Mathworld Data
5114                 </p>
5115               </td>
5116 <td>
5117                 <p>
5118                   <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
5119                 </p>
5120               </td>
5121 <td>
5122                 <p>
5123                   <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
5124                 </p>
5125               </td>
5126 <td>
5127                 <p>
5128                   <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
5129                 </p>
5130               </td>
5131 <td>
5132                 <p>
5133                   <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
5134                 </p>
5135               </td>
5136 </tr>
5137 <tr>
5138 <td>
5139                 <p>
5140                   Elliptic Integral D: Random Data
5141                 </p>
5142               </td>
5143 <td>
5144                 <p>
5145                   <span class="blue">Max = 1.27&#949; (Mean = 0.355&#949;)</span>
5146                 </p>
5147               </td>
5148 <td>
5149                 <p>
5150                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5151                 </p>
5152               </td>
5153 <td>
5154                 <p>
5155                   <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
5156                 </p>
5157               </td>
5158 <td>
5159                 <p>
5160                   <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
5161                 </p>
5162               </td>
5163 </tr>
5164 </tbody>
5165 </table></div>
5166 </div>
5167 <br class="table-break"><div class="table">
5168 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rc"></a><p class="title"><b>Table&#160;17.34.&#160;Error rates for ellint_rc</b></p>
5169 <div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
5170 <colgroup>
5171 <col>
5172 <col>
5173 <col>
5174 <col>
5175 <col>
5176 </colgroup>
5177 <thead><tr>
5178 <th>
5179               </th>
5180 <th>
5181                 <p>
5182                   Microsoft Visual C++ version 12.0<br> Win32<br> double
5183                 </p>
5184               </th>
5185 <th>
5186                 <p>
5187                   GNU C++ version 5.1.0<br> linux<br> double
5188                 </p>
5189               </th>
5190 <th>
5191                 <p>
5192                   GNU C++ version 5.1.0<br> linux<br> long double
5193                 </p>
5194               </th>
5195 <th>
5196                 <p>
5197                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
5198                 </p>
5199               </th>
5200 </tr></thead>
5201 <tbody><tr>
5202 <td>
5203                 <p>
5204                   RC: Random data
5205                 </p>
5206               </td>
5207 <td>
5208                 <p>
5209                   <span class="blue">Max = 0.962&#949; (Mean = 0.407&#949;)</span>
5210                 </p>
5211               </td>
5212 <td>
5213                 <p>
5214                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5215                   1.16:</em></span> Max = 2.4&#949; (Mean = 0.624&#949;))
5216                 </p>
5217               </td>
5218 <td>
5219                 <p>
5220                   <span class="blue">Max = 0.995&#949; (Mean = 0.433&#949;)</span>
5221                 </p>
5222               </td>
5223 <td>
5224                 <p>
5225                   <span class="blue">Max = 0.995&#949; (Mean = 0.438&#949;)</span>
5226                 </p>
5227               </td>
5228 </tr></tbody>
5229 </table></div>
5230 </div>
5231 <br class="table-break"><div class="table">
5232 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rd"></a><p class="title"><b>Table&#160;17.35.&#160;Error rates for ellint_rd</b></p>
5233 <div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
5234 <colgroup>
5235 <col>
5236 <col>
5237 <col>
5238 <col>
5239 <col>
5240 </colgroup>
5241 <thead><tr>
5242 <th>
5243               </th>
5244 <th>
5245                 <p>
5246                   Microsoft Visual C++ version 12.0<br> Win32<br> double
5247                 </p>
5248               </th>
5249 <th>
5250                 <p>
5251                   GNU C++ version 5.1.0<br> linux<br> double
5252                 </p>
5253               </th>
5254 <th>
5255                 <p>
5256                   GNU C++ version 5.1.0<br> linux<br> long double
5257                 </p>
5258               </th>
5259 <th>
5260                 <p>
5261                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
5262                 </p>
5263               </th>
5264 </tr></thead>
5265 <tbody>
5266 <tr>
5267 <td>
5268                 <p>
5269                   RD: Random data
5270                 </p>
5271               </td>
5272 <td>
5273                 <p>
5274                   <span class="blue">Max = 2.16&#949; (Mean = 0.803&#949;)</span>
5275                 </p>
5276               </td>
5277 <td>
5278                 <p>
5279                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5280                   1.16:</em></span> Max = 2.59&#949; (Mean = 0.878&#949;))
5281                 </p>
5282               </td>
5283 <td>
5284                 <p>
5285                   <span class="blue">Max = 2.73&#949; (Mean = 0.831&#949;)</span>
5286                 </p>
5287               </td>
5288 <td>
5289                 <p>
5290                   <span class="blue">Max = 2.73&#949; (Mean = 0.829&#949;)</span>
5291                 </p>
5292               </td>
5293 </tr>
5294 <tr>
5295 <td>
5296                 <p>
5297                   RD: y = z
5298                 </p>
5299               </td>
5300 <td>
5301                 <p>
5302                   <span class="blue">Max = 16.5&#949; (Mean = 0.843&#949;)</span>
5303                 </p>
5304               </td>
5305 <td>
5306                 <p>
5307                   <span class="blue">Max = 0.896&#949; (Mean = 0.022&#949;)</span><br> <br>
5308                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.88&#949; (Mean = 0.839&#949;))
5309                 </p>
5310               </td>
5311 <td>
5312                 <p>
5313                   <span class="blue">Max = 2.65&#949; (Mean = 0.82&#949;)</span>
5314                 </p>
5315               </td>
5316 <td>
5317                 <p>
5318                   <span class="blue">Max = 2.65&#949; (Mean = 0.819&#949;)</span>
5319                 </p>
5320               </td>
5321 </tr>
5322 <tr>
5323 <td>
5324                 <p>
5325                   RD: x = y
5326                 </p>
5327               </td>
5328 <td>
5329                 <p>
5330                   <span class="blue">Max = 3.51&#949; (Mean = 0.816&#949;)</span>
5331                 </p>
5332               </td>
5333 <td>
5334                 <p>
5335                   <span class="blue">Max = 0.824&#949; (Mean = 0.0272&#949;)</span><br>
5336                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.74&#949; (Mean = 0.84&#949;))
5337                 </p>
5338               </td>
5339 <td>
5340                 <p>
5341                   <span class="blue">Max = 2.85&#949; (Mean = 0.865&#949;)</span>
5342                 </p>
5343               </td>
5344 <td>
5345                 <p>
5346                   <span class="blue">Max = 2.85&#949; (Mean = 0.865&#949;)</span>
5347                 </p>
5348               </td>
5349 </tr>
5350 <tr>
5351 <td>
5352                 <p>
5353                   RD: x = 0, y = z
5354                 </p>
5355               </td>
5356 <td>
5357                 <p>
5358                   <span class="blue">Max = 1.16&#949; (Mean = 0.493&#949;)</span>
5359                 </p>
5360               </td>
5361 <td>
5362                 <p>
5363                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5364                   1.16:</em></span> Max = 2&#949; (Mean = 0.656&#949;))
5365                 </p>
5366               </td>
5367 <td>
5368                 <p>
5369                   <span class="blue">Max = 1.19&#949; (Mean = 0.522&#949;)</span>
5370                 </p>
5371               </td>
5372 <td>
5373                 <p>
5374                   <span class="blue">Max = 1.19&#949; (Mean = 0.522&#949;)</span>
5375                 </p>
5376               </td>
5377 </tr>
5378 <tr>
5379 <td>
5380                 <p>
5381                   RD: x = y = z
5382                 </p>
5383               </td>
5384 <td>
5385                 <p>
5386                   <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
5387                 </p>
5388               </td>
5389 <td>
5390                 <p>
5391                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5392                   1.16:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
5393                 </p>
5394               </td>
5395 <td>
5396                 <p>
5397                   <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
5398                 </p>
5399               </td>
5400 <td>
5401                 <p>
5402                   <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
5403                 </p>
5404               </td>
5405 </tr>
5406 <tr>
5407 <td>
5408                 <p>
5409                   RD: x = 0
5410                 </p>
5411               </td>
5412 <td>
5413                 <p>
5414                   <span class="blue">Max = 2.64&#949; (Mean = 0.894&#949;)</span>
5415                 </p>
5416               </td>
5417 <td>
5418                 <p>
5419                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5420                   1.16:</em></span> Max = 2.85&#949; (Mean = 0.781&#949;))
5421                 </p>
5422               </td>
5423 <td>
5424                 <p>
5425                   <span class="blue">Max = 2.79&#949; (Mean = 0.883&#949;)</span>
5426                 </p>
5427               </td>
5428 <td>
5429                 <p>
5430                   <span class="blue">Max = 2.79&#949; (Mean = 0.883&#949;)</span>
5431                 </p>
5432               </td>
5433 </tr>
5434 </tbody>
5435 </table></div>
5436 </div>
5437 <br class="table-break"><div class="table">
5438 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rf"></a><p class="title"><b>Table&#160;17.36.&#160;Error rates for ellint_rf</b></p>
5439 <div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
5440 <colgroup>
5441 <col>
5442 <col>
5443 <col>
5444 <col>
5445 <col>
5446 </colgroup>
5447 <thead><tr>
5448 <th>
5449               </th>
5450 <th>
5451                 <p>
5452                   Microsoft Visual C++ version 12.0<br> Win32<br> double
5453                 </p>
5454               </th>
5455 <th>
5456                 <p>
5457                   GNU C++ version 5.1.0<br> linux<br> double
5458                 </p>
5459               </th>
5460 <th>
5461                 <p>
5462                   GNU C++ version 5.1.0<br> linux<br> long double
5463                 </p>
5464               </th>
5465 <th>
5466                 <p>
5467                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
5468                 </p>
5469               </th>
5470 </tr></thead>
5471 <tbody>
5472 <tr>
5473 <td>
5474                 <p>
5475                   RF: Random data
5476                 </p>
5477               </td>
5478 <td>
5479                 <p>
5480                   <span class="blue">Max = 2.02&#949; (Mean = 0.677&#949;)</span>
5481                 </p>
5482               </td>
5483 <td>
5484                 <p>
5485                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5486                   1.16:</em></span> Max = 2.73&#949; (Mean = 0.804&#949;))
5487                 </p>
5488               </td>
5489 <td>
5490                 <p>
5491                   <span class="blue">Max = 2.54&#949; (Mean = 0.674&#949;)</span>
5492                 </p>
5493               </td>
5494 <td>
5495                 <p>
5496                   <span class="blue">Max = 2.54&#949; (Mean = 0.674&#949;)</span>
5497                 </p>
5498               </td>
5499 </tr>
5500 <tr>
5501 <td>
5502                 <p>
5503                   RF: x = y = z
5504                 </p>
5505               </td>
5506 <td>
5507                 <p>
5508                   <span class="blue">Max = 0.999&#949; (Mean = 0.335&#949;)</span>
5509                 </p>
5510               </td>
5511 <td>
5512                 <p>
5513                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5514                   1.16:</em></span> Max = 0.999&#949; (Mean = 0.34&#949;))
5515                 </p>
5516               </td>
5517 <td>
5518                 <p>
5519                   <span class="blue">Max = 0.991&#949; (Mean = 0.345&#949;)</span>
5520                 </p>
5521               </td>
5522 <td>
5523                 <p>
5524                   <span class="blue">Max = 0.991&#949; (Mean = 0.345&#949;)</span>
5525                 </p>
5526               </td>
5527 </tr>
5528 <tr>
5529 <td>
5530                 <p>
5531                   RF: x = y or y = z or x = z
5532                 </p>
5533               </td>
5534 <td>
5535                 <p>
5536                   <span class="blue">Max = 1.21&#949; (Mean = 0.394&#949;)</span>
5537                 </p>
5538               </td>
5539 <td>
5540                 <p>
5541                   <span class="blue">Max = 0.536&#949; (Mean = 0.00658&#949;)</span><br>
5542                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.89&#949; (Mean = 0.749&#949;))
5543                 </p>
5544               </td>
5545 <td>
5546                 <p>
5547                   <span class="blue">Max = 1.95&#949; (Mean = 0.418&#949;)</span>
5548                 </p>
5549               </td>
5550 <td>
5551                 <p>
5552                   <span class="blue">Max = 1.57&#949; (Mean = 0.418&#949;)</span>
5553                 </p>
5554               </td>
5555 </tr>
5556 <tr>
5557 <td>
5558                 <p>
5559                   RF: x = 0, y = z
5560                 </p>
5561               </td>
5562 <td>
5563                 <p>
5564                   <span class="blue">Max = 0.999&#949; (Mean = 0.407&#949;)</span>
5565                 </p>
5566               </td>
5567 <td>
5568                 <p>
5569                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5570                   1.16:</em></span> Max = 1.29&#949; (Mean = 0.527&#949;))
5571                 </p>
5572               </td>
5573 <td>
5574                 <p>
5575                   <span class="blue">Max = 0.894&#949; (Mean = 0.338&#949;)</span>
5576                 </p>
5577               </td>
5578 <td>
5579                 <p>
5580                   <span class="blue">Max = 0.894&#949; (Mean = 0.338&#949;)</span>
5581                 </p>
5582               </td>
5583 </tr>
5584 <tr>
5585 <td>
5586                 <p>
5587                   RF: z = 0
5588                 </p>
5589               </td>
5590 <td>
5591                 <p>
5592                   <span class="blue">Max = 1.89&#949; (Mean = 0.587&#949;)</span>
5593                 </p>
5594               </td>
5595 <td>
5596                 <p>
5597                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5598                   1.16:</em></span> Max = 2.54&#949; (Mean = 0.781&#949;))
5599                 </p>
5600               </td>
5601 <td>
5602                 <p>
5603                   <span class="blue">Max = 1.7&#949; (Mean = 0.539&#949;)</span>
5604                 </p>
5605               </td>
5606 <td>
5607                 <p>
5608                   <span class="blue">Max = 1.7&#949; (Mean = 0.539&#949;)</span>
5609                 </p>
5610               </td>
5611 </tr>
5612 </tbody>
5613 </table></div>
5614 </div>
5615 <br class="table-break"><div class="table">
5616 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rg"></a><p class="title"><b>Table&#160;17.37.&#160;Error rates for ellint_rg</b></p>
5617 <div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
5618 <colgroup>
5619 <col>
5620 <col>
5621 <col>
5622 <col>
5623 <col>
5624 </colgroup>
5625 <thead><tr>
5626 <th>
5627               </th>
5628 <th>
5629                 <p>
5630                   Microsoft Visual C++ version 12.0<br> Win32<br> double
5631                 </p>
5632               </th>
5633 <th>
5634                 <p>
5635                   GNU C++ version 5.1.0<br> linux<br> double
5636                 </p>
5637               </th>
5638 <th>
5639                 <p>
5640                   GNU C++ version 5.1.0<br> linux<br> long double
5641                 </p>
5642               </th>
5643 <th>
5644                 <p>
5645                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
5646                 </p>
5647               </th>
5648 </tr></thead>
5649 <tbody>
5650 <tr>
5651 <td>
5652                 <p>
5653                   RG: Random Data
5654                 </p>
5655               </td>
5656 <td>
5657                 <p>
5658                   <span class="blue">Max = 3.65&#949; (Mean = 0.929&#949;)</span>
5659                 </p>
5660               </td>
5661 <td>
5662                 <p>
5663                   <span class="blue">Max = 0.983&#949; (Mean = 0.0172&#949;)</span><br>
5664                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.983&#949; (Mean = 0.0172&#949;))
5665                 </p>
5666               </td>
5667 <td>
5668                 <p>
5669                   <span class="blue">Max = 3.95&#949; (Mean = 0.951&#949;)</span>
5670                 </p>
5671               </td>
5672 <td>
5673                 <p>
5674                   <span class="blue">Max = 3.95&#949; (Mean = 0.951&#949;)</span>
5675                 </p>
5676               </td>
5677 </tr>
5678 <tr>
5679 <td>
5680                 <p>
5681                   RG: two values 0
5682                 </p>
5683               </td>
5684 <td>
5685                 <p>
5686                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5687                 </p>
5688               </td>
5689 <td>
5690                 <p>
5691                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5692                   1.16:</em></span> Max = 0&#949; (Mean = 0&#949;))
5693                 </p>
5694               </td>
5695 <td>
5696                 <p>
5697                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5698                 </p>
5699               </td>
5700 <td>
5701                 <p>
5702                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
5703                 </p>
5704               </td>
5705 </tr>
5706 <tr>
5707 <td>
5708                 <p>
5709                   RG: All values the same or zero
5710                 </p>
5711               </td>
5712 <td>
5713                 <p>
5714                   <span class="blue">Max = 1.06&#949; (Mean = 0.348&#949;)</span>
5715                 </p>
5716               </td>
5717 <td>
5718                 <p>
5719                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5720                   1.16:</em></span> Max = 0&#949; (Mean = 0&#949;))
5721                 </p>
5722               </td>
5723 <td>
5724                 <p>
5725                   <span class="blue">Max = 0.992&#949; (Mean = 0.288&#949;)</span>
5726                 </p>
5727               </td>
5728 <td>
5729                 <p>
5730                   <span class="blue">Max = 0.992&#949; (Mean = 0.288&#949;)</span>
5731                 </p>
5732               </td>
5733 </tr>
5734 <tr>
5735 <td>
5736                 <p>
5737                   RG: two values the same
5738                 </p>
5739               </td>
5740 <td>
5741                 <p>
5742                   <span class="blue">Max = 1.96&#949; (Mean = 0.374&#949;)</span>
5743                 </p>
5744               </td>
5745 <td>
5746                 <p>
5747                   <span class="blue">Max = 0.594&#949; (Mean = 0.0103&#949;)</span><br>
5748                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.594&#949; (Mean = 0.0103&#949;))
5749                 </p>
5750               </td>
5751 <td>
5752                 <p>
5753                   <span class="blue">Max = 1.51&#949; (Mean = 0.404&#949;)</span>
5754                 </p>
5755               </td>
5756 <td>
5757                 <p>
5758                   <span class="blue">Max = 1.51&#949; (Mean = 0.404&#949;)</span>
5759                 </p>
5760               </td>
5761 </tr>
5762 <tr>
5763 <td>
5764                 <p>
5765                   RG: one value zero
5766                 </p>
5767               </td>
5768 <td>
5769                 <p>
5770                   <span class="blue">Max = 1.96&#949; (Mean = 0.674&#949;)</span>
5771                 </p>
5772               </td>
5773 <td>
5774                 <p>
5775                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5776                   1.16:</em></span> Max = 0&#949; (Mean = 0&#949;))
5777                 </p>
5778               </td>
5779 <td>
5780                 <p>
5781                   <span class="blue">Max = 2.14&#949; (Mean = 0.722&#949;)</span>
5782                 </p>
5783               </td>
5784 <td>
5785                 <p>
5786                   <span class="blue">Max = 2.14&#949; (Mean = 0.722&#949;)</span>
5787                 </p>
5788               </td>
5789 </tr>
5790 </tbody>
5791 </table></div>
5792 </div>
5793 <br class="table-break"><div class="table">
5794 <a name="math_toolkit.logs_and_tables.all_table.table_ellint_rj"></a><p class="title"><b>Table&#160;17.38.&#160;Error rates for ellint_rj</b></p>
5795 <div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
5796 <colgroup>
5797 <col>
5798 <col>
5799 <col>
5800 <col>
5801 <col>
5802 </colgroup>
5803 <thead><tr>
5804 <th>
5805               </th>
5806 <th>
5807                 <p>
5808                   Microsoft Visual C++ version 12.0<br> Win32<br> double
5809                 </p>
5810               </th>
5811 <th>
5812                 <p>
5813                   GNU C++ version 5.1.0<br> linux<br> double
5814                 </p>
5815               </th>
5816 <th>
5817                 <p>
5818                   GNU C++ version 5.1.0<br> linux<br> long double
5819                 </p>
5820               </th>
5821 <th>
5822                 <p>
5823                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
5824                 </p>
5825               </th>
5826 </tr></thead>
5827 <tbody>
5828 <tr>
5829 <td>
5830                 <p>
5831                   RJ: Random data
5832                 </p>
5833               </td>
5834 <td>
5835                 <p>
5836                   <span class="blue">Max = 119&#949; (Mean = 4.32&#949;)</span>
5837                 </p>
5838               </td>
5839 <td>
5840                 <p>
5841                   <span class="blue">Max = 0.52&#949; (Mean = 0.0184&#949;)</span><br> <br>
5842                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.57&#949; (Mean = 0.704&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ellint_rj_GSL_1_16_RJ_Random_data">And
5843                   other failures.</a>)
5844                 </p>
5845               </td>
5846 <td>
5847                 <p>
5848                   <span class="blue">Max = 186&#949; (Mean = 6.67&#949;)</span>
5849                 </p>
5850               </td>
5851 <td>
5852                 <p>
5853                   <span class="blue">Max = 186&#949; (Mean = 6.7&#949;)</span>
5854                 </p>
5855               </td>
5856 </tr>
5857 <tr>
5858 <td>
5859                 <p>
5860                   RJ: 4 Equal Values
5861                 </p>
5862               </td>
5863 <td>
5864                 <p>
5865                   <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
5866                 </p>
5867               </td>
5868 <td>
5869                 <p>
5870                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5871                   1.16:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
5872                 </p>
5873               </td>
5874 <td>
5875                 <p>
5876                   <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
5877                 </p>
5878               </td>
5879 <td>
5880                 <p>
5881                   <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
5882                 </p>
5883               </td>
5884 </tr>
5885 <tr>
5886 <td>
5887                 <p>
5888                   RJ: 3 Equal Values
5889                 </p>
5890               </td>
5891 <td>
5892                 <p>
5893                   <span class="blue">Max = 39.9&#949; (Mean = 1.12&#949;)</span>
5894                 </p>
5895               </td>
5896 <td>
5897                 <p>
5898                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
5899                   1.16:</em></span> Max = 3.96&#949; (Mean = 1.06&#949;))
5900                 </p>
5901               </td>
5902 <td>
5903                 <p>
5904                   <span class="blue">Max = 20.8&#949; (Mean = 0.986&#949;)</span>
5905                 </p>
5906               </td>
5907 <td>
5908                 <p>
5909                   <span class="blue">Max = 18.2&#949; (Mean = 0.917&#949;)</span>
5910                 </p>
5911               </td>
5912 </tr>
5913 <tr>
5914 <td>
5915                 <p>
5916                   RJ: 2 Equal Values
5917                 </p>
5918               </td>
5919 <td>
5920                 <p>
5921                   <span class="blue">Max = 214&#949; (Mean = 5.05&#949;)</span>
5922                 </p>
5923               </td>
5924 <td>
5925                 <p>
5926                   <span class="blue">Max = 0.6&#949; (Mean = 0.0228&#949;)</span><br> <br>
5927                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.57&#949; (Mean = 0.754&#949;))
5928                 </p>
5929               </td>
5930 <td>
5931                 <p>
5932                   <span class="blue">Max = 220&#949; (Mean = 6.64&#949;)</span>
5933                 </p>
5934               </td>
5935 <td>
5936                 <p>
5937                   <span class="blue">Max = 135&#949; (Mean = 5.3&#949;)</span>
5938                 </p>
5939               </td>
5940 </tr>
5941 <tr>
5942 <td>
5943                 <p>
5944                   RJ: Equal z and p
5945                 </p>
5946               </td>
5947 <td>
5948                 <p>
5949                   <span class="blue">Max = 15.4&#949; (Mean = 1.05&#949;)</span>
5950                 </p>
5951               </td>
5952 <td>
5953                 <p>
5954                   <span class="blue">Max = 0.742&#949; (Mean = 0.0166&#949;)</span><br>
5955                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.62&#949; (Mean = 0.699&#949;))
5956                 </p>
5957               </td>
5958 <td>
5959                 <p>
5960                   <span class="blue">Max = 17.2&#949; (Mean = 1.16&#949;)</span>
5961                 </p>
5962               </td>
5963 <td>
5964                 <p>
5965                   <span class="blue">Max = 16.6&#949; (Mean = 1.15&#949;)</span>
5966                 </p>
5967               </td>
5968 </tr>
5969 </tbody>
5970 </table></div>
5971 </div>
5972 <br class="table-break"><div class="table">
5973 <a name="math_toolkit.logs_and_tables.all_table.table_erf"></a><p class="title"><b>Table&#160;17.39.&#160;Error rates for erf</b></p>
5974 <div class="table-contents"><table class="table" summary="Error rates for erf">
5975 <colgroup>
5976 <col>
5977 <col>
5978 <col>
5979 <col>
5980 <col>
5981 </colgroup>
5982 <thead><tr>
5983 <th>
5984               </th>
5985 <th>
5986                 <p>
5987                   Microsoft Visual C++ version 12.0<br> Win32<br> double
5988                 </p>
5989               </th>
5990 <th>
5991                 <p>
5992                   GNU C++ version 5.1.0<br> linux<br> long double
5993                 </p>
5994               </th>
5995 <th>
5996                 <p>
5997                   GNU C++ version 5.1.0<br> linux<br> double
5998                 </p>
5999               </th>
6000 <th>
6001                 <p>
6002                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6003                 </p>
6004               </th>
6005 </tr></thead>
6006 <tbody>
6007 <tr>
6008 <td>
6009                 <p>
6010                   Erf Function: Small Values
6011                 </p>
6012               </td>
6013 <td>
6014                 <p>
6015                   <span class="blue">Max = 0.996&#949; (Mean = 0.182&#949;)</span><br> <br>
6016                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.57&#949; (Mean = 0.317&#949;))
6017                 </p>
6018               </td>
6019 <td>
6020                 <p>
6021                   <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
6022                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))<br>
6023                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))
6024                 </p>
6025               </td>
6026 <td>
6027                 <p>
6028                   <span class="blue">Max = 0.841&#949; (Mean = 0.0687&#949;)</span><br>
6029                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.06&#949; (Mean = 0.319&#949;))<br>
6030                   (<span class="emphasis"><em>Cephes:</em></span> Max = 1.13&#949; (Mean = 0.442&#949;))
6031                 </p>
6032               </td>
6033 <td>
6034                 <p>
6035                   <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
6036                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.194&#949;))
6037                 </p>
6038               </td>
6039 </tr>
6040 <tr>
6041 <td>
6042                 <p>
6043                   Erf Function: Medium Values
6044                 </p>
6045               </td>
6046 <td>
6047                 <p>
6048                   <span class="blue">Max = 1&#949; (Mean = 0.169&#949;)</span><br> <br>
6049                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.19&#949; (Mean = 0.244&#949;))
6050                 </p>
6051               </td>
6052 <td>
6053                 <p>
6054                   <span class="blue">Max = 1.5&#949; (Mean = 0.193&#949;)</span><br> <br>
6055                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))<br>
6056                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))
6057                 </p>
6058               </td>
6059 <td>
6060                 <p>
6061                   <span class="blue">Max = 1&#949; (Mean = 0.119&#949;)</span><br> <br>
6062                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.31&#949; (Mean = 0.368&#949;))<br>
6063                   (<span class="emphasis"><em>Cephes:</em></span> Max = 1.34&#949; (Mean = 0.279&#949;))
6064                 </p>
6065               </td>
6066 <td>
6067                 <p>
6068                   <span class="blue">Max = 1.5&#949; (Mean = 0.202&#949;)</span><br> <br>
6069                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.071&#949;))
6070                 </p>
6071               </td>
6072 </tr>
6073 <tr>
6074 <td>
6075                 <p>
6076                   Erf Function: Large Values
6077                 </p>
6078               </td>
6079 <td>
6080                 <p>
6081                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6082                   Max = 0&#949; (Mean = 0&#949;))
6083                 </p>
6084               </td>
6085 <td>
6086                 <p>
6087                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span>
6088                   Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6089                   Max = 0&#949; (Mean = 0&#949;))
6090                 </p>
6091               </td>
6092 <td>
6093                 <p>
6094                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6095                   1.16:</em></span> Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
6096                   Max = 0&#949; (Mean = 0&#949;))
6097                 </p>
6098               </td>
6099 <td>
6100                 <p>
6101                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6102                   Max = 0&#949; (Mean = 0&#949;))
6103                 </p>
6104               </td>
6105 </tr>
6106 </tbody>
6107 </table></div>
6108 </div>
6109 <br class="table-break"><div class="table">
6110 <a name="math_toolkit.logs_and_tables.all_table.table_erf_inv"></a><p class="title"><b>Table&#160;17.40.&#160;Error rates for erf_inv</b></p>
6111 <div class="table-contents"><table class="table" summary="Error rates for erf_inv">
6112 <colgroup>
6113 <col>
6114 <col>
6115 <col>
6116 <col>
6117 <col>
6118 </colgroup>
6119 <thead><tr>
6120 <th>
6121               </th>
6122 <th>
6123                 <p>
6124                   Microsoft Visual C++ version 12.0<br> Win32<br> double
6125                 </p>
6126               </th>
6127 <th>
6128                 <p>
6129                   GNU C++ version 5.1.0<br> linux<br> double
6130                 </p>
6131               </th>
6132 <th>
6133                 <p>
6134                   GNU C++ version 5.1.0<br> linux<br> long double
6135                 </p>
6136               </th>
6137 <th>
6138                 <p>
6139                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6140                 </p>
6141               </th>
6142 </tr></thead>
6143 <tbody><tr>
6144 <td>
6145                 <p>
6146                   Inverse Erf Function
6147                 </p>
6148               </td>
6149 <td>
6150                 <p>
6151                   <span class="blue">Max = 1.09&#949; (Mean = 0.502&#949;)</span>
6152                 </p>
6153               </td>
6154 <td>
6155                 <p>
6156                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
6157                 </p>
6158               </td>
6159 <td>
6160                 <p>
6161                   <span class="blue">Max = 0.996&#949; (Mean = 0.389&#949;)</span>
6162                 </p>
6163               </td>
6164 <td>
6165                 <p>
6166                   <span class="blue">Max = 0.996&#949; (Mean = 0.385&#949;)</span>
6167                 </p>
6168               </td>
6169 </tr></tbody>
6170 </table></div>
6171 </div>
6172 <br class="table-break"><div class="table">
6173 <a name="math_toolkit.logs_and_tables.all_table.table_erfc"></a><p class="title"><b>Table&#160;17.41.&#160;Error rates for erfc</b></p>
6174 <div class="table-contents"><table class="table" summary="Error rates for erfc">
6175 <colgroup>
6176 <col>
6177 <col>
6178 <col>
6179 <col>
6180 <col>
6181 </colgroup>
6182 <thead><tr>
6183 <th>
6184               </th>
6185 <th>
6186                 <p>
6187                   Microsoft Visual C++ version 12.0<br> Win32<br> double
6188                 </p>
6189               </th>
6190 <th>
6191                 <p>
6192                   GNU C++ version 5.1.0<br> linux<br> long double
6193                 </p>
6194               </th>
6195 <th>
6196                 <p>
6197                   GNU C++ version 5.1.0<br> linux<br> double
6198                 </p>
6199               </th>
6200 <th>
6201                 <p>
6202                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6203                 </p>
6204               </th>
6205 </tr></thead>
6206 <tbody>
6207 <tr>
6208 <td>
6209                 <p>
6210                   Erf Function: Small Values
6211                 </p>
6212               </td>
6213 <td>
6214                 <p>
6215                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6216                   Max = 0&#949; (Mean = 0&#949;))
6217                 </p>
6218               </td>
6219 <td>
6220                 <p>
6221                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span>
6222                   Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6223                   Max = 0&#949; (Mean = 0&#949;))
6224                 </p>
6225               </td>
6226 <td>
6227                 <p>
6228                   <span class="blue">Max = 0.658&#949; (Mean = 0.0537&#949;)</span><br>
6229                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.01&#949; (Mean = 0.485&#949;))<br>
6230                   (<span class="emphasis"><em>Cephes:</em></span> Max = 0.786&#949; (Mean = 0.0642&#949;))
6231                 </p>
6232               </td>
6233 <td>
6234                 <p>
6235                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6236                   Max = 0&#949; (Mean = 0&#949;))
6237                 </p>
6238               </td>
6239 </tr>
6240 <tr>
6241 <td>
6242                 <p>
6243                   Erf Function: Medium Values
6244                 </p>
6245               </td>
6246 <td>
6247                 <p>
6248                   <span class="blue">Max = 1.65&#949; (Mean = 0.373&#949;)</span><br> <br>
6249                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.36&#949; (Mean = 0.539&#949;))
6250                 </p>
6251               </td>
6252 <td>
6253                 <p>
6254                   <span class="blue">Max = 1.76&#949; (Mean = 0.365&#949;)</span><br> <br>
6255                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))<br>
6256                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))
6257                 </p>
6258               </td>
6259 <td>
6260                 <p>
6261                   <span class="blue">Max = 0.983&#949; (Mean = 0.213&#949;)</span><br> <br>
6262                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.64&#949; (Mean = 0.662&#949;))<br>
6263                   (<span class="emphasis"><em>Cephes:</em></span> Max = 3.59&#949; (Mean = 0.779&#949;))
6264                 </p>
6265               </td>
6266 <td>
6267                 <p>
6268                   <span class="blue">Max = 1.76&#949; (Mean = 0.383&#949;)</span><br> <br>
6269                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.81&#949; (Mean = 0.739&#949;))
6270                 </p>
6271               </td>
6272 </tr>
6273 <tr>
6274 <td>
6275                 <p>
6276                   Erf Function: Large Values
6277                 </p>
6278               </td>
6279 <td>
6280                 <p>
6281                   <span class="blue">Max = 1.14&#949; (Mean = 0.248&#949;)</span><br> <br>
6282                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.331&#949;))
6283                 </p>
6284               </td>
6285 <td>
6286                 <p>
6287                   <span class="blue">Max = 1.57&#949; (Mean = 0.542&#949;)</span><br> <br>
6288                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))<br>
6289                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))
6290                 </p>
6291               </td>
6292 <td>
6293                 <p>
6294                   <span class="blue">Max = 0.868&#949; (Mean = 0.147&#949;)</span><br> <br>
6295                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.9&#949; (Mean = 0.472&#949;))<br>
6296                   (<span class="emphasis"><em>Cephes:</em></span> Max = 2.74&#949; (Mean = 0.413&#949;))
6297                 </p>
6298               </td>
6299 <td>
6300                 <p>
6301                   <span class="blue">Max = 1.57&#949; (Mean = 0.564&#949;)</span><br> <br>
6302                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 4.91&#949; (Mean = 1.54&#949;))
6303                 </p>
6304               </td>
6305 </tr>
6306 </tbody>
6307 </table></div>
6308 </div>
6309 <br class="table-break"><div class="table">
6310 <a name="math_toolkit.logs_and_tables.all_table.table_erfc_inv"></a><p class="title"><b>Table&#160;17.42.&#160;Error rates for erfc_inv</b></p>
6311 <div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
6312 <colgroup>
6313 <col>
6314 <col>
6315 <col>
6316 <col>
6317 <col>
6318 </colgroup>
6319 <thead><tr>
6320 <th>
6321               </th>
6322 <th>
6323                 <p>
6324                   Microsoft Visual C++ version 12.0<br> Win32<br> double
6325                 </p>
6326               </th>
6327 <th>
6328                 <p>
6329                   GNU C++ version 5.1.0<br> linux<br> double
6330                 </p>
6331               </th>
6332 <th>
6333                 <p>
6334                   GNU C++ version 5.1.0<br> linux<br> long double
6335                 </p>
6336               </th>
6337 <th>
6338                 <p>
6339                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6340                 </p>
6341               </th>
6342 </tr></thead>
6343 <tbody>
6344 <tr>
6345 <td>
6346                 <p>
6347                   Inverse Erfc Function
6348                 </p>
6349               </td>
6350 <td>
6351                 <p>
6352                   <span class="blue">Max = 1&#949; (Mean = 0.491&#949;)</span>
6353                 </p>
6354               </td>
6355 <td>
6356                 <p>
6357                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
6358                 </p>
6359               </td>
6360 <td>
6361                 <p>
6362                   <span class="blue">Max = 0.996&#949; (Mean = 0.397&#949;)</span>
6363                 </p>
6364               </td>
6365 <td>
6366                 <p>
6367                   <span class="blue">Max = 0.996&#949; (Mean = 0.397&#949;)</span>
6368                 </p>
6369               </td>
6370 </tr>
6371 <tr>
6372 <td>
6373                 <p>
6374                   Inverse Erfc Function: extreme values
6375                 </p>
6376               </td>
6377 <td>
6378               </td>
6379 <td>
6380               </td>
6381 <td>
6382                 <p>
6383                   <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
6384                 </p>
6385               </td>
6386 <td>
6387                 <p>
6388                   <span class="blue">Max = 1.62&#949; (Mean = 0.385&#949;)</span>
6389                 </p>
6390               </td>
6391 </tr>
6392 </tbody>
6393 </table></div>
6394 </div>
6395 <br class="table-break"><div class="table">
6396 <a name="math_toolkit.logs_and_tables.all_table.table_expint_Ei_"></a><p class="title"><b>Table&#160;17.43.&#160;Error rates for expint (Ei)</b></p>
6397 <div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
6398 <colgroup>
6399 <col>
6400 <col>
6401 <col>
6402 <col>
6403 <col>
6404 </colgroup>
6405 <thead><tr>
6406 <th>
6407               </th>
6408 <th>
6409                 <p>
6410                   Microsoft Visual C++ version 12.0<br> Win32<br> double
6411                 </p>
6412               </th>
6413 <th>
6414                 <p>
6415                   GNU C++ version 5.1.0<br> linux<br> long double
6416                 </p>
6417               </th>
6418 <th>
6419                 <p>
6420                   GNU C++ version 5.1.0<br> linux<br> double
6421                 </p>
6422               </th>
6423 <th>
6424                 <p>
6425                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6426                 </p>
6427               </th>
6428 </tr></thead>
6429 <tbody>
6430 <tr>
6431 <td>
6432                 <p>
6433                   Exponential Integral Ei
6434                 </p>
6435               </td>
6436 <td>
6437                 <p>
6438                   <span class="blue">Max = 1.43&#949; (Mean = 0.541&#949;)</span>
6439                 </p>
6440               </td>
6441 <td>
6442                 <p>
6443                   <span class="blue">Max = 5.05&#949; (Mean = 0.821&#949;)</span><br> <br>
6444                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 14.1&#949; (Mean = 2.43&#949;)
6445                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_expint_Ei___tr1_cmath__Exponential_Integral_Ei">And
6446                   other failures.</a>)
6447                 </p>
6448               </td>
6449 <td>
6450                 <p>
6451                   <span class="blue">Max = 0.994&#949; (Mean = 0.142&#949;)</span><br> <br>
6452                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.96&#949; (Mean = 0.703&#949;))<br>
6453                   (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean
6454                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_expint_Ei__Cephes_Exponential_Integral_Ei">And
6455                   other failures.</a>)</span>
6456                 </p>
6457               </td>
6458 <td>
6459                 <p>
6460                   <span class="blue">Max = 3.34&#949; (Mean = 0.631&#949;)</span>
6461                 </p>
6462               </td>
6463 </tr>
6464 <tr>
6465 <td>
6466                 <p>
6467                   Exponential Integral Ei: double exponent range
6468                 </p>
6469               </td>
6470 <td>
6471                 <p>
6472                   <span class="blue">Max = 1.7&#949; (Mean = 0.66&#949;)</span>
6473                 </p>
6474               </td>
6475 <td>
6476                 <p>
6477                   <span class="blue">Max = 1.72&#949; (Mean = 0.593&#949;)</span><br> <br>
6478                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 3.11&#949; (Mean = 1.13&#949;))
6479                 </p>
6480               </td>
6481 <td>
6482                 <p>
6483                   <span class="blue">Max = 0.998&#949; (Mean = 0.156&#949;)</span><br> <br>
6484                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5&#949; (Mean = 0.612&#949;))<br>
6485                   (<span class="emphasis"><em>Cephes:</em></span> Max = 1.77&#949; (Mean = 0.644&#949;))
6486                 </p>
6487               </td>
6488 <td>
6489                 <p>
6490                   <span class="blue">Max = 1.72&#949; (Mean = 0.618&#949;)</span>
6491                 </p>
6492               </td>
6493 </tr>
6494 <tr>
6495 <td>
6496                 <p>
6497                   Exponential Integral Ei: long exponent range
6498                 </p>
6499               </td>
6500 <td>
6501               </td>
6502 <td>
6503                 <p>
6504                   <span class="blue">Max = 1.98&#949; (Mean = 0.595&#949;)</span><br> <br>
6505                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.93&#949; (Mean = 0.855&#949;))
6506                 </p>
6507               </td>
6508 <td>
6509               </td>
6510 <td>
6511                 <p>
6512                   <span class="blue">Max = 1.98&#949; (Mean = 0.575&#949;)</span>
6513                 </p>
6514               </td>
6515 </tr>
6516 </tbody>
6517 </table></div>
6518 </div>
6519 <br class="table-break"><div class="table">
6520 <a name="math_toolkit.logs_and_tables.all_table.table_expint_En_"></a><p class="title"><b>Table&#160;17.44.&#160;Error rates for expint (En)</b></p>
6521 <div class="table-contents"><table class="table" summary="Error rates for expint (En)">
6522 <colgroup>
6523 <col>
6524 <col>
6525 <col>
6526 <col>
6527 <col>
6528 </colgroup>
6529 <thead><tr>
6530 <th>
6531               </th>
6532 <th>
6533                 <p>
6534                   Microsoft Visual C++ version 12.0<br> Win32<br> double
6535                 </p>
6536               </th>
6537 <th>
6538                 <p>
6539                   GNU C++ version 5.1.0<br> linux<br> double
6540                 </p>
6541               </th>
6542 <th>
6543                 <p>
6544                   GNU C++ version 5.1.0<br> linux<br> long double
6545                 </p>
6546               </th>
6547 <th>
6548                 <p>
6549                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6550                 </p>
6551               </th>
6552 </tr></thead>
6553 <tbody>
6554 <tr>
6555 <td>
6556                 <p>
6557                   Exponential Integral En
6558                 </p>
6559               </td>
6560 <td>
6561                 <p>
6562                   <span class="blue">Max = 7.16&#949; (Mean = 1.85&#949;)</span>
6563                 </p>
6564               </td>
6565 <td>
6566                 <p>
6567                   <span class="blue">Max = 0.589&#949; (Mean = 0.0331&#949;)</span><br>
6568                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 58.5&#949; (Mean = 17.1&#949;))
6569                 </p>
6570               </td>
6571 <td>
6572                 <p>
6573                   <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
6574                 </p>
6575               </td>
6576 <td>
6577                 <p>
6578                   <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
6579                 </p>
6580               </td>
6581 </tr>
6582 <tr>
6583 <td>
6584                 <p>
6585                   Exponential Integral En: small z values
6586                 </p>
6587               </td>
6588 <td>
6589                 <p>
6590                   <span class="blue">Max = 2.62&#949; (Mean = 0.531&#949;)</span>
6591                 </p>
6592               </td>
6593 <td>
6594                 <p>
6595                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6596                   1.16:</em></span> Max = 115&#949; (Mean = 23.6&#949;))
6597                 </p>
6598               </td>
6599 <td>
6600                 <p>
6601                   <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
6602                 </p>
6603               </td>
6604 <td>
6605                 <p>
6606                   <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
6607                 </p>
6608               </td>
6609 </tr>
6610 <tr>
6611 <td>
6612                 <p>
6613                   Exponential Integral E1
6614                 </p>
6615               </td>
6616 <td>
6617                 <p>
6618                   <span class="blue">Max = 0.988&#949; (Mean = 0.486&#949;)</span>
6619                 </p>
6620               </td>
6621 <td>
6622                 <p>
6623                   <span class="blue">Max = 0.556&#949; (Mean = 0.0625&#949;)</span><br>
6624                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.988&#949; (Mean = 0.469&#949;))
6625                 </p>
6626               </td>
6627 <td>
6628                 <p>
6629                   <span class="blue">Max = 0.965&#949; (Mean = 0.414&#949;)</span>
6630                 </p>
6631               </td>
6632 <td>
6633                 <p>
6634                   <span class="blue">Max = 0.965&#949; (Mean = 0.409&#949;)</span>
6635                 </p>
6636               </td>
6637 </tr>
6638 </tbody>
6639 </table></div>
6640 </div>
6641 <br class="table-break"><div class="table">
6642 <a name="math_toolkit.logs_and_tables.all_table.table_expm1"></a><p class="title"><b>Table&#160;17.45.&#160;Error rates for expm1</b></p>
6643 <div class="table-contents"><table class="table" summary="Error rates for expm1">
6644 <colgroup>
6645 <col>
6646 <col>
6647 <col>
6648 <col>
6649 <col>
6650 </colgroup>
6651 <thead><tr>
6652 <th>
6653               </th>
6654 <th>
6655                 <p>
6656                   Microsoft Visual C++ version 12.0<br> Win32<br> double
6657                 </p>
6658               </th>
6659 <th>
6660                 <p>
6661                   GNU C++ version 5.1.0<br> linux<br> double
6662                 </p>
6663               </th>
6664 <th>
6665                 <p>
6666                   GNU C++ version 5.1.0<br> linux<br> long double
6667                 </p>
6668               </th>
6669 <th>
6670                 <p>
6671                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6672                 </p>
6673               </th>
6674 </tr></thead>
6675 <tbody><tr>
6676 <td>
6677                 <p>
6678                   Random test data
6679                 </p>
6680               </td>
6681 <td>
6682                 <p>
6683                   <span class="blue">Max = 0.996&#949; (Mean = 0.283&#949;)</span><br> <br>
6684                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.31&#949; (Mean = 0.496&#949;))
6685                 </p>
6686               </td>
6687 <td>
6688                 <p>
6689                   <span class="blue">Max = 0.793&#949; (Mean = 0.126&#949;)</span><br> <br>
6690                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.793&#949; (Mean = 0.126&#949;))<br>
6691                   (<span class="emphasis"><em>Cephes:</em></span> Max = 1.53&#949; (Mean = 0.535&#949;))
6692                 </p>
6693               </td>
6694 <td>
6695                 <p>
6696                   <span class="blue">Max = 0.992&#949; (Mean = 0.402&#949;)</span><br> <br>
6697                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> <span class="red">Max
6698                   = 1.26e+19&#949; (Mean = 4.89e+18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_expm1__tr1_cmath__Random_test_data">And
6699                   other failures.</a>)</span><br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
6700                   Max = 0.992&#949; (Mean = 0.402&#949;))
6701                 </p>
6702               </td>
6703 <td>
6704                 <p>
6705                   <span class="blue">Max = 1.31&#949; (Mean = 0.406&#949;)</span><br> <br>
6706                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.996&#949; (Mean = 0.426&#949;))
6707                 </p>
6708               </td>
6709 </tr></tbody>
6710 </table></div>
6711 </div>
6712 <br class="table-break"><div class="table">
6713 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p"></a><p class="title"><b>Table&#160;17.46.&#160;Error rates for gamma_p</b></p>
6714 <div class="table-contents"><table class="table" summary="Error rates for gamma_p">
6715 <colgroup>
6716 <col>
6717 <col>
6718 <col>
6719 <col>
6720 <col>
6721 </colgroup>
6722 <thead><tr>
6723 <th>
6724               </th>
6725 <th>
6726                 <p>
6727                   Microsoft Visual C++ version 12.0<br> Win32<br> double
6728                 </p>
6729               </th>
6730 <th>
6731                 <p>
6732                   GNU C++ version 5.1.0<br> linux<br> double
6733                 </p>
6734               </th>
6735 <th>
6736                 <p>
6737                   GNU C++ version 5.1.0<br> linux<br> long double
6738                 </p>
6739               </th>
6740 <th>
6741                 <p>
6742                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6743                 </p>
6744               </th>
6745 </tr></thead>
6746 <tbody>
6747 <tr>
6748 <td>
6749                 <p>
6750                   tgamma(a, z) medium values
6751                 </p>
6752               </td>
6753 <td>
6754                 <p>
6755                   <span class="blue">Max = 35.1&#949; (Mean = 6.97&#949;)</span>
6756                 </p>
6757               </td>
6758 <td>
6759                 <p>
6760                   <span class="blue">Max = 0.955&#949; (Mean = 0.05&#949;)</span><br> <br>
6761                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 342&#949; (Mean = 45.8&#949;))<br> (<span class="emphasis"><em>Rmath
6762                   3.0.2:</em></span> Max = 389&#949; (Mean = 44&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
6763                   Max = 492&#949; (Mean = 101&#949;))
6764                 </p>
6765               </td>
6766 <td>
6767                 <p>
6768                   <span class="blue">Max = 41&#949; (Mean = 8.09&#949;)</span>
6769                 </p>
6770               </td>
6771 <td>
6772                 <p>
6773                   <span class="blue">Max = 239&#949; (Mean = 30.2&#949;)</span>
6774                 </p>
6775               </td>
6776 </tr>
6777 <tr>
6778 <td>
6779                 <p>
6780                   tgamma(a, z) small values
6781                 </p>
6782               </td>
6783 <td>
6784                 <p>
6785                   <span class="blue">Max = 1.54&#949; (Mean = 0.439&#949;)</span>
6786                 </p>
6787               </td>
6788 <td>
6789                 <p>
6790                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6791                   1.16:</em></span> Max = 4.82&#949; (Mean = 0.758&#949;))<br> (<span class="emphasis"><em>Rmath
6792                   3.0.2:</em></span> Max = 1.01&#949; (Mean = 0.306&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
6793                   Max = 21&#949; (Mean = 5.65&#949;))
6794                 </p>
6795               </td>
6796 <td>
6797                 <p>
6798                   <span class="blue">Max = 2&#949; (Mean = 0.461&#949;)</span>
6799                 </p>
6800               </td>
6801 <td>
6802                 <p>
6803                   <span class="blue">Max = 2&#949; (Mean = 0.472&#949;)</span>
6804                 </p>
6805               </td>
6806 </tr>
6807 <tr>
6808 <td>
6809                 <p>
6810                   tgamma(a, z) large values
6811                 </p>
6812               </td>
6813 <td>
6814                 <p>
6815                   <span class="blue">Max = 244&#949; (Mean = 20.2&#949;)</span>
6816                 </p>
6817               </td>
6818 <td>
6819                 <p>
6820                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6821                   1.16:</em></span> Max = 1.02e+03&#949; (Mean = 105&#949;))<br> (<span class="emphasis"><em>Rmath
6822                   3.0.2:</em></span> Max = 1.11e+03&#949; (Mean = 67.5&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
6823                   Max = 8.18e+06&#949; (Mean = 7.69e+05&#949;))
6824                 </p>
6825               </td>
6826 <td>
6827                 <p>
6828                   <span class="blue">Max = 3.08e+04&#949; (Mean = 1.86e+03&#949;)</span>
6829                 </p>
6830               </td>
6831 <td>
6832                 <p>
6833                   <span class="blue">Max = 3.02e+04&#949; (Mean = 1.91e+03&#949;)</span>
6834                 </p>
6835               </td>
6836 </tr>
6837 <tr>
6838 <td>
6839                 <p>
6840                   tgamma(a, z) integer and half integer values
6841                 </p>
6842               </td>
6843 <td>
6844                 <p>
6845                   <span class="blue">Max = 13&#949; (Mean = 2.93&#949;)</span>
6846                 </p>
6847               </td>
6848 <td>
6849                 <p>
6850                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
6851                   1.16:</em></span> Max = 128&#949; (Mean = 22.6&#949;))<br> (<span class="emphasis"><em>Rmath
6852                   3.0.2:</em></span> Max = 66.2&#949; (Mean = 12.2&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
6853                   Max = 83.6&#949; (Mean = 22.2&#949;))
6854                 </p>
6855               </td>
6856 <td>
6857                 <p>
6858                   <span class="blue">Max = 11.8&#949; (Mean = 2.65&#949;)</span>
6859                 </p>
6860               </td>
6861 <td>
6862                 <p>
6863                   <span class="blue">Max = 71.6&#949; (Mean = 9.47&#949;)</span>
6864                 </p>
6865               </td>
6866 </tr>
6867 </tbody>
6868 </table></div>
6869 </div>
6870 <br class="table-break"><div class="table">
6871 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inv"></a><p class="title"><b>Table&#160;17.47.&#160;Error rates for gamma_p_inv</b></p>
6872 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
6873 <colgroup>
6874 <col>
6875 <col>
6876 <col>
6877 <col>
6878 <col>
6879 </colgroup>
6880 <thead><tr>
6881 <th>
6882               </th>
6883 <th>
6884                 <p>
6885                   Microsoft Visual C++ version 12.0<br> Win32<br> double
6886                 </p>
6887               </th>
6888 <th>
6889                 <p>
6890                   GNU C++ version 5.1.0<br> linux<br> double
6891                 </p>
6892               </th>
6893 <th>
6894                 <p>
6895                   GNU C++ version 5.1.0<br> linux<br> long double
6896                 </p>
6897               </th>
6898 <th>
6899                 <p>
6900                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
6901                 </p>
6902               </th>
6903 </tr></thead>
6904 <tbody>
6905 <tr>
6906 <td>
6907                 <p>
6908                   incomplete gamma inverse(a, z) medium values
6909                 </p>
6910               </td>
6911 <td>
6912                 <p>
6913                   <span class="blue">Max = 1.01&#949; (Mean = 0.307&#949;)</span>
6914                 </p>
6915               </td>
6916 <td>
6917                 <p>
6918                   <span class="blue">Max = 0.993&#949; (Mean = 0.15&#949;)</span><br> <br>
6919                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.88&#949; (Mean = 0.868&#949;))
6920                 </p>
6921               </td>
6922 <td>
6923                 <p>
6924                   <span class="blue">Max = 1.62&#949; (Mean = 0.365&#949;)</span>
6925                 </p>
6926               </td>
6927 <td>
6928                 <p>
6929                   <span class="blue">Max = 1.86&#949; (Mean = 0.405&#949;)</span>
6930                 </p>
6931               </td>
6932 </tr>
6933 <tr>
6934 <td>
6935                 <p>
6936                   incomplete gamma inverse(a, z) large values
6937                 </p>
6938               </td>
6939 <td>
6940                 <p>
6941                   <span class="blue">Max = 0.924&#949; (Mean = 0.118&#949;)</span>
6942                 </p>
6943               </td>
6944 <td>
6945                 <p>
6946                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
6947                   3.0.2:</em></span> Max = 0.816&#949; (Mean = 0.0874&#949;))
6948                 </p>
6949               </td>
6950 <td>
6951                 <p>
6952                   <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
6953                 </p>
6954               </td>
6955 <td>
6956                 <p>
6957                   <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
6958                 </p>
6959               </td>
6960 </tr>
6961 <tr>
6962 <td>
6963                 <p>
6964                   incomplete gamma inverse(a, z) small values
6965                 </p>
6966               </td>
6967 <td>
6968                 <p>
6969                   <span class="blue">Max = 1.1e+003&#949; (Mean = 108&#949;)</span>
6970                 </p>
6971               </td>
6972 <td>
6973                 <p>
6974                   <span class="blue">Max = 441&#949; (Mean = 53.9&#949;)</span><br> <br>
6975                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 547&#949; (Mean = 61.6&#949;))
6976                 </p>
6977               </td>
6978 <td>
6979                 <p>
6980                   <span class="blue">Max = 9.17e+03&#949; (Mean = 1.32e+03&#949;)</span>
6981                 </p>
6982               </td>
6983 <td>
6984                 <p>
6985                   <span class="blue">Max = 1.09e+04&#949; (Mean = 1.46e+03&#949;)</span>
6986                 </p>
6987               </td>
6988 </tr>
6989 </tbody>
6990 </table></div>
6991 </div>
6992 <br class="table-break"><div class="table">
6993 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inva"></a><p class="title"><b>Table&#160;17.48.&#160;Error rates for gamma_p_inva</b></p>
6994 <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
6995 <colgroup>
6996 <col>
6997 <col>
6998 <col>
6999 <col>
7000 <col>
7001 </colgroup>
7002 <thead><tr>
7003 <th>
7004               </th>
7005 <th>
7006                 <p>
7007                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7008                 </p>
7009               </th>
7010 <th>
7011                 <p>
7012                   GNU C++ version 5.1.0<br> linux<br> double
7013                 </p>
7014               </th>
7015 <th>
7016                 <p>
7017                   GNU C++ version 5.1.0<br> linux<br> long double
7018                 </p>
7019               </th>
7020 <th>
7021                 <p>
7022                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7023                 </p>
7024               </th>
7025 </tr></thead>
7026 <tbody><tr>
7027 <td>
7028                 <p>
7029                   Incomplete gamma inverses.
7030                 </p>
7031               </td>
7032 <td>
7033                 <p>
7034                   <span class="blue">Max = 3.52&#949; (Mean = 0.997&#949;)</span>
7035                 </p>
7036               </td>
7037 <td>
7038                 <p>
7039                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7040                 </p>
7041               </td>
7042 <td>
7043                 <p>
7044                   <span class="blue">Max = 6.44&#949; (Mean = 1.1&#949;)</span>
7045                 </p>
7046               </td>
7047 <td>
7048                 <p>
7049                   <span class="blue">Max = 4.08&#949; (Mean = 1.12&#949;)</span>
7050                 </p>
7051               </td>
7052 </tr></tbody>
7053 </table></div>
7054 </div>
7055 <br class="table-break"><div class="table">
7056 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q"></a><p class="title"><b>Table&#160;17.49.&#160;Error rates for gamma_q</b></p>
7057 <div class="table-contents"><table class="table" summary="Error rates for gamma_q">
7058 <colgroup>
7059 <col>
7060 <col>
7061 <col>
7062 <col>
7063 <col>
7064 </colgroup>
7065 <thead><tr>
7066 <th>
7067               </th>
7068 <th>
7069                 <p>
7070                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7071                 </p>
7072               </th>
7073 <th>
7074                 <p>
7075                   GNU C++ version 5.1.0<br> linux<br> double
7076                 </p>
7077               </th>
7078 <th>
7079                 <p>
7080                   GNU C++ version 5.1.0<br> linux<br> long double
7081                 </p>
7082               </th>
7083 <th>
7084                 <p>
7085                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7086                 </p>
7087               </th>
7088 </tr></thead>
7089 <tbody>
7090 <tr>
7091 <td>
7092                 <p>
7093                   tgamma(a, z) medium values
7094                 </p>
7095               </td>
7096 <td>
7097                 <p>
7098                   <span class="blue">Max = 23.7&#949; (Mean = 4.03&#949;)</span>
7099                 </p>
7100               </td>
7101 <td>
7102                 <p>
7103                   <span class="blue">Max = 0.927&#949; (Mean = 0.035&#949;)</span><br> <br>
7104                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 201&#949; (Mean = 13.5&#949;))<br> (<span class="emphasis"><em>Rmath
7105                   3.0.2:</em></span> Max = 131&#949; (Mean = 12.7&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
7106                   Max = 388&#949; (Mean = 93.8&#949;))
7107                 </p>
7108               </td>
7109 <td>
7110                 <p>
7111                   <span class="blue">Max = 31.3&#949; (Mean = 6.56&#949;)</span>
7112                 </p>
7113               </td>
7114 <td>
7115                 <p>
7116                   <span class="blue">Max = 199&#949; (Mean = 26.6&#949;)</span>
7117                 </p>
7118               </td>
7119 </tr>
7120 <tr>
7121 <td>
7122                 <p>
7123                   tgamma(a, z) small values
7124                 </p>
7125               </td>
7126 <td>
7127                 <p>
7128                   <span class="blue">Max = 2.26&#949; (Mean = 0.732&#949;)</span>
7129                 </p>
7130               </td>
7131 <td>
7132                 <p>
7133                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7134                   1.16:</em></span> <span class="red">Max = 1.38e+10&#949; (Mean = 1.05e+09&#949;))</span><br>
7135                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 65.6&#949; (Mean = 11&#949;))<br>
7136                   (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = 3.42e+11&#949; (Mean
7137                   = 4.1e+10&#949;))</span>
7138                 </p>
7139               </td>
7140 <td>
7141                 <p>
7142                   <span class="blue">Max = 2.45&#949; (Mean = 0.832&#949;)</span>
7143                 </p>
7144               </td>
7145 <td>
7146                 <p>
7147                   <span class="blue">Max = 2.25&#949; (Mean = 0.81&#949;)</span>
7148                 </p>
7149               </td>
7150 </tr>
7151 <tr>
7152 <td>
7153                 <p>
7154                   tgamma(a, z) large values
7155                 </p>
7156               </td>
7157 <td>
7158                 <p>
7159                   <span class="blue">Max = 470&#949; (Mean = 31.5&#949;)</span>
7160                 </p>
7161               </td>
7162 <td>
7163                 <p>
7164                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7165                   1.16:</em></span> Max = 2.71e+04&#949; (Mean = 2.16e+03&#949;))<br> (<span class="emphasis"><em>Rmath
7166                   3.0.2:</em></span> Max = 1.02e+03&#949; (Mean = 62.7&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
7167                   Max = 8.17e+06&#949; (Mean = 7.7e+05&#949;))
7168                 </p>
7169               </td>
7170 <td>
7171                 <p>
7172                   <span class="blue">Max = 6.82e+03&#949; (Mean = 414&#949;)</span>
7173                 </p>
7174               </td>
7175 <td>
7176                 <p>
7177                   <span class="blue">Max = 1.15e+04&#949; (Mean = 733&#949;)</span>
7178                 </p>
7179               </td>
7180 </tr>
7181 <tr>
7182 <td>
7183                 <p>
7184                   tgamma(a, z) integer and half integer values
7185                 </p>
7186               </td>
7187 <td>
7188                 <p>
7189                   <span class="blue">Max = 8.48&#949; (Mean = 1.42&#949;)</span>
7190                 </p>
7191               </td>
7192 <td>
7193                 <p>
7194                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7195                   1.16:</em></span> Max = 118&#949; (Mean = 12.5&#949;))<br> (<span class="emphasis"><em>Rmath
7196                   3.0.2:</em></span> Max = 138&#949; (Mean = 16.9&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
7197                   Max = 129&#949; (Mean = 26.5&#949;))
7198                 </p>
7199               </td>
7200 <td>
7201                 <p>
7202                   <span class="blue">Max = 11.1&#949; (Mean = 2.09&#949;)</span>
7203                 </p>
7204               </td>
7205 <td>
7206                 <p>
7207                   <span class="blue">Max = 54.7&#949; (Mean = 6.16&#949;)</span>
7208                 </p>
7209               </td>
7210 </tr>
7211 </tbody>
7212 </table></div>
7213 </div>
7214 <br class="table-break"><div class="table">
7215 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inv"></a><p class="title"><b>Table&#160;17.50.&#160;Error rates for gamma_q_inv</b></p>
7216 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
7217 <colgroup>
7218 <col>
7219 <col>
7220 <col>
7221 <col>
7222 <col>
7223 </colgroup>
7224 <thead><tr>
7225 <th>
7226               </th>
7227 <th>
7228                 <p>
7229                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7230                 </p>
7231               </th>
7232 <th>
7233                 <p>
7234                   GNU C++ version 5.1.0<br> linux<br> double
7235                 </p>
7236               </th>
7237 <th>
7238                 <p>
7239                   GNU C++ version 5.1.0<br> linux<br> long double
7240                 </p>
7241               </th>
7242 <th>
7243                 <p>
7244                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7245                 </p>
7246               </th>
7247 </tr></thead>
7248 <tbody>
7249 <tr>
7250 <td>
7251                 <p>
7252                   incomplete gamma inverse(a, z) medium values
7253                 </p>
7254               </td>
7255 <td>
7256                 <p>
7257                   <span class="blue">Max = 3.46&#949; (Mean = 0.475&#949;)</span>
7258                 </p>
7259               </td>
7260 <td>
7261                 <p>
7262                   <span class="blue">Max = 0.912&#949; (Mean = 0.154&#949;)</span><br> <br>
7263                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 4.66&#949; (Mean = 0.792&#949;))
7264                 </p>
7265               </td>
7266 <td>
7267                 <p>
7268                   <span class="blue">Max = 6.2&#949; (Mean = 0.659&#949;)</span>
7269                 </p>
7270               </td>
7271 <td>
7272                 <p>
7273                   <span class="blue">Max = 6.2&#949; (Mean = 0.661&#949;)</span>
7274                 </p>
7275               </td>
7276 </tr>
7277 <tr>
7278 <td>
7279                 <p>
7280                   incomplete gamma inverse(a, z) large values
7281                 </p>
7282               </td>
7283 <td>
7284                 <p>
7285                   <span class="blue">Max = 0.814&#949; (Mean = 0.0856&#949;)</span>
7286                 </p>
7287               </td>
7288 <td>
7289                 <p>
7290                   <span class="blue">Max = 0.894&#949; (Mean = 0.0915&#949;)</span><br>
7291                   <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.894&#949; (Mean = 0.106&#949;))
7292                 </p>
7293               </td>
7294 <td>
7295                 <p>
7296                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7297                 </p>
7298               </td>
7299 <td>
7300                 <p>
7301                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7302                 </p>
7303               </td>
7304 </tr>
7305 <tr>
7306 <td>
7307                 <p>
7308                   incomplete gamma inverse(a, z) small values
7309                 </p>
7310               </td>
7311 <td>
7312                 <p>
7313                   <span class="blue">Max = 451&#949; (Mean = 65&#949;)</span>
7314                 </p>
7315               </td>
7316 <td>
7317                 <p>
7318                   <span class="blue">Max = 292&#949; (Mean = 36.4&#949;)</span><br> <br>
7319                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 415&#949; (Mean = 48.7&#949;))
7320                 </p>
7321               </td>
7322 <td>
7323                 <p>
7324                   <span class="blue">Max = 8.28e+03&#949; (Mean = 963&#949;)</span>
7325                 </p>
7326               </td>
7327 <td>
7328                 <p>
7329                   <span class="blue">Max = 8.98e+03&#949; (Mean = 877&#949;)</span>
7330                 </p>
7331               </td>
7332 </tr>
7333 </tbody>
7334 </table></div>
7335 </div>
7336 <br class="table-break"><div class="table">
7337 <a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inva"></a><p class="title"><b>Table&#160;17.51.&#160;Error rates for gamma_q_inva</b></p>
7338 <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
7339 <colgroup>
7340 <col>
7341 <col>
7342 <col>
7343 <col>
7344 <col>
7345 </colgroup>
7346 <thead><tr>
7347 <th>
7348               </th>
7349 <th>
7350                 <p>
7351                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7352                 </p>
7353               </th>
7354 <th>
7355                 <p>
7356                   GNU C++ version 5.1.0<br> linux<br> double
7357                 </p>
7358               </th>
7359 <th>
7360                 <p>
7361                   GNU C++ version 5.1.0<br> linux<br> long double
7362                 </p>
7363               </th>
7364 <th>
7365                 <p>
7366                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7367                 </p>
7368               </th>
7369 </tr></thead>
7370 <tbody><tr>
7371 <td>
7372                 <p>
7373                   Incomplete gamma inverses.
7374                 </p>
7375               </td>
7376 <td>
7377                 <p>
7378                   <span class="blue">Max = 5.64&#949; (Mean = 1.09&#949;)</span>
7379                 </p>
7380               </td>
7381 <td>
7382                 <p>
7383                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7384                 </p>
7385               </td>
7386 <td>
7387                 <p>
7388                   <span class="blue">Max = 6.91&#949; (Mean = 1.17&#949;)</span>
7389                 </p>
7390               </td>
7391 <td>
7392                 <p>
7393                   <span class="blue">Max = 7.86&#949; (Mean = 1.25&#949;)</span>
7394                 </p>
7395               </td>
7396 </tr></tbody>
7397 </table></div>
7398 </div>
7399 <br class="table-break"><div class="table">
7400 <a name="math_toolkit.logs_and_tables.all_table.table_hermite"></a><p class="title"><b>Table&#160;17.52.&#160;Error rates for hermite</b></p>
7401 <div class="table-contents"><table class="table" summary="Error rates for hermite">
7402 <colgroup>
7403 <col>
7404 <col>
7405 <col>
7406 <col>
7407 <col>
7408 </colgroup>
7409 <thead><tr>
7410 <th>
7411               </th>
7412 <th>
7413                 <p>
7414                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7415                 </p>
7416               </th>
7417 <th>
7418                 <p>
7419                   GNU C++ version 5.1.0<br> linux<br> double
7420                 </p>
7421               </th>
7422 <th>
7423                 <p>
7424                   GNU C++ version 5.1.0<br> linux<br> long double
7425                 </p>
7426               </th>
7427 <th>
7428                 <p>
7429                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7430                 </p>
7431               </th>
7432 </tr></thead>
7433 <tbody><tr>
7434 <td>
7435                 <p>
7436                   Hermite Polynomials
7437                 </p>
7438               </td>
7439 <td>
7440                 <p>
7441                   <span class="blue">Max = 4.46&#949; (Mean = 1.41&#949;)</span>
7442                 </p>
7443               </td>
7444 <td>
7445                 <p>
7446                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7447                 </p>
7448               </td>
7449 <td>
7450                 <p>
7451                   <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
7452                 </p>
7453               </td>
7454 <td>
7455                 <p>
7456                   <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
7457                 </p>
7458               </td>
7459 </tr></tbody>
7460 </table></div>
7461 </div>
7462 <br class="table-break"><div class="table">
7463 <a name="math_toolkit.logs_and_tables.all_table.table_heuman_lambda"></a><p class="title"><b>Table&#160;17.53.&#160;Error rates for heuman_lambda</b></p>
7464 <div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
7465 <colgroup>
7466 <col>
7467 <col>
7468 <col>
7469 <col>
7470 <col>
7471 </colgroup>
7472 <thead><tr>
7473 <th>
7474               </th>
7475 <th>
7476                 <p>
7477                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7478                 </p>
7479               </th>
7480 <th>
7481                 <p>
7482                   GNU C++ version 5.1.0<br> linux<br> double
7483                 </p>
7484               </th>
7485 <th>
7486                 <p>
7487                   GNU C++ version 5.1.0<br> linux<br> long double
7488                 </p>
7489               </th>
7490 <th>
7491                 <p>
7492                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7493                 </p>
7494               </th>
7495 </tr></thead>
7496 <tbody>
7497 <tr>
7498 <td>
7499                 <p>
7500                   Elliptic Integral Jacobi Zeta: Mathworld Data
7501                 </p>
7502               </td>
7503 <td>
7504                 <p>
7505                   <span class="blue">Max = 1.08&#949; (Mean = 0.734&#949;)</span>
7506                 </p>
7507               </td>
7508 <td>
7509                 <p>
7510                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7511                 </p>
7512               </td>
7513 <td>
7514                 <p>
7515                   <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
7516                 </p>
7517               </td>
7518 <td>
7519                 <p>
7520                   <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
7521                 </p>
7522               </td>
7523 </tr>
7524 <tr>
7525 <td>
7526                 <p>
7527                   Elliptic Integral Heuman Lambda: Random Data
7528                 </p>
7529               </td>
7530 <td>
7531                 <p>
7532                   <span class="blue">Max = 2.12&#949; (Mean = 0.59&#949;)</span>
7533                 </p>
7534               </td>
7535 <td>
7536                 <p>
7537                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
7538                 </p>
7539               </td>
7540 <td>
7541                 <p>
7542                   <span class="blue">Max = 3.82&#949; (Mean = 0.609&#949;)</span>
7543                 </p>
7544               </td>
7545 <td>
7546                 <p>
7547                   <span class="blue">Max = 3.82&#949; (Mean = 0.608&#949;)</span>
7548                 </p>
7549               </td>
7550 </tr>
7551 </tbody>
7552 </table></div>
7553 </div>
7554 <br class="table-break"><div class="table">
7555 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta"></a><p class="title"><b>Table&#160;17.54.&#160;Error rates for ibeta</b></p>
7556 <div class="table-contents"><table class="table" summary="Error rates for ibeta">
7557 <colgroup>
7558 <col>
7559 <col>
7560 <col>
7561 <col>
7562 <col>
7563 </colgroup>
7564 <thead><tr>
7565 <th>
7566               </th>
7567 <th>
7568                 <p>
7569                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7570                 </p>
7571               </th>
7572 <th>
7573                 <p>
7574                   GNU C++ version 5.1.0<br> linux<br> double
7575                 </p>
7576               </th>
7577 <th>
7578                 <p>
7579                   GNU C++ version 5.1.0<br> linux<br> long double
7580                 </p>
7581               </th>
7582 <th>
7583                 <p>
7584                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7585                 </p>
7586               </th>
7587 </tr></thead>
7588 <tbody>
7589 <tr>
7590 <td>
7591                 <p>
7592                   Incomplete Beta Function: Small Values
7593                 </p>
7594               </td>
7595 <td>
7596                 <p>
7597                   <span class="blue">Max = 9.42&#949; (Mean = 2.24&#949;)</span>
7598                 </p>
7599               </td>
7600 <td>
7601                 <p>
7602                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7603                   1.16:</em></span> Max = 682&#949; (Mean = 32.6&#949;))<br> (<span class="emphasis"><em>Rmath
7604                   3.0.2:</em></span> Max = 22.9&#949; (Mean = 3.35&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
7605                   Max = 22.7&#949; (Mean = 1.69&#949;))
7606                 </p>
7607               </td>
7608 <td>
7609                 <p>
7610                   <span class="blue">Max = 6.27&#949; (Mean = 1.7&#949;)</span>
7611                 </p>
7612               </td>
7613 <td>
7614                 <p>
7615                   <span class="blue">Max = 21.3&#949; (Mean = 2.74&#949;)</span>
7616                 </p>
7617               </td>
7618 </tr>
7619 <tr>
7620 <td>
7621                 <p>
7622                   Incomplete Beta Function: Medium Values
7623                 </p>
7624               </td>
7625 <td>
7626                 <p>
7627                   <span class="blue">Max = 108&#949; (Mean = 16.3&#949;)</span>
7628                 </p>
7629               </td>
7630 <td>
7631                 <p>
7632                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7633                   1.16:</em></span> Max = 690&#949; (Mean = 151&#949;))<br> (<span class="emphasis"><em>Rmath
7634                   3.0.2:</em></span> Max = 232&#949; (Mean = 27.9&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
7635                   Max = 1.55e+03&#949; (Mean = 121&#949;))
7636                 </p>
7637               </td>
7638 <td>
7639                 <p>
7640                   <span class="blue">Max = 51.4&#949; (Mean = 12&#949;)</span>
7641                 </p>
7642               </td>
7643 <td>
7644                 <p>
7645                   <span class="blue">Max = 124&#949; (Mean = 18.4&#949;)</span>
7646                 </p>
7647               </td>
7648 </tr>
7649 <tr>
7650 <td>
7651                 <p>
7652                   Incomplete Beta Function: Large and Diverse Values
7653                 </p>
7654               </td>
7655 <td>
7656                 <p>
7657                   <span class="blue">Max = 1.19e+003&#949; (Mean = 59.5&#949;)</span>
7658                 </p>
7659               </td>
7660 <td>
7661                 <p>
7662                   <span class="blue">Max = 1.26&#949; (Mean = 0.063&#949;)</span><br> <br>
7663                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.9e+05&#949; (Mean = 1.82e+04&#949;)
7664                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibeta_GSL_1_16_Incomplete_Beta_Function_Large_and_Diverse_Values">And
7665                   other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span>
7666                   Max = 574&#949; (Mean = 49.4&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span> Max
7667                   = 5.92e+05&#949; (Mean = 2.17e+04&#949;))
7668                 </p>
7669               </td>
7670 <td>
7671                 <p>
7672                   <span class="blue">Max = 1.96e+04&#949; (Mean = 997&#949;)</span>
7673                 </p>
7674               </td>
7675 <td>
7676                 <p>
7677                   <span class="blue">Max = 4.98e+04&#949; (Mean = 2.07e+03&#949;)</span>
7678                 </p>
7679               </td>
7680 </tr>
7681 <tr>
7682 <td>
7683                 <p>
7684                   Incomplete Beta Function: Small Integer Values
7685                 </p>
7686               </td>
7687 <td>
7688                 <p>
7689                   <span class="blue">Max = 3.69&#949; (Mean = 0.765&#949;)</span>
7690                 </p>
7691               </td>
7692 <td>
7693                 <p>
7694                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
7695                   1.16:</em></span> Max = 254&#949; (Mean = 50.9&#949;))<br> (<span class="emphasis"><em>Rmath
7696                   3.0.2:</em></span> Max = 62.2&#949; (Mean = 8.95&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
7697                   Max = 7.96&#949; (Mean = 1.3&#949;))
7698                 </p>
7699               </td>
7700 <td>
7701                 <p>
7702                   <span class="blue">Max = 4.45&#949; (Mean = 0.814&#949;)</span>
7703                 </p>
7704               </td>
7705 <td>
7706                 <p>
7707                   <span class="blue">Max = 44.5&#949; (Mean = 10.1&#949;)</span>
7708                 </p>
7709               </td>
7710 </tr>
7711 </tbody>
7712 </table></div>
7713 </div>
7714 <br class="table-break"><div class="table">
7715 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inv"></a><p class="title"><b>Table&#160;17.55.&#160;Error rates for ibeta_inv</b></p>
7716 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
7717 <colgroup>
7718 <col>
7719 <col>
7720 <col>
7721 <col>
7722 <col>
7723 </colgroup>
7724 <thead><tr>
7725 <th>
7726               </th>
7727 <th>
7728                 <p>
7729                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7730                 </p>
7731               </th>
7732 <th>
7733                 <p>
7734                   GNU C++ version 5.1.0<br> linux<br> double
7735                 </p>
7736               </th>
7737 <th>
7738                 <p>
7739                   GNU C++ version 5.1.0<br> linux<br> long double
7740                 </p>
7741               </th>
7742 <th>
7743                 <p>
7744                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7745                 </p>
7746               </th>
7747 </tr></thead>
7748 <tbody><tr>
7749 <td>
7750                 <p>
7751                   Inverse incomplete beta
7752                 </p>
7753               </td>
7754 <td>
7755                 <p>
7756                   <span class="blue">Max = 7.08e+003&#949; (Mean = 244&#949;)</span>
7757                 </p>
7758               </td>
7759 <td>
7760                 <p>
7761                   <span class="blue">Max = 3.21&#949; (Mean = 0.158&#949;)</span><br> <br>
7762                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean
7763                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibeta_inv_Rmath_3_0_2_Inverse_incomplete_beta">And
7764                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
7765                   <span class="red">Max = 1.28e+10&#949; (Mean = 5.17e+08&#949;))</span>
7766                 </p>
7767               </td>
7768 <td>
7769                 <p>
7770                   <span class="blue">Max = 4.53e+04&#949; (Mean = 2.93e+03&#949;)</span>
7771                 </p>
7772               </td>
7773 <td>
7774                 <p>
7775                   <span class="blue">Max = 4.22e+04&#949; (Mean = 2.8e+03&#949;)</span>
7776                 </p>
7777               </td>
7778 </tr></tbody>
7779 </table></div>
7780 </div>
7781 <br class="table-break"><div class="table">
7782 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inva"></a><p class="title"><b>Table&#160;17.56.&#160;Error rates for ibeta_inva</b></p>
7783 <div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
7784 <colgroup>
7785 <col>
7786 <col>
7787 <col>
7788 <col>
7789 <col>
7790 </colgroup>
7791 <thead><tr>
7792 <th>
7793               </th>
7794 <th>
7795                 <p>
7796                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7797                 </p>
7798               </th>
7799 <th>
7800                 <p>
7801                   GNU C++ version 5.1.0<br> linux<br> double
7802                 </p>
7803               </th>
7804 <th>
7805                 <p>
7806                   GNU C++ version 5.1.0<br> linux<br> long double
7807                 </p>
7808               </th>
7809 <th>
7810                 <p>
7811                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7812                 </p>
7813               </th>
7814 </tr></thead>
7815 <tbody><tr>
7816 <td>
7817                 <p>
7818                   Inverse incomplete beta
7819                 </p>
7820               </td>
7821 <td>
7822                 <p>
7823                   <span class="blue">Max = 395&#949; (Mean = 24.7&#949;)</span>
7824                 </p>
7825               </td>
7826 <td>
7827                 <p>
7828                   <span class="blue">Max = 0.602&#949; (Mean = 0.0239&#949;)</span>
7829                 </p>
7830               </td>
7831 <td>
7832                 <p>
7833                   <span class="blue">Max = 377&#949; (Mean = 25.1&#949;)</span>
7834                 </p>
7835               </td>
7836 <td>
7837                 <p>
7838                   <span class="blue">Max = 438&#949; (Mean = 31.6&#949;)</span>
7839                 </p>
7840               </td>
7841 </tr></tbody>
7842 </table></div>
7843 </div>
7844 <br class="table-break"><div class="table">
7845 <a name="math_toolkit.logs_and_tables.all_table.table_ibeta_invb"></a><p class="title"><b>Table&#160;17.57.&#160;Error rates for ibeta_invb</b></p>
7846 <div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
7847 <colgroup>
7848 <col>
7849 <col>
7850 <col>
7851 <col>
7852 <col>
7853 </colgroup>
7854 <thead><tr>
7855 <th>
7856               </th>
7857 <th>
7858                 <p>
7859                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7860                 </p>
7861               </th>
7862 <th>
7863                 <p>
7864                   GNU C++ version 5.1.0<br> linux<br> double
7865                 </p>
7866               </th>
7867 <th>
7868                 <p>
7869                   GNU C++ version 5.1.0<br> linux<br> long double
7870                 </p>
7871               </th>
7872 <th>
7873                 <p>
7874                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7875                 </p>
7876               </th>
7877 </tr></thead>
7878 <tbody><tr>
7879 <td>
7880                 <p>
7881                   Inverse incomplete beta
7882                 </p>
7883               </td>
7884 <td>
7885                 <p>
7886                   <span class="blue">Max = 409&#949; (Mean = 17.9&#949;)</span>
7887                 </p>
7888               </td>
7889 <td>
7890                 <p>
7891                   <span class="blue">Max = 0.836&#949; (Mean = 0.0491&#949;)</span>
7892                 </p>
7893               </td>
7894 <td>
7895                 <p>
7896                   <span class="blue">Max = 407&#949; (Mean = 27.2&#949;)</span>
7897                 </p>
7898               </td>
7899 <td>
7900                 <p>
7901                   <span class="blue">Max = 407&#949; (Mean = 24.4&#949;)</span>
7902                 </p>
7903               </td>
7904 </tr></tbody>
7905 </table></div>
7906 </div>
7907 <br class="table-break"><div class="table">
7908 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac"></a><p class="title"><b>Table&#160;17.58.&#160;Error rates for ibetac</b></p>
7909 <div class="table-contents"><table class="table" summary="Error rates for ibetac">
7910 <colgroup>
7911 <col>
7912 <col>
7913 <col>
7914 <col>
7915 <col>
7916 </colgroup>
7917 <thead><tr>
7918 <th>
7919               </th>
7920 <th>
7921                 <p>
7922                   Microsoft Visual C++ version 12.0<br> Win32<br> double
7923                 </p>
7924               </th>
7925 <th>
7926                 <p>
7927                   GNU C++ version 5.1.0<br> linux<br> double
7928                 </p>
7929               </th>
7930 <th>
7931                 <p>
7932                   GNU C++ version 5.1.0<br> linux<br> long double
7933                 </p>
7934               </th>
7935 <th>
7936                 <p>
7937                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
7938                 </p>
7939               </th>
7940 </tr></thead>
7941 <tbody>
7942 <tr>
7943 <td>
7944                 <p>
7945                   Incomplete Beta Function: Small Values
7946                 </p>
7947               </td>
7948 <td>
7949                 <p>
7950                   <span class="blue">Max = 6.56&#949; (Mean = 1.88&#949;)</span>
7951                 </p>
7952               </td>
7953 <td>
7954                 <p>
7955                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
7956                   3.0.2:</em></span> Max = 22.4&#949; (Mean = 3.67&#949;))
7957                 </p>
7958               </td>
7959 <td>
7960                 <p>
7961                   <span class="blue">Max = 8.47&#949; (Mean = 1.68&#949;)</span>
7962                 </p>
7963               </td>
7964 <td>
7965                 <p>
7966                   <span class="blue">Max = 13.8&#949; (Mean = 2.69&#949;)</span>
7967                 </p>
7968               </td>
7969 </tr>
7970 <tr>
7971 <td>
7972                 <p>
7973                   Incomplete Beta Function: Medium Values
7974                 </p>
7975               </td>
7976 <td>
7977                 <p>
7978                   <span class="blue">Max = 56.2&#949; (Mean = 14.1&#949;)</span>
7979                 </p>
7980               </td>
7981 <td>
7982                 <p>
7983                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
7984                   3.0.2:</em></span> Max = 204&#949; (Mean = 25.8&#949;))
7985                 </p>
7986               </td>
7987 <td>
7988                 <p>
7989                   <span class="blue">Max = 75.3&#949; (Mean = 11.3&#949;)</span>
7990                 </p>
7991               </td>
7992 <td>
7993                 <p>
7994                   <span class="blue">Max = 132&#949; (Mean = 19.8&#949;)</span>
7995                 </p>
7996               </td>
7997 </tr>
7998 <tr>
7999 <td>
8000                 <p>
8001                   Incomplete Beta Function: Large and Diverse Values
8002                 </p>
8003               </td>
8004 <td>
8005                 <p>
8006                   <span class="blue">Max = 1.87e+003&#949; (Mean = 93.8&#949;)</span>
8007                 </p>
8008               </td>
8009 <td>
8010                 <p>
8011                   <span class="blue">Max = 0.981&#949; (Mean = 0.0638&#949;)</span><br>
8012                   <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 889&#949; (Mean = 68.4&#949;))
8013                 </p>
8014               </td>
8015 <td>
8016                 <p>
8017                   <span class="blue">Max = 3.45e+04&#949; (Mean = 1.32e+03&#949;)</span>
8018                 </p>
8019               </td>
8020 <td>
8021                 <p>
8022                   <span class="blue">Max = 4.26e+04&#949; (Mean = 1.54e+03&#949;)</span>
8023                 </p>
8024               </td>
8025 </tr>
8026 <tr>
8027 <td>
8028                 <p>
8029                   Incomplete Beta Function: Small Integer Values
8030                 </p>
8031               </td>
8032 <td>
8033                 <p>
8034                   <span class="blue">Max = 6.37&#949; (Mean = 1.03&#949;)</span>
8035                 </p>
8036               </td>
8037 <td>
8038                 <p>
8039                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
8040                   3.0.2:</em></span> Max = 84.6&#949; (Mean = 18&#949;))
8041                 </p>
8042               </td>
8043 <td>
8044                 <p>
8045                   <span class="blue">Max = 5.34&#949; (Mean = 1.11&#949;)</span>
8046                 </p>
8047               </td>
8048 <td>
8049                 <p>
8050                   <span class="blue">Max = 107&#949; (Mean = 17.1&#949;)</span>
8051                 </p>
8052               </td>
8053 </tr>
8054 </tbody>
8055 </table></div>
8056 </div>
8057 <br class="table-break"><div class="table">
8058 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inv"></a><p class="title"><b>Table&#160;17.59.&#160;Error rates for ibetac_inv</b></p>
8059 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
8060 <colgroup>
8061 <col>
8062 <col>
8063 <col>
8064 <col>
8065 <col>
8066 </colgroup>
8067 <thead><tr>
8068 <th>
8069               </th>
8070 <th>
8071                 <p>
8072                   Microsoft Visual C++ version 12.0<br> Win32<br> double
8073                 </p>
8074               </th>
8075 <th>
8076                 <p>
8077                   GNU C++ version 5.1.0<br> linux<br> double
8078                 </p>
8079               </th>
8080 <th>
8081                 <p>
8082                   GNU C++ version 5.1.0<br> linux<br> long double
8083                 </p>
8084               </th>
8085 <th>
8086                 <p>
8087                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
8088                 </p>
8089               </th>
8090 </tr></thead>
8091 <tbody><tr>
8092 <td>
8093                 <p>
8094                   Inverse incomplete beta
8095                 </p>
8096               </td>
8097 <td>
8098                 <p>
8099                   <span class="blue">Max = 5.53e+003&#949; (Mean = 220&#949;)</span>
8100                 </p>
8101               </td>
8102 <td>
8103                 <p>
8104                   <span class="blue">Max = 1.71&#949; (Mean = 0.108&#949;)</span><br> <br>
8105                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean
8106                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_ibetac_inv_Rmath_3_0_2_Inverse_incomplete_beta">And
8107                   other failures.</a>)</span><br> (<span class="emphasis"><em>Cephes:</em></span>
8108                   Max = 1.71&#949; (Mean = 0.108&#949;))
8109                 </p>
8110               </td>
8111 <td>
8112                 <p>
8113                   <span class="blue">Max = 6.17e+04&#949; (Mean = 3.77e+03&#949;)</span>
8114                 </p>
8115               </td>
8116 <td>
8117                 <p>
8118                   <span class="blue">Max = 5.15e+04&#949; (Mean = 3.51e+03&#949;)</span>
8119                 </p>
8120               </td>
8121 </tr></tbody>
8122 </table></div>
8123 </div>
8124 <br class="table-break"><div class="table">
8125 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inva"></a><p class="title"><b>Table&#160;17.60.&#160;Error rates for ibetac_inva</b></p>
8126 <div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
8127 <colgroup>
8128 <col>
8129 <col>
8130 <col>
8131 <col>
8132 <col>
8133 </colgroup>
8134 <thead><tr>
8135 <th>
8136               </th>
8137 <th>
8138                 <p>
8139                   Microsoft Visual C++ version 12.0<br> Win32<br> double
8140                 </p>
8141               </th>
8142 <th>
8143                 <p>
8144                   GNU C++ version 5.1.0<br> linux<br> double
8145                 </p>
8146               </th>
8147 <th>
8148                 <p>
8149                   GNU C++ version 5.1.0<br> linux<br> long double
8150                 </p>
8151               </th>
8152 <th>
8153                 <p>
8154                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
8155                 </p>
8156               </th>
8157 </tr></thead>
8158 <tbody><tr>
8159 <td>
8160                 <p>
8161                   Inverse incomplete beta
8162                 </p>
8163               </td>
8164 <td>
8165                 <p>
8166                   <span class="blue">Max = 408&#949; (Mean = 27.8&#949;)</span>
8167                 </p>
8168               </td>
8169 <td>
8170                 <p>
8171                   <span class="blue">Max = 0.683&#949; (Mean = 0.0271&#949;)</span>
8172                 </p>
8173               </td>
8174 <td>
8175                 <p>
8176                   <span class="blue">Max = 382&#949; (Mean = 22.2&#949;)</span>
8177                 </p>
8178               </td>
8179 <td>
8180                 <p>
8181                   <span class="blue">Max = 315&#949; (Mean = 23.7&#949;)</span>
8182                 </p>
8183               </td>
8184 </tr></tbody>
8185 </table></div>
8186 </div>
8187 <br class="table-break"><div class="table">
8188 <a name="math_toolkit.logs_and_tables.all_table.table_ibetac_invb"></a><p class="title"><b>Table&#160;17.61.&#160;Error rates for ibetac_invb</b></p>
8189 <div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
8190 <colgroup>
8191 <col>
8192 <col>
8193 <col>
8194 <col>
8195 <col>
8196 </colgroup>
8197 <thead><tr>
8198 <th>
8199               </th>
8200 <th>
8201                 <p>
8202                   Microsoft Visual C++ version 12.0<br> Win32<br> double
8203                 </p>
8204               </th>
8205 <th>
8206                 <p>
8207                   GNU C++ version 5.1.0<br> linux<br> double
8208                 </p>
8209               </th>
8210 <th>
8211                 <p>
8212                   GNU C++ version 5.1.0<br> linux<br> long double
8213                 </p>
8214               </th>
8215 <th>
8216                 <p>
8217                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
8218                 </p>
8219               </th>
8220 </tr></thead>
8221 <tbody><tr>
8222 <td>
8223                 <p>
8224                   Inverse incomplete beta
8225                 </p>
8226               </td>
8227 <td>
8228                 <p>
8229                   <span class="blue">Max = 329&#949; (Mean = 18.2&#949;)</span>
8230                 </p>
8231               </td>
8232 <td>
8233                 <p>
8234                   <span class="blue">Max = 0.724&#949; (Mean = 0.0303&#949;)</span>
8235                 </p>
8236               </td>
8237 <td>
8238                 <p>
8239                   <span class="blue">Max = 317&#949; (Mean = 19.7&#949;)</span>
8240                 </p>
8241               </td>
8242 <td>
8243                 <p>
8244                   <span class="blue">Max = 369&#949; (Mean = 21.7&#949;)</span>
8245                 </p>
8246               </td>
8247 </tr></tbody>
8248 </table></div>
8249 </div>
8250 <br class="table-break"><div class="table">
8251 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_cn"></a><p class="title"><b>Table&#160;17.62.&#160;Error rates for jacobi_cn</b></p>
8252 <div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
8253 <colgroup>
8254 <col>
8255 <col>
8256 <col>
8257 <col>
8258 <col>
8259 </colgroup>
8260 <thead><tr>
8261 <th>
8262               </th>
8263 <th>
8264                 <p>
8265                   Microsoft Visual C++ version 12.0<br> Win32<br> double
8266                 </p>
8267               </th>
8268 <th>
8269                 <p>
8270                   GNU C++ version 5.1.0<br> linux<br> double
8271                 </p>
8272               </th>
8273 <th>
8274                 <p>
8275                   GNU C++ version 5.1.0<br> linux<br> long double
8276                 </p>
8277               </th>
8278 <th>
8279                 <p>
8280                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
8281                 </p>
8282               </th>
8283 </tr></thead>
8284 <tbody>
8285 <tr>
8286 <td>
8287                 <p>
8288                   Jacobi Elliptic: Mathworld Data
8289                 </p>
8290               </td>
8291 <td>
8292                 <p>
8293                   <span class="blue">Max = 45.8&#949; (Mean = 11.4&#949;)</span>
8294                 </p>
8295               </td>
8296 <td>
8297                 <p>
8298                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8299                   1.16:</em></span> Max = 17.3&#949; (Mean = 4.29&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
8300                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
8301                   other failures.</a>)</span>
8302                 </p>
8303               </td>
8304 <td>
8305                 <p>
8306                   <span class="blue">Max = 71.6&#949; (Mean = 19.3&#949;)</span>
8307                 </p>
8308               </td>
8309 <td>
8310                 <p>
8311                   <span class="blue">Max = 71.6&#949; (Mean = 19.4&#949;)</span>
8312                 </p>
8313               </td>
8314 </tr>
8315 <tr>
8316 <td>
8317                 <p>
8318                   Jacobi Elliptic: Random Data
8319                 </p>
8320               </td>
8321 <td>
8322                 <p>
8323                   <span class="blue">Max = 1.83&#949; (Mean = 0.455&#949;)</span>
8324                 </p>
8325               </td>
8326 <td>
8327                 <p>
8328                   <span class="blue">Max = 0.816&#949; (Mean = 0.0563&#949;)</span><br>
8329                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 2.43&#949; (Mean = 0.803&#949;))<br>
8330                   (<span class="emphasis"><em>Cephes:</em></span> Max = 1.83&#949; (Mean = 0.437&#949;))
8331                 </p>
8332               </td>
8333 <td>
8334                 <p>
8335                   <span class="blue">Max = 1.68&#949; (Mean = 0.443&#949;)</span>
8336                 </p>
8337               </td>
8338 <td>
8339                 <p>
8340                   <span class="blue">Max = 1.68&#949; (Mean = 0.454&#949;)</span>
8341                 </p>
8342               </td>
8343 </tr>
8344 <tr>
8345 <td>
8346                 <p>
8347                   Jacobi Elliptic: Random Small Values
8348                 </p>
8349               </td>
8350 <td>
8351                 <p>
8352                   <span class="blue">Max = 26.2&#949; (Mean = 1.17&#949;)</span>
8353                 </p>
8354               </td>
8355 <td>
8356                 <p>
8357                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8358                   1.16:</em></span> Max = 55.2&#949; (Mean = 1.64&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
8359                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
8360                   other failures.</a>)</span>
8361                 </p>
8362               </td>
8363 <td>
8364                 <p>
8365                   <span class="blue">Max = 10.4&#949; (Mean = 0.594&#949;)</span>
8366                 </p>
8367               </td>
8368 <td>
8369                 <p>
8370                   <span class="blue">Max = 10.4&#949; (Mean = 0.602&#949;)</span>
8371                 </p>
8372               </td>
8373 </tr>
8374 <tr>
8375 <td>
8376                 <p>
8377                   Jacobi Elliptic: Modulus near 1
8378                 </p>
8379               </td>
8380 <td>
8381                 <p>
8382                   <span class="blue">Max = 513&#949; (Mean = 126&#949;)</span>
8383                 </p>
8384               </td>
8385 <td>
8386                 <p>
8387                   <span class="blue">Max = 0.919&#949; (Mean = 0.127&#949;)</span><br> <br>
8388                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
8389                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_cn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
8390                   other failures.</a>)</span>
8391                 </p>
8392               </td>
8393 <td>
8394                 <p>
8395                   <span class="blue">Max = 675&#949; (Mean = 87.1&#949;)</span>
8396                 </p>
8397               </td>
8398 <td>
8399                 <p>
8400                   <span class="blue">Max = 675&#949; (Mean = 86.8&#949;)</span>
8401                 </p>
8402               </td>
8403 </tr>
8404 <tr>
8405 <td>
8406                 <p>
8407                   Jacobi Elliptic: Large Phi
8408                 </p>
8409               </td>
8410 <td>
8411                 <p>
8412                   <span class="blue">Max = 3.27e+004&#949; (Mean = 1.93e+003&#949;)</span>
8413                 </p>
8414               </td>
8415 <td>
8416                 <p>
8417                   <span class="blue">Max = 14.2&#949; (Mean = 0.927&#949;)</span><br> <br>
8418                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 5.92e+03&#949; (Mean = 477&#949;))<br>
8419                   (<span class="emphasis"><em>Cephes:</em></span> Max = 3.27e+04&#949; (Mean = 1.93e+03&#949;))
8420                 </p>
8421               </td>
8422 <td>
8423                 <p>
8424                   <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
8425                 </p>
8426               </td>
8427 <td>
8428                 <p>
8429                   <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
8430                 </p>
8431               </td>
8432 </tr>
8433 </tbody>
8434 </table></div>
8435 </div>
8436 <br class="table-break"><div class="table">
8437 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_dn"></a><p class="title"><b>Table&#160;17.63.&#160;Error rates for jacobi_dn</b></p>
8438 <div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
8439 <colgroup>
8440 <col>
8441 <col>
8442 <col>
8443 <col>
8444 <col>
8445 </colgroup>
8446 <thead><tr>
8447 <th>
8448               </th>
8449 <th>
8450                 <p>
8451                   Microsoft Visual C++ version 12.0<br> Win32<br> double
8452                 </p>
8453               </th>
8454 <th>
8455                 <p>
8456                   GNU C++ version 5.1.0<br> linux<br> double
8457                 </p>
8458               </th>
8459 <th>
8460                 <p>
8461                   GNU C++ version 5.1.0<br> linux<br> long double
8462                 </p>
8463               </th>
8464 <th>
8465                 <p>
8466                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
8467                 </p>
8468               </th>
8469 </tr></thead>
8470 <tbody>
8471 <tr>
8472 <td>
8473                 <p>
8474                   Jacobi Elliptic: Mathworld Data
8475                 </p>
8476               </td>
8477 <td>
8478                 <p>
8479                   <span class="blue">Max = 34.3&#949; (Mean = 8.71&#949;)</span>
8480                 </p>
8481               </td>
8482 <td>
8483                 <p>
8484                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8485                   1.16:</em></span> Max = 2.82&#949; (Mean = 1.18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
8486                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
8487                   other failures.</a>)</span>
8488                 </p>
8489               </td>
8490 <td>
8491                 <p>
8492                   <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
8493                 </p>
8494               </td>
8495 <td>
8496                 <p>
8497                   <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
8498                 </p>
8499               </td>
8500 </tr>
8501 <tr>
8502 <td>
8503                 <p>
8504                   Jacobi Elliptic: Random Data
8505                 </p>
8506               </td>
8507 <td>
8508                 <p>
8509                   <span class="blue">Max = 1.52&#949; (Mean = 0.466&#949;)</span>
8510                 </p>
8511               </td>
8512 <td>
8513                 <p>
8514                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8515                   1.16:</em></span> Max = 3&#949; (Mean = 0.61&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
8516                   Max = 1.49&#949; (Mean = 0.321&#949;))
8517                 </p>
8518               </td>
8519 <td>
8520                 <p>
8521                   <span class="blue">Max = 1.53&#949; (Mean = 0.473&#949;)</span>
8522                 </p>
8523               </td>
8524 <td>
8525                 <p>
8526                   <span class="blue">Max = 1.53&#949; (Mean = 0.481&#949;)</span>
8527                 </p>
8528               </td>
8529 </tr>
8530 <tr>
8531 <td>
8532                 <p>
8533                   Jacobi Elliptic: Random Small Values
8534                 </p>
8535               </td>
8536 <td>
8537                 <p>
8538                   <span class="blue">Max = 16.1&#949; (Mean = 0.685&#949;)</span>
8539                 </p>
8540               </td>
8541 <td>
8542                 <p>
8543                   <span class="blue">Max = 0.5&#949; (Mean = 0.0122&#949;)</span><br> <br>
8544                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.5&#949; (Mean = 0.391&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
8545                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
8546                   other failures.</a>)</span>
8547                 </p>
8548               </td>
8549 <td>
8550                 <p>
8551                   <span class="blue">Max = 22.4&#949; (Mean = 0.777&#949;)</span>
8552                 </p>
8553               </td>
8554 <td>
8555                 <p>
8556                   <span class="blue">Max = 22.4&#949; (Mean = 0.763&#949;)</span>
8557                 </p>
8558               </td>
8559 </tr>
8560 <tr>
8561 <td>
8562                 <p>
8563                   Jacobi Elliptic: Modulus near 1
8564                 </p>
8565               </td>
8566 <td>
8567                 <p>
8568                   <span class="blue">Max = 6.24e+003&#949; (Mean = 482&#949;)</span>
8569                 </p>
8570               </td>
8571 <td>
8572                 <p>
8573                   <span class="blue">Max = 2.28&#949; (Mean = 0.194&#949;)</span><br> <br>
8574                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
8575                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_dn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
8576                   other failures.</a>)</span>
8577                 </p>
8578               </td>
8579 <td>
8580                 <p>
8581                   <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
8582                 </p>
8583               </td>
8584 <td>
8585                 <p>
8586                   <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
8587                 </p>
8588               </td>
8589 </tr>
8590 <tr>
8591 <td>
8592                 <p>
8593                   Jacobi Elliptic: Large Phi
8594                 </p>
8595               </td>
8596 <td>
8597                 <p>
8598                   <span class="blue">Max = 1.67e+004&#949; (Mean = 1e+003&#949;)</span>
8599                 </p>
8600               </td>
8601 <td>
8602                 <p>
8603                   <span class="blue">Max = 14.1&#949; (Mean = 0.897&#949;)</span><br> <br>
8604                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121&#949; (Mean = 22&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
8605                   Max = 196&#949; (Mean = 30.2&#949;))
8606                 </p>
8607               </td>
8608 <td>
8609                 <p>
8610                   <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
8611                 </p>
8612               </td>
8613 <td>
8614                 <p>
8615                   <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
8616                 </p>
8617               </td>
8618 </tr>
8619 </tbody>
8620 </table></div>
8621 </div>
8622 <br class="table-break"><div class="table">
8623 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_sn"></a><p class="title"><b>Table&#160;17.64.&#160;Error rates for jacobi_sn</b></p>
8624 <div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
8625 <colgroup>
8626 <col>
8627 <col>
8628 <col>
8629 <col>
8630 <col>
8631 </colgroup>
8632 <thead><tr>
8633 <th>
8634               </th>
8635 <th>
8636                 <p>
8637                   Microsoft Visual C++ version 12.0<br> Win32<br> double
8638                 </p>
8639               </th>
8640 <th>
8641                 <p>
8642                   GNU C++ version 5.1.0<br> linux<br> double
8643                 </p>
8644               </th>
8645 <th>
8646                 <p>
8647                   GNU C++ version 5.1.0<br> linux<br> long double
8648                 </p>
8649               </th>
8650 <th>
8651                 <p>
8652                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
8653                 </p>
8654               </th>
8655 </tr></thead>
8656 <tbody>
8657 <tr>
8658 <td>
8659                 <p>
8660                   Jacobi Elliptic: Mathworld Data
8661                 </p>
8662               </td>
8663 <td>
8664                 <p>
8665                   <span class="blue">Max = 481&#949; (Mean = 113&#949;)</span>
8666                 </p>
8667               </td>
8668 <td>
8669                 <p>
8670                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8671                   1.16:</em></span> Max = 588&#949; (Mean = 146&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Mathworld_Data">And
8672                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Mathworld_Data">And
8673                   other failures.</a>)</span>
8674                 </p>
8675               </td>
8676 <td>
8677                 <p>
8678                   <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
8679                 </p>
8680               </td>
8681 <td>
8682                 <p>
8683                   <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
8684                 </p>
8685               </td>
8686 </tr>
8687 <tr>
8688 <td>
8689                 <p>
8690                   Jacobi Elliptic: Random Data
8691                 </p>
8692               </td>
8693 <td>
8694                 <p>
8695                   <span class="blue">Max = 1.92&#949; (Mean = 0.567&#949;)</span>
8696                 </p>
8697               </td>
8698 <td>
8699                 <p>
8700                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8701                   1.16:</em></span> Max = 4.02&#949; (Mean = 1.07&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
8702                   Max = 1.92&#949; (Mean = 0.567&#949;))
8703                 </p>
8704               </td>
8705 <td>
8706                 <p>
8707                   <span class="blue">Max = 2.01&#949; (Mean = 0.584&#949;)</span>
8708                 </p>
8709               </td>
8710 <td>
8711                 <p>
8712                   <span class="blue">Max = 2.01&#949; (Mean = 0.593&#949;)</span>
8713                 </p>
8714               </td>
8715 </tr>
8716 <tr>
8717 <td>
8718                 <p>
8719                   Jacobi Elliptic: Random Small Values
8720                 </p>
8721               </td>
8722 <td>
8723                 <p>
8724                   <span class="blue">Max = 2.11&#949; (Mean = 0.385&#949;)</span>
8725                 </p>
8726               </td>
8727 <td>
8728                 <p>
8729                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8730                   1.16:</em></span> Max = 11.7&#949; (Mean = 1.65&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Random_Small_Values">And
8731                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Random_Small_Values">And
8732                   other failures.</a>)</span>
8733                 </p>
8734               </td>
8735 <td>
8736                 <p>
8737                   <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
8738                 </p>
8739               </td>
8740 <td>
8741                 <p>
8742                   <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
8743                 </p>
8744               </td>
8745 </tr>
8746 <tr>
8747 <td>
8748                 <p>
8749                   Jacobi Elliptic: Modulus near 1
8750                 </p>
8751               </td>
8752 <td>
8753                 <p>
8754                   <span class="blue">Max = 23.2&#949; (Mean = 1.85&#949;)</span>
8755                 </p>
8756               </td>
8757 <td>
8758                 <p>
8759                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
8760                   1.16:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_GSL_1_16_Jacobi_Elliptic_Modulus_near_1">And
8761                   other failures.</a>)<br> (<span class="emphasis"><em>Cephes:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_jacobi_sn_Cephes_Jacobi_Elliptic_Modulus_near_1">And
8762                   other failures.</a>)</span>
8763                 </p>
8764               </td>
8765 <td>
8766                 <p>
8767                   <span class="blue">Max = 109&#949; (Mean = 7.35&#949;)</span>
8768                 </p>
8769               </td>
8770 <td>
8771                 <p>
8772                   <span class="blue">Max = 109&#949; (Mean = 7.38&#949;)</span>
8773                 </p>
8774               </td>
8775 </tr>
8776 <tr>
8777 <td>
8778                 <p>
8779                   Jacobi Elliptic: Large Phi
8780                 </p>
8781               </td>
8782 <td>
8783                 <p>
8784                   <span class="blue">Max = 4.36e+004&#949; (Mean = 2.54e+003&#949;)</span>
8785                 </p>
8786               </td>
8787 <td>
8788                 <p>
8789                   <span class="blue">Max = 12&#949; (Mean = 0.771&#949;)</span><br> <br>
8790                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.54e+04&#949; (Mean = 2.63e+03&#949;))<br>
8791                   (<span class="emphasis"><em>Cephes:</em></span> Max = 4.36e+04&#949; (Mean = 2.54e+03&#949;))
8792                 </p>
8793               </td>
8794 <td>
8795                 <p>
8796                   <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
8797                 </p>
8798               </td>
8799 <td>
8800                 <p>
8801                   <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
8802                 </p>
8803               </td>
8804 </tr>
8805 </tbody>
8806 </table></div>
8807 </div>
8808 <br class="table-break"><div class="table">
8809 <a name="math_toolkit.logs_and_tables.all_table.table_jacobi_zeta"></a><p class="title"><b>Table&#160;17.65.&#160;Error rates for jacobi_zeta</b></p>
8810 <div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
8811 <colgroup>
8812 <col>
8813 <col>
8814 <col>
8815 <col>
8816 <col>
8817 </colgroup>
8818 <thead><tr>
8819 <th>
8820               </th>
8821 <th>
8822                 <p>
8823                   Microsoft Visual C++ version 12.0<br> Win32<br> double
8824                 </p>
8825               </th>
8826 <th>
8827                 <p>
8828                   GNU C++ version 5.1.0<br> linux<br> double
8829                 </p>
8830               </th>
8831 <th>
8832                 <p>
8833                   GNU C++ version 5.1.0<br> linux<br> long double
8834                 </p>
8835               </th>
8836 <th>
8837                 <p>
8838                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
8839                 </p>
8840               </th>
8841 </tr></thead>
8842 <tbody>
8843 <tr>
8844 <td>
8845                 <p>
8846                   Elliptic Integral Jacobi Zeta: Mathworld Data
8847                 </p>
8848               </td>
8849 <td>
8850                 <p>
8851                   <span class="blue">Max = 0.505&#949; (Mean = 0.119&#949;)</span>
8852                 </p>
8853               </td>
8854 <td>
8855                 <p>
8856                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
8857                 </p>
8858               </td>
8859 <td>
8860                 <p>
8861                   <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
8862                 </p>
8863               </td>
8864 <td>
8865                 <p>
8866                   <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
8867                 </p>
8868               </td>
8869 </tr>
8870 <tr>
8871 <td>
8872                 <p>
8873                   Elliptic Integral Jacobi Zeta: Random Data
8874                 </p>
8875               </td>
8876 <td>
8877                 <p>
8878                   <span class="blue">Max = 3.89&#949; (Mean = 0.818&#949;)</span>
8879                 </p>
8880               </td>
8881 <td>
8882                 <p>
8883                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
8884                 </p>
8885               </td>
8886 <td>
8887                 <p>
8888                   <span class="blue">Max = 2.99&#949; (Mean = 0.824&#949;)</span>
8889                 </p>
8890               </td>
8891 <td>
8892                 <p>
8893                   <span class="blue">Max = 3.96&#949; (Mean = 1.06&#949;)</span>
8894                 </p>
8895               </td>
8896 </tr>
8897 <tr>
8898 <td>
8899                 <p>
8900                   Elliptic Integral Jacobi Zeta: Large Phi Values
8901                 </p>
8902               </td>
8903 <td>
8904                 <p>
8905                   <span class="blue">Max = 2.92&#949; (Mean = 0.964&#949;)</span>
8906                 </p>
8907               </td>
8908 <td>
8909                 <p>
8910                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
8911                 </p>
8912               </td>
8913 <td>
8914                 <p>
8915                   <span class="blue">Max = 2.92&#949; (Mean = 0.951&#949;)</span>
8916                 </p>
8917               </td>
8918 <td>
8919                 <p>
8920                   <span class="blue">Max = 3.05&#949; (Mean = 1.13&#949;)</span>
8921                 </p>
8922               </td>
8923 </tr>
8924 </tbody>
8925 </table></div>
8926 </div>
8927 <br class="table-break"><div class="table">
8928 <a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_m_x_"></a><p class="title"><b>Table&#160;17.66.&#160;Error rates for laguerre(n, m, x)</b></p>
8929 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
8930 <colgroup>
8931 <col>
8932 <col>
8933 <col>
8934 <col>
8935 <col>
8936 </colgroup>
8937 <thead><tr>
8938 <th>
8939               </th>
8940 <th>
8941                 <p>
8942                   Microsoft Visual C++ version 12.0<br> Win32<br> double
8943                 </p>
8944               </th>
8945 <th>
8946                 <p>
8947                   GNU C++ version 5.1.0<br> linux<br> double
8948                 </p>
8949               </th>
8950 <th>
8951                 <p>
8952                   GNU C++ version 5.1.0<br> linux<br> long double
8953                 </p>
8954               </th>
8955 <th>
8956                 <p>
8957                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
8958                 </p>
8959               </th>
8960 </tr></thead>
8961 <tbody><tr>
8962 <td>
8963                 <p>
8964                   Associated Laguerre Polynomials
8965                 </p>
8966               </td>
8967 <td>
8968                 <p>
8969                   <span class="blue">Max = 434&#949; (Mean = 11.1&#949;)</span>
8970                 </p>
8971               </td>
8972 <td>
8973                 <p>
8974                   <span class="blue">Max = 0.84&#949; (Mean = 0.0358&#949;)</span><br> <br>
8975                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 434&#949; (Mean = 10.7&#949;))
8976                 </p>
8977               </td>
8978 <td>
8979                 <p>
8980                   <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span><br> <br>
8981                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 206&#949; (Mean = 6.86&#949;))
8982                 </p>
8983               </td>
8984 <td>
8985                 <p>
8986                   <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span>
8987                 </p>
8988               </td>
8989 </tr></tbody>
8990 </table></div>
8991 </div>
8992 <br class="table-break"><div class="table">
8993 <a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_x_"></a><p class="title"><b>Table&#160;17.67.&#160;Error rates for laguerre(n, x)</b></p>
8994 <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
8995 <colgroup>
8996 <col>
8997 <col>
8998 <col>
8999 <col>
9000 <col>
9001 </colgroup>
9002 <thead><tr>
9003 <th>
9004               </th>
9005 <th>
9006                 <p>
9007                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9008                 </p>
9009               </th>
9010 <th>
9011                 <p>
9012                   GNU C++ version 5.1.0<br> linux<br> double
9013                 </p>
9014               </th>
9015 <th>
9016                 <p>
9017                   GNU C++ version 5.1.0<br> linux<br> long double
9018                 </p>
9019               </th>
9020 <th>
9021                 <p>
9022                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9023                 </p>
9024               </th>
9025 </tr></thead>
9026 <tbody><tr>
9027 <td>
9028                 <p>
9029                   Laguerre Polynomials
9030                 </p>
9031               </td>
9032 <td>
9033                 <p>
9034                   <span class="blue">Max = 3.1e+003&#949; (Mean = 185&#949;)</span>
9035                 </p>
9036               </td>
9037 <td>
9038                 <p>
9039                   <span class="blue">Max = 6.82&#949; (Mean = 0.408&#949;)</span><br> <br>
9040                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 3.1e+03&#949; (Mean = 185&#949;))
9041                 </p>
9042               </td>
9043 <td>
9044                 <p>
9045                   <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span><br>
9046                   <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 4.2e+03&#949; (Mean
9047                   = 251&#949;))
9048                 </p>
9049               </td>
9050 <td>
9051                 <p>
9052                   <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span>
9053                 </p>
9054               </td>
9055 </tr></tbody>
9056 </table></div>
9057 </div>
9058 <br class="table-break"><div class="table">
9059 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_p"></a><p class="title"><b>Table&#160;17.68.&#160;Error rates for legendre_p</b></p>
9060 <div class="table-contents"><table class="table" summary="Error rates for legendre_p">
9061 <colgroup>
9062 <col>
9063 <col>
9064 <col>
9065 <col>
9066 <col>
9067 </colgroup>
9068 <thead><tr>
9069 <th>
9070               </th>
9071 <th>
9072                 <p>
9073                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9074                 </p>
9075               </th>
9076 <th>
9077                 <p>
9078                   GNU C++ version 5.1.0<br> linux<br> double
9079                 </p>
9080               </th>
9081 <th>
9082                 <p>
9083                   GNU C++ version 5.1.0<br> linux<br> long double
9084                 </p>
9085               </th>
9086 <th>
9087                 <p>
9088                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9089                 </p>
9090               </th>
9091 </tr></thead>
9092 <tbody>
9093 <tr>
9094 <td>
9095                 <p>
9096                   Legendre Polynomials: Small Values
9097                 </p>
9098               </td>
9099 <td>
9100                 <p>
9101                   <span class="blue">Max = 211&#949; (Mean = 20.4&#949;)</span>
9102                 </p>
9103               </td>
9104 <td>
9105                 <p>
9106                   <span class="blue">Max = 0.732&#949; (Mean = 0.0619&#949;)</span><br>
9107                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 211&#949; (Mean = 20.4&#949;))
9108                 </p>
9109               </td>
9110 <td>
9111                 <p>
9112                   <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span><br> <br>
9113                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 124&#949; (Mean = 13.2&#949;))
9114                 </p>
9115               </td>
9116 <td>
9117                 <p>
9118                   <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span>
9119                 </p>
9120               </td>
9121 </tr>
9122 <tr>
9123 <td>
9124                 <p>
9125                   Legendre Polynomials: Large Values
9126                 </p>
9127               </td>
9128 <td>
9129                 <p>
9130                   <span class="blue">Max = 300&#949; (Mean = 33.2&#949;)</span>
9131                 </p>
9132               </td>
9133 <td>
9134                 <p>
9135                   <span class="blue">Max = 0.632&#949; (Mean = 0.0693&#949;)</span><br>
9136                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 300&#949; (Mean = 33.2&#949;))
9137                 </p>
9138               </td>
9139 <td>
9140                 <p>
9141                   <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span><br> <br>
9142                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 343&#949; (Mean = 32.1&#949;))
9143                 </p>
9144               </td>
9145 <td>
9146                 <p>
9147                   <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span>
9148                 </p>
9149               </td>
9150 </tr>
9151 </tbody>
9152 </table></div>
9153 </div>
9154 <br class="table-break"><div class="table">
9155 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;17.69.&#160;Error rates for legendre_p (associated)</b></p>
9156 <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
9157 <colgroup>
9158 <col>
9159 <col>
9160 <col>
9161 <col>
9162 <col>
9163 </colgroup>
9164 <thead><tr>
9165 <th>
9166               </th>
9167 <th>
9168                 <p>
9169                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9170                 </p>
9171               </th>
9172 <th>
9173                 <p>
9174                   GNU C++ version 5.1.0<br> linux<br> double
9175                 </p>
9176               </th>
9177 <th>
9178                 <p>
9179                   GNU C++ version 5.1.0<br> linux<br> long double
9180                 </p>
9181               </th>
9182 <th>
9183                 <p>
9184                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9185                 </p>
9186               </th>
9187 </tr></thead>
9188 <tbody><tr>
9189 <td>
9190                 <p>
9191                   Associated Legendre Polynomials: Small Values
9192                 </p>
9193               </td>
9194 <td>
9195                 <p>
9196                   <span class="blue">Max = 121&#949; (Mean = 7.14&#949;)</span>
9197                 </p>
9198               </td>
9199 <td>
9200                 <p>
9201                   <span class="blue">Max = 0.999&#949; (Mean = 0.05&#949;)</span><br> <br>
9202                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 121&#949; (Mean = 6.75&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_legendre_p_associated__GSL_1_16_Associated_Legendre_Polynomials_Small_Values">And
9203                   other failures.</a>)
9204                 </p>
9205               </td>
9206 <td>
9207                 <p>
9208                   <span class="blue">Max = 175&#949; (Mean = 9.88&#949;)</span><br> <br>
9209                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 175&#949; (Mean = 9.36&#949;)
9210                   <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_long_double_legendre_p_associated___tr1_cmath__Associated_Legendre_Polynomials_Small_Values">And
9211                   other failures.</a>)
9212                 </p>
9213               </td>
9214 <td>
9215                 <p>
9216                   <span class="blue">Max = 77.7&#949; (Mean = 5.59&#949;)</span>
9217                 </p>
9218               </td>
9219 </tr></tbody>
9220 </table></div>
9221 </div>
9222 <br class="table-break"><div class="table">
9223 <a name="math_toolkit.logs_and_tables.all_table.table_legendre_q"></a><p class="title"><b>Table&#160;17.70.&#160;Error rates for legendre_q</b></p>
9224 <div class="table-contents"><table class="table" summary="Error rates for legendre_q">
9225 <colgroup>
9226 <col>
9227 <col>
9228 <col>
9229 <col>
9230 <col>
9231 </colgroup>
9232 <thead><tr>
9233 <th>
9234               </th>
9235 <th>
9236                 <p>
9237                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9238                 </p>
9239               </th>
9240 <th>
9241                 <p>
9242                   GNU C++ version 5.1.0<br> linux<br> double
9243                 </p>
9244               </th>
9245 <th>
9246                 <p>
9247                   GNU C++ version 5.1.0<br> linux<br> long double
9248                 </p>
9249               </th>
9250 <th>
9251                 <p>
9252                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9253                 </p>
9254               </th>
9255 </tr></thead>
9256 <tbody>
9257 <tr>
9258 <td>
9259                 <p>
9260                   Legendre Polynomials: Small Values
9261                 </p>
9262               </td>
9263 <td>
9264                 <p>
9265                   <span class="blue">Max = 46.4&#949; (Mean = 7.32&#949;)</span>
9266                 </p>
9267               </td>
9268 <td>
9269                 <p>
9270                   <span class="blue">Max = 0.612&#949; (Mean = 0.0517&#949;)</span><br>
9271                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 46.4&#949; (Mean = 7.46&#949;))
9272                 </p>
9273               </td>
9274 <td>
9275                 <p>
9276                   <span class="blue">Max = 50.9&#949; (Mean = 9&#949;)</span>
9277                 </p>
9278               </td>
9279 <td>
9280                 <p>
9281                   <span class="blue">Max = 50.9&#949; (Mean = 8.98&#949;)</span>
9282                 </p>
9283               </td>
9284 </tr>
9285 <tr>
9286 <td>
9287                 <p>
9288                   Legendre Polynomials: Large Values
9289                 </p>
9290               </td>
9291 <td>
9292                 <p>
9293                   <span class="blue">Max = 4.6e+003&#949; (Mean = 366&#949;)</span>
9294                 </p>
9295               </td>
9296 <td>
9297                 <p>
9298                   <span class="blue">Max = 2.49&#949; (Mean = 0.202&#949;)</span><br> <br>
9299                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 4.6e+03&#949; (Mean = 366&#949;))
9300                 </p>
9301               </td>
9302 <td>
9303                 <p>
9304                   <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
9305                 </p>
9306               </td>
9307 <td>
9308                 <p>
9309                   <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
9310                 </p>
9311               </td>
9312 </tr>
9313 </tbody>
9314 </table></div>
9315 </div>
9316 <br class="table-break"><div class="table">
9317 <a name="math_toolkit.logs_and_tables.all_table.table_lgamma"></a><p class="title"><b>Table&#160;17.71.&#160;Error rates for lgamma</b></p>
9318 <div class="table-contents"><table class="table" summary="Error rates for lgamma">
9319 <colgroup>
9320 <col>
9321 <col>
9322 <col>
9323 <col>
9324 <col>
9325 </colgroup>
9326 <thead><tr>
9327 <th>
9328               </th>
9329 <th>
9330                 <p>
9331                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9332                 </p>
9333               </th>
9334 <th>
9335                 <p>
9336                   GNU C++ version 5.1.0<br> linux<br> double
9337                 </p>
9338               </th>
9339 <th>
9340                 <p>
9341                   GNU C++ version 5.1.0<br> linux<br> long double
9342                 </p>
9343               </th>
9344 <th>
9345                 <p>
9346                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9347                 </p>
9348               </th>
9349 </tr></thead>
9350 <tbody>
9351 <tr>
9352 <td>
9353                 <p>
9354                   factorials
9355                 </p>
9356               </td>
9357 <td>
9358                 <p>
9359                   <span class="blue">Max = 0.914&#949; (Mean = 0.167&#949;)</span><br> <br>
9360                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.958&#949; (Mean = 0.38&#949;))
9361                 </p>
9362               </td>
9363 <td>
9364                 <p>
9365                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9366                   1.16:</em></span> Max = 33.6&#949; (Mean = 2.78&#949;))<br> (<span class="emphasis"><em>Rmath
9367                   3.0.2:</em></span> Max = 1.55&#949; (Mean = 0.592&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
9368                   Max = 1.55&#949; (Mean = 0.512&#949;))
9369                 </p>
9370               </td>
9371 <td>
9372                 <p>
9373                   <span class="blue">Max = 0.991&#949; (Mean = 0.311&#949;)</span><br> <br>
9374                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))<br>
9375                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))
9376                 </p>
9377               </td>
9378 <td>
9379                 <p>
9380                   <span class="blue">Max = 0.991&#949; (Mean = 0.383&#949;)</span><br> <br>
9381                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.36&#949; (Mean = 0.476&#949;))
9382                 </p>
9383               </td>
9384 </tr>
9385 <tr>
9386 <td>
9387                 <p>
9388                   near 0
9389                 </p>
9390               </td>
9391 <td>
9392                 <p>
9393                   <span class="blue">Max = 0.964&#949; (Mean = 0.462&#949;)</span><br> <br>
9394                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.962&#949; (Mean = 0.372&#949;))
9395                 </p>
9396               </td>
9397 <td>
9398                 <p>
9399                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9400                   1.16:</em></span> Max = 5.21&#949; (Mean = 1.57&#949;))<br> (<span class="emphasis"><em>Rmath
9401                   3.0.2:</em></span> Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
9402                   Max = 1.16&#949; (Mean = 0.341&#949;))
9403                 </p>
9404               </td>
9405 <td>
9406                 <p>
9407                   <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
9408                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))<br>
9409                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
9410                 </p>
9411               </td>
9412 <td>
9413                 <p>
9414                   <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
9415                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
9416                 </p>
9417               </td>
9418 </tr>
9419 <tr>
9420 <td>
9421                 <p>
9422                   near 1
9423                 </p>
9424               </td>
9425 <td>
9426                 <p>
9427                   <span class="blue">Max = 0.867&#949; (Mean = 0.468&#949;)</span><br> <br>
9428                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.906&#949; (Mean = 0.565&#949;))
9429                 </p>
9430               </td>
9431 <td>
9432                 <p>
9433                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9434                   1.16:</em></span> Max = 442&#949; (Mean = 88.8&#949;))<br> (<span class="emphasis"><em>Rmath
9435                   3.0.2:</em></span> Max = 7.99e+04&#949; (Mean = 1.68e+04&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
9436                   Max = 1.14e+05&#949; (Mean = 2.64e+04&#949;))
9437                 </p>
9438               </td>
9439 <td>
9440                 <p>
9441                   <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
9442                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))<br>
9443                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))
9444                 </p>
9445               </td>
9446 <td>
9447                 <p>
9448                   <span class="blue">Max = 0.866&#949; (Mean = 0.355&#949;)</span><br> <br>
9449                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.71&#949; (Mean = 0.581&#949;))
9450                 </p>
9451               </td>
9452 </tr>
9453 <tr>
9454 <td>
9455                 <p>
9456                   near 2
9457                 </p>
9458               </td>
9459 <td>
9460                 <p>
9461                   <span class="blue">Max = 0.591&#949; (Mean = 0.159&#949;)</span><br> <br>
9462                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.473&#949;))
9463                 </p>
9464               </td>
9465 <td>
9466                 <p>
9467                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9468                   1.16:</em></span> Max = 1.17e+03&#949; (Mean = 274&#949;))<br> (<span class="emphasis"><em>Rmath
9469                   3.0.2:</em></span> Max = 2.63e+05&#949; (Mean = 5.84e+04&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
9470                   Max = 5.08e+05&#949; (Mean = 9.04e+04&#949;))
9471                 </p>
9472               </td>
9473 <td>
9474                 <p>
9475                   <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
9476                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))<br>
9477                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))
9478                 </p>
9479               </td>
9480 <td>
9481                 <p>
9482                   <span class="blue">Max = 0.878&#949; (Mean = 0.241&#949;)</span><br> <br>
9483                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.598&#949; (Mean = 0.235&#949;))
9484                 </p>
9485               </td>
9486 </tr>
9487 <tr>
9488 <td>
9489                 <p>
9490                   near -10
9491                 </p>
9492               </td>
9493 <td>
9494                 <p>
9495                   <span class="blue">Max = 4.22&#949; (Mean = 1.33&#949;)</span><br> <br>
9496                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.444&#949;))
9497                 </p>
9498               </td>
9499 <td>
9500                 <p>
9501                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9502                   1.16:</em></span> Max = 24.9&#949; (Mean = 4.6&#949;))<br> (<span class="emphasis"><em>Rmath
9503                   3.0.2:</em></span> Max = 2.41e+05&#949; (Mean = 4.29e+04&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
9504                   Max = 0.997&#949; (Mean = 0.429&#949;))
9505                 </p>
9506               </td>
9507 <td>
9508                 <p>
9509                   <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
9510                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 3.01&#949; (Mean = 0.86&#949;))<br>
9511                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.01&#949; (Mean = 0.86&#949;))
9512                 </p>
9513               </td>
9514 <td>
9515                 <p>
9516                   <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
9517                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.04&#949; (Mean = 1.01&#949;))
9518                 </p>
9519               </td>
9520 </tr>
9521 <tr>
9522 <td>
9523                 <p>
9524                   near -55
9525                 </p>
9526               </td>
9527 <td>
9528                 <p>
9529                   <span class="blue">Max = 0.821&#949; (Mean = 0.419&#949;)</span><br> <br>
9530                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 249&#949; (Mean = 43.1&#949;))
9531                 </p>
9532               </td>
9533 <td>
9534                 <p>
9535                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
9536                   1.16:</em></span> Max = 7.02&#949; (Mean = 1.47&#949;))<br> (<span class="emphasis"><em>Rmath
9537                   3.0.2:</em></span> Max = 4.08e+04&#949; (Mean = 7.26e+03&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
9538                   Max = 1.64&#949; (Mean = 0.693&#949;))
9539                 </p>
9540               </td>
9541 <td>
9542                 <p>
9543                   <span class="blue">Max = 0.821&#949; (Mean = 0.513&#949;)</span><br> <br>
9544                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))<br>
9545                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))
9546                 </p>
9547               </td>
9548 <td>
9549                 <p>
9550                   <span class="blue">Max = 1.59&#949; (Mean = 0.587&#949;)</span><br> <br>
9551                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.821&#949; (Mean = 0.674&#949;))
9552                 </p>
9553               </td>
9554 </tr>
9555 </tbody>
9556 </table></div>
9557 </div>
9558 <br class="table-break"><div class="table">
9559 <a name="math_toolkit.logs_and_tables.all_table.table_log1p"></a><p class="title"><b>Table&#160;17.72.&#160;Error rates for log1p</b></p>
9560 <div class="table-contents"><table class="table" summary="Error rates for log1p">
9561 <colgroup>
9562 <col>
9563 <col>
9564 <col>
9565 <col>
9566 <col>
9567 </colgroup>
9568 <thead><tr>
9569 <th>
9570               </th>
9571 <th>
9572                 <p>
9573                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9574                 </p>
9575               </th>
9576 <th>
9577                 <p>
9578                   GNU C++ version 5.1.0<br> linux<br> double
9579                 </p>
9580               </th>
9581 <th>
9582                 <p>
9583                   GNU C++ version 5.1.0<br> linux<br> long double
9584                 </p>
9585               </th>
9586 <th>
9587                 <p>
9588                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9589                 </p>
9590               </th>
9591 </tr></thead>
9592 <tbody><tr>
9593 <td>
9594                 <p>
9595                   Random test data
9596                 </p>
9597               </td>
9598 <td>
9599                 <p>
9600                   <span class="blue">Max = 0.509&#949; (Mean = 0.057&#949;)</span><br> <br>
9601                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.509&#949; (Mean = 0.057&#949;))
9602                 </p>
9603               </td>
9604 <td>
9605                 <p>
9606                   <span class="blue">Max = 0.846&#949; (Mean = 0.153&#949;)</span><br> <br>
9607                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 0.846&#949; (Mean = 0.153&#949;))<br>
9608                   (<span class="emphasis"><em>Cephes:</em></span> Max = 0.799&#949; (Mean = 0.122&#949;))
9609                 </p>
9610               </td>
9611 <td>
9612                 <p>
9613                   <span class="blue">Max = 0.818&#949; (Mean = 0.227&#949;)</span><br> <br>
9614                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))<br>
9615                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))
9616                 </p>
9617               </td>
9618 <td>
9619                 <p>
9620                   <span class="blue">Max = 1.53&#949; (Mean = 0.627&#949;)</span><br> <br>
9621                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.249&#949;))
9622                 </p>
9623               </td>
9624 </tr></tbody>
9625 </table></div>
9626 </div>
9627 <br class="table-break"><div class="table">
9628 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF"></a><p class="title"><b>Table&#160;17.73.&#160;Error rates for non central beta CDF</b></p>
9629 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
9630 <colgroup>
9631 <col>
9632 <col>
9633 <col>
9634 <col>
9635 <col>
9636 </colgroup>
9637 <thead><tr>
9638 <th>
9639               </th>
9640 <th>
9641                 <p>
9642                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9643                 </p>
9644               </th>
9645 <th>
9646                 <p>
9647                   GNU C++ version 5.1.0<br> linux<br> double
9648                 </p>
9649               </th>
9650 <th>
9651                 <p>
9652                   GNU C++ version 5.1.0<br> linux<br> long double
9653                 </p>
9654               </th>
9655 <th>
9656                 <p>
9657                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9658                 </p>
9659               </th>
9660 </tr></thead>
9661 <tbody>
9662 <tr>
9663 <td>
9664                 <p>
9665                   Non Central Beta, medium parameters
9666                 </p>
9667               </td>
9668 <td>
9669                 <p>
9670                   <span class="blue">Max = 240&#949; (Mean = 31&#949;)</span>
9671                 </p>
9672               </td>
9673 <td>
9674                 <p>
9675                   <span class="blue">Max = 0.998&#949; (Mean = 0.0659&#949;)</span><br>
9676                   <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
9677                   = 1.46e+26&#949; (Mean = 3.5e+24&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_Rmath_3_0_2_Non_Central_Beta_medium_parameters">And
9678                   other failures.</a>)</span>
9679                 </p>
9680               </td>
9681 <td>
9682                 <p>
9683                   <span class="blue">Max = 825&#949; (Mean = 27.4&#949;)</span>
9684                 </p>
9685               </td>
9686 <td>
9687                 <p>
9688                   <span class="blue">Max = 832&#949; (Mean = 38.1&#949;)</span>
9689                 </p>
9690               </td>
9691 </tr>
9692 <tr>
9693 <td>
9694                 <p>
9695                   Non Central Beta, large parameters
9696                 </p>
9697               </td>
9698 <td>
9699                 <p>
9700                   <span class="blue">Max = 3.41e+003&#949; (Mean = 475&#949;)</span>
9701                 </p>
9702               </td>
9703 <td>
9704                 <p>
9705                   <span class="blue">Max = 1.18&#949; (Mean = 0.175&#949;)</span><br> <br>
9706                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = 1.01e+36&#949; (Mean
9707                   = 1.19e+35&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_Rmath_3_0_2_Non_Central_Beta_large_parameters">And
9708                   other failures.</a>)</span>
9709                 </p>
9710               </td>
9711 <td>
9712                 <p>
9713                   <span class="blue">Max = 2.5e+04&#949; (Mean = 3.78e+03&#949;)</span>
9714                 </p>
9715               </td>
9716 <td>
9717                 <p>
9718                   <span class="blue">Max = 2.57e+04&#949; (Mean = 4.43e+03&#949;)</span>
9719                 </p>
9720               </td>
9721 </tr>
9722 </tbody>
9723 </table></div>
9724 </div>
9725 <br class="table-break"><div class="table">
9726 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table&#160;17.74.&#160;Error rates for non central beta CDF complement</b></p>
9727 <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
9728 <colgroup>
9729 <col>
9730 <col>
9731 <col>
9732 <col>
9733 <col>
9734 </colgroup>
9735 <thead><tr>
9736 <th>
9737               </th>
9738 <th>
9739                 <p>
9740                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9741                 </p>
9742               </th>
9743 <th>
9744                 <p>
9745                   GNU C++ version 5.1.0<br> linux<br> double
9746                 </p>
9747               </th>
9748 <th>
9749                 <p>
9750                   GNU C++ version 5.1.0<br> linux<br> long double
9751                 </p>
9752               </th>
9753 <th>
9754                 <p>
9755                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9756                 </p>
9757               </th>
9758 </tr></thead>
9759 <tbody>
9760 <tr>
9761 <td>
9762                 <p>
9763                   Non Central Beta, medium parameters
9764                 </p>
9765               </td>
9766 <td>
9767                 <p>
9768                   <span class="blue">Max = 619&#949; (Mean = 62.7&#949;)</span>
9769                 </p>
9770               </td>
9771 <td>
9772                 <p>
9773                   <span class="blue">Max = 0.998&#949; (Mean = 0.0957&#949;)</span><br>
9774                   <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
9775                   = 7.5e+97&#949; (Mean = 1.37e+96&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_0_2_Non_Central_Beta_medium_parameters">And
9776                   other failures.</a>)</span>
9777                 </p>
9778               </td>
9779 <td>
9780                 <p>
9781                   <span class="blue">Max = 396&#949; (Mean = 50.7&#949;)</span>
9782                 </p>
9783               </td>
9784 <td>
9785                 <p>
9786                   <span class="blue">Max = 554&#949; (Mean = 57.3&#949;)</span>
9787                 </p>
9788               </td>
9789 </tr>
9790 <tr>
9791 <td>
9792                 <p>
9793                   Non Central Beta, large parameters
9794                 </p>
9795               </td>
9796 <td>
9797                 <p>
9798                   <span class="blue">Max = 8.67e+003&#949; (Mean = 1.04e+003&#949;)</span>
9799                 </p>
9800               </td>
9801 <td>
9802                 <p>
9803                   <span class="blue">Max = 0.986&#949; (Mean = 0.188&#949;)</span><br> <br>
9804                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean
9805                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_0_2_Non_Central_Beta_large_parameters">And
9806                   other failures.</a>)</span>
9807                 </p>
9808               </td>
9809 <td>
9810                 <p>
9811                   <span class="blue">Max = 6.83e+03&#949; (Mean = 993&#949;)</span>
9812                 </p>
9813               </td>
9814 <td>
9815                 <p>
9816                   <span class="blue">Max = 3.56e+03&#949; (Mean = 704&#949;)</span>
9817                 </p>
9818               </td>
9819 </tr>
9820 </tbody>
9821 </table></div>
9822 </div>
9823 <br class="table-break"><div class="table">
9824 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table&#160;17.75.&#160;Error rates for non central chi squared CDF</b></p>
9825 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
9826 <colgroup>
9827 <col>
9828 <col>
9829 <col>
9830 <col>
9831 <col>
9832 </colgroup>
9833 <thead><tr>
9834 <th>
9835               </th>
9836 <th>
9837                 <p>
9838                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9839                 </p>
9840               </th>
9841 <th>
9842                 <p>
9843                   GNU C++ version 5.1.0<br> linux<br> double
9844                 </p>
9845               </th>
9846 <th>
9847                 <p>
9848                   GNU C++ version 5.1.0<br> linux<br> long double
9849                 </p>
9850               </th>
9851 <th>
9852                 <p>
9853                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9854                 </p>
9855               </th>
9856 </tr></thead>
9857 <tbody>
9858 <tr>
9859 <td>
9860                 <p>
9861                   Non Central Chi Squared, medium parameters
9862                 </p>
9863               </td>
9864 <td>
9865                 <p>
9866                   <span class="blue">Max = 48.9&#949; (Mean = 10&#949;)</span>
9867                 </p>
9868               </td>
9869 <td>
9870                 <p>
9871                   <span class="blue">Max = 0.99&#949; (Mean = 0.0529&#949;)</span><br> <br>
9872                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 727&#949; (Mean = 121&#949;))
9873                 </p>
9874               </td>
9875 <td>
9876                 <p>
9877                   <span class="blue">Max = 46.5&#949; (Mean = 10.3&#949;)</span>
9878                 </p>
9879               </td>
9880 <td>
9881                 <p>
9882                   <span class="blue">Max = 115&#949; (Mean = 13.9&#949;)</span>
9883                 </p>
9884               </td>
9885 </tr>
9886 <tr>
9887 <td>
9888                 <p>
9889                   Non Central Chi Squared, large parameters
9890                 </p>
9891               </td>
9892 <td>
9893                 <p>
9894                   <span class="blue">Max = 9.79e+003&#949; (Mean = 723&#949;)</span>
9895                 </p>
9896               </td>
9897 <td>
9898                 <p>
9899                   <span class="blue">Max = 1.07&#949; (Mean = 0.102&#949;)</span><br> <br>
9900                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = 3.27e+08&#949; (Mean
9901                   = 2.23e+07&#949;))</span>
9902                 </p>
9903               </td>
9904 <td>
9905                 <p>
9906                   <span class="blue">Max = 3.07e+03&#949; (Mean = 336&#949;)</span>
9907                 </p>
9908               </td>
9909 <td>
9910                 <p>
9911                   <span class="blue">Max = 6.17e+03&#949; (Mean = 677&#949;)</span>
9912                 </p>
9913               </td>
9914 </tr>
9915 </tbody>
9916 </table></div>
9917 </div>
9918 <br class="table-break"><div class="table">
9919 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table&#160;17.76.&#160;Error rates for non central chi squared CDF complement</b></p>
9920 <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
9921 <colgroup>
9922 <col>
9923 <col>
9924 <col>
9925 <col>
9926 <col>
9927 </colgroup>
9928 <thead><tr>
9929 <th>
9930               </th>
9931 <th>
9932                 <p>
9933                   Microsoft Visual C++ version 12.0<br> Win32<br> double
9934                 </p>
9935               </th>
9936 <th>
9937                 <p>
9938                   GNU C++ version 5.1.0<br> linux<br> double
9939                 </p>
9940               </th>
9941 <th>
9942                 <p>
9943                   GNU C++ version 5.1.0<br> linux<br> long double
9944                 </p>
9945               </th>
9946 <th>
9947                 <p>
9948                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
9949                 </p>
9950               </th>
9951 </tr></thead>
9952 <tbody>
9953 <tr>
9954 <td>
9955                 <p>
9956                   Non Central Chi Squared, medium parameters
9957                 </p>
9958               </td>
9959 <td>
9960                 <p>
9961                   <span class="blue">Max = 98.6&#949; (Mean = 15.8&#949;)</span>
9962                 </p>
9963               </td>
9964 <td>
9965                 <p>
9966                   <span class="blue">Max = 0.96&#949; (Mean = 0.0635&#949;)</span><br> <br>
9967                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean
9968                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_0_2_Non_Central_Chi_Squared_medium_parameters">And
9969                   other failures.</a>)</span>
9970                 </p>
9971               </td>
9972 <td>
9973                 <p>
9974                   <span class="blue">Max = 107&#949; (Mean = 17.1&#949;)</span>
9975                 </p>
9976               </td>
9977 <td>
9978                 <p>
9979                   <span class="blue">Max = 171&#949; (Mean = 22.8&#949;)</span>
9980                 </p>
9981               </td>
9982 </tr>
9983 <tr>
9984 <td>
9985                 <p>
9986                   Non Central Chi Squared, large parameters
9987                 </p>
9988               </td>
9989 <td>
9990                 <p>
9991                   <span class="blue">Max = 5.43e+003&#949; (Mean = 705&#949;)</span>
9992                 </p>
9993               </td>
9994 <td>
9995                 <p>
9996                   <span class="blue">Max = 2.11&#949; (Mean = 0.278&#949;)</span><br> <br>
9997                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean
9998                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_0_2_Non_Central_Chi_Squared_large_parameters">And
9999                   other failures.</a>)</span>
10000                 </p>
10001               </td>
10002 <td>
10003                 <p>
10004                   <span class="blue">Max = 5.02e+03&#949; (Mean = 630&#949;)</span>
10005                 </p>
10006               </td>
10007 <td>
10008                 <p>
10009                   <span class="blue">Max = 5.1e+03&#949; (Mean = 577&#949;)</span>
10010                 </p>
10011               </td>
10012 </tr>
10013 </tbody>
10014 </table></div>
10015 </div>
10016 <br class="table-break"><div class="table">
10017 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF"></a><p class="title"><b>Table&#160;17.77.&#160;Error rates for non central t CDF</b></p>
10018 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
10019 <colgroup>
10020 <col>
10021 <col>
10022 <col>
10023 <col>
10024 <col>
10025 </colgroup>
10026 <thead><tr>
10027 <th>
10028               </th>
10029 <th>
10030                 <p>
10031                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10032                 </p>
10033               </th>
10034 <th>
10035                 <p>
10036                   GNU C++ version 5.1.0<br> linux<br> double
10037                 </p>
10038               </th>
10039 <th>
10040                 <p>
10041                   GNU C++ version 5.1.0<br> linux<br> long double
10042                 </p>
10043               </th>
10044 <th>
10045                 <p>
10046                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10047                 </p>
10048               </th>
10049 </tr></thead>
10050 <tbody>
10051 <tr>
10052 <td>
10053                 <p>
10054                   Non Central T
10055                 </p>
10056               </td>
10057 <td>
10058                 <p>
10059                   <span class="blue">Max = 138&#949; (Mean = 31.5&#949;)</span>
10060                 </p>
10061               </td>
10062 <td>
10063                 <p>
10064                   <span class="blue">Max = 0.796&#949; (Mean = 0.0691&#949;)</span><br>
10065                   <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
10066                   = 5.28e+15&#949; (Mean = 8.49e+14&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_t_CDF_Rmath_3_0_2_Non_Central_T">And
10067                   other failures.</a>)</span>
10068                 </p>
10069               </td>
10070 <td>
10071                 <p>
10072                   <span class="blue">Max = 141&#949; (Mean = 31.1&#949;)</span>
10073                 </p>
10074               </td>
10075 <td>
10076                 <p>
10077                   <span class="blue">Max = 145&#949; (Mean = 30.2&#949;)</span>
10078                 </p>
10079               </td>
10080 </tr>
10081 <tr>
10082 <td>
10083                 <p>
10084                   Non Central T (small non-centrality)
10085                 </p>
10086               </td>
10087 <td>
10088                 <p>
10089                   <span class="blue">Max = 3.61&#949; (Mean = 1.03&#949;)</span>
10090                 </p>
10091               </td>
10092 <td>
10093                 <p>
10094                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
10095                   3.0.2:</em></span> Max = 2.09e+03&#949; (Mean = 244&#949;))
10096                 </p>
10097               </td>
10098 <td>
10099                 <p>
10100                   <span class="blue">Max = 7.86&#949; (Mean = 1.69&#949;)</span>
10101                 </p>
10102               </td>
10103 <td>
10104                 <p>
10105                   <span class="blue">Max = 9.15&#949; (Mean = 2.25&#949;)</span>
10106                 </p>
10107               </td>
10108 </tr>
10109 <tr>
10110 <td>
10111                 <p>
10112                   Non Central T (large parameters)
10113                 </p>
10114               </td>
10115 <td>
10116                 <p>
10117                   <span class="blue">Max = 286&#949; (Mean = 62.8&#949;)</span>
10118                 </p>
10119               </td>
10120 <td>
10121                 <p>
10122                   <span class="blue">Max = 257&#949; (Mean = 72.1&#949;)</span><br> <br>
10123                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.46&#949; (Mean = 0.657&#949;))
10124                 </p>
10125               </td>
10126 <td>
10127                 <p>
10128                   <span class="blue">Max = 5.26e+05&#949; (Mean = 1.48e+05&#949;)</span>
10129                 </p>
10130               </td>
10131 <td>
10132                 <p>
10133                   <span class="blue">Max = 5.24e+05&#949; (Mean = 1.47e+05&#949;)</span>
10134                 </p>
10135               </td>
10136 </tr>
10137 </tbody>
10138 </table></div>
10139 </div>
10140 <br class="table-break"><div class="table">
10141 <a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF_complement"></a><p class="title"><b>Table&#160;17.78.&#160;Error rates for non central t CDF complement</b></p>
10142 <div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
10143 <colgroup>
10144 <col>
10145 <col>
10146 <col>
10147 <col>
10148 <col>
10149 </colgroup>
10150 <thead><tr>
10151 <th>
10152               </th>
10153 <th>
10154                 <p>
10155                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10156                 </p>
10157               </th>
10158 <th>
10159                 <p>
10160                   GNU C++ version 5.1.0<br> linux<br> double
10161                 </p>
10162               </th>
10163 <th>
10164                 <p>
10165                   GNU C++ version 5.1.0<br> linux<br> long double
10166                 </p>
10167               </th>
10168 <th>
10169                 <p>
10170                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10171                 </p>
10172               </th>
10173 </tr></thead>
10174 <tbody>
10175 <tr>
10176 <td>
10177                 <p>
10178                   Non Central T
10179                 </p>
10180               </td>
10181 <td>
10182                 <p>
10183                   <span class="blue">Max = 150&#949; (Mean = 32.3&#949;)</span>
10184                 </p>
10185               </td>
10186 <td>
10187                 <p>
10188                   <span class="blue">Max = 0.707&#949; (Mean = 0.0497&#949;)</span><br>
10189                   <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
10190                   = 6.19e+15&#949; (Mean = 6.72e+14&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_0_2_Non_Central_T">And
10191                   other failures.</a>)</span>
10192                 </p>
10193               </td>
10194 <td>
10195                 <p>
10196                   <span class="blue">Max = 203&#949; (Mean = 31.8&#949;)</span>
10197                 </p>
10198               </td>
10199 <td>
10200                 <p>
10201                   <span class="blue">Max = 340&#949; (Mean = 43.6&#949;)</span>
10202                 </p>
10203               </td>
10204 </tr>
10205 <tr>
10206 <td>
10207                 <p>
10208                   Non Central T (small non-centrality)
10209                 </p>
10210               </td>
10211 <td>
10212                 <p>
10213                   <span class="blue">Max = 5.21&#949; (Mean = 1.43&#949;)</span>
10214                 </p>
10215               </td>
10216 <td>
10217                 <p>
10218                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
10219                   3.0.2:</em></span> Max = 1.87e+03&#949; (Mean = 263&#949;))
10220                 </p>
10221               </td>
10222 <td>
10223                 <p>
10224                   <span class="blue">Max = 7.48&#949; (Mean = 1.86&#949;)</span>
10225                 </p>
10226               </td>
10227 <td>
10228                 <p>
10229                   <span class="blue">Max = 10.9&#949; (Mean = 2.43&#949;)</span>
10230                 </p>
10231               </td>
10232 </tr>
10233 <tr>
10234 <td>
10235                 <p>
10236                   Non Central T (large parameters)
10237                 </p>
10238               </td>
10239 <td>
10240                 <p>
10241                   <span class="blue">Max = 227&#949; (Mean = 50.4&#949;)</span>
10242                 </p>
10243               </td>
10244 <td>
10245                 <p>
10246                   <span class="blue">Max = 478&#949; (Mean = 96.3&#949;)</span><br> <br>
10247                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 2.24&#949; (Mean = 0.945&#949;))
10248                 </p>
10249               </td>
10250 <td>
10251                 <p>
10252                   <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
10253                 </p>
10254               </td>
10255 <td>
10256                 <p>
10257                   <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
10258                 </p>
10259               </td>
10260 </tr>
10261 </tbody>
10262 </table></div>
10263 </div>
10264 <br class="table-break"><div class="table">
10265 <a name="math_toolkit.logs_and_tables.all_table.table_owens_t"></a><p class="title"><b>Table&#160;17.79.&#160;Error rates for owens_t</b></p>
10266 <div class="table-contents"><table class="table" summary="Error rates for owens_t">
10267 <colgroup>
10268 <col>
10269 <col>
10270 <col>
10271 <col>
10272 <col>
10273 </colgroup>
10274 <thead><tr>
10275 <th>
10276               </th>
10277 <th>
10278                 <p>
10279                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10280                 </p>
10281               </th>
10282 <th>
10283                 <p>
10284                   GNU C++ version 5.1.0<br> linux<br> double
10285                 </p>
10286               </th>
10287 <th>
10288                 <p>
10289                   GNU C++ version 5.1.0<br> linux<br> long double
10290                 </p>
10291               </th>
10292 <th>
10293                 <p>
10294                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10295                 </p>
10296               </th>
10297 </tr></thead>
10298 <tbody>
10299 <tr>
10300 <td>
10301                 <p>
10302                   Owens T (medium small values)
10303                 </p>
10304               </td>
10305 <td>
10306                 <p>
10307                   <span class="blue">Max = 4.37&#949; (Mean = 0.973&#949;)</span>
10308                 </p>
10309               </td>
10310 <td>
10311                 <p>
10312                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10313                 </p>
10314               </td>
10315 <td>
10316                 <p>
10317                   <span class="blue">Max = 3.34&#949; (Mean = 0.942&#949;)</span>
10318                 </p>
10319               </td>
10320 <td>
10321                 <p>
10322                   <span class="blue">Max = 3.34&#949; (Mean = 0.91&#949;)</span>
10323                 </p>
10324               </td>
10325 </tr>
10326 <tr>
10327 <td>
10328                 <p>
10329                   Owens T (large and diverse values)
10330                 </p>
10331               </td>
10332 <td>
10333                 <p>
10334                   <span class="blue">Max = 3.78&#949; (Mean = 0.621&#949;)</span>
10335                 </p>
10336               </td>
10337 <td>
10338                 <p>
10339                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10340                 </p>
10341               </td>
10342 <td>
10343                 <p>
10344                   <span class="blue">Max = 49&#949; (Mean = 2.16&#949;)</span>
10345                 </p>
10346               </td>
10347 <td>
10348                 <p>
10349                   <span class="blue">Max = 24.5&#949; (Mean = 1.38&#949;)</span>
10350                 </p>
10351               </td>
10352 </tr>
10353 </tbody>
10354 </table></div>
10355 </div>
10356 <br class="table-break"><div class="table">
10357 <a name="math_toolkit.logs_and_tables.all_table.table_polygamma"></a><p class="title"><b>Table&#160;17.80.&#160;Error rates for polygamma</b></p>
10358 <div class="table-contents"><table class="table" summary="Error rates for polygamma">
10359 <colgroup>
10360 <col>
10361 <col>
10362 <col>
10363 <col>
10364 <col>
10365 </colgroup>
10366 <thead><tr>
10367 <th>
10368               </th>
10369 <th>
10370                 <p>
10371                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10372                 </p>
10373               </th>
10374 <th>
10375                 <p>
10376                   GNU C++ version 5.1.0<br> linux<br> double
10377                 </p>
10378               </th>
10379 <th>
10380                 <p>
10381                   GNU C++ version 5.1.0<br> linux<br> long double
10382                 </p>
10383               </th>
10384 <th>
10385                 <p>
10386                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10387                 </p>
10388               </th>
10389 </tr></thead>
10390 <tbody>
10391 <tr>
10392 <td>
10393                 <p>
10394                   Mathematica Data
10395                 </p>
10396               </td>
10397 <td>
10398                 <p>
10399                   <span class="blue">Max = 6.34&#949; (Mean = 1.53&#949;)</span>
10400                 </p>
10401               </td>
10402 <td>
10403                 <p>
10404                   <span class="blue">Max = 0.824&#949; (Mean = 0.0574&#949;)</span><br>
10405                   <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 108&#949; (Mean = 15.2&#949;))<br>
10406                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 62.9&#949; (Mean = 12.8&#949;))
10407                 </p>
10408               </td>
10409 <td>
10410                 <p>
10411                   <span class="blue">Max = 7.38&#949; (Mean = 1.84&#949;)</span>
10412                 </p>
10413               </td>
10414 <td>
10415                 <p>
10416                   <span class="blue">Max = 18.3&#949; (Mean = 4.16&#949;)</span>
10417                 </p>
10418               </td>
10419 </tr>
10420 <tr>
10421 <td>
10422                 <p>
10423                   Mathematica Data - large arguments
10424                 </p>
10425               </td>
10426 <td>
10427                 <p>
10428                   <span class="blue">Max = 150&#949; (Mean = 15.1&#949;)</span>
10429                 </p>
10430               </td>
10431 <td>
10432                 <p>
10433                   <span class="blue">Max = 0.998&#949; (Mean = 0.0592&#949;)</span><br>
10434                   <br> (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max
10435                   = 1.71e+56&#949; (Mean = 1.01e+55&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_large_arguments">And
10436                   other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10437                   Max = 244&#949; (Mean = 32.8&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_large_arguments">And
10438                   other failures.</a>)
10439                 </p>
10440               </td>
10441 <td>
10442                 <p>
10443                   <span class="blue">Max = 2.23&#949; (Mean = 0.323&#949;)</span>
10444                 </p>
10445               </td>
10446 <td>
10447                 <p>
10448                   <span class="blue">Max = 2.35&#949; (Mean = 0.34&#949;)</span>
10449                 </p>
10450               </td>
10451 </tr>
10452 <tr>
10453 <td>
10454                 <p>
10455                   Mathematica Data - negative arguments
10456                 </p>
10457               </td>
10458 <td>
10459                 <p>
10460                   <span class="blue">Max = 497&#949; (Mean = 129&#949;)</span>
10461                 </p>
10462               </td>
10463 <td>
10464                 <p>
10465                   <span class="blue">Max = 0.516&#949; (Mean = 0.022&#949;)</span><br> <br>
10466                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean
10467                   = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_negative_arguments">And
10468                   other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10469                   Max = 36.6&#949; (Mean = 3.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_negative_arguments">And
10470                   other failures.</a>)
10471                 </p>
10472               </td>
10473 <td>
10474                 <p>
10475                   <span class="blue">Max = 269&#949; (Mean = 87.7&#949;)</span>
10476                 </p>
10477               </td>
10478 <td>
10479                 <p>
10480                   <span class="blue">Max = 269&#949; (Mean = 87.9&#949;)</span>
10481                 </p>
10482               </td>
10483 </tr>
10484 <tr>
10485 <td>
10486                 <p>
10487                   Mathematica Data - large negative arguments
10488                 </p>
10489               </td>
10490 <td>
10491                 <p>
10492                   <span class="blue">Max = 162&#949; (Mean = 101&#949;)</span>
10493                 </p>
10494               </td>
10495 <td>
10496                 <p>
10497                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
10498                   3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_large_negative_arguments">And
10499                   other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10500                   Max = 1.79&#949; (Mean = 0.197&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_large_negative_arguments">And
10501                   other failures.</a>)
10502                 </p>
10503               </td>
10504 <td>
10505                 <p>
10506                   <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
10507                 </p>
10508               </td>
10509 <td>
10510                 <p>
10511                   <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
10512                 </p>
10513               </td>
10514 </tr>
10515 <tr>
10516 <td>
10517                 <p>
10518                   Mathematica Data - small arguments
10519                 </p>
10520               </td>
10521 <td>
10522                 <p>
10523                   <span class="blue">Max = 3&#949; (Mean = 0.496&#949;)</span>
10524                 </p>
10525               </td>
10526 <td>
10527                 <p>
10528                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
10529                   3.0.2:</em></span> Max = 106&#949; (Mean = 20&#949;))<br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10530                   Max = 15.2&#949; (Mean = 5.03&#949;))
10531                 </p>
10532               </td>
10533 <td>
10534                 <p>
10535                   <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
10536                 </p>
10537               </td>
10538 <td>
10539                 <p>
10540                   <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
10541                 </p>
10542               </td>
10543 </tr>
10544 <tr>
10545 <td>
10546                 <p>
10547                   Mathematica Data - Large orders and other bug cases
10548                 </p>
10549               </td>
10550 <td>
10551                 <p>
10552                   <span class="blue">Max = 200&#949; (Mean = 57.2&#949;)</span>
10553                 </p>
10554               </td>
10555 <td>
10556                 <p>
10557                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
10558                   3.0.2:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_Rmath_3_0_2_Mathematica_Data_Large_orders_and_other_bug_cases">And
10559                   other failures.</a>)</span><br> (<span class="emphasis"><em>GSL 1.16:</em></span>
10560                   Max = 151&#949; (Mean = 39.3&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_polygamma_GSL_1_16_Mathematica_Data_Large_orders_and_other_bug_cases">And
10561                   other failures.</a>)
10562                 </p>
10563               </td>
10564 <td>
10565                 <p>
10566                   <span class="blue">Max = 54.5&#949; (Mean = 13.3&#949;)</span>
10567                 </p>
10568               </td>
10569 <td>
10570                 <p>
10571                   <span class="blue">Max = 90.1&#949; (Mean = 30.6&#949;)</span>
10572                 </p>
10573               </td>
10574 </tr>
10575 </tbody>
10576 </table></div>
10577 </div>
10578 <br class="table-break"><div class="table">
10579 <a name="math_toolkit.logs_and_tables.all_table.table_powm1"></a><p class="title"><b>Table&#160;17.81.&#160;Error rates for powm1</b></p>
10580 <div class="table-contents"><table class="table" summary="Error rates for powm1">
10581 <colgroup>
10582 <col>
10583 <col>
10584 <col>
10585 <col>
10586 <col>
10587 </colgroup>
10588 <thead><tr>
10589 <th>
10590               </th>
10591 <th>
10592                 <p>
10593                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10594                 </p>
10595               </th>
10596 <th>
10597                 <p>
10598                   GNU C++ version 5.1.0<br> linux<br> double
10599                 </p>
10600               </th>
10601 <th>
10602                 <p>
10603                   GNU C++ version 5.1.0<br> linux<br> long double
10604                 </p>
10605               </th>
10606 <th>
10607                 <p>
10608                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10609                 </p>
10610               </th>
10611 </tr></thead>
10612 <tbody><tr>
10613 <td>
10614                 <p>
10615                   powm1
10616                 </p>
10617               </td>
10618 <td>
10619                 <p>
10620                   <span class="blue">Max = 1.99&#949; (Mean = 0.461&#949;)</span>
10621                 </p>
10622               </td>
10623 <td>
10624                 <p>
10625                   <span class="blue">Max = 1.26&#949; (Mean = 0.428&#949;)</span>
10626                 </p>
10627               </td>
10628 <td>
10629                 <p>
10630                   <span class="blue">Max = 2.04&#949; (Mean = 0.521&#949;)</span>
10631                 </p>
10632               </td>
10633 <td>
10634                 <p>
10635                   <span class="blue">Max = 2.14&#949; (Mean = 0.498&#949;)</span>
10636                 </p>
10637               </td>
10638 </tr></tbody>
10639 </table></div>
10640 </div>
10641 <br class="table-break"><div class="table">
10642 <a name="math_toolkit.logs_and_tables.all_table.table_sin_pi"></a><p class="title"><b>Table&#160;17.82.&#160;Error rates for sin_pi</b></p>
10643 <div class="table-contents"><table class="table" summary="Error rates for sin_pi">
10644 <colgroup>
10645 <col>
10646 <col>
10647 <col>
10648 <col>
10649 <col>
10650 </colgroup>
10651 <thead><tr>
10652 <th>
10653               </th>
10654 <th>
10655                 <p>
10656                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10657                 </p>
10658               </th>
10659 <th>
10660                 <p>
10661                   GNU C++ version 5.1.0<br> linux<br> double
10662                 </p>
10663               </th>
10664 <th>
10665                 <p>
10666                   GNU C++ version 5.1.0<br> linux<br> long double
10667                 </p>
10668               </th>
10669 <th>
10670                 <p>
10671                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10672                 </p>
10673               </th>
10674 </tr></thead>
10675 <tbody>
10676 <tr>
10677 <td>
10678                 <p>
10679                   sin_pi and cos_pi
10680                 </p>
10681               </td>
10682 <td>
10683                 <p>
10684                   <span class="blue">Max = 0.99&#949; (Mean = 0.328&#949;)</span>
10685                 </p>
10686               </td>
10687 <td>
10688                 <p>
10689                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10690                 </p>
10691               </td>
10692 <td>
10693                 <p>
10694                   <span class="blue">Max = 0.996&#949; (Mean = 0.335&#949;)</span>
10695                 </p>
10696               </td>
10697 <td>
10698                 <p>
10699                   <span class="blue">Max = 0.996&#949; (Mean = 0.336&#949;)</span>
10700                 </p>
10701               </td>
10702 </tr>
10703 <tr>
10704 <td>
10705                 <p>
10706                   sin_pi and cos_pi near integers and half integers
10707                 </p>
10708               </td>
10709 <td>
10710                 <p>
10711                   <span class="blue">Max = 0.996&#949; (Mean = 0.343&#949;)</span>
10712                 </p>
10713               </td>
10714 <td>
10715                 <p>
10716                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
10717                 </p>
10718               </td>
10719 <td>
10720                 <p>
10721                   <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
10722                 </p>
10723               </td>
10724 <td>
10725                 <p>
10726                   <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
10727                 </p>
10728               </td>
10729 </tr>
10730 </tbody>
10731 </table></div>
10732 </div>
10733 <br class="table-break"><div class="table">
10734 <a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel"></a><p class="title"><b>Table&#160;17.83.&#160;Error rates for sph_bessel</b></p>
10735 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
10736 <colgroup>
10737 <col>
10738 <col>
10739 <col>
10740 <col>
10741 <col>
10742 </colgroup>
10743 <thead><tr>
10744 <th>
10745               </th>
10746 <th>
10747                 <p>
10748                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10749                 </p>
10750               </th>
10751 <th>
10752                 <p>
10753                   GNU C++ version 5.1.0<br> linux<br> long double
10754                 </p>
10755               </th>
10756 <th>
10757                 <p>
10758                   GNU C++ version 5.1.0<br> linux<br> double
10759                 </p>
10760               </th>
10761 <th>
10762                 <p>
10763                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10764                 </p>
10765               </th>
10766 </tr></thead>
10767 <tbody><tr>
10768 <td>
10769                 <p>
10770                   Bessel j: Random Data
10771                 </p>
10772               </td>
10773 <td>
10774                 <p>
10775                   <span class="blue">Max = 245&#949; (Mean = 16.3&#949;)</span>
10776                 </p>
10777               </td>
10778 <td>
10779                 <p>
10780                   <span class="blue">Max = 243&#949; (Mean = 13.3&#949;)</span><br> <br>
10781                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.91e+06&#949; (Mean =
10782                   1.09e+05&#949;))
10783                 </p>
10784               </td>
10785 <td>
10786                 <p>
10787                   <span class="blue">Max = 0.978&#949; (Mean = 0.0539&#949;)</span><br>
10788                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.79e+03&#949; (Mean = 107&#949;))
10789                 </p>
10790               </td>
10791 <td>
10792                 <p>
10793                   <span class="blue">Max = 243&#949; (Mean = 33.7&#949;)</span>
10794                 </p>
10795               </td>
10796 </tr></tbody>
10797 </table></div>
10798 </div>
10799 <br class="table-break"><div class="table">
10800 <a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel_prime"></a><p class="title"><b>Table&#160;17.84.&#160;Error rates for sph_bessel_prime</b></p>
10801 <div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
10802 <colgroup>
10803 <col>
10804 <col>
10805 <col>
10806 <col>
10807 <col>
10808 </colgroup>
10809 <thead><tr>
10810 <th>
10811               </th>
10812 <th>
10813                 <p>
10814                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10815                 </p>
10816               </th>
10817 <th>
10818                 <p>
10819                   GNU C++ version 5.1.0<br> linux<br> double
10820                 </p>
10821               </th>
10822 <th>
10823                 <p>
10824                   GNU C++ version 5.1.0<br> linux<br> long double
10825                 </p>
10826               </th>
10827 <th>
10828                 <p>
10829                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10830                 </p>
10831               </th>
10832 </tr></thead>
10833 <tbody><tr>
10834 <td>
10835                 <p>
10836                   Bessel j': Random Data
10837                 </p>
10838               </td>
10839 <td>
10840                 <p>
10841                   <span class="blue">Max = 307&#949; (Mean = 25.2&#949;)</span>
10842                 </p>
10843               </td>
10844 <td>
10845                 <p>
10846                   <span class="blue">Max = 0.753&#949; (Mean = 0.0343&#949;)</span>
10847                 </p>
10848               </td>
10849 <td>
10850                 <p>
10851                   <span class="blue">Max = 167&#949; (Mean = 12&#949;)</span>
10852                 </p>
10853               </td>
10854 <td>
10855                 <p>
10856                   <span class="blue">Max = 167&#949; (Mean = 33.2&#949;)</span>
10857                 </p>
10858               </td>
10859 </tr></tbody>
10860 </table></div>
10861 </div>
10862 <br class="table-break"><div class="table">
10863 <a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann"></a><p class="title"><b>Table&#160;17.85.&#160;Error rates for sph_neumann</b></p>
10864 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
10865 <colgroup>
10866 <col>
10867 <col>
10868 <col>
10869 <col>
10870 <col>
10871 </colgroup>
10872 <thead><tr>
10873 <th>
10874               </th>
10875 <th>
10876                 <p>
10877                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10878                 </p>
10879               </th>
10880 <th>
10881                 <p>
10882                   GNU C++ version 5.1.0<br> linux<br> double
10883                 </p>
10884               </th>
10885 <th>
10886                 <p>
10887                   GNU C++ version 5.1.0<br> linux<br> long double
10888                 </p>
10889               </th>
10890 <th>
10891                 <p>
10892                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10893                 </p>
10894               </th>
10895 </tr></thead>
10896 <tbody><tr>
10897 <td>
10898                 <p>
10899                   y: Random Data
10900                 </p>
10901               </td>
10902 <td>
10903                 <p>
10904                   <span class="blue">Max = 281&#949; (Mean = 31.1&#949;)</span>
10905                 </p>
10906               </td>
10907 <td>
10908                 <p>
10909                   <span class="blue">Max = 0.995&#949; (Mean = 0.0665&#949;)</span><br>
10910                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 8.5e+04&#949; (Mean = 5.33e+03&#949;))
10911                 </p>
10912               </td>
10913 <td>
10914                 <p>
10915                   <span class="blue">Max = 234&#949; (Mean = 19.5&#949;)</span><br> <br>
10916                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.6e+06&#949; (Mean = 1.4e+05&#949;))
10917                 </p>
10918               </td>
10919 <td>
10920                 <p>
10921                   <span class="blue">Max = 234&#949; (Mean = 19.8&#949;)</span>
10922                 </p>
10923               </td>
10924 </tr></tbody>
10925 </table></div>
10926 </div>
10927 <br class="table-break"><div class="table">
10928 <a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann_prime"></a><p class="title"><b>Table&#160;17.86.&#160;Error rates for sph_neumann_prime</b></p>
10929 <div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
10930 <colgroup>
10931 <col>
10932 <col>
10933 <col>
10934 <col>
10935 <col>
10936 </colgroup>
10937 <thead><tr>
10938 <th>
10939               </th>
10940 <th>
10941                 <p>
10942                   Microsoft Visual C++ version 12.0<br> Win32<br> double
10943                 </p>
10944               </th>
10945 <th>
10946                 <p>
10947                   GNU C++ version 5.1.0<br> linux<br> double
10948                 </p>
10949               </th>
10950 <th>
10951                 <p>
10952                   GNU C++ version 5.1.0<br> linux<br> long double
10953                 </p>
10954               </th>
10955 <th>
10956                 <p>
10957                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
10958                 </p>
10959               </th>
10960 </tr></thead>
10961 <tbody><tr>
10962 <td>
10963                 <p>
10964                   y': Random Data
10965                 </p>
10966               </td>
10967 <td>
10968                 <p>
10969                   <span class="blue">Max = 296&#949; (Mean = 25.6&#949;)</span>
10970                 </p>
10971               </td>
10972 <td>
10973                 <p>
10974                   <span class="blue">Max = 0.752&#949; (Mean = 0.062&#949;)</span>
10975                 </p>
10976               </td>
10977 <td>
10978                 <p>
10979                   <span class="blue">Max = 158&#949; (Mean = 18.8&#949;)</span>
10980                 </p>
10981               </td>
10982 <td>
10983                 <p>
10984                   <span class="blue">Max = 158&#949; (Mean = 20.2&#949;)</span>
10985                 </p>
10986               </td>
10987 </tr></tbody>
10988 </table></div>
10989 </div>
10990 <br class="table-break"><div class="table">
10991 <a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_i"></a><p class="title"><b>Table&#160;17.87.&#160;Error rates for spherical_harmonic_i</b></p>
10992 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
10993 <colgroup>
10994 <col>
10995 <col>
10996 <col>
10997 <col>
10998 <col>
10999 </colgroup>
11000 <thead><tr>
11001 <th>
11002               </th>
11003 <th>
11004                 <p>
11005                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11006                 </p>
11007               </th>
11008 <th>
11009                 <p>
11010                   GNU C++ version 5.1.0<br> linux<br> double
11011                 </p>
11012               </th>
11013 <th>
11014                 <p>
11015                   GNU C++ version 5.1.0<br> linux<br> long double
11016                 </p>
11017               </th>
11018 <th>
11019                 <p>
11020                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11021                 </p>
11022               </th>
11023 </tr></thead>
11024 <tbody><tr>
11025 <td>
11026                 <p>
11027                   Spherical Harmonics
11028                 </p>
11029               </td>
11030 <td>
11031                 <p>
11032                   <span class="blue">Max = 2.27e+004&#949; (Mean = 725&#949;)</span>
11033                 </p>
11034               </td>
11035 <td>
11036                 <p>
11037                   <span class="blue">Max = 1.36&#949; (Mean = 0.0765&#949;)</span>
11038                 </p>
11039               </td>
11040 <td>
11041                 <p>
11042                   <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
11043                 </p>
11044               </td>
11045 <td>
11046                 <p>
11047                   <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
11048                 </p>
11049               </td>
11050 </tr></tbody>
11051 </table></div>
11052 </div>
11053 <br class="table-break"><div class="table">
11054 <a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_r"></a><p class="title"><b>Table&#160;17.88.&#160;Error rates for spherical_harmonic_r</b></p>
11055 <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
11056 <colgroup>
11057 <col>
11058 <col>
11059 <col>
11060 <col>
11061 <col>
11062 </colgroup>
11063 <thead><tr>
11064 <th>
11065               </th>
11066 <th>
11067                 <p>
11068                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11069                 </p>
11070               </th>
11071 <th>
11072                 <p>
11073                   GNU C++ version 5.1.0<br> linux<br> double
11074                 </p>
11075               </th>
11076 <th>
11077                 <p>
11078                   GNU C++ version 5.1.0<br> linux<br> long double
11079                 </p>
11080               </th>
11081 <th>
11082                 <p>
11083                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11084                 </p>
11085               </th>
11086 </tr></thead>
11087 <tbody><tr>
11088 <td>
11089                 <p>
11090                   Spherical Harmonics
11091                 </p>
11092               </td>
11093 <td>
11094                 <p>
11095                   <span class="blue">Max = 2.27e+004&#949; (Mean = 725&#949;)</span>
11096                 </p>
11097               </td>
11098 <td>
11099                 <p>
11100                   <span class="blue">Max = 1.58&#949; (Mean = 0.0707&#949;)</span>
11101                 </p>
11102               </td>
11103 <td>
11104                 <p>
11105                   <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
11106                 </p>
11107               </td>
11108 <td>
11109                 <p>
11110                   <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
11111                 </p>
11112               </td>
11113 </tr></tbody>
11114 </table></div>
11115 </div>
11116 <br class="table-break"><div class="table">
11117 <a name="math_toolkit.logs_and_tables.all_table.table_sqrt1pm1"></a><p class="title"><b>Table&#160;17.89.&#160;Error rates for sqrt1pm1</b></p>
11118 <div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
11119 <colgroup>
11120 <col>
11121 <col>
11122 <col>
11123 <col>
11124 <col>
11125 </colgroup>
11126 <thead><tr>
11127 <th>
11128               </th>
11129 <th>
11130                 <p>
11131                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11132                 </p>
11133               </th>
11134 <th>
11135                 <p>
11136                   GNU C++ version 5.1.0<br> linux<br> double
11137                 </p>
11138               </th>
11139 <th>
11140                 <p>
11141                   GNU C++ version 5.1.0<br> linux<br> long double
11142                 </p>
11143               </th>
11144 <th>
11145                 <p>
11146                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11147                 </p>
11148               </th>
11149 </tr></thead>
11150 <tbody><tr>
11151 <td>
11152                 <p>
11153                   sqrt1pm1
11154                 </p>
11155               </td>
11156 <td>
11157                 <p>
11158                   <span class="blue">Max = 1.36&#949; (Mean = 0.44&#949;)</span>
11159                 </p>
11160               </td>
11161 <td>
11162                 <p>
11163                   <span class="blue">Max = 1.3&#949; (Mean = 0.404&#949;)</span>
11164                 </p>
11165               </td>
11166 <td>
11167                 <p>
11168                   <span class="blue">Max = 1.33&#949; (Mean = 0.409&#949;)</span>
11169                 </p>
11170               </td>
11171 <td>
11172                 <p>
11173                   <span class="blue">Max = 1.54&#949; (Mean = 0.568&#949;)</span>
11174                 </p>
11175               </td>
11176 </tr></tbody>
11177 </table></div>
11178 </div>
11179 <br class="table-break"><div class="table">
11180 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma"></a><p class="title"><b>Table&#160;17.90.&#160;Error rates for tgamma</b></p>
11181 <div class="table-contents"><table class="table" summary="Error rates for tgamma">
11182 <colgroup>
11183 <col>
11184 <col>
11185 <col>
11186 <col>
11187 <col>
11188 </colgroup>
11189 <thead><tr>
11190 <th>
11191               </th>
11192 <th>
11193                 <p>
11194                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11195                 </p>
11196               </th>
11197 <th>
11198                 <p>
11199                   GNU C++ version 5.1.0<br> linux<br> double
11200                 </p>
11201               </th>
11202 <th>
11203                 <p>
11204                   GNU C++ version 5.1.0<br> linux<br> long double
11205                 </p>
11206               </th>
11207 <th>
11208                 <p>
11209                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11210                 </p>
11211               </th>
11212 </tr></thead>
11213 <tbody>
11214 <tr>
11215 <td>
11216                 <p>
11217                   factorials
11218                 </p>
11219               </td>
11220 <td>
11221                 <p>
11222                   <span class="blue">Max = 1.85&#949; (Mean = 0.491&#949;)</span><br> <br>
11223                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.17&#949; (Mean = 0.928&#949;))
11224                 </p>
11225               </td>
11226 <td>
11227                 <p>
11228                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11229                   1.16:</em></span> Max = 3.95&#949; (Mean = 0.783&#949;))<br> (<span class="emphasis"><em>Rmath
11230                   3.0.2:</em></span> Max = 314&#949; (Mean = 93.4&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
11231                   Max = 3.19&#949; (Mean = 0.884&#949;))
11232                 </p>
11233               </td>
11234 <td>
11235                 <p>
11236                   <span class="blue">Max = 1.96&#949; (Mean = 0.483&#949;)</span><br> <br>
11237                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))<br>
11238                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))
11239                 </p>
11240               </td>
11241 <td>
11242                 <p>
11243                   <span class="blue">Max = 172&#949; (Mean = 41&#949;)</span><br> <br>
11244                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11245                 </p>
11246               </td>
11247 </tr>
11248 <tr>
11249 <td>
11250                 <p>
11251                   near 0
11252                 </p>
11253               </td>
11254 <td>
11255                 <p>
11256                   <span class="blue">Max = 1.96&#949; (Mean = 0.684&#949;)</span><br> <br>
11257                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.405&#949;))
11258                 </p>
11259               </td>
11260 <td>
11261                 <p>
11262                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11263                   1.16:</em></span> Max = 4.51&#949; (Mean = 1.92&#949;))<br> (<span class="emphasis"><em>Rmath
11264                   3.0.2:</em></span> Max = 1&#949; (Mean = 0.335&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
11265                   Max = 1&#949; (Mean = 0.548&#949;))
11266                 </p>
11267               </td>
11268 <td>
11269                 <p>
11270                   <span class="blue">Max = 2&#949; (Mean = 0.73&#949;)</span><br> <br>
11271                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1&#949; (Mean = 0.376&#949;))<br>
11272                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.376&#949;))
11273                 </p>
11274               </td>
11275 <td>
11276                 <p>
11277                   <span class="blue">Max = 2&#949; (Mean = 0.647&#949;)</span><br> <br>
11278                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.5&#949; (Mean = 0.0791&#949;))
11279                 </p>
11280               </td>
11281 </tr>
11282 <tr>
11283 <td>
11284                 <p>
11285                   near 1
11286                 </p>
11287               </td>
11288 <td>
11289                 <p>
11290                   <span class="blue">Max = 2&#949; (Mean = 0.865&#949;)</span><br> <br>
11291                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.4&#949;))
11292                 </p>
11293               </td>
11294 <td>
11295                 <p>
11296                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11297                   1.16:</em></span> Max = 4.41&#949; (Mean = 1.81&#949;))<br> (<span class="emphasis"><em>Rmath
11298                   3.0.2:</em></span> Max = 1&#949; (Mean = 0.32&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
11299                   Max = 1&#949; (Mean = 0.518&#949;))
11300                 </p>
11301               </td>
11302 <td>
11303                 <p>
11304                   <span class="blue">Max = 2&#949; (Mean = 0.85&#949;)</span><br> <br>
11305                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))<br>
11306                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))
11307                 </p>
11308               </td>
11309 <td>
11310                 <p>
11311                   <span class="blue">Max = 3.01&#949; (Mean = 1.06&#949;)</span><br> <br>
11312                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.175&#949;))
11313                 </p>
11314               </td>
11315 </tr>
11316 <tr>
11317 <td>
11318                 <p>
11319                   near 2
11320                 </p>
11321               </td>
11322 <td>
11323                 <p>
11324                   <span class="blue">Max = 2&#949; (Mean = 0.995&#949;)</span><br> <br>
11325                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11326                 </p>
11327               </td>
11328 <td>
11329                 <p>
11330                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11331                   1.16:</em></span> Max = 7.95&#949; (Mean = 3.12&#949;))<br> (<span class="emphasis"><em>Rmath
11332                   3.0.2:</em></span> Max = 1&#949; (Mean = 0.191&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
11333                   Max = 1.09&#949; (Mean = 0.502&#949;))
11334                 </p>
11335               </td>
11336 <td>
11337                 <p>
11338                   <span class="blue">Max = 2&#949; (Mean = 0.913&#949;)</span><br> <br>
11339                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))<br>
11340                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))
11341                 </p>
11342               </td>
11343 <td>
11344                 <p>
11345                   <span class="blue">Max = 5.01&#949; (Mean = 1.89&#949;)</span><br> <br>
11346                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11347                 </p>
11348               </td>
11349 </tr>
11350 <tr>
11351 <td>
11352                 <p>
11353                   near -10
11354                 </p>
11355               </td>
11356 <td>
11357                 <p>
11358                   <span class="blue">Max = 1.73&#949; (Mean = 0.729&#949;)</span><br> <br>
11359                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.866&#949; (Mean = 0.445&#949;))
11360                 </p>
11361               </td>
11362 <td>
11363                 <p>
11364                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11365                   1.16:</em></span> Max = 2.6&#949; (Mean = 1.05&#949;))<br> (<span class="emphasis"><em>Rmath
11366                   3.0.2:</em></span> Max = 6.34e+05&#949; (Mean = 1.2e+05&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
11367                   Max = 2.6&#949; (Mean = 0.956&#949;))
11368                 </p>
11369               </td>
11370 <td>
11371                 <p>
11372                   <span class="blue">Max = 2.6&#949; (Mean = 0.985&#949;)</span><br> <br>
11373                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))<br>
11374                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))
11375                 </p>
11376               </td>
11377 <td>
11378                 <p>
11379                   <span class="blue">Max = 1.75&#949; (Mean = 0.819&#949;)</span><br> <br>
11380                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11381                 </p>
11382               </td>
11383 </tr>
11384 <tr>
11385 <td>
11386                 <p>
11387                   near -55
11388                 </p>
11389               </td>
11390 <td>
11391                 <p>
11392                   <span class="blue">Max = 1.8&#949; (Mean = 0.817&#949;)</span><br> <br>
11393                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.87e+004&#949; (Mean = 6.71e+003&#949;))
11394                 </p>
11395               </td>
11396 <td>
11397                 <p>
11398                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11399                   1.16:</em></span> Max = 1.8&#949; (Mean = 0.782&#949;))<br> (<span class="emphasis"><em>Rmath
11400                   3.0.2:</em></span> Max = 6.36e+06&#949; (Mean = 1.13e+06&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
11401                   Max = 2.7&#949; (Mean = 0.988&#949;))
11402                 </p>
11403               </td>
11404 <td>
11405                 <p>
11406                   <span class="blue">Max = 1.8&#949; (Mean = 0.847&#949;)</span><br> <br>
11407                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))<br>
11408                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))
11409                 </p>
11410               </td>
11411 <td>
11412                 <p>
11413                   <span class="blue">Max = 98.5&#949; (Mean = 53.4&#949;)</span><br> <br>
11414                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
11415                 </p>
11416               </td>
11417 </tr>
11418 </tbody>
11419 </table></div>
11420 </div>
11421 <br class="table-break"><div class="table">
11422 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma1pm1"></a><p class="title"><b>Table&#160;17.91.&#160;Error rates for tgamma1pm1</b></p>
11423 <div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
11424 <colgroup>
11425 <col>
11426 <col>
11427 <col>
11428 <col>
11429 <col>
11430 </colgroup>
11431 <thead><tr>
11432 <th>
11433               </th>
11434 <th>
11435                 <p>
11436                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11437                 </p>
11438               </th>
11439 <th>
11440                 <p>
11441                   GNU C++ version 5.1.0<br> linux<br> double
11442                 </p>
11443               </th>
11444 <th>
11445                 <p>
11446                   GNU C++ version 5.1.0<br> linux<br> long double
11447                 </p>
11448               </th>
11449 <th>
11450                 <p>
11451                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11452                 </p>
11453               </th>
11454 </tr></thead>
11455 <tbody><tr>
11456 <td>
11457                 <p>
11458                   tgamma1pm1(dz)
11459                 </p>
11460               </td>
11461 <td>
11462                 <p>
11463                   <span class="blue">Max = 0.982&#949; (Mean = 0.399&#949;)</span>
11464                 </p>
11465               </td>
11466 <td>
11467                 <p>
11468                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11469                 </p>
11470               </td>
11471 <td>
11472                 <p>
11473                   <span class="blue">Max = 1.12&#949; (Mean = 0.49&#949;)</span>
11474                 </p>
11475               </td>
11476 <td>
11477                 <p>
11478                   <span class="blue">Max = 3.97&#949; (Mean = 0.713&#949;)</span>
11479                 </p>
11480               </td>
11481 </tr></tbody>
11482 </table></div>
11483 </div>
11484 <br class="table-break"><div class="table">
11485 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_delta_ratio"></a><p class="title"><b>Table&#160;17.92.&#160;Error rates for tgamma_delta_ratio</b></p>
11486 <div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
11487 <colgroup>
11488 <col>
11489 <col>
11490 <col>
11491 <col>
11492 <col>
11493 </colgroup>
11494 <thead><tr>
11495 <th>
11496               </th>
11497 <th>
11498                 <p>
11499                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11500                 </p>
11501               </th>
11502 <th>
11503                 <p>
11504                   GNU C++ version 5.1.0<br> linux<br> double
11505                 </p>
11506               </th>
11507 <th>
11508                 <p>
11509                   GNU C++ version 5.1.0<br> linux<br> long double
11510                 </p>
11511               </th>
11512 <th>
11513                 <p>
11514                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11515                 </p>
11516               </th>
11517 </tr></thead>
11518 <tbody>
11519 <tr>
11520 <td>
11521                 <p>
11522                   tgamma + small delta ratios
11523                 </p>
11524               </td>
11525 <td>
11526                 <p>
11527                   <span class="blue">Max = 10.1&#949; (Mean = 1.25&#949;)</span>
11528                 </p>
11529               </td>
11530 <td>
11531                 <p>
11532                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11533                 </p>
11534               </td>
11535 <td>
11536                 <p>
11537                   <span class="blue">Max = 5.56&#949; (Mean = 0.969&#949;)</span>
11538                 </p>
11539               </td>
11540 <td>
11541                 <p>
11542                   <span class="blue">Max = 15.4&#949; (Mean = 2.09&#949;)</span>
11543                 </p>
11544               </td>
11545 </tr>
11546 <tr>
11547 <td>
11548                 <p>
11549                   tgamma + small delta ratios (negative delta)
11550                 </p>
11551               </td>
11552 <td>
11553                 <p>
11554                   <span class="blue">Max = 8.04&#949; (Mean = 1.31&#949;)</span>
11555                 </p>
11556               </td>
11557 <td>
11558                 <p>
11559                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11560                 </p>
11561               </td>
11562 <td>
11563                 <p>
11564                   <span class="blue">Max = 8.67&#949; (Mean = 1.29&#949;)</span>
11565                 </p>
11566               </td>
11567 <td>
11568                 <p>
11569                   <span class="blue">Max = 18.3&#949; (Mean = 2.03&#949;)</span>
11570                 </p>
11571               </td>
11572 </tr>
11573 <tr>
11574 <td>
11575                 <p>
11576                   tgamma + small integer ratios
11577                 </p>
11578               </td>
11579 <td>
11580                 <p>
11581                   <span class="blue">Max = 2.74&#949; (Mean = 0.736&#949;)</span>
11582                 </p>
11583               </td>
11584 <td>
11585                 <p>
11586                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11587                 </p>
11588               </td>
11589 <td>
11590                 <p>
11591                   <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
11592                 </p>
11593               </td>
11594 <td>
11595                 <p>
11596                   <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
11597                 </p>
11598               </td>
11599 </tr>
11600 <tr>
11601 <td>
11602                 <p>
11603                   tgamma + small integer ratios (negative delta)
11604                 </p>
11605               </td>
11606 <td>
11607                 <p>
11608                   <span class="blue">Max = 2.15&#949; (Mean = 0.685&#949;)</span>
11609                 </p>
11610               </td>
11611 <td>
11612                 <p>
11613                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11614                 </p>
11615               </td>
11616 <td>
11617                 <p>
11618                   <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
11619                 </p>
11620               </td>
11621 <td>
11622                 <p>
11623                   <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
11624                 </p>
11625               </td>
11626 </tr>
11627 <tr>
11628 <td>
11629                 <p>
11630                   integer tgamma ratios
11631                 </p>
11632               </td>
11633 <td>
11634                 <p>
11635                   <span class="blue">Max = 0.968&#949; (Mean = 0.386&#949;)</span>
11636                 </p>
11637               </td>
11638 <td>
11639                 <p>
11640                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11641                 </p>
11642               </td>
11643 <td>
11644                 <p>
11645                   <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
11646                 </p>
11647               </td>
11648 <td>
11649                 <p>
11650                   <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
11651                 </p>
11652               </td>
11653 </tr>
11654 <tr>
11655 <td>
11656                 <p>
11657                   integer tgamma ratios (negative delta)
11658                 </p>
11659               </td>
11660 <td>
11661                 <p>
11662                   <span class="blue">Max = 0.974&#949; (Mean = 0.184&#949;)</span>
11663                 </p>
11664               </td>
11665 <td>
11666                 <p>
11667                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11668                 </p>
11669               </td>
11670 <td>
11671                 <p>
11672                   <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
11673                 </p>
11674               </td>
11675 <td>
11676                 <p>
11677                   <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
11678                 </p>
11679               </td>
11680 </tr>
11681 </tbody>
11682 </table></div>
11683 </div>
11684 <br class="table-break"><div class="table">
11685 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_incomplete_"></a><p class="title"><b>Table&#160;17.93.&#160;Error rates for tgamma (incomplete)</b></p>
11686 <div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
11687 <colgroup>
11688 <col>
11689 <col>
11690 <col>
11691 <col>
11692 <col>
11693 </colgroup>
11694 <thead><tr>
11695 <th>
11696               </th>
11697 <th>
11698                 <p>
11699                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11700                 </p>
11701               </th>
11702 <th>
11703                 <p>
11704                   GNU C++ version 5.1.0<br> linux<br> double
11705                 </p>
11706               </th>
11707 <th>
11708                 <p>
11709                   GNU C++ version 5.1.0<br> linux<br> long double
11710                 </p>
11711               </th>
11712 <th>
11713                 <p>
11714                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11715                 </p>
11716               </th>
11717 </tr></thead>
11718 <tbody>
11719 <tr>
11720 <td>
11721                 <p>
11722                   tgamma(a, z) medium values
11723                 </p>
11724               </td>
11725 <td>
11726                 <p>
11727                   <span class="blue">Max = 8.14&#949; (Mean = 1.71&#949;)</span>
11728                 </p>
11729               </td>
11730 <td>
11731                 <p>
11732                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11733                   1.16:</em></span> Max = 200&#949; (Mean = 13.3&#949;))
11734                 </p>
11735               </td>
11736 <td>
11737                 <p>
11738                   <span class="blue">Max = 7.35&#949; (Mean = 1.69&#949;)</span>
11739                 </p>
11740               </td>
11741 <td>
11742                 <p>
11743                   <span class="blue">Max = 412&#949; (Mean = 95.5&#949;)</span>
11744                 </p>
11745               </td>
11746 </tr>
11747 <tr>
11748 <td>
11749                 <p>
11750                   tgamma(a, z) small values
11751                 </p>
11752               </td>
11753 <td>
11754                 <p>
11755                   <span class="blue">Max = 2.53&#949; (Mean = 0.66&#949;)</span>
11756                 </p>
11757               </td>
11758 <td>
11759                 <p>
11760                   <span class="blue">Max = 0.753&#949; (Mean = 0.0474&#949;)</span><br>
11761                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> <span class="red">Max =
11762                   1.38e+10&#949; (Mean = 1.05e+09&#949;))</span>
11763                 </p>
11764               </td>
11765 <td>
11766                 <p>
11767                   <span class="blue">Max = 2.13&#949; (Mean = 0.717&#949;)</span>
11768                 </p>
11769               </td>
11770 <td>
11771                 <p>
11772                   <span class="blue">Max = 2.13&#949; (Mean = 0.712&#949;)</span>
11773                 </p>
11774               </td>
11775 </tr>
11776 <tr>
11777 <td>
11778                 <p>
11779                   tgamma(a, z) integer and half integer values
11780                 </p>
11781               </td>
11782 <td>
11783                 <p>
11784                   <span class="blue">Max = 5.16&#949; (Mean = 1.44&#949;)</span>
11785                 </p>
11786               </td>
11787 <td>
11788                 <p>
11789                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11790                   1.16:</em></span> Max = 117&#949; (Mean = 12.5&#949;))
11791                 </p>
11792               </td>
11793 <td>
11794                 <p>
11795                   <span class="blue">Max = 5.52&#949; (Mean = 1.52&#949;)</span>
11796                 </p>
11797               </td>
11798 <td>
11799                 <p>
11800                   <span class="blue">Max = 79.6&#949; (Mean = 20.9&#949;)</span>
11801                 </p>
11802               </td>
11803 </tr>
11804 </tbody>
11805 </table></div>
11806 </div>
11807 <br class="table-break"><div class="table">
11808 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_lower"></a><p class="title"><b>Table&#160;17.94.&#160;Error rates for tgamma_lower</b></p>
11809 <div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
11810 <colgroup>
11811 <col>
11812 <col>
11813 <col>
11814 <col>
11815 <col>
11816 </colgroup>
11817 <thead><tr>
11818 <th>
11819               </th>
11820 <th>
11821                 <p>
11822                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11823                 </p>
11824               </th>
11825 <th>
11826                 <p>
11827                   GNU C++ version 5.1.0<br> linux<br> double
11828                 </p>
11829               </th>
11830 <th>
11831                 <p>
11832                   GNU C++ version 5.1.0<br> linux<br> long double
11833                 </p>
11834               </th>
11835 <th>
11836                 <p>
11837                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11838                 </p>
11839               </th>
11840 </tr></thead>
11841 <tbody>
11842 <tr>
11843 <td>
11844                 <p>
11845                   tgamma(a, z) medium values
11846                 </p>
11847               </td>
11848 <td>
11849                 <p>
11850                   <span class="blue">Max = 5.62&#949; (Mean = 1.43&#949;)</span>
11851                 </p>
11852               </td>
11853 <td>
11854                 <p>
11855                   <span class="blue">Max = 0.833&#949; (Mean = 0.0315&#949;)</span><br>
11856                   <br> (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 0.833&#949; (Mean = 0.0315&#949;))
11857                 </p>
11858               </td>
11859 <td>
11860                 <p>
11861                   <span class="blue">Max = 6.79&#949; (Mean = 1.38&#949;)</span>
11862                 </p>
11863               </td>
11864 <td>
11865                 <p>
11866                   <span class="blue">Max = 363&#949; (Mean = 63.8&#949;)</span>
11867                 </p>
11868               </td>
11869 </tr>
11870 <tr>
11871 <td>
11872                 <p>
11873                   tgamma(a, z) small values
11874                 </p>
11875               </td>
11876 <td>
11877                 <p>
11878                   <span class="blue">Max = 1.57&#949; (Mean = 0.527&#949;)</span>
11879                 </p>
11880               </td>
11881 <td>
11882                 <p>
11883                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11884                   1.16:</em></span> Max = 0&#949; (Mean = 0&#949;))
11885                 </p>
11886               </td>
11887 <td>
11888                 <p>
11889                   <span class="blue">Max = 1.97&#949; (Mean = 0.552&#949;)</span>
11890                 </p>
11891               </td>
11892 <td>
11893                 <p>
11894                   <span class="blue">Max = 1.97&#949; (Mean = 0.567&#949;)</span>
11895                 </p>
11896               </td>
11897 </tr>
11898 <tr>
11899 <td>
11900                 <p>
11901                   tgamma(a, z) integer and half integer values
11902                 </p>
11903               </td>
11904 <td>
11905                 <p>
11906                   <span class="blue">Max = 2.69&#949; (Mean = 0.866&#949;)</span>
11907                 </p>
11908               </td>
11909 <td>
11910                 <p>
11911                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
11912                   1.16:</em></span> Max = 0&#949; (Mean = 0&#949;))
11913                 </p>
11914               </td>
11915 <td>
11916                 <p>
11917                   <span class="blue">Max = 4.83&#949; (Mean = 1.12&#949;)</span>
11918                 </p>
11919               </td>
11920 <td>
11921                 <p>
11922                   <span class="blue">Max = 84.7&#949; (Mean = 17.5&#949;)</span>
11923                 </p>
11924               </td>
11925 </tr>
11926 </tbody>
11927 </table></div>
11928 </div>
11929 <br class="table-break"><div class="table">
11930 <a name="math_toolkit.logs_and_tables.all_table.table_tgamma_ratio"></a><p class="title"><b>Table&#160;17.95.&#160;Error rates for tgamma_ratio</b></p>
11931 <div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
11932 <colgroup>
11933 <col>
11934 <col>
11935 <col>
11936 <col>
11937 <col>
11938 </colgroup>
11939 <thead><tr>
11940 <th>
11941               </th>
11942 <th>
11943                 <p>
11944                   Microsoft Visual C++ version 12.0<br> Win32<br> double
11945                 </p>
11946               </th>
11947 <th>
11948                 <p>
11949                   GNU C++ version 5.1.0<br> linux<br> double
11950                 </p>
11951               </th>
11952 <th>
11953                 <p>
11954                   GNU C++ version 5.1.0<br> linux<br> long double
11955                 </p>
11956               </th>
11957 <th>
11958                 <p>
11959                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
11960                 </p>
11961               </th>
11962 </tr></thead>
11963 <tbody><tr>
11964 <td>
11965                 <p>
11966                   tgamma ratios
11967                 </p>
11968               </td>
11969 <td>
11970                 <p>
11971                   <span class="blue">Max = 3.66&#949; (Mean = 1.27&#949;)</span>
11972                 </p>
11973               </td>
11974 <td>
11975                 <p>
11976                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
11977                 </p>
11978               </td>
11979 <td>
11980                 <p>
11981                   <span class="blue">Max = 3.09&#949; (Mean = 1.15&#949;)</span>
11982                 </p>
11983               </td>
11984 <td>
11985                 <p>
11986                   <span class="blue">Max = 174&#949; (Mean = 61.2&#949;)</span>
11987                 </p>
11988               </td>
11989 </tr></tbody>
11990 </table></div>
11991 </div>
11992 <br class="table-break"><div class="table">
11993 <a name="math_toolkit.logs_and_tables.all_table.table_trigamma"></a><p class="title"><b>Table&#160;17.96.&#160;Error rates for trigamma</b></p>
11994 <div class="table-contents"><table class="table" summary="Error rates for trigamma">
11995 <colgroup>
11996 <col>
11997 <col>
11998 <col>
11999 <col>
12000 <col>
12001 </colgroup>
12002 <thead><tr>
12003 <th>
12004               </th>
12005 <th>
12006                 <p>
12007                   Microsoft Visual C++ version 12.0<br> Win32<br> double
12008                 </p>
12009               </th>
12010 <th>
12011                 <p>
12012                   GNU C++ version 5.1.0<br> linux<br> double
12013                 </p>
12014               </th>
12015 <th>
12016                 <p>
12017                   GNU C++ version 5.1.0<br> linux<br> long double
12018                 </p>
12019               </th>
12020 <th>
12021                 <p>
12022                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
12023                 </p>
12024               </th>
12025 </tr></thead>
12026 <tbody><tr>
12027 <td>
12028                 <p>
12029                   Mathematica Data
12030                 </p>
12031               </td>
12032 <td>
12033                 <p>
12034                   <span class="blue">Max = 1&#949; (Mean = 0.382&#949;)</span>
12035                 </p>
12036               </td>
12037 <td>
12038                 <p>
12039                   <span class="blue">Max = 0.998&#949; (Mean = 0.105&#949;)</span><br> <br>
12040                   (<span class="emphasis"><em>Rmath 3.0.2:</em></span> Max = 1.34e+04&#949; (Mean = 1.51e+03&#949;))<br>
12041                   (<span class="emphasis"><em>GSL 1.16:</em></span> Max = 1.34e+04&#949; (Mean = 1.49e+03&#949;))
12042                 </p>
12043               </td>
12044 <td>
12045                 <p>
12046                   <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
12047                 </p>
12048               </td>
12049 <td>
12050                 <p>
12051                   <span class="blue">Max = 1.28&#949; (Mean = 0.447&#949;)</span>
12052                 </p>
12053               </td>
12054 </tr></tbody>
12055 </table></div>
12056 </div>
12057 <br class="table-break"><div class="table">
12058 <a name="math_toolkit.logs_and_tables.all_table.table_zeta"></a><p class="title"><b>Table&#160;17.97.&#160;Error rates for zeta</b></p>
12059 <div class="table-contents"><table class="table" summary="Error rates for zeta">
12060 <colgroup>
12061 <col>
12062 <col>
12063 <col>
12064 <col>
12065 <col>
12066 </colgroup>
12067 <thead><tr>
12068 <th>
12069               </th>
12070 <th>
12071                 <p>
12072                   Microsoft Visual C++ version 12.0<br> Win32<br> double
12073                 </p>
12074               </th>
12075 <th>
12076                 <p>
12077                   GNU C++ version 5.1.0<br> linux<br> double
12078                 </p>
12079               </th>
12080 <th>
12081                 <p>
12082                   GNU C++ version 5.1.0<br> linux<br> long double
12083                 </p>
12084               </th>
12085 <th>
12086                 <p>
12087                   Sun compiler version 0x5130<br> Sun Solaris<br> long double
12088                 </p>
12089               </th>
12090 </tr></thead>
12091 <tbody>
12092 <tr>
12093 <td>
12094                 <p>
12095                   Zeta: Random values greater than 1
12096                 </p>
12097               </td>
12098 <td>
12099                 <p>
12100                   <span class="blue">Max = 0.836&#949; (Mean = 0.093&#949;)</span>
12101                 </p>
12102               </td>
12103 <td>
12104                 <p>
12105                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12106                   1.16:</em></span> Max = 8.69&#949; (Mean = 1.03&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
12107                   <span class="red">Max = 4.49e+33&#949; (Mean = 6.85e+32&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Random_values_greater_than_1">And
12108                   other failures.</a>)</span>
12109                 </p>
12110               </td>
12111 <td>
12112                 <p>
12113                   <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span><br>
12114                   <br> (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 5.45&#949; (Mean
12115                   = 1&#949;))
12116                 </p>
12117               </td>
12118 <td>
12119                 <p>
12120                   <span class="blue">Max = 0.846&#949; (Mean = 0.0743&#949;)</span>
12121                 </p>
12122               </td>
12123 </tr>
12124 <tr>
12125 <td>
12126                 <p>
12127                   Zeta: Random values less than 1
12128                 </p>
12129               </td>
12130 <td>
12131                 <p>
12132                   <span class="blue">Max = 7.03&#949; (Mean = 2.98&#949;)</span>
12133                 </p>
12134               </td>
12135 <td>
12136                 <p>
12137                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12138                   1.16:</em></span> Max = 137&#949; (Mean = 13.8&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
12139                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Random_values_less_than_1">And
12140                   other failures.</a>)</span>
12141                 </p>
12142               </td>
12143 <td>
12144                 <p>
12145                   <span class="blue">Max = 7.03&#949; (Mean = 2.71&#949;)</span><br> <br>
12146                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 538&#949; (Mean = 59.3&#949;))
12147                 </p>
12148               </td>
12149 <td>
12150                 <p>
12151                   <span class="blue">Max = 70.1&#949; (Mean = 17.1&#949;)</span>
12152                 </p>
12153               </td>
12154 </tr>
12155 <tr>
12156 <td>
12157                 <p>
12158                   Zeta: Values close to and greater than 1
12159                 </p>
12160               </td>
12161 <td>
12162                 <p>
12163                   <span class="blue">Max = 0.994&#949; (Mean = 0.421&#949;)</span>
12164                 </p>
12165               </td>
12166 <td>
12167                 <p>
12168                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12169                   1.16:</em></span> Max = 7.73&#949; (Mean = 4.07&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
12170                   <span class="red">Max = 6.77e+15&#949; (Mean = 1.52e+15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Values_close_to_and_greater_than_1">And
12171                   other failures.</a>)</span>
12172                 </p>
12173               </td>
12174 <td>
12175                 <p>
12176                   <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span><br> <br>
12177                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.9e+06&#949; (Mean = 5.11e+05&#949;))
12178                 </p>
12179               </td>
12180 <td>
12181                 <p>
12182                   <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span>
12183                 </p>
12184               </td>
12185 </tr>
12186 <tr>
12187 <td>
12188                 <p>
12189                   Zeta: Values close to and less than 1
12190                 </p>
12191               </td>
12192 <td>
12193                 <p>
12194                   <span class="blue">Max = 0.991&#949; (Mean = 0.375&#949;)</span>
12195                 </p>
12196               </td>
12197 <td>
12198                 <p>
12199                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12200                   1.16:</em></span> Max = 0.991&#949; (Mean = 0.28&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
12201                   <span class="red">Max = 8.66e+15&#949; (Mean = 1.9e+15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Values_close_to_and_less_than_1">And
12202                   other failures.</a>)</span>
12203                 </p>
12204               </td>
12205 <td>
12206                 <p>
12207                   <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span><br> <br>
12208                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 8.53e+06&#949; (Mean =
12209                   1.87e+06&#949;))
12210                 </p>
12211               </td>
12212 <td>
12213                 <p>
12214                   <span class="blue">Max = 0.998&#949; (Mean = 0.568&#949;)</span>
12215                 </p>
12216               </td>
12217 </tr>
12218 <tr>
12219 <td>
12220                 <p>
12221                   Zeta: Integer arguments
12222                 </p>
12223               </td>
12224 <td>
12225                 <p>
12226                   <span class="blue">Max = 6.5&#949; (Mean = 2.17&#949;)</span>
12227                 </p>
12228               </td>
12229 <td>
12230                 <p>
12231                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
12232                   1.16:</em></span> Max = 3.75&#949; (Mean = 1.1&#949;))<br> (<span class="emphasis"><em>Cephes:</em></span>
12233                   <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_5_1_0_linux_double_zeta_Cephes_Zeta_Integer_arguments">And
12234                   other failures.</a>)</span>
12235                 </p>
12236               </td>
12237 <td>
12238                 <p>
12239                   <span class="blue">Max = 9&#949; (Mean = 3.06&#949;)</span><br> <br>
12240                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 70.3&#949; (Mean = 17.4&#949;))
12241                 </p>
12242               </td>
12243 <td>
12244                 <p>
12245                   <span class="blue">Max = 21&#949; (Mean = 7.13&#949;)</span>
12246                 </p>
12247               </td>
12248 </tr>
12249 </tbody>
12250 </table></div>
12251 </div>
12252 <br class="table-break">
12253 </div>
12254 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
12255 <td align="left"></td>
12256 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
12257       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
12258       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
12259       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
12260         Distributed under the Boost Software License, Version 1.0. (See accompanying
12261         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>)
12262       </p>
12263 </div></td>
12264 </tr></table>
12265 <hr>
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