ceph/src/boost/libs/math/test/test_tr1.cpp

   1 //  (C) Copyright John Maddock 2008.
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 #define BOOST_TEST_MAIN
   7 #include <boost/test/unit_test.hpp>
   8 #include <boost/test/floating_point_comparison.hpp>
   9 #include <boost/math/tools/precision.hpp>
  10 #include <math.h>  // ldexpf
  11 #include <iostream>
  12 #include <iomanip>
  13
  14 #ifdef TEST_STD
  15 #include <cmath>
  16 namespace tr1 = std::tr1;
  17 #else
  18 #include <boost/math/tr1.hpp>
  19 namespace tr1 = boost::math::tr1;
  20 #endif
  21
  22 #ifdef _MSC_VER
  23 #  pragma warning (disable : 4100) // unreferenced formal parameter
  24 // Can't just comment parameter out because reference or not depends on macro define.
  25 #endif
  26
  27 void test_values(float, const char* name)
  28 {
  29    std::cout << "Testing type " << name << std::endl;
  30 #ifndef TEST_LD
  31    //
  32    // First the C99 math functions:
  33    //
  34    float eps = boost::math::tools::epsilon<float>();
  35    BOOST_CHECK_CLOSE(tr1::acoshf(std::cosh(0.5f)), 0.5f, 5000 * eps);
  36    BOOST_CHECK_CLOSE(tr1::asinhf(std::sinh(0.5f)), 0.5f, 5000 * eps);
  37    BOOST_CHECK_CLOSE(tr1::atanhf(std::tanh(0.5f)), 0.5f, 5000 * eps);
  38
  39    BOOST_CHECK_CLOSE(tr1::cbrtf(1.5f * 1.5f * 1.5f), 1.5f, 5000 * eps);
  40
  41    BOOST_CHECK(tr1::copysignf(1.0f, 1.0f) == 1.0f);
  42    BOOST_CHECK(tr1::copysignf(1.0f, -1.0f) == -1.0f);
  43    BOOST_CHECK(tr1::copysignf(-1.0f, 1.0f) == 1.0f);
  44    BOOST_CHECK(tr1::copysignf(-1.0f, -1.0f) == -1.0f);
  45
  46    BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(0.125)), static_cast<float>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
  47    BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(0.5)), static_cast<float>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
  48    BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(1)), static_cast<float>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
  49    BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(5)), static_cast<float>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
  50    BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(-0.125)), static_cast<float>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
  51    BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(-0.5)), static_cast<float>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
  52    BOOST_CHECK_CLOSE(tr1::erfcf(static_cast<float>(0)), static_cast<float>(1), eps * 1000);
  53
  54    BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(0.125)), static_cast<float>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
  55    BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(0.5)), static_cast<float>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
  56    BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(1)), static_cast<float>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
  57    BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(5)), static_cast<float>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
  58    BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(-0.125)), static_cast<float>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
  59    BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(-0.5)), static_cast<float>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
  60    BOOST_CHECK_CLOSE(tr1::erff(static_cast<float>(0)), static_cast<float>(0), eps * 1000);
  61
  62    BOOST_CHECK_CLOSE(tr1::log1pf(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
  63    BOOST_CHECK_CLOSE(tr1::expm1f(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
  64    BOOST_CHECK_CLOSE(tr1::log1pf(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
  65    BOOST_CHECK_CLOSE(tr1::expm1f(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
  66
  67    BOOST_CHECK_EQUAL(tr1::fmaxf(0.1f, -0.1f), 0.1f);
  68    BOOST_CHECK_EQUAL(tr1::fminf(0.1f, -0.1f), -0.1f);
  69
  70    BOOST_CHECK_CLOSE(tr1::hypotf(1.0f, 3.0f), std::sqrt(10.0f), eps * 500);
  71
  72    BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(3.5)), static_cast<float>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
  73    BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(0.125)), static_cast<float>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
  74    BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(-0.125)), static_cast<float>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
  75    BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(-3.125)), static_cast<float>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
  76    BOOST_CHECK_CLOSE(tr1::lgammaf(static_cast<float>(-53249.0/1024)), static_cast<float>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
  77
  78    BOOST_CHECK_CLOSE(tr1::tgammaf(static_cast<float>(3.5)), static_cast<float>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
  79    BOOST_CHECK_CLOSE(tr1::tgammaf(static_cast<float>(0.125)), static_cast<float>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
  80    BOOST_CHECK_CLOSE(tr1::tgammaf(static_cast<float>(-0.125)), static_cast<float>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
  81    BOOST_CHECK_CLOSE(tr1::tgammaf(static_cast<float>(-3.125)), static_cast<float>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
  82
  83 #ifdef BOOST_HAS_LONG_LONG
  84    BOOST_CHECK(tr1::llroundf(2.5f) == 3LL);
  85    BOOST_CHECK(tr1::llroundf(2.25f) == 2LL);
  86 #endif
  87    BOOST_CHECK(tr1::lroundf(2.5f) == 3L);
  88    BOOST_CHECK(tr1::lroundf(2.25f) == 2L);
  89    BOOST_CHECK(tr1::roundf(2.5f) == 3.0f);
  90    BOOST_CHECK(tr1::roundf(2.25f) == 2.0f);
  91
  92    BOOST_CHECK(tr1::nextafterf(1.0f, 2.0f) > 1.0f);
  93    BOOST_CHECK(tr1::nextafterf(1.0f, -2.0f) < 1.0f);
  94    BOOST_CHECK(tr1::nextafterf(tr1::nextafterf(1.0f, 2.0f), -2.0f) == 1.0f);
  95    BOOST_CHECK(tr1::nextafterf(tr1::nextafterf(1.0f, -2.0f), 2.0f) == 1.0f);
  96    BOOST_CHECK(tr1::nextafterf(1.0f, 2.0f) > 1.0f);
  97    BOOST_CHECK(tr1::nextafterf(1.0f, -2.0f) < 1.0f);
  98    BOOST_CHECK(tr1::nextafterf(tr1::nextafterf(1.0f, 2.0f), -2.0f) == 1.0f);
  99    BOOST_CHECK(tr1::nextafterf(tr1::nextafterf(1.0f, -2.0f), 2.0f) == 1.0f);
 100
 101    BOOST_CHECK(tr1::truncf(2.5f) == 2.0f);
 102    BOOST_CHECK(tr1::truncf(2.25f) == 2.0f);
 103
 104    //
 105    // And again but without the "f" suffix on the function names:
 106    //
 107    BOOST_CHECK_CLOSE(tr1::acosh(std::cosh(0.5f)), 0.5f, 5000 * eps);
 108    BOOST_CHECK_CLOSE(tr1::asinh(std::sinh(0.5f)), 0.5f, 5000 * eps);
 109    BOOST_CHECK_CLOSE(tr1::atanh(std::tanh(0.5f)), 0.5f, 5000 * eps);
 110
 111    BOOST_CHECK_CLOSE(tr1::cbrt(1.5f * 1.5f * 1.5f), 1.5f, 5000 * eps);
 112
 113    BOOST_CHECK(tr1::copysign(1.0f, 1.0f) == 1.0f);
 114    BOOST_CHECK(tr1::copysign(1.0f, -1.0f) == -1.0f);
 115    BOOST_CHECK(tr1::copysign(-1.0f, 1.0f) == 1.0f);
 116    BOOST_CHECK(tr1::copysign(-1.0f, -1.0f) == -1.0f);
 117
 118    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0.125)), static_cast<float>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
 119    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0.5)), static_cast<float>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
 120    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(1)), static_cast<float>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
 121    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(5)), static_cast<float>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
 122    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(-0.125)), static_cast<float>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
 123    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(-0.5)), static_cast<float>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
 124    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<float>(0)), static_cast<float>(1), eps * 1000);
 125
 126    BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0.125)), static_cast<float>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
 127    BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0.5)), static_cast<float>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
 128    BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(1)), static_cast<float>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
 129    BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(5)), static_cast<float>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
 130    BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(-0.125)), static_cast<float>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
 131    BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(-0.5)), static_cast<float>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
 132    BOOST_CHECK_CLOSE(tr1::erf(static_cast<float>(0)), static_cast<float>(0), eps * 1000);
 133
 134    BOOST_CHECK_CLOSE(tr1::log1p(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
 135    BOOST_CHECK_CLOSE(tr1::expm1(static_cast<float>(0.582029759883880615234375e0)), static_cast<float>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
 136    BOOST_CHECK_CLOSE(tr1::log1p(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
 137    BOOST_CHECK_CLOSE(tr1::expm1(static_cast<float>(-0.2047410048544406890869140625e-1)), static_cast<float>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
 138
 139    BOOST_CHECK_EQUAL(tr1::fmax(0.1f, -0.1f), 0.1f);
 140    BOOST_CHECK_EQUAL(tr1::fmin(0.1f, -0.1f), -0.1f);
 141
 142    BOOST_CHECK_CLOSE(tr1::hypot(1.0f, 3.0f), std::sqrt(10.0f), eps * 500);
 143
 144    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(3.5)), static_cast<float>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
 145    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(0.125)), static_cast<float>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
 146    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-0.125)), static_cast<float>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
 147    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-3.125)), static_cast<float>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
 148    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<float>(-53249.0/1024)), static_cast<float>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
 149
 150    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(3.5)), static_cast<float>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
 151    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(0.125)), static_cast<float>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
 152    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(-0.125)), static_cast<float>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
 153    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<float>(-3.125)), static_cast<float>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
 154
 155 #ifdef BOOST_HAS_LONG_LONG
 156    BOOST_CHECK(tr1::llround(2.5f) == 3LL);
 157    BOOST_CHECK(tr1::llround(2.25f) == 2LL);
 158 #endif
 159    BOOST_CHECK(tr1::lround(2.5f) == 3L);
 160    BOOST_CHECK(tr1::lround(2.25f) == 2L);
 161    BOOST_CHECK(tr1::round(2.5f) == 3.0f);
 162    BOOST_CHECK(tr1::round(2.25f) == 2.0f);
 163
 164    BOOST_CHECK(tr1::nextafter(1.0f, 2.0f) > 1.0f);
 165    BOOST_CHECK(tr1::nextafter(1.0f, -2.0f) < 1.0f);
 166    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, 2.0f), -2.0f) == 1.0f);
 167    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, -2.0f), 2.0f) == 1.0f);
 168    BOOST_CHECK(tr1::nextafter(1.0f, 2.0f) > 1.0f);
 169    BOOST_CHECK(tr1::nextafter(1.0f, -2.0f) < 1.0f);
 170    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, 2.0f), -2.0f) == 1.0f);
 171    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0f, -2.0f), 2.0f) == 1.0f);
 172
 173    BOOST_CHECK(tr1::trunc(2.5f) == 2.0f);
 174    BOOST_CHECK(tr1::trunc(2.25f) == 2.0f);
 175
 176    //
 177    // Now for the TR1 math functions:
 178    //
 179    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(4, 5, static_cast<float>(0.5L)), static_cast<float>(88.31510416666666666666666666666666666667L), eps * 100);
 180    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 0, static_cast<float>(2.5L)), static_cast<float>(-0.8802526766660982969576719576719576719577L), eps * 100);
 181    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 1, static_cast<float>(4.5L)), static_cast<float>(1.564311458042689732142857142857142857143L), eps * 100);
 182    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 6, static_cast<float>(8.5L)), static_cast<float>(20.51596541066649098875661375661375661376L), eps * 100);
 183    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(10, 12, static_cast<float>(12.5L)), static_cast<float>(-199.5560968456234671241181657848324514991L), eps * 100);
 184    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerref(50, 40, static_cast<float>(12.5L)), static_cast<float>(-4.996769495006119488583146995907246595400e16L), eps * 100);
 185
 186    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
 187    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(4, static_cast<float>(0.5L)), static_cast<float>(-0.3307291666666666666666666666666666666667L), eps * 100);
 188    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(7, static_cast<float>(0.5L)), static_cast<float>(-0.5183392237103174603174603174603174603175L), eps * 100);
 189    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(20, static_cast<float>(0.5L)), static_cast<float>(0.3120174870800154148915399248893113634676L), eps * 100);
 190    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(50, static_cast<float>(0.5L)), static_cast<float>(-0.3181388060269979064951118308575628226834L), eps * 100);
 191
 192    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(1, static_cast<float>(-0.5L)), static_cast<float>(1.5L), eps * 100);
 193    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(4, static_cast<float>(-0.5L)), static_cast<float>(3.835937500000000000000000000000000000000L), eps * 100);
 194    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(7, static_cast<float>(-0.5L)), static_cast<float>(7.950934709821428571428571428571428571429L), eps * 100);
 195    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(20, static_cast<float>(-0.5L)), static_cast<float>(76.12915699869631476833699787070874048223L), eps * 100);
 196    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(50, static_cast<float>(-0.5L)), static_cast<float>(2307.428631277506570629232863491518399720L), eps * 100);
 197
 198    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(1, static_cast<float>(4.5L)), static_cast<float>(-3.500000000000000000000000000000000000000L), eps * 100);
 199    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(4, static_cast<float>(4.5L)), static_cast<float>(0.08593750000000000000000000000000000000000L), eps * 100);
 200    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(7, static_cast<float>(4.5L)), static_cast<float>(-1.036928013392857142857142857142857142857L), eps * 100);
 201    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(20, static_cast<float>(4.5L)), static_cast<float>(1.437239150257817378525582974722170737587L), eps * 100);
 202    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerref(50, static_cast<float>(4.5L)), static_cast<float>(-0.7795068145562651416494321484050019245248L), eps * 100);
 203
 204    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(4, 2, static_cast<float>(0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
 205    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(7, 5, static_cast<float>(0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
 206    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(4, 2, static_cast<float>(-0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
 207    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendref(7, 5, static_cast<float>(-0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
 208
 209    BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
 210    BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(4, static_cast<float>(0.5L)), static_cast<float>(-0.2890625000000000000000000000000000000000L), eps * 100);
 211    BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(7, static_cast<float>(0.5L)), static_cast<float>(0.2231445312500000000000000000000000000000L), eps * 100);
 212    BOOST_CHECK_CLOSE_FRACTION(tr1::legendref(40, static_cast<float>(0.5L)), static_cast<float>(-0.09542943523261546936538467572384923220258L), eps * 100);
 213
 214    float sv = eps / 1024;
 215    BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(1), static_cast<float>(1)), static_cast<float>(1), eps * 20 * 100);
 216    BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(1), static_cast<float>(4)), static_cast<float>(0.25), eps * 20 * 100);
 217    BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), static_cast<float>(1)), static_cast<float>(0.25), eps * 20 * 100);
 218    BOOST_CHECK_CLOSE(tr1::betaf(sv, static_cast<float>(4)), 1/sv, eps * 20 * 100);
 219    BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), sv), 1/sv, eps * 20 * 100);
 220    BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(4), static_cast<float>(20)), static_cast<float>(0.00002823263692828910220214568040654997176736L), eps * 20 * 100);
 221    BOOST_CHECK_CLOSE(tr1::betaf(static_cast<float>(0.0125L), static_cast<float>(0.000023L)), static_cast<float>(43558.24045647538375006349016083320744662L), eps * 20 * 100);
 222
 223    BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
 224    BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(0.125)), static_cast<float>(1.5769867712158131421244030532288080803822271060839), eps * 5000);
 225    BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(0.25)), static_cast<float>(1.5962422221317835101489690714979498795055744578951), eps * 5000);
 226    BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(300)/1024), static_cast<float>(1.6062331054696636704261124078746600894998873503208), eps * 5000);
 227    BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(400)/1024), static_cast<float>(1.6364782007562008756208066125715722889067992997614), eps * 5000);
 228    BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(-0.5)), static_cast<float>(1.6857503548125960428712036577990769895008008941411), eps * 5000);
 229    BOOST_CHECK_CLOSE(tr1::comp_ellint_1f(static_cast<float>(-0.75)), static_cast<float>(1.9109897807518291965531482187613425592531451316788), eps * 5000);
 230
 231    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-1)), static_cast<float>(1), eps * 5000);
 232    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
 233    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(100) / 1024), static_cast<float>(1.5670445330545086723323795143598956428788609133377), eps * 5000);
 234    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(200) / 1024), static_cast<float>(1.5557071588766556854463404816624361127847775545087), eps * 5000);
 235    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(300) / 1024), static_cast<float>(1.5365278991162754883035625322482669608948678755743), eps * 5000);
 236    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(400) / 1024), static_cast<float>(1.5090417763083482272165682786143770446401437564021), eps * 5000);
 237    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-0.5)), static_cast<float>(1.4674622093394271554597952669909161360253617523272), eps * 5000);
 238    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-600) / 1024), static_cast<float>(1.4257538571071297192428217218834579920545946473778), eps * 5000);
 239    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-800) / 1024), static_cast<float>(1.2927868476159125056958680222998765985004489572909), eps * 5000);
 240    BOOST_CHECK_CLOSE(tr1::comp_ellint_2f(static_cast<float>(-900) / 1024), static_cast<float>(1.1966864890248739524112920627353824133420353430982), eps * 5000);
 241
 242    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0.2), static_cast<float>(0)), static_cast<float>(1.586867847454166237308008033828114192951), eps * 5000);
 243    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0.4), static_cast<float>(0)), static_cast<float>(1.639999865864511206865258329748601457626), eps * 5000);
 244    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(1.57079632679489661923132169163975144209858469968755291048747), eps * 5000);
 245    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(2.221441469079183123507940495030346849307), eps * 5000);
 246    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(0.3), static_cast<float>(-4)), static_cast<float>(0.712708870925620061597924858162260293305195624270730660081949), eps * 5000);
 247    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(-0.5), static_cast<float>(-1e+05)), static_cast<float>(0.00496944596485066055800109163256108604615568144080386919012831), eps * 5000);
 248    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(-0.75), static_cast<float>(-1e+10)), static_cast<float>(0.0000157080225184890546939710019277357161497407143903832703317801), eps * 5000);
 249    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(-0.875), static_cast<float>(1) / 1024), static_cast<float>(2.18674503176462374414944618968850352696579451638002110619287), eps * 5000);
 250    BOOST_CHECK_CLOSE(tr1::comp_ellint_3f(static_cast<float>(-0.875), static_cast<float>(1023)/1024), static_cast<float>(101.045289804941384100960063898569538919135722087486350366997), eps * 5000);
 251
 252    BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(2.25), static_cast<float>(1)/(1024*1024)), static_cast<float>(2.34379212133481347189068464680335815256364262507955635911656e-15), eps * 5000);
 253    BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(0.0583514045989371500460946536220735787163510569634133670181210), eps * 5000);
 254    BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-5) + static_cast<float>(1)/1024, static_cast<float>(2.125)), static_cast<float>(0.0267920938009571023702933210070984416052633027166975342895062), eps * 5000);
 255    BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(597.577606961369169607937419869926705730305175364662688426534), eps * 5000);
 256    BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474005665181350367684623930576333542989766867888186478185e35), eps * 5000);
 257    BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(50)), static_cast<float>(1.07153277202900671531087024688681954238311679648319534644743e20), eps * 5000);
 258    BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694757392660413922181531984160871678224178890247540320), eps * 5000);
 259    BOOST_CHECK_CLOSE(tr1::cyl_bessel_if(static_cast<float>(-144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694672763190927440969155740243346136463461655104698748), eps * 5000);
 260
 261    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(2457)/1024, static_cast<float>(1)/1024), static_cast<float>(3.80739920118603335646474073457326714709615200130620574875292e-9), eps * 5000);
 262    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(0.0281933076257506091621579544064767140470089107926550720453038), eps * 5000);
 263    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-5.5), static_cast<float>(3217)/1024), static_cast<float>(-2.55820064470647911823175836997490971806135336759164272675969), eps * 5000);
 264    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(2.449843111985605522111159013846599118397e-03), eps * 5000);
 265    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.5), static_cast<float>(1e+04)), static_cast<float>(0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
 266    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.5), static_cast<float>(1e+06)), static_cast<float>(-0.000747424248595630177396350688505919533097973148718960064663632), eps * 5000);
 267    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.125), static_cast<float>(1e+06)), static_cast<float>(-0.000776600124835704280633640911329691642748783663198207360238214), eps * 5000);
 268    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(5.875), static_cast<float>(1e+06)), static_cast<float>(-0.000466322721115193071631008581529503095819705088484386434589780), eps * 5000);
 269    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(0.5), static_cast<float>(101)), static_cast<float>(0.0358874487875643822020496677692429287863419555699447066226409), eps * 5000);
 270    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(0.00244984311198560552211115901384659911839737686676766460822577), eps * 5000);
 271    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-5.5), static_cast<float>(1e+06)), static_cast<float>(0.000279243200433579511095229508894156656558211060453622750659554), eps * 5000);
 272    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-0.5), static_cast<float>(101)), static_cast<float>(0.0708184798097594268482290389188138201440114881159344944791454), eps * 5000);
 273    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474013160494695750009004222225969090304185981836460288562e35), eps * 5000);
 274    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(15)), static_cast<float>(-0.0902239288885423309568944543848111461724911781719692852541489), eps * 5000);
 275    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547064914615137807616774867984047583596945624129838091326863), eps * 5000);
 276    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(10486074) / (1024*1024), static_cast<float>(2e+04)), static_cast<float>(-0.00556783614400875611650958980796060611309029233226596737701688), eps * 5000);
 277    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547613660316806551338637153942604550779513947674222863858713), eps * 5000);
 278
 279    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(0.5), static_cast<float>(0.875)), static_cast<float>(0.558532231646608646115729767013630967055657943463362504577189), eps * 5000);
 280    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(0.5), static_cast<float>(1.125)), static_cast<float>(0.383621010650189547146769320487006220295290256657827220786527), eps * 5000);
 281    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(2.25), static_cast<float>(std::ldexp(1.0, -30))), static_cast<float>(5.62397392719283271332307799146649700147907612095185712015604e20), eps * 5000);
 282    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(1.30623288775012596319554857587765179889689223531159532808379), eps * 5000);
 283    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(0.0000733045300798502164644836879577484533096239574909573072142667), eps * 5000);
 284    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(-5.5), static_cast<float>(100)), static_cast<float>(5.41274555306792267322084448693957747924412508020839543293369e-45), eps * 5000);
 285    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(10240)/1024, static_cast<float>(1)/1024), static_cast<float>(2.35522579263922076203415803966825431039900000000993410734978e38), eps * 5000);
 286    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(10240)/1024, static_cast<float>(10)), static_cast<float>(0.00161425530039067002345725193091329085443750382929208307802221), eps * 5000);
 287    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(144793)/1024, static_cast<float>(100)), static_cast<float>(1.39565245860302528069481472855619216759142225046370312329416e-6), eps * 5000);
 288    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kf(static_cast<float>(144793)/1024, static_cast<float>(200)), static_cast<float>(9.11950412043225432171915100042647230802198254567007382956336e-68), eps * 5000);
 289
 290    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(0.5), static_cast<float>(1) / (1024*1024)), static_cast<float>(-817.033790261762580469303126467917092806755460418223776544122), eps * 5000);
 291    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(-2.61489440328417468776474188539366752698192046890955453259866), eps * 5000);
 292    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-5.5), static_cast<float>(3.125)), static_cast<float>(-0.0274994493896489729948109971802244976377957234563871795364056), eps * 5000);
 293    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(-0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
 294    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(-1.50382374389531766117868938966858995093408410498915220070230e38), eps * 5000);
 295    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(0.0583041891319026009955779707640455341990844522293730214223545), eps * 5000);
 296    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(141.75), static_cast<float>(1e+02)), static_cast<float>(-5.38829231428696507293191118661269920130838607482708483122068e9), eps * 5000);
 297    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(141.75), static_cast<float>(2e+04)), static_cast<float>(-0.00376577888677186194728129112270988602876597726657372330194186), eps * 5000);
 298    BOOST_CHECK_CLOSE(tr1::cyl_neumannf(static_cast<float>(-141.75), static_cast<float>(1e+02)), static_cast<float>(-3.81009803444766877495905954105669819951653361036342457919021e9), eps * 5000);
 299
 300    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(0), eps * 5000);
 301    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0), static_cast<float>(-10)), static_cast<float>(-10), eps * 5000);
 302    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(-1), static_cast<float>(-1)), static_cast<float>(-1.2261911708835170708130609674719067527242483502207), eps * 5000);
 303    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.875), static_cast<float>(-4)), static_cast<float>(-5.3190556182262405182189463092940736859067548232647), eps * 5000);
 304    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(-0.625), static_cast<float>(8)), static_cast<float>(9.0419973860310100524448893214394562615252527557062), eps * 5000);
 305    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.875), static_cast<float>(1e-05)), static_cast<float>(0.000010000000000127604166668510945638036143355898993088), eps * 5000);
 306    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(10)/1024, static_cast<float>(1e+05)), static_cast<float>(100002.38431454899771096037307519328741455615271038), eps * 5000);
 307    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(1), static_cast<float>(1e-20)), static_cast<float>(1.0000000000000000000000000000000000000000166666667e-20), eps * 5000);
 308    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(1e-20), static_cast<float>(1e-20)), static_cast<float>(1.000000000000000e-20), eps * 5000);
 309    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(400)/1024, static_cast<float>(1e+20)), static_cast<float>(1.0418143796499216839719289963154558027005142709763e20), eps * 5000);
 310    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(2)), static_cast<float>(2.1765877052210673672479877957388515321497888026770), eps * 5000);
 311    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(4)), static_cast<float>(4.2543274975235836861894752787874633017836785640477), eps * 5000);
 312    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(6)), static_cast<float>(6.4588766202317746302999080620490579800463614807916), eps * 5000);
 313    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(10)), static_cast<float>(10.697409951222544858346795279378531495869386960090), eps * 5000);
 314    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(-2)), static_cast<float>(-2.1765877052210673672479877957388515321497888026770), eps * 5000);
 315    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(-4)), static_cast<float>(-4.2543274975235836861894752787874633017836785640477), eps * 5000);
 316    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(-6)), static_cast<float>(-6.4588766202317746302999080620490579800463614807916), eps * 5000);
 317    BOOST_CHECK_CLOSE(tr1::ellint_1f(static_cast<float>(0.5), static_cast<float>(-10)), static_cast<float>(-10.697409951222544858346795279378531495869386960090), eps * 5000);
 318
 319    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(0), eps * 5000);
 320    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(0), static_cast<float>(-10)), static_cast<float>(-10), eps * 5000);
 321    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(-1), static_cast<float>(-1)), static_cast<float>(-0.84147098480789650665250232163029899962256306079837), eps * 5000);
 322    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(900) / 1024, static_cast<float>(-4)), static_cast<float>(-3.1756145986492562317862928524528520686391383168377), eps * 5000);
 323    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(-600) / 1024, static_cast<float>(8)), static_cast<float>(7.2473147180505693037677015377802777959345489333465), eps * 5000);
 324    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(800) / 1024, static_cast<float>(1e-05)), static_cast<float>(9.999999999898274739584436515967055859383969942432E-6), eps * 5000);
 325    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(100) / 1024, static_cast<float>(1e+05)), static_cast<float>(99761.153306972066658135668386691227343323331995888), eps * 5000);
 326    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(-0.5), static_cast<float>(1e+10)), static_cast<float>(9.3421545766487137036576748555295222252286528414669e9), eps * 5000);
 327    BOOST_CHECK_CLOSE(tr1::ellint_2f(static_cast<float>(400) / 1024, ldexp(static_cast<float>(1), 66)), static_cast<float>(7.0886102721911705466476846969992069994308167515242e19), eps * 5000);
 328
 329    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1), static_cast<float>(-1)), static_cast<float>(-1.557407724654902230506974807458360173087), eps * 5000);
 330    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.4), static_cast<float>(0), static_cast<float>(-4)), static_cast<float>(-4.153623371196831087495427530365430979011), eps * 5000);
 331    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(-0.6), static_cast<float>(0), static_cast<float>(8)), static_cast<float>(8.935930619078575123490612395578518914416), eps * 5000);
 332    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.501246705365439492445236118603525029757890291780157969500480), eps * 5000);
 333    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.5), eps * 5000);
 334    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(-2), static_cast<float>(0.5)), static_cast<float>(0.437501067017546278595664813509803743009132067629603474488486), eps * 5000);
 335    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.25), static_cast<float>(0.5)), static_cast<float>(0.510269830229213412212501938035914557628394166585442994564135), eps * 5000);
 336    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.5)), static_cast<float>(0.533293253875952645421201146925578536430596894471541312806165), eps * 5000);
 337    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.75)), static_cast<float>(0.871827580412760575085768367421866079353646112288567703061975), eps * 5000);
 338    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1), static_cast<float>(0.25)), static_cast<float>(0.255341921221036266504482236490473678204201638800822621740476), eps * 5000);
 339    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(2), static_cast<float>(0.25)), static_cast<float>(0.261119051639220165094943572468224137699644963125853641716219), eps * 5000);
 340    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0), static_cast<float>(1023)/1024, static_cast<float>(1.5)), static_cast<float>(13.2821612239764190363647953338544569682942329604483733197131), eps * 5000);
 341    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(-1)), static_cast<float>(-1.228014414316220642611298946293865487807), eps * 5000);
 342    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(1e+10)), static_cast<float>(1.536591003599172091573590441336982730551e+10), eps * 5000);
 343    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.75), static_cast<float>(-1e+05), static_cast<float>(10)), static_cast<float>(0.0347926099493147087821620459290460547131012904008557007934290), eps * 5000);
 344    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(10)), static_cast<float>(0.000109956202759561502329123384755016959364346382187364656768212), eps * 5000);
 345    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1e+20)), static_cast<float>(1.00000626665567332602765201107198822183913978895904937646809e15), eps * 5000);
 346    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1608)/1024), static_cast<float>(0.0000157080616044072676127333183571107873332593142625043567690379), eps * 5000);
 347    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.875), 1-static_cast<float>(1) / 1024, static_cast<float>(1e+20)), static_cast<float>(6.43274293944380717581167058274600202023334985100499739678963e21), eps * 5000);
 348    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(50), static_cast<float>(0.1)), static_cast<float>(0.124573770342749525407523258569507331686458866564082916835900), eps * 5000);
 349    BOOST_CHECK_CLOSE(tr1::ellint_3f(static_cast<float>(0.25), static_cast<float>(1.125), static_cast<float>(1)), static_cast<float>(1.77299767784815770192352979665283069318388205110727241629752), eps * 5000);
 350
 351    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(1)/1024), static_cast<float>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000);
 352    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(0.125)), static_cast<float>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000);
 353    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(0.5)), static_cast<float>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000);
 354    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(1)), static_cast<float>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000);
 355    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(50.5)), static_cast<float>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000);
 356    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-1)/1024), static_cast<float>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000);
 357    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-0.125)), static_cast<float>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000);
 358    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-0.5)), static_cast<float>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000);
 359    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-1)), static_cast<float>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000);
 360    BOOST_CHECK_CLOSE(tr1::expintf(static_cast<float>(-50.5)), static_cast<float>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000);
 361
 362    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(0, static_cast<float>(1)), static_cast<float>(1.L), 100 * eps);
 363    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(1)), static_cast<float>(2.L), 100 * eps);
 364    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(2)), static_cast<float>(4.L), 100 * eps);
 365    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(10)), static_cast<float>(20), 100 * eps);
 366    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(100)), static_cast<float>(200), 100 * eps);
 367    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(1, static_cast<float>(1e6)), static_cast<float>(2e6), 100 * eps);
 368    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(30)), static_cast<float>(5.896624628001300E+17L), 100 * eps);
 369    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(1000)), static_cast<float>(1.023976960161280E+33L), 100 * eps);
 370    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
 371    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(10, static_cast<float>(-10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
 372    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-10)), static_cast<float>(-7.880000000000000E+3L), 100 * eps);
 373    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-1000)), static_cast<float>(-7.999988000000000E+9L), 100 * eps);
 374    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitef(3, static_cast<float>(-1000000)), static_cast<float>(-7.999999999988000E+18L), 100 * eps);
 375
 376    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0.125)), static_cast<float>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000);
 377    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1023) / static_cast<float>(1024)), static_cast<float>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000);
 378    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1025) / static_cast<float>(1024)), static_cast<float>(1024.5772867695045940578681624248887776501597556226L), eps * 5000);
 379    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0.5)), static_cast<float>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000);
 380    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(1.125)), static_cast<float>(8.5862412945105752999607544082693023591996301183069L), eps * 5000);
 381    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(2)), static_cast<float>(1.6449340668482264364724151666460251892189499012068L), eps * 5000);
 382    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(3.5)), static_cast<float>(1.1267338673170566464278124918549842722219969574036L), eps * 5000);
 383    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(4)), static_cast<float>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000);
 384    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(4 + static_cast<float>(1) / 1024), static_cast<float>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000);
 385    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(4.5)), static_cast<float>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000);
 386    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(6.5)), static_cast<float>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000);
 387    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(7.5)), static_cast<float>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000);
 388    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(8.125)), static_cast<float>(1.0037305205308161603183307711439385250181080293472L), eps * 5000);
 389    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(16.125)), static_cast<float>(1.0000140128224754088474783648500235958510030511915L), eps * 5000);
 390    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(0)), static_cast<float>(-0.5L), eps * 5000);
 391    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-0.125)), static_cast<float>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000);
 392    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-1)), static_cast<float>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000);
 393    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-2)), static_cast<float>(0L), eps * 5000);
 394    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-2.5)), static_cast<float>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000 * 3);
 395    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-3)), static_cast<float>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000);
 396    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-4)), static_cast<float>(0), eps * 5000);
 397    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-20)), static_cast<float>(0), eps * 5000 * 100);
 398    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-21)), static_cast<float>(-281.46014492753623188405797101449275362318840579710L), eps * 5000 * 100);
 399    BOOST_CHECK_CLOSE(tr1::riemann_zetaf(static_cast<float>(-30.125)), static_cast<float>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000 * 100);
 400
 401    BOOST_CHECK_CLOSE(tr1::sph_besself(0, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.9999657468461303487880990241993035937654e0),  eps * 5000 * 100);
 402    BOOST_CHECK_CLOSE(tr1::sph_besself(0, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.9999483203249623334100130061926184665364e0),  eps * 5000 * 100);
 403    BOOST_CHECK_CLOSE(tr1::sph_besself(2, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.1370120120703995134662099191103188366059e-4),  eps * 5000 * 100);
 404    BOOST_CHECK_CLOSE(tr1::sph_besself(2, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.2067173265753174063228459655801741280461e-4),  eps * 5000 * 100);
 405    BOOST_CHECK_CLOSE(tr1::sph_besself(7, static_cast<float>(0.1252804412841796875e3)), static_cast<float>(0.7887555711993028736906736576314283291289e-2),  eps * 5000 * 100);
 406    BOOST_CHECK_CLOSE(tr1::sph_besself(7, static_cast<float>(0.25554705810546875e3)), static_cast<float>(-0.1463292767579579943284849187188066532514e-2),  eps * 5000 * 100);
 407
 408    BOOST_CHECK_CLOSE(tr1::sph_neumannf(0, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.2249212131304610409189209411089291558038e1), eps * 5000 * 100);
 409    BOOST_CHECK_CLOSE(tr1::sph_neumannf(0, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1213309779166084571756446746977955970241e1),   eps * 5000 * 100);
 410    BOOST_CHECK_CLOSE(tr1::sph_neumannf(2, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.4541702641837159203058389758895634766256e2),   eps * 5000 * 100);
 411    BOOST_CHECK_CLOSE(tr1::sph_neumannf(2, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1156112621471167110574129561700037138981e2),   eps * 5000 * 100);
 412    BOOST_CHECK_CLOSE(tr1::sph_neumannf(10, static_cast<float>(0.1097540378570556640625e1)), static_cast<float>(-0.2427889658115064857278886600528596240123e9),   eps * 5000 * 100);
 413    BOOST_CHECK_CLOSE(tr1::sph_neumannf(10, static_cast<float>(0.30944411754608154296875e1)), static_cast<float>(-0.3394649246350136450439882104151313759251e4),   eps * 5000 * 100);
 414
 415    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendref(3, 2, static_cast<float>(0.5)), static_cast<float>(0.2061460599687871330692286791802688341213L), eps * 5000);
 416    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendref(40, 15, static_cast<float>(0.75)), static_cast<float>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000);
 417
 418    //
 419    // Now all over again but without the "f" suffix on the function names this time:
 420    //
 421    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(4, 5, static_cast<float>(0.5L)), static_cast<float>(88.31510416666666666666666666666666666667L), eps * 100);
 422    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 0, static_cast<float>(2.5L)), static_cast<float>(-0.8802526766660982969576719576719576719577L), eps * 100);
 423    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 1, static_cast<float>(4.5L)), static_cast<float>(1.564311458042689732142857142857142857143L), eps * 100);
 424    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 6, static_cast<float>(8.5L)), static_cast<float>(20.51596541066649098875661375661375661376L), eps * 100);
 425    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 12, static_cast<float>(12.5L)), static_cast<float>(-199.5560968456234671241181657848324514991L), eps * 100);
 426    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(50, 40, static_cast<float>(12.5L)), static_cast<float>(-4.996769495006119488583146995907246595400e16L), eps * 100);
 427
 428    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
 429    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(0.5L)), static_cast<float>(-0.3307291666666666666666666666666666666667L), eps * 100);
 430    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(0.5L)), static_cast<float>(-0.5183392237103174603174603174603174603175L), eps * 100);
 431    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(0.5L)), static_cast<float>(0.3120174870800154148915399248893113634676L), eps * 100);
 432    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(0.5L)), static_cast<float>(-0.3181388060269979064951118308575628226834L), eps * 100);
 433
 434    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(-0.5L)), static_cast<float>(1.5L), eps * 100);
 435    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(-0.5L)), static_cast<float>(3.835937500000000000000000000000000000000L), eps * 100);
 436    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(-0.5L)), static_cast<float>(7.950934709821428571428571428571428571429L), eps * 100);
 437    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(-0.5L)), static_cast<float>(76.12915699869631476833699787070874048223L), eps * 100);
 438    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(-0.5L)), static_cast<float>(2307.428631277506570629232863491518399720L), eps * 100);
 439
 440    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<float>(4.5L)), static_cast<float>(-3.500000000000000000000000000000000000000L), eps * 100);
 441    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<float>(4.5L)), static_cast<float>(0.08593750000000000000000000000000000000000L), eps * 100);
 442    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<float>(4.5L)), static_cast<float>(-1.036928013392857142857142857142857142857L), eps * 100);
 443    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<float>(4.5L)), static_cast<float>(1.437239150257817378525582974722170737587L), eps * 100);
 444    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<float>(4.5L)), static_cast<float>(-0.7795068145562651416494321484050019245248L), eps * 100);
 445
 446    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<float>(0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
 447    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<float>(0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
 448    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<float>(-0.5L)), static_cast<float>(4.218750000000000000000000000000000000000L), eps * 100);
 449    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<float>(-0.5L)), static_cast<float>(5696.789530152175143607977274672800795328L), eps * 100);
 450
 451    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(1, static_cast<float>(0.5L)), static_cast<float>(0.5L), eps * 100);
 452    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(4, static_cast<float>(0.5L)), static_cast<float>(-0.2890625000000000000000000000000000000000L), eps * 100);
 453    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(7, static_cast<float>(0.5L)), static_cast<float>(0.2231445312500000000000000000000000000000L), eps * 100);
 454    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(40, static_cast<float>(0.5L)), static_cast<float>(-0.09542943523261546936538467572384923220258L), eps * 100);
 455
 456    BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(1), static_cast<float>(1)), static_cast<float>(1), eps * 20 * 100);
 457    BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(1), static_cast<float>(4)), static_cast<float>(0.25), eps * 20 * 100);
 458    BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), static_cast<float>(1)), static_cast<float>(0.25), eps * 20 * 100);
 459    BOOST_CHECK_CLOSE(tr1::beta(sv, static_cast<float>(4)), 1/sv, eps * 20 * 100);
 460    BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), sv), 1/sv, eps * 20 * 100);
 461    BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(4), static_cast<float>(20)), static_cast<float>(0.00002823263692828910220214568040654997176736L), eps * 20 * 100);
 462    BOOST_CHECK_CLOSE(tr1::beta(static_cast<float>(0.0125L), static_cast<float>(0.000023L)), static_cast<float>(43558.24045647538375006349016083320744662L), eps * 20 * 100);
 463
 464    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
 465    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0.125)), static_cast<float>(1.5769867712158131421244030532288080803822271060839), eps * 5000);
 466    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(0.25)), static_cast<float>(1.5962422221317835101489690714979498795055744578951), eps * 5000);
 467    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(300)/1024), static_cast<float>(1.6062331054696636704261124078746600894998873503208), eps * 5000);
 468    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(400)/1024), static_cast<float>(1.6364782007562008756208066125715722889067992997614), eps * 5000);
 469    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(-0.5)), static_cast<float>(1.6857503548125960428712036577990769895008008941411), eps * 5000);
 470    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<float>(-0.75)), static_cast<float>(1.9109897807518291965531482187613425592531451316788), eps * 5000);
 471
 472    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-1)), static_cast<float>(1), eps * 5000);
 473    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(0)), static_cast<float>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
 474    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(100) / 1024), static_cast<float>(1.5670445330545086723323795143598956428788609133377), eps * 5000);
 475    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(200) / 1024), static_cast<float>(1.5557071588766556854463404816624361127847775545087), eps * 5000);
 476    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(300) / 1024), static_cast<float>(1.5365278991162754883035625322482669608948678755743), eps * 5000);
 477    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(400) / 1024), static_cast<float>(1.5090417763083482272165682786143770446401437564021), eps * 5000);
 478    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-0.5)), static_cast<float>(1.4674622093394271554597952669909161360253617523272), eps * 5000);
 479    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-600) / 1024), static_cast<float>(1.4257538571071297192428217218834579920545946473778), eps * 5000);
 480    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-800) / 1024), static_cast<float>(1.2927868476159125056958680222998765985004489572909), eps * 5000);
 481    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<float>(-900) / 1024), static_cast<float>(1.1966864890248739524112920627353824133420353430982), eps * 5000);
 482
 483    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.2), static_cast<float>(0)), static_cast<float>(1.586867847454166237308008033828114192951), eps * 5000);
 484    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.4), static_cast<float>(0)), static_cast<float>(1.639999865864511206865258329748601457626), eps * 5000);
 485    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(1.57079632679489661923132169163975144209858469968755291048747), eps * 5000);
 486    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(2.221441469079183123507940495030346849307), eps * 5000);
 487    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(0.3), static_cast<float>(-4)), static_cast<float>(0.712708870925620061597924858162260293305195624270730660081949), eps * 5000);
 488    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.5), static_cast<float>(-1e+05)), static_cast<float>(0.00496944596485066055800109163256108604615568144080386919012831), eps * 5000);
 489    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.75), static_cast<float>(-1e+10)), static_cast<float>(0.0000157080225184890546939710019277357161497407143903832703317801), eps * 5000);
 490    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.875), static_cast<float>(1) / 1024), static_cast<float>(2.18674503176462374414944618968850352696579451638002110619287), eps * 5000);
 491    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<float>(-0.875), static_cast<float>(1023)/1024), static_cast<float>(101.045289804941384100960063898569538919135722087486350366997), eps * 5000);
 492
 493    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(2.25), static_cast<float>(1)/(1024*1024)), static_cast<float>(2.34379212133481347189068464680335815256364262507955635911656e-15), eps * 5000);
 494    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(0.0583514045989371500460946536220735787163510569634133670181210), eps * 5000);
 495    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-5) + static_cast<float>(1)/1024, static_cast<float>(2.125)), static_cast<float>(0.0267920938009571023702933210070984416052633027166975342895062), eps * 5000);
 496    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(597.577606961369169607937419869926705730305175364662688426534), eps * 5000);
 497    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474005665181350367684623930576333542989766867888186478185e35), eps * 5000);
 498    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-10486074)/(1024*1024), static_cast<float>(50)), static_cast<float>(1.07153277202900671531087024688681954238311679648319534644743e20), eps * 5000);
 499    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694757392660413922181531984160871678224178890247540320), eps * 5000);
 500    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<float>(-144794)/1024, static_cast<float>(100)), static_cast<float>(2066.27694672763190927440969155740243346136463461655104698748), eps * 5000);
 501
 502    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(2457)/1024, static_cast<float>(1)/1024), static_cast<float>(3.80739920118603335646474073457326714709615200130620574875292e-9), eps * 5000);
 503    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(0.0281933076257506091621579544064767140470089107926550720453038), eps * 5000);
 504    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(3217)/1024), static_cast<float>(-2.55820064470647911823175836997490971806135336759164272675969), eps * 5000);
 505    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(2.449843111985605522111159013846599118397e-03), eps * 5000);
 506    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(1e+04)), static_cast<float>(0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
 507    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.5), static_cast<float>(1e+06)), static_cast<float>(-0.000747424248595630177396350688505919533097973148718960064663632), eps * 5000);
 508    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.125), static_cast<float>(1e+06)), static_cast<float>(-0.000776600124835704280633640911329691642748783663198207360238214), eps * 5000);
 509    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(5.875), static_cast<float>(1e+06)), static_cast<float>(-0.000466322721115193071631008581529503095819705088484386434589780), eps * 5000);
 510    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(0.5), static_cast<float>(101)), static_cast<float>(0.0358874487875643822020496677692429287863419555699447066226409), eps * 5000);
 511    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(0.00244984311198560552211115901384659911839737686676766460822577), eps * 5000);
 512    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-5.5), static_cast<float>(1e+06)), static_cast<float>(0.000279243200433579511095229508894156656558211060453622750659554), eps * 5000);
 513    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-0.5), static_cast<float>(101)), static_cast<float>(0.0708184798097594268482290389188138201440114881159344944791454), eps * 5000);
 514    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(1.41474013160494695750009004222225969090304185981836460288562e35), eps * 5000);
 515    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(15)), static_cast<float>(-0.0902239288885423309568944543848111461724911781719692852541489), eps * 5000);
 516    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547064914615137807616774867984047583596945624129838091326863), eps * 5000);
 517    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(10486074) / (1024*1024), static_cast<float>(2e+04)), static_cast<float>(-0.00556783614400875611650958980796060611309029233226596737701688), eps * 5000);
 518    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(-0.0547613660316806551338637153942604550779513947674222863858713), eps * 5000);
 519
 520    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(0.5), static_cast<float>(0.875)), static_cast<float>(0.558532231646608646115729767013630967055657943463362504577189), eps * 5000);
 521    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(0.5), static_cast<float>(1.125)), static_cast<float>(0.383621010650189547146769320487006220295290256657827220786527), eps * 5000);
 522    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(2.25), static_cast<float>(std::ldexp(1.0, -30))), static_cast<float>(5.62397392719283271332307799146649700147907612095185712015604e20), eps * 5000);
 523    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(5.5), static_cast<float>(3217)/1024), static_cast<float>(1.30623288775012596319554857587765179889689223531159532808379), eps * 5000);
 524    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(-5.5), static_cast<float>(10)), static_cast<float>(0.0000733045300798502164644836879577484533096239574909573072142667), eps * 5000);
 525    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(-5.5), static_cast<float>(100)), static_cast<float>(5.41274555306792267322084448693957747924412508020839543293369e-45), eps * 5000);
 526    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(10240)/1024, static_cast<float>(1)/1024), static_cast<float>(2.35522579263922076203415803966825431039900000000993410734978e38), eps * 5000);
 527    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(10240)/1024, static_cast<float>(10)), static_cast<float>(0.00161425530039067002345725193091329085443750382929208307802221), eps * 5000);
 528    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(144793)/1024, static_cast<float>(100)), static_cast<float>(1.39565245860302528069481472855619216759142225046370312329416e-6), eps * 5000);
 529    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<float>(144793)/1024, static_cast<float>(200)), static_cast<float>(9.11950412043225432171915100042647230802198254567007382956336e-68), eps * 5000);
 530
 531    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(0.5), static_cast<float>(1) / (1024*1024)), static_cast<float>(-817.033790261762580469303126467917092806755460418223776544122), eps * 5000);
 532    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(5.5), static_cast<float>(3.125)), static_cast<float>(-2.61489440328417468776474188539366752698192046890955453259866), eps * 5000);
 533    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-5.5), static_cast<float>(3.125)), static_cast<float>(-0.0274994493896489729948109971802244976377957234563871795364056), eps * 5000);
 534    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-5.5), static_cast<float>(1e+04)), static_cast<float>(-0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
 535    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1)/1024), static_cast<float>(-1.50382374389531766117868938966858995093408410498915220070230e38), eps * 5000);
 536    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-10486074) / (1024*1024), static_cast<float>(1e+02)), static_cast<float>(0.0583041891319026009955779707640455341990844522293730214223545), eps * 5000);
 537    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(141.75), static_cast<float>(1e+02)), static_cast<float>(-5.38829231428696507293191118661269920130838607482708483122068e9), eps * 5000);
 538    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(141.75), static_cast<float>(2e+04)), static_cast<float>(-0.00376577888677186194728129112270988602876597726657372330194186), eps * 5000);
 539    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<float>(-141.75), static_cast<float>(1e+02)), static_cast<float>(-3.81009803444766877495905954105669819951653361036342457919021e9), eps * 5000);
 540
 541    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(0), eps * 5000);
 542    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0), static_cast<float>(-10)), static_cast<float>(-10), eps * 5000);
 543    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(-1), static_cast<float>(-1)), static_cast<float>(-1.2261911708835170708130609674719067527242483502207), eps * 5000);
 544    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.875), static_cast<float>(-4)), static_cast<float>(-5.3190556182262405182189463092940736859067548232647), eps * 5000);
 545    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(-0.625), static_cast<float>(8)), static_cast<float>(9.0419973860310100524448893214394562615252527557062), eps * 5000);
 546    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.875), static_cast<float>(1e-05)), static_cast<float>(0.000010000000000127604166668510945638036143355898993088), eps * 5000);
 547    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(10)/1024, static_cast<float>(1e+05)), static_cast<float>(100002.38431454899771096037307519328741455615271038), eps * 5000);
 548    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(1), static_cast<float>(1e-20)), static_cast<float>(1.0000000000000000000000000000000000000000166666667e-20), eps * 5000);
 549    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(1e-20), static_cast<float>(1e-20)), static_cast<float>(1.000000000000000e-20), eps * 5000);
 550    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(400)/1024, static_cast<float>(1e+20)), static_cast<float>(1.0418143796499216839719289963154558027005142709763e20), eps * 5000);
 551    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(2)), static_cast<float>(2.1765877052210673672479877957388515321497888026770), eps * 5000);
 552    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(4)), static_cast<float>(4.2543274975235836861894752787874633017836785640477), eps * 5000);
 553    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(6)), static_cast<float>(6.4588766202317746302999080620490579800463614807916), eps * 5000);
 554    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(10)), static_cast<float>(10.697409951222544858346795279378531495869386960090), eps * 5000);
 555    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(-2)), static_cast<float>(-2.1765877052210673672479877957388515321497888026770), eps * 5000);
 556    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(-4)), static_cast<float>(-4.2543274975235836861894752787874633017836785640477), eps * 5000);
 557    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(-6)), static_cast<float>(-6.4588766202317746302999080620490579800463614807916), eps * 5000);
 558    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<float>(0.5), static_cast<float>(-10)), static_cast<float>(-10.697409951222544858346795279378531495869386960090), eps * 5000);
 559
 560    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(0), static_cast<float>(0)), static_cast<float>(0), eps * 5000);
 561    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(0), static_cast<float>(-10)), static_cast<float>(-10), eps * 5000);
 562    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(-1), static_cast<float>(-1)), static_cast<float>(-0.84147098480789650665250232163029899962256306079837), eps * 5000);
 563    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(900) / 1024, static_cast<float>(-4)), static_cast<float>(-3.1756145986492562317862928524528520686391383168377), eps * 5000);
 564    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(-600) / 1024, static_cast<float>(8)), static_cast<float>(7.2473147180505693037677015377802777959345489333465), eps * 5000);
 565    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(800) / 1024, static_cast<float>(1e-05)), static_cast<float>(9.999999999898274739584436515967055859383969942432E-6), eps * 5000);
 566    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(100) / 1024, static_cast<float>(1e+05)), static_cast<float>(99761.153306972066658135668386691227343323331995888), eps * 5000);
 567    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(-0.5), static_cast<float>(1e+10)), static_cast<float>(9.3421545766487137036576748555295222252286528414669e9), eps * 5000);
 568    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<float>(400) / 1024, static_cast<float>(ldexp(static_cast<double>(1), 66))), static_cast<float>(7.0886102721911705466476846969992069994308167515242e19), eps * 5000);
 569
 570    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(1), static_cast<float>(-1)), static_cast<float>(-1.557407724654902230506974807458360173087), eps * 5000);
 571    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.4), static_cast<float>(0), static_cast<float>(-4)), static_cast<float>(-4.153623371196831087495427530365430979011), eps * 5000);
 572    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(-0.6), static_cast<float>(0), static_cast<float>(8)), static_cast<float>(8.935930619078575123490612395578518914416), eps * 5000);
 573    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.25), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.501246705365439492445236118603525029757890291780157969500480), eps * 5000);
 574    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(0), static_cast<float>(0.5)), static_cast<float>(0.5), eps * 5000);
 575    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(-2), static_cast<float>(0.5)), static_cast<float>(0.437501067017546278595664813509803743009132067629603474488486), eps * 5000);
 576    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(0.25), static_cast<float>(0.5)), static_cast<float>(0.510269830229213412212501938035914557628394166585442994564135), eps * 5000);
 577    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.5)), static_cast<float>(0.533293253875952645421201146925578536430596894471541312806165), eps * 5000);
 578    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(0.75), static_cast<float>(0.75)), static_cast<float>(0.871827580412760575085768367421866079353646112288567703061975), eps * 5000);
 579    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(1), static_cast<float>(0.25)), static_cast<float>(0.255341921221036266504482236490473678204201638800822621740476), eps * 5000);
 580    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(2), static_cast<float>(0.25)), static_cast<float>(0.261119051639220165094943572468224137699644963125853641716219), eps * 5000);
 581    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0), static_cast<float>(1023)/1024, static_cast<float>(1.5)), static_cast<float>(13.2821612239764190363647953338544569682942329604483733197131), eps * 5000);
 582    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(-1)), static_cast<float>(-1.228014414316220642611298946293865487807), eps * 5000);
 583    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.5), static_cast<float>(0.5), static_cast<float>(1e+10)), static_cast<float>(1.536591003599172091573590441336982730551e+10), eps * 5000);
 584    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.75), static_cast<float>(-1e+05), static_cast<float>(10)), static_cast<float>(0.0347926099493147087821620459290460547131012904008557007934290), eps * 5000);
 585    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(10)), static_cast<float>(0.000109956202759561502329123384755016959364346382187364656768212), eps * 5000);
 586    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1e+20)), static_cast<float>(1.00000626665567332602765201107198822183913978895904937646809e15), eps * 5000);
 587    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.875), static_cast<float>(-1e+10), static_cast<float>(1608)/1024), static_cast<float>(0.0000157080616044072676127333183571107873332593142625043567690379), eps * 5000);
 588    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.875), 1-static_cast<float>(1) / 1024, static_cast<float>(1e+20)), static_cast<float>(6.43274293944380717581167058274600202023334985100499739678963e21), eps * 5000);
 589    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.25), static_cast<float>(50), static_cast<float>(0.1)), static_cast<float>(0.124573770342749525407523258569507331686458866564082916835900), eps * 5000);
 590    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<float>(0.25), static_cast<float>(1.125), static_cast<float>(1)), static_cast<float>(1.77299767784815770192352979665283069318388205110727241629752), eps * 5000);
 591
 592    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(1)/1024), static_cast<float>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000);
 593    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(0.125)), static_cast<float>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000);
 594    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(0.5)), static_cast<float>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000);
 595    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(1)), static_cast<float>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000);
 596    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(50.5)), static_cast<float>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000);
 597    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-1)/1024), static_cast<float>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000);
 598    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-0.125)), static_cast<float>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000);
 599    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-0.5)), static_cast<float>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000);
 600    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-1)), static_cast<float>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000);
 601    BOOST_CHECK_CLOSE(tr1::expint(static_cast<float>(-50.5)), static_cast<float>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000);
 602
 603    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(0, static_cast<float>(1)), static_cast<float>(1.L), 100 * eps);
 604    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(1)), static_cast<float>(2.L), 100 * eps);
 605    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(2)), static_cast<float>(4.L), 100 * eps);
 606    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(10)), static_cast<float>(20), 100 * eps);
 607    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(100)), static_cast<float>(200), 100 * eps);
 608    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<float>(1e6)), static_cast<float>(2e6), 100 * eps);
 609    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<float>(30)), static_cast<float>(5.896624628001300E+17L), 100 * eps);
 610    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<float>(1000)), static_cast<float>(1.023976960161280E+33L), 100 * eps);
 611    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<float>(10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
 612    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<float>(-10)), static_cast<float>(8.093278209760000E+12L), 100 * eps);
 613    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<float>(-10)), static_cast<float>(-7.880000000000000E+3L), 100 * eps);
 614    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<float>(-1000)), static_cast<float>(-7.999988000000000E+9L), 100 * eps);
 615    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<float>(-1000000)), static_cast<float>(-7.999999999988000E+18L), 100 * eps);
 616
 617    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(0.125)), static_cast<float>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000);
 618    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(1023) / static_cast<float>(1024)), static_cast<float>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000);
 619    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(1025) / static_cast<float>(1024)), static_cast<float>(1024.5772867695045940578681624248887776501597556226L), eps * 5000);
 620    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(0.5)), static_cast<float>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000);
 621    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(1.125)), static_cast<float>(8.5862412945105752999607544082693023591996301183069L), eps * 5000);
 622    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(2)), static_cast<float>(1.6449340668482264364724151666460251892189499012068L), eps * 5000);
 623    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(3.5)), static_cast<float>(1.1267338673170566464278124918549842722219969574036L), eps * 5000);
 624    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(4)), static_cast<float>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000);
 625    BOOST_CHECK_CLOSE(tr1::riemann_zeta(4 + static_cast<float>(1) / 1024), static_cast<float>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000);
 626    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(4.5)), static_cast<float>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000);
 627    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(6.5)), static_cast<float>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000);
 628    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(7.5)), static_cast<float>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000);
 629    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(8.125)), static_cast<float>(1.0037305205308161603183307711439385250181080293472L), eps * 5000);
 630    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(16.125)), static_cast<float>(1.0000140128224754088474783648500235958510030511915L), eps * 5000);
 631    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(0)), static_cast<float>(-0.5L), eps * 5000);
 632    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-0.125)), static_cast<float>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000);
 633    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-1)), static_cast<float>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000);
 634    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-2)), static_cast<float>(0L), eps * 5000);
 635    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-2.5)), static_cast<float>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000 * 3);
 636    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-3)), static_cast<float>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000);
 637    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-4)), static_cast<float>(0), eps * 5000);
 638    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-20)), static_cast<float>(0), eps * 5000 * 100);
 639    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-21)), static_cast<float>(-281.46014492753623188405797101449275362318840579710L), eps * 5000 * 100);
 640    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<float>(-30.125)), static_cast<float>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000 * 100);
 641
 642    BOOST_CHECK_CLOSE(tr1::sph_bessel(0, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.9999657468461303487880990241993035937654e0),  eps * 5000 * 100);
 643    BOOST_CHECK_CLOSE(tr1::sph_bessel(0, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.9999483203249623334100130061926184665364e0),  eps * 5000 * 100);
 644    BOOST_CHECK_CLOSE(tr1::sph_bessel(2, static_cast<float>(0.1433600485324859619140625e-1)), static_cast<float>(0.1370120120703995134662099191103188366059e-4),  eps * 5000 * 100);
 645    BOOST_CHECK_CLOSE(tr1::sph_bessel(2, static_cast<float>(0.1760916970670223236083984375e-1)), static_cast<float>(0.2067173265753174063228459655801741280461e-4),  eps * 5000 * 100);
 646    BOOST_CHECK_CLOSE(tr1::sph_bessel(7, static_cast<float>(0.1252804412841796875e3)), static_cast<float>(0.7887555711993028736906736576314283291289e-2),  eps * 5000 * 100);
 647    BOOST_CHECK_CLOSE(tr1::sph_bessel(7, static_cast<float>(0.25554705810546875e3)), static_cast<float>(-0.1463292767579579943284849187188066532514e-2),  eps * 5000 * 100);
 648
 649    BOOST_CHECK_CLOSE(tr1::sph_neumann(0, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.2249212131304610409189209411089291558038e1), eps * 5000 * 100);
 650    BOOST_CHECK_CLOSE(tr1::sph_neumann(0, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1213309779166084571756446746977955970241e1),   eps * 5000 * 100);
 651    BOOST_CHECK_CLOSE(tr1::sph_neumann(2, static_cast<float>(0.408089816570281982421875e0)), static_cast<float>(-0.4541702641837159203058389758895634766256e2),   eps * 5000 * 100);
 652    BOOST_CHECK_CLOSE(tr1::sph_neumann(2, static_cast<float>(0.6540834903717041015625e0)), static_cast<float>(-0.1156112621471167110574129561700037138981e2),   eps * 5000 * 100);
 653    BOOST_CHECK_CLOSE(tr1::sph_neumann(10, static_cast<float>(0.1097540378570556640625e1)), static_cast<float>(-0.2427889658115064857278886600528596240123e9),   eps * 5000 * 100);
 654    BOOST_CHECK_CLOSE(tr1::sph_neumann(10, static_cast<float>(0.30944411754608154296875e1)), static_cast<float>(-0.3394649246350136450439882104151313759251e4),   eps * 5000 * 100);
 655
 656    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(3, 2, static_cast<float>(0.5)), static_cast<float>(0.2061460599687871330692286791802688341213L), eps * 5000);
 657    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(40, 15, static_cast<float>(0.75)), static_cast<float>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000);
 658 #endif
 659 }
 660
 661 void test_values(double, const char* name)
 662 {
 663    std::cout << "Testing type " << name << std::endl;
 664
 665 #ifndef TEST_LD
 666    double eps = boost::math::tools::epsilon<double>();
 667    BOOST_CHECK_CLOSE(tr1::acosh(std::cosh(0.5)), 0.5, 500 * eps);
 668    BOOST_CHECK_CLOSE(tr1::asinh(std::sinh(0.5)), 0.5, 500 * eps);
 669    BOOST_CHECK_CLOSE(tr1::atanh(std::tanh(0.5)), 0.5, 500 * eps);
 670
 671    BOOST_CHECK_CLOSE(tr1::cbrt(1.5 * 1.5 * 1.5), 1.5, 500 * eps);
 672
 673    BOOST_CHECK(tr1::copysign(1.0, 1.0) == 1.0);
 674    BOOST_CHECK(tr1::copysign(1.0, -1.0) == -1.0);
 675    BOOST_CHECK(tr1::copysign(-1.0, 1.0) == 1.0);
 676    BOOST_CHECK(tr1::copysign(-1.0, -1.0) == -1.0);
 677
 678    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(0.125)), static_cast<double>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
 679    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(0.5)), static_cast<double>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
 680    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(1)), static_cast<double>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
 681    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(5)), static_cast<double>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
 682    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(-0.125)), static_cast<double>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
 683    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(-0.5)), static_cast<double>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
 684    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<double>(0)), static_cast<double>(1), eps * 1000);
 685
 686    BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(0.125)), static_cast<double>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
 687    BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(0.5)), static_cast<double>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
 688    BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(1)), static_cast<double>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
 689    BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(5)), static_cast<double>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
 690    BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(-0.125)), static_cast<double>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
 691    BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(-0.5)), static_cast<double>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
 692    BOOST_CHECK_CLOSE(tr1::erf(static_cast<double>(0)), static_cast<double>(0), eps * 1000);
 693
 694    BOOST_CHECK_CLOSE(tr1::log1p(static_cast<double>(0.582029759883880615234375e0)), static_cast<double>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
 695    BOOST_CHECK_CLOSE(tr1::expm1(static_cast<double>(0.582029759883880615234375e0)), static_cast<double>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
 696    BOOST_CHECK_CLOSE(tr1::log1p(static_cast<double>(-0.2047410048544406890869140625e-1)), static_cast<double>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
 697    BOOST_CHECK_CLOSE(tr1::expm1(static_cast<double>(-0.2047410048544406890869140625e-1)), static_cast<double>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
 698
 699    BOOST_CHECK_EQUAL(tr1::fmax(0.1, -0.1), 0.1);
 700    BOOST_CHECK_EQUAL(tr1::fmin(0.1, -0.1), -0.1);
 701
 702    BOOST_CHECK_CLOSE(tr1::hypot(1.0, 3.0), std::sqrt(10.0), eps * 500);
 703
 704    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(3.5)), static_cast<double>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
 705    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(0.125)), static_cast<double>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
 706    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(-0.125)), static_cast<double>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
 707    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(-3.125)), static_cast<double>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
 708    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<double>(-53249.0/1024)), static_cast<double>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
 709
 710    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<double>(3.5)), static_cast<double>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
 711    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<double>(0.125)), static_cast<double>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
 712    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<double>(-0.125)), static_cast<double>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
 713    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<double>(-3.125)), static_cast<double>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
 714
 715 #ifdef BOOST_HAS_LONG_LONG
 716    BOOST_CHECK(tr1::llround(2.5) == 3LL);
 717    BOOST_CHECK(tr1::llround(2.25) == 2LL);
 718 #endif
 719    BOOST_CHECK(tr1::lround(2.5) == 3L);
 720    BOOST_CHECK(tr1::lround(2.25) == 2L);
 721    BOOST_CHECK(tr1::round(2.5) == 3.0);
 722    BOOST_CHECK(tr1::round(2.25) == 2.0);
 723
 724    BOOST_CHECK(tr1::nextafter(1.0, 2.0) > 1.0);
 725    BOOST_CHECK(tr1::nextafter(1.0, -2.0) < 1.0);
 726    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0, 2.0), -2.0) == 1.0);
 727    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0, -2.0), 2.0) == 1.0);
 728    BOOST_CHECK(tr1::nextafter(1.0, 2.0) > 1.0);
 729    BOOST_CHECK(tr1::nextafter(1.0, -2.0) < 1.0);
 730    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0, 2.0), -2.0) == 1.0);
 731    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0, -2.0), 2.0) == 1.0);
 732
 733    BOOST_CHECK(tr1::trunc(2.5) == 2.0);
 734    BOOST_CHECK(tr1::trunc(2.25) == 2.0);
 735
 736    //
 737    // Now the TR1 functions:
 738    //
 739    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(4, 5, static_cast<double>(0.5L)), static_cast<double>(88.31510416666666666666666666666666666667L), eps * 100);
 740    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 0, static_cast<double>(2.5L)), static_cast<double>(-0.8802526766660982969576719576719576719577L), eps * 100);
 741    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 1, static_cast<double>(4.5L)), static_cast<double>(1.564311458042689732142857142857142857143L), eps * 100);
 742    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 6, static_cast<double>(8.5L)), static_cast<double>(20.51596541066649098875661375661375661376L), eps * 100);
 743    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10, 12, static_cast<double>(12.5L)), static_cast<double>(-199.5560968456234671241181657848324514991L), eps * 100);
 744    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(50, 40, static_cast<double>(12.5L)), static_cast<double>(-4.996769495006119488583146995907246595400e16L), eps * 100);
 745
 746    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<double>(0.5L)), static_cast<double>(0.5L), eps * 100);
 747    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<double>(0.5L)), static_cast<double>(-0.3307291666666666666666666666666666666667L), eps * 100);
 748    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<double>(0.5L)), static_cast<double>(-0.5183392237103174603174603174603174603175L), eps * 100);
 749    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<double>(0.5L)), static_cast<double>(0.3120174870800154148915399248893113634676L), eps * 100);
 750    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<double>(0.5L)), static_cast<double>(-0.3181388060269979064951118308575628226834L), eps * 100);
 751
 752    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<double>(-0.5L)), static_cast<double>(1.5L), eps * 100);
 753    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<double>(-0.5L)), static_cast<double>(3.835937500000000000000000000000000000000L), eps * 100);
 754    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<double>(-0.5L)), static_cast<double>(7.950934709821428571428571428571428571429L), eps * 100);
 755    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<double>(-0.5L)), static_cast<double>(76.12915699869631476833699787070874048223L), eps * 100);
 756    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<double>(-0.5L)), static_cast<double>(2307.428631277506570629232863491518399720L), eps * 100);
 757
 758    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1, static_cast<double>(4.5L)), static_cast<double>(-3.500000000000000000000000000000000000000L), eps * 100);
 759    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4, static_cast<double>(4.5L)), static_cast<double>(0.08593750000000000000000000000000000000000L), eps * 100);
 760    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7, static_cast<double>(4.5L)), static_cast<double>(-1.036928013392857142857142857142857142857L), eps * 100);
 761    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20, static_cast<double>(4.5L)), static_cast<double>(1.437239150257817378525582974722170737587L), eps * 100);
 762    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50, static_cast<double>(4.5L)), static_cast<double>(-0.7795068145562651416494321484050019245248L), eps * 100);
 763
 764    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<double>(0.5L)), static_cast<double>(4.218750000000000000000000000000000000000L), eps * 100);
 765    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<double>(0.5L)), static_cast<double>(5696.789530152175143607977274672800795328L), eps * 100);
 766    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4, 2, static_cast<double>(-0.5L)), static_cast<double>(4.218750000000000000000000000000000000000L), eps * 100);
 767    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7, 5, static_cast<double>(-0.5L)), static_cast<double>(5696.789530152175143607977274672800795328L), eps * 100);
 768
 769    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(1, static_cast<double>(0.5L)), static_cast<double>(0.5L), eps * 100);
 770    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(4, static_cast<double>(0.5L)), static_cast<double>(-0.2890625000000000000000000000000000000000L), eps * 100);
 771    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(7, static_cast<double>(0.5L)), static_cast<double>(0.2231445312500000000000000000000000000000L), eps * 100);
 772    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(40, static_cast<double>(0.5L)), static_cast<double>(-0.09542943523261546936538467572384923220258L), eps * 100);
 773
 774    double sv = eps / 1024;
 775
 776    BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(1), static_cast<double>(1)), static_cast<double>(1), eps * 20 * 100);
 777    BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(1), static_cast<double>(4)), static_cast<double>(0.25), eps * 20 * 100);
 778    BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(4), static_cast<double>(1)), static_cast<double>(0.25), eps * 20 * 100);
 779    BOOST_CHECK_CLOSE(tr1::beta(sv, static_cast<double>(4)), 1/sv, eps * 20 * 100);
 780    BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(4), sv), 1/sv, eps * 20 * 100);
 781    BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(4), static_cast<double>(20)), static_cast<double>(0.00002823263692828910220214568040654997176736L), eps * 20 * 100);
 782    BOOST_CHECK_CLOSE(tr1::beta(static_cast<double>(0.0125L), static_cast<double>(0.000023L)), static_cast<double>(43558.24045647538375006349016083320744662L), eps * 20 * 100);
 783
 784    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(0)), static_cast<double>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
 785    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(0.125)), static_cast<double>(1.5769867712158131421244030532288080803822271060839), eps * 5000);
 786    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(0.25)), static_cast<double>(1.5962422221317835101489690714979498795055744578951), eps * 5000);
 787    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(300)/1024), static_cast<double>(1.6062331054696636704261124078746600894998873503208), eps * 5000);
 788    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(400)/1024), static_cast<double>(1.6364782007562008756208066125715722889067992997614), eps * 5000);
 789    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(-0.5)), static_cast<double>(1.6857503548125960428712036577990769895008008941411), eps * 5000);
 790    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<double>(-0.75)), static_cast<double>(1.9109897807518291965531482187613425592531451316788), eps * 5000);
 791
 792    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-1)), static_cast<double>(1), eps * 5000);
 793    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(0)), static_cast<double>(1.5707963267948966192313216916397514420985846996876), eps * 5000);
 794    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(100) / 1024), static_cast<double>(1.5670445330545086723323795143598956428788609133377), eps * 5000);
 795    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(200) / 1024), static_cast<double>(1.5557071588766556854463404816624361127847775545087), eps * 5000);
 796    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(300) / 1024), static_cast<double>(1.5365278991162754883035625322482669608948678755743), eps * 5000);
 797    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(400) / 1024), static_cast<double>(1.5090417763083482272165682786143770446401437564021), eps * 5000);
 798    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-0.5)), static_cast<double>(1.4674622093394271554597952669909161360253617523272), eps * 5000);
 799    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-600) / 1024), static_cast<double>(1.4257538571071297192428217218834579920545946473778), eps * 5000);
 800    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-800) / 1024), static_cast<double>(1.2927868476159125056958680222998765985004489572909), eps * 5000);
 801    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<double>(-900) / 1024), static_cast<double>(1.1966864890248739524112920627353824133420353430982), eps * 5000);
 802
 803    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0.2), static_cast<double>(0)), static_cast<double>(1.586867847454166237308008033828114192951), eps * 5000);
 804    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0.4), static_cast<double>(0)), static_cast<double>(1.639999865864511206865258329748601457626), eps * 5000);
 805    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0), static_cast<double>(0)), static_cast<double>(1.57079632679489661923132169163975144209858469968755291048747), eps * 5000);
 806    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0), static_cast<double>(0.5)), static_cast<double>(2.221441469079183123507940495030346849307), eps * 5000);
 807    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(0.3), static_cast<double>(-4)), static_cast<double>(0.712708870925620061597924858162260293305195624270730660081949), eps * 5000);
 808    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(-0.5), static_cast<double>(-1e+05)), static_cast<double>(0.00496944596485066055800109163256108604615568144080386919012831), eps * 5000);
 809    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(-0.75), static_cast<double>(-1e+10)), static_cast<double>(0.0000157080225184890546939710019277357161497407143903832703317801), eps * 5000);
 810    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(-0.875), static_cast<double>(1) / 1024), static_cast<double>(2.18674503176462374414944618968850352696579451638002110619287), eps * 5000);
 811    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<double>(-0.875), static_cast<double>(1023)/1024), static_cast<double>(101.045289804941384100960063898569538919135722087486350366997), eps * 5000);
 812
 813    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(2.25), static_cast<double>(1)/(1024*1024)), static_cast<double>(2.34379212133481347189068464680335815256364262507955635911656e-15), eps * 5000);
 814    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(5.5), static_cast<double>(3.125)), static_cast<double>(0.0583514045989371500460946536220735787163510569634133670181210), eps * 5000);
 815    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-5) + static_cast<double>(1)/1024, static_cast<double>(2.125)), static_cast<double>(0.0267920938009571023702933210070984416052633027166975342895062), eps * 5000);
 816    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-5.5), static_cast<double>(10)), static_cast<double>(597.577606961369169607937419869926705730305175364662688426534), eps * 5000);
 817    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-10486074)/(1024*1024), static_cast<double>(1)/1024), static_cast<double>(1.41474005665181350367684623930576333542989766867888186478185e35), eps * 5000);
 818    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-10486074)/(1024*1024), static_cast<double>(50)), static_cast<double>(1.07153277202900671531087024688681954238311679648319534644743e20), eps * 5000);
 819    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(144794)/1024, static_cast<double>(100)), static_cast<double>(2066.27694757392660413922181531984160871678224178890247540320), eps * 5000);
 820    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<double>(-144794)/1024, static_cast<double>(100)), static_cast<double>(2066.27694672763190927440969155740243346136463461655104698748), eps * 5000);
 821
 822    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(2457)/1024, static_cast<double>(1)/1024), static_cast<double>(3.80739920118603335646474073457326714709615200130620574875292e-9), eps * 5000);
 823    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.5), static_cast<double>(3217)/1024), static_cast<double>(0.0281933076257506091621579544064767140470089107926550720453038), eps * 5000);
 824    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-5.5), static_cast<double>(3217)/1024), static_cast<double>(-2.55820064470647911823175836997490971806135336759164272675969), eps * 5000);
 825    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-5.5), static_cast<double>(1e+04)), static_cast<double>(2.449843111985605522111159013846599118397e-03), eps * 5000);
 826    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.5), static_cast<double>(1e+04)), static_cast<double>(0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
 827    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.5), static_cast<double>(1e+06)), static_cast<double>(-0.000747424248595630177396350688505919533097973148718960064663632), eps * 5000);
 828    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.125), static_cast<double>(1e+06)), static_cast<double>(-0.000776600124835704280633640911329691642748783663198207360238214), eps * 5000);
 829    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(5.875), static_cast<double>(1e+06)), static_cast<double>(-0.000466322721115193071631008581529503095819705088484386434589780), eps * 5000);
 830    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(0.5), static_cast<double>(101)), static_cast<double>(0.0358874487875643822020496677692429287863419555699447066226409), eps * 5000);
 831    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-5.5), static_cast<double>(1e+04)), static_cast<double>(0.00244984311198560552211115901384659911839737686676766460822577), eps * 5000);
 832    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-5.5), static_cast<double>(1e+06)), static_cast<double>(0.000279243200433579511095229508894156656558211060453622750659554), eps * 5000);
 833    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-0.5), static_cast<double>(101)), static_cast<double>(0.0708184798097594268482290389188138201440114881159344944791454), eps * 5000);
 834    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(1)/1024), static_cast<double>(1.41474013160494695750009004222225969090304185981836460288562e35), eps * 5000);
 835    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(15)), static_cast<double>(-0.0902239288885423309568944543848111461724911781719692852541489), eps * 5000);
 836    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(10486074) / (1024*1024), static_cast<double>(1e+02)), static_cast<double>(-0.0547064914615137807616774867984047583596945624129838091326863), eps * 5000);
 837    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(10486074) / (1024*1024), static_cast<double>(2e+04)), static_cast<double>(-0.00556783614400875611650958980796060611309029233226596737701688), eps * 5000);
 838    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(1e+02)), static_cast<double>(-0.0547613660316806551338637153942604550779513947674222863858713), eps * 5000);
 839
 840    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(0.5), static_cast<double>(0.875)), static_cast<double>(0.558532231646608646115729767013630967055657943463362504577189), eps * 5000);
 841    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(0.5), static_cast<double>(1.125)), static_cast<double>(0.383621010650189547146769320487006220295290256657827220786527), eps * 5000);
 842    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(2.25), static_cast<double>(std::ldexp(1.0, -30))), static_cast<double>(5.62397392719283271332307799146649700147907612095185712015604e20), eps * 5000);
 843    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(5.5), static_cast<double>(3217)/1024), static_cast<double>(1.30623288775012596319554857587765179889689223531159532808379), eps * 5000);
 844    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(-5.5), static_cast<double>(10)), static_cast<double>(0.0000733045300798502164644836879577484533096239574909573072142667), eps * 5000);
 845    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(-5.5), static_cast<double>(100)), static_cast<double>(5.41274555306792267322084448693957747924412508020839543293369e-45), eps * 5000);
 846    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(10240)/1024, static_cast<double>(1)/1024), static_cast<double>(2.35522579263922076203415803966825431039900000000993410734978e38), eps * 5000);
 847    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(10240)/1024, static_cast<double>(10)), static_cast<double>(0.00161425530039067002345725193091329085443750382929208307802221), eps * 5000);
 848    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(144793)/1024, static_cast<double>(100)), static_cast<double>(1.39565245860302528069481472855619216759142225046370312329416e-6), eps * 5000);
 849    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<double>(144793)/1024, static_cast<double>(200)), static_cast<double>(9.11950412043225432171915100042647230802198254567007382956336e-68), eps * 5000);
 850
 851    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(0.5), static_cast<double>(1) / (1024*1024)), static_cast<double>(-817.033790261762580469303126467917092806755460418223776544122), eps * 5000);
 852    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(5.5), static_cast<double>(3.125)), static_cast<double>(-2.61489440328417468776474188539366752698192046890955453259866), eps * 5000);
 853    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-5.5), static_cast<double>(3.125)), static_cast<double>(-0.0274994493896489729948109971802244976377957234563871795364056), eps * 5000);
 854    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-5.5), static_cast<double>(1e+04)), static_cast<double>(-0.00759343502722670361395585198154817047185480147294665270646578), eps * 5000);
 855    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(1)/1024), static_cast<double>(-1.50382374389531766117868938966858995093408410498915220070230e38), eps * 5000);
 856    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-10486074) / (1024*1024), static_cast<double>(1e+02)), static_cast<double>(0.0583041891319026009955779707640455341990844522293730214223545), eps * 5000);
 857    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(141.75), static_cast<double>(1e+02)), static_cast<double>(-5.38829231428696507293191118661269920130838607482708483122068e9), eps * 5000);
 858    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(141.75), static_cast<double>(2e+04)), static_cast<double>(-0.00376577888677186194728129112270988602876597726657372330194186), eps * 5000);
 859    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<double>(-141.75), static_cast<double>(1e+02)), static_cast<double>(-3.81009803444766877495905954105669819951653361036342457919021e9), eps * 5000);
 860
 861    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0), static_cast<double>(0)), static_cast<double>(0), eps * 5000);
 862    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0), static_cast<double>(-10)), static_cast<double>(-10), eps * 5000);
 863    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(-1), static_cast<double>(-1)), static_cast<double>(-1.2261911708835170708130609674719067527242483502207), eps * 5000);
 864    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.875), static_cast<double>(-4)), static_cast<double>(-5.3190556182262405182189463092940736859067548232647), eps * 5000);
 865    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(-0.625), static_cast<double>(8)), static_cast<double>(9.0419973860310100524448893214394562615252527557062), eps * 5000);
 866    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.875), static_cast<double>(1e-05)), static_cast<double>(0.000010000000000127604166668510945638036143355898993088), eps * 5000);
 867    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(10)/1024, static_cast<double>(1e+05)), static_cast<double>(100002.38431454899771096037307519328741455615271038), eps * 5000);
 868    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(1), static_cast<double>(1e-20)), static_cast<double>(1.0000000000000000000000000000000000000000166666667e-20), eps * 5000);
 869    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(1e-20), static_cast<double>(1e-20)), static_cast<double>(1.000000000000000e-20), eps * 5000);
 870    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(400)/1024, static_cast<double>(1e+20)), static_cast<double>(1.0418143796499216839719289963154558027005142709763e20), eps * 5000);
 871    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(2)), static_cast<double>(2.1765877052210673672479877957388515321497888026770), eps * 5000);
 872    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(4)), static_cast<double>(4.2543274975235836861894752787874633017836785640477), eps * 5000);
 873    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(6)), static_cast<double>(6.4588766202317746302999080620490579800463614807916), eps * 5000);
 874    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(10)), static_cast<double>(10.697409951222544858346795279378531495869386960090), eps * 5000);
 875    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(-2)), static_cast<double>(-2.1765877052210673672479877957388515321497888026770), eps * 5000);
 876    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(-4)), static_cast<double>(-4.2543274975235836861894752787874633017836785640477), eps * 5000);
 877    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(-6)), static_cast<double>(-6.4588766202317746302999080620490579800463614807916), eps * 5000);
 878    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<double>(0.5), static_cast<double>(-10)), static_cast<double>(-10.697409951222544858346795279378531495869386960090), eps * 5000);
 879
 880    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(0), static_cast<double>(0)), static_cast<double>(0), eps * 5000);
 881    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(0), static_cast<double>(-10)), static_cast<double>(-10), eps * 5000);
 882    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(-1), static_cast<double>(-1)), static_cast<double>(-0.84147098480789650665250232163029899962256306079837), eps * 5000);
 883    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(900) / 1024, static_cast<double>(-4)), static_cast<double>(-3.1756145986492562317862928524528520686391383168377), eps * 5000);
 884    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(-600) / 1024, static_cast<double>(8)), static_cast<double>(7.2473147180505693037677015377802777959345489333465), eps * 5000);
 885    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(800) / 1024, static_cast<double>(1e-05)), static_cast<double>(9.999999999898274739584436515967055859383969942432E-6), eps * 5000);
 886    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(100) / 1024, static_cast<double>(1e+05)), static_cast<double>(99761.153306972066658135668386691227343323331995888), eps * 5000);
 887    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(-0.5), static_cast<double>(1e+10)), static_cast<double>(9.3421545766487137036576748555295222252286528414669e9), eps * 5000);
 888    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<double>(400) / 1024, ldexp(static_cast<double>(1), 66)), static_cast<double>(7.0886102721911705466476846969992069994308167515242e19), eps * 5000);
 889
 890    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(1), static_cast<double>(-1)), static_cast<double>(-1.557407724654902230506974807458360173087), eps * 5000);
 891    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.4), static_cast<double>(0), static_cast<double>(-4)), static_cast<double>(-4.153623371196831087495427530365430979011), eps * 5000);
 892    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(-0.6), static_cast<double>(0), static_cast<double>(8)), static_cast<double>(8.935930619078575123490612395578518914416), eps * 5000);
 893    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.25), static_cast<double>(0), static_cast<double>(0.5)), static_cast<double>(0.501246705365439492445236118603525029757890291780157969500480), eps * 5000);
 894    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(0), static_cast<double>(0.5)), static_cast<double>(0.5), eps * 5000);
 895    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(-2), static_cast<double>(0.5)), static_cast<double>(0.437501067017546278595664813509803743009132067629603474488486), eps * 5000);
 896    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(0.25), static_cast<double>(0.5)), static_cast<double>(0.510269830229213412212501938035914557628394166585442994564135), eps * 5000);
 897    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(0.75), static_cast<double>(0.5)), static_cast<double>(0.533293253875952645421201146925578536430596894471541312806165), eps * 5000);
 898    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(0.75), static_cast<double>(0.75)), static_cast<double>(0.871827580412760575085768367421866079353646112288567703061975), eps * 5000);
 899    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(1), static_cast<double>(0.25)), static_cast<double>(0.255341921221036266504482236490473678204201638800822621740476), eps * 5000);
 900    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(2), static_cast<double>(0.25)), static_cast<double>(0.261119051639220165094943572468224137699644963125853641716219), eps * 5000);
 901    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0), static_cast<double>(1023)/1024, static_cast<double>(1.5)), static_cast<double>(13.2821612239764190363647953338544569682942329604483733197131), eps * 5000);
 902    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.5), static_cast<double>(0.5), static_cast<double>(-1)), static_cast<double>(-1.228014414316220642611298946293865487807), eps * 5000);
 903    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.5), static_cast<double>(0.5), static_cast<double>(1e+10)), static_cast<double>(1.536591003599172091573590441336982730551e+10), eps * 5000);
 904    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.75), static_cast<double>(-1e+05), static_cast<double>(10)), static_cast<double>(0.0347926099493147087821620459290460547131012904008557007934290), eps * 5000);
 905    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.875), static_cast<double>(-1e+10), static_cast<double>(10)), static_cast<double>(0.000109956202759561502329123384755016959364346382187364656768212), eps * 5000);
 906    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.875), static_cast<double>(-1e+10), static_cast<double>(1e+20)), static_cast<double>(1.00000626665567332602765201107198822183913978895904937646809e15), eps * 5000);
 907    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.875), static_cast<double>(-1e+10), static_cast<double>(1608)/1024), static_cast<double>(0.0000157080616044072676127333183571107873332593142625043567690379), eps * 5000);
 908    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.875), 1-static_cast<double>(1) / 1024, static_cast<double>(1e+20)), static_cast<double>(6.43274293944380717581167058274600202023334985100499739678963e21), eps * 5000);
 909    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.25), static_cast<double>(50), static_cast<double>(0.1)), static_cast<double>(0.124573770342749525407523258569507331686458866564082916835900), eps * 5000);
 910    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<double>(0.25), static_cast<double>(1.125), static_cast<double>(1)), static_cast<double>(1.77299767784815770192352979665283069318388205110727241629752), eps * 5000);
 911
 912    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(1)/1024), static_cast<double>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000);
 913    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(0.125)), static_cast<double>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000);
 914    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(0.5)), static_cast<double>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000);
 915    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(1)), static_cast<double>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000);
 916    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(50.5)), static_cast<double>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000);
 917    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-1)/1024), static_cast<double>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000);
 918    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-0.125)), static_cast<double>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000);
 919    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-0.5)), static_cast<double>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000);
 920    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-1)), static_cast<double>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000);
 921    BOOST_CHECK_CLOSE(tr1::expint(static_cast<double>(-50.5)), static_cast<double>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000);
 922
 923    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(0, static_cast<double>(1)), static_cast<double>(1.L), 100 * eps);
 924    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(1)), static_cast<double>(2.L), 100 * eps);
 925    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(2)), static_cast<double>(4.L), 100 * eps);
 926    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(10)), static_cast<double>(20), 100 * eps);
 927    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(100)), static_cast<double>(200), 100 * eps);
 928    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1, static_cast<double>(1e6)), static_cast<double>(2e6), 100 * eps);
 929    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<double>(30)), static_cast<double>(5.896624628001300E+17L), 100 * eps);
 930    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<double>(1000)), static_cast<double>(1.023976960161280E+33L), 100 * eps);
 931    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<double>(10)), static_cast<double>(8.093278209760000E+12L), 100 * eps);
 932    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10, static_cast<double>(-10)), static_cast<double>(8.093278209760000E+12L), 100 * eps);
 933    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<double>(-10)), static_cast<double>(-7.880000000000000E+3L), 100 * eps);
 934    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<double>(-1000)), static_cast<double>(-7.999988000000000E+9L), 100 * eps);
 935    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3, static_cast<double>(-1000000)), static_cast<double>(-7.999999999988000E+18L), 100 * eps);
 936
 937    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(0.125)), static_cast<double>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000);
 938    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(1023) / static_cast<double>(1024)), static_cast<double>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000);
 939    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(1025) / static_cast<double>(1024)), static_cast<double>(1024.5772867695045940578681624248887776501597556226L), eps * 5000);
 940    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(0.5)), static_cast<double>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000);
 941    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(1.125)), static_cast<double>(8.5862412945105752999607544082693023591996301183069L), eps * 5000);
 942    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(2)), static_cast<double>(1.6449340668482264364724151666460251892189499012068L), eps * 5000);
 943    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(3.5)), static_cast<double>(1.1267338673170566464278124918549842722219969574036L), eps * 5000);
 944    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(4)), static_cast<double>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000);
 945    BOOST_CHECK_CLOSE(tr1::riemann_zeta(4 + static_cast<double>(1) / 1024), static_cast<double>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000);
 946    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(4.5)), static_cast<double>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000);
 947    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(6.5)), static_cast<double>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000);
 948    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(7.5)), static_cast<double>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000);
 949    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(8.125)), static_cast<double>(1.0037305205308161603183307711439385250181080293472L), eps * 5000);
 950    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(16.125)), static_cast<double>(1.0000140128224754088474783648500235958510030511915L), eps * 5000);
 951    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(0)), static_cast<double>(-0.5L), eps * 5000);
 952    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-0.125)), static_cast<double>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000);
 953    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-1)), static_cast<double>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000);
 954    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-2)), static_cast<double>(0L), eps * 5000);
 955    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-2.5)), static_cast<double>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000 * 3);
 956    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-3)), static_cast<double>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000);
 957    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-4)), static_cast<double>(0), eps * 5000);
 958    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-20)), static_cast<double>(0), eps * 5000 * 100);
 959    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-21)), static_cast<double>(-281.46014492753623188405797101449275362318840579710L), eps * 5000 * 100);
 960    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<double>(-30.125)), static_cast<double>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000 * 100);
 961
 962    BOOST_CHECK_CLOSE(tr1::sph_bessel(0, static_cast<double>(0.1433600485324859619140625e-1)), static_cast<double>(0.9999657468461303487880990241993035937654e0),  eps * 5000 * 100);
 963    BOOST_CHECK_CLOSE(tr1::sph_bessel(0, static_cast<double>(0.1760916970670223236083984375e-1)), static_cast<double>(0.9999483203249623334100130061926184665364e0),  eps * 5000 * 100);
 964    BOOST_CHECK_CLOSE(tr1::sph_bessel(2, static_cast<double>(0.1433600485324859619140625e-1)), static_cast<double>(0.1370120120703995134662099191103188366059e-4),  eps * 5000 * 100);
 965    BOOST_CHECK_CLOSE(tr1::sph_bessel(2, static_cast<double>(0.1760916970670223236083984375e-1)), static_cast<double>(0.2067173265753174063228459655801741280461e-4),  eps * 5000 * 100);
 966    BOOST_CHECK_CLOSE(tr1::sph_bessel(7, static_cast<double>(0.1252804412841796875e3)), static_cast<double>(0.7887555711993028736906736576314283291289e-2),  eps * 5000 * 100);
 967    BOOST_CHECK_CLOSE(tr1::sph_bessel(7, static_cast<double>(0.25554705810546875e3)), static_cast<double>(-0.1463292767579579943284849187188066532514e-2),  eps * 5000 * 100);
 968
 969    BOOST_CHECK_CLOSE(tr1::sph_neumann(0, static_cast<double>(0.408089816570281982421875e0)), static_cast<double>(-0.2249212131304610409189209411089291558038e1), eps * 5000 * 100);
 970    BOOST_CHECK_CLOSE(tr1::sph_neumann(0, static_cast<double>(0.6540834903717041015625e0)), static_cast<double>(-0.1213309779166084571756446746977955970241e1),   eps * 5000 * 100);
 971    BOOST_CHECK_CLOSE(tr1::sph_neumann(2, static_cast<double>(0.408089816570281982421875e0)), static_cast<double>(-0.4541702641837159203058389758895634766256e2),   eps * 5000 * 100);
 972    BOOST_CHECK_CLOSE(tr1::sph_neumann(2, static_cast<double>(0.6540834903717041015625e0)), static_cast<double>(-0.1156112621471167110574129561700037138981e2),   eps * 5000 * 100);
 973    BOOST_CHECK_CLOSE(tr1::sph_neumann(10, static_cast<double>(0.1097540378570556640625e1)), static_cast<double>(-0.2427889658115064857278886600528596240123e9),   eps * 5000 * 100);
 974    BOOST_CHECK_CLOSE(tr1::sph_neumann(10, static_cast<double>(0.30944411754608154296875e1)), static_cast<double>(-0.3394649246350136450439882104151313759251e4),   eps * 5000 * 100);
 975
 976    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(3, 2, static_cast<double>(0.5)), static_cast<double>(0.2061460599687871330692286791802688341213L), eps * 5000);
 977    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(40, 15, static_cast<double>(0.75)), static_cast<double>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000);
 978 #endif
 979 }
 980
 981 void test_values(long double, const char* name)
 982 {
 983 #ifdef TEST_LD
 984 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 985    std::cout << "Testing type " << name << std::endl;
 986
 987    long double eps = boost::math::tools::epsilon<long double>();
 988    BOOST_CHECK_CLOSE(tr1::acoshl(std::cosh(0.5L)), 0.5L, 5000 * eps);
 989    BOOST_CHECK_CLOSE(tr1::asinhl(std::sinh(0.5L)), 0.5L, 5000 * eps);
 990    BOOST_CHECK_CLOSE(tr1::atanhl(std::tanh(0.5L)), 0.5L, 5000 * eps);
 991
 992    BOOST_CHECK_CLOSE(tr1::cbrtl(1.5L * 1.5L * 1.5L), 1.5L, 5000 * eps);
 993
 994    BOOST_CHECK(tr1::copysignl(1.0L, 1.0L) == 1.0L);
 995    BOOST_CHECK(tr1::copysignl(1.0L, -1.0L) == -1.0L);
 996    BOOST_CHECK(tr1::copysignl(-1.0L, 1.0L) == 1.0L);
 997    BOOST_CHECK(tr1::copysignl(-1.0L, -1.0L) == -1.0L);
 998
 999    BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(0.125)), static_cast<long double>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
1000    BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(0.5)), static_cast<long double>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
1001    BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(1)), static_cast<long double>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
1002    BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(5)), static_cast<long double>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
1003    BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(-0.125)), static_cast<long double>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
1004    BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(-0.5)), static_cast<long double>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
1005    BOOST_CHECK_CLOSE(tr1::erfcl(static_cast<long double>(0)), static_cast<long double>(1), eps * 1000);
1006
1007    BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(0.125)), static_cast<long double>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
1008    BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(0.5)), static_cast<long double>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
1009    BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(1)), static_cast<long double>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
1010    BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(5)), static_cast<long double>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
1011    BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(-0.125)), static_cast<long double>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
1012    BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(-0.5)), static_cast<long double>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
1013    BOOST_CHECK_CLOSE(tr1::erfl(static_cast<long double>(0)), static_cast<long double>(0), eps * 1000);
1014
1015    BOOST_CHECK_CLOSE(tr1::log1pl(static_cast<long double>(0.582029759883880615234375e0)), static_cast<long double>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
1016    BOOST_CHECK_CLOSE(tr1::expm1l(static_cast<long double>(0.582029759883880615234375e0)), static_cast<long double>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
1017    BOOST_CHECK_CLOSE(tr1::log1pl(static_cast<long double>(-0.2047410048544406890869140625e-1)), static_cast<long double>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
1018    BOOST_CHECK_CLOSE(tr1::expm1l(static_cast<long double>(-0.2047410048544406890869140625e-1)), static_cast<long double>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
1019
1020    BOOST_CHECK_EQUAL(tr1::fmaxl(0.1L, -0.1L), 0.1L);
1021    BOOST_CHECK_EQUAL(tr1::fminl(0.1L, -0.1L), -0.1L);
1022
1023    BOOST_CHECK_CLOSE(tr1::hypotl(1.0L, 3.0L), std::sqrt(10.0L), eps * 500);
1024
1025    BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(3.5)), static_cast<long double>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
1026    BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(0.125)), static_cast<long double>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
1027    BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(-0.125)), static_cast<long double>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
1028    BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(-3.125)), static_cast<long double>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
1029    BOOST_CHECK_CLOSE(tr1::lgammal(static_cast<long double>(-53249.0/1024)), static_cast<long double>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
1030
1031    BOOST_CHECK_CLOSE(tr1::tgammal(static_cast<long double>(3.5)), static_cast<long double>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
1032    BOOST_CHECK_CLOSE(tr1::tgammal(static_cast<long double>(0.125)), static_cast<long double>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
1033    BOOST_CHECK_CLOSE(tr1::tgammal(static_cast<long double>(-0.125)), static_cast<long double>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
1034    BOOST_CHECK_CLOSE(tr1::tgammal(static_cast<long double>(-3.125)), static_cast<long double>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
1035
1036 #ifdef BOOST_HAS_LONG_LONG
1037    BOOST_CHECK(tr1::llroundl(2.5L) == 3LL);
1038    BOOST_CHECK(tr1::llroundl(2.25L) == 2LL);
1039 #endif
1040    BOOST_CHECK(tr1::lroundl(2.5L) == 3L);
1041    BOOST_CHECK(tr1::lroundl(2.25L) == 2L);
1042    BOOST_CHECK(tr1::roundl(2.5L) == 3.0L);
1043    BOOST_CHECK(tr1::roundl(2.25L) == 2.0L);
1044
1045    BOOST_CHECK(tr1::nextafterl(1.0L, 2.0L) > 1.0L);
1046    BOOST_CHECK(tr1::nextafterl(1.0L, -2.0L) < 1.0L);
1047    BOOST_CHECK(tr1::nextafterl(tr1::nextafterl(1.0L, 2.0L), -2.0L) == 1.0L);
1048    BOOST_CHECK(tr1::nextafterl(tr1::nextafterl(1.0L, -2.0L), 2.0L) == 1.0L);
1049    BOOST_CHECK(tr1::nextafterl(1.0L, 2.0L) > 1.0L);
1050    BOOST_CHECK(tr1::nextafterl(1.0L, -2.0L) < 1.0L);
1051    BOOST_CHECK(tr1::nextafterl(tr1::nextafterl(1.0L, 2.0L), -2.0L) == 1.0L);
1052    BOOST_CHECK(tr1::nextafterl(tr1::nextafterl(1.0L, -2.0L), 2.0L) == 1.0L);
1053
1054    BOOST_CHECK(tr1::truncl(2.5L) == 2.0L);
1055    BOOST_CHECK(tr1::truncl(2.25L) == 2.0L);
1056
1057    //
1058    // And again but without the "l" suffix on the function names:
1059    //
1060    BOOST_CHECK_CLOSE(tr1::acosh(std::cosh(0.5L)), 0.5L, 5000 * eps);
1061    BOOST_CHECK_CLOSE(tr1::asinh(std::sinh(0.5L)), 0.5L, 5000 * eps);
1062    BOOST_CHECK_CLOSE(tr1::atanh(std::tanh(0.5L)), 0.5L, 5000 * eps);
1063
1064    BOOST_CHECK_CLOSE(tr1::cbrt(1.5L * 1.5L * 1.5L), 1.5L, 5000 * eps);
1065
1066    BOOST_CHECK(tr1::copysign(1.0L, 1.0L) == 1.0L);
1067    BOOST_CHECK(tr1::copysign(1.0L, -1.0L) == -1.0L);
1068    BOOST_CHECK(tr1::copysign(-1.0L, 1.0L) == 1.0L);
1069    BOOST_CHECK(tr1::copysign(-1.0L, -1.0L) == -1.0L);
1070
1071    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(0.125)), static_cast<long double>(0.85968379519866618260697055347837660181302041685015L), eps * 1000);
1072    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(0.5)), static_cast<long double>(0.47950012218695346231725334610803547126354842424204L), eps * 1000);
1073    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(1)), static_cast<long double>(0.15729920705028513065877936491739074070393300203370L), eps * 1000);
1074    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(5)), static_cast<long double>(1.5374597944280348501883434853833788901180503147234e-12L), eps * 1000);
1075    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(-0.125)), static_cast<long double>(1.1403162048013338173930294465216233981869795831498L), eps * 1000);
1076    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(-0.5)), static_cast<long double>(1.5204998778130465376827466538919645287364515757580L), eps * 1000);
1077    BOOST_CHECK_CLOSE(tr1::erfc(static_cast<long double>(0)), static_cast<long double>(1), eps * 1000);
1078
1079    BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(0.125)), static_cast<long double>(0.14031620480133381739302944652162339818697958314985L), eps * 1000);
1080    BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(0.5)), static_cast<long double>(0.52049987781304653768274665389196452873645157575796L), eps * 1000);
1081    BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(1)), static_cast<long double>(0.84270079294971486934122063508260925929606699796630L), eps * 1000);
1082    BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(5)), static_cast<long double>(0.9999999999984625402055719651498116565146166211099L), eps * 1000);
1083    BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(-0.125)), static_cast<long double>(-0.14031620480133381739302944652162339818697958314985L), eps * 1000);
1084    BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(-0.5)), static_cast<long double>(-0.52049987781304653768274665389196452873645157575796L), eps * 1000);
1085    BOOST_CHECK_CLOSE(tr1::erf(static_cast<long double>(0)), static_cast<long double>(0), eps * 1000);
1086
1087    BOOST_CHECK_CLOSE(tr1::log1p(static_cast<long double>(0.582029759883880615234375e0)), static_cast<long double>(0.4587086807259736626531803258754840111707e0L), eps * 1000);
1088    BOOST_CHECK_CLOSE(tr1::expm1(static_cast<long double>(0.582029759883880615234375e0)), static_cast<long double>(0.7896673415707786528734865994546559029663e0L), eps * 1000);
1089    BOOST_CHECK_CLOSE(tr1::log1p(static_cast<long double>(-0.2047410048544406890869140625e-1)), static_cast<long double>(-0.2068660038044094868521052319477265955827e-1L), eps * 1000);
1090    BOOST_CHECK_CLOSE(tr1::expm1(static_cast<long double>(-0.2047410048544406890869140625e-1)), static_cast<long double>(-0.2026592921724753704129022027337835687888e-1L), eps * 1000);
1091
1092    BOOST_CHECK_EQUAL(tr1::fmax(0.1L, -0.1L), 0.1L);
1093    BOOST_CHECK_EQUAL(tr1::fmin(0.1L, -0.1L), -0.1L);
1094
1095    BOOST_CHECK_CLOSE(tr1::hypot(1.0L, 3.0L), std::sqrt(10.0L), eps * 500);
1096
1097    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(3.5)), static_cast<long double>(1.2009736023470742248160218814507129957702389154682L), 5000 * eps);
1098    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(0.125)), static_cast<long double>(2.0194183575537963453202905211670995899482809521344L), 5000 * eps);
1099    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(-0.125)), static_cast<long double>(2.1653002489051702517540619481440174064962195287626L), 5000 * eps);
1100    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(-3.125)), static_cast<long double>(0.1543111276840418242676072830970532952413339012367L), 5000 * eps);
1101    BOOST_CHECK_CLOSE(tr1::lgamma(static_cast<long double>(-53249.0/1024)), static_cast<long double>(-149.43323093420259741100038126078721302600128285894L), 5000 * eps);
1102
1103    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<long double>(3.5)), static_cast<long double>(3.3233509704478425511840640312646472177454052302295L), 5000 * eps);
1104    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<long double>(0.125)), static_cast<long double>(7.5339415987976119046992298412151336246104195881491L), 5000 * eps);
1105    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<long double>(-0.125)), static_cast<long double>(-8.7172188593831756100190140408231437691829605421405L), 5000 * eps);
1106    BOOST_CHECK_CLOSE(tr1::tgamma(static_cast<long double>(-3.125)), static_cast<long double>(1.1668538708507675587790157356605097019141636072094L), 5000 * eps);
1107
1108 #ifdef BOOST_HAS_LONG_LONG
1109    BOOST_CHECK(tr1::llround(2.5L) == 3LL);
1110    BOOST_CHECK(tr1::llround(2.25L) == 2LL);
1111 #endif
1112    BOOST_CHECK(tr1::lround(2.5L) == 3L);
1113    BOOST_CHECK(tr1::lround(2.25L) == 2L);
1114    BOOST_CHECK(tr1::round(2.5L) == 3.0L);
1115    BOOST_CHECK(tr1::round(2.25L) == 2.0L);
1116
1117    BOOST_CHECK(tr1::nextafter(1.0L, 2.0L) > 1.0L);
1118    BOOST_CHECK(tr1::nextafter(1.0L, -2.0L) < 1.0L);
1119    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0L, 2.0L), -2.0L) == 1.0L);
1120    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0L, -2.0L), 2.0L) == 1.0L);
1121    BOOST_CHECK(tr1::nextafter(1.0L, 2.0L) > 1.0L);
1122    BOOST_CHECK(tr1::nextafter(1.0L, -2.0L) < 1.0L);
1123    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0L, 2.0L), -2.0L) == 1.0L);
1124    BOOST_CHECK(tr1::nextafter(tr1::nextafter(1.0L, -2.0L), 2.0L) == 1.0L);
1125
1126    BOOST_CHECK(tr1::trunc(2.5L) == 2.0L);
1127    BOOST_CHECK(tr1::trunc(2.25L) == 2.0L);
1128
1129    //
1130    // Now for the TR1 math functions:
1131    //
1132    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(4L, 5L, static_cast<long double>(0.5L)), static_cast<long double>(88.31510416666666666666666666666666666667L), eps * 100L);
1133    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(10L, 0L, static_cast<long double>(2.5L)), static_cast<long double>(-0.8802526766660982969576719576719576719577L), eps * 100L);
1134    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(10L, 1L, static_cast<long double>(4.5L)), static_cast<long double>(1.564311458042689732142857142857142857143L), eps * 100L);
1135    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(10L, 6L, static_cast<long double>(8.5L)), static_cast<long double>(20.51596541066649098875661375661375661376L), eps * 100L);
1136    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(10L, 12L, static_cast<long double>(12.5L)), static_cast<long double>(-199.5560968456234671241181657848324514991L), eps * 100L);
1137    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerrel(50L, 40L, static_cast<long double>(12.5L)), static_cast<long double>(-4.996769495006119488583146995907246595400e16L), eps * 100L);
1138
1139    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(1L, static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 100L);
1140    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(4L, static_cast<long double>(0.5L)), static_cast<long double>(-0.3307291666666666666666666666666666666667L), eps * 100L);
1141    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(7L, static_cast<long double>(0.5L)), static_cast<long double>(-0.5183392237103174603174603174603174603175L), eps * 100L);
1142    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(20L, static_cast<long double>(0.5L)), static_cast<long double>(0.3120174870800154148915399248893113634676L), eps * 100L);
1143    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(50L, static_cast<long double>(0.5L)), static_cast<long double>(-0.3181388060269979064951118308575628226834L), eps * 100L);
1144
1145    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(1L, static_cast<long double>(-0.5L)), static_cast<long double>(1.5L), eps * 100L);
1146    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(4L, static_cast<long double>(-0.5L)), static_cast<long double>(3.835937500000000000000000000000000000000L), eps * 100L);
1147    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(7L, static_cast<long double>(-0.5L)), static_cast<long double>(7.950934709821428571428571428571428571429L), eps * 100L);
1148    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(20L, static_cast<long double>(-0.5L)), static_cast<long double>(76.12915699869631476833699787070874048223L), eps * 100L);
1149    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(50L, static_cast<long double>(-0.5L)), static_cast<long double>(2307.428631277506570629232863491518399720L), eps * 100L);
1150
1151    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(1L, static_cast<long double>(4.5L)), static_cast<long double>(-3.500000000000000000000000000000000000000L), eps * 100L);
1152    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(4L, static_cast<long double>(4.5L)), static_cast<long double>(0.08593750000000000000000000000000000000000L), eps * 100L);
1153    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(7L, static_cast<long double>(4.5L)), static_cast<long double>(-1.036928013392857142857142857142857142857L), eps * 100L);
1154    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(20L, static_cast<long double>(4.5L)), static_cast<long double>(1.437239150257817378525582974722170737587L), eps * 100L);
1155    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerrel(50L, static_cast<long double>(4.5L)), static_cast<long double>(-0.7795068145562651416494321484050019245248L), eps * 100L);
1156
1157    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendrel(4L, 2L, static_cast<long double>(0.5L)), static_cast<long double>(4.218750000000000000000000000000000000000L), eps * 100L);
1158    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendrel(7L, 5L, static_cast<long double>(0.5L)), static_cast<long double>(5696.789530152175143607977274672800795328L), eps * 100L);
1159    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendrel(4L, 2L, static_cast<long double>(-0.5L)), static_cast<long double>(4.218750000000000000000000000000000000000L), eps * 100L);
1160    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendrel(7L, 5L, static_cast<long double>(-0.5L)), static_cast<long double>(5696.789530152175143607977274672800795328L), eps * 100L);
1161
1162    BOOST_CHECK_CLOSE_FRACTION(tr1::legendrel(1L, static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 100L);
1163    BOOST_CHECK_CLOSE_FRACTION(tr1::legendrel(4L, static_cast<long double>(0.5L)), static_cast<long double>(-0.2890625000000000000000000000000000000000L), eps * 100L);
1164    BOOST_CHECK_CLOSE_FRACTION(tr1::legendrel(7L, static_cast<long double>(0.5L)), static_cast<long double>(0.2231445312500000000000000000000000000000L), eps * 100L);
1165    BOOST_CHECK_CLOSE_FRACTION(tr1::legendrel(40L, static_cast<long double>(0.5L)), static_cast<long double>(-0.09542943523261546936538467572384923220258L), eps * 100L);
1166
1167    long double sv = eps / 1024;
1168    BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(1L), static_cast<long double>(1L)), static_cast<long double>(1L), eps * 20L * 100L);
1169    BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(1L), static_cast<long double>(4L)), static_cast<long double>(0.25L), eps * 20L * 100L);
1170    BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(4L), static_cast<long double>(1L)), static_cast<long double>(0.25L), eps * 20L * 100L);
1171    BOOST_CHECK_CLOSE(tr1::betal(sv, static_cast<long double>(4L)), 1/sv, eps * 20L * 100L);
1172    BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(4L), sv), 1/sv, eps * 20L * 100L);
1173    BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(4L), static_cast<long double>(20L)), static_cast<long double>(0.00002823263692828910220214568040654997176736L), eps * 20L * 100L);
1174    BOOST_CHECK_CLOSE(tr1::betal(static_cast<long double>(0.0125L), static_cast<long double>(0.000023L)), static_cast<long double>(43558.24045647538375006349016083320744662L), eps * 20L * 100L);
1175
1176    BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(0L)), static_cast<long double>(1.5707963267948966192313216916397514420985846996876L), eps * 5000L);
1177    BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(0.125L)), static_cast<long double>(1.5769867712158131421244030532288080803822271060839L), eps * 5000L);
1178    BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(0.25L)), static_cast<long double>(1.5962422221317835101489690714979498795055744578951L), eps * 5000L);
1179    BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(300L)/1024L), static_cast<long double>(1.6062331054696636704261124078746600894998873503208L), eps * 5000L);
1180    BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(400L)/1024L), static_cast<long double>(1.6364782007562008756208066125715722889067992997614L), eps * 5000L);
1181    BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(-0.5L)), static_cast<long double>(1.6857503548125960428712036577990769895008008941411L), eps * 5000L);
1182    BOOST_CHECK_CLOSE(tr1::comp_ellint_1l(static_cast<long double>(-0.75L)), static_cast<long double>(1.9109897807518291965531482187613425592531451316788L), eps * 5000L);
1183
1184    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-1L)), static_cast<long double>(1L), eps * 5000L);
1185    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(0L)), static_cast<long double>(1.5707963267948966192313216916397514420985846996876L), eps * 5000L);
1186    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(100L) / 1024L), static_cast<long double>(1.5670445330545086723323795143598956428788609133377L), eps * 5000L);
1187    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(200L) / 1024L), static_cast<long double>(1.5557071588766556854463404816624361127847775545087L), eps * 5000L);
1188    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(300L) / 1024L), static_cast<long double>(1.5365278991162754883035625322482669608948678755743L), eps * 5000L);
1189    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(400L) / 1024L), static_cast<long double>(1.5090417763083482272165682786143770446401437564021L), eps * 5000L);
1190    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-0.5L)), static_cast<long double>(1.4674622093394271554597952669909161360253617523272L), eps * 5000L);
1191    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-600L) / 1024L), static_cast<long double>(1.4257538571071297192428217218834579920545946473778L), eps * 5000L);
1192    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-800L) / 1024L), static_cast<long double>(1.2927868476159125056958680222998765985004489572909L), eps * 5000L);
1193    BOOST_CHECK_CLOSE(tr1::comp_ellint_2l(static_cast<long double>(-900L) / 1024L), static_cast<long double>(1.1966864890248739524112920627353824133420353430982L), eps * 5000L);
1194
1195    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0.2L), static_cast<long double>(0L)), static_cast<long double>(1.586867847454166237308008033828114192951L), eps * 5000L);
1196    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0.4L), static_cast<long double>(0L)), static_cast<long double>(1.639999865864511206865258329748601457626L), eps * 5000L);
1197    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(1.57079632679489661923132169163975144209858469968755291048747L), eps * 5000L);
1198    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(2.221441469079183123507940495030346849307L), eps * 5000L);
1199    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(0.3L), static_cast<long double>(-4L)), static_cast<long double>(0.712708870925620061597924858162260293305195624270730660081949L), eps * 5000L);
1200    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(-0.5L), static_cast<long double>(-1e+05L)), static_cast<long double>(0.00496944596485066055800109163256108604615568144080386919012831L), eps * 5000L);
1201    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(-0.75L), static_cast<long double>(-1e+10L)), static_cast<long double>(0.0000157080225184890546939710019277357161497407143903832703317801L), eps * 5000L);
1202    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(-0.875L), static_cast<long double>(1L) / 1024L), static_cast<long double>(2.18674503176462374414944618968850352696579451638002110619287L), eps * 5000L);
1203    BOOST_CHECK_CLOSE(tr1::comp_ellint_3l(static_cast<long double>(-0.875L), static_cast<long double>(1023L)/1024L), static_cast<long double>(101.045289804941384100960063898569538919135722087486350366997L), eps * 5000L);
1204
1205    BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(2.25L), static_cast<long double>(1L)/(1024*1024L)), static_cast<long double>(2.34379212133481347189068464680335815256364262507955635911656e-15L), eps * 5000L);
1206    BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(5.5L), static_cast<long double>(3.125L)), static_cast<long double>(0.0583514045989371500460946536220735787163510569634133670181210L), eps * 5000L);
1207    BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-5L) + static_cast<long double>(1L)/1024L, static_cast<long double>(2.125L)), static_cast<long double>(0.0267920938009571023702933210070984416052633027166975342895062L), eps * 5000L);
1208    BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-5.5L), static_cast<long double>(10L)), static_cast<long double>(597.577606961369169607937419869926705730305175364662688426534L), eps * 5000L);
1209    BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-10486074L)/(1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(1.41474005665181350367684623930576333542989766867888186478185e35L), eps * 5000L);
1210    BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-10486074L)/(1024*1024L), static_cast<long double>(50L)), static_cast<long double>(1.07153277202900671531087024688681954238311679648319534644743e20L), eps * 5000L);
1211    BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(144794L)/1024L, static_cast<long double>(100L)), static_cast<long double>(2066.27694757392660413922181531984160871678224178890247540320L), eps * 5000L);
1212    BOOST_CHECK_CLOSE(tr1::cyl_bessel_il(static_cast<long double>(-144794L)/1024L, static_cast<long double>(100L)), static_cast<long double>(2066.27694672763190927440969155740243346136463461655104698748L), eps * 5000L);
1213
1214    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(2457L)/1024L, static_cast<long double>(1L)/1024L), static_cast<long double>(3.80739920118603335646474073457326714709615200130620574875292e-9L), eps * 50000L);
1215    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(0.0281933076257506091621579544064767140470089107926550720453038L), eps * 5000L);
1216    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(-2.55820064470647911823175836997490971806135336759164272675969L), eps * 5000L);
1217    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(2.449843111985605522111159013846599118397e-03L), eps * 50000L);
1218    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(0.00759343502722670361395585198154817047185480147294665270646578L), eps * 5000L);
1219    //BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.5L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000747424248595630177396350688505919533097973148718960064663632L), eps * 50000L);
1220    //BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.125L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000776600124835704280633640911329691642748783663198207360238214L), eps * 50000L);
1221    //BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(5.875L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000466322721115193071631008581529503095819705088484386434589780L), eps * 50000L);
1222    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(0.5L), static_cast<long double>(101L)), static_cast<long double>(0.0358874487875643822020496677692429287863419555699447066226409L), eps * 5000L);
1223    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(0.00244984311198560552211115901384659911839737686676766460822577L), eps * 50000L);
1224    //BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-5.5L), static_cast<long double>(1e+06L)), static_cast<long double>(0.000279243200433579511095229508894156656558211060453622750659554L), eps * 50000L);
1225    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-0.5L), static_cast<long double>(101L)), static_cast<long double>(0.0708184798097594268482290389188138201440114881159344944791454L), eps * 5000L);
1226    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(1.41474013160494695750009004222225969090304185981836460288562e35L), eps * 5000L);
1227    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(15L)), static_cast<long double>(-0.0902239288885423309568944543848111461724911781719692852541489L), eps * 5000L);
1228    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(-0.0547064914615137807616774867984047583596945624129838091326863L), eps * 5000L);
1229    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(10486074L) / (1024*1024L), static_cast<long double>(2e+04L)), static_cast<long double>(-0.00556783614400875611650958980796060611309029233226596737701688L), eps * 5000L);
1230    BOOST_CHECK_CLOSE(tr1::cyl_bessel_jl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(-0.0547613660316806551338637153942604550779513947674222863858713L), eps * 5000L);
1231
1232    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(0.5L), static_cast<long double>(0.875L)), static_cast<long double>(0.558532231646608646115729767013630967055657943463362504577189L), eps * 5000L);
1233    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(0.5L), static_cast<long double>(1.125L)), static_cast<long double>(0.383621010650189547146769320487006220295290256657827220786527L), eps * 5000L);
1234    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(2.25L), static_cast<long double>(std::ldexp(1.0L, -30L))), static_cast<long double>(5.62397392719283271332307799146649700147907612095185712015604e20L), eps * 5000L);
1235    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(1.30623288775012596319554857587765179889689223531159532808379L), eps * 5000L);
1236    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(-5.5L), static_cast<long double>(10L)), static_cast<long double>(0.0000733045300798502164644836879577484533096239574909573072142667L), eps * 5000L);
1237    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(-5.5L), static_cast<long double>(100L)), static_cast<long double>(5.41274555306792267322084448693957747924412508020839543293369e-45L), eps * 5000L);
1238    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(10240L)/1024L, static_cast<long double>(1L)/1024L), static_cast<long double>(2.35522579263922076203415803966825431039900000000993410734978e38L), eps * 5000L);
1239    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(10240L)/1024L, static_cast<long double>(10L)), static_cast<long double>(0.00161425530039067002345725193091329085443750382929208307802221L), eps * 5000L);
1240    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(144793L)/1024L, static_cast<long double>(100L)), static_cast<long double>(1.39565245860302528069481472855619216759142225046370312329416e-6L), eps * 5000L);
1241    BOOST_CHECK_CLOSE(tr1::cyl_bessel_kl(static_cast<long double>(144793L)/1024L, static_cast<long double>(200L)), static_cast<long double>(9.11950412043225432171915100042647230802198254567007382956336e-68L), eps * 7000L);
1242
1243    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(0.5L), static_cast<long double>(1L) / (1024*1024L)), static_cast<long double>(-817.033790261762580469303126467917092806755460418223776544122L), eps * 5000L);
1244    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(5.5L), static_cast<long double>(3.125L)), static_cast<long double>(-2.61489440328417468776474188539366752698192046890955453259866L), eps * 5000L);
1245    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-5.5L), static_cast<long double>(3.125L)), static_cast<long double>(-0.0274994493896489729948109971802244976377957234563871795364056L), eps * 5000L);
1246    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(-0.00759343502722670361395585198154817047185480147294665270646578L), eps * 5000L);
1247    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(-1.50382374389531766117868938966858995093408410498915220070230e38L), eps * 5000L);
1248    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(0.0583041891319026009955779707640455341990844522293730214223545L), eps * 5000L);
1249    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(141.75L), static_cast<long double>(1e+02L)), static_cast<long double>(-5.38829231428696507293191118661269920130838607482708483122068e9L), eps * 5000L);
1250    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(141.75L), static_cast<long double>(2e+04L)), static_cast<long double>(-0.00376577888677186194728129112270988602876597726657372330194186L), eps * 50000L);
1251    BOOST_CHECK_CLOSE(tr1::cyl_neumannl(static_cast<long double>(-141.75L), static_cast<long double>(1e+02L)), static_cast<long double>(-3.81009803444766877495905954105669819951653361036342457919021e9L), eps * 5000L);
1252
1253    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(0L), eps * 5000L);
1254    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0L), static_cast<long double>(-10L)), static_cast<long double>(-10L), eps * 5000L);
1255    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(-1L), static_cast<long double>(-1L)), static_cast<long double>(-1.2261911708835170708130609674719067527242483502207L), eps * 5000L);
1256    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.875L), static_cast<long double>(-4L)), static_cast<long double>(-5.3190556182262405182189463092940736859067548232647L), eps * 5000L);
1257    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(-0.625L), static_cast<long double>(8L)), static_cast<long double>(9.0419973860310100524448893214394562615252527557062L), eps * 5000L);
1258    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.875L), static_cast<long double>(1e-05L)), static_cast<long double>(0.000010000000000127604166668510945638036143355898993088L), eps * 5000L);
1259    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(10L)/1024L, static_cast<long double>(1e+05L)), static_cast<long double>(100002.38431454899771096037307519328741455615271038L), eps * 5000L);
1260    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(1L), static_cast<long double>(1e-20L)), static_cast<long double>(1.0000000000000000000000000000000000000000166666667e-20L), eps * 5000L);
1261    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(1e-20L), static_cast<long double>(1e-20L)), static_cast<long double>(1.000000000000000e-20L), eps * 5000L);
1262    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(400L)/1024L, static_cast<long double>(1e+20L)), static_cast<long double>(1.0418143796499216839719289963154558027005142709763e20L), eps * 5000L);
1263    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(2L)), static_cast<long double>(2.1765877052210673672479877957388515321497888026770L), eps * 5000L);
1264    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(4L)), static_cast<long double>(4.2543274975235836861894752787874633017836785640477L), eps * 5000L);
1265    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(6L)), static_cast<long double>(6.4588766202317746302999080620490579800463614807916L), eps * 5000L);
1266    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(10L)), static_cast<long double>(10.697409951222544858346795279378531495869386960090L), eps * 5000L);
1267    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(-2L)), static_cast<long double>(-2.1765877052210673672479877957388515321497888026770L), eps * 5000L);
1268    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(-4L)), static_cast<long double>(-4.2543274975235836861894752787874633017836785640477L), eps * 5000L);
1269    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(-6L)), static_cast<long double>(-6.4588766202317746302999080620490579800463614807916L), eps * 5000L);
1270    BOOST_CHECK_CLOSE(tr1::ellint_1l(static_cast<long double>(0.5L), static_cast<long double>(-10L)), static_cast<long double>(-10.697409951222544858346795279378531495869386960090L), eps * 5000L);
1271
1272    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(0L), eps * 5000L);
1273    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(0L), static_cast<long double>(-10L)), static_cast<long double>(-10L), eps * 5000L);
1274    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(-1L), static_cast<long double>(-1L)), static_cast<long double>(-0.84147098480789650665250232163029899962256306079837L), eps * 5000L);
1275    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(900L) / 1024L, static_cast<long double>(-4L)), static_cast<long double>(-3.1756145986492562317862928524528520686391383168377L), eps * 5000L);
1276    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(-600L) / 1024L, static_cast<long double>(8L)), static_cast<long double>(7.2473147180505693037677015377802777959345489333465L), eps * 5000L);
1277    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(800L) / 1024L, static_cast<long double>(1e-05L)), static_cast<long double>(9.999999999898274739584436515967055859383969942432E-6L), eps * 5000L);
1278    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(100L) / 1024L, static_cast<long double>(1e+05L)), static_cast<long double>(99761.153306972066658135668386691227343323331995888L), eps * 5000L);
1279    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(-0.5L), static_cast<long double>(1e+10L)), static_cast<long double>(9.3421545766487137036576748555295222252286528414669e9L), eps * 5000L);
1280    BOOST_CHECK_CLOSE(tr1::ellint_2l(static_cast<long double>(400L) / 1024L, ldexp(static_cast<long double>(1L), 66L)), static_cast<long double>(7.0886102721911705466476846969992069994308167515242e19L), eps * 5000L);
1281
1282    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(1L), static_cast<long double>(-1L)), static_cast<long double>(-1.557407724654902230506974807458360173087L), eps * 5000L);
1283    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.4L), static_cast<long double>(0L), static_cast<long double>(-4L)), static_cast<long double>(-4.153623371196831087495427530365430979011L), eps * 5000L);
1284    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(-0.6L), static_cast<long double>(0L), static_cast<long double>(8L)), static_cast<long double>(8.935930619078575123490612395578518914416L), eps * 5000L);
1285    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.25L), static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(0.501246705365439492445236118603525029757890291780157969500480L), eps * 5000L);
1286    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 5000L);
1287    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(-2L), static_cast<long double>(0.5L)), static_cast<long double>(0.437501067017546278595664813509803743009132067629603474488486L), eps * 5000L);
1288    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(0.25L), static_cast<long double>(0.5L)), static_cast<long double>(0.510269830229213412212501938035914557628394166585442994564135L), eps * 5000L);
1289    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(0.75L), static_cast<long double>(0.5L)), static_cast<long double>(0.533293253875952645421201146925578536430596894471541312806165L), eps * 5000L);
1290    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(0.75L), static_cast<long double>(0.75L)), static_cast<long double>(0.871827580412760575085768367421866079353646112288567703061975L), eps * 5000L);
1291    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(1L), static_cast<long double>(0.25L)), static_cast<long double>(0.255341921221036266504482236490473678204201638800822621740476L), eps * 5000L);
1292    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(2L), static_cast<long double>(0.25L)), static_cast<long double>(0.261119051639220165094943572468224137699644963125853641716219L), eps * 5000L);
1293    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0L), static_cast<long double>(1023L)/1024L, static_cast<long double>(1.5L)), static_cast<long double>(13.2821612239764190363647953338544569682942329604483733197131L), eps * 5000L);
1294    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.5L), static_cast<long double>(0.5L), static_cast<long double>(-1L)), static_cast<long double>(-1.228014414316220642611298946293865487807L), eps * 5000L);
1295    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.5L), static_cast<long double>(0.5L), static_cast<long double>(1e+10L)), static_cast<long double>(1.536591003599172091573590441336982730551e+10L), eps * 5000L);
1296    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.75L), static_cast<long double>(-1e+05L), static_cast<long double>(10L)), static_cast<long double>(0.0347926099493147087821620459290460547131012904008557007934290L), eps * 5000L);
1297    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(10L)), static_cast<long double>(0.000109956202759561502329123384755016959364346382187364656768212L), eps * 5000L);
1298    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(1e+20L)), static_cast<long double>(1.00000626665567332602765201107198822183913978895904937646809e15L), eps * 5000L);
1299    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(1608L)/1024L), static_cast<long double>(0.0000157080616044072676127333183571107873332593142625043567690379L), eps * 5000L);
1300    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.875L), 1-static_cast<long double>(1L) / 1024L, static_cast<long double>(1e+20L)), static_cast<long double>(6.43274293944380717581167058274600202023334985100499739678963e21L), eps * 5000L);
1301    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.25L), static_cast<long double>(50L), static_cast<long double>(0.1L)), static_cast<long double>(0.124573770342749525407523258569507331686458866564082916835900L), eps * 5000L);
1302    BOOST_CHECK_CLOSE(tr1::ellint_3l(static_cast<long double>(0.25L), static_cast<long double>(1.125L), static_cast<long double>(1L)), static_cast<long double>(1.77299767784815770192352979665283069318388205110727241629752L), eps * 5000L);
1303
1304    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(1L)/1024L), static_cast<long double>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000L);
1305    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(0.125L)), static_cast<long double>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000L);
1306    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(0.5L)), static_cast<long double>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000L);
1307    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(1L)), static_cast<long double>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000L);
1308    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(50.5L)), static_cast<long double>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000L);
1309    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-1L)/1024L), static_cast<long double>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000L);
1310    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-0.125L)), static_cast<long double>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000L);
1311    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-0.5L)), static_cast<long double>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000L);
1312    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-1L)), static_cast<long double>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000L);
1313    BOOST_CHECK_CLOSE(tr1::expintl(static_cast<long double>(-50.5L)), static_cast<long double>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000L);
1314
1315    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(0L, static_cast<long double>(1L)), static_cast<long double>(1.L), 100L * eps);
1316    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(1L)), static_cast<long double>(2.L), 100L * eps);
1317    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(2L)), static_cast<long double>(4.L), 100L * eps);
1318    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(10L)), static_cast<long double>(20L), 100L * eps);
1319    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(100L)), static_cast<long double>(200L), 100L * eps);
1320    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(1L, static_cast<long double>(1e6L)), static_cast<long double>(2e6L), 100L * eps);
1321    //BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(10L, static_cast<long double>(30L)), static_cast<long double>(5.896624628001300E+17L), 1000L * eps);
1322    //BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(10L, static_cast<long double>(1000L)), static_cast<long double>(1.023976960161280E+33L), 1000L * eps);
1323    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(10L, static_cast<long double>(10L)), static_cast<long double>(8.093278209760000E+12L), 100L * eps);
1324    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(10L, static_cast<long double>(-10L)), static_cast<long double>(8.093278209760000E+12L), 100L * eps);
1325    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(3L, static_cast<long double>(-10L)), static_cast<long double>(-7.880000000000000E+3L), 100L * eps);
1326    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(3L, static_cast<long double>(-1000L)), static_cast<long double>(-7.999988000000000E+9L), 100L * eps);
1327    BOOST_CHECK_CLOSE_FRACTION(tr1::hermitel(3L, static_cast<long double>(-1000000L)), static_cast<long double>(-7.999999999988000E+18L), 100L * eps);
1328
1329    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(0.125L)), static_cast<long double>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000L);
1330    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(1023L) / static_cast<long double>(1024L)), static_cast<long double>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000L);
1331    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(1025L) / static_cast<long double>(1024L)), static_cast<long double>(1024.5772867695045940578681624248887776501597556226L), eps * 5000L);
1332    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(0.5L)), static_cast<long double>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000L);
1333    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(1.125L)), static_cast<long double>(8.5862412945105752999607544082693023591996301183069L), eps * 5000L);
1334    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(2L)), static_cast<long double>(1.6449340668482264364724151666460251892189499012068L), eps * 5000L);
1335    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(3.5L)), static_cast<long double>(1.1267338673170566464278124918549842722219969574036L), eps * 5000L);
1336    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(4L)), static_cast<long double>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000L);
1337    BOOST_CHECK_CLOSE(tr1::riemann_zetal(4L + static_cast<long double>(1L) / 1024L), static_cast<long double>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000L);
1338    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(4.5L)), static_cast<long double>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000L);
1339    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(6.5L)), static_cast<long double>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000L);
1340    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(7.5L)), static_cast<long double>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000L);
1341    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(8.125L)), static_cast<long double>(1.0037305205308161603183307711439385250181080293472L), eps * 5000L);
1342    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(16.125L)), static_cast<long double>(1.0000140128224754088474783648500235958510030511915L), eps * 5000L);
1343    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(0L)), static_cast<long double>(-0.5L), eps * 5000L);
1344    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-0.125L)), static_cast<long double>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000L);
1345    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-1L)), static_cast<long double>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000L);
1346    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-2L)), static_cast<long double>(0L), eps * 5000L);
1347    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-2.5L)), static_cast<long double>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000L * 3L);
1348    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-3L)), static_cast<long double>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000L);
1349    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-4L)), static_cast<long double>(0L), eps * 5000L);
1350    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-20L)), static_cast<long double>(0L), eps * 5000L * 100L);
1351    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-21L)), static_cast<long double>(-281.46014492753623188405797101449275362318840579710L), eps * 5000L * 100L);
1352    BOOST_CHECK_CLOSE(tr1::riemann_zetal(static_cast<long double>(-30.125L)), static_cast<long double>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000L * 100L);
1353
1354    BOOST_CHECK_CLOSE(tr1::sph_bessell(0L, static_cast<long double>(0.1433600485324859619140625e-1L)), static_cast<long double>(0.9999657468461303487880990241993035937654e0L),  eps * 5000L * 100L);
1355    BOOST_CHECK_CLOSE(tr1::sph_bessell(0L, static_cast<long double>(0.1760916970670223236083984375e-1L)), static_cast<long double>(0.9999483203249623334100130061926184665364e0L),  eps * 5000L * 100L);
1356    BOOST_CHECK_CLOSE(tr1::sph_bessell(2L, static_cast<long double>(0.1433600485324859619140625e-1L)), static_cast<long double>(0.1370120120703995134662099191103188366059e-4L),  eps * 5000L * 100L);
1357    BOOST_CHECK_CLOSE(tr1::sph_bessell(2L, static_cast<long double>(0.1760916970670223236083984375e-1L)), static_cast<long double>(0.2067173265753174063228459655801741280461e-4L),  eps * 5000L * 100L);
1358    BOOST_CHECK_CLOSE(tr1::sph_bessell(7L, static_cast<long double>(0.1252804412841796875e3L)), static_cast<long double>(0.7887555711993028736906736576314283291289e-2L),  eps * 50000L * 100L);
1359    BOOST_CHECK_CLOSE(tr1::sph_bessell(7L, static_cast<long double>(0.25554705810546875e3L)), static_cast<long double>(-0.1463292767579579943284849187188066532514e-2L),  eps * 5000L * 100L);
1360
1361    BOOST_CHECK_CLOSE(tr1::sph_neumannl(0L, static_cast<long double>(0.408089816570281982421875e0L)), static_cast<long double>(-0.2249212131304610409189209411089291558038e1L), eps * 5000L * 100L);
1362    BOOST_CHECK_CLOSE(tr1::sph_neumannl(0L, static_cast<long double>(0.6540834903717041015625e0L)), static_cast<long double>(-0.1213309779166084571756446746977955970241e1L),   eps * 5000L * 100L);
1363    BOOST_CHECK_CLOSE(tr1::sph_neumannl(2L, static_cast<long double>(0.408089816570281982421875e0L)), static_cast<long double>(-0.4541702641837159203058389758895634766256e2L),   eps * 5000L * 100L);
1364    BOOST_CHECK_CLOSE(tr1::sph_neumannl(2L, static_cast<long double>(0.6540834903717041015625e0L)), static_cast<long double>(-0.1156112621471167110574129561700037138981e2L),   eps * 5000L * 100L);
1365    BOOST_CHECK_CLOSE(tr1::sph_neumannl(10L, static_cast<long double>(0.1097540378570556640625e1L)), static_cast<long double>(-0.2427889658115064857278886600528596240123e9L),   eps * 5000L * 100L);
1366    BOOST_CHECK_CLOSE(tr1::sph_neumannl(10L, static_cast<long double>(0.30944411754608154296875e1L)), static_cast<long double>(-0.3394649246350136450439882104151313759251e4L),   eps * 5000L * 100L);
1367
1368    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendrel(3L, 2L, static_cast<long double>(0.5L)), static_cast<long double>(0.2061460599687871330692286791802688341213L), eps * 5000L);
1369    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendrel(40L, 15L, static_cast<long double>(0.75L)), static_cast<long double>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000L);
1370
1371    //
1372    // Now all over again but without the "f" suffix on the function names this time:
1373    //
1374    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(4L, 5L, static_cast<long double>(0.5L)), static_cast<long double>(88.31510416666666666666666666666666666667L), eps * 100L);
1375    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10L, 0L, static_cast<long double>(2.5L)), static_cast<long double>(-0.8802526766660982969576719576719576719577L), eps * 100L);
1376    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10L, 1L, static_cast<long double>(4.5L)), static_cast<long double>(1.564311458042689732142857142857142857143L), eps * 100L);
1377    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10L, 6L, static_cast<long double>(8.5L)), static_cast<long double>(20.51596541066649098875661375661375661376L), eps * 100L);
1378    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(10L, 12L, static_cast<long double>(12.5L)), static_cast<long double>(-199.5560968456234671241181657848324514991L), eps * 100L);
1379    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_laguerre(50L, 40L, static_cast<long double>(12.5L)), static_cast<long double>(-4.996769495006119488583146995907246595400e16L), eps * 100L);
1380
1381    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1L, static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 100L);
1382    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4L, static_cast<long double>(0.5L)), static_cast<long double>(-0.3307291666666666666666666666666666666667L), eps * 100L);
1383    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7L, static_cast<long double>(0.5L)), static_cast<long double>(-0.5183392237103174603174603174603174603175L), eps * 100L);
1384    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20L, static_cast<long double>(0.5L)), static_cast<long double>(0.3120174870800154148915399248893113634676L), eps * 100L);
1385    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50L, static_cast<long double>(0.5L)), static_cast<long double>(-0.3181388060269979064951118308575628226834L), eps * 100L);
1386
1387    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1L, static_cast<long double>(-0.5L)), static_cast<long double>(1.5L), eps * 100L);
1388    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4L, static_cast<long double>(-0.5L)), static_cast<long double>(3.835937500000000000000000000000000000000L), eps * 100L);
1389    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7L, static_cast<long double>(-0.5L)), static_cast<long double>(7.950934709821428571428571428571428571429L), eps * 100L);
1390    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20L, static_cast<long double>(-0.5L)), static_cast<long double>(76.12915699869631476833699787070874048223L), eps * 100L);
1391    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50L, static_cast<long double>(-0.5L)), static_cast<long double>(2307.428631277506570629232863491518399720L), eps * 100L);
1392
1393    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(1L, static_cast<long double>(4.5L)), static_cast<long double>(-3.500000000000000000000000000000000000000L), eps * 100L);
1394    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(4L, static_cast<long double>(4.5L)), static_cast<long double>(0.08593750000000000000000000000000000000000L), eps * 100L);
1395    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(7L, static_cast<long double>(4.5L)), static_cast<long double>(-1.036928013392857142857142857142857142857L), eps * 100L);
1396    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(20L, static_cast<long double>(4.5L)), static_cast<long double>(1.437239150257817378525582974722170737587L), eps * 100L);
1397    BOOST_CHECK_CLOSE_FRACTION(tr1::laguerre(50L, static_cast<long double>(4.5L)), static_cast<long double>(-0.7795068145562651416494321484050019245248L), eps * 100L);
1398
1399    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4L, 2L, static_cast<long double>(0.5L)), static_cast<long double>(4.218750000000000000000000000000000000000L), eps * 100L);
1400    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7L, 5L, static_cast<long double>(0.5L)), static_cast<long double>(5696.789530152175143607977274672800795328L), eps * 100L);
1401    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(4L, 2L, static_cast<long double>(-0.5L)), static_cast<long double>(4.218750000000000000000000000000000000000L), eps * 100L);
1402    BOOST_CHECK_CLOSE_FRACTION(tr1::assoc_legendre(7L, 5L, static_cast<long double>(-0.5L)), static_cast<long double>(5696.789530152175143607977274672800795328L), eps * 100L);
1403
1404    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(1L, static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 100L);
1405    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(4L, static_cast<long double>(0.5L)), static_cast<long double>(-0.2890625000000000000000000000000000000000L), eps * 100L);
1406    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(7L, static_cast<long double>(0.5L)), static_cast<long double>(0.2231445312500000000000000000000000000000L), eps * 100L);
1407    BOOST_CHECK_CLOSE_FRACTION(tr1::legendre(40L, static_cast<long double>(0.5L)), static_cast<long double>(-0.09542943523261546936538467572384923220258L), eps * 100L);
1408
1409    BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(1L), static_cast<long double>(1L)), static_cast<long double>(1L), eps * 20L * 100L);
1410    BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(1L), static_cast<long double>(4L)), static_cast<long double>(0.25L), eps * 20L * 100L);
1411    BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(4L), static_cast<long double>(1L)), static_cast<long double>(0.25L), eps * 20L * 100L);
1412    BOOST_CHECK_CLOSE(tr1::beta(sv, static_cast<long double>(4L)), 1/sv, eps * 20L * 100L);
1413    BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(4L), sv), 1/sv, eps * 20L * 100L);
1414    BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(4L), static_cast<long double>(20L)), static_cast<long double>(0.00002823263692828910220214568040654997176736L), eps * 20L * 100L);
1415    BOOST_CHECK_CLOSE(tr1::beta(static_cast<long double>(0.0125L), static_cast<long double>(0.000023L)), static_cast<long double>(43558.24045647538375006349016083320744662L), eps * 20L * 100L);
1416
1417    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(0L)), static_cast<long double>(1.5707963267948966192313216916397514420985846996876L), eps * 5000L);
1418    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(0.125L)), static_cast<long double>(1.5769867712158131421244030532288080803822271060839L), eps * 5000L);
1419    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(0.25L)), static_cast<long double>(1.5962422221317835101489690714979498795055744578951L), eps * 5000L);
1420    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(300L)/1024L), static_cast<long double>(1.6062331054696636704261124078746600894998873503208L), eps * 5000L);
1421    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(400L)/1024L), static_cast<long double>(1.6364782007562008756208066125715722889067992997614L), eps * 5000L);
1422    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(-0.5L)), static_cast<long double>(1.6857503548125960428712036577990769895008008941411L), eps * 5000L);
1423    BOOST_CHECK_CLOSE(tr1::comp_ellint_1(static_cast<long double>(-0.75L)), static_cast<long double>(1.9109897807518291965531482187613425592531451316788L), eps * 5000L);
1424
1425    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-1L)), static_cast<long double>(1L), eps * 5000L);
1426    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(0L)), static_cast<long double>(1.5707963267948966192313216916397514420985846996876L), eps * 5000L);
1427    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(100L) / 1024L), static_cast<long double>(1.5670445330545086723323795143598956428788609133377L), eps * 5000L);
1428    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(200L) / 1024L), static_cast<long double>(1.5557071588766556854463404816624361127847775545087L), eps * 5000L);
1429    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(300L) / 1024L), static_cast<long double>(1.5365278991162754883035625322482669608948678755743L), eps * 5000L);
1430    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(400L) / 1024L), static_cast<long double>(1.5090417763083482272165682786143770446401437564021L), eps * 5000L);
1431    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-0.5L)), static_cast<long double>(1.4674622093394271554597952669909161360253617523272L), eps * 5000L);
1432    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-600L) / 1024L), static_cast<long double>(1.4257538571071297192428217218834579920545946473778L), eps * 5000L);
1433    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-800L) / 1024L), static_cast<long double>(1.2927868476159125056958680222998765985004489572909L), eps * 5000L);
1434    BOOST_CHECK_CLOSE(tr1::comp_ellint_2(static_cast<long double>(-900L) / 1024L), static_cast<long double>(1.1966864890248739524112920627353824133420353430982L), eps * 5000L);
1435
1436    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0.2L), static_cast<long double>(0L)), static_cast<long double>(1.586867847454166237308008033828114192951L), eps * 5000L);
1437    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0.4L), static_cast<long double>(0L)), static_cast<long double>(1.639999865864511206865258329748601457626L), eps * 5000L);
1438    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(1.57079632679489661923132169163975144209858469968755291048747L), eps * 5000L);
1439    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(2.221441469079183123507940495030346849307L), eps * 5000L);
1440    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(0.3L), static_cast<long double>(-4L)), static_cast<long double>(0.712708870925620061597924858162260293305195624270730660081949L), eps * 5000L);
1441    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(-0.5L), static_cast<long double>(-1e+05L)), static_cast<long double>(0.00496944596485066055800109163256108604615568144080386919012831L), eps * 5000L);
1442    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(-0.75L), static_cast<long double>(-1e+10L)), static_cast<long double>(0.0000157080225184890546939710019277357161497407143903832703317801L), eps * 5000L);
1443    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(-0.875L), static_cast<long double>(1L) / 1024L), static_cast<long double>(2.18674503176462374414944618968850352696579451638002110619287L), eps * 5000L);
1444    BOOST_CHECK_CLOSE(tr1::comp_ellint_3(static_cast<long double>(-0.875L), static_cast<long double>(1023L)/1024L), static_cast<long double>(101.045289804941384100960063898569538919135722087486350366997L), eps * 5000L);
1445
1446    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(2.25L), static_cast<long double>(1L)/(1024*1024L)), static_cast<long double>(2.34379212133481347189068464680335815256364262507955635911656e-15L), eps * 5000L);
1447    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(5.5L), static_cast<long double>(3.125L)), static_cast<long double>(0.0583514045989371500460946536220735787163510569634133670181210L), eps * 5000L);
1448    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-5L) + static_cast<long double>(1L)/1024L, static_cast<long double>(2.125L)), static_cast<long double>(0.0267920938009571023702933210070984416052633027166975342895062L), eps * 5000L);
1449    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-5.5L), static_cast<long double>(10L)), static_cast<long double>(597.577606961369169607937419869926705730305175364662688426534L), eps * 5000L);
1450    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-10486074L)/(1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(1.41474005665181350367684623930576333542989766867888186478185e35L), eps * 5000L);
1451    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-10486074L)/(1024*1024L), static_cast<long double>(50L)), static_cast<long double>(1.07153277202900671531087024688681954238311679648319534644743e20L), eps * 5000L);
1452    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(144794L)/1024L, static_cast<long double>(100L)), static_cast<long double>(2066.27694757392660413922181531984160871678224178890247540320L), eps * 5000L);
1453    BOOST_CHECK_CLOSE(tr1::cyl_bessel_i(static_cast<long double>(-144794L)/1024L, static_cast<long double>(100L)), static_cast<long double>(2066.27694672763190927440969155740243346136463461655104698748L), eps * 5000L);
1454
1455    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(2457L)/1024L, static_cast<long double>(1L)/1024L), static_cast<long double>(3.80739920118603335646474073457326714709615200130620574875292e-9L), eps * 5000L);
1456    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(0.0281933076257506091621579544064767140470089107926550720453038L), eps * 5000L);
1457    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(-2.55820064470647911823175836997490971806135336759164272675969L), eps * 5000L);
1458    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(2.449843111985605522111159013846599118397e-03L), eps * 50000L);
1459    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(0.00759343502722670361395585198154817047185480147294665270646578L), eps * 5000L);
1460    //BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.5L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000747424248595630177396350688505919533097973148718960064663632L), eps * 50000L);
1461    //BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.125L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000776600124835704280633640911329691642748783663198207360238214L), eps * 50000L);
1462    //BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(5.875L), static_cast<long double>(1e+06L)), static_cast<long double>(-0.000466322721115193071631008581529503095819705088484386434589780L), eps * 50000L);
1463    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(0.5L), static_cast<long double>(101L)), static_cast<long double>(0.0358874487875643822020496677692429287863419555699447066226409L), eps * 5000L);
1464    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(0.00244984311198560552211115901384659911839737686676766460822577L), eps * 50000L);
1465    //BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-5.5L), static_cast<long double>(1e+06L)), static_cast<long double>(0.000279243200433579511095229508894156656558211060453622750659554L), eps * 50000L);
1466    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-0.5L), static_cast<long double>(101L)), static_cast<long double>(0.0708184798097594268482290389188138201440114881159344944791454L), eps * 5000L);
1467    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(1.41474013160494695750009004222225969090304185981836460288562e35L), eps * 5000L);
1468    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(15L)), static_cast<long double>(-0.0902239288885423309568944543848111461724911781719692852541489L), eps * 5000L);
1469    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(-0.0547064914615137807616774867984047583596945624129838091326863L), eps * 5000L);
1470    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(10486074L) / (1024*1024L), static_cast<long double>(2e+04L)), static_cast<long double>(-0.00556783614400875611650958980796060611309029233226596737701688L), eps * 5000L);
1471    BOOST_CHECK_CLOSE(tr1::cyl_bessel_j(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(-0.0547613660316806551338637153942604550779513947674222863858713L), eps * 5000L);
1472
1473    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(0.5L), static_cast<long double>(0.875L)), static_cast<long double>(0.558532231646608646115729767013630967055657943463362504577189L), eps * 5000L);
1474    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(0.5L), static_cast<long double>(1.125L)), static_cast<long double>(0.383621010650189547146769320487006220295290256657827220786527L), eps * 5000L);
1475    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(2.25L), static_cast<long double>(std::ldexp(1.0L, -30L))), static_cast<long double>(5.62397392719283271332307799146649700147907612095185712015604e20L), eps * 5000L);
1476    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(5.5L), static_cast<long double>(3217L)/1024L), static_cast<long double>(1.30623288775012596319554857587765179889689223531159532808379L), eps * 5000L);
1477    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(-5.5L), static_cast<long double>(10L)), static_cast<long double>(0.0000733045300798502164644836879577484533096239574909573072142667L), eps * 5000L);
1478    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(-5.5L), static_cast<long double>(100L)), static_cast<long double>(5.41274555306792267322084448693957747924412508020839543293369e-45L), eps * 5000L);
1479    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(10240L)/1024L, static_cast<long double>(1L)/1024L), static_cast<long double>(2.35522579263922076203415803966825431039900000000993410734978e38L), eps * 5000L);
1480    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(10240L)/1024L, static_cast<long double>(10L)), static_cast<long double>(0.00161425530039067002345725193091329085443750382929208307802221L), eps * 5000L);
1481    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(144793L)/1024L, static_cast<long double>(100L)), static_cast<long double>(1.39565245860302528069481472855619216759142225046370312329416e-6L), eps * 5000L);
1482    BOOST_CHECK_CLOSE(tr1::cyl_bessel_k(static_cast<long double>(144793L)/1024L, static_cast<long double>(200L)), static_cast<long double>(9.11950412043225432171915100042647230802198254567007382956336e-68L), eps * 7000L);
1483
1484    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(0.5L), static_cast<long double>(1L) / (1024*1024L)), static_cast<long double>(-817.033790261762580469303126467917092806755460418223776544122L), eps * 5000L);
1485    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(5.5L), static_cast<long double>(3.125L)), static_cast<long double>(-2.61489440328417468776474188539366752698192046890955453259866L), eps * 5000L);
1486    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-5.5L), static_cast<long double>(3.125L)), static_cast<long double>(-0.0274994493896489729948109971802244976377957234563871795364056L), eps * 5000L);
1487    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-5.5L), static_cast<long double>(1e+04L)), static_cast<long double>(-0.00759343502722670361395585198154817047185480147294665270646578L), eps * 5000L);
1488    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1L)/1024L), static_cast<long double>(-1.50382374389531766117868938966858995093408410498915220070230e38L), eps * 5000L);
1489    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-10486074L) / (1024*1024L), static_cast<long double>(1e+02L)), static_cast<long double>(0.0583041891319026009955779707640455341990844522293730214223545L), eps * 5000L);
1490    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(141.75L), static_cast<long double>(1e+02L)), static_cast<long double>(-5.38829231428696507293191118661269920130838607482708483122068e9L), eps * 5000L);
1491    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(141.75L), static_cast<long double>(2e+04L)), static_cast<long double>(-0.00376577888677186194728129112270988602876597726657372330194186L), eps * 50000L);
1492    BOOST_CHECK_CLOSE(tr1::cyl_neumann(static_cast<long double>(-141.75L), static_cast<long double>(1e+02L)), static_cast<long double>(-3.81009803444766877495905954105669819951653361036342457919021e9L), eps * 5000L);
1493
1494    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(0L), eps * 5000L);
1495    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0L), static_cast<long double>(-10L)), static_cast<long double>(-10L), eps * 5000L);
1496    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(-1L), static_cast<long double>(-1L)), static_cast<long double>(-1.2261911708835170708130609674719067527242483502207L), eps * 5000L);
1497    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.875L), static_cast<long double>(-4L)), static_cast<long double>(-5.3190556182262405182189463092940736859067548232647L), eps * 5000L);
1498    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(-0.625L), static_cast<long double>(8L)), static_cast<long double>(9.0419973860310100524448893214394562615252527557062L), eps * 5000L);
1499    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.875L), static_cast<long double>(1e-05L)), static_cast<long double>(0.000010000000000127604166668510945638036143355898993088L), eps * 5000L);
1500    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(10L)/1024L, static_cast<long double>(1e+05L)), static_cast<long double>(100002.38431454899771096037307519328741455615271038L), eps * 5000L);
1501    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(1L), static_cast<long double>(1e-20L)), static_cast<long double>(1.0000000000000000000000000000000000000000166666667e-20L), eps * 5000L);
1502    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(1e-20L), static_cast<long double>(1e-20L)), static_cast<long double>(1.000000000000000e-20L), eps * 5000L);
1503    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(400L)/1024L, static_cast<long double>(1e+20L)), static_cast<long double>(1.0418143796499216839719289963154558027005142709763e20L), eps * 5000L);
1504    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(2L)), static_cast<long double>(2.1765877052210673672479877957388515321497888026770L), eps * 5000L);
1505    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(4L)), static_cast<long double>(4.2543274975235836861894752787874633017836785640477L), eps * 5000L);
1506    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(6L)), static_cast<long double>(6.4588766202317746302999080620490579800463614807916L), eps * 5000L);
1507    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(10L)), static_cast<long double>(10.697409951222544858346795279378531495869386960090L), eps * 5000L);
1508    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(-2L)), static_cast<long double>(-2.1765877052210673672479877957388515321497888026770L), eps * 5000L);
1509    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(-4L)), static_cast<long double>(-4.2543274975235836861894752787874633017836785640477L), eps * 5000L);
1510    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(-6L)), static_cast<long double>(-6.4588766202317746302999080620490579800463614807916L), eps * 5000L);
1511    BOOST_CHECK_CLOSE(tr1::ellint_1(static_cast<long double>(0.5L), static_cast<long double>(-10L)), static_cast<long double>(-10.697409951222544858346795279378531495869386960090L), eps * 5000L);
1512
1513    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(0L), static_cast<long double>(0L)), static_cast<long double>(0L), eps * 5000L);
1514    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(0L), static_cast<long double>(-10L)), static_cast<long double>(-10L), eps * 5000L);
1515    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(-1L), static_cast<long double>(-1L)), static_cast<long double>(-0.84147098480789650665250232163029899962256306079837L), eps * 5000L);
1516    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(900L) / 1024L, static_cast<long double>(-4L)), static_cast<long double>(-3.1756145986492562317862928524528520686391383168377L), eps * 5000L);
1517    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(-600L) / 1024L, static_cast<long double>(8L)), static_cast<long double>(7.2473147180505693037677015377802777959345489333465L), eps * 5000L);
1518    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(800L) / 1024L, static_cast<long double>(1e-05L)), static_cast<long double>(9.999999999898274739584436515967055859383969942432E-6L), eps * 5000L);
1519    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(100L) / 1024L, static_cast<long double>(1e+05L)), static_cast<long double>(99761.153306972066658135668386691227343323331995888L), eps * 5000L);
1520    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(-0.5L), static_cast<long double>(1e+10L)), static_cast<long double>(9.3421545766487137036576748555295222252286528414669e9L), eps * 5000L);
1521    BOOST_CHECK_CLOSE(tr1::ellint_2(static_cast<long double>(400L) / 1024L, ldexp(static_cast<long double>(1L), 66L)), static_cast<long double>(7.0886102721911705466476846969992069994308167515242e19L), eps * 5000L);
1522
1523    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(1L), static_cast<long double>(-1L)), static_cast<long double>(-1.557407724654902230506974807458360173087L), eps * 5000L);
1524    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.4L), static_cast<long double>(0L), static_cast<long double>(-4L)), static_cast<long double>(-4.153623371196831087495427530365430979011L), eps * 5000L);
1525    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(-0.6L), static_cast<long double>(0L), static_cast<long double>(8L)), static_cast<long double>(8.935930619078575123490612395578518914416L), eps * 5000L);
1526    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.25L), static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(0.501246705365439492445236118603525029757890291780157969500480L), eps * 5000L);
1527    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(0L), static_cast<long double>(0.5L)), static_cast<long double>(0.5L), eps * 5000L);
1528    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(-2L), static_cast<long double>(0.5L)), static_cast<long double>(0.437501067017546278595664813509803743009132067629603474488486L), eps * 5000L);
1529    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(0.25L), static_cast<long double>(0.5L)), static_cast<long double>(0.510269830229213412212501938035914557628394166585442994564135L), eps * 5000L);
1530    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(0.75L), static_cast<long double>(0.5L)), static_cast<long double>(0.533293253875952645421201146925578536430596894471541312806165L), eps * 5000L);
1531    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(0.75L), static_cast<long double>(0.75L)), static_cast<long double>(0.871827580412760575085768367421866079353646112288567703061975L), eps * 5000L);
1532    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(1L), static_cast<long double>(0.25L)), static_cast<long double>(0.255341921221036266504482236490473678204201638800822621740476L), eps * 5000L);
1533    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(2L), static_cast<long double>(0.25L)), static_cast<long double>(0.261119051639220165094943572468224137699644963125853641716219L), eps * 5000L);
1534    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0L), static_cast<long double>(1023L)/1024L, static_cast<long double>(1.5L)), static_cast<long double>(13.2821612239764190363647953338544569682942329604483733197131L), eps * 5000L);
1535    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.5L), static_cast<long double>(0.5L), static_cast<long double>(-1L)), static_cast<long double>(-1.228014414316220642611298946293865487807L), eps * 5000L);
1536    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.5L), static_cast<long double>(0.5L), static_cast<long double>(1e+10L)), static_cast<long double>(1.536591003599172091573590441336982730551e+10L), eps * 5000L);
1537    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.75L), static_cast<long double>(-1e+05L), static_cast<long double>(10L)), static_cast<long double>(0.0347926099493147087821620459290460547131012904008557007934290L), eps * 5000L);
1538    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(10L)), static_cast<long double>(0.000109956202759561502329123384755016959364346382187364656768212L), eps * 5000L);
1539    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(1e+20L)), static_cast<long double>(1.00000626665567332602765201107198822183913978895904937646809e15L), eps * 5000L);
1540    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.875L), static_cast<long double>(-1e+10L), static_cast<long double>(1608L)/1024L), static_cast<long double>(0.0000157080616044072676127333183571107873332593142625043567690379L), eps * 5000L);
1541    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.875L), 1-static_cast<long double>(1L) / 1024L, static_cast<long double>(1e+20L)), static_cast<long double>(6.43274293944380717581167058274600202023334985100499739678963e21L), eps * 5000L);
1542    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.25L), static_cast<long double>(50L), static_cast<long double>(0.1L)), static_cast<long double>(0.124573770342749525407523258569507331686458866564082916835900L), eps * 5000L);
1543    BOOST_CHECK_CLOSE(tr1::ellint_3(static_cast<long double>(0.25L), static_cast<long double>(1.125L), static_cast<long double>(1L)), static_cast<long double>(1.77299767784815770192352979665283069318388205110727241629752L), eps * 5000L);
1544
1545    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(1L)/1024L), static_cast<long double>(-6.35327933972759151358547423727042905862963067106751711596065L), eps * 5000L);
1546    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(0.125L)), static_cast<long double>(-1.37320852494298333781545045921206470808223543321810480716122L), eps * 5000L);
1547    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(0.5L)), static_cast<long double>(0.454219904863173579920523812662802365281405554352642045162818L), eps * 5000L);
1548    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(1L)), static_cast<long double>(1.89511781635593675546652093433163426901706058173270759164623L), eps * 5000L);
1549    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(50.5L)), static_cast<long double>(1.72763195602911805201155668940185673806099654090456049881069e20L), eps * 5000L);
1550    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-1L)/1024L), static_cast<long double>(-6.35523246483107180261445551935803221293763008553775821607264L), eps * 5000L);
1551    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-0.125L)), static_cast<long double>(-1.62342564058416879145630692462440887363310605737209536579267L), eps * 5000L);
1552    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-0.5L)), static_cast<long double>(-0.559773594776160811746795939315085235226846890316353515248293L), eps * 5000L);
1553    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-1L)), static_cast<long double>(-0.219383934395520273677163775460121649031047293406908207577979L), eps * 5000L);
1554    BOOST_CHECK_CLOSE(tr1::expint(static_cast<long double>(-50.5L)), static_cast<long double>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), eps * 5000L);
1555
1556    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(0L, static_cast<long double>(1L)), static_cast<long double>(1.L), 100L * eps);
1557    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(1L)), static_cast<long double>(2.L), 100L * eps);
1558    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(2L)), static_cast<long double>(4.L), 100L * eps);
1559    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(10L)), static_cast<long double>(20L), 100L * eps);
1560    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(100L)), static_cast<long double>(200L), 100L * eps);
1561    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(1L, static_cast<long double>(1e6L)), static_cast<long double>(2e6L), 100L * eps);
1562    //BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10L, static_cast<long double>(30L)), static_cast<long double>(5.896624628001300E+17L), 100L * eps);
1563    //BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10L, static_cast<long double>(1000L)), static_cast<long double>(1.023976960161280E+33L), 100L * eps);
1564    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10L, static_cast<long double>(10L)), static_cast<long double>(8.093278209760000E+12L), 100L * eps);
1565    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(10L, static_cast<long double>(-10L)), static_cast<long double>(8.093278209760000E+12L), 100L * eps);
1566    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3L, static_cast<long double>(-10L)), static_cast<long double>(-7.880000000000000E+3L), 100L * eps);
1567    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3L, static_cast<long double>(-1000L)), static_cast<long double>(-7.999988000000000E+9L), 100L * eps);
1568    BOOST_CHECK_CLOSE_FRACTION(tr1::hermite(3L, static_cast<long double>(-1000000L)), static_cast<long double>(-7.999999999988000E+18L), 100L * eps);
1569
1570    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(0.125L)), static_cast<long double>(-0.63277562349869525529352526763564627152686379131122L), eps * 5000L);
1571    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(1023L) / static_cast<long double>(1024L)), static_cast<long double>(-1023.4228554489429786541032870895167448906103303056L), eps * 5000L);
1572    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(1025L) / static_cast<long double>(1024L)), static_cast<long double>(1024.5772867695045940578681624248887776501597556226L), eps * 5000L);
1573    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(0.5L)), static_cast<long double>(-1.46035450880958681288949915251529801246722933101258149054289L), eps * 5000L);
1574    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(1.125L)), static_cast<long double>(8.5862412945105752999607544082693023591996301183069L), eps * 5000L);
1575    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(2L)), static_cast<long double>(1.6449340668482264364724151666460251892189499012068L), eps * 5000L);
1576    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(3.5L)), static_cast<long double>(1.1267338673170566464278124918549842722219969574036L), eps * 5000L);
1577    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(4L)), static_cast<long double>(1.08232323371113819151600369654116790277475095191872690768298L), eps * 5000L);
1578    BOOST_CHECK_CLOSE(tr1::riemann_zeta(4L + static_cast<long double>(1L) / 1024L), static_cast<long double>(1.08225596856391369799036835439238249195298434901488518878804L), eps * 5000L);
1579    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(4.5L)), static_cast<long double>(1.05470751076145426402296728896028011727249383295625173068468L), eps * 5000L);
1580    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(6.5L)), static_cast<long double>(1.01200589988852479610078491680478352908773213619144808841031L), eps * 5000L);
1581    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(7.5L)), static_cast<long double>(1.00582672753652280770224164440459408011782510096320822989663L), eps * 5000L);
1582    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(8.125L)), static_cast<long double>(1.0037305205308161603183307711439385250181080293472L), eps * 5000L);
1583    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(16.125L)), static_cast<long double>(1.0000140128224754088474783648500235958510030511915L), eps * 5000L);
1584    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(0L)), static_cast<long double>(-0.5L), eps * 5000L);
1585    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-0.125L)), static_cast<long double>(-0.39906966894504503550986928301421235400280637468895L), eps * 5000L);
1586    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-1L)), static_cast<long double>(-0.083333333333333333333333333333333333333333333333333L), eps * 5000L);
1587    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-2L)), static_cast<long double>(0L), eps * 5000L);
1588    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-2.5L)), static_cast<long double>(0.0085169287778503305423585670283444869362759902200745L), eps * 5000L * 3L);
1589    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-3L)), static_cast<long double>(0.0083333333333333333333333333333333333333333333333333L), eps * 5000L);
1590    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-4L)), static_cast<long double>(0L), eps * 5000L);
1591    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-20L)), static_cast<long double>(0L), eps * 5000L * 100L);
1592    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-21L)), static_cast<long double>(-281.46014492753623188405797101449275362318840579710L), eps * 5000L * 100L);
1593    BOOST_CHECK_CLOSE(tr1::riemann_zeta(static_cast<long double>(-30.125L)), static_cast<long double>(2.2762941726834511267740045451463455513839970804578e7L), eps * 5000L * 100L);
1594
1595    BOOST_CHECK_CLOSE(tr1::sph_bessel(0L, static_cast<long double>(0.1433600485324859619140625e-1L)), static_cast<long double>(0.9999657468461303487880990241993035937654e0L),  eps * 5000L * 100L);
1596    BOOST_CHECK_CLOSE(tr1::sph_bessel(0L, static_cast<long double>(0.1760916970670223236083984375e-1L)), static_cast<long double>(0.9999483203249623334100130061926184665364e0L),  eps * 5000L * 100L);
1597    BOOST_CHECK_CLOSE(tr1::sph_bessel(2L, static_cast<long double>(0.1433600485324859619140625e-1L)), static_cast<long double>(0.1370120120703995134662099191103188366059e-4L),  eps * 5000L * 100L);
1598    BOOST_CHECK_CLOSE(tr1::sph_bessel(2L, static_cast<long double>(0.1760916970670223236083984375e-1L)), static_cast<long double>(0.2067173265753174063228459655801741280461e-4L),  eps * 5000L * 100L);
1599    BOOST_CHECK_CLOSE(tr1::sph_bessel(7L, static_cast<long double>(0.1252804412841796875e3L)), static_cast<long double>(0.7887555711993028736906736576314283291289e-2L),  eps * 5000L * 100L);
1600    BOOST_CHECK_CLOSE(tr1::sph_bessel(7L, static_cast<long double>(0.25554705810546875e3L)), static_cast<long double>(-0.1463292767579579943284849187188066532514e-2L),  eps * 5000L * 100L);
1601
1602    BOOST_CHECK_CLOSE(tr1::sph_neumann(0L, static_cast<long double>(0.408089816570281982421875e0L)), static_cast<long double>(-0.2249212131304610409189209411089291558038e1L), eps * 5000L * 100L);
1603    BOOST_CHECK_CLOSE(tr1::sph_neumann(0L, static_cast<long double>(0.6540834903717041015625e0L)), static_cast<long double>(-0.1213309779166084571756446746977955970241e1L),   eps * 5000L * 100L);
1604    BOOST_CHECK_CLOSE(tr1::sph_neumann(2L, static_cast<long double>(0.408089816570281982421875e0L)), static_cast<long double>(-0.4541702641837159203058389758895634766256e2L),   eps * 5000L * 100L);
1605    BOOST_CHECK_CLOSE(tr1::sph_neumann(2L, static_cast<long double>(0.6540834903717041015625e0L)), static_cast<long double>(-0.1156112621471167110574129561700037138981e2L),   eps * 5000L * 100L);
1606    BOOST_CHECK_CLOSE(tr1::sph_neumann(10L, static_cast<long double>(0.1097540378570556640625e1L)), static_cast<long double>(-0.2427889658115064857278886600528596240123e9L),   eps * 5000L * 100L);
1607    BOOST_CHECK_CLOSE(tr1::sph_neumann(10L, static_cast<long double>(0.30944411754608154296875e1L)), static_cast<long double>(-0.3394649246350136450439882104151313759251e4L),   eps * 5000L * 100L);
1608
1609    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(3L, 2L, static_cast<long double>(0.5L)), static_cast<long double>(0.2061460599687871330692286791802688341213L), eps * 5000L);
1610    BOOST_CHECK_CLOSE_FRACTION(tr1::sph_legendre(40L, 15L, static_cast<long double>(0.75L)), static_cast<long double>(-0.406036847302819452666908966769096223205057182668333862900509L), eps * 5000L);
1611 #endif
1612 #endif
1613 }
1614
1615 BOOST_AUTO_TEST_CASE( test_main )
1616 {
1617 #ifndef TEST_LD
1618    test_values(1.0f, "float");
1619    test_values(1.0, "double");
1620 #else
1621 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
1622    test_values(1.0L, "long double");
1623 #endif
1624 #endif
1625
1626 }
1627