libstdc++-v3/testsuite/special_functions/08_cyl_bessel_j/check_value.cc

   1 // { dg-do run { target c++11 } }
   2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   3 //
   4 // Copyright (C) 2016-2017 Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 3, or (at your option)
  10 // any later version.
  11 //
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16 //
  17 // You should have received a copy of the GNU General Public License along
  18 // with this library; see the file COPYING3.  If not see
  19 // <http://www.gnu.org/licenses/>.
  20
  21 //  cyl_bessel_j
  22 //  Compare against values generated by the GNU Scientific Library.
  23 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  24 #include <limits>
  25 #include <cmath>
  26 #if defined(__TEST_DEBUG)
  27 #  include <iostream>
  28 #  define VERIFY(A) \
  29   if (!(A)) \
  30     { \
  31       std::cout << "line " << __LINE__ \
  32         << "  max_abs_frac = " << max_abs_frac \
  33         << std::endl; \
  34     }
  35 #else
  36 #  include <testsuite_hooks.h>
  37 #endif
  38 #include <specfun_testcase.h>
  39
  40
  41 // Test data for nu=0.0000000000000000.
  42 // max(|f - f_GSL|): 1.6653345369377348e-16
  43 // max(|f - f_GSL| / |f_GSL|): 6.5276306654894409e-16
  44 const testcase_cyl_bessel_j<double>
  45 data001[21] =
  46 {
  47   { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000 },
  48   { 0.98443592929585266, 0.0000000000000000, 0.25000000000000000 },
  49   { 0.93846980724081297, 0.0000000000000000, 0.50000000000000000 },
  50   { 0.86424227516664853, 0.0000000000000000, 0.75000000000000000 },
  51   { 0.76519768655796661, 0.0000000000000000, 1.0000000000000000 },
  52   { 0.64590608527128535, 0.0000000000000000, 1.2500000000000000 },
  53   { 0.51182767173591814, 0.0000000000000000, 1.5000000000000000 },
  54   { 0.36903253018515075, 0.0000000000000000, 1.7500000000000000 },
  55   { 0.22389077914123562, 0.0000000000000000, 2.0000000000000000 },
  56   { 0.082749851288734022, 0.0000000000000000, 2.2500000000000000 },
  57   { -0.048383776468197998, 0.0000000000000000, 2.5000000000000000 },
  58   { -0.16414142780851368, 0.0000000000000000, 2.7500000000000000 },
  59   { -0.26005195490193334, 0.0000000000000000, 3.0000000000000000 },
  60   { -0.33275080217061132, 0.0000000000000000, 3.2500000000000000 },
  61   { -0.38012773998726335, 0.0000000000000000, 3.5000000000000000 },
  62   { -0.40140605493617426, 0.0000000000000000, 3.7500000000000000 },
  63   { -0.39714980986384740, 0.0000000000000000, 4.0000000000000000 },
  64   { -0.36919977029989554, 0.0000000000000000, 4.2500000000000000 },
  65   { -0.32054250898512149, 0.0000000000000000, 4.5000000000000000 },
  66   { -0.25512082749137405, 0.0000000000000000, 4.7500000000000000 },
  67   { -0.17759677131433835, 0.0000000000000000, 5.0000000000000000 },
  68 };
  69 const double toler001 = 2.5000000000000020e-13;
  70
  71 // Test data for nu=0.33333333333333331.
  72 // max(|f - f_GSL|): 7.7715611723760958e-16
  73 // max(|f - f_GSL| / |f_GSL|): 1.2121143083098064e-15
  74 const testcase_cyl_bessel_j<double>
  75 data002[21] =
  76 {
  77   { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000 },
  78   { 0.55338359549647709, 0.33333333333333331, 0.25000000000000000 },
  79   { 0.67283082949794537, 0.33333333333333331, 0.50000000000000000 },
  80   { 0.72490863199379008, 0.33333333333333331, 0.75000000000000000 },
  81   { 0.73087640216944760, 0.33333333333333331, 1.0000000000000000 },
  82   { 0.69953374433894455, 0.33333333333333331, 1.2500000000000000 },
  83   { 0.63713263706489176, 0.33333333333333331, 1.5000000000000000 },
  84   { 0.54956352730788460, 0.33333333333333331, 1.7500000000000000 },
  85   { 0.44293981814857586, 0.33333333333333331, 2.0000000000000000 },
  86   { 0.32366988946292502, 0.33333333333333331, 2.2500000000000000 },
  87   { 0.19832093341860796, 0.33333333333333331, 2.5000000000000000 },
  88   { 0.073389637874297489, 0.33333333333333331, 2.7500000000000000 },
  89   { -0.044963820940233351, 0.33333333333333331, 3.0000000000000000 },
  90   { -0.15118395956666372, 0.33333333333333331, 3.2500000000000000 },
  91   { -0.24056593952693625, 0.33333333333333331, 3.5000000000000000 },
  92   { -0.30946094681921288, 0.33333333333333331, 3.7500000000000000 },
  93   { -0.35542737345457609, 0.33333333333333331, 4.0000000000000000 },
  94   { -0.37731852825457068, 0.33333333333333331, 4.2500000000000000 },
  95   { -0.37530189159358079, 0.33333333333333331, 4.5000000000000000 },
  96   { -0.35080916720916927, 0.33333333333333331, 4.7500000000000000 },
  97   { -0.30642046380026405, 0.33333333333333331, 5.0000000000000000 },
  98 };
  99 const double toler002 = 2.5000000000000020e-13;
 100
 101 // Test data for nu=0.50000000000000000.
 102 // max(|f - f_GSL|): 7.7715611723760958e-16
 103 // max(|f - f_GSL| / |f_GSL|): 1.1959227189513475e-15
 104 const testcase_cyl_bessel_j<double>
 105 data003[21] =
 106 {
 107   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000 },
 108   { 0.39479959874136972, 0.50000000000000000, 0.25000000000000000 },
 109   { 0.54097378993452760, 0.50000000000000000, 0.50000000000000000 },
 110   { 0.62800587637588623, 0.50000000000000000, 0.75000000000000000 },
 111   { 0.67139670714180244, 0.50000000000000000, 1.0000000000000000 },
 112   { 0.67724253810014312, 0.50000000000000000, 1.2500000000000000 },
 113   { 0.64983807475374655, 0.50000000000000000, 1.5000000000000000 },
 114   { 0.59348525447147382, 0.50000000000000000, 1.7500000000000000 },
 115   { 0.51301613656182721, 0.50000000000000000, 2.0000000000000000 },
 116   { 0.41387506064759982, 0.50000000000000000, 2.2500000000000000 },
 117   { 0.30200490606236535, 0.50000000000000000, 2.5000000000000000 },
 118   { 0.18363332138431521, 0.50000000000000000, 2.7500000000000000 },
 119   { 0.065008182877375753, 0.50000000000000000, 3.0000000000000000 },
 120   { -0.047885729975898544, 0.50000000000000000, 3.2500000000000000 },
 121   { -0.14960456964952620, 0.50000000000000000, 3.5000000000000000 },
 122   { -0.23549801845815513, 0.50000000000000000, 3.7500000000000000 },
 123   { -0.30192051329163944, 0.50000000000000000, 4.0000000000000000 },
 124   { -0.34638850218952444, 0.50000000000000000, 4.2500000000000000 },
 125   { -0.36767487332724025, 0.50000000000000000, 4.5000000000000000 },
 126   { -0.36583563802350400, 0.50000000000000000, 4.7500000000000000 },
 127   { -0.34216798479816180, 0.50000000000000000, 5.0000000000000000 },
 128 };
 129 const double toler003 = 2.5000000000000020e-13;
 130
 131 // Test data for nu=0.66666666666666663.
 132 // max(|f - f_GSL|): 7.7715611723760958e-16
 133 // max(|f - f_GSL| / |f_GSL|): 1.4163878424300161e-15
 134 const testcase_cyl_bessel_j<double>
 135 data004[21] =
 136 {
 137   { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000 },
 138   { 0.27434438998865135, 0.66666666666666663, 0.25000000000000000 },
 139   { 0.42331075068448321, 0.66666666666666663, 0.50000000000000000 },
 140   { 0.52870551548162792, 0.66666666666666663, 0.75000000000000000 },
 141   { 0.59794997367362801, 0.66666666666666663, 1.0000000000000000 },
 142   { 0.63338726889075891, 0.66666666666666663, 1.2500000000000000 },
 143   { 0.63673234502877385, 0.66666666666666663, 1.5000000000000000 },
 144   { 0.61022230460131899, 0.66666666666666663, 1.7500000000000000 },
 145   { 0.55696967691913712, 0.66666666666666663, 2.0000000000000000 },
 146   { 0.48101276749106114, 0.66666666666666663, 2.2500000000000000 },
 147   { 0.38721242477084306, 0.66666666666666663, 2.5000000000000000 },
 148   { 0.28105724771080542, 0.66666666666666663, 2.7500000000000000 },
 149   { 0.16841218049067044, 0.66666666666666663, 3.0000000000000000 },
 150   { 0.055235893475364915, 0.66666666666666663, 3.2500000000000000 },
 151   { -0.052711584404031925, 0.66666666666666663, 3.5000000000000000 },
 152   { -0.15015178042293029, 0.66666666666666663, 3.7500000000000000 },
 153   { -0.23254408502670390, 0.66666666666666663, 4.0000000000000000 },
 154   { -0.29630067002972543, 0.66666666666666663, 4.2500000000000000 },
 155   { -0.33894810189777724, 0.66666666666666663, 4.5000000000000000 },
 156   { -0.35922706960321099, 0.66666666666666663, 4.7500000000000000 },
 157   { -0.35712533549168868, 0.66666666666666663, 5.0000000000000000 },
 158 };
 159 const double toler004 = 2.5000000000000020e-13;
 160
 161 // Test data for nu=1.0000000000000000.
 162 // max(|f - f_GSL|): 2.2204460492503131e-16
 163 // max(|f - f_GSL| / |f_GSL|): 6.7783500059747526e-16
 164 const testcase_cyl_bessel_j<double>
 165 data005[21] =
 166 {
 167   { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000 },
 168   { 0.12402597732272694, 1.0000000000000000, 0.25000000000000000 },
 169   { 0.24226845767487390, 1.0000000000000000, 0.50000000000000000 },
 170   { 0.34924360217486222, 1.0000000000000000, 0.75000000000000000 },
 171   { 0.44005058574493355, 1.0000000000000000, 1.0000000000000000 },
 172   { 0.51062326031988059, 1.0000000000000000, 1.2500000000000000 },
 173   { 0.55793650791009952, 1.0000000000000000, 1.5000000000000000 },
 174   { 0.58015619763899240, 1.0000000000000000, 1.7500000000000000 },
 175   { 0.57672480775687363, 1.0000000000000000, 2.0000000000000000 },
 176   { 0.54837835664696011, 1.0000000000000000, 2.2500000000000000 },
 177   { 0.49709410246427416, 1.0000000000000000, 2.5000000000000000 },
 178   { 0.42597230295790256, 1.0000000000000000, 2.7500000000000000 },
 179   { 0.33905895852593648, 1.0000000000000000, 3.0000000000000000 },
 180   { 0.24111968801520400, 1.0000000000000000, 3.2500000000000000 },
 181   { 0.13737752736232706, 1.0000000000000000, 3.5000000000000000 },
 182   { 0.033229349129679724, 1.0000000000000000, 3.7500000000000000 },
 183   { -0.066043328023549230, 1.0000000000000000, 4.0000000000000000 },
 184   { -0.15555319297834286, 1.0000000000000000, 4.2500000000000000 },
 185   { -0.23106043192337070, 1.0000000000000000, 4.5000000000000000 },
 186   { -0.28918679864711044, 1.0000000000000000, 4.7500000000000000 },
 187   { -0.32757913759146529, 1.0000000000000000, 5.0000000000000000 },
 188 };
 189 const double toler005 = 2.5000000000000020e-13;
 190
 191 // Test data for nu=2.0000000000000000.
 192 // max(|f - f_GSL|): 5.5511151231257827e-17
 193 // max(|f - f_GSL| / |f_GSL|): 2.4155555971238584e-16
 194 const testcase_cyl_bessel_j<double>
 195 data006[21] =
 196 {
 197   { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000 },
 198   { 0.0077718892859626760, 2.0000000000000000, 0.25000000000000000 },
 199   { 0.030604023458682638, 2.0000000000000000, 0.50000000000000000 },
 200   { 0.067073997299650551, 2.0000000000000000, 0.75000000000000000 },
 201   { 0.11490348493190047, 2.0000000000000000, 1.0000000000000000 },
 202   { 0.17109113124052350, 2.0000000000000000, 1.2500000000000000 },
 203   { 0.23208767214421472, 2.0000000000000000, 1.5000000000000000 },
 204   { 0.29400312425941216, 2.0000000000000000, 1.7500000000000000 },
 205   { 0.35283402861563773, 2.0000000000000000, 2.0000000000000000 },
 206   { 0.40469757684189717, 2.0000000000000000, 2.2500000000000000 },
 207   { 0.44605905843961718, 2.0000000000000000, 2.5000000000000000 },
 208   { 0.47393946632335160, 2.0000000000000000, 2.7500000000000000 },
 209   { 0.48609126058589119, 2.0000000000000000, 3.0000000000000000 },
 210   { 0.48113214864150627, 2.0000000000000000, 3.2500000000000000 },
 211   { 0.45862918419430765, 2.0000000000000000, 3.5000000000000000 },
 212   { 0.41912837447200352, 2.0000000000000000, 3.7500000000000000 },
 213   { 0.36412814585207293, 2.0000000000000000, 4.0000000000000000 },
 214   { 0.29599826772185189, 2.0000000000000000, 4.2500000000000000 },
 215   { 0.21784898368584549, 2.0000000000000000, 4.5000000000000000 },
 216   { 0.13335796490311685, 2.0000000000000000, 4.7500000000000000 },
 217   { 0.046565116277751971, 2.0000000000000000, 5.0000000000000000 },
 218 };
 219 const double toler006 = 2.5000000000000020e-13;
 220
 221 // Test data for nu=5.0000000000000000.
 222 // max(|f - f_GSL|): 1.3877787807814457e-16
 223 // max(|f - f_GSL| / |f_GSL|): 1.4609680807504906e-15
 224 const testcase_cyl_bessel_j<double>
 225 data007[21] =
 226 {
 227   { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000 },
 228   { 2.5365161587472413e-07, 5.0000000000000000, 0.25000000000000000 },
 229   { 8.0536272413574753e-06, 5.0000000000000000, 0.50000000000000000 },
 230   { 6.0364166510576438e-05, 5.0000000000000000, 0.75000000000000000 },
 231   { 0.00024975773021123450, 5.0000000000000000, 1.0000000000000000 },
 232   { 0.00074440885254749821, 5.0000000000000000, 1.2500000000000000 },
 233   { 0.0017994217673606111, 5.0000000000000000, 1.5000000000000000 },
 234   { 0.0037577257273157133, 5.0000000000000000, 1.7500000000000000 },
 235   { 0.0070396297558716842, 5.0000000000000000, 2.0000000000000000 },
 236   { 0.012121078633445751, 5.0000000000000000, 2.2500000000000000 },
 237   { 0.019501625134503223, 5.0000000000000000, 2.5000000000000000 },
 238   { 0.029664058320006174, 5.0000000000000000, 2.7500000000000000 },
 239   { 0.043028434877047578, 5.0000000000000000, 3.0000000000000000 },
 240   { 0.059903888098560426, 5.0000000000000000, 3.2500000000000000 },
 241   { 0.080441986647991792, 5.0000000000000000, 3.5000000000000000 },
 242   { 0.10459554742314070, 5.0000000000000000, 3.7500000000000000 },
 243   { 0.13208665604709827, 5.0000000000000000, 4.0000000000000000 },
 244   { 0.16238721643623680, 5.0000000000000000, 4.2500000000000000 },
 245   { 0.19471465863871368, 5.0000000000000000, 4.5000000000000000 },
 246   { 0.22804452118769436, 5.0000000000000000, 4.7500000000000000 },
 247   { 0.26114054612017007, 5.0000000000000000, 5.0000000000000000 },
 248 };
 249 const double toler007 = 2.5000000000000020e-13;
 250
 251 // Test data for nu=10.000000000000000.
 252 // max(|f - f_GSL|): 3.2526065174565133e-18
 253 // max(|f - f_GSL| / |f_GSL|): 3.9336732209858561e-15
 254 const testcase_cyl_bessel_j<double>
 255 data008[21] =
 256 {
 257   { 0.0000000000000000, 10.000000000000000, 0.0000000000000000 },
 258   { 2.5628321598050096e-16, 10.000000000000000, 0.25000000000000000 },
 259   { 2.6131773608228023e-13, 10.000000000000000, 0.50000000000000000 },
 260   { 1.4962171311759677e-11, 10.000000000000000, 0.75000000000000000 },
 261   { 2.6306151236874524e-10, 10.000000000000000, 1.0000000000000000 },
 262   { 2.4187548221114514e-09, 10.000000000000000, 1.2500000000000000 },
 263   { 1.4743269078039996e-08, 10.000000000000000, 1.5000000000000000 },
 264   { 6.7608502849897560e-08, 10.000000000000000, 1.7500000000000000 },
 265   { 2.5153862827167358e-07, 10.000000000000000, 2.0000000000000000 },
 266   { 7.9717051583730038e-07, 10.000000000000000, 2.2500000000000000 },
 267   { 2.2247284173983839e-06, 10.000000000000000, 2.5000000000000000 },
 268   { 5.5985475639210430e-06, 10.000000000000000, 2.7500000000000000 },
 269   { 1.2928351645715880e-05, 10.000000000000000, 3.0000000000000000 },
 270   { 2.7761691354244538e-05, 10.000000000000000, 3.2500000000000000 },
 271   { 5.6009495875078844e-05, 10.000000000000000, 3.5000000000000000 },
 272   { 0.00010703761729231951, 10.000000000000000, 3.7500000000000000 },
 273   { 0.00019504055466003446, 10.000000000000000, 4.0000000000000000 },
 274   { 0.00034068888474064193, 10.000000000000000, 4.2500000000000000 },
 275   { 0.00057300977667164505, 10.000000000000000, 4.5000000000000000 },
 276   { 0.00093142172588886810, 10.000000000000000, 4.7500000000000000 },
 277   { 0.0014678026473104744, 10.000000000000000, 5.0000000000000000 },
 278 };
 279 const double toler008 = 2.5000000000000020e-13;
 280
 281 // Test data for nu=20.000000000000000.
 282 // max(|f - f_GSL|): 1.9387045606711586e-26
 283 // max(|f - f_GSL| / |f_GSL|): 2.1275572270326799e-15
 284 const testcase_cyl_bessel_j<double>
 285 data009[21] =
 286 {
 287   { 0.0000000000000000, 20.000000000000000, 0.0000000000000000 },
 288   { 3.5624805510586969e-37, 20.000000000000000, 0.25000000000000000 },
 289   { 3.7272019617047132e-31, 20.000000000000000, 0.50000000000000000 },
 290   { 1.2347870693633488e-27, 20.000000000000000, 0.75000000000000000 },
 291   { 3.8735030085246562e-25, 20.000000000000000, 1.0000000000000000 },
 292   { 3.3372897667043766e-23, 20.000000000000000, 1.2500000000000000 },
 293   { 1.2689972189332558e-21, 20.000000000000000, 1.5000000000000000 },
 294   { 2.7427715944032989e-20, 20.000000000000000, 1.7500000000000000 },
 295   { 3.9189728050907524e-19, 20.000000000000000, 2.0000000000000000 },
 296   { 4.0805232551365158e-18, 20.000000000000000, 2.2500000000000000 },
 297   { 3.3090793836587786e-17, 20.000000000000000, 2.5000000000000000 },
 298   { 2.1915404680645990e-16, 20.000000000000000, 2.7500000000000000 },
 299   { 1.2275946737992981e-15, 20.000000000000000, 3.0000000000000000 },
 300   { 5.9727663938305382e-15, 20.000000000000000, 3.2500000000000000 },
 301   { 2.5768553102807590e-14, 20.000000000000000, 3.5000000000000000 },
 302   { 1.0021112208287217e-13, 20.000000000000000, 3.7500000000000000 },
 303   { 3.5595116285938516e-13, 20.000000000000000, 4.0000000000000000 },
 304   { 1.1673622958555074e-12, 20.000000000000000, 4.2500000000000000 },
 305   { 3.5665470983611762e-12, 20.000000000000000, 4.5000000000000000 },
 306   { 1.0227564044880958e-11, 20.000000000000000, 4.7500000000000000 },
 307   { 2.7703300521289426e-11, 20.000000000000000, 5.0000000000000000 },
 308 };
 309 const double toler009 = 2.5000000000000020e-13;
 310 //  cyl_bessel_j
 311
 312 // Test data for nu=0.0000000000000000.
 313 // max(|f - f_GSL|): 7.6709472107694410e-15
 314 // max(|f - f_GSL| / |f_GSL|): 4.1048891312746575e-13
 315 const testcase_cyl_bessel_j<double>
 316 data010[21] =
 317 {
 318   { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000 },
 319   { -0.17759677131433835, 0.0000000000000000, 5.0000000000000000 },
 320   { -0.24593576445134835, 0.0000000000000000, 10.000000000000000 },
 321   { -0.014224472826780771, 0.0000000000000000, 15.000000000000000 },
 322   { 0.16702466434058319, 0.0000000000000000, 20.000000000000000 },
 323   { 0.096266783275958154, 0.0000000000000000, 25.000000000000000 },
 324   { -0.086367983581040142, 0.0000000000000000, 30.000000000000000 },
 325   { -0.12684568275631256, 0.0000000000000000, 35.000000000000000 },
 326   { 0.0073668905842374085, 0.0000000000000000, 40.000000000000000 },
 327   { 0.11581867067325631, 0.0000000000000000, 45.000000000000000 },
 328   { 0.055812327669251746, 0.0000000000000000, 50.000000000000000 },
 329   { -0.074548302648236808, 0.0000000000000000, 55.000000000000000 },
 330   { -0.091471804089061859, 0.0000000000000000, 60.000000000000000 },
 331   { 0.018687343227677979, 0.0000000000000000, 65.000000000000000 },
 332   { 0.094908726483013545, 0.0000000000000000, 70.000000000000000 },
 333   { 0.034643913805097008, 0.0000000000000000, 75.000000000000000 },
 334   { -0.069742165512210033, 0.0000000000000000, 80.000000000000000 },
 335   { -0.070940394796273273, 0.0000000000000000, 85.000000000000000 },
 336   { 0.026630016699969526, 0.0000000000000000, 90.000000000000000 },
 337   { 0.081811967783384135, 0.0000000000000000, 95.000000000000000 },
 338   { 0.019985850304223170, 0.0000000000000000, 100.00000000000000 },
 339 };
 340 const double toler010 = 2.5000000000000014e-11;
 341
 342 // Test data for nu=0.33333333333333331.
 343 // max(|f - f_GSL|): 7.9311557321659620e-15
 344 // max(|f - f_GSL| / |f_GSL|): 4.2444155318123211e-12
 345 const testcase_cyl_bessel_j<double>
 346 data011[21] =
 347 {
 348   { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000 },
 349   { -0.30642046380026405, 0.33333333333333331, 5.0000000000000000 },
 350   { -0.18614516704869571, 0.33333333333333331, 10.000000000000000 },
 351   { 0.089740004221152650, 0.33333333333333331, 15.000000000000000 },
 352   { 0.17606058001293901, 0.33333333333333331, 20.000000000000000 },
 353   { 0.020097162141383233, 0.33333333333333331, 25.000000000000000 },
 354   { -0.13334053387426159, 0.33333333333333331, 30.000000000000000 },
 355   { -0.087118009397765497, 0.33333333333333331, 35.000000000000000 },
 356   { 0.069202942818858179, 0.33333333333333331, 40.000000000000000 },
 357   { 0.11387616964518317, 0.33333333333333331, 45.000000000000000 },
 358   { -0.00057226680771808045, 0.33333333333333331, 50.000000000000000 },
 359   { -0.10331600929280822, 0.33333333333333331, 55.000000000000000 },
 360   { -0.055618147270528003, 0.33333333333333331, 60.000000000000000 },
 361   { 0.064711954014113948, 0.33333333333333331, 65.000000000000000 },
 362   { 0.086879926462481605, 0.33333333333333331, 70.000000000000000 },
 363   { -0.012614484229891068, 0.33333333333333331, 75.000000000000000 },
 364   { -0.088199784400034537, 0.33333333333333331, 80.000000000000000 },
 365   { -0.036703611076564523, 0.33333333333333331, 85.000000000000000 },
 366   { 0.062916286828779547, 0.33333333333333331, 90.000000000000000 },
 367   { 0.069465244416806030, 0.33333333333333331, 95.000000000000000 },
 368   { -0.021271244853702364, 0.33333333333333331, 100.00000000000000 },
 369 };
 370 const double toler011 = 2.5000000000000017e-10;
 371
 372 // Test data for nu=0.50000000000000000.
 373 // max(|f - f_GSL|): 7.4246164771807344e-15
 374 // max(|f - f_GSL| / |f_GSL|): 3.6725252809051799e-13
 375 const testcase_cyl_bessel_j<double>
 376 data012[21] =
 377 {
 378   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000 },
 379   { -0.34216798479816180, 0.50000000000000000, 5.0000000000000000 },
 380   { -0.13726373575505049, 0.50000000000000000, 10.000000000000000 },
 381   { 0.13396768882243937, 0.50000000000000000, 15.000000000000000 },
 382   { 0.16288076385502984, 0.50000000000000000, 20.000000000000000 },
 383   { -0.021120283599650493, 0.50000000000000000, 25.000000000000000 },
 384   { -0.14392965337039987, 0.50000000000000000, 30.000000000000000 },
 385   { -0.057747757589458777, 0.50000000000000000, 35.000000000000000 },
 386   { 0.094000962389533649, 0.50000000000000000, 40.000000000000000 },
 387   { 0.10120783324271411, 0.50000000000000000, 45.000000000000000 },
 388   { -0.029605831888924641, 0.50000000000000000, 50.000000000000000 },
 389   { -0.10756039213265806, 0.50000000000000000, 55.000000000000000 },
 390   { -0.031397461182520438, 0.50000000000000000, 60.000000000000000 },
 391   { 0.081827430775628554, 0.50000000000000000, 65.000000000000000 },
 392   { 0.073802429539054554, 0.50000000000000000, 70.000000000000000 },
 393   { -0.035727009681702615, 0.50000000000000000, 75.000000000000000 },
 394   { -0.088661035811765460, 0.50000000000000000, 80.000000000000000 },
 395   { -0.015238065106312516, 0.50000000000000000, 85.000000000000000 },
 396   { 0.075189068550269425, 0.50000000000000000, 90.000000000000000 },
 397   { 0.055932643481494133, 0.50000000000000000, 95.000000000000000 },
 398   { -0.040402132716252127, 0.50000000000000000, 100.00000000000000 },
 399 };
 400 const double toler012 = 2.5000000000000014e-11;
 401
 402 // Test data for nu=0.66666666666666663.
 403 // max(|f - f_GSL|): 6.3629657098829284e-15
 404 // max(|f - f_GSL| / |f_GSL|): 1.2254869540384518e-12
 405 const testcase_cyl_bessel_j<double>
 406 data013[21] =
 407 {
 408   { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000 },
 409   { -0.35712533549168868, 0.66666666666666663, 5.0000000000000000 },
 410   { -0.080149603304315808, 0.66666666666666663, 10.000000000000000 },
 411   { 0.16918875175798079, 0.66666666666666663, 15.000000000000000 },
 412   { 0.13904826122116531, 0.66666666666666663, 20.000000000000000 },
 413   { -0.060770629698497600, 0.66666666666666663, 25.000000000000000 },
 414   { -0.14489851974205062, 0.66666666666666663, 30.000000000000000 },
 415   { -0.024604880159644394, 0.66666666666666663, 35.000000000000000 },
 416   { 0.11243936464912010, 0.66666666666666663, 40.000000000000000 },
 417   { 0.081776275512525309, 0.66666666666666663, 45.000000000000000 },
 418   { -0.056589908749367777, 0.66666666666666663, 50.000000000000000 },
 419   { -0.10455814523765931, 0.66666666666666663, 55.000000000000000 },
 420   { -0.0051030148548608456, 0.66666666666666663, 60.000000000000000 },
 421   { 0.093398227061639236, 0.66666666666666663, 65.000000000000000 },
 422   { 0.055763883611864913, 0.66666666666666663, 70.000000000000000 },
 423   { -0.056395322915757364, 0.66666666666666663, 75.000000000000000 },
 424   { -0.083131347805783087, 0.66666666666666663, 80.000000000000000 },
 425   { 0.0072315397874096648, 0.66666666666666663, 85.000000000000000 },
 426   { 0.082362798520905250, 0.66666666666666663, 90.000000000000000 },
 427   { 0.038630504403446168, 0.66666666666666663, 95.000000000000000 },
 428   { -0.056778819380529734, 0.66666666666666663, 100.00000000000000 },
 429 };
 430 const double toler013 = 1.0000000000000006e-10;
 431
 432 // Test data for nu=1.0000000000000000.
 433 // max(|f - f_GSL|): 7.1435912740724916e-15
 434 // max(|f - f_GSL| / |f_GSL|): 1.7857949645087573e-12
 435 const testcase_cyl_bessel_j<double>
 436 data014[21] =
 437 {
 438   { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000 },
 439   { -0.32757913759146529, 1.0000000000000000, 5.0000000000000000 },
 440   { 0.043472746168861459, 1.0000000000000000, 10.000000000000000 },
 441   { 0.20510403861352280, 1.0000000000000000, 15.000000000000000 },
 442   { 0.066833124175850078, 1.0000000000000000, 20.000000000000000 },
 443   { -0.12535024958028990, 1.0000000000000000, 25.000000000000000 },
 444   { -0.11875106261662294, 1.0000000000000000, 30.000000000000000 },
 445   { 0.043990942179625646, 1.0000000000000000, 35.000000000000000 },
 446   { 0.12603831803758500, 1.0000000000000000, 40.000000000000000 },
 447   { 0.028348854376424561, 1.0000000000000000, 45.000000000000000 },
 448   { -0.097511828125175129, 1.0000000000000000, 50.000000000000000 },
 449   { -0.078250038308684711, 1.0000000000000000, 55.000000000000000 },
 450   { 0.046598383758166370, 1.0000000000000000, 60.000000000000000 },
 451   { 0.097330172226126929, 1.0000000000000000, 65.000000000000000 },
 452   { 0.0099877887848385128, 1.0000000000000000, 70.000000000000000 },
 453   { -0.085139995044829081, 1.0000000000000000, 75.000000000000000 },
 454   { -0.056057296675712555, 1.0000000000000000, 80.000000000000000 },
 455   { 0.049151460334891130, 1.0000000000000000, 85.000000000000000 },
 456   { 0.079925646708868092, 1.0000000000000000, 90.000000000000000 },
 457   { -0.0023925612997269283, 1.0000000000000000, 95.000000000000000 },
 458   { -0.077145352014112129, 1.0000000000000000, 100.00000000000000 },
 459 };
 460 const double toler014 = 1.0000000000000006e-10;
 461
 462 // Test data for nu=2.0000000000000000.
 463 // max(|f - f_GSL|): 7.6050277186823223e-15
 464 // max(|f - f_GSL| / |f_GSL|): 2.0010877493528614e-12
 465 const testcase_cyl_bessel_j<double>
 466 data015[21] =
 467 {
 468   { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000 },
 469   { 0.046565116277751971, 2.0000000000000000, 5.0000000000000000 },
 470   { 0.25463031368512068, 2.0000000000000000, 10.000000000000000 },
 471   { 0.041571677975250486, 2.0000000000000000, 15.000000000000000 },
 472   { -0.16034135192299820, 2.0000000000000000, 20.000000000000000 },
 473   { -0.10629480324238134, 2.0000000000000000, 25.000000000000000 },
 474   { 0.078451246073265299, 2.0000000000000000, 30.000000000000000 },
 475   { 0.12935945088086259, 2.0000000000000000, 35.000000000000000 },
 476   { -0.0010649746823579794, 2.0000000000000000, 40.000000000000000 },
 477   { -0.11455872158985966, 2.0000000000000000, 45.000000000000000 },
 478   { -0.059712800794258863, 2.0000000000000000, 50.000000000000000 },
 479   { 0.071702846709739240, 2.0000000000000000, 55.000000000000000 },
 480   { 0.093025083547667420, 2.0000000000000000, 60.000000000000000 },
 481   { -0.015692568697643128, 2.0000000000000000, 65.000000000000000 },
 482   { -0.094623361089161029, 2.0000000000000000, 70.000000000000000 },
 483   { -0.036914313672959179, 2.0000000000000000, 75.000000000000000 },
 484   { 0.068340733095317172, 2.0000000000000000, 80.000000000000000 },
 485   { 0.072096899745329540, 2.0000000000000000, 85.000000000000000 },
 486   { -0.024853891217550248, 2.0000000000000000, 90.000000000000000 },
 487   { -0.081862337494957332, 2.0000000000000000, 95.000000000000000 },
 488   { -0.021528757344505364, 2.0000000000000000, 100.00000000000000 },
 489 };
 490 const double toler015 = 2.5000000000000017e-10;
 491
 492 // Test data for nu=5.0000000000000000.
 493 // max(|f - f_GSL|): 6.8521577301083880e-15
 494 // max(|f - f_GSL| / |f_GSL|): 5.6813560677959848e-13
 495 const testcase_cyl_bessel_j<double>
 496 data016[21] =
 497 {
 498   { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000 },
 499   { 0.26114054612017007, 5.0000000000000000, 5.0000000000000000 },
 500   { -0.23406152818679371, 5.0000000000000000, 10.000000000000000 },
 501   { 0.13045613456502966, 5.0000000000000000, 15.000000000000000 },
 502   { 0.15116976798239498, 5.0000000000000000, 20.000000000000000 },
 503   { -0.066007995398422933, 5.0000000000000000, 25.000000000000000 },
 504   { -0.14324029551207709, 5.0000000000000000, 30.000000000000000 },
 505   { -0.0015053072953907251, 5.0000000000000000, 35.000000000000000 },
 506   { 0.12257346597711777, 5.0000000000000000, 40.000000000000000 },
 507   { 0.057984499200954109, 5.0000000000000000, 45.000000000000000 },
 508   { -0.081400247696569616, 5.0000000000000000, 50.000000000000000 },
 509   { -0.092569895786432765, 5.0000000000000000, 55.000000000000000 },
 510   { 0.027454744228344204, 5.0000000000000000, 60.000000000000000 },
 511   { 0.099110527701539025, 5.0000000000000000, 65.000000000000000 },
 512   { 0.026058129823895364, 5.0000000000000000, 70.000000000000000 },
 513   { -0.078523977013751398, 5.0000000000000000, 75.000000000000000 },
 514   { -0.065862349140031584, 5.0000000000000000, 80.000000000000000 },
 515   { 0.038669072284680979, 5.0000000000000000, 85.000000000000000 },
 516   { 0.082759319528415157, 5.0000000000000000, 90.000000000000000 },
 517   { 0.0079423372702472871, 5.0000000000000000, 95.000000000000000 },
 518   { -0.074195736964513898, 5.0000000000000000, 100.00000000000000 },
 519 };
 520 const double toler016 = 5.0000000000000028e-11;
 521
 522 // Test data for nu=10.000000000000000.
 523 // max(|f - f_GSL|): 7.2303274478713320e-15
 524 // max(|f - f_GSL| / |f_GSL|): 3.6974790630140835e-13
 525 const testcase_cyl_bessel_j<double>
 526 data017[21] =
 527 {
 528   { 0.0000000000000000, 10.000000000000000, 0.0000000000000000 },
 529   { 0.0014678026473104744, 10.000000000000000, 5.0000000000000000 },
 530   { 0.20748610663335865, 10.000000000000000, 10.000000000000000 },
 531   { -0.090071811047659087, 10.000000000000000, 15.000000000000000 },
 532   { 0.18648255802394512, 10.000000000000000, 20.000000000000000 },
 533   { -0.075179843948523312, 10.000000000000000, 25.000000000000000 },
 534   { -0.12987689399858882, 10.000000000000000, 30.000000000000000 },
 535   { 0.063546391343962866, 10.000000000000000, 35.000000000000000 },
 536   { 0.11938336278226094, 10.000000000000000, 40.000000000000000 },
 537   { -0.026971402475010831, 10.000000000000000, 45.000000000000000 },
 538   { -0.11384784914946940, 10.000000000000000, 50.000000000000000 },
 539   { -0.015773790303746080, 10.000000000000000, 55.000000000000000 },
 540   { 0.097177143328071064, 10.000000000000000, 60.000000000000000 },
 541   { 0.054617389951112129, 10.000000000000000, 65.000000000000000 },
 542   { -0.065870338561952013, 10.000000000000000, 70.000000000000000 },
 543   { -0.080417867891894437, 10.000000000000000, 75.000000000000000 },
 544   { 0.024043850978184747, 10.000000000000000, 80.000000000000000 },
 545   { 0.086824832700067869, 10.000000000000000, 85.000000000000000 },
 546   { 0.019554748856312299, 10.000000000000000, 90.000000000000000 },
 547   { -0.072341598669443757, 10.000000000000000, 95.000000000000000 },
 548   { -0.054732176935472096, 10.000000000000000, 100.00000000000000 },
 549 };
 550 const double toler017 = 2.5000000000000014e-11;
 551
 552 // Test data for nu=20.000000000000000.
 553 // max(|f - f_GSL|): 7.7177847446208148e-15
 554 // max(|f - f_GSL| / |f_GSL|): 1.1191513260854523e-12
 555 const testcase_cyl_bessel_j<double>
 556 data018[21] =
 557 {
 558   { 0.0000000000000000, 20.000000000000000, 0.0000000000000000 },
 559   { 2.7703300521289426e-11, 20.000000000000000, 5.0000000000000000 },
 560   { 1.1513369247813403e-05, 20.000000000000000, 10.000000000000000 },
 561   { 0.0073602340792234934, 20.000000000000000, 15.000000000000000 },
 562   { 0.16474777377532665, 20.000000000000000, 20.000000000000000 },
 563   { 0.051994049228303307, 20.000000000000000, 25.000000000000000 },
 564   { 0.0048310199934040923, 20.000000000000000, 30.000000000000000 },
 565   { -0.10927417397178038, 20.000000000000000, 35.000000000000000 },
 566   { 0.12779393355084889, 20.000000000000000, 40.000000000000000 },
 567   { 0.0047633437900313621, 20.000000000000000, 45.000000000000000 },
 568   { -0.11670435275957974, 20.000000000000000, 50.000000000000000 },
 569   { 0.025389204574566639, 20.000000000000000, 55.000000000000000 },
 570   { 0.10266020557876326, 20.000000000000000, 60.000000000000000 },
 571   { -0.023138582263434154, 20.000000000000000, 65.000000000000000 },
 572   { -0.096058573489952365, 20.000000000000000, 70.000000000000000 },
 573   { 0.0068961047221522270, 20.000000000000000, 75.000000000000000 },
 574   { 0.090565405489918357, 20.000000000000000, 80.000000000000000 },
 575   { 0.015985497599497172, 20.000000000000000, 85.000000000000000 },
 576   { -0.080345344044422534, 20.000000000000000, 90.000000000000000 },
 577   { -0.040253075701614051, 20.000000000000000, 95.000000000000000 },
 578   { 0.062217458498338672, 20.000000000000000, 100.00000000000000 },
 579 };
 580 const double toler018 = 1.0000000000000006e-10;
 581
 582 // Test data for nu=50.000000000000000.
 583 // max(|f - f_GSL|): 6.6543992538470320e-15
 584 // max(|f - f_GSL| / |f_GSL|): 1.6466369526724007e-13
 585 const testcase_cyl_bessel_j<double>
 586 data019[21] =
 587 {
 588   { 0.0000000000000000, 50.000000000000000, 0.0000000000000000 },
 589   { 2.2942476159525415e-45, 50.000000000000000, 5.0000000000000000 },
 590   { 1.7845136078715964e-30, 50.000000000000000, 10.000000000000000 },
 591   { 6.1060519495338733e-22, 50.000000000000000, 15.000000000000000 },
 592   { 4.4510392847006872e-16, 50.000000000000000, 20.000000000000000 },
 593   { 9.7561594280229808e-12, 50.000000000000000, 25.000000000000000 },
 594   { 2.0581656631564172e-08, 50.000000000000000, 30.000000000000000 },
 595   { 7.6069951699272960e-06, 50.000000000000000, 35.000000000000000 },
 596   { 0.00068185243531768309, 50.000000000000000, 40.000000000000000 },
 597   { 0.017284343240791214, 50.000000000000000, 45.000000000000000 },
 598   { 0.12140902189761507, 50.000000000000000, 50.000000000000000 },
 599   { 0.13594720957176012, 50.000000000000000, 55.000000000000000 },
 600   { -0.13798273148535209, 50.000000000000000, 60.000000000000000 },
 601   { 0.12116217746619409, 50.000000000000000, 65.000000000000000 },
 602   { -0.11394866738787145, 50.000000000000000, 70.000000000000000 },
 603   { 0.094076799581573348, 50.000000000000000, 75.000000000000000 },
 604   { -0.039457764590251347, 50.000000000000000, 80.000000000000000 },
 605   { -0.040412060734136383, 50.000000000000000, 85.000000000000000 },
 606   { 0.090802099838032266, 50.000000000000000, 90.000000000000000 },
 607   { -0.055979156267280165, 50.000000000000000, 95.000000000000000 },
 608   { -0.038698339728525440, 50.000000000000000, 100.00000000000000 },
 609 };
 610 const double toler019 = 1.0000000000000006e-11;
 611
 612 // Test data for nu=100.00000000000000.
 613 // max(|f - f_GSL|): 4.8138576458356397e-17
 614 // max(|f - f_GSL| / |f_GSL|): 1.0835289187603112e-13
 615 const testcase_cyl_bessel_j<double>
 616 data020[21] =
 617 {
 618   { 0.0000000000000000, 100.00000000000000, 0.0000000000000000 },
 619   { 6.2677893955418763e-119, 100.00000000000000, 5.0000000000000000 },
 620   { 6.5973160641553816e-89, 100.00000000000000, 10.000000000000000 },
 621   { 1.9660095611249536e-71, 100.00000000000000, 15.000000000000000 },
 622   { 3.9617550943362524e-59, 100.00000000000000, 20.000000000000000 },
 623   { 1.1064482655301687e-49, 100.00000000000000, 25.000000000000000 },
 624   { 4.5788015281752354e-42, 100.00000000000000, 30.000000000000000 },
 625   { 9.9210206714732606e-36, 100.00000000000000, 35.000000000000000 },
 626   { 2.3866062996027414e-30, 100.00000000000000, 40.000000000000000 },
 627   { 1.0329791804565538e-25, 100.00000000000000, 45.000000000000000 },
 628   { 1.1159273690838340e-21, 100.00000000000000, 50.000000000000000 },
 629   { 3.7899753451900682e-18, 100.00000000000000, 55.000000000000000 },
 630   { 4.7832744078781205e-15, 100.00000000000000, 60.000000000000000 },
 631   { 2.5375564579490517e-12, 100.00000000000000, 65.000000000000000 },
 632   { 6.1982452141641260e-10, 100.00000000000000, 70.000000000000000 },
 633   { 7.4479005905904457e-08, 100.00000000000000, 75.000000000000000 },
 634   { 4.6065530648234948e-06, 100.00000000000000, 80.000000000000000 },
 635   { 0.00015043869999501765, 100.00000000000000, 85.000000000000000 },
 636   { 0.0026021305819963472, 100.00000000000000, 90.000000000000000 },
 637   { 0.023150768009428030, 100.00000000000000, 95.000000000000000 },
 638   { 0.096366673295861571, 100.00000000000000, 100.00000000000000 },
 639 };
 640 const double toler020 = 1.0000000000000006e-11;
 641
 642 template<typename Tp, unsigned int Num>
 643   void
 644   test(const testcase_cyl_bessel_j<Tp> (&data)[Num], Tp toler)
 645   {
 646     const Tp eps = std::numeric_limits<Tp>::epsilon();
 647     Tp max_abs_diff = -Tp(1);
 648     Tp max_abs_frac = -Tp(1);
 649     unsigned int num_datum = Num;
 650     for (unsigned int i = 0; i < num_datum; ++i)
 651       {
 652         const Tp f = std::cyl_bessel_j(data[i].nu, data[i].x);
 653         const Tp f0 = data[i].f0;
 654         const Tp diff = f - f0;
 655         if (std::abs(diff) > max_abs_diff)
 656           max_abs_diff = std::abs(diff);
 657         if (std::abs(f0) > Tp(10) * eps
 658          && std::abs(f) > Tp(10) * eps)
 659           {
 660             const Tp frac = diff / f0;
 661             if (std::abs(frac) > max_abs_frac)
 662               max_abs_frac = std::abs(frac);
 663           }
 664       }
 665     VERIFY(max_abs_frac < toler);
 666   }
 667
 668 int
 669 main()
 670 {
 671   test(data001, toler001);
 672   test(data002, toler002);
 673   test(data003, toler003);
 674   test(data004, toler004);
 675   test(data005, toler005);
 676   test(data006, toler006);
 677   test(data007, toler007);
 678   test(data008, toler008);
 679   test(data009, toler009);
 680   test(data010, toler010);
 681   test(data011, toler011);
 682   test(data012, toler012);
 683   test(data013, toler013);
 684   test(data014, toler014);
 685   test(data015, toler015);
 686   test(data016, toler016);
 687   test(data017, toler017);
 688   test(data018, toler018);
 689   test(data019, toler019);
 690   test(data020, toler020);
 691   return 0;
 692 }