libstdc++-v3/testsuite/special_functions/07_cyl_bessel_i/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_i
  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|): 2.8421709430404007e-14
  43 // max(|f - f_GSL| / |f_GSL|): 1.3916073135966565e-15
  44 const testcase_cyl_bessel_i<double>
  45 data001[21] =
  46 {
  47   { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000 },
  48   { 1.0156861412236078, 0.0000000000000000, 0.25000000000000000 },
  49   { 1.0634833707413236, 0.0000000000000000, 0.50000000000000000 },
  50   { 1.1456467780440014, 0.0000000000000000, 0.75000000000000000 },
  51   { 1.2660658777520082, 0.0000000000000000, 1.0000000000000000 },
  52   { 1.4304687177218294, 0.0000000000000000, 1.2500000000000000 },
  53   { 1.6467231897728904, 0.0000000000000000, 1.5000000000000000 },
  54   { 1.9252521538585023, 0.0000000000000000, 1.7500000000000000 },
  55   { 2.2795853023360668, 0.0000000000000000, 2.0000000000000000 },
  56   { 2.7270783071907951, 0.0000000000000000, 2.2500000000000000 },
  57   { 3.2898391440501231, 0.0000000000000000, 2.5000000000000000 },
  58   { 3.9959131072376550, 0.0000000000000000, 2.7500000000000000 },
  59   { 4.8807925858650245, 0.0000000000000000, 3.0000000000000000 },
  60   { 5.9893359979395138, 0.0000000000000000, 3.2500000000000000 },
  61   { 7.3782034322254750, 0.0000000000000000, 3.5000000000000000 },
  62   { 9.1189458608445655, 0.0000000000000000, 3.7500000000000000 },
  63   { 11.301921952136325, 0.0000000000000000, 4.0000000000000000 },
  64   { 14.041263683000595, 0.0000000000000000, 4.2500000000000000 },
  65   { 17.481171855609272, 0.0000000000000000, 4.5000000000000000 },
  66   { 21.803898740902120, 0.0000000000000000, 4.7500000000000000 },
  67   { 27.239871823604439, 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|): 1.0658141036401503e-14
  73 // max(|f - f_GSL| / |f_GSL|): 1.1056193696204194e-15
  74 const testcase_cyl_bessel_i<double>
  75 data002[21] =
  76 {
  77   { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000 },
  78   { 0.56650686557808660, 0.33333333333333331, 0.25000000000000000 },
  79   { 0.73897315642511863, 0.33333333333333331, 0.50000000000000000 },
  80   { 0.89532320365836804, 0.33333333333333331, 0.75000000000000000 },
  81   { 1.0646313978895285, 0.33333333333333331, 1.0000000000000000 },
  82   { 1.2623776732605250, 0.33333333333333331, 1.2500000000000000 },
  83   { 1.5014290000224382, 0.33333333333333331, 1.5000000000000000 },
  84   { 1.7951195525946044, 0.33333333333333331, 1.7500000000000000 },
  85   { 2.1587825813728614, 0.33333333333333331, 2.0000000000000000 },
  86   { 2.6109134564811405, 0.33333333333333331, 2.2500000000000000 },
  87   { 3.1743242297241938, 0.33333333333333331, 2.5000000000000000 },
  88   { 3.8774551722182107, 0.33333333333333331, 2.7500000000000000 },
  89   { 4.7559569371646946, 0.33333333333333331, 3.0000000000000000 },
  90   { 5.8546499652731825, 0.33333333333333331, 3.2500000000000000 },
  91   { 7.2299798619171147, 0.33333333333333331, 3.5000000000000000 },
  92   { 8.9531114355506318, 0.33333333333333331, 3.7500000000000000 },
  93   { 11.113838389991479, 0.33333333333333331, 4.0000000000000000 },
  94   { 13.825531136529117, 0.33333333333333331, 4.2500000000000000 },
  95   { 17.231403968478318, 0.33333333333333331, 4.5000000000000000 },
  96   { 21.512458099556554, 0.33333333333333331, 4.7500000000000000 },
  97   { 26.897553069268362, 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|): 1.4210854715202004e-14
 103 // max(|f - f_GSL| / |f_GSL|): 1.2805693909168510e-15
 104 const testcase_cyl_bessel_i<double>
 105 data003[21] =
 106 {
 107   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000 },
 108   { 0.40311093489975897, 0.50000000000000000, 0.25000000000000000 },
 109   { 0.58799308679041573, 0.50000000000000000, 0.50000000000000000 },
 110   { 0.75761498638991298, 0.50000000000000000, 0.75000000000000000 },
 111   { 0.93767488824548695, 0.50000000000000000, 1.0000000000000000 },
 112   { 1.1432089853159872, 0.50000000000000000, 1.2500000000000000 },
 113   { 1.3871617204034761, 0.50000000000000000, 1.5000000000000000 },
 114   { 1.6830217804556815, 0.50000000000000000, 1.7500000000000000 },
 115   { 2.0462368630890526, 0.50000000000000000, 2.0000000000000000 },
 116   { 2.4953405089360041, 0.50000000000000000, 2.2500000000000000 },
 117   { 3.0530935381967175, 0.50000000000000000, 2.5000000000000000 },
 118   { 3.7477882494879449, 0.50000000000000000, 2.7500000000000000 },
 119   { 4.6148229034075969, 0.50000000000000000, 3.0000000000000000 },
 120   { 5.6986505325335495, 0.50000000000000000, 3.2500000000000000 },
 121   { 7.0552194086911877, 0.50000000000000000, 3.5000000000000000 },
 122   { 8.7550467841188944, 0.50000000000000000, 3.7500000000000000 },
 123   { 10.887101798588422, 0.50000000000000000, 4.0000000000000000 },
 124   { 13.563718712579764, 0.50000000000000000, 4.2500000000000000 },
 125   { 16.926820080158183, 0.50000000000000000, 4.5000000000000000 },
 126   { 21.155804306570005, 0.50000000000000000, 4.7500000000000000 },
 127   { 26.477547497559065, 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|): 1.2434497875801753e-14
 133 // max(|f - f_GSL| / |f_GSL|): 1.3900778397944649e-15
 134 const testcase_cyl_bessel_i<double>
 135 data004[21] =
 136 {
 137   { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000 },
 138   { 0.27953690613200438, 0.66666666666666663, 0.25000000000000000 },
 139   { 0.45628323113556879, 0.66666666666666663, 0.50000000000000000 },
 140   { 0.62594569838182612, 0.66666666666666663, 0.75000000000000000 },
 141   { 0.80752128860612948, 0.66666666666666663, 1.0000000000000000 },
 142   { 1.0139484513577168, 0.66666666666666663, 1.2500000000000000 },
 143   { 1.2572918396962991, 0.66666666666666663, 1.5000000000000000 },
 144   { 1.5505806938325577, 0.66666666666666663, 1.7500000000000000 },
 145   { 1.9089492968236206, 0.66666666666666663, 2.0000000000000000 },
 146   { 2.3506463490300331, 0.66666666666666663, 2.2500000000000000 },
 147   { 2.8981161894224892, 0.66666666666666663, 2.5000000000000000 },
 148   { 3.5792654911068720, 0.66666666666666663, 2.7500000000000000 },
 149   { 4.4290087213549505, 0.66666666666666663, 3.0000000000000000 },
 150   { 5.4911895720097688, 0.66666666666666663, 3.2500000000000000 },
 151   { 6.8209918044137305, 0.66666666666666663, 3.5000000000000000 },
 152   { 8.4879784249619767, 0.66666666666666663, 3.7500000000000000 },
 153   { 10.579932774013002, 0.66666666666666663, 4.0000000000000000 },
 154   { 13.207720355482458, 0.66666666666666663, 4.2500000000000000 },
 155   { 16.511448404200543, 0.66666666666666663, 4.5000000000000000 },
 156   { 20.668274532832392, 0.66666666666666663, 4.7500000000000000 },
 157   { 25.902310583215122, 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|): 3.5527136788005009e-15
 163 // max(|f - f_GSL| / |f_GSL|): 2.2031887547040326e-16
 164 const testcase_cyl_bessel_i<double>
 165 data005[21] =
 166 {
 167   { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000 },
 168   { 0.12597910894546793, 1.0000000000000000, 0.25000000000000000 },
 169   { 0.25789430539089631, 1.0000000000000000, 0.50000000000000000 },
 170   { 0.40199246158092228, 1.0000000000000000, 0.75000000000000000 },
 171   { 0.56515910399248503, 1.0000000000000000, 1.0000000000000000 },
 172   { 0.75528141834074725, 1.0000000000000000, 1.2500000000000000 },
 173   { 0.98166642857790720, 1.0000000000000000, 1.5000000000000000 },
 174   { 1.2555375122401731, 1.0000000000000000, 1.7500000000000000 },
 175   { 1.5906368546373291, 1.0000000000000000, 2.0000000000000000 },
 176   { 2.0039674569295931, 1.0000000000000000, 2.2500000000000000 },
 177   { 2.5167162452886984, 1.0000000000000000, 2.5000000000000000 },
 178   { 3.1554101386190028, 1.0000000000000000, 2.7500000000000000 },
 179   { 3.9533702174026097, 1.0000000000000000, 3.0000000000000000 },
 180   { 4.9525461659085490, 1.0000000000000000, 3.2500000000000000 },
 181   { 6.2058349222583642, 1.0000000000000000, 3.5000000000000000 },
 182   { 7.7800152298244161, 1.0000000000000000, 3.7500000000000000 },
 183   { 9.7594651537044488, 1.0000000000000000, 4.0000000000000000 },
 184   { 12.250874667409304, 1.0000000000000000, 4.2500000000000000 },
 185   { 15.389222753735924, 1.0000000000000000, 4.5000000000000000 },
 186   { 19.345361447520226, 1.0000000000000000, 4.7500000000000000 },
 187   { 24.335642142450524, 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|): 1.7763568394002505e-15
 193 // max(|f - f_GSL| / |f_GSL|): 2.2089187702829171e-16
 194 const testcase_cyl_bessel_i<double>
 195 data006[21] =
 196 {
 197   { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000 },
 198   { 0.0078532696598645167, 2.0000000000000000, 0.25000000000000000 },
 199   { 0.031906149177738249, 2.0000000000000000, 0.50000000000000000 },
 200   { 0.073666880494875436, 2.0000000000000000, 0.75000000000000000 },
 201   { 0.13574766976703831, 2.0000000000000000, 1.0000000000000000 },
 202   { 0.22201844837663415, 2.0000000000000000, 1.2500000000000000 },
 203   { 0.33783461833568068, 2.0000000000000000, 1.5000000000000000 },
 204   { 0.49035213986973319, 2.0000000000000000, 1.7500000000000000 },
 205   { 0.68894844769873831, 2.0000000000000000, 2.0000000000000000 },
 206   { 0.94577390103115722, 2.0000000000000000, 2.2500000000000000 },
 207   { 1.2764661478191643, 2.0000000000000000, 2.5000000000000000 },
 208   { 1.7010693700601991, 2.0000000000000000, 2.7500000000000000 },
 209   { 2.2452124409299512, 2.0000000000000000, 3.0000000000000000 },
 210   { 2.9416152804573357, 2.0000000000000000, 3.2500000000000000 },
 211   { 3.8320120480778415, 2.0000000000000000, 3.5000000000000000 },
 212   { 4.9696044049382113, 2.0000000000000000, 3.7500000000000000 },
 213   { 6.4221893752841046, 2.0000000000000000, 4.0000000000000000 },
 214   { 8.2761461924550552, 2.0000000000000000, 4.2500000000000000 },
 215   { 10.641517298393307, 2.0000000000000000, 4.5000000000000000 },
 216   { 13.658483394577813, 2.0000000000000000, 4.7500000000000000 },
 217   { 17.505614966624233, 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|): 8.8817841970012523e-16
 223 // max(|f - f_GSL| / |f_GSL|): 1.6610041744866592e-15
 224 const testcase_cyl_bessel_i<double>
 225 data007[21] =
 226 {
 227   { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000 },
 228   { 2.5497616449882785e-07, 5.0000000000000000, 0.25000000000000000 },
 229   { 8.2231713131092646e-06, 5.0000000000000000, 0.50000000000000000 },
 230   { 6.3261122739811725e-05, 5.0000000000000000, 0.75000000000000000 },
 231   { 0.00027146315595697195, 5.0000000000000000, 1.0000000000000000 },
 232   { 0.00084793613616686856, 5.0000000000000000, 1.2500000000000000 },
 233   { 0.0021705595690975554, 5.0000000000000000, 1.5000000000000000 },
 234   { 0.0048504513371845394, 5.0000000000000000, 1.7500000000000000 },
 235   { 0.0098256793231317023, 5.0000000000000000, 2.0000000000000000 },
 236   { 0.018486577941045829, 5.0000000000000000, 2.2500000000000000 },
 237   { 0.032843475172023219, 5.0000000000000000, 2.5000000000000000 },
 238   { 0.055750882754221943, 5.0000000000000000, 2.7500000000000000 },
 239   { 0.091206477661513338, 5.0000000000000000, 3.0000000000000000 },
 240   { 0.14474880546308083, 5.0000000000000000, 3.2500000000000000 },
 241   { 0.22398495470190780, 5.0000000000000000, 3.5000000000000000 },
 242   { 0.33928899170999866, 5.0000000000000000, 3.7500000000000000 },
 243   { 0.50472436311316626, 5.0000000000000000, 4.0000000000000000 },
 244   { 0.73925961816682961, 5.0000000000000000, 4.2500000000000000 },
 245   { 1.0683677743764699, 5.0000000000000000, 4.5000000000000000 },
 246   { 1.5261268693599621, 5.0000000000000000, 4.7500000000000000 },
 247   { 2.1579745473225476, 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|): 9.5409791178724390e-18
 253 // max(|f - f_GSL| / |f_GSL|): 3.9173270279899483e-15
 254 const testcase_cyl_bessel_i<double>
 255 data008[21] =
 256 {
 257   { 0.0000000000000000, 10.000000000000000, 0.0000000000000000 },
 258   { 2.5701232848571186e-16, 10.000000000000000, 0.25000000000000000 },
 259   { 2.6430419258812784e-13, 10.000000000000000, 0.50000000000000000 },
 260   { 1.5349659676120412e-11, 10.000000000000000, 0.75000000000000000 },
 261   { 2.7529480398368732e-10, 10.000000000000000, 1.0000000000000000 },
 262   { 2.5967897782035928e-09, 10.000000000000000, 1.2500000000000000 },
 263   { 1.6330924437799743e-08, 10.000000000000000, 1.5000000000000000 },
 264   { 7.7706676834614093e-08, 10.000000000000000, 1.7500000000000000 },
 265   { 3.0169638793506839e-07, 10.000000000000000, 2.0000000000000000 },
 266   { 1.0034459057774481e-06, 10.000000000000000, 2.2500000000000000 },
 267   { 2.9557436109680578e-06, 10.000000000000000, 2.5000000000000000 },
 268   { 7.8955603774082724e-06, 10.000000000000000, 2.7500000000000000 },
 269   { 1.9464393470612970e-05, 10.000000000000000, 3.0000000000000000 },
 270   { 4.4875369479742435e-05, 10.000000000000000, 3.2500000000000000 },
 271   { 9.7760848514528916e-05, 10.000000000000000, 3.5000000000000000 },
 272   { 0.00020289011210063493, 10.000000000000000, 3.7500000000000000 },
 273   { 0.00040378896132693047, 10.000000000000000, 4.0000000000000000 },
 274   { 0.00077478519551669892, 10.000000000000000, 4.2500000000000000 },
 275   { 0.0014397060684919682, 10.000000000000000, 4.5000000000000000 },
 276   { 0.0026004486016189452, 10.000000000000000, 4.7500000000000000 },
 277   { 0.0045800444191760525, 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|): 2.9080568410067379e-26
 283 // max(|f - f_GSL| / |f_GSL|): 2.1318627676504474e-15
 284 const testcase_cyl_bessel_i<double>
 285 data009[21] =
 286 {
 287   { 0.0000000000000000, 20.000000000000000, 0.0000000000000000 },
 288   { 3.5677858077910353e-37, 20.000000000000000, 0.25000000000000000 },
 289   { 3.7494538480790194e-31, 20.000000000000000, 0.50000000000000000 },
 290   { 1.2514356342425337e-27, 20.000000000000000, 0.75000000000000000 },
 291   { 3.9668359858190197e-25, 20.000000000000000, 1.0000000000000000 },
 292   { 3.4637832909868234e-23, 20.000000000000000, 1.2500000000000000 },
 293   { 1.3388331839683472e-21, 20.000000000000000, 1.5000000000000000 },
 294   { 2.9502376732679751e-20, 20.000000000000000, 1.7500000000000000 },
 295   { 4.3105605761095479e-19, 20.000000000000000, 2.0000000000000000 },
 296   { 4.6032451406433059e-18, 20.000000000000000, 2.2500000000000000 },
 297   { 3.8400317244170310e-17, 20.000000000000000, 2.5000000000000000 },
 298   { 2.6239115263043263e-16, 20.000000000000000, 2.7500000000000000 },
 299   { 1.5209660019426689e-15, 20.000000000000000, 3.0000000000000000 },
 300   { 7.6806450728249953e-15, 20.000000000000000, 3.2500000000000000 },
 301   { 3.4495528847222945e-14, 20.000000000000000, 3.5000000000000000 },
 302   { 1.4006589294850672e-13, 20.000000000000000, 3.7500000000000000 },
 303   { 5.2100734221993044e-13, 20.000000000000000, 4.0000000000000000 },
 304   { 1.7946903269488168e-12, 20.000000000000000, 4.2500000000000000 },
 305   { 5.7763830562279683e-12, 20.000000000000000, 4.5000000000000000 },
 306   { 1.7502433074548735e-11, 20.000000000000000, 4.7500000000000000 },
 307   { 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000 },
 308 };
 309 const double toler009 = 2.5000000000000020e-13;
 310 //  cyl_bessel_i
 311
 312 // Test data for nu=0.0000000000000000.
 313 // max(|f - f_GSL|): 2.5687255815171641e+28
 314 // max(|f - f_GSL| / |f_GSL|): 2.3922901025046178e-14
 315 const testcase_cyl_bessel_i<double>
 316 data010[21] =
 317 {
 318   { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000 },
 319   { 27.239871823604439, 0.0000000000000000, 5.0000000000000000 },
 320   { 2815.7166284662558, 0.0000000000000000, 10.000000000000000 },
 321   { 339649.37329791381, 0.0000000000000000, 15.000000000000000 },
 322   { 43558282.559553474, 0.0000000000000000, 20.000000000000000 },
 323   { 5774560606.4663124, 0.0000000000000000, 25.000000000000000 },
 324   { 781672297823.97925, 0.0000000000000000, 30.000000000000000 },
 325   { 107338818494514.42, 0.0000000000000000, 35.000000000000000 },
 326   { 14894774793419918., 0.0000000000000000, 40.000000000000000 },
 327   { 2.0834140751773164e+18, 0.0000000000000000, 45.000000000000000 },
 328   { 2.9325537838493457e+20, 0.0000000000000000, 50.000000000000000 },
 329   { 4.1487895607332160e+22, 0.0000000000000000, 55.000000000000000 },
 330   { 5.8940770556098216e+24, 0.0000000000000000, 60.000000000000000 },
 331   { 8.4030398456255596e+26, 0.0000000000000000, 65.000000000000000 },
 332   { 1.2015889579125424e+29, 0.0000000000000000, 70.000000000000000 },
 333   { 1.7226390780357976e+31, 0.0000000000000000, 75.000000000000000 },
 334   { 2.4751784043341661e+33, 0.0000000000000000, 80.000000000000000 },
 335   { 3.5634776304081403e+35, 0.0000000000000000, 85.000000000000000 },
 336   { 5.1392383455086475e+37, 0.0000000000000000, 90.000000000000000 },
 337   { 7.4233258618752072e+39, 0.0000000000000000, 95.000000000000000 },
 338   { 1.0737517071310986e+42, 0.0000000000000000, 100.00000000000000 },
 339 };
 340 const double toler010 = 2.5000000000000015e-12;
 341
 342 // Test data for nu=0.33333333333333331.
 343 // max(|f - f_GSL|): 1.0831975343747077e+28
 344 // max(|f - f_GSL| / |f_GSL|): 1.2017640663876795e-14
 345 const testcase_cyl_bessel_i<double>
 346 data011[21] =
 347 {
 348   { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000 },
 349   { 26.897553069268362, 0.33333333333333331, 5.0000000000000000 },
 350   { 2799.2396097056790, 0.33333333333333331, 10.000000000000000 },
 351   { 338348.63146593666, 0.33333333333333331, 15.000000000000000 },
 352   { 43434263.927938424, 0.33333333333333331, 20.000000000000000 },
 353   { 5761474759.6213636, 0.33333333333333331, 25.000000000000000 },
 354   { 780201111830.30237, 0.33333333333333331, 30.000000000000000 },
 355   { 107166066959051.91, 0.33333333333333331, 35.000000000000000 },
 356   { 14873836574083764., 0.33333333333333331, 40.000000000000000 },
 357   { 2.0808143020217085e+18, 0.33333333333333331, 45.000000000000000 },
 358   { 2.9292639365644226e+20, 0.33333333333333331, 50.000000000000000 },
 359   { 4.1445621624120489e+22, 0.33333333333333331, 55.000000000000000 },
 360   { 5.8885758374365916e+24, 0.33333333333333331, 60.000000000000000 },
 361   { 8.3958047021083955e+26, 0.33333333333333331, 65.000000000000000 },
 362   { 1.2006287819446431e+29, 0.33333333333333331, 70.000000000000000 },
 363   { 1.7213548977150022e+31, 0.33333333333333331, 75.000000000000000 },
 364   { 2.4734492458444449e+33, 0.33333333333333331, 80.000000000000000 },
 365   { 3.5611354547857122e+35, 0.33333333333333331, 85.000000000000000 },
 366   { 5.1360491295551848e+37, 0.33333333333333331, 90.000000000000000 },
 367   { 7.4189629097600431e+39, 0.33333333333333331, 95.000000000000000 },
 368   { 1.0731523308358370e+42, 0.33333333333333331, 100.00000000000000 },
 369 };
 370 const double toler011 = 1.0000000000000008e-12;
 371
 372 // Test data for nu=0.50000000000000000.
 373 // max(|f - f_GSL|): 6.9634127209802640e+27
 374 // max(|f - f_GSL| / |f_GSL|): 1.1904152155149629e-14
 375 const testcase_cyl_bessel_i<double>
 376 data012[21] =
 377 {
 378   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000 },
 379   { 26.477547497559065, 0.50000000000000000, 5.0000000000000000 },
 380   { 2778.7846038745711, 0.50000000000000000, 10.000000000000000 },
 381   { 336729.88718706399, 0.50000000000000000, 15.000000000000000 },
 382   { 43279746.272428922, 0.50000000000000000, 20.000000000000000 },
 383   { 5745159748.3464680, 0.50000000000000000, 25.000000000000000 },
 384   { 778366068840.44580, 0.50000000000000000, 30.000000000000000 },
 385   { 106950522408567.66, 0.50000000000000000, 35.000000000000000 },
 386   { 14847705549021962., 0.50000000000000000, 40.000000000000000 },
 387   { 2.0775691824625661e+18, 0.50000000000000000, 45.000000000000000 },
 388   { 2.9251568529912984e+20, 0.50000000000000000, 50.000000000000000 },
 389   { 4.1392840094781220e+22, 0.50000000000000000, 55.000000000000000 },
 390   { 5.8817065760751945e+24, 0.50000000000000000, 60.000000000000000 },
 391   { 8.3867695787277258e+26, 0.50000000000000000, 65.000000000000000 },
 392   { 1.1994296461653203e+29, 0.50000000000000000, 70.000000000000000 },
 393   { 1.7197510246063334e+31, 0.50000000000000000, 75.000000000000000 },
 394   { 2.4712895036230794e+33, 0.50000000000000000, 80.000000000000000 },
 395   { 3.5582099086757769e+35, 0.50000000000000000, 85.000000000000000 },
 396   { 5.1320654031231128e+37, 0.50000000000000000, 90.000000000000000 },
 397   { 7.4135128383495239e+39, 0.50000000000000000, 95.000000000000000 },
 398   { 1.0724035825423179e+42, 0.50000000000000000, 100.00000000000000 },
 399 };
 400 const double toler012 = 1.0000000000000008e-12;
 401
 402 // Test data for nu=0.66666666666666663.
 403 // max(|f - f_GSL|): 4.4875326424095035e+27
 404 // max(|f - f_GSL| / |f_GSL|): 8.8432218147527708e-15
 405 const testcase_cyl_bessel_i<double>
 406 data013[21] =
 407 {
 408   { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000 },
 409   { 25.902310583215122, 0.66666666666666663, 5.0000000000000000 },
 410   { 2750.4090423459315, 0.66666666666666663, 10.000000000000000 },
 411   { 334476.98138574377, 0.66666666666666663, 15.000000000000000 },
 412   { 43064361.686912313, 0.66666666666666663, 20.000000000000000 },
 413   { 5722397441.9603882, 0.66666666666666663, 25.000000000000000 },
 414   { 775804343498.02661, 0.66666666666666663, 30.000000000000000 },
 415   { 106649495512800.88, 0.66666666666666663, 35.000000000000000 },
 416   { 14811199896983756., 0.66666666666666663, 40.000000000000000 },
 417   { 2.0730345814356961e+18, 0.66666666666666663, 45.000000000000000 },
 418   { 2.9194166755257467e+20, 0.66666666666666663, 50.000000000000000 },
 419   { 4.1319059569935374e+22, 0.66666666666666663, 55.000000000000000 },
 420   { 5.8721031476386222e+24, 0.66666666666666663, 60.000000000000000 },
 421   { 8.3741368248217844e+26, 0.66666666666666663, 65.000000000000000 },
 422   { 1.1977528777008688e+29, 0.66666666666666663, 70.000000000000000 },
 423   { 1.7175081240014333e+31, 0.66666666666666663, 75.000000000000000 },
 424   { 2.4682690458513916e+33, 0.66666666666666663, 80.000000000000000 },
 425   { 3.5541181975850724e+35, 0.66666666666666663, 85.000000000000000 },
 426   { 5.1264933963228892e+37, 0.66666666666666663, 90.000000000000000 },
 427   { 7.4058894880134064e+39, 0.66666666666666663, 95.000000000000000 },
 428   { 1.0713562154788124e+42, 0.66666666666666663, 100.00000000000000 },
 429 };
 430 const double toler013 = 5.0000000000000039e-13;
 431
 432 // Test data for nu=1.0000000000000000.
 433 // max(|f - f_GSL|): 5.7254726816948838e+27
 434 // max(|f - f_GSL| / |f_GSL|): 7.0819761463168391e-15
 435 const testcase_cyl_bessel_i<double>
 436 data014[21] =
 437 {
 438   { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000 },
 439   { 24.335642142450524, 1.0000000000000000, 5.0000000000000000 },
 440   { 2670.9883037012560, 1.0000000000000000, 10.000000000000000 },
 441   { 328124.92197020649, 1.0000000000000000, 15.000000000000000 },
 442   { 42454973.385127783, 1.0000000000000000, 20.000000000000000 },
 443   { 5657865129.8787022, 1.0000000000000000, 25.000000000000000 },
 444   { 768532038938.95667, 1.0000000000000000, 30.000000000000000 },
 445   { 105794126051896.17, 1.0000000000000000, 35.000000000000000 },
 446   { 14707396163259354., 1.0000000000000000, 40.000000000000000 },
 447   { 2.0601334620815780e+18, 1.0000000000000000, 45.000000000000000 },
 448   { 2.9030785901035638e+20, 1.0000000000000000, 50.000000000000000 },
 449   { 4.1108986452992812e+22, 1.0000000000000000, 55.000000000000000 },
 450   { 5.8447515883904527e+24, 1.0000000000000000, 60.000000000000000 },
 451   { 8.3381485471501302e+26, 1.0000000000000000, 65.000000000000000 },
 452   { 1.1929750788892366e+29, 1.0000000000000000, 70.000000000000000 },
 453   { 1.7111160152965382e+31, 1.0000000000000000, 75.000000000000000 },
 454   { 2.4596595795675343e+33, 1.0000000000000000, 80.000000000000000 },
 455   { 3.5424536064404024e+35, 1.0000000000000000, 85.000000000000000 },
 456   { 5.1106068152566129e+37, 1.0000000000000000, 90.000000000000000 },
 457   { 7.3841518091360182e+39, 1.0000000000000000, 95.000000000000000 },
 458   { 1.0683693903381569e+42, 1.0000000000000000, 100.00000000000000 },
 459 };
 460 const double toler014 = 5.0000000000000039e-13;
 461
 462 // Test data for nu=2.0000000000000000.
 463 // max(|f - f_GSL|): 6.3444427013375739e+27
 464 // max(|f - f_GSL| / |f_GSL|): 6.0286366727804324e-15
 465 const testcase_cyl_bessel_i<double>
 466 data015[21] =
 467 {
 468   { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000 },
 469   { 17.505614966624233, 2.0000000000000000, 5.0000000000000000 },
 470   { 2281.5189677260046, 2.0000000000000000, 10.000000000000000 },
 471   { 295899.38370188628, 2.0000000000000000, 15.000000000000000 },
 472   { 39312785.221040756, 2.0000000000000000, 20.000000000000000 },
 473   { 5321931396.0760155, 2.0000000000000000, 25.000000000000000 },
 474   { 730436828561.38013, 2.0000000000000000, 30.000000000000000 },
 475   { 101293439862977.19, 2.0000000000000000, 35.000000000000000 },
 476   { 14159404985256922., 2.0000000000000000, 40.000000000000000 },
 477   { 1.9918525879736883e+18, 2.0000000000000000, 45.000000000000000 },
 478   { 2.8164306402451938e+20, 2.0000000000000000, 50.000000000000000 },
 479   { 3.9993023372677540e+22, 2.0000000000000000, 55.000000000000000 },
 480   { 5.6992520026634433e+24, 2.0000000000000000, 60.000000000000000 },
 481   { 8.1464814287900378e+26, 2.0000000000000000, 65.000000000000000 },
 482   { 1.1675039556585663e+29, 2.0000000000000000, 70.000000000000000 },
 483   { 1.6770093176278926e+31, 2.0000000000000000, 75.000000000000000 },
 484   { 2.4136869148449879e+33, 2.0000000000000000, 80.000000000000000 },
 485   { 3.4801257808448186e+35, 2.0000000000000000, 85.000000000000000 },
 486   { 5.0256693051696307e+37, 2.0000000000000000, 90.000000000000000 },
 487   { 7.2678700343145818e+39, 2.0000000000000000, 95.000000000000000 },
 488   { 1.0523843193243042e+42, 2.0000000000000000, 100.00000000000000 },
 489 };
 490 const double toler015 = 5.0000000000000039e-13;
 491
 492 // Test data for nu=5.0000000000000000.
 493 // max(|f - f_GSL|): 7.7371252455336267e+26
 494 // max(|f - f_GSL| / |f_GSL|): 1.6729319922562276e-15
 495 const testcase_cyl_bessel_i<double>
 496 data016[21] =
 497 {
 498   { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000 },
 499   { 2.1579745473225476, 5.0000000000000000, 5.0000000000000000 },
 500   { 777.18828640326012, 5.0000000000000000, 10.000000000000000 },
 501   { 144572.01120063409, 5.0000000000000000, 15.000000000000000 },
 502   { 23018392.213413671, 5.0000000000000000, 20.000000000000000 },
 503   { 3472466208.7419176, 5.0000000000000000, 25.000000000000000 },
 504   { 512151465476.93494, 5.0000000000000000, 30.000000000000000 },
 505   { 74756743552251.547, 5.0000000000000000, 35.000000000000000 },
 506   { 10858318337624280., 5.0000000000000000, 40.000000000000000 },
 507   { 1.5736087399245911e+18, 5.0000000000000000, 45.000000000000000 },
 508   { 2.2785483079112825e+20, 5.0000000000000000, 50.000000000000000 },
 509   { 3.2989391052963687e+22, 5.0000000000000000, 55.000000000000000 },
 510   { 4.7777652072561732e+24, 5.0000000000000000, 60.000000000000000 },
 511   { 6.9232165147172657e+26, 5.0000000000000000, 65.000000000000000 },
 512   { 1.0038643002095155e+29, 5.0000000000000000, 70.000000000000000 },
 513   { 1.4566328222327073e+31, 5.0000000000000000, 75.000000000000000 },
 514   { 2.1151488565944835e+33, 5.0000000000000000, 80.000000000000000 },
 515   { 3.0735883450768239e+35, 5.0000000000000000, 85.000000000000000 },
 516   { 4.4694790189230327e+37, 5.0000000000000000, 90.000000000000000 },
 517   { 6.5037505570430995e+39, 5.0000000000000000, 95.000000000000000 },
 518   { 9.4700938730355882e+41, 5.0000000000000000, 100.00000000000000 },
 519 };
 520 const double toler016 = 2.5000000000000020e-13;
 521
 522 // Test data for nu=10.000000000000000.
 523 // max(|f - f_GSL|): 2.3211375736600880e+26
 524 // max(|f - f_GSL| / |f_GSL|): 3.0834307473515225e-15
 525 const testcase_cyl_bessel_i<double>
 526 data017[21] =
 527 {
 528   { 0.0000000000000000, 10.000000000000000, 0.0000000000000000 },
 529   { 0.0045800444191760525, 10.000000000000000, 5.0000000000000000 },
 530   { 21.891706163723381, 10.000000000000000, 10.000000000000000 },
 531   { 12267.475049806462, 10.000000000000000, 15.000000000000000 },
 532   { 3540200.2090195213, 10.000000000000000, 20.000000000000000 },
 533   { 771298871.17072666, 10.000000000000000, 25.000000000000000 },
 534   { 145831809975.96710, 10.000000000000000, 30.000000000000000 },
 535   { 25449470018534.777, 10.000000000000000, 35.000000000000000 },
 536   { 4228469210516757.5, 10.000000000000000, 40.000000000000000 },
 537   { 6.8049404557505165e+17, 10.000000000000000, 45.000000000000000 },
 538   { 1.0715971594776370e+20, 10.000000000000000, 50.000000000000000 },
 539   { 1.6618215752886714e+22, 10.000000000000000, 55.000000000000000 },
 540   { 2.5486246072566784e+24, 10.000000000000000, 60.000000000000000 },
 541   { 3.8764628702155481e+26, 10.000000000000000, 65.000000000000000 },
 542   { 5.8592538145409686e+28, 10.000000000000000, 70.000000000000000 },
 543   { 8.8135370711317444e+30, 10.000000000000000, 75.000000000000000 },
 544   { 1.3207418268325279e+33, 10.000000000000000, 80.000000000000000 },
 545   { 1.9732791360862190e+35, 10.000000000000000, 85.000000000000000 },
 546   { 2.9411893748384672e+37, 10.000000000000000, 90.000000000000000 },
 547   { 4.3754494922439984e+39, 10.000000000000000, 95.000000000000000 },
 548   { 6.4989755247201446e+41, 10.000000000000000, 100.00000000000000 },
 549 };
 550 const double toler017 = 2.5000000000000020e-13;
 551
 552 // Test data for nu=20.000000000000000.
 553 // max(|f - f_GSL|): 1.9342813113834067e+25
 554 // max(|f - f_GSL| / |f_GSL|): 4.7061265485304859e-15
 555 const testcase_cyl_bessel_i<double>
 556 data018[21] =
 557 {
 558   { 0.0000000000000000, 20.000000000000000, 0.0000000000000000 },
 559   { 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000 },
 560   { 0.00012507997356449481, 20.000000000000000, 10.000000000000000 },
 561   { 1.6470152535015836, 20.000000000000000, 15.000000000000000 },
 562   { 3188.7503288536154, 20.000000000000000, 20.000000000000000 },
 563   { 2449840.5422952301, 20.000000000000000, 25.000000000000000 },
 564   { 1126985104.4483771, 20.000000000000000, 30.000000000000000 },
 565   { 379617876611.88580, 20.000000000000000, 35.000000000000000 },
 566   { 104459633129479.89, 20.000000000000000, 40.000000000000000 },
 567   { 25039579987216524., 20.000000000000000, 45.000000000000000 },
 568   { 5.4420084027529984e+18, 20.000000000000000, 50.000000000000000 },
 569   { 1.1007498584335495e+21, 20.000000000000000, 55.000000000000000 },
 570   { 2.1091734863057236e+23, 20.000000000000000, 60.000000000000000 },
 571   { 3.8763618091286899e+25, 20.000000000000000, 65.000000000000000 },
 572   { 6.8946130527930870e+27, 20.000000000000000, 70.000000000000000 },
 573   { 1.1946319948836447e+30, 20.000000000000000, 75.000000000000000 },
 574   { 2.0265314377577587e+32, 20.000000000000000, 80.000000000000000 },
 575   { 3.3784665214179985e+34, 20.000000000000000, 85.000000000000000 },
 576   { 5.5516089411796646e+36, 20.000000000000000, 90.000000000000000 },
 577   { 9.0129310795305151e+38, 20.000000000000000, 95.000000000000000 },
 578   { 1.4483461256427176e+41, 20.000000000000000, 100.00000000000000 },
 579 };
 580 const double toler018 = 2.5000000000000020e-13;
 581
 582 // Test data for nu=50.000000000000000.
 583 // max(|f - f_GSL|): 4.5452777397620335e+22
 584 // max(|f - f_GSL| / |f_GSL|): 6.0191728870880627e-14
 585 const testcase_cyl_bessel_i<double>
 586 data019[21] =
 587 {
 588   { 0.0000000000000000, 50.000000000000000, 0.0000000000000000 },
 589   { 2.9314696468108517e-45, 50.000000000000000, 5.0000000000000000 },
 590   { 4.7568945607268442e-30, 50.000000000000000, 10.000000000000000 },
 591   { 5.5468372730667069e-21, 50.000000000000000, 15.000000000000000 },
 592   { 2.2551205757604056e-14, 50.000000000000000, 20.000000000000000 },
 593   { 4.5344251866130257e-09, 50.000000000000000, 25.000000000000000 },
 594   { 0.00014590106916468940, 50.000000000000000, 30.000000000000000 },
 595   { 1.3965549457254882, 50.000000000000000, 35.000000000000000 },
 596   { 5726.8656631289896, 50.000000000000000, 40.000000000000000 },
 597   { 12672593.113027781, 50.000000000000000, 45.000000000000000 },
 598   { 17650802430.016712, 50.000000000000000, 50.000000000000000 },
 599   { 17220231607789.926, 50.000000000000000, 55.000000000000000 },
 600   { 12704607933652176., 50.000000000000000, 60.000000000000000 },
 601   { 7.4989491942193725e+18, 50.000000000000000, 65.000000000000000 },
 602   { 3.6944034898904922e+21, 50.000000000000000, 70.000000000000000 },
 603   { 1.5691634774370186e+24, 50.000000000000000, 75.000000000000000 },
 604   { 5.8927749458163587e+26, 50.000000000000000, 80.000000000000000 },
 605   { 1.9958849054749339e+29, 50.000000000000000, 85.000000000000000 },
 606   { 6.1946050361781500e+31, 50.000000000000000, 90.000000000000000 },
 607   { 1.7845429728697119e+34, 50.000000000000000, 95.000000000000000 },
 608   { 4.8219580855940819e+36, 50.000000000000000, 100.00000000000000 },
 609 };
 610 const double toler019 = 5.0000000000000029e-12;
 611
 612 // Test data for nu=100.00000000000000.
 613 // max(|f - f_GSL|): 186646528.00000000
 614 // max(|f - f_GSL| / |f_GSL|): 2.8278213985558577e-13
 615 const testcase_cyl_bessel_i<double>
 616 data020[21] =
 617 {
 618   { 0.0000000000000000, 100.00000000000000, 0.0000000000000000 },
 619   { 7.0935514885313123e-119, 100.00000000000000, 5.0000000000000000 },
 620   { 1.0823442017492018e-88, 100.00000000000000, 10.000000000000000 },
 621   { 5.9887888536468904e-71, 100.00000000000000, 15.000000000000000 },
 622   { 2.8703193216428771e-58, 100.00000000000000, 20.000000000000000 },
 623   { 2.4426896913122370e-48, 100.00000000000000, 25.000000000000000 },
 624   { 3.9476420053334271e-40, 100.00000000000000, 30.000000000000000 },
 625   { 4.2836596180818780e-33, 100.00000000000000, 35.000000000000000 },
 626   { 6.6249380222596129e-27, 100.00000000000000, 40.000000000000000 },
 627   { 2.3702587262788900e-21, 100.00000000000000, 45.000000000000000 },
 628   { 2.7278879470966917e-16, 100.00000000000000, 50.000000000000000 },
 629   { 1.2763258878228082e-11, 100.00000000000000, 55.000000000000000 },
 630   { 2.8832770906491972e-07, 100.00000000000000, 60.000000000000000 },
 631   { 0.0035805902717061227, 100.00000000000000, 65.000000000000000 },
 632   { 27.017219102595387, 100.00000000000000, 70.000000000000000 },
 633   { 134001.44891209516, 100.00000000000000, 75.000000000000000 },
 634   { 465194832.85060996, 100.00000000000000, 80.000000000000000 },
 635   { 1189280653119.4814, 100.00000000000000, 85.000000000000000 },
 636   { 2334119331258728.0, 100.00000000000000, 90.000000000000000 },
 637   { 3.6399223078502436e+18, 100.00000000000000, 95.000000000000000 },
 638   { 4.6415349416162005e+21, 100.00000000000000, 100.00000000000000 },
 639 };
 640 const double toler020 = 2.5000000000000014e-11;
 641
 642 template<typename Tp, unsigned int Num>
 643   void
 644   test(const testcase_cyl_bessel_i<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_i(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 }