libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/08_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) 2016-2021 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 <tr1/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 // Test data for nu=0.0000000000000000.
  41 // max(|f - f_GSL|): 5.2402526762307389e-14 at index 12
  42 // max(|f - f_GSL| / |f_GSL|): 1.0747725055352992e-14
  43 // mean(f - f_GSL): -1.9624513654326576e-14
  44 // variance(f - f_GSL): 4.0630093099383162e-30
  45 // stddev(f - f_GSL): 2.0156907773610308e-15
  46 const testcase_cyl_bessel_i<double>
  47 data007[21] =
  48 {
  49   { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000, 0.0 },
  50   { 1.0156861412236078, 0.0000000000000000, 0.25000000000000000, 0.0 },
  51   { 1.0634833707413236, 0.0000000000000000, 0.50000000000000000, 0.0 },
  52   { 1.1456467780440014, 0.0000000000000000, 0.75000000000000000, 0.0 },
  53   { 1.2660658777520082, 0.0000000000000000, 1.0000000000000000, 0.0 },
  54   { 1.4304687177218294, 0.0000000000000000, 1.2500000000000000, 0.0 },
  55   { 1.6467231897728904, 0.0000000000000000, 1.5000000000000000, 0.0 },
  56   { 1.9252521538585021, 0.0000000000000000, 1.7500000000000000, 0.0 },
  57   { 2.2795853023360668, 0.0000000000000000, 2.0000000000000000, 0.0 },
  58   { 2.7270783071907951, 0.0000000000000000, 2.2500000000000000, 0.0 },
  59   { 3.2898391440501231, 0.0000000000000000, 2.5000000000000000, 0.0 },
  60   { 3.9959131072376550, 0.0000000000000000, 2.7500000000000000, 0.0 },
  61   { 4.8807925858650245, 0.0000000000000000, 3.0000000000000000, 0.0 },
  62   { 5.9893359979395138, 0.0000000000000000, 3.2500000000000000, 0.0 },
  63   { 7.3782034322254750, 0.0000000000000000, 3.5000000000000000, 0.0 },
  64   { 9.1189458608445655, 0.0000000000000000, 3.7500000000000000, 0.0 },
  65   { 11.301921952136325, 0.0000000000000000, 4.0000000000000000, 0.0 },
  66   { 14.041263683000595, 0.0000000000000000, 4.2500000000000000, 0.0 },
  67   { 17.481171855609272, 0.0000000000000000, 4.5000000000000000, 0.0 },
  68   { 21.803898740902120, 0.0000000000000000, 4.7500000000000000, 0.0 },
  69   { 27.239871823604439, 0.0000000000000000, 5.0000000000000000, 0.0 },
  70 };
  71 const double toler007 = 1.0000000000000008e-12;
  72
  73 // Test data for nu=0.33333333333333331.
  74 // max(|f - f_GSL|): 6.2172489379008766e-15 at index 14
  75 // max(|f - f_GSL| / |f_GSL|): 9.1624880778907085e-16
  76 // mean(f - f_GSL): 1.1525172350870673e-15
  77 // variance(f - f_GSL): 6.9735538801568761e-32
  78 // stddev(f - f_GSL): 2.6407487347638500e-16
  79 const testcase_cyl_bessel_i<double>
  80 data008[21] =
  81 {
  82   { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000, 0.0 },
  83   { 0.56650686557808660, 0.33333333333333331, 0.25000000000000000, 0.0 },
  84   { 0.73897315642511863, 0.33333333333333331, 0.50000000000000000, 0.0 },
  85   { 0.89532320365836815, 0.33333333333333331, 0.75000000000000000, 0.0 },
  86   { 1.0646313978895283, 0.33333333333333331, 1.0000000000000000, 0.0 },
  87   { 1.2623776732605250, 0.33333333333333331, 1.2500000000000000, 0.0 },
  88   { 1.5014290000224382, 0.33333333333333331, 1.5000000000000000, 0.0 },
  89   { 1.7951195525946040, 0.33333333333333331, 1.7500000000000000, 0.0 },
  90   { 2.1587825813728614, 0.33333333333333331, 2.0000000000000000, 0.0 },
  91   { 2.6109134564811405, 0.33333333333333331, 2.2500000000000000, 0.0 },
  92   { 3.1743242297241938, 0.33333333333333331, 2.5000000000000000, 0.0 },
  93   { 3.8774551722182093, 0.33333333333333331, 2.7500000000000000, 0.0 },
  94   { 4.7559569371646946, 0.33333333333333331, 3.0000000000000000, 0.0 },
  95   { 5.8546499652731825, 0.33333333333333331, 3.2500000000000000, 0.0 },
  96   { 7.2299798619171129, 0.33333333333333331, 3.5000000000000000, 0.0 },
  97   { 8.9531114355506318, 0.33333333333333331, 3.7500000000000000, 0.0 },
  98   { 11.113838389991479, 0.33333333333333331, 4.0000000000000000, 0.0 },
  99   { 13.825531136529117, 0.33333333333333331, 4.2500000000000000, 0.0 },
 100   { 17.231403968478318, 0.33333333333333331, 4.5000000000000000, 0.0 },
 101   { 21.512458099556554, 0.33333333333333331, 4.7500000000000000, 0.0 },
 102   { 26.897553069268362, 0.33333333333333331, 5.0000000000000000, 0.0 },
 103 };
 104 const double toler008 = 2.5000000000000020e-13;
 105
 106 // Test data for nu=0.50000000000000000.
 107 // max(|f - f_GSL|): 1.4210854715202004e-14 at index 19
 108 // max(|f - f_GSL| / |f_GSL|): 9.6042704318763827e-16
 109 // mean(f - f_GSL): 1.9296733523246769e-16
 110 // variance(f - f_GSL): 1.9549106045027772e-33
 111 // stddev(f - f_GSL): 4.4214371017835108e-17
 112 const testcase_cyl_bessel_i<double>
 113 data009[21] =
 114 {
 115   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, 0.0 },
 116   { 0.40311093489975897, 0.50000000000000000, 0.25000000000000000, 0.0 },
 117   { 0.58799308679041573, 0.50000000000000000, 0.50000000000000000, 0.0 },
 118   { 0.75761498638991298, 0.50000000000000000, 0.75000000000000000, 0.0 },
 119   { 0.93767488824548695, 0.50000000000000000, 1.0000000000000000, 0.0 },
 120   { 1.1432089853159872, 0.50000000000000000, 1.2500000000000000, 0.0 },
 121   { 1.3871617204034761, 0.50000000000000000, 1.5000000000000000, 0.0 },
 122   { 1.6830217804556813, 0.50000000000000000, 1.7500000000000000, 0.0 },
 123   { 2.0462368630890526, 0.50000000000000000, 2.0000000000000000, 0.0 },
 124   { 2.4953405089360046, 0.50000000000000000, 2.2500000000000000, 0.0 },
 125   { 3.0530935381967175, 0.50000000000000000, 2.5000000000000000, 0.0 },
 126   { 3.7477882494879449, 0.50000000000000000, 2.7500000000000000, 0.0 },
 127   { 4.6148229034075969, 0.50000000000000000, 3.0000000000000000, 0.0 },
 128   { 5.6986505325335486, 0.50000000000000000, 3.2500000000000000, 0.0 },
 129   { 7.0552194086911859, 0.50000000000000000, 3.5000000000000000, 0.0 },
 130   { 8.7550467841188979, 0.50000000000000000, 3.7500000000000000, 0.0 },
 131   { 10.887101798588422, 0.50000000000000000, 4.0000000000000000, 0.0 },
 132   { 13.563718712579764, 0.50000000000000000, 4.2500000000000000, 0.0 },
 133   { 16.926820080158183, 0.50000000000000000, 4.5000000000000000, 0.0 },
 134   { 21.155804306570005, 0.50000000000000000, 4.7500000000000000, 0.0 },
 135   { 26.477547497559065, 0.50000000000000000, 5.0000000000000000, 0.0 },
 136 };
 137 const double toler009 = 2.5000000000000020e-13;
 138
 139 // Test data for nu=0.66666666666666663.
 140 // max(|f - f_GSL|): 1.9539925233402755e-14 at index 16
 141 // max(|f - f_GSL| / |f_GSL|): 2.2100364323953014e-15
 142 // mean(f - f_GSL): -5.2312651565075830e-15
 143 // variance(f - f_GSL): 1.4792059082391298e-31
 144 // stddev(f - f_GSL): 3.8460446022363414e-16
 145 const testcase_cyl_bessel_i<double>
 146 data010[21] =
 147 {
 148   { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000, 0.0 },
 149   { 0.27953690613200444, 0.66666666666666663, 0.25000000000000000, 0.0 },
 150   { 0.45628323113556890, 0.66666666666666663, 0.50000000000000000, 0.0 },
 151   { 0.62594569838182623, 0.66666666666666663, 0.75000000000000000, 0.0 },
 152   { 0.80752128860612971, 0.66666666666666663, 1.0000000000000000, 0.0 },
 153   { 1.0139484513577173, 0.66666666666666663, 1.2500000000000000, 0.0 },
 154   { 1.2572918396962993, 0.66666666666666663, 1.5000000000000000, 0.0 },
 155   { 1.5505806938325581, 0.66666666666666663, 1.7500000000000000, 0.0 },
 156   { 1.9089492968236210, 0.66666666666666663, 2.0000000000000000, 0.0 },
 157   { 2.3506463490300340, 0.66666666666666663, 2.2500000000000000, 0.0 },
 158   { 2.8981161894224896, 0.66666666666666663, 2.5000000000000000, 0.0 },
 159   { 3.5792654911068724, 0.66666666666666663, 2.7500000000000000, 0.0 },
 160   { 4.4290087213549514, 0.66666666666666663, 3.0000000000000000, 0.0 },
 161   { 5.4911895720097705, 0.66666666666666663, 3.2500000000000000, 0.0 },
 162   { 6.8209918044137305, 0.66666666666666663, 3.5000000000000000, 0.0 },
 163   { 8.4879784249619785, 0.66666666666666663, 3.7500000000000000, 0.0 },
 164   { 10.579932774013004, 0.66666666666666663, 4.0000000000000000, 0.0 },
 165   { 13.207720355482458, 0.66666666666666663, 4.2500000000000000, 0.0 },
 166   { 16.511448404200543, 0.66666666666666663, 4.5000000000000000, 0.0 },
 167   { 20.668274532832392, 0.66666666666666663, 4.7500000000000000, 0.0 },
 168   { 25.902310583215122, 0.66666666666666663, 5.0000000000000000, 0.0 },
 169 };
 170 const double toler010 = 2.5000000000000020e-13;
 171
 172 // Test data for nu=1.0000000000000000.
 173 // max(|f - f_GSL|): 1.2967404927621828e-13 at index 17
 174 // max(|f - f_GSL| / |f_GSL|): 1.0977631741433893e-14
 175 // mean(f - f_GSL): -3.0188814411265717e-14
 176 // variance(f - f_GSL): 3.7247797767076778e-29
 177 // stddev(f - f_GSL): 6.1030973912495271e-15
 178 const testcase_cyl_bessel_i<double>
 179 data011[21] =
 180 {
 181   { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000, 0.0 },
 182   { 0.12597910894546793, 1.0000000000000000, 0.25000000000000000, 0.0 },
 183   { 0.25789430539089631, 1.0000000000000000, 0.50000000000000000, 0.0 },
 184   { 0.40199246158092228, 1.0000000000000000, 0.75000000000000000, 0.0 },
 185   { 0.56515910399248503, 1.0000000000000000, 1.0000000000000000, 0.0 },
 186   { 0.75528141834074725, 1.0000000000000000, 1.2500000000000000, 0.0 },
 187   { 0.98166642857790720, 1.0000000000000000, 1.5000000000000000, 0.0 },
 188   { 1.2555375122401728, 1.0000000000000000, 1.7500000000000000, 0.0 },
 189   { 1.5906368546373291, 1.0000000000000000, 2.0000000000000000, 0.0 },
 190   { 2.0039674569295931, 1.0000000000000000, 2.2500000000000000, 0.0 },
 191   { 2.5167162452886984, 1.0000000000000000, 2.5000000000000000, 0.0 },
 192   { 3.1554101386190028, 1.0000000000000000, 2.7500000000000000, 0.0 },
 193   { 3.9533702174026097, 1.0000000000000000, 3.0000000000000000, 0.0 },
 194   { 4.9525461659085490, 1.0000000000000000, 3.2500000000000000, 0.0 },
 195   { 6.2058349222583642, 1.0000000000000000, 3.5000000000000000, 0.0 },
 196   { 7.7800152298244170, 1.0000000000000000, 3.7500000000000000, 0.0 },
 197   { 9.7594651537044523, 1.0000000000000000, 4.0000000000000000, 0.0 },
 198   { 12.250874667409304, 1.0000000000000000, 4.2500000000000000, 0.0 },
 199   { 15.389222753735924, 1.0000000000000000, 4.5000000000000000, 0.0 },
 200   { 19.345361447520226, 1.0000000000000000, 4.7500000000000000, 0.0 },
 201   { 24.335642142450524, 1.0000000000000000, 5.0000000000000000, 0.0 },
 202 };
 203 const double toler011 = 1.0000000000000008e-12;
 204
 205 // Test data for nu=2.0000000000000000.
 206 // max(|f - f_GSL|): 1.8474111129762605e-13 at index 20
 207 // max(|f - f_GSL| / |f_GSL|): 1.0796880796865132e-14
 208 // mean(f - f_GSL): -3.8692841919903068e-14
 209 // variance(f - f_GSL): 1.1198300918819667e-27
 210 // stddev(f - f_GSL): 3.3463862477035829e-14
 211 const testcase_cyl_bessel_i<double>
 212 data012[21] =
 213 {
 214   { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000, 0.0 },
 215   { 0.0078532696598645167, 2.0000000000000000, 0.25000000000000000, 0.0 },
 216   { 0.031906149177738249, 2.0000000000000000, 0.50000000000000000, 0.0 },
 217   { 0.073666880494875436, 2.0000000000000000, 0.75000000000000000, 0.0 },
 218   { 0.13574766976703831, 2.0000000000000000, 1.0000000000000000, 0.0 },
 219   { 0.22201844837663415, 2.0000000000000000, 1.2500000000000000, 0.0 },
 220   { 0.33783461833568068, 2.0000000000000000, 1.5000000000000000, 0.0 },
 221   { 0.49035213986973314, 2.0000000000000000, 1.7500000000000000, 0.0 },
 222   { 0.68894844769873831, 2.0000000000000000, 2.0000000000000000, 0.0 },
 223   { 0.94577390103115722, 2.0000000000000000, 2.2500000000000000, 0.0 },
 224   { 1.2764661478191643, 2.0000000000000000, 2.5000000000000000, 0.0 },
 225   { 1.7010693700601991, 2.0000000000000000, 2.7500000000000000, 0.0 },
 226   { 2.2452124409299512, 2.0000000000000000, 3.0000000000000000, 0.0 },
 227   { 2.9416152804573357, 2.0000000000000000, 3.2500000000000000, 0.0 },
 228   { 3.8320120480778415, 2.0000000000000000, 3.5000000000000000, 0.0 },
 229   { 4.9696044049382113, 2.0000000000000000, 3.7500000000000000, 0.0 },
 230   { 6.4221893752841055, 2.0000000000000000, 4.0000000000000000, 0.0 },
 231   { 8.2761461924550552, 2.0000000000000000, 4.2500000000000000, 0.0 },
 232   { 10.641517298393307, 2.0000000000000000, 4.5000000000000000, 0.0 },
 233   { 13.658483394577813, 2.0000000000000000, 4.7500000000000000, 0.0 },
 234   { 17.505614966624233, 2.0000000000000000, 5.0000000000000000, 0.0 },
 235 };
 236 const double toler012 = 1.0000000000000008e-12;
 237
 238 // Test data for nu=5.0000000000000000.
 239 // max(|f - f_GSL|): 2.2204460492503131e-14 at index 20
 240 // max(|f - f_GSL| / |f_GSL|): 1.1379865680381910e-14
 241 // mean(f - f_GSL): -3.4502652328999478e-15
 242 // variance(f - f_GSL): 1.8465291591354433e-29
 243 // stddev(f - f_GSL): 4.2971259687556788e-15
 244 const testcase_cyl_bessel_i<double>
 245 data013[21] =
 246 {
 247   { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000, 0.0 },
 248   { 2.5497616449882785e-07, 5.0000000000000000, 0.25000000000000000, 0.0 },
 249   { 8.2231713131092646e-06, 5.0000000000000000, 0.50000000000000000, 0.0 },
 250   { 6.3261122739811725e-05, 5.0000000000000000, 0.75000000000000000, 0.0 },
 251   { 0.00027146315595697195, 5.0000000000000000, 1.0000000000000000, 0.0 },
 252   { 0.00084793613616686856, 5.0000000000000000, 1.2500000000000000, 0.0 },
 253   { 0.0021705595690975554, 5.0000000000000000, 1.5000000000000000, 0.0 },
 254   { 0.0048504513371845385, 5.0000000000000000, 1.7500000000000000, 0.0 },
 255   { 0.0098256793231317023, 5.0000000000000000, 2.0000000000000000, 0.0 },
 256   { 0.018486577941045829, 5.0000000000000000, 2.2500000000000000, 0.0 },
 257   { 0.032843475172023219, 5.0000000000000000, 2.5000000000000000, 0.0 },
 258   { 0.055750882754221943, 5.0000000000000000, 2.7500000000000000, 0.0 },
 259   { 0.091206477661513338, 5.0000000000000000, 3.0000000000000000, 0.0 },
 260   { 0.14474880546308083, 5.0000000000000000, 3.2500000000000000, 0.0 },
 261   { 0.22398495470190780, 5.0000000000000000, 3.5000000000000000, 0.0 },
 262   { 0.33928899170999877, 5.0000000000000000, 3.7500000000000000, 0.0 },
 263   { 0.50472436311316637, 5.0000000000000000, 4.0000000000000000, 0.0 },
 264   { 0.73925961816682961, 5.0000000000000000, 4.2500000000000000, 0.0 },
 265   { 1.0683677743764701, 5.0000000000000000, 4.5000000000000000, 0.0 },
 266   { 1.5261268693599621, 5.0000000000000000, 4.7500000000000000, 0.0 },
 267   { 2.1579745473225476, 5.0000000000000000, 5.0000000000000000, 0.0 },
 268 };
 269 const double toler013 = 1.0000000000000008e-12;
 270
 271 // Test data for nu=10.000000000000000.
 272 // max(|f - f_GSL|): 5.0306980803327406e-17 at index 20
 273 // max(|f - f_GSL| / |f_GSL|): 1.2741587624782699e-14
 274 // mean(f - f_GSL): -5.4602116438803446e-18
 275 // variance(f - f_GSL): 1.0558971696213844e-34
 276 // stddev(f - f_GSL): 1.0275685717368863e-17
 277 const testcase_cyl_bessel_i<double>
 278 data014[21] =
 279 {
 280   { 0.0000000000000000, 10.000000000000000, 0.0000000000000000, 0.0 },
 281   { 2.5701232848571186e-16, 10.000000000000000, 0.25000000000000000, 0.0 },
 282   { 2.6430419258812784e-13, 10.000000000000000, 0.50000000000000000, 0.0 },
 283   { 1.5349659676120412e-11, 10.000000000000000, 0.75000000000000000, 0.0 },
 284   { 2.7529480398368732e-10, 10.000000000000000, 1.0000000000000000, 0.0 },
 285   { 2.5967897782035928e-09, 10.000000000000000, 1.2500000000000000, 0.0 },
 286   { 1.6330924437799743e-08, 10.000000000000000, 1.5000000000000000, 0.0 },
 287   { 7.7706676834614079e-08, 10.000000000000000, 1.7500000000000000, 0.0 },
 288   { 3.0169638793506839e-07, 10.000000000000000, 2.0000000000000000, 0.0 },
 289   { 1.0034459057774481e-06, 10.000000000000000, 2.2500000000000000, 0.0 },
 290   { 2.9557436109680578e-06, 10.000000000000000, 2.5000000000000000, 0.0 },
 291   { 7.8955603774082724e-06, 10.000000000000000, 2.7500000000000000, 0.0 },
 292   { 1.9464393470612970e-05, 10.000000000000000, 3.0000000000000000, 0.0 },
 293   { 4.4875369479742435e-05, 10.000000000000000, 3.2500000000000000, 0.0 },
 294   { 9.7760848514528916e-05, 10.000000000000000, 3.5000000000000000, 0.0 },
 295   { 0.00020289011210063496, 10.000000000000000, 3.7500000000000000, 0.0 },
 296   { 0.00040378896132693058, 10.000000000000000, 4.0000000000000000, 0.0 },
 297   { 0.00077478519551669892, 10.000000000000000, 4.2500000000000000, 0.0 },
 298   { 0.0014397060684919682, 10.000000000000000, 4.5000000000000000, 0.0 },
 299   { 0.0026004486016189452, 10.000000000000000, 4.7500000000000000, 0.0 },
 300   { 0.0045800444191760525, 10.000000000000000, 5.0000000000000000, 0.0 },
 301 };
 302 const double toler014 = 1.0000000000000008e-12;
 303
 304 // Test data for nu=20.000000000000000.
 305 // max(|f - f_GSL|): 6.9147129330604657e-25 at index 20
 306 // max(|f - f_GSL| / |f_GSL|): 1.6061319023473306e-14
 307 // mean(f - f_GSL): -5.1436249496041580e-26
 308 // variance(f - f_GSL): 2.1506355008505938e-50
 309 // stddev(f - f_GSL): 1.4665045178418625e-25
 310 const testcase_cyl_bessel_i<double>
 311 data015[21] =
 312 {
 313   { 0.0000000000000000, 20.000000000000000, 0.0000000000000000, 0.0 },
 314   { 3.5677858077910353e-37, 20.000000000000000, 0.25000000000000000, 0.0 },
 315   { 3.7494538480790194e-31, 20.000000000000000, 0.50000000000000000, 0.0 },
 316   { 1.2514356342425337e-27, 20.000000000000000, 0.75000000000000000, 0.0 },
 317   { 3.9668359858190197e-25, 20.000000000000000, 1.0000000000000000, 0.0 },
 318   { 3.4637832909868234e-23, 20.000000000000000, 1.2500000000000000, 0.0 },
 319   { 1.3388331839683472e-21, 20.000000000000000, 1.5000000000000000, 0.0 },
 320   { 2.9502376732679751e-20, 20.000000000000000, 1.7500000000000000, 0.0 },
 321   { 4.3105605761095479e-19, 20.000000000000000, 2.0000000000000000, 0.0 },
 322   { 4.6032451406433059e-18, 20.000000000000000, 2.2500000000000000, 0.0 },
 323   { 3.8400317244170310e-17, 20.000000000000000, 2.5000000000000000, 0.0 },
 324   { 2.6239115263043263e-16, 20.000000000000000, 2.7500000000000000, 0.0 },
 325   { 1.5209660019426689e-15, 20.000000000000000, 3.0000000000000000, 0.0 },
 326   { 7.6806450728249953e-15, 20.000000000000000, 3.2500000000000000, 0.0 },
 327   { 3.4495528847222945e-14, 20.000000000000000, 3.5000000000000000, 0.0 },
 328   { 1.4006589294850677e-13, 20.000000000000000, 3.7500000000000000, 0.0 },
 329   { 5.2100734221993054e-13, 20.000000000000000, 4.0000000000000000, 0.0 },
 330   { 1.7946903269488168e-12, 20.000000000000000, 4.2500000000000000, 0.0 },
 331   { 5.7763830562279699e-12, 20.000000000000000, 4.5000000000000000, 0.0 },
 332   { 1.7502433074548735e-11, 20.000000000000000, 4.7500000000000000, 0.0 },
 333   { 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000, 0.0 },
 334 };
 335 const double toler015 = 1.0000000000000008e-12;
 336 //  cyl_bessel_i
 337
 338 // Test data for nu=0.0000000000000000.
 339 // max(|f - f_GSL|): 2.5841998320082313e+28 at index 20
 340 // max(|f - f_GSL| / |f_GSL|): 2.4067014886642843e-14
 341 // mean(f - f_GSL): -1.2242902567974868e+27
 342 // variance(f - f_GSL): inf
 343 // stddev(f - f_GSL): inf
 344 const testcase_cyl_bessel_i<double>
 345 data016[21] =
 346 {
 347   { 1.0000000000000000, 0.0000000000000000, 0.0000000000000000, 0.0 },
 348   { 27.239871823604439, 0.0000000000000000, 5.0000000000000000, 0.0 },
 349   { 2815.7166284662558, 0.0000000000000000, 10.000000000000000, 0.0 },
 350   { 339649.37329791381, 0.0000000000000000, 15.000000000000000, 0.0 },
 351   { 43558282.559553474, 0.0000000000000000, 20.000000000000000, 0.0 },
 352   { 5774560606.4663124, 0.0000000000000000, 25.000000000000000, 0.0 },
 353   { 781672297823.97925, 0.0000000000000000, 30.000000000000000, 0.0 },
 354   { 107338818494514.42, 0.0000000000000000, 35.000000000000000, 0.0 },
 355   { 14894774793419916., 0.0000000000000000, 40.000000000000000, 0.0 },
 356   { 2.0834140751773164e+18, 0.0000000000000000, 45.000000000000000, 0.0 },
 357   { 2.9325537838493457e+20, 0.0000000000000000, 50.000000000000000, 0.0 },
 358   { 4.1487895607332160e+22, 0.0000000000000000, 55.000000000000000, 0.0 },
 359   { 5.8940770556098216e+24, 0.0000000000000000, 60.000000000000000, 0.0 },
 360   { 8.4030398456255582e+26, 0.0000000000000000, 65.000000000000000, 0.0 },
 361   { 1.2015889579125424e+29, 0.0000000000000000, 70.000000000000000, 0.0 },
 362   { 1.7226390780357976e+31, 0.0000000000000000, 75.000000000000000, 0.0 },
 363   { 2.4751784043341661e+33, 0.0000000000000000, 80.000000000000000, 0.0 },
 364   { 3.5634776304081403e+35, 0.0000000000000000, 85.000000000000000, 0.0 },
 365   { 5.1392383455086475e+37, 0.0000000000000000, 90.000000000000000, 0.0 },
 366   { 7.4233258618752072e+39, 0.0000000000000000, 95.000000000000000, 0.0 },
 367   { 1.0737517071310986e+42, 0.0000000000000000, 100.00000000000000, 0.0 },
 368 };
 369 const double toler016 = 2.5000000000000015e-12;
 370
 371 // Test data for nu=0.33333333333333331.
 372 // max(|f - f_GSL|): 1.0986717848657750e+28 at index 20
 373 // max(|f - f_GSL| / |f_GSL|): 1.2017640663876795e-14
 374 // mean(f - f_GSL): -5.2068252642007974e+26
 375 // variance(f - f_GSL): inf
 376 // stddev(f - f_GSL): inf
 377 const testcase_cyl_bessel_i<double>
 378 data017[21] =
 379 {
 380   { 0.0000000000000000, 0.33333333333333331, 0.0000000000000000, 0.0 },
 381   { 26.897553069268362, 0.33333333333333331, 5.0000000000000000, 0.0 },
 382   { 2799.2396097056790, 0.33333333333333331, 10.000000000000000, 0.0 },
 383   { 338348.63146593666, 0.33333333333333331, 15.000000000000000, 0.0 },
 384   { 43434263.927938424, 0.33333333333333331, 20.000000000000000, 0.0 },
 385   { 5761474759.6213636, 0.33333333333333331, 25.000000000000000, 0.0 },
 386   { 780201111830.30237, 0.33333333333333331, 30.000000000000000, 0.0 },
 387   { 107166066959051.91, 0.33333333333333331, 35.000000000000000, 0.0 },
 388   { 14873836574083762., 0.33333333333333331, 40.000000000000000, 0.0 },
 389   { 2.0808143020217085e+18, 0.33333333333333331, 45.000000000000000, 0.0 },
 390   { 2.9292639365644226e+20, 0.33333333333333331, 50.000000000000000, 0.0 },
 391   { 4.1445621624120489e+22, 0.33333333333333331, 55.000000000000000, 0.0 },
 392   { 5.8885758374365916e+24, 0.33333333333333331, 60.000000000000000, 0.0 },
 393   { 8.3958047021083941e+26, 0.33333333333333331, 65.000000000000000, 0.0 },
 394   { 1.2006287819446431e+29, 0.33333333333333331, 70.000000000000000, 0.0 },
 395   { 1.7213548977150022e+31, 0.33333333333333331, 75.000000000000000, 0.0 },
 396   { 2.4734492458444449e+33, 0.33333333333333331, 80.000000000000000, 0.0 },
 397   { 3.5611354547857122e+35, 0.33333333333333331, 85.000000000000000, 0.0 },
 398   { 5.1360491295551848e+37, 0.33333333333333331, 90.000000000000000, 0.0 },
 399   { 7.4189629097600431e+39, 0.33333333333333331, 95.000000000000000, 0.0 },
 400   { 1.0731523308358370e+42, 0.33333333333333331, 100.00000000000000, 0.0 },
 401 };
 402 const double toler017 = 1.0000000000000008e-12;
 403
 404 // Test data for nu=0.50000000000000000.
 405 // max(|f - f_GSL|): 7.1181552258909366e+27 at index 20
 406 // max(|f - f_GSL| / |f_GSL|): 1.2230293310085236e-14
 407 // mean(f - f_GSL): -3.3462733503919608e+26
 408 // variance(f - f_GSL): inf
 409 // stddev(f - f_GSL): inf
 410 const testcase_cyl_bessel_i<double>
 411 data018[21] =
 412 {
 413   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, 0.0 },
 414   { 26.477547497559065, 0.50000000000000000, 5.0000000000000000, 0.0 },
 415   { 2778.7846038745711, 0.50000000000000000, 10.000000000000000, 0.0 },
 416   { 336729.88718706399, 0.50000000000000000, 15.000000000000000, 0.0 },
 417   { 43279746.272428922, 0.50000000000000000, 20.000000000000000, 0.0 },
 418   { 5745159748.3464680, 0.50000000000000000, 25.000000000000000, 0.0 },
 419   { 778366068840.44580, 0.50000000000000000, 30.000000000000000, 0.0 },
 420   { 106950522408567.66, 0.50000000000000000, 35.000000000000000, 0.0 },
 421   { 14847705549021960., 0.50000000000000000, 40.000000000000000, 0.0 },
 422   { 2.0775691824625661e+18, 0.50000000000000000, 45.000000000000000, 0.0 },
 423   { 2.9251568529912984e+20, 0.50000000000000000, 50.000000000000000, 0.0 },
 424   { 4.1392840094781220e+22, 0.50000000000000000, 55.000000000000000, 0.0 },
 425   { 5.8817065760751945e+24, 0.50000000000000000, 60.000000000000000, 0.0 },
 426   { 8.3867695787277245e+26, 0.50000000000000000, 65.000000000000000, 0.0 },
 427   { 1.1994296461653203e+29, 0.50000000000000000, 70.000000000000000, 0.0 },
 428   { 1.7197510246063334e+31, 0.50000000000000000, 75.000000000000000, 0.0 },
 429   { 2.4712895036230794e+33, 0.50000000000000000, 80.000000000000000, 0.0 },
 430   { 3.5582099086757769e+35, 0.50000000000000000, 85.000000000000000, 0.0 },
 431   { 5.1320654031231128e+37, 0.50000000000000000, 90.000000000000000, 0.0 },
 432   { 7.4135128383495239e+39, 0.50000000000000000, 95.000000000000000, 0.0 },
 433   { 1.0724035825423179e+42, 0.50000000000000000, 100.00000000000000, 0.0 },
 434 };
 435 const double toler018 = 1.0000000000000008e-12;
 436
 437 // Test data for nu=0.66666666666666663.
 438 // max(|f - f_GSL|): 4.6422751473201760e+27 at index 20
 439 // max(|f - f_GSL| / |f_GSL|): 8.8432218147527708e-15
 440 // mean(f - f_GSL): -2.2367290021744526e+26
 441 // variance(f - f_GSL): inf
 442 // stddev(f - f_GSL): inf
 443 const testcase_cyl_bessel_i<double>
 444 data019[21] =
 445 {
 446   { 0.0000000000000000, 0.66666666666666663, 0.0000000000000000, 0.0 },
 447   { 25.902310583215122, 0.66666666666666663, 5.0000000000000000, 0.0 },
 448   { 2750.4090423459315, 0.66666666666666663, 10.000000000000000, 0.0 },
 449   { 334476.98138574377, 0.66666666666666663, 15.000000000000000, 0.0 },
 450   { 43064361.686912313, 0.66666666666666663, 20.000000000000000, 0.0 },
 451   { 5722397441.9603882, 0.66666666666666663, 25.000000000000000, 0.0 },
 452   { 775804343498.02661, 0.66666666666666663, 30.000000000000000, 0.0 },
 453   { 106649495512800.88, 0.66666666666666663, 35.000000000000000, 0.0 },
 454   { 14811199896983754., 0.66666666666666663, 40.000000000000000, 0.0 },
 455   { 2.0730345814356961e+18, 0.66666666666666663, 45.000000000000000, 0.0 },
 456   { 2.9194166755257467e+20, 0.66666666666666663, 50.000000000000000, 0.0 },
 457   { 4.1319059569935374e+22, 0.66666666666666663, 55.000000000000000, 0.0 },
 458   { 5.8721031476386222e+24, 0.66666666666666663, 60.000000000000000, 0.0 },
 459   { 8.3741368248217830e+26, 0.66666666666666663, 65.000000000000000, 0.0 },
 460   { 1.1977528777008688e+29, 0.66666666666666663, 70.000000000000000, 0.0 },
 461   { 1.7175081240014333e+31, 0.66666666666666663, 75.000000000000000, 0.0 },
 462   { 2.4682690458513916e+33, 0.66666666666666663, 80.000000000000000, 0.0 },
 463   { 3.5541181975850724e+35, 0.66666666666666663, 85.000000000000000, 0.0 },
 464   { 5.1264933963228892e+37, 0.66666666666666663, 90.000000000000000, 0.0 },
 465   { 7.4058894880134064e+39, 0.66666666666666663, 95.000000000000000, 0.0 },
 466   { 1.0713562154788124e+42, 0.66666666666666663, 100.00000000000000, 0.0 },
 467 };
 468 const double toler019 = 5.0000000000000039e-13;
 469
 470 // Test data for nu=1.0000000000000000.
 471 // max(|f - f_GSL|): 5.4159876718735387e+27 at index 20
 472 // max(|f - f_GSL| / |f_GSL|): 7.0819761463168391e-15
 473 // mean(f - f_GSL): 2.5933470782682662e+26
 474 // variance(f - f_GSL): inf
 475 // stddev(f - f_GSL): inf
 476 const testcase_cyl_bessel_i<double>
 477 data020[21] =
 478 {
 479   { 0.0000000000000000, 1.0000000000000000, 0.0000000000000000, 0.0 },
 480   { 24.335642142450524, 1.0000000000000000, 5.0000000000000000, 0.0 },
 481   { 2670.9883037012560, 1.0000000000000000, 10.000000000000000, 0.0 },
 482   { 328124.92197020649, 1.0000000000000000, 15.000000000000000, 0.0 },
 483   { 42454973.385127783, 1.0000000000000000, 20.000000000000000, 0.0 },
 484   { 5657865129.8787022, 1.0000000000000000, 25.000000000000000, 0.0 },
 485   { 768532038938.95667, 1.0000000000000000, 30.000000000000000, 0.0 },
 486   { 105794126051896.17, 1.0000000000000000, 35.000000000000000, 0.0 },
 487   { 14707396163259352., 1.0000000000000000, 40.000000000000000, 0.0 },
 488   { 2.0601334620815780e+18, 1.0000000000000000, 45.000000000000000, 0.0 },
 489   { 2.9030785901035638e+20, 1.0000000000000000, 50.000000000000000, 0.0 },
 490   { 4.1108986452992812e+22, 1.0000000000000000, 55.000000000000000, 0.0 },
 491   { 5.8447515883904527e+24, 1.0000000000000000, 60.000000000000000, 0.0 },
 492   { 8.3381485471501288e+26, 1.0000000000000000, 65.000000000000000, 0.0 },
 493   { 1.1929750788892366e+29, 1.0000000000000000, 70.000000000000000, 0.0 },
 494   { 1.7111160152965382e+31, 1.0000000000000000, 75.000000000000000, 0.0 },
 495   { 2.4596595795675343e+33, 1.0000000000000000, 80.000000000000000, 0.0 },
 496   { 3.5424536064404024e+35, 1.0000000000000000, 85.000000000000000, 0.0 },
 497   { 5.1106068152566129e+37, 1.0000000000000000, 90.000000000000000, 0.0 },
 498   { 7.3841518091360182e+39, 1.0000000000000000, 95.000000000000000, 0.0 },
 499   { 1.0683693903381569e+42, 1.0000000000000000, 100.00000000000000, 0.0 },
 500 };
 501 const double toler020 = 5.0000000000000039e-13;
 502
 503 // Test data for nu=2.0000000000000000.
 504 // max(|f - f_GSL|): 6.1897001964269014e+27 at index 20
 505 // max(|f - f_GSL| / |f_GSL|): 1.0553248866140883e-14
 506 // mean(f - f_GSL): 2.9514880793266611e+26
 507 // variance(f - f_GSL): inf
 508 // stddev(f - f_GSL): inf
 509 const testcase_cyl_bessel_i<double>
 510 data021[21] =
 511 {
 512   { 0.0000000000000000, 2.0000000000000000, 0.0000000000000000, 0.0 },
 513   { 17.505614966624233, 2.0000000000000000, 5.0000000000000000, 0.0 },
 514   { 2281.5189677260046, 2.0000000000000000, 10.000000000000000, 0.0 },
 515   { 295899.38370188628, 2.0000000000000000, 15.000000000000000, 0.0 },
 516   { 39312785.221040756, 2.0000000000000000, 20.000000000000000, 0.0 },
 517   { 5321931396.0760155, 2.0000000000000000, 25.000000000000000, 0.0 },
 518   { 730436828561.38013, 2.0000000000000000, 30.000000000000000, 0.0 },
 519   { 101293439862977.19, 2.0000000000000000, 35.000000000000000, 0.0 },
 520   { 14159404985256920., 2.0000000000000000, 40.000000000000000, 0.0 },
 521   { 1.9918525879736883e+18, 2.0000000000000000, 45.000000000000000, 0.0 },
 522   { 2.8164306402451938e+20, 2.0000000000000000, 50.000000000000000, 0.0 },
 523   { 3.9993023372677540e+22, 2.0000000000000000, 55.000000000000000, 0.0 },
 524   { 5.6992520026634433e+24, 2.0000000000000000, 60.000000000000000, 0.0 },
 525   { 8.1464814287900364e+26, 2.0000000000000000, 65.000000000000000, 0.0 },
 526   { 1.1675039556585663e+29, 2.0000000000000000, 70.000000000000000, 0.0 },
 527   { 1.6770093176278926e+31, 2.0000000000000000, 75.000000000000000, 0.0 },
 528   { 2.4136869148449879e+33, 2.0000000000000000, 80.000000000000000, 0.0 },
 529   { 3.4801257808448186e+35, 2.0000000000000000, 85.000000000000000, 0.0 },
 530   { 5.0256693051696307e+37, 2.0000000000000000, 90.000000000000000, 0.0 },
 531   { 7.2678700343145818e+39, 2.0000000000000000, 95.000000000000000, 0.0 },
 532   { 1.0523843193243042e+42, 2.0000000000000000, 100.00000000000000, 0.0 },
 533 };
 534 const double toler021 = 1.0000000000000008e-12;
 535
 536 // Test data for nu=5.0000000000000000.
 537 // max(|f - f_GSL|): 1.0831975343747077e+27 at index 20
 538 // max(|f - f_GSL| / |f_GSL|): 1.0289491375166011e-14
 539 // mean(f - f_GSL): -5.2041812077613416e+25
 540 // variance(f - f_GSL): inf
 541 // stddev(f - f_GSL): inf
 542 const testcase_cyl_bessel_i<double>
 543 data022[21] =
 544 {
 545   { 0.0000000000000000, 5.0000000000000000, 0.0000000000000000, 0.0 },
 546   { 2.1579745473225476, 5.0000000000000000, 5.0000000000000000, 0.0 },
 547   { 777.18828640326012, 5.0000000000000000, 10.000000000000000, 0.0 },
 548   { 144572.01120063409, 5.0000000000000000, 15.000000000000000, 0.0 },
 549   { 23018392.213413671, 5.0000000000000000, 20.000000000000000, 0.0 },
 550   { 3472466208.7419176, 5.0000000000000000, 25.000000000000000, 0.0 },
 551   { 512151465476.93494, 5.0000000000000000, 30.000000000000000, 0.0 },
 552   { 74756743552251.547, 5.0000000000000000, 35.000000000000000, 0.0 },
 553   { 10858318337624278., 5.0000000000000000, 40.000000000000000, 0.0 },
 554   { 1.5736087399245911e+18, 5.0000000000000000, 45.000000000000000, 0.0 },
 555   { 2.2785483079112825e+20, 5.0000000000000000, 50.000000000000000, 0.0 },
 556   { 3.2989391052963687e+22, 5.0000000000000000, 55.000000000000000, 0.0 },
 557   { 4.7777652072561732e+24, 5.0000000000000000, 60.000000000000000, 0.0 },
 558   { 6.9232165147172657e+26, 5.0000000000000000, 65.000000000000000, 0.0 },
 559   { 1.0038643002095155e+29, 5.0000000000000000, 70.000000000000000, 0.0 },
 560   { 1.4566328222327073e+31, 5.0000000000000000, 75.000000000000000, 0.0 },
 561   { 2.1151488565944835e+33, 5.0000000000000000, 80.000000000000000, 0.0 },
 562   { 3.0735883450768239e+35, 5.0000000000000000, 85.000000000000000, 0.0 },
 563   { 4.4694790189230327e+37, 5.0000000000000000, 90.000000000000000, 0.0 },
 564   { 6.5037505570430995e+39, 5.0000000000000000, 95.000000000000000, 0.0 },
 565   { 9.4700938730355882e+41, 5.0000000000000000, 100.00000000000000, 0.0 },
 566 };
 567 const double toler022 = 1.0000000000000008e-12;
 568
 569 // Test data for nu=10.000000000000000.
 570 // max(|f - f_GSL|): 1.5474250491067253e+26 at index 20
 571 // max(|f - f_GSL| / |f_GSL|): 1.2009151331790140e-14
 572 // mean(f - f_GSL): 7.4845081675400805e+24
 573 // variance(f - f_GSL): inf
 574 // stddev(f - f_GSL): inf
 575 const testcase_cyl_bessel_i<double>
 576 data023[21] =
 577 {
 578   { 0.0000000000000000, 10.000000000000000, 0.0000000000000000, 0.0 },
 579   { 0.0045800444191760525, 10.000000000000000, 5.0000000000000000, 0.0 },
 580   { 21.891706163723381, 10.000000000000000, 10.000000000000000, 0.0 },
 581   { 12267.475049806462, 10.000000000000000, 15.000000000000000, 0.0 },
 582   { 3540200.2090195213, 10.000000000000000, 20.000000000000000, 0.0 },
 583   { 771298871.17072666, 10.000000000000000, 25.000000000000000, 0.0 },
 584   { 145831809975.96710, 10.000000000000000, 30.000000000000000, 0.0 },
 585   { 25449470018534.777, 10.000000000000000, 35.000000000000000, 0.0 },
 586   { 4228469210516757.0, 10.000000000000000, 40.000000000000000, 0.0 },
 587   { 6.8049404557505165e+17, 10.000000000000000, 45.000000000000000, 0.0 },
 588   { 1.0715971594776370e+20, 10.000000000000000, 50.000000000000000, 0.0 },
 589   { 1.6618215752886714e+22, 10.000000000000000, 55.000000000000000, 0.0 },
 590   { 2.5486246072566784e+24, 10.000000000000000, 60.000000000000000, 0.0 },
 591   { 3.8764628702155475e+26, 10.000000000000000, 65.000000000000000, 0.0 },
 592   { 5.8592538145409686e+28, 10.000000000000000, 70.000000000000000, 0.0 },
 593   { 8.8135370711317444e+30, 10.000000000000000, 75.000000000000000, 0.0 },
 594   { 1.3207418268325279e+33, 10.000000000000000, 80.000000000000000, 0.0 },
 595   { 1.9732791360862190e+35, 10.000000000000000, 85.000000000000000, 0.0 },
 596   { 2.9411893748384672e+37, 10.000000000000000, 90.000000000000000, 0.0 },
 597   { 4.3754494922439984e+39, 10.000000000000000, 95.000000000000000, 0.0 },
 598   { 6.4989755247201446e+41, 10.000000000000000, 100.00000000000000, 0.0 },
 599 };
 600 const double toler023 = 1.0000000000000008e-12;
 601
 602 // Test data for nu=20.000000000000000.
 603 // max(|f - f_GSL|): 1.9342813113834067e+25 at index 20
 604 // max(|f - f_GSL| / |f_GSL|): 1.5819230756119302e-14
 605 // mean(f - f_GSL): 1.0213821732843951e+24
 606 // variance(f - f_GSL): inf
 607 // stddev(f - f_GSL): inf
 608 const testcase_cyl_bessel_i<double>
 609 data024[21] =
 610 {
 611   { 0.0000000000000000, 20.000000000000000, 0.0000000000000000, 0.0 },
 612   { 5.0242393579718066e-11, 20.000000000000000, 5.0000000000000000, 0.0 },
 613   { 0.00012507997356449481, 20.000000000000000, 10.000000000000000, 0.0 },
 614   { 1.6470152535015836, 20.000000000000000, 15.000000000000000, 0.0 },
 615   { 3188.7503288536154, 20.000000000000000, 20.000000000000000, 0.0 },
 616   { 2449840.5422952301, 20.000000000000000, 25.000000000000000, 0.0 },
 617   { 1126985104.4483771, 20.000000000000000, 30.000000000000000, 0.0 },
 618   { 379617876611.88580, 20.000000000000000, 35.000000000000000, 0.0 },
 619   { 104459633129479.88, 20.000000000000000, 40.000000000000000, 0.0 },
 620   { 25039579987216524., 20.000000000000000, 45.000000000000000, 0.0 },
 621   { 5.4420084027529984e+18, 20.000000000000000, 50.000000000000000, 0.0 },
 622   { 1.1007498584335495e+21, 20.000000000000000, 55.000000000000000, 0.0 },
 623   { 2.1091734863057236e+23, 20.000000000000000, 60.000000000000000, 0.0 },
 624   { 3.8763618091286891e+25, 20.000000000000000, 65.000000000000000, 0.0 },
 625   { 6.8946130527930870e+27, 20.000000000000000, 70.000000000000000, 0.0 },
 626   { 1.1946319948836447e+30, 20.000000000000000, 75.000000000000000, 0.0 },
 627   { 2.0265314377577587e+32, 20.000000000000000, 80.000000000000000, 0.0 },
 628   { 3.3784665214179985e+34, 20.000000000000000, 85.000000000000000, 0.0 },
 629   { 5.5516089411796646e+36, 20.000000000000000, 90.000000000000000, 0.0 },
 630   { 9.0129310795305151e+38, 20.000000000000000, 95.000000000000000, 0.0 },
 631   { 1.4483461256427176e+41, 20.000000000000000, 100.00000000000000, 0.0 },
 632 };
 633 const double toler024 = 1.0000000000000008e-12;
 634
 635 // Test data for nu=50.000000000000000.
 636 // max(|f - f_GSL|): 4.4862481587261630e+22 at index 20
 637 // max(|f - f_GSL| / |f_GSL|): 6.0191728870880627e-14
 638 // mean(f - f_GSL): 2.1246678955085789e+21
 639 // variance(f - f_GSL): inf
 640 // stddev(f - f_GSL): inf
 641 const testcase_cyl_bessel_i<double>
 642 data025[21] =
 643 {
 644   { 0.0000000000000000, 50.000000000000000, 0.0000000000000000, 0.0 },
 645   { 2.9314696468108517e-45, 50.000000000000000, 5.0000000000000000, 0.0 },
 646   { 4.7568945607268435e-30, 50.000000000000000, 10.000000000000000, 0.0 },
 647   { 5.5468372730667069e-21, 50.000000000000000, 15.000000000000000, 0.0 },
 648   { 2.2551205757604056e-14, 50.000000000000000, 20.000000000000000, 0.0 },
 649   { 4.5344251866130257e-09, 50.000000000000000, 25.000000000000000, 0.0 },
 650   { 0.00014590106916468940, 50.000000000000000, 30.000000000000000, 0.0 },
 651   { 1.3965549457254882, 50.000000000000000, 35.000000000000000, 0.0 },
 652   { 5726.8656631289887, 50.000000000000000, 40.000000000000000, 0.0 },
 653   { 12672593.113027781, 50.000000000000000, 45.000000000000000, 0.0 },
 654   { 17650802430.016712, 50.000000000000000, 50.000000000000000, 0.0 },
 655   { 17220231607789.926, 50.000000000000000, 55.000000000000000, 0.0 },
 656   { 12704607933652176., 50.000000000000000, 60.000000000000000, 0.0 },
 657   { 7.4989491942193715e+18, 50.000000000000000, 65.000000000000000, 0.0 },
 658   { 3.6944034898904922e+21, 50.000000000000000, 70.000000000000000, 0.0 },
 659   { 1.5691634774370186e+24, 50.000000000000000, 75.000000000000000, 0.0 },
 660   { 5.8927749458163587e+26, 50.000000000000000, 80.000000000000000, 0.0 },
 661   { 1.9958849054749339e+29, 50.000000000000000, 85.000000000000000, 0.0 },
 662   { 6.1946050361781500e+31, 50.000000000000000, 90.000000000000000, 0.0 },
 663   { 1.7845429728697119e+34, 50.000000000000000, 95.000000000000000, 0.0 },
 664   { 4.8219580855940819e+36, 50.000000000000000, 100.00000000000000, 0.0 },
 665 };
 666 const double toler025 = 5.0000000000000029e-12;
 667
 668 // Test data for nu=100.00000000000000.
 669 // max(|f - f_GSL|): 185597952.00000000 at index 20
 670 // max(|f - f_GSL| / |f_GSL|): 2.8278213985558577e-13
 671 // mean(f - f_GSL): 8855366.2060860656
 672 // variance(f - f_GSL): 4.2527168883984777e+19
 673 // stddev(f - f_GSL): 6521285830.5693655
 674 const testcase_cyl_bessel_i<double>
 675 data026[21] =
 676 {
 677   { 0.0000000000000000, 100.00000000000000, 0.0000000000000000, 0.0 },
 678   { 7.0935514885313123e-119, 100.00000000000000, 5.0000000000000000, 0.0 },
 679   { 1.0823442017492015e-88, 100.00000000000000, 10.000000000000000, 0.0 },
 680   { 5.9887888536468904e-71, 100.00000000000000, 15.000000000000000, 0.0 },
 681   { 2.8703193216428771e-58, 100.00000000000000, 20.000000000000000, 0.0 },
 682   { 2.4426896913122370e-48, 100.00000000000000, 25.000000000000000, 0.0 },
 683   { 3.9476420053334271e-40, 100.00000000000000, 30.000000000000000, 0.0 },
 684   { 4.2836596180818780e-33, 100.00000000000000, 35.000000000000000, 0.0 },
 685   { 6.6249380222596129e-27, 100.00000000000000, 40.000000000000000, 0.0 },
 686   { 2.3702587262788900e-21, 100.00000000000000, 45.000000000000000, 0.0 },
 687   { 2.7278879470966917e-16, 100.00000000000000, 50.000000000000000, 0.0 },
 688   { 1.2763258878228082e-11, 100.00000000000000, 55.000000000000000, 0.0 },
 689   { 2.8832770906491972e-07, 100.00000000000000, 60.000000000000000, 0.0 },
 690   { 0.0035805902717061223, 100.00000000000000, 65.000000000000000, 0.0 },
 691   { 27.017219102595387, 100.00000000000000, 70.000000000000000, 0.0 },
 692   { 134001.44891209516, 100.00000000000000, 75.000000000000000, 0.0 },
 693   { 465194832.85060996, 100.00000000000000, 80.000000000000000, 0.0 },
 694   { 1189280653119.4814, 100.00000000000000, 85.000000000000000, 0.0 },
 695   { 2334119331258728.0, 100.00000000000000, 90.000000000000000, 0.0 },
 696   { 3.6399223078502436e+18, 100.00000000000000, 95.000000000000000, 0.0 },
 697   { 4.6415349416162005e+21, 100.00000000000000, 100.00000000000000, 0.0 },
 698 };
 699 const double toler026 = 2.5000000000000014e-11;
 700
 701 template<typename Ret, unsigned int Num>
 702   void
 703   test(const testcase_cyl_bessel_i<Ret> (&data)[Num], Ret toler)
 704   {
 705     bool test __attribute__((unused)) = true;
 706     const Ret eps = std::numeric_limits<Ret>::epsilon();
 707     Ret max_abs_diff = -Ret(1);
 708     Ret max_abs_frac = -Ret(1);
 709     unsigned int num_datum = Num;
 710     for (unsigned int i = 0; i < num_datum; ++i)
 711       {
 712         const Ret f = std::tr1::cyl_bessel_i(data[i].nu, data[i].x);
 713         const Ret f0 = data[i].f0;
 714         const Ret diff = f - f0;
 715         if (std::abs(diff) > max_abs_diff)
 716           max_abs_diff = std::abs(diff);
 717         if (std::abs(f0) > Ret(10) * eps
 718          && std::abs(f) > Ret(10) * eps)
 719           {
 720             const Ret frac = diff / f0;
 721             if (std::abs(frac) > max_abs_frac)
 722               max_abs_frac = std::abs(frac);
 723           }
 724       }
 725     VERIFY(max_abs_frac < toler);
 726   }
 727
 728 int
 729 main()
 730 {
 731   test(data007, toler007);
 732   test(data008, toler008);
 733   test(data009, toler009);
 734   test(data010, toler010);
 735   test(data011, toler011);
 736   test(data012, toler012);
 737   test(data013, toler013);
 738   test(data014, toler014);
 739   test(data015, toler015);
 740   test(data016, toler016);
 741   test(data017, toler017);
 742   test(data018, toler018);
 743   test(data019, toler019);
 744   test(data020, toler020);
 745   test(data021, toler021);
 746   test(data022, toler022);
 747   test(data023, toler023);
 748   test(data024, toler024);
 749   test(data025, toler025);
 750   test(data026, toler026);
 751   return 0;
 752 }