libstdc++-v3/testsuite/special_functions/10_cyl_neumann/check_value.cc

   1 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   2 //
   3 // Copyright (C) 2016 Free Software Foundation, Inc.
   4 //
   5 // This file is part of the GNU ISO C++ Library.  This library is free
   6 // software; you can redistribute it and/or modify it under the
   7 // terms of the GNU General Public License as published by the
   8 // Free Software Foundation; either version 3, or (at your option)
   9 // any later version.
  10 //
  11 // This library is distributed in the hope that it will be useful,
  12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14 // GNU General Public License for more details.
  15 //
  16 // You should have received a copy of the GNU General Public License along
  17 // with this library; see the file COPYING3.  If not see
  18 // <http://www.gnu.org/licenses/>.
  19
  20 //  cyl_neumann
  21 //  Compare against values generated by the GNU Scientific Library.
  22 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  23 #include <limits>
  24 #include <cmath>
  25 #if defined(__TEST_DEBUG)
  26 #  include <iostream>
  27 #  define VERIFY(A) \
  28   if (!(A)) \
  29     { \
  30       std::cout << "line " << __LINE__ \
  31         << "  max_abs_frac = " << max_abs_frac \
  32         << std::endl; \
  33     }
  34 #else
  35 #  include <testsuite_hooks.h>
  36 #endif
  37 #include <specfun_testcase.h>
  38
  39
  40 // Test data for nu=0.0000000000000000.
  41 // max(|f - f_GSL|): 1.6653345369377348e-16
  42 // max(|f - f_GSL| / |f_GSL|): 2.6623873675138176e-15
  43 const testcase_cyl_neumann<double>
  44 data001[20] =
  45 {
  46   { -0.93157302493005878, 0.0000000000000000, 0.25000000000000000 },
  47   { -0.44451873350670656, 0.0000000000000000, 0.50000000000000000 },
  48   { -0.13717276938577236, 0.0000000000000000, 0.75000000000000000 },
  49   { 0.088256964215676942, 0.0000000000000000, 1.0000000000000000 },
  50   { 0.25821685159454072, 0.0000000000000000, 1.2500000000000000 },
  51   { 0.38244892379775886, 0.0000000000000000, 1.5000000000000000 },
  52   { 0.46549262864690610, 0.0000000000000000, 1.7500000000000000 },
  53   { 0.51037567264974493, 0.0000000000000000, 2.0000000000000000 },
  54   { 0.52006476245727862, 0.0000000000000000, 2.2500000000000000 },
  55   { 0.49807035961523194, 0.0000000000000000, 2.5000000000000000 },
  56   { 0.44865872156913222, 0.0000000000000000, 2.7500000000000000 },
  57   { 0.37685001001279045, 0.0000000000000000, 3.0000000000000000 },
  58   { 0.28828690267308710, 0.0000000000000000, 3.2500000000000000 },
  59   { 0.18902194392082688, 0.0000000000000000, 3.5000000000000000 },
  60   { 0.085256756977362638, 0.0000000000000000, 3.7500000000000000 },
  61   { -0.016940739325064763, 0.0000000000000000, 4.0000000000000000 },
  62   { -0.11191885116160770, 0.0000000000000000, 4.2500000000000000 },
  63   { -0.19470500862950454, 0.0000000000000000, 4.5000000000000000 },
  64   { -0.26123250323497549, 0.0000000000000000, 4.7500000000000000 },
  65   { -0.30851762524903359, 0.0000000000000000, 5.0000000000000000 },
  66 };
  67 const double toler001 = 2.5000000000000020e-13;
  68
  69 // Test data for nu=0.33333333333333331.
  70 // max(|f - f_GSL|): 5.8286708792820718e-16
  71 // max(|f - f_GSL| / |f_GSL|): 1.7769445360534625e-14
  72 const testcase_cyl_neumann<double>
  73 data002[20] =
  74 {
  75   { -1.3461842332051077, 0.33333333333333331, 0.25000000000000000 },
  76   { -0.84062782604337771, 0.33333333333333331, 0.50000000000000000 },
  77   { -0.52488281484097077, 0.33333333333333331, 0.75000000000000000 },
  78   { -0.27880164127599205, 0.33333333333333331, 1.0000000000000000 },
  79   { -0.074321349727836453, 0.33333333333333331, 1.2500000000000000 },
  80   { 0.096610087766627981, 0.33333333333333331, 1.5000000000000000 },
  81   { 0.23582564494922068, 0.33333333333333331, 1.7500000000000000 },
  82   { 0.34319996626034494, 0.33333333333333331, 2.0000000000000000 },
  83   { 0.41835668452349323, 0.33333333333333331, 2.2500000000000000 },
  84   { 0.46145947419129157, 0.33333333333333331, 2.5000000000000000 },
  85   { 0.47358926135786023, 0.33333333333333331, 2.7500000000000000 },
  86   { 0.45689303457230640, 0.33333333333333331, 3.0000000000000000 },
  87   { 0.41458485697347386, 0.33333333333333331, 3.2500000000000000 },
  88   { 0.35084133277859947, 0.33333333333333331, 3.5000000000000000 },
  89   { 0.27061914527820891, 0.33333333333333331, 3.7500000000000000 },
  90   { 0.17941676634394862, 0.33333333333333331, 4.0000000000000000 },
  91   { 0.083000434191526043, 0.33333333333333331, 4.2500000000000000 },
  92   { -0.012886361627105348, 0.33333333333333331, 4.5000000000000000 },
  93   { -0.10281143123935124, 0.33333333333333331, 4.7500000000000000 },
  94   { -0.18192321129343850, 0.33333333333333331, 5.0000000000000000 },
  95 };
  96 const double toler002 = 1.0000000000000008e-12;
  97
  98 // Test data for nu=0.50000000000000000.
  99 // max(|f - f_GSL|): 4.4408920985006262e-16
 100 // max(|f - f_GSL| / |f_GSL|): 5.7217850214577088e-15
 101 const testcase_cyl_neumann<double>
 102 data003[20] =
 103 {
 104   { -1.5461605241060765, 0.50000000000000000, 0.25000000000000000 },
 105   { -0.99024588024340454, 0.50000000000000000, 0.50000000000000000 },
 106   { -0.67411792914454460, 0.50000000000000000, 0.75000000000000000 },
 107   { -0.43109886801837594, 0.50000000000000000, 1.0000000000000000 },
 108   { -0.22502969244466481, 0.50000000000000000, 1.2500000000000000 },
 109   { -0.046083165893097265, 0.50000000000000000, 1.5000000000000000 },
 110   { 0.10750804524368722, 0.50000000000000000, 1.7500000000000000 },
 111   { 0.23478571040624849, 0.50000000000000000, 2.0000000000000000 },
 112   { 0.33414002338271825, 0.50000000000000000, 2.2500000000000000 },
 113   { 0.40427830223905686, 0.50000000000000000, 2.5000000000000000 },
 114   { 0.44472115119490507, 0.50000000000000000, 2.7500000000000000 },
 115   { 0.45604882079463316, 0.50000000000000000, 3.0000000000000000 },
 116   { 0.43998859501924370, 0.50000000000000000, 3.2500000000000000 },
 117   { 0.39938682536304909, 0.50000000000000000, 3.5000000000000000 },
 118   { 0.33809163836693340, 0.50000000000000000, 3.7500000000000000 },
 119   { 0.26076607667717877, 0.50000000000000000, 4.0000000000000000 },
 120   { 0.17264962544644955, 0.50000000000000000, 4.2500000000000000 },
 121   { 0.079285862862978548, 0.50000000000000000, 4.5000000000000000 },
 122   { -0.013765943019498003, 0.50000000000000000, 4.7500000000000000 },
 123   { -0.10121770918510846, 0.50000000000000000, 5.0000000000000000 },
 124 };
 125 const double toler003 = 5.0000000000000039e-13;
 126
 127 // Test data for nu=0.66666666666666663.
 128 // max(|f - f_GSL|): 1.4988010832439613e-15
 129 // max(|f - f_GSL| / |f_GSL|): 6.3663053018318525e-15
 130 const testcase_cyl_neumann<double>
 131 data004[20] =
 132 {
 133   { -1.8021638417426857, 0.66666666666666663, 0.25000000000000000 },
 134   { -1.1316060101031435, 0.66666666666666663, 0.50000000000000000 },
 135   { -0.80251156358450737, 0.66666666666666663, 0.75000000000000000 },
 136   { -0.56270321497463327, 0.66666666666666663, 1.0000000000000000 },
 137   { -0.36007453643432208, 0.66666666666666663, 1.2500000000000000 },
 138   { -0.18017937469615020, 0.66666666666666663, 1.5000000000000000 },
 139   { -0.019885608758103752, 0.66666666666666663, 1.7500000000000000 },
 140   { 0.11989345361903521, 0.66666666666666663, 2.0000000000000000 },
 141   { 0.23690889836358039, 0.66666666666666663, 2.2500000000000000 },
 142   { 0.32882045742954535, 0.66666666666666663, 2.5000000000000000 },
 143   { 0.39385133784531856, 0.66666666666666663, 2.7500000000000000 },
 144   { 0.43115101690935642, 0.66666666666666663, 3.0000000000000000 },
 145   { 0.44098127351445843, 0.66666666666666663, 3.2500000000000000 },
 146   { 0.42477631413456485, 0.66666666666666663, 3.5000000000000000 },
 147   { 0.38510384155620386, 0.66666666666666663, 3.7500000000000000 },
 148   { 0.32554526794354366, 0.66666666666666663, 4.0000000000000000 },
 149   { 0.25051080073878446, 0.66666666666666663, 4.2500000000000000 },
 150   { 0.16500507211842136, 0.66666666666666663, 4.5000000000000000 },
 151   { 0.074359649728861360, 0.66666666666666663, 4.7500000000000000 },
 152   { -0.016050662643389627, 0.66666666666666663, 5.0000000000000000 },
 153 };
 154 const double toler004 = 5.0000000000000039e-13;
 155
 156 // Test data for nu=1.0000000000000000.
 157 // max(|f - f_GSL|): 9.1593399531575415e-16
 158 // max(|f - f_GSL| / |f_GSL|): 3.3683879467319323e-14
 159 const testcase_cyl_neumann<double>
 160 data005[13] =
 161 {
 162   { -0.10703243154093699, 1.0000000000000000, 2.0000000000000000 },
 163   { 0.027192057738017056, 1.0000000000000000, 2.2500000000000000 },
 164   { 0.14591813796678599, 1.0000000000000000, 2.5000000000000000 },
 165   { 0.24601900149738354, 1.0000000000000000, 2.7500000000000000 },
 166   { 0.32467442479180003, 1.0000000000000000, 3.0000000000000000 },
 167   { 0.37977777371708382, 1.0000000000000000, 3.2500000000000000 },
 168   { 0.41018841788751170, 1.0000000000000000, 3.5000000000000000 },
 169   { 0.41586877934522715, 1.0000000000000000, 3.7500000000000000 },
 170   { 0.39792571055709991, 1.0000000000000000, 4.0000000000000000 },
 171   { 0.35856889308385076, 1.0000000000000000, 4.2500000000000000 },
 172   { 0.30099732306965449, 1.0000000000000000, 4.5000000000000000 },
 173   { 0.22922559673872217, 1.0000000000000000, 4.7500000000000000 },
 174   { 0.14786314339122700, 1.0000000000000000, 5.0000000000000000 },
 175 };
 176 const double toler005 = 2.5000000000000015e-12;
 177
 178 // Test data for nu=2.0000000000000000.
 179 // max(|f - f_GSL|): 6.1062266354383610e-16
 180 // max(|f - f_GSL| / |f_GSL|): 1.2540693630135021e-14
 181 const testcase_cyl_neumann<double>
 182 data006[20] =
 183 {
 184   { -20.701268809592200, 2.0000000000000000, 0.25000000000000000 },
 185   { -5.4413708371742668, 2.0000000000000000, 0.50000000000000000 },
 186   { -2.6297460326656559, 2.0000000000000000, 0.75000000000000000 },
 187   { -1.6506826068162548, 2.0000000000000000, 1.0000000000000000 },
 188   { -1.1931993101785539, 2.0000000000000000, 1.2500000000000000 },
 189   { -0.93219375976297369, 2.0000000000000000, 1.5000000000000000 },
 190   { -0.75574746972832973, 2.0000000000000000, 1.7500000000000000 },
 191   { -0.61740810419068193, 2.0000000000000000, 2.0000000000000000 },
 192   { -0.49589404446793012, 2.0000000000000000, 2.2500000000000000 },
 193   { -0.38133584924180314, 2.0000000000000000, 2.5000000000000000 },
 194   { -0.26973581138921693, 2.0000000000000000, 2.7500000000000000 },
 195   { -0.16040039348492377, 2.0000000000000000, 3.0000000000000000 },
 196   { -0.054577503462573951, 2.0000000000000000, 3.2500000000000000 },
 197   { 0.045371437729179787, 2.0000000000000000, 3.5000000000000000 },
 198   { 0.13653992534009185, 2.0000000000000000, 3.7500000000000000 },
 199   { 0.21590359460361472, 2.0000000000000000, 4.0000000000000000 },
 200   { 0.28065715378930217, 2.0000000000000000, 4.2500000000000000 },
 201   { 0.32848159666046206, 2.0000000000000000, 4.5000000000000000 },
 202   { 0.35774854396706901, 2.0000000000000000, 4.7500000000000000 },
 203   { 0.36766288260552438, 2.0000000000000000, 5.0000000000000000 },
 204 };
 205 const double toler006 = 1.0000000000000008e-12;
 206
 207 // Test data for nu=5.0000000000000000.
 208 // max(|f - f_GSL|): 8.8817841970012523e-15
 209 // max(|f - f_GSL| / |f_GSL|): 1.6846903979704834e-15
 210 const testcase_cyl_neumann<double>
 211 data007[13] =
 212 {
 213   { -9.9359891284819675, 5.0000000000000000, 2.0000000000000000 },
 214   { -5.9446343848076424, 5.0000000000000000, 2.2500000000000000 },
 215   { -3.8301760007407522, 5.0000000000000000, 2.5000000000000000 },
 216   { -2.6287042009459087, 5.0000000000000000, 2.7500000000000000 },
 217   { -1.9059459538286738, 5.0000000000000000, 3.0000000000000000 },
 218   { -1.4498157389142654, 5.0000000000000000, 3.2500000000000000 },
 219   { -1.1494603169763686, 5.0000000000000000, 3.5000000000000000 },
 220   { -0.94343105151431672, 5.0000000000000000, 3.7500000000000000 },
 221   { -0.79585142111419982, 5.0000000000000000, 4.0000000000000000 },
 222   { -0.68479288173907016, 5.0000000000000000, 4.2500000000000000 },
 223   { -0.59631936513587558, 5.0000000000000000, 4.5000000000000000 },
 224   { -0.52130838331747587, 5.0000000000000000, 4.7500000000000000 },
 225   { -0.45369482249110193, 5.0000000000000000, 5.0000000000000000 },
 226 };
 227 const double toler007 = 2.5000000000000020e-13;
 228
 229 // Test data for nu=10.000000000000000.
 230 // max(|f - f_GSL|): 2.3841857910156250e-07
 231 // max(|f - f_GSL| / |f_GSL|): 1.4991559422183497e-15
 232 const testcase_cyl_neumann<double>
 233 data008[20] =
 234 {
 235   { -124241617095379.48, 10.000000000000000, 0.25000000000000000 },
 236   { -121963623349.56966, 10.000000000000000, 0.50000000000000000 },
 237   { -2133501638.9057348, 10.000000000000000, 0.75000000000000000 },
 238   { -121618014.27868921, 10.000000000000000, 1.0000000000000000 },
 239   { -13265210.158452792, 10.000000000000000, 1.2500000000000000 },
 240   { -2183993.0260864049, 10.000000000000000, 1.5000000000000000 },
 241   { -478274.82386541169, 10.000000000000000, 1.7500000000000000 },
 242   { -129184.54220803917, 10.000000000000000, 2.0000000000000000 },
 243   { -40993.254794381690, 10.000000000000000, 2.2500000000000000 },
 244   { -14782.847716021070, 10.000000000000000, 2.5000000000000000 },
 245   { -5916.5330998776262, 10.000000000000000, 2.7500000000000000 },
 246   { -2582.6071294842995, 10.000000000000000, 3.0000000000000000 },
 247   { -1213.3423564023892, 10.000000000000000, 3.2500000000000000 },
 248   { -607.27437834125760, 10.000000000000000, 3.5000000000000000 },
 249   { -321.17461059752202, 10.000000000000000, 3.7500000000000000 },
 250   { -178.33055590796428, 10.000000000000000, 4.0000000000000000 },
 251   { -103.40496587570090, 10.000000000000000, 4.2500000000000000 },
 252   { -62.345024619781434, 10.000000000000000, 4.5000000000000000 },
 253   { -38.944510430296937, 10.000000000000000, 4.7500000000000000 },
 254   { -25.129110095610095, 10.000000000000000, 5.0000000000000000 },
 255 };
 256 const double toler008 = 2.5000000000000020e-13;
 257
 258 // Test data for nu=20.000000000000000.
 259 // max(|f - f_GSL|): 6442450944.0000000
 260 // max(|f - f_GSL| / |f_GSL|): 1.6458221996165416e-15
 261 const testcase_cyl_neumann<double>
 262 data009[20] =
 263 {
 264   { -4.4678815064152581e+34, 20.000000000000000, 0.25000000000000000 },
 265   { -4.2714301215659088e+28, 20.000000000000000, 0.50000000000000000 },
 266   { -1.2898357375834223e+25, 20.000000000000000, 0.75000000000000000 },
 267   { -4.1139703148355065e+22, 20.000000000000000, 1.0000000000000000 },
 268   { -4.7783533372148580e+20, 20.000000000000000, 1.2500000000000000 },
 269   { -1.2577301772964241e+19, 20.000000000000000, 1.5000000000000000 },
 270   { -5.8251041176649626e+17, 20.000000000000000, 1.7500000000000000 },
 271   { -40816513889983640., 20.000000000000000, 2.0000000000000000 },
 272   { -3925339868516418.5, 20.000000000000000, 2.2500000000000000 },
 273   { -484776559582090.25, 20.000000000000000, 2.5000000000000000 },
 274   { -73320655044814.469, 20.000000000000000, 2.7500000000000000 },
 275   { -13113540041757.449, 20.000000000000000, 3.0000000000000000 },
 276   { -2700669268882.7139, 20.000000000000000, 3.2500000000000000 },
 277   { -627339518240.21240, 20.000000000000000, 3.5000000000000000 },
 278   { -161695236802.71753, 20.000000000000000, 3.7500000000000000 },
 279   { -45637199262.220100, 20.000000000000000, 4.0000000000000000 },
 280   { -13953299213.925377, 20.000000000000000, 4.2500000000000000 },
 281   { -4580215756.5691023, 20.000000000000000, 4.5000000000000000 },
 282   { -1602110715.5159132, 20.000000000000000, 4.7500000000000000 },
 283   { -593396529.69143200, 20.000000000000000, 5.0000000000000000 },
 284 };
 285 const double toler009 = 2.5000000000000020e-13;
 286
 287 // Test data for nu=50.000000000000000.
 288 // max(|f - f_GSL|): 6.4703872001161536e+68
 289 // max(|f - f_GSL| / |f_GSL|): 3.7730746786493403e-15
 290 const testcase_cyl_neumann<double>
 291 data010[20] =
 292 {
 293   { -2.7643487471155969e+107, 50.000000000000000, 0.25000000000000000 },
 294   { -2.4575848224461092e+92, 50.000000000000000, 0.50000000000000000 },
 295   { -3.8604508467683829e+83, 50.000000000000000, 0.75000000000000000 },
 296   { -2.1911428126053411e+77, 50.000000000000000, 1.0000000000000000 },
 297   { -3.1362926828833165e+72, 50.000000000000000, 1.2500000000000000 },
 298   { -3.4584216846550566e+68, 50.000000000000000, 1.5000000000000000 },
 299   { -1.5607714080312795e+65, 50.000000000000000, 1.7500000000000000 },
 300   { -1.9761505765184128e+62, 50.000000000000000, 2.0000000000000000 },
 301   { -5.5023640499231188e+59, 50.000000000000000, 2.2500000000000000 },
 302   { -2.8530384545826849e+57, 50.000000000000000, 2.5000000000000000 },
 303   { -2.4467169322684809e+55, 50.000000000000000, 2.7500000000000000 },
 304   { -3.1793891461005181e+53, 50.000000000000000, 3.0000000000000000 },
 305   { -5.8573901231568658e+51, 50.000000000000000, 3.2500000000000000 },
 306   { -1.4528262197760965e+50, 50.000000000000000, 3.5000000000000000 },
 307   { -4.6566569870478635e+48, 50.000000000000000, 3.7500000000000000 },
 308   { -1.8661134361400254e+47, 50.000000000000000, 4.0000000000000000 },
 309   { -9.1005883612255402e+45, 50.000000000000000, 4.2500000000000000 },
 310   { -5.2813777542386141e+44, 50.000000000000000, 4.5000000000000000 },
 311   { -3.5795477722116469e+43, 50.000000000000000, 4.7500000000000000 },
 312   { -2.7888370175838930e+42, 50.000000000000000, 5.0000000000000000 },
 313 };
 314 const double toler010 = 2.5000000000000020e-13;
 315
 316 // Test data for nu=100.00000000000000.
 317 // max(|f - f_GSL|): 1.6136484921850493e+233
 318 // max(|f - f_GSL| / |f_GSL|): 3.7090973947899002e-13
 319 const testcase_cyl_neumann<double>
 320 data011[20] =
 321 {
 322   { -6.0523080585856754e+245, 100.00000000000000, 0.25000000000000000 },
 323   { -4.7766903780412668e+215, 100.00000000000000, 0.50000000000000000 },
 324   { -1.1758283017660654e+198, 100.00000000000000, 0.75000000000000000 },
 325   { -3.7752878101091316e+185, 100.00000000000000, 1.0000000000000000 },
 326   { -7.7013290730008304e+175, 100.00000000000000, 1.2500000000000000 },
 327   { -9.3152624794288802e+167, 100.00000000000000, 1.5000000000000000 },
 328   { -1.8854163374247264e+161, 100.00000000000000, 1.7500000000000000 },
 329   { -3.0008260488569689e+155, 100.00000000000000, 2.0000000000000000 },
 330   { -2.3075650873777408e+150, 100.00000000000000, 2.2500000000000000 },
 331   { -6.1476258561369381e+145, 100.00000000000000, 2.5000000000000000 },
 332   { -4.4758816234829593e+141, 100.00000000000000, 2.7500000000000000 },
 333   { -7.4747961023547846e+137, 100.00000000000000, 3.0000000000000000 },
 334   { -2.5067022766900123e+134, 100.00000000000000, 3.2500000000000000 },
 335   { -1.5222488313431896e+131, 100.00000000000000, 3.5000000000000000 },
 336   { -1.5422392812241397e+128, 100.00000000000000, 3.7500000000000000 },
 337   { -2.4400857387551062e+125, 100.00000000000000, 4.0000000000000000 },
 338   { -5.7118153392422278e+122, 100.00000000000000, 4.2500000000000000 },
 339   { -1.8915420905194465e+120, 100.00000000000000, 4.5000000000000000 },
 340   { -8.5357945104770158e+117, 100.00000000000000, 4.7500000000000000 },
 341   { -5.0848639160196196e+115, 100.00000000000000, 5.0000000000000000 },
 342 };
 343 const double toler011 = 2.5000000000000014e-11;
 344 //  cyl_neumann
 345
 346 // Test data for nu=0.0000000000000000.
 347 // max(|f - f_GSL|): 7.1245093158367467e-15
 348 // max(|f - f_GSL| / |f_GSL|): 1.5215931554460198e-12
 349 const testcase_cyl_neumann<double>
 350 data012[20] =
 351 {
 352   { -0.30851762524903359, 0.0000000000000000, 5.0000000000000000 },
 353   { 0.055671167283599457, 0.0000000000000000, 10.000000000000000 },
 354   { 0.20546429603891822, 0.0000000000000000, 15.000000000000000 },
 355   { 0.062640596809384053, 0.0000000000000000, 20.000000000000000 },
 356   { -0.12724943226800617, 0.0000000000000000, 25.000000000000000 },
 357   { -0.11729573168666413, 0.0000000000000000, 30.000000000000000 },
 358   { 0.045797987195155689, 0.0000000000000000, 35.000000000000000 },
 359   { 0.12593641705826092, 0.0000000000000000, 40.000000000000000 },
 360   { 0.027060469763313333, 0.0000000000000000, 45.000000000000000 },
 361   { -0.098064995470077118, 0.0000000000000000, 50.000000000000000 },
 362   { -0.077569178730412594, 0.0000000000000000, 55.000000000000000 },
 363   { 0.047358952209449426, 0.0000000000000000, 60.000000000000000 },
 364   { 0.097183557740181920, 0.0000000000000000, 65.000000000000000 },
 365   { 0.0093096664589409992, 0.0000000000000000, 70.000000000000000 },
 366   { -0.085369047647775656, 0.0000000000000000, 75.000000000000000 },
 367   { -0.055620339089770016, 0.0000000000000000, 80.000000000000000 },
 368   { 0.049567884951494251, 0.0000000000000000, 85.000000000000000 },
 369   { 0.079776475854877751, 0.0000000000000000, 90.000000000000000 },
 370   { -0.0028230995861232107, 0.0000000000000000, 95.000000000000000 },
 371   { -0.077244313365083153, 0.0000000000000000, 100.00000000000000 },
 372 };
 373 const double toler012 = 1.0000000000000006e-10;
 374
 375 // Test data for nu=0.33333333333333331.
 376 // max(|f - f_GSL|): 6.4392935428259079e-15
 377 // max(|f - f_GSL| / |f_GSL|): 4.0229312517518102e-13
 378 const testcase_cyl_neumann<double>
 379 data013[20] =
 380 {
 381   { -0.18192321129343850, 0.33333333333333331, 5.0000000000000000 },
 382   { 0.17020111788268760, 0.33333333333333331, 10.000000000000000 },
 383   { 0.18540507541540796, 0.33333333333333331, 15.000000000000000 },
 384   { -0.028777707635715043, 0.33333333333333331, 20.000000000000000 },
 385   { -0.15829741864944163, 0.33333333333333331, 25.000000000000000 },
 386   { -0.058645772316705209, 0.33333333333333331, 30.000000000000000 },
 387   { 0.10294930308870617, 0.33333333333333331, 35.000000000000000 },
 388   { 0.10547870367098922, 0.33333333333333331, 40.000000000000000 },
 389   { -0.034334228816010816, 0.33333333333333331, 45.000000000000000 },
 390   { -0.11283489933031279, 0.33333333333333331, 50.000000000000000 },
 391   { -0.030007358986895105, 0.33333333333333331, 55.000000000000000 },
 392   { 0.086699173295718121, 0.33333333333333331, 60.000000000000000 },
 393   { 0.074875579668878658, 0.33333333333333331, 65.000000000000000 },
 394   { -0.039323246374552680, 0.33333333333333331, 70.000000000000000 },
 395   { -0.091263539574475236, 0.33333333333333331, 75.000000000000000 },
 396   { -0.013358849535984318, 0.33333333333333331, 80.000000000000000 },
 397   { 0.078373575537830198, 0.33333333333333331, 85.000000000000000 },
 398   { 0.055812482883955940, 0.33333333333333331, 90.000000000000000 },
 399   { -0.043310380106990683, 0.33333333333333331, 95.000000000000000 },
 400   { -0.076900504962136559, 0.33333333333333331, 100.00000000000000 },
 401 };
 402 const double toler013 = 2.5000000000000014e-11;
 403
 404 // Test data for nu=0.50000000000000000.
 405 // max(|f - f_GSL|): 6.5988881026157742e-15
 406 // max(|f - f_GSL| / |f_GSL|): 6.0282403975230169e-13
 407 const testcase_cyl_neumann<double>
 408 data014[20] =
 409 {
 410   { -0.10121770918510846, 0.50000000000000000, 5.0000000000000000 },
 411   { 0.21170886633139810, 0.50000000000000000, 10.000000000000000 },
 412   { 0.15650551590730855, 0.50000000000000000, 15.000000000000000 },
 413   { -0.072806904785061938, 0.50000000000000000, 20.000000000000000 },
 414   { -0.15817308404205055, 0.50000000000000000, 25.000000000000000 },
 415   { -0.022470290598831138, 0.50000000000000000, 30.000000000000000 },
 416   { 0.12187835265849535, 0.50000000000000000, 35.000000000000000 },
 417   { 0.084138655676395377, 0.50000000000000000, 40.000000000000000 },
 418   { -0.062482641933003201, 0.50000000000000000, 45.000000000000000 },
 419   { -0.10888475635053954, 0.50000000000000000, 50.000000000000000 },
 420   { -0.0023805454010949376, 0.50000000000000000, 55.000000000000000 },
 421   { 0.098104683735037918, 0.50000000000000000, 60.000000000000000 },
 422   { 0.055663470218594434, 0.50000000000000000, 65.000000000000000 },
 423   { -0.060396767883824871, 0.50000000000000000, 70.000000000000000 },
 424   { -0.084922578922046868, 0.50000000000000000, 75.000000000000000 },
 425   { 0.0098472271924441284, 0.50000000000000000, 80.000000000000000 },
 426   { 0.085190643574343625, 0.50000000000000000, 85.000000000000000 },
 427   { 0.037684970437156268, 0.50000000000000000, 90.000000000000000 },
 428   { -0.059772904856097500, 0.50000000000000000, 95.000000000000000 },
 429   { -0.068803091468728109, 0.50000000000000000, 100.00000000000000 },
 430 };
 431 const double toler014 = 5.0000000000000028e-11;
 432
 433 // Test data for nu=0.66666666666666663.
 434 // max(|f - f_GSL|): 7.2442052356791464e-15
 435 // max(|f - f_GSL| / |f_GSL|): 4.1296144775547441e-13
 436 const testcase_cyl_neumann<double>
 437 data015[20] =
 438 {
 439   { -0.016050662643389627, 0.66666666666666663, 5.0000000000000000 },
 440   { 0.23937232657540733, 0.66666666666666663, 10.000000000000000 },
 441   { 0.11762106604241235, 0.66666666666666663, 15.000000000000000 },
 442   { -0.11182254014899558, 0.66666666666666663, 20.000000000000000 },
 443   { -0.14756582982938804, 0.66666666666666663, 25.000000000000000 },
 444   { 0.015078692908077713, 0.66666666666666663, 30.000000000000000 },
 445   { 0.13260911815705795, 0.66666666666666663, 35.000000000000000 },
 446   { 0.057217565989652698, 0.66666666666666663, 40.000000000000000 },
 447   { -0.086373755152382006, 0.66666666666666663, 45.000000000000000 },
 448   { -0.097624139208051616, 0.66666666666666663, 50.000000000000000 },
 449   { 0.025354902147023392, 0.66666666666666663, 55.000000000000000 },
 450   { 0.10288136476351206, 0.66666666666666663, 60.000000000000000 },
 451   { 0.032728379560128203, 0.66666666666666663, 65.000000000000000 },
 452   { -0.077363672735747818, 0.66666666666666663, 70.000000000000000 },
 453   { -0.072855870458293961, 0.66666666666666663, 75.000000000000000 },
 454   { 0.032358106046953543, 0.66666666666666663, 80.000000000000000 },
 455   { 0.086240651537394228, 0.66666666666666663, 85.000000000000000 },
 456   { 0.017029601697285190, 0.66666666666666663, 90.000000000000000 },
 457   { -0.072173520560584681, 0.66666666666666663, 95.000000000000000 },
 458   { -0.056057339204073887, 0.66666666666666663, 100.00000000000000 },
 459 };
 460 const double toler015 = 2.5000000000000014e-11;
 461
 462 // Test data for nu=1.0000000000000000.
 463 // max(|f - f_GSL|): 7.6640083168655337e-15
 464 // max(|f - f_GSL| / |f_GSL|): 4.2719333494531163e-13
 465 const testcase_cyl_neumann<double>
 466 data016[20] =
 467 {
 468   { 0.14786314339122700, 1.0000000000000000, 5.0000000000000000 },
 469   { 0.24901542420695386, 1.0000000000000000, 10.000000000000000 },
 470   { 0.021073628036873522, 1.0000000000000000, 15.000000000000000 },
 471   { -0.16551161436252115, 1.0000000000000000, 20.000000000000000 },
 472   { -0.098829964783237412, 1.0000000000000000, 25.000000000000000 },
 473   { 0.084425570661747135, 1.0000000000000000, 30.000000000000000 },
 474   { 0.12751273354559009, 1.0000000000000000, 35.000000000000000 },
 475   { -0.0057935058215497536, 1.0000000000000000, 40.000000000000000 },
 476   { -0.11552517964639945, 1.0000000000000000, 45.000000000000000 },
 477   { -0.056795668562014692, 1.0000000000000000, 50.000000000000000 },
 478   { 0.073846265432577926, 1.0000000000000000, 55.000000000000000 },
 479   { 0.091869609369866892, 1.0000000000000000, 60.000000000000000 },
 480   { -0.017940374275377362, 1.0000000000000000, 65.000000000000000 },
 481   { -0.094844652625716230, 1.0000000000000000, 70.000000000000000 },
 482   { -0.035213785160580421, 1.0000000000000000, 75.000000000000000 },
 483   { 0.069395913784588037, 1.0000000000000000, 80.000000000000000 },
 484   { 0.071233187582749768, 1.0000000000000000, 85.000000000000000 },
 485   { -0.026187238607768244, 1.0000000000000000, 90.000000000000000 },
 486   { -0.081827958724501215, 1.0000000000000000, 95.000000000000000 },
 487   { -0.020372312002759834, 1.0000000000000000, 100.00000000000000 },
 488 };
 489 const double toler016 = 2.5000000000000014e-11;
 490
 491 // Test data for nu=2.0000000000000000.
 492 // max(|f - f_GSL|): 7.1193051454088163e-15
 493 // max(|f - f_GSL| / |f_GSL|): 3.9371586401654762e-12
 494 const testcase_cyl_neumann<double>
 495 data017[20] =
 496 {
 497   { 0.36766288260552438, 2.0000000000000000, 5.0000000000000000 },
 498   { -0.0058680824422086830, 2.0000000000000000, 10.000000000000000 },
 499   { -0.20265447896733507, 2.0000000000000000, 15.000000000000000 },
 500   { -0.079191758245636165, 2.0000000000000000, 20.000000000000000 },
 501   { 0.11934303508534717, 2.0000000000000000, 25.000000000000000 },
 502   { 0.12292410306411394, 2.0000000000000000, 30.000000000000000 },
 503   { -0.038511545278264829, 2.0000000000000000, 35.000000000000000 },
 504   { -0.12622609234933840, 2.0000000000000000, 40.000000000000000 },
 505   { -0.032194922192042195, 2.0000000000000000, 45.000000000000000 },
 506   { 0.095793168727596537, 2.0000000000000000, 50.000000000000000 },
 507   { 0.080254497473415426, 2.0000000000000000, 55.000000000000000 },
 508   { -0.044296631897120527, 2.0000000000000000, 60.000000000000000 },
 509   { -0.097735569256347382, 2.0000000000000000, 65.000000000000000 },
 510   { -0.012019513676818605, 2.0000000000000000, 70.000000000000000 },
 511   { 0.084430013376826846, 2.0000000000000000, 75.000000000000000 },
 512   { 0.057355236934384719, 2.0000000000000000, 80.000000000000000 },
 513   { -0.047891809949547198, 2.0000000000000000, 85.000000000000000 },
 514   { -0.080358414490605934, 2.0000000000000000, 90.000000000000000 },
 515   { 0.0011004057182389746, 2.0000000000000000, 95.000000000000000 },
 516   { 0.076836867125027963, 2.0000000000000000, 100.00000000000000 },
 517 };
 518 const double toler017 = 2.5000000000000017e-10;
 519
 520 // Test data for nu=5.0000000000000000.
 521 // max(|f - f_GSL|): 7.8097792989562098e-15
 522 // max(|f - f_GSL| / |f_GSL|): 3.2731037832632215e-11
 523 const testcase_cyl_neumann<double>
 524 data018[20] =
 525 {
 526   { -0.45369482249110193, 5.0000000000000000, 5.0000000000000000 },
 527   { 0.13540304768936234, 5.0000000000000000, 10.000000000000000 },
 528   { 0.16717271575940015, 5.0000000000000000, 15.000000000000000 },
 529   { -0.10003576788953220, 5.0000000000000000, 20.000000000000000 },
 530   { -0.14705799311372267, 5.0000000000000000, 25.000000000000000 },
 531   { 0.031627359289264301, 5.0000000000000000, 30.000000000000000 },
 532   { 0.13554781474770028, 5.0000000000000000, 35.000000000000000 },
 533   { 0.031869448780850247, 5.0000000000000000, 40.000000000000000 },
 534   { -0.10426932700176872, 5.0000000000000000, 45.000000000000000 },
 535   { -0.078548413913081594, 5.0000000000000000, 50.000000000000000 },
 536   { 0.055257033062858375, 5.0000000000000000, 55.000000000000000 },
 537   { 0.099464632840450887, 5.0000000000000000, 60.000000000000000 },
 538   { 0.00023860469499595305, 5.0000000000000000, 65.000000000000000 },
 539   { -0.091861802216406052, 5.0000000000000000, 70.000000000000000 },
 540   { -0.048383671296970042, 5.0000000000000000, 75.000000000000000 },
 541   { 0.060293667104896316, 5.0000000000000000, 80.000000000000000 },
 542   { 0.077506166682733996, 5.0000000000000000, 85.000000000000000 },
 543   { -0.015338764062239767, 5.0000000000000000, 90.000000000000000 },
 544   { -0.081531504045514361, 5.0000000000000000, 95.000000000000000 },
 545   { -0.029480196281661937, 5.0000000000000000, 100.00000000000000 },
 546 };
 547 const double toler018 = 2.5000000000000013e-09;
 548
 549 // Test data for nu=10.000000000000000.
 550 // max(|f - f_GSL|): 1.7763568394002505e-14
 551 // max(|f - f_GSL| / |f_GSL|): 2.7466153115234563e-12
 552 const testcase_cyl_neumann<double>
 553 data019[20] =
 554 {
 555   { -25.129110095610095, 10.000000000000000, 5.0000000000000000 },
 556   { -0.35981415218340279, 10.000000000000000, 10.000000000000000 },
 557   { 0.21997141360195577, 10.000000000000000, 15.000000000000000 },
 558   { -0.043894653515658105, 10.000000000000000, 20.000000000000000 },
 559   { -0.14871839049980651, 10.000000000000000, 25.000000000000000 },
 560   { 0.075056702122397012, 10.000000000000000, 30.000000000000000 },
 561   { 0.12222473135000546, 10.000000000000000, 35.000000000000000 },
 562   { -0.046723877232677985, 10.000000000000000, 40.000000000000000 },
 563   { -0.11739339009322181, 10.000000000000000, 45.000000000000000 },
 564   { 0.0057238971820535930, 10.000000000000000, 50.000000000000000 },
 565   { 0.10733910125831631, 10.000000000000000, 55.000000000000000 },
 566   { 0.036290350559545478, 10.000000000000000, 60.000000000000000 },
 567   { -0.083239127691715667, 10.000000000000000, 65.000000000000000 },
 568   { -0.069639384138314858, 10.000000000000000, 70.000000000000000 },
 569   { 0.045798335061325066, 10.000000000000000, 75.000000000000000 },
 570   { 0.086269195064844456, 10.000000000000000, 80.000000000000000 },
 571   { -0.0018234674126248740, 10.000000000000000, 85.000000000000000 },
 572   { -0.082067762371231284, 10.000000000000000, 90.000000000000000 },
 573   { -0.038798074754578089, 10.000000000000000, 95.000000000000000 },
 574   { 0.058331574236414913, 10.000000000000000, 100.00000000000000 },
 575 };
 576 const double toler019 = 2.5000000000000017e-10;
 577
 578 // Test data for nu=20.000000000000000.
 579 // max(|f - f_GSL|): 7.1525573730468750e-07
 580 // max(|f - f_GSL| / |f_GSL|): 1.7017552833615218e-12
 581 const testcase_cyl_neumann<double>
 582 data020[20] =
 583 {
 584   { -593396529.69143200, 20.000000000000000, 5.0000000000000000 },
 585   { -1597.4838482696259, 20.000000000000000, 10.000000000000000 },
 586   { -3.3087330924737621, 20.000000000000000, 15.000000000000000 },
 587   { -0.28548945860020319, 20.000000000000000, 20.000000000000000 },
 588   { 0.19804074776289243, 20.000000000000000, 25.000000000000000 },
 589   { -0.16848153948742683, 20.000000000000000, 30.000000000000000 },
 590   { 0.10102784152594022, 20.000000000000000, 35.000000000000000 },
 591   { 0.045161820565805755, 20.000000000000000, 40.000000000000000 },
 592   { -0.12556489308015448, 20.000000000000000, 45.000000000000000 },
 593   { 0.016442633948115834, 20.000000000000000, 50.000000000000000 },
 594   { 0.10853448778255181, 20.000000000000000, 55.000000000000000 },
 595   { -0.026721408520664701, 20.000000000000000, 60.000000000000000 },
 596   { -0.098780425256324175, 20.000000000000000, 65.000000000000000 },
 597   { 0.016201957786018233, 20.000000000000000, 70.000000000000000 },
 598   { 0.093591198265063721, 20.000000000000000, 75.000000000000000 },
 599   { 0.0040484400737296200, 20.000000000000000, 80.000000000000000 },
 600   { -0.086314929459920531, 20.000000000000000, 85.000000000000000 },
 601   { -0.028274110097231530, 20.000000000000000, 90.000000000000000 },
 602   { 0.072349520791638741, 20.000000000000000, 95.000000000000000 },
 603   { 0.051247973076188474, 20.000000000000000, 100.00000000000000 },
 604 };
 605 const double toler020 = 1.0000000000000006e-10;
 606
 607 // Test data for nu=50.000000000000000.
 608 // max(|f - f_GSL|): 1.0522490333925732e+28
 609 // max(|f - f_GSL| / |f_GSL|): 2.6658726302692481e-12
 610 const testcase_cyl_neumann<double>
 611 data021[20] =
 612 {
 613   { -2.7888370175838930e+42, 50.000000000000000, 5.0000000000000000 },
 614   { -3.6410665018007421e+27, 50.000000000000000, 10.000000000000000 },
 615   { -1.0929732912175415e+19, 50.000000000000000, 15.000000000000000 },
 616   { -15606426801663.734, 50.000000000000000, 20.000000000000000 },
 617   { -753573251.44662738, 50.000000000000000, 25.000000000000000 },
 618   { -386759.32602734759, 50.000000000000000, 30.000000000000000 },
 619   { -1172.8690492895323, 50.000000000000000, 35.000000000000000 },
 620   { -15.615608873419944, 50.000000000000000, 40.000000000000000 },
 621   { -0.87058346204176895, 50.000000000000000, 45.000000000000000 },
 622   { -0.21031655464397747, 50.000000000000000, 50.000000000000000 },
 623   { 0.093048240412999389, 50.000000000000000, 55.000000000000000 },
 624   { 0.0086417699626744754, 50.000000000000000, 60.000000000000000 },
 625   { -0.025019788459222037, 50.000000000000000, 65.000000000000000 },
 626   { -0.0014815155191909152, 50.000000000000000, 70.000000000000000 },
 627   { 0.050335774732164121, 50.000000000000000, 75.000000000000000 },
 628   { -0.092924250967987232, 50.000000000000000, 80.000000000000000 },
 629   { 0.087332463030205698, 50.000000000000000, 85.000000000000000 },
 630   { -0.016164237701651860, 50.000000000000000, 90.000000000000000 },
 631   { -0.068897613820457934, 50.000000000000000, 95.000000000000000 },
 632   { 0.076505263944803045, 50.000000000000000, 100.00000000000000 },
 633 };
 634 const double toler021 = 2.5000000000000017e-10;
 635
 636 // Test data for nu=100.00000000000000.
 637 // max(|f - f_GSL|): 6.3342780989716025e+102
 638 // max(|f - f_GSL| / |f_GSL|): 1.2681517765786818e-13
 639 const testcase_cyl_neumann<double>
 640 data022[20] =
 641 {
 642   { -5.0848639160196196e+115, 100.00000000000000, 5.0000000000000000 },
 643   { -4.8491482711800252e+85, 100.00000000000000, 10.000000000000000 },
 644   { -1.6375955323195320e+68, 100.00000000000000, 15.000000000000000 },
 645   { -8.2002648144679126e+55, 100.00000000000000, 20.000000000000000 },
 646   { -2.9712216432562368e+46, 100.00000000000000, 25.000000000000000 },
 647   { -7.2875284708240751e+38, 100.00000000000000, 30.000000000000000 },
 648   { -3.4251079902108953e+32, 100.00000000000000, 35.000000000000000 },
 649   { -1.4552439438101802e+27, 100.00000000000000, 40.000000000000000 },
 650   { -3.4506612476220073e+22, 100.00000000000000, 45.000000000000000 },
 651   { -3.2938001882025953e+18, 100.00000000000000, 50.000000000000000 },
 652   { -1005686182055527.4, 100.00000000000000, 55.000000000000000 },
 653   { -831892881402.11377, 100.00000000000000, 60.000000000000000 },
 654   { -1650863778.0598330, 100.00000000000000, 65.000000000000000 },
 655   { -7192614.1976097794, 100.00000000000000, 70.000000000000000 },
 656   { -64639.072261231595, 100.00000000000000, 75.000000000000000 },
 657   { -1152.5905185698466, 100.00000000000000, 80.000000000000000 },
 658   { -40.250761402101560, 100.00000000000000, 85.000000000000000 },
 659   { -2.8307771387185459, 100.00000000000000, 90.000000000000000 },
 660   { -0.45762200495904848, 100.00000000000000, 95.000000000000000 },
 661   { -0.16692141141757652, 100.00000000000000, 100.00000000000000 },
 662 };
 663 const double toler022 = 1.0000000000000006e-11;
 664
 665 template<typename Tp, unsigned int Num>
 666   void
 667   test(const testcase_cyl_neumann<Tp> (&data)[Num], Tp toler)
 668   {
 669     bool test __attribute__((unused)) = true;
 670     const Tp eps = std::numeric_limits<Tp>::epsilon();
 671     Tp max_abs_diff = -Tp(1);
 672     Tp max_abs_frac = -Tp(1);
 673     unsigned int num_datum = Num;
 674     for (unsigned int i = 0; i < num_datum; ++i)
 675       {
 676         const Tp f = std::cyl_neumann(data[i].nu, data[i].x);
 677         const Tp f0 = data[i].f0;
 678         const Tp diff = f - f0;
 679         if (std::abs(diff) > max_abs_diff)
 680           max_abs_diff = std::abs(diff);
 681         if (std::abs(f0) > Tp(10) * eps
 682          && std::abs(f) > Tp(10) * eps)
 683           {
 684             const Tp frac = diff / f0;
 685             if (std::abs(frac) > max_abs_frac)
 686               max_abs_frac = std::abs(frac);
 687           }
 688       }
 689     VERIFY(max_abs_frac < toler);
 690   }
 691
 692 int
 693 main()
 694 {
 695   test(data001, toler001);
 696   test(data002, toler002);
 697   test(data003, toler003);
 698   test(data004, toler004);
 699   test(data005, toler005);
 700   test(data006, toler006);
 701   test(data007, toler007);
 702   test(data008, toler008);
 703   test(data009, toler009);
 704   test(data010, toler010);
 705   test(data011, toler011);
 706   test(data012, toler012);
 707   test(data013, toler013);
 708   test(data014, toler014);
 709   test(data015, toler015);
 710   test(data016, toler016);
 711   test(data017, toler017);
 712   test(data018, toler018);
 713   test(data019, toler019);
 714   test(data020, toler020);
 715   test(data021, toler021);
 716   test(data022, toler022);
 717   return 0;
 718 }