libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/check_value.cc

   1 // { dg-do run { target c++11 } }
   2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   3 //
   4 // Copyright (C) 2016-2018 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_neumann
  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|): 9.9920072216264089e-16 at index 7
  42 // max(|f - f_GSL| / |f_GSL|): 1.5769525176812613e-14
  43 // mean(f - f_GSL): 1.7173762412170391e-17
  44 // variance(f - f_GSL): 1.8144622474613909e-32
  45 // stddev(f - f_GSL): 1.3470197650596635e-16
  46 const testcase_cyl_neumann<double>
  47 data007[20] =
  48 {
  49   { -0.93157302493005878, 0.0000000000000000, 0.25000000000000000, 0.0 },
  50   { -0.44451873350670656, 0.0000000000000000, 0.50000000000000000, 0.0 },
  51   { -0.13717276938577236, 0.0000000000000000, 0.75000000000000000, 0.0 },
  52   { 0.088256964215676942, 0.0000000000000000, 1.0000000000000000, 0.0 },
  53   { 0.25821685159454072, 0.0000000000000000, 1.2500000000000000, 0.0 },
  54   { 0.38244892379775886, 0.0000000000000000, 1.5000000000000000, 0.0 },
  55   { 0.46549262864690610, 0.0000000000000000, 1.7500000000000000, 0.0 },
  56   { 0.51037567264974493, 0.0000000000000000, 2.0000000000000000, 0.0 },
  57   { 0.52006476245727862, 0.0000000000000000, 2.2500000000000000, 0.0 },
  58   { 0.49807035961523194, 0.0000000000000000, 2.5000000000000000, 0.0 },
  59   { 0.44865872156913222, 0.0000000000000000, 2.7500000000000000, 0.0 },
  60   { 0.37685001001279045, 0.0000000000000000, 3.0000000000000000, 0.0 },
  61   { 0.28828690267308710, 0.0000000000000000, 3.2500000000000000, 0.0 },
  62   { 0.18902194392082688, 0.0000000000000000, 3.5000000000000000, 0.0 },
  63   { 0.085256756977362638, 0.0000000000000000, 3.7500000000000000, 0.0 },
  64   { -0.016940739325064763, 0.0000000000000000, 4.0000000000000000, 0.0 },
  65   { -0.11191885116160770, 0.0000000000000000, 4.2500000000000000, 0.0 },
  66   { -0.19470500862950454, 0.0000000000000000, 4.5000000000000000, 0.0 },
  67   { -0.26123250323497549, 0.0000000000000000, 4.7500000000000000, 0.0 },
  68   { -0.30851762524903359, 0.0000000000000000, 5.0000000000000000, 0.0 },
  69 };
  70 const double toler007 = 1.0000000000000008e-12;
  71
  72 // Test data for nu=0.33333333333333331.
  73 // max(|f - f_GSL|): 1.7208456881689926e-15 at index 7
  74 // max(|f - f_GSL| / |f_GSL|): 5.0141196309547185e-15
  75 // mean(f - f_GSL): -1.8908485888147198e-17
  76 // variance(f - f_GSL): 4.0002408539583433e-33
  77 // stddev(f - f_GSL): 6.3247457292434642e-17
  78 const testcase_cyl_neumann<double>
  79 data008[20] =
  80 {
  81   { -1.3461842332051073, 0.33333333333333331, 0.25000000000000000, 0.0 },
  82   { -0.84062782604337771, 0.33333333333333331, 0.50000000000000000, 0.0 },
  83   { -0.52488281484097088, 0.33333333333333331, 0.75000000000000000, 0.0 },
  84   { -0.27880164127599216, 0.33333333333333331, 1.0000000000000000, 0.0 },
  85   { -0.074321349727836453, 0.33333333333333331, 1.2500000000000000, 0.0 },
  86   { 0.096610087766627981, 0.33333333333333331, 1.5000000000000000, 0.0 },
  87   { 0.23582564494922068, 0.33333333333333331, 1.7500000000000000, 0.0 },
  88   { 0.34319996626034494, 0.33333333333333331, 2.0000000000000000, 0.0 },
  89   { 0.41835668452349323, 0.33333333333333331, 2.2500000000000000, 0.0 },
  90   { 0.46145947419129157, 0.33333333333333331, 2.5000000000000000, 0.0 },
  91   { 0.47358926135786023, 0.33333333333333331, 2.7500000000000000, 0.0 },
  92   { 0.45689303457230640, 0.33333333333333331, 3.0000000000000000, 0.0 },
  93   { 0.41458485697347386, 0.33333333333333331, 3.2500000000000000, 0.0 },
  94   { 0.35084133277859947, 0.33333333333333331, 3.5000000000000000, 0.0 },
  95   { 0.27061914527820891, 0.33333333333333331, 3.7500000000000000, 0.0 },
  96   { 0.17941676634394862, 0.33333333333333331, 4.0000000000000000, 0.0 },
  97   { 0.083000434191526043, 0.33333333333333331, 4.2500000000000000, 0.0 },
  98   { -0.012886361627105348, 0.33333333333333331, 4.5000000000000000, 0.0 },
  99   { -0.10281143123935124, 0.33333333333333331, 4.7500000000000000, 0.0 },
 100   { -0.18192321129343850, 0.33333333333333331, 5.0000000000000000, 0.0 },
 101 };
 102 const double toler008 = 5.0000000000000039e-13;
 103
 104 // Test data for nu=0.50000000000000000.
 105 // max(|f - f_GSL|): 5.5511151231257827e-16 at index 1
 106 // max(|f - f_GSL| / |f_GSL|): 6.6252247616878728e-15
 107 // mean(f - f_GSL): -8.0924850154318048e-17
 108 // variance(f - f_GSL): 1.5661893379337934e-34
 109 // stddev(f - f_GSL): 1.2514748650827124e-17
 110 const testcase_cyl_neumann<double>
 111 data009[20] =
 112 {
 113   { -1.5461605241060765, 0.50000000000000000, 0.25000000000000000, 0.0 },
 114   { -0.99024588024340454, 0.50000000000000000, 0.50000000000000000, 0.0 },
 115   { -0.67411792914454438, 0.50000000000000000, 0.75000000000000000, 0.0 },
 116   { -0.43109886801837571, 0.50000000000000000, 1.0000000000000000, 0.0 },
 117   { -0.22502969244466481, 0.50000000000000000, 1.2500000000000000, 0.0 },
 118   { -0.046083165893097265, 0.50000000000000000, 1.5000000000000000, 0.0 },
 119   { 0.10750804524368722, 0.50000000000000000, 1.7500000000000000, 0.0 },
 120   { 0.23478571040624849, 0.50000000000000000, 2.0000000000000000, 0.0 },
 121   { 0.33414002338271825, 0.50000000000000000, 2.2500000000000000, 0.0 },
 122   { 0.40427830223905686, 0.50000000000000000, 2.5000000000000000, 0.0 },
 123   { 0.44472115119490507, 0.50000000000000000, 2.7500000000000000, 0.0 },
 124   { 0.45604882079463316, 0.50000000000000000, 3.0000000000000000, 0.0 },
 125   { 0.43998859501924370, 0.50000000000000000, 3.2500000000000000, 0.0 },
 126   { 0.39938682536304909, 0.50000000000000000, 3.5000000000000000, 0.0 },
 127   { 0.33809163836693340, 0.50000000000000000, 3.7500000000000000, 0.0 },
 128   { 0.26076607667717877, 0.50000000000000000, 4.0000000000000000, 0.0 },
 129   { 0.17264962544644955, 0.50000000000000000, 4.2500000000000000, 0.0 },
 130   { 0.079285862862978548, 0.50000000000000000, 4.5000000000000000, 0.0 },
 131   { -0.013765943019498003, 0.50000000000000000, 4.7500000000000000, 0.0 },
 132   { -0.10121770918510846, 0.50000000000000000, 5.0000000000000000, 0.0 },
 133 };
 134 const double toler009 = 5.0000000000000039e-13;
 135
 136 // Test data for nu=0.66666666666666663.
 137 // max(|f - f_GSL|): 1.0547118733938987e-15 at index 9
 138 // max(|f - f_GSL| / |f_GSL|): 7.7816158152055799e-15
 139 // mean(f - f_GSL): 1.0772632785815972e-16
 140 // variance(f - f_GSL): 1.6340061794441914e-35
 141 // stddev(f - f_GSL): 4.0422842297940791e-18
 142 const testcase_cyl_neumann<double>
 143 data010[20] =
 144 {
 145   { -1.8021638417426857, 0.66666666666666663, 0.25000000000000000, 0.0 },
 146   { -1.1316060101031435, 0.66666666666666663, 0.50000000000000000, 0.0 },
 147   { -0.80251156358450748, 0.66666666666666663, 0.75000000000000000, 0.0 },
 148   { -0.56270321497463327, 0.66666666666666663, 1.0000000000000000, 0.0 },
 149   { -0.36007453643432208, 0.66666666666666663, 1.2500000000000000, 0.0 },
 150   { -0.18017937469615020, 0.66666666666666663, 1.5000000000000000, 0.0 },
 151   { -0.019885608758103752, 0.66666666666666663, 1.7500000000000000, 0.0 },
 152   { 0.11989345361903521, 0.66666666666666663, 2.0000000000000000, 0.0 },
 153   { 0.23690889836358039, 0.66666666666666663, 2.2500000000000000, 0.0 },
 154   { 0.32882045742954535, 0.66666666666666663, 2.5000000000000000, 0.0 },
 155   { 0.39385133784531856, 0.66666666666666663, 2.7500000000000000, 0.0 },
 156   { 0.43115101690935642, 0.66666666666666663, 3.0000000000000000, 0.0 },
 157   { 0.44098127351445843, 0.66666666666666663, 3.2500000000000000, 0.0 },
 158   { 0.42477631413456485, 0.66666666666666663, 3.5000000000000000, 0.0 },
 159   { 0.38510384155620386, 0.66666666666666663, 3.7500000000000000, 0.0 },
 160   { 0.32554526794354366, 0.66666666666666663, 4.0000000000000000, 0.0 },
 161   { 0.25051080073878446, 0.66666666666666663, 4.2500000000000000, 0.0 },
 162   { 0.16500507211842136, 0.66666666666666663, 4.5000000000000000, 0.0 },
 163   { 0.074359649728861360, 0.66666666666666663, 4.7500000000000000, 0.0 },
 164   { -0.016050662643389627, 0.66666666666666663, 5.0000000000000000, 0.0 },
 165 };
 166 const double toler010 = 5.0000000000000039e-13;
 167
 168 // Test data for nu=1.0000000000000000.
 169 // max(|f - f_GSL|): 8.5001450322863548e-16 at index 8
 170 // max(|f - f_GSL| / |f_GSL|): 3.1259660869292553e-14
 171 // mean(f - f_GSL): 8.2746309804093703e-17
 172 // variance(f - f_GSL): 1.0590097247613155e-33
 173 // stddev(f - f_GSL): 3.2542429607534157e-17
 174 const testcase_cyl_neumann<double>
 175 data011[20] =
 176 {
 177   { -2.7041052293152825, 1.0000000000000000, 0.25000000000000000, 0.0 },
 178   { -1.4714723926702433, 1.0000000000000000, 0.50000000000000000, 0.0 },
 179   { -1.0375945507692856, 1.0000000000000000, 0.75000000000000000, 0.0 },
 180   { -0.78121282130028891, 1.0000000000000000, 1.0000000000000000, 0.0 },
 181   { -0.58436403661500824, 1.0000000000000000, 1.2500000000000000, 0.0 },
 182   { -0.41230862697391119, 1.0000000000000000, 1.5000000000000000, 0.0 },
 183   { -0.25397298594624573, 1.0000000000000000, 1.7500000000000000, 0.0 },
 184   { -0.10703243154093699, 1.0000000000000000, 2.0000000000000000, 0.0 },
 185   { 0.027192057738017056, 1.0000000000000000, 2.2500000000000000, 0.0 },
 186   { 0.14591813796678599, 1.0000000000000000, 2.5000000000000000, 0.0 },
 187   { 0.24601900149738354, 1.0000000000000000, 2.7500000000000000, 0.0 },
 188   { 0.32467442479180003, 1.0000000000000000, 3.0000000000000000, 0.0 },
 189   { 0.37977777371708382, 1.0000000000000000, 3.2500000000000000, 0.0 },
 190   { 0.41018841788751170, 1.0000000000000000, 3.5000000000000000, 0.0 },
 191   { 0.41586877934522715, 1.0000000000000000, 3.7500000000000000, 0.0 },
 192   { 0.39792571055709991, 1.0000000000000000, 4.0000000000000000, 0.0 },
 193   { 0.35856889308385076, 1.0000000000000000, 4.2500000000000000, 0.0 },
 194   { 0.30099732306965449, 1.0000000000000000, 4.5000000000000000, 0.0 },
 195   { 0.22922559673872217, 1.0000000000000000, 4.7500000000000000, 0.0 },
 196   { 0.14786314339122700, 1.0000000000000000, 5.0000000000000000, 0.0 },
 197 };
 198 const double toler011 = 2.5000000000000015e-12;
 199
 200 // Test data for nu=2.0000000000000000.
 201 // max(|f - f_GSL|): 1.0547118733938987e-15 at index 8
 202 // max(|f - f_GSL| / |f_GSL|): 1.1776017189273130e-14
 203 // mean(f - f_GSL): 1.4502288259166106e-16
 204 // variance(f - f_GSL): 2.5634607708533707e-35
 205 // stddev(f - f_GSL): 5.0630630757016755e-18
 206 const testcase_cyl_neumann<double>
 207 data012[20] =
 208 {
 209   { -20.701268809592200, 2.0000000000000000, 0.25000000000000000, 0.0 },
 210   { -5.4413708371742668, 2.0000000000000000, 0.50000000000000000, 0.0 },
 211   { -2.6297460326656559, 2.0000000000000000, 0.75000000000000000, 0.0 },
 212   { -1.6506826068162548, 2.0000000000000000, 1.0000000000000000, 0.0 },
 213   { -1.1931993101785539, 2.0000000000000000, 1.2500000000000000, 0.0 },
 214   { -0.93219375976297369, 2.0000000000000000, 1.5000000000000000, 0.0 },
 215   { -0.75574746972832973, 2.0000000000000000, 1.7500000000000000, 0.0 },
 216   { -0.61740810419068193, 2.0000000000000000, 2.0000000000000000, 0.0 },
 217   { -0.49589404446793012, 2.0000000000000000, 2.2500000000000000, 0.0 },
 218   { -0.38133584924180314, 2.0000000000000000, 2.5000000000000000, 0.0 },
 219   { -0.26973581138921693, 2.0000000000000000, 2.7500000000000000, 0.0 },
 220   { -0.16040039348492377, 2.0000000000000000, 3.0000000000000000, 0.0 },
 221   { -0.054577503462573951, 2.0000000000000000, 3.2500000000000000, 0.0 },
 222   { 0.045371437729179787, 2.0000000000000000, 3.5000000000000000, 0.0 },
 223   { 0.13653992534009185, 2.0000000000000000, 3.7500000000000000, 0.0 },
 224   { 0.21590359460361472, 2.0000000000000000, 4.0000000000000000, 0.0 },
 225   { 0.28065715378930217, 2.0000000000000000, 4.2500000000000000, 0.0 },
 226   { 0.32848159666046206, 2.0000000000000000, 4.5000000000000000, 0.0 },
 227   { 0.35774854396706901, 2.0000000000000000, 4.7500000000000000, 0.0 },
 228   { 0.36766288260552438, 2.0000000000000000, 5.0000000000000000, 0.0 },
 229 };
 230 const double toler012 = 1.0000000000000008e-12;
 231
 232 // Test data for nu=5.0000000000000000.
 233 // max(|f - f_GSL|): 2.8421709430404007e-14 at index 4
 234 // max(|f - f_GSL| / |f_GSL|): 1.0726804245235588e-15
 235 // mean(f - f_GSL): -1.8762769116165144e-15
 236 // variance(f - f_GSL): 2.7042659892362611e-31
 237 // stddev(f - f_GSL): 5.2002557525916566e-16
 238 const testcase_cyl_neumann<double>
 239 data013[20] =
 240 {
 241   { -251309.48151852371, 5.0000000000000000, 0.25000000000000000, 0.0 },
 242   { -7946.3014788074752, 5.0000000000000000, 0.50000000000000000, 0.0 },
 243   { -1067.2468952289760, 5.0000000000000000, 0.75000000000000000, 0.0 },
 244   { -260.40586662581228, 5.0000000000000000, 1.0000000000000000, 0.0 },
 245   { -88.474252441880395, 5.0000000000000000, 1.2500000000000000, 0.0 },
 246   { -37.190308395498064, 5.0000000000000000, 1.5000000000000000, 0.0 },
 247   { -18.165774988201832, 5.0000000000000000, 1.7500000000000000, 0.0 },
 248   { -9.9359891284819675, 5.0000000000000000, 2.0000000000000000, 0.0 },
 249   { -5.9446343848076424, 5.0000000000000000, 2.2500000000000000, 0.0 },
 250   { -3.8301760007407522, 5.0000000000000000, 2.5000000000000000, 0.0 },
 251   { -2.6287042009459087, 5.0000000000000000, 2.7500000000000000, 0.0 },
 252   { -1.9059459538286738, 5.0000000000000000, 3.0000000000000000, 0.0 },
 253   { -1.4498157389142654, 5.0000000000000000, 3.2500000000000000, 0.0 },
 254   { -1.1494603169763686, 5.0000000000000000, 3.5000000000000000, 0.0 },
 255   { -0.94343105151431672, 5.0000000000000000, 3.7500000000000000, 0.0 },
 256   { -0.79585142111419982, 5.0000000000000000, 4.0000000000000000, 0.0 },
 257   { -0.68479288173907016, 5.0000000000000000, 4.2500000000000000, 0.0 },
 258   { -0.59631936513587558, 5.0000000000000000, 4.5000000000000000, 0.0 },
 259   { -0.52130838331747587, 5.0000000000000000, 4.7500000000000000, 0.0 },
 260   { -0.45369482249110193, 5.0000000000000000, 5.0000000000000000, 0.0 },
 261 };
 262 const double toler013 = 2.5000000000000020e-13;
 263
 264 // Test data for nu=10.000000000000000.
 265 // max(|f - f_GSL|): 2.3841857910156250e-07 at index 2
 266 // max(|f - f_GSL| / |f_GSL|): 1.2724057074663479e-15
 267 // mean(f - f_GSL): 1.1408855549177588e-08
 268 // variance(f - f_GSL): 7.2112307216715587e-18
 269 // stddev(f - f_GSL): 2.6853734789916205e-09
 270 const testcase_cyl_neumann<double>
 271 data014[20] =
 272 {
 273   { -124241617095379.48, 10.000000000000000, 0.25000000000000000, 0.0 },
 274   { -121963623349.56966, 10.000000000000000, 0.50000000000000000, 0.0 },
 275   { -2133501638.9057348, 10.000000000000000, 0.75000000000000000, 0.0 },
 276   { -121618014.27868921, 10.000000000000000, 1.0000000000000000, 0.0 },
 277   { -13265210.158452792, 10.000000000000000, 1.2500000000000000, 0.0 },
 278   { -2183993.0260864049, 10.000000000000000, 1.5000000000000000, 0.0 },
 279   { -478274.82386541169, 10.000000000000000, 1.7500000000000000, 0.0 },
 280   { -129184.54220803917, 10.000000000000000, 2.0000000000000000, 0.0 },
 281   { -40993.254794381690, 10.000000000000000, 2.2500000000000000, 0.0 },
 282   { -14782.847716021070, 10.000000000000000, 2.5000000000000000, 0.0 },
 283   { -5916.5330998776262, 10.000000000000000, 2.7500000000000000, 0.0 },
 284   { -2582.6071294842995, 10.000000000000000, 3.0000000000000000, 0.0 },
 285   { -1213.3423564023892, 10.000000000000000, 3.2500000000000000, 0.0 },
 286   { -607.27437834125760, 10.000000000000000, 3.5000000000000000, 0.0 },
 287   { -321.17461059752202, 10.000000000000000, 3.7500000000000000, 0.0 },
 288   { -178.33055590796428, 10.000000000000000, 4.0000000000000000, 0.0 },
 289   { -103.40496587570090, 10.000000000000000, 4.2500000000000000, 0.0 },
 290   { -62.345024619781434, 10.000000000000000, 4.5000000000000000, 0.0 },
 291   { -38.944510430296937, 10.000000000000000, 4.7500000000000000, 0.0 },
 292   { -25.129110095610095, 10.000000000000000, 5.0000000000000000, 0.0 },
 293 };
 294 const double toler014 = 2.5000000000000020e-13;
 295
 296 // Test data for nu=20.000000000000000.
 297 // max(|f - f_GSL|): 6442450944.0000000 at index 2
 298 // max(|f - f_GSL| / |f_GSL|): 1.8080382211114952e-15
 299 // mean(f - f_GSL): 322083865.10024977
 300 // variance(f - f_GSL): inf
 301 // stddev(f - f_GSL): inf
 302 const testcase_cyl_neumann<double>
 303 data015[20] =
 304 {
 305   { -4.4678815064152581e+34, 20.000000000000000, 0.25000000000000000, 0.0 },
 306   { -4.2714301215659088e+28, 20.000000000000000, 0.50000000000000000, 0.0 },
 307   { -1.2898357375834223e+25, 20.000000000000000, 0.75000000000000000, 0.0 },
 308   { -4.1139703148355065e+22, 20.000000000000000, 1.0000000000000000, 0.0 },
 309   { -4.7783533372148580e+20, 20.000000000000000, 1.2500000000000000, 0.0 },
 310   { -1.2577301772964241e+19, 20.000000000000000, 1.5000000000000000, 0.0 },
 311   { -5.8251041176649626e+17, 20.000000000000000, 1.7500000000000000, 0.0 },
 312   { -40816513889983640., 20.000000000000000, 2.0000000000000000, 0.0 },
 313   { -3925339868516418.5, 20.000000000000000, 2.2500000000000000, 0.0 },
 314   { -484776559582090.25, 20.000000000000000, 2.5000000000000000, 0.0 },
 315   { -73320655044814.469, 20.000000000000000, 2.7500000000000000, 0.0 },
 316   { -13113540041757.449, 20.000000000000000, 3.0000000000000000, 0.0 },
 317   { -2700669268882.7139, 20.000000000000000, 3.2500000000000000, 0.0 },
 318   { -627339518240.21240, 20.000000000000000, 3.5000000000000000, 0.0 },
 319   { -161695236802.71753, 20.000000000000000, 3.7500000000000000, 0.0 },
 320   { -45637199262.220100, 20.000000000000000, 4.0000000000000000, 0.0 },
 321   { -13953299213.925377, 20.000000000000000, 4.2500000000000000, 0.0 },
 322   { -4580215756.5691023, 20.000000000000000, 4.5000000000000000, 0.0 },
 323   { -1602110715.5159132, 20.000000000000000, 4.7500000000000000, 0.0 },
 324   { -593396529.69143200, 20.000000000000000, 5.0000000000000000, 0.0 },
 325 };
 326 const double toler015 = 2.5000000000000020e-13;
 327
 328 // Test data for nu=50.000000000000000.
 329 // max(|f - f_GSL|): 6.4703872001161536e+68 at index 2
 330 // max(|f - f_GSL| / |f_GSL|): 3.7730746786493403e-15
 331 // mean(f - f_GSL): 3.2351936000129644e+67
 332 // variance(f - f_GSL): inf
 333 // stddev(f - f_GSL): inf
 334 const testcase_cyl_neumann<double>
 335 data016[20] =
 336 {
 337   { -2.7643487471155969e+107, 50.000000000000000, 0.25000000000000000, 0.0 },
 338   { -2.4575848224461092e+92, 50.000000000000000, 0.50000000000000000, 0.0 },
 339   { -3.8604508467683829e+83, 50.000000000000000, 0.75000000000000000, 0.0 },
 340   { -2.1911428126053411e+77, 50.000000000000000, 1.0000000000000000, 0.0 },
 341   { -3.1362926828833165e+72, 50.000000000000000, 1.2500000000000000, 0.0 },
 342   { -3.4584216846550566e+68, 50.000000000000000, 1.5000000000000000, 0.0 },
 343   { -1.5607714080312795e+65, 50.000000000000000, 1.7500000000000000, 0.0 },
 344   { -1.9761505765184128e+62, 50.000000000000000, 2.0000000000000000, 0.0 },
 345   { -5.5023640499231188e+59, 50.000000000000000, 2.2500000000000000, 0.0 },
 346   { -2.8530384545826849e+57, 50.000000000000000, 2.5000000000000000, 0.0 },
 347   { -2.4467169322684809e+55, 50.000000000000000, 2.7500000000000000, 0.0 },
 348   { -3.1793891461005181e+53, 50.000000000000000, 3.0000000000000000, 0.0 },
 349   { -5.8573901231568658e+51, 50.000000000000000, 3.2500000000000000, 0.0 },
 350   { -1.4528262197760965e+50, 50.000000000000000, 3.5000000000000000, 0.0 },
 351   { -4.6566569870478635e+48, 50.000000000000000, 3.7500000000000000, 0.0 },
 352   { -1.8661134361400254e+47, 50.000000000000000, 4.0000000000000000, 0.0 },
 353   { -9.1005883612255402e+45, 50.000000000000000, 4.2500000000000000, 0.0 },
 354   { -5.2813777542386141e+44, 50.000000000000000, 4.5000000000000000, 0.0 },
 355   { -3.5795477722116469e+43, 50.000000000000000, 4.7500000000000000, 0.0 },
 356   { -2.7888370175838930e+42, 50.000000000000000, 5.0000000000000000, 0.0 },
 357 };
 358 const double toler016 = 2.5000000000000020e-13;
 359
 360 // Test data for nu=100.00000000000000.
 361 // max(|f - f_GSL|): 1.6126781683773614e+233 at index 0
 362 // max(|f - f_GSL| / |f_GSL|): 3.9669044390244564e-13
 363 // mean(f - f_GSL): -8.0633908418868065e+231
 364 // variance(f - f_GSL): inf
 365 // stddev(f - f_GSL): inf
 366 const testcase_cyl_neumann<double>
 367 data017[20] =
 368 {
 369   { -6.0523080585856763e+245, 100.00000000000000, 0.25000000000000000, 0.0 },
 370   { -4.7766903780412668e+215, 100.00000000000000, 0.50000000000000000, 0.0 },
 371   { -1.1758283017660654e+198, 100.00000000000000, 0.75000000000000000, 0.0 },
 372   { -3.7752878101091316e+185, 100.00000000000000, 1.0000000000000000, 0.0 },
 373   { -7.7013290729995187e+175, 100.00000000000000, 1.2500000000000000, 0.0 },
 374   { -9.3152624794288802e+167, 100.00000000000000, 1.5000000000000000, 0.0 },
 375   { -1.8854163374247264e+161, 100.00000000000000, 1.7500000000000000, 0.0 },
 376   { -3.0008260488566283e+155, 100.00000000000000, 2.0000000000000000, 0.0 },
 377   { -2.3075650873777408e+150, 100.00000000000000, 2.2500000000000000, 0.0 },
 378   { -6.1476258561369381e+145, 100.00000000000000, 2.5000000000000000, 0.0 },
 379   { -4.4758816234829593e+141, 100.00000000000000, 2.7500000000000000, 0.0 },
 380   { -7.4747961023547862e+137, 100.00000000000000, 3.0000000000000000, 0.0 },
 381   { -2.5067022766901547e+134, 100.00000000000000, 3.2500000000000000, 0.0 },
 382   { -1.5222488313432757e+131, 100.00000000000000, 3.5000000000000000, 0.0 },
 383   { -1.5422392812241399e+128, 100.00000000000000, 3.7500000000000000, 0.0 },
 384   { -2.4400857387551062e+125, 100.00000000000000, 4.0000000000000000, 0.0 },
 385   { -5.7118153392422293e+122, 100.00000000000000, 4.2500000000000000, 0.0 },
 386   { -1.8915420905193392e+120, 100.00000000000000, 4.5000000000000000, 0.0 },
 387   { -8.5357945104770158e+117, 100.00000000000000, 4.7500000000000000, 0.0 },
 388   { -5.0848639160196196e+115, 100.00000000000000, 5.0000000000000000, 0.0 },
 389 };
 390 const double toler017 = 2.5000000000000014e-11;
 391 //  cyl_neumann
 392
 393 // Test data for nu=0.0000000000000000.
 394 // max(|f - f_GSL|): 7.1210398688847931e-15 at index 13
 395 // max(|f - f_GSL| / |f_GSL|): 1.5217467741391491e-12
 396 // mean(f - f_GSL): 7.2554809382729962e-17
 397 // variance(f - f_GSL): 8.8801597233792556e-32
 398 // stddev(f - f_GSL): 2.9799596848580446e-16
 399 const testcase_cyl_neumann<double>
 400 data018[20] =
 401 {
 402   { -0.30851762524903359, 0.0000000000000000, 5.0000000000000000, 0.0 },
 403   { 0.055671167283599457, 0.0000000000000000, 10.000000000000000, 0.0 },
 404   { 0.20546429603891822, 0.0000000000000000, 15.000000000000000, 0.0 },
 405   { 0.062640596809384053, 0.0000000000000000, 20.000000000000000, 0.0 },
 406   { -0.12724943226800617, 0.0000000000000000, 25.000000000000000, 0.0 },
 407   { -0.11729573168666413, 0.0000000000000000, 30.000000000000000, 0.0 },
 408   { 0.045797987195155689, 0.0000000000000000, 35.000000000000000, 0.0 },
 409   { 0.12593641705826092, 0.0000000000000000, 40.000000000000000, 0.0 },
 410   { 0.027060469763313333, 0.0000000000000000, 45.000000000000000, 0.0 },
 411   { -0.098064995470077118, 0.0000000000000000, 50.000000000000000, 0.0 },
 412   { -0.077569178730412594, 0.0000000000000000, 55.000000000000000, 0.0 },
 413   { 0.047358952209449426, 0.0000000000000000, 60.000000000000000, 0.0 },
 414   { 0.097183557740181920, 0.0000000000000000, 65.000000000000000, 0.0 },
 415   { 0.0093096664589409992, 0.0000000000000000, 70.000000000000000, 0.0 },
 416   { -0.085369047647775656, 0.0000000000000000, 75.000000000000000, 0.0 },
 417   { -0.055620339089770016, 0.0000000000000000, 80.000000000000000, 0.0 },
 418   { 0.049567884951494251, 0.0000000000000000, 85.000000000000000, 0.0 },
 419   { 0.079776475854877751, 0.0000000000000000, 90.000000000000000, 0.0 },
 420   { -0.0028230995861232107, 0.0000000000000000, 95.000000000000000, 0.0 },
 421   { -0.077244313365083153, 0.0000000000000000, 100.00000000000000, 0.0 },
 422 };
 423 const double toler018 = 1.0000000000000006e-10;
 424
 425 // Test data for nu=0.33333333333333331.
 426 // max(|f - f_GSL|): 6.4392935428259079e-15 at index 13
 427 // max(|f - f_GSL| / |f_GSL|): 4.0255283668271825e-13
 428 // mean(f - f_GSL): 4.0124153999343550e-16
 429 // variance(f - f_GSL): 5.5447658140741534e-32
 430 // stddev(f - f_GSL): 2.3547326417396418e-16
 431 const testcase_cyl_neumann<double>
 432 data019[20] =
 433 {
 434   { -0.18192321129343850, 0.33333333333333331, 5.0000000000000000, 0.0 },
 435   { 0.17020111788268760, 0.33333333333333331, 10.000000000000000, 0.0 },
 436   { 0.18540507541540796, 0.33333333333333331, 15.000000000000000, 0.0 },
 437   { -0.028777707635715043, 0.33333333333333331, 20.000000000000000, 0.0 },
 438   { -0.15829741864944163, 0.33333333333333331, 25.000000000000000, 0.0 },
 439   { -0.058645772316705209, 0.33333333333333331, 30.000000000000000, 0.0 },
 440   { 0.10294930308870617, 0.33333333333333331, 35.000000000000000, 0.0 },
 441   { 0.10547870367098922, 0.33333333333333331, 40.000000000000000, 0.0 },
 442   { -0.034334228816010816, 0.33333333333333331, 45.000000000000000, 0.0 },
 443   { -0.11283489933031279, 0.33333333333333331, 50.000000000000000, 0.0 },
 444   { -0.030007358986895105, 0.33333333333333331, 55.000000000000000, 0.0 },
 445   { 0.086699173295718121, 0.33333333333333331, 60.000000000000000, 0.0 },
 446   { 0.074875579668878658, 0.33333333333333331, 65.000000000000000, 0.0 },
 447   { -0.039323246374552680, 0.33333333333333331, 70.000000000000000, 0.0 },
 448   { -0.091263539574475236, 0.33333333333333331, 75.000000000000000, 0.0 },
 449   { -0.013358849535984318, 0.33333333333333331, 80.000000000000000, 0.0 },
 450   { 0.078373575537830198, 0.33333333333333331, 85.000000000000000, 0.0 },
 451   { 0.055812482883955940, 0.33333333333333331, 90.000000000000000, 0.0 },
 452   { -0.043310380106990683, 0.33333333333333331, 95.000000000000000, 0.0 },
 453   { -0.076900504962136559, 0.33333333333333331, 100.00000000000000, 0.0 },
 454 };
 455 const double toler019 = 2.5000000000000014e-11;
 456
 457 // Test data for nu=0.50000000000000000.
 458 // max(|f - f_GSL|): 6.5919492087118670e-15 at index 12
 459 // max(|f - f_GSL| / |f_GSL|): 6.0282403975230169e-13
 460 // mean(f - f_GSL): 4.4870791110485090e-16
 461 // variance(f - f_GSL): 2.2330752394717835e-31
 462 // stddev(f - f_GSL): 4.7255425503023288e-16
 463 const testcase_cyl_neumann<double>
 464 data020[20] =
 465 {
 466   { -0.10121770918510846, 0.50000000000000000, 5.0000000000000000, 0.0 },
 467   { 0.21170886633139810, 0.50000000000000000, 10.000000000000000, 0.0 },
 468   { 0.15650551590730855, 0.50000000000000000, 15.000000000000000, 0.0 },
 469   { -0.072806904785061938, 0.50000000000000000, 20.000000000000000, 0.0 },
 470   { -0.15817308404205055, 0.50000000000000000, 25.000000000000000, 0.0 },
 471   { -0.022470290598831138, 0.50000000000000000, 30.000000000000000, 0.0 },
 472   { 0.12187835265849535, 0.50000000000000000, 35.000000000000000, 0.0 },
 473   { 0.084138655676395377, 0.50000000000000000, 40.000000000000000, 0.0 },
 474   { -0.062482641933003201, 0.50000000000000000, 45.000000000000000, 0.0 },
 475   { -0.10888475635053954, 0.50000000000000000, 50.000000000000000, 0.0 },
 476   { -0.0023805454010949376, 0.50000000000000000, 55.000000000000000, 0.0 },
 477   { 0.098104683735037918, 0.50000000000000000, 60.000000000000000, 0.0 },
 478   { 0.055663470218594434, 0.50000000000000000, 65.000000000000000, 0.0 },
 479   { -0.060396767883824871, 0.50000000000000000, 70.000000000000000, 0.0 },
 480   { -0.084922578922046868, 0.50000000000000000, 75.000000000000000, 0.0 },
 481   { 0.0098472271924441284, 0.50000000000000000, 80.000000000000000, 0.0 },
 482   { 0.085190643574343625, 0.50000000000000000, 85.000000000000000, 0.0 },
 483   { 0.037684970437156268, 0.50000000000000000, 90.000000000000000, 0.0 },
 484   { -0.059772904856097500, 0.50000000000000000, 95.000000000000000, 0.0 },
 485   { -0.068803091468728109, 0.50000000000000000, 100.00000000000000, 0.0 },
 486 };
 487 const double toler020 = 5.0000000000000028e-11;
 488
 489 // Test data for nu=0.66666666666666663.
 490 // max(|f - f_GSL|): 7.2372663417752392e-15 at index 12
 491 // max(|f - f_GSL| / |f_GSL|): 4.1336890848340281e-13
 492 // mean(f - f_GSL): 4.6646714269016339e-16
 493 // variance(f - f_GSL): 4.7228390491049495e-31
 494 // stddev(f - f_GSL): 6.8722915021882980e-16
 495 const testcase_cyl_neumann<double>
 496 data021[20] =
 497 {
 498   { -0.016050662643389627, 0.66666666666666663, 5.0000000000000000, 0.0 },
 499   { 0.23937232657540733, 0.66666666666666663, 10.000000000000000, 0.0 },
 500   { 0.11762106604241235, 0.66666666666666663, 15.000000000000000, 0.0 },
 501   { -0.11182254014899558, 0.66666666666666663, 20.000000000000000, 0.0 },
 502   { -0.14756582982938804, 0.66666666666666663, 25.000000000000000, 0.0 },
 503   { 0.015078692908077713, 0.66666666666666663, 30.000000000000000, 0.0 },
 504   { 0.13260911815705795, 0.66666666666666663, 35.000000000000000, 0.0 },
 505   { 0.057217565989652698, 0.66666666666666663, 40.000000000000000, 0.0 },
 506   { -0.086373755152382006, 0.66666666666666663, 45.000000000000000, 0.0 },
 507   { -0.097624139208051616, 0.66666666666666663, 50.000000000000000, 0.0 },
 508   { 0.025354902147023392, 0.66666666666666663, 55.000000000000000, 0.0 },
 509   { 0.10288136476351206, 0.66666666666666663, 60.000000000000000, 0.0 },
 510   { 0.032728379560128203, 0.66666666666666663, 65.000000000000000, 0.0 },
 511   { -0.077363672735747818, 0.66666666666666663, 70.000000000000000, 0.0 },
 512   { -0.072855870458293961, 0.66666666666666663, 75.000000000000000, 0.0 },
 513   { 0.032358106046953543, 0.66666666666666663, 80.000000000000000, 0.0 },
 514   { 0.086240651537394228, 0.66666666666666663, 85.000000000000000, 0.0 },
 515   { 0.017029601697285190, 0.66666666666666663, 90.000000000000000, 0.0 },
 516   { -0.072173520560584681, 0.66666666666666663, 95.000000000000000, 0.0 },
 517   { -0.056057339204073887, 0.66666666666666663, 100.00000000000000, 0.0 },
 518 };
 519 const double toler021 = 2.5000000000000014e-11;
 520
 521 // Test data for nu=1.0000000000000000.
 522 // max(|f - f_GSL|): 7.6570694229616265e-15 at index 12
 523 // max(|f - f_GSL| / |f_GSL|): 4.2680655963073912e-13
 524 // mean(f - f_GSL): 4.9712838012805347e-16
 525 // variance(f - f_GSL): 8.8456847510770884e-31
 526 // stddev(f - f_GSL): 9.4051500525388153e-16
 527 const testcase_cyl_neumann<double>
 528 data022[20] =
 529 {
 530   { 0.14786314339122700, 1.0000000000000000, 5.0000000000000000, 0.0 },
 531   { 0.24901542420695386, 1.0000000000000000, 10.000000000000000, 0.0 },
 532   { 0.021073628036873522, 1.0000000000000000, 15.000000000000000, 0.0 },
 533   { -0.16551161436252115, 1.0000000000000000, 20.000000000000000, 0.0 },
 534   { -0.098829964783237412, 1.0000000000000000, 25.000000000000000, 0.0 },
 535   { 0.084425570661747135, 1.0000000000000000, 30.000000000000000, 0.0 },
 536   { 0.12751273354559009, 1.0000000000000000, 35.000000000000000, 0.0 },
 537   { -0.0057935058215497536, 1.0000000000000000, 40.000000000000000, 0.0 },
 538   { -0.11552517964639945, 1.0000000000000000, 45.000000000000000, 0.0 },
 539   { -0.056795668562014692, 1.0000000000000000, 50.000000000000000, 0.0 },
 540   { 0.073846265432577926, 1.0000000000000000, 55.000000000000000, 0.0 },
 541   { 0.091869609369866892, 1.0000000000000000, 60.000000000000000, 0.0 },
 542   { -0.017940374275377362, 1.0000000000000000, 65.000000000000000, 0.0 },
 543   { -0.094844652625716230, 1.0000000000000000, 70.000000000000000, 0.0 },
 544   { -0.035213785160580421, 1.0000000000000000, 75.000000000000000, 0.0 },
 545   { 0.069395913784588037, 1.0000000000000000, 80.000000000000000, 0.0 },
 546   { 0.071233187582749768, 1.0000000000000000, 85.000000000000000, 0.0 },
 547   { -0.026187238607768244, 1.0000000000000000, 90.000000000000000, 0.0 },
 548   { -0.081827958724501215, 1.0000000000000000, 95.000000000000000, 0.0 },
 549   { -0.020372312002759834, 1.0000000000000000, 100.00000000000000, 0.0 },
 550 };
 551 const double toler022 = 2.5000000000000014e-11;
 552
 553 // Test data for nu=2.0000000000000000.
 554 // max(|f - f_GSL|): 7.1210398688847931e-15 at index 13
 555 // max(|f - f_GSL| / |f_GSL|): 3.9367645301914862e-12
 556 // mean(f - f_GSL): -6.4293188828390413e-17
 557 // variance(f - f_GSL): 1.0170794505214399e-31
 558 // stddev(f - f_GSL): 3.1891683093268064e-16
 559 const testcase_cyl_neumann<double>
 560 data023[20] =
 561 {
 562   { 0.36766288260552438, 2.0000000000000000, 5.0000000000000000, 0.0 },
 563   { -0.0058680824422086830, 2.0000000000000000, 10.000000000000000, 0.0 },
 564   { -0.20265447896733507, 2.0000000000000000, 15.000000000000000, 0.0 },
 565   { -0.079191758245636165, 2.0000000000000000, 20.000000000000000, 0.0 },
 566   { 0.11934303508534717, 2.0000000000000000, 25.000000000000000, 0.0 },
 567   { 0.12292410306411394, 2.0000000000000000, 30.000000000000000, 0.0 },
 568   { -0.038511545278264829, 2.0000000000000000, 35.000000000000000, 0.0 },
 569   { -0.12622609234933840, 2.0000000000000000, 40.000000000000000, 0.0 },
 570   { -0.032194922192042195, 2.0000000000000000, 45.000000000000000, 0.0 },
 571   { 0.095793168727596537, 2.0000000000000000, 50.000000000000000, 0.0 },
 572   { 0.080254497473415426, 2.0000000000000000, 55.000000000000000, 0.0 },
 573   { -0.044296631897120527, 2.0000000000000000, 60.000000000000000, 0.0 },
 574   { -0.097735569256347382, 2.0000000000000000, 65.000000000000000, 0.0 },
 575   { -0.012019513676818605, 2.0000000000000000, 70.000000000000000, 0.0 },
 576   { 0.084430013376826846, 2.0000000000000000, 75.000000000000000, 0.0 },
 577   { 0.057355236934384719, 2.0000000000000000, 80.000000000000000, 0.0 },
 578   { -0.047891809949547198, 2.0000000000000000, 85.000000000000000, 0.0 },
 579   { -0.080358414490605934, 2.0000000000000000, 90.000000000000000, 0.0 },
 580   { 0.0011004057182389746, 2.0000000000000000, 95.000000000000000, 0.0 },
 581   { 0.076836867125027963, 2.0000000000000000, 100.00000000000000, 0.0 },
 582 };
 583 const double toler023 = 2.5000000000000017e-10;
 584
 585 // Test data for nu=5.0000000000000000.
 586 // max(|f - f_GSL|): 7.8125169094417357e-15 at index 12
 587 // max(|f - f_GSL| / |f_GSL|): 3.2742511246789352e-11
 588 // mean(f - f_GSL): 4.9826543715644767e-16
 589 // variance(f - f_GSL): 8.7640351124736941e-31
 590 // stddev(f - f_GSL): 9.3616425441658967e-16
 591 const testcase_cyl_neumann<double>
 592 data024[20] =
 593 {
 594   { -0.45369482249110193, 5.0000000000000000, 5.0000000000000000, 0.0 },
 595   { 0.13540304768936234, 5.0000000000000000, 10.000000000000000, 0.0 },
 596   { 0.16717271575940015, 5.0000000000000000, 15.000000000000000, 0.0 },
 597   { -0.10003576788953220, 5.0000000000000000, 20.000000000000000, 0.0 },
 598   { -0.14705799311372267, 5.0000000000000000, 25.000000000000000, 0.0 },
 599   { 0.031627359289264301, 5.0000000000000000, 30.000000000000000, 0.0 },
 600   { 0.13554781474770028, 5.0000000000000000, 35.000000000000000, 0.0 },
 601   { 0.031869448780850247, 5.0000000000000000, 40.000000000000000, 0.0 },
 602   { -0.10426932700176872, 5.0000000000000000, 45.000000000000000, 0.0 },
 603   { -0.078548413913081594, 5.0000000000000000, 50.000000000000000, 0.0 },
 604   { 0.055257033062858375, 5.0000000000000000, 55.000000000000000, 0.0 },
 605   { 0.099464632840450887, 5.0000000000000000, 60.000000000000000, 0.0 },
 606   { 0.00023860469499595305, 5.0000000000000000, 65.000000000000000, 0.0 },
 607   { -0.091861802216406052, 5.0000000000000000, 70.000000000000000, 0.0 },
 608   { -0.048383671296970042, 5.0000000000000000, 75.000000000000000, 0.0 },
 609   { 0.060293667104896316, 5.0000000000000000, 80.000000000000000, 0.0 },
 610   { 0.077506166682733996, 5.0000000000000000, 85.000000000000000, 0.0 },
 611   { -0.015338764062239767, 5.0000000000000000, 90.000000000000000, 0.0 },
 612   { -0.081531504045514361, 5.0000000000000000, 95.000000000000000, 0.0 },
 613   { -0.029480196281661937, 5.0000000000000000, 100.00000000000000, 0.0 },
 614 };
 615 const double toler024 = 2.5000000000000013e-09;
 616
 617 // Test data for nu=10.000000000000000.
 618 // max(|f - f_GSL|): 3.1974423109204508e-14 at index 0
 619 // max(|f - f_GSL| / |f_GSL|): 2.7474477272995600e-12
 620 // mean(f - f_GSL): -1.4525707026091795e-15
 621 // variance(f - f_GSL): 1.6326443279890062e-30
 622 // stddev(f - f_GSL): 1.2777497125763739e-15
 623 const testcase_cyl_neumann<double>
 624 data025[20] =
 625 {
 626   { -25.129110095610095, 10.000000000000000, 5.0000000000000000, 0.0 },
 627   { -0.35981415218340279, 10.000000000000000, 10.000000000000000, 0.0 },
 628   { 0.21997141360195577, 10.000000000000000, 15.000000000000000, 0.0 },
 629   { -0.043894653515658105, 10.000000000000000, 20.000000000000000, 0.0 },
 630   { -0.14871839049980651, 10.000000000000000, 25.000000000000000, 0.0 },
 631   { 0.075056702122397012, 10.000000000000000, 30.000000000000000, 0.0 },
 632   { 0.12222473135000546, 10.000000000000000, 35.000000000000000, 0.0 },
 633   { -0.046723877232677985, 10.000000000000000, 40.000000000000000, 0.0 },
 634   { -0.11739339009322181, 10.000000000000000, 45.000000000000000, 0.0 },
 635   { 0.0057238971820535930, 10.000000000000000, 50.000000000000000, 0.0 },
 636   { 0.10733910125831631, 10.000000000000000, 55.000000000000000, 0.0 },
 637   { 0.036290350559545478, 10.000000000000000, 60.000000000000000, 0.0 },
 638   { -0.083239127691715667, 10.000000000000000, 65.000000000000000, 0.0 },
 639   { -0.069639384138314858, 10.000000000000000, 70.000000000000000, 0.0 },
 640   { 0.045798335061325066, 10.000000000000000, 75.000000000000000, 0.0 },
 641   { 0.086269195064844456, 10.000000000000000, 80.000000000000000, 0.0 },
 642   { -0.0018234674126248740, 10.000000000000000, 85.000000000000000, 0.0 },
 643   { -0.082067762371231284, 10.000000000000000, 90.000000000000000, 0.0 },
 644   { -0.038798074754578089, 10.000000000000000, 95.000000000000000, 0.0 },
 645   { 0.058331574236414913, 10.000000000000000, 100.00000000000000, 0.0 },
 646 };
 647 const double toler025 = 2.5000000000000017e-10;
 648
 649 // Test data for nu=20.000000000000000.
 650 // max(|f - f_GSL|): 1.0728836059570312e-06 at index 0
 651 // max(|f - f_GSL| / |f_GSL|): 1.7026122670117101e-12
 652 // mean(f - f_GSL): -5.3644294743674170e-08
 653 // variance(f - f_GSL): 1.5942991469572787e-16
 654 // stddev(f - f_GSL): 1.2626555931675426e-08
 655 const testcase_cyl_neumann<double>
 656 data026[20] =
 657 {
 658   { -593396529.69143200, 20.000000000000000, 5.0000000000000000, 0.0 },
 659   { -1597.4838482696259, 20.000000000000000, 10.000000000000000, 0.0 },
 660   { -3.3087330924737621, 20.000000000000000, 15.000000000000000, 0.0 },
 661   { -0.28548945860020319, 20.000000000000000, 20.000000000000000, 0.0 },
 662   { 0.19804074776289243, 20.000000000000000, 25.000000000000000, 0.0 },
 663   { -0.16848153948742683, 20.000000000000000, 30.000000000000000, 0.0 },
 664   { 0.10102784152594022, 20.000000000000000, 35.000000000000000, 0.0 },
 665   { 0.045161820565805755, 20.000000000000000, 40.000000000000000, 0.0 },
 666   { -0.12556489308015448, 20.000000000000000, 45.000000000000000, 0.0 },
 667   { 0.016442633948115834, 20.000000000000000, 50.000000000000000, 0.0 },
 668   { 0.10853448778255181, 20.000000000000000, 55.000000000000000, 0.0 },
 669   { -0.026721408520664701, 20.000000000000000, 60.000000000000000, 0.0 },
 670   { -0.098780425256324175, 20.000000000000000, 65.000000000000000, 0.0 },
 671   { 0.016201957786018233, 20.000000000000000, 70.000000000000000, 0.0 },
 672   { 0.093591198265063721, 20.000000000000000, 75.000000000000000, 0.0 },
 673   { 0.0040484400737296200, 20.000000000000000, 80.000000000000000, 0.0 },
 674   { -0.086314929459920531, 20.000000000000000, 85.000000000000000, 0.0 },
 675   { -0.028274110097231530, 20.000000000000000, 90.000000000000000, 0.0 },
 676   { 0.072349520791638741, 20.000000000000000, 95.000000000000000, 0.0 },
 677   { 0.051247973076188474, 20.000000000000000, 100.00000000000000, 0.0 },
 678 };
 679 const double toler026 = 1.0000000000000006e-10;
 680
 681 // Test data for nu=50.000000000000000.
 682 // max(|f - f_GSL|): 1.0522490333925732e+28 at index 0
 683 // max(|f - f_GSL| / |f_GSL|): 2.6670435417133106e-12
 684 // mean(f - f_GSL): -5.2612451669628722e+26
 685 // variance(f - f_GSL): inf
 686 // stddev(f - f_GSL): inf
 687 const testcase_cyl_neumann<double>
 688 data027[20] =
 689 {
 690   { -2.7888370175838930e+42, 50.000000000000000, 5.0000000000000000, 0.0 },
 691   { -3.6410665018007421e+27, 50.000000000000000, 10.000000000000000, 0.0 },
 692   { -1.0929732912175415e+19, 50.000000000000000, 15.000000000000000, 0.0 },
 693   { -15606426801663.734, 50.000000000000000, 20.000000000000000, 0.0 },
 694   { -753573251.44662738, 50.000000000000000, 25.000000000000000, 0.0 },
 695   { -386759.32602734759, 50.000000000000000, 30.000000000000000, 0.0 },
 696   { -1172.8690492895323, 50.000000000000000, 35.000000000000000, 0.0 },
 697   { -15.615608873419944, 50.000000000000000, 40.000000000000000, 0.0 },
 698   { -0.87058346204176895, 50.000000000000000, 45.000000000000000, 0.0 },
 699   { -0.21031655464397747, 50.000000000000000, 50.000000000000000, 0.0 },
 700   { 0.093048240412999389, 50.000000000000000, 55.000000000000000, 0.0 },
 701   { 0.0086417699626744754, 50.000000000000000, 60.000000000000000, 0.0 },
 702   { -0.025019788459222037, 50.000000000000000, 65.000000000000000, 0.0 },
 703   { -0.0014815155191909152, 50.000000000000000, 70.000000000000000, 0.0 },
 704   { 0.050335774732164121, 50.000000000000000, 75.000000000000000, 0.0 },
 705   { -0.092924250967987232, 50.000000000000000, 80.000000000000000, 0.0 },
 706   { 0.087332463030205698, 50.000000000000000, 85.000000000000000, 0.0 },
 707   { -0.016164237701651860, 50.000000000000000, 90.000000000000000, 0.0 },
 708   { -0.068897613820457934, 50.000000000000000, 95.000000000000000, 0.0 },
 709   { 0.076505263944803045, 50.000000000000000, 100.00000000000000, 0.0 },
 710 };
 711 const double toler027 = 2.5000000000000017e-10;
 712
 713 // Test data for nu=100.00000000000000.
 714 // max(|f - f_GSL|): 6.3342780989716025e+102 at index 0
 715 // max(|f - f_GSL| / |f_GSL|): 1.2524955818061054e-13
 716 // mean(f - f_GSL): -3.1671390494858015e+101
 717 // variance(f - f_GSL): inf
 718 // stddev(f - f_GSL): inf
 719 const testcase_cyl_neumann<double>
 720 data028[20] =
 721 {
 722   { -5.0848639160196196e+115, 100.00000000000000, 5.0000000000000000, 0.0 },
 723   { -4.8491482711800252e+85, 100.00000000000000, 10.000000000000000, 0.0 },
 724   { -1.6375955323195320e+68, 100.00000000000000, 15.000000000000000, 0.0 },
 725   { -8.2002648144679115e+55, 100.00000000000000, 20.000000000000000, 0.0 },
 726   { -2.9712216432562368e+46, 100.00000000000000, 25.000000000000000, 0.0 },
 727   { -7.2875284708240751e+38, 100.00000000000000, 30.000000000000000, 0.0 },
 728   { -3.4251079902107980e+32, 100.00000000000000, 35.000000000000000, 0.0 },
 729   { -1.4552439438102214e+27, 100.00000000000000, 40.000000000000000, 0.0 },
 730   { -3.4506612476220073e+22, 100.00000000000000, 45.000000000000000, 0.0 },
 731   { -3.2938001882025477e+18, 100.00000000000000, 50.000000000000000, 0.0 },
 732   { -1005686182055520.4, 100.00000000000000, 55.000000000000000, 0.0 },
 733   { -831892881402.09033, 100.00000000000000, 60.000000000000000, 0.0 },
 734   { -1650863778.0598392, 100.00000000000000, 65.000000000000000, 0.0 },
 735   { -7192614.1976097794, 100.00000000000000, 70.000000000000000, 0.0 },
 736   { -64639.072261231595, 100.00000000000000, 75.000000000000000, 0.0 },
 737   { -1152.5905185698466, 100.00000000000000, 80.000000000000000, 0.0 },
 738   { -40.250761402101489, 100.00000000000000, 85.000000000000000, 0.0 },
 739   { -2.8307771387185294, 100.00000000000000, 90.000000000000000, 0.0 },
 740   { -0.45762200495904848, 100.00000000000000, 95.000000000000000, 0.0 },
 741   { -0.16692141141757652, 100.00000000000000, 100.00000000000000, 0.0 },
 742 };
 743 const double toler028 = 1.0000000000000006e-11;
 744
 745 template<typename Ret, unsigned int Num>
 746   void
 747   test(const testcase_cyl_neumann<Ret> (&data)[Num], Ret toler)
 748   {
 749     bool test __attribute__((unused)) = true;
 750     const Ret eps = std::numeric_limits<Ret>::epsilon();
 751     Ret max_abs_diff = -Ret(1);
 752     Ret max_abs_frac = -Ret(1);
 753     unsigned int num_datum = Num;
 754     for (unsigned int i = 0; i < num_datum; ++i)
 755       {
 756         const Ret f = std::tr1::cyl_neumann(data[i].nu, data[i].x);
 757         const Ret f0 = data[i].f0;
 758         const Ret diff = f - f0;
 759         if (std::abs(diff) > max_abs_diff)
 760           max_abs_diff = std::abs(diff);
 761         if (std::abs(f0) > Ret(10) * eps
 762          && std::abs(f) > Ret(10) * eps)
 763           {
 764             const Ret frac = diff / f0;
 765             if (std::abs(frac) > max_abs_frac)
 766               max_abs_frac = std::abs(frac);
 767           }
 768       }
 769     VERIFY(max_abs_frac < toler);
 770   }
 771
 772 int
 773 main()
 774 {
 775   test(data007, toler007);
 776   test(data008, toler008);
 777   test(data009, toler009);
 778   test(data010, toler010);
 779   test(data011, toler011);
 780   test(data012, toler012);
 781   test(data013, toler013);
 782   test(data014, toler014);
 783   test(data015, toler015);
 784   test(data016, toler016);
 785   test(data017, toler017);
 786   test(data018, toler018);
 787   test(data019, toler019);
 788   test(data020, toler020);
 789   test(data021, toler021);
 790   test(data022, toler022);
 791   test(data023, toler023);
 792   test(data024, toler024);
 793   test(data025, toler025);
 794   test(data026, toler026);
 795   test(data027, toler027);
 796   test(data028, toler028);
 797   return 0;
 798 }