libstdc++-v3/testsuite/special_functions/21_sph_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 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 //  sph_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 <cmath>
  26 #if defined(__TEST_DEBUG)
  27 #  include <iostream>
  28 #  define VERIFY(A) \
  29   if (!(A)) \
  30     { \
  31       std::cout << "line " << __LINE__ \
  32         << "  max_abs_frac = " << max_abs_frac \
  33         << std::endl; \
  34     }
  35 #else
  36 #  include <testsuite_hooks.h>
  37 #endif
  38 #include <specfun_testcase.h>
  39
  40
  41 // Test data for n=0.
  42 // max(|f - f_GSL|): 4.4408920985006262e-16
  43 // max(|f - f_GSL| / |f_GSL|): 4.8209634107822837e-15
  44 const testcase_sph_neumann<double>
  45 data001[20] =
  46 {
  47   { -3.8756496868425789, 0, 0.25000000000000000 },
  48   { -1.7551651237807455, 0, 0.50000000000000000 },
  49   { -0.97558515849842786, 0, 0.75000000000000000 },
  50   { -0.54030230586813977, 0, 1.0000000000000000 },
  51   { -0.25225788991621495, 0, 1.2500000000000000 },
  52   { -0.047158134445135273, 0, 1.5000000000000000 },
  53   { 0.10185488894256690, 0, 1.7500000000000000 },
  54   { 0.20807341827357120, 0, 2.0000000000000000 },
  55   { 0.27918827676566177, 0, 2.2500000000000000 },
  56   { 0.32045744621877348, 0, 2.5000000000000000 },
  57   { 0.33610995586635040, 0, 2.7500000000000000 },
  58   { 0.32999749886681512, 0, 3.0000000000000000 },
  59   { 0.30588605417862963, 0, 3.2500000000000000 },
  60   { 0.26755905351165610, 0, 3.5000000000000000 },
  61   { 0.21881582862388288, 0, 3.7500000000000000 },
  62   { 0.16341090521590299, 0, 4.0000000000000000 },
  63   { 0.10496176233265714, 0, 4.2500000000000000 },
  64   { 0.046843510984617719, 0, 4.5000000000000000 },
  65   { -0.0079162427132582220, 0, 4.7500000000000000 },
  66   { -0.056732437092645263, 0, 5.0000000000000000 },
  67 };
  68 const double toler001 = 2.5000000000000020e-13;
  69
  70 // Test data for n=1.
  71 // max(|f - f_GSL|): 3.5527136788005009e-15
  72 // max(|f - f_GSL| / |f_GSL|): 3.7472288263398607e-15
  73 const testcase_sph_neumann<double>
  74 data002[20] =
  75 {
  76   { -16.492214584388407, 1, 0.25000000000000000 },
  77   { -4.4691813247698970, 1, 0.50000000000000000 },
  78   { -2.2096318913623492, 1, 0.75000000000000000 },
  79   { -1.3817732906760363, 1, 1.0000000000000000 },
  80   { -0.96099400741744090, 1, 1.2500000000000000 },
  81   { -0.69643541403279308, 1, 1.5000000000000000 },
  82   { -0.50407489024649721, 1, 1.7500000000000000 },
  83   { -0.35061200427605527, 1, 2.0000000000000000 },
  84   { -0.22172663116544869, 1, 2.2500000000000000 },
  85   { -0.11120587915407318, 1, 2.5000000000000000 },
  86   { -0.016564013158538646, 1, 2.7500000000000000 },
  87   { 0.062959163602315973, 1, 3.0000000000000000 },
  88   { 0.12740959652576553, 1, 3.2500000000000000 },
  89   { 0.17666922320036457, 1, 3.5000000000000000 },
  90   { 0.21076723929766045, 1, 3.7500000000000000 },
  91   { 0.23005335013095779, 1, 4.0000000000000000 },
  92   { 0.23528261660264485, 1, 4.2500000000000000 },
  93   { 0.22763858414438104, 1, 4.5000000000000000 },
  94   { 0.20871085184465679, 1, 4.7500000000000000 },
  95   { 0.18043836751409864, 1, 5.0000000000000000 },
  96 };
  97 const double toler002 = 2.5000000000000020e-13;
  98
  99 // Test data for n=2.
 100 // max(|f - f_GSL|): 5.6843418860808015e-14
 101 // max(|f - f_GSL| / |f_GSL|): 2.4702749396271158e-15
 102 const testcase_sph_neumann<double>
 103 data003[20] =
 104 {
 105   { -194.03092532581832, 2, 0.25000000000000000 },
 106   { -25.059922824838637, 2, 0.50000000000000000 },
 107   { -7.8629424069509692, 2, 0.75000000000000000 },
 108   { -3.6050175661599688, 2, 1.0000000000000000 },
 109   { -2.0541277278856431, 2, 1.2500000000000000 },
 110   { -1.3457126936204509, 2, 1.5000000000000000 },
 111   { -0.96598327222227631, 2, 1.7500000000000000 },
 112   { -0.73399142468765399, 2, 2.0000000000000000 },
 113   { -0.57482378498626008, 2, 2.2500000000000000 },
 114   { -0.45390450120366133, 2, 2.5000000000000000 },
 115   { -0.35417978840293796, 2, 2.7500000000000000 },
 116   { -0.26703833526449916, 2, 3.0000000000000000 },
 117   { -0.18827719584715374, 2, 3.2500000000000000 },
 118   { -0.11612829076848646, 2, 3.5000000000000000 },
 119   { -0.050202037185754500, 2, 3.7500000000000000 },
 120   { 0.0091291073823153435, 2, 4.0000000000000000 },
 121   { 0.061120084680974532, 2, 4.2500000000000000 },
 122   { 0.10491554511163632, 2, 4.5000000000000000 },
 123   { 0.13973362282567303, 2, 4.7500000000000000 },
 124   { 0.16499545760110443, 2, 5.0000000000000000 },
 125 };
 126 const double toler003 = 2.5000000000000020e-13;
 127
 128 // Test data for n=5.
 129 // max(|f - f_GSL|): 4.6566128730773926e-10
 130 // max(|f - f_GSL| / |f_GSL|): 6.3451511503162099e-16
 131 const testcase_sph_neumann<double>
 132 data004[20] =
 133 {
 134   { -3884190.0626637731, 5, 0.25000000000000000 },
 135   { -61327.563166980639, 5, 0.50000000000000000 },
 136   { -5478.9529323190836, 5, 0.75000000000000000 },
 137   { -999.44034339223640, 5, 1.0000000000000000 },
 138   { -270.49720502942358, 5, 1.2500000000000000 },
 139   { -94.236110085232468, 5, 1.5000000000000000 },
 140   { -39.182827786584333, 5, 1.7500000000000000 },
 141   { -18.591445311190984, 5, 2.0000000000000000 },
 142   { -9.7821420203182274, 5, 2.2500000000000000 },
 143   { -5.5991001548063233, 5, 2.5000000000000000 },
 144   { -3.4400655233636823, 5, 2.7500000000000000 },
 145   { -2.2470233284653904, 5, 3.0000000000000000 },
 146   { -1.5491439945779160, 5, 3.2500000000000000 },
 147   { -1.1205896325654248, 5, 3.5000000000000000 },
 148   { -0.84592255605194844, 5, 3.7500000000000000 },
 149   { -0.66280126645045878, 5, 4.0000000000000000 },
 150   { -0.53589374436038528, 5, 4.2500000000000000 },
 151   { -0.44430324229090551, 5, 4.5000000000000000 },
 152   { -0.37520157232899892, 5, 4.7500000000000000 },
 153   { -0.32046504674973919, 5, 5.0000000000000000 },
 154 };
 155 const double toler004 = 2.5000000000000020e-13;
 156
 157 // Test data for n=10.
 158 // max(|f - f_GSL|): 0.50000000000000000
 159 // max(|f - f_GSL| / |f_GSL|): 1.2712694703401436e-15
 160 const testcase_sph_neumann<double>
 161 data005[20] =
 162 {
 163   { -2750653598174213.5, 10, 0.25000000000000000 },
 164   { -1349739281107.0554, 10, 0.50000000000000000 },
 165   { -15733380424.953760, 10, 0.75000000000000000 },
 166   { -672215008.25620842, 10, 1.0000000000000000 },
 167   { -58607405.988679446, 10, 1.2500000000000000 },
 168   { -8032728.8148234813, 10, 1.5000000000000000 },
 169   { -1505955.5720640516, 10, 1.7500000000000000 },
 170   { -355414.72008543846, 10, 2.0000000000000000 },
 171   { -100086.80374425423, 10, 2.2500000000000000 },
 172   { -32423.794085334419, 10, 2.5000000000000000 },
 173   { -11772.863161809979, 10, 2.7500000000000000 },
 174   { -4699.8591888113924, 10, 3.0000000000000000 },
 175   { -2033.0183273853759, 10, 3.2500000000000000 },
 176   { -942.19075028425493, 10, 3.5000000000000000 },
 177   { -463.65206971202474, 10, 3.7500000000000000 },
 178   { -240.53552987988931, 10, 4.0000000000000000 },
 179   { -130.78478404631085, 10, 4.2500000000000000 },
 180   { -74.170665501737531, 10, 4.5000000000000000 },
 181   { -43.698249898184983, 10, 4.7500000000000000 },
 182   { -26.656114405718711, 10, 5.0000000000000000 },
 183 };
 184 const double toler005 = 2.5000000000000020e-13;
 185
 186 // Test data for n=20.
 187 // max(|f - f_GSL|): 2.9514790517935283e+20
 188 // max(|f - f_GSL| / |f_GSL|): 1.9896573344672978e-15
 189 const testcase_sph_neumann<double>
 190 data006[20] =
 191 {
 192   { -1.4077591402542251e+36, 20, 0.25000000000000000 },
 193   { -6.7288761838234712e+29, 20, 0.50000000000000000 },
 194   { -1.3544611382105945e+26, 20, 0.75000000000000000 },
 195   { -3.2395922185789833e+23, 20, 1.0000000000000000 },
 196   { -3.0096416715953060e+21, 20, 1.2500000000000000 },
 197   { -6.5999646851668173e+19, 20, 1.5000000000000000 },
 198   { -2.6193364753070735e+18, 20, 1.7500000000000000 },
 199   { -1.6054364928152224e+17, 20, 2.0000000000000000 },
 200   { -13719071872797762., 20, 2.2500000000000000 },
 201   { -1524247248298953.8, 20, 2.5000000000000000 },
 202   { -209484650509384.06, 20, 2.7500000000000000 },
 203   { -34327545666696.488, 20, 3.0000000000000000 },
 204   { -6522260876203.3174, 20, 3.2500000000000000 },
 205   { -1406018871897.2307, 20, 3.5000000000000000 },
 206   { -338025193731.78882, 20, 3.7500000000000000 },
 207   { -89381690326.018677, 20, 4.0000000000000000 },
 208   { -25701805899.474934, 20, 4.2500000000000000 },
 209   { -7961859734.2407761, 20, 4.5000000000000000 },
 210   { -2636237230.0850010, 20, 4.7500000000000000 },
 211   { -926795140.30575466, 20, 5.0000000000000000 },
 212 };
 213 const double toler006 = 2.5000000000000020e-13;
 214
 215 // Test data for n=50.
 216 // max(|f - f_GSL|): 2.0859248397665138e+93
 217 // max(|f - f_GSL| / |f_GSL|): 7.3237119407125301e-14
 218 const testcase_sph_neumann<double>
 219 data007[20] =
 220 {
 221   { -1.3823742808004061e+109, 50, 0.25000000000000000 },
 222   { -6.1447912922121694e+93, 50, 0.50000000000000000 },
 223   { -6.4348494908900529e+84, 50, 0.75000000000000000 },
 224   { -2.7391922846297569e+78, 50, 1.0000000000000000 },
 225   { -3.1365037573299931e+73, 50, 1.2500000000000000 },
 226   { -2.8821098528635756e+69, 50, 1.5000000000000000 },
 227   { -1.1148255024189452e+66, 50, 1.7500000000000000 },
 228   { -1.2350219443670970e+63, 50, 2.0000000000000000 },
 229   { -3.0565226939717125e+60, 50, 2.2500000000000000 },
 230   { -1.4262702131152733e+58, 50, 2.5000000000000000 },
 231   { -1.1118745474840939e+56, 50, 2.7500000000000000 },
 232   { -1.3243260716629126e+54, 50, 3.0000000000000000 },
 233   { -2.2519472094129334e+52, 50, 3.2500000000000000 },
 234   { -5.1861507201100364e+50, 50, 3.5000000000000000 },
 235   { -1.5513212909461383e+49, 50, 3.7500000000000000 },
 236   { -5.8276471407899822e+47, 50, 4.0000000000000000 },
 237   { -2.6745414086542661e+46, 50, 4.2500000000000000 },
 238   { -1.4657308996352322e+45, 50, 4.5000000000000000 },
 239   { -9.4102674366685358e+43, 50, 4.7500000000000000 },
 240   { -6.9641091882698388e+42, 50, 5.0000000000000000 },
 241 };
 242 const double toler007 = 5.0000000000000029e-12;
 243
 244 // Test data for n=100.
 245 // max(|f - f_GSL|): 2.4840289476811343e+232
 246 // max(|f - f_GSL| / |f_GSL|): 9.0555289224453335e-14
 247 const testcase_sph_neumann<double>
 248 data008[20] =
 249 {
 250   { -4.2856109460516407e+247, 100, 0.25000000000000000 },
 251   { -1.6911720011753781e+217, 100, 0.50000000000000000 },
 252   { -2.7753107402139484e+199, 100, 0.75000000000000000 },
 253   { -6.6830794632586774e+186, 100, 1.0000000000000000 },
 254   { -1.0906342369729277e+177, 100, 1.2500000000000000 },
 255   { -1.0993184254131119e+169, 100, 1.5000000000000000 },
 256   { -1.9071480498141315e+162, 100, 1.7500000000000000 },
 257   { -2.6559558301924957e+156, 100, 2.0000000000000000 },
 258   { -1.8154136926485787e+151, 100, 2.2500000000000000 },
 259   { -4.3527631662111383e+146, 100, 2.5000000000000000 },
 260   { -2.8809537014100589e+142, 100, 2.7500000000000000 },
 261   { -4.4102229953033134e+138, 100, 3.0000000000000000 },
 262   { -1.3651904154045514e+135, 100, 3.2500000000000000 },
 263   { -7.6980749101080730e+131, 100, 3.5000000000000000 },
 264   { -7.2790553499254927e+128, 100, 3.7500000000000000 },
 265   { -1.0796647795893970e+126, 100, 4.0000000000000000 },
 266   { -2.3785795774445298e+123, 100, 4.2500000000000000 },
 267   { -7.4391596631955861e+120, 100, 4.5000000000000000 },
 268   { -3.1802258278279400e+118, 100, 4.7500000000000000 },
 269   { -1.7997139826259740e+116, 100, 5.0000000000000000 },
 270 };
 271 const double toler008 = 5.0000000000000029e-12;
 272 //  sph_neumann
 273
 274 // Test data for n=0.
 275 // max(|f - f_GSL|): 1.0165479569224090e-15
 276 // max(|f - f_GSL| / |f_GSL|): 5.9073915926662418e-13
 277 const testcase_sph_neumann<double>
 278 data009[20] =
 279 {
 280   { -0.056732437092645263, 0, 5.0000000000000000 },
 281   { 0.083907152907645249, 0, 10.000000000000000 },
 282   { 0.050645860857254747, 0, 15.000000000000000 },
 283   { -0.020404103090669597, 0, 20.000000000000000 },
 284   { -0.039648112474538942, 0, 25.000000000000000 },
 285   { -0.0051417149962528020, 0, 30.000000000000000 },
 286   { 0.025819777288328762, 0, 35.000000000000000 },
 287   { 0.016673451541306544, 0, 40.000000000000000 },
 288   { -0.011673821973727327, 0, 45.000000000000000 },
 289   { -0.019299320569842265, 0, 50.000000000000000 },
 290   { -0.00040230465930828606, 0, 55.000000000000000 },
 291   { 0.015873549673585938, 0, 60.000000000000000 },
 292   { 0.0086531361728949541, 0, 65.000000000000000 },
 293   { -0.0090474171869471404, 0, 70.000000000000000 },
 294   { -0.012290016929663325, 0, 75.000000000000000 },
 295   { 0.0013798405479880944, 0, 80.000000000000000 },
 296   { 0.011580901686988727, 0, 85.000000000000000 },
 297   { 0.0049785957347685574, 0, 90.000000000000000 },
 298   { -0.0076860374841559963, 0, 95.000000000000000 },
 299   { -0.0086231887228768404, 0, 100.00000000000000 },
 300 };
 301 const double toler009 = 5.0000000000000028e-11;
 302
 303 // Test data for n=1.
 304 // max(|f - f_GSL|): 1.0529771499179219e-15
 305 // max(|f - f_GSL| / |f_GSL|): 3.5182047773188613e-13
 306 const testcase_sph_neumann<double>
 307 data010[20] =
 308 {
 309   { 0.18043836751409864, 1, 5.0000000000000000 },
 310   { 0.062792826379701502, 1, 10.000000000000000 },
 311   { -0.039976131953324147, 1, 15.000000000000000 },
 312   { -0.046667467690914864, 1, 20.000000000000000 },
 313   { 0.0037081455049293634, 1, 25.000000000000000 },
 314   { 0.032762996969886965, 1, 30.000000000000000 },
 315   { 0.012971498479556563, 1, 35.000000000000000 },
 316   { -0.018210992723451058, 1, 40.000000000000000 },
 317   { -0.019168385477952129, 1, 45.000000000000000 },
 318   { 0.0048615106626817301, 1, 50.000000000000000 },
 319   { 0.018170052158169303, 1, 55.000000000000000 },
 320   { 0.0053447361795967109, 1, 60.000000000000000 },
 321   { -0.012587316051033977, 1, 65.000000000000000 },
 322   { -0.011184829982069090, 1, 70.000000000000000 },
 323   { 0.0050065549130635621, 1, 75.000000000000000 },
 324   { 0.012440856180892041, 1, 80.000000000000000 },
 325   { 0.0022077237839479508, 1, 85.000000000000000 },
 326   { -0.0098779785318421041, 1, 90.000000000000000 },
 327   { -0.0072731342338976518, 1, 95.000000000000000 },
 328   { 0.0049774245238688201, 1, 100.00000000000000 },
 329 };
 330 const double toler010 = 2.5000000000000014e-11;
 331
 332 // Test data for n=2.
 333 // max(|f - f_GSL|): 9.7144514654701197e-16
 334 // max(|f - f_GSL| / |f_GSL|): 8.9389761338979581e-13
 335 const testcase_sph_neumann<double>
 336 data011[20] =
 337 {
 338   { 0.16499545760110443, 2, 5.0000000000000000 },
 339   { -0.065069304993734783, 2, 10.000000000000000 },
 340   { -0.058641087247919575, 2, 15.000000000000000 },
 341   { 0.013403982937032370, 2, 20.000000000000000 },
 342   { 0.040093089935130458, 2, 25.000000000000000 },
 343   { 0.0084180146932414986, 2, 30.000000000000000 },
 344   { -0.024707934561509628, 2, 35.000000000000000 },
 345   { -0.018039275995565374, 2, 40.000000000000000 },
 346   { 0.010395929608530518, 2, 45.000000000000000 },
 347   { 0.019591011209603170, 2, 50.000000000000000 },
 348   { 0.0013933984133902479, 2, 55.000000000000000 },
 349   { -0.015606312864606101, 2, 60.000000000000000 },
 350   { -0.0092340892214042153, 2, 65.000000000000000 },
 351   { 0.0085680673305727519, 2, 70.000000000000000 },
 352   { 0.012490279126185866, 2, 75.000000000000000 },
 353   { -0.00091330844120464274, 2, 80.000000000000000 },
 354   { -0.011502982024025860, 2, 85.000000000000000 },
 355   { -0.0053078616858299611, 2, 90.000000000000000 },
 356   { 0.0074563595609802797, 2, 95.000000000000000 },
 357   { 0.0087725114585929052, 2, 100.00000000000000 },
 358 };
 359 const double toler011 = 5.0000000000000028e-11;
 360
 361 // Test data for n=5.
 362 // max(|f - f_GSL|): 1.1327744298128550e-15
 363 // max(|f - f_GSL| / |f_GSL|): 6.2024335299315527e-13
 364 const testcase_sph_neumann<double>
 365 data012[20] =
 366 {
 367   { -0.32046504674973919, 5, 5.0000000000000000 },
 368   { 0.093833541678691818, 5, 10.000000000000000 },
 369   { 0.020475698281859061, 5, 15.000000000000000 },
 370   { -0.048172347757372780, 5, 20.000000000000000 },
 371   { -0.018309489232548347, 5, 25.000000000000000 },
 372   { 0.026639390496569996, 5, 30.000000000000000 },
 373   { 0.022006038985576210, 5, 35.000000000000000 },
 374   { -0.011268975348057965, 5, 40.000000000000000 },
 375   { -0.021770388372274858, 5, 45.000000000000000 },
 376   { -0.00069711319645853701, 5, 50.000000000000000 },
 377   { 0.017439589450220901, 5, 55.000000000000000 },
 378   { 0.0088699170919343089, 5, 60.000000000000000 },
 379   { -0.010421334444951861, 5, 65.000000000000000 },
 380   { -0.012746769858008553, 5, 70.000000000000000 },
 381   { 0.0026282888028967737, 5, 75.000000000000000 },
 382   { 0.012477658581324189, 5, 80.000000000000000 },
 383   { 0.0040771816818182642, 5, 85.000000000000000 },
 384   { -0.0089777759570579818, 5, 90.000000000000000 },
 385   { -0.0083184557896676149, 5, 95.000000000000000 },
 386   { 0.0037206784862748965, 5, 100.00000000000000 },
 387 };
 388 const double toler012 = 5.0000000000000028e-11;
 389
 390 // Test data for n=10.
 391 // max(|f - f_GSL|): 1.0658141036401503e-14
 392 // max(|f - f_GSL| / |f_GSL|): 7.3655649039219020e-13
 393 const testcase_sph_neumann<double>
 394 data013[20] =
 395 {
 396   { -26.656114405718711, 10, 5.0000000000000000 },
 397   { -0.17245367208805784, 10, 10.000000000000000 },
 398   { 0.078461689849642580, 10, 15.000000000000000 },
 399   { -0.036843410496289961, 10, 20.000000000000000 },
 400   { -0.021158339301097475, 10, 25.000000000000000 },
 401   { 0.031219591064754939, 10, 30.000000000000000 },
 402   { 0.012840593422414807, 10, 35.000000000000000 },
 403   { -0.021803068636888072, 10, 40.000000000000000 },
 404   { -0.014071636804469044, 10, 45.000000000000000 },
 405   { 0.013524687511158758, 10, 50.000000000000000 },
 406   { 0.015684932653180595, 10, 55.000000000000000 },
 407   { -0.0056356895567262122, 10, 60.000000000000000 },
 408   { -0.015364490270315362, 10, 65.000000000000000 },
 409   { -0.0014525575672261295, 10, 70.000000000000000 },
 410   { 0.012648951699549433, 10, 75.000000000000000 },
 411   { 0.0068571608061120367, 10, 80.000000000000000 },
 412   { -0.0080151152941401460, 10, 85.000000000000000 },
 413   { -0.0098139742219019149, 10, 90.000000000000000 },
 414   { 0.0025002854072314951, 10, 95.000000000000000 },
 415   { 0.010025777373636155, 10, 100.00000000000000 },
 416 };
 417 const double toler013 = 5.0000000000000028e-11;
 418
 419 // Test data for n=20.
 420 // max(|f - f_GSL|): 1.0728836059570312e-06
 421 // max(|f - f_GSL| / |f_GSL|): 1.0496253232407487e-11
 422 const testcase_sph_neumann<double>
 423 data014[20] =
 424 {
 425   { -926795140.30575466, 20, 5.0000000000000000 },
 426   { -1211.2106053526036, 20, 10.000000000000000 },
 427   { -1.5559965765652175, 20, 15.000000000000000 },
 428   { -0.093401132250914398, 20, 20.000000000000000 },
 429   { 0.044031985675276462, 20, 25.000000000000000 },
 430   { -0.036078033606613907, 20, 30.000000000000000 },
 431   { 0.029828405631319645, 20, 35.000000000000000 },
 432   { -0.0048414810986760759, 20, 40.000000000000000 },
 433   { -0.020504694681516944, 20, 45.000000000000000 },
 434   { 0.013759531302541216, 20, 50.000000000000000 },
 435   { 0.012783038861734196, 20, 55.000000000000000 },
 436   { -0.013117009421906418, 20, 60.000000000000000 },
 437   { -0.010338106075674407, 20, 65.000000000000000 },
 438   { 0.010538610814111244, 20, 70.000000000000000 },
 439   { 0.010200029094273744, 20, 75.000000000000000 },
 440   { -0.0073123450945617122, 20, 80.000000000000000 },
 441   { -0.010581510354950906, 20, 85.000000000000000 },
 442   { 0.0036866374015298723, 20, 90.000000000000000 },
 443   { 0.010498384318338270, 20, 95.000000000000000 },
 444   { 5.6317293788334978e-05, 20, 100.00000000000000 },
 445 };
 446 const double toler014 = 1.0000000000000007e-09;
 447
 448 // Test data for n=50.
 449 // max(|f - f_GSL|): 5.1003129618557667e+29
 450 // max(|f - f_GSL| / |f_GSL|): 4.9443320929884463e-13
 451 const testcase_sph_neumann<double>
 452 data015[20] =
 453 {
 454   { -6.9641091882698388e+42, 50, 5.0000000000000000 },
 455   { -4.5282272723512023e+27, 50, 10.000000000000000 },
 456   { -9.0004902645887037e+18, 50, 15.000000000000000 },
 457   { -9542541667002.5117, 50, 20.000000000000000 },
 458   { -363518140.71026671, 50, 25.000000000000000 },
 459   { -152551.57233157745, 50, 30.000000000000000 },
 460   { -386.26599186208625, 50, 35.000000000000000 },
 461   { -4.3290507947291035, 50, 40.000000000000000 },
 462   { -0.19968460851503758, 50, 45.000000000000000 },
 463   { -0.041900001504607758, 50, 50.000000000000000 },
 464   { 0.010696040672421902, 50, 55.000000000000000 },
 465   { 0.0078198768555267188, 50, 60.000000000000000 },
 466   { -0.010088474938191242, 50, 65.000000000000000 },
 467   { 0.0062423671279824801, 50, 70.000000000000000 },
 468   { 0.0011284242794941733, 50, 75.000000000000000 },
 469   { -0.0093934266037485562, 50, 80.000000000000000 },
 470   { 0.013108079602843424, 50, 85.000000000000000 },
 471   { -0.0075396607225722626, 50, 90.000000000000000 },
 472   { -0.0042605703552836558, 50, 95.000000000000000 },
 473   { 0.010747822973682470, 50, 100.00000000000000 },
 474 };
 475 const double toler015 = 2.5000000000000014e-11;
 476
 477 // Test data for n=100.
 478 // max(|f - f_GSL|): 3.0796490204944808e+102
 479 // max(|f - f_GSL| / |f_GSL|): 4.6209003006798690e-14
 480 const testcase_sph_neumann<double>
 481 data016[20] =
 482 {
 483   { -1.7997139826259740e+116, 100, 5.0000000000000000 },
 484   { -8.5732263093296268e+85, 100, 10.000000000000000 },
 485   { -1.9270658593711677e+68, 100, 15.000000000000000 },
 486   { -7.2208893582952385e+55, 100, 20.000000000000000 },
 487   { -2.0868752613007946e+46, 100, 25.000000000000000 },
 488   { -4.2496124023612646e+38, 100, 30.000000000000000 },
 489   { -1.7042898348910271e+32, 100, 35.000000000000000 },
 490   { -6.3021565260724554e+26, 100, 40.000000000000000 },
 491   { -1.3199917400494367e+22, 100, 45.000000000000000 },
 492   { -1.1256928913265988e+18, 100, 50.000000000000000 },
 493   { -309801083340343.25, 100, 55.000000000000000 },
 494   { -232585620046.64737, 100, 60.000000000000000 },
 495   { -421135935.93756074, 100, 65.000000000000000 },
 496   { -1680637.4531202621, 100, 70.000000000000000 },
 497   { -13868.302591128844, 100, 75.000000000000000 },
 498   { -227.24385709173322, 100, 80.000000000000000 },
 499   { -7.2807038787138731, 100, 85.000000000000000 },
 500   { -0.46648154448250878, 100, 90.000000000000000 },
 501   { -0.067270772720654556, 100, 95.000000000000000 },
 502   { -0.022983850491562267, 100, 100.00000000000000 },
 503 };
 504 const double toler016 = 2.5000000000000015e-12;
 505
 506 template<typename Tp, unsigned int Num>
 507   void
 508   test(const testcase_sph_neumann<Tp> (&data)[Num], Tp toler)
 509   {
 510     bool test __attribute__((unused)) = true;
 511     const Tp eps = std::numeric_limits<Tp>::epsilon();
 512     Tp max_abs_diff = -Tp(1);
 513     Tp max_abs_frac = -Tp(1);
 514     unsigned int num_datum = Num;
 515     for (unsigned int i = 0; i < num_datum; ++i)
 516       {
 517         const Tp f = std::sph_neumann(data[i].n, data[i].x);
 518         const Tp f0 = data[i].f0;
 519         const Tp diff = f - f0;
 520         if (std::abs(diff) > max_abs_diff)
 521           max_abs_diff = std::abs(diff);
 522         if (std::abs(f0) > Tp(10) * eps
 523          && std::abs(f) > Tp(10) * eps)
 524           {
 525             const Tp frac = diff / f0;
 526             if (std::abs(frac) > max_abs_frac)
 527               max_abs_frac = std::abs(frac);
 528           }
 529       }
 530     VERIFY(max_abs_frac < toler);
 531   }
 532
 533 int
 534 main()
 535 {
 536   test(data001, toler001);
 537   test(data002, toler002);
 538   test(data003, toler003);
 539   test(data004, toler004);
 540   test(data005, toler005);
 541   test(data006, toler006);
 542   test(data007, toler007);
 543   test(data008, toler008);
 544   test(data009, toler009);
 545   test(data010, toler010);
 546   test(data011, toler011);
 547   test(data012, toler012);
 548   test(data013, toler013);
 549   test(data014, toler014);
 550   test(data015, toler015);
 551   test(data016, toler016);
 552   return 0;
 553 }