// 2007-02-04  Edward Smith-Rowland <3dw4rd@verizon.net>
//
// Copyright (C) 2007-2017 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING3.  If not see
// <http://www.gnu.org/licenses/>.

//  sph_neumann


//  Compare against values generated by the GNU Scientific Library.
//  The GSL can be found on the web: http://www.gnu.org/software/gsl/

#include <tr1/cmath>
#if defined(__TEST_DEBUG)
#include <iostream>
#define VERIFY(A) \
if (!(A)) \
  { \
    std::cout << "line " << __LINE__ \
      << "  max_abs_frac = " << max_abs_frac \
      << std::endl; \
  }
#else
#include <testsuite_hooks.h>
#endif
#include "../testcase.h"


// Test data for n=0.
testcase_sph_neumann<double> data001[] = {
  { -3.8756496868425789, 0, 0.25000000000000000 },
  { -1.7551651237807455, 0, 0.50000000000000000 },
  { -0.97558515849842786, 0, 0.75000000000000000 },
  { -0.54030230586813977, 0, 1.0000000000000000 },
  { -0.25225788991621495, 0, 1.2500000000000000 },
  { -0.047158134445135273, 0, 1.5000000000000000 },
  { 0.10185488894256690, 0, 1.7500000000000000 },
  { 0.20807341827357120, 0, 2.0000000000000000 },
  { 0.27918827676566177, 0, 2.2500000000000000 },
  { 0.32045744621877348, 0, 2.5000000000000000 },
  { 0.33610995586635040, 0, 2.7500000000000000 },
  { 0.32999749886681512, 0, 3.0000000000000000 },
  { 0.30588605417862963, 0, 3.2500000000000000 },
  { 0.26755905351165610, 0, 3.5000000000000000 },
  { 0.21881582862388288, 0, 3.7500000000000000 },
  { 0.16341090521590299, 0, 4.0000000000000000 },
  { 0.10496176233265714, 0, 4.2500000000000000 },
  { 0.046843510984617719, 0, 4.5000000000000000 },
  { -0.0079162427132582220, 0, 4.7500000000000000 },
  { -0.056732437092645263, 0, 5.0000000000000000 },
};

// Test function for n=0.
template<typename Tp>
  void
  test001()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data001)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data001[i].n), Tp(data001[i].x));
	const Tp f0 = data001[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  }

// Test data for n=1.
testcase_sph_neumann<double> data002[] = {
  { -16.492214584388407, 1, 0.25000000000000000 },
  { -4.4691813247698970, 1, 0.50000000000000000 },
  { -2.2096318913623492, 1, 0.75000000000000000 },
  { -1.3817732906760363, 1, 1.0000000000000000 },
  { -0.96099400741744090, 1, 1.2500000000000000 },
  { -0.69643541403279308, 1, 1.5000000000000000 },
  { -0.50407489024649721, 1, 1.7500000000000000 },
  { -0.35061200427605527, 1, 2.0000000000000000 },
  { -0.22172663116544869, 1, 2.2500000000000000 },
  { -0.11120587915407318, 1, 2.5000000000000000 },
  { -0.016564013158538646, 1, 2.7500000000000000 },
  { 0.062959163602315973, 1, 3.0000000000000000 },
  { 0.12740959652576553, 1, 3.2500000000000000 },
  { 0.17666922320036457, 1, 3.5000000000000000 },
  { 0.21076723929766045, 1, 3.7500000000000000 },
  { 0.23005335013095779, 1, 4.0000000000000000 },
  { 0.23528261660264485, 1, 4.2500000000000000 },
  { 0.22763858414438104, 1, 4.5000000000000000 },
  { 0.20871085184465679, 1, 4.7500000000000000 },
  { 0.18043836751409864, 1, 5.0000000000000000 },
};

// Test function for n=1.
template<typename Tp>
  void
  test002()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data002)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data002[i].n), Tp(data002[i].x));
	const Tp f0 = data002[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  }

// Test data for n=2.
testcase_sph_neumann<double> data003[] = {
  { -194.03092532581832, 2, 0.25000000000000000 },
  { -25.059922824838637, 2, 0.50000000000000000 },
  { -7.8629424069509692, 2, 0.75000000000000000 },
  { -3.6050175661599688, 2, 1.0000000000000000 },
  { -2.0541277278856431, 2, 1.2500000000000000 },
  { -1.3457126936204509, 2, 1.5000000000000000 },
  { -0.96598327222227631, 2, 1.7500000000000000 },
  { -0.73399142468765399, 2, 2.0000000000000000 },
  { -0.57482378498626008, 2, 2.2500000000000000 },
  { -0.45390450120366133, 2, 2.5000000000000000 },
  { -0.35417978840293796, 2, 2.7500000000000000 },
  { -0.26703833526449916, 2, 3.0000000000000000 },
  { -0.18827719584715374, 2, 3.2500000000000000 },
  { -0.11612829076848646, 2, 3.5000000000000000 },
  { -0.050202037185754500, 2, 3.7500000000000000 },
  { 0.0091291073823153435, 2, 4.0000000000000000 },
  { 0.061120084680974532, 2, 4.2500000000000000 },
  { 0.10491554511163632, 2, 4.5000000000000000 },
  { 0.13973362282567303, 2, 4.7500000000000000 },
  { 0.16499545760110443, 2, 5.0000000000000000 },
};

// Test function for n=2.
template<typename Tp>
  void
  test003()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data003)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data003[i].n), Tp(data003[i].x));
	const Tp f0 = data003[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  }

// Test data for n=5.
testcase_sph_neumann<double> data004[] = {
  { -3884190.0626637731, 5, 0.25000000000000000 },
  { -61327.563166980639, 5, 0.50000000000000000 },
  { -5478.9529323190836, 5, 0.75000000000000000 },
  { -999.44034339223640, 5, 1.0000000000000000 },
  { -270.49720502942358, 5, 1.2500000000000000 },
  { -94.236110085232468, 5, 1.5000000000000000 },
  { -39.182827786584333, 5, 1.7500000000000000 },
  { -18.591445311190984, 5, 2.0000000000000000 },
  { -9.7821420203182274, 5, 2.2500000000000000 },
  { -5.5991001548063233, 5, 2.5000000000000000 },
  { -3.4400655233636823, 5, 2.7500000000000000 },
  { -2.2470233284653904, 5, 3.0000000000000000 },
  { -1.5491439945779160, 5, 3.2500000000000000 },
  { -1.1205896325654248, 5, 3.5000000000000000 },
  { -0.84592255605194844, 5, 3.7500000000000000 },
  { -0.66280126645045878, 5, 4.0000000000000000 },
  { -0.53589374436038528, 5, 4.2500000000000000 },
  { -0.44430324229090551, 5, 4.5000000000000000 },
  { -0.37520157232899892, 5, 4.7500000000000000 },
  { -0.32046504674973919, 5, 5.0000000000000000 },
};

// Test function for n=5.
template<typename Tp>
  void
  test004()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data004)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data004[i].n), Tp(data004[i].x));
	const Tp f0 = data004[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  }

// Test data for n=10.
testcase_sph_neumann<double> data005[] = {
  { -2750653598174213.5, 10, 0.25000000000000000 },
  { -1349739281107.0554, 10, 0.50000000000000000 },
  { -15733380424.953760, 10, 0.75000000000000000 },
  { -672215008.25620842, 10, 1.0000000000000000 },
  { -58607405.988679446, 10, 1.2500000000000000 },
  { -8032728.8148234813, 10, 1.5000000000000000 },
  { -1505955.5720640516, 10, 1.7500000000000000 },
  { -355414.72008543846, 10, 2.0000000000000000 },
  { -100086.80374425423, 10, 2.2500000000000000 },
  { -32423.794085334419, 10, 2.5000000000000000 },
  { -11772.863161809979, 10, 2.7500000000000000 },
  { -4699.8591888113924, 10, 3.0000000000000000 },
  { -2033.0183273853759, 10, 3.2500000000000000 },
  { -942.19075028425493, 10, 3.5000000000000000 },
  { -463.65206971202474, 10, 3.7500000000000000 },
  { -240.53552987988931, 10, 4.0000000000000000 },
  { -130.78478404631085, 10, 4.2500000000000000 },
  { -74.170665501737531, 10, 4.5000000000000000 },
  { -43.698249898184983, 10, 4.7500000000000000 },
  { -26.656114405718711, 10, 5.0000000000000000 },
};

// Test function for n=10.
template<typename Tp>
  void
  test005()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data005)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data005[i].n), Tp(data005[i].x));
	const Tp f0 = data005[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  }

// Test data for n=20.
testcase_sph_neumann<double> data006[] = {
  { -1.4077591402542251e+36, 20, 0.25000000000000000 },
  { -6.7288761838234712e+29, 20, 0.50000000000000000 },
  { -1.3544611382105945e+26, 20, 0.75000000000000000 },
  { -3.2395922185789833e+23, 20, 1.0000000000000000 },
  { -3.0096416715953060e+21, 20, 1.2500000000000000 },
  { -6.5999646851668173e+19, 20, 1.5000000000000000 },
  { -2.6193364753070735e+18, 20, 1.7500000000000000 },
  { -1.6054364928152224e+17, 20, 2.0000000000000000 },
  { -13719071872797762., 20, 2.2500000000000000 },
  { -1524247248298953.8, 20, 2.5000000000000000 },
  { -209484650509384.06, 20, 2.7500000000000000 },
  { -34327545666696.488, 20, 3.0000000000000000 },
  { -6522260876203.3174, 20, 3.2500000000000000 },
  { -1406018871897.2307, 20, 3.5000000000000000 },
  { -338025193731.78882, 20, 3.7500000000000000 },
  { -89381690326.018677, 20, 4.0000000000000000 },
  { -25701805899.474934, 20, 4.2500000000000000 },
  { -7961859734.2407761, 20, 4.5000000000000000 },
  { -2636237230.0850010, 20, 4.7500000000000000 },
  { -926795140.30575466, 20, 5.0000000000000000 },
};

// Test function for n=20.
template<typename Tp>
  void
  test006()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data006)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data006[i].n), Tp(data006[i].x));
	const Tp f0 = data006[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  }

// Test data for n=50.
testcase_sph_neumann<double> data007[] = {
  { -1.3823742808004061e+109, 50, 0.25000000000000000 },
  { -6.1447912922121694e+93, 50, 0.50000000000000000 },
  { -6.4348494908900529e+84, 50, 0.75000000000000000 },
  { -2.7391922846297569e+78, 50, 1.0000000000000000 },
  { -3.1365037573299931e+73, 50, 1.2500000000000000 },
  { -2.8821098528635756e+69, 50, 1.5000000000000000 },
  { -1.1148255024189452e+66, 50, 1.7500000000000000 },
  { -1.2350219443670970e+63, 50, 2.0000000000000000 },
  { -3.0565226939717125e+60, 50, 2.2500000000000000 },
  { -1.4262702131152733e+58, 50, 2.5000000000000000 },
  { -1.1118745474840939e+56, 50, 2.7500000000000000 },
  { -1.3243260716629126e+54, 50, 3.0000000000000000 },
  { -2.2519472094129334e+52, 50, 3.2500000000000000 },
  { -5.1861507201100364e+50, 50, 3.5000000000000000 },
  { -1.5513212909461383e+49, 50, 3.7500000000000000 },
  { -5.8276471407899822e+47, 50, 4.0000000000000000 },
  { -2.6745414086542661e+46, 50, 4.2500000000000000 },
  { -1.4657308996352322e+45, 50, 4.5000000000000000 },
  { -9.4102674366685358e+43, 50, 4.7500000000000000 },
  { -6.9641091882698388e+42, 50, 5.0000000000000000 },
};

// Test function for n=50.
template<typename Tp>
  void
  test007()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data007)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data007[i].n), Tp(data007[i].x));
	const Tp f0 = data007[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(5.0000000000000029e-12));
  }

// Test data for n=100.
testcase_sph_neumann<double> data008[] = {
  { -4.2856109460516407e+247, 100, 0.25000000000000000 },
  { -1.6911720011753781e+217, 100, 0.50000000000000000 },
  { -2.7753107402139484e+199, 100, 0.75000000000000000 },
  { -6.6830794632586774e+186, 100, 1.0000000000000000 },
  { -1.0906342369729277e+177, 100, 1.2500000000000000 },
  { -1.0993184254131119e+169, 100, 1.5000000000000000 },
  { -1.9071480498141315e+162, 100, 1.7500000000000000 },
  { -2.6559558301924957e+156, 100, 2.0000000000000000 },
  { -1.8154136926485787e+151, 100, 2.2500000000000000 },
  { -4.3527631662111383e+146, 100, 2.5000000000000000 },
  { -2.8809537014100589e+142, 100, 2.7500000000000000 },
  { -4.4102229953033134e+138, 100, 3.0000000000000000 },
  { -1.3651904154045514e+135, 100, 3.2500000000000000 },
  { -7.6980749101080730e+131, 100, 3.5000000000000000 },
  { -7.2790553499254927e+128, 100, 3.7500000000000000 },
  { -1.0796647795893970e+126, 100, 4.0000000000000000 },
  { -2.3785795774445298e+123, 100, 4.2500000000000000 },
  { -7.4391596631955861e+120, 100, 4.5000000000000000 },
  { -3.1802258278279400e+118, 100, 4.7500000000000000 },
  { -1.7997139826259740e+116, 100, 5.0000000000000000 },
};

// Test function for n=100.
template<typename Tp>
  void
  test008()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data008)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data008[i].n), Tp(data008[i].x));
	const Tp f0 = data008[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(5.0000000000000029e-12));
  }
//  sph_neumann

// Test data for n=0.
testcase_sph_neumann<double> data009[] = {
  { -0.056732437092645263, 0, 5.0000000000000000 },
  { 0.083907152907645249, 0, 10.000000000000000 },
  { 0.050645860857254747, 0, 15.000000000000000 },
  { -0.020404103090669597, 0, 20.000000000000000 },
  { -0.039648112474538942, 0, 25.000000000000000 },
  { -0.0051417149962528020, 0, 30.000000000000000 },
  { 0.025819777288328762, 0, 35.000000000000000 },
  { 0.016673451541306544, 0, 40.000000000000000 },
  { -0.011673821973727327, 0, 45.000000000000000 },
  { -0.019299320569842265, 0, 50.000000000000000 },
  { -0.00040230465930828606, 0, 55.000000000000000 },
  { 0.015873549673585938, 0, 60.000000000000000 },
  { 0.0086531361728949541, 0, 65.000000000000000 },
  { -0.0090474171869471404, 0, 70.000000000000000 },
  { -0.012290016929663325, 0, 75.000000000000000 },
  { 0.0013798405479880944, 0, 80.000000000000000 },
  { 0.011580901686988727, 0, 85.000000000000000 },
  { 0.0049785957347685574, 0, 90.000000000000000 },
  { -0.0076860374841559963, 0, 95.000000000000000 },
  { -0.0086231887228768404, 0, 100.00000000000000 },
};

// Test function for n=0.
template<typename Tp>
  void
  test009()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data009)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data009[i].n), Tp(data009[i].x));
	const Tp f0 = data009[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(5.0000000000000028e-11));
  }

// Test data for n=1.
testcase_sph_neumann<double> data010[] = {
  { 0.18043836751409864, 1, 5.0000000000000000 },
  { 0.062792826379701502, 1, 10.000000000000000 },
  { -0.039976131953324147, 1, 15.000000000000000 },
  { -0.046667467690914864, 1, 20.000000000000000 },
  { 0.0037081455049293634, 1, 25.000000000000000 },
  { 0.032762996969886965, 1, 30.000000000000000 },
  { 0.012971498479556563, 1, 35.000000000000000 },
  { -0.018210992723451058, 1, 40.000000000000000 },
  { -0.019168385477952129, 1, 45.000000000000000 },
  { 0.0048615106626817301, 1, 50.000000000000000 },
  { 0.018170052158169303, 1, 55.000000000000000 },
  { 0.0053447361795967109, 1, 60.000000000000000 },
  { -0.012587316051033977, 1, 65.000000000000000 },
  { -0.011184829982069090, 1, 70.000000000000000 },
  { 0.0050065549130635621, 1, 75.000000000000000 },
  { 0.012440856180892041, 1, 80.000000000000000 },
  { 0.0022077237839479508, 1, 85.000000000000000 },
  { -0.0098779785318421041, 1, 90.000000000000000 },
  { -0.0072731342338976518, 1, 95.000000000000000 },
  { 0.0049774245238688201, 1, 100.00000000000000 },
};

// Test function for n=1.
template<typename Tp>
  void
  test010()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data010)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data010[i].n), Tp(data010[i].x));
	const Tp f0 = data010[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000014e-11));
  }

// Test data for n=2.
testcase_sph_neumann<double> data011[] = {
  { 0.16499545760110443, 2, 5.0000000000000000 },
  { -0.065069304993734783, 2, 10.000000000000000 },
  { -0.058641087247919575, 2, 15.000000000000000 },
  { 0.013403982937032370, 2, 20.000000000000000 },
  { 0.040093089935130458, 2, 25.000000000000000 },
  { 0.0084180146932414986, 2, 30.000000000000000 },
  { -0.024707934561509628, 2, 35.000000000000000 },
  { -0.018039275995565374, 2, 40.000000000000000 },
  { 0.010395929608530518, 2, 45.000000000000000 },
  { 0.019591011209603170, 2, 50.000000000000000 },
  { 0.0013933984133902479, 2, 55.000000000000000 },
  { -0.015606312864606101, 2, 60.000000000000000 },
  { -0.0092340892214042153, 2, 65.000000000000000 },
  { 0.0085680673305727519, 2, 70.000000000000000 },
  { 0.012490279126185866, 2, 75.000000000000000 },
  { -0.00091330844120464274, 2, 80.000000000000000 },
  { -0.011502982024025860, 2, 85.000000000000000 },
  { -0.0053078616858299611, 2, 90.000000000000000 },
  { 0.0074563595609802797, 2, 95.000000000000000 },
  { 0.0087725114585929052, 2, 100.00000000000000 },
};

// Test function for n=2.
template<typename Tp>
  void
  test011()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data011)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data011[i].n), Tp(data011[i].x));
	const Tp f0 = data011[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(5.0000000000000028e-11));
  }

// Test data for n=5.
testcase_sph_neumann<double> data012[] = {
  { -0.32046504674973919, 5, 5.0000000000000000 },
  { 0.093833541678691818, 5, 10.000000000000000 },
  { 0.020475698281859061, 5, 15.000000000000000 },
  { -0.048172347757372780, 5, 20.000000000000000 },
  { -0.018309489232548347, 5, 25.000000000000000 },
  { 0.026639390496569996, 5, 30.000000000000000 },
  { 0.022006038985576210, 5, 35.000000000000000 },
  { -0.011268975348057965, 5, 40.000000000000000 },
  { -0.021770388372274858, 5, 45.000000000000000 },
  { -0.00069711319645853701, 5, 50.000000000000000 },
  { 0.017439589450220901, 5, 55.000000000000000 },
  { 0.0088699170919343089, 5, 60.000000000000000 },
  { -0.010421334444951861, 5, 65.000000000000000 },
  { -0.012746769858008553, 5, 70.000000000000000 },
  { 0.0026282888028967737, 5, 75.000000000000000 },
  { 0.012477658581324189, 5, 80.000000000000000 },
  { 0.0040771816818182642, 5, 85.000000000000000 },
  { -0.0089777759570579818, 5, 90.000000000000000 },
  { -0.0083184557896676149, 5, 95.000000000000000 },
  { 0.0037206784862748965, 5, 100.00000000000000 },
};

// Test function for n=5.
template<typename Tp>
  void
  test012()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data012)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data012[i].n), Tp(data012[i].x));
	const Tp f0 = data012[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(5.0000000000000028e-11));
  }

// Test data for n=10.
testcase_sph_neumann<double> data013[] = {
  { -26.656114405718711, 10, 5.0000000000000000 },
  { -0.17245367208805784, 10, 10.000000000000000 },
  { 0.078461689849642580, 10, 15.000000000000000 },
  { -0.036843410496289961, 10, 20.000000000000000 },
  { -0.021158339301097475, 10, 25.000000000000000 },
  { 0.031219591064754939, 10, 30.000000000000000 },
  { 0.012840593422414807, 10, 35.000000000000000 },
  { -0.021803068636888072, 10, 40.000000000000000 },
  { -0.014071636804469044, 10, 45.000000000000000 },
  { 0.013524687511158758, 10, 50.000000000000000 },
  { 0.015684932653180595, 10, 55.000000000000000 },
  { -0.0056356895567262122, 10, 60.000000000000000 },
  { -0.015364490270315362, 10, 65.000000000000000 },
  { -0.0014525575672261295, 10, 70.000000000000000 },
  { 0.012648951699549433, 10, 75.000000000000000 },
  { 0.0068571608061120367, 10, 80.000000000000000 },
  { -0.0080151152941401460, 10, 85.000000000000000 },
  { -0.0098139742219019149, 10, 90.000000000000000 },
  { 0.0025002854072314951, 10, 95.000000000000000 },
  { 0.010025777373636155, 10, 100.00000000000000 },
};

// Test function for n=10.
template<typename Tp>
  void
  test013()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data013)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data013[i].n), Tp(data013[i].x));
	const Tp f0 = data013[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(5.0000000000000028e-11));
  }

// Test data for n=20.
testcase_sph_neumann<double> data014[] = {
  { -926795140.30575466, 20, 5.0000000000000000 },
  { -1211.2106053526036, 20, 10.000000000000000 },
  { -1.5559965765652175, 20, 15.000000000000000 },
  { -0.093401132250914398, 20, 20.000000000000000 },
  { 0.044031985675276462, 20, 25.000000000000000 },
  { -0.036078033606613907, 20, 30.000000000000000 },
  { 0.029828405631319645, 20, 35.000000000000000 },
  { -0.0048414810986760759, 20, 40.000000000000000 },
  { -0.020504694681516944, 20, 45.000000000000000 },
  { 0.013759531302541216, 20, 50.000000000000000 },
  { 0.012783038861734196, 20, 55.000000000000000 },
  { -0.013117009421906418, 20, 60.000000000000000 },
  { -0.010338106075674407, 20, 65.000000000000000 },
  { 0.010538610814111244, 20, 70.000000000000000 },
  { 0.010200029094273744, 20, 75.000000000000000 },
  { -0.0073123450945617122, 20, 80.000000000000000 },
  { -0.010581510354950906, 20, 85.000000000000000 },
  { 0.0036866374015298723, 20, 90.000000000000000 },
  { 0.010498384318338270, 20, 95.000000000000000 },
  { 5.6317293788334978e-05, 20, 100.00000000000000 },
};

// Test function for n=20.
template<typename Tp>
  void
  test014()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data014)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data014[i].n), Tp(data014[i].x));
	const Tp f0 = data014[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(1.0000000000000007e-09));
  }

// Test data for n=50.
testcase_sph_neumann<double> data015[] = {
  { -6.9641091882698388e+42, 50, 5.0000000000000000 },
  { -4.5282272723512023e+27, 50, 10.000000000000000 },
  { -9.0004902645887037e+18, 50, 15.000000000000000 },
  { -9542541667002.5117, 50, 20.000000000000000 },
  { -363518140.71026671, 50, 25.000000000000000 },
  { -152551.57233157745, 50, 30.000000000000000 },
  { -386.26599186208625, 50, 35.000000000000000 },
  { -4.3290507947291035, 50, 40.000000000000000 },
  { -0.19968460851503758, 50, 45.000000000000000 },
  { -0.041900001504607758, 50, 50.000000000000000 },
  { 0.010696040672421902, 50, 55.000000000000000 },
  { 0.0078198768555267188, 50, 60.000000000000000 },
  { -0.010088474938191242, 50, 65.000000000000000 },
  { 0.0062423671279824801, 50, 70.000000000000000 },
  { 0.0011284242794941733, 50, 75.000000000000000 },
  { -0.0093934266037485562, 50, 80.000000000000000 },
  { 0.013108079602843424, 50, 85.000000000000000 },
  { -0.0075396607225722626, 50, 90.000000000000000 },
  { -0.0042605703552836558, 50, 95.000000000000000 },
  { 0.010747822973682470, 50, 100.00000000000000 },
};

// Test function for n=50.
template<typename Tp>
  void
  test015()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data015)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data015[i].n), Tp(data015[i].x));
	const Tp f0 = data015[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000014e-11));
  }

// Test data for n=100.
testcase_sph_neumann<double> data016[] = {
  { -1.7997139826259740e+116, 100, 5.0000000000000000 },
  { -8.5732263093296268e+85, 100, 10.000000000000000 },
  { -1.9270658593711677e+68, 100, 15.000000000000000 },
  { -7.2208893582952385e+55, 100, 20.000000000000000 },
  { -2.0868752613007946e+46, 100, 25.000000000000000 },
  { -4.2496124023612646e+38, 100, 30.000000000000000 },
  { -1.7042898348910271e+32, 100, 35.000000000000000 },
  { -6.3021565260724554e+26, 100, 40.000000000000000 },
  { -1.3199917400494367e+22, 100, 45.000000000000000 },
  { -1.1256928913265988e+18, 100, 50.000000000000000 },
  { -309801083340343.25, 100, 55.000000000000000 },
  { -232585620046.64737, 100, 60.000000000000000 },
  { -421135935.93756074, 100, 65.000000000000000 },
  { -1680637.4531202621, 100, 70.000000000000000 },
  { -13868.302591128844, 100, 75.000000000000000 },
  { -227.24385709173322, 100, 80.000000000000000 },
  { -7.2807038787138731, 100, 85.000000000000000 },
  { -0.46648154448250878, 100, 90.000000000000000 },
  { -0.067270772720654556, 100, 95.000000000000000 },
  { -0.022983850491562267, 100, 100.00000000000000 },
};

// Test function for n=100.
template<typename Tp>
  void
  test016()
  {
    const Tp eps = std::numeric_limits<Tp>::epsilon();
    Tp max_abs_diff = -Tp(1);
    Tp max_abs_frac = -Tp(1);
    unsigned int num_datum = sizeof(data016)
			   / sizeof(testcase_sph_neumann<double>);
    for (unsigned int i = 0; i < num_datum; ++i)
      {
	const Tp f = std::tr1::sph_neumann(Tp(data016[i].n), Tp(data016[i].x));
	const Tp f0 = data016[i].f0;
	const Tp diff = f - f0;
	if (std::abs(diff) > max_abs_diff)
	  max_abs_diff = std::abs(diff);
	if (std::abs(f0) > Tp(10) * eps
	 && std::abs(f) > Tp(10) * eps)
	  {
	    const Tp frac = diff / f0;
	    if (std::abs(frac) > max_abs_frac)
	      max_abs_frac = std::abs(frac);
	  }
      }
    VERIFY(max_abs_frac < Tp(2.5000000000000015e-12));
  }

int
main()
{
  test001<double>();
  test002<double>();
  test003<double>();
  test004<double>();
  test005<double>();
  test006<double>();
  test007<double>();
  test008<double>();
  test009<double>();
  test010<double>();
  test011<double>();
  test012<double>();
  test013<double>();
  test014<double>();
  test015<double>();
  test016<double>();
  return 0;
}