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jeremybenn |
// 2007-02-04 Edward Smith-Rowland <3dw4rd@verizon.net>
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//
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// Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the
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// terms of the GNU General Public License as published by the
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// Free Software Foundation; either version 3, or (at your option)
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// any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License along
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// with this library; see the file COPYING3. If not see
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// <http://www.gnu.org/licenses/>.
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// ellint_3
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// Compare against values generated by the GNU Scientific Library.
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// The GSL can be found on the web: http://www.gnu.org/software/gsl/
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#include <tr1/cmath>
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#if defined(__TEST_DEBUG)
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#include <iostream>
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#define VERIFY(A) \
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if (!(A)) \
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{ \
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std::cout << "line " << __LINE__ \
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<< " max_abs_frac = " << max_abs_frac \
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<< std::endl; \
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}
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#else
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#include <testsuite_hooks.h>
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#endif
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#include "../testcase.h"
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// Test data for k=-0.90000000000000002, nu=0.0000000000000000.
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testcase_ellint_3<double> data001[] = {
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{ -0.0000000000000000, -0.90000000000000002, 0.0000000000000000,
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0.0000000000000000 },
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{ 0.17525427376115027, -0.90000000000000002, 0.0000000000000000,
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0.17453292519943295 },
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{ 0.35492464591297446, -0.90000000000000002, 0.0000000000000000,
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0.34906585039886590 },
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{ 0.54388221416157134, -0.90000000000000002, 0.0000000000000000,
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0.52359877559829882 },
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{ 0.74797400423532523, -0.90000000000000002, 0.0000000000000000,
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0.69813170079773179 },
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{ 0.97463898451966458, -0.90000000000000002, 0.0000000000000000,
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0.87266462599716477 },
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{ 1.2334463254523440, -0.90000000000000002, 0.0000000000000000,
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1.0471975511965976 },
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{ 1.5355247765594910, -0.90000000000000002, 0.0000000000000000,
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1.2217304763960306 },
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{ 1.8882928567775124, -0.90000000000000002, 0.0000000000000000,
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1.3962634015954636 },
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{ 2.2805491384227703, -0.90000000000000002, 0.0000000000000000,
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1.5707963267948966 },
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};
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// Test function for k=-0.90000000000000002, nu=0.0000000000000000.
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template <typename Tp>
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void test001()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data001)
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/ sizeof(testcase_ellint_3<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::ellint_3(Tp(data001[i].k), Tp(data001[i].nu),
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Tp(data001[i].phi));
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const Tp f0 = data001[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for k=-0.90000000000000002, nu=0.10000000000000001.
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testcase_ellint_3<double> data002[] = {
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{ -0.0000000000000000, -0.90000000000000002, 0.10000000000000001,
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0.0000000000000000 },
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{ 0.17507714233254659, -0.90000000000000002, 0.10000000000000001,
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0.17453292519943295 },
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{ 0.35350932904326521, -0.90000000000000002, 0.10000000000000001,
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0.34906585039886590 },
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{ 0.53911129989870998, -0.90000000000000002, 0.10000000000000001,
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0.52359877559829882 },
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{ 0.73666644254508429, -0.90000000000000002, 0.10000000000000001,
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0.69813170079773179 },
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{ 0.95250736612100184, -0.90000000000000002, 0.10000000000000001,
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0.87266462599716477 },
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{ 1.1950199550905594, -0.90000000000000002, 0.10000000000000001,
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1.0471975511965976 },
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{ 1.4741687286340848, -0.90000000000000002, 0.10000000000000001,
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1.2217304763960306 },
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{ 1.7968678183506059, -0.90000000000000002, 0.10000000000000001,
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1.3962634015954636 },
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{ 2.1537868513875287, -0.90000000000000002, 0.10000000000000001,
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1.5707963267948966 },
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};
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// Test function for k=-0.90000000000000002, nu=0.10000000000000001.
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template <typename Tp>
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void test002()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data002)
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/ sizeof(testcase_ellint_3<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::ellint_3(Tp(data002[i].k), Tp(data002[i].nu),
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Tp(data002[i].phi));
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const Tp f0 = data002[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for k=-0.90000000000000002, nu=0.20000000000000001.
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testcase_ellint_3<double> data003[] = {
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{ -0.0000000000000000, -0.90000000000000002, 0.20000000000000001,
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0.0000000000000000 },
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{ 0.17490065089140930, -0.90000000000000002, 0.20000000000000001,
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0.17453292519943295 },
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{ 0.35211377590661436, -0.90000000000000002, 0.20000000000000001,
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0.34906585039886590 },
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{ 0.53448220334204122, -0.90000000000000002, 0.20000000000000001,
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0.52359877559829882 },
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{ 0.72591368943179613, -0.90000000000000002, 0.20000000000000001,
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0.69813170079773179 },
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{ 0.93192539780038763, -0.90000000000000002, 0.20000000000000001,
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0.87266462599716477 },
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{ 1.1600809679692683, -0.90000000000000002, 0.20000000000000001,
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1.0471975511965976 },
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{ 1.4195407225882508, -0.90000000000000002, 0.20000000000000001,
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1.2217304763960306 },
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{ 1.7168966476424528, -0.90000000000000002, 0.20000000000000001,
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1.3962634015954636 },
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{ 2.0443194576468890, -0.90000000000000002, 0.20000000000000001,
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1.5707963267948966 },
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};
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// Test function for k=-0.90000000000000002, nu=0.20000000000000001.
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template <typename Tp>
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void test003()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data003)
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/ sizeof(testcase_ellint_3<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::ellint_3(Tp(data003[i].k), Tp(data003[i].nu),
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Tp(data003[i].phi));
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const Tp f0 = data003[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for k=-0.90000000000000002, nu=0.29999999999999999.
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testcase_ellint_3<double> data004[] = {
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{ -0.0000000000000000, -0.90000000000000002, 0.29999999999999999,
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0.0000000000000000 },
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{ 0.17472479532647534, -0.90000000000000002, 0.29999999999999999,
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0.17453292519943295 },
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{ 0.35073750187374114, -0.90000000000000002, 0.29999999999999999,
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0.34906585039886590 },
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{ 0.52998766129466979, -0.90000000000000002, 0.29999999999999999,
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0.52359877559829882 },
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{ 0.71566993548699587, -0.90000000000000002, 0.29999999999999999,
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0.69813170079773179 },
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{ 0.91271517762560195, -0.90000000000000002, 0.29999999999999999,
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0.87266462599716477 },
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{ 1.1281241199843370, -0.90000000000000002, 0.29999999999999999,
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1.0471975511965976 },
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{ 1.3704929576917448, -0.90000000000000002, 0.29999999999999999,
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1.2217304763960306 },
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{ 1.6461981511487715, -0.90000000000000002, 0.29999999999999999,
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1.3962634015954636 },
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{ 1.9486280260314426, -0.90000000000000002, 0.29999999999999999,
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1.5707963267948966 },
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};
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// Test function for k=-0.90000000000000002, nu=0.29999999999999999.
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template <typename Tp>
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void test004()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data004)
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/ sizeof(testcase_ellint_3<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::ellint_3(Tp(data004[i].k), Tp(data004[i].nu),
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Tp(data004[i].phi));
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const Tp f0 = data004[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for k=-0.90000000000000002, nu=0.40000000000000002.
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testcase_ellint_3<double> data005[] = {
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{ -0.0000000000000000, -0.90000000000000002, 0.40000000000000002,
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| 253 |
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0.0000000000000000 },
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| 254 |
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{ 0.17454957156468839, -0.90000000000000002, 0.40000000000000002,
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| 255 |
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0.17453292519943295 },
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| 256 |
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{ 0.34938003933330430, -0.90000000000000002, 0.40000000000000002,
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| 257 |
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0.34906585039886590 },
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| 258 |
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{ 0.52562093533067455, -0.90000000000000002, 0.40000000000000002,
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| 259 |
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0.52359877559829882 },
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| 260 |
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{ 0.70589461324915703, -0.90000000000000002, 0.40000000000000002,
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| 261 |
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0.69813170079773179 },
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| 262 |
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{ 0.89472658511942849, -0.90000000000000002, 0.40000000000000002,
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| 263 |
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0.87266462599716477 },
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| 264 |
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{ 1.0987419542323440, -0.90000000000000002, 0.40000000000000002,
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| 265 |
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1.0471975511965976 },
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| 266 |
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{ 1.3261349565496301, -0.90000000000000002, 0.40000000000000002,
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| 267 |
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1.2217304763960306 },
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| 268 |
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{ 1.5831293909853767, -0.90000000000000002, 0.40000000000000002,
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| 269 |
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1.3962634015954636 },
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| 270 |
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{ 1.8641114227238349, -0.90000000000000002, 0.40000000000000002,
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| 271 |
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1.5707963267948966 },
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| 272 |
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};
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| 274 |
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// Test function for k=-0.90000000000000002, nu=0.40000000000000002.
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| 275 |
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template <typename Tp>
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| 276 |
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void test005()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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| 279 |
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Tp max_abs_diff = -Tp(1);
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| 280 |
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Tp max_abs_frac = -Tp(1);
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| 281 |
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unsigned int num_datum = sizeof(data005)
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| 282 |
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/ sizeof(testcase_ellint_3<double>);
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| 283 |
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for (unsigned int i = 0; i < num_datum; ++i)
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| 284 |
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{
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| 285 |
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const Tp f = std::tr1::ellint_3(Tp(data005[i].k), Tp(data005[i].nu),
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| 286 |
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Tp(data005[i].phi));
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| 287 |
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const Tp f0 = data005[i].f0;
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| 288 |
|
|
const Tp diff = f - f0;
|
| 289 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 290 |
|
|
max_abs_diff = std::abs(diff);
|
| 291 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 292 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 293 |
|
|
{
|
| 294 |
|
|
const Tp frac = diff / f0;
|
| 295 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 296 |
|
|
max_abs_frac = std::abs(frac);
|
| 297 |
|
|
}
|
| 298 |
|
|
}
|
| 299 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 300 |
|
|
}
|
| 301 |
|
|
|
| 302 |
|
|
// Test data for k=-0.90000000000000002, nu=0.50000000000000000.
|
| 303 |
|
|
testcase_ellint_3<double> data006[] = {
|
| 304 |
|
|
{ -0.0000000000000000, -0.90000000000000002, 0.50000000000000000,
|
| 305 |
|
|
0.0000000000000000 },
|
| 306 |
|
|
{ 0.17437497557073336, -0.90000000000000002, 0.50000000000000000,
|
| 307 |
|
|
0.17453292519943295 },
|
| 308 |
|
|
{ 0.34804093691586013, -0.90000000000000002, 0.50000000000000000,
|
| 309 |
|
|
0.34906585039886590 },
|
| 310 |
|
|
{ 0.52137576320372914, -0.90000000000000002, 0.50000000000000000,
|
| 311 |
|
|
0.52359877559829882 },
|
| 312 |
|
|
{ 0.69655163996912284, -0.90000000000000002, 0.50000000000000000,
|
| 313 |
|
|
0.69813170079773179 },
|
| 314 |
|
|
{ 0.87783188683054236, -0.90000000000000002, 0.50000000000000000,
|
| 315 |
|
|
0.87266462599716477 },
|
| 316 |
|
|
{ 1.0716015959755185, -0.90000000000000002, 0.50000000000000000,
|
| 317 |
|
|
1.0471975511965976 },
|
| 318 |
|
|
{ 1.2857636916026747, -0.90000000000000002, 0.50000000000000000,
|
| 319 |
|
|
1.2217304763960306 },
|
| 320 |
|
|
{ 1.5264263913252365, -0.90000000000000002, 0.50000000000000000,
|
| 321 |
|
|
1.3962634015954636 },
|
| 322 |
|
|
{ 1.7888013241937861, -0.90000000000000002, 0.50000000000000000,
|
| 323 |
|
|
1.5707963267948966 },
|
| 324 |
|
|
};
|
| 325 |
|
|
|
| 326 |
|
|
// Test function for k=-0.90000000000000002, nu=0.50000000000000000.
|
| 327 |
|
|
template <typename Tp>
|
| 328 |
|
|
void test006()
|
| 329 |
|
|
{
|
| 330 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 331 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 332 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 333 |
|
|
unsigned int num_datum = sizeof(data006)
|
| 334 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 335 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 336 |
|
|
{
|
| 337 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data006[i].k), Tp(data006[i].nu),
|
| 338 |
|
|
Tp(data006[i].phi));
|
| 339 |
|
|
const Tp f0 = data006[i].f0;
|
| 340 |
|
|
const Tp diff = f - f0;
|
| 341 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 342 |
|
|
max_abs_diff = std::abs(diff);
|
| 343 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 344 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 345 |
|
|
{
|
| 346 |
|
|
const Tp frac = diff / f0;
|
| 347 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 348 |
|
|
max_abs_frac = std::abs(frac);
|
| 349 |
|
|
}
|
| 350 |
|
|
}
|
| 351 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 352 |
|
|
}
|
| 353 |
|
|
|
| 354 |
|
|
// Test data for k=-0.90000000000000002, nu=0.59999999999999998.
|
| 355 |
|
|
testcase_ellint_3<double> data007[] = {
|
| 356 |
|
|
{ -0.0000000000000000, -0.90000000000000002, 0.59999999999999998,
|
| 357 |
|
|
0.0000000000000000 },
|
| 358 |
|
|
{ 0.17420100334657815, -0.90000000000000002, 0.59999999999999998,
|
| 359 |
|
|
0.17453292519943295 },
|
| 360 |
|
|
{ 0.34671975876122157, -0.90000000000000002, 0.59999999999999998,
|
| 361 |
|
|
0.34906585039886590 },
|
| 362 |
|
|
{ 0.51724631570707968, -0.90000000000000002, 0.59999999999999998,
|
| 363 |
|
|
0.52359877559829882 },
|
| 364 |
|
|
{ 0.68760879113743056, -0.90000000000000002, 0.59999999999999998,
|
| 365 |
|
|
0.69813170079773179 },
|
| 366 |
|
|
{ 0.86192157779698364, -0.90000000000000002, 0.59999999999999998,
|
| 367 |
|
|
0.87266462599716477 },
|
| 368 |
|
|
{ 1.0464279696166354, -0.90000000000000002, 0.59999999999999998,
|
| 369 |
|
|
1.0471975511965976 },
|
| 370 |
|
|
{ 1.2488156247094004, -0.90000000000000002, 0.59999999999999998,
|
| 371 |
|
|
1.2217304763960306 },
|
| 372 |
|
|
{ 1.4750988777188474, -0.90000000000000002, 0.59999999999999998,
|
| 373 |
|
|
1.3962634015954636 },
|
| 374 |
|
|
{ 1.7211781128919523, -0.90000000000000002, 0.59999999999999998,
|
| 375 |
|
|
1.5707963267948966 },
|
| 376 |
|
|
};
|
| 377 |
|
|
|
| 378 |
|
|
// Test function for k=-0.90000000000000002, nu=0.59999999999999998.
|
| 379 |
|
|
template <typename Tp>
|
| 380 |
|
|
void test007()
|
| 381 |
|
|
{
|
| 382 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 383 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 384 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 385 |
|
|
unsigned int num_datum = sizeof(data007)
|
| 386 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 387 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 388 |
|
|
{
|
| 389 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data007[i].k), Tp(data007[i].nu),
|
| 390 |
|
|
Tp(data007[i].phi));
|
| 391 |
|
|
const Tp f0 = data007[i].f0;
|
| 392 |
|
|
const Tp diff = f - f0;
|
| 393 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 394 |
|
|
max_abs_diff = std::abs(diff);
|
| 395 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 396 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 397 |
|
|
{
|
| 398 |
|
|
const Tp frac = diff / f0;
|
| 399 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 400 |
|
|
max_abs_frac = std::abs(frac);
|
| 401 |
|
|
}
|
| 402 |
|
|
}
|
| 403 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 404 |
|
|
}
|
| 405 |
|
|
|
| 406 |
|
|
// Test data for k=-0.90000000000000002, nu=0.69999999999999996.
|
| 407 |
|
|
testcase_ellint_3<double> data008[] = {
|
| 408 |
|
|
{ -0.0000000000000000, -0.90000000000000002, 0.69999999999999996,
|
| 409 |
|
|
0.0000000000000000 },
|
| 410 |
|
|
{ 0.17402765093102210, -0.90000000000000002, 0.69999999999999996,
|
| 411 |
|
|
0.17453292519943295 },
|
| 412 |
|
|
{ 0.34541608382635131, -0.90000000000000002, 0.69999999999999996,
|
| 413 |
|
|
0.34906585039886590 },
|
| 414 |
|
|
{ 0.51322715827061705, -0.90000000000000002, 0.69999999999999996,
|
| 415 |
|
|
0.52359877559829882 },
|
| 416 |
|
|
{ 0.67903717872440306, -0.90000000000000002, 0.69999999999999996,
|
| 417 |
|
|
0.69813170079773179 },
|
| 418 |
|
|
{ 0.84690113601682671, -0.90000000000000002, 0.69999999999999996,
|
| 419 |
|
|
0.87266462599716477 },
|
| 420 |
|
|
{ 1.0229914311548418, -0.90000000000000002, 0.69999999999999996,
|
| 421 |
|
|
1.0471975511965976 },
|
| 422 |
|
|
{ 1.2148329639709381, -0.90000000000000002, 0.69999999999999996,
|
| 423 |
|
|
1.2217304763960306 },
|
| 424 |
|
|
{ 1.4283586501307806, -0.90000000000000002, 0.69999999999999996,
|
| 425 |
|
|
1.3962634015954636 },
|
| 426 |
|
|
{ 1.6600480747670938, -0.90000000000000002, 0.69999999999999996,
|
| 427 |
|
|
1.5707963267948966 },
|
| 428 |
|
|
};
|
| 429 |
|
|
|
| 430 |
|
|
// Test function for k=-0.90000000000000002, nu=0.69999999999999996.
|
| 431 |
|
|
template <typename Tp>
|
| 432 |
|
|
void test008()
|
| 433 |
|
|
{
|
| 434 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 435 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 436 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 437 |
|
|
unsigned int num_datum = sizeof(data008)
|
| 438 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 439 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 440 |
|
|
{
|
| 441 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data008[i].k), Tp(data008[i].nu),
|
| 442 |
|
|
Tp(data008[i].phi));
|
| 443 |
|
|
const Tp f0 = data008[i].f0;
|
| 444 |
|
|
const Tp diff = f - f0;
|
| 445 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 446 |
|
|
max_abs_diff = std::abs(diff);
|
| 447 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 448 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 449 |
|
|
{
|
| 450 |
|
|
const Tp frac = diff / f0;
|
| 451 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 452 |
|
|
max_abs_frac = std::abs(frac);
|
| 453 |
|
|
}
|
| 454 |
|
|
}
|
| 455 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 456 |
|
|
}
|
| 457 |
|
|
|
| 458 |
|
|
// Test data for k=-0.90000000000000002, nu=0.80000000000000004.
|
| 459 |
|
|
testcase_ellint_3<double> data009[] = {
|
| 460 |
|
|
{ -0.0000000000000000, -0.90000000000000002, 0.80000000000000004,
|
| 461 |
|
|
0.0000000000000000 },
|
| 462 |
|
|
{ 0.17385491439925149, -0.90000000000000002, 0.80000000000000004,
|
| 463 |
|
|
0.17453292519943295 },
|
| 464 |
|
|
{ 0.34412950523113928, -0.90000000000000002, 0.80000000000000004,
|
| 465 |
|
|
0.34906585039886590 },
|
| 466 |
|
|
{ 0.50931321668729612, -0.90000000000000002, 0.80000000000000004,
|
| 467 |
|
|
0.52359877559829882 },
|
| 468 |
|
|
{ 0.67081081392296349, -0.90000000000000002, 0.80000000000000004,
|
| 469 |
|
|
0.69813170079773179 },
|
| 470 |
|
|
{ 0.83268846097293259, -0.90000000000000002, 0.80000000000000004,
|
| 471 |
|
|
0.87266462599716477 },
|
| 472 |
|
|
{ 1.0010985015814027, -0.90000000000000002, 0.80000000000000004,
|
| 473 |
|
|
1.0471975511965976 },
|
| 474 |
|
|
{ 1.1834394045489678, -0.90000000000000002, 0.80000000000000004,
|
| 475 |
|
|
1.2217304763960306 },
|
| 476 |
|
|
{ 1.3855695891683188, -0.90000000000000002, 0.80000000000000004,
|
| 477 |
|
|
1.3962634015954636 },
|
| 478 |
|
|
{ 1.6044591960982204, -0.90000000000000002, 0.80000000000000004,
|
| 479 |
|
|
1.5707963267948966 },
|
| 480 |
|
|
};
|
| 481 |
|
|
|
| 482 |
|
|
// Test function for k=-0.90000000000000002, nu=0.80000000000000004.
|
| 483 |
|
|
template <typename Tp>
|
| 484 |
|
|
void test009()
|
| 485 |
|
|
{
|
| 486 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 487 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 488 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 489 |
|
|
unsigned int num_datum = sizeof(data009)
|
| 490 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 491 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 492 |
|
|
{
|
| 493 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data009[i].k), Tp(data009[i].nu),
|
| 494 |
|
|
Tp(data009[i].phi));
|
| 495 |
|
|
const Tp f0 = data009[i].f0;
|
| 496 |
|
|
const Tp diff = f - f0;
|
| 497 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 498 |
|
|
max_abs_diff = std::abs(diff);
|
| 499 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 500 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 501 |
|
|
{
|
| 502 |
|
|
const Tp frac = diff / f0;
|
| 503 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 504 |
|
|
max_abs_frac = std::abs(frac);
|
| 505 |
|
|
}
|
| 506 |
|
|
}
|
| 507 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 508 |
|
|
}
|
| 509 |
|
|
|
| 510 |
|
|
// Test data for k=-0.90000000000000002, nu=0.90000000000000002.
|
| 511 |
|
|
testcase_ellint_3<double> data010[] = {
|
| 512 |
|
|
{ -0.0000000000000000, -0.90000000000000002, 0.90000000000000002,
|
| 513 |
|
|
0.0000000000000000 },
|
| 514 |
|
|
{ 0.17368278986240138, -0.90000000000000002, 0.90000000000000002,
|
| 515 |
|
|
0.17453292519943295 },
|
| 516 |
|
|
{ 0.34285962963961397, -0.90000000000000002, 0.90000000000000002,
|
| 517 |
|
|
0.34906585039886590 },
|
| 518 |
|
|
{ 0.50549974644993323, -0.90000000000000002, 0.90000000000000002,
|
| 519 |
|
|
0.52359877559829882 },
|
| 520 |
|
|
{ 0.66290623857720898, -0.90000000000000002, 0.90000000000000002,
|
| 521 |
|
|
0.69813170079773179 },
|
| 522 |
|
|
{ 0.81921183128847164, -0.90000000000000002, 0.90000000000000002,
|
| 523 |
|
|
0.87266462599716477 },
|
| 524 |
|
|
{ 0.98058481956066390, -0.90000000000000002, 0.90000000000000002,
|
| 525 |
|
|
1.0471975511965976 },
|
| 526 |
|
|
{ 1.1543223520473567, -0.90000000000000002, 0.90000000000000002,
|
| 527 |
|
|
1.2217304763960306 },
|
| 528 |
|
|
{ 1.3462119782292938, -0.90000000000000002, 0.90000000000000002,
|
| 529 |
|
|
1.3962634015954636 },
|
| 530 |
|
|
{ 1.5536420236310946, -0.90000000000000002, 0.90000000000000002,
|
| 531 |
|
|
1.5707963267948966 },
|
| 532 |
|
|
};
|
| 533 |
|
|
|
| 534 |
|
|
// Test function for k=-0.90000000000000002, nu=0.90000000000000002.
|
| 535 |
|
|
template <typename Tp>
|
| 536 |
|
|
void test010()
|
| 537 |
|
|
{
|
| 538 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 539 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 540 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 541 |
|
|
unsigned int num_datum = sizeof(data010)
|
| 542 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 543 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 544 |
|
|
{
|
| 545 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data010[i].k), Tp(data010[i].nu),
|
| 546 |
|
|
Tp(data010[i].phi));
|
| 547 |
|
|
const Tp f0 = data010[i].f0;
|
| 548 |
|
|
const Tp diff = f - f0;
|
| 549 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 550 |
|
|
max_abs_diff = std::abs(diff);
|
| 551 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 552 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 553 |
|
|
{
|
| 554 |
|
|
const Tp frac = diff / f0;
|
| 555 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 556 |
|
|
max_abs_frac = std::abs(frac);
|
| 557 |
|
|
}
|
| 558 |
|
|
}
|
| 559 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 560 |
|
|
}
|
| 561 |
|
|
|
| 562 |
|
|
// Test data for k=-0.80000000000000004, nu=0.0000000000000000.
|
| 563 |
|
|
testcase_ellint_3<double> data011[] = {
|
| 564 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.0000000000000000,
|
| 565 |
|
|
0.0000000000000000 },
|
| 566 |
|
|
{ 0.17510154241338902, -0.80000000000000004, 0.0000000000000000,
|
| 567 |
|
|
0.17453292519943295 },
|
| 568 |
|
|
{ 0.35365068839779390, -0.80000000000000004, 0.0000000000000000,
|
| 569 |
|
|
0.34906585039886590 },
|
| 570 |
|
|
{ 0.53926804409084561, -0.80000000000000004, 0.0000000000000000,
|
| 571 |
|
|
0.52359877559829882 },
|
| 572 |
|
|
{ 0.73587926028070383, -0.80000000000000004, 0.0000000000000000,
|
| 573 |
|
|
0.69813170079773179 },
|
| 574 |
|
|
{ 0.94770942970071170, -0.80000000000000004, 0.0000000000000000,
|
| 575 |
|
|
0.87266462599716477 },
|
| 576 |
|
|
{ 1.1789022995388239, -0.80000000000000004, 0.0000000000000000,
|
| 577 |
|
|
1.0471975511965976 },
|
| 578 |
|
|
{ 1.4323027881876009, -0.80000000000000004, 0.0000000000000000,
|
| 579 |
|
|
1.2217304763960306 },
|
| 580 |
|
|
{ 1.7069629739121674, -0.80000000000000004, 0.0000000000000000,
|
| 581 |
|
|
1.3962634015954636 },
|
| 582 |
|
|
{ 1.9953027776647296, -0.80000000000000004, 0.0000000000000000,
|
| 583 |
|
|
1.5707963267948966 },
|
| 584 |
|
|
};
|
| 585 |
|
|
|
| 586 |
|
|
// Test function for k=-0.80000000000000004, nu=0.0000000000000000.
|
| 587 |
|
|
template <typename Tp>
|
| 588 |
|
|
void test011()
|
| 589 |
|
|
{
|
| 590 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 591 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 592 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 593 |
|
|
unsigned int num_datum = sizeof(data011)
|
| 594 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 595 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 596 |
|
|
{
|
| 597 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data011[i].k), Tp(data011[i].nu),
|
| 598 |
|
|
Tp(data011[i].phi));
|
| 599 |
|
|
const Tp f0 = data011[i].f0;
|
| 600 |
|
|
const Tp diff = f - f0;
|
| 601 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 602 |
|
|
max_abs_diff = std::abs(diff);
|
| 603 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 604 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 605 |
|
|
{
|
| 606 |
|
|
const Tp frac = diff / f0;
|
| 607 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 608 |
|
|
max_abs_frac = std::abs(frac);
|
| 609 |
|
|
}
|
| 610 |
|
|
}
|
| 611 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 612 |
|
|
}
|
| 613 |
|
|
|
| 614 |
|
|
// Test data for k=-0.80000000000000004, nu=0.10000000000000001.
|
| 615 |
|
|
testcase_ellint_3<double> data012[] = {
|
| 616 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.10000000000000001,
|
| 617 |
|
|
0.0000000000000000 },
|
| 618 |
|
|
{ 0.17492468824017166, -0.80000000000000004, 0.10000000000000001,
|
| 619 |
|
|
0.17453292519943295 },
|
| 620 |
|
|
{ 0.35224443521476911, -0.80000000000000004, 0.10000000000000001,
|
| 621 |
|
|
0.34906585039886590 },
|
| 622 |
|
|
{ 0.53456851853226961, -0.80000000000000004, 0.10000000000000001,
|
| 623 |
|
|
0.52359877559829882 },
|
| 624 |
|
|
{ 0.72488875602364944, -0.80000000000000004, 0.10000000000000001,
|
| 625 |
|
|
0.69813170079773179 },
|
| 626 |
|
|
{ 0.92661354274638952, -0.80000000000000004, 0.10000000000000001,
|
| 627 |
|
|
0.87266462599716477 },
|
| 628 |
|
|
{ 1.1432651144499077, -0.80000000000000004, 0.10000000000000001,
|
| 629 |
|
|
1.0471975511965976 },
|
| 630 |
|
|
{ 1.3774479927211429, -0.80000000000000004, 0.10000000000000001,
|
| 631 |
|
|
1.2217304763960306 },
|
| 632 |
|
|
{ 1.6287092337196041, -0.80000000000000004, 0.10000000000000001,
|
| 633 |
|
|
1.3962634015954636 },
|
| 634 |
|
|
{ 1.8910755418379521, -0.80000000000000004, 0.10000000000000001,
|
| 635 |
|
|
1.5707963267948966 },
|
| 636 |
|
|
};
|
| 637 |
|
|
|
| 638 |
|
|
// Test function for k=-0.80000000000000004, nu=0.10000000000000001.
|
| 639 |
|
|
template <typename Tp>
|
| 640 |
|
|
void test012()
|
| 641 |
|
|
{
|
| 642 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 643 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 644 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 645 |
|
|
unsigned int num_datum = sizeof(data012)
|
| 646 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 647 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 648 |
|
|
{
|
| 649 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data012[i].k), Tp(data012[i].nu),
|
| 650 |
|
|
Tp(data012[i].phi));
|
| 651 |
|
|
const Tp f0 = data012[i].f0;
|
| 652 |
|
|
const Tp diff = f - f0;
|
| 653 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 654 |
|
|
max_abs_diff = std::abs(diff);
|
| 655 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 656 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 657 |
|
|
{
|
| 658 |
|
|
const Tp frac = diff / f0;
|
| 659 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 660 |
|
|
max_abs_frac = std::abs(frac);
|
| 661 |
|
|
}
|
| 662 |
|
|
}
|
| 663 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 664 |
|
|
}
|
| 665 |
|
|
|
| 666 |
|
|
// Test data for k=-0.80000000000000004, nu=0.20000000000000001.
|
| 667 |
|
|
testcase_ellint_3<double> data013[] = {
|
| 668 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.20000000000000001,
|
| 669 |
|
|
0.0000000000000000 },
|
| 670 |
|
|
{ 0.17474847286224943, -0.80000000000000004, 0.20000000000000001,
|
| 671 |
|
|
0.17453292519943295 },
|
| 672 |
|
|
{ 0.35085779529084682, -0.80000000000000004, 0.20000000000000001,
|
| 673 |
|
|
0.34906585039886590 },
|
| 674 |
|
|
{ 0.53000829263059157, -0.80000000000000004, 0.20000000000000001,
|
| 675 |
|
|
0.52359877559829882 },
|
| 676 |
|
|
{ 0.71443466027453406, -0.80000000000000004, 0.20000000000000001,
|
| 677 |
|
|
0.69813170079773179 },
|
| 678 |
|
|
{ 0.90698196872715420, -0.80000000000000004, 0.20000000000000001,
|
| 679 |
|
|
0.87266462599716477 },
|
| 680 |
|
|
{ 1.1108198200558581, -0.80000000000000004, 0.20000000000000001,
|
| 681 |
|
|
1.0471975511965976 },
|
| 682 |
|
|
{ 1.3284988909963957, -0.80000000000000004, 0.20000000000000001,
|
| 683 |
|
|
1.2217304763960306 },
|
| 684 |
|
|
{ 1.5600369318140328, -0.80000000000000004, 0.20000000000000001,
|
| 685 |
|
|
1.3962634015954636 },
|
| 686 |
|
|
{ 1.8007226661734588, -0.80000000000000004, 0.20000000000000001,
|
| 687 |
|
|
1.5707963267948966 },
|
| 688 |
|
|
};
|
| 689 |
|
|
|
| 690 |
|
|
// Test function for k=-0.80000000000000004, nu=0.20000000000000001.
|
| 691 |
|
|
template <typename Tp>
|
| 692 |
|
|
void test013()
|
| 693 |
|
|
{
|
| 694 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 695 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 696 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 697 |
|
|
unsigned int num_datum = sizeof(data013)
|
| 698 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 699 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 700 |
|
|
{
|
| 701 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data013[i].k), Tp(data013[i].nu),
|
| 702 |
|
|
Tp(data013[i].phi));
|
| 703 |
|
|
const Tp f0 = data013[i].f0;
|
| 704 |
|
|
const Tp diff = f - f0;
|
| 705 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 706 |
|
|
max_abs_diff = std::abs(diff);
|
| 707 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 708 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 709 |
|
|
{
|
| 710 |
|
|
const Tp frac = diff / f0;
|
| 711 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 712 |
|
|
max_abs_frac = std::abs(frac);
|
| 713 |
|
|
}
|
| 714 |
|
|
}
|
| 715 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 716 |
|
|
}
|
| 717 |
|
|
|
| 718 |
|
|
// Test data for k=-0.80000000000000004, nu=0.29999999999999999.
|
| 719 |
|
|
testcase_ellint_3<double> data014[] = {
|
| 720 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.29999999999999999,
|
| 721 |
|
|
0.0000000000000000 },
|
| 722 |
|
|
{ 0.17457289217669891, -0.80000000000000004, 0.29999999999999999,
|
| 723 |
|
|
0.17453292519943295 },
|
| 724 |
|
|
{ 0.34949028801501258, -0.80000000000000004, 0.29999999999999999,
|
| 725 |
|
|
0.34906585039886590 },
|
| 726 |
|
|
{ 0.52558024362769318, -0.80000000000000004, 0.29999999999999999,
|
| 727 |
|
|
0.52359877559829882 },
|
| 728 |
|
|
{ 0.70447281740094914, -0.80000000000000004, 0.29999999999999999,
|
| 729 |
|
|
0.69813170079773179 },
|
| 730 |
|
|
{ 0.88864745641528986, -0.80000000000000004, 0.29999999999999999,
|
| 731 |
|
|
0.87266462599716477 },
|
| 732 |
|
|
{ 1.0811075819341465, -0.80000000000000004, 0.29999999999999999,
|
| 733 |
|
|
1.0471975511965976 },
|
| 734 |
|
|
{ 1.2844589654082377, -0.80000000000000004, 0.29999999999999999,
|
| 735 |
|
|
1.2217304763960306 },
|
| 736 |
|
|
{ 1.4991461361277849, -0.80000000000000004, 0.29999999999999999,
|
| 737 |
|
|
1.3962634015954636 },
|
| 738 |
|
|
{ 1.7214611048717301, -0.80000000000000004, 0.29999999999999999,
|
| 739 |
|
|
1.5707963267948966 },
|
| 740 |
|
|
};
|
| 741 |
|
|
|
| 742 |
|
|
// Test function for k=-0.80000000000000004, nu=0.29999999999999999.
|
| 743 |
|
|
template <typename Tp>
|
| 744 |
|
|
void test014()
|
| 745 |
|
|
{
|
| 746 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 747 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 748 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 749 |
|
|
unsigned int num_datum = sizeof(data014)
|
| 750 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 751 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 752 |
|
|
{
|
| 753 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data014[i].k), Tp(data014[i].nu),
|
| 754 |
|
|
Tp(data014[i].phi));
|
| 755 |
|
|
const Tp f0 = data014[i].f0;
|
| 756 |
|
|
const Tp diff = f - f0;
|
| 757 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 758 |
|
|
max_abs_diff = std::abs(diff);
|
| 759 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 760 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 761 |
|
|
{
|
| 762 |
|
|
const Tp frac = diff / f0;
|
| 763 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 764 |
|
|
max_abs_frac = std::abs(frac);
|
| 765 |
|
|
}
|
| 766 |
|
|
}
|
| 767 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 768 |
|
|
}
|
| 769 |
|
|
|
| 770 |
|
|
// Test data for k=-0.80000000000000004, nu=0.40000000000000002.
|
| 771 |
|
|
testcase_ellint_3<double> data015[] = {
|
| 772 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.40000000000000002,
|
| 773 |
|
|
0.0000000000000000 },
|
| 774 |
|
|
{ 0.17439794211872178, -0.80000000000000004, 0.40000000000000002,
|
| 775 |
|
|
0.17453292519943295 },
|
| 776 |
|
|
{ 0.34814144964568972, -0.80000000000000004, 0.40000000000000002,
|
| 777 |
|
|
0.34906585039886590 },
|
| 778 |
|
|
{ 0.52127776285273075, -0.80000000000000004, 0.40000000000000002,
|
| 779 |
|
|
0.52359877559829882 },
|
| 780 |
|
|
{ 0.69496411438966599, -0.80000000000000004, 0.40000000000000002,
|
| 781 |
|
|
0.69813170079773179 },
|
| 782 |
|
|
{ 0.87146878427509589, -0.80000000000000004, 0.40000000000000002,
|
| 783 |
|
|
0.87266462599716477 },
|
| 784 |
|
|
{ 1.0537579024937762, -0.80000000000000004, 0.40000000000000002,
|
| 785 |
|
|
1.0471975511965976 },
|
| 786 |
|
|
{ 1.2445534387922637, -0.80000000000000004, 0.40000000000000002,
|
| 787 |
|
|
1.2217304763960306 },
|
| 788 |
|
|
{ 1.4446769766361993, -0.80000000000000004, 0.40000000000000002,
|
| 789 |
|
|
1.3962634015954636 },
|
| 790 |
|
|
{ 1.6512267838651289, -0.80000000000000004, 0.40000000000000002,
|
| 791 |
|
|
1.5707963267948966 },
|
| 792 |
|
|
};
|
| 793 |
|
|
|
| 794 |
|
|
// Test function for k=-0.80000000000000004, nu=0.40000000000000002.
|
| 795 |
|
|
template <typename Tp>
|
| 796 |
|
|
void test015()
|
| 797 |
|
|
{
|
| 798 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 799 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 800 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 801 |
|
|
unsigned int num_datum = sizeof(data015)
|
| 802 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 803 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 804 |
|
|
{
|
| 805 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data015[i].k), Tp(data015[i].nu),
|
| 806 |
|
|
Tp(data015[i].phi));
|
| 807 |
|
|
const Tp f0 = data015[i].f0;
|
| 808 |
|
|
const Tp diff = f - f0;
|
| 809 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 810 |
|
|
max_abs_diff = std::abs(diff);
|
| 811 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 812 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 813 |
|
|
{
|
| 814 |
|
|
const Tp frac = diff / f0;
|
| 815 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 816 |
|
|
max_abs_frac = std::abs(frac);
|
| 817 |
|
|
}
|
| 818 |
|
|
}
|
| 819 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 820 |
|
|
}
|
| 821 |
|
|
|
| 822 |
|
|
// Test data for k=-0.80000000000000004, nu=0.50000000000000000.
|
| 823 |
|
|
testcase_ellint_3<double> data016[] = {
|
| 824 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.50000000000000000,
|
| 825 |
|
|
0.0000000000000000 },
|
| 826 |
|
|
{ 0.17422361866118047, -0.80000000000000004, 0.50000000000000000,
|
| 827 |
|
|
0.17453292519943295 },
|
| 828 |
|
|
{ 0.34681083254170475, -0.80000000000000004, 0.50000000000000000,
|
| 829 |
|
|
0.34906585039886590 },
|
| 830 |
|
|
{ 0.51709470815494440, -0.80000000000000004, 0.50000000000000000,
|
| 831 |
|
|
0.52359877559829882 },
|
| 832 |
|
|
{ 0.68587375344080259, -0.80000000000000004, 0.50000000000000000,
|
| 833 |
|
|
0.69813170079773179 },
|
| 834 |
|
|
{ 0.85532571852810624, -0.80000000000000004, 0.50000000000000000,
|
| 835 |
|
|
0.87266462599716477 },
|
| 836 |
|
|
{ 1.0284677391874906, -0.80000000000000004, 0.50000000000000000,
|
| 837 |
|
|
1.0471975511965976 },
|
| 838 |
|
|
{ 1.2081693942686225, -0.80000000000000004, 0.50000000000000000,
|
| 839 |
|
|
1.2217304763960306 },
|
| 840 |
|
|
{ 1.3955803006426311, -0.80000000000000004, 0.50000000000000000,
|
| 841 |
|
|
1.3962634015954636 },
|
| 842 |
|
|
{ 1.5884528947755532, -0.80000000000000004, 0.50000000000000000,
|
| 843 |
|
|
1.5707963267948966 },
|
| 844 |
|
|
};
|
| 845 |
|
|
|
| 846 |
|
|
// Test function for k=-0.80000000000000004, nu=0.50000000000000000.
|
| 847 |
|
|
template <typename Tp>
|
| 848 |
|
|
void test016()
|
| 849 |
|
|
{
|
| 850 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 851 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 852 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 853 |
|
|
unsigned int num_datum = sizeof(data016)
|
| 854 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 855 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 856 |
|
|
{
|
| 857 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data016[i].k), Tp(data016[i].nu),
|
| 858 |
|
|
Tp(data016[i].phi));
|
| 859 |
|
|
const Tp f0 = data016[i].f0;
|
| 860 |
|
|
const Tp diff = f - f0;
|
| 861 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 862 |
|
|
max_abs_diff = std::abs(diff);
|
| 863 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 864 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 865 |
|
|
{
|
| 866 |
|
|
const Tp frac = diff / f0;
|
| 867 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 868 |
|
|
max_abs_frac = std::abs(frac);
|
| 869 |
|
|
}
|
| 870 |
|
|
}
|
| 871 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 872 |
|
|
}
|
| 873 |
|
|
|
| 874 |
|
|
// Test data for k=-0.80000000000000004, nu=0.59999999999999998.
|
| 875 |
|
|
testcase_ellint_3<double> data017[] = {
|
| 876 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.59999999999999998,
|
| 877 |
|
|
0.0000000000000000 },
|
| 878 |
|
|
{ 0.17404991781414092, -0.80000000000000004, 0.59999999999999998,
|
| 879 |
|
|
0.17453292519943295 },
|
| 880 |
|
|
{ 0.34549800443625167, -0.80000000000000004, 0.59999999999999998,
|
| 881 |
|
|
0.34906585039886590 },
|
| 882 |
|
|
{ 0.51302536167001556, -0.80000000000000004, 0.59999999999999998,
|
| 883 |
|
|
0.52359877559829882 },
|
| 884 |
|
|
{ 0.67717065003912258, -0.80000000000000004, 0.59999999999999998,
|
| 885 |
|
|
0.69813170079773179 },
|
| 886 |
|
|
{ 0.84011512421134416, -0.80000000000000004, 0.59999999999999998,
|
| 887 |
|
|
0.87266462599716477 },
|
| 888 |
|
|
{ 1.0049863847088742, -0.80000000000000004, 0.59999999999999998,
|
| 889 |
|
|
1.0471975511965976 },
|
| 890 |
|
|
{ 1.1748145941898918, -0.80000000000000004, 0.59999999999999998,
|
| 891 |
|
|
1.2217304763960306 },
|
| 892 |
|
|
{ 1.3510319699755071, -0.80000000000000004, 0.59999999999999998,
|
| 893 |
|
|
1.3962634015954636 },
|
| 894 |
|
|
{ 1.5319262547427865, -0.80000000000000004, 0.59999999999999998,
|
| 895 |
|
|
1.5707963267948966 },
|
| 896 |
|
|
};
|
| 897 |
|
|
|
| 898 |
|
|
// Test function for k=-0.80000000000000004, nu=0.59999999999999998.
|
| 899 |
|
|
template <typename Tp>
|
| 900 |
|
|
void test017()
|
| 901 |
|
|
{
|
| 902 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 903 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 904 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 905 |
|
|
unsigned int num_datum = sizeof(data017)
|
| 906 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 907 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 908 |
|
|
{
|
| 909 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data017[i].k), Tp(data017[i].nu),
|
| 910 |
|
|
Tp(data017[i].phi));
|
| 911 |
|
|
const Tp f0 = data017[i].f0;
|
| 912 |
|
|
const Tp diff = f - f0;
|
| 913 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 914 |
|
|
max_abs_diff = std::abs(diff);
|
| 915 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 916 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 917 |
|
|
{
|
| 918 |
|
|
const Tp frac = diff / f0;
|
| 919 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 920 |
|
|
max_abs_frac = std::abs(frac);
|
| 921 |
|
|
}
|
| 922 |
|
|
}
|
| 923 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 924 |
|
|
}
|
| 925 |
|
|
|
| 926 |
|
|
// Test data for k=-0.80000000000000004, nu=0.69999999999999996.
|
| 927 |
|
|
testcase_ellint_3<double> data018[] = {
|
| 928 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.69999999999999996,
|
| 929 |
|
|
0.0000000000000000 },
|
| 930 |
|
|
{ 0.17387683562442202, -0.80000000000000004, 0.69999999999999996,
|
| 931 |
|
|
0.17453292519943295 },
|
| 932 |
|
|
{ 0.34420254775101611, -0.80000000000000004, 0.69999999999999996,
|
| 933 |
|
|
0.34906585039886590 },
|
| 934 |
|
|
{ 0.50906439222143685, -0.80000000000000004, 0.69999999999999996,
|
| 935 |
|
|
0.52359877559829882 },
|
| 936 |
|
|
{ 0.66882693152688433, -0.80000000000000004, 0.69999999999999996,
|
| 937 |
|
|
0.69813170079773179 },
|
| 938 |
|
|
{ 0.82574792844091316, -0.80000000000000004, 0.69999999999999996,
|
| 939 |
|
|
0.87266462599716477 },
|
| 940 |
|
|
{ 0.98310431309490953, -0.80000000000000004, 0.69999999999999996,
|
| 941 |
|
|
1.0471975511965976 },
|
| 942 |
|
|
{ 1.1440884535113258, -0.80000000000000004, 0.69999999999999996,
|
| 943 |
|
|
1.2217304763960306 },
|
| 944 |
|
|
{ 1.3103743938952537, -0.80000000000000004, 0.69999999999999996,
|
| 945 |
|
|
1.3962634015954636 },
|
| 946 |
|
|
{ 1.4806912324625332, -0.80000000000000004, 0.69999999999999996,
|
| 947 |
|
|
1.5707963267948966 },
|
| 948 |
|
|
};
|
| 949 |
|
|
|
| 950 |
|
|
// Test function for k=-0.80000000000000004, nu=0.69999999999999996.
|
| 951 |
|
|
template <typename Tp>
|
| 952 |
|
|
void test018()
|
| 953 |
|
|
{
|
| 954 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 955 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 956 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 957 |
|
|
unsigned int num_datum = sizeof(data018)
|
| 958 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 959 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 960 |
|
|
{
|
| 961 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data018[i].k), Tp(data018[i].nu),
|
| 962 |
|
|
Tp(data018[i].phi));
|
| 963 |
|
|
const Tp f0 = data018[i].f0;
|
| 964 |
|
|
const Tp diff = f - f0;
|
| 965 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 966 |
|
|
max_abs_diff = std::abs(diff);
|
| 967 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 968 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 969 |
|
|
{
|
| 970 |
|
|
const Tp frac = diff / f0;
|
| 971 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 972 |
|
|
max_abs_frac = std::abs(frac);
|
| 973 |
|
|
}
|
| 974 |
|
|
}
|
| 975 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 976 |
|
|
}
|
| 977 |
|
|
|
| 978 |
|
|
// Test data for k=-0.80000000000000004, nu=0.80000000000000004.
|
| 979 |
|
|
testcase_ellint_3<double> data019[] = {
|
| 980 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.80000000000000004,
|
| 981 |
|
|
0.0000000000000000 },
|
| 982 |
|
|
{ 0.17370436817515206, -0.80000000000000004, 0.80000000000000004,
|
| 983 |
|
|
0.17453292519943295 },
|
| 984 |
|
|
{ 0.34292405894783395, -0.80000000000000004, 0.80000000000000004,
|
| 985 |
|
|
0.34906585039886590 },
|
| 986 |
|
|
{ 0.50520682176250087, -0.80000000000000004, 0.80000000000000004,
|
| 987 |
|
|
0.52359877559829882 },
|
| 988 |
|
|
{ 0.66081751679736189, -0.80000000000000004, 0.80000000000000004,
|
| 989 |
|
|
0.69813170079773179 },
|
| 990 |
|
|
{ 0.81214672249355102, -0.80000000000000004, 0.80000000000000004,
|
| 991 |
|
|
0.87266462599716477 },
|
| 992 |
|
|
{ 0.96264481387685574, -0.80000000000000004, 0.80000000000000004,
|
| 993 |
|
|
1.0471975511965976 },
|
| 994 |
|
|
{ 1.1156611352656258, -0.80000000000000004, 0.80000000000000004,
|
| 995 |
|
|
1.2217304763960306 },
|
| 996 |
|
|
{ 1.2730756225143889, -0.80000000000000004, 0.80000000000000004,
|
| 997 |
|
|
1.3962634015954636 },
|
| 998 |
|
|
{ 1.4339837018309474, -0.80000000000000004, 0.80000000000000004,
|
| 999 |
|
|
1.5707963267948966 },
|
| 1000 |
|
|
};
|
| 1001 |
|
|
|
| 1002 |
|
|
// Test function for k=-0.80000000000000004, nu=0.80000000000000004.
|
| 1003 |
|
|
template <typename Tp>
|
| 1004 |
|
|
void test019()
|
| 1005 |
|
|
{
|
| 1006 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1007 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1008 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1009 |
|
|
unsigned int num_datum = sizeof(data019)
|
| 1010 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1011 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1012 |
|
|
{
|
| 1013 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data019[i].k), Tp(data019[i].nu),
|
| 1014 |
|
|
Tp(data019[i].phi));
|
| 1015 |
|
|
const Tp f0 = data019[i].f0;
|
| 1016 |
|
|
const Tp diff = f - f0;
|
| 1017 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1018 |
|
|
max_abs_diff = std::abs(diff);
|
| 1019 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1020 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1021 |
|
|
{
|
| 1022 |
|
|
const Tp frac = diff / f0;
|
| 1023 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1024 |
|
|
max_abs_frac = std::abs(frac);
|
| 1025 |
|
|
}
|
| 1026 |
|
|
}
|
| 1027 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1028 |
|
|
}
|
| 1029 |
|
|
|
| 1030 |
|
|
// Test data for k=-0.80000000000000004, nu=0.90000000000000002.
|
| 1031 |
|
|
testcase_ellint_3<double> data020[] = {
|
| 1032 |
|
|
{ -0.0000000000000000, -0.80000000000000004, 0.90000000000000002,
|
| 1033 |
|
|
0.0000000000000000 },
|
| 1034 |
|
|
{ 0.17353251158533153, -0.80000000000000004, 0.90000000000000002,
|
| 1035 |
|
|
0.17453292519943295 },
|
| 1036 |
|
|
{ 0.34166214791545768, -0.80000000000000004, 0.90000000000000002,
|
| 1037 |
|
|
0.34906585039886590 },
|
| 1038 |
|
|
{ 0.50144799535130580, -0.80000000000000004, 0.90000000000000002,
|
| 1039 |
|
|
0.52359877559829882 },
|
| 1040 |
|
|
{ 0.65311976193814447, -0.80000000000000004, 0.90000000000000002,
|
| 1041 |
|
|
0.69813170079773179 },
|
| 1042 |
|
|
{ 0.79924384892320866, -0.80000000000000004, 0.90000000000000002,
|
| 1043 |
|
|
0.87266462599716477 },
|
| 1044 |
|
|
{ 0.94345762353365625, -0.80000000000000004, 0.90000000000000002,
|
| 1045 |
|
|
1.0471975511965976 },
|
| 1046 |
|
|
{ 1.0892582069219159, -0.80000000000000004, 0.90000000000000002,
|
| 1047 |
|
|
1.2217304763960306 },
|
| 1048 |
|
|
{ 1.2387000876610268, -0.80000000000000004, 0.90000000000000002,
|
| 1049 |
|
|
1.3962634015954636 },
|
| 1050 |
|
|
{ 1.3911845406776222, -0.80000000000000004, 0.90000000000000002,
|
| 1051 |
|
|
1.5707963267948966 },
|
| 1052 |
|
|
};
|
| 1053 |
|
|
|
| 1054 |
|
|
// Test function for k=-0.80000000000000004, nu=0.90000000000000002.
|
| 1055 |
|
|
template <typename Tp>
|
| 1056 |
|
|
void test020()
|
| 1057 |
|
|
{
|
| 1058 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1059 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1060 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1061 |
|
|
unsigned int num_datum = sizeof(data020)
|
| 1062 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1063 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1064 |
|
|
{
|
| 1065 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data020[i].k), Tp(data020[i].nu),
|
| 1066 |
|
|
Tp(data020[i].phi));
|
| 1067 |
|
|
const Tp f0 = data020[i].f0;
|
| 1068 |
|
|
const Tp diff = f - f0;
|
| 1069 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1070 |
|
|
max_abs_diff = std::abs(diff);
|
| 1071 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1072 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1073 |
|
|
{
|
| 1074 |
|
|
const Tp frac = diff / f0;
|
| 1075 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1076 |
|
|
max_abs_frac = std::abs(frac);
|
| 1077 |
|
|
}
|
| 1078 |
|
|
}
|
| 1079 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1080 |
|
|
}
|
| 1081 |
|
|
|
| 1082 |
|
|
// Test data for k=-0.69999999999999996, nu=0.0000000000000000.
|
| 1083 |
|
|
testcase_ellint_3<double> data021[] = {
|
| 1084 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.0000000000000000,
|
| 1085 |
|
|
0.0000000000000000 },
|
| 1086 |
|
|
{ 0.17496737466916720, -0.69999999999999996, 0.0000000000000000,
|
| 1087 |
|
|
0.17453292519943295 },
|
| 1088 |
|
|
{ 0.35254687535677925, -0.69999999999999996, 0.0000000000000000,
|
| 1089 |
|
|
0.34906585039886590 },
|
| 1090 |
|
|
{ 0.53536740275997130, -0.69999999999999996, 0.0000000000000000,
|
| 1091 |
|
|
0.52359877559829882 },
|
| 1092 |
|
|
{ 0.72603797651684465, -0.69999999999999996, 0.0000000000000000,
|
| 1093 |
|
|
0.69813170079773179 },
|
| 1094 |
|
|
{ 0.92698296348313458, -0.69999999999999996, 0.0000000000000000,
|
| 1095 |
|
|
0.87266462599716477 },
|
| 1096 |
|
|
{ 1.1400447527693316, -0.69999999999999996, 0.0000000000000000,
|
| 1097 |
|
|
1.0471975511965976 },
|
| 1098 |
|
|
{ 1.3657668117194071, -0.69999999999999996, 0.0000000000000000,
|
| 1099 |
|
|
1.2217304763960306 },
|
| 1100 |
|
|
{ 1.6024686895959159, -0.69999999999999996, 0.0000000000000000,
|
| 1101 |
|
|
1.3962634015954636 },
|
| 1102 |
|
|
{ 1.8456939983747236, -0.69999999999999996, 0.0000000000000000,
|
| 1103 |
|
|
1.5707963267948966 },
|
| 1104 |
|
|
};
|
| 1105 |
|
|
|
| 1106 |
|
|
// Test function for k=-0.69999999999999996, nu=0.0000000000000000.
|
| 1107 |
|
|
template <typename Tp>
|
| 1108 |
|
|
void test021()
|
| 1109 |
|
|
{
|
| 1110 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1111 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1112 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1113 |
|
|
unsigned int num_datum = sizeof(data021)
|
| 1114 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1115 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1116 |
|
|
{
|
| 1117 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data021[i].k), Tp(data021[i].nu),
|
| 1118 |
|
|
Tp(data021[i].phi));
|
| 1119 |
|
|
const Tp f0 = data021[i].f0;
|
| 1120 |
|
|
const Tp diff = f - f0;
|
| 1121 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1122 |
|
|
max_abs_diff = std::abs(diff);
|
| 1123 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1124 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1125 |
|
|
{
|
| 1126 |
|
|
const Tp frac = diff / f0;
|
| 1127 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1128 |
|
|
max_abs_frac = std::abs(frac);
|
| 1129 |
|
|
}
|
| 1130 |
|
|
}
|
| 1131 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1132 |
|
|
}
|
| 1133 |
|
|
|
| 1134 |
|
|
// Test data for k=-0.69999999999999996, nu=0.10000000000000001.
|
| 1135 |
|
|
testcase_ellint_3<double> data022[] = {
|
| 1136 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.10000000000000001,
|
| 1137 |
|
|
0.0000000000000000 },
|
| 1138 |
|
|
{ 0.17479076384884681, -0.69999999999999996, 0.10000000000000001,
|
| 1139 |
|
|
0.17453292519943295 },
|
| 1140 |
|
|
{ 0.35114844900396364, -0.69999999999999996, 0.10000000000000001,
|
| 1141 |
|
|
0.34906585039886590 },
|
| 1142 |
|
|
{ 0.53072776947527012, -0.69999999999999996, 0.10000000000000001,
|
| 1143 |
|
|
0.52359877559829882 },
|
| 1144 |
|
|
{ 0.71530198262386246, -0.69999999999999996, 0.10000000000000001,
|
| 1145 |
|
|
0.69813170079773179 },
|
| 1146 |
|
|
{ 0.90666760677828306, -0.69999999999999996, 0.10000000000000001,
|
| 1147 |
|
|
0.87266462599716477 },
|
| 1148 |
|
|
{ 1.1063366517438080, -0.69999999999999996, 0.10000000000000001,
|
| 1149 |
|
|
1.0471975511965976 },
|
| 1150 |
|
|
{ 1.3149477243092147, -0.69999999999999996, 0.10000000000000001,
|
| 1151 |
|
|
1.2217304763960306 },
|
| 1152 |
|
|
{ 1.5314886725038925, -0.69999999999999996, 0.10000000000000001,
|
| 1153 |
|
|
1.3962634015954636 },
|
| 1154 |
|
|
{ 1.7528050171757608, -0.69999999999999996, 0.10000000000000001,
|
| 1155 |
|
|
1.5707963267948966 },
|
| 1156 |
|
|
};
|
| 1157 |
|
|
|
| 1158 |
|
|
// Test function for k=-0.69999999999999996, nu=0.10000000000000001.
|
| 1159 |
|
|
template <typename Tp>
|
| 1160 |
|
|
void test022()
|
| 1161 |
|
|
{
|
| 1162 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1163 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1164 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1165 |
|
|
unsigned int num_datum = sizeof(data022)
|
| 1166 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1167 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1168 |
|
|
{
|
| 1169 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data022[i].k), Tp(data022[i].nu),
|
| 1170 |
|
|
Tp(data022[i].phi));
|
| 1171 |
|
|
const Tp f0 = data022[i].f0;
|
| 1172 |
|
|
const Tp diff = f - f0;
|
| 1173 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1174 |
|
|
max_abs_diff = std::abs(diff);
|
| 1175 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1176 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1177 |
|
|
{
|
| 1178 |
|
|
const Tp frac = diff / f0;
|
| 1179 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1180 |
|
|
max_abs_frac = std::abs(frac);
|
| 1181 |
|
|
}
|
| 1182 |
|
|
}
|
| 1183 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1184 |
|
|
}
|
| 1185 |
|
|
|
| 1186 |
|
|
// Test data for k=-0.69999999999999996, nu=0.20000000000000001.
|
| 1187 |
|
|
testcase_ellint_3<double> data023[] = {
|
| 1188 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.20000000000000001,
|
| 1189 |
|
|
0.0000000000000000 },
|
| 1190 |
|
|
{ 0.17461479077791472, -0.69999999999999996, 0.20000000000000001,
|
| 1191 |
|
|
0.17453292519943295 },
|
| 1192 |
|
|
{ 0.34976950621407538, -0.69999999999999996, 0.20000000000000001,
|
| 1193 |
|
|
0.34906585039886590 },
|
| 1194 |
|
|
{ 0.52622533231350188, -0.69999999999999996, 0.20000000000000001,
|
| 1195 |
|
|
0.52359877559829882 },
|
| 1196 |
|
|
{ 0.70508774017895226, -0.69999999999999996, 0.20000000000000001,
|
| 1197 |
|
|
0.69813170079773179 },
|
| 1198 |
|
|
{ 0.88775302531730294, -0.69999999999999996, 0.20000000000000001,
|
| 1199 |
|
|
0.87266462599716477 },
|
| 1200 |
|
|
{ 1.0756195476149006, -0.69999999999999996, 0.20000000000000001,
|
| 1201 |
|
|
1.0471975511965976 },
|
| 1202 |
|
|
{ 1.2695349716654372, -0.69999999999999996, 0.20000000000000001,
|
| 1203 |
|
|
1.2217304763960306 },
|
| 1204 |
|
|
{ 1.4690814617070540, -0.69999999999999996, 0.20000000000000001,
|
| 1205 |
|
|
1.3962634015954636 },
|
| 1206 |
|
|
{ 1.6721098780092147, -0.69999999999999996, 0.20000000000000001,
|
| 1207 |
|
|
1.5707963267948966 },
|
| 1208 |
|
|
};
|
| 1209 |
|
|
|
| 1210 |
|
|
// Test function for k=-0.69999999999999996, nu=0.20000000000000001.
|
| 1211 |
|
|
template <typename Tp>
|
| 1212 |
|
|
void test023()
|
| 1213 |
|
|
{
|
| 1214 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1215 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1216 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1217 |
|
|
unsigned int num_datum = sizeof(data023)
|
| 1218 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1219 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1220 |
|
|
{
|
| 1221 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data023[i].k), Tp(data023[i].nu),
|
| 1222 |
|
|
Tp(data023[i].phi));
|
| 1223 |
|
|
const Tp f0 = data023[i].f0;
|
| 1224 |
|
|
const Tp diff = f - f0;
|
| 1225 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1226 |
|
|
max_abs_diff = std::abs(diff);
|
| 1227 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1228 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1229 |
|
|
{
|
| 1230 |
|
|
const Tp frac = diff / f0;
|
| 1231 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1232 |
|
|
max_abs_frac = std::abs(frac);
|
| 1233 |
|
|
}
|
| 1234 |
|
|
}
|
| 1235 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1236 |
|
|
}
|
| 1237 |
|
|
|
| 1238 |
|
|
// Test data for k=-0.69999999999999996, nu=0.29999999999999999.
|
| 1239 |
|
|
testcase_ellint_3<double> data024[] = {
|
| 1240 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.29999999999999999,
|
| 1241 |
|
|
0.0000000000000000 },
|
| 1242 |
|
|
{ 0.17443945136076172, -0.69999999999999996, 0.29999999999999999,
|
| 1243 |
|
|
0.17453292519943295 },
|
| 1244 |
|
|
{ 0.34840956983535287, -0.69999999999999996, 0.29999999999999999,
|
| 1245 |
|
|
0.34906585039886590 },
|
| 1246 |
|
|
{ 0.52185308551329179, -0.69999999999999996, 0.29999999999999999,
|
| 1247 |
|
|
0.52359877559829882 },
|
| 1248 |
|
|
{ 0.69535240431168266, -0.69999999999999996, 0.29999999999999999,
|
| 1249 |
|
|
0.69813170079773179 },
|
| 1250 |
|
|
{ 0.87007983473964923, -0.69999999999999996, 0.29999999999999999,
|
| 1251 |
|
|
0.87266462599716477 },
|
| 1252 |
|
|
{ 1.0474657975577066, -0.69999999999999996, 0.29999999999999999,
|
| 1253 |
|
|
1.0471975511965976 },
|
| 1254 |
|
|
{ 1.2286225419931889, -0.69999999999999996, 0.29999999999999999,
|
| 1255 |
|
|
1.2217304763960306 },
|
| 1256 |
|
|
{ 1.4136490671013271, -0.69999999999999996, 0.29999999999999999,
|
| 1257 |
|
|
1.3962634015954636 },
|
| 1258 |
|
|
{ 1.6011813647733213, -0.69999999999999996, 0.29999999999999999,
|
| 1259 |
|
|
1.5707963267948966 },
|
| 1260 |
|
|
};
|
| 1261 |
|
|
|
| 1262 |
|
|
// Test function for k=-0.69999999999999996, nu=0.29999999999999999.
|
| 1263 |
|
|
template <typename Tp>
|
| 1264 |
|
|
void test024()
|
| 1265 |
|
|
{
|
| 1266 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1267 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1268 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1269 |
|
|
unsigned int num_datum = sizeof(data024)
|
| 1270 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1271 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1272 |
|
|
{
|
| 1273 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data024[i].k), Tp(data024[i].nu),
|
| 1274 |
|
|
Tp(data024[i].phi));
|
| 1275 |
|
|
const Tp f0 = data024[i].f0;
|
| 1276 |
|
|
const Tp diff = f - f0;
|
| 1277 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1278 |
|
|
max_abs_diff = std::abs(diff);
|
| 1279 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1280 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1281 |
|
|
{
|
| 1282 |
|
|
const Tp frac = diff / f0;
|
| 1283 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1284 |
|
|
max_abs_frac = std::abs(frac);
|
| 1285 |
|
|
}
|
| 1286 |
|
|
}
|
| 1287 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1288 |
|
|
}
|
| 1289 |
|
|
|
| 1290 |
|
|
// Test data for k=-0.69999999999999996, nu=0.40000000000000002.
|
| 1291 |
|
|
testcase_ellint_3<double> data025[] = {
|
| 1292 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.40000000000000002,
|
| 1293 |
|
|
0.0000000000000000 },
|
| 1294 |
|
|
{ 0.17426474153983226, -0.69999999999999996, 0.40000000000000002,
|
| 1295 |
|
|
0.17453292519943295 },
|
| 1296 |
|
|
{ 0.34706817945773732, -0.69999999999999996, 0.40000000000000002,
|
| 1297 |
|
|
0.34906585039886590 },
|
| 1298 |
|
|
{ 0.51760452851738159, -0.69999999999999996, 0.40000000000000002,
|
| 1299 |
|
|
0.52359877559829882 },
|
| 1300 |
|
|
{ 0.68605801534722766, -0.69999999999999996, 0.40000000000000002,
|
| 1301 |
|
|
0.69813170079773179 },
|
| 1302 |
|
|
{ 0.85351339387296532, -0.69999999999999996, 0.40000000000000002,
|
| 1303 |
|
|
0.87266462599716477 },
|
| 1304 |
|
|
{ 1.0215297967969537, -0.69999999999999996, 0.40000000000000002,
|
| 1305 |
|
|
1.0471975511965976 },
|
| 1306 |
|
|
{ 1.1915051074460528, -0.69999999999999996, 0.40000000000000002,
|
| 1307 |
|
|
1.2217304763960306 },
|
| 1308 |
|
|
{ 1.3639821911744707, -0.69999999999999996, 0.40000000000000002,
|
| 1309 |
|
|
1.3962634015954636 },
|
| 1310 |
|
|
{ 1.5382162002954762, -0.69999999999999996, 0.40000000000000002,
|
| 1311 |
|
|
1.5707963267948966 },
|
| 1312 |
|
|
};
|
| 1313 |
|
|
|
| 1314 |
|
|
// Test function for k=-0.69999999999999996, nu=0.40000000000000002.
|
| 1315 |
|
|
template <typename Tp>
|
| 1316 |
|
|
void test025()
|
| 1317 |
|
|
{
|
| 1318 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1319 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1320 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1321 |
|
|
unsigned int num_datum = sizeof(data025)
|
| 1322 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1323 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1324 |
|
|
{
|
| 1325 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data025[i].k), Tp(data025[i].nu),
|
| 1326 |
|
|
Tp(data025[i].phi));
|
| 1327 |
|
|
const Tp f0 = data025[i].f0;
|
| 1328 |
|
|
const Tp diff = f - f0;
|
| 1329 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1330 |
|
|
max_abs_diff = std::abs(diff);
|
| 1331 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1332 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1333 |
|
|
{
|
| 1334 |
|
|
const Tp frac = diff / f0;
|
| 1335 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1336 |
|
|
max_abs_frac = std::abs(frac);
|
| 1337 |
|
|
}
|
| 1338 |
|
|
}
|
| 1339 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1340 |
|
|
}
|
| 1341 |
|
|
|
| 1342 |
|
|
// Test data for k=-0.69999999999999996, nu=0.50000000000000000.
|
| 1343 |
|
|
testcase_ellint_3<double> data026[] = {
|
| 1344 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.50000000000000000,
|
| 1345 |
|
|
0.0000000000000000 },
|
| 1346 |
|
|
{ 0.17409065729516093, -0.69999999999999996, 0.50000000000000000,
|
| 1347 |
|
|
0.17453292519943295 },
|
| 1348 |
|
|
{ 0.34574489064986091, -0.69999999999999996, 0.50000000000000000,
|
| 1349 |
|
|
0.34906585039886590 },
|
| 1350 |
|
|
{ 0.51347361925579793, -0.69999999999999996, 0.50000000000000000,
|
| 1351 |
|
|
0.52359877559829882 },
|
| 1352 |
|
|
{ 0.67717079489579290, -0.69999999999999996, 0.50000000000000000,
|
| 1353 |
|
|
0.69813170079773179 },
|
| 1354 |
|
|
{ 0.83793902055292280, -0.69999999999999996, 0.50000000000000000,
|
| 1355 |
|
|
0.87266462599716477 },
|
| 1356 |
|
|
{ 0.99752863545289705, -0.69999999999999996, 0.50000000000000000,
|
| 1357 |
|
|
1.0471975511965976 },
|
| 1358 |
|
|
{ 1.1576240080401499, -0.69999999999999996, 0.50000000000000000,
|
| 1359 |
|
|
1.2217304763960306 },
|
| 1360 |
|
|
{ 1.3191464023923762, -0.69999999999999996, 0.50000000000000000,
|
| 1361 |
|
|
1.3962634015954636 },
|
| 1362 |
|
|
{ 1.4818433192178544, -0.69999999999999996, 0.50000000000000000,
|
| 1363 |
|
|
1.5707963267948966 },
|
| 1364 |
|
|
};
|
| 1365 |
|
|
|
| 1366 |
|
|
// Test function for k=-0.69999999999999996, nu=0.50000000000000000.
|
| 1367 |
|
|
template <typename Tp>
|
| 1368 |
|
|
void test026()
|
| 1369 |
|
|
{
|
| 1370 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1371 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1372 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1373 |
|
|
unsigned int num_datum = sizeof(data026)
|
| 1374 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1375 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1376 |
|
|
{
|
| 1377 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data026[i].k), Tp(data026[i].nu),
|
| 1378 |
|
|
Tp(data026[i].phi));
|
| 1379 |
|
|
const Tp f0 = data026[i].f0;
|
| 1380 |
|
|
const Tp diff = f - f0;
|
| 1381 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1382 |
|
|
max_abs_diff = std::abs(diff);
|
| 1383 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1384 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1385 |
|
|
{
|
| 1386 |
|
|
const Tp frac = diff / f0;
|
| 1387 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1388 |
|
|
max_abs_frac = std::abs(frac);
|
| 1389 |
|
|
}
|
| 1390 |
|
|
}
|
| 1391 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1392 |
|
|
}
|
| 1393 |
|
|
|
| 1394 |
|
|
// Test data for k=-0.69999999999999996, nu=0.59999999999999998.
|
| 1395 |
|
|
testcase_ellint_3<double> data027[] = {
|
| 1396 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.59999999999999998,
|
| 1397 |
|
|
0.0000000000000000 },
|
| 1398 |
|
|
{ 0.17391719464391611, -0.69999999999999996, 0.59999999999999998,
|
| 1399 |
|
|
0.17453292519943295 },
|
| 1400 |
|
|
{ 0.34443927423869031, -0.69999999999999996, 0.59999999999999998,
|
| 1401 |
|
|
0.34906585039886590 },
|
| 1402 |
|
|
{ 0.50945473266486074, -0.69999999999999996, 0.59999999999999998,
|
| 1403 |
|
|
0.52359877559829882 },
|
| 1404 |
|
|
{ 0.66866056326513823, -0.69999999999999996, 0.59999999999999998,
|
| 1405 |
|
|
0.69813170079773179 },
|
| 1406 |
|
|
{ 0.82325830002337352, -0.69999999999999996, 0.59999999999999998,
|
| 1407 |
|
|
0.87266462599716477 },
|
| 1408 |
|
|
{ 0.97522808245669357, -0.69999999999999996, 0.59999999999999998,
|
| 1409 |
|
|
1.0471975511965976 },
|
| 1410 |
|
|
{ 1.1265300613705282, -0.69999999999999996, 0.59999999999999998,
|
| 1411 |
|
|
1.2217304763960306 },
|
| 1412 |
|
|
{ 1.2784066076152003, -0.69999999999999996, 0.59999999999999998,
|
| 1413 |
|
|
1.3962634015954636 },
|
| 1414 |
|
|
{ 1.4309994736080540, -0.69999999999999996, 0.59999999999999998,
|
| 1415 |
|
|
1.5707963267948966 },
|
| 1416 |
|
|
};
|
| 1417 |
|
|
|
| 1418 |
|
|
// Test function for k=-0.69999999999999996, nu=0.59999999999999998.
|
| 1419 |
|
|
template <typename Tp>
|
| 1420 |
|
|
void test027()
|
| 1421 |
|
|
{
|
| 1422 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1423 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1424 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1425 |
|
|
unsigned int num_datum = sizeof(data027)
|
| 1426 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1427 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1428 |
|
|
{
|
| 1429 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data027[i].k), Tp(data027[i].nu),
|
| 1430 |
|
|
Tp(data027[i].phi));
|
| 1431 |
|
|
const Tp f0 = data027[i].f0;
|
| 1432 |
|
|
const Tp diff = f - f0;
|
| 1433 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1434 |
|
|
max_abs_diff = std::abs(diff);
|
| 1435 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1436 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1437 |
|
|
{
|
| 1438 |
|
|
const Tp frac = diff / f0;
|
| 1439 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1440 |
|
|
max_abs_frac = std::abs(frac);
|
| 1441 |
|
|
}
|
| 1442 |
|
|
}
|
| 1443 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1444 |
|
|
}
|
| 1445 |
|
|
|
| 1446 |
|
|
// Test data for k=-0.69999999999999996, nu=0.69999999999999996.
|
| 1447 |
|
|
testcase_ellint_3<double> data028[] = {
|
| 1448 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.69999999999999996,
|
| 1449 |
|
|
0.0000000000000000 },
|
| 1450 |
|
|
{ 0.17374434963995028, -0.69999999999999996, 0.69999999999999996,
|
| 1451 |
|
|
0.17453292519943295 },
|
| 1452 |
|
|
{ 0.34315091562900674, -0.69999999999999996, 0.69999999999999996,
|
| 1453 |
|
|
0.34906585039886590 },
|
| 1454 |
|
|
{ 0.50554262375653358, -0.69999999999999996, 0.69999999999999996,
|
| 1455 |
|
|
0.52359877559829882 },
|
| 1456 |
|
|
{ 0.66050025406305812, -0.69999999999999996, 0.69999999999999996,
|
| 1457 |
|
|
0.69813170079773179 },
|
| 1458 |
|
|
{ 0.80938620118847404, -0.69999999999999996, 0.69999999999999996,
|
| 1459 |
|
|
0.87266462599716477 },
|
| 1460 |
|
|
{ 0.95443223855852144, -0.69999999999999996, 0.69999999999999996,
|
| 1461 |
|
|
1.0471975511965976 },
|
| 1462 |
|
|
{ 1.0978573207128302, -0.69999999999999996, 0.69999999999999996,
|
| 1463 |
|
|
1.2217304763960306 },
|
| 1464 |
|
|
{ 1.2411754575007123, -0.69999999999999996, 0.69999999999999996,
|
| 1465 |
|
|
1.3962634015954636 },
|
| 1466 |
|
|
{ 1.3848459188329196, -0.69999999999999996, 0.69999999999999996,
|
| 1467 |
|
|
1.5707963267948966 },
|
| 1468 |
|
|
};
|
| 1469 |
|
|
|
| 1470 |
|
|
// Test function for k=-0.69999999999999996, nu=0.69999999999999996.
|
| 1471 |
|
|
template <typename Tp>
|
| 1472 |
|
|
void test028()
|
| 1473 |
|
|
{
|
| 1474 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1475 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1476 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1477 |
|
|
unsigned int num_datum = sizeof(data028)
|
| 1478 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1479 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1480 |
|
|
{
|
| 1481 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data028[i].k), Tp(data028[i].nu),
|
| 1482 |
|
|
Tp(data028[i].phi));
|
| 1483 |
|
|
const Tp f0 = data028[i].f0;
|
| 1484 |
|
|
const Tp diff = f - f0;
|
| 1485 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1486 |
|
|
max_abs_diff = std::abs(diff);
|
| 1487 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1488 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1489 |
|
|
{
|
| 1490 |
|
|
const Tp frac = diff / f0;
|
| 1491 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1492 |
|
|
max_abs_frac = std::abs(frac);
|
| 1493 |
|
|
}
|
| 1494 |
|
|
}
|
| 1495 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1496 |
|
|
}
|
| 1497 |
|
|
|
| 1498 |
|
|
// Test data for k=-0.69999999999999996, nu=0.80000000000000004.
|
| 1499 |
|
|
testcase_ellint_3<double> data029[] = {
|
| 1500 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.80000000000000004,
|
| 1501 |
|
|
0.0000000000000000 },
|
| 1502 |
|
|
{ 0.17357211837335737, -0.69999999999999996, 0.80000000000000004,
|
| 1503 |
|
|
0.17453292519943295 },
|
| 1504 |
|
|
{ 0.34187941416012108, -0.69999999999999996, 0.80000000000000004,
|
| 1505 |
|
|
0.34906585039886590 },
|
| 1506 |
|
|
{ 0.50173239465478270, -0.69999999999999996, 0.80000000000000004,
|
| 1507 |
|
|
0.52359877559829882 },
|
| 1508 |
|
|
{ 0.65266550725988315, -0.69999999999999996, 0.80000000000000004,
|
| 1509 |
|
|
0.69813170079773179 },
|
| 1510 |
|
|
{ 0.79624879865249298, -0.69999999999999996, 0.80000000000000004,
|
| 1511 |
|
|
0.87266462599716477 },
|
| 1512 |
|
|
{ 0.93497577043296920, -0.69999999999999996, 0.80000000000000004,
|
| 1513 |
|
|
1.0471975511965976 },
|
| 1514 |
|
|
{ 1.0713041566930748, -0.69999999999999996, 0.80000000000000004,
|
| 1515 |
|
|
1.2217304763960306 },
|
| 1516 |
|
|
{ 1.2069772023255652, -0.69999999999999996, 0.80000000000000004,
|
| 1517 |
|
|
1.3962634015954636 },
|
| 1518 |
|
|
{ 1.3427110650397533, -0.69999999999999996, 0.80000000000000004,
|
| 1519 |
|
|
1.5707963267948966 },
|
| 1520 |
|
|
};
|
| 1521 |
|
|
|
| 1522 |
|
|
// Test function for k=-0.69999999999999996, nu=0.80000000000000004.
|
| 1523 |
|
|
template <typename Tp>
|
| 1524 |
|
|
void test029()
|
| 1525 |
|
|
{
|
| 1526 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1527 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1528 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1529 |
|
|
unsigned int num_datum = sizeof(data029)
|
| 1530 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1531 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1532 |
|
|
{
|
| 1533 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data029[i].k), Tp(data029[i].nu),
|
| 1534 |
|
|
Tp(data029[i].phi));
|
| 1535 |
|
|
const Tp f0 = data029[i].f0;
|
| 1536 |
|
|
const Tp diff = f - f0;
|
| 1537 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1538 |
|
|
max_abs_diff = std::abs(diff);
|
| 1539 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1540 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1541 |
|
|
{
|
| 1542 |
|
|
const Tp frac = diff / f0;
|
| 1543 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1544 |
|
|
max_abs_frac = std::abs(frac);
|
| 1545 |
|
|
}
|
| 1546 |
|
|
}
|
| 1547 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1548 |
|
|
}
|
| 1549 |
|
|
|
| 1550 |
|
|
// Test data for k=-0.69999999999999996, nu=0.90000000000000002.
|
| 1551 |
|
|
testcase_ellint_3<double> data030[] = {
|
| 1552 |
|
|
{ -0.0000000000000000, -0.69999999999999996, 0.90000000000000002,
|
| 1553 |
|
|
0.0000000000000000 },
|
| 1554 |
|
|
{ 0.17340049697003634, -0.69999999999999996, 0.90000000000000002,
|
| 1555 |
|
|
0.17453292519943295 },
|
| 1556 |
|
|
{ 0.34062438249741556, -0.69999999999999996, 0.90000000000000002,
|
| 1557 |
|
|
0.34906585039886590 },
|
| 1558 |
|
|
{ 0.49801946510076878, -0.69999999999999996, 0.90000000000000002,
|
| 1559 |
|
|
0.52359877559829882 },
|
| 1560 |
|
|
{ 0.64513432604750487, -0.69999999999999996, 0.90000000000000002,
|
| 1561 |
|
|
0.69813170079773179 },
|
| 1562 |
|
|
{ 0.78378145487573758, -0.69999999999999996, 0.90000000000000002,
|
| 1563 |
|
|
0.87266462599716477 },
|
| 1564 |
|
|
{ 0.91671799500854634, -0.69999999999999996, 0.90000000000000002,
|
| 1565 |
|
|
1.0471975511965976 },
|
| 1566 |
|
|
{ 1.0466193579463123, -0.69999999999999996, 0.90000000000000002,
|
| 1567 |
|
|
1.2217304763960306 },
|
| 1568 |
|
|
{ 1.1754218079199146, -0.69999999999999996, 0.90000000000000002,
|
| 1569 |
|
|
1.3962634015954636 },
|
| 1570 |
|
|
{ 1.3040500499695911, -0.69999999999999996, 0.90000000000000002,
|
| 1571 |
|
|
1.5707963267948966 },
|
| 1572 |
|
|
};
|
| 1573 |
|
|
|
| 1574 |
|
|
// Test function for k=-0.69999999999999996, nu=0.90000000000000002.
|
| 1575 |
|
|
template <typename Tp>
|
| 1576 |
|
|
void test030()
|
| 1577 |
|
|
{
|
| 1578 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1579 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1580 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1581 |
|
|
unsigned int num_datum = sizeof(data030)
|
| 1582 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1583 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1584 |
|
|
{
|
| 1585 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data030[i].k), Tp(data030[i].nu),
|
| 1586 |
|
|
Tp(data030[i].phi));
|
| 1587 |
|
|
const Tp f0 = data030[i].f0;
|
| 1588 |
|
|
const Tp diff = f - f0;
|
| 1589 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1590 |
|
|
max_abs_diff = std::abs(diff);
|
| 1591 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1592 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1593 |
|
|
{
|
| 1594 |
|
|
const Tp frac = diff / f0;
|
| 1595 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1596 |
|
|
max_abs_frac = std::abs(frac);
|
| 1597 |
|
|
}
|
| 1598 |
|
|
}
|
| 1599 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1600 |
|
|
}
|
| 1601 |
|
|
|
| 1602 |
|
|
// Test data for k=-0.59999999999999998, nu=0.0000000000000000.
|
| 1603 |
|
|
testcase_ellint_3<double> data031[] = {
|
| 1604 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.0000000000000000,
|
| 1605 |
|
|
0.0000000000000000 },
|
| 1606 |
|
|
{ 0.17485154362988362, -0.59999999999999998, 0.0000000000000000,
|
| 1607 |
|
|
0.17453292519943295 },
|
| 1608 |
|
|
{ 0.35160509865544326, -0.59999999999999998, 0.0000000000000000,
|
| 1609 |
|
|
0.34906585039886590 },
|
| 1610 |
|
|
{ 0.53210652578446160, -0.59999999999999998, 0.0000000000000000,
|
| 1611 |
|
|
0.52359877559829882 },
|
| 1612 |
|
|
{ 0.71805304664485670, -0.59999999999999998, 0.0000000000000000,
|
| 1613 |
|
|
0.69813170079773179 },
|
| 1614 |
|
|
{ 0.91082759030195970, -0.59999999999999998, 0.0000000000000000,
|
| 1615 |
|
|
0.87266462599716477 },
|
| 1616 |
|
|
{ 1.1112333229323361, -0.59999999999999998, 0.0000000000000000,
|
| 1617 |
|
|
1.0471975511965976 },
|
| 1618 |
|
|
{ 1.3191461190365270, -0.59999999999999998, 0.0000000000000000,
|
| 1619 |
|
|
1.2217304763960306 },
|
| 1620 |
|
|
{ 1.5332022105084773, -0.59999999999999998, 0.0000000000000000,
|
| 1621 |
|
|
1.3962634015954636 },
|
| 1622 |
|
|
{ 1.7507538029157526, -0.59999999999999998, 0.0000000000000000,
|
| 1623 |
|
|
1.5707963267948966 },
|
| 1624 |
|
|
};
|
| 1625 |
|
|
|
| 1626 |
|
|
// Test function for k=-0.59999999999999998, nu=0.0000000000000000.
|
| 1627 |
|
|
template <typename Tp>
|
| 1628 |
|
|
void test031()
|
| 1629 |
|
|
{
|
| 1630 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1631 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1632 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1633 |
|
|
unsigned int num_datum = sizeof(data031)
|
| 1634 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1635 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1636 |
|
|
{
|
| 1637 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data031[i].k), Tp(data031[i].nu),
|
| 1638 |
|
|
Tp(data031[i].phi));
|
| 1639 |
|
|
const Tp f0 = data031[i].f0;
|
| 1640 |
|
|
const Tp diff = f - f0;
|
| 1641 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1642 |
|
|
max_abs_diff = std::abs(diff);
|
| 1643 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1644 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1645 |
|
|
{
|
| 1646 |
|
|
const Tp frac = diff / f0;
|
| 1647 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1648 |
|
|
max_abs_frac = std::abs(frac);
|
| 1649 |
|
|
}
|
| 1650 |
|
|
}
|
| 1651 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1652 |
|
|
}
|
| 1653 |
|
|
|
| 1654 |
|
|
// Test data for k=-0.59999999999999998, nu=0.10000000000000001.
|
| 1655 |
|
|
testcase_ellint_3<double> data032[] = {
|
| 1656 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.10000000000000001,
|
| 1657 |
|
|
0.0000000000000000 },
|
| 1658 |
|
|
{ 0.17467514275022014, -0.59999999999999998, 0.10000000000000001,
|
| 1659 |
|
|
0.17453292519943295 },
|
| 1660 |
|
|
{ 0.35021333086258255, -0.59999999999999998, 0.10000000000000001,
|
| 1661 |
|
|
0.34906585039886590 },
|
| 1662 |
|
|
{ 0.52751664092962713, -0.59999999999999998, 0.10000000000000001,
|
| 1663 |
|
|
0.52359877559829882 },
|
| 1664 |
|
|
{ 0.70752126971957885, -0.59999999999999998, 0.10000000000000001,
|
| 1665 |
|
|
0.69813170079773179 },
|
| 1666 |
|
|
{ 0.89111058756112871, -0.59999999999999998, 0.10000000000000001,
|
| 1667 |
|
|
0.87266462599716477 },
|
| 1668 |
|
|
{ 1.0789241202877768, -0.59999999999999998, 0.10000000000000001,
|
| 1669 |
|
|
1.0471975511965976 },
|
| 1670 |
|
|
{ 1.2710800210399946, -0.59999999999999998, 0.10000000000000001,
|
| 1671 |
|
|
1.2217304763960306 },
|
| 1672 |
|
|
{ 1.4669060574440276, -0.59999999999999998, 0.10000000000000001,
|
| 1673 |
|
|
1.3962634015954636 },
|
| 1674 |
|
|
{ 1.6648615773343014, -0.59999999999999998, 0.10000000000000001,
|
| 1675 |
|
|
1.5707963267948966 },
|
| 1676 |
|
|
};
|
| 1677 |
|
|
|
| 1678 |
|
|
// Test function for k=-0.59999999999999998, nu=0.10000000000000001.
|
| 1679 |
|
|
template <typename Tp>
|
| 1680 |
|
|
void test032()
|
| 1681 |
|
|
{
|
| 1682 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1683 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1684 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1685 |
|
|
unsigned int num_datum = sizeof(data032)
|
| 1686 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1687 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1688 |
|
|
{
|
| 1689 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data032[i].k), Tp(data032[i].nu),
|
| 1690 |
|
|
Tp(data032[i].phi));
|
| 1691 |
|
|
const Tp f0 = data032[i].f0;
|
| 1692 |
|
|
const Tp diff = f - f0;
|
| 1693 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1694 |
|
|
max_abs_diff = std::abs(diff);
|
| 1695 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1696 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1697 |
|
|
{
|
| 1698 |
|
|
const Tp frac = diff / f0;
|
| 1699 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1700 |
|
|
max_abs_frac = std::abs(frac);
|
| 1701 |
|
|
}
|
| 1702 |
|
|
}
|
| 1703 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1704 |
|
|
}
|
| 1705 |
|
|
|
| 1706 |
|
|
// Test data for k=-0.59999999999999998, nu=0.20000000000000001.
|
| 1707 |
|
|
testcase_ellint_3<double> data033[] = {
|
| 1708 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.20000000000000001,
|
| 1709 |
|
|
0.0000000000000000 },
|
| 1710 |
|
|
{ 0.17449937871800653, -0.59999999999999998, 0.20000000000000001,
|
| 1711 |
|
|
0.17453292519943295 },
|
| 1712 |
|
|
{ 0.34884093647346553, -0.59999999999999998, 0.20000000000000001,
|
| 1713 |
|
|
0.34906585039886590 },
|
| 1714 |
|
|
{ 0.52306221119844110, -0.59999999999999998, 0.20000000000000001,
|
| 1715 |
|
|
0.52359877559829882 },
|
| 1716 |
|
|
{ 0.69749955678982223, -0.59999999999999998, 0.20000000000000001,
|
| 1717 |
|
|
0.69813170079773179 },
|
| 1718 |
|
|
{ 0.87274610682416853, -0.59999999999999998, 0.20000000000000001,
|
| 1719 |
|
|
0.87266462599716477 },
|
| 1720 |
|
|
{ 1.0494620540750792, -0.59999999999999998, 0.20000000000000001,
|
| 1721 |
|
|
1.0471975511965976 },
|
| 1722 |
|
|
{ 1.2280847305507339, -0.59999999999999998, 0.20000000000000001,
|
| 1723 |
|
|
1.2217304763960306 },
|
| 1724 |
|
|
{ 1.4085436279696886, -0.59999999999999998, 0.20000000000000001,
|
| 1725 |
|
|
1.3962634015954636 },
|
| 1726 |
|
|
{ 1.5901418016279374, -0.59999999999999998, 0.20000000000000001,
|
| 1727 |
|
|
1.5707963267948966 },
|
| 1728 |
|
|
};
|
| 1729 |
|
|
|
| 1730 |
|
|
// Test function for k=-0.59999999999999998, nu=0.20000000000000001.
|
| 1731 |
|
|
template <typename Tp>
|
| 1732 |
|
|
void test033()
|
| 1733 |
|
|
{
|
| 1734 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1735 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1736 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1737 |
|
|
unsigned int num_datum = sizeof(data033)
|
| 1738 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1739 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1740 |
|
|
{
|
| 1741 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data033[i].k), Tp(data033[i].nu),
|
| 1742 |
|
|
Tp(data033[i].phi));
|
| 1743 |
|
|
const Tp f0 = data033[i].f0;
|
| 1744 |
|
|
const Tp diff = f - f0;
|
| 1745 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1746 |
|
|
max_abs_diff = std::abs(diff);
|
| 1747 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1748 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1749 |
|
|
{
|
| 1750 |
|
|
const Tp frac = diff / f0;
|
| 1751 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1752 |
|
|
max_abs_frac = std::abs(frac);
|
| 1753 |
|
|
}
|
| 1754 |
|
|
}
|
| 1755 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1756 |
|
|
}
|
| 1757 |
|
|
|
| 1758 |
|
|
// Test data for k=-0.59999999999999998, nu=0.29999999999999999.
|
| 1759 |
|
|
testcase_ellint_3<double> data034[] = {
|
| 1760 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.29999999999999999,
|
| 1761 |
|
|
0.0000000000000000 },
|
| 1762 |
|
|
{ 0.17432424744393935, -0.59999999999999998, 0.29999999999999999,
|
| 1763 |
|
|
0.17453292519943295 },
|
| 1764 |
|
|
{ 0.34748744127146447, -0.59999999999999998, 0.29999999999999999,
|
| 1765 |
|
|
0.34906585039886590 },
|
| 1766 |
|
|
{ 0.51873632743924847, -0.59999999999999998, 0.29999999999999999,
|
| 1767 |
|
|
0.52359877559829882 },
|
| 1768 |
|
|
{ 0.68794610396313127, -0.59999999999999998, 0.29999999999999999,
|
| 1769 |
|
|
0.69813170079773179 },
|
| 1770 |
|
|
{ 0.85558070175468726, -0.59999999999999998, 0.29999999999999999,
|
| 1771 |
|
|
0.87266462599716477 },
|
| 1772 |
|
|
{ 1.0224416343605653, -0.59999999999999998, 0.29999999999999999,
|
| 1773 |
|
|
1.0471975511965976 },
|
| 1774 |
|
|
{ 1.1893144457936788, -0.59999999999999998, 0.29999999999999999,
|
| 1775 |
|
|
1.2217304763960306 },
|
| 1776 |
|
|
{ 1.3566435377982575, -0.59999999999999998, 0.29999999999999999,
|
| 1777 |
|
|
1.3962634015954636 },
|
| 1778 |
|
|
{ 1.5243814243493585, -0.59999999999999998, 0.29999999999999999,
|
| 1779 |
|
|
1.5707963267948966 },
|
| 1780 |
|
|
};
|
| 1781 |
|
|
|
| 1782 |
|
|
// Test function for k=-0.59999999999999998, nu=0.29999999999999999.
|
| 1783 |
|
|
template <typename Tp>
|
| 1784 |
|
|
void test034()
|
| 1785 |
|
|
{
|
| 1786 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1787 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1788 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1789 |
|
|
unsigned int num_datum = sizeof(data034)
|
| 1790 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1791 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1792 |
|
|
{
|
| 1793 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data034[i].k), Tp(data034[i].nu),
|
| 1794 |
|
|
Tp(data034[i].phi));
|
| 1795 |
|
|
const Tp f0 = data034[i].f0;
|
| 1796 |
|
|
const Tp diff = f - f0;
|
| 1797 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1798 |
|
|
max_abs_diff = std::abs(diff);
|
| 1799 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1800 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1801 |
|
|
{
|
| 1802 |
|
|
const Tp frac = diff / f0;
|
| 1803 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1804 |
|
|
max_abs_frac = std::abs(frac);
|
| 1805 |
|
|
}
|
| 1806 |
|
|
}
|
| 1807 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1808 |
|
|
}
|
| 1809 |
|
|
|
| 1810 |
|
|
// Test data for k=-0.59999999999999998, nu=0.40000000000000002.
|
| 1811 |
|
|
testcase_ellint_3<double> data035[] = {
|
| 1812 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.40000000000000002,
|
| 1813 |
|
|
0.0000000000000000 },
|
| 1814 |
|
|
{ 0.17414974487670720, -0.59999999999999998, 0.40000000000000002,
|
| 1815 |
|
|
0.17453292519943295 },
|
| 1816 |
|
|
{ 0.34615238767335027, -0.59999999999999998, 0.40000000000000002,
|
| 1817 |
|
|
0.34906585039886590 },
|
| 1818 |
|
|
{ 0.51453257838108579, -0.59999999999999998, 0.40000000000000002,
|
| 1819 |
|
|
0.52359877559829882 },
|
| 1820 |
|
|
{ 0.67882386787534410, -0.59999999999999998, 0.40000000000000002,
|
| 1821 |
|
|
0.69813170079773179 },
|
| 1822 |
|
|
{ 0.83948470233173578, -0.59999999999999998, 0.40000000000000002,
|
| 1823 |
|
|
0.87266462599716477 },
|
| 1824 |
|
|
{ 0.99753496200073977, -0.59999999999999998, 0.40000000000000002,
|
| 1825 |
|
|
1.0471975511965976 },
|
| 1826 |
|
|
{ 1.1541101404388487, -0.59999999999999998, 0.40000000000000002,
|
| 1827 |
|
|
1.2217304763960306 },
|
| 1828 |
|
|
{ 1.3100911323398814, -0.59999999999999998, 0.40000000000000002,
|
| 1829 |
|
|
1.3962634015954636 },
|
| 1830 |
|
|
{ 1.4659345278069984, -0.59999999999999998, 0.40000000000000002,
|
| 1831 |
|
|
1.5707963267948966 },
|
| 1832 |
|
|
};
|
| 1833 |
|
|
|
| 1834 |
|
|
// Test function for k=-0.59999999999999998, nu=0.40000000000000002.
|
| 1835 |
|
|
template <typename Tp>
|
| 1836 |
|
|
void test035()
|
| 1837 |
|
|
{
|
| 1838 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1839 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1840 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1841 |
|
|
unsigned int num_datum = sizeof(data035)
|
| 1842 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1843 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1844 |
|
|
{
|
| 1845 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data035[i].k), Tp(data035[i].nu),
|
| 1846 |
|
|
Tp(data035[i].phi));
|
| 1847 |
|
|
const Tp f0 = data035[i].f0;
|
| 1848 |
|
|
const Tp diff = f - f0;
|
| 1849 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1850 |
|
|
max_abs_diff = std::abs(diff);
|
| 1851 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1852 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1853 |
|
|
{
|
| 1854 |
|
|
const Tp frac = diff / f0;
|
| 1855 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1856 |
|
|
max_abs_frac = std::abs(frac);
|
| 1857 |
|
|
}
|
| 1858 |
|
|
}
|
| 1859 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1860 |
|
|
}
|
| 1861 |
|
|
|
| 1862 |
|
|
// Test data for k=-0.59999999999999998, nu=0.50000000000000000.
|
| 1863 |
|
|
testcase_ellint_3<double> data036[] = {
|
| 1864 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.50000000000000000,
|
| 1865 |
|
|
0.0000000000000000 },
|
| 1866 |
|
|
{ 0.17397586700252810, -0.59999999999999998, 0.50000000000000000,
|
| 1867 |
|
|
0.17453292519943295 },
|
| 1868 |
|
|
{ 0.34483533397138516, -0.59999999999999998, 0.50000000000000000,
|
| 1869 |
|
|
0.34906585039886590 },
|
| 1870 |
|
|
{ 0.51044500461706499, -0.59999999999999998, 0.50000000000000000,
|
| 1871 |
|
|
0.52359877559829882 },
|
| 1872 |
|
|
{ 0.67009988034712675, -0.59999999999999998, 0.50000000000000000,
|
| 1873 |
|
|
0.69813170079773179 },
|
| 1874 |
|
|
{ 0.82434762375735193, -0.59999999999999998, 0.50000000000000000,
|
| 1875 |
|
|
0.87266462599716477 },
|
| 1876 |
|
|
{ 0.97447346702798998, -0.59999999999999998, 0.50000000000000000,
|
| 1877 |
|
|
1.0471975511965976 },
|
| 1878 |
|
|
{ 1.1219494000522143, -0.59999999999999998, 0.50000000000000000,
|
| 1879 |
|
|
1.2217304763960306 },
|
| 1880 |
|
|
{ 1.2680242605954486, -0.59999999999999998, 0.50000000000000000,
|
| 1881 |
|
|
1.3962634015954636 },
|
| 1882 |
|
|
{ 1.4135484285693078, -0.59999999999999998, 0.50000000000000000,
|
| 1883 |
|
|
1.5707963267948966 },
|
| 1884 |
|
|
};
|
| 1885 |
|
|
|
| 1886 |
|
|
// Test function for k=-0.59999999999999998, nu=0.50000000000000000.
|
| 1887 |
|
|
template <typename Tp>
|
| 1888 |
|
|
void test036()
|
| 1889 |
|
|
{
|
| 1890 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1891 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1892 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1893 |
|
|
unsigned int num_datum = sizeof(data036)
|
| 1894 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1895 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1896 |
|
|
{
|
| 1897 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data036[i].k), Tp(data036[i].nu),
|
| 1898 |
|
|
Tp(data036[i].phi));
|
| 1899 |
|
|
const Tp f0 = data036[i].f0;
|
| 1900 |
|
|
const Tp diff = f - f0;
|
| 1901 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1902 |
|
|
max_abs_diff = std::abs(diff);
|
| 1903 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1904 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1905 |
|
|
{
|
| 1906 |
|
|
const Tp frac = diff / f0;
|
| 1907 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1908 |
|
|
max_abs_frac = std::abs(frac);
|
| 1909 |
|
|
}
|
| 1910 |
|
|
}
|
| 1911 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1912 |
|
|
}
|
| 1913 |
|
|
|
| 1914 |
|
|
// Test data for k=-0.59999999999999998, nu=0.59999999999999998.
|
| 1915 |
|
|
testcase_ellint_3<double> data037[] = {
|
| 1916 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.59999999999999998,
|
| 1917 |
|
|
0.0000000000000000 },
|
| 1918 |
|
|
{ 0.17380260984469356, -0.59999999999999998, 0.59999999999999998,
|
| 1919 |
|
|
0.17453292519943295 },
|
| 1920 |
|
|
{ 0.34353585361777839, -0.59999999999999998, 0.59999999999999998,
|
| 1921 |
|
|
0.34906585039886590 },
|
| 1922 |
|
|
{ 0.50646805774321402, -0.59999999999999998, 0.59999999999999998,
|
| 1923 |
|
|
0.52359877559829882 },
|
| 1924 |
|
|
{ 0.66174468108625517, -0.59999999999999998, 0.59999999999999998,
|
| 1925 |
|
|
0.69813170079773179 },
|
| 1926 |
|
|
{ 0.81007462280278408, -0.59999999999999998, 0.59999999999999998,
|
| 1927 |
|
|
0.87266462599716477 },
|
| 1928 |
|
|
{ 0.95303466945718729, -0.59999999999999998, 0.59999999999999998,
|
| 1929 |
|
|
1.0471975511965976 },
|
| 1930 |
|
|
{ 1.0924118588677503, -0.59999999999999998, 0.59999999999999998,
|
| 1931 |
|
|
1.2217304763960306 },
|
| 1932 |
|
|
{ 1.2297640574847937, -0.59999999999999998, 0.59999999999999998,
|
| 1933 |
|
|
1.3962634015954636 },
|
| 1934 |
|
|
{ 1.3662507535812816, -0.59999999999999998, 0.59999999999999998,
|
| 1935 |
|
|
1.5707963267948966 },
|
| 1936 |
|
|
};
|
| 1937 |
|
|
|
| 1938 |
|
|
// Test function for k=-0.59999999999999998, nu=0.59999999999999998.
|
| 1939 |
|
|
template <typename Tp>
|
| 1940 |
|
|
void test037()
|
| 1941 |
|
|
{
|
| 1942 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1943 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1944 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1945 |
|
|
unsigned int num_datum = sizeof(data037)
|
| 1946 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1947 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1948 |
|
|
{
|
| 1949 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data037[i].k), Tp(data037[i].nu),
|
| 1950 |
|
|
Tp(data037[i].phi));
|
| 1951 |
|
|
const Tp f0 = data037[i].f0;
|
| 1952 |
|
|
const Tp diff = f - f0;
|
| 1953 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1954 |
|
|
max_abs_diff = std::abs(diff);
|
| 1955 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1956 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1957 |
|
|
{
|
| 1958 |
|
|
const Tp frac = diff / f0;
|
| 1959 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1960 |
|
|
max_abs_frac = std::abs(frac);
|
| 1961 |
|
|
}
|
| 1962 |
|
|
}
|
| 1963 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1964 |
|
|
}
|
| 1965 |
|
|
|
| 1966 |
|
|
// Test data for k=-0.59999999999999998, nu=0.69999999999999996.
|
| 1967 |
|
|
testcase_ellint_3<double> data038[] = {
|
| 1968 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.69999999999999996,
|
| 1969 |
|
|
0.0000000000000000 },
|
| 1970 |
|
|
{ 0.17362996946312009, -0.59999999999999998, 0.69999999999999996,
|
| 1971 |
|
|
0.17453292519943295 },
|
| 1972 |
|
|
{ 0.34225353454870588, -0.59999999999999998, 0.69999999999999996,
|
| 1973 |
|
|
0.34906585039886590 },
|
| 1974 |
|
|
{ 0.50259656397799546, -0.59999999999999998, 0.69999999999999996,
|
| 1975 |
|
|
0.52359877559829882 },
|
| 1976 |
|
|
{ 0.65373184496628944, -0.59999999999999998, 0.69999999999999996,
|
| 1977 |
|
|
0.69813170079773179 },
|
| 1978 |
|
|
{ 0.79658372884056439, -0.59999999999999998, 0.69999999999999996,
|
| 1979 |
|
|
0.87266462599716477 },
|
| 1980 |
|
|
{ 0.93303240100245421, -0.59999999999999998, 0.69999999999999996,
|
| 1981 |
|
|
1.0471975511965976 },
|
| 1982 |
|
|
{ 1.0651547944716557, -0.59999999999999998, 0.69999999999999996,
|
| 1983 |
|
|
1.2217304763960306 },
|
| 1984 |
|
|
{ 1.1947676204853441, -0.59999999999999998, 0.69999999999999996,
|
| 1985 |
|
|
1.3962634015954636 },
|
| 1986 |
|
|
{ 1.3232737468822811, -0.59999999999999998, 0.69999999999999996,
|
| 1987 |
|
|
1.5707963267948966 },
|
| 1988 |
|
|
};
|
| 1989 |
|
|
|
| 1990 |
|
|
// Test function for k=-0.59999999999999998, nu=0.69999999999999996.
|
| 1991 |
|
|
template <typename Tp>
|
| 1992 |
|
|
void test038()
|
| 1993 |
|
|
{
|
| 1994 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1995 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1996 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1997 |
|
|
unsigned int num_datum = sizeof(data038)
|
| 1998 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 1999 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2000 |
|
|
{
|
| 2001 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data038[i].k), Tp(data038[i].nu),
|
| 2002 |
|
|
Tp(data038[i].phi));
|
| 2003 |
|
|
const Tp f0 = data038[i].f0;
|
| 2004 |
|
|
const Tp diff = f - f0;
|
| 2005 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2006 |
|
|
max_abs_diff = std::abs(diff);
|
| 2007 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2008 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2009 |
|
|
{
|
| 2010 |
|
|
const Tp frac = diff / f0;
|
| 2011 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2012 |
|
|
max_abs_frac = std::abs(frac);
|
| 2013 |
|
|
}
|
| 2014 |
|
|
}
|
| 2015 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2016 |
|
|
}
|
| 2017 |
|
|
|
| 2018 |
|
|
// Test data for k=-0.59999999999999998, nu=0.80000000000000004.
|
| 2019 |
|
|
testcase_ellint_3<double> data039[] = {
|
| 2020 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.80000000000000004,
|
| 2021 |
|
|
0.0000000000000000 },
|
| 2022 |
|
|
{ 0.17345794195390687, -0.59999999999999998, 0.80000000000000004,
|
| 2023 |
|
|
0.17453292519943295 },
|
| 2024 |
|
|
{ 0.34098797854531027, -0.59999999999999998, 0.80000000000000004,
|
| 2025 |
|
|
0.34906585039886590 },
|
| 2026 |
|
|
{ 0.49882569168826230, -0.59999999999999998, 0.80000000000000004,
|
| 2027 |
|
|
0.52359877559829882 },
|
| 2028 |
|
|
{ 0.64603758566475511, -0.59999999999999998, 0.80000000000000004,
|
| 2029 |
|
|
0.69813170079773179 },
|
| 2030 |
|
|
{ 0.78380365594769730, -0.59999999999999998, 0.80000000000000004,
|
| 2031 |
|
|
0.87266462599716477 },
|
| 2032 |
|
|
{ 0.91430946255611190, -0.59999999999999998, 0.80000000000000004,
|
| 2033 |
|
|
1.0471975511965976 },
|
| 2034 |
|
|
{ 1.0398955217270607, -0.59999999999999998, 0.80000000000000004,
|
| 2035 |
|
|
1.2217304763960306 },
|
| 2036 |
|
|
{ 1.1625948314277676, -0.59999999999999998, 0.80000000000000004,
|
| 2037 |
|
|
1.3962634015954636 },
|
| 2038 |
|
|
{ 1.2840021261752192, -0.59999999999999998, 0.80000000000000004,
|
| 2039 |
|
|
1.5707963267948966 },
|
| 2040 |
|
|
};
|
| 2041 |
|
|
|
| 2042 |
|
|
// Test function for k=-0.59999999999999998, nu=0.80000000000000004.
|
| 2043 |
|
|
template <typename Tp>
|
| 2044 |
|
|
void test039()
|
| 2045 |
|
|
{
|
| 2046 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2047 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2048 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2049 |
|
|
unsigned int num_datum = sizeof(data039)
|
| 2050 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2051 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2052 |
|
|
{
|
| 2053 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data039[i].k), Tp(data039[i].nu),
|
| 2054 |
|
|
Tp(data039[i].phi));
|
| 2055 |
|
|
const Tp f0 = data039[i].f0;
|
| 2056 |
|
|
const Tp diff = f - f0;
|
| 2057 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2058 |
|
|
max_abs_diff = std::abs(diff);
|
| 2059 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2060 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2061 |
|
|
{
|
| 2062 |
|
|
const Tp frac = diff / f0;
|
| 2063 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2064 |
|
|
max_abs_frac = std::abs(frac);
|
| 2065 |
|
|
}
|
| 2066 |
|
|
}
|
| 2067 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2068 |
|
|
}
|
| 2069 |
|
|
|
| 2070 |
|
|
// Test data for k=-0.59999999999999998, nu=0.90000000000000002.
|
| 2071 |
|
|
testcase_ellint_3<double> data040[] = {
|
| 2072 |
|
|
{ -0.0000000000000000, -0.59999999999999998, 0.90000000000000002,
|
| 2073 |
|
|
0.0000000000000000 },
|
| 2074 |
|
|
{ 0.17328652344890033, -0.59999999999999998, 0.90000000000000002,
|
| 2075 |
|
|
0.17453292519943295 },
|
| 2076 |
|
|
{ 0.33973880062929018, -0.59999999999999998, 0.90000000000000002,
|
| 2077 |
|
|
0.34906585039886590 },
|
| 2078 |
|
|
{ 0.49515092233122765, -0.59999999999999998, 0.90000000000000002,
|
| 2079 |
|
|
0.52359877559829882 },
|
| 2080 |
|
|
{ 0.63864042139737043, -0.59999999999999998, 0.90000000000000002,
|
| 2081 |
|
|
0.69813170079773179 },
|
| 2082 |
|
|
{ 0.77167205646538850, -0.59999999999999998, 0.90000000000000002,
|
| 2083 |
|
|
0.87266462599716477 },
|
| 2084 |
|
|
{ 0.89673202848034383, -0.59999999999999998, 0.90000000000000002,
|
| 2085 |
|
|
1.0471975511965976 },
|
| 2086 |
|
|
{ 1.0163984492661304, -0.59999999999999998, 0.90000000000000002,
|
| 2087 |
|
|
1.2217304763960306 },
|
| 2088 |
|
|
{ 1.1328845785162431, -0.59999999999999998, 0.90000000000000002,
|
| 2089 |
|
|
1.3962634015954636 },
|
| 2090 |
|
|
{ 1.2479362973851875, -0.59999999999999998, 0.90000000000000002,
|
| 2091 |
|
|
1.5707963267948966 },
|
| 2092 |
|
|
};
|
| 2093 |
|
|
|
| 2094 |
|
|
// Test function for k=-0.59999999999999998, nu=0.90000000000000002.
|
| 2095 |
|
|
template <typename Tp>
|
| 2096 |
|
|
void test040()
|
| 2097 |
|
|
{
|
| 2098 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2099 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2100 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2101 |
|
|
unsigned int num_datum = sizeof(data040)
|
| 2102 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2103 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2104 |
|
|
{
|
| 2105 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data040[i].k), Tp(data040[i].nu),
|
| 2106 |
|
|
Tp(data040[i].phi));
|
| 2107 |
|
|
const Tp f0 = data040[i].f0;
|
| 2108 |
|
|
const Tp diff = f - f0;
|
| 2109 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2110 |
|
|
max_abs_diff = std::abs(diff);
|
| 2111 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2112 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2113 |
|
|
{
|
| 2114 |
|
|
const Tp frac = diff / f0;
|
| 2115 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2116 |
|
|
max_abs_frac = std::abs(frac);
|
| 2117 |
|
|
}
|
| 2118 |
|
|
}
|
| 2119 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2120 |
|
|
}
|
| 2121 |
|
|
|
| 2122 |
|
|
// Test data for k=-0.50000000000000000, nu=0.0000000000000000.
|
| 2123 |
|
|
testcase_ellint_3<double> data041[] = {
|
| 2124 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.0000000000000000,
|
| 2125 |
|
|
0.0000000000000000 },
|
| 2126 |
|
|
{ 0.17475385514035785, -0.50000000000000000, 0.0000000000000000,
|
| 2127 |
|
|
0.17453292519943295 },
|
| 2128 |
|
|
{ 0.35081868470101585, -0.50000000000000000, 0.0000000000000000,
|
| 2129 |
|
|
0.34906585039886590 },
|
| 2130 |
|
|
{ 0.52942862705190585, -0.50000000000000000, 0.0000000000000000,
|
| 2131 |
|
|
0.52359877559829882 },
|
| 2132 |
|
|
{ 0.71164727562630326, -0.50000000000000000, 0.0000000000000000,
|
| 2133 |
|
|
0.69813170079773179 },
|
| 2134 |
|
|
{ 0.89824523594227768, -0.50000000000000000, 0.0000000000000000,
|
| 2135 |
|
|
0.87266462599716477 },
|
| 2136 |
|
|
{ 1.0895506700518851, -0.50000000000000000, 0.0000000000000000,
|
| 2137 |
|
|
1.0471975511965976 },
|
| 2138 |
|
|
{ 1.2853005857432933, -0.50000000000000000, 0.0000000000000000,
|
| 2139 |
|
|
1.2217304763960306 },
|
| 2140 |
|
|
{ 1.4845545520549484, -0.50000000000000000, 0.0000000000000000,
|
| 2141 |
|
|
1.3962634015954636 },
|
| 2142 |
|
|
{ 1.6857503548125963, -0.50000000000000000, 0.0000000000000000,
|
| 2143 |
|
|
1.5707963267948966 },
|
| 2144 |
|
|
};
|
| 2145 |
|
|
|
| 2146 |
|
|
// Test function for k=-0.50000000000000000, nu=0.0000000000000000.
|
| 2147 |
|
|
template <typename Tp>
|
| 2148 |
|
|
void test041()
|
| 2149 |
|
|
{
|
| 2150 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2151 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2152 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2153 |
|
|
unsigned int num_datum = sizeof(data041)
|
| 2154 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2155 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2156 |
|
|
{
|
| 2157 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data041[i].k), Tp(data041[i].nu),
|
| 2158 |
|
|
Tp(data041[i].phi));
|
| 2159 |
|
|
const Tp f0 = data041[i].f0;
|
| 2160 |
|
|
const Tp diff = f - f0;
|
| 2161 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2162 |
|
|
max_abs_diff = std::abs(diff);
|
| 2163 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2164 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2165 |
|
|
{
|
| 2166 |
|
|
const Tp frac = diff / f0;
|
| 2167 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2168 |
|
|
max_abs_frac = std::abs(frac);
|
| 2169 |
|
|
}
|
| 2170 |
|
|
}
|
| 2171 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2172 |
|
|
}
|
| 2173 |
|
|
|
| 2174 |
|
|
// Test data for k=-0.50000000000000000, nu=0.10000000000000001.
|
| 2175 |
|
|
testcase_ellint_3<double> data042[] = {
|
| 2176 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.10000000000000001,
|
| 2177 |
|
|
0.0000000000000000 },
|
| 2178 |
|
|
{ 0.17457763120814676, -0.50000000000000000, 0.10000000000000001,
|
| 2179 |
|
|
0.17453292519943295 },
|
| 2180 |
|
|
{ 0.34943246340849154, -0.50000000000000000, 0.10000000000000001,
|
| 2181 |
|
|
0.34906585039886590 },
|
| 2182 |
|
|
{ 0.52487937869610801, -0.50000000000000000, 0.10000000000000001,
|
| 2183 |
|
|
0.52359877559829882 },
|
| 2184 |
|
|
{ 0.70127785096388395, -0.50000000000000000, 0.10000000000000001,
|
| 2185 |
|
|
0.69813170079773179 },
|
| 2186 |
|
|
{ 0.87898815988624479, -0.50000000000000000, 0.10000000000000001,
|
| 2187 |
|
|
0.87266462599716477 },
|
| 2188 |
|
|
{ 1.0582764576094172, -0.50000000000000000, 0.10000000000000001,
|
| 2189 |
|
|
1.0471975511965976 },
|
| 2190 |
|
|
{ 1.2391936844060207, -0.50000000000000000, 0.10000000000000001,
|
| 2191 |
|
|
1.2217304763960306 },
|
| 2192 |
|
|
{ 1.4214793542995841, -0.50000000000000000, 0.10000000000000001,
|
| 2193 |
|
|
1.3962634015954636 },
|
| 2194 |
|
|
{ 1.6045524936084892, -0.50000000000000000, 0.10000000000000001,
|
| 2195 |
|
|
1.5707963267948966 },
|
| 2196 |
|
|
};
|
| 2197 |
|
|
|
| 2198 |
|
|
// Test function for k=-0.50000000000000000, nu=0.10000000000000001.
|
| 2199 |
|
|
template <typename Tp>
|
| 2200 |
|
|
void test042()
|
| 2201 |
|
|
{
|
| 2202 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2203 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2204 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2205 |
|
|
unsigned int num_datum = sizeof(data042)
|
| 2206 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2207 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2208 |
|
|
{
|
| 2209 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data042[i].k), Tp(data042[i].nu),
|
| 2210 |
|
|
Tp(data042[i].phi));
|
| 2211 |
|
|
const Tp f0 = data042[i].f0;
|
| 2212 |
|
|
const Tp diff = f - f0;
|
| 2213 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2214 |
|
|
max_abs_diff = std::abs(diff);
|
| 2215 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2216 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2217 |
|
|
{
|
| 2218 |
|
|
const Tp frac = diff / f0;
|
| 2219 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2220 |
|
|
max_abs_frac = std::abs(frac);
|
| 2221 |
|
|
}
|
| 2222 |
|
|
}
|
| 2223 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2224 |
|
|
}
|
| 2225 |
|
|
|
| 2226 |
|
|
// Test data for k=-0.50000000000000000, nu=0.20000000000000001.
|
| 2227 |
|
|
testcase_ellint_3<double> data043[] = {
|
| 2228 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.20000000000000001,
|
| 2229 |
|
|
0.0000000000000000 },
|
| 2230 |
|
|
{ 0.17440204336345433, -0.50000000000000000, 0.20000000000000001,
|
| 2231 |
|
|
0.17453292519943295 },
|
| 2232 |
|
|
{ 0.34806552388338824, -0.50000000000000000, 0.20000000000000001,
|
| 2233 |
|
|
0.34906585039886590 },
|
| 2234 |
|
|
{ 0.52046416757129821, -0.50000000000000000, 0.20000000000000001,
|
| 2235 |
|
|
0.52359877559829882 },
|
| 2236 |
|
|
{ 0.69140924550993876, -0.50000000000000000, 0.20000000000000001,
|
| 2237 |
|
|
0.69813170079773179 },
|
| 2238 |
|
|
{ 0.86104678636125520, -0.50000000000000000, 0.20000000000000001,
|
| 2239 |
|
|
0.87266462599716477 },
|
| 2240 |
|
|
{ 1.0297439459053981, -0.50000000000000000, 0.20000000000000001,
|
| 2241 |
|
|
1.0471975511965976 },
|
| 2242 |
|
|
{ 1.1979214112912036, -0.50000000000000000, 0.20000000000000001,
|
| 2243 |
|
|
1.2217304763960306 },
|
| 2244 |
|
|
{ 1.3659033858648930, -0.50000000000000000, 0.20000000000000001,
|
| 2245 |
|
|
1.3962634015954636 },
|
| 2246 |
|
|
{ 1.5338490483665983, -0.50000000000000000, 0.20000000000000001,
|
| 2247 |
|
|
1.5707963267948966 },
|
| 2248 |
|
|
};
|
| 2249 |
|
|
|
| 2250 |
|
|
// Test function for k=-0.50000000000000000, nu=0.20000000000000001.
|
| 2251 |
|
|
template <typename Tp>
|
| 2252 |
|
|
void test043()
|
| 2253 |
|
|
{
|
| 2254 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2255 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2256 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2257 |
|
|
unsigned int num_datum = sizeof(data043)
|
| 2258 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2259 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2260 |
|
|
{
|
| 2261 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data043[i].k), Tp(data043[i].nu),
|
| 2262 |
|
|
Tp(data043[i].phi));
|
| 2263 |
|
|
const Tp f0 = data043[i].f0;
|
| 2264 |
|
|
const Tp diff = f - f0;
|
| 2265 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2266 |
|
|
max_abs_diff = std::abs(diff);
|
| 2267 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2268 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2269 |
|
|
{
|
| 2270 |
|
|
const Tp frac = diff / f0;
|
| 2271 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2272 |
|
|
max_abs_frac = std::abs(frac);
|
| 2273 |
|
|
}
|
| 2274 |
|
|
}
|
| 2275 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2276 |
|
|
}
|
| 2277 |
|
|
|
| 2278 |
|
|
// Test data for k=-0.50000000000000000, nu=0.29999999999999999.
|
| 2279 |
|
|
testcase_ellint_3<double> data044[] = {
|
| 2280 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.29999999999999999,
|
| 2281 |
|
|
0.0000000000000000 },
|
| 2282 |
|
|
{ 0.17422708752228896, -0.50000000000000000, 0.29999999999999999,
|
| 2283 |
|
|
0.17453292519943295 },
|
| 2284 |
|
|
{ 0.34671739434855858, -0.50000000000000000, 0.29999999999999999,
|
| 2285 |
|
|
0.34906585039886590 },
|
| 2286 |
|
|
{ 0.51617616305641889, -0.50000000000000000, 0.29999999999999999,
|
| 2287 |
|
|
0.52359877559829882 },
|
| 2288 |
|
|
{ 0.68200047612545178, -0.50000000000000000, 0.29999999999999999,
|
| 2289 |
|
|
0.69813170079773179 },
|
| 2290 |
|
|
{ 0.84427217869498372, -0.50000000000000000, 0.29999999999999999,
|
| 2291 |
|
|
0.87266462599716477 },
|
| 2292 |
|
|
{ 1.0035637821389782, -0.50000000000000000, 0.29999999999999999,
|
| 2293 |
|
|
1.0471975511965976 },
|
| 2294 |
|
|
{ 1.1606800483933113, -0.50000000000000000, 0.29999999999999999,
|
| 2295 |
|
|
1.2217304763960306 },
|
| 2296 |
|
|
{ 1.3164407134643459, -0.50000000000000000, 0.29999999999999999,
|
| 2297 |
|
|
1.3962634015954636 },
|
| 2298 |
|
|
{ 1.4715681939859637, -0.50000000000000000, 0.29999999999999999,
|
| 2299 |
|
|
1.5707963267948966 },
|
| 2300 |
|
|
};
|
| 2301 |
|
|
|
| 2302 |
|
|
// Test function for k=-0.50000000000000000, nu=0.29999999999999999.
|
| 2303 |
|
|
template <typename Tp>
|
| 2304 |
|
|
void test044()
|
| 2305 |
|
|
{
|
| 2306 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2307 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2308 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2309 |
|
|
unsigned int num_datum = sizeof(data044)
|
| 2310 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2311 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2312 |
|
|
{
|
| 2313 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data044[i].k), Tp(data044[i].nu),
|
| 2314 |
|
|
Tp(data044[i].phi));
|
| 2315 |
|
|
const Tp f0 = data044[i].f0;
|
| 2316 |
|
|
const Tp diff = f - f0;
|
| 2317 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2318 |
|
|
max_abs_diff = std::abs(diff);
|
| 2319 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2320 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2321 |
|
|
{
|
| 2322 |
|
|
const Tp frac = diff / f0;
|
| 2323 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2324 |
|
|
max_abs_frac = std::abs(frac);
|
| 2325 |
|
|
}
|
| 2326 |
|
|
}
|
| 2327 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2328 |
|
|
}
|
| 2329 |
|
|
|
| 2330 |
|
|
// Test data for k=-0.50000000000000000, nu=0.40000000000000002.
|
| 2331 |
|
|
testcase_ellint_3<double> data045[] = {
|
| 2332 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.40000000000000002,
|
| 2333 |
|
|
0.0000000000000000 },
|
| 2334 |
|
|
{ 0.17405275963859917, -0.50000000000000000, 0.40000000000000002,
|
| 2335 |
|
|
0.17453292519943295 },
|
| 2336 |
|
|
{ 0.34538761957029329, -0.50000000000000000, 0.40000000000000002,
|
| 2337 |
|
|
0.34906585039886590 },
|
| 2338 |
|
|
{ 0.51200902646603919, -0.50000000000000000, 0.40000000000000002,
|
| 2339 |
|
|
0.52359877559829882 },
|
| 2340 |
|
|
{ 0.67301522212868792, -0.50000000000000000, 0.40000000000000002,
|
| 2341 |
|
|
0.69813170079773179 },
|
| 2342 |
|
|
{ 0.82853844466313320, -0.50000000000000000, 0.40000000000000002,
|
| 2343 |
|
|
0.87266462599716477 },
|
| 2344 |
|
|
{ 0.97942097862681488, -0.50000000000000000, 0.40000000000000002,
|
| 2345 |
|
|
1.0471975511965976 },
|
| 2346 |
|
|
{ 1.1268429801220616, -0.50000000000000000, 0.40000000000000002,
|
| 2347 |
|
|
1.2217304763960306 },
|
| 2348 |
|
|
{ 1.2720406704533922, -0.50000000000000000, 0.40000000000000002,
|
| 2349 |
|
|
1.3962634015954636 },
|
| 2350 |
|
|
{ 1.4161679518465340, -0.50000000000000000, 0.40000000000000002,
|
| 2351 |
|
|
1.5707963267948966 },
|
| 2352 |
|
|
};
|
| 2353 |
|
|
|
| 2354 |
|
|
// Test function for k=-0.50000000000000000, nu=0.40000000000000002.
|
| 2355 |
|
|
template <typename Tp>
|
| 2356 |
|
|
void test045()
|
| 2357 |
|
|
{
|
| 2358 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2359 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2360 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2361 |
|
|
unsigned int num_datum = sizeof(data045)
|
| 2362 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2363 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2364 |
|
|
{
|
| 2365 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data045[i].k), Tp(data045[i].nu),
|
| 2366 |
|
|
Tp(data045[i].phi));
|
| 2367 |
|
|
const Tp f0 = data045[i].f0;
|
| 2368 |
|
|
const Tp diff = f - f0;
|
| 2369 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2370 |
|
|
max_abs_diff = std::abs(diff);
|
| 2371 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2372 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2373 |
|
|
{
|
| 2374 |
|
|
const Tp frac = diff / f0;
|
| 2375 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2376 |
|
|
max_abs_frac = std::abs(frac);
|
| 2377 |
|
|
}
|
| 2378 |
|
|
}
|
| 2379 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2380 |
|
|
}
|
| 2381 |
|
|
|
| 2382 |
|
|
// Test data for k=-0.50000000000000000, nu=0.50000000000000000.
|
| 2383 |
|
|
testcase_ellint_3<double> data046[] = {
|
| 2384 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.50000000000000000,
|
| 2385 |
|
|
0.0000000000000000 },
|
| 2386 |
|
|
{ 0.17387905570381157, -0.50000000000000000, 0.50000000000000000,
|
| 2387 |
|
|
0.17453292519943295 },
|
| 2388 |
|
|
{ 0.34407576010465207, -0.50000000000000000, 0.50000000000000000,
|
| 2389 |
|
|
0.34906585039886590 },
|
| 2390 |
|
|
{ 0.50795686560160835, -0.50000000000000000, 0.50000000000000000,
|
| 2391 |
|
|
0.52359877559829882 },
|
| 2392 |
|
|
{ 0.66442115453330175, -0.50000000000000000, 0.50000000000000000,
|
| 2393 |
|
|
0.69813170079773179 },
|
| 2394 |
|
|
{ 0.81373829119355345, -0.50000000000000000, 0.50000000000000000,
|
| 2395 |
|
|
0.87266462599716477 },
|
| 2396 |
|
|
{ 0.95705743313235825, -0.50000000000000000, 0.50000000000000000,
|
| 2397 |
|
|
1.0471975511965976 },
|
| 2398 |
|
|
{ 1.0959131991362556, -0.50000000000000000, 0.50000000000000000,
|
| 2399 |
|
|
1.2217304763960306 },
|
| 2400 |
|
|
{ 1.2318900529754597, -0.50000000000000000, 0.50000000000000000,
|
| 2401 |
|
|
1.3962634015954636 },
|
| 2402 |
|
|
{ 1.3664739530045971, -0.50000000000000000, 0.50000000000000000,
|
| 2403 |
|
|
1.5707963267948966 },
|
| 2404 |
|
|
};
|
| 2405 |
|
|
|
| 2406 |
|
|
// Test function for k=-0.50000000000000000, nu=0.50000000000000000.
|
| 2407 |
|
|
template <typename Tp>
|
| 2408 |
|
|
void test046()
|
| 2409 |
|
|
{
|
| 2410 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2411 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2412 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2413 |
|
|
unsigned int num_datum = sizeof(data046)
|
| 2414 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2415 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2416 |
|
|
{
|
| 2417 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data046[i].k), Tp(data046[i].nu),
|
| 2418 |
|
|
Tp(data046[i].phi));
|
| 2419 |
|
|
const Tp f0 = data046[i].f0;
|
| 2420 |
|
|
const Tp diff = f - f0;
|
| 2421 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2422 |
|
|
max_abs_diff = std::abs(diff);
|
| 2423 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2424 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2425 |
|
|
{
|
| 2426 |
|
|
const Tp frac = diff / f0;
|
| 2427 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2428 |
|
|
max_abs_frac = std::abs(frac);
|
| 2429 |
|
|
}
|
| 2430 |
|
|
}
|
| 2431 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2432 |
|
|
}
|
| 2433 |
|
|
|
| 2434 |
|
|
// Test data for k=-0.50000000000000000, nu=0.59999999999999998.
|
| 2435 |
|
|
testcase_ellint_3<double> data047[] = {
|
| 2436 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.59999999999999998,
|
| 2437 |
|
|
0.0000000000000000 },
|
| 2438 |
|
|
{ 0.17370597174637581, -0.50000000000000000, 0.59999999999999998,
|
| 2439 |
|
|
0.17453292519943295 },
|
| 2440 |
|
|
{ 0.34278139158591414, -0.50000000000000000, 0.59999999999999998,
|
| 2441 |
|
|
0.34906585039886590 },
|
| 2442 |
|
|
{ 0.50401419439302719, -0.50000000000000000, 0.59999999999999998,
|
| 2443 |
|
|
0.52359877559829882 },
|
| 2444 |
|
|
{ 0.65618938076167221, -0.50000000000000000, 0.59999999999999998,
|
| 2445 |
|
|
0.69813170079773179 },
|
| 2446 |
|
|
{ 0.79977959248855424, -0.50000000000000000, 0.59999999999999998,
|
| 2447 |
|
|
0.87266462599716477 },
|
| 2448 |
|
|
{ 0.93625925190753545, -0.50000000000000000, 0.59999999999999998,
|
| 2449 |
|
|
1.0471975511965976 },
|
| 2450 |
|
|
{ 1.0674905658379710, -0.50000000000000000, 0.59999999999999998,
|
| 2451 |
|
|
1.2217304763960306 },
|
| 2452 |
|
|
{ 1.1953481298023048, -0.50000000000000000, 0.59999999999999998,
|
| 2453 |
|
|
1.3962634015954636 },
|
| 2454 |
|
|
{ 1.3215740290190876, -0.50000000000000000, 0.59999999999999998,
|
| 2455 |
|
|
1.5707963267948966 },
|
| 2456 |
|
|
};
|
| 2457 |
|
|
|
| 2458 |
|
|
// Test function for k=-0.50000000000000000, nu=0.59999999999999998.
|
| 2459 |
|
|
template <typename Tp>
|
| 2460 |
|
|
void test047()
|
| 2461 |
|
|
{
|
| 2462 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2463 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2464 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2465 |
|
|
unsigned int num_datum = sizeof(data047)
|
| 2466 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2467 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2468 |
|
|
{
|
| 2469 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data047[i].k), Tp(data047[i].nu),
|
| 2470 |
|
|
Tp(data047[i].phi));
|
| 2471 |
|
|
const Tp f0 = data047[i].f0;
|
| 2472 |
|
|
const Tp diff = f - f0;
|
| 2473 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2474 |
|
|
max_abs_diff = std::abs(diff);
|
| 2475 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2476 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2477 |
|
|
{
|
| 2478 |
|
|
const Tp frac = diff / f0;
|
| 2479 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2480 |
|
|
max_abs_frac = std::abs(frac);
|
| 2481 |
|
|
}
|
| 2482 |
|
|
}
|
| 2483 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2484 |
|
|
}
|
| 2485 |
|
|
|
| 2486 |
|
|
// Test data for k=-0.50000000000000000, nu=0.69999999999999996.
|
| 2487 |
|
|
testcase_ellint_3<double> data048[] = {
|
| 2488 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.69999999999999996,
|
| 2489 |
|
|
0.0000000000000000 },
|
| 2490 |
|
|
{ 0.17353350383131641, -0.50000000000000000, 0.69999999999999996,
|
| 2491 |
|
|
0.17453292519943295 },
|
| 2492 |
|
|
{ 0.34150410405436771, -0.50000000000000000, 0.69999999999999996,
|
| 2493 |
|
|
0.34906585039886590 },
|
| 2494 |
|
|
{ 0.50017589696443487, -0.50000000000000000, 0.69999999999999996,
|
| 2495 |
|
|
0.52359877559829882 },
|
| 2496 |
|
|
{ 0.64829398188419962, -0.50000000000000000, 0.69999999999999996,
|
| 2497 |
|
|
0.69813170079773179 },
|
| 2498 |
|
|
{ 0.78658270782402073, -0.50000000000000000, 0.69999999999999996,
|
| 2499 |
|
|
0.87266462599716477 },
|
| 2500 |
|
|
{ 0.91684738336675053, -0.50000000000000000, 0.69999999999999996,
|
| 2501 |
|
|
1.0471975511965976 },
|
| 2502 |
|
|
{ 1.0412486789555937, -0.50000000000000000, 0.69999999999999996,
|
| 2503 |
|
|
1.2217304763960306 },
|
| 2504 |
|
|
{ 1.1619021847612001, -0.50000000000000000, 0.69999999999999996,
|
| 2505 |
|
|
1.3962634015954636 },
|
| 2506 |
|
|
{ 1.2807475181182502, -0.50000000000000000, 0.69999999999999996,
|
| 2507 |
|
|
1.5707963267948966 },
|
| 2508 |
|
|
};
|
| 2509 |
|
|
|
| 2510 |
|
|
// Test function for k=-0.50000000000000000, nu=0.69999999999999996.
|
| 2511 |
|
|
template <typename Tp>
|
| 2512 |
|
|
void test048()
|
| 2513 |
|
|
{
|
| 2514 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2515 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2516 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2517 |
|
|
unsigned int num_datum = sizeof(data048)
|
| 2518 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2519 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2520 |
|
|
{
|
| 2521 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data048[i].k), Tp(data048[i].nu),
|
| 2522 |
|
|
Tp(data048[i].phi));
|
| 2523 |
|
|
const Tp f0 = data048[i].f0;
|
| 2524 |
|
|
const Tp diff = f - f0;
|
| 2525 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2526 |
|
|
max_abs_diff = std::abs(diff);
|
| 2527 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2528 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2529 |
|
|
{
|
| 2530 |
|
|
const Tp frac = diff / f0;
|
| 2531 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2532 |
|
|
max_abs_frac = std::abs(frac);
|
| 2533 |
|
|
}
|
| 2534 |
|
|
}
|
| 2535 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2536 |
|
|
}
|
| 2537 |
|
|
|
| 2538 |
|
|
// Test data for k=-0.50000000000000000, nu=0.80000000000000004.
|
| 2539 |
|
|
testcase_ellint_3<double> data049[] = {
|
| 2540 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.80000000000000004,
|
| 2541 |
|
|
0.0000000000000000 },
|
| 2542 |
|
|
{ 0.17336164805979126, -0.50000000000000000, 0.80000000000000004,
|
| 2543 |
|
|
0.17453292519943295 },
|
| 2544 |
|
|
{ 0.34024350132086773, -0.50000000000000000, 0.80000000000000004,
|
| 2545 |
|
|
0.34906585039886590 },
|
| 2546 |
|
|
{ 0.49643719555734084, -0.50000000000000000, 0.80000000000000004,
|
| 2547 |
|
|
0.52359877559829882 },
|
| 2548 |
|
|
{ 0.64071162456976150, -0.50000000000000000, 0.80000000000000004,
|
| 2549 |
|
|
0.69813170079773179 },
|
| 2550 |
|
|
{ 0.77407836177211908, -0.50000000000000000, 0.80000000000000004,
|
| 2551 |
|
|
0.87266462599716477 },
|
| 2552 |
|
|
{ 0.89867058251905652, -0.50000000000000000, 0.80000000000000004,
|
| 2553 |
|
|
1.0471975511965976 },
|
| 2554 |
|
|
{ 1.0169181822134912, -0.50000000000000000, 0.80000000000000004,
|
| 2555 |
|
|
1.2217304763960306 },
|
| 2556 |
|
|
{ 1.1311363312779448, -0.50000000000000000, 0.80000000000000004,
|
| 2557 |
|
|
1.3962634015954636 },
|
| 2558 |
|
|
{ 1.2434165408189539, -0.50000000000000000, 0.80000000000000004,
|
| 2559 |
|
|
1.5707963267948966 },
|
| 2560 |
|
|
};
|
| 2561 |
|
|
|
| 2562 |
|
|
// Test function for k=-0.50000000000000000, nu=0.80000000000000004.
|
| 2563 |
|
|
template <typename Tp>
|
| 2564 |
|
|
void test049()
|
| 2565 |
|
|
{
|
| 2566 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2567 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2568 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2569 |
|
|
unsigned int num_datum = sizeof(data049)
|
| 2570 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2571 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2572 |
|
|
{
|
| 2573 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data049[i].k), Tp(data049[i].nu),
|
| 2574 |
|
|
Tp(data049[i].phi));
|
| 2575 |
|
|
const Tp f0 = data049[i].f0;
|
| 2576 |
|
|
const Tp diff = f - f0;
|
| 2577 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2578 |
|
|
max_abs_diff = std::abs(diff);
|
| 2579 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2580 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2581 |
|
|
{
|
| 2582 |
|
|
const Tp frac = diff / f0;
|
| 2583 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2584 |
|
|
max_abs_frac = std::abs(frac);
|
| 2585 |
|
|
}
|
| 2586 |
|
|
}
|
| 2587 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2588 |
|
|
}
|
| 2589 |
|
|
|
| 2590 |
|
|
// Test data for k=-0.50000000000000000, nu=0.90000000000000002.
|
| 2591 |
|
|
testcase_ellint_3<double> data050[] = {
|
| 2592 |
|
|
{ -0.0000000000000000, -0.50000000000000000, 0.90000000000000002,
|
| 2593 |
|
|
0.0000000000000000 },
|
| 2594 |
|
|
{ 0.17319040056865681, -0.50000000000000000, 0.90000000000000002,
|
| 2595 |
|
|
0.17453292519943295 },
|
| 2596 |
|
|
{ 0.33899920036578557, -0.50000000000000000, 0.90000000000000002,
|
| 2597 |
|
|
0.34906585039886590 },
|
| 2598 |
|
|
{ 0.49279362182695186, -0.50000000000000000, 0.90000000000000002,
|
| 2599 |
|
|
0.52359877559829882 },
|
| 2600 |
|
|
{ 0.63342123379746151, -0.50000000000000000, 0.90000000000000002,
|
| 2601 |
|
|
0.69813170079773179 },
|
| 2602 |
|
|
{ 0.76220595179550321, -0.50000000000000000, 0.90000000000000002,
|
| 2603 |
|
|
0.87266462599716477 },
|
| 2604 |
|
|
{ 0.88160004743532294, -0.50000000000000000, 0.90000000000000002,
|
| 2605 |
|
|
1.0471975511965976 },
|
| 2606 |
|
|
{ 0.99427448642310134, -0.50000000000000000, 0.90000000000000002,
|
| 2607 |
|
|
1.2217304763960306 },
|
| 2608 |
|
|
{ 1.1027091512470093, -0.50000000000000000, 0.90000000000000002,
|
| 2609 |
|
|
1.3962634015954636 },
|
| 2610 |
|
|
{ 1.2091116095504744, -0.50000000000000000, 0.90000000000000002,
|
| 2611 |
|
|
1.5707963267948966 },
|
| 2612 |
|
|
};
|
| 2613 |
|
|
|
| 2614 |
|
|
// Test function for k=-0.50000000000000000, nu=0.90000000000000002.
|
| 2615 |
|
|
template <typename Tp>
|
| 2616 |
|
|
void test050()
|
| 2617 |
|
|
{
|
| 2618 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2619 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2620 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2621 |
|
|
unsigned int num_datum = sizeof(data050)
|
| 2622 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2623 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2624 |
|
|
{
|
| 2625 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data050[i].k), Tp(data050[i].nu),
|
| 2626 |
|
|
Tp(data050[i].phi));
|
| 2627 |
|
|
const Tp f0 = data050[i].f0;
|
| 2628 |
|
|
const Tp diff = f - f0;
|
| 2629 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2630 |
|
|
max_abs_diff = std::abs(diff);
|
| 2631 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2632 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2633 |
|
|
{
|
| 2634 |
|
|
const Tp frac = diff / f0;
|
| 2635 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2636 |
|
|
max_abs_frac = std::abs(frac);
|
| 2637 |
|
|
}
|
| 2638 |
|
|
}
|
| 2639 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2640 |
|
|
}
|
| 2641 |
|
|
|
| 2642 |
|
|
// Test data for k=-0.40000000000000002, nu=0.0000000000000000.
|
| 2643 |
|
|
testcase_ellint_3<double> data051[] = {
|
| 2644 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.0000000000000000,
|
| 2645 |
|
|
0.0000000000000000 },
|
| 2646 |
|
|
{ 0.17467414669441531, -0.40000000000000002, 0.0000000000000000,
|
| 2647 |
|
|
0.17453292519943295 },
|
| 2648 |
|
|
{ 0.35018222772483443, -0.40000000000000002, 0.0000000000000000,
|
| 2649 |
|
|
0.34906585039886590 },
|
| 2650 |
|
|
{ 0.52729015917508748, -0.40000000000000002, 0.0000000000000000,
|
| 2651 |
|
|
0.52359877559829882 },
|
| 2652 |
|
|
{ 0.70662374407341255, -0.40000000000000002, 0.0000000000000000,
|
| 2653 |
|
|
0.69813170079773179 },
|
| 2654 |
|
|
{ 0.88859210497602170, -0.40000000000000002, 0.0000000000000000,
|
| 2655 |
|
|
0.87266462599716477 },
|
| 2656 |
|
|
{ 1.0733136290471379, -0.40000000000000002, 0.0000000000000000,
|
| 2657 |
|
|
1.0471975511965976 },
|
| 2658 |
|
|
{ 1.2605612170157061, -0.40000000000000002, 0.0000000000000000,
|
| 2659 |
|
|
1.2217304763960306 },
|
| 2660 |
|
|
{ 1.4497513956433437, -0.40000000000000002, 0.0000000000000000,
|
| 2661 |
|
|
1.3962634015954636 },
|
| 2662 |
|
|
{ 1.6399998658645112, -0.40000000000000002, 0.0000000000000000,
|
| 2663 |
|
|
1.5707963267948966 },
|
| 2664 |
|
|
};
|
| 2665 |
|
|
|
| 2666 |
|
|
// Test function for k=-0.40000000000000002, nu=0.0000000000000000.
|
| 2667 |
|
|
template <typename Tp>
|
| 2668 |
|
|
void test051()
|
| 2669 |
|
|
{
|
| 2670 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2671 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2672 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2673 |
|
|
unsigned int num_datum = sizeof(data051)
|
| 2674 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2675 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2676 |
|
|
{
|
| 2677 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data051[i].k), Tp(data051[i].nu),
|
| 2678 |
|
|
Tp(data051[i].phi));
|
| 2679 |
|
|
const Tp f0 = data051[i].f0;
|
| 2680 |
|
|
const Tp diff = f - f0;
|
| 2681 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2682 |
|
|
max_abs_diff = std::abs(diff);
|
| 2683 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2684 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2685 |
|
|
{
|
| 2686 |
|
|
const Tp frac = diff / f0;
|
| 2687 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2688 |
|
|
max_abs_frac = std::abs(frac);
|
| 2689 |
|
|
}
|
| 2690 |
|
|
}
|
| 2691 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2692 |
|
|
}
|
| 2693 |
|
|
|
| 2694 |
|
|
// Test data for k=-0.40000000000000002, nu=0.10000000000000001.
|
| 2695 |
|
|
testcase_ellint_3<double> data052[] = {
|
| 2696 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.10000000000000001,
|
| 2697 |
|
|
0.0000000000000000 },
|
| 2698 |
|
|
{ 0.17449806706684673, -0.40000000000000002, 0.10000000000000001,
|
| 2699 |
|
|
0.17453292519943295 },
|
| 2700 |
|
|
{ 0.34880048623856075, -0.40000000000000002, 0.10000000000000001,
|
| 2701 |
|
|
0.34906585039886590 },
|
| 2702 |
|
|
{ 0.52277322065757403, -0.40000000000000002, 0.10000000000000001,
|
| 2703 |
|
|
0.52359877559829882 },
|
| 2704 |
|
|
{ 0.69638072056918376, -0.40000000000000002, 0.10000000000000001,
|
| 2705 |
|
|
0.69813170079773179 },
|
| 2706 |
|
|
{ 0.86968426619831540, -0.40000000000000002, 0.10000000000000001,
|
| 2707 |
|
|
0.87266462599716477 },
|
| 2708 |
|
|
{ 1.0428044206578095, -0.40000000000000002, 0.10000000000000001,
|
| 2709 |
|
|
1.0471975511965976 },
|
| 2710 |
|
|
{ 1.2158651158274378, -0.40000000000000002, 0.10000000000000001,
|
| 2711 |
|
|
1.2217304763960306 },
|
| 2712 |
|
|
{ 1.3889447129893322, -0.40000000000000002, 0.10000000000000001,
|
| 2713 |
|
|
1.3962634015954636 },
|
| 2714 |
|
|
{ 1.5620566886683604, -0.40000000000000002, 0.10000000000000001,
|
| 2715 |
|
|
1.5707963267948966 },
|
| 2716 |
|
|
};
|
| 2717 |
|
|
|
| 2718 |
|
|
// Test function for k=-0.40000000000000002, nu=0.10000000000000001.
|
| 2719 |
|
|
template <typename Tp>
|
| 2720 |
|
|
void test052()
|
| 2721 |
|
|
{
|
| 2722 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2723 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2724 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2725 |
|
|
unsigned int num_datum = sizeof(data052)
|
| 2726 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2727 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2728 |
|
|
{
|
| 2729 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data052[i].k), Tp(data052[i].nu),
|
| 2730 |
|
|
Tp(data052[i].phi));
|
| 2731 |
|
|
const Tp f0 = data052[i].f0;
|
| 2732 |
|
|
const Tp diff = f - f0;
|
| 2733 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2734 |
|
|
max_abs_diff = std::abs(diff);
|
| 2735 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2736 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2737 |
|
|
{
|
| 2738 |
|
|
const Tp frac = diff / f0;
|
| 2739 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2740 |
|
|
max_abs_frac = std::abs(frac);
|
| 2741 |
|
|
}
|
| 2742 |
|
|
}
|
| 2743 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2744 |
|
|
}
|
| 2745 |
|
|
|
| 2746 |
|
|
// Test data for k=-0.40000000000000002, nu=0.20000000000000001.
|
| 2747 |
|
|
testcase_ellint_3<double> data053[] = {
|
| 2748 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.20000000000000001,
|
| 2749 |
|
|
0.0000000000000000 },
|
| 2750 |
|
|
{ 0.17432262290723399, -0.40000000000000002, 0.20000000000000001,
|
| 2751 |
|
|
0.17453292519943295 },
|
| 2752 |
|
|
{ 0.34743795258968596, -0.40000000000000002, 0.20000000000000001,
|
| 2753 |
|
|
0.34906585039886590 },
|
| 2754 |
|
|
{ 0.51838919472805123, -0.40000000000000002, 0.20000000000000001,
|
| 2755 |
|
|
0.52359877559829882 },
|
| 2756 |
|
|
{ 0.68663134739057918, -0.40000000000000002, 0.20000000000000001,
|
| 2757 |
|
|
0.69813170079773179 },
|
| 2758 |
|
|
{ 0.85206432981833979, -0.40000000000000002, 0.20000000000000001,
|
| 2759 |
|
|
0.87266462599716477 },
|
| 2760 |
|
|
{ 1.0149595349004430, -0.40000000000000002, 0.20000000000000001,
|
| 2761 |
|
|
1.0471975511965976 },
|
| 2762 |
|
|
{ 1.1758349405464676, -0.40000000000000002, 0.20000000000000001,
|
| 2763 |
|
|
1.2217304763960306 },
|
| 2764 |
|
|
{ 1.3353337673882635, -0.40000000000000002, 0.20000000000000001,
|
| 2765 |
|
|
1.3962634015954636 },
|
| 2766 |
|
|
{ 1.4941414344266770, -0.40000000000000002, 0.20000000000000001,
|
| 2767 |
|
|
1.5707963267948966 },
|
| 2768 |
|
|
};
|
| 2769 |
|
|
|
| 2770 |
|
|
// Test function for k=-0.40000000000000002, nu=0.20000000000000001.
|
| 2771 |
|
|
template <typename Tp>
|
| 2772 |
|
|
void test053()
|
| 2773 |
|
|
{
|
| 2774 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2775 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2776 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2777 |
|
|
unsigned int num_datum = sizeof(data053)
|
| 2778 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2779 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2780 |
|
|
{
|
| 2781 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data053[i].k), Tp(data053[i].nu),
|
| 2782 |
|
|
Tp(data053[i].phi));
|
| 2783 |
|
|
const Tp f0 = data053[i].f0;
|
| 2784 |
|
|
const Tp diff = f - f0;
|
| 2785 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2786 |
|
|
max_abs_diff = std::abs(diff);
|
| 2787 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2788 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2789 |
|
|
{
|
| 2790 |
|
|
const Tp frac = diff / f0;
|
| 2791 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2792 |
|
|
max_abs_frac = std::abs(frac);
|
| 2793 |
|
|
}
|
| 2794 |
|
|
}
|
| 2795 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2796 |
|
|
}
|
| 2797 |
|
|
|
| 2798 |
|
|
// Test data for k=-0.40000000000000002, nu=0.29999999999999999.
|
| 2799 |
|
|
testcase_ellint_3<double> data054[] = {
|
| 2800 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.29999999999999999,
|
| 2801 |
|
|
0.0000000000000000 },
|
| 2802 |
|
|
{ 0.17414781013591543, -0.40000000000000002, 0.29999999999999999,
|
| 2803 |
|
|
0.17453292519943295 },
|
| 2804 |
|
|
{ 0.34609415696777285, -0.40000000000000002, 0.29999999999999999,
|
| 2805 |
|
|
0.34906585039886590 },
|
| 2806 |
|
|
{ 0.51413131295862546, -0.40000000000000002, 0.29999999999999999,
|
| 2807 |
|
|
0.52359877559829882 },
|
| 2808 |
|
|
{ 0.67733527622935630, -0.40000000000000002, 0.29999999999999999,
|
| 2809 |
|
|
0.69813170079773179 },
|
| 2810 |
|
|
{ 0.83558675182733266, -0.40000000000000002, 0.29999999999999999,
|
| 2811 |
|
|
0.87266462599716477 },
|
| 2812 |
|
|
{ 0.98940140808865906, -0.40000000000000002, 0.29999999999999999,
|
| 2813 |
|
|
1.0471975511965976 },
|
| 2814 |
|
|
{ 1.1396968797728058, -0.40000000000000002, 0.29999999999999999,
|
| 2815 |
|
|
1.2217304763960306 },
|
| 2816 |
|
|
{ 1.2875920037865087, -0.40000000000000002, 0.29999999999999999,
|
| 2817 |
|
|
1.3962634015954636 },
|
| 2818 |
|
|
{ 1.4342789859950078, -0.40000000000000002, 0.29999999999999999,
|
| 2819 |
|
|
1.5707963267948966 },
|
| 2820 |
|
|
};
|
| 2821 |
|
|
|
| 2822 |
|
|
// Test function for k=-0.40000000000000002, nu=0.29999999999999999.
|
| 2823 |
|
|
template <typename Tp>
|
| 2824 |
|
|
void test054()
|
| 2825 |
|
|
{
|
| 2826 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2827 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2828 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2829 |
|
|
unsigned int num_datum = sizeof(data054)
|
| 2830 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2831 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2832 |
|
|
{
|
| 2833 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data054[i].k), Tp(data054[i].nu),
|
| 2834 |
|
|
Tp(data054[i].phi));
|
| 2835 |
|
|
const Tp f0 = data054[i].f0;
|
| 2836 |
|
|
const Tp diff = f - f0;
|
| 2837 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2838 |
|
|
max_abs_diff = std::abs(diff);
|
| 2839 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2840 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2841 |
|
|
{
|
| 2842 |
|
|
const Tp frac = diff / f0;
|
| 2843 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2844 |
|
|
max_abs_frac = std::abs(frac);
|
| 2845 |
|
|
}
|
| 2846 |
|
|
}
|
| 2847 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2848 |
|
|
}
|
| 2849 |
|
|
|
| 2850 |
|
|
// Test data for k=-0.40000000000000002, nu=0.40000000000000002.
|
| 2851 |
|
|
testcase_ellint_3<double> data055[] = {
|
| 2852 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.40000000000000002,
|
| 2853 |
|
|
0.0000000000000000 },
|
| 2854 |
|
|
{ 0.17397362471112710, -0.40000000000000002, 0.40000000000000002,
|
| 2855 |
|
|
0.17453292519943295 },
|
| 2856 |
|
|
{ 0.34476864603333196, -0.40000000000000002, 0.40000000000000002,
|
| 2857 |
|
|
0.34906585039886590 },
|
| 2858 |
|
|
{ 0.50999329415379357, -0.40000000000000002, 0.40000000000000002,
|
| 2859 |
|
|
0.52359877559829882 },
|
| 2860 |
|
|
{ 0.66845674551396017, -0.40000000000000002, 0.40000000000000002,
|
| 2861 |
|
|
0.69813170079773179 },
|
| 2862 |
|
|
{ 0.82012848346231748, -0.40000000000000002, 0.40000000000000002,
|
| 2863 |
|
|
0.87266462599716477 },
|
| 2864 |
|
|
{ 0.96582449258349057, -0.40000000000000002, 0.40000000000000002,
|
| 2865 |
|
|
1.0471975511965976 },
|
| 2866 |
|
|
{ 1.1068473749476286, -0.40000000000000002, 0.40000000000000002,
|
| 2867 |
|
|
1.2217304763960306 },
|
| 2868 |
|
|
{ 1.2447132729159986, -0.40000000000000002, 0.40000000000000002,
|
| 2869 |
|
|
1.3962634015954636 },
|
| 2870 |
|
|
{ 1.3809986210732901, -0.40000000000000002, 0.40000000000000002,
|
| 2871 |
|
|
1.5707963267948966 },
|
| 2872 |
|
|
};
|
| 2873 |
|
|
|
| 2874 |
|
|
// Test function for k=-0.40000000000000002, nu=0.40000000000000002.
|
| 2875 |
|
|
template <typename Tp>
|
| 2876 |
|
|
void test055()
|
| 2877 |
|
|
{
|
| 2878 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2879 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2880 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2881 |
|
|
unsigned int num_datum = sizeof(data055)
|
| 2882 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2883 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2884 |
|
|
{
|
| 2885 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data055[i].k), Tp(data055[i].nu),
|
| 2886 |
|
|
Tp(data055[i].phi));
|
| 2887 |
|
|
const Tp f0 = data055[i].f0;
|
| 2888 |
|
|
const Tp diff = f - f0;
|
| 2889 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2890 |
|
|
max_abs_diff = std::abs(diff);
|
| 2891 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2892 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2893 |
|
|
{
|
| 2894 |
|
|
const Tp frac = diff / f0;
|
| 2895 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2896 |
|
|
max_abs_frac = std::abs(frac);
|
| 2897 |
|
|
}
|
| 2898 |
|
|
}
|
| 2899 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2900 |
|
|
}
|
| 2901 |
|
|
|
| 2902 |
|
|
// Test data for k=-0.40000000000000002, nu=0.50000000000000000.
|
| 2903 |
|
|
testcase_ellint_3<double> data056[] = {
|
| 2904 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.50000000000000000,
|
| 2905 |
|
|
0.0000000000000000 },
|
| 2906 |
|
|
{ 0.17380006262854139, -0.40000000000000002, 0.50000000000000000,
|
| 2907 |
|
|
0.17453292519943295 },
|
| 2908 |
|
|
{ 0.34346098216756610, -0.40000000000000002, 0.50000000000000000,
|
| 2909 |
|
|
0.34906585039886590 },
|
| 2910 |
|
|
{ 0.50596929935059420, -0.40000000000000002, 0.50000000000000000,
|
| 2911 |
|
|
0.52359877559829882 },
|
| 2912 |
|
|
{ 0.65996392089131262, -0.40000000000000002, 0.50000000000000000,
|
| 2913 |
|
|
0.69813170079773179 },
|
| 2914 |
|
|
{ 0.80558463511364786, -0.40000000000000002, 0.50000000000000000,
|
| 2915 |
|
|
0.87266462599716477 },
|
| 2916 |
|
|
{ 0.94397834522857704, -0.40000000000000002, 0.50000000000000000,
|
| 2917 |
|
|
1.0471975511965976 },
|
| 2918 |
|
|
{ 1.0768075114108115, -0.40000000000000002, 0.50000000000000000,
|
| 2919 |
|
|
1.2217304763960306 },
|
| 2920 |
|
|
{ 1.2059184624251329, -0.40000000000000002, 0.50000000000000000,
|
| 2921 |
|
|
1.3962634015954636 },
|
| 2922 |
|
|
{ 1.3331797176377398, -0.40000000000000002, 0.50000000000000000,
|
| 2923 |
|
|
1.5707963267948966 },
|
| 2924 |
|
|
};
|
| 2925 |
|
|
|
| 2926 |
|
|
// Test function for k=-0.40000000000000002, nu=0.50000000000000000.
|
| 2927 |
|
|
template <typename Tp>
|
| 2928 |
|
|
void test056()
|
| 2929 |
|
|
{
|
| 2930 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2931 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2932 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2933 |
|
|
unsigned int num_datum = sizeof(data056)
|
| 2934 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2935 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2936 |
|
|
{
|
| 2937 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data056[i].k), Tp(data056[i].nu),
|
| 2938 |
|
|
Tp(data056[i].phi));
|
| 2939 |
|
|
const Tp f0 = data056[i].f0;
|
| 2940 |
|
|
const Tp diff = f - f0;
|
| 2941 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2942 |
|
|
max_abs_diff = std::abs(diff);
|
| 2943 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2944 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2945 |
|
|
{
|
| 2946 |
|
|
const Tp frac = diff / f0;
|
| 2947 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2948 |
|
|
max_abs_frac = std::abs(frac);
|
| 2949 |
|
|
}
|
| 2950 |
|
|
}
|
| 2951 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2952 |
|
|
}
|
| 2953 |
|
|
|
| 2954 |
|
|
// Test data for k=-0.40000000000000002, nu=0.59999999999999998.
|
| 2955 |
|
|
testcase_ellint_3<double> data057[] = {
|
| 2956 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.59999999999999998,
|
| 2957 |
|
|
0.0000000000000000 },
|
| 2958 |
|
|
{ 0.17362711992081248, -0.40000000000000002, 0.59999999999999998,
|
| 2959 |
|
|
0.17453292519943295 },
|
| 2960 |
|
|
{ 0.34217074276403953, -0.40000000000000002, 0.59999999999999998,
|
| 2961 |
|
|
0.34906585039886590 },
|
| 2962 |
|
|
{ 0.50205389185761617, -0.40000000000000002, 0.59999999999999998,
|
| 2963 |
|
|
0.52359877559829882 },
|
| 2964 |
|
|
{ 0.65182834920372745, -0.40000000000000002, 0.59999999999999998,
|
| 2965 |
|
|
0.69813170079773179 },
|
| 2966 |
|
|
{ 0.79186512820565136, -0.40000000000000002, 0.59999999999999998,
|
| 2967 |
|
|
0.87266462599716477 },
|
| 2968 |
|
|
{ 0.92365535916287134, -0.40000000000000002, 0.59999999999999998,
|
| 2969 |
|
|
1.0471975511965976 },
|
| 2970 |
|
|
{ 1.0491915663957907, -0.40000000000000002, 0.59999999999999998,
|
| 2971 |
|
|
1.2217304763960306 },
|
| 2972 |
|
|
{ 1.1705934291745104, -0.40000000000000002, 0.59999999999999998,
|
| 2973 |
|
|
1.3962634015954636 },
|
| 2974 |
|
|
{ 1.2899514672527024, -0.40000000000000002, 0.59999999999999998,
|
| 2975 |
|
|
1.5707963267948966 },
|
| 2976 |
|
|
};
|
| 2977 |
|
|
|
| 2978 |
|
|
// Test function for k=-0.40000000000000002, nu=0.59999999999999998.
|
| 2979 |
|
|
template <typename Tp>
|
| 2980 |
|
|
void test057()
|
| 2981 |
|
|
{
|
| 2982 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2983 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2984 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2985 |
|
|
unsigned int num_datum = sizeof(data057)
|
| 2986 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 2987 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2988 |
|
|
{
|
| 2989 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data057[i].k), Tp(data057[i].nu),
|
| 2990 |
|
|
Tp(data057[i].phi));
|
| 2991 |
|
|
const Tp f0 = data057[i].f0;
|
| 2992 |
|
|
const Tp diff = f - f0;
|
| 2993 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2994 |
|
|
max_abs_diff = std::abs(diff);
|
| 2995 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2996 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2997 |
|
|
{
|
| 2998 |
|
|
const Tp frac = diff / f0;
|
| 2999 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3000 |
|
|
max_abs_frac = std::abs(frac);
|
| 3001 |
|
|
}
|
| 3002 |
|
|
}
|
| 3003 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3004 |
|
|
}
|
| 3005 |
|
|
|
| 3006 |
|
|
// Test data for k=-0.40000000000000002, nu=0.69999999999999996.
|
| 3007 |
|
|
testcase_ellint_3<double> data058[] = {
|
| 3008 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.69999999999999996,
|
| 3009 |
|
|
0.0000000000000000 },
|
| 3010 |
|
|
{ 0.17345479265712871, -0.40000000000000002, 0.69999999999999996,
|
| 3011 |
|
|
0.17453292519943295 },
|
| 3012 |
|
|
{ 0.34089751955950354, -0.40000000000000002, 0.69999999999999996,
|
| 3013 |
|
|
0.34906585039886590 },
|
| 3014 |
|
|
{ 0.49824200167361343, -0.40000000000000002, 0.69999999999999996,
|
| 3015 |
|
|
0.52359877559829882 },
|
| 3016 |
|
|
{ 0.64402450341199413, -0.40000000000000002, 0.69999999999999996,
|
| 3017 |
|
|
0.69813170079773179 },
|
| 3018 |
|
|
{ 0.77889207804122873, -0.40000000000000002, 0.69999999999999996,
|
| 3019 |
|
|
0.87266462599716477 },
|
| 3020 |
|
|
{ 0.90468169720957992, -0.40000000000000002, 0.69999999999999996,
|
| 3021 |
|
|
1.0471975511965976 },
|
| 3022 |
|
|
{ 1.0236847823692916, -0.40000000000000002, 0.69999999999999996,
|
| 3023 |
|
|
1.2217304763960306 },
|
| 3024 |
|
|
{ 1.1382465247425164, -0.40000000000000002, 0.69999999999999996,
|
| 3025 |
|
|
1.3962634015954636 },
|
| 3026 |
|
|
{ 1.2506255923253344, -0.40000000000000002, 0.69999999999999996,
|
| 3027 |
|
|
1.5707963267948966 },
|
| 3028 |
|
|
};
|
| 3029 |
|
|
|
| 3030 |
|
|
// Test function for k=-0.40000000000000002, nu=0.69999999999999996.
|
| 3031 |
|
|
template <typename Tp>
|
| 3032 |
|
|
void test058()
|
| 3033 |
|
|
{
|
| 3034 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3035 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3036 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3037 |
|
|
unsigned int num_datum = sizeof(data058)
|
| 3038 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3039 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3040 |
|
|
{
|
| 3041 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data058[i].k), Tp(data058[i].nu),
|
| 3042 |
|
|
Tp(data058[i].phi));
|
| 3043 |
|
|
const Tp f0 = data058[i].f0;
|
| 3044 |
|
|
const Tp diff = f - f0;
|
| 3045 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3046 |
|
|
max_abs_diff = std::abs(diff);
|
| 3047 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3048 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3049 |
|
|
{
|
| 3050 |
|
|
const Tp frac = diff / f0;
|
| 3051 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3052 |
|
|
max_abs_frac = std::abs(frac);
|
| 3053 |
|
|
}
|
| 3054 |
|
|
}
|
| 3055 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3056 |
|
|
}
|
| 3057 |
|
|
|
| 3058 |
|
|
// Test data for k=-0.40000000000000002, nu=0.80000000000000004.
|
| 3059 |
|
|
testcase_ellint_3<double> data059[] = {
|
| 3060 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.80000000000000004,
|
| 3061 |
|
|
0.0000000000000000 },
|
| 3062 |
|
|
{ 0.17328307694277156, -0.40000000000000002, 0.80000000000000004,
|
| 3063 |
|
|
0.17453292519943295 },
|
| 3064 |
|
|
{ 0.33964091800132007, -0.40000000000000002, 0.80000000000000004,
|
| 3065 |
|
|
0.34906585039886590 },
|
| 3066 |
|
|
{ 0.49452889372467451, -0.40000000000000002, 0.80000000000000004,
|
| 3067 |
|
|
0.52359877559829882 },
|
| 3068 |
|
|
{ 0.63652940095937327, -0.40000000000000002, 0.80000000000000004,
|
| 3069 |
|
|
0.69813170079773179 },
|
| 3070 |
|
|
{ 0.76659772511159097, -0.40000000000000002, 0.80000000000000004,
|
| 3071 |
|
|
0.87266462599716477 },
|
| 3072 |
|
|
{ 0.88691047977338111, -0.40000000000000002, 0.80000000000000004,
|
| 3073 |
|
|
1.0471975511965976 },
|
| 3074 |
|
|
{ 1.0000273200611638, -0.40000000000000002, 0.80000000000000004,
|
| 3075 |
|
|
1.2217304763960306 },
|
| 3076 |
|
|
{ 1.1084787902188007, -0.40000000000000002, 0.80000000000000004,
|
| 3077 |
|
|
1.3962634015954636 },
|
| 3078 |
|
|
{ 1.2146499565727209, -0.40000000000000002, 0.80000000000000004,
|
| 3079 |
|
|
1.5707963267948966 },
|
| 3080 |
|
|
};
|
| 3081 |
|
|
|
| 3082 |
|
|
// Test function for k=-0.40000000000000002, nu=0.80000000000000004.
|
| 3083 |
|
|
template <typename Tp>
|
| 3084 |
|
|
void test059()
|
| 3085 |
|
|
{
|
| 3086 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3087 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3088 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3089 |
|
|
unsigned int num_datum = sizeof(data059)
|
| 3090 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3091 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3092 |
|
|
{
|
| 3093 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data059[i].k), Tp(data059[i].nu),
|
| 3094 |
|
|
Tp(data059[i].phi));
|
| 3095 |
|
|
const Tp f0 = data059[i].f0;
|
| 3096 |
|
|
const Tp diff = f - f0;
|
| 3097 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3098 |
|
|
max_abs_diff = std::abs(diff);
|
| 3099 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3100 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3101 |
|
|
{
|
| 3102 |
|
|
const Tp frac = diff / f0;
|
| 3103 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3104 |
|
|
max_abs_frac = std::abs(frac);
|
| 3105 |
|
|
}
|
| 3106 |
|
|
}
|
| 3107 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3108 |
|
|
}
|
| 3109 |
|
|
|
| 3110 |
|
|
// Test data for k=-0.40000000000000002, nu=0.90000000000000002.
|
| 3111 |
|
|
testcase_ellint_3<double> data060[] = {
|
| 3112 |
|
|
{ -0.0000000000000000, -0.40000000000000002, 0.90000000000000002,
|
| 3113 |
|
|
0.0000000000000000 },
|
| 3114 |
|
|
{ 0.17311196891868130, -0.40000000000000002, 0.90000000000000002,
|
| 3115 |
|
|
0.17453292519943295 },
|
| 3116 |
|
|
{ 0.33840055664911906, -0.40000000000000002, 0.90000000000000002,
|
| 3117 |
|
|
0.34906585039886590 },
|
| 3118 |
|
|
{ 0.49091013944075340, -0.40000000000000002, 0.90000000000000002,
|
| 3119 |
|
|
0.52359877559829882 },
|
| 3120 |
|
|
{ 0.62932228186809591, -0.40000000000000002, 0.90000000000000002,
|
| 3121 |
|
|
0.69813170079773179 },
|
| 3122 |
|
|
{ 0.75492278323019801, -0.40000000000000002, 0.90000000000000002,
|
| 3123 |
|
|
0.87266462599716477 },
|
| 3124 |
|
|
{ 0.87021659043854294, -0.40000000000000002, 0.90000000000000002,
|
| 3125 |
|
|
1.0471975511965976 },
|
| 3126 |
|
|
{ 0.97800245228239246, -0.40000000000000002, 0.90000000000000002,
|
| 3127 |
|
|
1.2217304763960306 },
|
| 3128 |
|
|
{ 1.0809625773173694, -0.40000000000000002, 0.90000000000000002,
|
| 3129 |
|
|
1.3962634015954636 },
|
| 3130 |
|
|
{ 1.1815758115929846, -0.40000000000000002, 0.90000000000000002,
|
| 3131 |
|
|
1.5707963267948966 },
|
| 3132 |
|
|
};
|
| 3133 |
|
|
|
| 3134 |
|
|
// Test function for k=-0.40000000000000002, nu=0.90000000000000002.
|
| 3135 |
|
|
template <typename Tp>
|
| 3136 |
|
|
void test060()
|
| 3137 |
|
|
{
|
| 3138 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3139 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3140 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3141 |
|
|
unsigned int num_datum = sizeof(data060)
|
| 3142 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3143 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3144 |
|
|
{
|
| 3145 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data060[i].k), Tp(data060[i].nu),
|
| 3146 |
|
|
Tp(data060[i].phi));
|
| 3147 |
|
|
const Tp f0 = data060[i].f0;
|
| 3148 |
|
|
const Tp diff = f - f0;
|
| 3149 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3150 |
|
|
max_abs_diff = std::abs(diff);
|
| 3151 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3152 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3153 |
|
|
{
|
| 3154 |
|
|
const Tp frac = diff / f0;
|
| 3155 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3156 |
|
|
max_abs_frac = std::abs(frac);
|
| 3157 |
|
|
}
|
| 3158 |
|
|
}
|
| 3159 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3160 |
|
|
}
|
| 3161 |
|
|
|
| 3162 |
|
|
// Test data for k=-0.30000000000000004, nu=0.0000000000000000.
|
| 3163 |
|
|
testcase_ellint_3<double> data061[] = {
|
| 3164 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.0000000000000000,
|
| 3165 |
|
|
0.0000000000000000 },
|
| 3166 |
|
|
{ 0.17461228653000102, -0.30000000000000004, 0.0000000000000000,
|
| 3167 |
|
|
0.17453292519943295 },
|
| 3168 |
|
|
{ 0.34969146102798415, -0.30000000000000004, 0.0000000000000000,
|
| 3169 |
|
|
0.34906585039886590 },
|
| 3170 |
|
|
{ 0.52565822873726320, -0.30000000000000004, 0.0000000000000000,
|
| 3171 |
|
|
0.52359877559829882 },
|
| 3172 |
|
|
{ 0.70284226512408532, -0.30000000000000004, 0.0000000000000000,
|
| 3173 |
|
|
0.69813170079773179 },
|
| 3174 |
|
|
{ 0.88144139195111182, -0.30000000000000004, 0.0000000000000000,
|
| 3175 |
|
|
0.87266462599716477 },
|
| 3176 |
|
|
{ 1.0614897067260523, -0.30000000000000004, 0.0000000000000000,
|
| 3177 |
|
|
1.0471975511965976 },
|
| 3178 |
|
|
{ 1.2428416824174218, -0.30000000000000004, 0.0000000000000000,
|
| 3179 |
|
|
1.2217304763960306 },
|
| 3180 |
|
|
{ 1.4251795877015925, -0.30000000000000004, 0.0000000000000000,
|
| 3181 |
|
|
1.3962634015954636 },
|
| 3182 |
|
|
{ 1.6080486199305126, -0.30000000000000004, 0.0000000000000000,
|
| 3183 |
|
|
1.5707963267948966 },
|
| 3184 |
|
|
};
|
| 3185 |
|
|
|
| 3186 |
|
|
// Test function for k=-0.30000000000000004, nu=0.0000000000000000.
|
| 3187 |
|
|
template <typename Tp>
|
| 3188 |
|
|
void test061()
|
| 3189 |
|
|
{
|
| 3190 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3191 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3192 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3193 |
|
|
unsigned int num_datum = sizeof(data061)
|
| 3194 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3195 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3196 |
|
|
{
|
| 3197 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data061[i].k), Tp(data061[i].nu),
|
| 3198 |
|
|
Tp(data061[i].phi));
|
| 3199 |
|
|
const Tp f0 = data061[i].f0;
|
| 3200 |
|
|
const Tp diff = f - f0;
|
| 3201 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3202 |
|
|
max_abs_diff = std::abs(diff);
|
| 3203 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3204 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3205 |
|
|
{
|
| 3206 |
|
|
const Tp frac = diff / f0;
|
| 3207 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3208 |
|
|
max_abs_frac = std::abs(frac);
|
| 3209 |
|
|
}
|
| 3210 |
|
|
}
|
| 3211 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3212 |
|
|
}
|
| 3213 |
|
|
|
| 3214 |
|
|
// Test data for k=-0.30000000000000004, nu=0.10000000000000001.
|
| 3215 |
|
|
testcase_ellint_3<double> data062[] = {
|
| 3216 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.10000000000000001,
|
| 3217 |
|
|
0.0000000000000000 },
|
| 3218 |
|
|
{ 0.17443631884814378, -0.30000000000000004, 0.10000000000000001,
|
| 3219 |
|
|
0.17453292519943295 },
|
| 3220 |
|
|
{ 0.34831316835124926, -0.30000000000000004, 0.10000000000000001,
|
| 3221 |
|
|
0.34906585039886590 },
|
| 3222 |
|
|
{ 0.52116586276523857, -0.30000000000000004, 0.10000000000000001,
|
| 3223 |
|
|
0.52359877559829882 },
|
| 3224 |
|
|
{ 0.69269385837910036, -0.30000000000000004, 0.10000000000000001,
|
| 3225 |
|
|
0.69813170079773179 },
|
| 3226 |
|
|
{ 0.86279023163070856, -0.30000000000000004, 0.10000000000000001,
|
| 3227 |
|
|
0.87266462599716477 },
|
| 3228 |
|
|
{ 1.0315321461438265, -0.30000000000000004, 0.10000000000000001,
|
| 3229 |
|
|
1.0471975511965976 },
|
| 3230 |
|
|
{ 1.1991449111869024, -0.30000000000000004, 0.10000000000000001,
|
| 3231 |
|
|
1.2217304763960306 },
|
| 3232 |
|
|
{ 1.3659561780923211, -0.30000000000000004, 0.10000000000000001,
|
| 3233 |
|
|
1.3962634015954636 },
|
| 3234 |
|
|
{ 1.5323534693557526, -0.30000000000000004, 0.10000000000000001,
|
| 3235 |
|
|
1.5707963267948966 },
|
| 3236 |
|
|
};
|
| 3237 |
|
|
|
| 3238 |
|
|
// Test function for k=-0.30000000000000004, nu=0.10000000000000001.
|
| 3239 |
|
|
template <typename Tp>
|
| 3240 |
|
|
void test062()
|
| 3241 |
|
|
{
|
| 3242 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3243 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3244 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3245 |
|
|
unsigned int num_datum = sizeof(data062)
|
| 3246 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3247 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3248 |
|
|
{
|
| 3249 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data062[i].k), Tp(data062[i].nu),
|
| 3250 |
|
|
Tp(data062[i].phi));
|
| 3251 |
|
|
const Tp f0 = data062[i].f0;
|
| 3252 |
|
|
const Tp diff = f - f0;
|
| 3253 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3254 |
|
|
max_abs_diff = std::abs(diff);
|
| 3255 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3256 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3257 |
|
|
{
|
| 3258 |
|
|
const Tp frac = diff / f0;
|
| 3259 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3260 |
|
|
max_abs_frac = std::abs(frac);
|
| 3261 |
|
|
}
|
| 3262 |
|
|
}
|
| 3263 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3264 |
|
|
}
|
| 3265 |
|
|
|
| 3266 |
|
|
// Test data for k=-0.30000000000000004, nu=0.20000000000000001.
|
| 3267 |
|
|
testcase_ellint_3<double> data063[] = {
|
| 3268 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.20000000000000001,
|
| 3269 |
|
|
0.0000000000000000 },
|
| 3270 |
|
|
{ 0.17426098615372090, -0.30000000000000004, 0.20000000000000001,
|
| 3271 |
|
|
0.17453292519943295 },
|
| 3272 |
|
|
{ 0.34695402664689923, -0.30000000000000004, 0.20000000000000001,
|
| 3273 |
|
|
0.34906585039886590 },
|
| 3274 |
|
|
{ 0.51680555567038933, -0.30000000000000004, 0.20000000000000001,
|
| 3275 |
|
|
0.52359877559829882 },
|
| 3276 |
|
|
{ 0.68303375225260210, -0.30000000000000004, 0.20000000000000001,
|
| 3277 |
|
|
0.69813170079773179 },
|
| 3278 |
|
|
{ 0.84540662891295026, -0.30000000000000004, 0.20000000000000001,
|
| 3279 |
|
|
0.87266462599716477 },
|
| 3280 |
|
|
{ 1.0041834051646927, -0.30000000000000004, 0.20000000000000001,
|
| 3281 |
|
|
1.0471975511965976 },
|
| 3282 |
|
|
{ 1.1599952702345711, -0.30000000000000004, 0.20000000000000001,
|
| 3283 |
|
|
1.2217304763960306 },
|
| 3284 |
|
|
{ 1.3137179520499163, -0.30000000000000004, 0.20000000000000001,
|
| 3285 |
|
|
1.3962634015954636 },
|
| 3286 |
|
|
{ 1.4663658145259875, -0.30000000000000004, 0.20000000000000001,
|
| 3287 |
|
|
1.5707963267948966 },
|
| 3288 |
|
|
};
|
| 3289 |
|
|
|
| 3290 |
|
|
// Test function for k=-0.30000000000000004, nu=0.20000000000000001.
|
| 3291 |
|
|
template <typename Tp>
|
| 3292 |
|
|
void test063()
|
| 3293 |
|
|
{
|
| 3294 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3295 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3296 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3297 |
|
|
unsigned int num_datum = sizeof(data063)
|
| 3298 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3299 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3300 |
|
|
{
|
| 3301 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data063[i].k), Tp(data063[i].nu),
|
| 3302 |
|
|
Tp(data063[i].phi));
|
| 3303 |
|
|
const Tp f0 = data063[i].f0;
|
| 3304 |
|
|
const Tp diff = f - f0;
|
| 3305 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3306 |
|
|
max_abs_diff = std::abs(diff);
|
| 3307 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3308 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3309 |
|
|
{
|
| 3310 |
|
|
const Tp frac = diff / f0;
|
| 3311 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3312 |
|
|
max_abs_frac = std::abs(frac);
|
| 3313 |
|
|
}
|
| 3314 |
|
|
}
|
| 3315 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3316 |
|
|
}
|
| 3317 |
|
|
|
| 3318 |
|
|
// Test data for k=-0.30000000000000004, nu=0.29999999999999999.
|
| 3319 |
|
|
testcase_ellint_3<double> data064[] = {
|
| 3320 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.29999999999999999,
|
| 3321 |
|
|
0.0000000000000000 },
|
| 3322 |
|
|
{ 0.17408628437042845, -0.30000000000000004, 0.29999999999999999,
|
| 3323 |
|
|
0.17453292519943295 },
|
| 3324 |
|
|
{ 0.34561356761638401, -0.30000000000000004, 0.29999999999999999,
|
| 3325 |
|
|
0.34906585039886590 },
|
| 3326 |
|
|
{ 0.51257058617875850, -0.30000000000000004, 0.29999999999999999,
|
| 3327 |
|
|
0.52359877559829882 },
|
| 3328 |
|
|
{ 0.67382207124602866, -0.30000000000000004, 0.29999999999999999,
|
| 3329 |
|
|
0.69813170079773179 },
|
| 3330 |
|
|
{ 0.82914751587825131, -0.30000000000000004, 0.29999999999999999,
|
| 3331 |
|
|
0.87266462599716477 },
|
| 3332 |
|
|
{ 0.97907434814374950, -0.30000000000000004, 0.29999999999999999,
|
| 3333 |
|
|
1.0471975511965976 },
|
| 3334 |
|
|
{ 1.1246399297351584, -0.30000000000000004, 0.29999999999999999,
|
| 3335 |
|
|
1.2217304763960306 },
|
| 3336 |
|
|
{ 1.2671793970398146, -0.30000000000000004, 0.29999999999999999,
|
| 3337 |
|
|
1.3962634015954636 },
|
| 3338 |
|
|
{ 1.4081767433479089, -0.30000000000000004, 0.29999999999999999,
|
| 3339 |
|
|
1.5707963267948966 },
|
| 3340 |
|
|
};
|
| 3341 |
|
|
|
| 3342 |
|
|
// Test function for k=-0.30000000000000004, nu=0.29999999999999999.
|
| 3343 |
|
|
template <typename Tp>
|
| 3344 |
|
|
void test064()
|
| 3345 |
|
|
{
|
| 3346 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3347 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3348 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3349 |
|
|
unsigned int num_datum = sizeof(data064)
|
| 3350 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3351 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3352 |
|
|
{
|
| 3353 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data064[i].k), Tp(data064[i].nu),
|
| 3354 |
|
|
Tp(data064[i].phi));
|
| 3355 |
|
|
const Tp f0 = data064[i].f0;
|
| 3356 |
|
|
const Tp diff = f - f0;
|
| 3357 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3358 |
|
|
max_abs_diff = std::abs(diff);
|
| 3359 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3360 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3361 |
|
|
{
|
| 3362 |
|
|
const Tp frac = diff / f0;
|
| 3363 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3364 |
|
|
max_abs_frac = std::abs(frac);
|
| 3365 |
|
|
}
|
| 3366 |
|
|
}
|
| 3367 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3368 |
|
|
}
|
| 3369 |
|
|
|
| 3370 |
|
|
// Test data for k=-0.30000000000000004, nu=0.40000000000000002.
|
| 3371 |
|
|
testcase_ellint_3<double> data065[] = {
|
| 3372 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.40000000000000002,
|
| 3373 |
|
|
0.0000000000000000 },
|
| 3374 |
|
|
{ 0.17391220945982730, -0.30000000000000004, 0.40000000000000002,
|
| 3375 |
|
|
0.17453292519943295 },
|
| 3376 |
|
|
{ 0.34429133937639689, -0.30000000000000004, 0.40000000000000002,
|
| 3377 |
|
|
0.34906585039886590 },
|
| 3378 |
|
|
{ 0.50845471668581632, -0.30000000000000004, 0.40000000000000002,
|
| 3379 |
|
|
0.52359877559829882 },
|
| 3380 |
|
|
{ 0.66502347027873854, -0.30000000000000004, 0.40000000000000002,
|
| 3381 |
|
|
0.69813170079773179 },
|
| 3382 |
|
|
{ 0.81389191978012254, -0.30000000000000004, 0.40000000000000002,
|
| 3383 |
|
|
0.87266462599716477 },
|
| 3384 |
|
|
{ 0.95590618002140593, -0.30000000000000004, 0.40000000000000002,
|
| 3385 |
|
|
1.0471975511965976 },
|
| 3386 |
|
|
{ 1.0924915195213121, -0.30000000000000004, 0.40000000000000002,
|
| 3387 |
|
|
1.2217304763960306 },
|
| 3388 |
|
|
{ 1.2253651604038058, -0.30000000000000004, 0.40000000000000002,
|
| 3389 |
|
|
1.3962634015954636 },
|
| 3390 |
|
|
{ 1.3563643538969761, -0.30000000000000004, 0.40000000000000002,
|
| 3391 |
|
|
1.5707963267948966 },
|
| 3392 |
|
|
};
|
| 3393 |
|
|
|
| 3394 |
|
|
// Test function for k=-0.30000000000000004, nu=0.40000000000000002.
|
| 3395 |
|
|
template <typename Tp>
|
| 3396 |
|
|
void test065()
|
| 3397 |
|
|
{
|
| 3398 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3399 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3400 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3401 |
|
|
unsigned int num_datum = sizeof(data065)
|
| 3402 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3403 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3404 |
|
|
{
|
| 3405 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data065[i].k), Tp(data065[i].nu),
|
| 3406 |
|
|
Tp(data065[i].phi));
|
| 3407 |
|
|
const Tp f0 = data065[i].f0;
|
| 3408 |
|
|
const Tp diff = f - f0;
|
| 3409 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3410 |
|
|
max_abs_diff = std::abs(diff);
|
| 3411 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3412 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3413 |
|
|
{
|
| 3414 |
|
|
const Tp frac = diff / f0;
|
| 3415 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3416 |
|
|
max_abs_frac = std::abs(frac);
|
| 3417 |
|
|
}
|
| 3418 |
|
|
}
|
| 3419 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3420 |
|
|
}
|
| 3421 |
|
|
|
| 3422 |
|
|
// Test data for k=-0.30000000000000004, nu=0.50000000000000000.
|
| 3423 |
|
|
testcase_ellint_3<double> data066[] = {
|
| 3424 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.50000000000000000,
|
| 3425 |
|
|
0.0000000000000000 },
|
| 3426 |
|
|
{ 0.17373875742088235, -0.30000000000000004, 0.50000000000000000,
|
| 3427 |
|
|
0.17453292519943295 },
|
| 3428 |
|
|
{ 0.34298690571124157, -0.30000000000000004, 0.50000000000000000,
|
| 3429 |
|
|
0.34906585039886590 },
|
| 3430 |
|
|
{ 0.50445214859646936, -0.30000000000000004, 0.50000000000000000,
|
| 3431 |
|
|
0.52359877559829882 },
|
| 3432 |
|
|
{ 0.65660648352418516, -0.30000000000000004, 0.50000000000000000,
|
| 3433 |
|
|
0.69813170079773179 },
|
| 3434 |
|
|
{ 0.79953670639287289, -0.30000000000000004, 0.50000000000000000,
|
| 3435 |
|
|
0.87266462599716477 },
|
| 3436 |
|
|
{ 0.93443393926588558, -0.30000000000000004, 0.50000000000000000,
|
| 3437 |
|
|
1.0471975511965976 },
|
| 3438 |
|
|
{ 1.0630838369016911, -0.30000000000000004, 0.50000000000000000,
|
| 3439 |
|
|
1.2217304763960306 },
|
| 3440 |
|
|
{ 1.1875197325653026, -0.30000000000000004, 0.50000000000000000,
|
| 3441 |
|
|
1.3962634015954636 },
|
| 3442 |
|
|
{ 1.3098448759814960, -0.30000000000000004, 0.50000000000000000,
|
| 3443 |
|
|
1.5707963267948966 },
|
| 3444 |
|
|
};
|
| 3445 |
|
|
|
| 3446 |
|
|
// Test function for k=-0.30000000000000004, nu=0.50000000000000000.
|
| 3447 |
|
|
template <typename Tp>
|
| 3448 |
|
|
void test066()
|
| 3449 |
|
|
{
|
| 3450 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3451 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3452 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3453 |
|
|
unsigned int num_datum = sizeof(data066)
|
| 3454 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3455 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3456 |
|
|
{
|
| 3457 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data066[i].k), Tp(data066[i].nu),
|
| 3458 |
|
|
Tp(data066[i].phi));
|
| 3459 |
|
|
const Tp f0 = data066[i].f0;
|
| 3460 |
|
|
const Tp diff = f - f0;
|
| 3461 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3462 |
|
|
max_abs_diff = std::abs(diff);
|
| 3463 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3464 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3465 |
|
|
{
|
| 3466 |
|
|
const Tp frac = diff / f0;
|
| 3467 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3468 |
|
|
max_abs_frac = std::abs(frac);
|
| 3469 |
|
|
}
|
| 3470 |
|
|
}
|
| 3471 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3472 |
|
|
}
|
| 3473 |
|
|
|
| 3474 |
|
|
// Test data for k=-0.30000000000000004, nu=0.59999999999999998.
|
| 3475 |
|
|
testcase_ellint_3<double> data067[] = {
|
| 3476 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.59999999999999998,
|
| 3477 |
|
|
0.0000000000000000 },
|
| 3478 |
|
|
{ 0.17356592428950826, -0.30000000000000004, 0.59999999999999998,
|
| 3479 |
|
|
0.17453292519943295 },
|
| 3480 |
|
|
{ 0.34169984536697379, -0.30000000000000004, 0.59999999999999998,
|
| 3481 |
|
|
0.34906585039886590 },
|
| 3482 |
|
|
{ 0.50055748266498457, -0.30000000000000004, 0.59999999999999998,
|
| 3483 |
|
|
0.52359877559829882 },
|
| 3484 |
|
|
{ 0.64854298527106768, -0.30000000000000004, 0.59999999999999998,
|
| 3485 |
|
|
0.69813170079773179 },
|
| 3486 |
|
|
{ 0.78599329284207431, -0.30000000000000004, 0.59999999999999998,
|
| 3487 |
|
|
0.87266462599716477 },
|
| 3488 |
|
|
{ 0.91445452089128221, -0.30000000000000004, 0.59999999999999998,
|
| 3489 |
|
|
1.0471975511965976 },
|
| 3490 |
|
|
{ 1.0360412952290587, -0.30000000000000004, 0.59999999999999998,
|
| 3491 |
|
|
1.2217304763960306 },
|
| 3492 |
|
|
{ 1.1530473919778639, -0.30000000000000004, 0.59999999999999998,
|
| 3493 |
|
|
1.3962634015954636 },
|
| 3494 |
|
|
{ 1.2677758800420666, -0.30000000000000004, 0.59999999999999998,
|
| 3495 |
|
|
1.5707963267948966 },
|
| 3496 |
|
|
};
|
| 3497 |
|
|
|
| 3498 |
|
|
// Test function for k=-0.30000000000000004, nu=0.59999999999999998.
|
| 3499 |
|
|
template <typename Tp>
|
| 3500 |
|
|
void test067()
|
| 3501 |
|
|
{
|
| 3502 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3503 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3504 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3505 |
|
|
unsigned int num_datum = sizeof(data067)
|
| 3506 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3507 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3508 |
|
|
{
|
| 3509 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data067[i].k), Tp(data067[i].nu),
|
| 3510 |
|
|
Tp(data067[i].phi));
|
| 3511 |
|
|
const Tp f0 = data067[i].f0;
|
| 3512 |
|
|
const Tp diff = f - f0;
|
| 3513 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3514 |
|
|
max_abs_diff = std::abs(diff);
|
| 3515 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3516 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3517 |
|
|
{
|
| 3518 |
|
|
const Tp frac = diff / f0;
|
| 3519 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3520 |
|
|
max_abs_frac = std::abs(frac);
|
| 3521 |
|
|
}
|
| 3522 |
|
|
}
|
| 3523 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3524 |
|
|
}
|
| 3525 |
|
|
|
| 3526 |
|
|
// Test data for k=-0.30000000000000004, nu=0.69999999999999996.
|
| 3527 |
|
|
testcase_ellint_3<double> data068[] = {
|
| 3528 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.69999999999999996,
|
| 3529 |
|
|
0.0000000000000000 },
|
| 3530 |
|
|
{ 0.17339370613812227, -0.30000000000000004, 0.69999999999999996,
|
| 3531 |
|
|
0.17453292519943295 },
|
| 3532 |
|
|
{ 0.34042975138455933, -0.30000000000000004, 0.69999999999999996,
|
| 3533 |
|
|
0.34906585039886590 },
|
| 3534 |
|
|
{ 0.49676568368075985, -0.30000000000000004, 0.69999999999999996,
|
| 3535 |
|
|
0.52359877559829882 },
|
| 3536 |
|
|
{ 0.64080774055753720, -0.30000000000000004, 0.69999999999999996,
|
| 3537 |
|
|
0.69813170079773179 },
|
| 3538 |
|
|
{ 0.77318507779667278, -0.30000000000000004, 0.69999999999999996,
|
| 3539 |
|
|
0.87266462599716477 },
|
| 3540 |
|
|
{ 0.89579782346548631, -0.30000000000000004, 0.69999999999999996,
|
| 3541 |
|
|
1.0471975511965976 },
|
| 3542 |
|
|
{ 1.0110573286052202, -0.30000000000000004, 0.69999999999999996,
|
| 3543 |
|
|
1.2217304763960306 },
|
| 3544 |
|
|
{ 1.1214710972949633, -0.30000000000000004, 0.69999999999999996,
|
| 3545 |
|
|
1.3962634015954636 },
|
| 3546 |
|
|
{ 1.2294913236274980, -0.30000000000000004, 0.69999999999999996,
|
| 3547 |
|
|
1.5707963267948966 },
|
| 3548 |
|
|
};
|
| 3549 |
|
|
|
| 3550 |
|
|
// Test function for k=-0.30000000000000004, nu=0.69999999999999996.
|
| 3551 |
|
|
template <typename Tp>
|
| 3552 |
|
|
void test068()
|
| 3553 |
|
|
{
|
| 3554 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3555 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3556 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3557 |
|
|
unsigned int num_datum = sizeof(data068)
|
| 3558 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3559 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3560 |
|
|
{
|
| 3561 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data068[i].k), Tp(data068[i].nu),
|
| 3562 |
|
|
Tp(data068[i].phi));
|
| 3563 |
|
|
const Tp f0 = data068[i].f0;
|
| 3564 |
|
|
const Tp diff = f - f0;
|
| 3565 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3566 |
|
|
max_abs_diff = std::abs(diff);
|
| 3567 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3568 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3569 |
|
|
{
|
| 3570 |
|
|
const Tp frac = diff / f0;
|
| 3571 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3572 |
|
|
max_abs_frac = std::abs(frac);
|
| 3573 |
|
|
}
|
| 3574 |
|
|
}
|
| 3575 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3576 |
|
|
}
|
| 3577 |
|
|
|
| 3578 |
|
|
// Test data for k=-0.30000000000000004, nu=0.80000000000000004.
|
| 3579 |
|
|
testcase_ellint_3<double> data069[] = {
|
| 3580 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.80000000000000004,
|
| 3581 |
|
|
0.0000000000000000 },
|
| 3582 |
|
|
{ 0.17322209907520361, -0.30000000000000004, 0.80000000000000004,
|
| 3583 |
|
|
0.17453292519943295 },
|
| 3584 |
|
|
{ 0.33917623046949996, -0.30000000000000004, 0.80000000000000004,
|
| 3585 |
|
|
0.34906585039886590 },
|
| 3586 |
|
|
{ 0.49307204894329176, -0.30000000000000004, 0.80000000000000004,
|
| 3587 |
|
|
0.52359877559829882 },
|
| 3588 |
|
|
{ 0.63337802830291723, -0.30000000000000004, 0.80000000000000004,
|
| 3589 |
|
|
0.69813170079773179 },
|
| 3590 |
|
|
{ 0.76104540997689407, -0.30000000000000004, 0.80000000000000004,
|
| 3591 |
|
|
0.87266462599716477 },
|
| 3592 |
|
|
{ 0.87832009635450736, -0.30000000000000004, 0.80000000000000004,
|
| 3593 |
|
|
1.0471975511965976 },
|
| 3594 |
|
|
{ 0.98787879723171790, -0.30000000000000004, 0.80000000000000004,
|
| 3595 |
|
|
1.2217304763960306 },
|
| 3596 |
|
|
{ 1.0924036340069336, -0.30000000000000004, 0.80000000000000004,
|
| 3597 |
|
|
1.3962634015954636 },
|
| 3598 |
|
|
{ 1.1944567571590046, -0.30000000000000004, 0.80000000000000004,
|
| 3599 |
|
|
1.5707963267948966 },
|
| 3600 |
|
|
};
|
| 3601 |
|
|
|
| 3602 |
|
|
// Test function for k=-0.30000000000000004, nu=0.80000000000000004.
|
| 3603 |
|
|
template <typename Tp>
|
| 3604 |
|
|
void test069()
|
| 3605 |
|
|
{
|
| 3606 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3607 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3608 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3609 |
|
|
unsigned int num_datum = sizeof(data069)
|
| 3610 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3611 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3612 |
|
|
{
|
| 3613 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data069[i].k), Tp(data069[i].nu),
|
| 3614 |
|
|
Tp(data069[i].phi));
|
| 3615 |
|
|
const Tp f0 = data069[i].f0;
|
| 3616 |
|
|
const Tp diff = f - f0;
|
| 3617 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3618 |
|
|
max_abs_diff = std::abs(diff);
|
| 3619 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3620 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3621 |
|
|
{
|
| 3622 |
|
|
const Tp frac = diff / f0;
|
| 3623 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3624 |
|
|
max_abs_frac = std::abs(frac);
|
| 3625 |
|
|
}
|
| 3626 |
|
|
}
|
| 3627 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3628 |
|
|
}
|
| 3629 |
|
|
|
| 3630 |
|
|
// Test data for k=-0.30000000000000004, nu=0.90000000000000002.
|
| 3631 |
|
|
testcase_ellint_3<double> data070[] = {
|
| 3632 |
|
|
{ -0.0000000000000000, -0.30000000000000004, 0.90000000000000002,
|
| 3633 |
|
|
0.0000000000000000 },
|
| 3634 |
|
|
{ 0.17305109924485948, -0.30000000000000004, 0.90000000000000002,
|
| 3635 |
|
|
0.17453292519943295 },
|
| 3636 |
|
|
{ 0.33793890239556984, -0.30000000000000004, 0.90000000000000002,
|
| 3637 |
|
|
0.34906585039886590 },
|
| 3638 |
|
|
{ 0.48947218005089738, -0.30000000000000004, 0.90000000000000002,
|
| 3639 |
|
|
0.52359877559829882 },
|
| 3640 |
|
|
{ 0.62623332340775151, -0.30000000000000004, 0.90000000000000002,
|
| 3641 |
|
|
0.69813170079773179 },
|
| 3642 |
|
|
{ 0.74951596581511148, -0.30000000000000004, 0.90000000000000002,
|
| 3643 |
|
|
0.87266462599716477 },
|
| 3644 |
|
|
{ 0.86189886597756005, -0.30000000000000004, 0.90000000000000002,
|
| 3645 |
|
|
1.0471975511965976 },
|
| 3646 |
|
|
{ 0.96629451153092005, -0.30000000000000004, 0.90000000000000002,
|
| 3647 |
|
|
1.2217304763960306 },
|
| 3648 |
|
|
{ 1.0655269133492680, -0.30000000000000004, 0.90000000000000002,
|
| 3649 |
|
|
1.3962634015954636 },
|
| 3650 |
|
|
{ 1.1622376896064912, -0.30000000000000004, 0.90000000000000002,
|
| 3651 |
|
|
1.5707963267948966 },
|
| 3652 |
|
|
};
|
| 3653 |
|
|
|
| 3654 |
|
|
// Test function for k=-0.30000000000000004, nu=0.90000000000000002.
|
| 3655 |
|
|
template <typename Tp>
|
| 3656 |
|
|
void test070()
|
| 3657 |
|
|
{
|
| 3658 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3659 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3660 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3661 |
|
|
unsigned int num_datum = sizeof(data070)
|
| 3662 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3663 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3664 |
|
|
{
|
| 3665 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data070[i].k), Tp(data070[i].nu),
|
| 3666 |
|
|
Tp(data070[i].phi));
|
| 3667 |
|
|
const Tp f0 = data070[i].f0;
|
| 3668 |
|
|
const Tp diff = f - f0;
|
| 3669 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3670 |
|
|
max_abs_diff = std::abs(diff);
|
| 3671 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3672 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3673 |
|
|
{
|
| 3674 |
|
|
const Tp frac = diff / f0;
|
| 3675 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3676 |
|
|
max_abs_frac = std::abs(frac);
|
| 3677 |
|
|
}
|
| 3678 |
|
|
}
|
| 3679 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3680 |
|
|
}
|
| 3681 |
|
|
|
| 3682 |
|
|
// Test data for k=-0.19999999999999996, nu=0.0000000000000000.
|
| 3683 |
|
|
testcase_ellint_3<double> data071[] = {
|
| 3684 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.0000000000000000,
|
| 3685 |
|
|
0.0000000000000000 },
|
| 3686 |
|
|
{ 0.17456817290292811, -0.19999999999999996, 0.0000000000000000,
|
| 3687 |
|
|
0.17453292519943295 },
|
| 3688 |
|
|
{ 0.34934315932086801, -0.19999999999999996, 0.0000000000000000,
|
| 3689 |
|
|
0.34906585039886590 },
|
| 3690 |
|
|
{ 0.52450880529443988, -0.19999999999999996, 0.0000000000000000,
|
| 3691 |
|
|
0.52359877559829882 },
|
| 3692 |
|
|
{ 0.70020491009844910, -0.19999999999999996, 0.0000000000000000,
|
| 3693 |
|
|
0.69813170079773179 },
|
| 3694 |
|
|
{ 0.87651006649967955, -0.19999999999999996, 0.0000000000000000,
|
| 3695 |
|
|
0.87266462599716477 },
|
| 3696 |
|
|
{ 1.0534305870298994, -0.19999999999999996, 0.0000000000000000,
|
| 3697 |
|
|
1.0471975511965976 },
|
| 3698 |
|
|
{ 1.2308975521670784, -0.19999999999999996, 0.0000000000000000,
|
| 3699 |
|
|
1.2217304763960306 },
|
| 3700 |
|
|
{ 1.4087733584990738, -0.19999999999999996, 0.0000000000000000,
|
| 3701 |
|
|
1.3962634015954636 },
|
| 3702 |
|
|
{ 1.5868678474541664, -0.19999999999999996, 0.0000000000000000,
|
| 3703 |
|
|
1.5707963267948966 },
|
| 3704 |
|
|
};
|
| 3705 |
|
|
|
| 3706 |
|
|
// Test function for k=-0.19999999999999996, nu=0.0000000000000000.
|
| 3707 |
|
|
template <typename Tp>
|
| 3708 |
|
|
void test071()
|
| 3709 |
|
|
{
|
| 3710 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3711 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3712 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3713 |
|
|
unsigned int num_datum = sizeof(data071)
|
| 3714 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3715 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3716 |
|
|
{
|
| 3717 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data071[i].k), Tp(data071[i].nu),
|
| 3718 |
|
|
Tp(data071[i].phi));
|
| 3719 |
|
|
const Tp f0 = data071[i].f0;
|
| 3720 |
|
|
const Tp diff = f - f0;
|
| 3721 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3722 |
|
|
max_abs_diff = std::abs(diff);
|
| 3723 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3724 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3725 |
|
|
{
|
| 3726 |
|
|
const Tp frac = diff / f0;
|
| 3727 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3728 |
|
|
max_abs_frac = std::abs(frac);
|
| 3729 |
|
|
}
|
| 3730 |
|
|
}
|
| 3731 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3732 |
|
|
}
|
| 3733 |
|
|
|
| 3734 |
|
|
// Test data for k=-0.19999999999999996, nu=0.10000000000000001.
|
| 3735 |
|
|
testcase_ellint_3<double> data072[] = {
|
| 3736 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.10000000000000001,
|
| 3737 |
|
|
0.0000000000000000 },
|
| 3738 |
|
|
{ 0.17439228502691750, -0.19999999999999996, 0.10000000000000001,
|
| 3739 |
|
|
0.17453292519943295 },
|
| 3740 |
|
|
{ 0.34796731137565740, -0.19999999999999996, 0.10000000000000001,
|
| 3741 |
|
|
0.34906585039886590 },
|
| 3742 |
|
|
{ 0.52003370294544848, -0.19999999999999996, 0.10000000000000001,
|
| 3743 |
|
|
0.52359877559829882 },
|
| 3744 |
|
|
{ 0.69012222258631495, -0.19999999999999996, 0.10000000000000001,
|
| 3745 |
|
|
0.69813170079773179 },
|
| 3746 |
|
|
{ 0.85803491465566772, -0.19999999999999996, 0.10000000000000001,
|
| 3747 |
|
|
0.87266462599716477 },
|
| 3748 |
|
|
{ 1.0238463961099364, -0.19999999999999996, 0.10000000000000001,
|
| 3749 |
|
|
1.0471975511965976 },
|
| 3750 |
|
|
{ 1.1878691059202153, -0.19999999999999996, 0.10000000000000001,
|
| 3751 |
|
|
1.2217304763960306 },
|
| 3752 |
|
|
{ 1.3505985031831940, -0.19999999999999996, 0.10000000000000001,
|
| 3753 |
|
|
1.3962634015954636 },
|
| 3754 |
|
|
{ 1.5126513474261092, -0.19999999999999996, 0.10000000000000001,
|
| 3755 |
|
|
1.5707963267948966 },
|
| 3756 |
|
|
};
|
| 3757 |
|
|
|
| 3758 |
|
|
// Test function for k=-0.19999999999999996, nu=0.10000000000000001.
|
| 3759 |
|
|
template <typename Tp>
|
| 3760 |
|
|
void test072()
|
| 3761 |
|
|
{
|
| 3762 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3763 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3764 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3765 |
|
|
unsigned int num_datum = sizeof(data072)
|
| 3766 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3767 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3768 |
|
|
{
|
| 3769 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data072[i].k), Tp(data072[i].nu),
|
| 3770 |
|
|
Tp(data072[i].phi));
|
| 3771 |
|
|
const Tp f0 = data072[i].f0;
|
| 3772 |
|
|
const Tp diff = f - f0;
|
| 3773 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3774 |
|
|
max_abs_diff = std::abs(diff);
|
| 3775 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3776 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3777 |
|
|
{
|
| 3778 |
|
|
const Tp frac = diff / f0;
|
| 3779 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3780 |
|
|
max_abs_frac = std::abs(frac);
|
| 3781 |
|
|
}
|
| 3782 |
|
|
}
|
| 3783 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3784 |
|
|
}
|
| 3785 |
|
|
|
| 3786 |
|
|
// Test data for k=-0.19999999999999996, nu=0.20000000000000001.
|
| 3787 |
|
|
testcase_ellint_3<double> data073[] = {
|
| 3788 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.20000000000000001,
|
| 3789 |
|
|
0.0000000000000000 },
|
| 3790 |
|
|
{ 0.17421703179583750, -0.19999999999999996, 0.20000000000000001,
|
| 3791 |
|
|
0.17453292519943295 },
|
| 3792 |
|
|
{ 0.34661057411998791, -0.19999999999999996, 0.20000000000000001,
|
| 3793 |
|
|
0.34906585039886590 },
|
| 3794 |
|
|
{ 0.51569006052647393, -0.19999999999999996, 0.20000000000000001,
|
| 3795 |
|
|
0.52359877559829882 },
|
| 3796 |
|
|
{ 0.68052412821107278, -0.19999999999999996, 0.20000000000000001,
|
| 3797 |
|
|
0.69813170079773179 },
|
| 3798 |
|
|
{ 0.84081341263313825, -0.19999999999999996, 0.20000000000000001,
|
| 3799 |
|
|
0.87266462599716477 },
|
| 3800 |
|
|
{ 0.99683359988842890, -0.19999999999999996, 0.20000000000000001,
|
| 3801 |
|
|
1.0471975511965976 },
|
| 3802 |
|
|
{ 1.1493086715118852, -0.19999999999999996, 0.20000000000000001,
|
| 3803 |
|
|
1.2217304763960306 },
|
| 3804 |
|
|
{ 1.2992699693957541, -0.19999999999999996, 0.20000000000000001,
|
| 3805 |
|
|
1.3962634015954636 },
|
| 3806 |
|
|
{ 1.4479323932249568, -0.19999999999999996, 0.20000000000000001,
|
| 3807 |
|
|
1.5707963267948966 },
|
| 3808 |
|
|
};
|
| 3809 |
|
|
|
| 3810 |
|
|
// Test function for k=-0.19999999999999996, nu=0.20000000000000001.
|
| 3811 |
|
|
template <typename Tp>
|
| 3812 |
|
|
void test073()
|
| 3813 |
|
|
{
|
| 3814 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3815 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3816 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3817 |
|
|
unsigned int num_datum = sizeof(data073)
|
| 3818 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3819 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3820 |
|
|
{
|
| 3821 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data073[i].k), Tp(data073[i].nu),
|
| 3822 |
|
|
Tp(data073[i].phi));
|
| 3823 |
|
|
const Tp f0 = data073[i].f0;
|
| 3824 |
|
|
const Tp diff = f - f0;
|
| 3825 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3826 |
|
|
max_abs_diff = std::abs(diff);
|
| 3827 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3828 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3829 |
|
|
{
|
| 3830 |
|
|
const Tp frac = diff / f0;
|
| 3831 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3832 |
|
|
max_abs_frac = std::abs(frac);
|
| 3833 |
|
|
}
|
| 3834 |
|
|
}
|
| 3835 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3836 |
|
|
}
|
| 3837 |
|
|
|
| 3838 |
|
|
// Test data for k=-0.19999999999999996, nu=0.29999999999999999.
|
| 3839 |
|
|
testcase_ellint_3<double> data074[] = {
|
| 3840 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.29999999999999999,
|
| 3841 |
|
|
0.0000000000000000 },
|
| 3842 |
|
|
{ 0.17404240913577707, -0.19999999999999996, 0.29999999999999999,
|
| 3843 |
|
|
0.17453292519943295 },
|
| 3844 |
|
|
{ 0.34527248032587193, -0.19999999999999996, 0.29999999999999999,
|
| 3845 |
|
|
0.34906585039886590 },
|
| 3846 |
|
|
{ 0.51147118981668416, -0.19999999999999996, 0.29999999999999999,
|
| 3847 |
|
|
0.52359877559829882 },
|
| 3848 |
|
|
{ 0.67137107867777635, -0.19999999999999996, 0.29999999999999999,
|
| 3849 |
|
|
0.69813170079773179 },
|
| 3850 |
|
|
{ 0.82470418188668893, -0.19999999999999996, 0.29999999999999999,
|
| 3851 |
|
|
0.87266462599716477 },
|
| 3852 |
|
|
{ 0.97202873223594299, -0.19999999999999996, 0.29999999999999999,
|
| 3853 |
|
|
1.0471975511965976 },
|
| 3854 |
|
|
{ 1.1144773569375266, -0.19999999999999996, 0.29999999999999999,
|
| 3855 |
|
|
1.2217304763960306 },
|
| 3856 |
|
|
{ 1.2535292433701000, -0.19999999999999996, 0.29999999999999999,
|
| 3857 |
|
|
1.3962634015954636 },
|
| 3858 |
|
|
{ 1.3908453514752481, -0.19999999999999996, 0.29999999999999999,
|
| 3859 |
|
|
1.5707963267948966 },
|
| 3860 |
|
|
};
|
| 3861 |
|
|
|
| 3862 |
|
|
// Test function for k=-0.19999999999999996, nu=0.29999999999999999.
|
| 3863 |
|
|
template <typename Tp>
|
| 3864 |
|
|
void test074()
|
| 3865 |
|
|
{
|
| 3866 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3867 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3868 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3869 |
|
|
unsigned int num_datum = sizeof(data074)
|
| 3870 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3871 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3872 |
|
|
{
|
| 3873 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data074[i].k), Tp(data074[i].nu),
|
| 3874 |
|
|
Tp(data074[i].phi));
|
| 3875 |
|
|
const Tp f0 = data074[i].f0;
|
| 3876 |
|
|
const Tp diff = f - f0;
|
| 3877 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3878 |
|
|
max_abs_diff = std::abs(diff);
|
| 3879 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3880 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3881 |
|
|
{
|
| 3882 |
|
|
const Tp frac = diff / f0;
|
| 3883 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3884 |
|
|
max_abs_frac = std::abs(frac);
|
| 3885 |
|
|
}
|
| 3886 |
|
|
}
|
| 3887 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3888 |
|
|
}
|
| 3889 |
|
|
|
| 3890 |
|
|
// Test data for k=-0.19999999999999996, nu=0.40000000000000002.
|
| 3891 |
|
|
testcase_ellint_3<double> data075[] = {
|
| 3892 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.40000000000000002,
|
| 3893 |
|
|
0.0000000000000000 },
|
| 3894 |
|
|
{ 0.17386841301066677, -0.19999999999999996, 0.40000000000000002,
|
| 3895 |
|
|
0.17453292519943295 },
|
| 3896 |
|
|
{ 0.34395257914113253, -0.19999999999999996, 0.40000000000000002,
|
| 3897 |
|
|
0.34906585039886590 },
|
| 3898 |
|
|
{ 0.50737088376869466, -0.19999999999999996, 0.40000000000000002,
|
| 3899 |
|
|
0.52359877559829882 },
|
| 3900 |
|
|
{ 0.66262801717277664, -0.19999999999999996, 0.40000000000000002,
|
| 3901 |
|
|
0.69813170079773179 },
|
| 3902 |
|
|
{ 0.80958766645079094, -0.19999999999999996, 0.40000000000000002,
|
| 3903 |
|
|
0.87266462599716477 },
|
| 3904 |
|
|
{ 0.94913754236162040, -0.19999999999999996, 0.40000000000000002,
|
| 3905 |
|
|
1.0471975511965976 },
|
| 3906 |
|
|
{ 1.0827985514223000, -0.19999999999999996, 0.40000000000000002,
|
| 3907 |
|
|
1.2217304763960306 },
|
| 3908 |
|
|
{ 1.2124212429050478, -0.19999999999999996, 0.40000000000000002,
|
| 3909 |
|
|
1.3962634015954636 },
|
| 3910 |
|
|
{ 1.3400002519661010, -0.19999999999999996, 0.40000000000000002,
|
| 3911 |
|
|
1.5707963267948966 },
|
| 3912 |
|
|
};
|
| 3913 |
|
|
|
| 3914 |
|
|
// Test function for k=-0.19999999999999996, nu=0.40000000000000002.
|
| 3915 |
|
|
template <typename Tp>
|
| 3916 |
|
|
void test075()
|
| 3917 |
|
|
{
|
| 3918 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3919 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3920 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3921 |
|
|
unsigned int num_datum = sizeof(data075)
|
| 3922 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3923 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3924 |
|
|
{
|
| 3925 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data075[i].k), Tp(data075[i].nu),
|
| 3926 |
|
|
Tp(data075[i].phi));
|
| 3927 |
|
|
const Tp f0 = data075[i].f0;
|
| 3928 |
|
|
const Tp diff = f - f0;
|
| 3929 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3930 |
|
|
max_abs_diff = std::abs(diff);
|
| 3931 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3932 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3933 |
|
|
{
|
| 3934 |
|
|
const Tp frac = diff / f0;
|
| 3935 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3936 |
|
|
max_abs_frac = std::abs(frac);
|
| 3937 |
|
|
}
|
| 3938 |
|
|
}
|
| 3939 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3940 |
|
|
}
|
| 3941 |
|
|
|
| 3942 |
|
|
// Test data for k=-0.19999999999999996, nu=0.50000000000000000.
|
| 3943 |
|
|
testcase_ellint_3<double> data076[] = {
|
| 3944 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.50000000000000000,
|
| 3945 |
|
|
0.0000000000000000 },
|
| 3946 |
|
|
{ 0.17369503942181802, -0.19999999999999996, 0.50000000000000000,
|
| 3947 |
|
|
0.17453292519943295 },
|
| 3948 |
|
|
{ 0.34265043534362660, -0.19999999999999996, 0.50000000000000000,
|
| 3949 |
|
|
0.34906585039886590 },
|
| 3950 |
|
|
{ 0.50338337208655415, -0.19999999999999996, 0.50000000000000000,
|
| 3951 |
|
|
0.52359877559829882 },
|
| 3952 |
|
|
{ 0.65426373297163642, -0.19999999999999996, 0.50000000000000000,
|
| 3953 |
|
|
0.69813170079773179 },
|
| 3954 |
|
|
{ 0.79536193036145808, -0.19999999999999996, 0.50000000000000000,
|
| 3955 |
|
|
0.87266462599716477 },
|
| 3956 |
|
|
{ 0.92791875910061605, -0.19999999999999996, 0.50000000000000000,
|
| 3957 |
|
|
1.0471975511965976 },
|
| 3958 |
|
|
{ 1.0538145052725829, -0.19999999999999996, 0.50000000000000000,
|
| 3959 |
|
|
1.2217304763960306 },
|
| 3960 |
|
|
{ 1.1752060022875899, -0.19999999999999996, 0.50000000000000000,
|
| 3961 |
|
|
1.3962634015954636 },
|
| 3962 |
|
|
{ 1.2943374404397376, -0.19999999999999996, 0.50000000000000000,
|
| 3963 |
|
|
1.5707963267948966 },
|
| 3964 |
|
|
};
|
| 3965 |
|
|
|
| 3966 |
|
|
// Test function for k=-0.19999999999999996, nu=0.50000000000000000.
|
| 3967 |
|
|
template <typename Tp>
|
| 3968 |
|
|
void test076()
|
| 3969 |
|
|
{
|
| 3970 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 3971 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 3972 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 3973 |
|
|
unsigned int num_datum = sizeof(data076)
|
| 3974 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 3975 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 3976 |
|
|
{
|
| 3977 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data076[i].k), Tp(data076[i].nu),
|
| 3978 |
|
|
Tp(data076[i].phi));
|
| 3979 |
|
|
const Tp f0 = data076[i].f0;
|
| 3980 |
|
|
const Tp diff = f - f0;
|
| 3981 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 3982 |
|
|
max_abs_diff = std::abs(diff);
|
| 3983 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 3984 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 3985 |
|
|
{
|
| 3986 |
|
|
const Tp frac = diff / f0;
|
| 3987 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 3988 |
|
|
max_abs_frac = std::abs(frac);
|
| 3989 |
|
|
}
|
| 3990 |
|
|
}
|
| 3991 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 3992 |
|
|
}
|
| 3993 |
|
|
|
| 3994 |
|
|
// Test data for k=-0.19999999999999996, nu=0.59999999999999998.
|
| 3995 |
|
|
testcase_ellint_3<double> data077[] = {
|
| 3996 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.59999999999999998,
|
| 3997 |
|
|
0.0000000000000000 },
|
| 3998 |
|
|
{ 0.17352228440746928, -0.19999999999999996, 0.59999999999999998,
|
| 3999 |
|
|
0.17453292519943295 },
|
| 4000 |
|
|
{ 0.34136562863713626, -0.19999999999999996, 0.59999999999999998,
|
| 4001 |
|
|
0.34906585039886590 },
|
| 4002 |
|
|
{ 0.49950328177638481, -0.19999999999999996, 0.59999999999999998,
|
| 4003 |
|
|
0.52359877559829882 },
|
| 4004 |
|
|
{ 0.64625032705690832, -0.19999999999999996, 0.59999999999999998,
|
| 4005 |
|
|
0.69813170079773179 },
|
| 4006 |
|
|
{ 0.78193941198403094, -0.19999999999999996, 0.59999999999999998,
|
| 4007 |
|
|
0.87266462599716477 },
|
| 4008 |
|
|
{ 0.90817230934317128, -0.19999999999999996, 0.59999999999999998,
|
| 4009 |
|
|
1.0471975511965976 },
|
| 4010 |
|
|
{ 1.0271563751276462, -0.19999999999999996, 0.59999999999999998,
|
| 4011 |
|
|
1.2217304763960306 },
|
| 4012 |
|
|
{ 1.1412999379040518, -0.19999999999999996, 0.59999999999999998,
|
| 4013 |
|
|
1.3962634015954636 },
|
| 4014 |
|
|
{ 1.2530330675914561, -0.19999999999999996, 0.59999999999999998,
|
| 4015 |
|
|
1.5707963267948966 },
|
| 4016 |
|
|
};
|
| 4017 |
|
|
|
| 4018 |
|
|
// Test function for k=-0.19999999999999996, nu=0.59999999999999998.
|
| 4019 |
|
|
template <typename Tp>
|
| 4020 |
|
|
void test077()
|
| 4021 |
|
|
{
|
| 4022 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4023 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4024 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4025 |
|
|
unsigned int num_datum = sizeof(data077)
|
| 4026 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4027 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4028 |
|
|
{
|
| 4029 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data077[i].k), Tp(data077[i].nu),
|
| 4030 |
|
|
Tp(data077[i].phi));
|
| 4031 |
|
|
const Tp f0 = data077[i].f0;
|
| 4032 |
|
|
const Tp diff = f - f0;
|
| 4033 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4034 |
|
|
max_abs_diff = std::abs(diff);
|
| 4035 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4036 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4037 |
|
|
{
|
| 4038 |
|
|
const Tp frac = diff / f0;
|
| 4039 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4040 |
|
|
max_abs_frac = std::abs(frac);
|
| 4041 |
|
|
}
|
| 4042 |
|
|
}
|
| 4043 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4044 |
|
|
}
|
| 4045 |
|
|
|
| 4046 |
|
|
// Test data for k=-0.19999999999999996, nu=0.69999999999999996.
|
| 4047 |
|
|
testcase_ellint_3<double> data078[] = {
|
| 4048 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.69999999999999996,
|
| 4049 |
|
|
0.0000000000000000 },
|
| 4050 |
|
|
{ 0.17335014404233898, -0.19999999999999996, 0.69999999999999996,
|
| 4051 |
|
|
0.17453292519943295 },
|
| 4052 |
|
|
{ 0.34009775298617811, -0.19999999999999996, 0.69999999999999996,
|
| 4053 |
|
|
0.34906585039886590 },
|
| 4054 |
|
|
{ 0.49572560201923810, -0.19999999999999996, 0.69999999999999996,
|
| 4055 |
|
|
0.52359877559829882 },
|
| 4056 |
|
|
{ 0.63856276669886525, -0.19999999999999996, 0.69999999999999996,
|
| 4057 |
|
|
0.69813170079773179 },
|
| 4058 |
|
|
{ 0.76924438644867565, -0.19999999999999996, 0.69999999999999996,
|
| 4059 |
|
|
0.87266462599716477 },
|
| 4060 |
|
|
{ 0.88973060843856466, -0.19999999999999996, 0.69999999999999996,
|
| 4061 |
|
|
1.0471975511965976 },
|
| 4062 |
|
|
{ 1.0025230471636377, -0.19999999999999996, 0.69999999999999996,
|
| 4063 |
|
|
1.2217304763960306 },
|
| 4064 |
|
|
{ 1.1102356376093103, -0.19999999999999996, 0.69999999999999996,
|
| 4065 |
|
|
1.3962634015954636 },
|
| 4066 |
|
|
{ 1.2154356555075867, -0.19999999999999996, 0.69999999999999996,
|
| 4067 |
|
|
1.5707963267948966 },
|
| 4068 |
|
|
};
|
| 4069 |
|
|
|
| 4070 |
|
|
// Test function for k=-0.19999999999999996, nu=0.69999999999999996.
|
| 4071 |
|
|
template <typename Tp>
|
| 4072 |
|
|
void test078()
|
| 4073 |
|
|
{
|
| 4074 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4075 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4076 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4077 |
|
|
unsigned int num_datum = sizeof(data078)
|
| 4078 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4079 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4080 |
|
|
{
|
| 4081 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data078[i].k), Tp(data078[i].nu),
|
| 4082 |
|
|
Tp(data078[i].phi));
|
| 4083 |
|
|
const Tp f0 = data078[i].f0;
|
| 4084 |
|
|
const Tp diff = f - f0;
|
| 4085 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4086 |
|
|
max_abs_diff = std::abs(diff);
|
| 4087 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4088 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4089 |
|
|
{
|
| 4090 |
|
|
const Tp frac = diff / f0;
|
| 4091 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4092 |
|
|
max_abs_frac = std::abs(frac);
|
| 4093 |
|
|
}
|
| 4094 |
|
|
}
|
| 4095 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4096 |
|
|
}
|
| 4097 |
|
|
|
| 4098 |
|
|
// Test data for k=-0.19999999999999996, nu=0.80000000000000004.
|
| 4099 |
|
|
testcase_ellint_3<double> data079[] = {
|
| 4100 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.80000000000000004,
|
| 4101 |
|
|
0.0000000000000000 },
|
| 4102 |
|
|
{ 0.17317861443718541, -0.19999999999999996, 0.80000000000000004,
|
| 4103 |
|
|
0.17453292519943295 },
|
| 4104 |
|
|
{ 0.33884641598718701, -0.19999999999999996, 0.80000000000000004,
|
| 4105 |
|
|
0.34906585039886590 },
|
| 4106 |
|
|
{ 0.49204565281259494, -0.19999999999999996, 0.80000000000000004,
|
| 4107 |
|
|
0.52359877559829882 },
|
| 4108 |
|
|
{ 0.63117851188220353, -0.19999999999999996, 0.80000000000000004,
|
| 4109 |
|
|
0.69813170079773179 },
|
| 4110 |
|
|
{ 0.75721095949544170, -0.19999999999999996, 0.80000000000000004,
|
| 4111 |
|
|
0.87266462599716477 },
|
| 4112 |
|
|
{ 0.87245201443919118, -0.19999999999999996, 0.80000000000000004,
|
| 4113 |
|
|
1.0471975511965976 },
|
| 4114 |
|
|
{ 0.97966584238831089, -0.19999999999999996, 0.80000000000000004,
|
| 4115 |
|
|
1.2217304763960306 },
|
| 4116 |
|
|
{ 1.0816336325174360, -0.19999999999999996, 0.80000000000000004,
|
| 4117 |
|
|
1.3962634015954636 },
|
| 4118 |
|
|
{ 1.1810223448909913, -0.19999999999999996, 0.80000000000000004,
|
| 4119 |
|
|
1.5707963267948966 },
|
| 4120 |
|
|
};
|
| 4121 |
|
|
|
| 4122 |
|
|
// Test function for k=-0.19999999999999996, nu=0.80000000000000004.
|
| 4123 |
|
|
template <typename Tp>
|
| 4124 |
|
|
void test079()
|
| 4125 |
|
|
{
|
| 4126 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4127 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4128 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4129 |
|
|
unsigned int num_datum = sizeof(data079)
|
| 4130 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4131 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4132 |
|
|
{
|
| 4133 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data079[i].k), Tp(data079[i].nu),
|
| 4134 |
|
|
Tp(data079[i].phi));
|
| 4135 |
|
|
const Tp f0 = data079[i].f0;
|
| 4136 |
|
|
const Tp diff = f - f0;
|
| 4137 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4138 |
|
|
max_abs_diff = std::abs(diff);
|
| 4139 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4140 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4141 |
|
|
{
|
| 4142 |
|
|
const Tp frac = diff / f0;
|
| 4143 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4144 |
|
|
max_abs_frac = std::abs(frac);
|
| 4145 |
|
|
}
|
| 4146 |
|
|
}
|
| 4147 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4148 |
|
|
}
|
| 4149 |
|
|
|
| 4150 |
|
|
// Test data for k=-0.19999999999999996, nu=0.90000000000000002.
|
| 4151 |
|
|
testcase_ellint_3<double> data080[] = {
|
| 4152 |
|
|
{ -0.0000000000000000, -0.19999999999999996, 0.90000000000000002,
|
| 4153 |
|
|
0.0000000000000000 },
|
| 4154 |
|
|
{ 0.17300769173837280, -0.19999999999999996, 0.90000000000000002,
|
| 4155 |
|
|
0.17453292519943295 },
|
| 4156 |
|
|
{ 0.33761123827372508, -0.19999999999999996, 0.90000000000000002,
|
| 4157 |
|
|
0.34906585039886590 },
|
| 4158 |
|
|
{ 0.48845905690769426, -0.19999999999999996, 0.90000000000000002,
|
| 4159 |
|
|
0.52359877559829882 },
|
| 4160 |
|
|
{ 0.62407720017324986, -0.19999999999999996, 0.90000000000000002,
|
| 4161 |
|
|
0.69813170079773179 },
|
| 4162 |
|
|
{ 0.74578146525124289, -0.19999999999999996, 0.90000000000000002,
|
| 4163 |
|
|
0.87266462599716477 },
|
| 4164 |
|
|
{ 0.85621583540073076, -0.19999999999999996, 0.90000000000000002,
|
| 4165 |
|
|
1.0471975511965976 },
|
| 4166 |
|
|
{ 0.95837725988001199, -0.19999999999999996, 0.90000000000000002,
|
| 4167 |
|
|
1.2217304763960306 },
|
| 4168 |
|
|
{ 1.0551821412633928, -0.19999999999999996, 0.90000000000000002,
|
| 4169 |
|
|
1.3962634015954636 },
|
| 4170 |
|
|
{ 1.1493679916141863, -0.19999999999999996, 0.90000000000000002,
|
| 4171 |
|
|
1.5707963267948966 },
|
| 4172 |
|
|
};
|
| 4173 |
|
|
|
| 4174 |
|
|
// Test function for k=-0.19999999999999996, nu=0.90000000000000002.
|
| 4175 |
|
|
template <typename Tp>
|
| 4176 |
|
|
void test080()
|
| 4177 |
|
|
{
|
| 4178 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4179 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4180 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4181 |
|
|
unsigned int num_datum = sizeof(data080)
|
| 4182 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4183 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4184 |
|
|
{
|
| 4185 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data080[i].k), Tp(data080[i].nu),
|
| 4186 |
|
|
Tp(data080[i].phi));
|
| 4187 |
|
|
const Tp f0 = data080[i].f0;
|
| 4188 |
|
|
const Tp diff = f - f0;
|
| 4189 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4190 |
|
|
max_abs_diff = std::abs(diff);
|
| 4191 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4192 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4193 |
|
|
{
|
| 4194 |
|
|
const Tp frac = diff / f0;
|
| 4195 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4196 |
|
|
max_abs_frac = std::abs(frac);
|
| 4197 |
|
|
}
|
| 4198 |
|
|
}
|
| 4199 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4200 |
|
|
}
|
| 4201 |
|
|
|
| 4202 |
|
|
// Test data for k=-0.099999999999999978, nu=0.0000000000000000.
|
| 4203 |
|
|
testcase_ellint_3<double> data081[] = {
|
| 4204 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.0000000000000000,
|
| 4205 |
|
|
0.0000000000000000 },
|
| 4206 |
|
|
{ 0.17454173353063665, -0.099999999999999978, 0.0000000000000000,
|
| 4207 |
|
|
0.17453292519943295 },
|
| 4208 |
|
|
{ 0.34913506721468085, -0.099999999999999978, 0.0000000000000000,
|
| 4209 |
|
|
0.34906585039886590 },
|
| 4210 |
|
|
{ 0.52382550016538953, -0.099999999999999978, 0.0000000000000000,
|
| 4211 |
|
|
0.52359877559829882 },
|
| 4212 |
|
|
{ 0.69864700854177031, -0.099999999999999978, 0.0000000000000000,
|
| 4213 |
|
|
0.69813170079773179 },
|
| 4214 |
|
|
{ 0.87361792586964870, -0.099999999999999978, 0.0000000000000000,
|
| 4215 |
|
|
0.87266462599716477 },
|
| 4216 |
|
|
{ 1.0487386319621685, -0.099999999999999978, 0.0000000000000000,
|
| 4217 |
|
|
1.0471975511965976 },
|
| 4218 |
|
|
{ 1.2239913752078757, -0.099999999999999978, 0.0000000000000000,
|
| 4219 |
|
|
1.2217304763960306 },
|
| 4220 |
|
|
{ 1.3993423113684049, -0.099999999999999978, 0.0000000000000000,
|
| 4221 |
|
|
1.3962634015954636 },
|
| 4222 |
|
|
{ 1.5747455615173562, -0.099999999999999978, 0.0000000000000000,
|
| 4223 |
|
|
1.5707963267948966 },
|
| 4224 |
|
|
};
|
| 4225 |
|
|
|
| 4226 |
|
|
// Test function for k=-0.099999999999999978, nu=0.0000000000000000.
|
| 4227 |
|
|
template <typename Tp>
|
| 4228 |
|
|
void test081()
|
| 4229 |
|
|
{
|
| 4230 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4231 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4232 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4233 |
|
|
unsigned int num_datum = sizeof(data081)
|
| 4234 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4235 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4236 |
|
|
{
|
| 4237 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data081[i].k), Tp(data081[i].nu),
|
| 4238 |
|
|
Tp(data081[i].phi));
|
| 4239 |
|
|
const Tp f0 = data081[i].f0;
|
| 4240 |
|
|
const Tp diff = f - f0;
|
| 4241 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4242 |
|
|
max_abs_diff = std::abs(diff);
|
| 4243 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4244 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4245 |
|
|
{
|
| 4246 |
|
|
const Tp frac = diff / f0;
|
| 4247 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4248 |
|
|
max_abs_frac = std::abs(frac);
|
| 4249 |
|
|
}
|
| 4250 |
|
|
}
|
| 4251 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4252 |
|
|
}
|
| 4253 |
|
|
|
| 4254 |
|
|
// Test data for k=-0.099999999999999978, nu=0.10000000000000001.
|
| 4255 |
|
|
testcase_ellint_3<double> data082[] = {
|
| 4256 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.10000000000000001,
|
| 4257 |
|
|
0.0000000000000000 },
|
| 4258 |
|
|
{ 0.17436589347616618, -0.099999999999999978, 0.10000000000000001,
|
| 4259 |
|
|
0.17453292519943295 },
|
| 4260 |
|
|
{ 0.34776067871237354, -0.099999999999999978, 0.10000000000000001,
|
| 4261 |
|
|
0.34906585039886590 },
|
| 4262 |
|
|
{ 0.51936064354727807, -0.099999999999999978, 0.10000000000000001,
|
| 4263 |
|
|
0.52359877559829882 },
|
| 4264 |
|
|
{ 0.68860303749364360, -0.099999999999999978, 0.10000000000000001,
|
| 4265 |
|
|
0.69813170079773179 },
|
| 4266 |
|
|
{ 0.85524561882332051, -0.099999999999999978, 0.10000000000000001,
|
| 4267 |
|
|
0.87266462599716477 },
|
| 4268 |
|
|
{ 1.0193708301908337, -0.099999999999999978, 0.10000000000000001,
|
| 4269 |
|
|
1.0471975511965976 },
|
| 4270 |
|
|
{ 1.1813474067123044, -0.099999999999999978, 0.10000000000000001,
|
| 4271 |
|
|
1.2217304763960306 },
|
| 4272 |
|
|
{ 1.3417670770424983, -0.099999999999999978, 0.10000000000000001,
|
| 4273 |
|
|
1.3962634015954636 },
|
| 4274 |
|
|
{ 1.5013711111199950, -0.099999999999999978, 0.10000000000000001,
|
| 4275 |
|
|
1.5707963267948966 },
|
| 4276 |
|
|
};
|
| 4277 |
|
|
|
| 4278 |
|
|
// Test function for k=-0.099999999999999978, nu=0.10000000000000001.
|
| 4279 |
|
|
template <typename Tp>
|
| 4280 |
|
|
void test082()
|
| 4281 |
|
|
{
|
| 4282 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4283 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4284 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4285 |
|
|
unsigned int num_datum = sizeof(data082)
|
| 4286 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4287 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4288 |
|
|
{
|
| 4289 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data082[i].k), Tp(data082[i].nu),
|
| 4290 |
|
|
Tp(data082[i].phi));
|
| 4291 |
|
|
const Tp f0 = data082[i].f0;
|
| 4292 |
|
|
const Tp diff = f - f0;
|
| 4293 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4294 |
|
|
max_abs_diff = std::abs(diff);
|
| 4295 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4296 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4297 |
|
|
{
|
| 4298 |
|
|
const Tp frac = diff / f0;
|
| 4299 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4300 |
|
|
max_abs_frac = std::abs(frac);
|
| 4301 |
|
|
}
|
| 4302 |
|
|
}
|
| 4303 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4304 |
|
|
}
|
| 4305 |
|
|
|
| 4306 |
|
|
// Test data for k=-0.099999999999999978, nu=0.20000000000000001.
|
| 4307 |
|
|
testcase_ellint_3<double> data083[] = {
|
| 4308 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.20000000000000001,
|
| 4309 |
|
|
0.0000000000000000 },
|
| 4310 |
|
|
{ 0.17419068786141345, -0.099999999999999978, 0.20000000000000001,
|
| 4311 |
|
|
0.17453292519943295 },
|
| 4312 |
|
|
{ 0.34640537686230127, -0.099999999999999978, 0.20000000000000001,
|
| 4313 |
|
|
0.34906585039886590 },
|
| 4314 |
|
|
{ 0.51502689171753957, -0.099999999999999978, 0.20000000000000001,
|
| 4315 |
|
|
0.52359877559829882 },
|
| 4316 |
|
|
{ 0.67904147863672726, -0.099999999999999978, 0.20000000000000001,
|
| 4317 |
|
|
0.69813170079773179 },
|
| 4318 |
|
|
{ 0.83811885126105179, -0.099999999999999978, 0.20000000000000001,
|
| 4319 |
|
|
0.87266462599716477 },
|
| 4320 |
|
|
{ 0.99255278555742810, -0.099999999999999978, 0.20000000000000001,
|
| 4321 |
|
|
1.0471975511965976 },
|
| 4322 |
|
|
{ 1.1431260546194930, -0.099999999999999978, 0.20000000000000001,
|
| 4323 |
|
|
1.2217304763960306 },
|
| 4324 |
|
|
{ 1.2909589656532101, -0.099999999999999978, 0.20000000000000001,
|
| 4325 |
|
|
1.3962634015954636 },
|
| 4326 |
|
|
{ 1.4373749386463430, -0.099999999999999978, 0.20000000000000001,
|
| 4327 |
|
|
1.5707963267948966 },
|
| 4328 |
|
|
};
|
| 4329 |
|
|
|
| 4330 |
|
|
// Test function for k=-0.099999999999999978, nu=0.20000000000000001.
|
| 4331 |
|
|
template <typename Tp>
|
| 4332 |
|
|
void test083()
|
| 4333 |
|
|
{
|
| 4334 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4335 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4336 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4337 |
|
|
unsigned int num_datum = sizeof(data083)
|
| 4338 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4339 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4340 |
|
|
{
|
| 4341 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data083[i].k), Tp(data083[i].nu),
|
| 4342 |
|
|
Tp(data083[i].phi));
|
| 4343 |
|
|
const Tp f0 = data083[i].f0;
|
| 4344 |
|
|
const Tp diff = f - f0;
|
| 4345 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4346 |
|
|
max_abs_diff = std::abs(diff);
|
| 4347 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4348 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4349 |
|
|
{
|
| 4350 |
|
|
const Tp frac = diff / f0;
|
| 4351 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4352 |
|
|
max_abs_frac = std::abs(frac);
|
| 4353 |
|
|
}
|
| 4354 |
|
|
}
|
| 4355 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4356 |
|
|
}
|
| 4357 |
|
|
|
| 4358 |
|
|
// Test data for k=-0.099999999999999978, nu=0.29999999999999999.
|
| 4359 |
|
|
testcase_ellint_3<double> data084[] = {
|
| 4360 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.29999999999999999,
|
| 4361 |
|
|
0.0000000000000000 },
|
| 4362 |
|
|
{ 0.17401611261390110, -0.099999999999999978, 0.29999999999999999,
|
| 4363 |
|
|
0.17453292519943295 },
|
| 4364 |
|
|
{ 0.34506869507511767, -0.099999999999999978, 0.29999999999999999,
|
| 4365 |
|
|
0.34906585039886590 },
|
| 4366 |
|
|
{ 0.51081757604259870, -0.099999999999999978, 0.29999999999999999,
|
| 4367 |
|
|
0.52359877559829882 },
|
| 4368 |
|
|
{ 0.66992297597712303, -0.099999999999999978, 0.29999999999999999,
|
| 4369 |
|
|
0.69813170079773179 },
|
| 4370 |
|
|
{ 0.82209722856174228, -0.099999999999999978, 0.29999999999999999,
|
| 4371 |
|
|
0.87266462599716477 },
|
| 4372 |
|
|
{ 0.96792430487669612, -0.099999999999999978, 0.29999999999999999,
|
| 4373 |
|
|
1.0471975511965976 },
|
| 4374 |
|
|
{ 1.1085964108954092, -0.099999999999999978, 0.29999999999999999,
|
| 4375 |
|
|
1.2217304763960306 },
|
| 4376 |
|
|
{ 1.2456748370836999, -0.099999999999999978, 0.29999999999999999,
|
| 4377 |
|
|
1.3962634015954636 },
|
| 4378 |
|
|
{ 1.3809159606704959, -0.099999999999999978, 0.29999999999999999,
|
| 4379 |
|
|
1.5707963267948966 },
|
| 4380 |
|
|
};
|
| 4381 |
|
|
|
| 4382 |
|
|
// Test function for k=-0.099999999999999978, nu=0.29999999999999999.
|
| 4383 |
|
|
template <typename Tp>
|
| 4384 |
|
|
void test084()
|
| 4385 |
|
|
{
|
| 4386 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4387 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4388 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4389 |
|
|
unsigned int num_datum = sizeof(data084)
|
| 4390 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4391 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4392 |
|
|
{
|
| 4393 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data084[i].k), Tp(data084[i].nu),
|
| 4394 |
|
|
Tp(data084[i].phi));
|
| 4395 |
|
|
const Tp f0 = data084[i].f0;
|
| 4396 |
|
|
const Tp diff = f - f0;
|
| 4397 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4398 |
|
|
max_abs_diff = std::abs(diff);
|
| 4399 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4400 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4401 |
|
|
{
|
| 4402 |
|
|
const Tp frac = diff / f0;
|
| 4403 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4404 |
|
|
max_abs_frac = std::abs(frac);
|
| 4405 |
|
|
}
|
| 4406 |
|
|
}
|
| 4407 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4408 |
|
|
}
|
| 4409 |
|
|
|
| 4410 |
|
|
// Test data for k=-0.099999999999999978, nu=0.40000000000000002.
|
| 4411 |
|
|
testcase_ellint_3<double> data085[] = {
|
| 4412 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.40000000000000002,
|
| 4413 |
|
|
0.0000000000000000 },
|
| 4414 |
|
|
{ 0.17384216369897937, -0.099999999999999978, 0.40000000000000002,
|
| 4415 |
|
|
0.17453292519943295 },
|
| 4416 |
|
|
{ 0.34375018311376782, -0.099999999999999978, 0.40000000000000002,
|
| 4417 |
|
|
0.34906585039886590 },
|
| 4418 |
|
|
{ 0.50672650758380455, -0.099999999999999978, 0.40000000000000002,
|
| 4419 |
|
|
0.52359877559829882 },
|
| 4420 |
|
|
{ 0.66121264213337616, -0.099999999999999978, 0.40000000000000002,
|
| 4421 |
|
|
0.69813170079773179 },
|
| 4422 |
|
|
{ 0.80706202005774441, -0.099999999999999978, 0.40000000000000002,
|
| 4423 |
|
|
0.87266462599716477 },
|
| 4424 |
|
|
{ 0.94519376138245892, -0.099999999999999978, 0.40000000000000002,
|
| 4425 |
|
|
1.0471975511965976 },
|
| 4426 |
|
|
{ 1.0771880300759584, -0.099999999999999978, 0.40000000000000002,
|
| 4427 |
|
|
1.2217304763960306 },
|
| 4428 |
|
|
{ 1.2049711557188272, -0.099999999999999978, 0.40000000000000002,
|
| 4429 |
|
|
1.3962634015954636 },
|
| 4430 |
|
|
{ 1.3306223265207477, -0.099999999999999978, 0.40000000000000002,
|
| 4431 |
|
|
1.5707963267948966 },
|
| 4432 |
|
|
};
|
| 4433 |
|
|
|
| 4434 |
|
|
// Test function for k=-0.099999999999999978, nu=0.40000000000000002.
|
| 4435 |
|
|
template <typename Tp>
|
| 4436 |
|
|
void test085()
|
| 4437 |
|
|
{
|
| 4438 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4439 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4440 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4441 |
|
|
unsigned int num_datum = sizeof(data085)
|
| 4442 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4443 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4444 |
|
|
{
|
| 4445 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data085[i].k), Tp(data085[i].nu),
|
| 4446 |
|
|
Tp(data085[i].phi));
|
| 4447 |
|
|
const Tp f0 = data085[i].f0;
|
| 4448 |
|
|
const Tp diff = f - f0;
|
| 4449 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4450 |
|
|
max_abs_diff = std::abs(diff);
|
| 4451 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4452 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4453 |
|
|
{
|
| 4454 |
|
|
const Tp frac = diff / f0;
|
| 4455 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4456 |
|
|
max_abs_frac = std::abs(frac);
|
| 4457 |
|
|
}
|
| 4458 |
|
|
}
|
| 4459 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4460 |
|
|
}
|
| 4461 |
|
|
|
| 4462 |
|
|
// Test data for k=-0.099999999999999978, nu=0.50000000000000000.
|
| 4463 |
|
|
testcase_ellint_3<double> data086[] = {
|
| 4464 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.50000000000000000,
|
| 4465 |
|
|
0.0000000000000000 },
|
| 4466 |
|
|
{ 0.17366883711936554, -0.099999999999999978, 0.50000000000000000,
|
| 4467 |
|
|
0.17453292519943295 },
|
| 4468 |
|
|
{ 0.34244940634881876, -0.099999999999999978, 0.50000000000000000,
|
| 4469 |
|
|
0.34906585039886590 },
|
| 4470 |
|
|
{ 0.50274793281634378, -0.099999999999999978, 0.50000000000000000,
|
| 4471 |
|
|
0.52359877559829882 },
|
| 4472 |
|
|
{ 0.65287941633275093, -0.099999999999999978, 0.50000000000000000,
|
| 4473 |
|
|
0.69813170079773179 },
|
| 4474 |
|
|
{ 0.79291198790315398, -0.099999999999999978, 0.50000000000000000,
|
| 4475 |
|
|
0.87266462599716477 },
|
| 4476 |
|
|
{ 0.92412201537880345, -0.099999999999999978, 0.50000000000000000,
|
| 4477 |
|
|
1.0471975511965976 },
|
| 4478 |
|
|
{ 1.0484480076799370, -0.099999999999999978, 0.50000000000000000,
|
| 4479 |
|
|
1.2217304763960306 },
|
| 4480 |
|
|
{ 1.1681168130475206, -0.099999999999999978, 0.50000000000000000,
|
| 4481 |
|
|
1.3962634015954636 },
|
| 4482 |
|
|
{ 1.2854480708580160, -0.099999999999999978, 0.50000000000000000,
|
| 4483 |
|
|
1.5707963267948966 },
|
| 4484 |
|
|
};
|
| 4485 |
|
|
|
| 4486 |
|
|
// Test function for k=-0.099999999999999978, nu=0.50000000000000000.
|
| 4487 |
|
|
template <typename Tp>
|
| 4488 |
|
|
void test086()
|
| 4489 |
|
|
{
|
| 4490 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4491 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4492 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4493 |
|
|
unsigned int num_datum = sizeof(data086)
|
| 4494 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4495 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4496 |
|
|
{
|
| 4497 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data086[i].k), Tp(data086[i].nu),
|
| 4498 |
|
|
Tp(data086[i].phi));
|
| 4499 |
|
|
const Tp f0 = data086[i].f0;
|
| 4500 |
|
|
const Tp diff = f - f0;
|
| 4501 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4502 |
|
|
max_abs_diff = std::abs(diff);
|
| 4503 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4504 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4505 |
|
|
{
|
| 4506 |
|
|
const Tp frac = diff / f0;
|
| 4507 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4508 |
|
|
max_abs_frac = std::abs(frac);
|
| 4509 |
|
|
}
|
| 4510 |
|
|
}
|
| 4511 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4512 |
|
|
}
|
| 4513 |
|
|
|
| 4514 |
|
|
// Test data for k=-0.099999999999999978, nu=0.59999999999999998.
|
| 4515 |
|
|
testcase_ellint_3<double> data087[] = {
|
| 4516 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.59999999999999998,
|
| 4517 |
|
|
0.0000000000000000 },
|
| 4518 |
|
|
{ 0.17349612891469018, -0.099999999999999978, 0.59999999999999998,
|
| 4519 |
|
|
0.17453292519943295 },
|
| 4520 |
|
|
{ 0.34116594505539438, -0.099999999999999978, 0.59999999999999998,
|
| 4521 |
|
|
0.34906585039886590 },
|
| 4522 |
|
|
{ 0.49887649430466685, -0.099999999999999978, 0.59999999999999998,
|
| 4523 |
|
|
0.52359877559829882 },
|
| 4524 |
|
|
{ 0.64489553282165157, -0.099999999999999978, 0.59999999999999998,
|
| 4525 |
|
|
0.69813170079773179 },
|
| 4526 |
|
|
{ 0.77956016553782437, -0.099999999999999978, 0.59999999999999998,
|
| 4527 |
|
|
0.87266462599716477 },
|
| 4528 |
|
|
{ 0.90451074530096309, -0.099999999999999978, 0.59999999999999998,
|
| 4529 |
|
|
1.0471975511965976 },
|
| 4530 |
|
|
{ 1.0220113666961632, -0.099999999999999978, 0.59999999999999998,
|
| 4531 |
|
|
1.2217304763960306 },
|
| 4532 |
|
|
{ 1.1345351441065563, -0.099999999999999978, 0.59999999999999998,
|
| 4533 |
|
|
1.3962634015954636 },
|
| 4534 |
|
|
{ 1.2445798942989255, -0.099999999999999978, 0.59999999999999998,
|
| 4535 |
|
|
1.5707963267948966 },
|
| 4536 |
|
|
};
|
| 4537 |
|
|
|
| 4538 |
|
|
// Test function for k=-0.099999999999999978, nu=0.59999999999999998.
|
| 4539 |
|
|
template <typename Tp>
|
| 4540 |
|
|
void test087()
|
| 4541 |
|
|
{
|
| 4542 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4543 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4544 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4545 |
|
|
unsigned int num_datum = sizeof(data087)
|
| 4546 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4547 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4548 |
|
|
{
|
| 4549 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data087[i].k), Tp(data087[i].nu),
|
| 4550 |
|
|
Tp(data087[i].phi));
|
| 4551 |
|
|
const Tp f0 = data087[i].f0;
|
| 4552 |
|
|
const Tp diff = f - f0;
|
| 4553 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4554 |
|
|
max_abs_diff = std::abs(diff);
|
| 4555 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4556 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4557 |
|
|
{
|
| 4558 |
|
|
const Tp frac = diff / f0;
|
| 4559 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4560 |
|
|
max_abs_frac = std::abs(frac);
|
| 4561 |
|
|
}
|
| 4562 |
|
|
}
|
| 4563 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4564 |
|
|
}
|
| 4565 |
|
|
|
| 4566 |
|
|
// Test data for k=-0.099999999999999978, nu=0.69999999999999996.
|
| 4567 |
|
|
testcase_ellint_3<double> data088[] = {
|
| 4568 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.69999999999999996,
|
| 4569 |
|
|
0.0000000000000000 },
|
| 4570 |
|
|
{ 0.17332403516105052, -0.099999999999999978, 0.69999999999999996,
|
| 4571 |
|
|
0.17453292519943295 },
|
| 4572 |
|
|
{ 0.33989939374896877, -0.099999999999999978, 0.69999999999999996,
|
| 4573 |
|
|
0.34906585039886590 },
|
| 4574 |
|
|
{ 0.49510719568614081, -0.099999999999999978, 0.69999999999999996,
|
| 4575 |
|
|
0.52359877559829882 },
|
| 4576 |
|
|
{ 0.63723607776354974, -0.099999999999999978, 0.69999999999999996,
|
| 4577 |
|
|
0.69813170079773179 },
|
| 4578 |
|
|
{ 0.76693133887935327, -0.099999999999999978, 0.69999999999999996,
|
| 4579 |
|
|
0.87266462599716477 },
|
| 4580 |
|
|
{ 0.88619382078823827, -0.099999999999999978, 0.69999999999999996,
|
| 4581 |
|
|
1.0471975511965976 },
|
| 4582 |
|
|
{ 0.99758012018676490, -0.099999999999999978, 0.69999999999999996,
|
| 4583 |
|
|
1.2217304763960306 },
|
| 4584 |
|
|
{ 1.1037642270814410, -0.099999999999999978, 0.69999999999999996,
|
| 4585 |
|
|
1.3962634015954636 },
|
| 4586 |
|
|
{ 1.2073745911083187, -0.099999999999999978, 0.69999999999999996,
|
| 4587 |
|
|
1.5707963267948966 },
|
| 4588 |
|
|
};
|
| 4589 |
|
|
|
| 4590 |
|
|
// Test function for k=-0.099999999999999978, nu=0.69999999999999996.
|
| 4591 |
|
|
template <typename Tp>
|
| 4592 |
|
|
void test088()
|
| 4593 |
|
|
{
|
| 4594 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4595 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4596 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4597 |
|
|
unsigned int num_datum = sizeof(data088)
|
| 4598 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4599 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4600 |
|
|
{
|
| 4601 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data088[i].k), Tp(data088[i].nu),
|
| 4602 |
|
|
Tp(data088[i].phi));
|
| 4603 |
|
|
const Tp f0 = data088[i].f0;
|
| 4604 |
|
|
const Tp diff = f - f0;
|
| 4605 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4606 |
|
|
max_abs_diff = std::abs(diff);
|
| 4607 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4608 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4609 |
|
|
{
|
| 4610 |
|
|
const Tp frac = diff / f0;
|
| 4611 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4612 |
|
|
max_abs_frac = std::abs(frac);
|
| 4613 |
|
|
}
|
| 4614 |
|
|
}
|
| 4615 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4616 |
|
|
}
|
| 4617 |
|
|
|
| 4618 |
|
|
// Test data for k=-0.099999999999999978, nu=0.80000000000000004.
|
| 4619 |
|
|
testcase_ellint_3<double> data089[] = {
|
| 4620 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.80000000000000004,
|
| 4621 |
|
|
0.0000000000000000 },
|
| 4622 |
|
|
{ 0.17315255197057020, -0.099999999999999978, 0.80000000000000004,
|
| 4623 |
|
|
0.17453292519943295 },
|
| 4624 |
|
|
{ 0.33864936055747985, -0.099999999999999978, 0.80000000000000004,
|
| 4625 |
|
|
0.34906585039886590 },
|
| 4626 |
|
|
{ 0.49143537041117619, -0.099999999999999978, 0.80000000000000004,
|
| 4627 |
|
|
0.52359877559829882 },
|
| 4628 |
|
|
{ 0.62987861760047492, -0.099999999999999978, 0.80000000000000004,
|
| 4629 |
|
|
0.69813170079773179 },
|
| 4630 |
|
|
{ 0.75496005490917517, -0.099999999999999978, 0.80000000000000004,
|
| 4631 |
|
|
0.87266462599716477 },
|
| 4632 |
|
|
{ 0.86903081862701903, -0.099999999999999978, 0.80000000000000004,
|
| 4633 |
|
|
1.0471975511965976 },
|
| 4634 |
|
|
{ 0.97490814820725591, -0.099999999999999978, 0.80000000000000004,
|
| 4635 |
|
|
1.2217304763960306 },
|
| 4636 |
|
|
{ 1.0754290107171083, -0.099999999999999978, 0.80000000000000004,
|
| 4637 |
|
|
1.3962634015954636 },
|
| 4638 |
|
|
{ 1.1733158866987732, -0.099999999999999978, 0.80000000000000004,
|
| 4639 |
|
|
1.5707963267948966 },
|
| 4640 |
|
|
};
|
| 4641 |
|
|
|
| 4642 |
|
|
// Test function for k=-0.099999999999999978, nu=0.80000000000000004.
|
| 4643 |
|
|
template <typename Tp>
|
| 4644 |
|
|
void test089()
|
| 4645 |
|
|
{
|
| 4646 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4647 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4648 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4649 |
|
|
unsigned int num_datum = sizeof(data089)
|
| 4650 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4651 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4652 |
|
|
{
|
| 4653 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data089[i].k), Tp(data089[i].nu),
|
| 4654 |
|
|
Tp(data089[i].phi));
|
| 4655 |
|
|
const Tp f0 = data089[i].f0;
|
| 4656 |
|
|
const Tp diff = f - f0;
|
| 4657 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4658 |
|
|
max_abs_diff = std::abs(diff);
|
| 4659 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4660 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4661 |
|
|
{
|
| 4662 |
|
|
const Tp frac = diff / f0;
|
| 4663 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4664 |
|
|
max_abs_frac = std::abs(frac);
|
| 4665 |
|
|
}
|
| 4666 |
|
|
}
|
| 4667 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4668 |
|
|
}
|
| 4669 |
|
|
|
| 4670 |
|
|
// Test data for k=-0.099999999999999978, nu=0.90000000000000002.
|
| 4671 |
|
|
testcase_ellint_3<double> data090[] = {
|
| 4672 |
|
|
{ -0.0000000000000000, -0.099999999999999978, 0.90000000000000002,
|
| 4673 |
|
|
0.0000000000000000 },
|
| 4674 |
|
|
{ 0.17298167549096569, -0.099999999999999978, 0.90000000000000002,
|
| 4675 |
|
|
0.17453292519943295 },
|
| 4676 |
|
|
{ 0.33741546662741584, -0.099999999999999978, 0.90000000000000002,
|
| 4677 |
|
|
0.34906585039886590 },
|
| 4678 |
|
|
{ 0.48785665376856879, -0.099999999999999978, 0.90000000000000002,
|
| 4679 |
|
|
0.52359877559829882 },
|
| 4680 |
|
|
{ 0.62280288554518959, -0.099999999999999978, 0.90000000000000002,
|
| 4681 |
|
|
0.69813170079773179 },
|
| 4682 |
|
|
{ 0.74358903115455199, -0.099999999999999978, 0.90000000000000002,
|
| 4683 |
|
|
0.87266462599716477 },
|
| 4684 |
|
|
{ 0.85290207679298358, -0.099999999999999978, 0.90000000000000002,
|
| 4685 |
|
|
1.0471975511965976 },
|
| 4686 |
|
|
{ 0.95379006645397379, -0.099999999999999978, 0.90000000000000002,
|
| 4687 |
|
|
1.2217304763960306 },
|
| 4688 |
|
|
{ 1.0492213119872327, -0.099999999999999978, 0.90000000000000002,
|
| 4689 |
|
|
1.3962634015954636 },
|
| 4690 |
|
|
{ 1.1419839485283374, -0.099999999999999978, 0.90000000000000002,
|
| 4691 |
|
|
1.5707963267948966 },
|
| 4692 |
|
|
};
|
| 4693 |
|
|
|
| 4694 |
|
|
// Test function for k=-0.099999999999999978, nu=0.90000000000000002.
|
| 4695 |
|
|
template <typename Tp>
|
| 4696 |
|
|
void test090()
|
| 4697 |
|
|
{
|
| 4698 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4699 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4700 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4701 |
|
|
unsigned int num_datum = sizeof(data090)
|
| 4702 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4703 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4704 |
|
|
{
|
| 4705 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data090[i].k), Tp(data090[i].nu),
|
| 4706 |
|
|
Tp(data090[i].phi));
|
| 4707 |
|
|
const Tp f0 = data090[i].f0;
|
| 4708 |
|
|
const Tp diff = f - f0;
|
| 4709 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4710 |
|
|
max_abs_diff = std::abs(diff);
|
| 4711 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4712 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4713 |
|
|
{
|
| 4714 |
|
|
const Tp frac = diff / f0;
|
| 4715 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4716 |
|
|
max_abs_frac = std::abs(frac);
|
| 4717 |
|
|
}
|
| 4718 |
|
|
}
|
| 4719 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4720 |
|
|
}
|
| 4721 |
|
|
|
| 4722 |
|
|
// Test data for k=0.0000000000000000, nu=0.0000000000000000.
|
| 4723 |
|
|
testcase_ellint_3<double> data091[] = {
|
| 4724 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
|
| 4725 |
|
|
0.0000000000000000 },
|
| 4726 |
|
|
{ 0.17453292519943295, 0.0000000000000000, 0.0000000000000000,
|
| 4727 |
|
|
0.17453292519943295 },
|
| 4728 |
|
|
{ 0.34906585039886584, 0.0000000000000000, 0.0000000000000000,
|
| 4729 |
|
|
0.34906585039886590 },
|
| 4730 |
|
|
{ 0.52359877559829882, 0.0000000000000000, 0.0000000000000000,
|
| 4731 |
|
|
0.52359877559829882 },
|
| 4732 |
|
|
{ 0.69813170079773179, 0.0000000000000000, 0.0000000000000000,
|
| 4733 |
|
|
0.69813170079773179 },
|
| 4734 |
|
|
{ 0.87266462599716477, 0.0000000000000000, 0.0000000000000000,
|
| 4735 |
|
|
0.87266462599716477 },
|
| 4736 |
|
|
{ 1.0471975511965976, 0.0000000000000000, 0.0000000000000000,
|
| 4737 |
|
|
1.0471975511965976 },
|
| 4738 |
|
|
{ 1.2217304763960304, 0.0000000000000000, 0.0000000000000000,
|
| 4739 |
|
|
1.2217304763960306 },
|
| 4740 |
|
|
{ 1.3962634015954631, 0.0000000000000000, 0.0000000000000000,
|
| 4741 |
|
|
1.3962634015954636 },
|
| 4742 |
|
|
{ 1.5707963267948966, 0.0000000000000000, 0.0000000000000000,
|
| 4743 |
|
|
1.5707963267948966 },
|
| 4744 |
|
|
};
|
| 4745 |
|
|
|
| 4746 |
|
|
// Test function for k=0.0000000000000000, nu=0.0000000000000000.
|
| 4747 |
|
|
template <typename Tp>
|
| 4748 |
|
|
void test091()
|
| 4749 |
|
|
{
|
| 4750 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4751 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4752 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4753 |
|
|
unsigned int num_datum = sizeof(data091)
|
| 4754 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4755 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4756 |
|
|
{
|
| 4757 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data091[i].k), Tp(data091[i].nu),
|
| 4758 |
|
|
Tp(data091[i].phi));
|
| 4759 |
|
|
const Tp f0 = data091[i].f0;
|
| 4760 |
|
|
const Tp diff = f - f0;
|
| 4761 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4762 |
|
|
max_abs_diff = std::abs(diff);
|
| 4763 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4764 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4765 |
|
|
{
|
| 4766 |
|
|
const Tp frac = diff / f0;
|
| 4767 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4768 |
|
|
max_abs_frac = std::abs(frac);
|
| 4769 |
|
|
}
|
| 4770 |
|
|
}
|
| 4771 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4772 |
|
|
}
|
| 4773 |
|
|
|
| 4774 |
|
|
// Test data for k=0.0000000000000000, nu=0.10000000000000001.
|
| 4775 |
|
|
testcase_ellint_3<double> data092[] = {
|
| 4776 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.10000000000000001,
|
| 4777 |
|
|
0.0000000000000000 },
|
| 4778 |
|
|
{ 0.17435710107516608, 0.0000000000000000, 0.10000000000000001,
|
| 4779 |
|
|
0.17453292519943295 },
|
| 4780 |
|
|
{ 0.34769194715329604, 0.0000000000000000, 0.10000000000000001,
|
| 4781 |
|
|
0.34906585039886590 },
|
| 4782 |
|
|
{ 0.51913731575866118, 0.0000000000000000, 0.10000000000000001,
|
| 4783 |
|
|
0.52359877559829882 },
|
| 4784 |
|
|
{ 0.68810051897078461, 0.0000000000000000, 0.10000000000000001,
|
| 4785 |
|
|
0.69813170079773179 },
|
| 4786 |
|
|
{ 0.85432615661706823, 0.0000000000000000, 0.10000000000000001,
|
| 4787 |
|
|
0.87266462599716477 },
|
| 4788 |
|
|
{ 1.0179006647340796, 0.0000000000000000, 0.10000000000000001,
|
| 4789 |
|
|
1.0471975511965976 },
|
| 4790 |
|
|
{ 1.1792120640746322, 0.0000000000000000, 0.10000000000000001,
|
| 4791 |
|
|
1.2217304763960306 },
|
| 4792 |
|
|
{ 1.3388834245070498, 0.0000000000000000, 0.10000000000000001,
|
| 4793 |
|
|
1.3962634015954636 },
|
| 4794 |
|
|
{ 1.4976955329233277, 0.0000000000000000, 0.10000000000000001,
|
| 4795 |
|
|
1.5707963267948966 },
|
| 4796 |
|
|
};
|
| 4797 |
|
|
|
| 4798 |
|
|
// Test function for k=0.0000000000000000, nu=0.10000000000000001.
|
| 4799 |
|
|
template <typename Tp>
|
| 4800 |
|
|
void test092()
|
| 4801 |
|
|
{
|
| 4802 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4803 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4804 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4805 |
|
|
unsigned int num_datum = sizeof(data092)
|
| 4806 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4807 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4808 |
|
|
{
|
| 4809 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data092[i].k), Tp(data092[i].nu),
|
| 4810 |
|
|
Tp(data092[i].phi));
|
| 4811 |
|
|
const Tp f0 = data092[i].f0;
|
| 4812 |
|
|
const Tp diff = f - f0;
|
| 4813 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4814 |
|
|
max_abs_diff = std::abs(diff);
|
| 4815 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4816 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4817 |
|
|
{
|
| 4818 |
|
|
const Tp frac = diff / f0;
|
| 4819 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4820 |
|
|
max_abs_frac = std::abs(frac);
|
| 4821 |
|
|
}
|
| 4822 |
|
|
}
|
| 4823 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4824 |
|
|
}
|
| 4825 |
|
|
|
| 4826 |
|
|
// Test data for k=0.0000000000000000, nu=0.20000000000000001.
|
| 4827 |
|
|
testcase_ellint_3<double> data093[] = {
|
| 4828 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.20000000000000001,
|
| 4829 |
|
|
0.0000000000000000 },
|
| 4830 |
|
|
{ 0.17418191132226077, 0.0000000000000000, 0.20000000000000001,
|
| 4831 |
|
|
0.17453292519943295 },
|
| 4832 |
|
|
{ 0.34633712256943405, 0.0000000000000000, 0.20000000000000001,
|
| 4833 |
|
|
0.34906585039886590 },
|
| 4834 |
|
|
{ 0.51480684302043711, 0.0000000000000000, 0.20000000000000001,
|
| 4835 |
|
|
0.52359877559829882 },
|
| 4836 |
|
|
{ 0.67855102942481949, 0.0000000000000000, 0.20000000000000001,
|
| 4837 |
|
|
0.69813170079773179 },
|
| 4838 |
|
|
{ 0.83723056090326253, 0.0000000000000000, 0.20000000000000001,
|
| 4839 |
|
|
0.87266462599716477 },
|
| 4840 |
|
|
{ 0.99114645269578183, 0.0000000000000000, 0.20000000000000001,
|
| 4841 |
|
|
1.0471975511965976 },
|
| 4842 |
|
|
{ 1.1411014627915537, 0.0000000000000000, 0.20000000000000001,
|
| 4843 |
|
|
1.2217304763960306 },
|
| 4844 |
|
|
{ 1.2882448138013969, 0.0000000000000000, 0.20000000000000001,
|
| 4845 |
|
|
1.3962634015954636 },
|
| 4846 |
|
|
{ 1.4339343023863691, 0.0000000000000000, 0.20000000000000001,
|
| 4847 |
|
|
1.5707963267948966 },
|
| 4848 |
|
|
};
|
| 4849 |
|
|
|
| 4850 |
|
|
// Test function for k=0.0000000000000000, nu=0.20000000000000001.
|
| 4851 |
|
|
template <typename Tp>
|
| 4852 |
|
|
void test093()
|
| 4853 |
|
|
{
|
| 4854 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4855 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4856 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4857 |
|
|
unsigned int num_datum = sizeof(data093)
|
| 4858 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4859 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4860 |
|
|
{
|
| 4861 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data093[i].k), Tp(data093[i].nu),
|
| 4862 |
|
|
Tp(data093[i].phi));
|
| 4863 |
|
|
const Tp f0 = data093[i].f0;
|
| 4864 |
|
|
const Tp diff = f - f0;
|
| 4865 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4866 |
|
|
max_abs_diff = std::abs(diff);
|
| 4867 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4868 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4869 |
|
|
{
|
| 4870 |
|
|
const Tp frac = diff / f0;
|
| 4871 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4872 |
|
|
max_abs_frac = std::abs(frac);
|
| 4873 |
|
|
}
|
| 4874 |
|
|
}
|
| 4875 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4876 |
|
|
}
|
| 4877 |
|
|
|
| 4878 |
|
|
// Test data for k=0.0000000000000000, nu=0.29999999999999999.
|
| 4879 |
|
|
testcase_ellint_3<double> data094[] = {
|
| 4880 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.29999999999999999,
|
| 4881 |
|
|
0.0000000000000000 },
|
| 4882 |
|
|
{ 0.17400735186871727, 0.0000000000000000, 0.29999999999999999,
|
| 4883 |
|
|
0.17453292519943295 },
|
| 4884 |
|
|
{ 0.34500091027020219, 0.0000000000000000, 0.29999999999999999,
|
| 4885 |
|
|
0.34906585039886590 },
|
| 4886 |
|
|
{ 0.51060069523901541, 0.0000000000000000, 0.29999999999999999,
|
| 4887 |
|
|
0.52359877559829882 },
|
| 4888 |
|
|
{ 0.66944393961375459, 0.0000000000000000, 0.29999999999999999,
|
| 4889 |
|
|
0.69813170079773179 },
|
| 4890 |
|
|
{ 0.82123776744538157, 0.0000000000000000, 0.29999999999999999,
|
| 4891 |
|
|
0.87266462599716477 },
|
| 4892 |
|
|
{ 0.96657579245516523, 0.0000000000000000, 0.29999999999999999,
|
| 4893 |
|
|
1.0471975511965976 },
|
| 4894 |
|
|
{ 1.1066703663542414, 0.0000000000000000, 0.29999999999999999,
|
| 4895 |
|
|
1.2217304763960306 },
|
| 4896 |
|
|
{ 1.2431094251944901, 0.0000000000000000, 0.29999999999999999,
|
| 4897 |
|
|
1.3962634015954636 },
|
| 4898 |
|
|
{ 1.3776795151134889, 0.0000000000000000, 0.29999999999999999,
|
| 4899 |
|
|
1.5707963267948966 },
|
| 4900 |
|
|
};
|
| 4901 |
|
|
|
| 4902 |
|
|
// Test function for k=0.0000000000000000, nu=0.29999999999999999.
|
| 4903 |
|
|
template <typename Tp>
|
| 4904 |
|
|
void test094()
|
| 4905 |
|
|
{
|
| 4906 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4907 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4908 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4909 |
|
|
unsigned int num_datum = sizeof(data094)
|
| 4910 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4911 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4912 |
|
|
{
|
| 4913 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data094[i].k), Tp(data094[i].nu),
|
| 4914 |
|
|
Tp(data094[i].phi));
|
| 4915 |
|
|
const Tp f0 = data094[i].f0;
|
| 4916 |
|
|
const Tp diff = f - f0;
|
| 4917 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4918 |
|
|
max_abs_diff = std::abs(diff);
|
| 4919 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4920 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4921 |
|
|
{
|
| 4922 |
|
|
const Tp frac = diff / f0;
|
| 4923 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4924 |
|
|
max_abs_frac = std::abs(frac);
|
| 4925 |
|
|
}
|
| 4926 |
|
|
}
|
| 4927 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4928 |
|
|
}
|
| 4929 |
|
|
|
| 4930 |
|
|
// Test data for k=0.0000000000000000, nu=0.40000000000000002.
|
| 4931 |
|
|
testcase_ellint_3<double> data095[] = {
|
| 4932 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.40000000000000002,
|
| 4933 |
|
|
0.0000000000000000 },
|
| 4934 |
|
|
{ 0.17383341868035865, 0.0000000000000000, 0.40000000000000002,
|
| 4935 |
|
|
0.17453292519943295 },
|
| 4936 |
|
|
{ 0.34368286022299821, 0.0000000000000000, 0.40000000000000002,
|
| 4937 |
|
|
0.34906585039886590 },
|
| 4938 |
|
|
{ 0.50651268947499406, 0.0000000000000000, 0.40000000000000002,
|
| 4939 |
|
|
0.52359877559829882 },
|
| 4940 |
|
|
{ 0.66074441806097550, 0.0000000000000000, 0.40000000000000002,
|
| 4941 |
|
|
0.69813170079773179 },
|
| 4942 |
|
|
{ 0.80622931670113485, 0.0000000000000000, 0.40000000000000002,
|
| 4943 |
|
|
0.87266462599716477 },
|
| 4944 |
|
|
{ 0.94389791565435233, 0.0000000000000000, 0.40000000000000002,
|
| 4945 |
|
|
1.0471975511965976 },
|
| 4946 |
|
|
{ 1.0753503387899728, 0.0000000000000000, 0.40000000000000002,
|
| 4947 |
|
|
1.2217304763960306 },
|
| 4948 |
|
|
{ 1.2025374759127518, 0.0000000000000000, 0.40000000000000002,
|
| 4949 |
|
|
1.3962634015954636 },
|
| 4950 |
|
|
{ 1.3275651989026322, 0.0000000000000000, 0.40000000000000002,
|
| 4951 |
|
|
1.5707963267948966 },
|
| 4952 |
|
|
};
|
| 4953 |
|
|
|
| 4954 |
|
|
// Test function for k=0.0000000000000000, nu=0.40000000000000002.
|
| 4955 |
|
|
template <typename Tp>
|
| 4956 |
|
|
void test095()
|
| 4957 |
|
|
{
|
| 4958 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 4959 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 4960 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 4961 |
|
|
unsigned int num_datum = sizeof(data095)
|
| 4962 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 4963 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 4964 |
|
|
{
|
| 4965 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data095[i].k), Tp(data095[i].nu),
|
| 4966 |
|
|
Tp(data095[i].phi));
|
| 4967 |
|
|
const Tp f0 = data095[i].f0;
|
| 4968 |
|
|
const Tp diff = f - f0;
|
| 4969 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 4970 |
|
|
max_abs_diff = std::abs(diff);
|
| 4971 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 4972 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 4973 |
|
|
{
|
| 4974 |
|
|
const Tp frac = diff / f0;
|
| 4975 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 4976 |
|
|
max_abs_frac = std::abs(frac);
|
| 4977 |
|
|
}
|
| 4978 |
|
|
}
|
| 4979 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 4980 |
|
|
}
|
| 4981 |
|
|
|
| 4982 |
|
|
// Test data for k=0.0000000000000000, nu=0.50000000000000000.
|
| 4983 |
|
|
testcase_ellint_3<double> data096[] = {
|
| 4984 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.50000000000000000,
|
| 4985 |
|
|
0.0000000000000000 },
|
| 4986 |
|
|
{ 0.17366010776037047, 0.0000000000000000, 0.50000000000000000,
|
| 4987 |
|
|
0.17453292519943295 },
|
| 4988 |
|
|
{ 0.34238253799539309, 0.0000000000000000, 0.50000000000000000,
|
| 4989 |
|
|
0.34906585039886590 },
|
| 4990 |
|
|
{ 0.50253707775976408, 0.0000000000000000, 0.50000000000000000,
|
| 4991 |
|
|
0.52359877559829882 },
|
| 4992 |
|
|
{ 0.65242145347295766, 0.0000000000000000, 0.50000000000000000,
|
| 4993 |
|
|
0.69813170079773179 },
|
| 4994 |
|
|
{ 0.79210420018698058, 0.0000000000000000, 0.50000000000000000,
|
| 4995 |
|
|
0.87266462599716477 },
|
| 4996 |
|
|
{ 0.92287437995632193, 0.0000000000000000, 0.50000000000000000,
|
| 4997 |
|
|
1.0471975511965976 },
|
| 4998 |
|
|
{ 1.0466900550798661, 0.0000000000000000, 0.50000000000000000,
|
| 4999 |
|
|
1.2217304763960306 },
|
| 5000 |
|
|
{ 1.1658007366618623, 0.0000000000000000, 0.50000000000000000,
|
| 5001 |
|
|
1.3962634015954636 },
|
| 5002 |
|
|
{ 1.2825498301618641, 0.0000000000000000, 0.50000000000000000,
|
| 5003 |
|
|
1.5707963267948966 },
|
| 5004 |
|
|
};
|
| 5005 |
|
|
|
| 5006 |
|
|
// Test function for k=0.0000000000000000, nu=0.50000000000000000.
|
| 5007 |
|
|
template <typename Tp>
|
| 5008 |
|
|
void test096()
|
| 5009 |
|
|
{
|
| 5010 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5011 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5012 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5013 |
|
|
unsigned int num_datum = sizeof(data096)
|
| 5014 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5015 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5016 |
|
|
{
|
| 5017 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data096[i].k), Tp(data096[i].nu),
|
| 5018 |
|
|
Tp(data096[i].phi));
|
| 5019 |
|
|
const Tp f0 = data096[i].f0;
|
| 5020 |
|
|
const Tp diff = f - f0;
|
| 5021 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5022 |
|
|
max_abs_diff = std::abs(diff);
|
| 5023 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5024 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5025 |
|
|
{
|
| 5026 |
|
|
const Tp frac = diff / f0;
|
| 5027 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5028 |
|
|
max_abs_frac = std::abs(frac);
|
| 5029 |
|
|
}
|
| 5030 |
|
|
}
|
| 5031 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5032 |
|
|
}
|
| 5033 |
|
|
|
| 5034 |
|
|
// Test data for k=0.0000000000000000, nu=0.59999999999999998.
|
| 5035 |
|
|
testcase_ellint_3<double> data097[] = {
|
| 5036 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.59999999999999998,
|
| 5037 |
|
|
0.0000000000000000 },
|
| 5038 |
|
|
{ 0.17348741514884702, 0.0000000000000000, 0.59999999999999998,
|
| 5039 |
|
|
0.17453292519943295 },
|
| 5040 |
|
|
{ 0.34109952405241289, 0.0000000000000000, 0.59999999999999998,
|
| 5041 |
|
|
0.34906585039886590 },
|
| 5042 |
|
|
{ 0.49866850781226296, 0.0000000000000000, 0.59999999999999998,
|
| 5043 |
|
|
0.52359877559829882 },
|
| 5044 |
|
|
{ 0.64444732407062510, 0.0000000000000000, 0.59999999999999998,
|
| 5045 |
|
|
0.69813170079773179 },
|
| 5046 |
|
|
{ 0.77877564686544720, 0.0000000000000000, 0.59999999999999998,
|
| 5047 |
|
|
0.87266462599716477 },
|
| 5048 |
|
|
{ 0.90330743691883497, 0.0000000000000000, 0.59999999999999998,
|
| 5049 |
|
|
1.0471975511965976 },
|
| 5050 |
|
|
{ 1.0203257987604104, 0.0000000000000000, 0.59999999999999998,
|
| 5051 |
|
|
1.2217304763960306 },
|
| 5052 |
|
|
{ 1.1323247918768631, 0.0000000000000000, 0.59999999999999998,
|
| 5053 |
|
|
1.3962634015954636 },
|
| 5054 |
|
|
{ 1.2418235332245127, 0.0000000000000000, 0.59999999999999998,
|
| 5055 |
|
|
1.5707963267948966 },
|
| 5056 |
|
|
};
|
| 5057 |
|
|
|
| 5058 |
|
|
// Test function for k=0.0000000000000000, nu=0.59999999999999998.
|
| 5059 |
|
|
template <typename Tp>
|
| 5060 |
|
|
void test097()
|
| 5061 |
|
|
{
|
| 5062 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5063 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5064 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5065 |
|
|
unsigned int num_datum = sizeof(data097)
|
| 5066 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5067 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5068 |
|
|
{
|
| 5069 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data097[i].k), Tp(data097[i].nu),
|
| 5070 |
|
|
Tp(data097[i].phi));
|
| 5071 |
|
|
const Tp f0 = data097[i].f0;
|
| 5072 |
|
|
const Tp diff = f - f0;
|
| 5073 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5074 |
|
|
max_abs_diff = std::abs(diff);
|
| 5075 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5076 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5077 |
|
|
{
|
| 5078 |
|
|
const Tp frac = diff / f0;
|
| 5079 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5080 |
|
|
max_abs_frac = std::abs(frac);
|
| 5081 |
|
|
}
|
| 5082 |
|
|
}
|
| 5083 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5084 |
|
|
}
|
| 5085 |
|
|
|
| 5086 |
|
|
// Test data for k=0.0000000000000000, nu=0.69999999999999996.
|
| 5087 |
|
|
testcase_ellint_3<double> data098[] = {
|
| 5088 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.69999999999999996,
|
| 5089 |
|
|
0.0000000000000000 },
|
| 5090 |
|
|
{ 0.17331533692234477, 0.0000000000000000, 0.69999999999999996,
|
| 5091 |
|
|
0.17453292519943295 },
|
| 5092 |
|
|
{ 0.33983341309265941, 0.0000000000000000, 0.69999999999999996,
|
| 5093 |
|
|
0.34906585039886590 },
|
| 5094 |
|
|
{ 0.49490198805931990, 0.0000000000000000, 0.69999999999999996,
|
| 5095 |
|
|
0.52359877559829882 },
|
| 5096 |
|
|
{ 0.63679715525145308, 0.0000000000000000, 0.69999999999999996,
|
| 5097 |
|
|
0.69813170079773179 },
|
| 5098 |
|
|
{ 0.76616861049481944, 0.0000000000000000, 0.69999999999999996,
|
| 5099 |
|
|
0.87266462599716477 },
|
| 5100 |
|
|
{ 0.88503143209004220, 0.0000000000000000, 0.69999999999999996,
|
| 5101 |
|
|
1.0471975511965976 },
|
| 5102 |
|
|
{ 0.99596060249112173, 0.0000000000000000, 0.69999999999999996,
|
| 5103 |
|
|
1.2217304763960306 },
|
| 5104 |
|
|
{ 1.1016495050260424, 0.0000000000000000, 0.69999999999999996,
|
| 5105 |
|
|
1.3962634015954636 },
|
| 5106 |
|
|
{ 1.2047457872617382, 0.0000000000000000, 0.69999999999999996,
|
| 5107 |
|
|
1.5707963267948966 },
|
| 5108 |
|
|
};
|
| 5109 |
|
|
|
| 5110 |
|
|
// Test function for k=0.0000000000000000, nu=0.69999999999999996.
|
| 5111 |
|
|
template <typename Tp>
|
| 5112 |
|
|
void test098()
|
| 5113 |
|
|
{
|
| 5114 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5115 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5116 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5117 |
|
|
unsigned int num_datum = sizeof(data098)
|
| 5118 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5119 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5120 |
|
|
{
|
| 5121 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data098[i].k), Tp(data098[i].nu),
|
| 5122 |
|
|
Tp(data098[i].phi));
|
| 5123 |
|
|
const Tp f0 = data098[i].f0;
|
| 5124 |
|
|
const Tp diff = f - f0;
|
| 5125 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5126 |
|
|
max_abs_diff = std::abs(diff);
|
| 5127 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5128 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5129 |
|
|
{
|
| 5130 |
|
|
const Tp frac = diff / f0;
|
| 5131 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5132 |
|
|
max_abs_frac = std::abs(frac);
|
| 5133 |
|
|
}
|
| 5134 |
|
|
}
|
| 5135 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5136 |
|
|
}
|
| 5137 |
|
|
|
| 5138 |
|
|
// Test data for k=0.0000000000000000, nu=0.80000000000000004.
|
| 5139 |
|
|
testcase_ellint_3<double> data099[] = {
|
| 5140 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.80000000000000004,
|
| 5141 |
|
|
0.0000000000000000 },
|
| 5142 |
|
|
{ 0.17314386919344213, 0.0000000000000000, 0.80000000000000004,
|
| 5143 |
|
|
0.17453292519943295 },
|
| 5144 |
|
|
{ 0.33858381342073240, 0.0000000000000000, 0.80000000000000004,
|
| 5145 |
|
|
0.34906585039886590 },
|
| 5146 |
|
|
{ 0.49123285640844738, 0.0000000000000000, 0.80000000000000004,
|
| 5147 |
|
|
0.52359877559829882 },
|
| 5148 |
|
|
{ 0.62944854858904520, 0.0000000000000000, 0.80000000000000004,
|
| 5149 |
|
|
0.69813170079773179 },
|
| 5150 |
|
|
{ 0.75421778305499343, 0.0000000000000000, 0.80000000000000004,
|
| 5151 |
|
|
0.87266462599716477 },
|
| 5152 |
|
|
{ 0.86790634112156639, 0.0000000000000000, 0.80000000000000004,
|
| 5153 |
|
|
1.0471975511965976 },
|
| 5154 |
|
|
{ 0.97334918087427558, 0.0000000000000000, 0.80000000000000004,
|
| 5155 |
|
|
1.2217304763960306 },
|
| 5156 |
|
|
{ 1.0734012615283985, 0.0000000000000000, 0.80000000000000004,
|
| 5157 |
|
|
1.3962634015954636 },
|
| 5158 |
|
|
{ 1.1708024551734544, 0.0000000000000000, 0.80000000000000004,
|
| 5159 |
|
|
1.5707963267948966 },
|
| 5160 |
|
|
};
|
| 5161 |
|
|
|
| 5162 |
|
|
// Test function for k=0.0000000000000000, nu=0.80000000000000004.
|
| 5163 |
|
|
template <typename Tp>
|
| 5164 |
|
|
void test099()
|
| 5165 |
|
|
{
|
| 5166 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5167 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5168 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5169 |
|
|
unsigned int num_datum = sizeof(data099)
|
| 5170 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5171 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5172 |
|
|
{
|
| 5173 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data099[i].k), Tp(data099[i].nu),
|
| 5174 |
|
|
Tp(data099[i].phi));
|
| 5175 |
|
|
const Tp f0 = data099[i].f0;
|
| 5176 |
|
|
const Tp diff = f - f0;
|
| 5177 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5178 |
|
|
max_abs_diff = std::abs(diff);
|
| 5179 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5180 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5181 |
|
|
{
|
| 5182 |
|
|
const Tp frac = diff / f0;
|
| 5183 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5184 |
|
|
max_abs_frac = std::abs(frac);
|
| 5185 |
|
|
}
|
| 5186 |
|
|
}
|
| 5187 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5188 |
|
|
}
|
| 5189 |
|
|
|
| 5190 |
|
|
// Test data for k=0.0000000000000000, nu=0.90000000000000002.
|
| 5191 |
|
|
testcase_ellint_3<double> data100[] = {
|
| 5192 |
|
|
{ -0.0000000000000000, 0.0000000000000000, 0.90000000000000002,
|
| 5193 |
|
|
0.0000000000000000 },
|
| 5194 |
|
|
{ 0.17297300811030600, 0.0000000000000000, 0.90000000000000002,
|
| 5195 |
|
|
0.17453292519943295 },
|
| 5196 |
|
|
{ 0.33735034635360817, 0.0000000000000000, 0.90000000000000002,
|
| 5197 |
|
|
0.34906585039886590 },
|
| 5198 |
|
|
{ 0.48765675230233141, 0.0000000000000000, 0.90000000000000002,
|
| 5199 |
|
|
0.52359877559829882 },
|
| 5200 |
|
|
{ 0.62238126886123568, 0.0000000000000000, 0.90000000000000002,
|
| 5201 |
|
|
0.69813170079773179 },
|
| 5202 |
|
|
{ 0.74286600807269243, 0.0000000000000000, 0.90000000000000002,
|
| 5203 |
|
|
0.87266462599716477 },
|
| 5204 |
|
|
{ 0.85181283909264971, 0.0000000000000000, 0.90000000000000002,
|
| 5205 |
|
|
1.0471975511965976 },
|
| 5206 |
|
|
{ 0.95228683995371122, 0.0000000000000000, 0.90000000000000002,
|
| 5207 |
|
|
1.2217304763960306 },
|
| 5208 |
|
|
{ 1.0472730487412552, 0.0000000000000000, 0.90000000000000002,
|
| 5209 |
|
|
1.3962634015954636 },
|
| 5210 |
|
|
{ 1.1395754288497419, 0.0000000000000000, 0.90000000000000002,
|
| 5211 |
|
|
1.5707963267948966 },
|
| 5212 |
|
|
};
|
| 5213 |
|
|
|
| 5214 |
|
|
// Test function for k=0.0000000000000000, nu=0.90000000000000002.
|
| 5215 |
|
|
template <typename Tp>
|
| 5216 |
|
|
void test100()
|
| 5217 |
|
|
{
|
| 5218 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5219 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5220 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5221 |
|
|
unsigned int num_datum = sizeof(data100)
|
| 5222 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5223 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5224 |
|
|
{
|
| 5225 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data100[i].k), Tp(data100[i].nu),
|
| 5226 |
|
|
Tp(data100[i].phi));
|
| 5227 |
|
|
const Tp f0 = data100[i].f0;
|
| 5228 |
|
|
const Tp diff = f - f0;
|
| 5229 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5230 |
|
|
max_abs_diff = std::abs(diff);
|
| 5231 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5232 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5233 |
|
|
{
|
| 5234 |
|
|
const Tp frac = diff / f0;
|
| 5235 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5236 |
|
|
max_abs_frac = std::abs(frac);
|
| 5237 |
|
|
}
|
| 5238 |
|
|
}
|
| 5239 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5240 |
|
|
}
|
| 5241 |
|
|
|
| 5242 |
|
|
// Test data for k=0.10000000000000009, nu=0.0000000000000000.
|
| 5243 |
|
|
testcase_ellint_3<double> data101[] = {
|
| 5244 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.0000000000000000,
|
| 5245 |
|
|
0.0000000000000000 },
|
| 5246 |
|
|
{ 0.17454173353063665, 0.10000000000000009, 0.0000000000000000,
|
| 5247 |
|
|
0.17453292519943295 },
|
| 5248 |
|
|
{ 0.34913506721468085, 0.10000000000000009, 0.0000000000000000,
|
| 5249 |
|
|
0.34906585039886590 },
|
| 5250 |
|
|
{ 0.52382550016538953, 0.10000000000000009, 0.0000000000000000,
|
| 5251 |
|
|
0.52359877559829882 },
|
| 5252 |
|
|
{ 0.69864700854177031, 0.10000000000000009, 0.0000000000000000,
|
| 5253 |
|
|
0.69813170079773179 },
|
| 5254 |
|
|
{ 0.87361792586964870, 0.10000000000000009, 0.0000000000000000,
|
| 5255 |
|
|
0.87266462599716477 },
|
| 5256 |
|
|
{ 1.0487386319621685, 0.10000000000000009, 0.0000000000000000,
|
| 5257 |
|
|
1.0471975511965976 },
|
| 5258 |
|
|
{ 1.2239913752078757, 0.10000000000000009, 0.0000000000000000,
|
| 5259 |
|
|
1.2217304763960306 },
|
| 5260 |
|
|
{ 1.3993423113684049, 0.10000000000000009, 0.0000000000000000,
|
| 5261 |
|
|
1.3962634015954636 },
|
| 5262 |
|
|
{ 1.5747455615173562, 0.10000000000000009, 0.0000000000000000,
|
| 5263 |
|
|
1.5707963267948966 },
|
| 5264 |
|
|
};
|
| 5265 |
|
|
|
| 5266 |
|
|
// Test function for k=0.10000000000000009, nu=0.0000000000000000.
|
| 5267 |
|
|
template <typename Tp>
|
| 5268 |
|
|
void test101()
|
| 5269 |
|
|
{
|
| 5270 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5271 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5272 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5273 |
|
|
unsigned int num_datum = sizeof(data101)
|
| 5274 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5275 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5276 |
|
|
{
|
| 5277 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data101[i].k), Tp(data101[i].nu),
|
| 5278 |
|
|
Tp(data101[i].phi));
|
| 5279 |
|
|
const Tp f0 = data101[i].f0;
|
| 5280 |
|
|
const Tp diff = f - f0;
|
| 5281 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5282 |
|
|
max_abs_diff = std::abs(diff);
|
| 5283 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5284 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5285 |
|
|
{
|
| 5286 |
|
|
const Tp frac = diff / f0;
|
| 5287 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5288 |
|
|
max_abs_frac = std::abs(frac);
|
| 5289 |
|
|
}
|
| 5290 |
|
|
}
|
| 5291 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5292 |
|
|
}
|
| 5293 |
|
|
|
| 5294 |
|
|
// Test data for k=0.10000000000000009, nu=0.10000000000000001.
|
| 5295 |
|
|
testcase_ellint_3<double> data102[] = {
|
| 5296 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.10000000000000001,
|
| 5297 |
|
|
0.0000000000000000 },
|
| 5298 |
|
|
{ 0.17436589347616618, 0.10000000000000009, 0.10000000000000001,
|
| 5299 |
|
|
0.17453292519943295 },
|
| 5300 |
|
|
{ 0.34776067871237354, 0.10000000000000009, 0.10000000000000001,
|
| 5301 |
|
|
0.34906585039886590 },
|
| 5302 |
|
|
{ 0.51936064354727807, 0.10000000000000009, 0.10000000000000001,
|
| 5303 |
|
|
0.52359877559829882 },
|
| 5304 |
|
|
{ 0.68860303749364360, 0.10000000000000009, 0.10000000000000001,
|
| 5305 |
|
|
0.69813170079773179 },
|
| 5306 |
|
|
{ 0.85524561882332051, 0.10000000000000009, 0.10000000000000001,
|
| 5307 |
|
|
0.87266462599716477 },
|
| 5308 |
|
|
{ 1.0193708301908337, 0.10000000000000009, 0.10000000000000001,
|
| 5309 |
|
|
1.0471975511965976 },
|
| 5310 |
|
|
{ 1.1813474067123044, 0.10000000000000009, 0.10000000000000001,
|
| 5311 |
|
|
1.2217304763960306 },
|
| 5312 |
|
|
{ 1.3417670770424983, 0.10000000000000009, 0.10000000000000001,
|
| 5313 |
|
|
1.3962634015954636 },
|
| 5314 |
|
|
{ 1.5013711111199950, 0.10000000000000009, 0.10000000000000001,
|
| 5315 |
|
|
1.5707963267948966 },
|
| 5316 |
|
|
};
|
| 5317 |
|
|
|
| 5318 |
|
|
// Test function for k=0.10000000000000009, nu=0.10000000000000001.
|
| 5319 |
|
|
template <typename Tp>
|
| 5320 |
|
|
void test102()
|
| 5321 |
|
|
{
|
| 5322 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5323 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5324 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5325 |
|
|
unsigned int num_datum = sizeof(data102)
|
| 5326 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5327 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5328 |
|
|
{
|
| 5329 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data102[i].k), Tp(data102[i].nu),
|
| 5330 |
|
|
Tp(data102[i].phi));
|
| 5331 |
|
|
const Tp f0 = data102[i].f0;
|
| 5332 |
|
|
const Tp diff = f - f0;
|
| 5333 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5334 |
|
|
max_abs_diff = std::abs(diff);
|
| 5335 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5336 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5337 |
|
|
{
|
| 5338 |
|
|
const Tp frac = diff / f0;
|
| 5339 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5340 |
|
|
max_abs_frac = std::abs(frac);
|
| 5341 |
|
|
}
|
| 5342 |
|
|
}
|
| 5343 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5344 |
|
|
}
|
| 5345 |
|
|
|
| 5346 |
|
|
// Test data for k=0.10000000000000009, nu=0.20000000000000001.
|
| 5347 |
|
|
testcase_ellint_3<double> data103[] = {
|
| 5348 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.20000000000000001,
|
| 5349 |
|
|
0.0000000000000000 },
|
| 5350 |
|
|
{ 0.17419068786141345, 0.10000000000000009, 0.20000000000000001,
|
| 5351 |
|
|
0.17453292519943295 },
|
| 5352 |
|
|
{ 0.34640537686230127, 0.10000000000000009, 0.20000000000000001,
|
| 5353 |
|
|
0.34906585039886590 },
|
| 5354 |
|
|
{ 0.51502689171753957, 0.10000000000000009, 0.20000000000000001,
|
| 5355 |
|
|
0.52359877559829882 },
|
| 5356 |
|
|
{ 0.67904147863672726, 0.10000000000000009, 0.20000000000000001,
|
| 5357 |
|
|
0.69813170079773179 },
|
| 5358 |
|
|
{ 0.83811885126105179, 0.10000000000000009, 0.20000000000000001,
|
| 5359 |
|
|
0.87266462599716477 },
|
| 5360 |
|
|
{ 0.99255278555742810, 0.10000000000000009, 0.20000000000000001,
|
| 5361 |
|
|
1.0471975511965976 },
|
| 5362 |
|
|
{ 1.1431260546194930, 0.10000000000000009, 0.20000000000000001,
|
| 5363 |
|
|
1.2217304763960306 },
|
| 5364 |
|
|
{ 1.2909589656532101, 0.10000000000000009, 0.20000000000000001,
|
| 5365 |
|
|
1.3962634015954636 },
|
| 5366 |
|
|
{ 1.4373749386463430, 0.10000000000000009, 0.20000000000000001,
|
| 5367 |
|
|
1.5707963267948966 },
|
| 5368 |
|
|
};
|
| 5369 |
|
|
|
| 5370 |
|
|
// Test function for k=0.10000000000000009, nu=0.20000000000000001.
|
| 5371 |
|
|
template <typename Tp>
|
| 5372 |
|
|
void test103()
|
| 5373 |
|
|
{
|
| 5374 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5375 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5376 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5377 |
|
|
unsigned int num_datum = sizeof(data103)
|
| 5378 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5379 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5380 |
|
|
{
|
| 5381 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data103[i].k), Tp(data103[i].nu),
|
| 5382 |
|
|
Tp(data103[i].phi));
|
| 5383 |
|
|
const Tp f0 = data103[i].f0;
|
| 5384 |
|
|
const Tp diff = f - f0;
|
| 5385 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5386 |
|
|
max_abs_diff = std::abs(diff);
|
| 5387 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5388 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5389 |
|
|
{
|
| 5390 |
|
|
const Tp frac = diff / f0;
|
| 5391 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5392 |
|
|
max_abs_frac = std::abs(frac);
|
| 5393 |
|
|
}
|
| 5394 |
|
|
}
|
| 5395 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5396 |
|
|
}
|
| 5397 |
|
|
|
| 5398 |
|
|
// Test data for k=0.10000000000000009, nu=0.29999999999999999.
|
| 5399 |
|
|
testcase_ellint_3<double> data104[] = {
|
| 5400 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.29999999999999999,
|
| 5401 |
|
|
0.0000000000000000 },
|
| 5402 |
|
|
{ 0.17401611261390110, 0.10000000000000009, 0.29999999999999999,
|
| 5403 |
|
|
0.17453292519943295 },
|
| 5404 |
|
|
{ 0.34506869507511767, 0.10000000000000009, 0.29999999999999999,
|
| 5405 |
|
|
0.34906585039886590 },
|
| 5406 |
|
|
{ 0.51081757604259870, 0.10000000000000009, 0.29999999999999999,
|
| 5407 |
|
|
0.52359877559829882 },
|
| 5408 |
|
|
{ 0.66992297597712303, 0.10000000000000009, 0.29999999999999999,
|
| 5409 |
|
|
0.69813170079773179 },
|
| 5410 |
|
|
{ 0.82209722856174228, 0.10000000000000009, 0.29999999999999999,
|
| 5411 |
|
|
0.87266462599716477 },
|
| 5412 |
|
|
{ 0.96792430487669612, 0.10000000000000009, 0.29999999999999999,
|
| 5413 |
|
|
1.0471975511965976 },
|
| 5414 |
|
|
{ 1.1085964108954092, 0.10000000000000009, 0.29999999999999999,
|
| 5415 |
|
|
1.2217304763960306 },
|
| 5416 |
|
|
{ 1.2456748370836999, 0.10000000000000009, 0.29999999999999999,
|
| 5417 |
|
|
1.3962634015954636 },
|
| 5418 |
|
|
{ 1.3809159606704959, 0.10000000000000009, 0.29999999999999999,
|
| 5419 |
|
|
1.5707963267948966 },
|
| 5420 |
|
|
};
|
| 5421 |
|
|
|
| 5422 |
|
|
// Test function for k=0.10000000000000009, nu=0.29999999999999999.
|
| 5423 |
|
|
template <typename Tp>
|
| 5424 |
|
|
void test104()
|
| 5425 |
|
|
{
|
| 5426 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5427 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5428 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5429 |
|
|
unsigned int num_datum = sizeof(data104)
|
| 5430 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5431 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5432 |
|
|
{
|
| 5433 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data104[i].k), Tp(data104[i].nu),
|
| 5434 |
|
|
Tp(data104[i].phi));
|
| 5435 |
|
|
const Tp f0 = data104[i].f0;
|
| 5436 |
|
|
const Tp diff = f - f0;
|
| 5437 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5438 |
|
|
max_abs_diff = std::abs(diff);
|
| 5439 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5440 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5441 |
|
|
{
|
| 5442 |
|
|
const Tp frac = diff / f0;
|
| 5443 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5444 |
|
|
max_abs_frac = std::abs(frac);
|
| 5445 |
|
|
}
|
| 5446 |
|
|
}
|
| 5447 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5448 |
|
|
}
|
| 5449 |
|
|
|
| 5450 |
|
|
// Test data for k=0.10000000000000009, nu=0.40000000000000002.
|
| 5451 |
|
|
testcase_ellint_3<double> data105[] = {
|
| 5452 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.40000000000000002,
|
| 5453 |
|
|
0.0000000000000000 },
|
| 5454 |
|
|
{ 0.17384216369897937, 0.10000000000000009, 0.40000000000000002,
|
| 5455 |
|
|
0.17453292519943295 },
|
| 5456 |
|
|
{ 0.34375018311376782, 0.10000000000000009, 0.40000000000000002,
|
| 5457 |
|
|
0.34906585039886590 },
|
| 5458 |
|
|
{ 0.50672650758380455, 0.10000000000000009, 0.40000000000000002,
|
| 5459 |
|
|
0.52359877559829882 },
|
| 5460 |
|
|
{ 0.66121264213337616, 0.10000000000000009, 0.40000000000000002,
|
| 5461 |
|
|
0.69813170079773179 },
|
| 5462 |
|
|
{ 0.80706202005774441, 0.10000000000000009, 0.40000000000000002,
|
| 5463 |
|
|
0.87266462599716477 },
|
| 5464 |
|
|
{ 0.94519376138245892, 0.10000000000000009, 0.40000000000000002,
|
| 5465 |
|
|
1.0471975511965976 },
|
| 5466 |
|
|
{ 1.0771880300759584, 0.10000000000000009, 0.40000000000000002,
|
| 5467 |
|
|
1.2217304763960306 },
|
| 5468 |
|
|
{ 1.2049711557188272, 0.10000000000000009, 0.40000000000000002,
|
| 5469 |
|
|
1.3962634015954636 },
|
| 5470 |
|
|
{ 1.3306223265207477, 0.10000000000000009, 0.40000000000000002,
|
| 5471 |
|
|
1.5707963267948966 },
|
| 5472 |
|
|
};
|
| 5473 |
|
|
|
| 5474 |
|
|
// Test function for k=0.10000000000000009, nu=0.40000000000000002.
|
| 5475 |
|
|
template <typename Tp>
|
| 5476 |
|
|
void test105()
|
| 5477 |
|
|
{
|
| 5478 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5479 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5480 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5481 |
|
|
unsigned int num_datum = sizeof(data105)
|
| 5482 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5483 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5484 |
|
|
{
|
| 5485 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data105[i].k), Tp(data105[i].nu),
|
| 5486 |
|
|
Tp(data105[i].phi));
|
| 5487 |
|
|
const Tp f0 = data105[i].f0;
|
| 5488 |
|
|
const Tp diff = f - f0;
|
| 5489 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5490 |
|
|
max_abs_diff = std::abs(diff);
|
| 5491 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5492 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5493 |
|
|
{
|
| 5494 |
|
|
const Tp frac = diff / f0;
|
| 5495 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5496 |
|
|
max_abs_frac = std::abs(frac);
|
| 5497 |
|
|
}
|
| 5498 |
|
|
}
|
| 5499 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5500 |
|
|
}
|
| 5501 |
|
|
|
| 5502 |
|
|
// Test data for k=0.10000000000000009, nu=0.50000000000000000.
|
| 5503 |
|
|
testcase_ellint_3<double> data106[] = {
|
| 5504 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.50000000000000000,
|
| 5505 |
|
|
0.0000000000000000 },
|
| 5506 |
|
|
{ 0.17366883711936554, 0.10000000000000009, 0.50000000000000000,
|
| 5507 |
|
|
0.17453292519943295 },
|
| 5508 |
|
|
{ 0.34244940634881876, 0.10000000000000009, 0.50000000000000000,
|
| 5509 |
|
|
0.34906585039886590 },
|
| 5510 |
|
|
{ 0.50274793281634378, 0.10000000000000009, 0.50000000000000000,
|
| 5511 |
|
|
0.52359877559829882 },
|
| 5512 |
|
|
{ 0.65287941633275093, 0.10000000000000009, 0.50000000000000000,
|
| 5513 |
|
|
0.69813170079773179 },
|
| 5514 |
|
|
{ 0.79291198790315398, 0.10000000000000009, 0.50000000000000000,
|
| 5515 |
|
|
0.87266462599716477 },
|
| 5516 |
|
|
{ 0.92412201537880345, 0.10000000000000009, 0.50000000000000000,
|
| 5517 |
|
|
1.0471975511965976 },
|
| 5518 |
|
|
{ 1.0484480076799370, 0.10000000000000009, 0.50000000000000000,
|
| 5519 |
|
|
1.2217304763960306 },
|
| 5520 |
|
|
{ 1.1681168130475206, 0.10000000000000009, 0.50000000000000000,
|
| 5521 |
|
|
1.3962634015954636 },
|
| 5522 |
|
|
{ 1.2854480708580160, 0.10000000000000009, 0.50000000000000000,
|
| 5523 |
|
|
1.5707963267948966 },
|
| 5524 |
|
|
};
|
| 5525 |
|
|
|
| 5526 |
|
|
// Test function for k=0.10000000000000009, nu=0.50000000000000000.
|
| 5527 |
|
|
template <typename Tp>
|
| 5528 |
|
|
void test106()
|
| 5529 |
|
|
{
|
| 5530 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5531 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5532 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5533 |
|
|
unsigned int num_datum = sizeof(data106)
|
| 5534 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5535 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5536 |
|
|
{
|
| 5537 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data106[i].k), Tp(data106[i].nu),
|
| 5538 |
|
|
Tp(data106[i].phi));
|
| 5539 |
|
|
const Tp f0 = data106[i].f0;
|
| 5540 |
|
|
const Tp diff = f - f0;
|
| 5541 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5542 |
|
|
max_abs_diff = std::abs(diff);
|
| 5543 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5544 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5545 |
|
|
{
|
| 5546 |
|
|
const Tp frac = diff / f0;
|
| 5547 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5548 |
|
|
max_abs_frac = std::abs(frac);
|
| 5549 |
|
|
}
|
| 5550 |
|
|
}
|
| 5551 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5552 |
|
|
}
|
| 5553 |
|
|
|
| 5554 |
|
|
// Test data for k=0.10000000000000009, nu=0.59999999999999998.
|
| 5555 |
|
|
testcase_ellint_3<double> data107[] = {
|
| 5556 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.59999999999999998,
|
| 5557 |
|
|
0.0000000000000000 },
|
| 5558 |
|
|
{ 0.17349612891469018, 0.10000000000000009, 0.59999999999999998,
|
| 5559 |
|
|
0.17453292519943295 },
|
| 5560 |
|
|
{ 0.34116594505539438, 0.10000000000000009, 0.59999999999999998,
|
| 5561 |
|
|
0.34906585039886590 },
|
| 5562 |
|
|
{ 0.49887649430466685, 0.10000000000000009, 0.59999999999999998,
|
| 5563 |
|
|
0.52359877559829882 },
|
| 5564 |
|
|
{ 0.64489553282165157, 0.10000000000000009, 0.59999999999999998,
|
| 5565 |
|
|
0.69813170079773179 },
|
| 5566 |
|
|
{ 0.77956016553782437, 0.10000000000000009, 0.59999999999999998,
|
| 5567 |
|
|
0.87266462599716477 },
|
| 5568 |
|
|
{ 0.90451074530096309, 0.10000000000000009, 0.59999999999999998,
|
| 5569 |
|
|
1.0471975511965976 },
|
| 5570 |
|
|
{ 1.0220113666961632, 0.10000000000000009, 0.59999999999999998,
|
| 5571 |
|
|
1.2217304763960306 },
|
| 5572 |
|
|
{ 1.1345351441065563, 0.10000000000000009, 0.59999999999999998,
|
| 5573 |
|
|
1.3962634015954636 },
|
| 5574 |
|
|
{ 1.2445798942989255, 0.10000000000000009, 0.59999999999999998,
|
| 5575 |
|
|
1.5707963267948966 },
|
| 5576 |
|
|
};
|
| 5577 |
|
|
|
| 5578 |
|
|
// Test function for k=0.10000000000000009, nu=0.59999999999999998.
|
| 5579 |
|
|
template <typename Tp>
|
| 5580 |
|
|
void test107()
|
| 5581 |
|
|
{
|
| 5582 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5583 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5584 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5585 |
|
|
unsigned int num_datum = sizeof(data107)
|
| 5586 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5587 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5588 |
|
|
{
|
| 5589 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data107[i].k), Tp(data107[i].nu),
|
| 5590 |
|
|
Tp(data107[i].phi));
|
| 5591 |
|
|
const Tp f0 = data107[i].f0;
|
| 5592 |
|
|
const Tp diff = f - f0;
|
| 5593 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5594 |
|
|
max_abs_diff = std::abs(diff);
|
| 5595 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5596 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5597 |
|
|
{
|
| 5598 |
|
|
const Tp frac = diff / f0;
|
| 5599 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5600 |
|
|
max_abs_frac = std::abs(frac);
|
| 5601 |
|
|
}
|
| 5602 |
|
|
}
|
| 5603 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5604 |
|
|
}
|
| 5605 |
|
|
|
| 5606 |
|
|
// Test data for k=0.10000000000000009, nu=0.69999999999999996.
|
| 5607 |
|
|
testcase_ellint_3<double> data108[] = {
|
| 5608 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.69999999999999996,
|
| 5609 |
|
|
0.0000000000000000 },
|
| 5610 |
|
|
{ 0.17332403516105052, 0.10000000000000009, 0.69999999999999996,
|
| 5611 |
|
|
0.17453292519943295 },
|
| 5612 |
|
|
{ 0.33989939374896877, 0.10000000000000009, 0.69999999999999996,
|
| 5613 |
|
|
0.34906585039886590 },
|
| 5614 |
|
|
{ 0.49510719568614081, 0.10000000000000009, 0.69999999999999996,
|
| 5615 |
|
|
0.52359877559829882 },
|
| 5616 |
|
|
{ 0.63723607776354974, 0.10000000000000009, 0.69999999999999996,
|
| 5617 |
|
|
0.69813170079773179 },
|
| 5618 |
|
|
{ 0.76693133887935327, 0.10000000000000009, 0.69999999999999996,
|
| 5619 |
|
|
0.87266462599716477 },
|
| 5620 |
|
|
{ 0.88619382078823827, 0.10000000000000009, 0.69999999999999996,
|
| 5621 |
|
|
1.0471975511965976 },
|
| 5622 |
|
|
{ 0.99758012018676490, 0.10000000000000009, 0.69999999999999996,
|
| 5623 |
|
|
1.2217304763960306 },
|
| 5624 |
|
|
{ 1.1037642270814410, 0.10000000000000009, 0.69999999999999996,
|
| 5625 |
|
|
1.3962634015954636 },
|
| 5626 |
|
|
{ 1.2073745911083187, 0.10000000000000009, 0.69999999999999996,
|
| 5627 |
|
|
1.5707963267948966 },
|
| 5628 |
|
|
};
|
| 5629 |
|
|
|
| 5630 |
|
|
// Test function for k=0.10000000000000009, nu=0.69999999999999996.
|
| 5631 |
|
|
template <typename Tp>
|
| 5632 |
|
|
void test108()
|
| 5633 |
|
|
{
|
| 5634 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5635 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5636 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5637 |
|
|
unsigned int num_datum = sizeof(data108)
|
| 5638 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5639 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5640 |
|
|
{
|
| 5641 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data108[i].k), Tp(data108[i].nu),
|
| 5642 |
|
|
Tp(data108[i].phi));
|
| 5643 |
|
|
const Tp f0 = data108[i].f0;
|
| 5644 |
|
|
const Tp diff = f - f0;
|
| 5645 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5646 |
|
|
max_abs_diff = std::abs(diff);
|
| 5647 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5648 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5649 |
|
|
{
|
| 5650 |
|
|
const Tp frac = diff / f0;
|
| 5651 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5652 |
|
|
max_abs_frac = std::abs(frac);
|
| 5653 |
|
|
}
|
| 5654 |
|
|
}
|
| 5655 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5656 |
|
|
}
|
| 5657 |
|
|
|
| 5658 |
|
|
// Test data for k=0.10000000000000009, nu=0.80000000000000004.
|
| 5659 |
|
|
testcase_ellint_3<double> data109[] = {
|
| 5660 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.80000000000000004,
|
| 5661 |
|
|
0.0000000000000000 },
|
| 5662 |
|
|
{ 0.17315255197057020, 0.10000000000000009, 0.80000000000000004,
|
| 5663 |
|
|
0.17453292519943295 },
|
| 5664 |
|
|
{ 0.33864936055747985, 0.10000000000000009, 0.80000000000000004,
|
| 5665 |
|
|
0.34906585039886590 },
|
| 5666 |
|
|
{ 0.49143537041117619, 0.10000000000000009, 0.80000000000000004,
|
| 5667 |
|
|
0.52359877559829882 },
|
| 5668 |
|
|
{ 0.62987861760047492, 0.10000000000000009, 0.80000000000000004,
|
| 5669 |
|
|
0.69813170079773179 },
|
| 5670 |
|
|
{ 0.75496005490917517, 0.10000000000000009, 0.80000000000000004,
|
| 5671 |
|
|
0.87266462599716477 },
|
| 5672 |
|
|
{ 0.86903081862701903, 0.10000000000000009, 0.80000000000000004,
|
| 5673 |
|
|
1.0471975511965976 },
|
| 5674 |
|
|
{ 0.97490814820725591, 0.10000000000000009, 0.80000000000000004,
|
| 5675 |
|
|
1.2217304763960306 },
|
| 5676 |
|
|
{ 1.0754290107171083, 0.10000000000000009, 0.80000000000000004,
|
| 5677 |
|
|
1.3962634015954636 },
|
| 5678 |
|
|
{ 1.1733158866987732, 0.10000000000000009, 0.80000000000000004,
|
| 5679 |
|
|
1.5707963267948966 },
|
| 5680 |
|
|
};
|
| 5681 |
|
|
|
| 5682 |
|
|
// Test function for k=0.10000000000000009, nu=0.80000000000000004.
|
| 5683 |
|
|
template <typename Tp>
|
| 5684 |
|
|
void test109()
|
| 5685 |
|
|
{
|
| 5686 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5687 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5688 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5689 |
|
|
unsigned int num_datum = sizeof(data109)
|
| 5690 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5691 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5692 |
|
|
{
|
| 5693 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data109[i].k), Tp(data109[i].nu),
|
| 5694 |
|
|
Tp(data109[i].phi));
|
| 5695 |
|
|
const Tp f0 = data109[i].f0;
|
| 5696 |
|
|
const Tp diff = f - f0;
|
| 5697 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5698 |
|
|
max_abs_diff = std::abs(diff);
|
| 5699 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5700 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5701 |
|
|
{
|
| 5702 |
|
|
const Tp frac = diff / f0;
|
| 5703 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5704 |
|
|
max_abs_frac = std::abs(frac);
|
| 5705 |
|
|
}
|
| 5706 |
|
|
}
|
| 5707 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5708 |
|
|
}
|
| 5709 |
|
|
|
| 5710 |
|
|
// Test data for k=0.10000000000000009, nu=0.90000000000000002.
|
| 5711 |
|
|
testcase_ellint_3<double> data110[] = {
|
| 5712 |
|
|
{ -0.0000000000000000, 0.10000000000000009, 0.90000000000000002,
|
| 5713 |
|
|
0.0000000000000000 },
|
| 5714 |
|
|
{ 0.17298167549096569, 0.10000000000000009, 0.90000000000000002,
|
| 5715 |
|
|
0.17453292519943295 },
|
| 5716 |
|
|
{ 0.33741546662741584, 0.10000000000000009, 0.90000000000000002,
|
| 5717 |
|
|
0.34906585039886590 },
|
| 5718 |
|
|
{ 0.48785665376856879, 0.10000000000000009, 0.90000000000000002,
|
| 5719 |
|
|
0.52359877559829882 },
|
| 5720 |
|
|
{ 0.62280288554518959, 0.10000000000000009, 0.90000000000000002,
|
| 5721 |
|
|
0.69813170079773179 },
|
| 5722 |
|
|
{ 0.74358903115455199, 0.10000000000000009, 0.90000000000000002,
|
| 5723 |
|
|
0.87266462599716477 },
|
| 5724 |
|
|
{ 0.85290207679298358, 0.10000000000000009, 0.90000000000000002,
|
| 5725 |
|
|
1.0471975511965976 },
|
| 5726 |
|
|
{ 0.95379006645397379, 0.10000000000000009, 0.90000000000000002,
|
| 5727 |
|
|
1.2217304763960306 },
|
| 5728 |
|
|
{ 1.0492213119872327, 0.10000000000000009, 0.90000000000000002,
|
| 5729 |
|
|
1.3962634015954636 },
|
| 5730 |
|
|
{ 1.1419839485283374, 0.10000000000000009, 0.90000000000000002,
|
| 5731 |
|
|
1.5707963267948966 },
|
| 5732 |
|
|
};
|
| 5733 |
|
|
|
| 5734 |
|
|
// Test function for k=0.10000000000000009, nu=0.90000000000000002.
|
| 5735 |
|
|
template <typename Tp>
|
| 5736 |
|
|
void test110()
|
| 5737 |
|
|
{
|
| 5738 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5739 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5740 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5741 |
|
|
unsigned int num_datum = sizeof(data110)
|
| 5742 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5743 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5744 |
|
|
{
|
| 5745 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data110[i].k), Tp(data110[i].nu),
|
| 5746 |
|
|
Tp(data110[i].phi));
|
| 5747 |
|
|
const Tp f0 = data110[i].f0;
|
| 5748 |
|
|
const Tp diff = f - f0;
|
| 5749 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5750 |
|
|
max_abs_diff = std::abs(diff);
|
| 5751 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5752 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5753 |
|
|
{
|
| 5754 |
|
|
const Tp frac = diff / f0;
|
| 5755 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5756 |
|
|
max_abs_frac = std::abs(frac);
|
| 5757 |
|
|
}
|
| 5758 |
|
|
}
|
| 5759 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5760 |
|
|
}
|
| 5761 |
|
|
|
| 5762 |
|
|
// Test data for k=0.19999999999999996, nu=0.0000000000000000.
|
| 5763 |
|
|
testcase_ellint_3<double> data111[] = {
|
| 5764 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.0000000000000000,
|
| 5765 |
|
|
0.0000000000000000 },
|
| 5766 |
|
|
{ 0.17456817290292811, 0.19999999999999996, 0.0000000000000000,
|
| 5767 |
|
|
0.17453292519943295 },
|
| 5768 |
|
|
{ 0.34934315932086801, 0.19999999999999996, 0.0000000000000000,
|
| 5769 |
|
|
0.34906585039886590 },
|
| 5770 |
|
|
{ 0.52450880529443988, 0.19999999999999996, 0.0000000000000000,
|
| 5771 |
|
|
0.52359877559829882 },
|
| 5772 |
|
|
{ 0.70020491009844910, 0.19999999999999996, 0.0000000000000000,
|
| 5773 |
|
|
0.69813170079773179 },
|
| 5774 |
|
|
{ 0.87651006649967955, 0.19999999999999996, 0.0000000000000000,
|
| 5775 |
|
|
0.87266462599716477 },
|
| 5776 |
|
|
{ 1.0534305870298994, 0.19999999999999996, 0.0000000000000000,
|
| 5777 |
|
|
1.0471975511965976 },
|
| 5778 |
|
|
{ 1.2308975521670784, 0.19999999999999996, 0.0000000000000000,
|
| 5779 |
|
|
1.2217304763960306 },
|
| 5780 |
|
|
{ 1.4087733584990738, 0.19999999999999996, 0.0000000000000000,
|
| 5781 |
|
|
1.3962634015954636 },
|
| 5782 |
|
|
{ 1.5868678474541664, 0.19999999999999996, 0.0000000000000000,
|
| 5783 |
|
|
1.5707963267948966 },
|
| 5784 |
|
|
};
|
| 5785 |
|
|
|
| 5786 |
|
|
// Test function for k=0.19999999999999996, nu=0.0000000000000000.
|
| 5787 |
|
|
template <typename Tp>
|
| 5788 |
|
|
void test111()
|
| 5789 |
|
|
{
|
| 5790 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5791 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5792 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5793 |
|
|
unsigned int num_datum = sizeof(data111)
|
| 5794 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5795 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5796 |
|
|
{
|
| 5797 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data111[i].k), Tp(data111[i].nu),
|
| 5798 |
|
|
Tp(data111[i].phi));
|
| 5799 |
|
|
const Tp f0 = data111[i].f0;
|
| 5800 |
|
|
const Tp diff = f - f0;
|
| 5801 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5802 |
|
|
max_abs_diff = std::abs(diff);
|
| 5803 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5804 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5805 |
|
|
{
|
| 5806 |
|
|
const Tp frac = diff / f0;
|
| 5807 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5808 |
|
|
max_abs_frac = std::abs(frac);
|
| 5809 |
|
|
}
|
| 5810 |
|
|
}
|
| 5811 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5812 |
|
|
}
|
| 5813 |
|
|
|
| 5814 |
|
|
// Test data for k=0.19999999999999996, nu=0.10000000000000001.
|
| 5815 |
|
|
testcase_ellint_3<double> data112[] = {
|
| 5816 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.10000000000000001,
|
| 5817 |
|
|
0.0000000000000000 },
|
| 5818 |
|
|
{ 0.17439228502691750, 0.19999999999999996, 0.10000000000000001,
|
| 5819 |
|
|
0.17453292519943295 },
|
| 5820 |
|
|
{ 0.34796731137565740, 0.19999999999999996, 0.10000000000000001,
|
| 5821 |
|
|
0.34906585039886590 },
|
| 5822 |
|
|
{ 0.52003370294544848, 0.19999999999999996, 0.10000000000000001,
|
| 5823 |
|
|
0.52359877559829882 },
|
| 5824 |
|
|
{ 0.69012222258631495, 0.19999999999999996, 0.10000000000000001,
|
| 5825 |
|
|
0.69813170079773179 },
|
| 5826 |
|
|
{ 0.85803491465566772, 0.19999999999999996, 0.10000000000000001,
|
| 5827 |
|
|
0.87266462599716477 },
|
| 5828 |
|
|
{ 1.0238463961099364, 0.19999999999999996, 0.10000000000000001,
|
| 5829 |
|
|
1.0471975511965976 },
|
| 5830 |
|
|
{ 1.1878691059202153, 0.19999999999999996, 0.10000000000000001,
|
| 5831 |
|
|
1.2217304763960306 },
|
| 5832 |
|
|
{ 1.3505985031831940, 0.19999999999999996, 0.10000000000000001,
|
| 5833 |
|
|
1.3962634015954636 },
|
| 5834 |
|
|
{ 1.5126513474261092, 0.19999999999999996, 0.10000000000000001,
|
| 5835 |
|
|
1.5707963267948966 },
|
| 5836 |
|
|
};
|
| 5837 |
|
|
|
| 5838 |
|
|
// Test function for k=0.19999999999999996, nu=0.10000000000000001.
|
| 5839 |
|
|
template <typename Tp>
|
| 5840 |
|
|
void test112()
|
| 5841 |
|
|
{
|
| 5842 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5843 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5844 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5845 |
|
|
unsigned int num_datum = sizeof(data112)
|
| 5846 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5847 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5848 |
|
|
{
|
| 5849 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data112[i].k), Tp(data112[i].nu),
|
| 5850 |
|
|
Tp(data112[i].phi));
|
| 5851 |
|
|
const Tp f0 = data112[i].f0;
|
| 5852 |
|
|
const Tp diff = f - f0;
|
| 5853 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5854 |
|
|
max_abs_diff = std::abs(diff);
|
| 5855 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5856 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5857 |
|
|
{
|
| 5858 |
|
|
const Tp frac = diff / f0;
|
| 5859 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5860 |
|
|
max_abs_frac = std::abs(frac);
|
| 5861 |
|
|
}
|
| 5862 |
|
|
}
|
| 5863 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5864 |
|
|
}
|
| 5865 |
|
|
|
| 5866 |
|
|
// Test data for k=0.19999999999999996, nu=0.20000000000000001.
|
| 5867 |
|
|
testcase_ellint_3<double> data113[] = {
|
| 5868 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.20000000000000001,
|
| 5869 |
|
|
0.0000000000000000 },
|
| 5870 |
|
|
{ 0.17421703179583750, 0.19999999999999996, 0.20000000000000001,
|
| 5871 |
|
|
0.17453292519943295 },
|
| 5872 |
|
|
{ 0.34661057411998791, 0.19999999999999996, 0.20000000000000001,
|
| 5873 |
|
|
0.34906585039886590 },
|
| 5874 |
|
|
{ 0.51569006052647393, 0.19999999999999996, 0.20000000000000001,
|
| 5875 |
|
|
0.52359877559829882 },
|
| 5876 |
|
|
{ 0.68052412821107278, 0.19999999999999996, 0.20000000000000001,
|
| 5877 |
|
|
0.69813170079773179 },
|
| 5878 |
|
|
{ 0.84081341263313825, 0.19999999999999996, 0.20000000000000001,
|
| 5879 |
|
|
0.87266462599716477 },
|
| 5880 |
|
|
{ 0.99683359988842890, 0.19999999999999996, 0.20000000000000001,
|
| 5881 |
|
|
1.0471975511965976 },
|
| 5882 |
|
|
{ 1.1493086715118852, 0.19999999999999996, 0.20000000000000001,
|
| 5883 |
|
|
1.2217304763960306 },
|
| 5884 |
|
|
{ 1.2992699693957541, 0.19999999999999996, 0.20000000000000001,
|
| 5885 |
|
|
1.3962634015954636 },
|
| 5886 |
|
|
{ 1.4479323932249568, 0.19999999999999996, 0.20000000000000001,
|
| 5887 |
|
|
1.5707963267948966 },
|
| 5888 |
|
|
};
|
| 5889 |
|
|
|
| 5890 |
|
|
// Test function for k=0.19999999999999996, nu=0.20000000000000001.
|
| 5891 |
|
|
template <typename Tp>
|
| 5892 |
|
|
void test113()
|
| 5893 |
|
|
{
|
| 5894 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5895 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5896 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5897 |
|
|
unsigned int num_datum = sizeof(data113)
|
| 5898 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5899 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5900 |
|
|
{
|
| 5901 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data113[i].k), Tp(data113[i].nu),
|
| 5902 |
|
|
Tp(data113[i].phi));
|
| 5903 |
|
|
const Tp f0 = data113[i].f0;
|
| 5904 |
|
|
const Tp diff = f - f0;
|
| 5905 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5906 |
|
|
max_abs_diff = std::abs(diff);
|
| 5907 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5908 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5909 |
|
|
{
|
| 5910 |
|
|
const Tp frac = diff / f0;
|
| 5911 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5912 |
|
|
max_abs_frac = std::abs(frac);
|
| 5913 |
|
|
}
|
| 5914 |
|
|
}
|
| 5915 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5916 |
|
|
}
|
| 5917 |
|
|
|
| 5918 |
|
|
// Test data for k=0.19999999999999996, nu=0.29999999999999999.
|
| 5919 |
|
|
testcase_ellint_3<double> data114[] = {
|
| 5920 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.29999999999999999,
|
| 5921 |
|
|
0.0000000000000000 },
|
| 5922 |
|
|
{ 0.17404240913577707, 0.19999999999999996, 0.29999999999999999,
|
| 5923 |
|
|
0.17453292519943295 },
|
| 5924 |
|
|
{ 0.34527248032587193, 0.19999999999999996, 0.29999999999999999,
|
| 5925 |
|
|
0.34906585039886590 },
|
| 5926 |
|
|
{ 0.51147118981668416, 0.19999999999999996, 0.29999999999999999,
|
| 5927 |
|
|
0.52359877559829882 },
|
| 5928 |
|
|
{ 0.67137107867777635, 0.19999999999999996, 0.29999999999999999,
|
| 5929 |
|
|
0.69813170079773179 },
|
| 5930 |
|
|
{ 0.82470418188668893, 0.19999999999999996, 0.29999999999999999,
|
| 5931 |
|
|
0.87266462599716477 },
|
| 5932 |
|
|
{ 0.97202873223594299, 0.19999999999999996, 0.29999999999999999,
|
| 5933 |
|
|
1.0471975511965976 },
|
| 5934 |
|
|
{ 1.1144773569375266, 0.19999999999999996, 0.29999999999999999,
|
| 5935 |
|
|
1.2217304763960306 },
|
| 5936 |
|
|
{ 1.2535292433701000, 0.19999999999999996, 0.29999999999999999,
|
| 5937 |
|
|
1.3962634015954636 },
|
| 5938 |
|
|
{ 1.3908453514752481, 0.19999999999999996, 0.29999999999999999,
|
| 5939 |
|
|
1.5707963267948966 },
|
| 5940 |
|
|
};
|
| 5941 |
|
|
|
| 5942 |
|
|
// Test function for k=0.19999999999999996, nu=0.29999999999999999.
|
| 5943 |
|
|
template <typename Tp>
|
| 5944 |
|
|
void test114()
|
| 5945 |
|
|
{
|
| 5946 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5947 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 5948 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 5949 |
|
|
unsigned int num_datum = sizeof(data114)
|
| 5950 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 5951 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 5952 |
|
|
{
|
| 5953 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data114[i].k), Tp(data114[i].nu),
|
| 5954 |
|
|
Tp(data114[i].phi));
|
| 5955 |
|
|
const Tp f0 = data114[i].f0;
|
| 5956 |
|
|
const Tp diff = f - f0;
|
| 5957 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 5958 |
|
|
max_abs_diff = std::abs(diff);
|
| 5959 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 5960 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 5961 |
|
|
{
|
| 5962 |
|
|
const Tp frac = diff / f0;
|
| 5963 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 5964 |
|
|
max_abs_frac = std::abs(frac);
|
| 5965 |
|
|
}
|
| 5966 |
|
|
}
|
| 5967 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 5968 |
|
|
}
|
| 5969 |
|
|
|
| 5970 |
|
|
// Test data for k=0.19999999999999996, nu=0.40000000000000002.
|
| 5971 |
|
|
testcase_ellint_3<double> data115[] = {
|
| 5972 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.40000000000000002,
|
| 5973 |
|
|
0.0000000000000000 },
|
| 5974 |
|
|
{ 0.17386841301066677, 0.19999999999999996, 0.40000000000000002,
|
| 5975 |
|
|
0.17453292519943295 },
|
| 5976 |
|
|
{ 0.34395257914113253, 0.19999999999999996, 0.40000000000000002,
|
| 5977 |
|
|
0.34906585039886590 },
|
| 5978 |
|
|
{ 0.50737088376869466, 0.19999999999999996, 0.40000000000000002,
|
| 5979 |
|
|
0.52359877559829882 },
|
| 5980 |
|
|
{ 0.66262801717277664, 0.19999999999999996, 0.40000000000000002,
|
| 5981 |
|
|
0.69813170079773179 },
|
| 5982 |
|
|
{ 0.80958766645079094, 0.19999999999999996, 0.40000000000000002,
|
| 5983 |
|
|
0.87266462599716477 },
|
| 5984 |
|
|
{ 0.94913754236162040, 0.19999999999999996, 0.40000000000000002,
|
| 5985 |
|
|
1.0471975511965976 },
|
| 5986 |
|
|
{ 1.0827985514223000, 0.19999999999999996, 0.40000000000000002,
|
| 5987 |
|
|
1.2217304763960306 },
|
| 5988 |
|
|
{ 1.2124212429050478, 0.19999999999999996, 0.40000000000000002,
|
| 5989 |
|
|
1.3962634015954636 },
|
| 5990 |
|
|
{ 1.3400002519661010, 0.19999999999999996, 0.40000000000000002,
|
| 5991 |
|
|
1.5707963267948966 },
|
| 5992 |
|
|
};
|
| 5993 |
|
|
|
| 5994 |
|
|
// Test function for k=0.19999999999999996, nu=0.40000000000000002.
|
| 5995 |
|
|
template <typename Tp>
|
| 5996 |
|
|
void test115()
|
| 5997 |
|
|
{
|
| 5998 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 5999 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6000 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6001 |
|
|
unsigned int num_datum = sizeof(data115)
|
| 6002 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6003 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6004 |
|
|
{
|
| 6005 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data115[i].k), Tp(data115[i].nu),
|
| 6006 |
|
|
Tp(data115[i].phi));
|
| 6007 |
|
|
const Tp f0 = data115[i].f0;
|
| 6008 |
|
|
const Tp diff = f - f0;
|
| 6009 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6010 |
|
|
max_abs_diff = std::abs(diff);
|
| 6011 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6012 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6013 |
|
|
{
|
| 6014 |
|
|
const Tp frac = diff / f0;
|
| 6015 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6016 |
|
|
max_abs_frac = std::abs(frac);
|
| 6017 |
|
|
}
|
| 6018 |
|
|
}
|
| 6019 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6020 |
|
|
}
|
| 6021 |
|
|
|
| 6022 |
|
|
// Test data for k=0.19999999999999996, nu=0.50000000000000000.
|
| 6023 |
|
|
testcase_ellint_3<double> data116[] = {
|
| 6024 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.50000000000000000,
|
| 6025 |
|
|
0.0000000000000000 },
|
| 6026 |
|
|
{ 0.17369503942181802, 0.19999999999999996, 0.50000000000000000,
|
| 6027 |
|
|
0.17453292519943295 },
|
| 6028 |
|
|
{ 0.34265043534362660, 0.19999999999999996, 0.50000000000000000,
|
| 6029 |
|
|
0.34906585039886590 },
|
| 6030 |
|
|
{ 0.50338337208655415, 0.19999999999999996, 0.50000000000000000,
|
| 6031 |
|
|
0.52359877559829882 },
|
| 6032 |
|
|
{ 0.65426373297163642, 0.19999999999999996, 0.50000000000000000,
|
| 6033 |
|
|
0.69813170079773179 },
|
| 6034 |
|
|
{ 0.79536193036145808, 0.19999999999999996, 0.50000000000000000,
|
| 6035 |
|
|
0.87266462599716477 },
|
| 6036 |
|
|
{ 0.92791875910061605, 0.19999999999999996, 0.50000000000000000,
|
| 6037 |
|
|
1.0471975511965976 },
|
| 6038 |
|
|
{ 1.0538145052725829, 0.19999999999999996, 0.50000000000000000,
|
| 6039 |
|
|
1.2217304763960306 },
|
| 6040 |
|
|
{ 1.1752060022875899, 0.19999999999999996, 0.50000000000000000,
|
| 6041 |
|
|
1.3962634015954636 },
|
| 6042 |
|
|
{ 1.2943374404397376, 0.19999999999999996, 0.50000000000000000,
|
| 6043 |
|
|
1.5707963267948966 },
|
| 6044 |
|
|
};
|
| 6045 |
|
|
|
| 6046 |
|
|
// Test function for k=0.19999999999999996, nu=0.50000000000000000.
|
| 6047 |
|
|
template <typename Tp>
|
| 6048 |
|
|
void test116()
|
| 6049 |
|
|
{
|
| 6050 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6051 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6052 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6053 |
|
|
unsigned int num_datum = sizeof(data116)
|
| 6054 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6055 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6056 |
|
|
{
|
| 6057 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data116[i].k), Tp(data116[i].nu),
|
| 6058 |
|
|
Tp(data116[i].phi));
|
| 6059 |
|
|
const Tp f0 = data116[i].f0;
|
| 6060 |
|
|
const Tp diff = f - f0;
|
| 6061 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6062 |
|
|
max_abs_diff = std::abs(diff);
|
| 6063 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6064 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6065 |
|
|
{
|
| 6066 |
|
|
const Tp frac = diff / f0;
|
| 6067 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6068 |
|
|
max_abs_frac = std::abs(frac);
|
| 6069 |
|
|
}
|
| 6070 |
|
|
}
|
| 6071 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6072 |
|
|
}
|
| 6073 |
|
|
|
| 6074 |
|
|
// Test data for k=0.19999999999999996, nu=0.59999999999999998.
|
| 6075 |
|
|
testcase_ellint_3<double> data117[] = {
|
| 6076 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.59999999999999998,
|
| 6077 |
|
|
0.0000000000000000 },
|
| 6078 |
|
|
{ 0.17352228440746928, 0.19999999999999996, 0.59999999999999998,
|
| 6079 |
|
|
0.17453292519943295 },
|
| 6080 |
|
|
{ 0.34136562863713626, 0.19999999999999996, 0.59999999999999998,
|
| 6081 |
|
|
0.34906585039886590 },
|
| 6082 |
|
|
{ 0.49950328177638481, 0.19999999999999996, 0.59999999999999998,
|
| 6083 |
|
|
0.52359877559829882 },
|
| 6084 |
|
|
{ 0.64625032705690832, 0.19999999999999996, 0.59999999999999998,
|
| 6085 |
|
|
0.69813170079773179 },
|
| 6086 |
|
|
{ 0.78193941198403094, 0.19999999999999996, 0.59999999999999998,
|
| 6087 |
|
|
0.87266462599716477 },
|
| 6088 |
|
|
{ 0.90817230934317128, 0.19999999999999996, 0.59999999999999998,
|
| 6089 |
|
|
1.0471975511965976 },
|
| 6090 |
|
|
{ 1.0271563751276462, 0.19999999999999996, 0.59999999999999998,
|
| 6091 |
|
|
1.2217304763960306 },
|
| 6092 |
|
|
{ 1.1412999379040518, 0.19999999999999996, 0.59999999999999998,
|
| 6093 |
|
|
1.3962634015954636 },
|
| 6094 |
|
|
{ 1.2530330675914561, 0.19999999999999996, 0.59999999999999998,
|
| 6095 |
|
|
1.5707963267948966 },
|
| 6096 |
|
|
};
|
| 6097 |
|
|
|
| 6098 |
|
|
// Test function for k=0.19999999999999996, nu=0.59999999999999998.
|
| 6099 |
|
|
template <typename Tp>
|
| 6100 |
|
|
void test117()
|
| 6101 |
|
|
{
|
| 6102 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6103 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6104 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6105 |
|
|
unsigned int num_datum = sizeof(data117)
|
| 6106 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6107 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6108 |
|
|
{
|
| 6109 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data117[i].k), Tp(data117[i].nu),
|
| 6110 |
|
|
Tp(data117[i].phi));
|
| 6111 |
|
|
const Tp f0 = data117[i].f0;
|
| 6112 |
|
|
const Tp diff = f - f0;
|
| 6113 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6114 |
|
|
max_abs_diff = std::abs(diff);
|
| 6115 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6116 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6117 |
|
|
{
|
| 6118 |
|
|
const Tp frac = diff / f0;
|
| 6119 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6120 |
|
|
max_abs_frac = std::abs(frac);
|
| 6121 |
|
|
}
|
| 6122 |
|
|
}
|
| 6123 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6124 |
|
|
}
|
| 6125 |
|
|
|
| 6126 |
|
|
// Test data for k=0.19999999999999996, nu=0.69999999999999996.
|
| 6127 |
|
|
testcase_ellint_3<double> data118[] = {
|
| 6128 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.69999999999999996,
|
| 6129 |
|
|
0.0000000000000000 },
|
| 6130 |
|
|
{ 0.17335014404233898, 0.19999999999999996, 0.69999999999999996,
|
| 6131 |
|
|
0.17453292519943295 },
|
| 6132 |
|
|
{ 0.34009775298617811, 0.19999999999999996, 0.69999999999999996,
|
| 6133 |
|
|
0.34906585039886590 },
|
| 6134 |
|
|
{ 0.49572560201923810, 0.19999999999999996, 0.69999999999999996,
|
| 6135 |
|
|
0.52359877559829882 },
|
| 6136 |
|
|
{ 0.63856276669886525, 0.19999999999999996, 0.69999999999999996,
|
| 6137 |
|
|
0.69813170079773179 },
|
| 6138 |
|
|
{ 0.76924438644867565, 0.19999999999999996, 0.69999999999999996,
|
| 6139 |
|
|
0.87266462599716477 },
|
| 6140 |
|
|
{ 0.88973060843856466, 0.19999999999999996, 0.69999999999999996,
|
| 6141 |
|
|
1.0471975511965976 },
|
| 6142 |
|
|
{ 1.0025230471636377, 0.19999999999999996, 0.69999999999999996,
|
| 6143 |
|
|
1.2217304763960306 },
|
| 6144 |
|
|
{ 1.1102356376093103, 0.19999999999999996, 0.69999999999999996,
|
| 6145 |
|
|
1.3962634015954636 },
|
| 6146 |
|
|
{ 1.2154356555075867, 0.19999999999999996, 0.69999999999999996,
|
| 6147 |
|
|
1.5707963267948966 },
|
| 6148 |
|
|
};
|
| 6149 |
|
|
|
| 6150 |
|
|
// Test function for k=0.19999999999999996, nu=0.69999999999999996.
|
| 6151 |
|
|
template <typename Tp>
|
| 6152 |
|
|
void test118()
|
| 6153 |
|
|
{
|
| 6154 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6155 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6156 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6157 |
|
|
unsigned int num_datum = sizeof(data118)
|
| 6158 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6159 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6160 |
|
|
{
|
| 6161 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data118[i].k), Tp(data118[i].nu),
|
| 6162 |
|
|
Tp(data118[i].phi));
|
| 6163 |
|
|
const Tp f0 = data118[i].f0;
|
| 6164 |
|
|
const Tp diff = f - f0;
|
| 6165 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6166 |
|
|
max_abs_diff = std::abs(diff);
|
| 6167 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6168 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6169 |
|
|
{
|
| 6170 |
|
|
const Tp frac = diff / f0;
|
| 6171 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6172 |
|
|
max_abs_frac = std::abs(frac);
|
| 6173 |
|
|
}
|
| 6174 |
|
|
}
|
| 6175 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6176 |
|
|
}
|
| 6177 |
|
|
|
| 6178 |
|
|
// Test data for k=0.19999999999999996, nu=0.80000000000000004.
|
| 6179 |
|
|
testcase_ellint_3<double> data119[] = {
|
| 6180 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.80000000000000004,
|
| 6181 |
|
|
0.0000000000000000 },
|
| 6182 |
|
|
{ 0.17317861443718541, 0.19999999999999996, 0.80000000000000004,
|
| 6183 |
|
|
0.17453292519943295 },
|
| 6184 |
|
|
{ 0.33884641598718701, 0.19999999999999996, 0.80000000000000004,
|
| 6185 |
|
|
0.34906585039886590 },
|
| 6186 |
|
|
{ 0.49204565281259494, 0.19999999999999996, 0.80000000000000004,
|
| 6187 |
|
|
0.52359877559829882 },
|
| 6188 |
|
|
{ 0.63117851188220353, 0.19999999999999996, 0.80000000000000004,
|
| 6189 |
|
|
0.69813170079773179 },
|
| 6190 |
|
|
{ 0.75721095949544170, 0.19999999999999996, 0.80000000000000004,
|
| 6191 |
|
|
0.87266462599716477 },
|
| 6192 |
|
|
{ 0.87245201443919118, 0.19999999999999996, 0.80000000000000004,
|
| 6193 |
|
|
1.0471975511965976 },
|
| 6194 |
|
|
{ 0.97966584238831089, 0.19999999999999996, 0.80000000000000004,
|
| 6195 |
|
|
1.2217304763960306 },
|
| 6196 |
|
|
{ 1.0816336325174360, 0.19999999999999996, 0.80000000000000004,
|
| 6197 |
|
|
1.3962634015954636 },
|
| 6198 |
|
|
{ 1.1810223448909913, 0.19999999999999996, 0.80000000000000004,
|
| 6199 |
|
|
1.5707963267948966 },
|
| 6200 |
|
|
};
|
| 6201 |
|
|
|
| 6202 |
|
|
// Test function for k=0.19999999999999996, nu=0.80000000000000004.
|
| 6203 |
|
|
template <typename Tp>
|
| 6204 |
|
|
void test119()
|
| 6205 |
|
|
{
|
| 6206 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6207 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6208 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6209 |
|
|
unsigned int num_datum = sizeof(data119)
|
| 6210 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6211 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6212 |
|
|
{
|
| 6213 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data119[i].k), Tp(data119[i].nu),
|
| 6214 |
|
|
Tp(data119[i].phi));
|
| 6215 |
|
|
const Tp f0 = data119[i].f0;
|
| 6216 |
|
|
const Tp diff = f - f0;
|
| 6217 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6218 |
|
|
max_abs_diff = std::abs(diff);
|
| 6219 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6220 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6221 |
|
|
{
|
| 6222 |
|
|
const Tp frac = diff / f0;
|
| 6223 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6224 |
|
|
max_abs_frac = std::abs(frac);
|
| 6225 |
|
|
}
|
| 6226 |
|
|
}
|
| 6227 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6228 |
|
|
}
|
| 6229 |
|
|
|
| 6230 |
|
|
// Test data for k=0.19999999999999996, nu=0.90000000000000002.
|
| 6231 |
|
|
testcase_ellint_3<double> data120[] = {
|
| 6232 |
|
|
{ -0.0000000000000000, 0.19999999999999996, 0.90000000000000002,
|
| 6233 |
|
|
0.0000000000000000 },
|
| 6234 |
|
|
{ 0.17300769173837280, 0.19999999999999996, 0.90000000000000002,
|
| 6235 |
|
|
0.17453292519943295 },
|
| 6236 |
|
|
{ 0.33761123827372508, 0.19999999999999996, 0.90000000000000002,
|
| 6237 |
|
|
0.34906585039886590 },
|
| 6238 |
|
|
{ 0.48845905690769426, 0.19999999999999996, 0.90000000000000002,
|
| 6239 |
|
|
0.52359877559829882 },
|
| 6240 |
|
|
{ 0.62407720017324986, 0.19999999999999996, 0.90000000000000002,
|
| 6241 |
|
|
0.69813170079773179 },
|
| 6242 |
|
|
{ 0.74578146525124289, 0.19999999999999996, 0.90000000000000002,
|
| 6243 |
|
|
0.87266462599716477 },
|
| 6244 |
|
|
{ 0.85621583540073076, 0.19999999999999996, 0.90000000000000002,
|
| 6245 |
|
|
1.0471975511965976 },
|
| 6246 |
|
|
{ 0.95837725988001199, 0.19999999999999996, 0.90000000000000002,
|
| 6247 |
|
|
1.2217304763960306 },
|
| 6248 |
|
|
{ 1.0551821412633928, 0.19999999999999996, 0.90000000000000002,
|
| 6249 |
|
|
1.3962634015954636 },
|
| 6250 |
|
|
{ 1.1493679916141863, 0.19999999999999996, 0.90000000000000002,
|
| 6251 |
|
|
1.5707963267948966 },
|
| 6252 |
|
|
};
|
| 6253 |
|
|
|
| 6254 |
|
|
// Test function for k=0.19999999999999996, nu=0.90000000000000002.
|
| 6255 |
|
|
template <typename Tp>
|
| 6256 |
|
|
void test120()
|
| 6257 |
|
|
{
|
| 6258 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6259 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6260 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6261 |
|
|
unsigned int num_datum = sizeof(data120)
|
| 6262 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6263 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6264 |
|
|
{
|
| 6265 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data120[i].k), Tp(data120[i].nu),
|
| 6266 |
|
|
Tp(data120[i].phi));
|
| 6267 |
|
|
const Tp f0 = data120[i].f0;
|
| 6268 |
|
|
const Tp diff = f - f0;
|
| 6269 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6270 |
|
|
max_abs_diff = std::abs(diff);
|
| 6271 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6272 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6273 |
|
|
{
|
| 6274 |
|
|
const Tp frac = diff / f0;
|
| 6275 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6276 |
|
|
max_abs_frac = std::abs(frac);
|
| 6277 |
|
|
}
|
| 6278 |
|
|
}
|
| 6279 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6280 |
|
|
}
|
| 6281 |
|
|
|
| 6282 |
|
|
// Test data for k=0.30000000000000004, nu=0.0000000000000000.
|
| 6283 |
|
|
testcase_ellint_3<double> data121[] = {
|
| 6284 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.0000000000000000,
|
| 6285 |
|
|
0.0000000000000000 },
|
| 6286 |
|
|
{ 0.17461228653000102, 0.30000000000000004, 0.0000000000000000,
|
| 6287 |
|
|
0.17453292519943295 },
|
| 6288 |
|
|
{ 0.34969146102798415, 0.30000000000000004, 0.0000000000000000,
|
| 6289 |
|
|
0.34906585039886590 },
|
| 6290 |
|
|
{ 0.52565822873726320, 0.30000000000000004, 0.0000000000000000,
|
| 6291 |
|
|
0.52359877559829882 },
|
| 6292 |
|
|
{ 0.70284226512408532, 0.30000000000000004, 0.0000000000000000,
|
| 6293 |
|
|
0.69813170079773179 },
|
| 6294 |
|
|
{ 0.88144139195111182, 0.30000000000000004, 0.0000000000000000,
|
| 6295 |
|
|
0.87266462599716477 },
|
| 6296 |
|
|
{ 1.0614897067260523, 0.30000000000000004, 0.0000000000000000,
|
| 6297 |
|
|
1.0471975511965976 },
|
| 6298 |
|
|
{ 1.2428416824174218, 0.30000000000000004, 0.0000000000000000,
|
| 6299 |
|
|
1.2217304763960306 },
|
| 6300 |
|
|
{ 1.4251795877015925, 0.30000000000000004, 0.0000000000000000,
|
| 6301 |
|
|
1.3962634015954636 },
|
| 6302 |
|
|
{ 1.6080486199305126, 0.30000000000000004, 0.0000000000000000,
|
| 6303 |
|
|
1.5707963267948966 },
|
| 6304 |
|
|
};
|
| 6305 |
|
|
|
| 6306 |
|
|
// Test function for k=0.30000000000000004, nu=0.0000000000000000.
|
| 6307 |
|
|
template <typename Tp>
|
| 6308 |
|
|
void test121()
|
| 6309 |
|
|
{
|
| 6310 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6311 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6312 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6313 |
|
|
unsigned int num_datum = sizeof(data121)
|
| 6314 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6315 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6316 |
|
|
{
|
| 6317 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data121[i].k), Tp(data121[i].nu),
|
| 6318 |
|
|
Tp(data121[i].phi));
|
| 6319 |
|
|
const Tp f0 = data121[i].f0;
|
| 6320 |
|
|
const Tp diff = f - f0;
|
| 6321 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6322 |
|
|
max_abs_diff = std::abs(diff);
|
| 6323 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6324 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6325 |
|
|
{
|
| 6326 |
|
|
const Tp frac = diff / f0;
|
| 6327 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6328 |
|
|
max_abs_frac = std::abs(frac);
|
| 6329 |
|
|
}
|
| 6330 |
|
|
}
|
| 6331 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6332 |
|
|
}
|
| 6333 |
|
|
|
| 6334 |
|
|
// Test data for k=0.30000000000000004, nu=0.10000000000000001.
|
| 6335 |
|
|
testcase_ellint_3<double> data122[] = {
|
| 6336 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.10000000000000001,
|
| 6337 |
|
|
0.0000000000000000 },
|
| 6338 |
|
|
{ 0.17443631884814378, 0.30000000000000004, 0.10000000000000001,
|
| 6339 |
|
|
0.17453292519943295 },
|
| 6340 |
|
|
{ 0.34831316835124926, 0.30000000000000004, 0.10000000000000001,
|
| 6341 |
|
|
0.34906585039886590 },
|
| 6342 |
|
|
{ 0.52116586276523857, 0.30000000000000004, 0.10000000000000001,
|
| 6343 |
|
|
0.52359877559829882 },
|
| 6344 |
|
|
{ 0.69269385837910036, 0.30000000000000004, 0.10000000000000001,
|
| 6345 |
|
|
0.69813170079773179 },
|
| 6346 |
|
|
{ 0.86279023163070856, 0.30000000000000004, 0.10000000000000001,
|
| 6347 |
|
|
0.87266462599716477 },
|
| 6348 |
|
|
{ 1.0315321461438265, 0.30000000000000004, 0.10000000000000001,
|
| 6349 |
|
|
1.0471975511965976 },
|
| 6350 |
|
|
{ 1.1991449111869024, 0.30000000000000004, 0.10000000000000001,
|
| 6351 |
|
|
1.2217304763960306 },
|
| 6352 |
|
|
{ 1.3659561780923211, 0.30000000000000004, 0.10000000000000001,
|
| 6353 |
|
|
1.3962634015954636 },
|
| 6354 |
|
|
{ 1.5323534693557526, 0.30000000000000004, 0.10000000000000001,
|
| 6355 |
|
|
1.5707963267948966 },
|
| 6356 |
|
|
};
|
| 6357 |
|
|
|
| 6358 |
|
|
// Test function for k=0.30000000000000004, nu=0.10000000000000001.
|
| 6359 |
|
|
template <typename Tp>
|
| 6360 |
|
|
void test122()
|
| 6361 |
|
|
{
|
| 6362 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6363 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6364 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6365 |
|
|
unsigned int num_datum = sizeof(data122)
|
| 6366 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6367 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6368 |
|
|
{
|
| 6369 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data122[i].k), Tp(data122[i].nu),
|
| 6370 |
|
|
Tp(data122[i].phi));
|
| 6371 |
|
|
const Tp f0 = data122[i].f0;
|
| 6372 |
|
|
const Tp diff = f - f0;
|
| 6373 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6374 |
|
|
max_abs_diff = std::abs(diff);
|
| 6375 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6376 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6377 |
|
|
{
|
| 6378 |
|
|
const Tp frac = diff / f0;
|
| 6379 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6380 |
|
|
max_abs_frac = std::abs(frac);
|
| 6381 |
|
|
}
|
| 6382 |
|
|
}
|
| 6383 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6384 |
|
|
}
|
| 6385 |
|
|
|
| 6386 |
|
|
// Test data for k=0.30000000000000004, nu=0.20000000000000001.
|
| 6387 |
|
|
testcase_ellint_3<double> data123[] = {
|
| 6388 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.20000000000000001,
|
| 6389 |
|
|
0.0000000000000000 },
|
| 6390 |
|
|
{ 0.17426098615372090, 0.30000000000000004, 0.20000000000000001,
|
| 6391 |
|
|
0.17453292519943295 },
|
| 6392 |
|
|
{ 0.34695402664689923, 0.30000000000000004, 0.20000000000000001,
|
| 6393 |
|
|
0.34906585039886590 },
|
| 6394 |
|
|
{ 0.51680555567038933, 0.30000000000000004, 0.20000000000000001,
|
| 6395 |
|
|
0.52359877559829882 },
|
| 6396 |
|
|
{ 0.68303375225260210, 0.30000000000000004, 0.20000000000000001,
|
| 6397 |
|
|
0.69813170079773179 },
|
| 6398 |
|
|
{ 0.84540662891295026, 0.30000000000000004, 0.20000000000000001,
|
| 6399 |
|
|
0.87266462599716477 },
|
| 6400 |
|
|
{ 1.0041834051646927, 0.30000000000000004, 0.20000000000000001,
|
| 6401 |
|
|
1.0471975511965976 },
|
| 6402 |
|
|
{ 1.1599952702345711, 0.30000000000000004, 0.20000000000000001,
|
| 6403 |
|
|
1.2217304763960306 },
|
| 6404 |
|
|
{ 1.3137179520499163, 0.30000000000000004, 0.20000000000000001,
|
| 6405 |
|
|
1.3962634015954636 },
|
| 6406 |
|
|
{ 1.4663658145259875, 0.30000000000000004, 0.20000000000000001,
|
| 6407 |
|
|
1.5707963267948966 },
|
| 6408 |
|
|
};
|
| 6409 |
|
|
|
| 6410 |
|
|
// Test function for k=0.30000000000000004, nu=0.20000000000000001.
|
| 6411 |
|
|
template <typename Tp>
|
| 6412 |
|
|
void test123()
|
| 6413 |
|
|
{
|
| 6414 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6415 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6416 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6417 |
|
|
unsigned int num_datum = sizeof(data123)
|
| 6418 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6419 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6420 |
|
|
{
|
| 6421 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data123[i].k), Tp(data123[i].nu),
|
| 6422 |
|
|
Tp(data123[i].phi));
|
| 6423 |
|
|
const Tp f0 = data123[i].f0;
|
| 6424 |
|
|
const Tp diff = f - f0;
|
| 6425 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6426 |
|
|
max_abs_diff = std::abs(diff);
|
| 6427 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6428 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6429 |
|
|
{
|
| 6430 |
|
|
const Tp frac = diff / f0;
|
| 6431 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6432 |
|
|
max_abs_frac = std::abs(frac);
|
| 6433 |
|
|
}
|
| 6434 |
|
|
}
|
| 6435 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6436 |
|
|
}
|
| 6437 |
|
|
|
| 6438 |
|
|
// Test data for k=0.30000000000000004, nu=0.29999999999999999.
|
| 6439 |
|
|
testcase_ellint_3<double> data124[] = {
|
| 6440 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.29999999999999999,
|
| 6441 |
|
|
0.0000000000000000 },
|
| 6442 |
|
|
{ 0.17408628437042845, 0.30000000000000004, 0.29999999999999999,
|
| 6443 |
|
|
0.17453292519943295 },
|
| 6444 |
|
|
{ 0.34561356761638401, 0.30000000000000004, 0.29999999999999999,
|
| 6445 |
|
|
0.34906585039886590 },
|
| 6446 |
|
|
{ 0.51257058617875850, 0.30000000000000004, 0.29999999999999999,
|
| 6447 |
|
|
0.52359877559829882 },
|
| 6448 |
|
|
{ 0.67382207124602866, 0.30000000000000004, 0.29999999999999999,
|
| 6449 |
|
|
0.69813170079773179 },
|
| 6450 |
|
|
{ 0.82914751587825131, 0.30000000000000004, 0.29999999999999999,
|
| 6451 |
|
|
0.87266462599716477 },
|
| 6452 |
|
|
{ 0.97907434814374950, 0.30000000000000004, 0.29999999999999999,
|
| 6453 |
|
|
1.0471975511965976 },
|
| 6454 |
|
|
{ 1.1246399297351584, 0.30000000000000004, 0.29999999999999999,
|
| 6455 |
|
|
1.2217304763960306 },
|
| 6456 |
|
|
{ 1.2671793970398146, 0.30000000000000004, 0.29999999999999999,
|
| 6457 |
|
|
1.3962634015954636 },
|
| 6458 |
|
|
{ 1.4081767433479089, 0.30000000000000004, 0.29999999999999999,
|
| 6459 |
|
|
1.5707963267948966 },
|
| 6460 |
|
|
};
|
| 6461 |
|
|
|
| 6462 |
|
|
// Test function for k=0.30000000000000004, nu=0.29999999999999999.
|
| 6463 |
|
|
template <typename Tp>
|
| 6464 |
|
|
void test124()
|
| 6465 |
|
|
{
|
| 6466 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6467 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6468 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6469 |
|
|
unsigned int num_datum = sizeof(data124)
|
| 6470 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6471 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6472 |
|
|
{
|
| 6473 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data124[i].k), Tp(data124[i].nu),
|
| 6474 |
|
|
Tp(data124[i].phi));
|
| 6475 |
|
|
const Tp f0 = data124[i].f0;
|
| 6476 |
|
|
const Tp diff = f - f0;
|
| 6477 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6478 |
|
|
max_abs_diff = std::abs(diff);
|
| 6479 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6480 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6481 |
|
|
{
|
| 6482 |
|
|
const Tp frac = diff / f0;
|
| 6483 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6484 |
|
|
max_abs_frac = std::abs(frac);
|
| 6485 |
|
|
}
|
| 6486 |
|
|
}
|
| 6487 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6488 |
|
|
}
|
| 6489 |
|
|
|
| 6490 |
|
|
// Test data for k=0.30000000000000004, nu=0.40000000000000002.
|
| 6491 |
|
|
testcase_ellint_3<double> data125[] = {
|
| 6492 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.40000000000000002,
|
| 6493 |
|
|
0.0000000000000000 },
|
| 6494 |
|
|
{ 0.17391220945982730, 0.30000000000000004, 0.40000000000000002,
|
| 6495 |
|
|
0.17453292519943295 },
|
| 6496 |
|
|
{ 0.34429133937639689, 0.30000000000000004, 0.40000000000000002,
|
| 6497 |
|
|
0.34906585039886590 },
|
| 6498 |
|
|
{ 0.50845471668581632, 0.30000000000000004, 0.40000000000000002,
|
| 6499 |
|
|
0.52359877559829882 },
|
| 6500 |
|
|
{ 0.66502347027873854, 0.30000000000000004, 0.40000000000000002,
|
| 6501 |
|
|
0.69813170079773179 },
|
| 6502 |
|
|
{ 0.81389191978012254, 0.30000000000000004, 0.40000000000000002,
|
| 6503 |
|
|
0.87266462599716477 },
|
| 6504 |
|
|
{ 0.95590618002140593, 0.30000000000000004, 0.40000000000000002,
|
| 6505 |
|
|
1.0471975511965976 },
|
| 6506 |
|
|
{ 1.0924915195213121, 0.30000000000000004, 0.40000000000000002,
|
| 6507 |
|
|
1.2217304763960306 },
|
| 6508 |
|
|
{ 1.2253651604038058, 0.30000000000000004, 0.40000000000000002,
|
| 6509 |
|
|
1.3962634015954636 },
|
| 6510 |
|
|
{ 1.3563643538969761, 0.30000000000000004, 0.40000000000000002,
|
| 6511 |
|
|
1.5707963267948966 },
|
| 6512 |
|
|
};
|
| 6513 |
|
|
|
| 6514 |
|
|
// Test function for k=0.30000000000000004, nu=0.40000000000000002.
|
| 6515 |
|
|
template <typename Tp>
|
| 6516 |
|
|
void test125()
|
| 6517 |
|
|
{
|
| 6518 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6519 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6520 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6521 |
|
|
unsigned int num_datum = sizeof(data125)
|
| 6522 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6523 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6524 |
|
|
{
|
| 6525 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data125[i].k), Tp(data125[i].nu),
|
| 6526 |
|
|
Tp(data125[i].phi));
|
| 6527 |
|
|
const Tp f0 = data125[i].f0;
|
| 6528 |
|
|
const Tp diff = f - f0;
|
| 6529 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6530 |
|
|
max_abs_diff = std::abs(diff);
|
| 6531 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6532 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6533 |
|
|
{
|
| 6534 |
|
|
const Tp frac = diff / f0;
|
| 6535 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6536 |
|
|
max_abs_frac = std::abs(frac);
|
| 6537 |
|
|
}
|
| 6538 |
|
|
}
|
| 6539 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6540 |
|
|
}
|
| 6541 |
|
|
|
| 6542 |
|
|
// Test data for k=0.30000000000000004, nu=0.50000000000000000.
|
| 6543 |
|
|
testcase_ellint_3<double> data126[] = {
|
| 6544 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.50000000000000000,
|
| 6545 |
|
|
0.0000000000000000 },
|
| 6546 |
|
|
{ 0.17373875742088235, 0.30000000000000004, 0.50000000000000000,
|
| 6547 |
|
|
0.17453292519943295 },
|
| 6548 |
|
|
{ 0.34298690571124157, 0.30000000000000004, 0.50000000000000000,
|
| 6549 |
|
|
0.34906585039886590 },
|
| 6550 |
|
|
{ 0.50445214859646936, 0.30000000000000004, 0.50000000000000000,
|
| 6551 |
|
|
0.52359877559829882 },
|
| 6552 |
|
|
{ 0.65660648352418516, 0.30000000000000004, 0.50000000000000000,
|
| 6553 |
|
|
0.69813170079773179 },
|
| 6554 |
|
|
{ 0.79953670639287289, 0.30000000000000004, 0.50000000000000000,
|
| 6555 |
|
|
0.87266462599716477 },
|
| 6556 |
|
|
{ 0.93443393926588558, 0.30000000000000004, 0.50000000000000000,
|
| 6557 |
|
|
1.0471975511965976 },
|
| 6558 |
|
|
{ 1.0630838369016911, 0.30000000000000004, 0.50000000000000000,
|
| 6559 |
|
|
1.2217304763960306 },
|
| 6560 |
|
|
{ 1.1875197325653026, 0.30000000000000004, 0.50000000000000000,
|
| 6561 |
|
|
1.3962634015954636 },
|
| 6562 |
|
|
{ 1.3098448759814960, 0.30000000000000004, 0.50000000000000000,
|
| 6563 |
|
|
1.5707963267948966 },
|
| 6564 |
|
|
};
|
| 6565 |
|
|
|
| 6566 |
|
|
// Test function for k=0.30000000000000004, nu=0.50000000000000000.
|
| 6567 |
|
|
template <typename Tp>
|
| 6568 |
|
|
void test126()
|
| 6569 |
|
|
{
|
| 6570 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6571 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6572 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6573 |
|
|
unsigned int num_datum = sizeof(data126)
|
| 6574 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6575 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6576 |
|
|
{
|
| 6577 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data126[i].k), Tp(data126[i].nu),
|
| 6578 |
|
|
Tp(data126[i].phi));
|
| 6579 |
|
|
const Tp f0 = data126[i].f0;
|
| 6580 |
|
|
const Tp diff = f - f0;
|
| 6581 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6582 |
|
|
max_abs_diff = std::abs(diff);
|
| 6583 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6584 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6585 |
|
|
{
|
| 6586 |
|
|
const Tp frac = diff / f0;
|
| 6587 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6588 |
|
|
max_abs_frac = std::abs(frac);
|
| 6589 |
|
|
}
|
| 6590 |
|
|
}
|
| 6591 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6592 |
|
|
}
|
| 6593 |
|
|
|
| 6594 |
|
|
// Test data for k=0.30000000000000004, nu=0.59999999999999998.
|
| 6595 |
|
|
testcase_ellint_3<double> data127[] = {
|
| 6596 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.59999999999999998,
|
| 6597 |
|
|
0.0000000000000000 },
|
| 6598 |
|
|
{ 0.17356592428950826, 0.30000000000000004, 0.59999999999999998,
|
| 6599 |
|
|
0.17453292519943295 },
|
| 6600 |
|
|
{ 0.34169984536697379, 0.30000000000000004, 0.59999999999999998,
|
| 6601 |
|
|
0.34906585039886590 },
|
| 6602 |
|
|
{ 0.50055748266498457, 0.30000000000000004, 0.59999999999999998,
|
| 6603 |
|
|
0.52359877559829882 },
|
| 6604 |
|
|
{ 0.64854298527106768, 0.30000000000000004, 0.59999999999999998,
|
| 6605 |
|
|
0.69813170079773179 },
|
| 6606 |
|
|
{ 0.78599329284207431, 0.30000000000000004, 0.59999999999999998,
|
| 6607 |
|
|
0.87266462599716477 },
|
| 6608 |
|
|
{ 0.91445452089128221, 0.30000000000000004, 0.59999999999999998,
|
| 6609 |
|
|
1.0471975511965976 },
|
| 6610 |
|
|
{ 1.0360412952290587, 0.30000000000000004, 0.59999999999999998,
|
| 6611 |
|
|
1.2217304763960306 },
|
| 6612 |
|
|
{ 1.1530473919778639, 0.30000000000000004, 0.59999999999999998,
|
| 6613 |
|
|
1.3962634015954636 },
|
| 6614 |
|
|
{ 1.2677758800420666, 0.30000000000000004, 0.59999999999999998,
|
| 6615 |
|
|
1.5707963267948966 },
|
| 6616 |
|
|
};
|
| 6617 |
|
|
|
| 6618 |
|
|
// Test function for k=0.30000000000000004, nu=0.59999999999999998.
|
| 6619 |
|
|
template <typename Tp>
|
| 6620 |
|
|
void test127()
|
| 6621 |
|
|
{
|
| 6622 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6623 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6624 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6625 |
|
|
unsigned int num_datum = sizeof(data127)
|
| 6626 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6627 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6628 |
|
|
{
|
| 6629 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data127[i].k), Tp(data127[i].nu),
|
| 6630 |
|
|
Tp(data127[i].phi));
|
| 6631 |
|
|
const Tp f0 = data127[i].f0;
|
| 6632 |
|
|
const Tp diff = f - f0;
|
| 6633 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6634 |
|
|
max_abs_diff = std::abs(diff);
|
| 6635 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6636 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6637 |
|
|
{
|
| 6638 |
|
|
const Tp frac = diff / f0;
|
| 6639 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6640 |
|
|
max_abs_frac = std::abs(frac);
|
| 6641 |
|
|
}
|
| 6642 |
|
|
}
|
| 6643 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6644 |
|
|
}
|
| 6645 |
|
|
|
| 6646 |
|
|
// Test data for k=0.30000000000000004, nu=0.69999999999999996.
|
| 6647 |
|
|
testcase_ellint_3<double> data128[] = {
|
| 6648 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.69999999999999996,
|
| 6649 |
|
|
0.0000000000000000 },
|
| 6650 |
|
|
{ 0.17339370613812227, 0.30000000000000004, 0.69999999999999996,
|
| 6651 |
|
|
0.17453292519943295 },
|
| 6652 |
|
|
{ 0.34042975138455933, 0.30000000000000004, 0.69999999999999996,
|
| 6653 |
|
|
0.34906585039886590 },
|
| 6654 |
|
|
{ 0.49676568368075985, 0.30000000000000004, 0.69999999999999996,
|
| 6655 |
|
|
0.52359877559829882 },
|
| 6656 |
|
|
{ 0.64080774055753720, 0.30000000000000004, 0.69999999999999996,
|
| 6657 |
|
|
0.69813170079773179 },
|
| 6658 |
|
|
{ 0.77318507779667278, 0.30000000000000004, 0.69999999999999996,
|
| 6659 |
|
|
0.87266462599716477 },
|
| 6660 |
|
|
{ 0.89579782346548631, 0.30000000000000004, 0.69999999999999996,
|
| 6661 |
|
|
1.0471975511965976 },
|
| 6662 |
|
|
{ 1.0110573286052202, 0.30000000000000004, 0.69999999999999996,
|
| 6663 |
|
|
1.2217304763960306 },
|
| 6664 |
|
|
{ 1.1214710972949633, 0.30000000000000004, 0.69999999999999996,
|
| 6665 |
|
|
1.3962634015954636 },
|
| 6666 |
|
|
{ 1.2294913236274980, 0.30000000000000004, 0.69999999999999996,
|
| 6667 |
|
|
1.5707963267948966 },
|
| 6668 |
|
|
};
|
| 6669 |
|
|
|
| 6670 |
|
|
// Test function for k=0.30000000000000004, nu=0.69999999999999996.
|
| 6671 |
|
|
template <typename Tp>
|
| 6672 |
|
|
void test128()
|
| 6673 |
|
|
{
|
| 6674 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6675 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6676 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6677 |
|
|
unsigned int num_datum = sizeof(data128)
|
| 6678 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6679 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6680 |
|
|
{
|
| 6681 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data128[i].k), Tp(data128[i].nu),
|
| 6682 |
|
|
Tp(data128[i].phi));
|
| 6683 |
|
|
const Tp f0 = data128[i].f0;
|
| 6684 |
|
|
const Tp diff = f - f0;
|
| 6685 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6686 |
|
|
max_abs_diff = std::abs(diff);
|
| 6687 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6688 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6689 |
|
|
{
|
| 6690 |
|
|
const Tp frac = diff / f0;
|
| 6691 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6692 |
|
|
max_abs_frac = std::abs(frac);
|
| 6693 |
|
|
}
|
| 6694 |
|
|
}
|
| 6695 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6696 |
|
|
}
|
| 6697 |
|
|
|
| 6698 |
|
|
// Test data for k=0.30000000000000004, nu=0.80000000000000004.
|
| 6699 |
|
|
testcase_ellint_3<double> data129[] = {
|
| 6700 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.80000000000000004,
|
| 6701 |
|
|
0.0000000000000000 },
|
| 6702 |
|
|
{ 0.17322209907520361, 0.30000000000000004, 0.80000000000000004,
|
| 6703 |
|
|
0.17453292519943295 },
|
| 6704 |
|
|
{ 0.33917623046949996, 0.30000000000000004, 0.80000000000000004,
|
| 6705 |
|
|
0.34906585039886590 },
|
| 6706 |
|
|
{ 0.49307204894329176, 0.30000000000000004, 0.80000000000000004,
|
| 6707 |
|
|
0.52359877559829882 },
|
| 6708 |
|
|
{ 0.63337802830291723, 0.30000000000000004, 0.80000000000000004,
|
| 6709 |
|
|
0.69813170079773179 },
|
| 6710 |
|
|
{ 0.76104540997689407, 0.30000000000000004, 0.80000000000000004,
|
| 6711 |
|
|
0.87266462599716477 },
|
| 6712 |
|
|
{ 0.87832009635450736, 0.30000000000000004, 0.80000000000000004,
|
| 6713 |
|
|
1.0471975511965976 },
|
| 6714 |
|
|
{ 0.98787879723171790, 0.30000000000000004, 0.80000000000000004,
|
| 6715 |
|
|
1.2217304763960306 },
|
| 6716 |
|
|
{ 1.0924036340069336, 0.30000000000000004, 0.80000000000000004,
|
| 6717 |
|
|
1.3962634015954636 },
|
| 6718 |
|
|
{ 1.1944567571590046, 0.30000000000000004, 0.80000000000000004,
|
| 6719 |
|
|
1.5707963267948966 },
|
| 6720 |
|
|
};
|
| 6721 |
|
|
|
| 6722 |
|
|
// Test function for k=0.30000000000000004, nu=0.80000000000000004.
|
| 6723 |
|
|
template <typename Tp>
|
| 6724 |
|
|
void test129()
|
| 6725 |
|
|
{
|
| 6726 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6727 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6728 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6729 |
|
|
unsigned int num_datum = sizeof(data129)
|
| 6730 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6731 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6732 |
|
|
{
|
| 6733 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data129[i].k), Tp(data129[i].nu),
|
| 6734 |
|
|
Tp(data129[i].phi));
|
| 6735 |
|
|
const Tp f0 = data129[i].f0;
|
| 6736 |
|
|
const Tp diff = f - f0;
|
| 6737 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6738 |
|
|
max_abs_diff = std::abs(diff);
|
| 6739 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6740 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6741 |
|
|
{
|
| 6742 |
|
|
const Tp frac = diff / f0;
|
| 6743 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6744 |
|
|
max_abs_frac = std::abs(frac);
|
| 6745 |
|
|
}
|
| 6746 |
|
|
}
|
| 6747 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6748 |
|
|
}
|
| 6749 |
|
|
|
| 6750 |
|
|
// Test data for k=0.30000000000000004, nu=0.90000000000000002.
|
| 6751 |
|
|
testcase_ellint_3<double> data130[] = {
|
| 6752 |
|
|
{ -0.0000000000000000, 0.30000000000000004, 0.90000000000000002,
|
| 6753 |
|
|
0.0000000000000000 },
|
| 6754 |
|
|
{ 0.17305109924485948, 0.30000000000000004, 0.90000000000000002,
|
| 6755 |
|
|
0.17453292519943295 },
|
| 6756 |
|
|
{ 0.33793890239556984, 0.30000000000000004, 0.90000000000000002,
|
| 6757 |
|
|
0.34906585039886590 },
|
| 6758 |
|
|
{ 0.48947218005089738, 0.30000000000000004, 0.90000000000000002,
|
| 6759 |
|
|
0.52359877559829882 },
|
| 6760 |
|
|
{ 0.62623332340775151, 0.30000000000000004, 0.90000000000000002,
|
| 6761 |
|
|
0.69813170079773179 },
|
| 6762 |
|
|
{ 0.74951596581511148, 0.30000000000000004, 0.90000000000000002,
|
| 6763 |
|
|
0.87266462599716477 },
|
| 6764 |
|
|
{ 0.86189886597756005, 0.30000000000000004, 0.90000000000000002,
|
| 6765 |
|
|
1.0471975511965976 },
|
| 6766 |
|
|
{ 0.96629451153092005, 0.30000000000000004, 0.90000000000000002,
|
| 6767 |
|
|
1.2217304763960306 },
|
| 6768 |
|
|
{ 1.0655269133492680, 0.30000000000000004, 0.90000000000000002,
|
| 6769 |
|
|
1.3962634015954636 },
|
| 6770 |
|
|
{ 1.1622376896064912, 0.30000000000000004, 0.90000000000000002,
|
| 6771 |
|
|
1.5707963267948966 },
|
| 6772 |
|
|
};
|
| 6773 |
|
|
|
| 6774 |
|
|
// Test function for k=0.30000000000000004, nu=0.90000000000000002.
|
| 6775 |
|
|
template <typename Tp>
|
| 6776 |
|
|
void test130()
|
| 6777 |
|
|
{
|
| 6778 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6779 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6780 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6781 |
|
|
unsigned int num_datum = sizeof(data130)
|
| 6782 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6783 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6784 |
|
|
{
|
| 6785 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data130[i].k), Tp(data130[i].nu),
|
| 6786 |
|
|
Tp(data130[i].phi));
|
| 6787 |
|
|
const Tp f0 = data130[i].f0;
|
| 6788 |
|
|
const Tp diff = f - f0;
|
| 6789 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6790 |
|
|
max_abs_diff = std::abs(diff);
|
| 6791 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6792 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6793 |
|
|
{
|
| 6794 |
|
|
const Tp frac = diff / f0;
|
| 6795 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6796 |
|
|
max_abs_frac = std::abs(frac);
|
| 6797 |
|
|
}
|
| 6798 |
|
|
}
|
| 6799 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6800 |
|
|
}
|
| 6801 |
|
|
|
| 6802 |
|
|
// Test data for k=0.39999999999999991, nu=0.0000000000000000.
|
| 6803 |
|
|
testcase_ellint_3<double> data131[] = {
|
| 6804 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.0000000000000000,
|
| 6805 |
|
|
0.0000000000000000 },
|
| 6806 |
|
|
{ 0.17467414669441531, 0.39999999999999991, 0.0000000000000000,
|
| 6807 |
|
|
0.17453292519943295 },
|
| 6808 |
|
|
{ 0.35018222772483443, 0.39999999999999991, 0.0000000000000000,
|
| 6809 |
|
|
0.34906585039886590 },
|
| 6810 |
|
|
{ 0.52729015917508748, 0.39999999999999991, 0.0000000000000000,
|
| 6811 |
|
|
0.52359877559829882 },
|
| 6812 |
|
|
{ 0.70662374407341255, 0.39999999999999991, 0.0000000000000000,
|
| 6813 |
|
|
0.69813170079773179 },
|
| 6814 |
|
|
{ 0.88859210497602170, 0.39999999999999991, 0.0000000000000000,
|
| 6815 |
|
|
0.87266462599716477 },
|
| 6816 |
|
|
{ 1.0733136290471379, 0.39999999999999991, 0.0000000000000000,
|
| 6817 |
|
|
1.0471975511965976 },
|
| 6818 |
|
|
{ 1.2605612170157061, 0.39999999999999991, 0.0000000000000000,
|
| 6819 |
|
|
1.2217304763960306 },
|
| 6820 |
|
|
{ 1.4497513956433437, 0.39999999999999991, 0.0000000000000000,
|
| 6821 |
|
|
1.3962634015954636 },
|
| 6822 |
|
|
{ 1.6399998658645112, 0.39999999999999991, 0.0000000000000000,
|
| 6823 |
|
|
1.5707963267948966 },
|
| 6824 |
|
|
};
|
| 6825 |
|
|
|
| 6826 |
|
|
// Test function for k=0.39999999999999991, nu=0.0000000000000000.
|
| 6827 |
|
|
template <typename Tp>
|
| 6828 |
|
|
void test131()
|
| 6829 |
|
|
{
|
| 6830 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6831 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6832 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6833 |
|
|
unsigned int num_datum = sizeof(data131)
|
| 6834 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6835 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6836 |
|
|
{
|
| 6837 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data131[i].k), Tp(data131[i].nu),
|
| 6838 |
|
|
Tp(data131[i].phi));
|
| 6839 |
|
|
const Tp f0 = data131[i].f0;
|
| 6840 |
|
|
const Tp diff = f - f0;
|
| 6841 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6842 |
|
|
max_abs_diff = std::abs(diff);
|
| 6843 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6844 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6845 |
|
|
{
|
| 6846 |
|
|
const Tp frac = diff / f0;
|
| 6847 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6848 |
|
|
max_abs_frac = std::abs(frac);
|
| 6849 |
|
|
}
|
| 6850 |
|
|
}
|
| 6851 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6852 |
|
|
}
|
| 6853 |
|
|
|
| 6854 |
|
|
// Test data for k=0.39999999999999991, nu=0.10000000000000001.
|
| 6855 |
|
|
testcase_ellint_3<double> data132[] = {
|
| 6856 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.10000000000000001,
|
| 6857 |
|
|
0.0000000000000000 },
|
| 6858 |
|
|
{ 0.17449806706684673, 0.39999999999999991, 0.10000000000000001,
|
| 6859 |
|
|
0.17453292519943295 },
|
| 6860 |
|
|
{ 0.34880048623856075, 0.39999999999999991, 0.10000000000000001,
|
| 6861 |
|
|
0.34906585039886590 },
|
| 6862 |
|
|
{ 0.52277322065757403, 0.39999999999999991, 0.10000000000000001,
|
| 6863 |
|
|
0.52359877559829882 },
|
| 6864 |
|
|
{ 0.69638072056918376, 0.39999999999999991, 0.10000000000000001,
|
| 6865 |
|
|
0.69813170079773179 },
|
| 6866 |
|
|
{ 0.86968426619831540, 0.39999999999999991, 0.10000000000000001,
|
| 6867 |
|
|
0.87266462599716477 },
|
| 6868 |
|
|
{ 1.0428044206578095, 0.39999999999999991, 0.10000000000000001,
|
| 6869 |
|
|
1.0471975511965976 },
|
| 6870 |
|
|
{ 1.2158651158274378, 0.39999999999999991, 0.10000000000000001,
|
| 6871 |
|
|
1.2217304763960306 },
|
| 6872 |
|
|
{ 1.3889447129893322, 0.39999999999999991, 0.10000000000000001,
|
| 6873 |
|
|
1.3962634015954636 },
|
| 6874 |
|
|
{ 1.5620566886683604, 0.39999999999999991, 0.10000000000000001,
|
| 6875 |
|
|
1.5707963267948966 },
|
| 6876 |
|
|
};
|
| 6877 |
|
|
|
| 6878 |
|
|
// Test function for k=0.39999999999999991, nu=0.10000000000000001.
|
| 6879 |
|
|
template <typename Tp>
|
| 6880 |
|
|
void test132()
|
| 6881 |
|
|
{
|
| 6882 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6883 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6884 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6885 |
|
|
unsigned int num_datum = sizeof(data132)
|
| 6886 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6887 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6888 |
|
|
{
|
| 6889 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data132[i].k), Tp(data132[i].nu),
|
| 6890 |
|
|
Tp(data132[i].phi));
|
| 6891 |
|
|
const Tp f0 = data132[i].f0;
|
| 6892 |
|
|
const Tp diff = f - f0;
|
| 6893 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6894 |
|
|
max_abs_diff = std::abs(diff);
|
| 6895 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6896 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6897 |
|
|
{
|
| 6898 |
|
|
const Tp frac = diff / f0;
|
| 6899 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6900 |
|
|
max_abs_frac = std::abs(frac);
|
| 6901 |
|
|
}
|
| 6902 |
|
|
}
|
| 6903 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6904 |
|
|
}
|
| 6905 |
|
|
|
| 6906 |
|
|
// Test data for k=0.39999999999999991, nu=0.20000000000000001.
|
| 6907 |
|
|
testcase_ellint_3<double> data133[] = {
|
| 6908 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.20000000000000001,
|
| 6909 |
|
|
0.0000000000000000 },
|
| 6910 |
|
|
{ 0.17432262290723399, 0.39999999999999991, 0.20000000000000001,
|
| 6911 |
|
|
0.17453292519943295 },
|
| 6912 |
|
|
{ 0.34743795258968596, 0.39999999999999991, 0.20000000000000001,
|
| 6913 |
|
|
0.34906585039886590 },
|
| 6914 |
|
|
{ 0.51838919472805123, 0.39999999999999991, 0.20000000000000001,
|
| 6915 |
|
|
0.52359877559829882 },
|
| 6916 |
|
|
{ 0.68663134739057918, 0.39999999999999991, 0.20000000000000001,
|
| 6917 |
|
|
0.69813170079773179 },
|
| 6918 |
|
|
{ 0.85206432981833979, 0.39999999999999991, 0.20000000000000001,
|
| 6919 |
|
|
0.87266462599716477 },
|
| 6920 |
|
|
{ 1.0149595349004430, 0.39999999999999991, 0.20000000000000001,
|
| 6921 |
|
|
1.0471975511965976 },
|
| 6922 |
|
|
{ 1.1758349405464676, 0.39999999999999991, 0.20000000000000001,
|
| 6923 |
|
|
1.2217304763960306 },
|
| 6924 |
|
|
{ 1.3353337673882635, 0.39999999999999991, 0.20000000000000001,
|
| 6925 |
|
|
1.3962634015954636 },
|
| 6926 |
|
|
{ 1.4941414344266770, 0.39999999999999991, 0.20000000000000001,
|
| 6927 |
|
|
1.5707963267948966 },
|
| 6928 |
|
|
};
|
| 6929 |
|
|
|
| 6930 |
|
|
// Test function for k=0.39999999999999991, nu=0.20000000000000001.
|
| 6931 |
|
|
template <typename Tp>
|
| 6932 |
|
|
void test133()
|
| 6933 |
|
|
{
|
| 6934 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6935 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6936 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6937 |
|
|
unsigned int num_datum = sizeof(data133)
|
| 6938 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6939 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6940 |
|
|
{
|
| 6941 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data133[i].k), Tp(data133[i].nu),
|
| 6942 |
|
|
Tp(data133[i].phi));
|
| 6943 |
|
|
const Tp f0 = data133[i].f0;
|
| 6944 |
|
|
const Tp diff = f - f0;
|
| 6945 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6946 |
|
|
max_abs_diff = std::abs(diff);
|
| 6947 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 6948 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 6949 |
|
|
{
|
| 6950 |
|
|
const Tp frac = diff / f0;
|
| 6951 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 6952 |
|
|
max_abs_frac = std::abs(frac);
|
| 6953 |
|
|
}
|
| 6954 |
|
|
}
|
| 6955 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 6956 |
|
|
}
|
| 6957 |
|
|
|
| 6958 |
|
|
// Test data for k=0.39999999999999991, nu=0.29999999999999999.
|
| 6959 |
|
|
testcase_ellint_3<double> data134[] = {
|
| 6960 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.29999999999999999,
|
| 6961 |
|
|
0.0000000000000000 },
|
| 6962 |
|
|
{ 0.17414781013591543, 0.39999999999999991, 0.29999999999999999,
|
| 6963 |
|
|
0.17453292519943295 },
|
| 6964 |
|
|
{ 0.34609415696777285, 0.39999999999999991, 0.29999999999999999,
|
| 6965 |
|
|
0.34906585039886590 },
|
| 6966 |
|
|
{ 0.51413131295862546, 0.39999999999999991, 0.29999999999999999,
|
| 6967 |
|
|
0.52359877559829882 },
|
| 6968 |
|
|
{ 0.67733527622935630, 0.39999999999999991, 0.29999999999999999,
|
| 6969 |
|
|
0.69813170079773179 },
|
| 6970 |
|
|
{ 0.83558675182733266, 0.39999999999999991, 0.29999999999999999,
|
| 6971 |
|
|
0.87266462599716477 },
|
| 6972 |
|
|
{ 0.98940140808865906, 0.39999999999999991, 0.29999999999999999,
|
| 6973 |
|
|
1.0471975511965976 },
|
| 6974 |
|
|
{ 1.1396968797728058, 0.39999999999999991, 0.29999999999999999,
|
| 6975 |
|
|
1.2217304763960306 },
|
| 6976 |
|
|
{ 1.2875920037865087, 0.39999999999999991, 0.29999999999999999,
|
| 6977 |
|
|
1.3962634015954636 },
|
| 6978 |
|
|
{ 1.4342789859950078, 0.39999999999999991, 0.29999999999999999,
|
| 6979 |
|
|
1.5707963267948966 },
|
| 6980 |
|
|
};
|
| 6981 |
|
|
|
| 6982 |
|
|
// Test function for k=0.39999999999999991, nu=0.29999999999999999.
|
| 6983 |
|
|
template <typename Tp>
|
| 6984 |
|
|
void test134()
|
| 6985 |
|
|
{
|
| 6986 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 6987 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 6988 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 6989 |
|
|
unsigned int num_datum = sizeof(data134)
|
| 6990 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 6991 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 6992 |
|
|
{
|
| 6993 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data134[i].k), Tp(data134[i].nu),
|
| 6994 |
|
|
Tp(data134[i].phi));
|
| 6995 |
|
|
const Tp f0 = data134[i].f0;
|
| 6996 |
|
|
const Tp diff = f - f0;
|
| 6997 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 6998 |
|
|
max_abs_diff = std::abs(diff);
|
| 6999 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7000 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7001 |
|
|
{
|
| 7002 |
|
|
const Tp frac = diff / f0;
|
| 7003 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7004 |
|
|
max_abs_frac = std::abs(frac);
|
| 7005 |
|
|
}
|
| 7006 |
|
|
}
|
| 7007 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7008 |
|
|
}
|
| 7009 |
|
|
|
| 7010 |
|
|
// Test data for k=0.39999999999999991, nu=0.40000000000000002.
|
| 7011 |
|
|
testcase_ellint_3<double> data135[] = {
|
| 7012 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.40000000000000002,
|
| 7013 |
|
|
0.0000000000000000 },
|
| 7014 |
|
|
{ 0.17397362471112710, 0.39999999999999991, 0.40000000000000002,
|
| 7015 |
|
|
0.17453292519943295 },
|
| 7016 |
|
|
{ 0.34476864603333196, 0.39999999999999991, 0.40000000000000002,
|
| 7017 |
|
|
0.34906585039886590 },
|
| 7018 |
|
|
{ 0.50999329415379357, 0.39999999999999991, 0.40000000000000002,
|
| 7019 |
|
|
0.52359877559829882 },
|
| 7020 |
|
|
{ 0.66845674551396017, 0.39999999999999991, 0.40000000000000002,
|
| 7021 |
|
|
0.69813170079773179 },
|
| 7022 |
|
|
{ 0.82012848346231748, 0.39999999999999991, 0.40000000000000002,
|
| 7023 |
|
|
0.87266462599716477 },
|
| 7024 |
|
|
{ 0.96582449258349057, 0.39999999999999991, 0.40000000000000002,
|
| 7025 |
|
|
1.0471975511965976 },
|
| 7026 |
|
|
{ 1.1068473749476286, 0.39999999999999991, 0.40000000000000002,
|
| 7027 |
|
|
1.2217304763960306 },
|
| 7028 |
|
|
{ 1.2447132729159986, 0.39999999999999991, 0.40000000000000002,
|
| 7029 |
|
|
1.3962634015954636 },
|
| 7030 |
|
|
{ 1.3809986210732901, 0.39999999999999991, 0.40000000000000002,
|
| 7031 |
|
|
1.5707963267948966 },
|
| 7032 |
|
|
};
|
| 7033 |
|
|
|
| 7034 |
|
|
// Test function for k=0.39999999999999991, nu=0.40000000000000002.
|
| 7035 |
|
|
template <typename Tp>
|
| 7036 |
|
|
void test135()
|
| 7037 |
|
|
{
|
| 7038 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7039 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7040 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7041 |
|
|
unsigned int num_datum = sizeof(data135)
|
| 7042 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7043 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7044 |
|
|
{
|
| 7045 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data135[i].k), Tp(data135[i].nu),
|
| 7046 |
|
|
Tp(data135[i].phi));
|
| 7047 |
|
|
const Tp f0 = data135[i].f0;
|
| 7048 |
|
|
const Tp diff = f - f0;
|
| 7049 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7050 |
|
|
max_abs_diff = std::abs(diff);
|
| 7051 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7052 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7053 |
|
|
{
|
| 7054 |
|
|
const Tp frac = diff / f0;
|
| 7055 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7056 |
|
|
max_abs_frac = std::abs(frac);
|
| 7057 |
|
|
}
|
| 7058 |
|
|
}
|
| 7059 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7060 |
|
|
}
|
| 7061 |
|
|
|
| 7062 |
|
|
// Test data for k=0.39999999999999991, nu=0.50000000000000000.
|
| 7063 |
|
|
testcase_ellint_3<double> data136[] = {
|
| 7064 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.50000000000000000,
|
| 7065 |
|
|
0.0000000000000000 },
|
| 7066 |
|
|
{ 0.17380006262854139, 0.39999999999999991, 0.50000000000000000,
|
| 7067 |
|
|
0.17453292519943295 },
|
| 7068 |
|
|
{ 0.34346098216756610, 0.39999999999999991, 0.50000000000000000,
|
| 7069 |
|
|
0.34906585039886590 },
|
| 7070 |
|
|
{ 0.50596929935059420, 0.39999999999999991, 0.50000000000000000,
|
| 7071 |
|
|
0.52359877559829882 },
|
| 7072 |
|
|
{ 0.65996392089131262, 0.39999999999999991, 0.50000000000000000,
|
| 7073 |
|
|
0.69813170079773179 },
|
| 7074 |
|
|
{ 0.80558463511364786, 0.39999999999999991, 0.50000000000000000,
|
| 7075 |
|
|
0.87266462599716477 },
|
| 7076 |
|
|
{ 0.94397834522857704, 0.39999999999999991, 0.50000000000000000,
|
| 7077 |
|
|
1.0471975511965976 },
|
| 7078 |
|
|
{ 1.0768075114108115, 0.39999999999999991, 0.50000000000000000,
|
| 7079 |
|
|
1.2217304763960306 },
|
| 7080 |
|
|
{ 1.2059184624251329, 0.39999999999999991, 0.50000000000000000,
|
| 7081 |
|
|
1.3962634015954636 },
|
| 7082 |
|
|
{ 1.3331797176377398, 0.39999999999999991, 0.50000000000000000,
|
| 7083 |
|
|
1.5707963267948966 },
|
| 7084 |
|
|
};
|
| 7085 |
|
|
|
| 7086 |
|
|
// Test function for k=0.39999999999999991, nu=0.50000000000000000.
|
| 7087 |
|
|
template <typename Tp>
|
| 7088 |
|
|
void test136()
|
| 7089 |
|
|
{
|
| 7090 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7091 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7092 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7093 |
|
|
unsigned int num_datum = sizeof(data136)
|
| 7094 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7095 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7096 |
|
|
{
|
| 7097 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data136[i].k), Tp(data136[i].nu),
|
| 7098 |
|
|
Tp(data136[i].phi));
|
| 7099 |
|
|
const Tp f0 = data136[i].f0;
|
| 7100 |
|
|
const Tp diff = f - f0;
|
| 7101 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7102 |
|
|
max_abs_diff = std::abs(diff);
|
| 7103 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7104 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7105 |
|
|
{
|
| 7106 |
|
|
const Tp frac = diff / f0;
|
| 7107 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7108 |
|
|
max_abs_frac = std::abs(frac);
|
| 7109 |
|
|
}
|
| 7110 |
|
|
}
|
| 7111 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7112 |
|
|
}
|
| 7113 |
|
|
|
| 7114 |
|
|
// Test data for k=0.39999999999999991, nu=0.59999999999999998.
|
| 7115 |
|
|
testcase_ellint_3<double> data137[] = {
|
| 7116 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.59999999999999998,
|
| 7117 |
|
|
0.0000000000000000 },
|
| 7118 |
|
|
{ 0.17362711992081248, 0.39999999999999991, 0.59999999999999998,
|
| 7119 |
|
|
0.17453292519943295 },
|
| 7120 |
|
|
{ 0.34217074276403953, 0.39999999999999991, 0.59999999999999998,
|
| 7121 |
|
|
0.34906585039886590 },
|
| 7122 |
|
|
{ 0.50205389185761617, 0.39999999999999991, 0.59999999999999998,
|
| 7123 |
|
|
0.52359877559829882 },
|
| 7124 |
|
|
{ 0.65182834920372745, 0.39999999999999991, 0.59999999999999998,
|
| 7125 |
|
|
0.69813170079773179 },
|
| 7126 |
|
|
{ 0.79186512820565136, 0.39999999999999991, 0.59999999999999998,
|
| 7127 |
|
|
0.87266462599716477 },
|
| 7128 |
|
|
{ 0.92365535916287134, 0.39999999999999991, 0.59999999999999998,
|
| 7129 |
|
|
1.0471975511965976 },
|
| 7130 |
|
|
{ 1.0491915663957907, 0.39999999999999991, 0.59999999999999998,
|
| 7131 |
|
|
1.2217304763960306 },
|
| 7132 |
|
|
{ 1.1705934291745104, 0.39999999999999991, 0.59999999999999998,
|
| 7133 |
|
|
1.3962634015954636 },
|
| 7134 |
|
|
{ 1.2899514672527024, 0.39999999999999991, 0.59999999999999998,
|
| 7135 |
|
|
1.5707963267948966 },
|
| 7136 |
|
|
};
|
| 7137 |
|
|
|
| 7138 |
|
|
// Test function for k=0.39999999999999991, nu=0.59999999999999998.
|
| 7139 |
|
|
template <typename Tp>
|
| 7140 |
|
|
void test137()
|
| 7141 |
|
|
{
|
| 7142 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7143 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7144 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7145 |
|
|
unsigned int num_datum = sizeof(data137)
|
| 7146 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7147 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7148 |
|
|
{
|
| 7149 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data137[i].k), Tp(data137[i].nu),
|
| 7150 |
|
|
Tp(data137[i].phi));
|
| 7151 |
|
|
const Tp f0 = data137[i].f0;
|
| 7152 |
|
|
const Tp diff = f - f0;
|
| 7153 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7154 |
|
|
max_abs_diff = std::abs(diff);
|
| 7155 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7156 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7157 |
|
|
{
|
| 7158 |
|
|
const Tp frac = diff / f0;
|
| 7159 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7160 |
|
|
max_abs_frac = std::abs(frac);
|
| 7161 |
|
|
}
|
| 7162 |
|
|
}
|
| 7163 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7164 |
|
|
}
|
| 7165 |
|
|
|
| 7166 |
|
|
// Test data for k=0.39999999999999991, nu=0.69999999999999996.
|
| 7167 |
|
|
testcase_ellint_3<double> data138[] = {
|
| 7168 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.69999999999999996,
|
| 7169 |
|
|
0.0000000000000000 },
|
| 7170 |
|
|
{ 0.17345479265712871, 0.39999999999999991, 0.69999999999999996,
|
| 7171 |
|
|
0.17453292519943295 },
|
| 7172 |
|
|
{ 0.34089751955950354, 0.39999999999999991, 0.69999999999999996,
|
| 7173 |
|
|
0.34906585039886590 },
|
| 7174 |
|
|
{ 0.49824200167361343, 0.39999999999999991, 0.69999999999999996,
|
| 7175 |
|
|
0.52359877559829882 },
|
| 7176 |
|
|
{ 0.64402450341199413, 0.39999999999999991, 0.69999999999999996,
|
| 7177 |
|
|
0.69813170079773179 },
|
| 7178 |
|
|
{ 0.77889207804122873, 0.39999999999999991, 0.69999999999999996,
|
| 7179 |
|
|
0.87266462599716477 },
|
| 7180 |
|
|
{ 0.90468169720957992, 0.39999999999999991, 0.69999999999999996,
|
| 7181 |
|
|
1.0471975511965976 },
|
| 7182 |
|
|
{ 1.0236847823692916, 0.39999999999999991, 0.69999999999999996,
|
| 7183 |
|
|
1.2217304763960306 },
|
| 7184 |
|
|
{ 1.1382465247425164, 0.39999999999999991, 0.69999999999999996,
|
| 7185 |
|
|
1.3962634015954636 },
|
| 7186 |
|
|
{ 1.2506255923253344, 0.39999999999999991, 0.69999999999999996,
|
| 7187 |
|
|
1.5707963267948966 },
|
| 7188 |
|
|
};
|
| 7189 |
|
|
|
| 7190 |
|
|
// Test function for k=0.39999999999999991, nu=0.69999999999999996.
|
| 7191 |
|
|
template <typename Tp>
|
| 7192 |
|
|
void test138()
|
| 7193 |
|
|
{
|
| 7194 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7195 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7196 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7197 |
|
|
unsigned int num_datum = sizeof(data138)
|
| 7198 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7199 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7200 |
|
|
{
|
| 7201 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data138[i].k), Tp(data138[i].nu),
|
| 7202 |
|
|
Tp(data138[i].phi));
|
| 7203 |
|
|
const Tp f0 = data138[i].f0;
|
| 7204 |
|
|
const Tp diff = f - f0;
|
| 7205 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7206 |
|
|
max_abs_diff = std::abs(diff);
|
| 7207 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7208 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7209 |
|
|
{
|
| 7210 |
|
|
const Tp frac = diff / f0;
|
| 7211 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7212 |
|
|
max_abs_frac = std::abs(frac);
|
| 7213 |
|
|
}
|
| 7214 |
|
|
}
|
| 7215 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7216 |
|
|
}
|
| 7217 |
|
|
|
| 7218 |
|
|
// Test data for k=0.39999999999999991, nu=0.80000000000000004.
|
| 7219 |
|
|
testcase_ellint_3<double> data139[] = {
|
| 7220 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.80000000000000004,
|
| 7221 |
|
|
0.0000000000000000 },
|
| 7222 |
|
|
{ 0.17328307694277156, 0.39999999999999991, 0.80000000000000004,
|
| 7223 |
|
|
0.17453292519943295 },
|
| 7224 |
|
|
{ 0.33964091800132007, 0.39999999999999991, 0.80000000000000004,
|
| 7225 |
|
|
0.34906585039886590 },
|
| 7226 |
|
|
{ 0.49452889372467451, 0.39999999999999991, 0.80000000000000004,
|
| 7227 |
|
|
0.52359877559829882 },
|
| 7228 |
|
|
{ 0.63652940095937327, 0.39999999999999991, 0.80000000000000004,
|
| 7229 |
|
|
0.69813170079773179 },
|
| 7230 |
|
|
{ 0.76659772511159097, 0.39999999999999991, 0.80000000000000004,
|
| 7231 |
|
|
0.87266462599716477 },
|
| 7232 |
|
|
{ 0.88691047977338111, 0.39999999999999991, 0.80000000000000004,
|
| 7233 |
|
|
1.0471975511965976 },
|
| 7234 |
|
|
{ 1.0000273200611640, 0.39999999999999991, 0.80000000000000004,
|
| 7235 |
|
|
1.2217304763960306 },
|
| 7236 |
|
|
{ 1.1084787902188007, 0.39999999999999991, 0.80000000000000004,
|
| 7237 |
|
|
1.3962634015954636 },
|
| 7238 |
|
|
{ 1.2146499565727209, 0.39999999999999991, 0.80000000000000004,
|
| 7239 |
|
|
1.5707963267948966 },
|
| 7240 |
|
|
};
|
| 7241 |
|
|
|
| 7242 |
|
|
// Test function for k=0.39999999999999991, nu=0.80000000000000004.
|
| 7243 |
|
|
template <typename Tp>
|
| 7244 |
|
|
void test139()
|
| 7245 |
|
|
{
|
| 7246 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7247 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7248 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7249 |
|
|
unsigned int num_datum = sizeof(data139)
|
| 7250 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7251 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7252 |
|
|
{
|
| 7253 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data139[i].k), Tp(data139[i].nu),
|
| 7254 |
|
|
Tp(data139[i].phi));
|
| 7255 |
|
|
const Tp f0 = data139[i].f0;
|
| 7256 |
|
|
const Tp diff = f - f0;
|
| 7257 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7258 |
|
|
max_abs_diff = std::abs(diff);
|
| 7259 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7260 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7261 |
|
|
{
|
| 7262 |
|
|
const Tp frac = diff / f0;
|
| 7263 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7264 |
|
|
max_abs_frac = std::abs(frac);
|
| 7265 |
|
|
}
|
| 7266 |
|
|
}
|
| 7267 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7268 |
|
|
}
|
| 7269 |
|
|
|
| 7270 |
|
|
// Test data for k=0.39999999999999991, nu=0.90000000000000002.
|
| 7271 |
|
|
testcase_ellint_3<double> data140[] = {
|
| 7272 |
|
|
{ -0.0000000000000000, 0.39999999999999991, 0.90000000000000002,
|
| 7273 |
|
|
0.0000000000000000 },
|
| 7274 |
|
|
{ 0.17311196891868130, 0.39999999999999991, 0.90000000000000002,
|
| 7275 |
|
|
0.17453292519943295 },
|
| 7276 |
|
|
{ 0.33840055664911906, 0.39999999999999991, 0.90000000000000002,
|
| 7277 |
|
|
0.34906585039886590 },
|
| 7278 |
|
|
{ 0.49091013944075340, 0.39999999999999991, 0.90000000000000002,
|
| 7279 |
|
|
0.52359877559829882 },
|
| 7280 |
|
|
{ 0.62932228186809591, 0.39999999999999991, 0.90000000000000002,
|
| 7281 |
|
|
0.69813170079773179 },
|
| 7282 |
|
|
{ 0.75492278323019801, 0.39999999999999991, 0.90000000000000002,
|
| 7283 |
|
|
0.87266462599716477 },
|
| 7284 |
|
|
{ 0.87021659043854294, 0.39999999999999991, 0.90000000000000002,
|
| 7285 |
|
|
1.0471975511965976 },
|
| 7286 |
|
|
{ 0.97800245228239246, 0.39999999999999991, 0.90000000000000002,
|
| 7287 |
|
|
1.2217304763960306 },
|
| 7288 |
|
|
{ 1.0809625773173694, 0.39999999999999991, 0.90000000000000002,
|
| 7289 |
|
|
1.3962634015954636 },
|
| 7290 |
|
|
{ 1.1815758115929846, 0.39999999999999991, 0.90000000000000002,
|
| 7291 |
|
|
1.5707963267948966 },
|
| 7292 |
|
|
};
|
| 7293 |
|
|
|
| 7294 |
|
|
// Test function for k=0.39999999999999991, nu=0.90000000000000002.
|
| 7295 |
|
|
template <typename Tp>
|
| 7296 |
|
|
void test140()
|
| 7297 |
|
|
{
|
| 7298 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7299 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7300 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7301 |
|
|
unsigned int num_datum = sizeof(data140)
|
| 7302 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7303 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7304 |
|
|
{
|
| 7305 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data140[i].k), Tp(data140[i].nu),
|
| 7306 |
|
|
Tp(data140[i].phi));
|
| 7307 |
|
|
const Tp f0 = data140[i].f0;
|
| 7308 |
|
|
const Tp diff = f - f0;
|
| 7309 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7310 |
|
|
max_abs_diff = std::abs(diff);
|
| 7311 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7312 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7313 |
|
|
{
|
| 7314 |
|
|
const Tp frac = diff / f0;
|
| 7315 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7316 |
|
|
max_abs_frac = std::abs(frac);
|
| 7317 |
|
|
}
|
| 7318 |
|
|
}
|
| 7319 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7320 |
|
|
}
|
| 7321 |
|
|
|
| 7322 |
|
|
// Test data for k=0.50000000000000000, nu=0.0000000000000000.
|
| 7323 |
|
|
testcase_ellint_3<double> data141[] = {
|
| 7324 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.0000000000000000,
|
| 7325 |
|
|
0.0000000000000000 },
|
| 7326 |
|
|
{ 0.17475385514035785, 0.50000000000000000, 0.0000000000000000,
|
| 7327 |
|
|
0.17453292519943295 },
|
| 7328 |
|
|
{ 0.35081868470101585, 0.50000000000000000, 0.0000000000000000,
|
| 7329 |
|
|
0.34906585039886590 },
|
| 7330 |
|
|
{ 0.52942862705190585, 0.50000000000000000, 0.0000000000000000,
|
| 7331 |
|
|
0.52359877559829882 },
|
| 7332 |
|
|
{ 0.71164727562630326, 0.50000000000000000, 0.0000000000000000,
|
| 7333 |
|
|
0.69813170079773179 },
|
| 7334 |
|
|
{ 0.89824523594227768, 0.50000000000000000, 0.0000000000000000,
|
| 7335 |
|
|
0.87266462599716477 },
|
| 7336 |
|
|
{ 1.0895506700518851, 0.50000000000000000, 0.0000000000000000,
|
| 7337 |
|
|
1.0471975511965976 },
|
| 7338 |
|
|
{ 1.2853005857432933, 0.50000000000000000, 0.0000000000000000,
|
| 7339 |
|
|
1.2217304763960306 },
|
| 7340 |
|
|
{ 1.4845545520549484, 0.50000000000000000, 0.0000000000000000,
|
| 7341 |
|
|
1.3962634015954636 },
|
| 7342 |
|
|
{ 1.6857503548125963, 0.50000000000000000, 0.0000000000000000,
|
| 7343 |
|
|
1.5707963267948966 },
|
| 7344 |
|
|
};
|
| 7345 |
|
|
|
| 7346 |
|
|
// Test function for k=0.50000000000000000, nu=0.0000000000000000.
|
| 7347 |
|
|
template <typename Tp>
|
| 7348 |
|
|
void test141()
|
| 7349 |
|
|
{
|
| 7350 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7351 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7352 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7353 |
|
|
unsigned int num_datum = sizeof(data141)
|
| 7354 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7355 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7356 |
|
|
{
|
| 7357 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data141[i].k), Tp(data141[i].nu),
|
| 7358 |
|
|
Tp(data141[i].phi));
|
| 7359 |
|
|
const Tp f0 = data141[i].f0;
|
| 7360 |
|
|
const Tp diff = f - f0;
|
| 7361 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7362 |
|
|
max_abs_diff = std::abs(diff);
|
| 7363 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7364 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7365 |
|
|
{
|
| 7366 |
|
|
const Tp frac = diff / f0;
|
| 7367 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7368 |
|
|
max_abs_frac = std::abs(frac);
|
| 7369 |
|
|
}
|
| 7370 |
|
|
}
|
| 7371 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7372 |
|
|
}
|
| 7373 |
|
|
|
| 7374 |
|
|
// Test data for k=0.50000000000000000, nu=0.10000000000000001.
|
| 7375 |
|
|
testcase_ellint_3<double> data142[] = {
|
| 7376 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.10000000000000001,
|
| 7377 |
|
|
0.0000000000000000 },
|
| 7378 |
|
|
{ 0.17457763120814676, 0.50000000000000000, 0.10000000000000001,
|
| 7379 |
|
|
0.17453292519943295 },
|
| 7380 |
|
|
{ 0.34943246340849154, 0.50000000000000000, 0.10000000000000001,
|
| 7381 |
|
|
0.34906585039886590 },
|
| 7382 |
|
|
{ 0.52487937869610801, 0.50000000000000000, 0.10000000000000001,
|
| 7383 |
|
|
0.52359877559829882 },
|
| 7384 |
|
|
{ 0.70127785096388395, 0.50000000000000000, 0.10000000000000001,
|
| 7385 |
|
|
0.69813170079773179 },
|
| 7386 |
|
|
{ 0.87898815988624479, 0.50000000000000000, 0.10000000000000001,
|
| 7387 |
|
|
0.87266462599716477 },
|
| 7388 |
|
|
{ 1.0582764576094172, 0.50000000000000000, 0.10000000000000001,
|
| 7389 |
|
|
1.0471975511965976 },
|
| 7390 |
|
|
{ 1.2391936844060207, 0.50000000000000000, 0.10000000000000001,
|
| 7391 |
|
|
1.2217304763960306 },
|
| 7392 |
|
|
{ 1.4214793542995841, 0.50000000000000000, 0.10000000000000001,
|
| 7393 |
|
|
1.3962634015954636 },
|
| 7394 |
|
|
{ 1.6045524936084892, 0.50000000000000000, 0.10000000000000001,
|
| 7395 |
|
|
1.5707963267948966 },
|
| 7396 |
|
|
};
|
| 7397 |
|
|
|
| 7398 |
|
|
// Test function for k=0.50000000000000000, nu=0.10000000000000001.
|
| 7399 |
|
|
template <typename Tp>
|
| 7400 |
|
|
void test142()
|
| 7401 |
|
|
{
|
| 7402 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7403 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7404 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7405 |
|
|
unsigned int num_datum = sizeof(data142)
|
| 7406 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7407 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7408 |
|
|
{
|
| 7409 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data142[i].k), Tp(data142[i].nu),
|
| 7410 |
|
|
Tp(data142[i].phi));
|
| 7411 |
|
|
const Tp f0 = data142[i].f0;
|
| 7412 |
|
|
const Tp diff = f - f0;
|
| 7413 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7414 |
|
|
max_abs_diff = std::abs(diff);
|
| 7415 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7416 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7417 |
|
|
{
|
| 7418 |
|
|
const Tp frac = diff / f0;
|
| 7419 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7420 |
|
|
max_abs_frac = std::abs(frac);
|
| 7421 |
|
|
}
|
| 7422 |
|
|
}
|
| 7423 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7424 |
|
|
}
|
| 7425 |
|
|
|
| 7426 |
|
|
// Test data for k=0.50000000000000000, nu=0.20000000000000001.
|
| 7427 |
|
|
testcase_ellint_3<double> data143[] = {
|
| 7428 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.20000000000000001,
|
| 7429 |
|
|
0.0000000000000000 },
|
| 7430 |
|
|
{ 0.17440204336345433, 0.50000000000000000, 0.20000000000000001,
|
| 7431 |
|
|
0.17453292519943295 },
|
| 7432 |
|
|
{ 0.34806552388338824, 0.50000000000000000, 0.20000000000000001,
|
| 7433 |
|
|
0.34906585039886590 },
|
| 7434 |
|
|
{ 0.52046416757129821, 0.50000000000000000, 0.20000000000000001,
|
| 7435 |
|
|
0.52359877559829882 },
|
| 7436 |
|
|
{ 0.69140924550993876, 0.50000000000000000, 0.20000000000000001,
|
| 7437 |
|
|
0.69813170079773179 },
|
| 7438 |
|
|
{ 0.86104678636125520, 0.50000000000000000, 0.20000000000000001,
|
| 7439 |
|
|
0.87266462599716477 },
|
| 7440 |
|
|
{ 1.0297439459053981, 0.50000000000000000, 0.20000000000000001,
|
| 7441 |
|
|
1.0471975511965976 },
|
| 7442 |
|
|
{ 1.1979214112912036, 0.50000000000000000, 0.20000000000000001,
|
| 7443 |
|
|
1.2217304763960306 },
|
| 7444 |
|
|
{ 1.3659033858648930, 0.50000000000000000, 0.20000000000000001,
|
| 7445 |
|
|
1.3962634015954636 },
|
| 7446 |
|
|
{ 1.5338490483665983, 0.50000000000000000, 0.20000000000000001,
|
| 7447 |
|
|
1.5707963267948966 },
|
| 7448 |
|
|
};
|
| 7449 |
|
|
|
| 7450 |
|
|
// Test function for k=0.50000000000000000, nu=0.20000000000000001.
|
| 7451 |
|
|
template <typename Tp>
|
| 7452 |
|
|
void test143()
|
| 7453 |
|
|
{
|
| 7454 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7455 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7456 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7457 |
|
|
unsigned int num_datum = sizeof(data143)
|
| 7458 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7459 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7460 |
|
|
{
|
| 7461 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data143[i].k), Tp(data143[i].nu),
|
| 7462 |
|
|
Tp(data143[i].phi));
|
| 7463 |
|
|
const Tp f0 = data143[i].f0;
|
| 7464 |
|
|
const Tp diff = f - f0;
|
| 7465 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7466 |
|
|
max_abs_diff = std::abs(diff);
|
| 7467 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7468 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7469 |
|
|
{
|
| 7470 |
|
|
const Tp frac = diff / f0;
|
| 7471 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7472 |
|
|
max_abs_frac = std::abs(frac);
|
| 7473 |
|
|
}
|
| 7474 |
|
|
}
|
| 7475 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7476 |
|
|
}
|
| 7477 |
|
|
|
| 7478 |
|
|
// Test data for k=0.50000000000000000, nu=0.29999999999999999.
|
| 7479 |
|
|
testcase_ellint_3<double> data144[] = {
|
| 7480 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.29999999999999999,
|
| 7481 |
|
|
0.0000000000000000 },
|
| 7482 |
|
|
{ 0.17422708752228896, 0.50000000000000000, 0.29999999999999999,
|
| 7483 |
|
|
0.17453292519943295 },
|
| 7484 |
|
|
{ 0.34671739434855858, 0.50000000000000000, 0.29999999999999999,
|
| 7485 |
|
|
0.34906585039886590 },
|
| 7486 |
|
|
{ 0.51617616305641889, 0.50000000000000000, 0.29999999999999999,
|
| 7487 |
|
|
0.52359877559829882 },
|
| 7488 |
|
|
{ 0.68200047612545178, 0.50000000000000000, 0.29999999999999999,
|
| 7489 |
|
|
0.69813170079773179 },
|
| 7490 |
|
|
{ 0.84427217869498372, 0.50000000000000000, 0.29999999999999999,
|
| 7491 |
|
|
0.87266462599716477 },
|
| 7492 |
|
|
{ 1.0035637821389782, 0.50000000000000000, 0.29999999999999999,
|
| 7493 |
|
|
1.0471975511965976 },
|
| 7494 |
|
|
{ 1.1606800483933113, 0.50000000000000000, 0.29999999999999999,
|
| 7495 |
|
|
1.2217304763960306 },
|
| 7496 |
|
|
{ 1.3164407134643459, 0.50000000000000000, 0.29999999999999999,
|
| 7497 |
|
|
1.3962634015954636 },
|
| 7498 |
|
|
{ 1.4715681939859637, 0.50000000000000000, 0.29999999999999999,
|
| 7499 |
|
|
1.5707963267948966 },
|
| 7500 |
|
|
};
|
| 7501 |
|
|
|
| 7502 |
|
|
// Test function for k=0.50000000000000000, nu=0.29999999999999999.
|
| 7503 |
|
|
template <typename Tp>
|
| 7504 |
|
|
void test144()
|
| 7505 |
|
|
{
|
| 7506 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7507 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7508 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7509 |
|
|
unsigned int num_datum = sizeof(data144)
|
| 7510 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7511 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7512 |
|
|
{
|
| 7513 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data144[i].k), Tp(data144[i].nu),
|
| 7514 |
|
|
Tp(data144[i].phi));
|
| 7515 |
|
|
const Tp f0 = data144[i].f0;
|
| 7516 |
|
|
const Tp diff = f - f0;
|
| 7517 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7518 |
|
|
max_abs_diff = std::abs(diff);
|
| 7519 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7520 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7521 |
|
|
{
|
| 7522 |
|
|
const Tp frac = diff / f0;
|
| 7523 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7524 |
|
|
max_abs_frac = std::abs(frac);
|
| 7525 |
|
|
}
|
| 7526 |
|
|
}
|
| 7527 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7528 |
|
|
}
|
| 7529 |
|
|
|
| 7530 |
|
|
// Test data for k=0.50000000000000000, nu=0.40000000000000002.
|
| 7531 |
|
|
testcase_ellint_3<double> data145[] = {
|
| 7532 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.40000000000000002,
|
| 7533 |
|
|
0.0000000000000000 },
|
| 7534 |
|
|
{ 0.17405275963859917, 0.50000000000000000, 0.40000000000000002,
|
| 7535 |
|
|
0.17453292519943295 },
|
| 7536 |
|
|
{ 0.34538761957029329, 0.50000000000000000, 0.40000000000000002,
|
| 7537 |
|
|
0.34906585039886590 },
|
| 7538 |
|
|
{ 0.51200902646603919, 0.50000000000000000, 0.40000000000000002,
|
| 7539 |
|
|
0.52359877559829882 },
|
| 7540 |
|
|
{ 0.67301522212868792, 0.50000000000000000, 0.40000000000000002,
|
| 7541 |
|
|
0.69813170079773179 },
|
| 7542 |
|
|
{ 0.82853844466313320, 0.50000000000000000, 0.40000000000000002,
|
| 7543 |
|
|
0.87266462599716477 },
|
| 7544 |
|
|
{ 0.97942097862681488, 0.50000000000000000, 0.40000000000000002,
|
| 7545 |
|
|
1.0471975511965976 },
|
| 7546 |
|
|
{ 1.1268429801220616, 0.50000000000000000, 0.40000000000000002,
|
| 7547 |
|
|
1.2217304763960306 },
|
| 7548 |
|
|
{ 1.2720406704533922, 0.50000000000000000, 0.40000000000000002,
|
| 7549 |
|
|
1.3962634015954636 },
|
| 7550 |
|
|
{ 1.4161679518465340, 0.50000000000000000, 0.40000000000000002,
|
| 7551 |
|
|
1.5707963267948966 },
|
| 7552 |
|
|
};
|
| 7553 |
|
|
|
| 7554 |
|
|
// Test function for k=0.50000000000000000, nu=0.40000000000000002.
|
| 7555 |
|
|
template <typename Tp>
|
| 7556 |
|
|
void test145()
|
| 7557 |
|
|
{
|
| 7558 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7559 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7560 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7561 |
|
|
unsigned int num_datum = sizeof(data145)
|
| 7562 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7563 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7564 |
|
|
{
|
| 7565 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data145[i].k), Tp(data145[i].nu),
|
| 7566 |
|
|
Tp(data145[i].phi));
|
| 7567 |
|
|
const Tp f0 = data145[i].f0;
|
| 7568 |
|
|
const Tp diff = f - f0;
|
| 7569 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7570 |
|
|
max_abs_diff = std::abs(diff);
|
| 7571 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7572 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7573 |
|
|
{
|
| 7574 |
|
|
const Tp frac = diff / f0;
|
| 7575 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7576 |
|
|
max_abs_frac = std::abs(frac);
|
| 7577 |
|
|
}
|
| 7578 |
|
|
}
|
| 7579 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7580 |
|
|
}
|
| 7581 |
|
|
|
| 7582 |
|
|
// Test data for k=0.50000000000000000, nu=0.50000000000000000.
|
| 7583 |
|
|
testcase_ellint_3<double> data146[] = {
|
| 7584 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.50000000000000000,
|
| 7585 |
|
|
0.0000000000000000 },
|
| 7586 |
|
|
{ 0.17387905570381157, 0.50000000000000000, 0.50000000000000000,
|
| 7587 |
|
|
0.17453292519943295 },
|
| 7588 |
|
|
{ 0.34407576010465207, 0.50000000000000000, 0.50000000000000000,
|
| 7589 |
|
|
0.34906585039886590 },
|
| 7590 |
|
|
{ 0.50795686560160835, 0.50000000000000000, 0.50000000000000000,
|
| 7591 |
|
|
0.52359877559829882 },
|
| 7592 |
|
|
{ 0.66442115453330175, 0.50000000000000000, 0.50000000000000000,
|
| 7593 |
|
|
0.69813170079773179 },
|
| 7594 |
|
|
{ 0.81373829119355345, 0.50000000000000000, 0.50000000000000000,
|
| 7595 |
|
|
0.87266462599716477 },
|
| 7596 |
|
|
{ 0.95705743313235825, 0.50000000000000000, 0.50000000000000000,
|
| 7597 |
|
|
1.0471975511965976 },
|
| 7598 |
|
|
{ 1.0959131991362556, 0.50000000000000000, 0.50000000000000000,
|
| 7599 |
|
|
1.2217304763960306 },
|
| 7600 |
|
|
{ 1.2318900529754597, 0.50000000000000000, 0.50000000000000000,
|
| 7601 |
|
|
1.3962634015954636 },
|
| 7602 |
|
|
{ 1.3664739530045971, 0.50000000000000000, 0.50000000000000000,
|
| 7603 |
|
|
1.5707963267948966 },
|
| 7604 |
|
|
};
|
| 7605 |
|
|
|
| 7606 |
|
|
// Test function for k=0.50000000000000000, nu=0.50000000000000000.
|
| 7607 |
|
|
template <typename Tp>
|
| 7608 |
|
|
void test146()
|
| 7609 |
|
|
{
|
| 7610 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7611 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7612 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7613 |
|
|
unsigned int num_datum = sizeof(data146)
|
| 7614 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7615 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7616 |
|
|
{
|
| 7617 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data146[i].k), Tp(data146[i].nu),
|
| 7618 |
|
|
Tp(data146[i].phi));
|
| 7619 |
|
|
const Tp f0 = data146[i].f0;
|
| 7620 |
|
|
const Tp diff = f - f0;
|
| 7621 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7622 |
|
|
max_abs_diff = std::abs(diff);
|
| 7623 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7624 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7625 |
|
|
{
|
| 7626 |
|
|
const Tp frac = diff / f0;
|
| 7627 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7628 |
|
|
max_abs_frac = std::abs(frac);
|
| 7629 |
|
|
}
|
| 7630 |
|
|
}
|
| 7631 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7632 |
|
|
}
|
| 7633 |
|
|
|
| 7634 |
|
|
// Test data for k=0.50000000000000000, nu=0.59999999999999998.
|
| 7635 |
|
|
testcase_ellint_3<double> data147[] = {
|
| 7636 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.59999999999999998,
|
| 7637 |
|
|
0.0000000000000000 },
|
| 7638 |
|
|
{ 0.17370597174637581, 0.50000000000000000, 0.59999999999999998,
|
| 7639 |
|
|
0.17453292519943295 },
|
| 7640 |
|
|
{ 0.34278139158591414, 0.50000000000000000, 0.59999999999999998,
|
| 7641 |
|
|
0.34906585039886590 },
|
| 7642 |
|
|
{ 0.50401419439302719, 0.50000000000000000, 0.59999999999999998,
|
| 7643 |
|
|
0.52359877559829882 },
|
| 7644 |
|
|
{ 0.65618938076167221, 0.50000000000000000, 0.59999999999999998,
|
| 7645 |
|
|
0.69813170079773179 },
|
| 7646 |
|
|
{ 0.79977959248855424, 0.50000000000000000, 0.59999999999999998,
|
| 7647 |
|
|
0.87266462599716477 },
|
| 7648 |
|
|
{ 0.93625925190753545, 0.50000000000000000, 0.59999999999999998,
|
| 7649 |
|
|
1.0471975511965976 },
|
| 7650 |
|
|
{ 1.0674905658379710, 0.50000000000000000, 0.59999999999999998,
|
| 7651 |
|
|
1.2217304763960306 },
|
| 7652 |
|
|
{ 1.1953481298023048, 0.50000000000000000, 0.59999999999999998,
|
| 7653 |
|
|
1.3962634015954636 },
|
| 7654 |
|
|
{ 1.3215740290190876, 0.50000000000000000, 0.59999999999999998,
|
| 7655 |
|
|
1.5707963267948966 },
|
| 7656 |
|
|
};
|
| 7657 |
|
|
|
| 7658 |
|
|
// Test function for k=0.50000000000000000, nu=0.59999999999999998.
|
| 7659 |
|
|
template <typename Tp>
|
| 7660 |
|
|
void test147()
|
| 7661 |
|
|
{
|
| 7662 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7663 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7664 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7665 |
|
|
unsigned int num_datum = sizeof(data147)
|
| 7666 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7667 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7668 |
|
|
{
|
| 7669 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data147[i].k), Tp(data147[i].nu),
|
| 7670 |
|
|
Tp(data147[i].phi));
|
| 7671 |
|
|
const Tp f0 = data147[i].f0;
|
| 7672 |
|
|
const Tp diff = f - f0;
|
| 7673 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7674 |
|
|
max_abs_diff = std::abs(diff);
|
| 7675 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7676 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7677 |
|
|
{
|
| 7678 |
|
|
const Tp frac = diff / f0;
|
| 7679 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7680 |
|
|
max_abs_frac = std::abs(frac);
|
| 7681 |
|
|
}
|
| 7682 |
|
|
}
|
| 7683 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7684 |
|
|
}
|
| 7685 |
|
|
|
| 7686 |
|
|
// Test data for k=0.50000000000000000, nu=0.69999999999999996.
|
| 7687 |
|
|
testcase_ellint_3<double> data148[] = {
|
| 7688 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.69999999999999996,
|
| 7689 |
|
|
0.0000000000000000 },
|
| 7690 |
|
|
{ 0.17353350383131641, 0.50000000000000000, 0.69999999999999996,
|
| 7691 |
|
|
0.17453292519943295 },
|
| 7692 |
|
|
{ 0.34150410405436771, 0.50000000000000000, 0.69999999999999996,
|
| 7693 |
|
|
0.34906585039886590 },
|
| 7694 |
|
|
{ 0.50017589696443487, 0.50000000000000000, 0.69999999999999996,
|
| 7695 |
|
|
0.52359877559829882 },
|
| 7696 |
|
|
{ 0.64829398188419962, 0.50000000000000000, 0.69999999999999996,
|
| 7697 |
|
|
0.69813170079773179 },
|
| 7698 |
|
|
{ 0.78658270782402073, 0.50000000000000000, 0.69999999999999996,
|
| 7699 |
|
|
0.87266462599716477 },
|
| 7700 |
|
|
{ 0.91684738336675053, 0.50000000000000000, 0.69999999999999996,
|
| 7701 |
|
|
1.0471975511965976 },
|
| 7702 |
|
|
{ 1.0412486789555937, 0.50000000000000000, 0.69999999999999996,
|
| 7703 |
|
|
1.2217304763960306 },
|
| 7704 |
|
|
{ 1.1619021847612001, 0.50000000000000000, 0.69999999999999996,
|
| 7705 |
|
|
1.3962634015954636 },
|
| 7706 |
|
|
{ 1.2807475181182502, 0.50000000000000000, 0.69999999999999996,
|
| 7707 |
|
|
1.5707963267948966 },
|
| 7708 |
|
|
};
|
| 7709 |
|
|
|
| 7710 |
|
|
// Test function for k=0.50000000000000000, nu=0.69999999999999996.
|
| 7711 |
|
|
template <typename Tp>
|
| 7712 |
|
|
void test148()
|
| 7713 |
|
|
{
|
| 7714 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7715 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7716 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7717 |
|
|
unsigned int num_datum = sizeof(data148)
|
| 7718 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7719 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7720 |
|
|
{
|
| 7721 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data148[i].k), Tp(data148[i].nu),
|
| 7722 |
|
|
Tp(data148[i].phi));
|
| 7723 |
|
|
const Tp f0 = data148[i].f0;
|
| 7724 |
|
|
const Tp diff = f - f0;
|
| 7725 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7726 |
|
|
max_abs_diff = std::abs(diff);
|
| 7727 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7728 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7729 |
|
|
{
|
| 7730 |
|
|
const Tp frac = diff / f0;
|
| 7731 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7732 |
|
|
max_abs_frac = std::abs(frac);
|
| 7733 |
|
|
}
|
| 7734 |
|
|
}
|
| 7735 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7736 |
|
|
}
|
| 7737 |
|
|
|
| 7738 |
|
|
// Test data for k=0.50000000000000000, nu=0.80000000000000004.
|
| 7739 |
|
|
testcase_ellint_3<double> data149[] = {
|
| 7740 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.80000000000000004,
|
| 7741 |
|
|
0.0000000000000000 },
|
| 7742 |
|
|
{ 0.17336164805979126, 0.50000000000000000, 0.80000000000000004,
|
| 7743 |
|
|
0.17453292519943295 },
|
| 7744 |
|
|
{ 0.34024350132086773, 0.50000000000000000, 0.80000000000000004,
|
| 7745 |
|
|
0.34906585039886590 },
|
| 7746 |
|
|
{ 0.49643719555734084, 0.50000000000000000, 0.80000000000000004,
|
| 7747 |
|
|
0.52359877559829882 },
|
| 7748 |
|
|
{ 0.64071162456976150, 0.50000000000000000, 0.80000000000000004,
|
| 7749 |
|
|
0.69813170079773179 },
|
| 7750 |
|
|
{ 0.77407836177211908, 0.50000000000000000, 0.80000000000000004,
|
| 7751 |
|
|
0.87266462599716477 },
|
| 7752 |
|
|
{ 0.89867058251905652, 0.50000000000000000, 0.80000000000000004,
|
| 7753 |
|
|
1.0471975511965976 },
|
| 7754 |
|
|
{ 1.0169181822134912, 0.50000000000000000, 0.80000000000000004,
|
| 7755 |
|
|
1.2217304763960306 },
|
| 7756 |
|
|
{ 1.1311363312779448, 0.50000000000000000, 0.80000000000000004,
|
| 7757 |
|
|
1.3962634015954636 },
|
| 7758 |
|
|
{ 1.2434165408189539, 0.50000000000000000, 0.80000000000000004,
|
| 7759 |
|
|
1.5707963267948966 },
|
| 7760 |
|
|
};
|
| 7761 |
|
|
|
| 7762 |
|
|
// Test function for k=0.50000000000000000, nu=0.80000000000000004.
|
| 7763 |
|
|
template <typename Tp>
|
| 7764 |
|
|
void test149()
|
| 7765 |
|
|
{
|
| 7766 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7767 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7768 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7769 |
|
|
unsigned int num_datum = sizeof(data149)
|
| 7770 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7771 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7772 |
|
|
{
|
| 7773 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data149[i].k), Tp(data149[i].nu),
|
| 7774 |
|
|
Tp(data149[i].phi));
|
| 7775 |
|
|
const Tp f0 = data149[i].f0;
|
| 7776 |
|
|
const Tp diff = f - f0;
|
| 7777 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7778 |
|
|
max_abs_diff = std::abs(diff);
|
| 7779 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7780 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7781 |
|
|
{
|
| 7782 |
|
|
const Tp frac = diff / f0;
|
| 7783 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7784 |
|
|
max_abs_frac = std::abs(frac);
|
| 7785 |
|
|
}
|
| 7786 |
|
|
}
|
| 7787 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7788 |
|
|
}
|
| 7789 |
|
|
|
| 7790 |
|
|
// Test data for k=0.50000000000000000, nu=0.90000000000000002.
|
| 7791 |
|
|
testcase_ellint_3<double> data150[] = {
|
| 7792 |
|
|
{ -0.0000000000000000, 0.50000000000000000, 0.90000000000000002,
|
| 7793 |
|
|
0.0000000000000000 },
|
| 7794 |
|
|
{ 0.17319040056865681, 0.50000000000000000, 0.90000000000000002,
|
| 7795 |
|
|
0.17453292519943295 },
|
| 7796 |
|
|
{ 0.33899920036578557, 0.50000000000000000, 0.90000000000000002,
|
| 7797 |
|
|
0.34906585039886590 },
|
| 7798 |
|
|
{ 0.49279362182695186, 0.50000000000000000, 0.90000000000000002,
|
| 7799 |
|
|
0.52359877559829882 },
|
| 7800 |
|
|
{ 0.63342123379746151, 0.50000000000000000, 0.90000000000000002,
|
| 7801 |
|
|
0.69813170079773179 },
|
| 7802 |
|
|
{ 0.76220595179550321, 0.50000000000000000, 0.90000000000000002,
|
| 7803 |
|
|
0.87266462599716477 },
|
| 7804 |
|
|
{ 0.88160004743532294, 0.50000000000000000, 0.90000000000000002,
|
| 7805 |
|
|
1.0471975511965976 },
|
| 7806 |
|
|
{ 0.99427448642310134, 0.50000000000000000, 0.90000000000000002,
|
| 7807 |
|
|
1.2217304763960306 },
|
| 7808 |
|
|
{ 1.1027091512470093, 0.50000000000000000, 0.90000000000000002,
|
| 7809 |
|
|
1.3962634015954636 },
|
| 7810 |
|
|
{ 1.2091116095504744, 0.50000000000000000, 0.90000000000000002,
|
| 7811 |
|
|
1.5707963267948966 },
|
| 7812 |
|
|
};
|
| 7813 |
|
|
|
| 7814 |
|
|
// Test function for k=0.50000000000000000, nu=0.90000000000000002.
|
| 7815 |
|
|
template <typename Tp>
|
| 7816 |
|
|
void test150()
|
| 7817 |
|
|
{
|
| 7818 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7819 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7820 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7821 |
|
|
unsigned int num_datum = sizeof(data150)
|
| 7822 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7823 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7824 |
|
|
{
|
| 7825 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data150[i].k), Tp(data150[i].nu),
|
| 7826 |
|
|
Tp(data150[i].phi));
|
| 7827 |
|
|
const Tp f0 = data150[i].f0;
|
| 7828 |
|
|
const Tp diff = f - f0;
|
| 7829 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7830 |
|
|
max_abs_diff = std::abs(diff);
|
| 7831 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7832 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7833 |
|
|
{
|
| 7834 |
|
|
const Tp frac = diff / f0;
|
| 7835 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7836 |
|
|
max_abs_frac = std::abs(frac);
|
| 7837 |
|
|
}
|
| 7838 |
|
|
}
|
| 7839 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7840 |
|
|
}
|
| 7841 |
|
|
|
| 7842 |
|
|
// Test data for k=0.60000000000000009, nu=0.0000000000000000.
|
| 7843 |
|
|
testcase_ellint_3<double> data151[] = {
|
| 7844 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.0000000000000000,
|
| 7845 |
|
|
0.0000000000000000 },
|
| 7846 |
|
|
{ 0.17485154362988362, 0.60000000000000009, 0.0000000000000000,
|
| 7847 |
|
|
0.17453292519943295 },
|
| 7848 |
|
|
{ 0.35160509865544326, 0.60000000000000009, 0.0000000000000000,
|
| 7849 |
|
|
0.34906585039886590 },
|
| 7850 |
|
|
{ 0.53210652578446160, 0.60000000000000009, 0.0000000000000000,
|
| 7851 |
|
|
0.52359877559829882 },
|
| 7852 |
|
|
{ 0.71805304664485670, 0.60000000000000009, 0.0000000000000000,
|
| 7853 |
|
|
0.69813170079773179 },
|
| 7854 |
|
|
{ 0.91082759030195970, 0.60000000000000009, 0.0000000000000000,
|
| 7855 |
|
|
0.87266462599716477 },
|
| 7856 |
|
|
{ 1.1112333229323366, 0.60000000000000009, 0.0000000000000000,
|
| 7857 |
|
|
1.0471975511965976 },
|
| 7858 |
|
|
{ 1.3191461190365270, 0.60000000000000009, 0.0000000000000000,
|
| 7859 |
|
|
1.2217304763960306 },
|
| 7860 |
|
|
{ 1.5332022105084775, 0.60000000000000009, 0.0000000000000000,
|
| 7861 |
|
|
1.3962634015954636 },
|
| 7862 |
|
|
{ 1.7507538029157526, 0.60000000000000009, 0.0000000000000000,
|
| 7863 |
|
|
1.5707963267948966 },
|
| 7864 |
|
|
};
|
| 7865 |
|
|
|
| 7866 |
|
|
// Test function for k=0.60000000000000009, nu=0.0000000000000000.
|
| 7867 |
|
|
template <typename Tp>
|
| 7868 |
|
|
void test151()
|
| 7869 |
|
|
{
|
| 7870 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7871 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7872 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7873 |
|
|
unsigned int num_datum = sizeof(data151)
|
| 7874 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7875 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7876 |
|
|
{
|
| 7877 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data151[i].k), Tp(data151[i].nu),
|
| 7878 |
|
|
Tp(data151[i].phi));
|
| 7879 |
|
|
const Tp f0 = data151[i].f0;
|
| 7880 |
|
|
const Tp diff = f - f0;
|
| 7881 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7882 |
|
|
max_abs_diff = std::abs(diff);
|
| 7883 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7884 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7885 |
|
|
{
|
| 7886 |
|
|
const Tp frac = diff / f0;
|
| 7887 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7888 |
|
|
max_abs_frac = std::abs(frac);
|
| 7889 |
|
|
}
|
| 7890 |
|
|
}
|
| 7891 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7892 |
|
|
}
|
| 7893 |
|
|
|
| 7894 |
|
|
// Test data for k=0.60000000000000009, nu=0.10000000000000001.
|
| 7895 |
|
|
testcase_ellint_3<double> data152[] = {
|
| 7896 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.10000000000000001,
|
| 7897 |
|
|
0.0000000000000000 },
|
| 7898 |
|
|
{ 0.17467514275022014, 0.60000000000000009, 0.10000000000000001,
|
| 7899 |
|
|
0.17453292519943295 },
|
| 7900 |
|
|
{ 0.35021333086258255, 0.60000000000000009, 0.10000000000000001,
|
| 7901 |
|
|
0.34906585039886590 },
|
| 7902 |
|
|
{ 0.52751664092962713, 0.60000000000000009, 0.10000000000000001,
|
| 7903 |
|
|
0.52359877559829882 },
|
| 7904 |
|
|
{ 0.70752126971957885, 0.60000000000000009, 0.10000000000000001,
|
| 7905 |
|
|
0.69813170079773179 },
|
| 7906 |
|
|
{ 0.89111058756112871, 0.60000000000000009, 0.10000000000000001,
|
| 7907 |
|
|
0.87266462599716477 },
|
| 7908 |
|
|
{ 1.0789241202877773, 0.60000000000000009, 0.10000000000000001,
|
| 7909 |
|
|
1.0471975511965976 },
|
| 7910 |
|
|
{ 1.2710800210399946, 0.60000000000000009, 0.10000000000000001,
|
| 7911 |
|
|
1.2217304763960306 },
|
| 7912 |
|
|
{ 1.4669060574440278, 0.60000000000000009, 0.10000000000000001,
|
| 7913 |
|
|
1.3962634015954636 },
|
| 7914 |
|
|
{ 1.6648615773343014, 0.60000000000000009, 0.10000000000000001,
|
| 7915 |
|
|
1.5707963267948966 },
|
| 7916 |
|
|
};
|
| 7917 |
|
|
|
| 7918 |
|
|
// Test function for k=0.60000000000000009, nu=0.10000000000000001.
|
| 7919 |
|
|
template <typename Tp>
|
| 7920 |
|
|
void test152()
|
| 7921 |
|
|
{
|
| 7922 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7923 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7924 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7925 |
|
|
unsigned int num_datum = sizeof(data152)
|
| 7926 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7927 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7928 |
|
|
{
|
| 7929 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data152[i].k), Tp(data152[i].nu),
|
| 7930 |
|
|
Tp(data152[i].phi));
|
| 7931 |
|
|
const Tp f0 = data152[i].f0;
|
| 7932 |
|
|
const Tp diff = f - f0;
|
| 7933 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7934 |
|
|
max_abs_diff = std::abs(diff);
|
| 7935 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7936 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7937 |
|
|
{
|
| 7938 |
|
|
const Tp frac = diff / f0;
|
| 7939 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7940 |
|
|
max_abs_frac = std::abs(frac);
|
| 7941 |
|
|
}
|
| 7942 |
|
|
}
|
| 7943 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7944 |
|
|
}
|
| 7945 |
|
|
|
| 7946 |
|
|
// Test data for k=0.60000000000000009, nu=0.20000000000000001.
|
| 7947 |
|
|
testcase_ellint_3<double> data153[] = {
|
| 7948 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.20000000000000001,
|
| 7949 |
|
|
0.0000000000000000 },
|
| 7950 |
|
|
{ 0.17449937871800653, 0.60000000000000009, 0.20000000000000001,
|
| 7951 |
|
|
0.17453292519943295 },
|
| 7952 |
|
|
{ 0.34884093647346553, 0.60000000000000009, 0.20000000000000001,
|
| 7953 |
|
|
0.34906585039886590 },
|
| 7954 |
|
|
{ 0.52306221119844110, 0.60000000000000009, 0.20000000000000001,
|
| 7955 |
|
|
0.52359877559829882 },
|
| 7956 |
|
|
{ 0.69749955678982223, 0.60000000000000009, 0.20000000000000001,
|
| 7957 |
|
|
0.69813170079773179 },
|
| 7958 |
|
|
{ 0.87274610682416853, 0.60000000000000009, 0.20000000000000001,
|
| 7959 |
|
|
0.87266462599716477 },
|
| 7960 |
|
|
{ 1.0494620540750796, 0.60000000000000009, 0.20000000000000001,
|
| 7961 |
|
|
1.0471975511965976 },
|
| 7962 |
|
|
{ 1.2280847305507339, 0.60000000000000009, 0.20000000000000001,
|
| 7963 |
|
|
1.2217304763960306 },
|
| 7964 |
|
|
{ 1.4085436279696888, 0.60000000000000009, 0.20000000000000001,
|
| 7965 |
|
|
1.3962634015954636 },
|
| 7966 |
|
|
{ 1.5901418016279374, 0.60000000000000009, 0.20000000000000001,
|
| 7967 |
|
|
1.5707963267948966 },
|
| 7968 |
|
|
};
|
| 7969 |
|
|
|
| 7970 |
|
|
// Test function for k=0.60000000000000009, nu=0.20000000000000001.
|
| 7971 |
|
|
template <typename Tp>
|
| 7972 |
|
|
void test153()
|
| 7973 |
|
|
{
|
| 7974 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 7975 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 7976 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 7977 |
|
|
unsigned int num_datum = sizeof(data153)
|
| 7978 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 7979 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 7980 |
|
|
{
|
| 7981 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data153[i].k), Tp(data153[i].nu),
|
| 7982 |
|
|
Tp(data153[i].phi));
|
| 7983 |
|
|
const Tp f0 = data153[i].f0;
|
| 7984 |
|
|
const Tp diff = f - f0;
|
| 7985 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 7986 |
|
|
max_abs_diff = std::abs(diff);
|
| 7987 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 7988 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 7989 |
|
|
{
|
| 7990 |
|
|
const Tp frac = diff / f0;
|
| 7991 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 7992 |
|
|
max_abs_frac = std::abs(frac);
|
| 7993 |
|
|
}
|
| 7994 |
|
|
}
|
| 7995 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 7996 |
|
|
}
|
| 7997 |
|
|
|
| 7998 |
|
|
// Test data for k=0.60000000000000009, nu=0.29999999999999999.
|
| 7999 |
|
|
testcase_ellint_3<double> data154[] = {
|
| 8000 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.29999999999999999,
|
| 8001 |
|
|
0.0000000000000000 },
|
| 8002 |
|
|
{ 0.17432424744393935, 0.60000000000000009, 0.29999999999999999,
|
| 8003 |
|
|
0.17453292519943295 },
|
| 8004 |
|
|
{ 0.34748744127146447, 0.60000000000000009, 0.29999999999999999,
|
| 8005 |
|
|
0.34906585039886590 },
|
| 8006 |
|
|
{ 0.51873632743924847, 0.60000000000000009, 0.29999999999999999,
|
| 8007 |
|
|
0.52359877559829882 },
|
| 8008 |
|
|
{ 0.68794610396313127, 0.60000000000000009, 0.29999999999999999,
|
| 8009 |
|
|
0.69813170079773179 },
|
| 8010 |
|
|
{ 0.85558070175468726, 0.60000000000000009, 0.29999999999999999,
|
| 8011 |
|
|
0.87266462599716477 },
|
| 8012 |
|
|
{ 1.0224416343605658, 0.60000000000000009, 0.29999999999999999,
|
| 8013 |
|
|
1.0471975511965976 },
|
| 8014 |
|
|
{ 1.1893144457936788, 0.60000000000000009, 0.29999999999999999,
|
| 8015 |
|
|
1.2217304763960306 },
|
| 8016 |
|
|
{ 1.3566435377982575, 0.60000000000000009, 0.29999999999999999,
|
| 8017 |
|
|
1.3962634015954636 },
|
| 8018 |
|
|
{ 1.5243814243493585, 0.60000000000000009, 0.29999999999999999,
|
| 8019 |
|
|
1.5707963267948966 },
|
| 8020 |
|
|
};
|
| 8021 |
|
|
|
| 8022 |
|
|
// Test function for k=0.60000000000000009, nu=0.29999999999999999.
|
| 8023 |
|
|
template <typename Tp>
|
| 8024 |
|
|
void test154()
|
| 8025 |
|
|
{
|
| 8026 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8027 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8028 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8029 |
|
|
unsigned int num_datum = sizeof(data154)
|
| 8030 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8031 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8032 |
|
|
{
|
| 8033 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data154[i].k), Tp(data154[i].nu),
|
| 8034 |
|
|
Tp(data154[i].phi));
|
| 8035 |
|
|
const Tp f0 = data154[i].f0;
|
| 8036 |
|
|
const Tp diff = f - f0;
|
| 8037 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8038 |
|
|
max_abs_diff = std::abs(diff);
|
| 8039 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8040 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8041 |
|
|
{
|
| 8042 |
|
|
const Tp frac = diff / f0;
|
| 8043 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8044 |
|
|
max_abs_frac = std::abs(frac);
|
| 8045 |
|
|
}
|
| 8046 |
|
|
}
|
| 8047 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8048 |
|
|
}
|
| 8049 |
|
|
|
| 8050 |
|
|
// Test data for k=0.60000000000000009, nu=0.40000000000000002.
|
| 8051 |
|
|
testcase_ellint_3<double> data155[] = {
|
| 8052 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.40000000000000002,
|
| 8053 |
|
|
0.0000000000000000 },
|
| 8054 |
|
|
{ 0.17414974487670720, 0.60000000000000009, 0.40000000000000002,
|
| 8055 |
|
|
0.17453292519943295 },
|
| 8056 |
|
|
{ 0.34615238767335027, 0.60000000000000009, 0.40000000000000002,
|
| 8057 |
|
|
0.34906585039886590 },
|
| 8058 |
|
|
{ 0.51453257838108579, 0.60000000000000009, 0.40000000000000002,
|
| 8059 |
|
|
0.52359877559829882 },
|
| 8060 |
|
|
{ 0.67882386787534410, 0.60000000000000009, 0.40000000000000002,
|
| 8061 |
|
|
0.69813170079773179 },
|
| 8062 |
|
|
{ 0.83948470233173578, 0.60000000000000009, 0.40000000000000002,
|
| 8063 |
|
|
0.87266462599716477 },
|
| 8064 |
|
|
{ 0.99753496200074021, 0.60000000000000009, 0.40000000000000002,
|
| 8065 |
|
|
1.0471975511965976 },
|
| 8066 |
|
|
{ 1.1541101404388487, 0.60000000000000009, 0.40000000000000002,
|
| 8067 |
|
|
1.2217304763960306 },
|
| 8068 |
|
|
{ 1.3100911323398816, 0.60000000000000009, 0.40000000000000002,
|
| 8069 |
|
|
1.3962634015954636 },
|
| 8070 |
|
|
{ 1.4659345278069984, 0.60000000000000009, 0.40000000000000002,
|
| 8071 |
|
|
1.5707963267948966 },
|
| 8072 |
|
|
};
|
| 8073 |
|
|
|
| 8074 |
|
|
// Test function for k=0.60000000000000009, nu=0.40000000000000002.
|
| 8075 |
|
|
template <typename Tp>
|
| 8076 |
|
|
void test155()
|
| 8077 |
|
|
{
|
| 8078 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8079 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8080 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8081 |
|
|
unsigned int num_datum = sizeof(data155)
|
| 8082 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8083 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8084 |
|
|
{
|
| 8085 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data155[i].k), Tp(data155[i].nu),
|
| 8086 |
|
|
Tp(data155[i].phi));
|
| 8087 |
|
|
const Tp f0 = data155[i].f0;
|
| 8088 |
|
|
const Tp diff = f - f0;
|
| 8089 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8090 |
|
|
max_abs_diff = std::abs(diff);
|
| 8091 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8092 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8093 |
|
|
{
|
| 8094 |
|
|
const Tp frac = diff / f0;
|
| 8095 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8096 |
|
|
max_abs_frac = std::abs(frac);
|
| 8097 |
|
|
}
|
| 8098 |
|
|
}
|
| 8099 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8100 |
|
|
}
|
| 8101 |
|
|
|
| 8102 |
|
|
// Test data for k=0.60000000000000009, nu=0.50000000000000000.
|
| 8103 |
|
|
testcase_ellint_3<double> data156[] = {
|
| 8104 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.50000000000000000,
|
| 8105 |
|
|
0.0000000000000000 },
|
| 8106 |
|
|
{ 0.17397586700252810, 0.60000000000000009, 0.50000000000000000,
|
| 8107 |
|
|
0.17453292519943295 },
|
| 8108 |
|
|
{ 0.34483533397138516, 0.60000000000000009, 0.50000000000000000,
|
| 8109 |
|
|
0.34906585039886590 },
|
| 8110 |
|
|
{ 0.51044500461706499, 0.60000000000000009, 0.50000000000000000,
|
| 8111 |
|
|
0.52359877559829882 },
|
| 8112 |
|
|
{ 0.67009988034712675, 0.60000000000000009, 0.50000000000000000,
|
| 8113 |
|
|
0.69813170079773179 },
|
| 8114 |
|
|
{ 0.82434762375735193, 0.60000000000000009, 0.50000000000000000,
|
| 8115 |
|
|
0.87266462599716477 },
|
| 8116 |
|
|
{ 0.97447346702799043, 0.60000000000000009, 0.50000000000000000,
|
| 8117 |
|
|
1.0471975511965976 },
|
| 8118 |
|
|
{ 1.1219494000522143, 0.60000000000000009, 0.50000000000000000,
|
| 8119 |
|
|
1.2217304763960306 },
|
| 8120 |
|
|
{ 1.2680242605954488, 0.60000000000000009, 0.50000000000000000,
|
| 8121 |
|
|
1.3962634015954636 },
|
| 8122 |
|
|
{ 1.4135484285693078, 0.60000000000000009, 0.50000000000000000,
|
| 8123 |
|
|
1.5707963267948966 },
|
| 8124 |
|
|
};
|
| 8125 |
|
|
|
| 8126 |
|
|
// Test function for k=0.60000000000000009, nu=0.50000000000000000.
|
| 8127 |
|
|
template <typename Tp>
|
| 8128 |
|
|
void test156()
|
| 8129 |
|
|
{
|
| 8130 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8131 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8132 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8133 |
|
|
unsigned int num_datum = sizeof(data156)
|
| 8134 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8135 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8136 |
|
|
{
|
| 8137 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data156[i].k), Tp(data156[i].nu),
|
| 8138 |
|
|
Tp(data156[i].phi));
|
| 8139 |
|
|
const Tp f0 = data156[i].f0;
|
| 8140 |
|
|
const Tp diff = f - f0;
|
| 8141 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8142 |
|
|
max_abs_diff = std::abs(diff);
|
| 8143 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8144 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8145 |
|
|
{
|
| 8146 |
|
|
const Tp frac = diff / f0;
|
| 8147 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8148 |
|
|
max_abs_frac = std::abs(frac);
|
| 8149 |
|
|
}
|
| 8150 |
|
|
}
|
| 8151 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8152 |
|
|
}
|
| 8153 |
|
|
|
| 8154 |
|
|
// Test data for k=0.60000000000000009, nu=0.59999999999999998.
|
| 8155 |
|
|
testcase_ellint_3<double> data157[] = {
|
| 8156 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.59999999999999998,
|
| 8157 |
|
|
0.0000000000000000 },
|
| 8158 |
|
|
{ 0.17380260984469356, 0.60000000000000009, 0.59999999999999998,
|
| 8159 |
|
|
0.17453292519943295 },
|
| 8160 |
|
|
{ 0.34353585361777839, 0.60000000000000009, 0.59999999999999998,
|
| 8161 |
|
|
0.34906585039886590 },
|
| 8162 |
|
|
{ 0.50646805774321402, 0.60000000000000009, 0.59999999999999998,
|
| 8163 |
|
|
0.52359877559829882 },
|
| 8164 |
|
|
{ 0.66174468108625517, 0.60000000000000009, 0.59999999999999998,
|
| 8165 |
|
|
0.69813170079773179 },
|
| 8166 |
|
|
{ 0.81007462280278408, 0.60000000000000009, 0.59999999999999998,
|
| 8167 |
|
|
0.87266462599716477 },
|
| 8168 |
|
|
{ 0.95303466945718773, 0.60000000000000009, 0.59999999999999998,
|
| 8169 |
|
|
1.0471975511965976 },
|
| 8170 |
|
|
{ 1.0924118588677503, 0.60000000000000009, 0.59999999999999998,
|
| 8171 |
|
|
1.2217304763960306 },
|
| 8172 |
|
|
{ 1.2297640574847937, 0.60000000000000009, 0.59999999999999998,
|
| 8173 |
|
|
1.3962634015954636 },
|
| 8174 |
|
|
{ 1.3662507535812816, 0.60000000000000009, 0.59999999999999998,
|
| 8175 |
|
|
1.5707963267948966 },
|
| 8176 |
|
|
};
|
| 8177 |
|
|
|
| 8178 |
|
|
// Test function for k=0.60000000000000009, nu=0.59999999999999998.
|
| 8179 |
|
|
template <typename Tp>
|
| 8180 |
|
|
void test157()
|
| 8181 |
|
|
{
|
| 8182 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8183 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8184 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8185 |
|
|
unsigned int num_datum = sizeof(data157)
|
| 8186 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8187 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8188 |
|
|
{
|
| 8189 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data157[i].k), Tp(data157[i].nu),
|
| 8190 |
|
|
Tp(data157[i].phi));
|
| 8191 |
|
|
const Tp f0 = data157[i].f0;
|
| 8192 |
|
|
const Tp diff = f - f0;
|
| 8193 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8194 |
|
|
max_abs_diff = std::abs(diff);
|
| 8195 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8196 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8197 |
|
|
{
|
| 8198 |
|
|
const Tp frac = diff / f0;
|
| 8199 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8200 |
|
|
max_abs_frac = std::abs(frac);
|
| 8201 |
|
|
}
|
| 8202 |
|
|
}
|
| 8203 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8204 |
|
|
}
|
| 8205 |
|
|
|
| 8206 |
|
|
// Test data for k=0.60000000000000009, nu=0.69999999999999996.
|
| 8207 |
|
|
testcase_ellint_3<double> data158[] = {
|
| 8208 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.69999999999999996,
|
| 8209 |
|
|
0.0000000000000000 },
|
| 8210 |
|
|
{ 0.17362996946312009, 0.60000000000000009, 0.69999999999999996,
|
| 8211 |
|
|
0.17453292519943295 },
|
| 8212 |
|
|
{ 0.34225353454870588, 0.60000000000000009, 0.69999999999999996,
|
| 8213 |
|
|
0.34906585039886590 },
|
| 8214 |
|
|
{ 0.50259656397799546, 0.60000000000000009, 0.69999999999999996,
|
| 8215 |
|
|
0.52359877559829882 },
|
| 8216 |
|
|
{ 0.65373184496628944, 0.60000000000000009, 0.69999999999999996,
|
| 8217 |
|
|
0.69813170079773179 },
|
| 8218 |
|
|
{ 0.79658372884056439, 0.60000000000000009, 0.69999999999999996,
|
| 8219 |
|
|
0.87266462599716477 },
|
| 8220 |
|
|
{ 0.93303240100245466, 0.60000000000000009, 0.69999999999999996,
|
| 8221 |
|
|
1.0471975511965976 },
|
| 8222 |
|
|
{ 1.0651547944716557, 0.60000000000000009, 0.69999999999999996,
|
| 8223 |
|
|
1.2217304763960306 },
|
| 8224 |
|
|
{ 1.1947676204853441, 0.60000000000000009, 0.69999999999999996,
|
| 8225 |
|
|
1.3962634015954636 },
|
| 8226 |
|
|
{ 1.3232737468822811, 0.60000000000000009, 0.69999999999999996,
|
| 8227 |
|
|
1.5707963267948966 },
|
| 8228 |
|
|
};
|
| 8229 |
|
|
|
| 8230 |
|
|
// Test function for k=0.60000000000000009, nu=0.69999999999999996.
|
| 8231 |
|
|
template <typename Tp>
|
| 8232 |
|
|
void test158()
|
| 8233 |
|
|
{
|
| 8234 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8235 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8236 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8237 |
|
|
unsigned int num_datum = sizeof(data158)
|
| 8238 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8239 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8240 |
|
|
{
|
| 8241 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data158[i].k), Tp(data158[i].nu),
|
| 8242 |
|
|
Tp(data158[i].phi));
|
| 8243 |
|
|
const Tp f0 = data158[i].f0;
|
| 8244 |
|
|
const Tp diff = f - f0;
|
| 8245 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8246 |
|
|
max_abs_diff = std::abs(diff);
|
| 8247 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8248 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8249 |
|
|
{
|
| 8250 |
|
|
const Tp frac = diff / f0;
|
| 8251 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8252 |
|
|
max_abs_frac = std::abs(frac);
|
| 8253 |
|
|
}
|
| 8254 |
|
|
}
|
| 8255 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8256 |
|
|
}
|
| 8257 |
|
|
|
| 8258 |
|
|
// Test data for k=0.60000000000000009, nu=0.80000000000000004.
|
| 8259 |
|
|
testcase_ellint_3<double> data159[] = {
|
| 8260 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.80000000000000004,
|
| 8261 |
|
|
0.0000000000000000 },
|
| 8262 |
|
|
{ 0.17345794195390687, 0.60000000000000009, 0.80000000000000004,
|
| 8263 |
|
|
0.17453292519943295 },
|
| 8264 |
|
|
{ 0.34098797854531027, 0.60000000000000009, 0.80000000000000004,
|
| 8265 |
|
|
0.34906585039886590 },
|
| 8266 |
|
|
{ 0.49882569168826230, 0.60000000000000009, 0.80000000000000004,
|
| 8267 |
|
|
0.52359877559829882 },
|
| 8268 |
|
|
{ 0.64603758566475511, 0.60000000000000009, 0.80000000000000004,
|
| 8269 |
|
|
0.69813170079773179 },
|
| 8270 |
|
|
{ 0.78380365594769730, 0.60000000000000009, 0.80000000000000004,
|
| 8271 |
|
|
0.87266462599716477 },
|
| 8272 |
|
|
{ 0.91430946255611223, 0.60000000000000009, 0.80000000000000004,
|
| 8273 |
|
|
1.0471975511965976 },
|
| 8274 |
|
|
{ 1.0398955217270607, 0.60000000000000009, 0.80000000000000004,
|
| 8275 |
|
|
1.2217304763960306 },
|
| 8276 |
|
|
{ 1.1625948314277679, 0.60000000000000009, 0.80000000000000004,
|
| 8277 |
|
|
1.3962634015954636 },
|
| 8278 |
|
|
{ 1.2840021261752192, 0.60000000000000009, 0.80000000000000004,
|
| 8279 |
|
|
1.5707963267948966 },
|
| 8280 |
|
|
};
|
| 8281 |
|
|
|
| 8282 |
|
|
// Test function for k=0.60000000000000009, nu=0.80000000000000004.
|
| 8283 |
|
|
template <typename Tp>
|
| 8284 |
|
|
void test159()
|
| 8285 |
|
|
{
|
| 8286 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8287 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8288 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8289 |
|
|
unsigned int num_datum = sizeof(data159)
|
| 8290 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8291 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8292 |
|
|
{
|
| 8293 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data159[i].k), Tp(data159[i].nu),
|
| 8294 |
|
|
Tp(data159[i].phi));
|
| 8295 |
|
|
const Tp f0 = data159[i].f0;
|
| 8296 |
|
|
const Tp diff = f - f0;
|
| 8297 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8298 |
|
|
max_abs_diff = std::abs(diff);
|
| 8299 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8300 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8301 |
|
|
{
|
| 8302 |
|
|
const Tp frac = diff / f0;
|
| 8303 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8304 |
|
|
max_abs_frac = std::abs(frac);
|
| 8305 |
|
|
}
|
| 8306 |
|
|
}
|
| 8307 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8308 |
|
|
}
|
| 8309 |
|
|
|
| 8310 |
|
|
// Test data for k=0.60000000000000009, nu=0.90000000000000002.
|
| 8311 |
|
|
testcase_ellint_3<double> data160[] = {
|
| 8312 |
|
|
{ -0.0000000000000000, 0.60000000000000009, 0.90000000000000002,
|
| 8313 |
|
|
0.0000000000000000 },
|
| 8314 |
|
|
{ 0.17328652344890033, 0.60000000000000009, 0.90000000000000002,
|
| 8315 |
|
|
0.17453292519943295 },
|
| 8316 |
|
|
{ 0.33973880062929018, 0.60000000000000009, 0.90000000000000002,
|
| 8317 |
|
|
0.34906585039886590 },
|
| 8318 |
|
|
{ 0.49515092233122765, 0.60000000000000009, 0.90000000000000002,
|
| 8319 |
|
|
0.52359877559829882 },
|
| 8320 |
|
|
{ 0.63864042139737043, 0.60000000000000009, 0.90000000000000002,
|
| 8321 |
|
|
0.69813170079773179 },
|
| 8322 |
|
|
{ 0.77167205646538850, 0.60000000000000009, 0.90000000000000002,
|
| 8323 |
|
|
0.87266462599716477 },
|
| 8324 |
|
|
{ 0.89673202848034428, 0.60000000000000009, 0.90000000000000002,
|
| 8325 |
|
|
1.0471975511965976 },
|
| 8326 |
|
|
{ 1.0163984492661304, 0.60000000000000009, 0.90000000000000002,
|
| 8327 |
|
|
1.2217304763960306 },
|
| 8328 |
|
|
{ 1.1328845785162431, 0.60000000000000009, 0.90000000000000002,
|
| 8329 |
|
|
1.3962634015954636 },
|
| 8330 |
|
|
{ 1.2479362973851875, 0.60000000000000009, 0.90000000000000002,
|
| 8331 |
|
|
1.5707963267948966 },
|
| 8332 |
|
|
};
|
| 8333 |
|
|
|
| 8334 |
|
|
// Test function for k=0.60000000000000009, nu=0.90000000000000002.
|
| 8335 |
|
|
template <typename Tp>
|
| 8336 |
|
|
void test160()
|
| 8337 |
|
|
{
|
| 8338 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8339 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8340 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8341 |
|
|
unsigned int num_datum = sizeof(data160)
|
| 8342 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8343 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8344 |
|
|
{
|
| 8345 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data160[i].k), Tp(data160[i].nu),
|
| 8346 |
|
|
Tp(data160[i].phi));
|
| 8347 |
|
|
const Tp f0 = data160[i].f0;
|
| 8348 |
|
|
const Tp diff = f - f0;
|
| 8349 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8350 |
|
|
max_abs_diff = std::abs(diff);
|
| 8351 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8352 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8353 |
|
|
{
|
| 8354 |
|
|
const Tp frac = diff / f0;
|
| 8355 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8356 |
|
|
max_abs_frac = std::abs(frac);
|
| 8357 |
|
|
}
|
| 8358 |
|
|
}
|
| 8359 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8360 |
|
|
}
|
| 8361 |
|
|
|
| 8362 |
|
|
// Test data for k=0.69999999999999996, nu=0.0000000000000000.
|
| 8363 |
|
|
testcase_ellint_3<double> data161[] = {
|
| 8364 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.0000000000000000,
|
| 8365 |
|
|
0.0000000000000000 },
|
| 8366 |
|
|
{ 0.17496737466916720, 0.69999999999999996, 0.0000000000000000,
|
| 8367 |
|
|
0.17453292519943295 },
|
| 8368 |
|
|
{ 0.35254687535677925, 0.69999999999999996, 0.0000000000000000,
|
| 8369 |
|
|
0.34906585039886590 },
|
| 8370 |
|
|
{ 0.53536740275997130, 0.69999999999999996, 0.0000000000000000,
|
| 8371 |
|
|
0.52359877559829882 },
|
| 8372 |
|
|
{ 0.72603797651684465, 0.69999999999999996, 0.0000000000000000,
|
| 8373 |
|
|
0.69813170079773179 },
|
| 8374 |
|
|
{ 0.92698296348313458, 0.69999999999999996, 0.0000000000000000,
|
| 8375 |
|
|
0.87266462599716477 },
|
| 8376 |
|
|
{ 1.1400447527693316, 0.69999999999999996, 0.0000000000000000,
|
| 8377 |
|
|
1.0471975511965976 },
|
| 8378 |
|
|
{ 1.3657668117194071, 0.69999999999999996, 0.0000000000000000,
|
| 8379 |
|
|
1.2217304763960306 },
|
| 8380 |
|
|
{ 1.6024686895959159, 0.69999999999999996, 0.0000000000000000,
|
| 8381 |
|
|
1.3962634015954636 },
|
| 8382 |
|
|
{ 1.8456939983747236, 0.69999999999999996, 0.0000000000000000,
|
| 8383 |
|
|
1.5707963267948966 },
|
| 8384 |
|
|
};
|
| 8385 |
|
|
|
| 8386 |
|
|
// Test function for k=0.69999999999999996, nu=0.0000000000000000.
|
| 8387 |
|
|
template <typename Tp>
|
| 8388 |
|
|
void test161()
|
| 8389 |
|
|
{
|
| 8390 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8391 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8392 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8393 |
|
|
unsigned int num_datum = sizeof(data161)
|
| 8394 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8395 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8396 |
|
|
{
|
| 8397 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data161[i].k), Tp(data161[i].nu),
|
| 8398 |
|
|
Tp(data161[i].phi));
|
| 8399 |
|
|
const Tp f0 = data161[i].f0;
|
| 8400 |
|
|
const Tp diff = f - f0;
|
| 8401 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8402 |
|
|
max_abs_diff = std::abs(diff);
|
| 8403 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8404 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8405 |
|
|
{
|
| 8406 |
|
|
const Tp frac = diff / f0;
|
| 8407 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8408 |
|
|
max_abs_frac = std::abs(frac);
|
| 8409 |
|
|
}
|
| 8410 |
|
|
}
|
| 8411 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8412 |
|
|
}
|
| 8413 |
|
|
|
| 8414 |
|
|
// Test data for k=0.69999999999999996, nu=0.10000000000000001.
|
| 8415 |
|
|
testcase_ellint_3<double> data162[] = {
|
| 8416 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.10000000000000001,
|
| 8417 |
|
|
0.0000000000000000 },
|
| 8418 |
|
|
{ 0.17479076384884681, 0.69999999999999996, 0.10000000000000001,
|
| 8419 |
|
|
0.17453292519943295 },
|
| 8420 |
|
|
{ 0.35114844900396364, 0.69999999999999996, 0.10000000000000001,
|
| 8421 |
|
|
0.34906585039886590 },
|
| 8422 |
|
|
{ 0.53072776947527012, 0.69999999999999996, 0.10000000000000001,
|
| 8423 |
|
|
0.52359877559829882 },
|
| 8424 |
|
|
{ 0.71530198262386246, 0.69999999999999996, 0.10000000000000001,
|
| 8425 |
|
|
0.69813170079773179 },
|
| 8426 |
|
|
{ 0.90666760677828306, 0.69999999999999996, 0.10000000000000001,
|
| 8427 |
|
|
0.87266462599716477 },
|
| 8428 |
|
|
{ 1.1063366517438080, 0.69999999999999996, 0.10000000000000001,
|
| 8429 |
|
|
1.0471975511965976 },
|
| 8430 |
|
|
{ 1.3149477243092147, 0.69999999999999996, 0.10000000000000001,
|
| 8431 |
|
|
1.2217304763960306 },
|
| 8432 |
|
|
{ 1.5314886725038925, 0.69999999999999996, 0.10000000000000001,
|
| 8433 |
|
|
1.3962634015954636 },
|
| 8434 |
|
|
{ 1.7528050171757608, 0.69999999999999996, 0.10000000000000001,
|
| 8435 |
|
|
1.5707963267948966 },
|
| 8436 |
|
|
};
|
| 8437 |
|
|
|
| 8438 |
|
|
// Test function for k=0.69999999999999996, nu=0.10000000000000001.
|
| 8439 |
|
|
template <typename Tp>
|
| 8440 |
|
|
void test162()
|
| 8441 |
|
|
{
|
| 8442 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8443 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8444 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8445 |
|
|
unsigned int num_datum = sizeof(data162)
|
| 8446 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8447 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8448 |
|
|
{
|
| 8449 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data162[i].k), Tp(data162[i].nu),
|
| 8450 |
|
|
Tp(data162[i].phi));
|
| 8451 |
|
|
const Tp f0 = data162[i].f0;
|
| 8452 |
|
|
const Tp diff = f - f0;
|
| 8453 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8454 |
|
|
max_abs_diff = std::abs(diff);
|
| 8455 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8456 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8457 |
|
|
{
|
| 8458 |
|
|
const Tp frac = diff / f0;
|
| 8459 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8460 |
|
|
max_abs_frac = std::abs(frac);
|
| 8461 |
|
|
}
|
| 8462 |
|
|
}
|
| 8463 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8464 |
|
|
}
|
| 8465 |
|
|
|
| 8466 |
|
|
// Test data for k=0.69999999999999996, nu=0.20000000000000001.
|
| 8467 |
|
|
testcase_ellint_3<double> data163[] = {
|
| 8468 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.20000000000000001,
|
| 8469 |
|
|
0.0000000000000000 },
|
| 8470 |
|
|
{ 0.17461479077791472, 0.69999999999999996, 0.20000000000000001,
|
| 8471 |
|
|
0.17453292519943295 },
|
| 8472 |
|
|
{ 0.34976950621407538, 0.69999999999999996, 0.20000000000000001,
|
| 8473 |
|
|
0.34906585039886590 },
|
| 8474 |
|
|
{ 0.52622533231350188, 0.69999999999999996, 0.20000000000000001,
|
| 8475 |
|
|
0.52359877559829882 },
|
| 8476 |
|
|
{ 0.70508774017895226, 0.69999999999999996, 0.20000000000000001,
|
| 8477 |
|
|
0.69813170079773179 },
|
| 8478 |
|
|
{ 0.88775302531730294, 0.69999999999999996, 0.20000000000000001,
|
| 8479 |
|
|
0.87266462599716477 },
|
| 8480 |
|
|
{ 1.0756195476149006, 0.69999999999999996, 0.20000000000000001,
|
| 8481 |
|
|
1.0471975511965976 },
|
| 8482 |
|
|
{ 1.2695349716654372, 0.69999999999999996, 0.20000000000000001,
|
| 8483 |
|
|
1.2217304763960306 },
|
| 8484 |
|
|
{ 1.4690814617070540, 0.69999999999999996, 0.20000000000000001,
|
| 8485 |
|
|
1.3962634015954636 },
|
| 8486 |
|
|
{ 1.6721098780092147, 0.69999999999999996, 0.20000000000000001,
|
| 8487 |
|
|
1.5707963267948966 },
|
| 8488 |
|
|
};
|
| 8489 |
|
|
|
| 8490 |
|
|
// Test function for k=0.69999999999999996, nu=0.20000000000000001.
|
| 8491 |
|
|
template <typename Tp>
|
| 8492 |
|
|
void test163()
|
| 8493 |
|
|
{
|
| 8494 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8495 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8496 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8497 |
|
|
unsigned int num_datum = sizeof(data163)
|
| 8498 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8499 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8500 |
|
|
{
|
| 8501 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data163[i].k), Tp(data163[i].nu),
|
| 8502 |
|
|
Tp(data163[i].phi));
|
| 8503 |
|
|
const Tp f0 = data163[i].f0;
|
| 8504 |
|
|
const Tp diff = f - f0;
|
| 8505 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8506 |
|
|
max_abs_diff = std::abs(diff);
|
| 8507 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8508 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8509 |
|
|
{
|
| 8510 |
|
|
const Tp frac = diff / f0;
|
| 8511 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8512 |
|
|
max_abs_frac = std::abs(frac);
|
| 8513 |
|
|
}
|
| 8514 |
|
|
}
|
| 8515 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8516 |
|
|
}
|
| 8517 |
|
|
|
| 8518 |
|
|
// Test data for k=0.69999999999999996, nu=0.29999999999999999.
|
| 8519 |
|
|
testcase_ellint_3<double> data164[] = {
|
| 8520 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.29999999999999999,
|
| 8521 |
|
|
0.0000000000000000 },
|
| 8522 |
|
|
{ 0.17443945136076172, 0.69999999999999996, 0.29999999999999999,
|
| 8523 |
|
|
0.17453292519943295 },
|
| 8524 |
|
|
{ 0.34840956983535287, 0.69999999999999996, 0.29999999999999999,
|
| 8525 |
|
|
0.34906585039886590 },
|
| 8526 |
|
|
{ 0.52185308551329179, 0.69999999999999996, 0.29999999999999999,
|
| 8527 |
|
|
0.52359877559829882 },
|
| 8528 |
|
|
{ 0.69535240431168266, 0.69999999999999996, 0.29999999999999999,
|
| 8529 |
|
|
0.69813170079773179 },
|
| 8530 |
|
|
{ 0.87007983473964923, 0.69999999999999996, 0.29999999999999999,
|
| 8531 |
|
|
0.87266462599716477 },
|
| 8532 |
|
|
{ 1.0474657975577066, 0.69999999999999996, 0.29999999999999999,
|
| 8533 |
|
|
1.0471975511965976 },
|
| 8534 |
|
|
{ 1.2286225419931889, 0.69999999999999996, 0.29999999999999999,
|
| 8535 |
|
|
1.2217304763960306 },
|
| 8536 |
|
|
{ 1.4136490671013271, 0.69999999999999996, 0.29999999999999999,
|
| 8537 |
|
|
1.3962634015954636 },
|
| 8538 |
|
|
{ 1.6011813647733213, 0.69999999999999996, 0.29999999999999999,
|
| 8539 |
|
|
1.5707963267948966 },
|
| 8540 |
|
|
};
|
| 8541 |
|
|
|
| 8542 |
|
|
// Test function for k=0.69999999999999996, nu=0.29999999999999999.
|
| 8543 |
|
|
template <typename Tp>
|
| 8544 |
|
|
void test164()
|
| 8545 |
|
|
{
|
| 8546 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8547 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8548 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8549 |
|
|
unsigned int num_datum = sizeof(data164)
|
| 8550 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8551 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8552 |
|
|
{
|
| 8553 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data164[i].k), Tp(data164[i].nu),
|
| 8554 |
|
|
Tp(data164[i].phi));
|
| 8555 |
|
|
const Tp f0 = data164[i].f0;
|
| 8556 |
|
|
const Tp diff = f - f0;
|
| 8557 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8558 |
|
|
max_abs_diff = std::abs(diff);
|
| 8559 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8560 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8561 |
|
|
{
|
| 8562 |
|
|
const Tp frac = diff / f0;
|
| 8563 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8564 |
|
|
max_abs_frac = std::abs(frac);
|
| 8565 |
|
|
}
|
| 8566 |
|
|
}
|
| 8567 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8568 |
|
|
}
|
| 8569 |
|
|
|
| 8570 |
|
|
// Test data for k=0.69999999999999996, nu=0.40000000000000002.
|
| 8571 |
|
|
testcase_ellint_3<double> data165[] = {
|
| 8572 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.40000000000000002,
|
| 8573 |
|
|
0.0000000000000000 },
|
| 8574 |
|
|
{ 0.17426474153983226, 0.69999999999999996, 0.40000000000000002,
|
| 8575 |
|
|
0.17453292519943295 },
|
| 8576 |
|
|
{ 0.34706817945773732, 0.69999999999999996, 0.40000000000000002,
|
| 8577 |
|
|
0.34906585039886590 },
|
| 8578 |
|
|
{ 0.51760452851738159, 0.69999999999999996, 0.40000000000000002,
|
| 8579 |
|
|
0.52359877559829882 },
|
| 8580 |
|
|
{ 0.68605801534722766, 0.69999999999999996, 0.40000000000000002,
|
| 8581 |
|
|
0.69813170079773179 },
|
| 8582 |
|
|
{ 0.85351339387296532, 0.69999999999999996, 0.40000000000000002,
|
| 8583 |
|
|
0.87266462599716477 },
|
| 8584 |
|
|
{ 1.0215297967969537, 0.69999999999999996, 0.40000000000000002,
|
| 8585 |
|
|
1.0471975511965976 },
|
| 8586 |
|
|
{ 1.1915051074460528, 0.69999999999999996, 0.40000000000000002,
|
| 8587 |
|
|
1.2217304763960306 },
|
| 8588 |
|
|
{ 1.3639821911744707, 0.69999999999999996, 0.40000000000000002,
|
| 8589 |
|
|
1.3962634015954636 },
|
| 8590 |
|
|
{ 1.5382162002954762, 0.69999999999999996, 0.40000000000000002,
|
| 8591 |
|
|
1.5707963267948966 },
|
| 8592 |
|
|
};
|
| 8593 |
|
|
|
| 8594 |
|
|
// Test function for k=0.69999999999999996, nu=0.40000000000000002.
|
| 8595 |
|
|
template <typename Tp>
|
| 8596 |
|
|
void test165()
|
| 8597 |
|
|
{
|
| 8598 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8599 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8600 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8601 |
|
|
unsigned int num_datum = sizeof(data165)
|
| 8602 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8603 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8604 |
|
|
{
|
| 8605 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data165[i].k), Tp(data165[i].nu),
|
| 8606 |
|
|
Tp(data165[i].phi));
|
| 8607 |
|
|
const Tp f0 = data165[i].f0;
|
| 8608 |
|
|
const Tp diff = f - f0;
|
| 8609 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8610 |
|
|
max_abs_diff = std::abs(diff);
|
| 8611 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8612 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8613 |
|
|
{
|
| 8614 |
|
|
const Tp frac = diff / f0;
|
| 8615 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8616 |
|
|
max_abs_frac = std::abs(frac);
|
| 8617 |
|
|
}
|
| 8618 |
|
|
}
|
| 8619 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8620 |
|
|
}
|
| 8621 |
|
|
|
| 8622 |
|
|
// Test data for k=0.69999999999999996, nu=0.50000000000000000.
|
| 8623 |
|
|
testcase_ellint_3<double> data166[] = {
|
| 8624 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.50000000000000000,
|
| 8625 |
|
|
0.0000000000000000 },
|
| 8626 |
|
|
{ 0.17409065729516093, 0.69999999999999996, 0.50000000000000000,
|
| 8627 |
|
|
0.17453292519943295 },
|
| 8628 |
|
|
{ 0.34574489064986091, 0.69999999999999996, 0.50000000000000000,
|
| 8629 |
|
|
0.34906585039886590 },
|
| 8630 |
|
|
{ 0.51347361925579793, 0.69999999999999996, 0.50000000000000000,
|
| 8631 |
|
|
0.52359877559829882 },
|
| 8632 |
|
|
{ 0.67717079489579290, 0.69999999999999996, 0.50000000000000000,
|
| 8633 |
|
|
0.69813170079773179 },
|
| 8634 |
|
|
{ 0.83793902055292280, 0.69999999999999996, 0.50000000000000000,
|
| 8635 |
|
|
0.87266462599716477 },
|
| 8636 |
|
|
{ 0.99752863545289705, 0.69999999999999996, 0.50000000000000000,
|
| 8637 |
|
|
1.0471975511965976 },
|
| 8638 |
|
|
{ 1.1576240080401499, 0.69999999999999996, 0.50000000000000000,
|
| 8639 |
|
|
1.2217304763960306 },
|
| 8640 |
|
|
{ 1.3191464023923762, 0.69999999999999996, 0.50000000000000000,
|
| 8641 |
|
|
1.3962634015954636 },
|
| 8642 |
|
|
{ 1.4818433192178544, 0.69999999999999996, 0.50000000000000000,
|
| 8643 |
|
|
1.5707963267948966 },
|
| 8644 |
|
|
};
|
| 8645 |
|
|
|
| 8646 |
|
|
// Test function for k=0.69999999999999996, nu=0.50000000000000000.
|
| 8647 |
|
|
template <typename Tp>
|
| 8648 |
|
|
void test166()
|
| 8649 |
|
|
{
|
| 8650 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8651 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8652 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8653 |
|
|
unsigned int num_datum = sizeof(data166)
|
| 8654 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8655 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8656 |
|
|
{
|
| 8657 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data166[i].k), Tp(data166[i].nu),
|
| 8658 |
|
|
Tp(data166[i].phi));
|
| 8659 |
|
|
const Tp f0 = data166[i].f0;
|
| 8660 |
|
|
const Tp diff = f - f0;
|
| 8661 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8662 |
|
|
max_abs_diff = std::abs(diff);
|
| 8663 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8664 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8665 |
|
|
{
|
| 8666 |
|
|
const Tp frac = diff / f0;
|
| 8667 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8668 |
|
|
max_abs_frac = std::abs(frac);
|
| 8669 |
|
|
}
|
| 8670 |
|
|
}
|
| 8671 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8672 |
|
|
}
|
| 8673 |
|
|
|
| 8674 |
|
|
// Test data for k=0.69999999999999996, nu=0.59999999999999998.
|
| 8675 |
|
|
testcase_ellint_3<double> data167[] = {
|
| 8676 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.59999999999999998,
|
| 8677 |
|
|
0.0000000000000000 },
|
| 8678 |
|
|
{ 0.17391719464391611, 0.69999999999999996, 0.59999999999999998,
|
| 8679 |
|
|
0.17453292519943295 },
|
| 8680 |
|
|
{ 0.34443927423869031, 0.69999999999999996, 0.59999999999999998,
|
| 8681 |
|
|
0.34906585039886590 },
|
| 8682 |
|
|
{ 0.50945473266486074, 0.69999999999999996, 0.59999999999999998,
|
| 8683 |
|
|
0.52359877559829882 },
|
| 8684 |
|
|
{ 0.66866056326513823, 0.69999999999999996, 0.59999999999999998,
|
| 8685 |
|
|
0.69813170079773179 },
|
| 8686 |
|
|
{ 0.82325830002337352, 0.69999999999999996, 0.59999999999999998,
|
| 8687 |
|
|
0.87266462599716477 },
|
| 8688 |
|
|
{ 0.97522808245669357, 0.69999999999999996, 0.59999999999999998,
|
| 8689 |
|
|
1.0471975511965976 },
|
| 8690 |
|
|
{ 1.1265300613705282, 0.69999999999999996, 0.59999999999999998,
|
| 8691 |
|
|
1.2217304763960306 },
|
| 8692 |
|
|
{ 1.2784066076152003, 0.69999999999999996, 0.59999999999999998,
|
| 8693 |
|
|
1.3962634015954636 },
|
| 8694 |
|
|
{ 1.4309994736080540, 0.69999999999999996, 0.59999999999999998,
|
| 8695 |
|
|
1.5707963267948966 },
|
| 8696 |
|
|
};
|
| 8697 |
|
|
|
| 8698 |
|
|
// Test function for k=0.69999999999999996, nu=0.59999999999999998.
|
| 8699 |
|
|
template <typename Tp>
|
| 8700 |
|
|
void test167()
|
| 8701 |
|
|
{
|
| 8702 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8703 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8704 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8705 |
|
|
unsigned int num_datum = sizeof(data167)
|
| 8706 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8707 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8708 |
|
|
{
|
| 8709 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data167[i].k), Tp(data167[i].nu),
|
| 8710 |
|
|
Tp(data167[i].phi));
|
| 8711 |
|
|
const Tp f0 = data167[i].f0;
|
| 8712 |
|
|
const Tp diff = f - f0;
|
| 8713 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8714 |
|
|
max_abs_diff = std::abs(diff);
|
| 8715 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8716 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8717 |
|
|
{
|
| 8718 |
|
|
const Tp frac = diff / f0;
|
| 8719 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8720 |
|
|
max_abs_frac = std::abs(frac);
|
| 8721 |
|
|
}
|
| 8722 |
|
|
}
|
| 8723 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8724 |
|
|
}
|
| 8725 |
|
|
|
| 8726 |
|
|
// Test data for k=0.69999999999999996, nu=0.69999999999999996.
|
| 8727 |
|
|
testcase_ellint_3<double> data168[] = {
|
| 8728 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.69999999999999996,
|
| 8729 |
|
|
0.0000000000000000 },
|
| 8730 |
|
|
{ 0.17374434963995028, 0.69999999999999996, 0.69999999999999996,
|
| 8731 |
|
|
0.17453292519943295 },
|
| 8732 |
|
|
{ 0.34315091562900674, 0.69999999999999996, 0.69999999999999996,
|
| 8733 |
|
|
0.34906585039886590 },
|
| 8734 |
|
|
{ 0.50554262375653358, 0.69999999999999996, 0.69999999999999996,
|
| 8735 |
|
|
0.52359877559829882 },
|
| 8736 |
|
|
{ 0.66050025406305812, 0.69999999999999996, 0.69999999999999996,
|
| 8737 |
|
|
0.69813170079773179 },
|
| 8738 |
|
|
{ 0.80938620118847404, 0.69999999999999996, 0.69999999999999996,
|
| 8739 |
|
|
0.87266462599716477 },
|
| 8740 |
|
|
{ 0.95443223855852144, 0.69999999999999996, 0.69999999999999996,
|
| 8741 |
|
|
1.0471975511965976 },
|
| 8742 |
|
|
{ 1.0978573207128302, 0.69999999999999996, 0.69999999999999996,
|
| 8743 |
|
|
1.2217304763960306 },
|
| 8744 |
|
|
{ 1.2411754575007123, 0.69999999999999996, 0.69999999999999996,
|
| 8745 |
|
|
1.3962634015954636 },
|
| 8746 |
|
|
{ 1.3848459188329196, 0.69999999999999996, 0.69999999999999996,
|
| 8747 |
|
|
1.5707963267948966 },
|
| 8748 |
|
|
};
|
| 8749 |
|
|
|
| 8750 |
|
|
// Test function for k=0.69999999999999996, nu=0.69999999999999996.
|
| 8751 |
|
|
template <typename Tp>
|
| 8752 |
|
|
void test168()
|
| 8753 |
|
|
{
|
| 8754 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8755 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8756 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8757 |
|
|
unsigned int num_datum = sizeof(data168)
|
| 8758 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8759 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8760 |
|
|
{
|
| 8761 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data168[i].k), Tp(data168[i].nu),
|
| 8762 |
|
|
Tp(data168[i].phi));
|
| 8763 |
|
|
const Tp f0 = data168[i].f0;
|
| 8764 |
|
|
const Tp diff = f - f0;
|
| 8765 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8766 |
|
|
max_abs_diff = std::abs(diff);
|
| 8767 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8768 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8769 |
|
|
{
|
| 8770 |
|
|
const Tp frac = diff / f0;
|
| 8771 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8772 |
|
|
max_abs_frac = std::abs(frac);
|
| 8773 |
|
|
}
|
| 8774 |
|
|
}
|
| 8775 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8776 |
|
|
}
|
| 8777 |
|
|
|
| 8778 |
|
|
// Test data for k=0.69999999999999996, nu=0.80000000000000004.
|
| 8779 |
|
|
testcase_ellint_3<double> data169[] = {
|
| 8780 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.80000000000000004,
|
| 8781 |
|
|
0.0000000000000000 },
|
| 8782 |
|
|
{ 0.17357211837335737, 0.69999999999999996, 0.80000000000000004,
|
| 8783 |
|
|
0.17453292519943295 },
|
| 8784 |
|
|
{ 0.34187941416012108, 0.69999999999999996, 0.80000000000000004,
|
| 8785 |
|
|
0.34906585039886590 },
|
| 8786 |
|
|
{ 0.50173239465478270, 0.69999999999999996, 0.80000000000000004,
|
| 8787 |
|
|
0.52359877559829882 },
|
| 8788 |
|
|
{ 0.65266550725988315, 0.69999999999999996, 0.80000000000000004,
|
| 8789 |
|
|
0.69813170079773179 },
|
| 8790 |
|
|
{ 0.79624879865249298, 0.69999999999999996, 0.80000000000000004,
|
| 8791 |
|
|
0.87266462599716477 },
|
| 8792 |
|
|
{ 0.93497577043296920, 0.69999999999999996, 0.80000000000000004,
|
| 8793 |
|
|
1.0471975511965976 },
|
| 8794 |
|
|
{ 1.0713041566930748, 0.69999999999999996, 0.80000000000000004,
|
| 8795 |
|
|
1.2217304763960306 },
|
| 8796 |
|
|
{ 1.2069772023255652, 0.69999999999999996, 0.80000000000000004,
|
| 8797 |
|
|
1.3962634015954636 },
|
| 8798 |
|
|
{ 1.3427110650397533, 0.69999999999999996, 0.80000000000000004,
|
| 8799 |
|
|
1.5707963267948966 },
|
| 8800 |
|
|
};
|
| 8801 |
|
|
|
| 8802 |
|
|
// Test function for k=0.69999999999999996, nu=0.80000000000000004.
|
| 8803 |
|
|
template <typename Tp>
|
| 8804 |
|
|
void test169()
|
| 8805 |
|
|
{
|
| 8806 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8807 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8808 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8809 |
|
|
unsigned int num_datum = sizeof(data169)
|
| 8810 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8811 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8812 |
|
|
{
|
| 8813 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data169[i].k), Tp(data169[i].nu),
|
| 8814 |
|
|
Tp(data169[i].phi));
|
| 8815 |
|
|
const Tp f0 = data169[i].f0;
|
| 8816 |
|
|
const Tp diff = f - f0;
|
| 8817 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8818 |
|
|
max_abs_diff = std::abs(diff);
|
| 8819 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8820 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8821 |
|
|
{
|
| 8822 |
|
|
const Tp frac = diff / f0;
|
| 8823 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8824 |
|
|
max_abs_frac = std::abs(frac);
|
| 8825 |
|
|
}
|
| 8826 |
|
|
}
|
| 8827 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8828 |
|
|
}
|
| 8829 |
|
|
|
| 8830 |
|
|
// Test data for k=0.69999999999999996, nu=0.90000000000000002.
|
| 8831 |
|
|
testcase_ellint_3<double> data170[] = {
|
| 8832 |
|
|
{ -0.0000000000000000, 0.69999999999999996, 0.90000000000000002,
|
| 8833 |
|
|
0.0000000000000000 },
|
| 8834 |
|
|
{ 0.17340049697003634, 0.69999999999999996, 0.90000000000000002,
|
| 8835 |
|
|
0.17453292519943295 },
|
| 8836 |
|
|
{ 0.34062438249741556, 0.69999999999999996, 0.90000000000000002,
|
| 8837 |
|
|
0.34906585039886590 },
|
| 8838 |
|
|
{ 0.49801946510076878, 0.69999999999999996, 0.90000000000000002,
|
| 8839 |
|
|
0.52359877559829882 },
|
| 8840 |
|
|
{ 0.64513432604750487, 0.69999999999999996, 0.90000000000000002,
|
| 8841 |
|
|
0.69813170079773179 },
|
| 8842 |
|
|
{ 0.78378145487573758, 0.69999999999999996, 0.90000000000000002,
|
| 8843 |
|
|
0.87266462599716477 },
|
| 8844 |
|
|
{ 0.91671799500854634, 0.69999999999999996, 0.90000000000000002,
|
| 8845 |
|
|
1.0471975511965976 },
|
| 8846 |
|
|
{ 1.0466193579463123, 0.69999999999999996, 0.90000000000000002,
|
| 8847 |
|
|
1.2217304763960306 },
|
| 8848 |
|
|
{ 1.1754218079199146, 0.69999999999999996, 0.90000000000000002,
|
| 8849 |
|
|
1.3962634015954636 },
|
| 8850 |
|
|
{ 1.3040500499695911, 0.69999999999999996, 0.90000000000000002,
|
| 8851 |
|
|
1.5707963267948966 },
|
| 8852 |
|
|
};
|
| 8853 |
|
|
|
| 8854 |
|
|
// Test function for k=0.69999999999999996, nu=0.90000000000000002.
|
| 8855 |
|
|
template <typename Tp>
|
| 8856 |
|
|
void test170()
|
| 8857 |
|
|
{
|
| 8858 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8859 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8860 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8861 |
|
|
unsigned int num_datum = sizeof(data170)
|
| 8862 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8863 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8864 |
|
|
{
|
| 8865 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data170[i].k), Tp(data170[i].nu),
|
| 8866 |
|
|
Tp(data170[i].phi));
|
| 8867 |
|
|
const Tp f0 = data170[i].f0;
|
| 8868 |
|
|
const Tp diff = f - f0;
|
| 8869 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8870 |
|
|
max_abs_diff = std::abs(diff);
|
| 8871 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8872 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8873 |
|
|
{
|
| 8874 |
|
|
const Tp frac = diff / f0;
|
| 8875 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8876 |
|
|
max_abs_frac = std::abs(frac);
|
| 8877 |
|
|
}
|
| 8878 |
|
|
}
|
| 8879 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8880 |
|
|
}
|
| 8881 |
|
|
|
| 8882 |
|
|
// Test data for k=0.80000000000000004, nu=0.0000000000000000.
|
| 8883 |
|
|
testcase_ellint_3<double> data171[] = {
|
| 8884 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.0000000000000000,
|
| 8885 |
|
|
0.0000000000000000 },
|
| 8886 |
|
|
{ 0.17510154241338902, 0.80000000000000004, 0.0000000000000000,
|
| 8887 |
|
|
0.17453292519943295 },
|
| 8888 |
|
|
{ 0.35365068839779390, 0.80000000000000004, 0.0000000000000000,
|
| 8889 |
|
|
0.34906585039886590 },
|
| 8890 |
|
|
{ 0.53926804409084561, 0.80000000000000004, 0.0000000000000000,
|
| 8891 |
|
|
0.52359877559829882 },
|
| 8892 |
|
|
{ 0.73587926028070383, 0.80000000000000004, 0.0000000000000000,
|
| 8893 |
|
|
0.69813170079773179 },
|
| 8894 |
|
|
{ 0.94770942970071170, 0.80000000000000004, 0.0000000000000000,
|
| 8895 |
|
|
0.87266462599716477 },
|
| 8896 |
|
|
{ 1.1789022995388239, 0.80000000000000004, 0.0000000000000000,
|
| 8897 |
|
|
1.0471975511965976 },
|
| 8898 |
|
|
{ 1.4323027881876009, 0.80000000000000004, 0.0000000000000000,
|
| 8899 |
|
|
1.2217304763960306 },
|
| 8900 |
|
|
{ 1.7069629739121674, 0.80000000000000004, 0.0000000000000000,
|
| 8901 |
|
|
1.3962634015954636 },
|
| 8902 |
|
|
{ 1.9953027776647296, 0.80000000000000004, 0.0000000000000000,
|
| 8903 |
|
|
1.5707963267948966 },
|
| 8904 |
|
|
};
|
| 8905 |
|
|
|
| 8906 |
|
|
// Test function for k=0.80000000000000004, nu=0.0000000000000000.
|
| 8907 |
|
|
template <typename Tp>
|
| 8908 |
|
|
void test171()
|
| 8909 |
|
|
{
|
| 8910 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8911 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8912 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8913 |
|
|
unsigned int num_datum = sizeof(data171)
|
| 8914 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8915 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8916 |
|
|
{
|
| 8917 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data171[i].k), Tp(data171[i].nu),
|
| 8918 |
|
|
Tp(data171[i].phi));
|
| 8919 |
|
|
const Tp f0 = data171[i].f0;
|
| 8920 |
|
|
const Tp diff = f - f0;
|
| 8921 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8922 |
|
|
max_abs_diff = std::abs(diff);
|
| 8923 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8924 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8925 |
|
|
{
|
| 8926 |
|
|
const Tp frac = diff / f0;
|
| 8927 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8928 |
|
|
max_abs_frac = std::abs(frac);
|
| 8929 |
|
|
}
|
| 8930 |
|
|
}
|
| 8931 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8932 |
|
|
}
|
| 8933 |
|
|
|
| 8934 |
|
|
// Test data for k=0.80000000000000004, nu=0.10000000000000001.
|
| 8935 |
|
|
testcase_ellint_3<double> data172[] = {
|
| 8936 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.10000000000000001,
|
| 8937 |
|
|
0.0000000000000000 },
|
| 8938 |
|
|
{ 0.17492468824017166, 0.80000000000000004, 0.10000000000000001,
|
| 8939 |
|
|
0.17453292519943295 },
|
| 8940 |
|
|
{ 0.35224443521476911, 0.80000000000000004, 0.10000000000000001,
|
| 8941 |
|
|
0.34906585039886590 },
|
| 8942 |
|
|
{ 0.53456851853226961, 0.80000000000000004, 0.10000000000000001,
|
| 8943 |
|
|
0.52359877559829882 },
|
| 8944 |
|
|
{ 0.72488875602364944, 0.80000000000000004, 0.10000000000000001,
|
| 8945 |
|
|
0.69813170079773179 },
|
| 8946 |
|
|
{ 0.92661354274638952, 0.80000000000000004, 0.10000000000000001,
|
| 8947 |
|
|
0.87266462599716477 },
|
| 8948 |
|
|
{ 1.1432651144499077, 0.80000000000000004, 0.10000000000000001,
|
| 8949 |
|
|
1.0471975511965976 },
|
| 8950 |
|
|
{ 1.3774479927211429, 0.80000000000000004, 0.10000000000000001,
|
| 8951 |
|
|
1.2217304763960306 },
|
| 8952 |
|
|
{ 1.6287092337196041, 0.80000000000000004, 0.10000000000000001,
|
| 8953 |
|
|
1.3962634015954636 },
|
| 8954 |
|
|
{ 1.8910755418379521, 0.80000000000000004, 0.10000000000000001,
|
| 8955 |
|
|
1.5707963267948966 },
|
| 8956 |
|
|
};
|
| 8957 |
|
|
|
| 8958 |
|
|
// Test function for k=0.80000000000000004, nu=0.10000000000000001.
|
| 8959 |
|
|
template <typename Tp>
|
| 8960 |
|
|
void test172()
|
| 8961 |
|
|
{
|
| 8962 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 8963 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 8964 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 8965 |
|
|
unsigned int num_datum = sizeof(data172)
|
| 8966 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 8967 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 8968 |
|
|
{
|
| 8969 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data172[i].k), Tp(data172[i].nu),
|
| 8970 |
|
|
Tp(data172[i].phi));
|
| 8971 |
|
|
const Tp f0 = data172[i].f0;
|
| 8972 |
|
|
const Tp diff = f - f0;
|
| 8973 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 8974 |
|
|
max_abs_diff = std::abs(diff);
|
| 8975 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 8976 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 8977 |
|
|
{
|
| 8978 |
|
|
const Tp frac = diff / f0;
|
| 8979 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 8980 |
|
|
max_abs_frac = std::abs(frac);
|
| 8981 |
|
|
}
|
| 8982 |
|
|
}
|
| 8983 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 8984 |
|
|
}
|
| 8985 |
|
|
|
| 8986 |
|
|
// Test data for k=0.80000000000000004, nu=0.20000000000000001.
|
| 8987 |
|
|
testcase_ellint_3<double> data173[] = {
|
| 8988 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.20000000000000001,
|
| 8989 |
|
|
0.0000000000000000 },
|
| 8990 |
|
|
{ 0.17474847286224943, 0.80000000000000004, 0.20000000000000001,
|
| 8991 |
|
|
0.17453292519943295 },
|
| 8992 |
|
|
{ 0.35085779529084682, 0.80000000000000004, 0.20000000000000001,
|
| 8993 |
|
|
0.34906585039886590 },
|
| 8994 |
|
|
{ 0.53000829263059157, 0.80000000000000004, 0.20000000000000001,
|
| 8995 |
|
|
0.52359877559829882 },
|
| 8996 |
|
|
{ 0.71443466027453406, 0.80000000000000004, 0.20000000000000001,
|
| 8997 |
|
|
0.69813170079773179 },
|
| 8998 |
|
|
{ 0.90698196872715420, 0.80000000000000004, 0.20000000000000001,
|
| 8999 |
|
|
0.87266462599716477 },
|
| 9000 |
|
|
{ 1.1108198200558581, 0.80000000000000004, 0.20000000000000001,
|
| 9001 |
|
|
1.0471975511965976 },
|
| 9002 |
|
|
{ 1.3284988909963957, 0.80000000000000004, 0.20000000000000001,
|
| 9003 |
|
|
1.2217304763960306 },
|
| 9004 |
|
|
{ 1.5600369318140328, 0.80000000000000004, 0.20000000000000001,
|
| 9005 |
|
|
1.3962634015954636 },
|
| 9006 |
|
|
{ 1.8007226661734588, 0.80000000000000004, 0.20000000000000001,
|
| 9007 |
|
|
1.5707963267948966 },
|
| 9008 |
|
|
};
|
| 9009 |
|
|
|
| 9010 |
|
|
// Test function for k=0.80000000000000004, nu=0.20000000000000001.
|
| 9011 |
|
|
template <typename Tp>
|
| 9012 |
|
|
void test173()
|
| 9013 |
|
|
{
|
| 9014 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9015 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9016 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9017 |
|
|
unsigned int num_datum = sizeof(data173)
|
| 9018 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9019 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9020 |
|
|
{
|
| 9021 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data173[i].k), Tp(data173[i].nu),
|
| 9022 |
|
|
Tp(data173[i].phi));
|
| 9023 |
|
|
const Tp f0 = data173[i].f0;
|
| 9024 |
|
|
const Tp diff = f - f0;
|
| 9025 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9026 |
|
|
max_abs_diff = std::abs(diff);
|
| 9027 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9028 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9029 |
|
|
{
|
| 9030 |
|
|
const Tp frac = diff / f0;
|
| 9031 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9032 |
|
|
max_abs_frac = std::abs(frac);
|
| 9033 |
|
|
}
|
| 9034 |
|
|
}
|
| 9035 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9036 |
|
|
}
|
| 9037 |
|
|
|
| 9038 |
|
|
// Test data for k=0.80000000000000004, nu=0.29999999999999999.
|
| 9039 |
|
|
testcase_ellint_3<double> data174[] = {
|
| 9040 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.29999999999999999,
|
| 9041 |
|
|
0.0000000000000000 },
|
| 9042 |
|
|
{ 0.17457289217669891, 0.80000000000000004, 0.29999999999999999,
|
| 9043 |
|
|
0.17453292519943295 },
|
| 9044 |
|
|
{ 0.34949028801501258, 0.80000000000000004, 0.29999999999999999,
|
| 9045 |
|
|
0.34906585039886590 },
|
| 9046 |
|
|
{ 0.52558024362769318, 0.80000000000000004, 0.29999999999999999,
|
| 9047 |
|
|
0.52359877559829882 },
|
| 9048 |
|
|
{ 0.70447281740094914, 0.80000000000000004, 0.29999999999999999,
|
| 9049 |
|
|
0.69813170079773179 },
|
| 9050 |
|
|
{ 0.88864745641528986, 0.80000000000000004, 0.29999999999999999,
|
| 9051 |
|
|
0.87266462599716477 },
|
| 9052 |
|
|
{ 1.0811075819341465, 0.80000000000000004, 0.29999999999999999,
|
| 9053 |
|
|
1.0471975511965976 },
|
| 9054 |
|
|
{ 1.2844589654082377, 0.80000000000000004, 0.29999999999999999,
|
| 9055 |
|
|
1.2217304763960306 },
|
| 9056 |
|
|
{ 1.4991461361277849, 0.80000000000000004, 0.29999999999999999,
|
| 9057 |
|
|
1.3962634015954636 },
|
| 9058 |
|
|
{ 1.7214611048717301, 0.80000000000000004, 0.29999999999999999,
|
| 9059 |
|
|
1.5707963267948966 },
|
| 9060 |
|
|
};
|
| 9061 |
|
|
|
| 9062 |
|
|
// Test function for k=0.80000000000000004, nu=0.29999999999999999.
|
| 9063 |
|
|
template <typename Tp>
|
| 9064 |
|
|
void test174()
|
| 9065 |
|
|
{
|
| 9066 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9067 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9068 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9069 |
|
|
unsigned int num_datum = sizeof(data174)
|
| 9070 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9071 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9072 |
|
|
{
|
| 9073 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data174[i].k), Tp(data174[i].nu),
|
| 9074 |
|
|
Tp(data174[i].phi));
|
| 9075 |
|
|
const Tp f0 = data174[i].f0;
|
| 9076 |
|
|
const Tp diff = f - f0;
|
| 9077 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9078 |
|
|
max_abs_diff = std::abs(diff);
|
| 9079 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9080 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9081 |
|
|
{
|
| 9082 |
|
|
const Tp frac = diff / f0;
|
| 9083 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9084 |
|
|
max_abs_frac = std::abs(frac);
|
| 9085 |
|
|
}
|
| 9086 |
|
|
}
|
| 9087 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9088 |
|
|
}
|
| 9089 |
|
|
|
| 9090 |
|
|
// Test data for k=0.80000000000000004, nu=0.40000000000000002.
|
| 9091 |
|
|
testcase_ellint_3<double> data175[] = {
|
| 9092 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.40000000000000002,
|
| 9093 |
|
|
0.0000000000000000 },
|
| 9094 |
|
|
{ 0.17439794211872178, 0.80000000000000004, 0.40000000000000002,
|
| 9095 |
|
|
0.17453292519943295 },
|
| 9096 |
|
|
{ 0.34814144964568972, 0.80000000000000004, 0.40000000000000002,
|
| 9097 |
|
|
0.34906585039886590 },
|
| 9098 |
|
|
{ 0.52127776285273075, 0.80000000000000004, 0.40000000000000002,
|
| 9099 |
|
|
0.52359877559829882 },
|
| 9100 |
|
|
{ 0.69496411438966599, 0.80000000000000004, 0.40000000000000002,
|
| 9101 |
|
|
0.69813170079773179 },
|
| 9102 |
|
|
{ 0.87146878427509589, 0.80000000000000004, 0.40000000000000002,
|
| 9103 |
|
|
0.87266462599716477 },
|
| 9104 |
|
|
{ 1.0537579024937762, 0.80000000000000004, 0.40000000000000002,
|
| 9105 |
|
|
1.0471975511965976 },
|
| 9106 |
|
|
{ 1.2445534387922637, 0.80000000000000004, 0.40000000000000002,
|
| 9107 |
|
|
1.2217304763960306 },
|
| 9108 |
|
|
{ 1.4446769766361993, 0.80000000000000004, 0.40000000000000002,
|
| 9109 |
|
|
1.3962634015954636 },
|
| 9110 |
|
|
{ 1.6512267838651289, 0.80000000000000004, 0.40000000000000002,
|
| 9111 |
|
|
1.5707963267948966 },
|
| 9112 |
|
|
};
|
| 9113 |
|
|
|
| 9114 |
|
|
// Test function for k=0.80000000000000004, nu=0.40000000000000002.
|
| 9115 |
|
|
template <typename Tp>
|
| 9116 |
|
|
void test175()
|
| 9117 |
|
|
{
|
| 9118 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9119 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9120 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9121 |
|
|
unsigned int num_datum = sizeof(data175)
|
| 9122 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9123 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9124 |
|
|
{
|
| 9125 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data175[i].k), Tp(data175[i].nu),
|
| 9126 |
|
|
Tp(data175[i].phi));
|
| 9127 |
|
|
const Tp f0 = data175[i].f0;
|
| 9128 |
|
|
const Tp diff = f - f0;
|
| 9129 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9130 |
|
|
max_abs_diff = std::abs(diff);
|
| 9131 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9132 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9133 |
|
|
{
|
| 9134 |
|
|
const Tp frac = diff / f0;
|
| 9135 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9136 |
|
|
max_abs_frac = std::abs(frac);
|
| 9137 |
|
|
}
|
| 9138 |
|
|
}
|
| 9139 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9140 |
|
|
}
|
| 9141 |
|
|
|
| 9142 |
|
|
// Test data for k=0.80000000000000004, nu=0.50000000000000000.
|
| 9143 |
|
|
testcase_ellint_3<double> data176[] = {
|
| 9144 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.50000000000000000,
|
| 9145 |
|
|
0.0000000000000000 },
|
| 9146 |
|
|
{ 0.17422361866118047, 0.80000000000000004, 0.50000000000000000,
|
| 9147 |
|
|
0.17453292519943295 },
|
| 9148 |
|
|
{ 0.34681083254170475, 0.80000000000000004, 0.50000000000000000,
|
| 9149 |
|
|
0.34906585039886590 },
|
| 9150 |
|
|
{ 0.51709470815494440, 0.80000000000000004, 0.50000000000000000,
|
| 9151 |
|
|
0.52359877559829882 },
|
| 9152 |
|
|
{ 0.68587375344080259, 0.80000000000000004, 0.50000000000000000,
|
| 9153 |
|
|
0.69813170079773179 },
|
| 9154 |
|
|
{ 0.85532571852810624, 0.80000000000000004, 0.50000000000000000,
|
| 9155 |
|
|
0.87266462599716477 },
|
| 9156 |
|
|
{ 1.0284677391874906, 0.80000000000000004, 0.50000000000000000,
|
| 9157 |
|
|
1.0471975511965976 },
|
| 9158 |
|
|
{ 1.2081693942686225, 0.80000000000000004, 0.50000000000000000,
|
| 9159 |
|
|
1.2217304763960306 },
|
| 9160 |
|
|
{ 1.3955803006426311, 0.80000000000000004, 0.50000000000000000,
|
| 9161 |
|
|
1.3962634015954636 },
|
| 9162 |
|
|
{ 1.5884528947755532, 0.80000000000000004, 0.50000000000000000,
|
| 9163 |
|
|
1.5707963267948966 },
|
| 9164 |
|
|
};
|
| 9165 |
|
|
|
| 9166 |
|
|
// Test function for k=0.80000000000000004, nu=0.50000000000000000.
|
| 9167 |
|
|
template <typename Tp>
|
| 9168 |
|
|
void test176()
|
| 9169 |
|
|
{
|
| 9170 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9171 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9172 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9173 |
|
|
unsigned int num_datum = sizeof(data176)
|
| 9174 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9175 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9176 |
|
|
{
|
| 9177 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data176[i].k), Tp(data176[i].nu),
|
| 9178 |
|
|
Tp(data176[i].phi));
|
| 9179 |
|
|
const Tp f0 = data176[i].f0;
|
| 9180 |
|
|
const Tp diff = f - f0;
|
| 9181 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9182 |
|
|
max_abs_diff = std::abs(diff);
|
| 9183 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9184 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9185 |
|
|
{
|
| 9186 |
|
|
const Tp frac = diff / f0;
|
| 9187 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9188 |
|
|
max_abs_frac = std::abs(frac);
|
| 9189 |
|
|
}
|
| 9190 |
|
|
}
|
| 9191 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9192 |
|
|
}
|
| 9193 |
|
|
|
| 9194 |
|
|
// Test data for k=0.80000000000000004, nu=0.59999999999999998.
|
| 9195 |
|
|
testcase_ellint_3<double> data177[] = {
|
| 9196 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.59999999999999998,
|
| 9197 |
|
|
0.0000000000000000 },
|
| 9198 |
|
|
{ 0.17404991781414092, 0.80000000000000004, 0.59999999999999998,
|
| 9199 |
|
|
0.17453292519943295 },
|
| 9200 |
|
|
{ 0.34549800443625167, 0.80000000000000004, 0.59999999999999998,
|
| 9201 |
|
|
0.34906585039886590 },
|
| 9202 |
|
|
{ 0.51302536167001556, 0.80000000000000004, 0.59999999999999998,
|
| 9203 |
|
|
0.52359877559829882 },
|
| 9204 |
|
|
{ 0.67717065003912258, 0.80000000000000004, 0.59999999999999998,
|
| 9205 |
|
|
0.69813170079773179 },
|
| 9206 |
|
|
{ 0.84011512421134416, 0.80000000000000004, 0.59999999999999998,
|
| 9207 |
|
|
0.87266462599716477 },
|
| 9208 |
|
|
{ 1.0049863847088742, 0.80000000000000004, 0.59999999999999998,
|
| 9209 |
|
|
1.0471975511965976 },
|
| 9210 |
|
|
{ 1.1748145941898918, 0.80000000000000004, 0.59999999999999998,
|
| 9211 |
|
|
1.2217304763960306 },
|
| 9212 |
|
|
{ 1.3510319699755071, 0.80000000000000004, 0.59999999999999998,
|
| 9213 |
|
|
1.3962634015954636 },
|
| 9214 |
|
|
{ 1.5319262547427865, 0.80000000000000004, 0.59999999999999998,
|
| 9215 |
|
|
1.5707963267948966 },
|
| 9216 |
|
|
};
|
| 9217 |
|
|
|
| 9218 |
|
|
// Test function for k=0.80000000000000004, nu=0.59999999999999998.
|
| 9219 |
|
|
template <typename Tp>
|
| 9220 |
|
|
void test177()
|
| 9221 |
|
|
{
|
| 9222 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9223 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9224 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9225 |
|
|
unsigned int num_datum = sizeof(data177)
|
| 9226 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9227 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9228 |
|
|
{
|
| 9229 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data177[i].k), Tp(data177[i].nu),
|
| 9230 |
|
|
Tp(data177[i].phi));
|
| 9231 |
|
|
const Tp f0 = data177[i].f0;
|
| 9232 |
|
|
const Tp diff = f - f0;
|
| 9233 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9234 |
|
|
max_abs_diff = std::abs(diff);
|
| 9235 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9236 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9237 |
|
|
{
|
| 9238 |
|
|
const Tp frac = diff / f0;
|
| 9239 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9240 |
|
|
max_abs_frac = std::abs(frac);
|
| 9241 |
|
|
}
|
| 9242 |
|
|
}
|
| 9243 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9244 |
|
|
}
|
| 9245 |
|
|
|
| 9246 |
|
|
// Test data for k=0.80000000000000004, nu=0.69999999999999996.
|
| 9247 |
|
|
testcase_ellint_3<double> data178[] = {
|
| 9248 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.69999999999999996,
|
| 9249 |
|
|
0.0000000000000000 },
|
| 9250 |
|
|
{ 0.17387683562442202, 0.80000000000000004, 0.69999999999999996,
|
| 9251 |
|
|
0.17453292519943295 },
|
| 9252 |
|
|
{ 0.34420254775101611, 0.80000000000000004, 0.69999999999999996,
|
| 9253 |
|
|
0.34906585039886590 },
|
| 9254 |
|
|
{ 0.50906439222143685, 0.80000000000000004, 0.69999999999999996,
|
| 9255 |
|
|
0.52359877559829882 },
|
| 9256 |
|
|
{ 0.66882693152688433, 0.80000000000000004, 0.69999999999999996,
|
| 9257 |
|
|
0.69813170079773179 },
|
| 9258 |
|
|
{ 0.82574792844091316, 0.80000000000000004, 0.69999999999999996,
|
| 9259 |
|
|
0.87266462599716477 },
|
| 9260 |
|
|
{ 0.98310431309490953, 0.80000000000000004, 0.69999999999999996,
|
| 9261 |
|
|
1.0471975511965976 },
|
| 9262 |
|
|
{ 1.1440884535113258, 0.80000000000000004, 0.69999999999999996,
|
| 9263 |
|
|
1.2217304763960306 },
|
| 9264 |
|
|
{ 1.3103743938952537, 0.80000000000000004, 0.69999999999999996,
|
| 9265 |
|
|
1.3962634015954636 },
|
| 9266 |
|
|
{ 1.4806912324625332, 0.80000000000000004, 0.69999999999999996,
|
| 9267 |
|
|
1.5707963267948966 },
|
| 9268 |
|
|
};
|
| 9269 |
|
|
|
| 9270 |
|
|
// Test function for k=0.80000000000000004, nu=0.69999999999999996.
|
| 9271 |
|
|
template <typename Tp>
|
| 9272 |
|
|
void test178()
|
| 9273 |
|
|
{
|
| 9274 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9275 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9276 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9277 |
|
|
unsigned int num_datum = sizeof(data178)
|
| 9278 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9279 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9280 |
|
|
{
|
| 9281 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data178[i].k), Tp(data178[i].nu),
|
| 9282 |
|
|
Tp(data178[i].phi));
|
| 9283 |
|
|
const Tp f0 = data178[i].f0;
|
| 9284 |
|
|
const Tp diff = f - f0;
|
| 9285 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9286 |
|
|
max_abs_diff = std::abs(diff);
|
| 9287 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9288 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9289 |
|
|
{
|
| 9290 |
|
|
const Tp frac = diff / f0;
|
| 9291 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9292 |
|
|
max_abs_frac = std::abs(frac);
|
| 9293 |
|
|
}
|
| 9294 |
|
|
}
|
| 9295 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9296 |
|
|
}
|
| 9297 |
|
|
|
| 9298 |
|
|
// Test data for k=0.80000000000000004, nu=0.80000000000000004.
|
| 9299 |
|
|
testcase_ellint_3<double> data179[] = {
|
| 9300 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.80000000000000004,
|
| 9301 |
|
|
0.0000000000000000 },
|
| 9302 |
|
|
{ 0.17370436817515206, 0.80000000000000004, 0.80000000000000004,
|
| 9303 |
|
|
0.17453292519943295 },
|
| 9304 |
|
|
{ 0.34292405894783395, 0.80000000000000004, 0.80000000000000004,
|
| 9305 |
|
|
0.34906585039886590 },
|
| 9306 |
|
|
{ 0.50520682176250087, 0.80000000000000004, 0.80000000000000004,
|
| 9307 |
|
|
0.52359877559829882 },
|
| 9308 |
|
|
{ 0.66081751679736189, 0.80000000000000004, 0.80000000000000004,
|
| 9309 |
|
|
0.69813170079773179 },
|
| 9310 |
|
|
{ 0.81214672249355102, 0.80000000000000004, 0.80000000000000004,
|
| 9311 |
|
|
0.87266462599716477 },
|
| 9312 |
|
|
{ 0.96264481387685574, 0.80000000000000004, 0.80000000000000004,
|
| 9313 |
|
|
1.0471975511965976 },
|
| 9314 |
|
|
{ 1.1156611352656258, 0.80000000000000004, 0.80000000000000004,
|
| 9315 |
|
|
1.2217304763960306 },
|
| 9316 |
|
|
{ 1.2730756225143889, 0.80000000000000004, 0.80000000000000004,
|
| 9317 |
|
|
1.3962634015954636 },
|
| 9318 |
|
|
{ 1.4339837018309474, 0.80000000000000004, 0.80000000000000004,
|
| 9319 |
|
|
1.5707963267948966 },
|
| 9320 |
|
|
};
|
| 9321 |
|
|
|
| 9322 |
|
|
// Test function for k=0.80000000000000004, nu=0.80000000000000004.
|
| 9323 |
|
|
template <typename Tp>
|
| 9324 |
|
|
void test179()
|
| 9325 |
|
|
{
|
| 9326 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9327 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9328 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9329 |
|
|
unsigned int num_datum = sizeof(data179)
|
| 9330 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9331 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9332 |
|
|
{
|
| 9333 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data179[i].k), Tp(data179[i].nu),
|
| 9334 |
|
|
Tp(data179[i].phi));
|
| 9335 |
|
|
const Tp f0 = data179[i].f0;
|
| 9336 |
|
|
const Tp diff = f - f0;
|
| 9337 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9338 |
|
|
max_abs_diff = std::abs(diff);
|
| 9339 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9340 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9341 |
|
|
{
|
| 9342 |
|
|
const Tp frac = diff / f0;
|
| 9343 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9344 |
|
|
max_abs_frac = std::abs(frac);
|
| 9345 |
|
|
}
|
| 9346 |
|
|
}
|
| 9347 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9348 |
|
|
}
|
| 9349 |
|
|
|
| 9350 |
|
|
// Test data for k=0.80000000000000004, nu=0.90000000000000002.
|
| 9351 |
|
|
testcase_ellint_3<double> data180[] = {
|
| 9352 |
|
|
{ -0.0000000000000000, 0.80000000000000004, 0.90000000000000002,
|
| 9353 |
|
|
0.0000000000000000 },
|
| 9354 |
|
|
{ 0.17353251158533153, 0.80000000000000004, 0.90000000000000002,
|
| 9355 |
|
|
0.17453292519943295 },
|
| 9356 |
|
|
{ 0.34166214791545768, 0.80000000000000004, 0.90000000000000002,
|
| 9357 |
|
|
0.34906585039886590 },
|
| 9358 |
|
|
{ 0.50144799535130580, 0.80000000000000004, 0.90000000000000002,
|
| 9359 |
|
|
0.52359877559829882 },
|
| 9360 |
|
|
{ 0.65311976193814447, 0.80000000000000004, 0.90000000000000002,
|
| 9361 |
|
|
0.69813170079773179 },
|
| 9362 |
|
|
{ 0.79924384892320866, 0.80000000000000004, 0.90000000000000002,
|
| 9363 |
|
|
0.87266462599716477 },
|
| 9364 |
|
|
{ 0.94345762353365625, 0.80000000000000004, 0.90000000000000002,
|
| 9365 |
|
|
1.0471975511965976 },
|
| 9366 |
|
|
{ 1.0892582069219159, 0.80000000000000004, 0.90000000000000002,
|
| 9367 |
|
|
1.2217304763960306 },
|
| 9368 |
|
|
{ 1.2387000876610268, 0.80000000000000004, 0.90000000000000002,
|
| 9369 |
|
|
1.3962634015954636 },
|
| 9370 |
|
|
{ 1.3911845406776222, 0.80000000000000004, 0.90000000000000002,
|
| 9371 |
|
|
1.5707963267948966 },
|
| 9372 |
|
|
};
|
| 9373 |
|
|
|
| 9374 |
|
|
// Test function for k=0.80000000000000004, nu=0.90000000000000002.
|
| 9375 |
|
|
template <typename Tp>
|
| 9376 |
|
|
void test180()
|
| 9377 |
|
|
{
|
| 9378 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9379 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9380 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9381 |
|
|
unsigned int num_datum = sizeof(data180)
|
| 9382 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9383 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9384 |
|
|
{
|
| 9385 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data180[i].k), Tp(data180[i].nu),
|
| 9386 |
|
|
Tp(data180[i].phi));
|
| 9387 |
|
|
const Tp f0 = data180[i].f0;
|
| 9388 |
|
|
const Tp diff = f - f0;
|
| 9389 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9390 |
|
|
max_abs_diff = std::abs(diff);
|
| 9391 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9392 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9393 |
|
|
{
|
| 9394 |
|
|
const Tp frac = diff / f0;
|
| 9395 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9396 |
|
|
max_abs_frac = std::abs(frac);
|
| 9397 |
|
|
}
|
| 9398 |
|
|
}
|
| 9399 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9400 |
|
|
}
|
| 9401 |
|
|
|
| 9402 |
|
|
// Test data for k=0.89999999999999991, nu=0.0000000000000000.
|
| 9403 |
|
|
testcase_ellint_3<double> data181[] = {
|
| 9404 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.0000000000000000,
|
| 9405 |
|
|
0.0000000000000000 },
|
| 9406 |
|
|
{ 0.17525427376115027, 0.89999999999999991, 0.0000000000000000,
|
| 9407 |
|
|
0.17453292519943295 },
|
| 9408 |
|
|
{ 0.35492464591297446, 0.89999999999999991, 0.0000000000000000,
|
| 9409 |
|
|
0.34906585039886590 },
|
| 9410 |
|
|
{ 0.54388221416157123, 0.89999999999999991, 0.0000000000000000,
|
| 9411 |
|
|
0.52359877559829882 },
|
| 9412 |
|
|
{ 0.74797400423532501, 0.89999999999999991, 0.0000000000000000,
|
| 9413 |
|
|
0.69813170079773179 },
|
| 9414 |
|
|
{ 0.97463898451966458, 0.89999999999999991, 0.0000000000000000,
|
| 9415 |
|
|
0.87266462599716477 },
|
| 9416 |
|
|
{ 1.2334463254523438, 0.89999999999999991, 0.0000000000000000,
|
| 9417 |
|
|
1.0471975511965976 },
|
| 9418 |
|
|
{ 1.5355247765594910, 0.89999999999999991, 0.0000000000000000,
|
| 9419 |
|
|
1.2217304763960306 },
|
| 9420 |
|
|
{ 1.8882928567775117, 0.89999999999999991, 0.0000000000000000,
|
| 9421 |
|
|
1.3962634015954636 },
|
| 9422 |
|
|
{ 2.2805491384227699, 0.89999999999999991, 0.0000000000000000,
|
| 9423 |
|
|
1.5707963267948966 },
|
| 9424 |
|
|
};
|
| 9425 |
|
|
|
| 9426 |
|
|
// Test function for k=0.89999999999999991, nu=0.0000000000000000.
|
| 9427 |
|
|
template <typename Tp>
|
| 9428 |
|
|
void test181()
|
| 9429 |
|
|
{
|
| 9430 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9431 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9432 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9433 |
|
|
unsigned int num_datum = sizeof(data181)
|
| 9434 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9435 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9436 |
|
|
{
|
| 9437 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data181[i].k), Tp(data181[i].nu),
|
| 9438 |
|
|
Tp(data181[i].phi));
|
| 9439 |
|
|
const Tp f0 = data181[i].f0;
|
| 9440 |
|
|
const Tp diff = f - f0;
|
| 9441 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9442 |
|
|
max_abs_diff = std::abs(diff);
|
| 9443 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9444 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9445 |
|
|
{
|
| 9446 |
|
|
const Tp frac = diff / f0;
|
| 9447 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9448 |
|
|
max_abs_frac = std::abs(frac);
|
| 9449 |
|
|
}
|
| 9450 |
|
|
}
|
| 9451 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9452 |
|
|
}
|
| 9453 |
|
|
|
| 9454 |
|
|
// Test data for k=0.89999999999999991, nu=0.10000000000000001.
|
| 9455 |
|
|
testcase_ellint_3<double> data182[] = {
|
| 9456 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.10000000000000001,
|
| 9457 |
|
|
0.0000000000000000 },
|
| 9458 |
|
|
{ 0.17507714233254659, 0.89999999999999991, 0.10000000000000001,
|
| 9459 |
|
|
0.17453292519943295 },
|
| 9460 |
|
|
{ 0.35350932904326521, 0.89999999999999991, 0.10000000000000001,
|
| 9461 |
|
|
0.34906585039886590 },
|
| 9462 |
|
|
{ 0.53911129989870987, 0.89999999999999991, 0.10000000000000001,
|
| 9463 |
|
|
0.52359877559829882 },
|
| 9464 |
|
|
{ 0.73666644254508407, 0.89999999999999991, 0.10000000000000001,
|
| 9465 |
|
|
0.69813170079773179 },
|
| 9466 |
|
|
{ 0.95250736612100184, 0.89999999999999991, 0.10000000000000001,
|
| 9467 |
|
|
0.87266462599716477 },
|
| 9468 |
|
|
{ 1.1950199550905591, 0.89999999999999991, 0.10000000000000001,
|
| 9469 |
|
|
1.0471975511965976 },
|
| 9470 |
|
|
{ 1.4741687286340848, 0.89999999999999991, 0.10000000000000001,
|
| 9471 |
|
|
1.2217304763960306 },
|
| 9472 |
|
|
{ 1.7968678183506053, 0.89999999999999991, 0.10000000000000001,
|
| 9473 |
|
|
1.3962634015954636 },
|
| 9474 |
|
|
{ 2.1537868513875282, 0.89999999999999991, 0.10000000000000001,
|
| 9475 |
|
|
1.5707963267948966 },
|
| 9476 |
|
|
};
|
| 9477 |
|
|
|
| 9478 |
|
|
// Test function for k=0.89999999999999991, nu=0.10000000000000001.
|
| 9479 |
|
|
template <typename Tp>
|
| 9480 |
|
|
void test182()
|
| 9481 |
|
|
{
|
| 9482 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9483 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9484 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9485 |
|
|
unsigned int num_datum = sizeof(data182)
|
| 9486 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9487 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9488 |
|
|
{
|
| 9489 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data182[i].k), Tp(data182[i].nu),
|
| 9490 |
|
|
Tp(data182[i].phi));
|
| 9491 |
|
|
const Tp f0 = data182[i].f0;
|
| 9492 |
|
|
const Tp diff = f - f0;
|
| 9493 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9494 |
|
|
max_abs_diff = std::abs(diff);
|
| 9495 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9496 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9497 |
|
|
{
|
| 9498 |
|
|
const Tp frac = diff / f0;
|
| 9499 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9500 |
|
|
max_abs_frac = std::abs(frac);
|
| 9501 |
|
|
}
|
| 9502 |
|
|
}
|
| 9503 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9504 |
|
|
}
|
| 9505 |
|
|
|
| 9506 |
|
|
// Test data for k=0.89999999999999991, nu=0.20000000000000001.
|
| 9507 |
|
|
testcase_ellint_3<double> data183[] = {
|
| 9508 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.20000000000000001,
|
| 9509 |
|
|
0.0000000000000000 },
|
| 9510 |
|
|
{ 0.17490065089140930, 0.89999999999999991, 0.20000000000000001,
|
| 9511 |
|
|
0.17453292519943295 },
|
| 9512 |
|
|
{ 0.35211377590661436, 0.89999999999999991, 0.20000000000000001,
|
| 9513 |
|
|
0.34906585039886590 },
|
| 9514 |
|
|
{ 0.53448220334204111, 0.89999999999999991, 0.20000000000000001,
|
| 9515 |
|
|
0.52359877559829882 },
|
| 9516 |
|
|
{ 0.72591368943179591, 0.89999999999999991, 0.20000000000000001,
|
| 9517 |
|
|
0.69813170079773179 },
|
| 9518 |
|
|
{ 0.93192539780038763, 0.89999999999999991, 0.20000000000000001,
|
| 9519 |
|
|
0.87266462599716477 },
|
| 9520 |
|
|
{ 1.1600809679692681, 0.89999999999999991, 0.20000000000000001,
|
| 9521 |
|
|
1.0471975511965976 },
|
| 9522 |
|
|
{ 1.4195407225882508, 0.89999999999999991, 0.20000000000000001,
|
| 9523 |
|
|
1.2217304763960306 },
|
| 9524 |
|
|
{ 1.7168966476424521, 0.89999999999999991, 0.20000000000000001,
|
| 9525 |
|
|
1.3962634015954636 },
|
| 9526 |
|
|
{ 2.0443194576468890, 0.89999999999999991, 0.20000000000000001,
|
| 9527 |
|
|
1.5707963267948966 },
|
| 9528 |
|
|
};
|
| 9529 |
|
|
|
| 9530 |
|
|
// Test function for k=0.89999999999999991, nu=0.20000000000000001.
|
| 9531 |
|
|
template <typename Tp>
|
| 9532 |
|
|
void test183()
|
| 9533 |
|
|
{
|
| 9534 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9535 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9536 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9537 |
|
|
unsigned int num_datum = sizeof(data183)
|
| 9538 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9539 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9540 |
|
|
{
|
| 9541 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data183[i].k), Tp(data183[i].nu),
|
| 9542 |
|
|
Tp(data183[i].phi));
|
| 9543 |
|
|
const Tp f0 = data183[i].f0;
|
| 9544 |
|
|
const Tp diff = f - f0;
|
| 9545 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9546 |
|
|
max_abs_diff = std::abs(diff);
|
| 9547 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9548 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9549 |
|
|
{
|
| 9550 |
|
|
const Tp frac = diff / f0;
|
| 9551 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9552 |
|
|
max_abs_frac = std::abs(frac);
|
| 9553 |
|
|
}
|
| 9554 |
|
|
}
|
| 9555 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9556 |
|
|
}
|
| 9557 |
|
|
|
| 9558 |
|
|
// Test data for k=0.89999999999999991, nu=0.29999999999999999.
|
| 9559 |
|
|
testcase_ellint_3<double> data184[] = {
|
| 9560 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.29999999999999999,
|
| 9561 |
|
|
0.0000000000000000 },
|
| 9562 |
|
|
{ 0.17472479532647534, 0.89999999999999991, 0.29999999999999999,
|
| 9563 |
|
|
0.17453292519943295 },
|
| 9564 |
|
|
{ 0.35073750187374114, 0.89999999999999991, 0.29999999999999999,
|
| 9565 |
|
|
0.34906585039886590 },
|
| 9566 |
|
|
{ 0.52998766129466968, 0.89999999999999991, 0.29999999999999999,
|
| 9567 |
|
|
0.52359877559829882 },
|
| 9568 |
|
|
{ 0.71566993548699565, 0.89999999999999991, 0.29999999999999999,
|
| 9569 |
|
|
0.69813170079773179 },
|
| 9570 |
|
|
{ 0.91271517762560195, 0.89999999999999991, 0.29999999999999999,
|
| 9571 |
|
|
0.87266462599716477 },
|
| 9572 |
|
|
{ 1.1281241199843368, 0.89999999999999991, 0.29999999999999999,
|
| 9573 |
|
|
1.0471975511965976 },
|
| 9574 |
|
|
{ 1.3704929576917448, 0.89999999999999991, 0.29999999999999999,
|
| 9575 |
|
|
1.2217304763960306 },
|
| 9576 |
|
|
{ 1.6461981511487711, 0.89999999999999991, 0.29999999999999999,
|
| 9577 |
|
|
1.3962634015954636 },
|
| 9578 |
|
|
{ 1.9486280260314424, 0.89999999999999991, 0.29999999999999999,
|
| 9579 |
|
|
1.5707963267948966 },
|
| 9580 |
|
|
};
|
| 9581 |
|
|
|
| 9582 |
|
|
// Test function for k=0.89999999999999991, nu=0.29999999999999999.
|
| 9583 |
|
|
template <typename Tp>
|
| 9584 |
|
|
void test184()
|
| 9585 |
|
|
{
|
| 9586 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9587 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9588 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9589 |
|
|
unsigned int num_datum = sizeof(data184)
|
| 9590 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9591 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9592 |
|
|
{
|
| 9593 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data184[i].k), Tp(data184[i].nu),
|
| 9594 |
|
|
Tp(data184[i].phi));
|
| 9595 |
|
|
const Tp f0 = data184[i].f0;
|
| 9596 |
|
|
const Tp diff = f - f0;
|
| 9597 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9598 |
|
|
max_abs_diff = std::abs(diff);
|
| 9599 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9600 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9601 |
|
|
{
|
| 9602 |
|
|
const Tp frac = diff / f0;
|
| 9603 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9604 |
|
|
max_abs_frac = std::abs(frac);
|
| 9605 |
|
|
}
|
| 9606 |
|
|
}
|
| 9607 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9608 |
|
|
}
|
| 9609 |
|
|
|
| 9610 |
|
|
// Test data for k=0.89999999999999991, nu=0.40000000000000002.
|
| 9611 |
|
|
testcase_ellint_3<double> data185[] = {
|
| 9612 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.40000000000000002,
|
| 9613 |
|
|
0.0000000000000000 },
|
| 9614 |
|
|
{ 0.17454957156468839, 0.89999999999999991, 0.40000000000000002,
|
| 9615 |
|
|
0.17453292519943295 },
|
| 9616 |
|
|
{ 0.34938003933330430, 0.89999999999999991, 0.40000000000000002,
|
| 9617 |
|
|
0.34906585039886590 },
|
| 9618 |
|
|
{ 0.52562093533067444, 0.89999999999999991, 0.40000000000000002,
|
| 9619 |
|
|
0.52359877559829882 },
|
| 9620 |
|
|
{ 0.70589461324915681, 0.89999999999999991, 0.40000000000000002,
|
| 9621 |
|
|
0.69813170079773179 },
|
| 9622 |
|
|
{ 0.89472658511942849, 0.89999999999999991, 0.40000000000000002,
|
| 9623 |
|
|
0.87266462599716477 },
|
| 9624 |
|
|
{ 1.0987419542323438, 0.89999999999999991, 0.40000000000000002,
|
| 9625 |
|
|
1.0471975511965976 },
|
| 9626 |
|
|
{ 1.3261349565496301, 0.89999999999999991, 0.40000000000000002,
|
| 9627 |
|
|
1.2217304763960306 },
|
| 9628 |
|
|
{ 1.5831293909853761, 0.89999999999999991, 0.40000000000000002,
|
| 9629 |
|
|
1.3962634015954636 },
|
| 9630 |
|
|
{ 1.8641114227238347, 0.89999999999999991, 0.40000000000000002,
|
| 9631 |
|
|
1.5707963267948966 },
|
| 9632 |
|
|
};
|
| 9633 |
|
|
|
| 9634 |
|
|
// Test function for k=0.89999999999999991, nu=0.40000000000000002.
|
| 9635 |
|
|
template <typename Tp>
|
| 9636 |
|
|
void test185()
|
| 9637 |
|
|
{
|
| 9638 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9639 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9640 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9641 |
|
|
unsigned int num_datum = sizeof(data185)
|
| 9642 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9643 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9644 |
|
|
{
|
| 9645 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data185[i].k), Tp(data185[i].nu),
|
| 9646 |
|
|
Tp(data185[i].phi));
|
| 9647 |
|
|
const Tp f0 = data185[i].f0;
|
| 9648 |
|
|
const Tp diff = f - f0;
|
| 9649 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9650 |
|
|
max_abs_diff = std::abs(diff);
|
| 9651 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9652 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9653 |
|
|
{
|
| 9654 |
|
|
const Tp frac = diff / f0;
|
| 9655 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9656 |
|
|
max_abs_frac = std::abs(frac);
|
| 9657 |
|
|
}
|
| 9658 |
|
|
}
|
| 9659 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9660 |
|
|
}
|
| 9661 |
|
|
|
| 9662 |
|
|
// Test data for k=0.89999999999999991, nu=0.50000000000000000.
|
| 9663 |
|
|
testcase_ellint_3<double> data186[] = {
|
| 9664 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.50000000000000000,
|
| 9665 |
|
|
0.0000000000000000 },
|
| 9666 |
|
|
{ 0.17437497557073336, 0.89999999999999991, 0.50000000000000000,
|
| 9667 |
|
|
0.17453292519943295 },
|
| 9668 |
|
|
{ 0.34804093691586013, 0.89999999999999991, 0.50000000000000000,
|
| 9669 |
|
|
0.34906585039886590 },
|
| 9670 |
|
|
{ 0.52137576320372903, 0.89999999999999991, 0.50000000000000000,
|
| 9671 |
|
|
0.52359877559829882 },
|
| 9672 |
|
|
{ 0.69655163996912262, 0.89999999999999991, 0.50000000000000000,
|
| 9673 |
|
|
0.69813170079773179 },
|
| 9674 |
|
|
{ 0.87783188683054236, 0.89999999999999991, 0.50000000000000000,
|
| 9675 |
|
|
0.87266462599716477 },
|
| 9676 |
|
|
{ 1.0716015959755183, 0.89999999999999991, 0.50000000000000000,
|
| 9677 |
|
|
1.0471975511965976 },
|
| 9678 |
|
|
{ 1.2857636916026749, 0.89999999999999991, 0.50000000000000000,
|
| 9679 |
|
|
1.2217304763960306 },
|
| 9680 |
|
|
{ 1.5264263913252358, 0.89999999999999991, 0.50000000000000000,
|
| 9681 |
|
|
1.3962634015954636 },
|
| 9682 |
|
|
{ 1.7888013241937859, 0.89999999999999991, 0.50000000000000000,
|
| 9683 |
|
|
1.5707963267948966 },
|
| 9684 |
|
|
};
|
| 9685 |
|
|
|
| 9686 |
|
|
// Test function for k=0.89999999999999991, nu=0.50000000000000000.
|
| 9687 |
|
|
template <typename Tp>
|
| 9688 |
|
|
void test186()
|
| 9689 |
|
|
{
|
| 9690 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9691 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9692 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9693 |
|
|
unsigned int num_datum = sizeof(data186)
|
| 9694 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9695 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9696 |
|
|
{
|
| 9697 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data186[i].k), Tp(data186[i].nu),
|
| 9698 |
|
|
Tp(data186[i].phi));
|
| 9699 |
|
|
const Tp f0 = data186[i].f0;
|
| 9700 |
|
|
const Tp diff = f - f0;
|
| 9701 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9702 |
|
|
max_abs_diff = std::abs(diff);
|
| 9703 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9704 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9705 |
|
|
{
|
| 9706 |
|
|
const Tp frac = diff / f0;
|
| 9707 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9708 |
|
|
max_abs_frac = std::abs(frac);
|
| 9709 |
|
|
}
|
| 9710 |
|
|
}
|
| 9711 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9712 |
|
|
}
|
| 9713 |
|
|
|
| 9714 |
|
|
// Test data for k=0.89999999999999991, nu=0.59999999999999998.
|
| 9715 |
|
|
testcase_ellint_3<double> data187[] = {
|
| 9716 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.59999999999999998,
|
| 9717 |
|
|
0.0000000000000000 },
|
| 9718 |
|
|
{ 0.17420100334657815, 0.89999999999999991, 0.59999999999999998,
|
| 9719 |
|
|
0.17453292519943295 },
|
| 9720 |
|
|
{ 0.34671975876122157, 0.89999999999999991, 0.59999999999999998,
|
| 9721 |
|
|
0.34906585039886590 },
|
| 9722 |
|
|
{ 0.51724631570707957, 0.89999999999999991, 0.59999999999999998,
|
| 9723 |
|
|
0.52359877559829882 },
|
| 9724 |
|
|
{ 0.68760879113743034, 0.89999999999999991, 0.59999999999999998,
|
| 9725 |
|
|
0.69813170079773179 },
|
| 9726 |
|
|
{ 0.86192157779698364, 0.89999999999999991, 0.59999999999999998,
|
| 9727 |
|
|
0.87266462599716477 },
|
| 9728 |
|
|
{ 1.0464279696166352, 0.89999999999999991, 0.59999999999999998,
|
| 9729 |
|
|
1.0471975511965976 },
|
| 9730 |
|
|
{ 1.2488156247094004, 0.89999999999999991, 0.59999999999999998,
|
| 9731 |
|
|
1.2217304763960306 },
|
| 9732 |
|
|
{ 1.4750988777188470, 0.89999999999999991, 0.59999999999999998,
|
| 9733 |
|
|
1.3962634015954636 },
|
| 9734 |
|
|
{ 1.7211781128919521, 0.89999999999999991, 0.59999999999999998,
|
| 9735 |
|
|
1.5707963267948966 },
|
| 9736 |
|
|
};
|
| 9737 |
|
|
|
| 9738 |
|
|
// Test function for k=0.89999999999999991, nu=0.59999999999999998.
|
| 9739 |
|
|
template <typename Tp>
|
| 9740 |
|
|
void test187()
|
| 9741 |
|
|
{
|
| 9742 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9743 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9744 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9745 |
|
|
unsigned int num_datum = sizeof(data187)
|
| 9746 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9747 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9748 |
|
|
{
|
| 9749 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data187[i].k), Tp(data187[i].nu),
|
| 9750 |
|
|
Tp(data187[i].phi));
|
| 9751 |
|
|
const Tp f0 = data187[i].f0;
|
| 9752 |
|
|
const Tp diff = f - f0;
|
| 9753 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9754 |
|
|
max_abs_diff = std::abs(diff);
|
| 9755 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9756 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9757 |
|
|
{
|
| 9758 |
|
|
const Tp frac = diff / f0;
|
| 9759 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9760 |
|
|
max_abs_frac = std::abs(frac);
|
| 9761 |
|
|
}
|
| 9762 |
|
|
}
|
| 9763 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9764 |
|
|
}
|
| 9765 |
|
|
|
| 9766 |
|
|
// Test data for k=0.89999999999999991, nu=0.69999999999999996.
|
| 9767 |
|
|
testcase_ellint_3<double> data188[] = {
|
| 9768 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.69999999999999996,
|
| 9769 |
|
|
0.0000000000000000 },
|
| 9770 |
|
|
{ 0.17402765093102210, 0.89999999999999991, 0.69999999999999996,
|
| 9771 |
|
|
0.17453292519943295 },
|
| 9772 |
|
|
{ 0.34541608382635131, 0.89999999999999991, 0.69999999999999996,
|
| 9773 |
|
|
0.34906585039886590 },
|
| 9774 |
|
|
{ 0.51322715827061693, 0.89999999999999991, 0.69999999999999996,
|
| 9775 |
|
|
0.52359877559829882 },
|
| 9776 |
|
|
{ 0.67903717872440283, 0.89999999999999991, 0.69999999999999996,
|
| 9777 |
|
|
0.69813170079773179 },
|
| 9778 |
|
|
{ 0.84690113601682671, 0.89999999999999991, 0.69999999999999996,
|
| 9779 |
|
|
0.87266462599716477 },
|
| 9780 |
|
|
{ 1.0229914311548416, 0.89999999999999991, 0.69999999999999996,
|
| 9781 |
|
|
1.0471975511965976 },
|
| 9782 |
|
|
{ 1.2148329639709381, 0.89999999999999991, 0.69999999999999996,
|
| 9783 |
|
|
1.2217304763960306 },
|
| 9784 |
|
|
{ 1.4283586501307799, 0.89999999999999991, 0.69999999999999996,
|
| 9785 |
|
|
1.3962634015954636 },
|
| 9786 |
|
|
{ 1.6600480747670936, 0.89999999999999991, 0.69999999999999996,
|
| 9787 |
|
|
1.5707963267948966 },
|
| 9788 |
|
|
};
|
| 9789 |
|
|
|
| 9790 |
|
|
// Test function for k=0.89999999999999991, nu=0.69999999999999996.
|
| 9791 |
|
|
template <typename Tp>
|
| 9792 |
|
|
void test188()
|
| 9793 |
|
|
{
|
| 9794 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9795 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9796 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9797 |
|
|
unsigned int num_datum = sizeof(data188)
|
| 9798 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9799 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9800 |
|
|
{
|
| 9801 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data188[i].k), Tp(data188[i].nu),
|
| 9802 |
|
|
Tp(data188[i].phi));
|
| 9803 |
|
|
const Tp f0 = data188[i].f0;
|
| 9804 |
|
|
const Tp diff = f - f0;
|
| 9805 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9806 |
|
|
max_abs_diff = std::abs(diff);
|
| 9807 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9808 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9809 |
|
|
{
|
| 9810 |
|
|
const Tp frac = diff / f0;
|
| 9811 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9812 |
|
|
max_abs_frac = std::abs(frac);
|
| 9813 |
|
|
}
|
| 9814 |
|
|
}
|
| 9815 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9816 |
|
|
}
|
| 9817 |
|
|
|
| 9818 |
|
|
// Test data for k=0.89999999999999991, nu=0.80000000000000004.
|
| 9819 |
|
|
testcase_ellint_3<double> data189[] = {
|
| 9820 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.80000000000000004,
|
| 9821 |
|
|
0.0000000000000000 },
|
| 9822 |
|
|
{ 0.17385491439925149, 0.89999999999999991, 0.80000000000000004,
|
| 9823 |
|
|
0.17453292519943295 },
|
| 9824 |
|
|
{ 0.34412950523113928, 0.89999999999999991, 0.80000000000000004,
|
| 9825 |
|
|
0.34906585039886590 },
|
| 9826 |
|
|
{ 0.50931321668729601, 0.89999999999999991, 0.80000000000000004,
|
| 9827 |
|
|
0.52359877559829882 },
|
| 9828 |
|
|
{ 0.67081081392296327, 0.89999999999999991, 0.80000000000000004,
|
| 9829 |
|
|
0.69813170079773179 },
|
| 9830 |
|
|
{ 0.83268846097293259, 0.89999999999999991, 0.80000000000000004,
|
| 9831 |
|
|
0.87266462599716477 },
|
| 9832 |
|
|
{ 1.0010985015814025, 0.89999999999999991, 0.80000000000000004,
|
| 9833 |
|
|
1.0471975511965976 },
|
| 9834 |
|
|
{ 1.1834394045489678, 0.89999999999999991, 0.80000000000000004,
|
| 9835 |
|
|
1.2217304763960306 },
|
| 9836 |
|
|
{ 1.3855695891683182, 0.89999999999999991, 0.80000000000000004,
|
| 9837 |
|
|
1.3962634015954636 },
|
| 9838 |
|
|
{ 1.6044591960982200, 0.89999999999999991, 0.80000000000000004,
|
| 9839 |
|
|
1.5707963267948966 },
|
| 9840 |
|
|
};
|
| 9841 |
|
|
|
| 9842 |
|
|
// Test function for k=0.89999999999999991, nu=0.80000000000000004.
|
| 9843 |
|
|
template <typename Tp>
|
| 9844 |
|
|
void test189()
|
| 9845 |
|
|
{
|
| 9846 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9847 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9848 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9849 |
|
|
unsigned int num_datum = sizeof(data189)
|
| 9850 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9851 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9852 |
|
|
{
|
| 9853 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data189[i].k), Tp(data189[i].nu),
|
| 9854 |
|
|
Tp(data189[i].phi));
|
| 9855 |
|
|
const Tp f0 = data189[i].f0;
|
| 9856 |
|
|
const Tp diff = f - f0;
|
| 9857 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9858 |
|
|
max_abs_diff = std::abs(diff);
|
| 9859 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9860 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9861 |
|
|
{
|
| 9862 |
|
|
const Tp frac = diff / f0;
|
| 9863 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9864 |
|
|
max_abs_frac = std::abs(frac);
|
| 9865 |
|
|
}
|
| 9866 |
|
|
}
|
| 9867 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9868 |
|
|
}
|
| 9869 |
|
|
|
| 9870 |
|
|
// Test data for k=0.89999999999999991, nu=0.90000000000000002.
|
| 9871 |
|
|
testcase_ellint_3<double> data190[] = {
|
| 9872 |
|
|
{ -0.0000000000000000, 0.89999999999999991, 0.90000000000000002,
|
| 9873 |
|
|
0.0000000000000000 },
|
| 9874 |
|
|
{ 0.17368278986240138, 0.89999999999999991, 0.90000000000000002,
|
| 9875 |
|
|
0.17453292519943295 },
|
| 9876 |
|
|
{ 0.34285962963961397, 0.89999999999999991, 0.90000000000000002,
|
| 9877 |
|
|
0.34906585039886590 },
|
| 9878 |
|
|
{ 0.50549974644993312, 0.89999999999999991, 0.90000000000000002,
|
| 9879 |
|
|
0.52359877559829882 },
|
| 9880 |
|
|
{ 0.66290623857720876, 0.89999999999999991, 0.90000000000000002,
|
| 9881 |
|
|
0.69813170079773179 },
|
| 9882 |
|
|
{ 0.81921183128847164, 0.89999999999999991, 0.90000000000000002,
|
| 9883 |
|
|
0.87266462599716477 },
|
| 9884 |
|
|
{ 0.98058481956066368, 0.89999999999999991, 0.90000000000000002,
|
| 9885 |
|
|
1.0471975511965976 },
|
| 9886 |
|
|
{ 1.1543223520473569, 0.89999999999999991, 0.90000000000000002,
|
| 9887 |
|
|
1.2217304763960306 },
|
| 9888 |
|
|
{ 1.3462119782292934, 0.89999999999999991, 0.90000000000000002,
|
| 9889 |
|
|
1.3962634015954636 },
|
| 9890 |
|
|
{ 1.5536420236310944, 0.89999999999999991, 0.90000000000000002,
|
| 9891 |
|
|
1.5707963267948966 },
|
| 9892 |
|
|
};
|
| 9893 |
|
|
|
| 9894 |
|
|
// Test function for k=0.89999999999999991, nu=0.90000000000000002.
|
| 9895 |
|
|
template <typename Tp>
|
| 9896 |
|
|
void test190()
|
| 9897 |
|
|
{
|
| 9898 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 9899 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 9900 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 9901 |
|
|
unsigned int num_datum = sizeof(data190)
|
| 9902 |
|
|
/ sizeof(testcase_ellint_3<double>);
|
| 9903 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 9904 |
|
|
{
|
| 9905 |
|
|
const Tp f = std::tr1::ellint_3(Tp(data190[i].k), Tp(data190[i].nu),
|
| 9906 |
|
|
Tp(data190[i].phi));
|
| 9907 |
|
|
const Tp f0 = data190[i].f0;
|
| 9908 |
|
|
const Tp diff = f - f0;
|
| 9909 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 9910 |
|
|
max_abs_diff = std::abs(diff);
|
| 9911 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 9912 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 9913 |
|
|
{
|
| 9914 |
|
|
const Tp frac = diff / f0;
|
| 9915 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 9916 |
|
|
max_abs_frac = std::abs(frac);
|
| 9917 |
|
|
}
|
| 9918 |
|
|
}
|
| 9919 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 9920 |
|
|
}
|
| 9921 |
|
|
|
| 9922 |
|
|
int main(int, char**)
|
| 9923 |
|
|
{
|
| 9924 |
|
|
test001<double>();
|
| 9925 |
|
|
test002<double>();
|
| 9926 |
|
|
test003<double>();
|
| 9927 |
|
|
test004<double>();
|
| 9928 |
|
|
test005<double>();
|
| 9929 |
|
|
test006<double>();
|
| 9930 |
|
|
test007<double>();
|
| 9931 |
|
|
test008<double>();
|
| 9932 |
|
|
test009<double>();
|
| 9933 |
|
|
test010<double>();
|
| 9934 |
|
|
test011<double>();
|
| 9935 |
|
|
test012<double>();
|
| 9936 |
|
|
test013<double>();
|
| 9937 |
|
|
test014<double>();
|
| 9938 |
|
|
test015<double>();
|
| 9939 |
|
|
test016<double>();
|
| 9940 |
|
|
test017<double>();
|
| 9941 |
|
|
test018<double>();
|
| 9942 |
|
|
test019<double>();
|
| 9943 |
|
|
test020<double>();
|
| 9944 |
|
|
test021<double>();
|
| 9945 |
|
|
test022<double>();
|
| 9946 |
|
|
test023<double>();
|
| 9947 |
|
|
test024<double>();
|
| 9948 |
|
|
test025<double>();
|
| 9949 |
|
|
test026<double>();
|
| 9950 |
|
|
test027<double>();
|
| 9951 |
|
|
test028<double>();
|
| 9952 |
|
|
test029<double>();
|
| 9953 |
|
|
test030<double>();
|
| 9954 |
|
|
test031<double>();
|
| 9955 |
|
|
test032<double>();
|
| 9956 |
|
|
test033<double>();
|
| 9957 |
|
|
test034<double>();
|
| 9958 |
|
|
test035<double>();
|
| 9959 |
|
|
test036<double>();
|
| 9960 |
|
|
test037<double>();
|
| 9961 |
|
|
test038<double>();
|
| 9962 |
|
|
test039<double>();
|
| 9963 |
|
|
test040<double>();
|
| 9964 |
|
|
test041<double>();
|
| 9965 |
|
|
test042<double>();
|
| 9966 |
|
|
test043<double>();
|
| 9967 |
|
|
test044<double>();
|
| 9968 |
|
|
test045<double>();
|
| 9969 |
|
|
test046<double>();
|
| 9970 |
|
|
test047<double>();
|
| 9971 |
|
|
test048<double>();
|
| 9972 |
|
|
test049<double>();
|
| 9973 |
|
|
test050<double>();
|
| 9974 |
|
|
test051<double>();
|
| 9975 |
|
|
test052<double>();
|
| 9976 |
|
|
test053<double>();
|
| 9977 |
|
|
test054<double>();
|
| 9978 |
|
|
test055<double>();
|
| 9979 |
|
|
test056<double>();
|
| 9980 |
|
|
test057<double>();
|
| 9981 |
|
|
test058<double>();
|
| 9982 |
|
|
test059<double>();
|
| 9983 |
|
|
test060<double>();
|
| 9984 |
|
|
test061<double>();
|
| 9985 |
|
|
test062<double>();
|
| 9986 |
|
|
test063<double>();
|
| 9987 |
|
|
test064<double>();
|
| 9988 |
|
|
test065<double>();
|
| 9989 |
|
|
test066<double>();
|
| 9990 |
|
|
test067<double>();
|
| 9991 |
|
|
test068<double>();
|
| 9992 |
|
|
test069<double>();
|
| 9993 |
|
|
test070<double>();
|
| 9994 |
|
|
test071<double>();
|
| 9995 |
|
|
test072<double>();
|
| 9996 |
|
|
test073<double>();
|
| 9997 |
|
|
test074<double>();
|
| 9998 |
|
|
test075<double>();
|
| 9999 |
|
|
test076<double>();
|
| 10000 |
|
|
test077<double>();
|
| 10001 |
|
|
test078<double>();
|
| 10002 |
|
|
test079<double>();
|
| 10003 |
|
|
test080<double>();
|
| 10004 |
|
|
test081<double>();
|
| 10005 |
|
|
test082<double>();
|
| 10006 |
|
|
test083<double>();
|
| 10007 |
|
|
test084<double>();
|
| 10008 |
|
|
test085<double>();
|
| 10009 |
|
|
test086<double>();
|
| 10010 |
|
|
test087<double>();
|
| 10011 |
|
|
test088<double>();
|
| 10012 |
|
|
test089<double>();
|
| 10013 |
|
|
test090<double>();
|
| 10014 |
|
|
test091<double>();
|
| 10015 |
|
|
test092<double>();
|
| 10016 |
|
|
test093<double>();
|
| 10017 |
|
|
test094<double>();
|
| 10018 |
|
|
test095<double>();
|
| 10019 |
|
|
test096<double>();
|
| 10020 |
|
|
test097<double>();
|
| 10021 |
|
|
test098<double>();
|
| 10022 |
|
|
test099<double>();
|
| 10023 |
|
|
test100<double>();
|
| 10024 |
|
|
test101<double>();
|
| 10025 |
|
|
test102<double>();
|
| 10026 |
|
|
test103<double>();
|
| 10027 |
|
|
test104<double>();
|
| 10028 |
|
|
test105<double>();
|
| 10029 |
|
|
test106<double>();
|
| 10030 |
|
|
test107<double>();
|
| 10031 |
|
|
test108<double>();
|
| 10032 |
|
|
test109<double>();
|
| 10033 |
|
|
test110<double>();
|
| 10034 |
|
|
test111<double>();
|
| 10035 |
|
|
test112<double>();
|
| 10036 |
|
|
test113<double>();
|
| 10037 |
|
|
test114<double>();
|
| 10038 |
|
|
test115<double>();
|
| 10039 |
|
|
test116<double>();
|
| 10040 |
|
|
test117<double>();
|
| 10041 |
|
|
test118<double>();
|
| 10042 |
|
|
test119<double>();
|
| 10043 |
|
|
test120<double>();
|
| 10044 |
|
|
test121<double>();
|
| 10045 |
|
|
test122<double>();
|
| 10046 |
|
|
test123<double>();
|
| 10047 |
|
|
test124<double>();
|
| 10048 |
|
|
test125<double>();
|
| 10049 |
|
|
test126<double>();
|
| 10050 |
|
|
test127<double>();
|
| 10051 |
|
|
test128<double>();
|
| 10052 |
|
|
test129<double>();
|
| 10053 |
|
|
test130<double>();
|
| 10054 |
|
|
test131<double>();
|
| 10055 |
|
|
test132<double>();
|
| 10056 |
|
|
test133<double>();
|
| 10057 |
|
|
test134<double>();
|
| 10058 |
|
|
test135<double>();
|
| 10059 |
|
|
test136<double>();
|
| 10060 |
|
|
test137<double>();
|
| 10061 |
|
|
test138<double>();
|
| 10062 |
|
|
test139<double>();
|
| 10063 |
|
|
test140<double>();
|
| 10064 |
|
|
test141<double>();
|
| 10065 |
|
|
test142<double>();
|
| 10066 |
|
|
test143<double>();
|
| 10067 |
|
|
test144<double>();
|
| 10068 |
|
|
test145<double>();
|
| 10069 |
|
|
test146<double>();
|
| 10070 |
|
|
test147<double>();
|
| 10071 |
|
|
test148<double>();
|
| 10072 |
|
|
test149<double>();
|
| 10073 |
|
|
test150<double>();
|
| 10074 |
|
|
test151<double>();
|
| 10075 |
|
|
test152<double>();
|
| 10076 |
|
|
test153<double>();
|
| 10077 |
|
|
test154<double>();
|
| 10078 |
|
|
test155<double>();
|
| 10079 |
|
|
test156<double>();
|
| 10080 |
|
|
test157<double>();
|
| 10081 |
|
|
test158<double>();
|
| 10082 |
|
|
test159<double>();
|
| 10083 |
|
|
test160<double>();
|
| 10084 |
|
|
test161<double>();
|
| 10085 |
|
|
test162<double>();
|
| 10086 |
|
|
test163<double>();
|
| 10087 |
|
|
test164<double>();
|
| 10088 |
|
|
test165<double>();
|
| 10089 |
|
|
test166<double>();
|
| 10090 |
|
|
test167<double>();
|
| 10091 |
|
|
test168<double>();
|
| 10092 |
|
|
test169<double>();
|
| 10093 |
|
|
test170<double>();
|
| 10094 |
|
|
test171<double>();
|
| 10095 |
|
|
test172<double>();
|
| 10096 |
|
|
test173<double>();
|
| 10097 |
|
|
test174<double>();
|
| 10098 |
|
|
test175<double>();
|
| 10099 |
|
|
test176<double>();
|
| 10100 |
|
|
test177<double>();
|
| 10101 |
|
|
test178<double>();
|
| 10102 |
|
|
test179<double>();
|
| 10103 |
|
|
test180<double>();
|
| 10104 |
|
|
test181<double>();
|
| 10105 |
|
|
test182<double>();
|
| 10106 |
|
|
test183<double>();
|
| 10107 |
|
|
test184<double>();
|
| 10108 |
|
|
test185<double>();
|
| 10109 |
|
|
test186<double>();
|
| 10110 |
|
|
test187<double>();
|
| 10111 |
|
|
test188<double>();
|
| 10112 |
|
|
test189<double>();
|
| 10113 |
|
|
test190<double>();
|
| 10114 |
|
|
return 0;
|
| 10115 |
|
|
}
|
