| // 2007-02-04 Edward Smith-Rowland <3dw4rd@verizon.net> |
| // |
| // Copyright (C) 2007, 2009 Free Software Foundation, Inc. |
| // |
| // This file is part of the GNU ISO C++ Library. This library is free |
| // software; you can redistribute it and/or modify it under the |
| // terms of the GNU General Public License as published by the |
| // Free Software Foundation; either version 3, or (at your option) |
| // any later version. |
| // |
| // This library is distributed in the hope that it will be useful, |
| // but WITHOUT ANY WARRANTY; without even the implied warranty of |
| // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| // GNU General Public License for more details. |
| // |
| // You should have received a copy of the GNU General Public License along |
| // with this library; see the file COPYING3. If not see |
| // <http://www.gnu.org/licenses/>. |
| |
| // ellint_1 |
| |
| |
| // Compare against values generated by the GNU Scientific Library. |
| // The GSL can be found on the web: http://www.gnu.org/software/gsl/ |
| |
| #include <tr1/cmath> |
| #if defined(__TEST_DEBUG) |
| #include <iostream> |
| #define VERIFY(A) \ |
| if (!(A)) \ |
| { \ |
| std::cout << "line " << __LINE__ \ |
| << " max_abs_frac = " << max_abs_frac \ |
| << std::endl; \ |
| } |
| #else |
| #include <testsuite_hooks.h> |
| #endif |
| #include "../testcase.h" |
| |
| |
| // Test data for k=-0.90000000000000002. |
| testcase_ellint_1<double> data001[] = { |
| { -0.0000000000000000, -0.90000000000000002, 0.0000000000000000 }, |
| { 0.17525427376115027, -0.90000000000000002, 0.17453292519943295 }, |
| { 0.35492464591297446, -0.90000000000000002, 0.34906585039886590 }, |
| { 0.54388221416157134, -0.90000000000000002, 0.52359877559829882 }, |
| { 0.74797400423532523, -0.90000000000000002, 0.69813170079773179 }, |
| { 0.97463898451966458, -0.90000000000000002, 0.87266462599716477 }, |
| { 1.2334463254523440, -0.90000000000000002, 1.0471975511965976 }, |
| { 1.5355247765594910, -0.90000000000000002, 1.2217304763960306 }, |
| { 1.8882928567775124, -0.90000000000000002, 1.3962634015954636 }, |
| { 2.2805491384227703, -0.90000000000000002, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.90000000000000002. |
| template <typename Tp> |
| void test001() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data001) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data001[i].k), Tp(data001[i].phi)); |
| const Tp f0 = data001[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=-0.80000000000000004. |
| testcase_ellint_1<double> data002[] = { |
| { -0.0000000000000000, -0.80000000000000004, 0.0000000000000000 }, |
| { 0.17510154241338902, -0.80000000000000004, 0.17453292519943295 }, |
| { 0.35365068839779390, -0.80000000000000004, 0.34906585039886590 }, |
| { 0.53926804409084561, -0.80000000000000004, 0.52359877559829882 }, |
| { 0.73587926028070383, -0.80000000000000004, 0.69813170079773179 }, |
| { 0.94770942970071170, -0.80000000000000004, 0.87266462599716477 }, |
| { 1.1789022995388239, -0.80000000000000004, 1.0471975511965976 }, |
| { 1.4323027881876009, -0.80000000000000004, 1.2217304763960306 }, |
| { 1.7069629739121674, -0.80000000000000004, 1.3962634015954636 }, |
| { 1.9953027776647296, -0.80000000000000004, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.80000000000000004. |
| template <typename Tp> |
| void test002() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data002) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data002[i].k), Tp(data002[i].phi)); |
| const Tp f0 = data002[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=-0.69999999999999996. |
| testcase_ellint_1<double> data003[] = { |
| { -0.0000000000000000, -0.69999999999999996, 0.0000000000000000 }, |
| { 0.17496737466916720, -0.69999999999999996, 0.17453292519943295 }, |
| { 0.35254687535677925, -0.69999999999999996, 0.34906585039886590 }, |
| { 0.53536740275997130, -0.69999999999999996, 0.52359877559829882 }, |
| { 0.72603797651684465, -0.69999999999999996, 0.69813170079773179 }, |
| { 0.92698296348313458, -0.69999999999999996, 0.87266462599716477 }, |
| { 1.1400447527693316, -0.69999999999999996, 1.0471975511965976 }, |
| { 1.3657668117194071, -0.69999999999999996, 1.2217304763960306 }, |
| { 1.6024686895959159, -0.69999999999999996, 1.3962634015954636 }, |
| { 1.8456939983747236, -0.69999999999999996, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.69999999999999996. |
| template <typename Tp> |
| void test003() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data003) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data003[i].k), Tp(data003[i].phi)); |
| const Tp f0 = data003[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=-0.59999999999999998. |
| testcase_ellint_1<double> data004[] = { |
| { -0.0000000000000000, -0.59999999999999998, 0.0000000000000000 }, |
| { 0.17485154362988362, -0.59999999999999998, 0.17453292519943295 }, |
| { 0.35160509865544326, -0.59999999999999998, 0.34906585039886590 }, |
| { 0.53210652578446160, -0.59999999999999998, 0.52359877559829882 }, |
| { 0.71805304664485670, -0.59999999999999998, 0.69813170079773179 }, |
| { 0.91082759030195970, -0.59999999999999998, 0.87266462599716477 }, |
| { 1.1112333229323361, -0.59999999999999998, 1.0471975511965976 }, |
| { 1.3191461190365270, -0.59999999999999998, 1.2217304763960306 }, |
| { 1.5332022105084773, -0.59999999999999998, 1.3962634015954636 }, |
| { 1.7507538029157526, -0.59999999999999998, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.59999999999999998. |
| template <typename Tp> |
| void test004() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data004) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data004[i].k), Tp(data004[i].phi)); |
| const Tp f0 = data004[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=-0.50000000000000000. |
| testcase_ellint_1<double> data005[] = { |
| { -0.0000000000000000, -0.50000000000000000, 0.0000000000000000 }, |
| { 0.17475385514035785, -0.50000000000000000, 0.17453292519943295 }, |
| { 0.35081868470101585, -0.50000000000000000, 0.34906585039886590 }, |
| { 0.52942862705190585, -0.50000000000000000, 0.52359877559829882 }, |
| { 0.71164727562630326, -0.50000000000000000, 0.69813170079773179 }, |
| { 0.89824523594227768, -0.50000000000000000, 0.87266462599716477 }, |
| { 1.0895506700518851, -0.50000000000000000, 1.0471975511965976 }, |
| { 1.2853005857432933, -0.50000000000000000, 1.2217304763960306 }, |
| { 1.4845545520549484, -0.50000000000000000, 1.3962634015954636 }, |
| { 1.6857503548125963, -0.50000000000000000, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.50000000000000000. |
| template <typename Tp> |
| void test005() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data005) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data005[i].k), Tp(data005[i].phi)); |
| const Tp f0 = data005[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=-0.40000000000000002. |
| testcase_ellint_1<double> data006[] = { |
| { -0.0000000000000000, -0.40000000000000002, 0.0000000000000000 }, |
| { 0.17467414669441531, -0.40000000000000002, 0.17453292519943295 }, |
| { 0.35018222772483443, -0.40000000000000002, 0.34906585039886590 }, |
| { 0.52729015917508748, -0.40000000000000002, 0.52359877559829882 }, |
| { 0.70662374407341255, -0.40000000000000002, 0.69813170079773179 }, |
| { 0.88859210497602170, -0.40000000000000002, 0.87266462599716477 }, |
| { 1.0733136290471379, -0.40000000000000002, 1.0471975511965976 }, |
| { 1.2605612170157061, -0.40000000000000002, 1.2217304763960306 }, |
| { 1.4497513956433437, -0.40000000000000002, 1.3962634015954636 }, |
| { 1.6399998658645112, -0.40000000000000002, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.40000000000000002. |
| template <typename Tp> |
| void test006() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data006) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data006[i].k), Tp(data006[i].phi)); |
| const Tp f0 = data006[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=-0.30000000000000004. |
| testcase_ellint_1<double> data007[] = { |
| { -0.0000000000000000, -0.30000000000000004, 0.0000000000000000 }, |
| { 0.17461228653000102, -0.30000000000000004, 0.17453292519943295 }, |
| { 0.34969146102798415, -0.30000000000000004, 0.34906585039886590 }, |
| { 0.52565822873726320, -0.30000000000000004, 0.52359877559829882 }, |
| { 0.70284226512408532, -0.30000000000000004, 0.69813170079773179 }, |
| { 0.88144139195111182, -0.30000000000000004, 0.87266462599716477 }, |
| { 1.0614897067260523, -0.30000000000000004, 1.0471975511965976 }, |
| { 1.2428416824174218, -0.30000000000000004, 1.2217304763960306 }, |
| { 1.4251795877015925, -0.30000000000000004, 1.3962634015954636 }, |
| { 1.6080486199305126, -0.30000000000000004, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.30000000000000004. |
| template <typename Tp> |
| void test007() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data007) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data007[i].k), Tp(data007[i].phi)); |
| const Tp f0 = data007[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=-0.19999999999999996. |
| testcase_ellint_1<double> data008[] = { |
| { -0.0000000000000000, -0.19999999999999996, 0.0000000000000000 }, |
| { 0.17456817290292811, -0.19999999999999996, 0.17453292519943295 }, |
| { 0.34934315932086801, -0.19999999999999996, 0.34906585039886590 }, |
| { 0.52450880529443988, -0.19999999999999996, 0.52359877559829882 }, |
| { 0.70020491009844910, -0.19999999999999996, 0.69813170079773179 }, |
| { 0.87651006649967955, -0.19999999999999996, 0.87266462599716477 }, |
| { 1.0534305870298994, -0.19999999999999996, 1.0471975511965976 }, |
| { 1.2308975521670784, -0.19999999999999996, 1.2217304763960306 }, |
| { 1.4087733584990738, -0.19999999999999996, 1.3962634015954636 }, |
| { 1.5868678474541664, -0.19999999999999996, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.19999999999999996. |
| template <typename Tp> |
| void test008() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data008) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data008[i].k), Tp(data008[i].phi)); |
| const Tp f0 = data008[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=-0.099999999999999978. |
| testcase_ellint_1<double> data009[] = { |
| { -0.0000000000000000, -0.099999999999999978, 0.0000000000000000 }, |
| { 0.17454173353063665, -0.099999999999999978, 0.17453292519943295 }, |
| { 0.34913506721468085, -0.099999999999999978, 0.34906585039886590 }, |
| { 0.52382550016538953, -0.099999999999999978, 0.52359877559829882 }, |
| { 0.69864700854177031, -0.099999999999999978, 0.69813170079773179 }, |
| { 0.87361792586964870, -0.099999999999999978, 0.87266462599716477 }, |
| { 1.0487386319621685, -0.099999999999999978, 1.0471975511965976 }, |
| { 1.2239913752078757, -0.099999999999999978, 1.2217304763960306 }, |
| { 1.3993423113684049, -0.099999999999999978, 1.3962634015954636 }, |
| { 1.5747455615173562, -0.099999999999999978, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=-0.099999999999999978. |
| template <typename Tp> |
| void test009() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data009) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data009[i].k), Tp(data009[i].phi)); |
| const Tp f0 = data009[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.0000000000000000. |
| testcase_ellint_1<double> data010[] = { |
| { -0.0000000000000000, 0.0000000000000000, 0.0000000000000000 }, |
| { 0.17453292519943295, 0.0000000000000000, 0.17453292519943295 }, |
| { 0.34906585039886584, 0.0000000000000000, 0.34906585039886590 }, |
| { 0.52359877559829882, 0.0000000000000000, 0.52359877559829882 }, |
| { 0.69813170079773179, 0.0000000000000000, 0.69813170079773179 }, |
| { 0.87266462599716477, 0.0000000000000000, 0.87266462599716477 }, |
| { 1.0471975511965976, 0.0000000000000000, 1.0471975511965976 }, |
| { 1.2217304763960304, 0.0000000000000000, 1.2217304763960306 }, |
| { 1.3962634015954631, 0.0000000000000000, 1.3962634015954636 }, |
| { 1.5707963267948966, 0.0000000000000000, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.0000000000000000. |
| template <typename Tp> |
| void test010() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data010) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data010[i].k), Tp(data010[i].phi)); |
| const Tp f0 = data010[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.10000000000000009. |
| testcase_ellint_1<double> data011[] = { |
| { -0.0000000000000000, 0.10000000000000009, 0.0000000000000000 }, |
| { 0.17454173353063665, 0.10000000000000009, 0.17453292519943295 }, |
| { 0.34913506721468085, 0.10000000000000009, 0.34906585039886590 }, |
| { 0.52382550016538953, 0.10000000000000009, 0.52359877559829882 }, |
| { 0.69864700854177031, 0.10000000000000009, 0.69813170079773179 }, |
| { 0.87361792586964870, 0.10000000000000009, 0.87266462599716477 }, |
| { 1.0487386319621685, 0.10000000000000009, 1.0471975511965976 }, |
| { 1.2239913752078757, 0.10000000000000009, 1.2217304763960306 }, |
| { 1.3993423113684049, 0.10000000000000009, 1.3962634015954636 }, |
| { 1.5747455615173562, 0.10000000000000009, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.10000000000000009. |
| template <typename Tp> |
| void test011() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data011) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data011[i].k), Tp(data011[i].phi)); |
| const Tp f0 = data011[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.19999999999999996. |
| testcase_ellint_1<double> data012[] = { |
| { -0.0000000000000000, 0.19999999999999996, 0.0000000000000000 }, |
| { 0.17456817290292811, 0.19999999999999996, 0.17453292519943295 }, |
| { 0.34934315932086801, 0.19999999999999996, 0.34906585039886590 }, |
| { 0.52450880529443988, 0.19999999999999996, 0.52359877559829882 }, |
| { 0.70020491009844910, 0.19999999999999996, 0.69813170079773179 }, |
| { 0.87651006649967955, 0.19999999999999996, 0.87266462599716477 }, |
| { 1.0534305870298994, 0.19999999999999996, 1.0471975511965976 }, |
| { 1.2308975521670784, 0.19999999999999996, 1.2217304763960306 }, |
| { 1.4087733584990738, 0.19999999999999996, 1.3962634015954636 }, |
| { 1.5868678474541664, 0.19999999999999996, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.19999999999999996. |
| template <typename Tp> |
| void test012() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data012) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data012[i].k), Tp(data012[i].phi)); |
| const Tp f0 = data012[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.30000000000000004. |
| testcase_ellint_1<double> data013[] = { |
| { -0.0000000000000000, 0.30000000000000004, 0.0000000000000000 }, |
| { 0.17461228653000102, 0.30000000000000004, 0.17453292519943295 }, |
| { 0.34969146102798415, 0.30000000000000004, 0.34906585039886590 }, |
| { 0.52565822873726320, 0.30000000000000004, 0.52359877559829882 }, |
| { 0.70284226512408532, 0.30000000000000004, 0.69813170079773179 }, |
| { 0.88144139195111182, 0.30000000000000004, 0.87266462599716477 }, |
| { 1.0614897067260523, 0.30000000000000004, 1.0471975511965976 }, |
| { 1.2428416824174218, 0.30000000000000004, 1.2217304763960306 }, |
| { 1.4251795877015925, 0.30000000000000004, 1.3962634015954636 }, |
| { 1.6080486199305126, 0.30000000000000004, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.30000000000000004. |
| template <typename Tp> |
| void test013() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data013) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data013[i].k), Tp(data013[i].phi)); |
| const Tp f0 = data013[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.39999999999999991. |
| testcase_ellint_1<double> data014[] = { |
| { -0.0000000000000000, 0.39999999999999991, 0.0000000000000000 }, |
| { 0.17467414669441531, 0.39999999999999991, 0.17453292519943295 }, |
| { 0.35018222772483443, 0.39999999999999991, 0.34906585039886590 }, |
| { 0.52729015917508748, 0.39999999999999991, 0.52359877559829882 }, |
| { 0.70662374407341255, 0.39999999999999991, 0.69813170079773179 }, |
| { 0.88859210497602170, 0.39999999999999991, 0.87266462599716477 }, |
| { 1.0733136290471379, 0.39999999999999991, 1.0471975511965976 }, |
| { 1.2605612170157061, 0.39999999999999991, 1.2217304763960306 }, |
| { 1.4497513956433437, 0.39999999999999991, 1.3962634015954636 }, |
| { 1.6399998658645112, 0.39999999999999991, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.39999999999999991. |
| template <typename Tp> |
| void test014() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data014) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data014[i].k), Tp(data014[i].phi)); |
| const Tp f0 = data014[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.50000000000000000. |
| testcase_ellint_1<double> data015[] = { |
| { -0.0000000000000000, 0.50000000000000000, 0.0000000000000000 }, |
| { 0.17475385514035785, 0.50000000000000000, 0.17453292519943295 }, |
| { 0.35081868470101585, 0.50000000000000000, 0.34906585039886590 }, |
| { 0.52942862705190585, 0.50000000000000000, 0.52359877559829882 }, |
| { 0.71164727562630326, 0.50000000000000000, 0.69813170079773179 }, |
| { 0.89824523594227768, 0.50000000000000000, 0.87266462599716477 }, |
| { 1.0895506700518851, 0.50000000000000000, 1.0471975511965976 }, |
| { 1.2853005857432933, 0.50000000000000000, 1.2217304763960306 }, |
| { 1.4845545520549484, 0.50000000000000000, 1.3962634015954636 }, |
| { 1.6857503548125963, 0.50000000000000000, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.50000000000000000. |
| template <typename Tp> |
| void test015() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data015) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data015[i].k), Tp(data015[i].phi)); |
| const Tp f0 = data015[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.60000000000000009. |
| testcase_ellint_1<double> data016[] = { |
| { -0.0000000000000000, 0.60000000000000009, 0.0000000000000000 }, |
| { 0.17485154362988362, 0.60000000000000009, 0.17453292519943295 }, |
| { 0.35160509865544326, 0.60000000000000009, 0.34906585039886590 }, |
| { 0.53210652578446160, 0.60000000000000009, 0.52359877559829882 }, |
| { 0.71805304664485670, 0.60000000000000009, 0.69813170079773179 }, |
| { 0.91082759030195970, 0.60000000000000009, 0.87266462599716477 }, |
| { 1.1112333229323366, 0.60000000000000009, 1.0471975511965976 }, |
| { 1.3191461190365270, 0.60000000000000009, 1.2217304763960306 }, |
| { 1.5332022105084775, 0.60000000000000009, 1.3962634015954636 }, |
| { 1.7507538029157526, 0.60000000000000009, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.60000000000000009. |
| template <typename Tp> |
| void test016() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data016) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data016[i].k), Tp(data016[i].phi)); |
| const Tp f0 = data016[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.69999999999999996. |
| testcase_ellint_1<double> data017[] = { |
| { -0.0000000000000000, 0.69999999999999996, 0.0000000000000000 }, |
| { 0.17496737466916720, 0.69999999999999996, 0.17453292519943295 }, |
| { 0.35254687535677925, 0.69999999999999996, 0.34906585039886590 }, |
| { 0.53536740275997130, 0.69999999999999996, 0.52359877559829882 }, |
| { 0.72603797651684465, 0.69999999999999996, 0.69813170079773179 }, |
| { 0.92698296348313458, 0.69999999999999996, 0.87266462599716477 }, |
| { 1.1400447527693316, 0.69999999999999996, 1.0471975511965976 }, |
| { 1.3657668117194071, 0.69999999999999996, 1.2217304763960306 }, |
| { 1.6024686895959159, 0.69999999999999996, 1.3962634015954636 }, |
| { 1.8456939983747236, 0.69999999999999996, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.69999999999999996. |
| template <typename Tp> |
| void test017() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data017) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data017[i].k), Tp(data017[i].phi)); |
| const Tp f0 = data017[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.80000000000000004. |
| testcase_ellint_1<double> data018[] = { |
| { -0.0000000000000000, 0.80000000000000004, 0.0000000000000000 }, |
| { 0.17510154241338902, 0.80000000000000004, 0.17453292519943295 }, |
| { 0.35365068839779390, 0.80000000000000004, 0.34906585039886590 }, |
| { 0.53926804409084561, 0.80000000000000004, 0.52359877559829882 }, |
| { 0.73587926028070383, 0.80000000000000004, 0.69813170079773179 }, |
| { 0.94770942970071170, 0.80000000000000004, 0.87266462599716477 }, |
| { 1.1789022995388239, 0.80000000000000004, 1.0471975511965976 }, |
| { 1.4323027881876009, 0.80000000000000004, 1.2217304763960306 }, |
| { 1.7069629739121674, 0.80000000000000004, 1.3962634015954636 }, |
| { 1.9953027776647296, 0.80000000000000004, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.80000000000000004. |
| template <typename Tp> |
| void test018() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data018) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data018[i].k), Tp(data018[i].phi)); |
| const Tp f0 = data018[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| // Test data for k=0.89999999999999991. |
| testcase_ellint_1<double> data019[] = { |
| { -0.0000000000000000, 0.89999999999999991, 0.0000000000000000 }, |
| { 0.17525427376115027, 0.89999999999999991, 0.17453292519943295 }, |
| { 0.35492464591297446, 0.89999999999999991, 0.34906585039886590 }, |
| { 0.54388221416157123, 0.89999999999999991, 0.52359877559829882 }, |
| { 0.74797400423532501, 0.89999999999999991, 0.69813170079773179 }, |
| { 0.97463898451966458, 0.89999999999999991, 0.87266462599716477 }, |
| { 1.2334463254523438, 0.89999999999999991, 1.0471975511965976 }, |
| { 1.5355247765594910, 0.89999999999999991, 1.2217304763960306 }, |
| { 1.8882928567775117, 0.89999999999999991, 1.3962634015954636 }, |
| { 2.2805491384227699, 0.89999999999999991, 1.5707963267948966 }, |
| }; |
| |
| // Test function for k=0.89999999999999991. |
| template <typename Tp> |
| void test019() |
| { |
| const Tp eps = std::numeric_limits<Tp>::epsilon(); |
| Tp max_abs_diff = -Tp(1); |
| Tp max_abs_frac = -Tp(1); |
| unsigned int num_datum = sizeof(data019) |
| / sizeof(testcase_ellint_1<double>); |
| for (unsigned int i = 0; i < num_datum; ++i) |
| { |
| const Tp f = std::tr1::ellint_1(Tp(data019[i].k), Tp(data019[i].phi)); |
| const Tp f0 = data019[i].f0; |
| const Tp diff = f - f0; |
| if (std::abs(diff) > max_abs_diff) |
| max_abs_diff = std::abs(diff); |
| if (std::abs(f0) > Tp(10) * eps |
| && std::abs(f) > Tp(10) * eps) |
| { |
| const Tp frac = diff / f0; |
| if (std::abs(frac) > max_abs_frac) |
| max_abs_frac = std::abs(frac); |
| } |
| } |
| VERIFY(max_abs_frac < Tp(2.5000000000000020e-13)); |
| } |
| |
| int main(int, char**) |
| { |
| test001<double>(); |
| test002<double>(); |
| test003<double>(); |
| test004<double>(); |
| test005<double>(); |
| test006<double>(); |
| test007<double>(); |
| test008<double>(); |
| test009<double>(); |
| test010<double>(); |
| test011<double>(); |
| test012<double>(); |
| test013<double>(); |
| test014<double>(); |
| test015<double>(); |
| test016<double>(); |
| test017<double>(); |
| test018<double>(); |
| test019<double>(); |
| return 0; |
| } |