diff options
Diffstat (limited to 'libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/check_value.cc')
| -rw-r--r-- | libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/check_value.cc | 16039 |
1 files changed, 6133 insertions, 9906 deletions
diff --git a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/check_value.cc b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/check_value.cc index 2e402c68793..e0bd7037480 100644 --- a/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/check_value.cc +++ b/libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/14_ellint_3/check_value.cc @@ -1,6 +1,7 @@ -// 2007-02-04 Edward Smith-Rowland <3dw4rd@verizon.net> +// { dg-do run { target c++11 } } +// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" } // -// Copyright (C) 2007-2017 Free Software Foundation, Inc. +// Copyright (C) 2016-2018 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 @@ -18,10098 +19,6324 @@ // <http://www.gnu.org/licenses/>. // ellint_3 - - // Compare against values generated by the GNU Scientific Library. // The GSL can be found on the web: http://www.gnu.org/software/gsl/ - +#include <limits> #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; \ - } +# include <iostream> +# define VERIFY(A) \ + if (!(A)) \ + { \ + std::cout << "line " << __LINE__ \ + << " max_abs_frac = " << max_abs_frac \ + << std::endl; \ + } #else -#include <testsuite_hooks.h> +# include <testsuite_hooks.h> #endif -#include "../testcase.h" - +#include <specfun_testcase.h> // Test data for k=-0.90000000000000002, nu=0.0000000000000000. -testcase_ellint_3<double> data001[] = { - { -0.0000000000000000, -0.90000000000000002, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17525427376115027, -0.90000000000000002, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35492464591297446, -0.90000000000000002, 0.0000000000000000, - 0.34906585039886590 }, - { 0.54388221416157134, -0.90000000000000002, 0.0000000000000000, - 0.52359877559829882 }, - { 0.74797400423532523, -0.90000000000000002, 0.0000000000000000, - 0.69813170079773179 }, - { 0.97463898451966458, -0.90000000000000002, 0.0000000000000000, - 0.87266462599716477 }, - { 1.2334463254523440, -0.90000000000000002, 0.0000000000000000, - 1.0471975511965976 }, - { 1.5355247765594910, -0.90000000000000002, 0.0000000000000000, - 1.2217304763960306 }, - { 1.8882928567775124, -0.90000000000000002, 0.0000000000000000, - 1.3962634015954636 }, - { 2.2805491384227703, -0.90000000000000002, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.0000000000000000. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data001[i].k), Tp(data001[i].nu), - 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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 5.7842011620951154e-16 +// mean(f - f_Boost): 5.8286708792820721e-17 +// variance(f - f_Boost): 4.1942474344433133e-34 +// stddev(f - f_Boost): 2.0479861900030756e-17 +const testcase_ellint_3<double> +data001[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17525427376115027, -0.90000000000000002, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35492464591297446, -0.90000000000000002, 0.0000000000000000, + 0.34906585039886590 }, + { 0.54388221416157123, -0.90000000000000002, 0.0000000000000000, + 0.52359877559829882 }, + { 0.74797400423532512, -0.90000000000000002, 0.0000000000000000, + 0.69813170079773179 }, + { 0.97463898451966446, -0.90000000000000002, 0.0000000000000000, + 0.87266462599716477 }, + { 1.2334463254523438, -0.90000000000000002, 0.0000000000000000, + 1.0471975511965976 }, + { 1.5355247765594913, -0.90000000000000002, 0.0000000000000000, + 1.2217304763960306 }, + { 1.8882928567775126, -0.90000000000000002, 0.0000000000000000, + 1.3962634015954636 }, + { 2.2805491384227703, -0.90000000000000002, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler001 = 2.5000000000000020e-13; // Test data for k=-0.90000000000000002, nu=0.10000000000000001. -testcase_ellint_3<double> data002[] = { - { -0.0000000000000000, -0.90000000000000002, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17507714233254659, -0.90000000000000002, 0.10000000000000001, - 0.17453292519943295 }, - { 0.35350932904326521, -0.90000000000000002, 0.10000000000000001, - 0.34906585039886590 }, - { 0.53911129989870998, -0.90000000000000002, 0.10000000000000001, - 0.52359877559829882 }, - { 0.73666644254508429, -0.90000000000000002, 0.10000000000000001, - 0.69813170079773179 }, - { 0.95250736612100184, -0.90000000000000002, 0.10000000000000001, - 0.87266462599716477 }, - { 1.1950199550905594, -0.90000000000000002, 0.10000000000000001, - 1.0471975511965976 }, - { 1.4741687286340848, -0.90000000000000002, 0.10000000000000001, - 1.2217304763960306 }, - { 1.7968678183506059, -0.90000000000000002, 0.10000000000000001, - 1.3962634015954636 }, - { 2.1537868513875287, -0.90000000000000002, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.10000000000000001. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data002[i].k), Tp(data002[i].nu), - 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)); -} +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.1500594295134815e-16 +// mean(f - f_Boost): 1.0269562977782698e-16 +// variance(f - f_Boost): 1.4388836606733082e-32 +// stddev(f - f_Boost): 1.1995347684303728e-16 +const testcase_ellint_3<double> +data002[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17543204932716244, -0.90000000000000002, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35636022898551184, -0.90000000000000002, 0.10000000000000001, + 0.34906585039886590 }, + { 0.54880278898382584, -0.90000000000000002, 0.10000000000000001, + 0.52359877559829882 }, + { 0.75988834774529268, -0.90000000000000002, 0.10000000000000001, + 0.69813170079773179 }, + { 0.99853303003568117, -0.90000000000000002, 0.10000000000000001, + 0.87266462599716477 }, + { 1.2759958823999022, -0.90000000000000002, 0.10000000000000001, + 1.0471975511965976 }, + { 1.6051187364639401, -0.90000000000000002, 0.10000000000000001, + 1.2217304763960306 }, + { 1.9941406879519472, -0.90000000000000002, 0.10000000000000001, + 1.3962634015954636 }, + { 2.4295011187834881, -0.90000000000000002, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler002 = 2.5000000000000020e-13; // Test data for k=-0.90000000000000002, nu=0.20000000000000001. -testcase_ellint_3<double> data003[] = { - { -0.0000000000000000, -0.90000000000000002, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17490065089140930, -0.90000000000000002, 0.20000000000000001, - 0.17453292519943295 }, - { 0.35211377590661436, -0.90000000000000002, 0.20000000000000001, - 0.34906585039886590 }, - { 0.53448220334204122, -0.90000000000000002, 0.20000000000000001, - 0.52359877559829882 }, - { 0.72591368943179613, -0.90000000000000002, 0.20000000000000001, - 0.69813170079773179 }, - { 0.93192539780038763, -0.90000000000000002, 0.20000000000000001, - 0.87266462599716477 }, - { 1.1600809679692683, -0.90000000000000002, 0.20000000000000001, - 1.0471975511965976 }, - { 1.4195407225882508, -0.90000000000000002, 0.20000000000000001, - 1.2217304763960306 }, - { 1.7168966476424528, -0.90000000000000002, 0.20000000000000001, - 1.3962634015954636 }, - { 2.0443194576468890, -0.90000000000000002, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.20000000000000001. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data003[i].k), Tp(data003[i].nu), - 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=-0.90000000000000002, nu=0.29999999999999999. -testcase_ellint_3<double> data004[] = { - { -0.0000000000000000, -0.90000000000000002, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17472479532647534, -0.90000000000000002, 0.29999999999999999, - 0.17453292519943295 }, - { 0.35073750187374114, -0.90000000000000002, 0.29999999999999999, - 0.34906585039886590 }, - { 0.52998766129466979, -0.90000000000000002, 0.29999999999999999, - 0.52359877559829882 }, - { 0.71566993548699587, -0.90000000000000002, 0.29999999999999999, - 0.69813170079773179 }, - { 0.91271517762560195, -0.90000000000000002, 0.29999999999999999, - 0.87266462599716477 }, - { 1.1281241199843370, -0.90000000000000002, 0.29999999999999999, - 1.0471975511965976 }, - { 1.3704929576917448, -0.90000000000000002, 0.29999999999999999, - 1.2217304763960306 }, - { 1.6461981511487715, -0.90000000000000002, 0.29999999999999999, - 1.3962634015954636 }, - { 1.9486280260314426, -0.90000000000000002, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.29999999999999999. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data004[i].k), Tp(data004[i].nu), - 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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 5.2711357908578066e-16 +// mean(f - f_Boost): 8.0491169285323847e-17 +// variance(f - f_Boost): 7.9985534974304465e-34 +// stddev(f - f_Boost): 2.8281714052423424e-17 +const testcase_ellint_3<double> +data003[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17561047321968409, -0.90000000000000002, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35781659944356109, -0.90000000000000002, 0.20000000000000001, + 0.34906585039886590 }, + { 0.55388150905215283, -0.90000000000000002, 0.20000000000000001, + 0.52359877559829882 }, + { 0.77246874123251441, -0.90000000000000002, 0.20000000000000001, + 0.69813170079773179 }, + { 1.0244466254771925, -0.90000000000000002, 0.20000000000000001, + 0.87266462599716477 }, + { 1.3234824077640801, -0.90000000000000002, 0.20000000000000001, + 1.0471975511965976 }, + { 1.6849848968804237, -0.90000000000000002, 0.20000000000000001, + 1.2217304763960306 }, + { 2.1185749045502273, -0.90000000000000002, 0.20000000000000001, + 1.3962634015954636 }, + { 2.6076835743348412, -0.90000000000000002, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler003 = 2.5000000000000020e-13; + +// Test data for k=-0.90000000000000002, nu=0.30000000000000004. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.9955372494296814e-16 +// mean(f - f_Boost): 5.8286708792820721e-17 +// variance(f - f_Boost): 4.1942474344433133e-34 +// stddev(f - f_Boost): 2.0479861900030756e-17 +const testcase_ellint_3<double> +data004[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17578954966746221, -0.90000000000000002, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35929429810867447, -0.90000000000000002, 0.30000000000000004, + 0.34906585039886590 }, + { 0.55912757154240811, -0.90000000000000002, 0.30000000000000004, + 0.52359877559829882 }, + { 0.78578314722025389, -0.90000000000000002, 0.30000000000000004, + 0.69813170079773179 }, + { 1.0526941001131365, -0.90000000000000002, 0.30000000000000004, + 0.87266462599716477 }, + { 1.3769682234538601, -0.90000000000000002, 0.30000000000000004, + 1.0471975511965976 }, + { 1.7779437432911238, -0.90000000000000002, 0.30000000000000004, + 1.2217304763960306 }, + { 2.2676509341813631, -0.90000000000000002, 0.30000000000000004, + 1.3962634015954636 }, + { 2.8256506968858512, -0.90000000000000002, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler004 = 2.5000000000000020e-13; // Test data for k=-0.90000000000000002, nu=0.40000000000000002. -testcase_ellint_3<double> data005[] = { - { -0.0000000000000000, -0.90000000000000002, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17454957156468839, -0.90000000000000002, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34938003933330430, -0.90000000000000002, 0.40000000000000002, - 0.34906585039886590 }, - { 0.52562093533067455, -0.90000000000000002, 0.40000000000000002, - 0.52359877559829882 }, - { 0.70589461324915703, -0.90000000000000002, 0.40000000000000002, - 0.69813170079773179 }, - { 0.89472658511942849, -0.90000000000000002, 0.40000000000000002, - 0.87266462599716477 }, - { 1.0987419542323440, -0.90000000000000002, 0.40000000000000002, - 1.0471975511965976 }, - { 1.3261349565496301, -0.90000000000000002, 0.40000000000000002, - 1.2217304763960306 }, - { 1.5831293909853767, -0.90000000000000002, 0.40000000000000002, - 1.3962634015954636 }, - { 1.8641114227238349, -0.90000000000000002, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.40000000000000002. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data005[i].k), Tp(data005[i].nu), - 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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.7042235432234642e-16 +// mean(f - f_Boost): 2.0261570199409106e-16 +// variance(f - f_Boost): 5.8024227149195491e-32 +// stddev(f - f_Boost): 2.4088218520512364e-16 +const testcase_ellint_3<double> +data005[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17596928293938452, -0.90000000000000002, 0.40000000000000002, + 0.17453292519943295 }, + { 0.36079388642472821, -0.90000000000000002, 0.40000000000000002, + 0.34906585039886590 }, + { 0.56455096667115612, -0.90000000000000002, 0.40000000000000002, + 0.52359877559829882 }, + { 0.79990996997869435, -0.90000000000000002, 0.40000000000000002, + 0.69813170079773179 }, + { 1.0836647913872215, -0.90000000000000002, 0.40000000000000002, + 0.87266462599716477 }, + { 1.4378726836091849, -0.90000000000000002, 0.40000000000000002, + 1.0471975511965976 }, + { 1.8880446720682853, -0.90000000000000002, 0.40000000000000002, + 1.2217304763960306 }, + { 2.4505848932025227, -0.90000000000000002, 0.40000000000000002, + 1.3962634015954636 }, + { 3.1000689868578615, -0.90000000000000002, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler005 = 2.5000000000000020e-13; // Test data for k=-0.90000000000000002, nu=0.50000000000000000. -testcase_ellint_3<double> data006[] = { - { -0.0000000000000000, -0.90000000000000002, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17437497557073336, -0.90000000000000002, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34804093691586013, -0.90000000000000002, 0.50000000000000000, - 0.34906585039886590 }, - { 0.52137576320372914, -0.90000000000000002, 0.50000000000000000, - 0.52359877559829882 }, - { 0.69655163996912284, -0.90000000000000002, 0.50000000000000000, - 0.69813170079773179 }, - { 0.87783188683054236, -0.90000000000000002, 0.50000000000000000, - 0.87266462599716477 }, - { 1.0716015959755185, -0.90000000000000002, 0.50000000000000000, - 1.0471975511965976 }, - { 1.2857636916026747, -0.90000000000000002, 0.50000000000000000, - 1.2217304763960306 }, - { 1.5264263913252365, -0.90000000000000002, 0.50000000000000000, - 1.3962634015954636 }, - { 1.7888013241937861, -0.90000000000000002, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.50000000000000000. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data006[i].k), Tp(data006[i].nu), - 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=-0.90000000000000002, nu=0.59999999999999998. -testcase_ellint_3<double> data007[] = { - { -0.0000000000000000, -0.90000000000000002, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17420100334657815, -0.90000000000000002, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34671975876122157, -0.90000000000000002, 0.59999999999999998, - 0.34906585039886590 }, - { 0.51724631570707968, -0.90000000000000002, 0.59999999999999998, - 0.52359877559829882 }, - { 0.68760879113743056, -0.90000000000000002, 0.59999999999999998, - 0.69813170079773179 }, - { 0.86192157779698364, -0.90000000000000002, 0.59999999999999998, - 0.87266462599716477 }, - { 1.0464279696166354, -0.90000000000000002, 0.59999999999999998, - 1.0471975511965976 }, - { 1.2488156247094004, -0.90000000000000002, 0.59999999999999998, - 1.2217304763960306 }, - { 1.4750988777188474, -0.90000000000000002, 0.59999999999999998, - 1.3962634015954636 }, - { 1.7211781128919523, -0.90000000000000002, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.59999999999999998. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data007[i].k), Tp(data007[i].nu), - 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=-0.90000000000000002, nu=0.69999999999999996. -testcase_ellint_3<double> data008[] = { - { -0.0000000000000000, -0.90000000000000002, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17402765093102210, -0.90000000000000002, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34541608382635131, -0.90000000000000002, 0.69999999999999996, - 0.34906585039886590 }, - { 0.51322715827061705, -0.90000000000000002, 0.69999999999999996, - 0.52359877559829882 }, - { 0.67903717872440306, -0.90000000000000002, 0.69999999999999996, - 0.69813170079773179 }, - { 0.84690113601682671, -0.90000000000000002, 0.69999999999999996, - 0.87266462599716477 }, - { 1.0229914311548418, -0.90000000000000002, 0.69999999999999996, - 1.0471975511965976 }, - { 1.2148329639709381, -0.90000000000000002, 0.69999999999999996, - 1.2217304763960306 }, - { 1.4283586501307806, -0.90000000000000002, 0.69999999999999996, - 1.3962634015954636 }, - { 1.6600480747670938, -0.90000000000000002, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.69999999999999996. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data008[i].k), Tp(data008[i].nu), - 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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 3.8944086593755267e-16 +// mean(f - f_Boost): 6.9388939039072284e-17 +// variance(f - f_Boost): 1.7333369499485123e-32 +// stddev(f - f_Boost): 1.3165625507162629e-16 +const testcase_ellint_3<double> +data006[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17614967734498183, -0.90000000000000002, 0.50000000000000000, + 0.17453292519943295 }, + { 0.36231594750319435, -0.90000000000000002, 0.50000000000000000, + 0.34906585039886590 }, + { 0.57016256984349567, -0.90000000000000002, 0.50000000000000000, + 0.52359877559829882 }, + { 0.81494025918293422, -0.90000000000000002, 0.50000000000000000, + 0.69813170079773179 }, + { 1.1178482279283477, -0.90000000000000002, 0.50000000000000000, + 0.87266462599716477 }, + { 1.5081455873012106, -0.90000000000000002, 0.50000000000000000, + 1.0471975511965976 }, + { 2.0213599730863998, -0.90000000000000002, 0.50000000000000000, + 1.2217304763960306 }, + { 2.6822467012926827, -0.90000000000000002, 0.50000000000000000, + 1.3962634015954636 }, + { 3.4591069002104677, -0.90000000000000002, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler006 = 2.5000000000000020e-13; + +// Test data for k=-0.90000000000000002, nu=0.60000000000000009. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.0602096790645418e-16 +// mean(f - f_Boost): 1.0269562977782698e-16 +// variance(f - f_Boost): 1.4388836606733082e-32 +// stddev(f - f_Boost): 1.1995347684303728e-16 +const testcase_ellint_3<double> +data007[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17633073723493825, -0.90000000000000002, 0.60000000000000009, + 0.17453292519943295 }, + { 0.36386108723492810, -0.90000000000000002, 0.60000000000000009, + 0.34906585039886590 }, + { 0.57597424744716241, -0.90000000000000002, 0.60000000000000009, + 0.52359877559829882 }, + { 0.83098051948501150, -0.90000000000000002, 0.60000000000000009, + 0.69813170079773179 }, + { 1.1558706545698916, -0.90000000000000002, 0.60000000000000009, + 0.87266462599716477 }, + { 1.5905576379415669, -0.90000000000000002, 0.60000000000000009, + 1.0471975511965976 }, + { 2.1875186010215080, -0.90000000000000002, 0.60000000000000009, + 1.2217304763960306 }, + { 2.9885767771316849, -0.90000000000000002, 0.60000000000000009, + 1.3962634015954636 }, + { 3.9549939883570224, -0.90000000000000002, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler007 = 2.5000000000000020e-13; + +// Test data for k=-0.90000000000000002, nu=0.70000000000000007. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 5.1938610791060186e-16 +// mean(f - f_Boost): 3.0253577421035517e-16 +// variance(f - f_Boost): 4.2342877557562532e-32 +// stddev(f - f_Boost): 2.0577385051935665e-16 +const testcase_ellint_3<double> +data008[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17651246700160939, -0.90000000000000002, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36542993547358982, -0.90000000000000002, 0.70000000000000007, + 0.34906585039886590 }, + { 0.58199897877674867, -0.90000000000000002, 0.70000000000000007, + 0.52359877559829882 }, + { 0.84815633587352857, -0.90000000000000002, 0.70000000000000007, + 0.69813170079773179 }, + { 1.1985495623872375, -0.90000000000000002, 0.70000000000000007, + 0.87266462599716477 }, + { 1.6892158134027688, -0.90000000000000002, 0.70000000000000007, + 1.0471975511965976 }, + { 2.4029722191094236, -0.90000000000000002, 0.70000000000000007, + 1.2217304763960306 }, + { 3.4201084941340052, -0.90000000000000002, 0.70000000000000007, + 1.3962634015954636 }, + { 4.6985482312992435, -0.90000000000000002, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler008 = 2.5000000000000020e-13; // Test data for k=-0.90000000000000002, nu=0.80000000000000004. -testcase_ellint_3<double> data009[] = { - { -0.0000000000000000, -0.90000000000000002, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17385491439925149, -0.90000000000000002, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34412950523113928, -0.90000000000000002, 0.80000000000000004, - 0.34906585039886590 }, - { 0.50931321668729612, -0.90000000000000002, 0.80000000000000004, - 0.52359877559829882 }, - { 0.67081081392296349, -0.90000000000000002, 0.80000000000000004, - 0.69813170079773179 }, - { 0.83268846097293259, -0.90000000000000002, 0.80000000000000004, - 0.87266462599716477 }, - { 1.0010985015814027, -0.90000000000000002, 0.80000000000000004, - 1.0471975511965976 }, - { 1.1834394045489678, -0.90000000000000002, 0.80000000000000004, - 1.2217304763960306 }, - { 1.3855695891683188, -0.90000000000000002, 0.80000000000000004, - 1.3962634015954636 }, - { 1.6044591960982204, -0.90000000000000002, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.80000000000000004. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data009[i].k), Tp(data009[i].nu), - 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)); -} +// max(|f - f_Boost|): 2.6645352591003757e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 6.5091520146032660e-16 +// mean(f - f_Boost): 2.8310687127941490e-16 +// variance(f - f_Boost): 9.8950000698295322e-33 +// stddev(f - f_Boost): 9.9473614943006532e-17 +const testcase_ellint_3<double> +data009[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17669487107954862, -0.90000000000000002, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36702314729628421, -0.90000000000000002, 0.80000000000000004, + 0.34906585039886590 }, + { 0.58825099711365492, -0.90000000000000002, 0.80000000000000004, + 0.52359877559829882 }, + { 0.86661711422209031, -0.90000000000000002, 0.80000000000000004, + 0.69813170079773179 }, + { 1.2469779109884802, -0.90000000000000002, 0.80000000000000004, + 0.87266462599716477 }, + { 1.8105469760531578, -0.90000000000000002, 0.80000000000000004, + 1.0471975511965976 }, + { 2.6989505165893752, -0.90000000000000002, 0.80000000000000004, + 1.2217304763960306 }, + { 4.0935213267757424, -0.90000000000000002, 0.80000000000000004, + 1.3962634015954636 }, + { 5.9820740813645710, -0.90000000000000002, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler009 = 2.5000000000000020e-13; // Test data for k=-0.90000000000000002, nu=0.90000000000000002. -testcase_ellint_3<double> data010[] = { - { -0.0000000000000000, -0.90000000000000002, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17368278986240138, -0.90000000000000002, 0.90000000000000002, - 0.17453292519943295 }, - { 0.34285962963961397, -0.90000000000000002, 0.90000000000000002, - 0.34906585039886590 }, - { 0.50549974644993323, -0.90000000000000002, 0.90000000000000002, - 0.52359877559829882 }, - { 0.66290623857720898, -0.90000000000000002, 0.90000000000000002, - 0.69813170079773179 }, - { 0.81921183128847164, -0.90000000000000002, 0.90000000000000002, - 0.87266462599716477 }, - { 0.98058481956066390, -0.90000000000000002, 0.90000000000000002, - 1.0471975511965976 }, - { 1.1543223520473567, -0.90000000000000002, 0.90000000000000002, - 1.2217304763960306 }, - { 1.3462119782292938, -0.90000000000000002, 0.90000000000000002, - 1.3962634015954636 }, - { 1.5536420236310946, -0.90000000000000002, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.90000000000000002, nu=0.90000000000000002. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data010[i].k), Tp(data010[i].nu), - 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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 8.2628580104449673e-16 +// mean(f - f_Boost): 8.5764728652293339e-16 +// variance(f - f_Boost): 8.9671393318321280e-31 +// stddev(f - f_Boost): 9.4694980499666013e-16 +const testcase_ellint_3<double> +data010[10] = +{ + { 0.0000000000000000, -0.90000000000000002, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17687795394604169, -0.90000000000000002, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36864140434751286, -0.90000000000000002, 0.90000000000000002, + 0.34906585039886590 }, + { 0.59474595366817051, -0.90000000000000002, 0.90000000000000002, + 0.52359877559829882 }, + { 0.88654237226056665, -0.90000000000000002, 0.90000000000000002, + 0.69813170079773179 }, + { 1.3026595810616726, -0.90000000000000002, 0.90000000000000002, + 0.87266462599716477 }, + { 1.9653635459278078, -0.90000000000000002, 0.90000000000000002, + 1.0471975511965976 }, + { 3.1451407527189463, -0.90000000000000002, 0.90000000000000002, + 1.2217304763960306 }, + { 5.3745230680316114, -0.90000000000000002, 0.90000000000000002, + 1.3962634015954636 }, + { 8.9942562031858682, -0.90000000000000002, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler010 = 2.5000000000000020e-13; // Test data for k=-0.80000000000000004, nu=0.0000000000000000. -testcase_ellint_3<double> data011[] = { - { -0.0000000000000000, -0.80000000000000004, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17510154241338902, -0.80000000000000004, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35365068839779390, -0.80000000000000004, 0.0000000000000000, - 0.34906585039886590 }, - { 0.53926804409084561, -0.80000000000000004, 0.0000000000000000, - 0.52359877559829882 }, - { 0.73587926028070383, -0.80000000000000004, 0.0000000000000000, - 0.69813170079773179 }, - { 0.94770942970071170, -0.80000000000000004, 0.0000000000000000, - 0.87266462599716477 }, - { 1.1789022995388239, -0.80000000000000004, 0.0000000000000000, - 1.0471975511965976 }, - { 1.4323027881876009, -0.80000000000000004, 0.0000000000000000, - 1.2217304763960306 }, - { 1.7069629739121674, -0.80000000000000004, 0.0000000000000000, - 1.3962634015954636 }, - { 1.9953027776647296, -0.80000000000000004, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.0000000000000000. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data011[i].k), Tp(data011[i].nu), - 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)); -} +// max(|f - f_Boost|): 1.5543122344752192e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 7.7898565163847540e-16 +// mean(f - f_Boost): 2.3869795029440865e-16 +// variance(f - f_Boost): 2.1368406725192426e-31 +// stddev(f - f_Boost): 4.6225974002926564e-16 +const testcase_ellint_3<double> +data011[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17510154241338899, -0.80000000000000004, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35365068839779396, -0.80000000000000004, 0.0000000000000000, + 0.34906585039886590 }, + { 0.53926804409084550, -0.80000000000000004, 0.0000000000000000, + 0.52359877559829882 }, + { 0.73587926028070372, -0.80000000000000004, 0.0000000000000000, + 0.69813170079773179 }, + { 0.94770942970071170, -0.80000000000000004, 0.0000000000000000, + 0.87266462599716477 }, + { 1.1789022995388236, -0.80000000000000004, 0.0000000000000000, + 1.0471975511965976 }, + { 1.4323027881876012, -0.80000000000000004, 0.0000000000000000, + 1.2217304763960306 }, + { 1.7069629739121677, -0.80000000000000004, 0.0000000000000000, + 1.3962634015954636 }, + { 1.9953027776647294, -0.80000000000000004, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler011 = 2.5000000000000020e-13; // Test data for k=-0.80000000000000004, nu=0.10000000000000001. -testcase_ellint_3<double> data012[] = { - { -0.0000000000000000, -0.80000000000000004, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17492468824017166, -0.80000000000000004, 0.10000000000000001, - 0.17453292519943295 }, - { 0.35224443521476911, -0.80000000000000004, 0.10000000000000001, - 0.34906585039886590 }, - { 0.53456851853226961, -0.80000000000000004, 0.10000000000000001, - 0.52359877559829882 }, - { 0.72488875602364944, -0.80000000000000004, 0.10000000000000001, - 0.69813170079773179 }, - { 0.92661354274638952, -0.80000000000000004, 0.10000000000000001, - 0.87266462599716477 }, - { 1.1432651144499077, -0.80000000000000004, 0.10000000000000001, - 1.0471975511965976 }, - { 1.3774479927211429, -0.80000000000000004, 0.10000000000000001, - 1.2217304763960306 }, - { 1.6287092337196041, -0.80000000000000004, 0.10000000000000001, - 1.3962634015954636 }, - { 1.8910755418379521, -0.80000000000000004, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.10000000000000001. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data012[i].k), Tp(data012[i].nu), - 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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 8.3898786942190374e-16 +// mean(f - f_Boost): 2.3869795029440865e-16 +// variance(f - f_Boost): 2.9190059990693968e-31 +// stddev(f - f_Boost): 5.4027826155319237e-16 +const testcase_ellint_3<double> +data012[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17527903952342144, -0.80000000000000004, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35507705313548549, -0.80000000000000004, 0.10000000000000001, + 0.34906585039886590 }, + { 0.54411455987643553, -0.80000000000000004, 0.10000000000000001, + 0.52359877559829882 }, + { 0.74745625666804383, -0.80000000000000004, 0.10000000000000001, + 0.69813170079773179 }, + { 0.97046953684238557, -0.80000000000000004, 0.10000000000000001, + 0.87266462599716477 }, + { 1.2183080025184605, -0.80000000000000004, 0.10000000000000001, + 1.0471975511965976 }, + { 1.4943711151994405, -0.80000000000000004, 0.10000000000000001, + 1.2217304763960306 }, + { 1.7972401309544201, -0.80000000000000004, 0.10000000000000001, + 1.3962634015954636 }, + { 2.1172616484005085, -0.80000000000000004, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler012 = 2.5000000000000020e-13; // Test data for k=-0.80000000000000004, nu=0.20000000000000001. -testcase_ellint_3<double> data013[] = { - { -0.0000000000000000, -0.80000000000000004, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17474847286224943, -0.80000000000000004, 0.20000000000000001, - 0.17453292519943295 }, - { 0.35085779529084682, -0.80000000000000004, 0.20000000000000001, - 0.34906585039886590 }, - { 0.53000829263059157, -0.80000000000000004, 0.20000000000000001, - 0.52359877559829882 }, - { 0.71443466027453406, -0.80000000000000004, 0.20000000000000001, - 0.69813170079773179 }, - { 0.90698196872715420, -0.80000000000000004, 0.20000000000000001, - 0.87266462599716477 }, - { 1.1108198200558581, -0.80000000000000004, 0.20000000000000001, - 1.0471975511965976 }, - { 1.3284988909963957, -0.80000000000000004, 0.20000000000000001, - 1.2217304763960306 }, - { 1.5600369318140328, -0.80000000000000004, 0.20000000000000001, - 1.3962634015954636 }, - { 1.8007226661734588, -0.80000000000000004, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.20000000000000001. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data013[i].k), Tp(data013[i].nu), - 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=-0.80000000000000004, nu=0.29999999999999999. -testcase_ellint_3<double> data014[] = { - { -0.0000000000000000, -0.80000000000000004, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17457289217669891, -0.80000000000000004, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34949028801501258, -0.80000000000000004, 0.29999999999999999, - 0.34906585039886590 }, - { 0.52558024362769318, -0.80000000000000004, 0.29999999999999999, - 0.52359877559829882 }, - { 0.70447281740094914, -0.80000000000000004, 0.29999999999999999, - 0.69813170079773179 }, - { 0.88864745641528986, -0.80000000000000004, 0.29999999999999999, - 0.87266462599716477 }, - { 1.0811075819341465, -0.80000000000000004, 0.29999999999999999, - 1.0471975511965976 }, - { 1.2844589654082377, -0.80000000000000004, 0.29999999999999999, - 1.2217304763960306 }, - { 1.4991461361277849, -0.80000000000000004, 0.29999999999999999, - 1.3962634015954636 }, - { 1.7214611048717301, -0.80000000000000004, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.29999999999999999. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data014[i].k), Tp(data014[i].nu), - 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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 7.8513740186068518e-16 +// mean(f - f_Boost): 2.8310687127941490e-16 +// variance(f - f_Boost): 2.7528339102381189e-31 +// stddev(f - f_Boost): 5.2467455724840699e-16 +const testcase_ellint_3<double> +data013[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17545718375086419, -0.80000000000000004, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35652404627248163, -0.80000000000000004, 0.20000000000000001, + 0.34906585039886590 }, + { 0.54911638512920913, -0.80000000000000004, 0.20000000000000001, + 0.52359877559829882 }, + { 0.75967684282131176, -0.80000000000000004, 0.20000000000000001, + 0.69813170079773179 }, + { 0.99513526893543769, -0.80000000000000004, 0.20000000000000001, + 0.87266462599716477 }, + { 1.2622192109995993, -0.80000000000000004, 0.20000000000000001, + 1.0471975511965976 }, + { 1.5654106676347741, -0.80000000000000004, 0.20000000000000001, + 1.2217304763960306 }, + { 1.9029531718534984, -0.80000000000000004, 0.20000000000000001, + 1.3962634015954636 }, + { 2.2624789434186798, -0.80000000000000004, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler013 = 2.5000000000000020e-13; + +// Test data for k=-0.80000000000000004, nu=0.30000000000000004. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 7.2825261583337354e-16 +// mean(f - f_Boost): 2.6367796834847468e-16 +// variance(f - f_Boost): 2.8249350208968825e-31 +// stddev(f - f_Boost): 5.3150117788175054e-16 +const testcase_ellint_3<double> +data014[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17563597931587369, -0.80000000000000004, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35799220412005128, -0.80000000000000004, 0.30000000000000004, + 0.34906585039886590 }, + { 0.55428253691111318, -0.80000000000000004, 0.30000000000000004, + 0.52359877559829882 }, + { 0.77260647376977365, -0.80000000000000004, 0.30000000000000004, + 0.69813170079773179 }, + { 1.0220015271210958, -0.80000000000000004, 0.30000000000000004, + 0.87266462599716477 }, + { 1.3115965312302671, -0.80000000000000004, 0.30000000000000004, + 1.0471975511965976 }, + { 1.6478518468813512, -0.80000000000000004, 0.30000000000000004, + 1.2217304763960306 }, + { 2.0290458414203481, -0.80000000000000004, 0.30000000000000004, + 1.3962634015954636 }, + { 2.4392042002725693, -0.80000000000000004, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler014 = 2.5000000000000020e-13; // Test data for k=-0.80000000000000004, nu=0.40000000000000002. -testcase_ellint_3<double> data015[] = { - { -0.0000000000000000, -0.80000000000000004, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17439794211872178, -0.80000000000000004, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34814144964568972, -0.80000000000000004, 0.40000000000000002, - 0.34906585039886590 }, - { 0.52127776285273075, -0.80000000000000004, 0.40000000000000002, - 0.52359877559829882 }, - { 0.69496411438966599, -0.80000000000000004, 0.40000000000000002, - 0.69813170079773179 }, - { 0.87146878427509589, -0.80000000000000004, 0.40000000000000002, - 0.87266462599716477 }, - { 1.0537579024937762, -0.80000000000000004, 0.40000000000000002, - 1.0471975511965976 }, - { 1.2445534387922637, -0.80000000000000004, 0.40000000000000002, - 1.2217304763960306 }, - { 1.4446769766361993, -0.80000000000000004, 0.40000000000000002, - 1.3962634015954636 }, - { 1.6512267838651289, -0.80000000000000004, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.40000000000000002. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data015[i].k), Tp(data015[i].nu), - 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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 8.3462748389836647e-16 +// mean(f - f_Boost): 3.3861802251067273e-16 +// variance(f - f_Boost): 4.3719465706454422e-31 +// stddev(f - f_Boost): 6.6120696991527871e-16 +const testcase_ellint_3<double> +data015[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17581543047866136, -0.80000000000000004, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35948208343061633, -0.80000000000000004, 0.40000000000000002, + 0.34906585039886590 }, + { 0.55962280893702021, -0.80000000000000004, 0.40000000000000002, + 0.52359877559829882 }, + { 0.78632063889234116, -0.80000000000000004, 0.40000000000000002, + 0.69813170079773179 }, + { 1.0514333069550323, -0.80000000000000004, 0.40000000000000002, + 0.87266462599716477 }, + { 1.3677213138838757, -0.80000000000000004, 0.40000000000000002, + 1.0471975511965976 }, + { 1.7451736773665165, -0.80000000000000004, 0.40000000000000002, + 1.2217304763960306 }, + { 2.1830100424586831, -0.80000000000000004, 0.40000000000000002, + 1.3962634015954636 }, + { 2.6604037035529724, -0.80000000000000004, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler015 = 2.5000000000000020e-13; // Test data for k=-0.80000000000000004, nu=0.50000000000000000. -testcase_ellint_3<double> data016[] = { - { -0.0000000000000000, -0.80000000000000004, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17422361866118047, -0.80000000000000004, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34681083254170475, -0.80000000000000004, 0.50000000000000000, - 0.34906585039886590 }, - { 0.51709470815494440, -0.80000000000000004, 0.50000000000000000, - 0.52359877559829882 }, - { 0.68587375344080259, -0.80000000000000004, 0.50000000000000000, - 0.69813170079773179 }, - { 0.85532571852810624, -0.80000000000000004, 0.50000000000000000, - 0.87266462599716477 }, - { 1.0284677391874906, -0.80000000000000004, 0.50000000000000000, - 1.0471975511965976 }, - { 1.2081693942686225, -0.80000000000000004, 0.50000000000000000, - 1.2217304763960306 }, - { 1.3955803006426311, -0.80000000000000004, 0.50000000000000000, - 1.3962634015954636 }, - { 1.5884528947755532, -0.80000000000000004, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.50000000000000000. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data016[i].k), Tp(data016[i].nu), - 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=-0.80000000000000004, nu=0.59999999999999998. -testcase_ellint_3<double> data017[] = { - { -0.0000000000000000, -0.80000000000000004, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17404991781414092, -0.80000000000000004, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34549800443625167, -0.80000000000000004, 0.59999999999999998, - 0.34906585039886590 }, - { 0.51302536167001556, -0.80000000000000004, 0.59999999999999998, - 0.52359877559829882 }, - { 0.67717065003912258, -0.80000000000000004, 0.59999999999999998, - 0.69813170079773179 }, - { 0.84011512421134416, -0.80000000000000004, 0.59999999999999998, - 0.87266462599716477 }, - { 1.0049863847088742, -0.80000000000000004, 0.59999999999999998, - 1.0471975511965976 }, - { 1.1748145941898918, -0.80000000000000004, 0.59999999999999998, - 1.2217304763960306 }, - { 1.3510319699755071, -0.80000000000000004, 0.59999999999999998, - 1.3962634015954636 }, - { 1.5319262547427865, -0.80000000000000004, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.59999999999999998. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data017[i].k), Tp(data017[i].nu), - 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, nu=0.69999999999999996. -testcase_ellint_3<double> data018[] = { - { -0.0000000000000000, -0.80000000000000004, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17387683562442202, -0.80000000000000004, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34420254775101611, -0.80000000000000004, 0.69999999999999996, - 0.34906585039886590 }, - { 0.50906439222143685, -0.80000000000000004, 0.69999999999999996, - 0.52359877559829882 }, - { 0.66882693152688433, -0.80000000000000004, 0.69999999999999996, - 0.69813170079773179 }, - { 0.82574792844091316, -0.80000000000000004, 0.69999999999999996, - 0.87266462599716477 }, - { 0.98310431309490953, -0.80000000000000004, 0.69999999999999996, - 1.0471975511965976 }, - { 1.1440884535113258, -0.80000000000000004, 0.69999999999999996, - 1.2217304763960306 }, - { 1.3103743938952537, -0.80000000000000004, 0.69999999999999996, - 1.3962634015954636 }, - { 1.4806912324625332, -0.80000000000000004, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.69999999999999996. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data018[i].k), Tp(data018[i].nu), - 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)); -} +// max(|f - f_Boost|): 2.6645352591003757e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 9.0388243828581744e-16 +// mean(f - f_Boost): 3.8580250105724191e-16 +// variance(f - f_Boost): 6.4106456575047741e-31 +// stddev(f - f_Boost): 8.0066507713929764e-16 +const testcase_ellint_3<double> +data016[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17599554153999472, -0.80000000000000004, 0.50000000000000000, + 0.17453292519943295 }, + { 0.36099426243351540, -0.80000000000000004, 0.50000000000000000, + 0.34906585039886590 }, + { 0.56514786174780673, -0.80000000000000004, 0.50000000000000000, + 0.52359877559829882 }, + { 0.80090697622371010, -0.80000000000000004, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0838891627679339, -0.80000000000000004, 0.50000000000000000, + 0.87266462599716477 }, + { 1.4323506654466280, -0.80000000000000004, 0.50000000000000000, + 1.0471975511965976 }, + { 1.8625761085390575, -0.80000000000000004, 0.50000000000000000, + 1.2217304763960306 }, + { 2.3768757305654766, -0.80000000000000004, 0.50000000000000000, + 1.3962634015954636 }, + { 2.9478781158239746, -0.80000000000000004, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler016 = 2.5000000000000020e-13; + +// Test data for k=-0.80000000000000004, nu=0.60000000000000009. +// max(|f - f_Boost|): 3.5527136788005009e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 1.0631099169042069e-15 +// mean(f - f_Boost): 4.8294701571194306e-16 +// variance(f - f_Boost): 1.1633910328160319e-30 +// stddev(f - f_Boost): 1.0786060600682865e-15 +const testcase_ellint_3<double> +data017[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17617631684170665, -0.80000000000000004, 0.60000000000000009, + 0.17453292519943295 }, + { 0.36252934193666231, -0.80000000000000004, 0.60000000000000009, + 0.34906585039886590 }, + { 0.57086932622945163, -0.80000000000000004, 0.60000000000000009, + 0.52359877559829882 }, + { 0.81646796740150973, -0.80000000000000004, 0.60000000000000009, + 0.69813170079773179 }, + { 1.1199552158519064, -0.80000000000000004, 0.60000000000000009, + 0.87266462599716477 }, + { 1.5079766673336394, -0.80000000000000004, 0.60000000000000009, + 1.0471975511965976 }, + { 2.0082747447038165, -0.80000000000000004, 0.60000000000000009, + 1.2217304763960306 }, + { 2.6315146066775523, -0.80000000000000004, 0.60000000000000009, + 1.3962634015954636 }, + { 3.3418121892288051, -0.80000000000000004, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler017 = 2.5000000000000020e-13; + +// Test data for k=-0.80000000000000004, nu=0.70000000000000007. +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.6544679145741375e-16 +// mean(f - f_Boost): 3.2751579226442120e-16 +// variance(f - f_Boost): 4.4236851331020672e-31 +// stddev(f - f_Boost): 6.6510789599147505e-16 +const testcase_ellint_3<double> +data018[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17635776076721221, -0.80000000000000004, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36408794649916976, -0.80000000000000004, 0.70000000000000007, + 0.34906585039886590 }, + { 0.57679992290624138, -0.80000000000000004, 0.70000000000000007, + 0.52359877559829882 }, + { 0.83312441418142813, -0.80000000000000004, 0.70000000000000007, + 0.69813170079773179 }, + { 1.1603958891464856, -0.80000000000000004, 0.70000000000000007, + 0.87266462599716477 }, + { 1.5982855143796213, -0.80000000000000004, 0.70000000000000007, + 1.0471975511965976 }, + { 2.1962484408371821, -0.80000000000000004, 0.70000000000000007, + 1.2217304763960306 }, + { 2.9873281786111869, -0.80000000000000004, 0.70000000000000007, + 1.3962634015954636 }, + { 3.9268876980046397, -0.80000000000000004, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler018 = 2.5000000000000020e-13; // Test data for k=-0.80000000000000004, nu=0.80000000000000004. -testcase_ellint_3<double> data019[] = { - { -0.0000000000000000, -0.80000000000000004, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17370436817515206, -0.80000000000000004, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34292405894783395, -0.80000000000000004, 0.80000000000000004, - 0.34906585039886590 }, - { 0.50520682176250087, -0.80000000000000004, 0.80000000000000004, - 0.52359877559829882 }, - { 0.66081751679736189, -0.80000000000000004, 0.80000000000000004, - 0.69813170079773179 }, - { 0.81214672249355102, -0.80000000000000004, 0.80000000000000004, - 0.87266462599716477 }, - { 0.96264481387685574, -0.80000000000000004, 0.80000000000000004, - 1.0471975511965976 }, - { 1.1156611352656258, -0.80000000000000004, 0.80000000000000004, - 1.2217304763960306 }, - { 1.2730756225143889, -0.80000000000000004, 0.80000000000000004, - 1.3962634015954636 }, - { 1.4339837018309474, -0.80000000000000004, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.80000000000000004. -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_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data019[i].k), Tp(data019[i].nu), - 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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 9.0176949165011079e-16 +// mean(f - f_Boost): 7.0499162063697436e-16 +// variance(f - f_Boost): 1.7230805408026989e-30 +// stddev(f - f_Boost): 1.3126616246400665e-15 +const testcase_ellint_3<double> +data019[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17653987774203392, -0.80000000000000004, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36567072568046877, -0.80000000000000004, 0.80000000000000004, + 0.34906585039886590 }, + { 0.58295359996558616, -0.80000000000000004, 0.80000000000000004, + 0.52359877559829882 }, + { 0.85101998309176108, -0.80000000000000004, 0.80000000000000004, + 0.69813170079773179 }, + { 1.2062322059736537, -0.80000000000000004, 0.80000000000000004, + 0.87266462599716477 }, + { 1.7090321420917429, -0.80000000000000004, 0.80000000000000004, + 1.0471975511965976 }, + { 2.4529058049405066, -0.80000000000000004, 0.80000000000000004, + 1.2217304763960306 }, + { 3.5368893360106948, -0.80000000000000004, 0.80000000000000004, + 1.3962634015954636 }, + { 4.9246422058196062, -0.80000000000000004, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler019 = 2.5000000000000020e-13; // Test data for k=-0.80000000000000004, nu=0.90000000000000002. -testcase_ellint_3<double> data020[] = { - { -0.0000000000000000, -0.80000000000000004, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17353251158533153, -0.80000000000000004, 0.90000000000000002, - 0.17453292519943295 }, - { 0.34166214791545768, -0.80000000000000004, 0.90000000000000002, - 0.34906585039886590 }, - { 0.50144799535130580, -0.80000000000000004, 0.90000000000000002, - 0.52359877559829882 }, - { 0.65311976193814447, -0.80000000000000004, 0.90000000000000002, - 0.69813170079773179 }, - { 0.79924384892320866, -0.80000000000000004, 0.90000000000000002, - 0.87266462599716477 }, - { 0.94345762353365625, -0.80000000000000004, 0.90000000000000002, - 1.0471975511965976 }, - { 1.0892582069219159, -0.80000000000000004, 0.90000000000000002, - 1.2217304763960306 }, - { 1.2387000876610268, -0.80000000000000004, 0.90000000000000002, - 1.3962634015954636 }, - { 1.3911845406776222, -0.80000000000000004, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.80000000000000004, nu=0.90000000000000002. -template <typename Tp> -void test020() -{ - 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(data020) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data020[i].k), Tp(data020[i].nu), - Tp(data020[i].phi)); - const Tp f0 = data020[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 7.7782721357365268e-16 +// mean(f - f_Boost): 8.9928064994637676e-16 +// variance(f - f_Boost): 1.5485199571025344e-30 +// stddev(f - f_Boost): 1.2443954183066307e-15 +const testcase_ellint_3<double> +data020[10] = +{ + { 0.0000000000000000, -0.80000000000000004, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17672267223433513, -0.80000000000000004, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36727835537196063, -0.80000000000000004, 0.90000000000000002, + 0.34906585039886590 }, + { 0.58934569363716649, -0.80000000000000004, 0.90000000000000002, + 0.52359877559829882 }, + { 0.87032723471138851, -0.80000000000000004, 0.90000000000000002, + 0.69813170079773179 }, + { 1.2588676111323349, -0.80000000000000004, 0.90000000000000002, + 0.87266462599716477 }, + { 1.8498731900660019, -0.80000000000000004, 0.90000000000000002, + 1.0471975511965976 }, + { 2.8368381299300420, -0.80000000000000004, 0.90000000000000002, + 1.2217304763960306 }, + { 4.5674844191654058, -0.80000000000000004, 0.90000000000000002, + 1.3962634015954636 }, + { 7.2263259298637115, -0.80000000000000004, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler020 = 2.5000000000000020e-13; // Test data for k=-0.69999999999999996, nu=0.0000000000000000. -testcase_ellint_3<double> data021[] = { - { -0.0000000000000000, -0.69999999999999996, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17496737466916720, -0.69999999999999996, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35254687535677925, -0.69999999999999996, 0.0000000000000000, - 0.34906585039886590 }, - { 0.53536740275997130, -0.69999999999999996, 0.0000000000000000, - 0.52359877559829882 }, - { 0.72603797651684465, -0.69999999999999996, 0.0000000000000000, - 0.69813170079773179 }, - { 0.92698296348313458, -0.69999999999999996, 0.0000000000000000, - 0.87266462599716477 }, - { 1.1400447527693316, -0.69999999999999996, 0.0000000000000000, - 1.0471975511965976 }, - { 1.3657668117194071, -0.69999999999999996, 0.0000000000000000, - 1.2217304763960306 }, - { 1.6024686895959159, -0.69999999999999996, 0.0000000000000000, - 1.3962634015954636 }, - { 1.8456939983747236, -0.69999999999999996, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.0000000000000000. -template <typename Tp> -void test021() -{ - 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(data021) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data021[i].k), Tp(data021[i].nu), - Tp(data021[i].phi)); - const Tp f0 = data021[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 5.5425633303580569e-16 +// mean(f - f_Boost): 7.7715611723760953e-17 +// variance(f - f_Boost): 7.4564398834547797e-34 +// stddev(f - f_Boost): 2.7306482533374340e-17 +const testcase_ellint_3<double> +data021[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17496737466916723, -0.69999999999999996, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35254687535677931, -0.69999999999999996, 0.0000000000000000, + 0.34906585039886590 }, + { 0.53536740275997130, -0.69999999999999996, 0.0000000000000000, + 0.52359877559829882 }, + { 0.72603797651684454, -0.69999999999999996, 0.0000000000000000, + 0.69813170079773179 }, + { 0.92698296348313447, -0.69999999999999996, 0.0000000000000000, + 0.87266462599716477 }, + { 1.1400447527693316, -0.69999999999999996, 0.0000000000000000, + 1.0471975511965976 }, + { 1.3657668117194071, -0.69999999999999996, 0.0000000000000000, + 1.2217304763960306 }, + { 1.6024686895959162, -0.69999999999999996, 0.0000000000000000, + 1.3962634015954636 }, + { 1.8456939983747234, -0.69999999999999996, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler021 = 2.5000000000000020e-13; // Test data for k=-0.69999999999999996, nu=0.10000000000000001. -testcase_ellint_3<double> data022[] = { - { -0.0000000000000000, -0.69999999999999996, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17479076384884681, -0.69999999999999996, 0.10000000000000001, - 0.17453292519943295 }, - { 0.35114844900396364, -0.69999999999999996, 0.10000000000000001, - 0.34906585039886590 }, - { 0.53072776947527012, -0.69999999999999996, 0.10000000000000001, - 0.52359877559829882 }, - { 0.71530198262386246, -0.69999999999999996, 0.10000000000000001, - 0.69813170079773179 }, - { 0.90666760677828306, -0.69999999999999996, 0.10000000000000001, - 0.87266462599716477 }, - { 1.1063366517438080, -0.69999999999999996, 0.10000000000000001, - 1.0471975511965976 }, - { 1.3149477243092147, -0.69999999999999996, 0.10000000000000001, - 1.2217304763960306 }, - { 1.5314886725038925, -0.69999999999999996, 0.10000000000000001, - 1.3962634015954636 }, - { 1.7528050171757608, -0.69999999999999996, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.10000000000000001. -template <typename Tp> -void test022() -{ - 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(data022) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data022[i].k), Tp(data022[i].nu), - Tp(data022[i].phi)); - const Tp f0 = data022[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 5.2736371663370261e-16 +// mean(f - f_Boost): 8.8817841970012528e-17 +// variance(f - f_Boost): 9.7390235212470591e-34 +// stddev(f - f_Boost): 3.1207408609570677e-17 +const testcase_ellint_3<double> +data022[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17514462737300920, -0.69999999999999996, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35396527997470451, -0.69999999999999996, 0.10000000000000001, + 0.34906585039886590 }, + { 0.54015179589433981, -0.69999999999999996, 0.10000000000000001, + 0.52359877559829882 }, + { 0.73734430854477728, -0.69999999999999996, 0.10000000000000001, + 0.69813170079773179 }, + { 0.94888950796697047, -0.69999999999999996, 0.10000000000000001, + 0.87266462599716477 }, + { 1.1772807959736322, -0.69999999999999996, 0.10000000000000001, + 1.0471975511965976 }, + { 1.4231796401075831, -0.69999999999999996, 0.10000000000000001, + 1.2217304763960306 }, + { 1.6841856799887469, -0.69999999999999996, 0.10000000000000001, + 1.3962634015954636 }, + { 1.9541347343119562, -0.69999999999999996, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler022 = 2.5000000000000020e-13; // Test data for k=-0.69999999999999996, nu=0.20000000000000001. -testcase_ellint_3<double> data023[] = { - { -0.0000000000000000, -0.69999999999999996, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17461479077791472, -0.69999999999999996, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34976950621407538, -0.69999999999999996, 0.20000000000000001, - 0.34906585039886590 }, - { 0.52622533231350188, -0.69999999999999996, 0.20000000000000001, - 0.52359877559829882 }, - { 0.70508774017895226, -0.69999999999999996, 0.20000000000000001, - 0.69813170079773179 }, - { 0.88775302531730294, -0.69999999999999996, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0756195476149006, -0.69999999999999996, 0.20000000000000001, - 1.0471975511965976 }, - { 1.2695349716654372, -0.69999999999999996, 0.20000000000000001, - 1.2217304763960306 }, - { 1.4690814617070540, -0.69999999999999996, 0.20000000000000001, - 1.3962634015954636 }, - { 1.6721098780092147, -0.69999999999999996, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.20000000000000001. -template <typename Tp> -void test023() -{ - 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(data023) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data023[i].k), Tp(data023[i].nu), - Tp(data023[i].phi)); - const Tp f0 = data023[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, nu=0.29999999999999999. -testcase_ellint_3<double> data024[] = { - { -0.0000000000000000, -0.69999999999999996, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17443945136076172, -0.69999999999999996, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34840956983535287, -0.69999999999999996, 0.29999999999999999, - 0.34906585039886590 }, - { 0.52185308551329179, -0.69999999999999996, 0.29999999999999999, - 0.52359877559829882 }, - { 0.69535240431168266, -0.69999999999999996, 0.29999999999999999, - 0.69813170079773179 }, - { 0.87007983473964923, -0.69999999999999996, 0.29999999999999999, - 0.87266462599716477 }, - { 1.0474657975577066, -0.69999999999999996, 0.29999999999999999, - 1.0471975511965976 }, - { 1.2286225419931889, -0.69999999999999996, 0.29999999999999999, - 1.2217304763960306 }, - { 1.4136490671013271, -0.69999999999999996, 0.29999999999999999, - 1.3962634015954636 }, - { 1.6011813647733213, -0.69999999999999996, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.29999999999999999. -template <typename Tp> -void test024() -{ - 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(data024) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data024[i].k), Tp(data024[i].nu), - Tp(data024[i].phi)); - const Tp f0 = data024[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.9907249355047774e-16 +// mean(f - f_Boost): 3.3306690738754695e-17 +// variance(f - f_Boost): 1.3695501826753678e-34 +// stddev(f - f_Boost): 1.1702778228589003e-17 +const testcase_ellint_3<double> +data023[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17532252613350796, -0.69999999999999996, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35540417596807522, -0.69999999999999996, 0.20000000000000001, + 0.34906585039886590 }, + { 0.54508913033361928, -0.69999999999999996, 0.20000000000000001, + 0.52359877559829882 }, + { 0.74927635777718415, -0.69999999999999996, 0.20000000000000001, + 0.69813170079773179 }, + { 0.97261706337936338, -0.69999999999999996, 0.20000000000000001, + 0.87266462599716477 }, + { 1.2187303976209327, -0.69999999999999996, 0.20000000000000001, + 1.0471975511965976 }, + { 1.4887796709222487, -0.69999999999999996, 0.20000000000000001, + 1.2217304763960306 }, + { 1.7796581281839212, -0.69999999999999996, 0.20000000000000001, + 1.3962634015954636 }, + { 2.0829290325820202, -0.69999999999999996, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler023 = 2.5000000000000020e-13; + +// Test data for k=-0.69999999999999996, nu=0.30000000000000004. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.6912897610535316e-16 +// mean(f - f_Boost): 1.6653345369377347e-17 +// variance(f - f_Boost): 2.6207864467918357e-32 +// stddev(f - f_Boost): 1.6188843216214787e-16 +const testcase_ellint_3<double> +data024[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17550107516328570, -0.69999999999999996, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35686409576571959, -0.69999999999999996, 0.30000000000000004, + 0.34906585039886590 }, + { 0.55018827316513352, -0.69999999999999996, 0.30000000000000004, + 0.52359877559829882 }, + { 0.76189759494390275, -0.69999999999999996, 0.30000000000000004, + 0.69813170079773179 }, + { 0.99844623430885615, -0.69999999999999996, 0.30000000000000004, + 0.87266462599716477 }, + { 1.2652862989039833, -0.69999999999999996, 0.30000000000000004, + 1.0471975511965976 }, + { 1.5647666808691361, -0.69999999999999996, 0.30000000000000004, + 1.2217304763960306 }, + { 1.8932499694938163, -0.69999999999999996, 0.30000000000000004, + 1.3962634015954636 }, + { 2.2392290510988535, -0.69999999999999996, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler024 = 2.5000000000000020e-13; // Test data for k=-0.69999999999999996, nu=0.40000000000000002. -testcase_ellint_3<double> data025[] = { - { -0.0000000000000000, -0.69999999999999996, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17426474153983226, -0.69999999999999996, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34706817945773732, -0.69999999999999996, 0.40000000000000002, - 0.34906585039886590 }, - { 0.51760452851738159, -0.69999999999999996, 0.40000000000000002, - 0.52359877559829882 }, - { 0.68605801534722766, -0.69999999999999996, 0.40000000000000002, - 0.69813170079773179 }, - { 0.85351339387296532, -0.69999999999999996, 0.40000000000000002, - 0.87266462599716477 }, - { 1.0215297967969537, -0.69999999999999996, 0.40000000000000002, - 1.0471975511965976 }, - { 1.1915051074460528, -0.69999999999999996, 0.40000000000000002, - 1.2217304763960306 }, - { 1.3639821911744707, -0.69999999999999996, 0.40000000000000002, - 1.3962634015954636 }, - { 1.5382162002954762, -0.69999999999999996, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.40000000000000002. -template <typename Tp> -void test025() -{ - 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(data025) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data025[i].k), Tp(data025[i].nu), - Tp(data025[i].phi)); - const Tp f0 = data025[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)); -} +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 6.5578567644745380e-16 +// mean(f - f_Boost): 1.4710455076283324e-16 +// variance(f - f_Boost): 2.6715739327327140e-33 +// stddev(f - f_Boost): 5.1687270509601433e-17 +const testcase_ellint_3<double> +data025[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17568027871494424, -0.69999999999999996, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35834559208180261, -0.69999999999999996, 0.40000000000000002, + 0.34906585039886590 }, + { 0.55545885451190613, -0.69999999999999996, 0.40000000000000002, + 0.52359877559829882 }, + { 0.77528120402568101, -0.69999999999999996, 0.40000000000000002, + 0.69813170079773179 }, + { 1.0267241287600319, -0.69999999999999996, 0.40000000000000002, + 0.87266462599716477 }, + { 1.3181380338980246, -0.69999999999999996, 0.40000000000000002, + 1.0471975511965976 }, + { 1.6542840785132085, -0.69999999999999996, 0.40000000000000002, + 1.2217304763960306 }, + { 2.0315595131131818, -0.69999999999999996, 0.40000000000000002, + 1.3962634015954636 }, + { 2.4342502915307875, -0.69999999999999996, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler025 = 2.5000000000000020e-13; // Test data for k=-0.69999999999999996, nu=0.50000000000000000. -testcase_ellint_3<double> data026[] = { - { -0.0000000000000000, -0.69999999999999996, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17409065729516093, -0.69999999999999996, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34574489064986091, -0.69999999999999996, 0.50000000000000000, - 0.34906585039886590 }, - { 0.51347361925579793, -0.69999999999999996, 0.50000000000000000, - 0.52359877559829882 }, - { 0.67717079489579290, -0.69999999999999996, 0.50000000000000000, - 0.69813170079773179 }, - { 0.83793902055292280, -0.69999999999999996, 0.50000000000000000, - 0.87266462599716477 }, - { 0.99752863545289705, -0.69999999999999996, 0.50000000000000000, - 1.0471975511965976 }, - { 1.1576240080401499, -0.69999999999999996, 0.50000000000000000, - 1.2217304763960306 }, - { 1.3191464023923762, -0.69999999999999996, 0.50000000000000000, - 1.3962634015954636 }, - { 1.4818433192178544, -0.69999999999999996, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.50000000000000000. -template <typename Tp> -void test026() -{ - 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(data026) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data026[i].k), Tp(data026[i].nu), - Tp(data026[i].phi)); - const Tp f0 = data026[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, nu=0.59999999999999998. -testcase_ellint_3<double> data027[] = { - { -0.0000000000000000, -0.69999999999999996, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17391719464391611, -0.69999999999999996, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34443927423869031, -0.69999999999999996, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50945473266486074, -0.69999999999999996, 0.59999999999999998, - 0.52359877559829882 }, - { 0.66866056326513823, -0.69999999999999996, 0.59999999999999998, - 0.69813170079773179 }, - { 0.82325830002337352, -0.69999999999999996, 0.59999999999999998, - 0.87266462599716477 }, - { 0.97522808245669357, -0.69999999999999996, 0.59999999999999998, - 1.0471975511965976 }, - { 1.1265300613705282, -0.69999999999999996, 0.59999999999999998, - 1.2217304763960306 }, - { 1.2784066076152003, -0.69999999999999996, 0.59999999999999998, - 1.3962634015954636 }, - { 1.4309994736080540, -0.69999999999999996, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.59999999999999998. -template <typename Tp> -void test027() -{ - 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(data027) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data027[i].k), Tp(data027[i].nu), - Tp(data027[i].phi)); - const Tp f0 = data027[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, nu=0.69999999999999996. -testcase_ellint_3<double> data028[] = { - { -0.0000000000000000, -0.69999999999999996, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17374434963995028, -0.69999999999999996, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34315091562900674, -0.69999999999999996, 0.69999999999999996, - 0.34906585039886590 }, - { 0.50554262375653358, -0.69999999999999996, 0.69999999999999996, - 0.52359877559829882 }, - { 0.66050025406305812, -0.69999999999999996, 0.69999999999999996, - 0.69813170079773179 }, - { 0.80938620118847404, -0.69999999999999996, 0.69999999999999996, - 0.87266462599716477 }, - { 0.95443223855852144, -0.69999999999999996, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0978573207128302, -0.69999999999999996, 0.69999999999999996, - 1.2217304763960306 }, - { 1.2411754575007123, -0.69999999999999996, 0.69999999999999996, - 1.3962634015954636 }, - { 1.3848459188329196, -0.69999999999999996, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.69999999999999996. -template <typename Tp> -void test028() -{ - 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(data028) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data028[i].k), Tp(data028[i].nu), - Tp(data028[i].phi)); - const Tp f0 = data028[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)); -} +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 6.0416041815443256e-16 +// mean(f - f_Boost): 1.9151347174783951e-16 +// variance(f - f_Boost): 7.8758646268991113e-33 +// stddev(f - f_Boost): 8.8746068233466605e-17 +const testcase_ellint_3<double> +data026[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17586014108156545, -0.69999999999999996, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35984923894341653, -0.69999999999999996, 0.50000000000000000, + 0.34906585039886590 }, + { 0.56091135606739995, -0.69999999999999996, 0.50000000000000000, + 0.52359877559829882 }, + { 0.78951212635197054, -0.69999999999999996, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0578865732938729, -0.69999999999999996, 0.50000000000000000, + 0.87266462599716477 }, + { 1.3789149005151722, -0.69999999999999996, 0.50000000000000000, + 1.0471975511965976 }, + { 1.7620212286086225, -0.69999999999999996, 0.50000000000000000, + 1.2217304763960306 }, + { 2.2051554347435585, -0.69999999999999996, 0.50000000000000000, + 1.3962634015954636 }, + { 2.6868019968236991, -0.69999999999999996, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler026 = 2.5000000000000020e-13; + +// Test data for k=-0.69999999999999996, nu=0.60000000000000009. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.6515644573247170e-16 +// mean(f - f_Boost): 9.9920072216264091e-17 +// variance(f - f_Boost): 1.2325951644078310e-33 +// stddev(f - f_Boost): 3.5108334685767011e-17 +const testcase_ellint_3<double> +data027[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17604066659721918, -0.69999999999999996, 0.60000000000000009, + 0.17453292519943295 }, + { 0.36137563278353424, -0.69999999999999996, 0.60000000000000009, + 0.34906585039886590 }, + { 0.56655721272747606, -0.69999999999999996, 0.60000000000000009, + 0.52359877559829882 }, + { 0.80468966552978305, -0.69999999999999996, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0924902943683852, -0.69999999999999996, 0.60000000000000009, + 0.87266462599716477 }, + { 1.4499247992499797, -0.69999999999999996, 0.60000000000000009, + 1.0471975511965976 }, + { 1.8953714382113815, -0.69999999999999996, 0.60000000000000009, + 1.2217304763960306 }, + { 2.4323229949248670, -0.69999999999999996, 0.60000000000000009, + 1.3962634015954636 }, + { 3.0314573496746742, -0.69999999999999996, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler027 = 2.5000000000000020e-13; + +// Test data for k=-0.69999999999999996, nu=0.70000000000000007. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.8475278552871384e-16 +// mean(f - f_Boost): 9.9920072216264091e-17 +// variance(f - f_Boost): 1.2325951644078310e-33 +// stddev(f - f_Boost): 3.5108334685767011e-17 +const testcase_ellint_3<double> +data028[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17622185963747933, -0.69999999999999996, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36292539360435261, -0.69999999999999996, 0.70000000000000007, + 0.34906585039886590 }, + { 0.57240892970150015, -0.69999999999999996, 0.70000000000000007, + 0.52359877559829882 }, + { 0.82093084713182629, -0.69999999999999996, 0.70000000000000007, + 0.69813170079773179 }, + { 1.1312609022179871, -0.69999999999999996, 0.70000000000000007, + 0.87266462599716477 }, + { 1.5345768067715795, -0.69999999999999996, 0.70000000000000007, + 1.0471975511965976 }, + { 2.0668847445934420, -0.69999999999999996, 0.70000000000000007, + 1.2217304763960306 }, + { 2.7483444537551240, -0.69999999999999996, 0.70000000000000007, + 1.3962634015954636 }, + { 3.5408408771788560, -0.69999999999999996, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler028 = 2.5000000000000020e-13; // Test data for k=-0.69999999999999996, nu=0.80000000000000004. -testcase_ellint_3<double> data029[] = { - { -0.0000000000000000, -0.69999999999999996, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17357211837335737, -0.69999999999999996, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34187941416012108, -0.69999999999999996, 0.80000000000000004, - 0.34906585039886590 }, - { 0.50173239465478270, -0.69999999999999996, 0.80000000000000004, - 0.52359877559829882 }, - { 0.65266550725988315, -0.69999999999999996, 0.80000000000000004, - 0.69813170079773179 }, - { 0.79624879865249298, -0.69999999999999996, 0.80000000000000004, - 0.87266462599716477 }, - { 0.93497577043296920, -0.69999999999999996, 0.80000000000000004, - 1.0471975511965976 }, - { 1.0713041566930748, -0.69999999999999996, 0.80000000000000004, - 1.2217304763960306 }, - { 1.2069772023255652, -0.69999999999999996, 0.80000000000000004, - 1.3962634015954636 }, - { 1.3427110650397533, -0.69999999999999996, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.80000000000000004. -template <typename Tp> -void test029() -{ - 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(data029) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data029[i].k), Tp(data029[i].nu), - Tp(data029[i].phi)); - const Tp f0 = data029[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 6.8664526853112274e-16 +// mean(f - f_Boost): 1.6930901125533636e-16 +// variance(f - f_Boost): 3.5389557150937801e-33 +// stddev(f - f_Boost): 5.9489122661994095e-17 +const testcase_ellint_3<double> +data029[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17640372461994805, -0.69999999999999996, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36449916621651091, -0.69999999999999996, 0.80000000000000004, + 0.34906585039886590 }, + { 0.57848021800372573, -0.69999999999999996, 0.80000000000000004, + 0.52359877559829882 }, + { 0.83837480968392586, -0.69999999999999996, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1751669030061143, -0.69999999999999996, 0.80000000000000004, + 0.87266462599716477 }, + { 1.6381851899173601, -0.69999999999999996, 0.80000000000000004, + 1.0471975511965976 }, + { 2.3002065924302197, -0.69999999999999996, 0.80000000000000004, + 1.2217304763960306 }, + { 3.2337600665337862, -0.69999999999999996, 0.80000000000000004, + 1.3962634015954636 }, + { 4.4042405729076961, -0.69999999999999996, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler029 = 2.5000000000000020e-13; // Test data for k=-0.69999999999999996, nu=0.90000000000000002. -testcase_ellint_3<double> data030[] = { - { -0.0000000000000000, -0.69999999999999996, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17340049697003634, -0.69999999999999996, 0.90000000000000002, - 0.17453292519943295 }, - { 0.34062438249741556, -0.69999999999999996, 0.90000000000000002, - 0.34906585039886590 }, - { 0.49801946510076878, -0.69999999999999996, 0.90000000000000002, - 0.52359877559829882 }, - { 0.64513432604750487, -0.69999999999999996, 0.90000000000000002, - 0.69813170079773179 }, - { 0.78378145487573758, -0.69999999999999996, 0.90000000000000002, - 0.87266462599716477 }, - { 0.91671799500854634, -0.69999999999999996, 0.90000000000000002, - 1.0471975511965976 }, - { 1.0466193579463123, -0.69999999999999996, 0.90000000000000002, - 1.2217304763960306 }, - { 1.1754218079199146, -0.69999999999999996, 0.90000000000000002, - 1.3962634015954636 }, - { 1.3040500499695911, -0.69999999999999996, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.69999999999999996, nu=0.90000000000000002. -template <typename Tp> -void test030() -{ - 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(data030) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data030[i].k), Tp(data030[i].nu), - Tp(data030[i].phi)); - const Tp f0 = data030[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)); -} +// max(|f - f_Boost|): 3.5527136788005009e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 8.5869439826269878e-16 +// mean(f - f_Boost): 6.7723604502134545e-16 +// variance(f - f_Boost): 4.8757508225668289e-31 +// stddev(f - f_Boost): 6.9826576763914390e-16 +const testcase_ellint_3<double> +data030[10] = +{ + { 0.0000000000000000, -0.69999999999999996, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17658626600478800, -0.69999999999999996, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36609762156017206, -0.69999999999999996, 0.90000000000000002, + 0.34906585039886590 }, + { 0.58478615187842409, -0.69999999999999996, 0.90000000000000002, + 0.52359877559829882 }, + { 0.85718862878291846, -0.69999999999999996, 0.90000000000000002, + 0.69813170079773179 }, + { 1.2255385617397643, -0.69999999999999996, 0.90000000000000002, + 0.87266462599716477 }, + { 1.7696521899992939, -0.69999999999999996, 0.90000000000000002, + 1.0471975511965976 }, + { 2.6476314987883502, -0.69999999999999996, 0.90000000000000002, + 1.2217304763960306 }, + { 4.1373434902898083, -0.69999999999999996, 0.90000000000000002, + 1.3962634015954636 }, + { 6.3796094177887746, -0.69999999999999996, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler030 = 2.5000000000000020e-13; // Test data for k=-0.59999999999999998, nu=0.0000000000000000. -testcase_ellint_3<double> data031[] = { - { -0.0000000000000000, -0.59999999999999998, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17485154362988362, -0.59999999999999998, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35160509865544326, -0.59999999999999998, 0.0000000000000000, - 0.34906585039886590 }, - { 0.53210652578446160, -0.59999999999999998, 0.0000000000000000, - 0.52359877559829882 }, - { 0.71805304664485670, -0.59999999999999998, 0.0000000000000000, - 0.69813170079773179 }, - { 0.91082759030195970, -0.59999999999999998, 0.0000000000000000, - 0.87266462599716477 }, - { 1.1112333229323361, -0.59999999999999998, 0.0000000000000000, - 1.0471975511965976 }, - { 1.3191461190365270, -0.59999999999999998, 0.0000000000000000, - 1.2217304763960306 }, - { 1.5332022105084773, -0.59999999999999998, 0.0000000000000000, - 1.3962634015954636 }, - { 1.7507538029157526, -0.59999999999999998, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.0000000000000000. -template <typename Tp> -void test031() -{ - 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(data031) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data031[i].k), Tp(data031[i].nu), - Tp(data031[i].phi)); - const Tp f0 = data031[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.3664899092028927e-16 +// mean(f - f_Boost): 5.2735593669694933e-17 +// variance(f - f_Boost): 3.4333862218458872e-34 +// stddev(f - f_Boost): 1.8529398861932589e-17 +const testcase_ellint_3<double> +data031[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17485154362988359, -0.59999999999999998, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35160509865544320, -0.59999999999999998, 0.0000000000000000, + 0.34906585039886590 }, + { 0.53210652578446138, -0.59999999999999998, 0.0000000000000000, + 0.52359877559829882 }, + { 0.71805304664485659, -0.59999999999999998, 0.0000000000000000, + 0.69813170079773179 }, + { 0.91082759030195981, -0.59999999999999998, 0.0000000000000000, + 0.87266462599716477 }, + { 1.1112333229323361, -0.59999999999999998, 0.0000000000000000, + 1.0471975511965976 }, + { 1.3191461190365270, -0.59999999999999998, 0.0000000000000000, + 1.2217304763960306 }, + { 1.5332022105084779, -0.59999999999999998, 0.0000000000000000, + 1.3962634015954636 }, + { 1.7507538029157523, -0.59999999999999998, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler031 = 2.5000000000000020e-13; // Test data for k=-0.59999999999999998, nu=0.10000000000000001. -testcase_ellint_3<double> data032[] = { - { -0.0000000000000000, -0.59999999999999998, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17467514275022014, -0.59999999999999998, 0.10000000000000001, - 0.17453292519943295 }, - { 0.35021333086258255, -0.59999999999999998, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52751664092962713, -0.59999999999999998, 0.10000000000000001, - 0.52359877559829882 }, - { 0.70752126971957885, -0.59999999999999998, 0.10000000000000001, - 0.69813170079773179 }, - { 0.89111058756112871, -0.59999999999999998, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0789241202877768, -0.59999999999999998, 0.10000000000000001, - 1.0471975511965976 }, - { 1.2710800210399946, -0.59999999999999998, 0.10000000000000001, - 1.2217304763960306 }, - { 1.4669060574440276, -0.59999999999999998, 0.10000000000000001, - 1.3962634015954636 }, - { 1.6648615773343014, -0.59999999999999998, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.10000000000000001. -template <typename Tp> -void test032() -{ - 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(data032) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data032[i].k), Tp(data032[i].nu), - Tp(data032[i].phi)); - const Tp f0 = data032[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.2335247010355137e-16 +// mean(f - f_Boost): 8.6042284408449634e-17 +// variance(f - f_Boost): 2.2835347143080263e-33 +// stddev(f - f_Boost): 4.7786344433405099e-17 +const testcase_ellint_3<double> +data032[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17502858548476194, -0.59999999999999998, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35301673150537388, -0.59999999999999998, 0.10000000000000001, + 0.34906585039886590 }, + { 0.53683932476326812, -0.59999999999999998, 0.10000000000000001, + 0.52359877559829882 }, + { 0.72914228589586771, -0.59999999999999998, 0.10000000000000001, + 0.69813170079773179 }, + { 0.93208036718354692, -0.59999999999999998, 0.10000000000000001, + 0.87266462599716477 }, + { 1.1468984688863377, -0.59999999999999998, 0.10000000000000001, + 1.0471975511965976 }, + { 1.3733904977062528, -0.59999999999999998, 0.10000000000000001, + 1.2217304763960306 }, + { 1.6094225663372157, -0.59999999999999998, 0.10000000000000001, + 1.3962634015954636 }, + { 1.8508766487100685, -0.59999999999999998, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler032 = 2.5000000000000020e-13; // Test data for k=-0.59999999999999998, nu=0.20000000000000001. -testcase_ellint_3<double> data033[] = { - { -0.0000000000000000, -0.59999999999999998, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17449937871800653, -0.59999999999999998, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34884093647346553, -0.59999999999999998, 0.20000000000000001, - 0.34906585039886590 }, - { 0.52306221119844110, -0.59999999999999998, 0.20000000000000001, - 0.52359877559829882 }, - { 0.69749955678982223, -0.59999999999999998, 0.20000000000000001, - 0.69813170079773179 }, - { 0.87274610682416853, -0.59999999999999998, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0494620540750792, -0.59999999999999998, 0.20000000000000001, - 1.0471975511965976 }, - { 1.2280847305507339, -0.59999999999999998, 0.20000000000000001, - 1.2217304763960306 }, - { 1.4085436279696886, -0.59999999999999998, 0.20000000000000001, - 1.3962634015954636 }, - { 1.5901418016279374, -0.59999999999999998, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.20000000000000001. -template <typename Tp> -void test033() -{ - 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(data033) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data033[i].k), Tp(data033[i].nu), - Tp(data033[i].phi)); - const Tp f0 = data033[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, nu=0.29999999999999999. -testcase_ellint_3<double> data034[] = { - { -0.0000000000000000, -0.59999999999999998, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17432424744393935, -0.59999999999999998, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34748744127146447, -0.59999999999999998, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51873632743924847, -0.59999999999999998, 0.29999999999999999, - 0.52359877559829882 }, - { 0.68794610396313127, -0.59999999999999998, 0.29999999999999999, - 0.69813170079773179 }, - { 0.85558070175468726, -0.59999999999999998, 0.29999999999999999, - 0.87266462599716477 }, - { 1.0224416343605653, -0.59999999999999998, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1893144457936788, -0.59999999999999998, 0.29999999999999999, - 1.2217304763960306 }, - { 1.3566435377982575, -0.59999999999999998, 0.29999999999999999, - 1.3962634015954636 }, - { 1.5243814243493585, -0.59999999999999998, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.29999999999999999. -template <typename Tp> -void test034() -{ - 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(data034) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data034[i].k), Tp(data034[i].nu), - Tp(data034[i].phi)); - const Tp f0 = data034[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.0940560416437693e-16 +// mean(f - f_Boost): 4.1633363423443370e-17 +// variance(f - f_Boost): 8.5834655546147173e-33 +// stddev(f - f_Boost): 9.2646994309662939e-17 +const testcase_ellint_3<double> +data033[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17520627248155893, -0.59999999999999998, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35444873935437748, -0.59999999999999998, 0.20000000000000001, + 0.34906585039886590 }, + { 0.54172310557682524, -0.59999999999999998, 0.20000000000000001, + 0.52359877559829882 }, + { 0.74084300280734672, -0.59999999999999998, 0.20000000000000001, + 0.69813170079773179 }, + { 0.95509001527006121, -0.59999999999999998, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1865688084431796, -0.59999999999999998, 0.20000000000000001, + 1.0471975511965976 }, + { 1.4352978868932598, -0.59999999999999998, 0.20000000000000001, + 1.2217304763960306 }, + { 1.6983400371331816, -0.59999999999999998, 0.20000000000000001, + 1.3962634015954636 }, + { 1.9695980282802215, -0.59999999999999998, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler033 = 2.5000000000000020e-13; + +// Test data for k=-0.59999999999999998, nu=0.30000000000000004. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.9470074709717020e-16 +// mean(f - f_Boost): 7.4940054162198071e-17 +// variance(f - f_Boost): 1.6823592487044846e-32 +// stddev(f - f_Boost): 1.2970579203352812e-16 +const testcase_ellint_3<double> +data034[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17538460882640122, -0.59999999999999998, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35590165133735557, -0.59999999999999998, 0.30000000000000004, + 0.34906585039886590 }, + { 0.54676661152254535, -0.59999999999999998, 0.30000000000000004, + 0.52359877559829882 }, + { 0.75321709418305305, -0.59999999999999998, 0.30000000000000004, + 0.69813170079773179 }, + { 0.98012637808992920, -0.59999999999999998, 0.30000000000000004, + 0.87266462599716477 }, + { 1.2310891277158875, -0.59999999999999998, 0.30000000000000004, + 1.0471975511965976 }, + { 1.5069157924585623, -0.59999999999999998, 0.30000000000000004, + 1.2217304763960306 }, + { 1.8039583598337940, -0.59999999999999998, 0.30000000000000004, + 1.3962634015954636 }, + { 2.1134154405060599, -0.59999999999999998, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler034 = 2.5000000000000020e-13; // Test data for k=-0.59999999999999998, nu=0.40000000000000002. -testcase_ellint_3<double> data035[] = { - { -0.0000000000000000, -0.59999999999999998, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17414974487670720, -0.59999999999999998, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34615238767335027, -0.59999999999999998, 0.40000000000000002, - 0.34906585039886590 }, - { 0.51453257838108579, -0.59999999999999998, 0.40000000000000002, - 0.52359877559829882 }, - { 0.67882386787534410, -0.59999999999999998, 0.40000000000000002, - 0.69813170079773179 }, - { 0.83948470233173578, -0.59999999999999998, 0.40000000000000002, - 0.87266462599716477 }, - { 0.99753496200073977, -0.59999999999999998, 0.40000000000000002, - 1.0471975511965976 }, - { 1.1541101404388487, -0.59999999999999998, 0.40000000000000002, - 1.2217304763960306 }, - { 1.3100911323398814, -0.59999999999999998, 0.40000000000000002, - 1.3962634015954636 }, - { 1.4659345278069984, -0.59999999999999998, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.40000000000000002. -template <typename Tp> -void test035() -{ - 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(data035) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data035[i].k), Tp(data035[i].nu), - Tp(data035[i].phi)); - const Tp f0 = data035[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.7909659715991921e-16 +// mean(f - f_Boost): -2.7755575615628915e-18 +// variance(f - f_Boost): 2.4044165394594425e-32 +// stddev(f - f_Boost): 1.5506181152880429e-16 +const testcase_ellint_3<double> +data035[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17556359876533037, -0.59999999999999998, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35737601674244679, -0.59999999999999998, 0.40000000000000002, + 0.34906585039886590 }, + { 0.55197933771320218, -0.59999999999999998, 0.40000000000000002, + 0.52359877559829882 }, + { 0.76633591620002894, -0.59999999999999998, 0.40000000000000002, + 0.69813170079773179 }, + { 1.0075231136019616, -0.59999999999999998, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2815842073813450, -0.59999999999999998, 0.40000000000000002, + 1.0471975511965976 }, + { 1.5911666941449827, -0.59999999999999998, 0.40000000000000002, + 1.2217304763960306 }, + { 1.9323227566025762, -0.59999999999999998, 0.40000000000000002, + 1.3962634015954636 }, + { 2.2925036420985130, -0.59999999999999998, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler035 = 2.5000000000000020e-13; // Test data for k=-0.59999999999999998, nu=0.50000000000000000. -testcase_ellint_3<double> data036[] = { - { -0.0000000000000000, -0.59999999999999998, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17397586700252810, -0.59999999999999998, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34483533397138516, -0.59999999999999998, 0.50000000000000000, - 0.34906585039886590 }, - { 0.51044500461706499, -0.59999999999999998, 0.50000000000000000, - 0.52359877559829882 }, - { 0.67009988034712675, -0.59999999999999998, 0.50000000000000000, - 0.69813170079773179 }, - { 0.82434762375735193, -0.59999999999999998, 0.50000000000000000, - 0.87266462599716477 }, - { 0.97447346702798998, -0.59999999999999998, 0.50000000000000000, - 1.0471975511965976 }, - { 1.1219494000522143, -0.59999999999999998, 0.50000000000000000, - 1.2217304763960306 }, - { 1.2680242605954486, -0.59999999999999998, 0.50000000000000000, - 1.3962634015954636 }, - { 1.4135484285693078, -0.59999999999999998, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.50000000000000000. -template <typename Tp> -void test036() -{ - 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(data036) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data036[i].k), Tp(data036[i].nu), - Tp(data036[i].phi)); - const Tp f0 = data036[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, nu=0.59999999999999998. -testcase_ellint_3<double> data037[] = { - { -0.0000000000000000, -0.59999999999999998, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17380260984469356, -0.59999999999999998, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34353585361777839, -0.59999999999999998, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50646805774321402, -0.59999999999999998, 0.59999999999999998, - 0.52359877559829882 }, - { 0.66174468108625517, -0.59999999999999998, 0.59999999999999998, - 0.69813170079773179 }, - { 0.81007462280278408, -0.59999999999999998, 0.59999999999999998, - 0.87266462599716477 }, - { 0.95303466945718729, -0.59999999999999998, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0924118588677503, -0.59999999999999998, 0.59999999999999998, - 1.2217304763960306 }, - { 1.2297640574847937, -0.59999999999999998, 0.59999999999999998, - 1.3962634015954636 }, - { 1.3662507535812816, -0.59999999999999998, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.59999999999999998. -template <typename Tp> -void test037() -{ - 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(data037) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data037[i].k), Tp(data037[i].nu), - Tp(data037[i].phi)); - const Tp f0 = data037[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, nu=0.69999999999999996. -testcase_ellint_3<double> data038[] = { - { -0.0000000000000000, -0.59999999999999998, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17362996946312009, -0.59999999999999998, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34225353454870588, -0.59999999999999998, 0.69999999999999996, - 0.34906585039886590 }, - { 0.50259656397799546, -0.59999999999999998, 0.69999999999999996, - 0.52359877559829882 }, - { 0.65373184496628944, -0.59999999999999998, 0.69999999999999996, - 0.69813170079773179 }, - { 0.79658372884056439, -0.59999999999999998, 0.69999999999999996, - 0.87266462599716477 }, - { 0.93303240100245421, -0.59999999999999998, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0651547944716557, -0.59999999999999998, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1947676204853441, -0.59999999999999998, 0.69999999999999996, - 1.3962634015954636 }, - { 1.3232737468822811, -0.59999999999999998, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.69999999999999996. -template <typename Tp> -void test038() -{ - 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(data038) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data038[i].k), Tp(data038[i].nu), - Tp(data038[i].phi)); - const Tp f0 = data038[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.6240126899196213e-16 +// mean(f - f_Boost): 9.1593399531575410e-17 +// variance(f - f_Boost): 1.0357223256482469e-33 +// stddev(f - f_Boost): 3.2182640128619758e-17 +const testcase_ellint_3<double> +data036[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17574324658480217, -0.59999999999999998, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35887240603169313, -0.59999999999999998, 0.50000000000000000, + 0.34906585039886590 }, + { 0.55737161826345261, -0.59999999999999998, 0.50000000000000000, + 0.52359877559829882 }, + { 0.78028227313077458, -0.59999999999999998, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0376989776486290, -0.59999999999999998, 0.50000000000000000, + 0.87266462599716477 }, + { 1.3395933991042925, -0.59999999999999998, 0.50000000000000000, + 1.0471975511965976 }, + { 1.6924049626591782, -0.59999999999999998, 0.50000000000000000, + 1.2217304763960306 }, + { 2.0931011856518920, -0.59999999999999998, 0.50000000000000000, + 1.3962634015954636 }, + { 2.5239007084492706, -0.59999999999999998, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler036 = 2.5000000000000020e-13; + +// Test data for k=-0.59999999999999998, nu=0.60000000000000009. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.6651378277398083e-16 +// mean(f - f_Boost): 1.1934897514720432e-16 +// variance(f - f_Boost): 1.7585404776158019e-33 +// stddev(f - f_Boost): 4.1934955319110598e-17 +const testcase_ellint_3<double> +data037[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17592355661219386, -0.59999999999999998, 0.60000000000000009, + 0.17453292519943295 }, + { 0.36039141192661606, -0.59999999999999998, 0.60000000000000009, + 0.34906585039886590 }, + { 0.56295472636903854, -0.59999999999999998, 0.60000000000000009, + 0.52359877559829882 }, + { 0.79515295130165986, -0.59999999999999998, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0711886441942242, -0.59999999999999998, 0.60000000000000009, + 0.87266462599716477 }, + { 1.4072952835139891, -0.59999999999999998, 0.60000000000000009, + 1.0471975511965976 }, + { 1.8174863977376825, -0.59999999999999998, 0.60000000000000009, + 1.2217304763960306 }, + { 2.3029921578542232, -0.59999999999999998, 0.60000000000000009, + 1.3962634015954636 }, + { 2.8388723099514972, -0.59999999999999998, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler037 = 2.5000000000000020e-13; + +// Test data for k=-0.59999999999999998, nu=0.70000000000000007. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.2451074234797436e-16 +// mean(f - f_Boost): 5.2735593669694933e-17 +// variance(f - f_Boost): 3.4333862218458872e-34 +// stddev(f - f_Boost): 1.8529398861932589e-17 +const testcase_ellint_3<double> +data038[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17610453321631936, -0.59999999999999998, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36193365056369764, -0.59999999999999998, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56874098962268527, -0.59999999999999998, 0.70000000000000007, + 0.52359877559829882 }, + { 0.81106198671477181, -0.59999999999999998, 0.70000000000000007, + 0.69813170079773179 }, + { 1.1086886419010082, -0.59999999999999998, 0.70000000000000007, + 0.87266462599716477 }, + { 1.4879048567239257, -0.59999999999999998, 0.70000000000000007, + 1.0471975511965976 }, + { 1.9780310073615923, -0.59999999999999998, 0.70000000000000007, + 1.2217304763960306 }, + { 2.5941545586772712, -0.59999999999999998, 0.70000000000000007, + 1.3962634015954636 }, + { 3.3029735898397155, -0.59999999999999998, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler038 = 2.5000000000000020e-13; // Test data for k=-0.59999999999999998, nu=0.80000000000000004. -testcase_ellint_3<double> data039[] = { - { -0.0000000000000000, -0.59999999999999998, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17345794195390687, -0.59999999999999998, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34098797854531027, -0.59999999999999998, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49882569168826230, -0.59999999999999998, 0.80000000000000004, - 0.52359877559829882 }, - { 0.64603758566475511, -0.59999999999999998, 0.80000000000000004, - 0.69813170079773179 }, - { 0.78380365594769730, -0.59999999999999998, 0.80000000000000004, - 0.87266462599716477 }, - { 0.91430946255611190, -0.59999999999999998, 0.80000000000000004, - 1.0471975511965976 }, - { 1.0398955217270607, -0.59999999999999998, 0.80000000000000004, - 1.2217304763960306 }, - { 1.1625948314277676, -0.59999999999999998, 0.80000000000000004, - 1.3962634015954636 }, - { 1.2840021261752192, -0.59999999999999998, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.80000000000000004. -template <typename Tp> -void test039() -{ - 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(data039) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data039[i].k), Tp(data039[i].nu), - Tp(data039[i].phi)); - const Tp f0 = data039[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)); -} +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.3826960061025914e-16 +// mean(f - f_Boost): 2.7478019859472625e-16 +// variance(f - f_Boost): 4.6451528105588637e-32 +// stddev(f - f_Boost): 2.1552616570984749e-16 +const testcase_ellint_3<double> +data039[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17628618080795252, -0.59999999999999998, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36349976272521012, -0.59999999999999998, 0.80000000000000004, + 0.34906585039886590 }, + { 0.57474392342151914, -0.59999999999999998, 0.80000000000000004, + 0.52359877559829882 }, + { 0.82814493499158159, -0.59999999999999998, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1511281795998280, -0.59999999999999998, 0.80000000000000004, + 0.87266462599716477 }, + { 1.5864286332503075, -0.59999999999999998, 0.80000000000000004, + 1.0471975511965976 }, + { 2.1958944866494527, -0.59999999999999998, 0.80000000000000004, + 1.2217304763960306 }, + { 3.0398358172574604, -0.59999999999999998, 0.80000000000000004, + 1.3962634015954636 }, + { 4.0867036409261832, -0.59999999999999998, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler039 = 2.5000000000000020e-13; // Test data for k=-0.59999999999999998, nu=0.90000000000000002. -testcase_ellint_3<double> data040[] = { - { -0.0000000000000000, -0.59999999999999998, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17328652344890033, -0.59999999999999998, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33973880062929018, -0.59999999999999998, 0.90000000000000002, - 0.34906585039886590 }, - { 0.49515092233122765, -0.59999999999999998, 0.90000000000000002, - 0.52359877559829882 }, - { 0.63864042139737043, -0.59999999999999998, 0.90000000000000002, - 0.69813170079773179 }, - { 0.77167205646538850, -0.59999999999999998, 0.90000000000000002, - 0.87266462599716477 }, - { 0.89673202848034383, -0.59999999999999998, 0.90000000000000002, - 1.0471975511965976 }, - { 1.0163984492661304, -0.59999999999999998, 0.90000000000000002, - 1.2217304763960306 }, - { 1.1328845785162431, -0.59999999999999998, 0.90000000000000002, - 1.3962634015954636 }, - { 1.2479362973851875, -0.59999999999999998, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.59999999999999998, nu=0.90000000000000002. -template <typename Tp> -void test040() -{ - 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(data040) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data040[i].k), Tp(data040[i].nu), - Tp(data040[i].phi)); - const Tp f0 = data040[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 5.7440178400898422e-16 +// mean(f - f_Boost): 5.0792703376600914e-16 +// variance(f - f_Boost): 1.9863137923719990e-31 +// stddev(f - f_Boost): 4.4568080420543122e-16 +const testcase_ellint_3<double> +data040[10] = +{ + { 0.0000000000000000, -0.59999999999999998, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17646850384035848, -0.59999999999999998, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36509041515134105, -0.59999999999999998, 0.90000000000000002, + 0.34906585039886590 }, + { 0.58097838596260631, -0.59999999999999998, 0.90000000000000002, + 0.52359877559829882 }, + { 0.84656453396163722, -0.59999999999999998, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1997828426963724, -0.59999999999999998, 0.90000000000000002, + 0.87266462599716477 }, + { 1.7112436789225605, -0.59999999999999998, 0.90000000000000002, + 1.0471975511965976 }, + { 2.5193168553672312, -0.59999999999999998, 0.90000000000000002, + 1.2217304763960306 }, + { 3.8656670488606686, -0.59999999999999998, 0.90000000000000002, + 1.3962634015954636 }, + { 5.8709993116265595, -0.59999999999999998, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler040 = 2.5000000000000020e-13; // Test data for k=-0.50000000000000000, nu=0.0000000000000000. -testcase_ellint_3<double> data041[] = { - { -0.0000000000000000, -0.50000000000000000, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17475385514035785, -0.50000000000000000, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35081868470101585, -0.50000000000000000, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52942862705190585, -0.50000000000000000, 0.0000000000000000, - 0.52359877559829882 }, - { 0.71164727562630326, -0.50000000000000000, 0.0000000000000000, - 0.69813170079773179 }, - { 0.89824523594227768, -0.50000000000000000, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0895506700518851, -0.50000000000000000, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2853005857432933, -0.50000000000000000, 0.0000000000000000, - 1.2217304763960306 }, - { 1.4845545520549484, -0.50000000000000000, 0.0000000000000000, - 1.3962634015954636 }, - { 1.6857503548125963, -0.50000000000000000, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.0000000000000000. -template <typename Tp> -void test041() -{ - 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(data041) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data041[i].k), Tp(data041[i].nu), - Tp(data041[i].phi)); - const Tp f0 = data041[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.4551389361831220e-16 +// mean(f - f_Boost): -1.3877787807814457e-17 +// variance(f - f_Boost): 2.5893058141206173e-32 +// stddev(f - f_Boost): 1.6091320064309879e-16 +const testcase_ellint_3<double> +data041[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17475385514035785, -0.50000000000000000, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35081868470101579, -0.50000000000000000, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52942862705190574, -0.50000000000000000, 0.0000000000000000, + 0.52359877559829882 }, + { 0.71164727562630326, -0.50000000000000000, 0.0000000000000000, + 0.69813170079773179 }, + { 0.89824523594227768, -0.50000000000000000, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0895506700518853, -0.50000000000000000, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2853005857432933, -0.50000000000000000, 0.0000000000000000, + 1.2217304763960306 }, + { 1.4845545520549488, -0.50000000000000000, 0.0000000000000000, + 1.3962634015954636 }, + { 1.6857503548125961, -0.50000000000000000, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler041 = 2.5000000000000020e-13; // Test data for k=-0.50000000000000000, nu=0.10000000000000001. -testcase_ellint_3<double> data042[] = { - { -0.0000000000000000, -0.50000000000000000, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17457763120814676, -0.50000000000000000, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34943246340849154, -0.50000000000000000, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52487937869610801, -0.50000000000000000, 0.10000000000000001, - 0.52359877559829882 }, - { 0.70127785096388395, -0.50000000000000000, 0.10000000000000001, - 0.69813170079773179 }, - { 0.87898815988624479, -0.50000000000000000, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0582764576094172, -0.50000000000000000, 0.10000000000000001, - 1.0471975511965976 }, - { 1.2391936844060207, -0.50000000000000000, 0.10000000000000001, - 1.2217304763960306 }, - { 1.4214793542995841, -0.50000000000000000, 0.10000000000000001, - 1.3962634015954636 }, - { 1.6045524936084892, -0.50000000000000000, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.10000000000000001. -template <typename Tp> -void test042() -{ - 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(data042) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data042[i].k), Tp(data042[i].nu), - Tp(data042[i].phi)); - const Tp f0 = data042[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)); -} +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.7416868347177582e-16 +// mean(f - f_Boost): 2.7755575615628915e-18 +// variance(f - f_Boost): 5.4326441655972001e-32 +// stddev(f - f_Boost): 2.3308033305273100e-16 +const testcase_ellint_3<double> +data042[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17493071928248824, -0.50000000000000000, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35222467688034798, -0.50000000000000000, 0.10000000000000001, + 0.34906585039886590 }, + { 0.53411928652008112, -0.50000000000000000, 0.10000000000000001, + 0.52359877559829882 }, + { 0.72256398117177589, -0.50000000000000000, 0.10000000000000001, + 0.69813170079773179 }, + { 0.91899583232771009, -0.50000000000000000, 0.10000000000000001, + 0.87266462599716477 }, + { 1.1240549163055360, -0.50000000000000000, 0.10000000000000001, + 1.0471975511965976 }, + { 1.3372938086286021, -0.50000000000000000, 0.10000000000000001, + 1.2217304763960306 }, + { 1.5570024469132429, -0.50000000000000000, 0.10000000000000001, + 1.3962634015954636 }, + { 1.7803034946545480, -0.50000000000000000, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler042 = 2.5000000000000020e-13; // Test data for k=-0.50000000000000000, nu=0.20000000000000001. -testcase_ellint_3<double> data043[] = { - { -0.0000000000000000, -0.50000000000000000, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17440204336345433, -0.50000000000000000, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34806552388338824, -0.50000000000000000, 0.20000000000000001, - 0.34906585039886590 }, - { 0.52046416757129821, -0.50000000000000000, 0.20000000000000001, - 0.52359877559829882 }, - { 0.69140924550993876, -0.50000000000000000, 0.20000000000000001, - 0.69813170079773179 }, - { 0.86104678636125520, -0.50000000000000000, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0297439459053981, -0.50000000000000000, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1979214112912036, -0.50000000000000000, 0.20000000000000001, - 1.2217304763960306 }, - { 1.3659033858648930, -0.50000000000000000, 0.20000000000000001, - 1.3962634015954636 }, - { 1.5338490483665983, -0.50000000000000000, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.20000000000000001. -template <typename Tp> -void test043() -{ - 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(data043) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data043[i].k), Tp(data043[i].nu), - Tp(data043[i].phi)); - const Tp f0 = data043[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, nu=0.29999999999999999. -testcase_ellint_3<double> data044[] = { - { -0.0000000000000000, -0.50000000000000000, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17422708752228896, -0.50000000000000000, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34671739434855858, -0.50000000000000000, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51617616305641889, -0.50000000000000000, 0.29999999999999999, - 0.52359877559829882 }, - { 0.68200047612545178, -0.50000000000000000, 0.29999999999999999, - 0.69813170079773179 }, - { 0.84427217869498372, -0.50000000000000000, 0.29999999999999999, - 0.87266462599716477 }, - { 1.0035637821389782, -0.50000000000000000, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1606800483933113, -0.50000000000000000, 0.29999999999999999, - 1.2217304763960306 }, - { 1.3164407134643459, -0.50000000000000000, 0.29999999999999999, - 1.3962634015954636 }, - { 1.4715681939859637, -0.50000000000000000, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.29999999999999999. -template <typename Tp> -void test044() -{ - 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(data044) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data044[i].k), Tp(data044[i].nu), - Tp(data044[i].phi)); - const Tp f0 = data044[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)); -} +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.1198767993730867e-16 +// mean(f - f_Boost): 2.7755575615628914e-17 +// variance(f - f_Boost): 5.0311947683004831e-32 +// stddev(f - f_Boost): 2.2430324938128922e-16 +const testcase_ellint_3<double> +data043[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17510822779582402, -0.50000000000000000, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35365094725531487, -0.50000000000000000, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53895933237328697, -0.50000000000000000, 0.20000000000000001, + 0.52359877559829882 }, + { 0.73408090840070794, -0.50000000000000000, 0.20000000000000001, + 0.69813170079773179 }, + { 0.94145442818535396, -0.50000000000000000, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1624120186296487, -0.50000000000000000, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3965823372867114, -0.50000000000000000, 0.20000000000000001, + 1.2217304763960306 }, + { 1.6414308440430099, -0.50000000000000000, 0.20000000000000001, + 1.3962634015954636 }, + { 1.8922947612264018, -0.50000000000000000, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler043 = 2.5000000000000020e-13; + +// Test data for k=-0.50000000000000000, nu=0.30000000000000004. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.3800262770228813e-16 +// mean(f - f_Boost): 5.8286708792820721e-17 +// variance(f - f_Boost): 8.5027191584278157e-32 +// stddev(f - f_Boost): 2.9159422419567599e-16 +const testcase_ellint_3<double> +data044[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17528638488102041, -0.50000000000000000, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35509802222332720, -0.50000000000000000, 0.30000000000000004, + 0.34906585039886590 }, + { 0.54395740731866193, -0.50000000000000000, 0.30000000000000004, + 0.52359877559829882 }, + { 0.74625871438752667, -0.50000000000000000, 0.30000000000000004, + 0.69813170079773179 }, + { 0.96588271186092023, -0.50000000000000000, 0.30000000000000004, + 0.87266462599716477 }, + { 1.2054319584357329, -0.50000000000000000, 0.30000000000000004, + 1.0471975511965976 }, + { 1.4651077994832871, -0.50000000000000000, 0.30000000000000004, + 1.2217304763960306 }, + { 1.7416018368052644, -0.50000000000000000, 0.30000000000000004, + 1.3962634015954636 }, + { 2.0277924458111314, -0.50000000000000000, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler044 = 2.5000000000000020e-13; // Test data for k=-0.50000000000000000, nu=0.40000000000000002. -testcase_ellint_3<double> data045[] = { - { -0.0000000000000000, -0.50000000000000000, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17405275963859917, -0.50000000000000000, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34538761957029329, -0.50000000000000000, 0.40000000000000002, - 0.34906585039886590 }, - { 0.51200902646603919, -0.50000000000000000, 0.40000000000000002, - 0.52359877559829882 }, - { 0.67301522212868792, -0.50000000000000000, 0.40000000000000002, - 0.69813170079773179 }, - { 0.82853844466313320, -0.50000000000000000, 0.40000000000000002, - 0.87266462599716477 }, - { 0.97942097862681488, -0.50000000000000000, 0.40000000000000002, - 1.0471975511965976 }, - { 1.1268429801220616, -0.50000000000000000, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2720406704533922, -0.50000000000000000, 0.40000000000000002, - 1.3962634015954636 }, - { 1.4161679518465340, -0.50000000000000000, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.40000000000000002. -template <typename Tp> -void test045() -{ - 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(data045) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data045[i].k), Tp(data045[i].nu), - Tp(data045[i].phi)); - const Tp f0 = data045[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.0439932918341581e-16 +// mean(f - f_Boost): 3.0531133177191807e-17 +// variance(f - f_Boost): 9.0809736800018602e-32 +// stddev(f - f_Boost): 3.0134653938616686e-16 +const testcase_ellint_3<double> +data045[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17546519477859268, -0.50000000000000000, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35656644822531680, -0.50000000000000000, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54912289677411319, -0.50000000000000000, 0.40000000000000002, + 0.52359877559829882 }, + { 0.75916731611690047, -0.50000000000000000, 0.40000000000000002, + 0.69813170079773179 }, + { 0.99260415631328214, -0.50000000000000000, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2541925856918670, -0.50000000000000000, 0.40000000000000002, + 1.0471975511965976 }, + { 1.5456393705347609, -0.50000000000000000, 0.40000000000000002, + 1.2217304763960306 }, + { 1.8631904972952076, -0.50000000000000000, 0.40000000000000002, + 1.3962634015954636 }, + { 2.1962905366178065, -0.50000000000000000, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler045 = 2.5000000000000020e-13; // Test data for k=-0.50000000000000000, nu=0.50000000000000000. -testcase_ellint_3<double> data046[] = { - { -0.0000000000000000, -0.50000000000000000, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17387905570381157, -0.50000000000000000, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34407576010465207, -0.50000000000000000, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50795686560160835, -0.50000000000000000, 0.50000000000000000, - 0.52359877559829882 }, - { 0.66442115453330175, -0.50000000000000000, 0.50000000000000000, - 0.69813170079773179 }, - { 0.81373829119355345, -0.50000000000000000, 0.50000000000000000, - 0.87266462599716477 }, - { 0.95705743313235825, -0.50000000000000000, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0959131991362556, -0.50000000000000000, 0.50000000000000000, - 1.2217304763960306 }, - { 1.2318900529754597, -0.50000000000000000, 0.50000000000000000, - 1.3962634015954636 }, - { 1.3664739530045971, -0.50000000000000000, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.50000000000000000. -template <typename Tp> -void test046() -{ - 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(data046) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data046[i].k), Tp(data046[i].nu), - Tp(data046[i].phi)); - const Tp f0 = data046[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, nu=0.59999999999999998. -testcase_ellint_3<double> data047[] = { - { -0.0000000000000000, -0.50000000000000000, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17370597174637581, -0.50000000000000000, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34278139158591414, -0.50000000000000000, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50401419439302719, -0.50000000000000000, 0.59999999999999998, - 0.52359877559829882 }, - { 0.65618938076167221, -0.50000000000000000, 0.59999999999999998, - 0.69813170079773179 }, - { 0.79977959248855424, -0.50000000000000000, 0.59999999999999998, - 0.87266462599716477 }, - { 0.93625925190753545, -0.50000000000000000, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0674905658379710, -0.50000000000000000, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1953481298023048, -0.50000000000000000, 0.59999999999999998, - 1.3962634015954636 }, - { 1.3215740290190876, -0.50000000000000000, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.59999999999999998. -template <typename Tp> -void test047() -{ - 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(data047) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data047[i].k), Tp(data047[i].nu), - Tp(data047[i].phi)); - const Tp f0 = data047[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, nu=0.69999999999999996. -testcase_ellint_3<double> data048[] = { - { -0.0000000000000000, -0.50000000000000000, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17353350383131641, -0.50000000000000000, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34150410405436771, -0.50000000000000000, 0.69999999999999996, - 0.34906585039886590 }, - { 0.50017589696443487, -0.50000000000000000, 0.69999999999999996, - 0.52359877559829882 }, - { 0.64829398188419962, -0.50000000000000000, 0.69999999999999996, - 0.69813170079773179 }, - { 0.78658270782402073, -0.50000000000000000, 0.69999999999999996, - 0.87266462599716477 }, - { 0.91684738336675053, -0.50000000000000000, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0412486789555937, -0.50000000000000000, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1619021847612001, -0.50000000000000000, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2807475181182502, -0.50000000000000000, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.69999999999999996. -template <typename Tp> -void test048() -{ - 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(data048) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data048[i].k), Tp(data048[i].nu), - Tp(data048[i].phi)); - const Tp f0 = data048[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.6797816859260978e-16 +// mean(f - f_Boost): 9.4368957093138303e-17 +// variance(f - f_Boost): 7.7794254682023874e-32 +// stddev(f - f_Boost): 2.7891621444803792e-16 +const testcase_ellint_3<double> +data046[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17564466176941509, -0.50000000000000000, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35805679276065394, -0.50000000000000000, 0.50000000000000000, + 0.34906585039886590 }, + { 0.55446601496200032, -0.50000000000000000, 0.50000000000000000, + 0.52359877559829882 }, + { 0.77288783578259013, -0.50000000000000000, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0220246013918972, -0.50000000000000000, 0.50000000000000000, + 0.87266462599716477 }, + { 1.3101681612463965, -0.50000000000000000, 0.50000000000000000, + 1.0471975511965976 }, + { 1.6422994881851025, -0.50000000000000000, 0.50000000000000000, + 1.2217304763960306 }, + { 2.0152636030998816, -0.50000000000000000, 0.50000000000000000, + 1.3962634015954636 }, + { 2.4136715042011945, -0.50000000000000000, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler046 = 2.5000000000000020e-13; + +// Test data for k=-0.50000000000000000, nu=0.60000000000000009. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.9178421578645735e-16 +// mean(f - f_Boost): 1.3322676295501878e-16 +// variance(f - f_Boost): 1.7749370367472766e-31 +// stddev(f - f_Boost): 4.2130001622920411e-16 +const testcase_ellint_3<double> +data047[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17582479017522740, -0.50000000000000000, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35956964546660036, -0.50000000000000000, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55999790372984193, -0.50000000000000000, 0.60000000000000009, + 0.52359877559829882 }, + { 0.78751507911209895, -0.50000000000000000, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0546620505035220, -0.50000000000000000, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3754438357425935, -0.50000000000000000, 0.60000000000000009, + 1.0471975511965976 }, + { 1.7615727400820127, -0.50000000000000000, 0.60000000000000009, + 1.2217304763960306 }, + { 2.2134638067565242, -0.50000000000000000, 0.60000000000000009, + 1.3962634015954636 }, + { 2.7090491861753558, -0.50000000000000000, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler047 = 2.5000000000000020e-13; + +// Test data for k=-0.50000000000000000, nu=0.70000000000000007. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.0745105182189226e-16 +// mean(f - f_Boost): 4.1633363423443370e-17 +// variance(f - f_Boost): 1.9996383743576116e-32 +// stddev(f - f_Boost): 1.4140857026211713e-16 +const testcase_ellint_3<double> +data048[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17600558435914915, -0.50000000000000000, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36110561926726259, -0.50000000000000000, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56573074641137111, -0.50000000000000000, 0.70000000000000007, + 0.52359877559829882 }, + { 0.80316073084237205, -0.50000000000000000, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0911910688131461, -0.50000000000000000, 0.70000000000000007, + 0.87266462599716477 }, + { 1.4530946406380640, -0.50000000000000000, 0.70000000000000007, + 1.0471975511965976 }, + { 1.9144386536785372, -0.50000000000000000, 0.70000000000000007, + 1.2217304763960306 }, + { 2.4878788958234970, -0.50000000000000000, 0.70000000000000007, + 1.3962634015954636 }, + { 3.1433945297859225, -0.50000000000000000, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler048 = 2.5000000000000020e-13; // Test data for k=-0.50000000000000000, nu=0.80000000000000004. -testcase_ellint_3<double> data049[] = { - { -0.0000000000000000, -0.50000000000000000, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17336164805979126, -0.50000000000000000, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34024350132086773, -0.50000000000000000, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49643719555734084, -0.50000000000000000, 0.80000000000000004, - 0.52359877559829882 }, - { 0.64071162456976150, -0.50000000000000000, 0.80000000000000004, - 0.69813170079773179 }, - { 0.77407836177211908, -0.50000000000000000, 0.80000000000000004, - 0.87266462599716477 }, - { 0.89867058251905652, -0.50000000000000000, 0.80000000000000004, - 1.0471975511965976 }, - { 1.0169181822134912, -0.50000000000000000, 0.80000000000000004, - 1.2217304763960306 }, - { 1.1311363312779448, -0.50000000000000000, 0.80000000000000004, - 1.3962634015954636 }, - { 1.2434165408189539, -0.50000000000000000, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.80000000000000004. -template <typename Tp> -void test049() -{ - 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(data049) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data049[i].k), Tp(data049[i].nu), - Tp(data049[i].phi)); - const Tp f0 = data049[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)); -} +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.4380477375534667e-16 +// mean(f - f_Boost): 2.3037127760972000e-16 +// variance(f - f_Boost): 1.4989821857033475e-31 +// stddev(f - f_Boost): 3.8716691306248618e-16 +const testcase_ellint_3<double> +data049[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17618704872620228, -0.50000000000000000, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36266535159745827, -0.50000000000000000, 0.80000000000000004, + 0.34906585039886590 }, + { 0.57167789954529158, -0.50000000000000000, 0.80000000000000004, + 0.52359877559829882 }, + { 0.81995752984315018, -0.50000000000000000, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1325112162158122, -0.50000000000000000, 0.80000000000000004, + 0.87266462599716477 }, + { 1.5479055930718042, -0.50000000000000000, 0.80000000000000004, + 1.0471975511965976 }, + { 2.1215243941010486, -0.50000000000000000, 0.80000000000000004, + 1.2217304763960306 }, + { 2.9069405767650132, -0.50000000000000000, 0.80000000000000004, + 1.3962634015954636 }, + { 3.8750701888108066, -0.50000000000000000, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler049 = 2.5000000000000020e-13; // Test data for k=-0.50000000000000000, nu=0.90000000000000002. -testcase_ellint_3<double> data050[] = { - { -0.0000000000000000, -0.50000000000000000, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17319040056865681, -0.50000000000000000, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33899920036578557, -0.50000000000000000, 0.90000000000000002, - 0.34906585039886590 }, - { 0.49279362182695186, -0.50000000000000000, 0.90000000000000002, - 0.52359877559829882 }, - { 0.63342123379746151, -0.50000000000000000, 0.90000000000000002, - 0.69813170079773179 }, - { 0.76220595179550321, -0.50000000000000000, 0.90000000000000002, - 0.87266462599716477 }, - { 0.88160004743532294, -0.50000000000000000, 0.90000000000000002, - 1.0471975511965976 }, - { 0.99427448642310134, -0.50000000000000000, 0.90000000000000002, - 1.2217304763960306 }, - { 1.1027091512470093, -0.50000000000000000, 0.90000000000000002, - 1.3962634015954636 }, - { 1.2091116095504744, -0.50000000000000000, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.50000000000000000, nu=0.90000000000000002. -template <typename Tp> -void test050() -{ - 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(data050) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data050[i].k), Tp(data050[i].nu), - Tp(data050[i].phi)); - const Tp f0 = data050[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, nu=0.0000000000000000. -testcase_ellint_3<double> data051[] = { - { -0.0000000000000000, -0.40000000000000002, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17467414669441531, -0.40000000000000002, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35018222772483443, -0.40000000000000002, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52729015917508748, -0.40000000000000002, 0.0000000000000000, - 0.52359877559829882 }, - { 0.70662374407341255, -0.40000000000000002, 0.0000000000000000, - 0.69813170079773179 }, - { 0.88859210497602170, -0.40000000000000002, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0733136290471379, -0.40000000000000002, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2605612170157061, -0.40000000000000002, 0.0000000000000000, - 1.2217304763960306 }, - { 1.4497513956433437, -0.40000000000000002, 0.0000000000000000, - 1.3962634015954636 }, - { 1.6399998658645112, -0.40000000000000002, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.0000000000000000. -template <typename Tp> -void test051() -{ - 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(data051) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data051[i].k), Tp(data051[i].nu), - Tp(data051[i].phi)); - const Tp f0 = data051[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, nu=0.10000000000000001. -testcase_ellint_3<double> data052[] = { - { -0.0000000000000000, -0.40000000000000002, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17449806706684673, -0.40000000000000002, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34880048623856075, -0.40000000000000002, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52277322065757403, -0.40000000000000002, 0.10000000000000001, - 0.52359877559829882 }, - { 0.69638072056918376, -0.40000000000000002, 0.10000000000000001, - 0.69813170079773179 }, - { 0.86968426619831540, -0.40000000000000002, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0428044206578095, -0.40000000000000002, 0.10000000000000001, - 1.0471975511965976 }, - { 1.2158651158274378, -0.40000000000000002, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3889447129893322, -0.40000000000000002, 0.10000000000000001, - 1.3962634015954636 }, - { 1.5620566886683604, -0.40000000000000002, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.10000000000000001. -template <typename Tp> -void test052() -{ - 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(data052) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data052[i].k), Tp(data052[i].nu), - Tp(data052[i].phi)); - const Tp f0 = data052[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, nu=0.20000000000000001. -testcase_ellint_3<double> data053[] = { - { -0.0000000000000000, -0.40000000000000002, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17432262290723399, -0.40000000000000002, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34743795258968596, -0.40000000000000002, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51838919472805123, -0.40000000000000002, 0.20000000000000001, - 0.52359877559829882 }, - { 0.68663134739057918, -0.40000000000000002, 0.20000000000000001, - 0.69813170079773179 }, - { 0.85206432981833979, -0.40000000000000002, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0149595349004430, -0.40000000000000002, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1758349405464676, -0.40000000000000002, 0.20000000000000001, - 1.2217304763960306 }, - { 1.3353337673882635, -0.40000000000000002, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4941414344266770, -0.40000000000000002, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.20000000000000001. -template <typename Tp> -void test053() -{ - 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(data053) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data053[i].k), Tp(data053[i].nu), - Tp(data053[i].phi)); - const Tp f0 = data053[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, nu=0.29999999999999999. -testcase_ellint_3<double> data054[] = { - { -0.0000000000000000, -0.40000000000000002, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17414781013591543, -0.40000000000000002, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34609415696777285, -0.40000000000000002, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51413131295862546, -0.40000000000000002, 0.29999999999999999, - 0.52359877559829882 }, - { 0.67733527622935630, -0.40000000000000002, 0.29999999999999999, - 0.69813170079773179 }, - { 0.83558675182733266, -0.40000000000000002, 0.29999999999999999, - 0.87266462599716477 }, - { 0.98940140808865906, -0.40000000000000002, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1396968797728058, -0.40000000000000002, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2875920037865087, -0.40000000000000002, 0.29999999999999999, - 1.3962634015954636 }, - { 1.4342789859950078, -0.40000000000000002, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.29999999999999999. -template <typename Tp> -void test054() -{ - 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(data054) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data054[i].k), Tp(data054[i].nu), - Tp(data054[i].phi)); - const Tp f0 = data054[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, nu=0.40000000000000002. -testcase_ellint_3<double> data055[] = { - { -0.0000000000000000, -0.40000000000000002, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17397362471112710, -0.40000000000000002, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34476864603333196, -0.40000000000000002, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50999329415379357, -0.40000000000000002, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66845674551396017, -0.40000000000000002, 0.40000000000000002, - 0.69813170079773179 }, - { 0.82012848346231748, -0.40000000000000002, 0.40000000000000002, - 0.87266462599716477 }, - { 0.96582449258349057, -0.40000000000000002, 0.40000000000000002, - 1.0471975511965976 }, - { 1.1068473749476286, -0.40000000000000002, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2447132729159986, -0.40000000000000002, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3809986210732901, -0.40000000000000002, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.40000000000000002. -template <typename Tp> -void test055() -{ - 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(data055) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data055[i].k), Tp(data055[i].nu), - Tp(data055[i].phi)); - const Tp f0 = data055[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, nu=0.50000000000000000. -testcase_ellint_3<double> data056[] = { - { -0.0000000000000000, -0.40000000000000002, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17380006262854139, -0.40000000000000002, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34346098216756610, -0.40000000000000002, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50596929935059420, -0.40000000000000002, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65996392089131262, -0.40000000000000002, 0.50000000000000000, - 0.69813170079773179 }, - { 0.80558463511364786, -0.40000000000000002, 0.50000000000000000, - 0.87266462599716477 }, - { 0.94397834522857704, -0.40000000000000002, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0768075114108115, -0.40000000000000002, 0.50000000000000000, - 1.2217304763960306 }, - { 1.2059184624251329, -0.40000000000000002, 0.50000000000000000, - 1.3962634015954636 }, - { 1.3331797176377398, -0.40000000000000002, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.50000000000000000. -template <typename Tp> -void test056() -{ - 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(data056) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data056[i].k), Tp(data056[i].nu), - Tp(data056[i].phi)); - const Tp f0 = data056[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, nu=0.59999999999999998. -testcase_ellint_3<double> data057[] = { - { -0.0000000000000000, -0.40000000000000002, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17362711992081248, -0.40000000000000002, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34217074276403953, -0.40000000000000002, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50205389185761617, -0.40000000000000002, 0.59999999999999998, - 0.52359877559829882 }, - { 0.65182834920372745, -0.40000000000000002, 0.59999999999999998, - 0.69813170079773179 }, - { 0.79186512820565136, -0.40000000000000002, 0.59999999999999998, - 0.87266462599716477 }, - { 0.92365535916287134, -0.40000000000000002, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0491915663957907, -0.40000000000000002, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1705934291745104, -0.40000000000000002, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2899514672527024, -0.40000000000000002, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.59999999999999998. -template <typename Tp> -void test057() -{ - 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(data057) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data057[i].k), Tp(data057[i].nu), - Tp(data057[i].phi)); - const Tp f0 = data057[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, nu=0.69999999999999996. -testcase_ellint_3<double> data058[] = { - { -0.0000000000000000, -0.40000000000000002, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17345479265712871, -0.40000000000000002, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34089751955950354, -0.40000000000000002, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49824200167361343, -0.40000000000000002, 0.69999999999999996, - 0.52359877559829882 }, - { 0.64402450341199413, -0.40000000000000002, 0.69999999999999996, - 0.69813170079773179 }, - { 0.77889207804122873, -0.40000000000000002, 0.69999999999999996, - 0.87266462599716477 }, - { 0.90468169720957992, -0.40000000000000002, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0236847823692916, -0.40000000000000002, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1382465247425164, -0.40000000000000002, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2506255923253344, -0.40000000000000002, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.69999999999999996. -template <typename Tp> -void test058() -{ - 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(data058) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data058[i].k), Tp(data058[i].nu), - Tp(data058[i].phi)); - const Tp f0 = data058[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, nu=0.80000000000000004. -testcase_ellint_3<double> data059[] = { - { -0.0000000000000000, -0.40000000000000002, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17328307694277156, -0.40000000000000002, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33964091800132007, -0.40000000000000002, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49452889372467451, -0.40000000000000002, 0.80000000000000004, - 0.52359877559829882 }, - { 0.63652940095937327, -0.40000000000000002, 0.80000000000000004, - 0.69813170079773179 }, - { 0.76659772511159097, -0.40000000000000002, 0.80000000000000004, - 0.87266462599716477 }, - { 0.88691047977338111, -0.40000000000000002, 0.80000000000000004, - 1.0471975511965976 }, - { 1.0000273200611638, -0.40000000000000002, 0.80000000000000004, - 1.2217304763960306 }, - { 1.1084787902188007, -0.40000000000000002, 0.80000000000000004, - 1.3962634015954636 }, - { 1.2146499565727209, -0.40000000000000002, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.80000000000000004. -template <typename Tp> -void test059() -{ - 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(data059) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data059[i].k), Tp(data059[i].nu), - Tp(data059[i].phi)); - const Tp f0 = data059[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, nu=0.90000000000000002. -testcase_ellint_3<double> data060[] = { - { -0.0000000000000000, -0.40000000000000002, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17311196891868130, -0.40000000000000002, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33840055664911906, -0.40000000000000002, 0.90000000000000002, - 0.34906585039886590 }, - { 0.49091013944075340, -0.40000000000000002, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62932228186809591, -0.40000000000000002, 0.90000000000000002, - 0.69813170079773179 }, - { 0.75492278323019801, -0.40000000000000002, 0.90000000000000002, - 0.87266462599716477 }, - { 0.87021659043854294, -0.40000000000000002, 0.90000000000000002, - 1.0471975511965976 }, - { 0.97800245228239246, -0.40000000000000002, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0809625773173694, -0.40000000000000002, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1815758115929846, -0.40000000000000002, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.40000000000000002, nu=0.90000000000000002. -template <typename Tp> -void test060() -{ - 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(data060) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data060[i].k), Tp(data060[i].nu), - Tp(data060[i].phi)); - const Tp f0 = data060[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, nu=0.0000000000000000. -testcase_ellint_3<double> data061[] = { - { -0.0000000000000000, -0.30000000000000004, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17461228653000102, -0.30000000000000004, 0.0000000000000000, - 0.17453292519943295 }, - { 0.34969146102798415, -0.30000000000000004, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52565822873726320, -0.30000000000000004, 0.0000000000000000, - 0.52359877559829882 }, - { 0.70284226512408532, -0.30000000000000004, 0.0000000000000000, - 0.69813170079773179 }, - { 0.88144139195111182, -0.30000000000000004, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0614897067260523, -0.30000000000000004, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2428416824174218, -0.30000000000000004, 0.0000000000000000, - 1.2217304763960306 }, - { 1.4251795877015925, -0.30000000000000004, 0.0000000000000000, - 1.3962634015954636 }, - { 1.6080486199305126, -0.30000000000000004, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.0000000000000000. -template <typename Tp> -void test061() -{ - 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(data061) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data061[i].k), Tp(data061[i].nu), - Tp(data061[i].phi)); - const Tp f0 = data061[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, nu=0.10000000000000001. -testcase_ellint_3<double> data062[] = { - { -0.0000000000000000, -0.30000000000000004, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17443631884814378, -0.30000000000000004, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34831316835124926, -0.30000000000000004, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52116586276523857, -0.30000000000000004, 0.10000000000000001, - 0.52359877559829882 }, - { 0.69269385837910036, -0.30000000000000004, 0.10000000000000001, - 0.69813170079773179 }, - { 0.86279023163070856, -0.30000000000000004, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0315321461438265, -0.30000000000000004, 0.10000000000000001, - 1.0471975511965976 }, - { 1.1991449111869024, -0.30000000000000004, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3659561780923211, -0.30000000000000004, 0.10000000000000001, - 1.3962634015954636 }, - { 1.5323534693557526, -0.30000000000000004, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.10000000000000001. -template <typename Tp> -void test062() -{ - 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(data062) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data062[i].k), Tp(data062[i].nu), - Tp(data062[i].phi)); - const Tp f0 = data062[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, nu=0.20000000000000001. -testcase_ellint_3<double> data063[] = { - { -0.0000000000000000, -0.30000000000000004, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17426098615372090, -0.30000000000000004, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34695402664689923, -0.30000000000000004, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51680555567038933, -0.30000000000000004, 0.20000000000000001, - 0.52359877559829882 }, - { 0.68303375225260210, -0.30000000000000004, 0.20000000000000001, - 0.69813170079773179 }, - { 0.84540662891295026, -0.30000000000000004, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0041834051646927, -0.30000000000000004, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1599952702345711, -0.30000000000000004, 0.20000000000000001, - 1.2217304763960306 }, - { 1.3137179520499163, -0.30000000000000004, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4663658145259875, -0.30000000000000004, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.20000000000000001. -template <typename Tp> -void test063() -{ - 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(data063) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data063[i].k), Tp(data063[i].nu), - Tp(data063[i].phi)); - const Tp f0 = data063[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, nu=0.29999999999999999. -testcase_ellint_3<double> data064[] = { - { -0.0000000000000000, -0.30000000000000004, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17408628437042845, -0.30000000000000004, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34561356761638401, -0.30000000000000004, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51257058617875850, -0.30000000000000004, 0.29999999999999999, - 0.52359877559829882 }, - { 0.67382207124602866, -0.30000000000000004, 0.29999999999999999, - 0.69813170079773179 }, - { 0.82914751587825131, -0.30000000000000004, 0.29999999999999999, - 0.87266462599716477 }, - { 0.97907434814374950, -0.30000000000000004, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1246399297351584, -0.30000000000000004, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2671793970398146, -0.30000000000000004, 0.29999999999999999, - 1.3962634015954636 }, - { 1.4081767433479089, -0.30000000000000004, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.29999999999999999. -template <typename Tp> -void test064() -{ - 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(data064) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data064[i].k), Tp(data064[i].nu), - Tp(data064[i].phi)); - const Tp f0 = data064[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, nu=0.40000000000000002. -testcase_ellint_3<double> data065[] = { - { -0.0000000000000000, -0.30000000000000004, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17391220945982730, -0.30000000000000004, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34429133937639689, -0.30000000000000004, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50845471668581632, -0.30000000000000004, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66502347027873854, -0.30000000000000004, 0.40000000000000002, - 0.69813170079773179 }, - { 0.81389191978012254, -0.30000000000000004, 0.40000000000000002, - 0.87266462599716477 }, - { 0.95590618002140593, -0.30000000000000004, 0.40000000000000002, - 1.0471975511965976 }, - { 1.0924915195213121, -0.30000000000000004, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2253651604038058, -0.30000000000000004, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3563643538969761, -0.30000000000000004, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.40000000000000002. -template <typename Tp> -void test065() -{ - 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(data065) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data065[i].k), Tp(data065[i].nu), - Tp(data065[i].phi)); - const Tp f0 = data065[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, nu=0.50000000000000000. -testcase_ellint_3<double> data066[] = { - { -0.0000000000000000, -0.30000000000000004, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17373875742088235, -0.30000000000000004, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34298690571124157, -0.30000000000000004, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50445214859646936, -0.30000000000000004, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65660648352418516, -0.30000000000000004, 0.50000000000000000, - 0.69813170079773179 }, - { 0.79953670639287289, -0.30000000000000004, 0.50000000000000000, - 0.87266462599716477 }, - { 0.93443393926588558, -0.30000000000000004, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0630838369016911, -0.30000000000000004, 0.50000000000000000, - 1.2217304763960306 }, - { 1.1875197325653026, -0.30000000000000004, 0.50000000000000000, - 1.3962634015954636 }, - { 1.3098448759814960, -0.30000000000000004, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.50000000000000000. -template <typename Tp> -void test066() -{ - 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(data066) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data066[i].k), Tp(data066[i].nu), - Tp(data066[i].phi)); - const Tp f0 = data066[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, nu=0.59999999999999998. -testcase_ellint_3<double> data067[] = { - { -0.0000000000000000, -0.30000000000000004, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17356592428950826, -0.30000000000000004, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34169984536697379, -0.30000000000000004, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50055748266498457, -0.30000000000000004, 0.59999999999999998, - 0.52359877559829882 }, - { 0.64854298527106768, -0.30000000000000004, 0.59999999999999998, - 0.69813170079773179 }, - { 0.78599329284207431, -0.30000000000000004, 0.59999999999999998, - 0.87266462599716477 }, - { 0.91445452089128221, -0.30000000000000004, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0360412952290587, -0.30000000000000004, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1530473919778639, -0.30000000000000004, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2677758800420666, -0.30000000000000004, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.59999999999999998. -template <typename Tp> -void test067() -{ - 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(data067) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data067[i].k), Tp(data067[i].nu), - Tp(data067[i].phi)); - const Tp f0 = data067[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, nu=0.69999999999999996. -testcase_ellint_3<double> data068[] = { - { -0.0000000000000000, -0.30000000000000004, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17339370613812227, -0.30000000000000004, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34042975138455933, -0.30000000000000004, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49676568368075985, -0.30000000000000004, 0.69999999999999996, - 0.52359877559829882 }, - { 0.64080774055753720, -0.30000000000000004, 0.69999999999999996, - 0.69813170079773179 }, - { 0.77318507779667278, -0.30000000000000004, 0.69999999999999996, - 0.87266462599716477 }, - { 0.89579782346548631, -0.30000000000000004, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0110573286052202, -0.30000000000000004, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1214710972949633, -0.30000000000000004, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2294913236274980, -0.30000000000000004, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.69999999999999996. -template <typename Tp> -void test068() -{ - 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(data068) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data068[i].k), Tp(data068[i].nu), - Tp(data068[i].phi)); - const Tp f0 = data068[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, nu=0.80000000000000004. -testcase_ellint_3<double> data069[] = { - { -0.0000000000000000, -0.30000000000000004, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17322209907520361, -0.30000000000000004, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33917623046949996, -0.30000000000000004, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49307204894329176, -0.30000000000000004, 0.80000000000000004, - 0.52359877559829882 }, - { 0.63337802830291723, -0.30000000000000004, 0.80000000000000004, - 0.69813170079773179 }, - { 0.76104540997689407, -0.30000000000000004, 0.80000000000000004, - 0.87266462599716477 }, - { 0.87832009635450736, -0.30000000000000004, 0.80000000000000004, - 1.0471975511965976 }, - { 0.98787879723171790, -0.30000000000000004, 0.80000000000000004, - 1.2217304763960306 }, - { 1.0924036340069336, -0.30000000000000004, 0.80000000000000004, - 1.3962634015954636 }, - { 1.1944567571590046, -0.30000000000000004, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.80000000000000004. -template <typename Tp> -void test069() -{ - 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(data069) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data069[i].k), Tp(data069[i].nu), - Tp(data069[i].phi)); - const Tp f0 = data069[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, nu=0.90000000000000002. -testcase_ellint_3<double> data070[] = { - { -0.0000000000000000, -0.30000000000000004, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17305109924485948, -0.30000000000000004, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33793890239556984, -0.30000000000000004, 0.90000000000000002, - 0.34906585039886590 }, - { 0.48947218005089738, -0.30000000000000004, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62623332340775151, -0.30000000000000004, 0.90000000000000002, - 0.69813170079773179 }, - { 0.74951596581511148, -0.30000000000000004, 0.90000000000000002, - 0.87266462599716477 }, - { 0.86189886597756005, -0.30000000000000004, 0.90000000000000002, - 1.0471975511965976 }, - { 0.96629451153092005, -0.30000000000000004, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0655269133492680, -0.30000000000000004, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1622376896064912, -0.30000000000000004, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.30000000000000004, nu=0.90000000000000002. -template <typename Tp> -void test070() -{ - 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(data070) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data070[i].k), Tp(data070[i].nu), - Tp(data070[i].phi)); - const Tp f0 = data070[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.6192315188521289e-16 +// mean(f - f_Boost): 3.5249581031848718e-16 +// variance(f - f_Boost): 2.5029385557256515e-31 +// stddev(f - f_Boost): 5.0029376927217987e-16 +const testcase_ellint_3<double> +data050[10] = +{ + { 0.0000000000000000, -0.50000000000000000, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17636918772384180, -0.50000000000000000, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36424950570740700, -0.50000000000000000, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57785404590231426, -0.50000000000000000, 0.90000000000000002, + 0.52359877559829882 }, + { 0.83806480521716531, -0.50000000000000000, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1798568683069752, -0.50000000000000000, 0.90000000000000002, + 0.87266462599716477 }, + { 1.6678766243739607, -0.50000000000000000, 0.90000000000000002, + 1.0471975511965976 }, + { 2.4282976450693483, -0.50000000000000000, 0.90000000000000002, + 1.2217304763960306 }, + { 3.6810787666126656, -0.50000000000000000, 0.90000000000000002, + 1.3962634015954636 }, + { 5.5355132096026454, -0.50000000000000000, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler050 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.0000000000000000. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.1423314994346225e-16 +// mean(f - f_Boost): 1.9428902930940238e-17 +// variance(f - f_Boost): 2.2263750157116445e-32 +// stddev(f - f_Boost): 1.4921042241450980e-16 +const testcase_ellint_3<double> +data051[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17467414669441528, -0.39999999999999991, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35018222772483443, -0.39999999999999991, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52729015917508748, -0.39999999999999991, 0.0000000000000000, + 0.52359877559829882 }, + { 0.70662374407341244, -0.39999999999999991, 0.0000000000000000, + 0.69813170079773179 }, + { 0.88859210497602159, -0.39999999999999991, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0733136290471381, -0.39999999999999991, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2605612170157066, -0.39999999999999991, 0.0000000000000000, + 1.2217304763960306 }, + { 1.4497513956433439, -0.39999999999999991, 0.0000000000000000, + 1.3962634015954636 }, + { 1.6399998658645112, -0.39999999999999991, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler051 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.10000000000000001. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.8489340395463703e-16 +// mean(f - f_Boost): 6.3837823915946496e-17 +// variance(f - f_Boost): 4.4785242050000272e-32 +// stddev(f - f_Boost): 2.1162523963365114e-16 +const testcase_ellint_3<double> +data052[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17485086590796767, -0.39999999999999991, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35158366412506992, -0.39999999999999991, 0.10000000000000001, + 0.34906585039886590 }, + { 0.53194731675711726, -0.39999999999999991, 0.10000000000000001, + 0.52359877559829882 }, + { 0.71740615528010931, -0.39999999999999991, 0.10000000000000001, + 0.69813170079773179 }, + { 0.90896157773487030, -0.39999999999999991, 0.10000000000000001, + 0.87266462599716477 }, + { 1.1069605483834348, -0.39999999999999991, 0.10000000000000001, + 1.0471975511965976 }, + { 1.3109353428823001, -0.39999999999999991, 0.10000000000000001, + 1.2217304763960306 }, + { 1.5195460789903448, -0.39999999999999991, 0.10000000000000001, + 1.3962634015954636 }, + { 1.7306968836847187, -0.39999999999999991, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler052 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.20000000000000001. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.0467985583872730e-16 +// mean(f - f_Boost): 8.6042284408449634e-17 +// variance(f - f_Boost): 1.5826864298542218e-32 +// stddev(f - f_Boost): 1.2580486595733180e-16 +const testcase_ellint_3<double> +data053[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17502822886437389, -0.39999999999999991, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35300530062530805, -0.39999999999999991, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53675259548210896, -0.39999999999999991, 0.20000000000000001, + 0.52359877559829882 }, + { 0.72878006428676934, -0.39999999999999991, 0.20000000000000001, + 0.69813170079773179 }, + { 0.93100219010583563, -0.39999999999999991, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1443487271187609, -0.39999999999999991, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3683427764108813, -0.39999999999999991, 0.20000000000000001, + 1.2217304763960306 }, + { 1.6008221459300933, -0.39999999999999991, 0.20000000000000001, + 1.3962634015954636 }, + { 1.8380358826317627, -0.39999999999999991, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler053 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.30000000000000004. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 2.9973414591826100e-16 +// mean(f - f_Boost): 8.6042284408449634e-17 +// variance(f - f_Boost): 1.5826864298542218e-32 +// stddev(f - f_Boost): 1.2580486595733180e-16 +const testcase_ellint_3<double> +data054[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17520623975982899, -0.39999999999999991, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35444766141612105, -0.39999999999999991, 0.30000000000000004, + 0.34906585039886590 }, + { 0.54171455841536009, -0.39999999999999991, 0.30000000000000004, + 0.52359877559829882 }, + { 0.74080517001084012, -0.39999999999999991, 0.30000000000000004, + 0.69813170079773179 }, + { 0.95496950509296563, -0.39999999999999991, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1862627879844718, -0.39999999999999991, 0.30000000000000004, + 1.0471975511965976 }, + { 1.4346501803799458, -0.39999999999999991, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6971744798077697, -0.39999999999999991, 0.30000000000000004, + 1.3962634015954636 }, + { 1.9677924132520139, -0.39999999999999991, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler054 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.40000000000000002. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.2577246923979600e-16 +// mean(f - f_Boost): 1.8596235662471373e-16 +// variance(f - f_Boost): 1.6222417021441306e-31 +// stddev(f - f_Boost): 4.0277061736727151e-16 +const testcase_ellint_3<double> +data055[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17538490283034375, -0.39999999999999991, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35591129064319948, -0.39999999999999991, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54684250413264535, -0.39999999999999991, 0.40000000000000002, + 0.52359877559829882 }, + { 0.75355027742668290, -0.39999999999999991, 0.40000000000000002, + 0.69813170079773179 }, + { 0.98117935026780634, -0.39999999999999991, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2337464222030734, -0.39999999999999991, 0.40000000000000002, + 1.0471975511965976 }, + { 1.5125183419289221, -0.39999999999999991, 0.40000000000000002, + 1.2217304763960306 }, + { 1.8140224451130311, -0.39999999999999991, 0.40000000000000002, + 1.3962634015954636 }, + { 2.1289968719280026, -0.39999999999999991, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler055 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.50000000000000000. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.8009196014748294e-16 +// mean(f - f_Boost): 1.6375789613221060e-16 +// variance(f - f_Boost): 6.4788283329186610e-32 +// stddev(f - f_Boost): 2.5453542647181080e-16 +const testcase_ellint_3<double> +data056[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17556422235224273, -0.39999999999999991, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35739675341763921, -0.39999999999999991, 0.50000000000000000, + 0.34906585039886590 }, + { 0.55214655195037188, -0.39999999999999991, 0.50000000000000000, + 0.52359877559829882 }, + { 0.76709520942047438, -0.39999999999999991, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0100278761577499, -0.39999999999999991, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2882265661384342, -0.39999999999999991, 0.50000000000000000, + 1.0471975511965976 }, + { 1.6059059780051874, -0.39999999999999991, 0.50000000000000000, + 1.2217304763960306 }, + { 1.9600182740224081, -0.39999999999999991, 0.50000000000000000, + 1.3962634015954636 }, + { 2.3367461373176508, -0.39999999999999991, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler056 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.60000000000000009. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 2.8411408870840790e-16 +// mean(f - f_Boost): 9.7144514654701197e-17 +// variance(f - f_Boost): 1.4860570558543486e-32 +// stddev(f - f_Boost): 1.2190393988113545e-16 +const testcase_ellint_3<double> +data057[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17574420264267029, -0.39999999999999991, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35890463689046265, -0.39999999999999991, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55763773975194486, -0.39999999999999991, 0.60000000000000009, + 0.52359877559829882 }, + { 0.78153324227761267, -0.39999999999999991, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0420205885765887, -0.39999999999999991, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3517205230381770, -0.39999999999999991, 0.60000000000000009, + 1.0471975511965976 }, + { 1.7210360970313896, -0.39999999999999991, 0.60000000000000009, + 1.2217304763960306 }, + { 2.1500780510169242, -0.39999999999999991, 0.60000000000000009, + 1.3962634015954636 }, + { 2.6186940209850191, -0.39999999999999991, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler057 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.70000000000000007. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.1553900340611668e-16 +// mean(f - f_Boost): 1.1657341758564144e-16 +// variance(f - f_Boost): 1.3242789405258207e-32 +// stddev(f - f_Boost): 1.1507731924779187e-16 +const testcase_ellint_3<double> +data058[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17592484806010436, -0.39999999999999991, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36043555139631439, -0.39999999999999991, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56332813669944881, -0.39999999999999991, 0.70000000000000007, + 0.52359877559829882 }, + { 0.79697424562157548, -0.39999999999999991, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0778155987523672, -0.39999999999999991, 0.70000000000000007, + 0.87266462599716477 }, + { 1.4272018169896268, -0.39999999999999991, 0.70000000000000007, + 1.0471975511965976 }, + { 1.8684377907453380, -0.39999999999999991, 0.70000000000000007, + 1.2217304763960306 }, + { 2.4128677409207469, -0.39999999999999991, 0.70000000000000007, + 1.3962634015954636 }, + { 3.0327078743873241, -0.39999999999999991, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler058 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.80000000000000004. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.5727642219519274e-16 +// mean(f - f_Boost): 2.1926904736346843e-16 +// variance(f - f_Boost): 1.5293405480859847e-31 +// stddev(f - f_Boost): 3.9106783913868252e-16 +const testcase_ellint_3<double> +data059[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17610616300487833, -0.39999999999999991, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36199013167171978, -0.39999999999999991, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56923097361842423, -0.39999999999999991, 0.80000000000000004, + 0.52359877559829882 }, + { 0.81354878456624347, -0.39999999999999991, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1182902719261825, -0.39999999999999991, 0.80000000000000004, + 0.87266462599716477 }, + { 1.5192950589409022, -0.39999999999999991, 0.80000000000000004, + 1.0471975511965976 }, + { 2.0678761710223981, -0.39999999999999991, 0.80000000000000004, + 1.2217304763960306 }, + { 2.8135222249879783, -0.39999999999999991, 0.80000000000000004, + 1.3962634015954636 }, + { 3.7289548002199902, -0.39999999999999991, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler059 = 2.5000000000000020e-13; + +// Test data for k=-0.39999999999999991, nu=0.90000000000000002. +// max(|f - f_Boost|): 2.6645352591003757e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.0221626338023938e-16 +// mean(f - f_Boost): 4.1910919179599658e-16 +// variance(f - f_Boost): 6.2246150910247033e-31 +// stddev(f - f_Boost): 7.8896229891070860e-16 +const testcase_ellint_3<double> +data060[10] = +{ + { 0.0000000000000000, -0.39999999999999991, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17628815191971123, -0.39999999999999991, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36356903815378772, -0.39999999999999991, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57536079447000310, -0.39999999999999991, 0.90000000000000002, + 0.52359877559829882 }, + { 0.83141355850172571, -0.39999999999999991, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1646481598721361, -0.39999999999999991, 0.90000000000000002, + 0.87266462599716477 }, + { 1.6357275034001995, -0.39999999999999991, 0.90000000000000002, + 1.0471975511965976 }, + { 2.3628787566572398, -0.39999999999999991, 0.90000000000000002, + 1.2217304763960306 }, + { 3.5521010369134958, -0.39999999999999991, 0.90000000000000002, + 1.3962634015954636 }, + { 5.3055535102872513, -0.39999999999999991, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler060 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.0000000000000000. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.2241249691539529e-16 +// mean(f - f_Boost): 4.9960036108132046e-17 +// variance(f - f_Boost): 4.6872855002064458e-32 +// stddev(f - f_Boost): 2.1650139722889657e-16 +const testcase_ellint_3<double> +data061[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17461228653000099, -0.29999999999999993, 0.0000000000000000, + 0.17453292519943295 }, + { 0.34969146102798421, -0.29999999999999993, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52565822873726309, -0.29999999999999993, 0.0000000000000000, + 0.52359877559829882 }, + { 0.70284226512408543, -0.29999999999999993, 0.0000000000000000, + 0.69813170079773179 }, + { 0.88144139195111171, -0.29999999999999993, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0614897067260520, -0.29999999999999993, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2428416824174220, -0.29999999999999993, 0.0000000000000000, + 1.2217304763960306 }, + { 1.4251795877015929, -0.29999999999999993, 0.0000000000000000, + 1.3962634015954636 }, + { 1.6080486199305126, -0.29999999999999993, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler061 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.10000000000000001. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.1872304407982844e-16 +// mean(f - f_Boost): 9.4368957093138303e-17 +// variance(f - f_Boost): 4.0359883022230488e-32 +// stddev(f - f_Boost): 2.0089769292411121e-16 +const testcase_ellint_3<double> +data062[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17478889331392972, -0.29999999999999993, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35108939018329183, -0.29999999999999993, 0.10000000000000001, + 0.34906585039886590 }, + { 0.53028990896115835, -0.29999999999999993, 0.10000000000000001, + 0.52359877559829882 }, + { 0.71352417052371409, -0.29999999999999993, 0.10000000000000001, + 0.69813170079773179 }, + { 0.90153086032405894, -0.29999999999999993, 0.10000000000000001, + 0.87266462599716477 }, + { 1.0945187977283313, -0.29999999999999993, 0.10000000000000001, + 1.0471975511965976 }, + { 1.2920699268385680, -0.29999999999999993, 0.10000000000000001, + 1.2217304763960306 }, + { 1.4931243665896394, -0.29999999999999993, 0.10000000000000001, + 1.3962634015954636 }, + { 1.6960848815118226, -0.29999999999999993, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler062 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.20000000000000001. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.2247497610332889e-16 +// mean(f - f_Boost): 1.1102230246251565e-16 +// variance(f - f_Boost): 3.8043060629871325e-32 +// stddev(f - f_Boost): 1.9504630380981672e-16 +const testcase_ellint_3<double> +data063[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17496614335337535, -0.29999999999999993, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35250745937139372, -0.29999999999999993, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53506875002836884, -0.29999999999999993, 0.20000000000000001, + 0.52359877559829882 }, + { 0.72479106622248191, -0.29999999999999993, 0.20000000000000001, + 0.69813170079773179 }, + { 0.92326451535891607, -0.29999999999999993, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1312092060698349, -0.29999999999999993, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3481473154592321, -0.29999999999999993, 0.20000000000000001, + 1.2217304763960306 }, + { 1.5722049569662748, -0.29999999999999993, 0.20000000000000001, + 1.3962634015954636 }, + { 1.8002173372290498, -0.29999999999999993, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler063 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.30000000000000004. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.1678685180047551e-16 +// mean(f - f_Boost): 1.0547118733938987e-16 +// variance(f - f_Boost): 7.5633408838247182e-32 +// stddev(f - f_Boost): 2.7501528837184157e-16 +const testcase_ellint_3<double> +data064[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17514404084107435, -0.29999999999999993, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35394619108645647, -0.29999999999999993, 0.30000000000000004, + 0.34906585039886590 }, + { 0.54000325463372689, -0.29999999999999993, 0.30000000000000004, + 0.52359877559829882 }, + { 0.73670193794067651, -0.29999999999999993, 0.30000000000000004, + 0.69813170079773179 }, + { 0.94689345491722177, -0.29999999999999993, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1723274608389140, -0.29999999999999993, 0.30000000000000004, + 1.0471975511965976 }, + { 1.4128880552936287, -0.29999999999999993, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6659010047449661, -0.29999999999999993, 0.30000000000000004, + 1.3962634015954636 }, + { 1.9260216862473254, -0.29999999999999993, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler064 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.40000000000000002. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.3983279132797385e-16 +// mean(f - f_Boost): 1.1657341758564144e-16 +// variance(f - f_Boost): 1.8245832308692586e-31 +// stddev(f - f_Boost): 4.2715140534349863e-16 +const testcase_ellint_3<double> +data065[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17532259000954434, -0.29999999999999993, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35540612770983693, -0.29999999999999993, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54510265552938919, -0.29999999999999993, 0.40000000000000002, + 0.52359877559829882 }, + { 0.74932476310965057, -0.29999999999999993, 0.40000000000000002, + 0.69813170079773179 }, + { 0.97272793583093109, -0.29999999999999993, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2188928987074241, -0.29999999999999993, 0.40000000000000002, + 1.0471975511965976 }, + { 1.4888771674085941, -0.29999999999999993, 0.40000000000000002, + 1.2217304763960306 }, + { 1.7794558498219191, -0.29999999999999993, 0.40000000000000002, + 1.3962634015954636 }, + { 2.0822121773175528, -0.29999999999999993, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler065 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.50000000000000000. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.0516138451673425e-16 +// mean(f - f_Boost): 4.7184478546569152e-17 +// variance(f - f_Boost): 1.9448563670505968e-32 +// stddev(f - f_Boost): 1.3945810722401896e-16 +const testcase_ellint_3<double> +data066[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17550179513158179, -0.29999999999999993, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35688783251681200, -0.29999999999999993, 0.50000000000000000, + 0.34906585039886590 }, + { 0.55037700010142798, -0.29999999999999993, 0.50000000000000000, + 0.52359877559829882 }, + { 0.76273839789895992, -0.29999999999999993, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0011570518830419, -0.29999999999999993, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2722987414055109, -0.29999999999999993, 0.50000000000000000, + 1.0471975511965976 }, + { 1.5799590511080066, -0.29999999999999993, 0.50000000000000000, + 1.2217304763960306 }, + { 1.9212367220124293, -0.29999999999999993, 0.50000000000000000, + 1.3962634015954636 }, + { 2.2833505881933971, -0.29999999999999993, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler066 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.60000000000000009. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.2121157428443725e-16 +// mean(f - f_Boost): 1.9428902930940239e-16 +// variance(f - f_Boost): 1.5987596229703424e-31 +// stddev(f - f_Boost): 3.9984492281012430e-16 +const testcase_ellint_3<double> +data067[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17568166052076745, -0.29999999999999993, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35839189074731181, -0.29999999999999993, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55583724744367558, -0.29999999999999993, 0.60000000000000009, + 0.52359877559829882 }, + { 0.77703498090888223, -0.29999999999999993, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0326772113675962, -0.29999999999999993, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3345139983717369, -0.29999999999999993, 0.60000000000000009, + 1.0471975511965976 }, + { 1.6921742922838403, -0.29999999999999993, 0.60000000000000009, + 1.2217304763960306 }, + { 2.1056608968472186, -0.29999999999999993, 0.60000000000000009, + 1.3962634015954636 }, + { 2.5560975528589061, -0.29999999999999993, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler067 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.70000000000000007. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.0088945789059381e-16 +// mean(f - f_Boost): 1.6653345369377348e-16 +// variance(f - f_Boost): 3.1994213989721786e-31 +// stddev(f - f_Boost): 5.6563428104846852e-16 +const testcase_ellint_3<double> +data068[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17586219053197988, -0.29999999999999993, 0.70000000000000007, + 0.17453292519943295 }, + { 0.35991891074557669, -0.29999999999999993, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56149538019961731, -0.29999999999999993, 0.70000000000000007, + 0.52359877559829882 }, + { 0.79232303189667685, -0.29999999999999993, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0679345542878826, -0.29999999999999993, 0.70000000000000007, + 0.87266462599716477 }, + { 1.4084400085913955, -0.29999999999999993, 0.70000000000000007, + 1.0471975511965976 }, + { 1.8357382859296454, -0.29999999999999993, 0.70000000000000007, + 1.2217304763960306 }, + { 2.3604197996171519, -0.29999999999999993, 0.70000000000000007, + 1.3962634015954636 }, + { 2.9562123549913872, -0.29999999999999993, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler068 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.80000000000000004. +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.1197887707781618e-16 +// mean(f - f_Boost): 3.4416913763379854e-16 +// variance(f - f_Boost): 4.3461914185990199e-31 +// stddev(f - f_Boost): 6.5925650687718054e-16 +const testcase_ellint_3<double> +data069[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17604338956191670, -0.29999999999999993, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36146952517410791, -0.29999999999999993, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56736453393774644, -0.29999999999999993, 0.80000000000000004, + 0.52359877559829882 }, + { 0.80873149979001091, -0.29999999999999993, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1077903069860620, -0.29999999999999993, 0.80000000000000004, + 0.87266462599716477 }, + { 1.4985874311132998, -0.29999999999999993, 0.80000000000000004, + 1.0471975511965976 }, + { 2.0298167266724954, -0.29999999999999993, 0.80000000000000004, + 1.2217304763960306 }, + { 2.7483929054985432, -0.29999999999999993, 0.80000000000000004, + 1.3962634015954636 }, + { 3.6283050484567170, -0.29999999999999993, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler069 = 2.5000000000000020e-13; + +// Test data for k=-0.29999999999999993, nu=0.90000000000000002. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 5.1301806687926828e-16 +// mean(f - f_Boost): 4.1633363423443370e-16 +// variance(f - f_Boost): 2.2835347143080263e-31 +// stddev(f - f_Boost): 4.7786344433405093e-16 +const testcase_ellint_3<double> +data070[10] = +{ + { 0.0000000000000000, -0.29999999999999993, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17622526204962433, -0.29999999999999993, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36304439230777141, -0.29999999999999993, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57345914744719195, -0.29999999999999993, 0.90000000000000002, + 0.52359877559829882 }, + { 0.82641512928845162, -0.29999999999999993, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1534256210757743, -0.29999999999999993, 0.90000000000000002, + 0.87266462599716477 }, + { 1.6124900353411677, -0.29999999999999993, 0.90000000000000002, + 1.0471975511965976 }, + { 2.3165905514845089, -0.29999999999999993, 0.90000000000000002, + 1.2217304763960306 }, + { 3.4625619526539824, -0.29999999999999993, 0.90000000000000002, + 1.3962634015954636 }, + { 5.1479514944016787, -0.29999999999999993, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler070 = 2.5000000000000020e-13; // Test data for k=-0.19999999999999996, nu=0.0000000000000000. -testcase_ellint_3<double> data071[] = { - { -0.0000000000000000, -0.19999999999999996, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17456817290292811, -0.19999999999999996, 0.0000000000000000, - 0.17453292519943295 }, - { 0.34934315932086801, -0.19999999999999996, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52450880529443988, -0.19999999999999996, 0.0000000000000000, - 0.52359877559829882 }, - { 0.70020491009844910, -0.19999999999999996, 0.0000000000000000, - 0.69813170079773179 }, - { 0.87651006649967955, -0.19999999999999996, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0534305870298994, -0.19999999999999996, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2308975521670784, -0.19999999999999996, 0.0000000000000000, - 1.2217304763960306 }, - { 1.4087733584990738, -0.19999999999999996, 0.0000000000000000, - 1.3962634015954636 }, - { 1.5868678474541664, -0.19999999999999996, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.0000000000000000. -template <typename Tp> -void test071() -{ - 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(data071) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data071[i].k), Tp(data071[i].nu), - Tp(data071[i].phi)); - const Tp f0 = data071[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 4.2156475739151676e-16 +// mean(f - f_Boost): -5.2735593669694933e-17 +// variance(f - f_Boost): 3.0473442641042680e-32 +// stddev(f - f_Boost): 1.7456644190978597e-16 +const testcase_ellint_3<double> +data071[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17456817290292806, -0.19999999999999996, 0.0000000000000000, + 0.17453292519943295 }, + { 0.34934315932086796, -0.19999999999999996, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52450880529443988, -0.19999999999999996, 0.0000000000000000, + 0.52359877559829882 }, + { 0.70020491009844887, -0.19999999999999996, 0.0000000000000000, + 0.69813170079773179 }, + { 0.87651006649967977, -0.19999999999999996, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0534305870298994, -0.19999999999999996, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2308975521670789, -0.19999999999999996, 0.0000000000000000, + 1.2217304763960306 }, + { 1.4087733584990738, -0.19999999999999996, 0.0000000000000000, + 1.3962634015954636 }, + { 1.5868678474541662, -0.19999999999999996, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler071 = 2.5000000000000020e-13; // Test data for k=-0.19999999999999996, nu=0.10000000000000001. -testcase_ellint_3<double> data072[] = { - { -0.0000000000000000, -0.19999999999999996, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17439228502691750, -0.19999999999999996, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34796731137565740, -0.19999999999999996, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52003370294544848, -0.19999999999999996, 0.10000000000000001, - 0.52359877559829882 }, - { 0.69012222258631495, -0.19999999999999996, 0.10000000000000001, - 0.69813170079773179 }, - { 0.85803491465566772, -0.19999999999999996, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0238463961099364, -0.19999999999999996, 0.10000000000000001, - 1.0471975511965976 }, - { 1.1878691059202153, -0.19999999999999996, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3505985031831940, -0.19999999999999996, 0.10000000000000001, - 1.3962634015954636 }, - { 1.5126513474261092, -0.19999999999999996, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.10000000000000001. -template <typename Tp> -void test072() -{ - 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(data072) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data072[i].k), Tp(data072[i].nu), - Tp(data072[i].phi)); - const Tp f0 = data072[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 4.0890622182605400e-16 +// mean(f - f_Boost): -3.8857805861880476e-17 +// variance(f - f_Boost): 2.8794792590749608e-32 +// stddev(f - f_Boost): 1.6969028431454054e-16 +const testcase_ellint_3<double> +data072[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17474469953608965, -0.19999999999999996, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35073860234984255, -0.19999999999999996, 0.10000000000000001, + 0.34906585039886590 }, + { 0.52912258712951521, -0.19999999999999996, 0.10000000000000001, + 0.52359877559829882 }, + { 0.71081701558898069, -0.19999999999999996, 0.10000000000000001, + 0.69813170079773179 }, + { 0.89640758521169384, -0.19999999999999996, 0.10000000000000001, + 0.87266462599716477 }, + { 1.0860417038089853, -0.19999999999999996, 0.10000000000000001, + 1.0471975511965976 }, + { 1.2793599255528623, -0.19999999999999996, 0.10000000000000001, + 1.2217304763960306 }, + { 1.4754938544089076, -0.19999999999999996, 0.10000000000000001, + 1.3962634015954636 }, + { 1.6731552050562593, -0.19999999999999996, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler072 = 2.5000000000000020e-13; // Test data for k=-0.19999999999999996, nu=0.20000000000000001. -testcase_ellint_3<double> data073[] = { - { -0.0000000000000000, -0.19999999999999996, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17421703179583750, -0.19999999999999996, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34661057411998791, -0.19999999999999996, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51569006052647393, -0.19999999999999996, 0.20000000000000001, - 0.52359877559829882 }, - { 0.68052412821107278, -0.19999999999999996, 0.20000000000000001, - 0.69813170079773179 }, - { 0.84081341263313825, -0.19999999999999996, 0.20000000000000001, - 0.87266462599716477 }, - { 0.99683359988842890, -0.19999999999999996, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1493086715118852, -0.19999999999999996, 0.20000000000000001, - 1.2217304763960306 }, - { 1.2992699693957541, -0.19999999999999996, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4479323932249568, -0.19999999999999996, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.20000000000000001. -template <typename Tp> -void test073() -{ - 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(data073) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data073[i].k), Tp(data073[i].nu), - Tp(data073[i].phi)); - const Tp f0 = data073[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, nu=0.29999999999999999. -testcase_ellint_3<double> data074[] = { - { -0.0000000000000000, -0.19999999999999996, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17404240913577707, -0.19999999999999996, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34527248032587193, -0.19999999999999996, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51147118981668416, -0.19999999999999996, 0.29999999999999999, - 0.52359877559829882 }, - { 0.67137107867777635, -0.19999999999999996, 0.29999999999999999, - 0.69813170079773179 }, - { 0.82470418188668893, -0.19999999999999996, 0.29999999999999999, - 0.87266462599716477 }, - { 0.97202873223594299, -0.19999999999999996, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1144773569375266, -0.19999999999999996, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2535292433701000, -0.19999999999999996, 0.29999999999999999, - 1.3962634015954636 }, - { 1.3908453514752481, -0.19999999999999996, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.29999999999999999. -template <typename Tp> -void test074() -{ - 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(data074) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data074[i].k), Tp(data074[i].nu), - Tp(data074[i].phi)); - const Tp f0 = data074[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 3.9570963716579749e-16 +// mean(f - f_Boost): -5.8286708792820721e-17 +// variance(f - f_Boost): 3.1158217732380362e-32 +// stddev(f - f_Boost): 1.7651690494788412e-16 +const testcase_ellint_3<double> +data073[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17492186907740698, -0.19999999999999996, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35215414286134267, -0.19999999999999996, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53388285615182440, -0.19999999999999996, 0.20000000000000001, + 0.52359877559829882 }, + { 0.72200960282688265, -0.19999999999999996, 0.20000000000000001, + 0.69813170079773179 }, + { 0.91793087614428526, -0.19999999999999996, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1222602841587976, -0.19999999999999996, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3345489407496247, -0.19999999999999996, 0.20000000000000001, + 1.2217304763960306 }, + { 1.5531225705475502, -0.19999999999999996, 0.20000000000000001, + 1.3962634015954636 }, + { 1.7751816279738935, -0.19999999999999996, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler073 = 2.5000000000000020e-13; + +// Test data for k=-0.19999999999999996, nu=0.30000000000000004. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.6785817924053817e-16 +// mean(f - f_Boost): -1.1102230246251566e-17 +// variance(f - f_Boost): 9.9840208317034302e-32 +// stddev(f - f_Boost): 3.1597501217190311e-16 +const testcase_ellint_3<double> +data074[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17509968571715159, -0.19999999999999996, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35359030214835629, -0.19999999999999996, 0.30000000000000004, + 0.34906585039886590 }, + { 0.53879807274537084, -0.19999999999999996, 0.30000000000000004, + 0.52359877559829882 }, + { 0.73384116418059731, -0.19999999999999996, 0.30000000000000004, + 0.69813170079773179 }, + { 0.94132799329524031, -0.19999999999999996, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1628407021801439, -0.19999999999999996, 0.30000000000000004, + 1.0471975511965976 }, + { 1.3982440216739438, -0.19999999999999996, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6450634983653640, -0.19999999999999996, 0.30000000000000004, + 1.3962634015954636 }, + { 1.8983924169967099, -0.19999999999999996, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler074 = 2.5000000000000020e-13; // Test data for k=-0.19999999999999996, nu=0.40000000000000002. -testcase_ellint_3<double> data075[] = { - { -0.0000000000000000, -0.19999999999999996, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17386841301066677, -0.19999999999999996, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34395257914113253, -0.19999999999999996, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50737088376869466, -0.19999999999999996, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66262801717277664, -0.19999999999999996, 0.40000000000000002, - 0.69813170079773179 }, - { 0.80958766645079094, -0.19999999999999996, 0.40000000000000002, - 0.87266462599716477 }, - { 0.94913754236162040, -0.19999999999999996, 0.40000000000000002, - 1.0471975511965976 }, - { 1.0827985514223000, -0.19999999999999996, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2124212429050478, -0.19999999999999996, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3400002519661010, -0.19999999999999996, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.40000000000000002. -template <typename Tp> -void test075() -{ - 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(data075) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data075[i].k), Tp(data075[i].nu), - Tp(data075[i].phi)); - const Tp f0 = data075[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.3298410018355870e-16 +// mean(f - f_Boost): 1.3877787807814457e-17 +// variance(f - f_Boost): 9.4370567274974557e-32 +// stddev(f - f_Boost): 3.0719792850046133e-16 +const testcase_ellint_3<double> +data075[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17527815368535152, -0.19999999999999996, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35504762134297801, -0.19999999999999996, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54387742353211344, -0.19999999999999996, 0.40000000000000002, + 0.52359877559829882 }, + { 0.74637910471804259, -0.19999999999999996, 0.40000000000000002, + 0.69813170079773179 }, + { 0.96690539714174639, -0.19999999999999996, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2087859420184757, -0.19999999999999996, 0.40000000000000002, + 1.0471975511965976 }, + { 1.4729799844168852, -0.19999999999999996, 0.40000000000000002, + 1.2217304763960306 }, + { 1.7564445064596661, -0.19999999999999996, 0.40000000000000002, + 1.3962634015954636 }, + { 2.0512956926676802, -0.19999999999999996, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler075 = 2.5000000000000020e-13; // Test data for k=-0.19999999999999996, nu=0.50000000000000000. -testcase_ellint_3<double> data076[] = { - { -0.0000000000000000, -0.19999999999999996, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17369503942181802, -0.19999999999999996, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34265043534362660, -0.19999999999999996, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50338337208655415, -0.19999999999999996, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65426373297163642, -0.19999999999999996, 0.50000000000000000, - 0.69813170079773179 }, - { 0.79536193036145808, -0.19999999999999996, 0.50000000000000000, - 0.87266462599716477 }, - { 0.92791875910061605, -0.19999999999999996, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0538145052725829, -0.19999999999999996, 0.50000000000000000, - 1.2217304763960306 }, - { 1.1752060022875899, -0.19999999999999996, 0.50000000000000000, - 1.3962634015954636 }, - { 1.2943374404397376, -0.19999999999999996, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.50000000000000000. -template <typename Tp> -void test076() -{ - 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(data076) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data076[i].k), Tp(data076[i].nu), - Tp(data076[i].phi)); - const Tp f0 = data076[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, nu=0.59999999999999998. -testcase_ellint_3<double> data077[] = { - { -0.0000000000000000, -0.19999999999999996, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17352228440746928, -0.19999999999999996, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34136562863713626, -0.19999999999999996, 0.59999999999999998, - 0.34906585039886590 }, - { 0.49950328177638481, -0.19999999999999996, 0.59999999999999998, - 0.52359877559829882 }, - { 0.64625032705690832, -0.19999999999999996, 0.59999999999999998, - 0.69813170079773179 }, - { 0.78193941198403094, -0.19999999999999996, 0.59999999999999998, - 0.87266462599716477 }, - { 0.90817230934317128, -0.19999999999999996, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0271563751276462, -0.19999999999999996, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1412999379040518, -0.19999999999999996, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2530330675914561, -0.19999999999999996, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.59999999999999998. -template <typename Tp> -void test077() -{ - 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(data077) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data077[i].k), Tp(data077[i].nu), - Tp(data077[i].phi)); - const Tp f0 = data077[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, nu=0.69999999999999996. -testcase_ellint_3<double> data078[] = { - { -0.0000000000000000, -0.19999999999999996, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17335014404233898, -0.19999999999999996, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34009775298617811, -0.19999999999999996, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49572560201923810, -0.19999999999999996, 0.69999999999999996, - 0.52359877559829882 }, - { 0.63856276669886525, -0.19999999999999996, 0.69999999999999996, - 0.69813170079773179 }, - { 0.76924438644867565, -0.19999999999999996, 0.69999999999999996, - 0.87266462599716477 }, - { 0.88973060843856466, -0.19999999999999996, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0025230471636377, -0.19999999999999996, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1102356376093103, -0.19999999999999996, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2154356555075867, -0.19999999999999996, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.69999999999999996. -template <typename Tp> -void test078() -{ - 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(data078) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data078[i].k), Tp(data078[i].nu), - Tp(data078[i].phi)); - const Tp f0 = data078[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.3841806057292116e-16 +// mean(f - f_Boost): 8.0491169285323847e-17 +// variance(f - f_Boost): 8.0538110429953348e-32 +// stddev(f - f_Boost): 2.8379237204328335e-16 +const testcase_ellint_3<double> +data076[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17545727725228877, -0.19999999999999996, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35652666242062175, -0.19999999999999996, 0.50000000000000000, + 0.34906585039886590 }, + { 0.54913090549102406, -0.19999999999999996, 0.50000000000000000, + 0.52359877559829882 }, + { 0.75970161209211551, -0.19999999999999996, 0.50000000000000000, + 0.69813170079773179 }, + { 0.99504737401590326, -0.19999999999999996, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2614666007124373, -0.19999999999999996, 0.50000000000000000, + 1.0471975511965976 }, + { 1.5625255355205496, -0.19999999999999996, 0.50000000000000000, + 1.2217304763960306 }, + { 1.8954460255613343, -0.19999999999999996, 0.50000000000000000, + 1.3962634015954636 }, + { 2.2481046259421302, -0.19999999999999996, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler076 = 2.5000000000000020e-13; + +// Test data for k=-0.19999999999999996, nu=0.60000000000000009. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.5317584994994743e-16 +// mean(f - f_Boost): -1.3877787807814457e-17 +// variance(f - f_Boost): 1.0045745697575397e-31 +// stddev(f - f_Boost): 3.1695024369095219e-16 +const testcase_ellint_3<double> +data077[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17563706072900442, -0.19999999999999996, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35802800926807238, -0.19999999999999996, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55456942250515051, -0.19999999999999996, 0.60000000000000009, + 0.52359877559829882 }, + { 0.77390003828438203, -0.19999999999999996, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0262441366366397, -0.19999999999999996, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3228192988439669, -0.19999999999999996, 0.60000000000000009, + 1.0471975511965976 }, + { 1.6728005754680795, -0.19999999999999996, 0.60000000000000009, + 1.2217304763960306 }, + { 2.0761587107468511, -0.19999999999999996, 0.60000000000000009, + 1.3962634015954636 }, + { 2.5148333891629315, -0.19999999999999996, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler077 = 2.5000000000000020e-13; + +// Test data for k=-0.19999999999999996, nu=0.70000000000000007. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.1818454249546518e-16 +// mean(f - f_Boost): 3.6082248300317589e-17 +// variance(f - f_Boost): 8.9638010532618564e-32 +// stddev(f - f_Boost): 2.9939607634806868e-16 +const testcase_ellint_3<double> +data078[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17581750846781172, -0.19999999999999996, 0.70000000000000007, + 0.17453292519943295 }, + { 0.35955226882028513, -0.19999999999999996, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56020489659466499, -0.19999999999999996, 0.70000000000000007, + 0.52359877559829882 }, + { 0.78908196988531487, -0.19999999999999996, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0611336754143517, -0.19999999999999996, 0.70000000000000007, + 0.87266462599716477 }, + { 1.3956969951058884, -0.19999999999999996, 0.70000000000000007, + 1.0471975511965976 }, + { 1.8138131612209609, -0.19999999999999996, 0.70000000000000007, + 1.2217304763960306 }, + { 2.3256365528879561, -0.19999999999999996, 0.70000000000000007, + 1.3962634015954636 }, + { 2.9058704854500963, -0.19999999999999996, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler078 = 2.5000000000000020e-13; // Test data for k=-0.19999999999999996, nu=0.80000000000000004. -testcase_ellint_3<double> data079[] = { - { -0.0000000000000000, -0.19999999999999996, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17317861443718541, -0.19999999999999996, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33884641598718701, -0.19999999999999996, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49204565281259494, -0.19999999999999996, 0.80000000000000004, - 0.52359877559829882 }, - { 0.63117851188220353, -0.19999999999999996, 0.80000000000000004, - 0.69813170079773179 }, - { 0.75721095949544170, -0.19999999999999996, 0.80000000000000004, - 0.87266462599716477 }, - { 0.87245201443919118, -0.19999999999999996, 0.80000000000000004, - 1.0471975511965976 }, - { 0.97966584238831089, -0.19999999999999996, 0.80000000000000004, - 1.2217304763960306 }, - { 1.0816336325174360, -0.19999999999999996, 0.80000000000000004, - 1.3962634015954636 }, - { 1.1810223448909913, -0.19999999999999996, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.80000000000000004. -template <typename Tp> -void test079() -{ - 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(data079) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data079[i].k), Tp(data079[i].nu), - Tp(data079[i].phi)); - const Tp f0 = data079[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.9866614515542431e-16 +// mean(f - f_Boost): 1.8318679906315082e-16 +// variance(f - f_Boost): 3.1335688610218711e-31 +// stddev(f - f_Boost): 5.5978289193417400e-16 +const testcase_ellint_3<double> +data079[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17599862486281712, -0.19999999999999996, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36110007227128776, -0.19999999999999996, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56605039658567224, -0.19999999999999996, 0.80000000000000004, + 0.52359877559829882 }, + { 0.80537523874517691, -0.19999999999999996, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1005662342414086, -0.19999999999999996, 0.80000000000000004, + 0.87266462599716477 }, + { 1.4845340298105778, -0.19999999999999996, 0.80000000000000004, + 1.0471975511965976 }, + { 2.0043332244969392, -0.19999999999999996, 0.80000000000000004, + 1.2217304763960306 }, + { 2.7052856676744761, -0.19999999999999996, 0.80000000000000004, + 1.3962634015954636 }, + { 3.5622166386422629, -0.19999999999999996, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler079 = 2.5000000000000020e-13; // Test data for k=-0.19999999999999996, nu=0.90000000000000002. -testcase_ellint_3<double> data080[] = { - { -0.0000000000000000, -0.19999999999999996, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17300769173837280, -0.19999999999999996, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33761123827372508, -0.19999999999999996, 0.90000000000000002, - 0.34906585039886590 }, - { 0.48845905690769426, -0.19999999999999996, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62407720017324986, -0.19999999999999996, 0.90000000000000002, - 0.69813170079773179 }, - { 0.74578146525124289, -0.19999999999999996, 0.90000000000000002, - 0.87266462599716477 }, - { 0.85621583540073076, -0.19999999999999996, 0.90000000000000002, - 1.0471975511965976 }, - { 0.95837725988001199, -0.19999999999999996, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0551821412633928, -0.19999999999999996, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1493679916141863, -0.19999999999999996, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.19999999999999996, nu=0.90000000000000002. -template <typename Tp> -void test080() -{ - 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(data080) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data080[i].k), Tp(data080[i].nu), - Tp(data080[i].phi)); - const Tp f0 = data080[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)); -} +// max(|f - f_Boost|): 2.6645352591003757e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.2817178727913890e-16 +// mean(f - f_Boost): 3.4694469519536142e-16 +// variance(f - f_Boost): 6.6311432369155086e-31 +// stddev(f - f_Boost): 8.1431831840598485e-16 +const testcase_ellint_3<double> +data080[10] = +{ + { 0.0000000000000000, -0.19999999999999996, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17618041435044951, -0.19999999999999996, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36267207636502929, -0.19999999999999996, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57212028758237743, -0.19999999999999996, 0.90000000000000002, + 0.52359877559829882 }, + { 0.82293323876704483, -0.19999999999999996, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1457077279880385, -0.19999999999999996, 0.90000000000000002, + 0.87266462599716477 }, + { 1.5967346899325681, -0.19999999999999996, 0.90000000000000002, + 1.0471975511965976 }, + { 2.2856537353421724, -0.19999999999999996, 0.90000000000000002, + 1.2217304763960306 }, + { 3.4034714304613902, -0.19999999999999996, 0.90000000000000002, + 1.3962634015954636 }, + { 5.0448269356200361, -0.19999999999999996, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler080 = 2.5000000000000020e-13; // Test data for k=-0.099999999999999978, nu=0.0000000000000000. -testcase_ellint_3<double> data081[] = { - { -0.0000000000000000, -0.099999999999999978, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17454173353063665, -0.099999999999999978, 0.0000000000000000, - 0.17453292519943295 }, - { 0.34913506721468085, -0.099999999999999978, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52382550016538953, -0.099999999999999978, 0.0000000000000000, - 0.52359877559829882 }, - { 0.69864700854177031, -0.099999999999999978, 0.0000000000000000, - 0.69813170079773179 }, - { 0.87361792586964870, -0.099999999999999978, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0487386319621685, -0.099999999999999978, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2239913752078757, -0.099999999999999978, 0.0000000000000000, - 1.2217304763960306 }, - { 1.3993423113684049, -0.099999999999999978, 0.0000000000000000, - 1.3962634015954636 }, - { 1.5747455615173562, -0.099999999999999978, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.0000000000000000. -template <typename Tp> -void test081() -{ - 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(data081) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data081[i].k), Tp(data081[i].nu), - Tp(data081[i].phi)); - const Tp f0 = data081[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.1735566504509645e-16 +// mean(f - f_Boost): -3.6082248300317589e-17 +// variance(f - f_Boost): 8.2258607846939269e-33 +// stddev(f - f_Boost): 9.0696531271564778e-17 +const testcase_ellint_3<double> +data081[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17454173353063662, -0.099999999999999978, 0.0000000000000000, + 0.17453292519943295 }, + { 0.34913506721468096, -0.099999999999999978, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52382550016538953, -0.099999999999999978, 0.0000000000000000, + 0.52359877559829882 }, + { 0.69864700854177020, -0.099999999999999978, 0.0000000000000000, + 0.69813170079773179 }, + { 0.87361792586964859, -0.099999999999999978, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0487386319621685, -0.099999999999999978, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2239913752078759, -0.099999999999999978, 0.0000000000000000, + 1.2217304763960306 }, + { 1.3993423113684051, -0.099999999999999978, 0.0000000000000000, + 1.3962634015954636 }, + { 1.5747455615173558, -0.099999999999999978, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler081 = 2.5000000000000020e-13; // Test data for k=-0.099999999999999978, nu=0.10000000000000001. -testcase_ellint_3<double> data082[] = { - { -0.0000000000000000, -0.099999999999999978, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17436589347616618, -0.099999999999999978, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34776067871237354, -0.099999999999999978, 0.10000000000000001, - 0.34906585039886590 }, - { 0.51936064354727807, -0.099999999999999978, 0.10000000000000001, - 0.52359877559829882 }, - { 0.68860303749364360, -0.099999999999999978, 0.10000000000000001, - 0.69813170079773179 }, - { 0.85524561882332051, -0.099999999999999978, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0193708301908337, -0.099999999999999978, 0.10000000000000001, - 1.0471975511965976 }, - { 1.1813474067123044, -0.099999999999999978, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3417670770424983, -0.099999999999999978, 0.10000000000000001, - 1.3962634015954636 }, - { 1.5013711111199950, -0.099999999999999978, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.10000000000000001. -template <typename Tp> -void test082() -{ - 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(data082) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data082[i].k), Tp(data082[i].nu), - Tp(data082[i].phi)); - const Tp f0 = data082[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.0305747373482148e-16 +// mean(f - f_Boost): -3.0531133177191807e-17 +// variance(f - f_Boost): 1.1508025840536076e-34 +// stddev(f - f_Boost): 1.0727546709539920e-17 +const testcase_ellint_3<double> +data082[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17471821213559732, -0.099999999999999978, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35052902610011138, -0.099999999999999978, 0.10000000000000001, + 0.34906585039886590 }, + { 0.52842865990255727, -0.099999999999999978, 0.10000000000000001, + 0.52359877559829882 }, + { 0.70921799731166713, -0.099999999999999978, 0.10000000000000001, + 0.69813170079773179 }, + { 0.89340330535868662, -0.099999999999999978, 0.10000000000000001, + 0.87266462599716477 }, + { 1.0811075784236857, -0.099999999999999978, 0.10000000000000001, + 1.0471975511965976 }, + { 1.2720133232666426, -0.099999999999999978, 0.10000000000000001, + 1.2217304763960306 }, + { 1.4653630031861395, -0.099999999999999978, 0.10000000000000001, + 1.3962634015954636 }, + { 1.6600374067558428, -0.099999999999999978, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler082 = 2.5000000000000020e-13; // Test data for k=-0.099999999999999978, nu=0.20000000000000001. -testcase_ellint_3<double> data083[] = { - { -0.0000000000000000, -0.099999999999999978, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17419068786141345, -0.099999999999999978, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34640537686230127, -0.099999999999999978, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51502689171753957, -0.099999999999999978, 0.20000000000000001, - 0.52359877559829882 }, - { 0.67904147863672726, -0.099999999999999978, 0.20000000000000001, - 0.69813170079773179 }, - { 0.83811885126105179, -0.099999999999999978, 0.20000000000000001, - 0.87266462599716477 }, - { 0.99255278555742810, -0.099999999999999978, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1431260546194930, -0.099999999999999978, 0.20000000000000001, - 1.2217304763960306 }, - { 1.2909589656532101, -0.099999999999999978, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4373749386463430, -0.099999999999999978, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.20000000000000001. -template <typename Tp> -void test083() -{ - 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(data083) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data083[i].k), Tp(data083[i].nu), - Tp(data083[i].phi)); - const Tp f0 = data083[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, nu=0.29999999999999999. -testcase_ellint_3<double> data084[] = { - { -0.0000000000000000, -0.099999999999999978, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17401611261390110, -0.099999999999999978, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34506869507511767, -0.099999999999999978, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51081757604259870, -0.099999999999999978, 0.29999999999999999, - 0.52359877559829882 }, - { 0.66992297597712303, -0.099999999999999978, 0.29999999999999999, - 0.69813170079773179 }, - { 0.82209722856174228, -0.099999999999999978, 0.29999999999999999, - 0.87266462599716477 }, - { 0.96792430487669612, -0.099999999999999978, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1085964108954092, -0.099999999999999978, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2456748370836999, -0.099999999999999978, 0.29999999999999999, - 1.3962634015954636 }, - { 1.3809159606704959, -0.099999999999999978, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.29999999999999999. -template <typename Tp> -void test084() -{ - 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(data084) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data084[i].k), Tp(data084[i].nu), - Tp(data084[i].phi)); - const Tp f0 = data084[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 1.6736714959992433e-16 +// mean(f - f_Boost): 5.5511151231257830e-18 +// variance(f - f_Boost): 3.8043060629871325e-36 +// stddev(f - f_Boost): 1.9504630380981673e-18 +const testcase_ellint_3<double> +data083[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17489533344059083, -0.099999999999999978, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35194305707815038, -0.099999999999999978, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53317790741512527, -0.099999999999999978, 0.20000000000000001, + 0.52359877559829882 }, + { 0.72036681615081222, -0.099999999999999978, 0.20000000000000001, + 0.69813170079773179 }, + { 0.91480372268244303, -0.099999999999999978, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1170528708071514, -0.099999999999999978, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3266916802718358, -0.099999999999999978, 0.20000000000000001, + 1.2217304763960306 }, + { 1.5421622241831547, -0.099999999999999978, 0.20000000000000001, + 1.3962634015954636 }, + { 1.7608656115083421, -0.099999999999999978, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler083 = 2.5000000000000020e-13; + +// Test data for k=-0.099999999999999978, nu=0.30000000000000004. +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 1.9186071760326645e-16 +// mean(f - f_Boost): -1.6653345369377347e-17 +// variance(f - f_Boost): 3.4238754566884194e-35 +// stddev(f - f_Boost): 5.8513891142945016e-18 +const testcase_ellint_3<double> +data084[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17507310163441189, -0.099999999999999978, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35337768072524217, -0.099999999999999978, 0.30000000000000004, + 0.34906585039886590 }, + { 0.53808167801629170, -0.099999999999999978, 0.30000000000000004, + 0.52359877559829882 }, + { 0.73215166755955019, -0.099999999999999978, 0.30000000000000004, + 0.69813170079773179 }, + { 0.93806546000201219, -0.099999999999999978, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1573218723395986, -0.099999999999999978, 0.30000000000000004, + 1.0471975511965976 }, + { 1.3897859679542097, -0.099999999999999978, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6331009404328622, -0.099999999999999978, 0.30000000000000004, + 1.3962634015954636 }, + { 1.8826015946315438, -0.099999999999999978, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler084 = 2.5000000000000020e-13; // Test data for k=-0.099999999999999978, nu=0.40000000000000002. -testcase_ellint_3<double> data085[] = { - { -0.0000000000000000, -0.099999999999999978, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17384216369897937, -0.099999999999999978, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34375018311376782, -0.099999999999999978, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50672650758380455, -0.099999999999999978, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66121264213337616, -0.099999999999999978, 0.40000000000000002, - 0.69813170079773179 }, - { 0.80706202005774441, -0.099999999999999978, 0.40000000000000002, - 0.87266462599716477 }, - { 0.94519376138245892, -0.099999999999999978, 0.40000000000000002, - 1.0471975511965976 }, - { 1.0771880300759584, -0.099999999999999978, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2049711557188272, -0.099999999999999978, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3306223265207477, -0.099999999999999978, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.40000000000000002. -template <typename Tp> -void test085() -{ - 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(data085) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data085[i].k), Tp(data085[i].nu), - Tp(data085[i].phi)); - const Tp f0 = data085[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.0338059536914377e-16 +// mean(f - f_Boost): 2.7755575615628914e-17 +// variance(f - f_Boost): 9.5107651574678308e-35 +// stddev(f - f_Boost): 9.7523151904908362e-18 +const testcase_ellint_3<double> +data085[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17525152094559704, -0.099999999999999978, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35483343742825979, -0.099999999999999978, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54314913099505446, -0.099999999999999978, 0.40000000000000002, + 0.52359877559829882 }, + { 0.74463962034766862, -0.099999999999999978, 0.40000000000000002, + 0.69813170079773179 }, + { 0.96349276837570441, -0.099999999999999978, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2029081382746343, -0.099999999999999978, 0.40000000000000002, + 1.0471975511965976 }, + { 1.4638022887050806, -0.099999999999999978, 0.40000000000000002, + 1.2217304763960306 }, + { 1.7432413830105224, -0.099999999999999978, 0.40000000000000002, + 1.3962634015954636 }, + { 2.0336367403076760, -0.099999999999999978, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler085 = 2.5000000000000020e-13; // Test data for k=-0.099999999999999978, nu=0.50000000000000000. -testcase_ellint_3<double> data086[] = { - { -0.0000000000000000, -0.099999999999999978, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17366883711936554, -0.099999999999999978, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34244940634881876, -0.099999999999999978, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50274793281634378, -0.099999999999999978, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65287941633275093, -0.099999999999999978, 0.50000000000000000, - 0.69813170079773179 }, - { 0.79291198790315398, -0.099999999999999978, 0.50000000000000000, - 0.87266462599716477 }, - { 0.92412201537880345, -0.099999999999999978, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0484480076799370, -0.099999999999999978, 0.50000000000000000, - 1.2217304763960306 }, - { 1.1681168130475206, -0.099999999999999978, 0.50000000000000000, - 1.3962634015954636 }, - { 1.2854480708580160, -0.099999999999999978, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.50000000000000000. -template <typename Tp> -void test086() -{ - 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(data086) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data086[i].k), Tp(data086[i].nu), - Tp(data086[i].phi)); - const Tp f0 = data086[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, nu=0.59999999999999998. -testcase_ellint_3<double> data087[] = { - { -0.0000000000000000, -0.099999999999999978, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17349612891469018, -0.099999999999999978, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34116594505539438, -0.099999999999999978, 0.59999999999999998, - 0.34906585039886590 }, - { 0.49887649430466685, -0.099999999999999978, 0.59999999999999998, - 0.52359877559829882 }, - { 0.64489553282165157, -0.099999999999999978, 0.59999999999999998, - 0.69813170079773179 }, - { 0.77956016553782437, -0.099999999999999978, 0.59999999999999998, - 0.87266462599716477 }, - { 0.90451074530096309, -0.099999999999999978, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0220113666961632, -0.099999999999999978, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1345351441065563, -0.099999999999999978, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2445798942989255, -0.099999999999999978, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.59999999999999998. -template <typename Tp> -void test087() -{ - 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(data087) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data087[i].k), Tp(data087[i].nu), - Tp(data087[i].phi)); - const Tp f0 = data087[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, nu=0.69999999999999996. -testcase_ellint_3<double> data088[] = { - { -0.0000000000000000, -0.099999999999999978, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17332403516105052, -0.099999999999999978, 0.69999999999999996, - 0.17453292519943295 }, - { 0.33989939374896877, -0.099999999999999978, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49510719568614081, -0.099999999999999978, 0.69999999999999996, - 0.52359877559829882 }, - { 0.63723607776354974, -0.099999999999999978, 0.69999999999999996, - 0.69813170079773179 }, - { 0.76693133887935327, -0.099999999999999978, 0.69999999999999996, - 0.87266462599716477 }, - { 0.88619382078823827, -0.099999999999999978, 0.69999999999999996, - 1.0471975511965976 }, - { 0.99758012018676490, -0.099999999999999978, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1037642270814410, -0.099999999999999978, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2073745911083187, -0.099999999999999978, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.69999999999999996. -template <typename Tp> -void test088() -{ - 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(data088) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data088[i].k), Tp(data088[i].nu), - Tp(data088[i].phi)); - const Tp f0 = data088[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.9864616042835278e-16 +// mean(f - f_Boost): 1.0547118733938987e-16 +// variance(f - f_Boost): 7.5633408838247182e-32 +// stddev(f - f_Boost): 2.7501528837184157e-16 +const testcase_ellint_3<double> +data086[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17543059564292182, -0.099999999999999978, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35631088838721664, -0.099999999999999978, 0.50000000000000000, + 0.34906585039886590 }, + { 0.54839023346436444, -0.099999999999999978, 0.50000000000000000, + 0.52359877559829882 }, + { 0.75790846946088830, -0.099999999999999978, 0.50000000000000000, + 0.69813170079773179 }, + { 0.99146713686720678, -0.099999999999999978, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2551692247937198, -0.099999999999999978, 0.50000000000000000, + 1.0471975511965976 }, + { 1.5524660788146873, -0.099999999999999978, 0.50000000000000000, + 1.2217304763960306 }, + { 1.8806578570830670, -0.099999999999999978, 0.50000000000000000, + 1.3962634015954636 }, + { 2.2279868912966849, -0.099999999999999978, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler086 = 2.5000000000000020e-13; + +// Test data for k=-0.099999999999999978, nu=0.60000000000000009. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.6726146516228014e-16 +// mean(f - f_Boost): -3.6082248300317589e-17 +// variance(f - f_Boost): 1.6073193116120635e-34 +// stddev(f - f_Boost): 1.2678009747638087e-17 +const testcase_ellint_3<double> +data087[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17561033003590576, -0.099999999999999978, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35781061668171932, -0.099999999999999978, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55381585659629196, -0.099999999999999978, 0.60000000000000009, + 0.52359877559829882 }, + { 0.77204910484575640, -0.099999999999999978, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0224751740393108, -0.099999999999999978, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3160230906351114, -0.099999999999999978, 0.60000000000000009, + 1.0471975511965976 }, + { 1.6616282844233206, -0.099999999999999978, 0.60000000000000009, + 1.2217304763960306 }, + { 2.0592555664850392, -0.099999999999999978, 0.60000000000000009, + 1.3962634015954636 }, + { 2.4913004919173822, -0.099999999999999978, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler087 = 2.5000000000000020e-13; + +// Test data for k=-0.099999999999999978, nu=0.70000000000000007. +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 5 +// max(|f - f_Boost| / |f_Boost|): 2.1004074871280821e-16 +// mean(f - f_Boost): 3.3306690738754695e-17 +// variance(f - f_Boost): 1.3695501826753678e-34 +// stddev(f - f_Boost): 1.1702778228589003e-17 +const testcase_ellint_3<double> +data088[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17579072847532518, -0.099999999999999978, 0.70000000000000007, + 0.17453292519943295 }, + { 0.35933322840606297, -0.099999999999999978, 0.70000000000000007, + 0.34906585039886590 }, + { 0.55943788649460324, -0.099999999999999978, 0.70000000000000007, + 0.52359877559829882 }, + { 0.78716856504031707, -0.099999999999999978, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0571501305617423, -0.099999999999999978, 0.70000000000000007, + 0.87266462599716477 }, + { 1.3882948301743525, -0.099999999999999978, 0.70000000000000007, + 1.0471975511965976 }, + { 1.8011785680114223, -0.099999999999999978, 0.70000000000000007, + 1.2217304763960306 }, + { 2.3057268183616464, -0.099999999999999978, 0.70000000000000007, + 1.3962634015954636 }, + { 2.8771910188009739, -0.099999999999999978, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler088 = 2.5000000000000020e-13; // Test data for k=-0.099999999999999978, nu=0.80000000000000004. -testcase_ellint_3<double> data089[] = { - { -0.0000000000000000, -0.099999999999999978, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17315255197057020, -0.099999999999999978, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33864936055747985, -0.099999999999999978, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49143537041117619, -0.099999999999999978, 0.80000000000000004, - 0.52359877559829882 }, - { 0.62987861760047492, -0.099999999999999978, 0.80000000000000004, - 0.69813170079773179 }, - { 0.75496005490917517, -0.099999999999999978, 0.80000000000000004, - 0.87266462599716477 }, - { 0.86903081862701903, -0.099999999999999978, 0.80000000000000004, - 1.0471975511965976 }, - { 0.97490814820725591, -0.099999999999999978, 0.80000000000000004, - 1.2217304763960306 }, - { 1.0754290107171083, -0.099999999999999978, 0.80000000000000004, - 1.3962634015954636 }, - { 1.1733158866987732, -0.099999999999999978, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.80000000000000004. -template <typename Tp> -void test089() -{ - 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(data089) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data089[i].k), Tp(data089[i].nu), - Tp(data089[i].phi)); - const Tp f0 = data089[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.3133043868392355e-16 +// mean(f - f_Boost): 1.8041124150158794e-16 +// variance(f - f_Boost): 6.1843750436434569e-32 +// stddev(f - f_Boost): 2.4868403735751633e-16 +const testcase_ellint_3<double> +data089[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17597179535373417, -0.099999999999999978, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36087935387831499, -0.099999999999999978, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56526935244526444, -0.099999999999999978, 0.80000000000000004, + 0.52359877559829882 }, + { 0.80339402590612397, -0.099999999999999978, 0.80000000000000004, + 0.69813170079773179 }, + { 1.0963358646374459, -0.099999999999999978, 0.80000000000000004, + 0.87266462599716477 }, + { 1.4763748483246868, -0.099999999999999978, 0.80000000000000004, + 1.0471975511965976 }, + { 1.9896610222794102, -0.099999999999999978, 0.80000000000000004, + 1.2217304763960306 }, + { 2.6806423920122024, -0.099999999999999978, 0.80000000000000004, + 1.3962634015954636 }, + { 3.5246199613295612, -0.099999999999999978, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler089 = 2.5000000000000020e-13; // Test data for k=-0.099999999999999978, nu=0.90000000000000002. -testcase_ellint_3<double> data090[] = { - { -0.0000000000000000, -0.099999999999999978, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17298167549096569, -0.099999999999999978, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33741546662741584, -0.099999999999999978, 0.90000000000000002, - 0.34906585039886590 }, - { 0.48785665376856879, -0.099999999999999978, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62280288554518959, -0.099999999999999978, 0.90000000000000002, - 0.69813170079773179 }, - { 0.74358903115455199, -0.099999999999999978, 0.90000000000000002, - 0.87266462599716477 }, - { 0.85290207679298358, -0.099999999999999978, 0.90000000000000002, - 1.0471975511965976 }, - { 0.95379006645397379, -0.099999999999999978, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0492213119872327, -0.099999999999999978, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1419839485283374, -0.099999999999999978, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=-0.099999999999999978, nu=0.90000000000000002. -template <typename Tp> -void test090() -{ - 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(data090) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data090[i].k), Tp(data090[i].nu), - Tp(data090[i].phi)); - const Tp f0 = data090[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.5624826890976725e-16 +// mean(f - f_Boost): 2.3314683517128288e-16 +// variance(f - f_Boost): 2.9401198977189756e-31 +// stddev(f - f_Boost): 5.4222872459129045e-16 +const testcase_ellint_3<double> +data090[10] = +{ + { 0.0000000000000000, -0.099999999999999978, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17615353510599349, -0.099999999999999978, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36244964892922371, -0.099999999999999978, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57132457590110530, -0.099999999999999978, 0.90000000000000002, + 0.52359877559829882 }, + { 0.82087808820385000, -0.099999999999999978, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1411894342144451, -0.099999999999999978, 0.90000000000000002, + 0.87266462599716477 }, + { 1.5875929286844597, -0.099999999999999978, 0.90000000000000002, + 1.0471975511965976 }, + { 2.2678622986596659, -0.099999999999999978, 0.90000000000000002, + 1.2217304763960306 }, + { 3.3697528941897903, -0.099999999999999978, 0.90000000000000002, + 1.3962634015954636 }, + { 4.9862890417305499, -0.099999999999999978, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler090 = 2.5000000000000020e-13; // Test data for k=0.0000000000000000, nu=0.0000000000000000. -testcase_ellint_3<double> data091[] = { - { -0.0000000000000000, 0.0000000000000000, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17453292519943295, 0.0000000000000000, 0.0000000000000000, - 0.17453292519943295 }, - { 0.34906585039886584, 0.0000000000000000, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52359877559829882, 0.0000000000000000, 0.0000000000000000, - 0.52359877559829882 }, - { 0.69813170079773179, 0.0000000000000000, 0.0000000000000000, - 0.69813170079773179 }, - { 0.87266462599716477, 0.0000000000000000, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0471975511965976, 0.0000000000000000, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2217304763960304, 0.0000000000000000, 0.0000000000000000, - 1.2217304763960306 }, - { 1.3962634015954631, 0.0000000000000000, 0.0000000000000000, - 1.3962634015954636 }, - { 1.5707963267948966, 0.0000000000000000, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.0000000000000000. -template <typename Tp> -void test091() -{ - 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(data091) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data091[i].k), Tp(data091[i].nu), - Tp(data091[i].phi)); - const Tp f0 = data091[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.1203697876423447e-16 +// mean(f - f_Boost): -1.9428902930940238e-17 +// variance(f - f_Boost): 4.6602749271592373e-35 +// stddev(f - f_Boost): 6.8266206333435850e-18 +const testcase_ellint_3<double> +data091[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17453292519943295, 0.0000000000000000, 0.0000000000000000, + 0.17453292519943295 }, + { 0.34906585039886590, 0.0000000000000000, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52359877559829882, 0.0000000000000000, 0.0000000000000000, + 0.52359877559829882 }, + { 0.69813170079773179, 0.0000000000000000, 0.0000000000000000, + 0.69813170079773179 }, + { 0.87266462599716477, 0.0000000000000000, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0471975511965976, 0.0000000000000000, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2217304763960306, 0.0000000000000000, 0.0000000000000000, + 1.2217304763960306 }, + { 1.3962634015954636, 0.0000000000000000, 0.0000000000000000, + 1.3962634015954636 }, + { 1.5707963267948966, 0.0000000000000000, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler091 = 2.5000000000000020e-13; // Test data for k=0.0000000000000000, nu=0.10000000000000001. -testcase_ellint_3<double> data092[] = { - { -0.0000000000000000, 0.0000000000000000, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17435710107516608, 0.0000000000000000, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34769194715329604, 0.0000000000000000, 0.10000000000000001, - 0.34906585039886590 }, - { 0.51913731575866118, 0.0000000000000000, 0.10000000000000001, - 0.52359877559829882 }, - { 0.68810051897078461, 0.0000000000000000, 0.10000000000000001, - 0.69813170079773179 }, - { 0.85432615661706823, 0.0000000000000000, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0179006647340796, 0.0000000000000000, 0.10000000000000001, - 1.0471975511965976 }, - { 1.1792120640746322, 0.0000000000000000, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3388834245070498, 0.0000000000000000, 0.10000000000000001, - 1.3962634015954636 }, - { 1.4976955329233277, 0.0000000000000000, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.10000000000000001. -template <typename Tp> -void test092() -{ - 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(data092) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data092[i].k), Tp(data092[i].nu), - Tp(data092[i].phi)); - const Tp f0 = data092[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.1019052604815601e-16 +// mean(f - f_Boost): 2.7755575615628915e-18 +// variance(f - f_Boost): 9.5107651574678312e-37 +// stddev(f - f_Boost): 9.7523151904908366e-19 +const testcase_ellint_3<double> +data092[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17470938780535167, 0.0000000000000000, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35045931581655582, 0.0000000000000000, 0.10000000000000001, + 0.34906585039886590 }, + { 0.52819841383849875, 0.0000000000000000, 0.10000000000000001, + 0.52359877559829882 }, + { 0.70868910807992958, 0.0000000000000000, 0.10000000000000001, + 0.69813170079773179 }, + { 0.89241311307249638, 0.0000000000000000, 0.10000000000000001, + 0.87266462599716477 }, + { 1.0794871444666669, 0.0000000000000000, 0.10000000000000001, + 1.0471975511965976 }, + { 1.2696086247356864, 0.0000000000000000, 0.10000000000000001, + 1.2217304763960306 }, + { 1.4620562617494721, 0.0000000000000000, 0.10000000000000001, + 1.3962634015954636 }, + { 1.6557647109660167, 0.0000000000000000, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler092 = 2.5000000000000020e-13; // Test data for k=0.0000000000000000, nu=0.20000000000000001. -testcase_ellint_3<double> data093[] = { - { -0.0000000000000000, 0.0000000000000000, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17418191132226077, 0.0000000000000000, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34633712256943405, 0.0000000000000000, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51480684302043711, 0.0000000000000000, 0.20000000000000001, - 0.52359877559829882 }, - { 0.67855102942481949, 0.0000000000000000, 0.20000000000000001, - 0.69813170079773179 }, - { 0.83723056090326253, 0.0000000000000000, 0.20000000000000001, - 0.87266462599716477 }, - { 0.99114645269578183, 0.0000000000000000, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1411014627915537, 0.0000000000000000, 0.20000000000000001, - 1.2217304763960306 }, - { 1.2882448138013969, 0.0000000000000000, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4339343023863691, 0.0000000000000000, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.20000000000000001. -template <typename Tp> -void test093() -{ - 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(data093) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data093[i].k), Tp(data093[i].nu), - Tp(data093[i].phi)); - const Tp f0 = data093[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, nu=0.29999999999999999. -testcase_ellint_3<double> data094[] = { - { -0.0000000000000000, 0.0000000000000000, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17400735186871727, 0.0000000000000000, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34500091027020219, 0.0000000000000000, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51060069523901541, 0.0000000000000000, 0.29999999999999999, - 0.52359877559829882 }, - { 0.66944393961375459, 0.0000000000000000, 0.29999999999999999, - 0.69813170079773179 }, - { 0.82123776744538157, 0.0000000000000000, 0.29999999999999999, - 0.87266462599716477 }, - { 0.96657579245516523, 0.0000000000000000, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1066703663542414, 0.0000000000000000, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2431094251944901, 0.0000000000000000, 0.29999999999999999, - 1.3962634015954636 }, - { 1.3776795151134889, 0.0000000000000000, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.29999999999999999. -template <typename Tp> -void test094() -{ - 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(data094) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data094[i].k), Tp(data094[i].nu), - Tp(data094[i].phi)); - const Tp f0 = data094[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.0831888697465320e-16 +// mean(f - f_Boost): -1.9428902930940238e-17 +// variance(f - f_Boost): 4.6602749271592373e-35 +// stddev(f - f_Boost): 6.8266206333435850e-18 +const testcase_ellint_3<double> +data093[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17488649304197776, 0.0000000000000000, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35187284488675424, 0.0000000000000000, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53294400750146131, 0.0000000000000000, 0.20000000000000001, + 0.52359877559829882 }, + { 0.71982347021822823, 0.0000000000000000, 0.20000000000000001, + 0.69813170079773179 }, + { 0.91377311030258745, 0.0000000000000000, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1153429007215137, 0.0000000000000000, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3241202847784086, 0.0000000000000000, 0.20000000000000001, + 1.2217304763960306 }, + { 1.5385854914338242, 0.0000000000000000, 0.20000000000000001, + 1.3962634015954636 }, + { 1.7562036827601815, 0.0000000000000000, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler093 = 2.5000000000000020e-13; + +// Test data for k=0.0000000000000000, nu=0.30000000000000004. +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.0642101770923591e-16 +// mean(f - f_Boost): -1.9428902930940238e-17 +// variance(f - f_Boost): 4.6602749271592373e-35 +// stddev(f - f_Boost): 6.8266206333435850e-18 +const testcase_ellint_3<double> +data094[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17506424509761404, 0.0000000000000000, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35330695794774630, 0.0000000000000000, 0.30000000000000004, + 0.34906585039886590 }, + { 0.53784398359522367, 0.0000000000000000, 0.30000000000000004, + 0.52359877559829882 }, + { 0.73159289408687844, 0.0000000000000000, 0.30000000000000004, + 0.69813170079773179 }, + { 0.93699031797084975, 0.0000000000000000, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1555098909390267, 0.0000000000000000, 0.30000000000000004, + 1.0471975511965976 }, + { 1.3870184960144325, 0.0000000000000000, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6291980835772994, 0.0000000000000000, 0.30000000000000004, + 1.3962634015954636 }, + { 1.8774607092226381, 0.0000000000000000, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler094 = 2.5000000000000020e-13; // Test data for k=0.0000000000000000, nu=0.40000000000000002. -testcase_ellint_3<double> data095[] = { - { -0.0000000000000000, 0.0000000000000000, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17383341868035865, 0.0000000000000000, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34368286022299821, 0.0000000000000000, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50651268947499406, 0.0000000000000000, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66074441806097550, 0.0000000000000000, 0.40000000000000002, - 0.69813170079773179 }, - { 0.80622931670113485, 0.0000000000000000, 0.40000000000000002, - 0.87266462599716477 }, - { 0.94389791565435233, 0.0000000000000000, 0.40000000000000002, - 1.0471975511965976 }, - { 1.0753503387899728, 0.0000000000000000, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2025374759127518, 0.0000000000000000, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3275651989026322, 0.0000000000000000, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.40000000000000002. -template <typename Tp> -void test095() -{ - 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(data095) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data095[i].k), Tp(data095[i].nu), - Tp(data095[i].phi)); - const Tp f0 = data095[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.0449580089795878e-16 +// mean(f - f_Boost): -1.9428902930940238e-17 +// variance(f - f_Boost): 4.6602749271592373e-35 +// stddev(f - f_Boost): 6.8266206333435850e-18 +const testcase_ellint_3<double> +data095[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17524264820030025, 0.0000000000000000, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35476219513871499, 0.0000000000000000, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54290749235440094, 0.0000000000000000, 0.40000000000000002, + 0.52359877559829882 }, + { 0.74406433757109913, 0.0000000000000000, 0.40000000000000002, + 0.69813170079773179 }, + { 0.96236826162553313, 0.0000000000000000, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2009785880262487, 0.0000000000000000, 0.40000000000000002, + 1.0471975511965976 }, + { 1.4608000106167567, 0.0000000000000000, 0.40000000000000002, + 1.2217304763960306 }, + { 1.7389349574753439, 0.0000000000000000, 0.40000000000000002, + 1.3962634015954636 }, + { 2.0278893379868057, 0.0000000000000000, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler095 = 2.5000000000000020e-13; // Test data for k=0.0000000000000000, nu=0.50000000000000000. -testcase_ellint_3<double> data096[] = { - { -0.0000000000000000, 0.0000000000000000, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17366010776037047, 0.0000000000000000, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34238253799539309, 0.0000000000000000, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50253707775976408, 0.0000000000000000, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65242145347295766, 0.0000000000000000, 0.50000000000000000, - 0.69813170079773179 }, - { 0.79210420018698058, 0.0000000000000000, 0.50000000000000000, - 0.87266462599716477 }, - { 0.92287437995632193, 0.0000000000000000, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0466900550798661, 0.0000000000000000, 0.50000000000000000, - 1.2217304763960306 }, - { 1.1658007366618623, 0.0000000000000000, 0.50000000000000000, - 1.3962634015954636 }, - { 1.2825498301618641, 0.0000000000000000, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.50000000000000000. -template <typename Tp> -void test096() -{ - 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(data096) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data096[i].k), Tp(data096[i].nu), - Tp(data096[i].phi)); - const Tp f0 = data096[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, nu=0.59999999999999998. -testcase_ellint_3<double> data097[] = { - { -0.0000000000000000, 0.0000000000000000, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17348741514884702, 0.0000000000000000, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34109952405241289, 0.0000000000000000, 0.59999999999999998, - 0.34906585039886590 }, - { 0.49866850781226296, 0.0000000000000000, 0.59999999999999998, - 0.52359877559829882 }, - { 0.64444732407062510, 0.0000000000000000, 0.59999999999999998, - 0.69813170079773179 }, - { 0.77877564686544720, 0.0000000000000000, 0.59999999999999998, - 0.87266462599716477 }, - { 0.90330743691883497, 0.0000000000000000, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0203257987604104, 0.0000000000000000, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1323247918768631, 0.0000000000000000, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2418235332245127, 0.0000000000000000, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.59999999999999998. -template <typename Tp> -void test097() -{ - 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(data097) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data097[i].k), Tp(data097[i].nu), - Tp(data097[i].phi)); - const Tp f0 = data097[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, nu=0.69999999999999996. -testcase_ellint_3<double> data098[] = { - { -0.0000000000000000, 0.0000000000000000, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17331533692234477, 0.0000000000000000, 0.69999999999999996, - 0.17453292519943295 }, - { 0.33983341309265941, 0.0000000000000000, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49490198805931990, 0.0000000000000000, 0.69999999999999996, - 0.52359877559829882 }, - { 0.63679715525145308, 0.0000000000000000, 0.69999999999999996, - 0.69813170079773179 }, - { 0.76616861049481944, 0.0000000000000000, 0.69999999999999996, - 0.87266462599716477 }, - { 0.88503143209004220, 0.0000000000000000, 0.69999999999999996, - 1.0471975511965976 }, - { 0.99596060249112173, 0.0000000000000000, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1016495050260424, 0.0000000000000000, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2047457872617382, 0.0000000000000000, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.69999999999999996. -template <typename Tp> -void test098() -{ - 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(data098) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data098[i].k), Tp(data098[i].nu), - Tp(data098[i].phi)); - const Tp f0 = data098[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.0254203825026289e-16 +// mean(f - f_Boost): -1.9428902930940238e-17 +// variance(f - f_Boost): 4.6602749271592373e-35 +// stddev(f - f_Boost): 6.8266206333435850e-18 +const testcase_ellint_3<double> +data096[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17542170661831016, 0.0000000000000000, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35623911740195419, 0.0000000000000000, 0.50000000000000000, + 0.34906585039886590 }, + { 0.54814449099863127, 0.0000000000000000, 0.50000000000000000, + 0.52359877559829882 }, + { 0.75731546607718081, 0.0000000000000000, 0.50000000000000000, + 0.69813170079773179 }, + { 0.99028751188233310, 0.0000000000000000, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2531022857760581, 0.0000000000000000, 0.50000000000000000, + 1.0471975511965976 }, + { 1.5491761777615785, 0.0000000000000000, 0.50000000000000000, + 1.2217304763960306 }, + { 1.8758359693666533, 0.0000000000000000, 0.50000000000000000, + 1.3962634015954636 }, + { 2.2214414690791831, 0.0000000000000000, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler096 = 2.5000000000000020e-13; + +// Test data for k=0.0000000000000000, nu=0.60000000000000009. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 2.1742785192400269e-16 +// mean(f - f_Boost): 1.3877787807814457e-17 +// variance(f - f_Boost): 2.3776912893669577e-35 +// stddev(f - f_Boost): 4.8761575952454181e-18 +const testcase_ellint_3<double> +data097[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17560142466065651, 0.0000000000000000, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35773830754879005, 0.0000000000000000, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55356583986445973, 0.0000000000000000, 0.60000000000000009, + 0.52359877559829882 }, + { 0.77143701715151514, 0.0000000000000000, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0212334940541210, 0.0000000000000000, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3137928444460387, 0.0000000000000000, 0.60000000000000009, + 1.0471975511965976 }, + { 1.6579755004159076, 0.0000000000000000, 0.60000000000000009, + 1.2217304763960306 }, + { 2.0537461418295506, 0.0000000000000000, 0.60000000000000009, + 1.3962634015954636 }, + { 2.4836470664490253, 0.0000000000000000, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler097 = 2.5000000000000020e-13; + +// Test data for k=0.0000000000000000, nu=0.70000000000000007. +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 4 +// max(|f - f_Boost| / |f_Boost|): 3.0903019454022601e-16 +// mean(f - f_Boost): -6.9388939039072284e-17 +// variance(f - f_Boost): 5.9442282234173945e-34 +// stddev(f - f_Boost): 2.4380787976227090e-17 +const testcase_ellint_3<double> +data098[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17578180667760368, 0.0000000000000000, 0.70000000000000007, + 0.17453292519943295 }, + { 0.35926037139410999, 0.0000000000000000, 0.70000000000000007, + 0.34906585039886590 }, + { 0.55918341315855080, 0.0000000000000000, 0.70000000000000007, + 0.52359877559829882 }, + { 0.78653584856932546, 0.0000000000000000, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0558379029273324, 0.0000000000000000, 0.70000000000000007, + 0.87266462599716477 }, + { 1.3858662544850615, 0.0000000000000000, 0.70000000000000007, + 1.0471975511965976 }, + { 1.7970491170359040, 0.0000000000000000, 0.70000000000000007, + 1.2217304763960306 }, + { 2.2992404490153917, 0.0000000000000000, 0.70000000000000007, + 1.3962634015954636 }, + { 2.8678686047727382, 0.0000000000000000, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler098 = 2.5000000000000020e-13; // Test data for k=0.0000000000000000, nu=0.80000000000000004. -testcase_ellint_3<double> data099[] = { - { -0.0000000000000000, 0.0000000000000000, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17314386919344213, 0.0000000000000000, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33858381342073240, 0.0000000000000000, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49123285640844738, 0.0000000000000000, 0.80000000000000004, - 0.52359877559829882 }, - { 0.62944854858904520, 0.0000000000000000, 0.80000000000000004, - 0.69813170079773179 }, - { 0.75421778305499343, 0.0000000000000000, 0.80000000000000004, - 0.87266462599716477 }, - { 0.86790634112156639, 0.0000000000000000, 0.80000000000000004, - 1.0471975511965976 }, - { 0.97334918087427558, 0.0000000000000000, 0.80000000000000004, - 1.2217304763960306 }, - { 1.0734012615283985, 0.0000000000000000, 0.80000000000000004, - 1.3962634015954636 }, - { 1.1708024551734544, 0.0000000000000000, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.80000000000000004. -template <typename Tp> -void test099() -{ - 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(data099) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data099[i].k), Tp(data099[i].nu), - Tp(data099[i].phi)); - const Tp f0 = data099[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.2373744057922657e-16 +// mean(f - f_Boost): 1.0269562977782698e-16 +// variance(f - f_Boost): 1.4388836606733082e-32 +// stddev(f - f_Boost): 1.1995347684303728e-16 +const testcase_ellint_3<double> +data099[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17596285706118869, 0.0000000000000000, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36080593896484231, 0.0000000000000000, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56501022706967863, 0.0000000000000000, 0.80000000000000004, + 0.52359877559829882 }, + { 0.80273891984116930, 0.0000000000000000, 0.80000000000000004, + 0.69813170079773179 }, + { 1.0949425007763358, 0.0000000000000000, 0.80000000000000004, + 0.87266462599716477 }, + { 1.4736985692253419, 0.0000000000000000, 0.80000000000000004, + 1.0471975511965976 }, + { 1.9848676587180696, 0.0000000000000000, 0.80000000000000004, + 1.2217304763960306 }, + { 2.6726187823193546, 0.0000000000000000, 0.80000000000000004, + 1.3962634015954636 }, + { 3.5124073655203634, 0.0000000000000000, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler099 = 2.5000000000000020e-13; // Test data for k=0.0000000000000000, nu=0.90000000000000002. -testcase_ellint_3<double> data100[] = { - { -0.0000000000000000, 0.0000000000000000, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17297300811030600, 0.0000000000000000, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33735034635360817, 0.0000000000000000, 0.90000000000000002, - 0.34906585039886590 }, - { 0.48765675230233141, 0.0000000000000000, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62238126886123568, 0.0000000000000000, 0.90000000000000002, - 0.69813170079773179 }, - { 0.74286600807269243, 0.0000000000000000, 0.90000000000000002, - 0.87266462599716477 }, - { 0.85181283909264971, 0.0000000000000000, 0.90000000000000002, - 1.0471975511965976 }, - { 0.95228683995371122, 0.0000000000000000, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0472730487412552, 0.0000000000000000, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1395754288497419, 0.0000000000000000, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.0000000000000000, nu=0.90000000000000002. -template <typename Tp> -void test100() -{ - 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(data100) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data100[i].k), Tp(data100[i].nu), - Tp(data100[i].phi)); - const Tp f0 = data100[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 6.6108624815885066e-16 +// mean(f - f_Boost): 2.1371793224034264e-16 +// variance(f - f_Boost): 5.6389326618626776e-33 +// stddev(f - f_Boost): 7.5092826966779442e-17 +const testcase_ellint_3<double> +data100[10] = +{ + { 0.0000000000000000, 0.0000000000000000, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17614458024574997, 0.0000000000000000, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36237566578821978, 0.0000000000000000, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57106058859196640, 0.0000000000000000, 0.90000000000000002, + 0.52359877559829882 }, + { 0.82019857015755915, 0.0000000000000000, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1397014388908147, 0.0000000000000000, 0.90000000000000002, + 0.87266462599716477 }, + { 1.5845952415154960, 0.0000000000000000, 0.90000000000000002, + 1.0471975511965976 }, + { 2.2620531413370775, 0.0000000000000000, 0.90000000000000002, + 1.2217304763960306 }, + { 3.3587842061975066, 0.0000000000000000, 0.90000000000000002, + 1.3962634015954636 }, + { 4.9672941328980507, 0.0000000000000000, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler100 = 2.5000000000000020e-13; // Test data for k=0.10000000000000009, nu=0.0000000000000000. -testcase_ellint_3<double> data101[] = { - { -0.0000000000000000, 0.10000000000000009, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17454173353063665, 0.10000000000000009, 0.0000000000000000, - 0.17453292519943295 }, - { 0.34913506721468085, 0.10000000000000009, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52382550016538953, 0.10000000000000009, 0.0000000000000000, - 0.52359877559829882 }, - { 0.69864700854177031, 0.10000000000000009, 0.0000000000000000, - 0.69813170079773179 }, - { 0.87361792586964870, 0.10000000000000009, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0487386319621685, 0.10000000000000009, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2239913752078757, 0.10000000000000009, 0.0000000000000000, - 1.2217304763960306 }, - { 1.3993423113684049, 0.10000000000000009, 0.0000000000000000, - 1.3962634015954636 }, - { 1.5747455615173562, 0.10000000000000009, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.0000000000000000. -template <typename Tp> -void test101() -{ - 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(data101) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data101[i].k), Tp(data101[i].nu), - Tp(data101[i].phi)); - const Tp f0 = data101[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.1735566504509645e-16 +// mean(f - f_Boost): -5.8286708792820721e-17 +// variance(f - f_Boost): 4.1942474344433133e-34 +// stddev(f - f_Boost): 2.0479861900030756e-17 +const testcase_ellint_3<double> +data101[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17454173353063662, 0.10000000000000009, 0.0000000000000000, + 0.17453292519943295 }, + { 0.34913506721468096, 0.10000000000000009, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52382550016538953, 0.10000000000000009, 0.0000000000000000, + 0.52359877559829882 }, + { 0.69864700854177020, 0.10000000000000009, 0.0000000000000000, + 0.69813170079773179 }, + { 0.87361792586964859, 0.10000000000000009, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0487386319621685, 0.10000000000000009, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2239913752078759, 0.10000000000000009, 0.0000000000000000, + 1.2217304763960306 }, + { 1.3993423113684051, 0.10000000000000009, 0.0000000000000000, + 1.3962634015954636 }, + { 1.5747455615173560, 0.10000000000000009, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler101 = 2.5000000000000020e-13; // Test data for k=0.10000000000000009, nu=0.10000000000000001. -testcase_ellint_3<double> data102[] = { - { -0.0000000000000000, 0.10000000000000009, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17436589347616618, 0.10000000000000009, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34776067871237354, 0.10000000000000009, 0.10000000000000001, - 0.34906585039886590 }, - { 0.51936064354727807, 0.10000000000000009, 0.10000000000000001, - 0.52359877559829882 }, - { 0.68860303749364360, 0.10000000000000009, 0.10000000000000001, - 0.69813170079773179 }, - { 0.85524561882332051, 0.10000000000000009, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0193708301908337, 0.10000000000000009, 0.10000000000000001, - 1.0471975511965976 }, - { 1.1813474067123044, 0.10000000000000009, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3417670770424983, 0.10000000000000009, 0.10000000000000001, - 1.3962634015954636 }, - { 1.5013711111199950, 0.10000000000000009, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.10000000000000001. -template <typename Tp> -void test102() -{ - 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(data102) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data102[i].k), Tp(data102[i].nu), - Tp(data102[i].phi)); - const Tp f0 = data102[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.0305747373482148e-16 +// mean(f - f_Boost): -3.0531133177191807e-17 +// variance(f - f_Boost): 1.1508025840536076e-34 +// stddev(f - f_Boost): 1.0727546709539920e-17 +const testcase_ellint_3<double> +data102[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17471821213559732, 0.10000000000000009, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35052902610011138, 0.10000000000000009, 0.10000000000000001, + 0.34906585039886590 }, + { 0.52842865990255727, 0.10000000000000009, 0.10000000000000001, + 0.52359877559829882 }, + { 0.70921799731166713, 0.10000000000000009, 0.10000000000000001, + 0.69813170079773179 }, + { 0.89340330535868662, 0.10000000000000009, 0.10000000000000001, + 0.87266462599716477 }, + { 1.0811075784236857, 0.10000000000000009, 0.10000000000000001, + 1.0471975511965976 }, + { 1.2720133232666426, 0.10000000000000009, 0.10000000000000001, + 1.2217304763960306 }, + { 1.4653630031861395, 0.10000000000000009, 0.10000000000000001, + 1.3962634015954636 }, + { 1.6600374067558428, 0.10000000000000009, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler102 = 2.5000000000000020e-13; // Test data for k=0.10000000000000009, nu=0.20000000000000001. -testcase_ellint_3<double> data103[] = { - { -0.0000000000000000, 0.10000000000000009, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17419068786141345, 0.10000000000000009, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34640537686230127, 0.10000000000000009, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51502689171753957, 0.10000000000000009, 0.20000000000000001, - 0.52359877559829882 }, - { 0.67904147863672726, 0.10000000000000009, 0.20000000000000001, - 0.69813170079773179 }, - { 0.83811885126105179, 0.10000000000000009, 0.20000000000000001, - 0.87266462599716477 }, - { 0.99255278555742810, 0.10000000000000009, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1431260546194930, 0.10000000000000009, 0.20000000000000001, - 1.2217304763960306 }, - { 1.2909589656532101, 0.10000000000000009, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4373749386463430, 0.10000000000000009, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.20000000000000001. -template <typename Tp> -void test103() -{ - 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(data103) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data103[i].k), Tp(data103[i].nu), - Tp(data103[i].phi)); - const Tp f0 = data103[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, nu=0.29999999999999999. -testcase_ellint_3<double> data104[] = { - { -0.0000000000000000, 0.10000000000000009, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17401611261390110, 0.10000000000000009, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34506869507511767, 0.10000000000000009, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51081757604259870, 0.10000000000000009, 0.29999999999999999, - 0.52359877559829882 }, - { 0.66992297597712303, 0.10000000000000009, 0.29999999999999999, - 0.69813170079773179 }, - { 0.82209722856174228, 0.10000000000000009, 0.29999999999999999, - 0.87266462599716477 }, - { 0.96792430487669612, 0.10000000000000009, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1085964108954092, 0.10000000000000009, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2456748370836999, 0.10000000000000009, 0.29999999999999999, - 1.3962634015954636 }, - { 1.3809159606704959, 0.10000000000000009, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.29999999999999999. -template <typename Tp> -void test104() -{ - 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(data104) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data104[i].k), Tp(data104[i].nu), - Tp(data104[i].phi)); - const Tp f0 = data104[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 1.6736714959992433e-16 +// mean(f - f_Boost): 5.5511151231257830e-18 +// variance(f - f_Boost): 3.8043060629871325e-36 +// stddev(f - f_Boost): 1.9504630380981673e-18 +const testcase_ellint_3<double> +data103[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17489533344059083, 0.10000000000000009, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35194305707815038, 0.10000000000000009, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53317790741512527, 0.10000000000000009, 0.20000000000000001, + 0.52359877559829882 }, + { 0.72036681615081222, 0.10000000000000009, 0.20000000000000001, + 0.69813170079773179 }, + { 0.91480372268244303, 0.10000000000000009, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1170528708071514, 0.10000000000000009, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3266916802718358, 0.10000000000000009, 0.20000000000000001, + 1.2217304763960306 }, + { 1.5421622241831547, 0.10000000000000009, 0.20000000000000001, + 1.3962634015954636 }, + { 1.7608656115083421, 0.10000000000000009, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler103 = 2.5000000000000020e-13; + +// Test data for k=0.10000000000000009, nu=0.30000000000000004. +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 1.9186071760326645e-16 +// mean(f - f_Boost): -1.6653345369377347e-17 +// variance(f - f_Boost): 3.4238754566884194e-35 +// stddev(f - f_Boost): 5.8513891142945016e-18 +const testcase_ellint_3<double> +data104[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17507310163441189, 0.10000000000000009, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35337768072524217, 0.10000000000000009, 0.30000000000000004, + 0.34906585039886590 }, + { 0.53808167801629170, 0.10000000000000009, 0.30000000000000004, + 0.52359877559829882 }, + { 0.73215166755955019, 0.10000000000000009, 0.30000000000000004, + 0.69813170079773179 }, + { 0.93806546000201219, 0.10000000000000009, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1573218723395986, 0.10000000000000009, 0.30000000000000004, + 1.0471975511965976 }, + { 1.3897859679542097, 0.10000000000000009, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6331009404328622, 0.10000000000000009, 0.30000000000000004, + 1.3962634015954636 }, + { 1.8826015946315438, 0.10000000000000009, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler104 = 2.5000000000000020e-13; // Test data for k=0.10000000000000009, nu=0.40000000000000002. -testcase_ellint_3<double> data105[] = { - { -0.0000000000000000, 0.10000000000000009, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17384216369897937, 0.10000000000000009, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34375018311376782, 0.10000000000000009, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50672650758380455, 0.10000000000000009, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66121264213337616, 0.10000000000000009, 0.40000000000000002, - 0.69813170079773179 }, - { 0.80706202005774441, 0.10000000000000009, 0.40000000000000002, - 0.87266462599716477 }, - { 0.94519376138245892, 0.10000000000000009, 0.40000000000000002, - 1.0471975511965976 }, - { 1.0771880300759584, 0.10000000000000009, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2049711557188272, 0.10000000000000009, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3306223265207477, 0.10000000000000009, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.40000000000000002. -template <typename Tp> -void test105() -{ - 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(data105) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data105[i].k), Tp(data105[i].nu), - Tp(data105[i].phi)); - const Tp f0 = data105[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.0338059536914377e-16 +// mean(f - f_Boost): 2.7755575615628914e-17 +// variance(f - f_Boost): 9.5107651574678308e-35 +// stddev(f - f_Boost): 9.7523151904908362e-18 +const testcase_ellint_3<double> +data105[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17525152094559704, 0.10000000000000009, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35483343742825979, 0.10000000000000009, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54314913099505446, 0.10000000000000009, 0.40000000000000002, + 0.52359877559829882 }, + { 0.74463962034766862, 0.10000000000000009, 0.40000000000000002, + 0.69813170079773179 }, + { 0.96349276837570441, 0.10000000000000009, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2029081382746343, 0.10000000000000009, 0.40000000000000002, + 1.0471975511965976 }, + { 1.4638022887050806, 0.10000000000000009, 0.40000000000000002, + 1.2217304763960306 }, + { 1.7432413830105224, 0.10000000000000009, 0.40000000000000002, + 1.3962634015954636 }, + { 2.0336367403076760, 0.10000000000000009, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler105 = 2.5000000000000020e-13; // Test data for k=0.10000000000000009, nu=0.50000000000000000. -testcase_ellint_3<double> data106[] = { - { -0.0000000000000000, 0.10000000000000009, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17366883711936554, 0.10000000000000009, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34244940634881876, 0.10000000000000009, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50274793281634378, 0.10000000000000009, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65287941633275093, 0.10000000000000009, 0.50000000000000000, - 0.69813170079773179 }, - { 0.79291198790315398, 0.10000000000000009, 0.50000000000000000, - 0.87266462599716477 }, - { 0.92412201537880345, 0.10000000000000009, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0484480076799370, 0.10000000000000009, 0.50000000000000000, - 1.2217304763960306 }, - { 1.1681168130475206, 0.10000000000000009, 0.50000000000000000, - 1.3962634015954636 }, - { 1.2854480708580160, 0.10000000000000009, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.50000000000000000. -template <typename Tp> -void test106() -{ - 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(data106) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data106[i].k), Tp(data106[i].nu), - Tp(data106[i].phi)); - const Tp f0 = data106[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, nu=0.59999999999999998. -testcase_ellint_3<double> data107[] = { - { -0.0000000000000000, 0.10000000000000009, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17349612891469018, 0.10000000000000009, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34116594505539438, 0.10000000000000009, 0.59999999999999998, - 0.34906585039886590 }, - { 0.49887649430466685, 0.10000000000000009, 0.59999999999999998, - 0.52359877559829882 }, - { 0.64489553282165157, 0.10000000000000009, 0.59999999999999998, - 0.69813170079773179 }, - { 0.77956016553782437, 0.10000000000000009, 0.59999999999999998, - 0.87266462599716477 }, - { 0.90451074530096309, 0.10000000000000009, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0220113666961632, 0.10000000000000009, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1345351441065563, 0.10000000000000009, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2445798942989255, 0.10000000000000009, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.59999999999999998. -template <typename Tp> -void test107() -{ - 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(data107) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data107[i].k), Tp(data107[i].nu), - Tp(data107[i].phi)); - const Tp f0 = data107[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, nu=0.69999999999999996. -testcase_ellint_3<double> data108[] = { - { -0.0000000000000000, 0.10000000000000009, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17332403516105052, 0.10000000000000009, 0.69999999999999996, - 0.17453292519943295 }, - { 0.33989939374896877, 0.10000000000000009, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49510719568614081, 0.10000000000000009, 0.69999999999999996, - 0.52359877559829882 }, - { 0.63723607776354974, 0.10000000000000009, 0.69999999999999996, - 0.69813170079773179 }, - { 0.76693133887935327, 0.10000000000000009, 0.69999999999999996, - 0.87266462599716477 }, - { 0.88619382078823827, 0.10000000000000009, 0.69999999999999996, - 1.0471975511965976 }, - { 0.99758012018676490, 0.10000000000000009, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1037642270814410, 0.10000000000000009, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2073745911083187, 0.10000000000000009, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.69999999999999996. -template <typename Tp> -void test108() -{ - 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(data108) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data108[i].k), Tp(data108[i].nu), - Tp(data108[i].phi)); - const Tp f0 = data108[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.9864616042835278e-16 +// mean(f - f_Boost): 9.4368957093138303e-17 +// variance(f - f_Boost): 7.7794254682023874e-32 +// stddev(f - f_Boost): 2.7891621444803792e-16 +const testcase_ellint_3<double> +data106[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17543059564292182, 0.10000000000000009, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35631088838721664, 0.10000000000000009, 0.50000000000000000, + 0.34906585039886590 }, + { 0.54839023346436455, 0.10000000000000009, 0.50000000000000000, + 0.52359877559829882 }, + { 0.75790846946088830, 0.10000000000000009, 0.50000000000000000, + 0.69813170079773179 }, + { 0.99146713686720678, 0.10000000000000009, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2551692247937198, 0.10000000000000009, 0.50000000000000000, + 1.0471975511965976 }, + { 1.5524660788146873, 0.10000000000000009, 0.50000000000000000, + 1.2217304763960306 }, + { 1.8806578570830670, 0.10000000000000009, 0.50000000000000000, + 1.3962634015954636 }, + { 2.2279868912966849, 0.10000000000000009, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler106 = 2.5000000000000020e-13; + +// Test data for k=0.10000000000000009, nu=0.60000000000000009. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.6726146516228014e-16 +// mean(f - f_Boost): -3.6082248300317589e-17 +// variance(f - f_Boost): 1.6073193116120635e-34 +// stddev(f - f_Boost): 1.2678009747638087e-17 +const testcase_ellint_3<double> +data107[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17561033003590576, 0.10000000000000009, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35781061668171932, 0.10000000000000009, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55381585659629196, 0.10000000000000009, 0.60000000000000009, + 0.52359877559829882 }, + { 0.77204910484575640, 0.10000000000000009, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0224751740393108, 0.10000000000000009, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3160230906351114, 0.10000000000000009, 0.60000000000000009, + 1.0471975511965976 }, + { 1.6616282844233206, 0.10000000000000009, 0.60000000000000009, + 1.2217304763960306 }, + { 2.0592555664850392, 0.10000000000000009, 0.60000000000000009, + 1.3962634015954636 }, + { 2.4913004919173822, 0.10000000000000009, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler107 = 2.5000000000000020e-13; + +// Test data for k=0.10000000000000009, nu=0.70000000000000007. +// max(|f - f_Boost|): 2.2204460492503131e-16 at index 5 +// max(|f - f_Boost| / |f_Boost|): 2.1004074871280821e-16 +// mean(f - f_Boost): 3.3306690738754695e-17 +// variance(f - f_Boost): 1.3695501826753678e-34 +// stddev(f - f_Boost): 1.1702778228589003e-17 +const testcase_ellint_3<double> +data108[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17579072847532518, 0.10000000000000009, 0.70000000000000007, + 0.17453292519943295 }, + { 0.35933322840606297, 0.10000000000000009, 0.70000000000000007, + 0.34906585039886590 }, + { 0.55943788649460324, 0.10000000000000009, 0.70000000000000007, + 0.52359877559829882 }, + { 0.78716856504031707, 0.10000000000000009, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0571501305617423, 0.10000000000000009, 0.70000000000000007, + 0.87266462599716477 }, + { 1.3882948301743525, 0.10000000000000009, 0.70000000000000007, + 1.0471975511965976 }, + { 1.8011785680114223, 0.10000000000000009, 0.70000000000000007, + 1.2217304763960306 }, + { 2.3057268183616464, 0.10000000000000009, 0.70000000000000007, + 1.3962634015954636 }, + { 2.8771910188009739, 0.10000000000000009, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler108 = 2.5000000000000020e-13; // Test data for k=0.10000000000000009, nu=0.80000000000000004. -testcase_ellint_3<double> data109[] = { - { -0.0000000000000000, 0.10000000000000009, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17315255197057020, 0.10000000000000009, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33864936055747985, 0.10000000000000009, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49143537041117619, 0.10000000000000009, 0.80000000000000004, - 0.52359877559829882 }, - { 0.62987861760047492, 0.10000000000000009, 0.80000000000000004, - 0.69813170079773179 }, - { 0.75496005490917517, 0.10000000000000009, 0.80000000000000004, - 0.87266462599716477 }, - { 0.86903081862701903, 0.10000000000000009, 0.80000000000000004, - 1.0471975511965976 }, - { 0.97490814820725591, 0.10000000000000009, 0.80000000000000004, - 1.2217304763960306 }, - { 1.0754290107171083, 0.10000000000000009, 0.80000000000000004, - 1.3962634015954636 }, - { 1.1733158866987732, 0.10000000000000009, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.80000000000000004. -template <typename Tp> -void test109() -{ - 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(data109) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data109[i].k), Tp(data109[i].nu), - Tp(data109[i].phi)); - const Tp f0 = data109[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.3133043868392355e-16 +// mean(f - f_Boost): 1.8041124150158794e-16 +// variance(f - f_Boost): 6.1843750436434569e-32 +// stddev(f - f_Boost): 2.4868403735751633e-16 +const testcase_ellint_3<double> +data109[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17597179535373417, 0.10000000000000009, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36087935387831499, 0.10000000000000009, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56526935244526444, 0.10000000000000009, 0.80000000000000004, + 0.52359877559829882 }, + { 0.80339402590612397, 0.10000000000000009, 0.80000000000000004, + 0.69813170079773179 }, + { 1.0963358646374459, 0.10000000000000009, 0.80000000000000004, + 0.87266462599716477 }, + { 1.4763748483246868, 0.10000000000000009, 0.80000000000000004, + 1.0471975511965976 }, + { 1.9896610222794102, 0.10000000000000009, 0.80000000000000004, + 1.2217304763960306 }, + { 2.6806423920122024, 0.10000000000000009, 0.80000000000000004, + 1.3962634015954636 }, + { 3.5246199613295612, 0.10000000000000009, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler109 = 2.5000000000000020e-13; // Test data for k=0.10000000000000009, nu=0.90000000000000002. -testcase_ellint_3<double> data110[] = { - { -0.0000000000000000, 0.10000000000000009, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17298167549096569, 0.10000000000000009, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33741546662741584, 0.10000000000000009, 0.90000000000000002, - 0.34906585039886590 }, - { 0.48785665376856879, 0.10000000000000009, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62280288554518959, 0.10000000000000009, 0.90000000000000002, - 0.69813170079773179 }, - { 0.74358903115455199, 0.10000000000000009, 0.90000000000000002, - 0.87266462599716477 }, - { 0.85290207679298358, 0.10000000000000009, 0.90000000000000002, - 1.0471975511965976 }, - { 0.95379006645397379, 0.10000000000000009, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0492213119872327, 0.10000000000000009, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1419839485283374, 0.10000000000000009, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.10000000000000009, nu=0.90000000000000002. -template <typename Tp> -void test110() -{ - 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(data110) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data110[i].k), Tp(data110[i].nu), - Tp(data110[i].phi)); - const Tp f0 = data110[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, nu=0.0000000000000000. -testcase_ellint_3<double> data111[] = { - { -0.0000000000000000, 0.19999999999999996, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17456817290292811, 0.19999999999999996, 0.0000000000000000, - 0.17453292519943295 }, - { 0.34934315932086801, 0.19999999999999996, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52450880529443988, 0.19999999999999996, 0.0000000000000000, - 0.52359877559829882 }, - { 0.70020491009844910, 0.19999999999999996, 0.0000000000000000, - 0.69813170079773179 }, - { 0.87651006649967955, 0.19999999999999996, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0534305870298994, 0.19999999999999996, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2308975521670784, 0.19999999999999996, 0.0000000000000000, - 1.2217304763960306 }, - { 1.4087733584990738, 0.19999999999999996, 0.0000000000000000, - 1.3962634015954636 }, - { 1.5868678474541664, 0.19999999999999996, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.0000000000000000. -template <typename Tp> -void test111() -{ - 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(data111) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data111[i].k), Tp(data111[i].nu), - Tp(data111[i].phi)); - const Tp f0 = data111[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, nu=0.10000000000000001. -testcase_ellint_3<double> data112[] = { - { -0.0000000000000000, 0.19999999999999996, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17439228502691750, 0.19999999999999996, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34796731137565740, 0.19999999999999996, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52003370294544848, 0.19999999999999996, 0.10000000000000001, - 0.52359877559829882 }, - { 0.69012222258631495, 0.19999999999999996, 0.10000000000000001, - 0.69813170079773179 }, - { 0.85803491465566772, 0.19999999999999996, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0238463961099364, 0.19999999999999996, 0.10000000000000001, - 1.0471975511965976 }, - { 1.1878691059202153, 0.19999999999999996, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3505985031831940, 0.19999999999999996, 0.10000000000000001, - 1.3962634015954636 }, - { 1.5126513474261092, 0.19999999999999996, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.10000000000000001. -template <typename Tp> -void test112() -{ - 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(data112) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data112[i].k), Tp(data112[i].nu), - Tp(data112[i].phi)); - const Tp f0 = data112[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, nu=0.20000000000000001. -testcase_ellint_3<double> data113[] = { - { -0.0000000000000000, 0.19999999999999996, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17421703179583750, 0.19999999999999996, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34661057411998791, 0.19999999999999996, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51569006052647393, 0.19999999999999996, 0.20000000000000001, - 0.52359877559829882 }, - { 0.68052412821107278, 0.19999999999999996, 0.20000000000000001, - 0.69813170079773179 }, - { 0.84081341263313825, 0.19999999999999996, 0.20000000000000001, - 0.87266462599716477 }, - { 0.99683359988842890, 0.19999999999999996, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1493086715118852, 0.19999999999999996, 0.20000000000000001, - 1.2217304763960306 }, - { 1.2992699693957541, 0.19999999999999996, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4479323932249568, 0.19999999999999996, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.20000000000000001. -template <typename Tp> -void test113() -{ - 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(data113) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data113[i].k), Tp(data113[i].nu), - Tp(data113[i].phi)); - const Tp f0 = data113[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, nu=0.29999999999999999. -testcase_ellint_3<double> data114[] = { - { -0.0000000000000000, 0.19999999999999996, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17404240913577707, 0.19999999999999996, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34527248032587193, 0.19999999999999996, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51147118981668416, 0.19999999999999996, 0.29999999999999999, - 0.52359877559829882 }, - { 0.67137107867777635, 0.19999999999999996, 0.29999999999999999, - 0.69813170079773179 }, - { 0.82470418188668893, 0.19999999999999996, 0.29999999999999999, - 0.87266462599716477 }, - { 0.97202873223594299, 0.19999999999999996, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1144773569375266, 0.19999999999999996, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2535292433701000, 0.19999999999999996, 0.29999999999999999, - 1.3962634015954636 }, - { 1.3908453514752481, 0.19999999999999996, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.29999999999999999. -template <typename Tp> -void test114() -{ - 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(data114) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data114[i].k), Tp(data114[i].nu), - Tp(data114[i].phi)); - const Tp f0 = data114[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, nu=0.40000000000000002. -testcase_ellint_3<double> data115[] = { - { -0.0000000000000000, 0.19999999999999996, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17386841301066677, 0.19999999999999996, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34395257914113253, 0.19999999999999996, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50737088376869466, 0.19999999999999996, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66262801717277664, 0.19999999999999996, 0.40000000000000002, - 0.69813170079773179 }, - { 0.80958766645079094, 0.19999999999999996, 0.40000000000000002, - 0.87266462599716477 }, - { 0.94913754236162040, 0.19999999999999996, 0.40000000000000002, - 1.0471975511965976 }, - { 1.0827985514223000, 0.19999999999999996, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2124212429050478, 0.19999999999999996, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3400002519661010, 0.19999999999999996, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.40000000000000002. -template <typename Tp> -void test115() -{ - 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(data115) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data115[i].k), Tp(data115[i].nu), - Tp(data115[i].phi)); - const Tp f0 = data115[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, nu=0.50000000000000000. -testcase_ellint_3<double> data116[] = { - { -0.0000000000000000, 0.19999999999999996, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17369503942181802, 0.19999999999999996, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34265043534362660, 0.19999999999999996, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50338337208655415, 0.19999999999999996, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65426373297163642, 0.19999999999999996, 0.50000000000000000, - 0.69813170079773179 }, - { 0.79536193036145808, 0.19999999999999996, 0.50000000000000000, - 0.87266462599716477 }, - { 0.92791875910061605, 0.19999999999999996, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0538145052725829, 0.19999999999999996, 0.50000000000000000, - 1.2217304763960306 }, - { 1.1752060022875899, 0.19999999999999996, 0.50000000000000000, - 1.3962634015954636 }, - { 1.2943374404397376, 0.19999999999999996, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.50000000000000000. -template <typename Tp> -void test116() -{ - 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(data116) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data116[i].k), Tp(data116[i].nu), - Tp(data116[i].phi)); - const Tp f0 = data116[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, nu=0.59999999999999998. -testcase_ellint_3<double> data117[] = { - { -0.0000000000000000, 0.19999999999999996, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17352228440746928, 0.19999999999999996, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34136562863713626, 0.19999999999999996, 0.59999999999999998, - 0.34906585039886590 }, - { 0.49950328177638481, 0.19999999999999996, 0.59999999999999998, - 0.52359877559829882 }, - { 0.64625032705690832, 0.19999999999999996, 0.59999999999999998, - 0.69813170079773179 }, - { 0.78193941198403094, 0.19999999999999996, 0.59999999999999998, - 0.87266462599716477 }, - { 0.90817230934317128, 0.19999999999999996, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0271563751276462, 0.19999999999999996, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1412999379040518, 0.19999999999999996, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2530330675914561, 0.19999999999999996, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.59999999999999998. -template <typename Tp> -void test117() -{ - 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(data117) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data117[i].k), Tp(data117[i].nu), - Tp(data117[i].phi)); - const Tp f0 = data117[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, nu=0.69999999999999996. -testcase_ellint_3<double> data118[] = { - { -0.0000000000000000, 0.19999999999999996, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17335014404233898, 0.19999999999999996, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34009775298617811, 0.19999999999999996, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49572560201923810, 0.19999999999999996, 0.69999999999999996, - 0.52359877559829882 }, - { 0.63856276669886525, 0.19999999999999996, 0.69999999999999996, - 0.69813170079773179 }, - { 0.76924438644867565, 0.19999999999999996, 0.69999999999999996, - 0.87266462599716477 }, - { 0.88973060843856466, 0.19999999999999996, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0025230471636377, 0.19999999999999996, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1102356376093103, 0.19999999999999996, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2154356555075867, 0.19999999999999996, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.69999999999999996. -template <typename Tp> -void test118() -{ - 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(data118) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data118[i].k), Tp(data118[i].nu), - Tp(data118[i].phi)); - const Tp f0 = data118[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, nu=0.80000000000000004. -testcase_ellint_3<double> data119[] = { - { -0.0000000000000000, 0.19999999999999996, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17317861443718541, 0.19999999999999996, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33884641598718701, 0.19999999999999996, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49204565281259494, 0.19999999999999996, 0.80000000000000004, - 0.52359877559829882 }, - { 0.63117851188220353, 0.19999999999999996, 0.80000000000000004, - 0.69813170079773179 }, - { 0.75721095949544170, 0.19999999999999996, 0.80000000000000004, - 0.87266462599716477 }, - { 0.87245201443919118, 0.19999999999999996, 0.80000000000000004, - 1.0471975511965976 }, - { 0.97966584238831089, 0.19999999999999996, 0.80000000000000004, - 1.2217304763960306 }, - { 1.0816336325174360, 0.19999999999999996, 0.80000000000000004, - 1.3962634015954636 }, - { 1.1810223448909913, 0.19999999999999996, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.80000000000000004. -template <typename Tp> -void test119() -{ - 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(data119) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data119[i].k), Tp(data119[i].nu), - Tp(data119[i].phi)); - const Tp f0 = data119[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, nu=0.90000000000000002. -testcase_ellint_3<double> data120[] = { - { -0.0000000000000000, 0.19999999999999996, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17300769173837280, 0.19999999999999996, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33761123827372508, 0.19999999999999996, 0.90000000000000002, - 0.34906585039886590 }, - { 0.48845905690769426, 0.19999999999999996, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62407720017324986, 0.19999999999999996, 0.90000000000000002, - 0.69813170079773179 }, - { 0.74578146525124289, 0.19999999999999996, 0.90000000000000002, - 0.87266462599716477 }, - { 0.85621583540073076, 0.19999999999999996, 0.90000000000000002, - 1.0471975511965976 }, - { 0.95837725988001199, 0.19999999999999996, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0551821412633928, 0.19999999999999996, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1493679916141863, 0.19999999999999996, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.19999999999999996, nu=0.90000000000000002. -template <typename Tp> -void test120() -{ - 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(data120) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data120[i].k), Tp(data120[i].nu), - Tp(data120[i].phi)); - const Tp f0 = data120[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.5624826890976725e-16 +// mean(f - f_Boost): 2.3314683517128288e-16 +// variance(f - f_Boost): 2.9401198977189756e-31 +// stddev(f - f_Boost): 5.4222872459129045e-16 +const testcase_ellint_3<double> +data110[10] = +{ + { 0.0000000000000000, 0.10000000000000009, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17615353510599349, 0.10000000000000009, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36244964892922371, 0.10000000000000009, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57132457590110530, 0.10000000000000009, 0.90000000000000002, + 0.52359877559829882 }, + { 0.82087808820385000, 0.10000000000000009, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1411894342144451, 0.10000000000000009, 0.90000000000000002, + 0.87266462599716477 }, + { 1.5875929286844597, 0.10000000000000009, 0.90000000000000002, + 1.0471975511965976 }, + { 2.2678622986596659, 0.10000000000000009, 0.90000000000000002, + 1.2217304763960306 }, + { 3.3697528941897903, 0.10000000000000009, 0.90000000000000002, + 1.3962634015954636 }, + { 4.9862890417305499, 0.10000000000000009, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler110 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.0000000000000000. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 4.2156475739151676e-16 +// mean(f - f_Boost): -5.2735593669694933e-17 +// variance(f - f_Boost): 3.0473442641042680e-32 +// stddev(f - f_Boost): 1.7456644190978597e-16 +const testcase_ellint_3<double> +data111[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17456817290292806, 0.20000000000000018, 0.0000000000000000, + 0.17453292519943295 }, + { 0.34934315932086796, 0.20000000000000018, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52450880529443988, 0.20000000000000018, 0.0000000000000000, + 0.52359877559829882 }, + { 0.70020491009844887, 0.20000000000000018, 0.0000000000000000, + 0.69813170079773179 }, + { 0.87651006649967977, 0.20000000000000018, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0534305870298994, 0.20000000000000018, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2308975521670789, 0.20000000000000018, 0.0000000000000000, + 1.2217304763960306 }, + { 1.4087733584990738, 0.20000000000000018, 0.0000000000000000, + 1.3962634015954636 }, + { 1.5868678474541662, 0.20000000000000018, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler111 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.10000000000000001. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 4.0890622182605400e-16 +// mean(f - f_Boost): -3.8857805861880476e-17 +// variance(f - f_Boost): 2.8794792590749608e-32 +// stddev(f - f_Boost): 1.6969028431454054e-16 +const testcase_ellint_3<double> +data112[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17474469953608965, 0.20000000000000018, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35073860234984255, 0.20000000000000018, 0.10000000000000001, + 0.34906585039886590 }, + { 0.52912258712951521, 0.20000000000000018, 0.10000000000000001, + 0.52359877559829882 }, + { 0.71081701558898069, 0.20000000000000018, 0.10000000000000001, + 0.69813170079773179 }, + { 0.89640758521169384, 0.20000000000000018, 0.10000000000000001, + 0.87266462599716477 }, + { 1.0860417038089853, 0.20000000000000018, 0.10000000000000001, + 1.0471975511965976 }, + { 1.2793599255528623, 0.20000000000000018, 0.10000000000000001, + 1.2217304763960306 }, + { 1.4754938544089076, 0.20000000000000018, 0.10000000000000001, + 1.3962634015954636 }, + { 1.6731552050562593, 0.20000000000000018, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler112 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.20000000000000001. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 3.9570963716579749e-16 +// mean(f - f_Boost): -5.8286708792820721e-17 +// variance(f - f_Boost): 3.1158217732380362e-32 +// stddev(f - f_Boost): 1.7651690494788412e-16 +const testcase_ellint_3<double> +data113[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17492186907740698, 0.20000000000000018, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35215414286134267, 0.20000000000000018, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53388285615182440, 0.20000000000000018, 0.20000000000000001, + 0.52359877559829882 }, + { 0.72200960282688265, 0.20000000000000018, 0.20000000000000001, + 0.69813170079773179 }, + { 0.91793087614428526, 0.20000000000000018, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1222602841587976, 0.20000000000000018, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3345489407496247, 0.20000000000000018, 0.20000000000000001, + 1.2217304763960306 }, + { 1.5531225705475502, 0.20000000000000018, 0.20000000000000001, + 1.3962634015954636 }, + { 1.7751816279738935, 0.20000000000000018, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler113 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.30000000000000004. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.6785817924053817e-16 +// mean(f - f_Boost): -1.1102230246251566e-17 +// variance(f - f_Boost): 9.9840208317034302e-32 +// stddev(f - f_Boost): 3.1597501217190311e-16 +const testcase_ellint_3<double> +data114[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17509968571715159, 0.20000000000000018, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35359030214835629, 0.20000000000000018, 0.30000000000000004, + 0.34906585039886590 }, + { 0.53879807274537084, 0.20000000000000018, 0.30000000000000004, + 0.52359877559829882 }, + { 0.73384116418059731, 0.20000000000000018, 0.30000000000000004, + 0.69813170079773179 }, + { 0.94132799329524031, 0.20000000000000018, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1628407021801439, 0.20000000000000018, 0.30000000000000004, + 1.0471975511965976 }, + { 1.3982440216739438, 0.20000000000000018, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6450634983653640, 0.20000000000000018, 0.30000000000000004, + 1.3962634015954636 }, + { 1.8983924169967099, 0.20000000000000018, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler114 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.40000000000000002. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 6 +// max(|f - f_Boost| / |f_Boost|): 3.6738449250038925e-16 +// mean(f - f_Boost): -3.0531133177191807e-17 +// variance(f - f_Boost): 2.7810428396951687e-32 +// stddev(f - f_Boost): 1.6676458975739331e-16 +const testcase_ellint_3<double> +data115[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17527815368535152, 0.20000000000000018, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35504762134297801, 0.20000000000000018, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54387742353211344, 0.20000000000000018, 0.40000000000000002, + 0.52359877559829882 }, + { 0.74637910471804259, 0.20000000000000018, 0.40000000000000002, + 0.69813170079773179 }, + { 0.96690539714174639, 0.20000000000000018, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2087859420184757, 0.20000000000000018, 0.40000000000000002, + 1.0471975511965976 }, + { 1.4729799844168852, 0.20000000000000018, 0.40000000000000002, + 1.2217304763960306 }, + { 1.7564445064596661, 0.20000000000000018, 0.40000000000000002, + 1.3962634015954636 }, + { 2.0512956926676806, 0.20000000000000018, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler115 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.50000000000000000. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.3841806057292116e-16 +// mean(f - f_Boost): 3.6082248300317589e-17 +// variance(f - f_Boost): 8.9638010532618564e-32 +// stddev(f - f_Boost): 2.9939607634806868e-16 +const testcase_ellint_3<double> +data116[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17545727725228877, 0.20000000000000018, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35652666242062175, 0.20000000000000018, 0.50000000000000000, + 0.34906585039886590 }, + { 0.54913090549102406, 0.20000000000000018, 0.50000000000000000, + 0.52359877559829882 }, + { 0.75970161209211551, 0.20000000000000018, 0.50000000000000000, + 0.69813170079773179 }, + { 0.99504737401590326, 0.20000000000000018, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2614666007124373, 0.20000000000000018, 0.50000000000000000, + 1.0471975511965976 }, + { 1.5625255355205498, 0.20000000000000018, 0.50000000000000000, + 1.2217304763960306 }, + { 1.8954460255613346, 0.20000000000000018, 0.50000000000000000, + 1.3962634015954636 }, + { 2.2481046259421302, 0.20000000000000018, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler116 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.60000000000000009. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.5317584994994743e-16 +// mean(f - f_Boost): -1.3877787807814457e-17 +// variance(f - f_Boost): 1.0045745697575397e-31 +// stddev(f - f_Boost): 3.1695024369095219e-16 +const testcase_ellint_3<double> +data117[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17563706072900442, 0.20000000000000018, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35802800926807238, 0.20000000000000018, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55456942250515051, 0.20000000000000018, 0.60000000000000009, + 0.52359877559829882 }, + { 0.77390003828438203, 0.20000000000000018, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0262441366366397, 0.20000000000000018, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3228192988439669, 0.20000000000000018, 0.60000000000000009, + 1.0471975511965976 }, + { 1.6728005754680795, 0.20000000000000018, 0.60000000000000009, + 1.2217304763960306 }, + { 2.0761587107468511, 0.20000000000000018, 0.60000000000000009, + 1.3962634015954636 }, + { 2.5148333891629315, 0.20000000000000018, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler117 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.70000000000000007. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.2209418045118284e-16 +// mean(f - f_Boost): 2.4980018054066023e-17 +// variance(f - f_Boost): 9.1989071679544611e-32 +// stddev(f - f_Boost): 3.0329700242426498e-16 +const testcase_ellint_3<double> +data118[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17581750846781172, 0.20000000000000018, 0.70000000000000007, + 0.17453292519943295 }, + { 0.35955226882028513, 0.20000000000000018, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56020489659466499, 0.20000000000000018, 0.70000000000000007, + 0.52359877559829882 }, + { 0.78908196988531498, 0.20000000000000018, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0611336754143517, 0.20000000000000018, 0.70000000000000007, + 0.87266462599716477 }, + { 1.3956969951058884, 0.20000000000000018, 0.70000000000000007, + 1.0471975511965976 }, + { 1.8138131612209609, 0.20000000000000018, 0.70000000000000007, + 1.2217304763960306 }, + { 2.3256365528879561, 0.20000000000000018, 0.70000000000000007, + 1.3962634015954636 }, + { 2.9058704854500963, 0.20000000000000018, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler118 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.80000000000000004. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.7399960886656824e-16 +// mean(f - f_Boost): 1.3877787807814457e-16 +// variance(f - f_Boost): 1.7585404776158019e-31 +// stddev(f - f_Boost): 4.1934955319110593e-16 +const testcase_ellint_3<double> +data119[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17599862486281712, 0.20000000000000018, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36110007227128776, 0.20000000000000018, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56605039658567224, 0.20000000000000018, 0.80000000000000004, + 0.52359877559829882 }, + { 0.80537523874517691, 0.20000000000000018, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1005662342414086, 0.20000000000000018, 0.80000000000000004, + 0.87266462599716477 }, + { 1.4845340298105778, 0.20000000000000018, 0.80000000000000004, + 1.0471975511965976 }, + { 2.0043332244969392, 0.20000000000000018, 0.80000000000000004, + 1.2217304763960306 }, + { 2.7052856676744761, 0.20000000000000018, 0.80000000000000004, + 1.3962634015954636 }, + { 3.5622166386422633, 0.20000000000000018, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler119 = 2.5000000000000020e-13; + +// Test data for k=0.20000000000000018, nu=0.90000000000000002. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.1718503329017390e-16 +// mean(f - f_Boost): 2.3592239273284576e-16 +// variance(f - f_Boost): 2.9295534376290287e-31 +// stddev(f - f_Boost): 5.4125349307224141e-16 +const testcase_ellint_3<double> +data120[10] = +{ + { 0.0000000000000000, 0.20000000000000018, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17618041435044951, 0.20000000000000018, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36267207636502929, 0.20000000000000018, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57212028758237743, 0.20000000000000018, 0.90000000000000002, + 0.52359877559829882 }, + { 0.82293323876704483, 0.20000000000000018, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1457077279880388, 0.20000000000000018, 0.90000000000000002, + 0.87266462599716477 }, + { 1.5967346899325681, 0.20000000000000018, 0.90000000000000002, + 1.0471975511965976 }, + { 2.2856537353421724, 0.20000000000000018, 0.90000000000000002, + 1.2217304763960306 }, + { 3.4034714304613902, 0.20000000000000018, 0.90000000000000002, + 1.3962634015954636 }, + { 5.0448269356200370, 0.20000000000000018, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler120 = 2.5000000000000020e-13; // Test data for k=0.30000000000000004, nu=0.0000000000000000. -testcase_ellint_3<double> data121[] = { - { -0.0000000000000000, 0.30000000000000004, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17461228653000102, 0.30000000000000004, 0.0000000000000000, - 0.17453292519943295 }, - { 0.34969146102798415, 0.30000000000000004, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52565822873726320, 0.30000000000000004, 0.0000000000000000, - 0.52359877559829882 }, - { 0.70284226512408532, 0.30000000000000004, 0.0000000000000000, - 0.69813170079773179 }, - { 0.88144139195111182, 0.30000000000000004, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0614897067260523, 0.30000000000000004, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2428416824174218, 0.30000000000000004, 0.0000000000000000, - 1.2217304763960306 }, - { 1.4251795877015925, 0.30000000000000004, 0.0000000000000000, - 1.3962634015954636 }, - { 1.6080486199305126, 0.30000000000000004, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.0000000000000000. -template <typename Tp> -void test121() -{ - 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(data121) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data121[i].k), Tp(data121[i].nu), - Tp(data121[i].phi)); - const Tp f0 = data121[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.2241249691539529e-16 +// mean(f - f_Boost): 2.7755575615628914e-17 +// variance(f - f_Boost): 2.1399221604302621e-32 +// stddev(f - f_Boost): 1.4628472785736254e-16 +const testcase_ellint_3<double> +data121[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17461228653000099, 0.30000000000000004, 0.0000000000000000, + 0.17453292519943295 }, + { 0.34969146102798421, 0.30000000000000004, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52565822873726309, 0.30000000000000004, 0.0000000000000000, + 0.52359877559829882 }, + { 0.70284226512408543, 0.30000000000000004, 0.0000000000000000, + 0.69813170079773179 }, + { 0.88144139195111171, 0.30000000000000004, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0614897067260520, 0.30000000000000004, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2428416824174220, 0.30000000000000004, 0.0000000000000000, + 1.2217304763960306 }, + { 1.4251795877015929, 0.30000000000000004, 0.0000000000000000, + 1.3962634015954636 }, + { 1.6080486199305128, 0.30000000000000004, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler121 = 2.5000000000000020e-13; // Test data for k=0.30000000000000004, nu=0.10000000000000001. -testcase_ellint_3<double> data122[] = { - { -0.0000000000000000, 0.30000000000000004, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17443631884814378, 0.30000000000000004, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34831316835124926, 0.30000000000000004, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52116586276523857, 0.30000000000000004, 0.10000000000000001, - 0.52359877559829882 }, - { 0.69269385837910036, 0.30000000000000004, 0.10000000000000001, - 0.69813170079773179 }, - { 0.86279023163070856, 0.30000000000000004, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0315321461438265, 0.30000000000000004, 0.10000000000000001, - 1.0471975511965976 }, - { 1.1991449111869024, 0.30000000000000004, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3659561780923211, 0.30000000000000004, 0.10000000000000001, - 1.3962634015954636 }, - { 1.5323534693557526, 0.30000000000000004, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.10000000000000001. -template <typename Tp> -void test122() -{ - 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(data122) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data122[i].k), Tp(data122[i].nu), - Tp(data122[i].phi)); - const Tp f0 = data122[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)); -} +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.1872304407982844e-16 +// mean(f - f_Boost): 7.2164496600635178e-17 +// variance(f - f_Boost): 4.3555500115139682e-32 +// stddev(f - f_Boost): 2.0869954507650391e-16 +const testcase_ellint_3<double> +data122[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17478889331392972, 0.30000000000000004, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35108939018329183, 0.30000000000000004, 0.10000000000000001, + 0.34906585039886590 }, + { 0.53028990896115835, 0.30000000000000004, 0.10000000000000001, + 0.52359877559829882 }, + { 0.71352417052371409, 0.30000000000000004, 0.10000000000000001, + 0.69813170079773179 }, + { 0.90153086032405894, 0.30000000000000004, 0.10000000000000001, + 0.87266462599716477 }, + { 1.0945187977283313, 0.30000000000000004, 0.10000000000000001, + 1.0471975511965976 }, + { 1.2920699268385683, 0.30000000000000004, 0.10000000000000001, + 1.2217304763960306 }, + { 1.4931243665896394, 0.30000000000000004, 0.10000000000000001, + 1.3962634015954636 }, + { 1.6960848815118226, 0.30000000000000004, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler122 = 2.5000000000000020e-13; // Test data for k=0.30000000000000004, nu=0.20000000000000001. -testcase_ellint_3<double> data123[] = { - { -0.0000000000000000, 0.30000000000000004, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17426098615372090, 0.30000000000000004, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34695402664689923, 0.30000000000000004, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51680555567038933, 0.30000000000000004, 0.20000000000000001, - 0.52359877559829882 }, - { 0.68303375225260210, 0.30000000000000004, 0.20000000000000001, - 0.69813170079773179 }, - { 0.84540662891295026, 0.30000000000000004, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0041834051646927, 0.30000000000000004, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1599952702345711, 0.30000000000000004, 0.20000000000000001, - 1.2217304763960306 }, - { 1.3137179520499163, 0.30000000000000004, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4663658145259875, 0.30000000000000004, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.20000000000000001. -template <typename Tp> -void test123() -{ - 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(data123) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data123[i].k), Tp(data123[i].nu), - Tp(data123[i].phi)); - const Tp f0 = data123[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, nu=0.29999999999999999. -testcase_ellint_3<double> data124[] = { - { -0.0000000000000000, 0.30000000000000004, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17408628437042845, 0.30000000000000004, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34561356761638401, 0.30000000000000004, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51257058617875850, 0.30000000000000004, 0.29999999999999999, - 0.52359877559829882 }, - { 0.67382207124602866, 0.30000000000000004, 0.29999999999999999, - 0.69813170079773179 }, - { 0.82914751587825131, 0.30000000000000004, 0.29999999999999999, - 0.87266462599716477 }, - { 0.97907434814374950, 0.30000000000000004, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1246399297351584, 0.30000000000000004, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2671793970398146, 0.30000000000000004, 0.29999999999999999, - 1.3962634015954636 }, - { 1.4081767433479089, 0.30000000000000004, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.29999999999999999. -template <typename Tp> -void test124() -{ - 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(data124) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data124[i].k), Tp(data124[i].nu), - Tp(data124[i].phi)); - const Tp f0 = data124[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.2247497610332889e-16 +// mean(f - f_Boost): 6.6613381477509390e-17 +// variance(f - f_Boost): 1.7591111235252501e-32 +// stddev(f - f_Boost): 1.3263148659067538e-16 +const testcase_ellint_3<double> +data123[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17496614335337535, 0.30000000000000004, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35250745937139372, 0.30000000000000004, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53506875002836884, 0.30000000000000004, 0.20000000000000001, + 0.52359877559829882 }, + { 0.72479106622248191, 0.30000000000000004, 0.20000000000000001, + 0.69813170079773179 }, + { 0.92326451535891607, 0.30000000000000004, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1312092060698349, 0.30000000000000004, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3481473154592321, 0.30000000000000004, 0.20000000000000001, + 1.2217304763960306 }, + { 1.5722049569662750, 0.30000000000000004, 0.20000000000000001, + 1.3962634015954636 }, + { 1.8002173372290500, 0.30000000000000004, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler123 = 2.5000000000000020e-13; + +// Test data for k=0.30000000000000004, nu=0.30000000000000004. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.1678685180047551e-16 +// mean(f - f_Boost): 1.0547118733938987e-16 +// variance(f - f_Boost): 7.5633408838247182e-32 +// stddev(f - f_Boost): 2.7501528837184157e-16 +const testcase_ellint_3<double> +data124[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17514404084107435, 0.30000000000000004, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35394619108645647, 0.30000000000000004, 0.30000000000000004, + 0.34906585039886590 }, + { 0.54000325463372689, 0.30000000000000004, 0.30000000000000004, + 0.52359877559829882 }, + { 0.73670193794067651, 0.30000000000000004, 0.30000000000000004, + 0.69813170079773179 }, + { 0.94689345491722177, 0.30000000000000004, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1723274608389140, 0.30000000000000004, 0.30000000000000004, + 1.0471975511965976 }, + { 1.4128880552936287, 0.30000000000000004, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6659010047449661, 0.30000000000000004, 0.30000000000000004, + 1.3962634015954636 }, + { 1.9260216862473254, 0.30000000000000004, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler124 = 2.5000000000000020e-13; // Test data for k=0.30000000000000004, nu=0.40000000000000002. -testcase_ellint_3<double> data125[] = { - { -0.0000000000000000, 0.30000000000000004, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17391220945982730, 0.30000000000000004, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34429133937639689, 0.30000000000000004, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50845471668581632, 0.30000000000000004, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66502347027873854, 0.30000000000000004, 0.40000000000000002, - 0.69813170079773179 }, - { 0.81389191978012254, 0.30000000000000004, 0.40000000000000002, - 0.87266462599716477 }, - { 0.95590618002140593, 0.30000000000000004, 0.40000000000000002, - 1.0471975511965976 }, - { 1.0924915195213121, 0.30000000000000004, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2253651604038058, 0.30000000000000004, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3563643538969761, 0.30000000000000004, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.40000000000000002. -template <typename Tp> -void test125() -{ - 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(data125) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data125[i].k), Tp(data125[i].nu), - Tp(data125[i].phi)); - const Tp f0 = data125[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)); -} +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.3983279132797385e-16 +// mean(f - f_Boost): 1.1657341758564144e-16 +// variance(f - f_Boost): 1.8245832308692586e-31 +// stddev(f - f_Boost): 4.2715140534349863e-16 +const testcase_ellint_3<double> +data125[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17532259000954434, 0.30000000000000004, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35540612770983693, 0.30000000000000004, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54510265552938919, 0.30000000000000004, 0.40000000000000002, + 0.52359877559829882 }, + { 0.74932476310965057, 0.30000000000000004, 0.40000000000000002, + 0.69813170079773179 }, + { 0.97272793583093109, 0.30000000000000004, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2188928987074241, 0.30000000000000004, 0.40000000000000002, + 1.0471975511965976 }, + { 1.4888771674085941, 0.30000000000000004, 0.40000000000000002, + 1.2217304763960306 }, + { 1.7794558498219191, 0.30000000000000004, 0.40000000000000002, + 1.3962634015954636 }, + { 2.0822121773175528, 0.30000000000000004, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler125 = 2.5000000000000020e-13; // Test data for k=0.30000000000000004, nu=0.50000000000000000. -testcase_ellint_3<double> data126[] = { - { -0.0000000000000000, 0.30000000000000004, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17373875742088235, 0.30000000000000004, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34298690571124157, 0.30000000000000004, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50445214859646936, 0.30000000000000004, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65660648352418516, 0.30000000000000004, 0.50000000000000000, - 0.69813170079773179 }, - { 0.79953670639287289, 0.30000000000000004, 0.50000000000000000, - 0.87266462599716477 }, - { 0.93443393926588558, 0.30000000000000004, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0630838369016911, 0.30000000000000004, 0.50000000000000000, - 1.2217304763960306 }, - { 1.1875197325653026, 0.30000000000000004, 0.50000000000000000, - 1.3962634015954636 }, - { 1.3098448759814960, 0.30000000000000004, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.50000000000000000. -template <typename Tp> -void test126() -{ - 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(data126) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data126[i].k), Tp(data126[i].nu), - Tp(data126[i].phi)); - const Tp f0 = data126[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, nu=0.59999999999999998. -testcase_ellint_3<double> data127[] = { - { -0.0000000000000000, 0.30000000000000004, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17356592428950826, 0.30000000000000004, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34169984536697379, 0.30000000000000004, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50055748266498457, 0.30000000000000004, 0.59999999999999998, - 0.52359877559829882 }, - { 0.64854298527106768, 0.30000000000000004, 0.59999999999999998, - 0.69813170079773179 }, - { 0.78599329284207431, 0.30000000000000004, 0.59999999999999998, - 0.87266462599716477 }, - { 0.91445452089128221, 0.30000000000000004, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0360412952290587, 0.30000000000000004, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1530473919778639, 0.30000000000000004, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2677758800420666, 0.30000000000000004, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.59999999999999998. -template <typename Tp> -void test127() -{ - 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(data127) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data127[i].k), Tp(data127[i].nu), - Tp(data127[i].phi)); - const Tp f0 = data127[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, nu=0.69999999999999996. -testcase_ellint_3<double> data128[] = { - { -0.0000000000000000, 0.30000000000000004, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17339370613812227, 0.30000000000000004, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34042975138455933, 0.30000000000000004, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49676568368075985, 0.30000000000000004, 0.69999999999999996, - 0.52359877559829882 }, - { 0.64080774055753720, 0.30000000000000004, 0.69999999999999996, - 0.69813170079773179 }, - { 0.77318507779667278, 0.30000000000000004, 0.69999999999999996, - 0.87266462599716477 }, - { 0.89579782346548631, 0.30000000000000004, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0110573286052202, 0.30000000000000004, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1214710972949633, 0.30000000000000004, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2294913236274980, 0.30000000000000004, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.69999999999999996. -template <typename Tp> -void test128() -{ - 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(data128) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data128[i].k), Tp(data128[i].nu), - Tp(data128[i].phi)); - const Tp f0 = data128[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.0516138451673425e-16 +// mean(f - f_Boost): 4.7184478546569152e-17 +// variance(f - f_Boost): 1.9448563670505968e-32 +// stddev(f - f_Boost): 1.3945810722401896e-16 +const testcase_ellint_3<double> +data126[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17550179513158179, 0.30000000000000004, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35688783251681200, 0.30000000000000004, 0.50000000000000000, + 0.34906585039886590 }, + { 0.55037700010142798, 0.30000000000000004, 0.50000000000000000, + 0.52359877559829882 }, + { 0.76273839789895992, 0.30000000000000004, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0011570518830419, 0.30000000000000004, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2722987414055109, 0.30000000000000004, 0.50000000000000000, + 1.0471975511965976 }, + { 1.5799590511080066, 0.30000000000000004, 0.50000000000000000, + 1.2217304763960306 }, + { 1.9212367220124293, 0.30000000000000004, 0.50000000000000000, + 1.3962634015954636 }, + { 2.2833505881933971, 0.30000000000000004, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler126 = 2.5000000000000020e-13; + +// Test data for k=0.30000000000000004, nu=0.60000000000000009. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.2121157428443725e-16 +// mean(f - f_Boost): 1.9428902930940239e-16 +// variance(f - f_Boost): 1.5987596229703424e-31 +// stddev(f - f_Boost): 3.9984492281012430e-16 +const testcase_ellint_3<double> +data127[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17568166052076745, 0.30000000000000004, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35839189074731181, 0.30000000000000004, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55583724744367558, 0.30000000000000004, 0.60000000000000009, + 0.52359877559829882 }, + { 0.77703498090888223, 0.30000000000000004, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0326772113675962, 0.30000000000000004, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3345139983717369, 0.30000000000000004, 0.60000000000000009, + 1.0471975511965976 }, + { 1.6921742922838403, 0.30000000000000004, 0.60000000000000009, + 1.2217304763960306 }, + { 2.1056608968472186, 0.30000000000000004, 0.60000000000000009, + 1.3962634015954636 }, + { 2.5560975528589061, 0.30000000000000004, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler127 = 2.5000000000000020e-13; + +// Test data for k=0.30000000000000004, nu=0.70000000000000007. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.0088945789059381e-16 +// mean(f - f_Boost): 2.1094237467877973e-16 +// variance(f - f_Boost): 3.0253363535298873e-31 +// stddev(f - f_Boost): 5.5003057674368314e-16 +const testcase_ellint_3<double> +data128[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17586219053197988, 0.30000000000000004, 0.70000000000000007, + 0.17453292519943295 }, + { 0.35991891074557669, 0.30000000000000004, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56149538019961731, 0.30000000000000004, 0.70000000000000007, + 0.52359877559829882 }, + { 0.79232303189667685, 0.30000000000000004, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0679345542878826, 0.30000000000000004, 0.70000000000000007, + 0.87266462599716477 }, + { 1.4084400085913955, 0.30000000000000004, 0.70000000000000007, + 1.0471975511965976 }, + { 1.8357382859296454, 0.30000000000000004, 0.70000000000000007, + 1.2217304763960306 }, + { 2.3604197996171519, 0.30000000000000004, 0.70000000000000007, + 1.3962634015954636 }, + { 2.9562123549913872, 0.30000000000000004, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler128 = 2.5000000000000020e-13; // Test data for k=0.30000000000000004, nu=0.80000000000000004. -testcase_ellint_3<double> data129[] = { - { -0.0000000000000000, 0.30000000000000004, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17322209907520361, 0.30000000000000004, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33917623046949996, 0.30000000000000004, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49307204894329176, 0.30000000000000004, 0.80000000000000004, - 0.52359877559829882 }, - { 0.63337802830291723, 0.30000000000000004, 0.80000000000000004, - 0.69813170079773179 }, - { 0.76104540997689407, 0.30000000000000004, 0.80000000000000004, - 0.87266462599716477 }, - { 0.87832009635450736, 0.30000000000000004, 0.80000000000000004, - 1.0471975511965976 }, - { 0.98787879723171790, 0.30000000000000004, 0.80000000000000004, - 1.2217304763960306 }, - { 1.0924036340069336, 0.30000000000000004, 0.80000000000000004, - 1.3962634015954636 }, - { 1.1944567571590046, 0.30000000000000004, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.80000000000000004. -template <typename Tp> -void test129() -{ - 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(data129) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data129[i].k), Tp(data129[i].nu), - Tp(data129[i].phi)); - const Tp f0 = data129[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 6.1197887707781618e-16 +// mean(f - f_Boost): 3.4416913763379854e-16 +// variance(f - f_Boost): 4.3461914185990199e-31 +// stddev(f - f_Boost): 6.5925650687718054e-16 +const testcase_ellint_3<double> +data129[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17604338956191670, 0.30000000000000004, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36146952517410791, 0.30000000000000004, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56736453393774644, 0.30000000000000004, 0.80000000000000004, + 0.52359877559829882 }, + { 0.80873149979001091, 0.30000000000000004, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1077903069860620, 0.30000000000000004, 0.80000000000000004, + 0.87266462599716477 }, + { 1.4985874311132998, 0.30000000000000004, 0.80000000000000004, + 1.0471975511965976 }, + { 2.0298167266724954, 0.30000000000000004, 0.80000000000000004, + 1.2217304763960306 }, + { 2.7483929054985432, 0.30000000000000004, 0.80000000000000004, + 1.3962634015954636 }, + { 3.6283050484567170, 0.30000000000000004, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler129 = 2.5000000000000020e-13; // Test data for k=0.30000000000000004, nu=0.90000000000000002. -testcase_ellint_3<double> data130[] = { - { -0.0000000000000000, 0.30000000000000004, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17305109924485948, 0.30000000000000004, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33793890239556984, 0.30000000000000004, 0.90000000000000002, - 0.34906585039886590 }, - { 0.48947218005089738, 0.30000000000000004, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62623332340775151, 0.30000000000000004, 0.90000000000000002, - 0.69813170079773179 }, - { 0.74951596581511148, 0.30000000000000004, 0.90000000000000002, - 0.87266462599716477 }, - { 0.86189886597756005, 0.30000000000000004, 0.90000000000000002, - 1.0471975511965976 }, - { 0.96629451153092005, 0.30000000000000004, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0655269133492680, 0.30000000000000004, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1622376896064912, 0.30000000000000004, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.30000000000000004, nu=0.90000000000000002. -template <typename Tp> -void test130() -{ - 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(data130) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data130[i].k), Tp(data130[i].nu), - Tp(data130[i].phi)); - const Tp f0 = data130[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, nu=0.0000000000000000. -testcase_ellint_3<double> data131[] = { - { -0.0000000000000000, 0.39999999999999991, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17467414669441531, 0.39999999999999991, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35018222772483443, 0.39999999999999991, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52729015917508748, 0.39999999999999991, 0.0000000000000000, - 0.52359877559829882 }, - { 0.70662374407341255, 0.39999999999999991, 0.0000000000000000, - 0.69813170079773179 }, - { 0.88859210497602170, 0.39999999999999991, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0733136290471379, 0.39999999999999991, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2605612170157061, 0.39999999999999991, 0.0000000000000000, - 1.2217304763960306 }, - { 1.4497513956433437, 0.39999999999999991, 0.0000000000000000, - 1.3962634015954636 }, - { 1.6399998658645112, 0.39999999999999991, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.0000000000000000. -template <typename Tp> -void test131() -{ - 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(data131) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data131[i].k), Tp(data131[i].nu), - Tp(data131[i].phi)); - const Tp f0 = data131[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, nu=0.10000000000000001. -testcase_ellint_3<double> data132[] = { - { -0.0000000000000000, 0.39999999999999991, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17449806706684673, 0.39999999999999991, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34880048623856075, 0.39999999999999991, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52277322065757403, 0.39999999999999991, 0.10000000000000001, - 0.52359877559829882 }, - { 0.69638072056918376, 0.39999999999999991, 0.10000000000000001, - 0.69813170079773179 }, - { 0.86968426619831540, 0.39999999999999991, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0428044206578095, 0.39999999999999991, 0.10000000000000001, - 1.0471975511965976 }, - { 1.2158651158274378, 0.39999999999999991, 0.10000000000000001, - 1.2217304763960306 }, - { 1.3889447129893322, 0.39999999999999991, 0.10000000000000001, - 1.3962634015954636 }, - { 1.5620566886683604, 0.39999999999999991, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.10000000000000001. -template <typename Tp> -void test132() -{ - 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(data132) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data132[i].k), Tp(data132[i].nu), - Tp(data132[i].phi)); - const Tp f0 = data132[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, nu=0.20000000000000001. -testcase_ellint_3<double> data133[] = { - { -0.0000000000000000, 0.39999999999999991, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17432262290723399, 0.39999999999999991, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34743795258968596, 0.39999999999999991, 0.20000000000000001, - 0.34906585039886590 }, - { 0.51838919472805123, 0.39999999999999991, 0.20000000000000001, - 0.52359877559829882 }, - { 0.68663134739057918, 0.39999999999999991, 0.20000000000000001, - 0.69813170079773179 }, - { 0.85206432981833979, 0.39999999999999991, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0149595349004430, 0.39999999999999991, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1758349405464676, 0.39999999999999991, 0.20000000000000001, - 1.2217304763960306 }, - { 1.3353337673882635, 0.39999999999999991, 0.20000000000000001, - 1.3962634015954636 }, - { 1.4941414344266770, 0.39999999999999991, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.20000000000000001. -template <typename Tp> -void test133() -{ - 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(data133) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data133[i].k), Tp(data133[i].nu), - Tp(data133[i].phi)); - const Tp f0 = data133[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, nu=0.29999999999999999. -testcase_ellint_3<double> data134[] = { - { -0.0000000000000000, 0.39999999999999991, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17414781013591543, 0.39999999999999991, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34609415696777285, 0.39999999999999991, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51413131295862546, 0.39999999999999991, 0.29999999999999999, - 0.52359877559829882 }, - { 0.67733527622935630, 0.39999999999999991, 0.29999999999999999, - 0.69813170079773179 }, - { 0.83558675182733266, 0.39999999999999991, 0.29999999999999999, - 0.87266462599716477 }, - { 0.98940140808865906, 0.39999999999999991, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1396968797728058, 0.39999999999999991, 0.29999999999999999, - 1.2217304763960306 }, - { 1.2875920037865087, 0.39999999999999991, 0.29999999999999999, - 1.3962634015954636 }, - { 1.4342789859950078, 0.39999999999999991, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.29999999999999999. -template <typename Tp> -void test134() -{ - 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(data134) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data134[i].k), Tp(data134[i].nu), - Tp(data134[i].phi)); - const Tp f0 = data134[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, nu=0.40000000000000002. -testcase_ellint_3<double> data135[] = { - { -0.0000000000000000, 0.39999999999999991, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17397362471112710, 0.39999999999999991, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34476864603333196, 0.39999999999999991, 0.40000000000000002, - 0.34906585039886590 }, - { 0.50999329415379357, 0.39999999999999991, 0.40000000000000002, - 0.52359877559829882 }, - { 0.66845674551396017, 0.39999999999999991, 0.40000000000000002, - 0.69813170079773179 }, - { 0.82012848346231748, 0.39999999999999991, 0.40000000000000002, - 0.87266462599716477 }, - { 0.96582449258349057, 0.39999999999999991, 0.40000000000000002, - 1.0471975511965976 }, - { 1.1068473749476286, 0.39999999999999991, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2447132729159986, 0.39999999999999991, 0.40000000000000002, - 1.3962634015954636 }, - { 1.3809986210732901, 0.39999999999999991, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.40000000000000002. -template <typename Tp> -void test135() -{ - 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(data135) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data135[i].k), Tp(data135[i].nu), - Tp(data135[i].phi)); - const Tp f0 = data135[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, nu=0.50000000000000000. -testcase_ellint_3<double> data136[] = { - { -0.0000000000000000, 0.39999999999999991, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17380006262854139, 0.39999999999999991, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34346098216756610, 0.39999999999999991, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50596929935059420, 0.39999999999999991, 0.50000000000000000, - 0.52359877559829882 }, - { 0.65996392089131262, 0.39999999999999991, 0.50000000000000000, - 0.69813170079773179 }, - { 0.80558463511364786, 0.39999999999999991, 0.50000000000000000, - 0.87266462599716477 }, - { 0.94397834522857704, 0.39999999999999991, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0768075114108115, 0.39999999999999991, 0.50000000000000000, - 1.2217304763960306 }, - { 1.2059184624251329, 0.39999999999999991, 0.50000000000000000, - 1.3962634015954636 }, - { 1.3331797176377398, 0.39999999999999991, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.50000000000000000. -template <typename Tp> -void test136() -{ - 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(data136) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data136[i].k), Tp(data136[i].nu), - Tp(data136[i].phi)); - const Tp f0 = data136[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, nu=0.59999999999999998. -testcase_ellint_3<double> data137[] = { - { -0.0000000000000000, 0.39999999999999991, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17362711992081248, 0.39999999999999991, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34217074276403953, 0.39999999999999991, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50205389185761617, 0.39999999999999991, 0.59999999999999998, - 0.52359877559829882 }, - { 0.65182834920372745, 0.39999999999999991, 0.59999999999999998, - 0.69813170079773179 }, - { 0.79186512820565136, 0.39999999999999991, 0.59999999999999998, - 0.87266462599716477 }, - { 0.92365535916287134, 0.39999999999999991, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0491915663957907, 0.39999999999999991, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1705934291745104, 0.39999999999999991, 0.59999999999999998, - 1.3962634015954636 }, - { 1.2899514672527024, 0.39999999999999991, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.59999999999999998. -template <typename Tp> -void test137() -{ - 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(data137) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data137[i].k), Tp(data137[i].nu), - Tp(data137[i].phi)); - const Tp f0 = data137[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, nu=0.69999999999999996. -testcase_ellint_3<double> data138[] = { - { -0.0000000000000000, 0.39999999999999991, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17345479265712871, 0.39999999999999991, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34089751955950354, 0.39999999999999991, 0.69999999999999996, - 0.34906585039886590 }, - { 0.49824200167361343, 0.39999999999999991, 0.69999999999999996, - 0.52359877559829882 }, - { 0.64402450341199413, 0.39999999999999991, 0.69999999999999996, - 0.69813170079773179 }, - { 0.77889207804122873, 0.39999999999999991, 0.69999999999999996, - 0.87266462599716477 }, - { 0.90468169720957992, 0.39999999999999991, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0236847823692916, 0.39999999999999991, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1382465247425164, 0.39999999999999991, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2506255923253344, 0.39999999999999991, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.69999999999999996. -template <typename Tp> -void test138() -{ - 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(data138) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data138[i].k), Tp(data138[i].nu), - Tp(data138[i].phi)); - const Tp f0 = data138[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, nu=0.80000000000000004. -testcase_ellint_3<double> data139[] = { - { -0.0000000000000000, 0.39999999999999991, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17328307694277156, 0.39999999999999991, 0.80000000000000004, - 0.17453292519943295 }, - { 0.33964091800132007, 0.39999999999999991, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49452889372467451, 0.39999999999999991, 0.80000000000000004, - 0.52359877559829882 }, - { 0.63652940095937327, 0.39999999999999991, 0.80000000000000004, - 0.69813170079773179 }, - { 0.76659772511159097, 0.39999999999999991, 0.80000000000000004, - 0.87266462599716477 }, - { 0.88691047977338111, 0.39999999999999991, 0.80000000000000004, - 1.0471975511965976 }, - { 1.0000273200611640, 0.39999999999999991, 0.80000000000000004, - 1.2217304763960306 }, - { 1.1084787902188007, 0.39999999999999991, 0.80000000000000004, - 1.3962634015954636 }, - { 1.2146499565727209, 0.39999999999999991, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.80000000000000004. -template <typename Tp> -void test139() -{ - 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(data139) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data139[i].k), Tp(data139[i].nu), - Tp(data139[i].phi)); - const Tp f0 = data139[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, nu=0.90000000000000002. -testcase_ellint_3<double> data140[] = { - { -0.0000000000000000, 0.39999999999999991, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17311196891868130, 0.39999999999999991, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33840055664911906, 0.39999999999999991, 0.90000000000000002, - 0.34906585039886590 }, - { 0.49091013944075340, 0.39999999999999991, 0.90000000000000002, - 0.52359877559829882 }, - { 0.62932228186809591, 0.39999999999999991, 0.90000000000000002, - 0.69813170079773179 }, - { 0.75492278323019801, 0.39999999999999991, 0.90000000000000002, - 0.87266462599716477 }, - { 0.87021659043854294, 0.39999999999999991, 0.90000000000000002, - 1.0471975511965976 }, - { 0.97800245228239246, 0.39999999999999991, 0.90000000000000002, - 1.2217304763960306 }, - { 1.0809625773173694, 0.39999999999999991, 0.90000000000000002, - 1.3962634015954636 }, - { 1.1815758115929846, 0.39999999999999991, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.39999999999999991, nu=0.90000000000000002. -template <typename Tp> -void test140() -{ - 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(data140) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data140[i].k), Tp(data140[i].nu), - Tp(data140[i].phi)); - const Tp f0 = data140[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 5.1301806687926828e-16 +// mean(f - f_Boost): 4.1633363423443370e-16 +// variance(f - f_Boost): 2.2835347143080263e-31 +// stddev(f - f_Boost): 4.7786344433405093e-16 +const testcase_ellint_3<double> +data130[10] = +{ + { 0.0000000000000000, 0.30000000000000004, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17622526204962433, 0.30000000000000004, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36304439230777141, 0.30000000000000004, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57345914744719195, 0.30000000000000004, 0.90000000000000002, + 0.52359877559829882 }, + { 0.82641512928845162, 0.30000000000000004, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1534256210757743, 0.30000000000000004, 0.90000000000000002, + 0.87266462599716477 }, + { 1.6124900353411677, 0.30000000000000004, 0.90000000000000002, + 1.0471975511965976 }, + { 2.3165905514845089, 0.30000000000000004, 0.90000000000000002, + 1.2217304763960306 }, + { 3.4625619526539824, 0.30000000000000004, 0.90000000000000002, + 1.3962634015954636 }, + { 5.1479514944016787, 0.30000000000000004, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler130 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.0000000000000000. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 1.0831445028587608e-15 +// mean(f - f_Boost): 1.7486012637846215e-16 +// variance(f - f_Boost): 3.1664095331106078e-31 +// stddev(f - f_Boost): 5.6270858649132121e-16 +const testcase_ellint_3<double> +data131[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17467414669441528, 0.40000000000000013, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35018222772483443, 0.40000000000000013, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52729015917508748, 0.40000000000000013, 0.0000000000000000, + 0.52359877559829882 }, + { 0.70662374407341244, 0.40000000000000013, 0.0000000000000000, + 0.69813170079773179 }, + { 0.88859210497602159, 0.40000000000000013, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0733136290471381, 0.40000000000000013, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2605612170157066, 0.40000000000000013, 0.0000000000000000, + 1.2217304763960306 }, + { 1.4497513956433439, 0.40000000000000013, 0.0000000000000000, + 1.3962634015954636 }, + { 1.6399998658645112, 0.40000000000000013, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler131 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.10000000000000001. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 1.0263824105456986e-15 +// mean(f - f_Boost): 1.7486012637846215e-16 +// variance(f - f_Boost): 3.1664095331106078e-31 +// stddev(f - f_Boost): 5.6270858649132121e-16 +const testcase_ellint_3<double> +data132[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17485086590796767, 0.40000000000000013, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35158366412506992, 0.40000000000000013, 0.10000000000000001, + 0.34906585039886590 }, + { 0.53194731675711726, 0.40000000000000013, 0.10000000000000001, + 0.52359877559829882 }, + { 0.71740615528010931, 0.40000000000000013, 0.10000000000000001, + 0.69813170079773179 }, + { 0.90896157773487030, 0.40000000000000013, 0.10000000000000001, + 0.87266462599716477 }, + { 1.1069605483834348, 0.40000000000000013, 0.10000000000000001, + 1.0471975511965976 }, + { 1.3109353428823001, 0.40000000000000013, 0.10000000000000001, + 1.2217304763960306 }, + { 1.5195460789903450, 0.40000000000000013, 0.10000000000000001, + 1.3962634015954636 }, + { 1.7306968836847190, 0.40000000000000013, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler132 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.20000000000000001. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 9.6644296021947179e-16 +// mean(f - f_Boost): 2.0816681711721685e-16 +// variance(f - f_Boost): 3.0360740073926687e-31 +// stddev(f - f_Boost): 5.5100580826273227e-16 +const testcase_ellint_3<double> +data133[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17502822886437389, 0.40000000000000013, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35300530062530805, 0.40000000000000013, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53675259548210896, 0.40000000000000013, 0.20000000000000001, + 0.52359877559829882 }, + { 0.72878006428676934, 0.40000000000000013, 0.20000000000000001, + 0.69813170079773179 }, + { 0.93100219010583574, 0.40000000000000013, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1443487271187611, 0.40000000000000013, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3683427764108813, 0.40000000000000013, 0.20000000000000001, + 1.2217304763960306 }, + { 1.6008221459300933, 0.40000000000000013, 0.20000000000000001, + 1.3962634015954636 }, + { 1.8380358826317627, 0.40000000000000013, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler133 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.30000000000000004. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 9.0271556462838835e-16 +// mean(f - f_Boost): 2.0816681711721685e-16 +// variance(f - f_Boost): 3.0360740073926687e-31 +// stddev(f - f_Boost): 5.5100580826273227e-16 +const testcase_ellint_3<double> +data134[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17520623975982899, 0.40000000000000013, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35444766141612105, 0.40000000000000013, 0.30000000000000004, + 0.34906585039886590 }, + { 0.54171455841536009, 0.40000000000000013, 0.30000000000000004, + 0.52359877559829882 }, + { 0.74080517001084012, 0.40000000000000013, 0.30000000000000004, + 0.69813170079773179 }, + { 0.95496950509296574, 0.40000000000000013, 0.30000000000000004, + 0.87266462599716477 }, + { 1.1862627879844718, 0.40000000000000013, 0.30000000000000004, + 1.0471975511965976 }, + { 1.4346501803799458, 0.40000000000000013, 0.30000000000000004, + 1.2217304763960306 }, + { 1.6971744798077699, 0.40000000000000013, 0.30000000000000004, + 1.3962634015954636 }, + { 1.9677924132520139, 0.40000000000000013, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler134 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.40000000000000002. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 8.3436329231972794e-16 +// mean(f - f_Boost): 2.3037127760972000e-16 +// variance(f - f_Boost): 2.9507053793392374e-31 +// stddev(f - f_Boost): 5.4320395611033958e-16 +const testcase_ellint_3<double> +data135[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17538490283034375, 0.40000000000000013, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35591129064319948, 0.40000000000000013, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54684250413264535, 0.40000000000000013, 0.40000000000000002, + 0.52359877559829882 }, + { 0.75355027742668290, 0.40000000000000013, 0.40000000000000002, + 0.69813170079773179 }, + { 0.98117935026780634, 0.40000000000000013, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2337464222030736, 0.40000000000000013, 0.40000000000000002, + 1.0471975511965976 }, + { 1.5125183419289221, 0.40000000000000013, 0.40000000000000002, + 1.2217304763960306 }, + { 1.8140224451130313, 0.40000000000000013, 0.40000000000000002, + 1.3962634015954636 }, + { 2.1289968719280026, 0.40000000000000013, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler135 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.50000000000000000. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.7013794022122431e-16 +// mean(f - f_Boost): 2.3037127760972000e-16 +// variance(f - f_Boost): 1.4989821857033475e-31 +// stddev(f - f_Boost): 3.8716691306248618e-16 +const testcase_ellint_3<double> +data136[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17556422235224273, 0.40000000000000013, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35739675341763921, 0.40000000000000013, 0.50000000000000000, + 0.34906585039886590 }, + { 0.55214655195037188, 0.40000000000000013, 0.50000000000000000, + 0.52359877559829882 }, + { 0.76709520942047438, 0.40000000000000013, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0100278761577499, 0.40000000000000013, 0.50000000000000000, + 0.87266462599716477 }, + { 1.2882265661384342, 0.40000000000000013, 0.50000000000000000, + 1.0471975511965976 }, + { 1.6059059780051876, 0.40000000000000013, 0.50000000000000000, + 1.2217304763960306 }, + { 1.9600182740224081, 0.40000000000000013, 0.50000000000000000, + 1.3962634015954636 }, + { 2.3367461373176512, 0.40000000000000013, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler136 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.60000000000000009. +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 8.4792115132836117e-16 +// mean(f - f_Boost): 2.3037127760972000e-16 +// variance(f - f_Boost): 4.8893797490374802e-31 +// stddev(f - f_Boost): 6.9924099915819294e-16 +const testcase_ellint_3<double> +data137[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17574420264267029, 0.40000000000000013, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35890463689046265, 0.40000000000000013, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55763773975194486, 0.40000000000000013, 0.60000000000000009, + 0.52359877559829882 }, + { 0.78153324227761267, 0.40000000000000013, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0420205885765887, 0.40000000000000013, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3517205230381770, 0.40000000000000013, 0.60000000000000009, + 1.0471975511965976 }, + { 1.7210360970313896, 0.40000000000000013, 0.60000000000000009, + 1.2217304763960306 }, + { 2.1500780510169246, 0.40000000000000013, 0.60000000000000009, + 1.3962634015954636 }, + { 2.6186940209850191, 0.40000000000000013, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler137 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.70000000000000007. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.8573292020719759e-16 +// mean(f - f_Boost): 2.2759572004815707e-16 +// variance(f - f_Boost): 2.9613098824898137e-31 +// stddev(f - f_Boost): 5.4417918762938862e-16 +const testcase_ellint_3<double> +data138[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17592484806010436, 0.40000000000000013, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36043555139631439, 0.40000000000000013, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56332813669944881, 0.40000000000000013, 0.70000000000000007, + 0.52359877559829882 }, + { 0.79697424562157548, 0.40000000000000013, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0778155987523672, 0.40000000000000013, 0.70000000000000007, + 0.87266462599716477 }, + { 1.4272018169896268, 0.40000000000000013, 0.70000000000000007, + 1.0471975511965976 }, + { 1.8684377907453382, 0.40000000000000013, 0.70000000000000007, + 1.2217304763960306 }, + { 2.4128677409207473, 0.40000000000000013, 0.70000000000000007, + 1.3962634015954636 }, + { 3.0327078743873246, 0.40000000000000013, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler138 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.80000000000000004. +// max(|f - f_Boost|): 3.5527136788005009e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 9.5273712585384737e-16 +// mean(f - f_Boost): 4.5241588253475131e-16 +// variance(f - f_Boost): 1.1866477068555882e-30 +// stddev(f - f_Boost): 1.0893336067778265e-15 +const testcase_ellint_3<double> +data139[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17610616300487833, 0.40000000000000013, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36199013167171978, 0.40000000000000013, 0.80000000000000004, + 0.34906585039886590 }, + { 0.56923097361842434, 0.40000000000000013, 0.80000000000000004, + 0.52359877559829882 }, + { 0.81354878456624347, 0.40000000000000013, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1182902719261825, 0.40000000000000013, 0.80000000000000004, + 0.87266462599716477 }, + { 1.5192950589409022, 0.40000000000000013, 0.80000000000000004, + 1.0471975511965976 }, + { 2.0678761710223981, 0.40000000000000013, 0.80000000000000004, + 1.2217304763960306 }, + { 2.8135222249879788, 0.40000000000000013, 0.80000000000000004, + 1.3962634015954636 }, + { 3.7289548002199902, 0.40000000000000013, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler139 = 2.5000000000000020e-13; + +// Test data for k=0.40000000000000013, nu=0.90000000000000002. +// max(|f - f_Boost|): 6.2172489379008766e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 1.1718379478872251e-15 +// mean(f - f_Boost): 8.4099394115355610e-16 +// variance(f - f_Boost): 3.5684096037099424e-30 +// stddev(f - f_Boost): 1.8890234523980751e-15 +const testcase_ellint_3<double> +data140[10] = +{ + { 0.0000000000000000, 0.40000000000000013, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17628815191971123, 0.40000000000000013, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36356903815378772, 0.40000000000000013, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57536079447000310, 0.40000000000000013, 0.90000000000000002, + 0.52359877559829882 }, + { 0.83141355850172571, 0.40000000000000013, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1646481598721361, 0.40000000000000013, 0.90000000000000002, + 0.87266462599716477 }, + { 1.6357275034001995, 0.40000000000000013, 0.90000000000000002, + 1.0471975511965976 }, + { 2.3628787566572402, 0.40000000000000013, 0.90000000000000002, + 1.2217304763960306 }, + { 3.5521010369134962, 0.40000000000000013, 0.90000000000000002, + 1.3962634015954636 }, + { 5.3055535102872513, 0.40000000000000013, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler140 = 2.5000000000000020e-13; // Test data for k=0.50000000000000000, nu=0.0000000000000000. -testcase_ellint_3<double> data141[] = { - { -0.0000000000000000, 0.50000000000000000, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17475385514035785, 0.50000000000000000, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35081868470101585, 0.50000000000000000, 0.0000000000000000, - 0.34906585039886590 }, - { 0.52942862705190585, 0.50000000000000000, 0.0000000000000000, - 0.52359877559829882 }, - { 0.71164727562630326, 0.50000000000000000, 0.0000000000000000, - 0.69813170079773179 }, - { 0.89824523594227768, 0.50000000000000000, 0.0000000000000000, - 0.87266462599716477 }, - { 1.0895506700518851, 0.50000000000000000, 0.0000000000000000, - 1.0471975511965976 }, - { 1.2853005857432933, 0.50000000000000000, 0.0000000000000000, - 1.2217304763960306 }, - { 1.4845545520549484, 0.50000000000000000, 0.0000000000000000, - 1.3962634015954636 }, - { 1.6857503548125963, 0.50000000000000000, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.0000000000000000. -template <typename Tp> -void test141() -{ - 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(data141) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data141[i].k), Tp(data141[i].nu), - Tp(data141[i].phi)); - const Tp f0 = data141[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.4551389361831220e-16 +// mean(f - f_Boost): -1.3877787807814457e-17 +// variance(f - f_Boost): 2.5893058141206173e-32 +// stddev(f - f_Boost): 1.6091320064309879e-16 +const testcase_ellint_3<double> +data141[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17475385514035785, 0.50000000000000000, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35081868470101579, 0.50000000000000000, 0.0000000000000000, + 0.34906585039886590 }, + { 0.52942862705190574, 0.50000000000000000, 0.0000000000000000, + 0.52359877559829882 }, + { 0.71164727562630326, 0.50000000000000000, 0.0000000000000000, + 0.69813170079773179 }, + { 0.89824523594227768, 0.50000000000000000, 0.0000000000000000, + 0.87266462599716477 }, + { 1.0895506700518853, 0.50000000000000000, 0.0000000000000000, + 1.0471975511965976 }, + { 1.2853005857432933, 0.50000000000000000, 0.0000000000000000, + 1.2217304763960306 }, + { 1.4845545520549488, 0.50000000000000000, 0.0000000000000000, + 1.3962634015954636 }, + { 1.6857503548125961, 0.50000000000000000, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler141 = 2.5000000000000020e-13; // Test data for k=0.50000000000000000, nu=0.10000000000000001. -testcase_ellint_3<double> data142[] = { - { -0.0000000000000000, 0.50000000000000000, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17457763120814676, 0.50000000000000000, 0.10000000000000001, - 0.17453292519943295 }, - { 0.34943246340849154, 0.50000000000000000, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52487937869610801, 0.50000000000000000, 0.10000000000000001, - 0.52359877559829882 }, - { 0.70127785096388395, 0.50000000000000000, 0.10000000000000001, - 0.69813170079773179 }, - { 0.87898815988624479, 0.50000000000000000, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0582764576094172, 0.50000000000000000, 0.10000000000000001, - 1.0471975511965976 }, - { 1.2391936844060207, 0.50000000000000000, 0.10000000000000001, - 1.2217304763960306 }, - { 1.4214793542995841, 0.50000000000000000, 0.10000000000000001, - 1.3962634015954636 }, - { 1.6045524936084892, 0.50000000000000000, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.10000000000000001. -template <typename Tp> -void test142() -{ - 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(data142) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data142[i].k), Tp(data142[i].nu), - Tp(data142[i].phi)); - const Tp f0 = data142[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)); -} +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.7416868347177582e-16 +// mean(f - f_Boost): 2.7755575615628915e-18 +// variance(f - f_Boost): 5.4326441655972001e-32 +// stddev(f - f_Boost): 2.3308033305273100e-16 +const testcase_ellint_3<double> +data142[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17493071928248824, 0.50000000000000000, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35222467688034798, 0.50000000000000000, 0.10000000000000001, + 0.34906585039886590 }, + { 0.53411928652008112, 0.50000000000000000, 0.10000000000000001, + 0.52359877559829882 }, + { 0.72256398117177589, 0.50000000000000000, 0.10000000000000001, + 0.69813170079773179 }, + { 0.91899583232771009, 0.50000000000000000, 0.10000000000000001, + 0.87266462599716477 }, + { 1.1240549163055360, 0.50000000000000000, 0.10000000000000001, + 1.0471975511965976 }, + { 1.3372938086286021, 0.50000000000000000, 0.10000000000000001, + 1.2217304763960306 }, + { 1.5570024469132429, 0.50000000000000000, 0.10000000000000001, + 1.3962634015954636 }, + { 1.7803034946545480, 0.50000000000000000, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler142 = 2.5000000000000020e-13; // Test data for k=0.50000000000000000, nu=0.20000000000000001. -testcase_ellint_3<double> data143[] = { - { -0.0000000000000000, 0.50000000000000000, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17440204336345433, 0.50000000000000000, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34806552388338824, 0.50000000000000000, 0.20000000000000001, - 0.34906585039886590 }, - { 0.52046416757129821, 0.50000000000000000, 0.20000000000000001, - 0.52359877559829882 }, - { 0.69140924550993876, 0.50000000000000000, 0.20000000000000001, - 0.69813170079773179 }, - { 0.86104678636125520, 0.50000000000000000, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0297439459053981, 0.50000000000000000, 0.20000000000000001, - 1.0471975511965976 }, - { 1.1979214112912036, 0.50000000000000000, 0.20000000000000001, - 1.2217304763960306 }, - { 1.3659033858648930, 0.50000000000000000, 0.20000000000000001, - 1.3962634015954636 }, - { 1.5338490483665983, 0.50000000000000000, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.20000000000000001. -template <typename Tp> -void test143() -{ - 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(data143) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data143[i].k), Tp(data143[i].nu), - Tp(data143[i].phi)); - const Tp f0 = data143[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, nu=0.29999999999999999. -testcase_ellint_3<double> data144[] = { - { -0.0000000000000000, 0.50000000000000000, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17422708752228896, 0.50000000000000000, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34671739434855858, 0.50000000000000000, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51617616305641889, 0.50000000000000000, 0.29999999999999999, - 0.52359877559829882 }, - { 0.68200047612545178, 0.50000000000000000, 0.29999999999999999, - 0.69813170079773179 }, - { 0.84427217869498372, 0.50000000000000000, 0.29999999999999999, - 0.87266462599716477 }, - { 1.0035637821389782, 0.50000000000000000, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1606800483933113, 0.50000000000000000, 0.29999999999999999, - 1.2217304763960306 }, - { 1.3164407134643459, 0.50000000000000000, 0.29999999999999999, - 1.3962634015954636 }, - { 1.4715681939859637, 0.50000000000000000, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.29999999999999999. -template <typename Tp> -void test144() -{ - 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(data144) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data144[i].k), Tp(data144[i].nu), - Tp(data144[i].phi)); - const Tp f0 = data144[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)); -} +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.1198767993730867e-16 +// mean(f - f_Boost): 2.7755575615628914e-17 +// variance(f - f_Boost): 5.0311947683004831e-32 +// stddev(f - f_Boost): 2.2430324938128922e-16 +const testcase_ellint_3<double> +data143[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17510822779582402, 0.50000000000000000, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35365094725531487, 0.50000000000000000, 0.20000000000000001, + 0.34906585039886590 }, + { 0.53895933237328697, 0.50000000000000000, 0.20000000000000001, + 0.52359877559829882 }, + { 0.73408090840070794, 0.50000000000000000, 0.20000000000000001, + 0.69813170079773179 }, + { 0.94145442818535396, 0.50000000000000000, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1624120186296487, 0.50000000000000000, 0.20000000000000001, + 1.0471975511965976 }, + { 1.3965823372867114, 0.50000000000000000, 0.20000000000000001, + 1.2217304763960306 }, + { 1.6414308440430099, 0.50000000000000000, 0.20000000000000001, + 1.3962634015954636 }, + { 1.8922947612264018, 0.50000000000000000, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler143 = 2.5000000000000020e-13; + +// Test data for k=0.50000000000000000, nu=0.30000000000000004. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.3800262770228813e-16 +// mean(f - f_Boost): 5.8286708792820721e-17 +// variance(f - f_Boost): 8.5027191584278157e-32 +// stddev(f - f_Boost): 2.9159422419567599e-16 +const testcase_ellint_3<double> +data144[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17528638488102041, 0.50000000000000000, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35509802222332720, 0.50000000000000000, 0.30000000000000004, + 0.34906585039886590 }, + { 0.54395740731866193, 0.50000000000000000, 0.30000000000000004, + 0.52359877559829882 }, + { 0.74625871438752667, 0.50000000000000000, 0.30000000000000004, + 0.69813170079773179 }, + { 0.96588271186092023, 0.50000000000000000, 0.30000000000000004, + 0.87266462599716477 }, + { 1.2054319584357329, 0.50000000000000000, 0.30000000000000004, + 1.0471975511965976 }, + { 1.4651077994832871, 0.50000000000000000, 0.30000000000000004, + 1.2217304763960306 }, + { 1.7416018368052644, 0.50000000000000000, 0.30000000000000004, + 1.3962634015954636 }, + { 2.0277924458111314, 0.50000000000000000, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler144 = 2.5000000000000020e-13; // Test data for k=0.50000000000000000, nu=0.40000000000000002. -testcase_ellint_3<double> data145[] = { - { -0.0000000000000000, 0.50000000000000000, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17405275963859917, 0.50000000000000000, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34538761957029329, 0.50000000000000000, 0.40000000000000002, - 0.34906585039886590 }, - { 0.51200902646603919, 0.50000000000000000, 0.40000000000000002, - 0.52359877559829882 }, - { 0.67301522212868792, 0.50000000000000000, 0.40000000000000002, - 0.69813170079773179 }, - { 0.82853844466313320, 0.50000000000000000, 0.40000000000000002, - 0.87266462599716477 }, - { 0.97942097862681488, 0.50000000000000000, 0.40000000000000002, - 1.0471975511965976 }, - { 1.1268429801220616, 0.50000000000000000, 0.40000000000000002, - 1.2217304763960306 }, - { 1.2720406704533922, 0.50000000000000000, 0.40000000000000002, - 1.3962634015954636 }, - { 1.4161679518465340, 0.50000000000000000, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.40000000000000002. -template <typename Tp> -void test145() -{ - 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(data145) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data145[i].k), Tp(data145[i].nu), - Tp(data145[i].phi)); - const Tp f0 = data145[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.0439932918341581e-16 +// mean(f - f_Boost): 3.0531133177191807e-17 +// variance(f - f_Boost): 9.0809736800018602e-32 +// stddev(f - f_Boost): 3.0134653938616686e-16 +const testcase_ellint_3<double> +data145[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17546519477859268, 0.50000000000000000, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35656644822531680, 0.50000000000000000, 0.40000000000000002, + 0.34906585039886590 }, + { 0.54912289677411319, 0.50000000000000000, 0.40000000000000002, + 0.52359877559829882 }, + { 0.75916731611690047, 0.50000000000000000, 0.40000000000000002, + 0.69813170079773179 }, + { 0.99260415631328214, 0.50000000000000000, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2541925856918670, 0.50000000000000000, 0.40000000000000002, + 1.0471975511965976 }, + { 1.5456393705347609, 0.50000000000000000, 0.40000000000000002, + 1.2217304763960306 }, + { 1.8631904972952076, 0.50000000000000000, 0.40000000000000002, + 1.3962634015954636 }, + { 2.1962905366178065, 0.50000000000000000, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler145 = 2.5000000000000020e-13; // Test data for k=0.50000000000000000, nu=0.50000000000000000. -testcase_ellint_3<double> data146[] = { - { -0.0000000000000000, 0.50000000000000000, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17387905570381157, 0.50000000000000000, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34407576010465207, 0.50000000000000000, 0.50000000000000000, - 0.34906585039886590 }, - { 0.50795686560160835, 0.50000000000000000, 0.50000000000000000, - 0.52359877559829882 }, - { 0.66442115453330175, 0.50000000000000000, 0.50000000000000000, - 0.69813170079773179 }, - { 0.81373829119355345, 0.50000000000000000, 0.50000000000000000, - 0.87266462599716477 }, - { 0.95705743313235825, 0.50000000000000000, 0.50000000000000000, - 1.0471975511965976 }, - { 1.0959131991362556, 0.50000000000000000, 0.50000000000000000, - 1.2217304763960306 }, - { 1.2318900529754597, 0.50000000000000000, 0.50000000000000000, - 1.3962634015954636 }, - { 1.3664739530045971, 0.50000000000000000, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.50000000000000000. -template <typename Tp> -void test146() -{ - 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(data146) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data146[i].k), Tp(data146[i].nu), - Tp(data146[i].phi)); - const Tp f0 = data146[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, nu=0.59999999999999998. -testcase_ellint_3<double> data147[] = { - { -0.0000000000000000, 0.50000000000000000, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17370597174637581, 0.50000000000000000, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34278139158591414, 0.50000000000000000, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50401419439302719, 0.50000000000000000, 0.59999999999999998, - 0.52359877559829882 }, - { 0.65618938076167221, 0.50000000000000000, 0.59999999999999998, - 0.69813170079773179 }, - { 0.79977959248855424, 0.50000000000000000, 0.59999999999999998, - 0.87266462599716477 }, - { 0.93625925190753545, 0.50000000000000000, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0674905658379710, 0.50000000000000000, 0.59999999999999998, - 1.2217304763960306 }, - { 1.1953481298023048, 0.50000000000000000, 0.59999999999999998, - 1.3962634015954636 }, - { 1.3215740290190876, 0.50000000000000000, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.59999999999999998. -template <typename Tp> -void test147() -{ - 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(data147) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data147[i].k), Tp(data147[i].nu), - Tp(data147[i].phi)); - const Tp f0 = data147[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, nu=0.69999999999999996. -testcase_ellint_3<double> data148[] = { - { -0.0000000000000000, 0.50000000000000000, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17353350383131641, 0.50000000000000000, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34150410405436771, 0.50000000000000000, 0.69999999999999996, - 0.34906585039886590 }, - { 0.50017589696443487, 0.50000000000000000, 0.69999999999999996, - 0.52359877559829882 }, - { 0.64829398188419962, 0.50000000000000000, 0.69999999999999996, - 0.69813170079773179 }, - { 0.78658270782402073, 0.50000000000000000, 0.69999999999999996, - 0.87266462599716477 }, - { 0.91684738336675053, 0.50000000000000000, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0412486789555937, 0.50000000000000000, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1619021847612001, 0.50000000000000000, 0.69999999999999996, - 1.3962634015954636 }, - { 1.2807475181182502, 0.50000000000000000, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.69999999999999996. -template <typename Tp> -void test148() -{ - 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(data148) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data148[i].k), Tp(data148[i].nu), - Tp(data148[i].phi)); - const Tp f0 = data148[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)); -} +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.6797816859260978e-16 +// mean(f - f_Boost): 9.4368957093138303e-17 +// variance(f - f_Boost): 7.7794254682023874e-32 +// stddev(f - f_Boost): 2.7891621444803792e-16 +const testcase_ellint_3<double> +data146[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17564466176941509, 0.50000000000000000, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35805679276065394, 0.50000000000000000, 0.50000000000000000, + 0.34906585039886590 }, + { 0.55446601496200032, 0.50000000000000000, 0.50000000000000000, + 0.52359877559829882 }, + { 0.77288783578259013, 0.50000000000000000, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0220246013918972, 0.50000000000000000, 0.50000000000000000, + 0.87266462599716477 }, + { 1.3101681612463965, 0.50000000000000000, 0.50000000000000000, + 1.0471975511965976 }, + { 1.6422994881851025, 0.50000000000000000, 0.50000000000000000, + 1.2217304763960306 }, + { 2.0152636030998816, 0.50000000000000000, 0.50000000000000000, + 1.3962634015954636 }, + { 2.4136715042011945, 0.50000000000000000, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler146 = 2.5000000000000020e-13; + +// Test data for k=0.50000000000000000, nu=0.60000000000000009. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.9178421578645735e-16 +// mean(f - f_Boost): 1.3322676295501878e-16 +// variance(f - f_Boost): 1.7749370367472766e-31 +// stddev(f - f_Boost): 4.2130001622920411e-16 +const testcase_ellint_3<double> +data147[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17582479017522740, 0.50000000000000000, 0.60000000000000009, + 0.17453292519943295 }, + { 0.35956964546660036, 0.50000000000000000, 0.60000000000000009, + 0.34906585039886590 }, + { 0.55999790372984193, 0.50000000000000000, 0.60000000000000009, + 0.52359877559829882 }, + { 0.78751507911209895, 0.50000000000000000, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0546620505035220, 0.50000000000000000, 0.60000000000000009, + 0.87266462599716477 }, + { 1.3754438357425935, 0.50000000000000000, 0.60000000000000009, + 1.0471975511965976 }, + { 1.7615727400820127, 0.50000000000000000, 0.60000000000000009, + 1.2217304763960306 }, + { 2.2134638067565242, 0.50000000000000000, 0.60000000000000009, + 1.3962634015954636 }, + { 2.7090491861753558, 0.50000000000000000, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler147 = 2.5000000000000020e-13; + +// Test data for k=0.50000000000000000, nu=0.70000000000000007. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.0745105182189226e-16 +// mean(f - f_Boost): 4.1633363423443370e-17 +// variance(f - f_Boost): 1.9996383743576116e-32 +// stddev(f - f_Boost): 1.4140857026211713e-16 +const testcase_ellint_3<double> +data148[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17600558435914915, 0.50000000000000000, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36110561926726259, 0.50000000000000000, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56573074641137111, 0.50000000000000000, 0.70000000000000007, + 0.52359877559829882 }, + { 0.80316073084237205, 0.50000000000000000, 0.70000000000000007, + 0.69813170079773179 }, + { 1.0911910688131461, 0.50000000000000000, 0.70000000000000007, + 0.87266462599716477 }, + { 1.4530946406380640, 0.50000000000000000, 0.70000000000000007, + 1.0471975511965976 }, + { 1.9144386536785372, 0.50000000000000000, 0.70000000000000007, + 1.2217304763960306 }, + { 2.4878788958234970, 0.50000000000000000, 0.70000000000000007, + 1.3962634015954636 }, + { 3.1433945297859225, 0.50000000000000000, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler148 = 2.5000000000000020e-13; // Test data for k=0.50000000000000000, nu=0.80000000000000004. -testcase_ellint_3<double> data149[] = { - { -0.0000000000000000, 0.50000000000000000, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17336164805979126, 0.50000000000000000, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34024350132086773, 0.50000000000000000, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49643719555734084, 0.50000000000000000, 0.80000000000000004, - 0.52359877559829882 }, - { 0.64071162456976150, 0.50000000000000000, 0.80000000000000004, - 0.69813170079773179 }, - { 0.77407836177211908, 0.50000000000000000, 0.80000000000000004, - 0.87266462599716477 }, - { 0.89867058251905652, 0.50000000000000000, 0.80000000000000004, - 1.0471975511965976 }, - { 1.0169181822134912, 0.50000000000000000, 0.80000000000000004, - 1.2217304763960306 }, - { 1.1311363312779448, 0.50000000000000000, 0.80000000000000004, - 1.3962634015954636 }, - { 1.2434165408189539, 0.50000000000000000, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.80000000000000004. -template <typename Tp> -void test149() -{ - 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(data149) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data149[i].k), Tp(data149[i].nu), - Tp(data149[i].phi)); - const Tp f0 = data149[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)); -} +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.4380477375534667e-16 +// mean(f - f_Boost): 2.3037127760972000e-16 +// variance(f - f_Boost): 1.4989821857033475e-31 +// stddev(f - f_Boost): 3.8716691306248618e-16 +const testcase_ellint_3<double> +data149[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17618704872620228, 0.50000000000000000, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36266535159745827, 0.50000000000000000, 0.80000000000000004, + 0.34906585039886590 }, + { 0.57167789954529158, 0.50000000000000000, 0.80000000000000004, + 0.52359877559829882 }, + { 0.81995752984315018, 0.50000000000000000, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1325112162158122, 0.50000000000000000, 0.80000000000000004, + 0.87266462599716477 }, + { 1.5479055930718042, 0.50000000000000000, 0.80000000000000004, + 1.0471975511965976 }, + { 2.1215243941010486, 0.50000000000000000, 0.80000000000000004, + 1.2217304763960306 }, + { 2.9069405767650132, 0.50000000000000000, 0.80000000000000004, + 1.3962634015954636 }, + { 3.8750701888108066, 0.50000000000000000, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler149 = 2.5000000000000020e-13; // Test data for k=0.50000000000000000, nu=0.90000000000000002. -testcase_ellint_3<double> data150[] = { - { -0.0000000000000000, 0.50000000000000000, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17319040056865681, 0.50000000000000000, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33899920036578557, 0.50000000000000000, 0.90000000000000002, - 0.34906585039886590 }, - { 0.49279362182695186, 0.50000000000000000, 0.90000000000000002, - 0.52359877559829882 }, - { 0.63342123379746151, 0.50000000000000000, 0.90000000000000002, - 0.69813170079773179 }, - { 0.76220595179550321, 0.50000000000000000, 0.90000000000000002, - 0.87266462599716477 }, - { 0.88160004743532294, 0.50000000000000000, 0.90000000000000002, - 1.0471975511965976 }, - { 0.99427448642310134, 0.50000000000000000, 0.90000000000000002, - 1.2217304763960306 }, - { 1.1027091512470093, 0.50000000000000000, 0.90000000000000002, - 1.3962634015954636 }, - { 1.2091116095504744, 0.50000000000000000, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.50000000000000000, nu=0.90000000000000002. -template <typename Tp> -void test150() -{ - 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(data150) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data150[i].k), Tp(data150[i].nu), - Tp(data150[i].phi)); - const Tp f0 = data150[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 3.6192315188521289e-16 +// mean(f - f_Boost): 3.5249581031848718e-16 +// variance(f - f_Boost): 2.5029385557256515e-31 +// stddev(f - f_Boost): 5.0029376927217987e-16 +const testcase_ellint_3<double> +data150[10] = +{ + { 0.0000000000000000, 0.50000000000000000, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17636918772384180, 0.50000000000000000, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36424950570740700, 0.50000000000000000, 0.90000000000000002, + 0.34906585039886590 }, + { 0.57785404590231426, 0.50000000000000000, 0.90000000000000002, + 0.52359877559829882 }, + { 0.83806480521716531, 0.50000000000000000, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1798568683069752, 0.50000000000000000, 0.90000000000000002, + 0.87266462599716477 }, + { 1.6678766243739607, 0.50000000000000000, 0.90000000000000002, + 1.0471975511965976 }, + { 2.4282976450693483, 0.50000000000000000, 0.90000000000000002, + 1.2217304763960306 }, + { 3.6810787666126656, 0.50000000000000000, 0.90000000000000002, + 1.3962634015954636 }, + { 5.5355132096026454, 0.50000000000000000, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler150 = 2.5000000000000020e-13; // Test data for k=0.60000000000000009, nu=0.0000000000000000. -testcase_ellint_3<double> data151[] = { - { -0.0000000000000000, 0.60000000000000009, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17485154362988362, 0.60000000000000009, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35160509865544326, 0.60000000000000009, 0.0000000000000000, - 0.34906585039886590 }, - { 0.53210652578446160, 0.60000000000000009, 0.0000000000000000, - 0.52359877559829882 }, - { 0.71805304664485670, 0.60000000000000009, 0.0000000000000000, - 0.69813170079773179 }, - { 0.91082759030195970, 0.60000000000000009, 0.0000000000000000, - 0.87266462599716477 }, - { 1.1112333229323366, 0.60000000000000009, 0.0000000000000000, - 1.0471975511965976 }, - { 1.3191461190365270, 0.60000000000000009, 0.0000000000000000, - 1.2217304763960306 }, - { 1.5332022105084775, 0.60000000000000009, 0.0000000000000000, - 1.3962634015954636 }, - { 1.7507538029157526, 0.60000000000000009, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.0000000000000000. -template <typename Tp> -void test151() -{ - 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(data151) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data151[i].k), Tp(data151[i].nu), - Tp(data151[i].phi)); - const Tp f0 = data151[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.3664899092028927e-16 +// mean(f - f_Boost): 3.0531133177191807e-17 +// variance(f - f_Boost): 7.8758646268991113e-33 +// stddev(f - f_Boost): 8.8746068233466605e-17 +const testcase_ellint_3<double> +data151[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17485154362988359, 0.60000000000000009, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35160509865544320, 0.60000000000000009, 0.0000000000000000, + 0.34906585039886590 }, + { 0.53210652578446138, 0.60000000000000009, 0.0000000000000000, + 0.52359877559829882 }, + { 0.71805304664485659, 0.60000000000000009, 0.0000000000000000, + 0.69813170079773179 }, + { 0.91082759030195981, 0.60000000000000009, 0.0000000000000000, + 0.87266462599716477 }, + { 1.1112333229323361, 0.60000000000000009, 0.0000000000000000, + 1.0471975511965976 }, + { 1.3191461190365270, 0.60000000000000009, 0.0000000000000000, + 1.2217304763960306 }, + { 1.5332022105084779, 0.60000000000000009, 0.0000000000000000, + 1.3962634015954636 }, + { 1.7507538029157526, 0.60000000000000009, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler151 = 2.5000000000000020e-13; // Test data for k=0.60000000000000009, nu=0.10000000000000001. -testcase_ellint_3<double> data152[] = { - { -0.0000000000000000, 0.60000000000000009, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17467514275022014, 0.60000000000000009, 0.10000000000000001, - 0.17453292519943295 }, - { 0.35021333086258255, 0.60000000000000009, 0.10000000000000001, - 0.34906585039886590 }, - { 0.52751664092962713, 0.60000000000000009, 0.10000000000000001, - 0.52359877559829882 }, - { 0.70752126971957885, 0.60000000000000009, 0.10000000000000001, - 0.69813170079773179 }, - { 0.89111058756112871, 0.60000000000000009, 0.10000000000000001, - 0.87266462599716477 }, - { 1.0789241202877773, 0.60000000000000009, 0.10000000000000001, - 1.0471975511965976 }, - { 1.2710800210399946, 0.60000000000000009, 0.10000000000000001, - 1.2217304763960306 }, - { 1.4669060574440278, 0.60000000000000009, 0.10000000000000001, - 1.3962634015954636 }, - { 1.6648615773343014, 0.60000000000000009, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.10000000000000001. -template <typename Tp> -void test152() -{ - 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(data152) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data152[i].k), Tp(data152[i].nu), - Tp(data152[i].phi)); - const Tp f0 = data152[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.2335247010355137e-16 +// mean(f - f_Boost): 8.6042284408449634e-17 +// variance(f - f_Boost): 2.2835347143080263e-33 +// stddev(f - f_Boost): 4.7786344433405099e-17 +const testcase_ellint_3<double> +data152[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17502858548476194, 0.60000000000000009, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35301673150537388, 0.60000000000000009, 0.10000000000000001, + 0.34906585039886590 }, + { 0.53683932476326812, 0.60000000000000009, 0.10000000000000001, + 0.52359877559829882 }, + { 0.72914228589586771, 0.60000000000000009, 0.10000000000000001, + 0.69813170079773179 }, + { 0.93208036718354692, 0.60000000000000009, 0.10000000000000001, + 0.87266462599716477 }, + { 1.1468984688863377, 0.60000000000000009, 0.10000000000000001, + 1.0471975511965976 }, + { 1.3733904977062528, 0.60000000000000009, 0.10000000000000001, + 1.2217304763960306 }, + { 1.6094225663372157, 0.60000000000000009, 0.10000000000000001, + 1.3962634015954636 }, + { 1.8508766487100685, 0.60000000000000009, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler152 = 2.5000000000000020e-13; // Test data for k=0.60000000000000009, nu=0.20000000000000001. -testcase_ellint_3<double> data153[] = { - { -0.0000000000000000, 0.60000000000000009, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17449937871800653, 0.60000000000000009, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34884093647346553, 0.60000000000000009, 0.20000000000000001, - 0.34906585039886590 }, - { 0.52306221119844110, 0.60000000000000009, 0.20000000000000001, - 0.52359877559829882 }, - { 0.69749955678982223, 0.60000000000000009, 0.20000000000000001, - 0.69813170079773179 }, - { 0.87274610682416853, 0.60000000000000009, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0494620540750796, 0.60000000000000009, 0.20000000000000001, - 1.0471975511965976 }, - { 1.2280847305507339, 0.60000000000000009, 0.20000000000000001, - 1.2217304763960306 }, - { 1.4085436279696888, 0.60000000000000009, 0.20000000000000001, - 1.3962634015954636 }, - { 1.5901418016279374, 0.60000000000000009, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.20000000000000001. -template <typename Tp> -void test153() -{ - 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(data153) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data153[i].k), Tp(data153[i].nu), - Tp(data153[i].phi)); - const Tp f0 = data153[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, nu=0.29999999999999999. -testcase_ellint_3<double> data154[] = { - { -0.0000000000000000, 0.60000000000000009, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17432424744393935, 0.60000000000000009, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34748744127146447, 0.60000000000000009, 0.29999999999999999, - 0.34906585039886590 }, - { 0.51873632743924847, 0.60000000000000009, 0.29999999999999999, - 0.52359877559829882 }, - { 0.68794610396313127, 0.60000000000000009, 0.29999999999999999, - 0.69813170079773179 }, - { 0.85558070175468726, 0.60000000000000009, 0.29999999999999999, - 0.87266462599716477 }, - { 1.0224416343605658, 0.60000000000000009, 0.29999999999999999, - 1.0471975511965976 }, - { 1.1893144457936788, 0.60000000000000009, 0.29999999999999999, - 1.2217304763960306 }, - { 1.3566435377982575, 0.60000000000000009, 0.29999999999999999, - 1.3962634015954636 }, - { 1.5243814243493585, 0.60000000000000009, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.29999999999999999. -template <typename Tp> -void test154() -{ - 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(data154) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data154[i].k), Tp(data154[i].nu), - Tp(data154[i].phi)); - const Tp f0 = data154[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 2.2547200163366559e-16 +// mean(f - f_Boost): -2.4980018054066023e-17 +// variance(f - f_Boost): 2.1685495635542404e-32 +// stddev(f - f_Boost): 1.4725995937641163e-16 +const testcase_ellint_3<double> +data153[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17520627248155893, 0.60000000000000009, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35444873935437748, 0.60000000000000009, 0.20000000000000001, + 0.34906585039886590 }, + { 0.54172310557682524, 0.60000000000000009, 0.20000000000000001, + 0.52359877559829882 }, + { 0.74084300280734672, 0.60000000000000009, 0.20000000000000001, + 0.69813170079773179 }, + { 0.95509001527006121, 0.60000000000000009, 0.20000000000000001, + 0.87266462599716477 }, + { 1.1865688084431796, 0.60000000000000009, 0.20000000000000001, + 1.0471975511965976 }, + { 1.4352978868932600, 0.60000000000000009, 0.20000000000000001, + 1.2217304763960306 }, + { 1.6983400371331818, 0.60000000000000009, 0.20000000000000001, + 1.3962634015954636 }, + { 1.9695980282802217, 0.60000000000000009, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler153 = 2.5000000000000020e-13; + +// Test data for k=0.60000000000000009, nu=0.30000000000000004. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.9470074709717020e-16 +// mean(f - f_Boost): 3.0531133177191807e-17 +// variance(f - f_Boost): 1.1508025840536076e-34 +// stddev(f - f_Boost): 1.0727546709539920e-17 +const testcase_ellint_3<double> +data154[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17538460882640122, 0.60000000000000009, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35590165133735557, 0.60000000000000009, 0.30000000000000004, + 0.34906585039886590 }, + { 0.54676661152254535, 0.60000000000000009, 0.30000000000000004, + 0.52359877559829882 }, + { 0.75321709418305305, 0.60000000000000009, 0.30000000000000004, + 0.69813170079773179 }, + { 0.98012637808992920, 0.60000000000000009, 0.30000000000000004, + 0.87266462599716477 }, + { 1.2310891277158875, 0.60000000000000009, 0.30000000000000004, + 1.0471975511965976 }, + { 1.5069157924585623, 0.60000000000000009, 0.30000000000000004, + 1.2217304763960306 }, + { 1.8039583598337940, 0.60000000000000009, 0.30000000000000004, + 1.3962634015954636 }, + { 2.1134154405060599, 0.60000000000000009, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler154 = 2.5000000000000020e-13; // Test data for k=0.60000000000000009, nu=0.40000000000000002. -testcase_ellint_3<double> data155[] = { - { -0.0000000000000000, 0.60000000000000009, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17414974487670720, 0.60000000000000009, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34615238767335027, 0.60000000000000009, 0.40000000000000002, - 0.34906585039886590 }, - { 0.51453257838108579, 0.60000000000000009, 0.40000000000000002, - 0.52359877559829882 }, - { 0.67882386787534410, 0.60000000000000009, 0.40000000000000002, - 0.69813170079773179 }, - { 0.83948470233173578, 0.60000000000000009, 0.40000000000000002, - 0.87266462599716477 }, - { 0.99753496200074021, 0.60000000000000009, 0.40000000000000002, - 1.0471975511965976 }, - { 1.1541101404388487, 0.60000000000000009, 0.40000000000000002, - 1.2217304763960306 }, - { 1.3100911323398816, 0.60000000000000009, 0.40000000000000002, - 1.3962634015954636 }, - { 1.4659345278069984, 0.60000000000000009, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.40000000000000002. -template <typename Tp> -void test155() -{ - 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(data155) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data155[i].k), Tp(data155[i].nu), - Tp(data155[i].phi)); - const Tp f0 = data155[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 2.8974839914337670e-16 +// mean(f - f_Boost): -1.3877787807814457e-17 +// variance(f - f_Boost): 2.2849613290816465e-32 +// stddev(f - f_Boost): 1.5116088545260797e-16 +const testcase_ellint_3<double> +data155[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17556359876533037, 0.60000000000000009, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35737601674244679, 0.60000000000000009, 0.40000000000000002, + 0.34906585039886590 }, + { 0.55197933771320218, 0.60000000000000009, 0.40000000000000002, + 0.52359877559829882 }, + { 0.76633591620002905, 0.60000000000000009, 0.40000000000000002, + 0.69813170079773179 }, + { 1.0075231136019616, 0.60000000000000009, 0.40000000000000002, + 0.87266462599716477 }, + { 1.2815842073813450, 0.60000000000000009, 0.40000000000000002, + 1.0471975511965976 }, + { 1.5911666941449827, 0.60000000000000009, 0.40000000000000002, + 1.2217304763960306 }, + { 1.9323227566025762, 0.60000000000000009, 0.40000000000000002, + 1.3962634015954636 }, + { 2.2925036420985130, 0.60000000000000009, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler155 = 2.5000000000000020e-13; // Test data for k=0.60000000000000009, nu=0.50000000000000000. -testcase_ellint_3<double> data156[] = { - { -0.0000000000000000, 0.60000000000000009, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17397586700252810, 0.60000000000000009, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34483533397138516, 0.60000000000000009, 0.50000000000000000, - 0.34906585039886590 }, - { 0.51044500461706499, 0.60000000000000009, 0.50000000000000000, - 0.52359877559829882 }, - { 0.67009988034712675, 0.60000000000000009, 0.50000000000000000, - 0.69813170079773179 }, - { 0.82434762375735193, 0.60000000000000009, 0.50000000000000000, - 0.87266462599716477 }, - { 0.97447346702799043, 0.60000000000000009, 0.50000000000000000, - 1.0471975511965976 }, - { 1.1219494000522143, 0.60000000000000009, 0.50000000000000000, - 1.2217304763960306 }, - { 1.2680242605954488, 0.60000000000000009, 0.50000000000000000, - 1.3962634015954636 }, - { 1.4135484285693078, 0.60000000000000009, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.50000000000000000. -template <typename Tp> -void test156() -{ - 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(data156) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data156[i].k), Tp(data156[i].nu), - Tp(data156[i].phi)); - const Tp f0 = data156[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, nu=0.59999999999999998. -testcase_ellint_3<double> data157[] = { - { -0.0000000000000000, 0.60000000000000009, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17380260984469356, 0.60000000000000009, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34353585361777839, 0.60000000000000009, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50646805774321402, 0.60000000000000009, 0.59999999999999998, - 0.52359877559829882 }, - { 0.66174468108625517, 0.60000000000000009, 0.59999999999999998, - 0.69813170079773179 }, - { 0.81007462280278408, 0.60000000000000009, 0.59999999999999998, - 0.87266462599716477 }, - { 0.95303466945718773, 0.60000000000000009, 0.59999999999999998, - 1.0471975511965976 }, - { 1.0924118588677503, 0.60000000000000009, 0.59999999999999998, - 1.2217304763960306 }, - { 1.2297640574847937, 0.60000000000000009, 0.59999999999999998, - 1.3962634015954636 }, - { 1.3662507535812816, 0.60000000000000009, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.59999999999999998. -template <typename Tp> -void test157() -{ - 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(data157) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data157[i].k), Tp(data157[i].nu), - Tp(data157[i].phi)); - const Tp f0 = data157[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, nu=0.69999999999999996. -testcase_ellint_3<double> data158[] = { - { -0.0000000000000000, 0.60000000000000009, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17362996946312009, 0.60000000000000009, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34225353454870588, 0.60000000000000009, 0.69999999999999996, - 0.34906585039886590 }, - { 0.50259656397799546, 0.60000000000000009, 0.69999999999999996, - 0.52359877559829882 }, - { 0.65373184496628944, 0.60000000000000009, 0.69999999999999996, - 0.69813170079773179 }, - { 0.79658372884056439, 0.60000000000000009, 0.69999999999999996, - 0.87266462599716477 }, - { 0.93303240100245466, 0.60000000000000009, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0651547944716557, 0.60000000000000009, 0.69999999999999996, - 1.2217304763960306 }, - { 1.1947676204853441, 0.60000000000000009, 0.69999999999999996, - 1.3962634015954636 }, - { 1.3232737468822811, 0.60000000000000009, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.69999999999999996. -template <typename Tp> -void test158() -{ - 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(data158) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data158[i].k), Tp(data158[i].nu), - Tp(data158[i].phi)); - const Tp f0 = data158[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 2.1397785842303966e-16 +// mean(f - f_Boost): 9.1593399531575410e-17 +// variance(f - f_Boost): 1.5339913122479866e-32 +// stddev(f - f_Boost): 1.2385440291923362e-16 +const testcase_ellint_3<double> +data156[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17574324658480217, 0.60000000000000009, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35887240603169313, 0.60000000000000009, 0.50000000000000000, + 0.34906585039886590 }, + { 0.55737161826345261, 0.60000000000000009, 0.50000000000000000, + 0.52359877559829882 }, + { 0.78028227313077458, 0.60000000000000009, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0376989776486290, 0.60000000000000009, 0.50000000000000000, + 0.87266462599716477 }, + { 1.3395933991042928, 0.60000000000000009, 0.50000000000000000, + 1.0471975511965976 }, + { 1.6924049626591784, 0.60000000000000009, 0.50000000000000000, + 1.2217304763960306 }, + { 2.0931011856518920, 0.60000000000000009, 0.50000000000000000, + 1.3962634015954636 }, + { 2.5239007084492711, 0.60000000000000009, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler156 = 2.5000000000000020e-13; + +// Test data for k=0.60000000000000009, nu=0.60000000000000009. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.6651378277398083e-16 +// mean(f - f_Boost): 1.1934897514720432e-16 +// variance(f - f_Boost): 1.7585404776158019e-33 +// stddev(f - f_Boost): 4.1934955319110598e-17 +const testcase_ellint_3<double> +data157[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17592355661219386, 0.60000000000000009, 0.60000000000000009, + 0.17453292519943295 }, + { 0.36039141192661606, 0.60000000000000009, 0.60000000000000009, + 0.34906585039886590 }, + { 0.56295472636903854, 0.60000000000000009, 0.60000000000000009, + 0.52359877559829882 }, + { 0.79515295130165986, 0.60000000000000009, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0711886441942242, 0.60000000000000009, 0.60000000000000009, + 0.87266462599716477 }, + { 1.4072952835139891, 0.60000000000000009, 0.60000000000000009, + 1.0471975511965976 }, + { 1.8174863977376825, 0.60000000000000009, 0.60000000000000009, + 1.2217304763960306 }, + { 2.3029921578542232, 0.60000000000000009, 0.60000000000000009, + 1.3962634015954636 }, + { 2.8388723099514972, 0.60000000000000009, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler157 = 2.5000000000000020e-13; + +// Test data for k=0.60000000000000009, nu=0.70000000000000007. +// max(|f - f_Boost|): 4.4408920985006262e-16 at index 9 +// max(|f - f_Boost| / |f_Boost|): 2.0027679235921772e-16 +// mean(f - f_Boost): -1.3877787807814457e-17 +// variance(f - f_Boost): 2.2849613290816465e-32 +// stddev(f - f_Boost): 1.5116088545260797e-16 +const testcase_ellint_3<double> +data158[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17610453321631936, 0.60000000000000009, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36193365056369764, 0.60000000000000009, 0.70000000000000007, + 0.34906585039886590 }, + { 0.56874098962268527, 0.60000000000000009, 0.70000000000000007, + 0.52359877559829882 }, + { 0.81106198671477181, 0.60000000000000009, 0.70000000000000007, + 0.69813170079773179 }, + { 1.1086886419010082, 0.60000000000000009, 0.70000000000000007, + 0.87266462599716477 }, + { 1.4879048567239257, 0.60000000000000009, 0.70000000000000007, + 1.0471975511965976 }, + { 1.9780310073615925, 0.60000000000000009, 0.70000000000000007, + 1.2217304763960306 }, + { 2.5941545586772712, 0.60000000000000009, 0.70000000000000007, + 1.3962634015954636 }, + { 3.3029735898397159, 0.60000000000000009, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler158 = 2.5000000000000020e-13; // Test data for k=0.60000000000000009, nu=0.80000000000000004. -testcase_ellint_3<double> data159[] = { - { -0.0000000000000000, 0.60000000000000009, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17345794195390687, 0.60000000000000009, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34098797854531027, 0.60000000000000009, 0.80000000000000004, - 0.34906585039886590 }, - { 0.49882569168826230, 0.60000000000000009, 0.80000000000000004, - 0.52359877559829882 }, - { 0.64603758566475511, 0.60000000000000009, 0.80000000000000004, - 0.69813170079773179 }, - { 0.78380365594769730, 0.60000000000000009, 0.80000000000000004, - 0.87266462599716477 }, - { 0.91430946255611223, 0.60000000000000009, 0.80000000000000004, - 1.0471975511965976 }, - { 1.0398955217270607, 0.60000000000000009, 0.80000000000000004, - 1.2217304763960306 }, - { 1.1625948314277679, 0.60000000000000009, 0.80000000000000004, - 1.3962634015954636 }, - { 1.2840021261752192, 0.60000000000000009, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.80000000000000004. -template <typename Tp> -void test159() -{ - 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(data159) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data159[i].k), Tp(data159[i].nu), - Tp(data159[i].phi)); - const Tp f0 = data159[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 7.3044933435043190e-16 +// mean(f - f_Boost): 2.6367796834847468e-16 +// variance(f - f_Boost): 8.5834655546147173e-33 +// stddev(f - f_Boost): 9.2646994309662939e-17 +const testcase_ellint_3<double> +data159[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17628618080795252, 0.60000000000000009, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36349976272521012, 0.60000000000000009, 0.80000000000000004, + 0.34906585039886590 }, + { 0.57474392342151914, 0.60000000000000009, 0.80000000000000004, + 0.52359877559829882 }, + { 0.82814493499158170, 0.60000000000000009, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1511281795998280, 0.60000000000000009, 0.80000000000000004, + 0.87266462599716477 }, + { 1.5864286332503075, 0.60000000000000009, 0.80000000000000004, + 1.0471975511965976 }, + { 2.1958944866494527, 0.60000000000000009, 0.80000000000000004, + 1.2217304763960306 }, + { 3.0398358172574604, 0.60000000000000009, 0.80000000000000004, + 1.3962634015954636 }, + { 4.0867036409261832, 0.60000000000000009, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler159 = 2.5000000000000020e-13; // Test data for k=0.60000000000000009, nu=0.90000000000000002. -testcase_ellint_3<double> data160[] = { - { -0.0000000000000000, 0.60000000000000009, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17328652344890033, 0.60000000000000009, 0.90000000000000002, - 0.17453292519943295 }, - { 0.33973880062929018, 0.60000000000000009, 0.90000000000000002, - 0.34906585039886590 }, - { 0.49515092233122765, 0.60000000000000009, 0.90000000000000002, - 0.52359877559829882 }, - { 0.63864042139737043, 0.60000000000000009, 0.90000000000000002, - 0.69813170079773179 }, - { 0.77167205646538850, 0.60000000000000009, 0.90000000000000002, - 0.87266462599716477 }, - { 0.89673202848034428, 0.60000000000000009, 0.90000000000000002, - 1.0471975511965976 }, - { 1.0163984492661304, 0.60000000000000009, 0.90000000000000002, - 1.2217304763960306 }, - { 1.1328845785162431, 0.60000000000000009, 0.90000000000000002, - 1.3962634015954636 }, - { 1.2479362973851875, 0.60000000000000009, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.60000000000000009, nu=0.90000000000000002. -template <typename Tp> -void test160() -{ - 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(data160) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data160[i].k), Tp(data160[i].nu), - Tp(data160[i].phi)); - const Tp f0 = data160[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, nu=0.0000000000000000. -testcase_ellint_3<double> data161[] = { - { -0.0000000000000000, 0.69999999999999996, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17496737466916720, 0.69999999999999996, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35254687535677925, 0.69999999999999996, 0.0000000000000000, - 0.34906585039886590 }, - { 0.53536740275997130, 0.69999999999999996, 0.0000000000000000, - 0.52359877559829882 }, - { 0.72603797651684465, 0.69999999999999996, 0.0000000000000000, - 0.69813170079773179 }, - { 0.92698296348313458, 0.69999999999999996, 0.0000000000000000, - 0.87266462599716477 }, - { 1.1400447527693316, 0.69999999999999996, 0.0000000000000000, - 1.0471975511965976 }, - { 1.3657668117194071, 0.69999999999999996, 0.0000000000000000, - 1.2217304763960306 }, - { 1.6024686895959159, 0.69999999999999996, 0.0000000000000000, - 1.3962634015954636 }, - { 1.8456939983747236, 0.69999999999999996, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.0000000000000000. -template <typename Tp> -void test161() -{ - 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(data161) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data161[i].k), Tp(data161[i].nu), - Tp(data161[i].phi)); - const Tp f0 = data161[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, nu=0.10000000000000001. -testcase_ellint_3<double> data162[] = { - { -0.0000000000000000, 0.69999999999999996, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17479076384884681, 0.69999999999999996, 0.10000000000000001, - 0.17453292519943295 }, - { 0.35114844900396364, 0.69999999999999996, 0.10000000000000001, - 0.34906585039886590 }, - { 0.53072776947527012, 0.69999999999999996, 0.10000000000000001, - 0.52359877559829882 }, - { 0.71530198262386246, 0.69999999999999996, 0.10000000000000001, - 0.69813170079773179 }, - { 0.90666760677828306, 0.69999999999999996, 0.10000000000000001, - 0.87266462599716477 }, - { 1.1063366517438080, 0.69999999999999996, 0.10000000000000001, - 1.0471975511965976 }, - { 1.3149477243092147, 0.69999999999999996, 0.10000000000000001, - 1.2217304763960306 }, - { 1.5314886725038925, 0.69999999999999996, 0.10000000000000001, - 1.3962634015954636 }, - { 1.7528050171757608, 0.69999999999999996, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.10000000000000001. -template <typename Tp> -void test162() -{ - 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(data162) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data162[i].k), Tp(data162[i].nu), - Tp(data162[i].phi)); - const Tp f0 = data162[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, nu=0.20000000000000001. -testcase_ellint_3<double> data163[] = { - { -0.0000000000000000, 0.69999999999999996, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17461479077791472, 0.69999999999999996, 0.20000000000000001, - 0.17453292519943295 }, - { 0.34976950621407538, 0.69999999999999996, 0.20000000000000001, - 0.34906585039886590 }, - { 0.52622533231350188, 0.69999999999999996, 0.20000000000000001, - 0.52359877559829882 }, - { 0.70508774017895226, 0.69999999999999996, 0.20000000000000001, - 0.69813170079773179 }, - { 0.88775302531730294, 0.69999999999999996, 0.20000000000000001, - 0.87266462599716477 }, - { 1.0756195476149006, 0.69999999999999996, 0.20000000000000001, - 1.0471975511965976 }, - { 1.2695349716654372, 0.69999999999999996, 0.20000000000000001, - 1.2217304763960306 }, - { 1.4690814617070540, 0.69999999999999996, 0.20000000000000001, - 1.3962634015954636 }, - { 1.6721098780092147, 0.69999999999999996, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.20000000000000001. -template <typename Tp> -void test163() -{ - 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(data163) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data163[i].k), Tp(data163[i].nu), - Tp(data163[i].phi)); - const Tp f0 = data163[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, nu=0.29999999999999999. -testcase_ellint_3<double> data164[] = { - { -0.0000000000000000, 0.69999999999999996, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17443945136076172, 0.69999999999999996, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34840956983535287, 0.69999999999999996, 0.29999999999999999, - 0.34906585039886590 }, - { 0.52185308551329179, 0.69999999999999996, 0.29999999999999999, - 0.52359877559829882 }, - { 0.69535240431168266, 0.69999999999999996, 0.29999999999999999, - 0.69813170079773179 }, - { 0.87007983473964923, 0.69999999999999996, 0.29999999999999999, - 0.87266462599716477 }, - { 1.0474657975577066, 0.69999999999999996, 0.29999999999999999, - 1.0471975511965976 }, - { 1.2286225419931889, 0.69999999999999996, 0.29999999999999999, - 1.2217304763960306 }, - { 1.4136490671013271, 0.69999999999999996, 0.29999999999999999, - 1.3962634015954636 }, - { 1.6011813647733213, 0.69999999999999996, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.29999999999999999. -template <typename Tp> -void test164() -{ - 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(data164) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data164[i].k), Tp(data164[i].nu), - Tp(data164[i].phi)); - const Tp f0 = data164[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, nu=0.40000000000000002. -testcase_ellint_3<double> data165[] = { - { -0.0000000000000000, 0.69999999999999996, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17426474153983226, 0.69999999999999996, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34706817945773732, 0.69999999999999996, 0.40000000000000002, - 0.34906585039886590 }, - { 0.51760452851738159, 0.69999999999999996, 0.40000000000000002, - 0.52359877559829882 }, - { 0.68605801534722766, 0.69999999999999996, 0.40000000000000002, - 0.69813170079773179 }, - { 0.85351339387296532, 0.69999999999999996, 0.40000000000000002, - 0.87266462599716477 }, - { 1.0215297967969537, 0.69999999999999996, 0.40000000000000002, - 1.0471975511965976 }, - { 1.1915051074460528, 0.69999999999999996, 0.40000000000000002, - 1.2217304763960306 }, - { 1.3639821911744707, 0.69999999999999996, 0.40000000000000002, - 1.3962634015954636 }, - { 1.5382162002954762, 0.69999999999999996, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.40000000000000002. -template <typename Tp> -void test165() -{ - 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(data165) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data165[i].k), Tp(data165[i].nu), - Tp(data165[i].phi)); - const Tp f0 = data165[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, nu=0.50000000000000000. -testcase_ellint_3<double> data166[] = { - { -0.0000000000000000, 0.69999999999999996, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17409065729516093, 0.69999999999999996, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34574489064986091, 0.69999999999999996, 0.50000000000000000, - 0.34906585039886590 }, - { 0.51347361925579793, 0.69999999999999996, 0.50000000000000000, - 0.52359877559829882 }, - { 0.67717079489579290, 0.69999999999999996, 0.50000000000000000, - 0.69813170079773179 }, - { 0.83793902055292280, 0.69999999999999996, 0.50000000000000000, - 0.87266462599716477 }, - { 0.99752863545289705, 0.69999999999999996, 0.50000000000000000, - 1.0471975511965976 }, - { 1.1576240080401499, 0.69999999999999996, 0.50000000000000000, - 1.2217304763960306 }, - { 1.3191464023923762, 0.69999999999999996, 0.50000000000000000, - 1.3962634015954636 }, - { 1.4818433192178544, 0.69999999999999996, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.50000000000000000. -template <typename Tp> -void test166() -{ - 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(data166) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data166[i].k), Tp(data166[i].nu), - Tp(data166[i].phi)); - const Tp f0 = data166[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, nu=0.59999999999999998. -testcase_ellint_3<double> data167[] = { - { -0.0000000000000000, 0.69999999999999996, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17391719464391611, 0.69999999999999996, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34443927423869031, 0.69999999999999996, 0.59999999999999998, - 0.34906585039886590 }, - { 0.50945473266486074, 0.69999999999999996, 0.59999999999999998, - 0.52359877559829882 }, - { 0.66866056326513823, 0.69999999999999996, 0.59999999999999998, - 0.69813170079773179 }, - { 0.82325830002337352, 0.69999999999999996, 0.59999999999999998, - 0.87266462599716477 }, - { 0.97522808245669357, 0.69999999999999996, 0.59999999999999998, - 1.0471975511965976 }, - { 1.1265300613705282, 0.69999999999999996, 0.59999999999999998, - 1.2217304763960306 }, - { 1.2784066076152003, 0.69999999999999996, 0.59999999999999998, - 1.3962634015954636 }, - { 1.4309994736080540, 0.69999999999999996, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.59999999999999998. -template <typename Tp> -void test167() -{ - 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(data167) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data167[i].k), Tp(data167[i].nu), - Tp(data167[i].phi)); - const Tp f0 = data167[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, nu=0.69999999999999996. -testcase_ellint_3<double> data168[] = { - { -0.0000000000000000, 0.69999999999999996, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17374434963995028, 0.69999999999999996, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34315091562900674, 0.69999999999999996, 0.69999999999999996, - 0.34906585039886590 }, - { 0.50554262375653358, 0.69999999999999996, 0.69999999999999996, - 0.52359877559829882 }, - { 0.66050025406305812, 0.69999999999999996, 0.69999999999999996, - 0.69813170079773179 }, - { 0.80938620118847404, 0.69999999999999996, 0.69999999999999996, - 0.87266462599716477 }, - { 0.95443223855852144, 0.69999999999999996, 0.69999999999999996, - 1.0471975511965976 }, - { 1.0978573207128302, 0.69999999999999996, 0.69999999999999996, - 1.2217304763960306 }, - { 1.2411754575007123, 0.69999999999999996, 0.69999999999999996, - 1.3962634015954636 }, - { 1.3848459188329196, 0.69999999999999996, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.69999999999999996. -template <typename Tp> -void test168() -{ - 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(data168) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data168[i].k), Tp(data168[i].nu), - Tp(data168[i].phi)); - const Tp f0 = data168[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, nu=0.80000000000000004. -testcase_ellint_3<double> data169[] = { - { -0.0000000000000000, 0.69999999999999996, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17357211837335737, 0.69999999999999996, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34187941416012108, 0.69999999999999996, 0.80000000000000004, - 0.34906585039886590 }, - { 0.50173239465478270, 0.69999999999999996, 0.80000000000000004, - 0.52359877559829882 }, - { 0.65266550725988315, 0.69999999999999996, 0.80000000000000004, - 0.69813170079773179 }, - { 0.79624879865249298, 0.69999999999999996, 0.80000000000000004, - 0.87266462599716477 }, - { 0.93497577043296920, 0.69999999999999996, 0.80000000000000004, - 1.0471975511965976 }, - { 1.0713041566930748, 0.69999999999999996, 0.80000000000000004, - 1.2217304763960306 }, - { 1.2069772023255652, 0.69999999999999996, 0.80000000000000004, - 1.3962634015954636 }, - { 1.3427110650397533, 0.69999999999999996, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.80000000000000004. -template <typename Tp> -void test169() -{ - 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(data169) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data169[i].k), Tp(data169[i].nu), - Tp(data169[i].phi)); - const Tp f0 = data169[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, nu=0.90000000000000002. -testcase_ellint_3<double> data170[] = { - { -0.0000000000000000, 0.69999999999999996, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17340049697003634, 0.69999999999999996, 0.90000000000000002, - 0.17453292519943295 }, - { 0.34062438249741556, 0.69999999999999996, 0.90000000000000002, - 0.34906585039886590 }, - { 0.49801946510076878, 0.69999999999999996, 0.90000000000000002, - 0.52359877559829882 }, - { 0.64513432604750487, 0.69999999999999996, 0.90000000000000002, - 0.69813170079773179 }, - { 0.78378145487573758, 0.69999999999999996, 0.90000000000000002, - 0.87266462599716477 }, - { 0.91671799500854634, 0.69999999999999996, 0.90000000000000002, - 1.0471975511965976 }, - { 1.0466193579463123, 0.69999999999999996, 0.90000000000000002, - 1.2217304763960306 }, - { 1.1754218079199146, 0.69999999999999996, 0.90000000000000002, - 1.3962634015954636 }, - { 1.3040500499695911, 0.69999999999999996, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.69999999999999996, nu=0.90000000000000002. -template <typename Tp> -void test170() -{ - 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(data170) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data170[i].k), Tp(data170[i].nu), - Tp(data170[i].phi)); - const Tp f0 = data170[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.5952142720718732e-16 +// mean(f - f_Boost): 4.6351811278100284e-16 +// variance(f - f_Boost): 2.1278339779151204e-31 +// stddev(f - f_Boost): 4.6128450851021651e-16 +const testcase_ellint_3<double> +data160[10] = +{ + { 0.0000000000000000, 0.60000000000000009, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17646850384035848, 0.60000000000000009, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36509041515134105, 0.60000000000000009, 0.90000000000000002, + 0.34906585039886590 }, + { 0.58097838596260631, 0.60000000000000009, 0.90000000000000002, + 0.52359877559829882 }, + { 0.84656453396163722, 0.60000000000000009, 0.90000000000000002, + 0.69813170079773179 }, + { 1.1997828426963724, 0.60000000000000009, 0.90000000000000002, + 0.87266462599716477 }, + { 1.7112436789225605, 0.60000000000000009, 0.90000000000000002, + 1.0471975511965976 }, + { 2.5193168553672312, 0.60000000000000009, 0.90000000000000002, + 1.2217304763960306 }, + { 3.8656670488606690, 0.60000000000000009, 0.90000000000000002, + 1.3962634015954636 }, + { 5.8709993116265604, 0.60000000000000009, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler160 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.0000000000000000. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.1569224977685422e-16 +// mean(f - f_Boost): 7.7715611723760953e-17 +// variance(f - f_Boost): 1.6571557210371951e-32 +// stddev(f - f_Boost): 1.2873056051447903e-16 +const testcase_ellint_3<double> +data161[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17496737466916723, 0.70000000000000018, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35254687535677931, 0.70000000000000018, 0.0000000000000000, + 0.34906585039886590 }, + { 0.53536740275997130, 0.70000000000000018, 0.0000000000000000, + 0.52359877559829882 }, + { 0.72603797651684454, 0.70000000000000018, 0.0000000000000000, + 0.69813170079773179 }, + { 0.92698296348313447, 0.70000000000000018, 0.0000000000000000, + 0.87266462599716477 }, + { 1.1400447527693318, 0.70000000000000018, 0.0000000000000000, + 1.0471975511965976 }, + { 1.3657668117194073, 0.70000000000000018, 0.0000000000000000, + 1.2217304763960306 }, + { 1.6024686895959164, 0.70000000000000018, 0.0000000000000000, + 1.3962634015954636 }, + { 1.8456939983747236, 0.70000000000000018, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler161 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.10000000000000001. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.9552278747527691e-16 +// mean(f - f_Boost): 1.1102230246251565e-16 +// variance(f - f_Boost): 1.3695501826753678e-32 +// stddev(f - f_Boost): 1.1702778228589004e-16 +const testcase_ellint_3<double> +data162[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17514462737300920, 0.70000000000000018, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35396527997470451, 0.70000000000000018, 0.10000000000000001, + 0.34906585039886590 }, + { 0.54015179589433981, 0.70000000000000018, 0.10000000000000001, + 0.52359877559829882 }, + { 0.73734430854477728, 0.70000000000000018, 0.10000000000000001, + 0.69813170079773179 }, + { 0.94888950796697047, 0.70000000000000018, 0.10000000000000001, + 0.87266462599716477 }, + { 1.1772807959736322, 0.70000000000000018, 0.10000000000000001, + 1.0471975511965976 }, + { 1.4231796401075834, 0.70000000000000018, 0.10000000000000001, + 1.2217304763960306 }, + { 1.6841856799887471, 0.70000000000000018, 0.10000000000000001, + 1.3962634015954636 }, + { 1.9541347343119564, 0.70000000000000018, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler162 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.20000000000000001. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.7430437016285820e-16 +// mean(f - f_Boost): 3.3306690738754695e-17 +// variance(f - f_Boost): 1.3695501826753678e-34 +// stddev(f - f_Boost): 1.1702778228589003e-17 +const testcase_ellint_3<double> +data163[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17532252613350796, 0.70000000000000018, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35540417596807522, 0.70000000000000018, 0.20000000000000001, + 0.34906585039886590 }, + { 0.54508913033361928, 0.70000000000000018, 0.20000000000000001, + 0.52359877559829882 }, + { 0.74927635777718415, 0.70000000000000018, 0.20000000000000001, + 0.69813170079773179 }, + { 0.97261706337936338, 0.70000000000000018, 0.20000000000000001, + 0.87266462599716477 }, + { 1.2187303976209327, 0.70000000000000018, 0.20000000000000001, + 1.0471975511965976 }, + { 1.4887796709222487, 0.70000000000000018, 0.20000000000000001, + 1.2217304763960306 }, + { 1.7796581281839214, 0.70000000000000018, 0.20000000000000001, + 1.3962634015954636 }, + { 2.0829290325820207, 0.70000000000000018, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler163 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.30000000000000004. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.2570807706941696e-16 +// mean(f - f_Boost): 8.8817841970012528e-17 +// variance(f - f_Boost): 1.5582437633995295e-32 +// stddev(f - f_Boost): 1.2482963443828271e-16 +const testcase_ellint_3<double> +data164[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17550107516328570, 0.70000000000000018, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35686409576571965, 0.70000000000000018, 0.30000000000000004, + 0.34906585039886590 }, + { 0.55018827316513352, 0.70000000000000018, 0.30000000000000004, + 0.52359877559829882 }, + { 0.76189759494390275, 0.70000000000000018, 0.30000000000000004, + 0.69813170079773179 }, + { 0.99844623430885626, 0.70000000000000018, 0.30000000000000004, + 0.87266462599716477 }, + { 1.2652862989039833, 0.70000000000000018, 0.30000000000000004, + 1.0471975511965976 }, + { 1.5647666808691361, 0.70000000000000018, 0.30000000000000004, + 1.2217304763960306 }, + { 1.8932499694938165, 0.70000000000000018, 0.30000000000000004, + 1.3962634015954636 }, + { 2.2392290510988535, 0.70000000000000018, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler164 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.40000000000000002. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.3719045096496910e-16 +// mean(f - f_Boost): 1.3600232051658169e-16 +// variance(f - f_Boost): 1.1718213750516114e-32 +// stddev(f - f_Boost): 1.0825069861444829e-16 +const testcase_ellint_3<double> +data165[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17568027871494424, 0.70000000000000018, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35834559208180261, 0.70000000000000018, 0.40000000000000002, + 0.34906585039886590 }, + { 0.55545885451190613, 0.70000000000000018, 0.40000000000000002, + 0.52359877559829882 }, + { 0.77528120402568113, 0.70000000000000018, 0.40000000000000002, + 0.69813170079773179 }, + { 1.0267241287600322, 0.70000000000000018, 0.40000000000000002, + 0.87266462599716477 }, + { 1.3181380338980246, 0.70000000000000018, 0.40000000000000002, + 1.0471975511965976 }, + { 1.6542840785132087, 0.70000000000000018, 0.40000000000000002, + 1.2217304763960306 }, + { 2.0315595131131823, 0.70000000000000018, 0.40000000000000002, + 1.3962634015954636 }, + { 2.4342502915307880, 0.70000000000000018, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler165 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.50000000000000000. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.0277361210295499e-16 +// mean(f - f_Boost): 1.6930901125533636e-16 +// variance(f - f_Boost): 6.3799163752809956e-32 +// stddev(f - f_Boost): 2.5258496343371268e-16 +const testcase_ellint_3<double> +data166[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17586014108156545, 0.70000000000000018, 0.50000000000000000, + 0.17453292519943295 }, + { 0.35984923894341653, 0.70000000000000018, 0.50000000000000000, + 0.34906585039886590 }, + { 0.56091135606739995, 0.70000000000000018, 0.50000000000000000, + 0.52359877559829882 }, + { 0.78951212635197054, 0.70000000000000018, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0578865732938731, 0.70000000000000018, 0.50000000000000000, + 0.87266462599716477 }, + { 1.3789149005151722, 0.70000000000000018, 0.50000000000000000, + 1.0471975511965976 }, + { 1.7620212286086228, 0.70000000000000018, 0.50000000000000000, + 1.2217304763960306 }, + { 2.2051554347435589, 0.70000000000000018, 0.50000000000000000, + 1.3962634015954636 }, + { 2.6868019968236996, 0.70000000000000018, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler166 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.60000000000000009. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.8597454441867134e-16 +// mean(f - f_Boost): 2.5535129566378598e-16 +// variance(f - f_Boost): 2.8561208198482198e-31 +// stddev(f - f_Boost): 5.3442687243889785e-16 +const testcase_ellint_3<double> +data167[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17604066659721918, 0.70000000000000018, 0.60000000000000009, + 0.17453292519943295 }, + { 0.36137563278353424, 0.70000000000000018, 0.60000000000000009, + 0.34906585039886590 }, + { 0.56655721272747606, 0.70000000000000018, 0.60000000000000009, + 0.52359877559829882 }, + { 0.80468966552978305, 0.70000000000000018, 0.60000000000000009, + 0.69813170079773179 }, + { 1.0924902943683852, 0.70000000000000018, 0.60000000000000009, + 0.87266462599716477 }, + { 1.4499247992499800, 0.70000000000000018, 0.60000000000000009, + 1.0471975511965976 }, + { 1.8953714382113818, 0.70000000000000018, 0.60000000000000009, + 1.2217304763960306 }, + { 2.4323229949248670, 0.70000000000000018, 0.60000000000000009, + 1.3962634015954636 }, + { 3.0314573496746746, 0.70000000000000018, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler167 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.70000000000000007. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 8 +// max(|f - f_Boost| / |f_Boost|): 3.2316852368580916e-16 +// mean(f - f_Boost): 7.7715611723760953e-17 +// variance(f - f_Boost): 7.4564398834547797e-34 +// stddev(f - f_Boost): 2.7306482533374340e-17 +const testcase_ellint_3<double> +data168[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17622185963747933, 0.70000000000000018, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36292539360435261, 0.70000000000000018, 0.70000000000000007, + 0.34906585039886590 }, + { 0.57240892970150015, 0.70000000000000018, 0.70000000000000007, + 0.52359877559829882 }, + { 0.82093084713182629, 0.70000000000000018, 0.70000000000000007, + 0.69813170079773179 }, + { 1.1312609022179871, 0.70000000000000018, 0.70000000000000007, + 0.87266462599716477 }, + { 1.5345768067715795, 0.70000000000000018, 0.70000000000000007, + 1.0471975511965976 }, + { 2.0668847445934424, 0.70000000000000018, 0.70000000000000007, + 1.2217304763960306 }, + { 2.7483444537551245, 0.70000000000000018, 0.70000000000000007, + 1.3962634015954636 }, + { 3.5408408771788569, 0.70000000000000018, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler168 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.80000000000000004. +// max(|f - f_Boost|): 1.3322676295501878e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.1198716111867353e-16 +// mean(f - f_Boost): 2.2482016248659419e-16 +// variance(f - f_Boost): 5.4326441655972001e-32 +// stddev(f - f_Boost): 2.3308033305273100e-16 +const testcase_ellint_3<double> +data169[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17640372461994805, 0.70000000000000018, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36449916621651091, 0.70000000000000018, 0.80000000000000004, + 0.34906585039886590 }, + { 0.57848021800372584, 0.70000000000000018, 0.80000000000000004, + 0.52359877559829882 }, + { 0.83837480968392586, 0.70000000000000018, 0.80000000000000004, + 0.69813170079773179 }, + { 1.1751669030061143, 0.70000000000000018, 0.80000000000000004, + 0.87266462599716477 }, + { 1.6381851899173603, 0.70000000000000018, 0.80000000000000004, + 1.0471975511965976 }, + { 2.3002065924302197, 0.70000000000000018, 0.80000000000000004, + 1.2217304763960306 }, + { 3.2337600665337871, 0.70000000000000018, 0.80000000000000004, + 1.3962634015954636 }, + { 4.4042405729076970, 0.70000000000000018, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler169 = 2.5000000000000020e-13; + +// Test data for k=0.70000000000000018, nu=0.90000000000000002. +// max(|f - f_Boost|): 3.5527136788005009e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 8.5869439826269878e-16 +// mean(f - f_Boost): 7.4384942649885490e-16 +// variance(f - f_Boost): 9.7403930714297352e-31 +// stddev(f - f_Boost): 9.8693429727767263e-16 +const testcase_ellint_3<double> +data170[10] = +{ + { 0.0000000000000000, 0.70000000000000018, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17658626600478800, 0.70000000000000018, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36609762156017206, 0.70000000000000018, 0.90000000000000002, + 0.34906585039886590 }, + { 0.58478615187842409, 0.70000000000000018, 0.90000000000000002, + 0.52359877559829882 }, + { 0.85718862878291846, 0.70000000000000018, 0.90000000000000002, + 0.69813170079773179 }, + { 1.2255385617397643, 0.70000000000000018, 0.90000000000000002, + 0.87266462599716477 }, + { 1.7696521899992941, 0.70000000000000018, 0.90000000000000002, + 1.0471975511965976 }, + { 2.6476314987883507, 0.70000000000000018, 0.90000000000000002, + 1.2217304763960306 }, + { 4.1373434902898083, 0.70000000000000018, 0.90000000000000002, + 1.3962634015954636 }, + { 6.3796094177887763, 0.70000000000000018, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler170 = 2.5000000000000020e-13; // Test data for k=0.80000000000000004, nu=0.0000000000000000. -testcase_ellint_3<double> data171[] = { - { -0.0000000000000000, 0.80000000000000004, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17510154241338902, 0.80000000000000004, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35365068839779390, 0.80000000000000004, 0.0000000000000000, - 0.34906585039886590 }, - { 0.53926804409084561, 0.80000000000000004, 0.0000000000000000, - 0.52359877559829882 }, - { 0.73587926028070383, 0.80000000000000004, 0.0000000000000000, - 0.69813170079773179 }, - { 0.94770942970071170, 0.80000000000000004, 0.0000000000000000, - 0.87266462599716477 }, - { 1.1789022995388239, 0.80000000000000004, 0.0000000000000000, - 1.0471975511965976 }, - { 1.4323027881876009, 0.80000000000000004, 0.0000000000000000, - 1.2217304763960306 }, - { 1.7069629739121674, 0.80000000000000004, 0.0000000000000000, - 1.3962634015954636 }, - { 1.9953027776647296, 0.80000000000000004, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.0000000000000000. -template <typename Tp> -void test171() -{ - 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(data171) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data171[i].k), Tp(data171[i].nu), - Tp(data171[i].phi)); - const Tp f0 = data171[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)); -} +// max(|f - f_Boost|): 1.5543122344752192e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 7.7898565163847540e-16 +// mean(f - f_Boost): 2.3869795029440865e-16 +// variance(f - f_Boost): 2.1368406725192426e-31 +// stddev(f - f_Boost): 4.6225974002926564e-16 +const testcase_ellint_3<double> +data171[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17510154241338899, 0.80000000000000004, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35365068839779396, 0.80000000000000004, 0.0000000000000000, + 0.34906585039886590 }, + { 0.53926804409084550, 0.80000000000000004, 0.0000000000000000, + 0.52359877559829882 }, + { 0.73587926028070372, 0.80000000000000004, 0.0000000000000000, + 0.69813170079773179 }, + { 0.94770942970071170, 0.80000000000000004, 0.0000000000000000, + 0.87266462599716477 }, + { 1.1789022995388236, 0.80000000000000004, 0.0000000000000000, + 1.0471975511965976 }, + { 1.4323027881876012, 0.80000000000000004, 0.0000000000000000, + 1.2217304763960306 }, + { 1.7069629739121677, 0.80000000000000004, 0.0000000000000000, + 1.3962634015954636 }, + { 1.9953027776647294, 0.80000000000000004, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler171 = 2.5000000000000020e-13; // Test data for k=0.80000000000000004, nu=0.10000000000000001. -testcase_ellint_3<double> data172[] = { - { -0.0000000000000000, 0.80000000000000004, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17492468824017166, 0.80000000000000004, 0.10000000000000001, - 0.17453292519943295 }, - { 0.35224443521476911, 0.80000000000000004, 0.10000000000000001, - 0.34906585039886590 }, - { 0.53456851853226961, 0.80000000000000004, 0.10000000000000001, - 0.52359877559829882 }, - { 0.72488875602364944, 0.80000000000000004, 0.10000000000000001, - 0.69813170079773179 }, - { 0.92661354274638952, 0.80000000000000004, 0.10000000000000001, - 0.87266462599716477 }, - { 1.1432651144499077, 0.80000000000000004, 0.10000000000000001, - 1.0471975511965976 }, - { 1.3774479927211429, 0.80000000000000004, 0.10000000000000001, - 1.2217304763960306 }, - { 1.6287092337196041, 0.80000000000000004, 0.10000000000000001, - 1.3962634015954636 }, - { 1.8910755418379521, 0.80000000000000004, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.10000000000000001. -template <typename Tp> -void test172() -{ - 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(data172) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data172[i].k), Tp(data172[i].nu), - Tp(data172[i].phi)); - const Tp f0 = data172[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 8.3898786942190374e-16 +// mean(f - f_Boost): 2.3869795029440865e-16 +// variance(f - f_Boost): 2.9190059990693968e-31 +// stddev(f - f_Boost): 5.4027826155319237e-16 +const testcase_ellint_3<double> +data172[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17527903952342144, 0.80000000000000004, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35507705313548549, 0.80000000000000004, 0.10000000000000001, + 0.34906585039886590 }, + { 0.54411455987643553, 0.80000000000000004, 0.10000000000000001, + 0.52359877559829882 }, + { 0.74745625666804383, 0.80000000000000004, 0.10000000000000001, + 0.69813170079773179 }, + { 0.97046953684238557, 0.80000000000000004, 0.10000000000000001, + 0.87266462599716477 }, + { 1.2183080025184605, 0.80000000000000004, 0.10000000000000001, + 1.0471975511965976 }, + { 1.4943711151994405, 0.80000000000000004, 0.10000000000000001, + 1.2217304763960306 }, + { 1.7972401309544201, 0.80000000000000004, 0.10000000000000001, + 1.3962634015954636 }, + { 2.1172616484005085, 0.80000000000000004, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler172 = 2.5000000000000020e-13; // Test data for k=0.80000000000000004, nu=0.20000000000000001. -testcase_ellint_3<double> data173[] = { - { -0.0000000000000000, 0.80000000000000004, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17474847286224943, 0.80000000000000004, 0.20000000000000001, - 0.17453292519943295 }, - { 0.35085779529084682, 0.80000000000000004, 0.20000000000000001, - 0.34906585039886590 }, - { 0.53000829263059157, 0.80000000000000004, 0.20000000000000001, - 0.52359877559829882 }, - { 0.71443466027453406, 0.80000000000000004, 0.20000000000000001, - 0.69813170079773179 }, - { 0.90698196872715420, 0.80000000000000004, 0.20000000000000001, - 0.87266462599716477 }, - { 1.1108198200558581, 0.80000000000000004, 0.20000000000000001, - 1.0471975511965976 }, - { 1.3284988909963957, 0.80000000000000004, 0.20000000000000001, - 1.2217304763960306 }, - { 1.5600369318140328, 0.80000000000000004, 0.20000000000000001, - 1.3962634015954636 }, - { 1.8007226661734588, 0.80000000000000004, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.20000000000000001. -template <typename Tp> -void test173() -{ - 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(data173) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data173[i].k), Tp(data173[i].nu), - Tp(data173[i].phi)); - const Tp f0 = data173[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, nu=0.29999999999999999. -testcase_ellint_3<double> data174[] = { - { -0.0000000000000000, 0.80000000000000004, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17457289217669891, 0.80000000000000004, 0.29999999999999999, - 0.17453292519943295 }, - { 0.34949028801501258, 0.80000000000000004, 0.29999999999999999, - 0.34906585039886590 }, - { 0.52558024362769318, 0.80000000000000004, 0.29999999999999999, - 0.52359877559829882 }, - { 0.70447281740094914, 0.80000000000000004, 0.29999999999999999, - 0.69813170079773179 }, - { 0.88864745641528986, 0.80000000000000004, 0.29999999999999999, - 0.87266462599716477 }, - { 1.0811075819341465, 0.80000000000000004, 0.29999999999999999, - 1.0471975511965976 }, - { 1.2844589654082377, 0.80000000000000004, 0.29999999999999999, - 1.2217304763960306 }, - { 1.4991461361277849, 0.80000000000000004, 0.29999999999999999, - 1.3962634015954636 }, - { 1.7214611048717301, 0.80000000000000004, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.29999999999999999. -template <typename Tp> -void test174() -{ - 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(data174) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data174[i].k), Tp(data174[i].nu), - Tp(data174[i].phi)); - const Tp f0 = data174[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)); -} +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 7.8513740186068518e-16 +// mean(f - f_Boost): 2.8310687127941490e-16 +// variance(f - f_Boost): 2.7528339102381189e-31 +// stddev(f - f_Boost): 5.2467455724840699e-16 +const testcase_ellint_3<double> +data173[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17545718375086419, 0.80000000000000004, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35652404627248163, 0.80000000000000004, 0.20000000000000001, + 0.34906585039886590 }, + { 0.54911638512920913, 0.80000000000000004, 0.20000000000000001, + 0.52359877559829882 }, + { 0.75967684282131176, 0.80000000000000004, 0.20000000000000001, + 0.69813170079773179 }, + { 0.99513526893543769, 0.80000000000000004, 0.20000000000000001, + 0.87266462599716477 }, + { 1.2622192109995993, 0.80000000000000004, 0.20000000000000001, + 1.0471975511965976 }, + { 1.5654106676347741, 0.80000000000000004, 0.20000000000000001, + 1.2217304763960306 }, + { 1.9029531718534984, 0.80000000000000004, 0.20000000000000001, + 1.3962634015954636 }, + { 2.2624789434186798, 0.80000000000000004, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler173 = 2.5000000000000020e-13; + +// Test data for k=0.80000000000000004, nu=0.30000000000000004. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 7.2825261583337354e-16 +// mean(f - f_Boost): 2.6367796834847468e-16 +// variance(f - f_Boost): 2.8249350208968825e-31 +// stddev(f - f_Boost): 5.3150117788175054e-16 +const testcase_ellint_3<double> +data174[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17563597931587369, 0.80000000000000004, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35799220412005128, 0.80000000000000004, 0.30000000000000004, + 0.34906585039886590 }, + { 0.55428253691111318, 0.80000000000000004, 0.30000000000000004, + 0.52359877559829882 }, + { 0.77260647376977365, 0.80000000000000004, 0.30000000000000004, + 0.69813170079773179 }, + { 1.0220015271210958, 0.80000000000000004, 0.30000000000000004, + 0.87266462599716477 }, + { 1.3115965312302671, 0.80000000000000004, 0.30000000000000004, + 1.0471975511965976 }, + { 1.6478518468813512, 0.80000000000000004, 0.30000000000000004, + 1.2217304763960306 }, + { 2.0290458414203481, 0.80000000000000004, 0.30000000000000004, + 1.3962634015954636 }, + { 2.4392042002725693, 0.80000000000000004, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler174 = 2.5000000000000020e-13; // Test data for k=0.80000000000000004, nu=0.40000000000000002. -testcase_ellint_3<double> data175[] = { - { -0.0000000000000000, 0.80000000000000004, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17439794211872178, 0.80000000000000004, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34814144964568972, 0.80000000000000004, 0.40000000000000002, - 0.34906585039886590 }, - { 0.52127776285273075, 0.80000000000000004, 0.40000000000000002, - 0.52359877559829882 }, - { 0.69496411438966599, 0.80000000000000004, 0.40000000000000002, - 0.69813170079773179 }, - { 0.87146878427509589, 0.80000000000000004, 0.40000000000000002, - 0.87266462599716477 }, - { 1.0537579024937762, 0.80000000000000004, 0.40000000000000002, - 1.0471975511965976 }, - { 1.2445534387922637, 0.80000000000000004, 0.40000000000000002, - 1.2217304763960306 }, - { 1.4446769766361993, 0.80000000000000004, 0.40000000000000002, - 1.3962634015954636 }, - { 1.6512267838651289, 0.80000000000000004, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.40000000000000002. -template <typename Tp> -void test175() -{ - 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(data175) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data175[i].k), Tp(data175[i].nu), - Tp(data175[i].phi)); - const Tp f0 = data175[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)); -} +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 8.3462748389836647e-16 +// mean(f - f_Boost): 3.3861802251067273e-16 +// variance(f - f_Boost): 4.3719465706454422e-31 +// stddev(f - f_Boost): 6.6120696991527871e-16 +const testcase_ellint_3<double> +data175[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17581543047866136, 0.80000000000000004, 0.40000000000000002, + 0.17453292519943295 }, + { 0.35948208343061633, 0.80000000000000004, 0.40000000000000002, + 0.34906585039886590 }, + { 0.55962280893702021, 0.80000000000000004, 0.40000000000000002, + 0.52359877559829882 }, + { 0.78632063889234116, 0.80000000000000004, 0.40000000000000002, + 0.69813170079773179 }, + { 1.0514333069550323, 0.80000000000000004, 0.40000000000000002, + 0.87266462599716477 }, + { 1.3677213138838757, 0.80000000000000004, 0.40000000000000002, + 1.0471975511965976 }, + { 1.7451736773665165, 0.80000000000000004, 0.40000000000000002, + 1.2217304763960306 }, + { 2.1830100424586831, 0.80000000000000004, 0.40000000000000002, + 1.3962634015954636 }, + { 2.6604037035529724, 0.80000000000000004, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler175 = 2.5000000000000020e-13; // Test data for k=0.80000000000000004, nu=0.50000000000000000. -testcase_ellint_3<double> data176[] = { - { -0.0000000000000000, 0.80000000000000004, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17422361866118047, 0.80000000000000004, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34681083254170475, 0.80000000000000004, 0.50000000000000000, - 0.34906585039886590 }, - { 0.51709470815494440, 0.80000000000000004, 0.50000000000000000, - 0.52359877559829882 }, - { 0.68587375344080259, 0.80000000000000004, 0.50000000000000000, - 0.69813170079773179 }, - { 0.85532571852810624, 0.80000000000000004, 0.50000000000000000, - 0.87266462599716477 }, - { 1.0284677391874906, 0.80000000000000004, 0.50000000000000000, - 1.0471975511965976 }, - { 1.2081693942686225, 0.80000000000000004, 0.50000000000000000, - 1.2217304763960306 }, - { 1.3955803006426311, 0.80000000000000004, 0.50000000000000000, - 1.3962634015954636 }, - { 1.5884528947755532, 0.80000000000000004, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.50000000000000000. -template <typename Tp> -void test176() -{ - 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(data176) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data176[i].k), Tp(data176[i].nu), - Tp(data176[i].phi)); - const Tp f0 = data176[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, nu=0.59999999999999998. -testcase_ellint_3<double> data177[] = { - { -0.0000000000000000, 0.80000000000000004, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17404991781414092, 0.80000000000000004, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34549800443625167, 0.80000000000000004, 0.59999999999999998, - 0.34906585039886590 }, - { 0.51302536167001556, 0.80000000000000004, 0.59999999999999998, - 0.52359877559829882 }, - { 0.67717065003912258, 0.80000000000000004, 0.59999999999999998, - 0.69813170079773179 }, - { 0.84011512421134416, 0.80000000000000004, 0.59999999999999998, - 0.87266462599716477 }, - { 1.0049863847088742, 0.80000000000000004, 0.59999999999999998, - 1.0471975511965976 }, - { 1.1748145941898918, 0.80000000000000004, 0.59999999999999998, - 1.2217304763960306 }, - { 1.3510319699755071, 0.80000000000000004, 0.59999999999999998, - 1.3962634015954636 }, - { 1.5319262547427865, 0.80000000000000004, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.59999999999999998. -template <typename Tp> -void test177() -{ - 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(data177) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data177[i].k), Tp(data177[i].nu), - Tp(data177[i].phi)); - const Tp f0 = data177[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, nu=0.69999999999999996. -testcase_ellint_3<double> data178[] = { - { -0.0000000000000000, 0.80000000000000004, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17387683562442202, 0.80000000000000004, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34420254775101611, 0.80000000000000004, 0.69999999999999996, - 0.34906585039886590 }, - { 0.50906439222143685, 0.80000000000000004, 0.69999999999999996, - 0.52359877559829882 }, - { 0.66882693152688433, 0.80000000000000004, 0.69999999999999996, - 0.69813170079773179 }, - { 0.82574792844091316, 0.80000000000000004, 0.69999999999999996, - 0.87266462599716477 }, - { 0.98310431309490953, 0.80000000000000004, 0.69999999999999996, - 1.0471975511965976 }, - { 1.1440884535113258, 0.80000000000000004, 0.69999999999999996, - 1.2217304763960306 }, - { 1.3103743938952537, 0.80000000000000004, 0.69999999999999996, - 1.3962634015954636 }, - { 1.4806912324625332, 0.80000000000000004, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.69999999999999996. -template <typename Tp> -void test178() -{ - 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(data178) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data178[i].k), Tp(data178[i].nu), - Tp(data178[i].phi)); - const Tp f0 = data178[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)); -} +// max(|f - f_Boost|): 2.6645352591003757e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 9.0388243828581744e-16 +// mean(f - f_Boost): 3.8580250105724191e-16 +// variance(f - f_Boost): 6.4106456575047741e-31 +// stddev(f - f_Boost): 8.0066507713929764e-16 +const testcase_ellint_3<double> +data176[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17599554153999472, 0.80000000000000004, 0.50000000000000000, + 0.17453292519943295 }, + { 0.36099426243351540, 0.80000000000000004, 0.50000000000000000, + 0.34906585039886590 }, + { 0.56514786174780673, 0.80000000000000004, 0.50000000000000000, + 0.52359877559829882 }, + { 0.80090697622371010, 0.80000000000000004, 0.50000000000000000, + 0.69813170079773179 }, + { 1.0838891627679339, 0.80000000000000004, 0.50000000000000000, + 0.87266462599716477 }, + { 1.4323506654466280, 0.80000000000000004, 0.50000000000000000, + 1.0471975511965976 }, + { 1.8625761085390575, 0.80000000000000004, 0.50000000000000000, + 1.2217304763960306 }, + { 2.3768757305654766, 0.80000000000000004, 0.50000000000000000, + 1.3962634015954636 }, + { 2.9478781158239746, 0.80000000000000004, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler176 = 2.5000000000000020e-13; + +// Test data for k=0.80000000000000004, nu=0.60000000000000009. +// max(|f - f_Boost|): 3.5527136788005009e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 1.0631099169042069e-15 +// mean(f - f_Boost): 4.8294701571194306e-16 +// variance(f - f_Boost): 1.1633910328160319e-30 +// stddev(f - f_Boost): 1.0786060600682865e-15 +const testcase_ellint_3<double> +data177[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17617631684170665, 0.80000000000000004, 0.60000000000000009, + 0.17453292519943295 }, + { 0.36252934193666231, 0.80000000000000004, 0.60000000000000009, + 0.34906585039886590 }, + { 0.57086932622945163, 0.80000000000000004, 0.60000000000000009, + 0.52359877559829882 }, + { 0.81646796740150973, 0.80000000000000004, 0.60000000000000009, + 0.69813170079773179 }, + { 1.1199552158519064, 0.80000000000000004, 0.60000000000000009, + 0.87266462599716477 }, + { 1.5079766673336394, 0.80000000000000004, 0.60000000000000009, + 1.0471975511965976 }, + { 2.0082747447038165, 0.80000000000000004, 0.60000000000000009, + 1.2217304763960306 }, + { 2.6315146066775523, 0.80000000000000004, 0.60000000000000009, + 1.3962634015954636 }, + { 3.3418121892288051, 0.80000000000000004, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler177 = 2.5000000000000020e-13; + +// Test data for k=0.80000000000000004, nu=0.70000000000000007. +// max(|f - f_Boost|): 2.2204460492503131e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.6544679145741375e-16 +// mean(f - f_Boost): 3.2751579226442120e-16 +// variance(f - f_Boost): 4.4236851331020672e-31 +// stddev(f - f_Boost): 6.6510789599147505e-16 +const testcase_ellint_3<double> +data178[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17635776076721221, 0.80000000000000004, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36408794649916976, 0.80000000000000004, 0.70000000000000007, + 0.34906585039886590 }, + { 0.57679992290624138, 0.80000000000000004, 0.70000000000000007, + 0.52359877559829882 }, + { 0.83312441418142813, 0.80000000000000004, 0.70000000000000007, + 0.69813170079773179 }, + { 1.1603958891464856, 0.80000000000000004, 0.70000000000000007, + 0.87266462599716477 }, + { 1.5982855143796213, 0.80000000000000004, 0.70000000000000007, + 1.0471975511965976 }, + { 2.1962484408371821, 0.80000000000000004, 0.70000000000000007, + 1.2217304763960306 }, + { 2.9873281786111869, 0.80000000000000004, 0.70000000000000007, + 1.3962634015954636 }, + { 3.9268876980046397, 0.80000000000000004, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler178 = 2.5000000000000020e-13; // Test data for k=0.80000000000000004, nu=0.80000000000000004. -testcase_ellint_3<double> data179[] = { - { -0.0000000000000000, 0.80000000000000004, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17370436817515206, 0.80000000000000004, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34292405894783395, 0.80000000000000004, 0.80000000000000004, - 0.34906585039886590 }, - { 0.50520682176250087, 0.80000000000000004, 0.80000000000000004, - 0.52359877559829882 }, - { 0.66081751679736189, 0.80000000000000004, 0.80000000000000004, - 0.69813170079773179 }, - { 0.81214672249355102, 0.80000000000000004, 0.80000000000000004, - 0.87266462599716477 }, - { 0.96264481387685574, 0.80000000000000004, 0.80000000000000004, - 1.0471975511965976 }, - { 1.1156611352656258, 0.80000000000000004, 0.80000000000000004, - 1.2217304763960306 }, - { 1.2730756225143889, 0.80000000000000004, 0.80000000000000004, - 1.3962634015954636 }, - { 1.4339837018309474, 0.80000000000000004, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.80000000000000004. -template <typename Tp> -void test179() -{ - 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(data179) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data179[i].k), Tp(data179[i].nu), - Tp(data179[i].phi)); - const Tp f0 = data179[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 9.0176949165011079e-16 +// mean(f - f_Boost): 7.0499162063697436e-16 +// variance(f - f_Boost): 1.7230805408026989e-30 +// stddev(f - f_Boost): 1.3126616246400665e-15 +const testcase_ellint_3<double> +data179[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17653987774203392, 0.80000000000000004, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36567072568046877, 0.80000000000000004, 0.80000000000000004, + 0.34906585039886590 }, + { 0.58295359996558616, 0.80000000000000004, 0.80000000000000004, + 0.52359877559829882 }, + { 0.85101998309176108, 0.80000000000000004, 0.80000000000000004, + 0.69813170079773179 }, + { 1.2062322059736537, 0.80000000000000004, 0.80000000000000004, + 0.87266462599716477 }, + { 1.7090321420917429, 0.80000000000000004, 0.80000000000000004, + 1.0471975511965976 }, + { 2.4529058049405066, 0.80000000000000004, 0.80000000000000004, + 1.2217304763960306 }, + { 3.5368893360106948, 0.80000000000000004, 0.80000000000000004, + 1.3962634015954636 }, + { 4.9246422058196062, 0.80000000000000004, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler179 = 2.5000000000000020e-13; // Test data for k=0.80000000000000004, nu=0.90000000000000002. -testcase_ellint_3<double> data180[] = { - { -0.0000000000000000, 0.80000000000000004, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17353251158533153, 0.80000000000000004, 0.90000000000000002, - 0.17453292519943295 }, - { 0.34166214791545768, 0.80000000000000004, 0.90000000000000002, - 0.34906585039886590 }, - { 0.50144799535130580, 0.80000000000000004, 0.90000000000000002, - 0.52359877559829882 }, - { 0.65311976193814447, 0.80000000000000004, 0.90000000000000002, - 0.69813170079773179 }, - { 0.79924384892320866, 0.80000000000000004, 0.90000000000000002, - 0.87266462599716477 }, - { 0.94345762353365625, 0.80000000000000004, 0.90000000000000002, - 1.0471975511965976 }, - { 1.0892582069219159, 0.80000000000000004, 0.90000000000000002, - 1.2217304763960306 }, - { 1.2387000876610268, 0.80000000000000004, 0.90000000000000002, - 1.3962634015954636 }, - { 1.3911845406776222, 0.80000000000000004, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.80000000000000004, nu=0.90000000000000002. -template <typename Tp> -void test180() -{ - 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(data180) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data180[i].k), Tp(data180[i].nu), - Tp(data180[i].phi)); - const Tp f0 = data180[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, nu=0.0000000000000000. -testcase_ellint_3<double> data181[] = { - { -0.0000000000000000, 0.89999999999999991, 0.0000000000000000, - 0.0000000000000000 }, - { 0.17525427376115027, 0.89999999999999991, 0.0000000000000000, - 0.17453292519943295 }, - { 0.35492464591297446, 0.89999999999999991, 0.0000000000000000, - 0.34906585039886590 }, - { 0.54388221416157123, 0.89999999999999991, 0.0000000000000000, - 0.52359877559829882 }, - { 0.74797400423532501, 0.89999999999999991, 0.0000000000000000, - 0.69813170079773179 }, - { 0.97463898451966458, 0.89999999999999991, 0.0000000000000000, - 0.87266462599716477 }, - { 1.2334463254523438, 0.89999999999999991, 0.0000000000000000, - 1.0471975511965976 }, - { 1.5355247765594910, 0.89999999999999991, 0.0000000000000000, - 1.2217304763960306 }, - { 1.8882928567775117, 0.89999999999999991, 0.0000000000000000, - 1.3962634015954636 }, - { 2.2805491384227699, 0.89999999999999991, 0.0000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.0000000000000000. -template <typename Tp> -void test181() -{ - 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(data181) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data181[i].k), Tp(data181[i].nu), - Tp(data181[i].phi)); - const Tp f0 = data181[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, nu=0.10000000000000001. -testcase_ellint_3<double> data182[] = { - { -0.0000000000000000, 0.89999999999999991, 0.10000000000000001, - 0.0000000000000000 }, - { 0.17507714233254659, 0.89999999999999991, 0.10000000000000001, - 0.17453292519943295 }, - { 0.35350932904326521, 0.89999999999999991, 0.10000000000000001, - 0.34906585039886590 }, - { 0.53911129989870987, 0.89999999999999991, 0.10000000000000001, - 0.52359877559829882 }, - { 0.73666644254508407, 0.89999999999999991, 0.10000000000000001, - 0.69813170079773179 }, - { 0.95250736612100184, 0.89999999999999991, 0.10000000000000001, - 0.87266462599716477 }, - { 1.1950199550905591, 0.89999999999999991, 0.10000000000000001, - 1.0471975511965976 }, - { 1.4741687286340848, 0.89999999999999991, 0.10000000000000001, - 1.2217304763960306 }, - { 1.7968678183506053, 0.89999999999999991, 0.10000000000000001, - 1.3962634015954636 }, - { 2.1537868513875282, 0.89999999999999991, 0.10000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.10000000000000001. -template <typename Tp> -void test182() -{ - 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(data182) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data182[i].k), Tp(data182[i].nu), - Tp(data182[i].phi)); - const Tp f0 = data182[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, nu=0.20000000000000001. -testcase_ellint_3<double> data183[] = { - { -0.0000000000000000, 0.89999999999999991, 0.20000000000000001, - 0.0000000000000000 }, - { 0.17490065089140930, 0.89999999999999991, 0.20000000000000001, - 0.17453292519943295 }, - { 0.35211377590661436, 0.89999999999999991, 0.20000000000000001, - 0.34906585039886590 }, - { 0.53448220334204111, 0.89999999999999991, 0.20000000000000001, - 0.52359877559829882 }, - { 0.72591368943179591, 0.89999999999999991, 0.20000000000000001, - 0.69813170079773179 }, - { 0.93192539780038763, 0.89999999999999991, 0.20000000000000001, - 0.87266462599716477 }, - { 1.1600809679692681, 0.89999999999999991, 0.20000000000000001, - 1.0471975511965976 }, - { 1.4195407225882508, 0.89999999999999991, 0.20000000000000001, - 1.2217304763960306 }, - { 1.7168966476424521, 0.89999999999999991, 0.20000000000000001, - 1.3962634015954636 }, - { 2.0443194576468890, 0.89999999999999991, 0.20000000000000001, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.20000000000000001. -template <typename Tp> -void test183() -{ - 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(data183) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data183[i].k), Tp(data183[i].nu), - Tp(data183[i].phi)); - const Tp f0 = data183[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, nu=0.29999999999999999. -testcase_ellint_3<double> data184[] = { - { -0.0000000000000000, 0.89999999999999991, 0.29999999999999999, - 0.0000000000000000 }, - { 0.17472479532647534, 0.89999999999999991, 0.29999999999999999, - 0.17453292519943295 }, - { 0.35073750187374114, 0.89999999999999991, 0.29999999999999999, - 0.34906585039886590 }, - { 0.52998766129466968, 0.89999999999999991, 0.29999999999999999, - 0.52359877559829882 }, - { 0.71566993548699565, 0.89999999999999991, 0.29999999999999999, - 0.69813170079773179 }, - { 0.91271517762560195, 0.89999999999999991, 0.29999999999999999, - 0.87266462599716477 }, - { 1.1281241199843368, 0.89999999999999991, 0.29999999999999999, - 1.0471975511965976 }, - { 1.3704929576917448, 0.89999999999999991, 0.29999999999999999, - 1.2217304763960306 }, - { 1.6461981511487711, 0.89999999999999991, 0.29999999999999999, - 1.3962634015954636 }, - { 1.9486280260314424, 0.89999999999999991, 0.29999999999999999, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.29999999999999999. -template <typename Tp> -void test184() -{ - 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(data184) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data184[i].k), Tp(data184[i].nu), - Tp(data184[i].phi)); - const Tp f0 = data184[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, nu=0.40000000000000002. -testcase_ellint_3<double> data185[] = { - { -0.0000000000000000, 0.89999999999999991, 0.40000000000000002, - 0.0000000000000000 }, - { 0.17454957156468839, 0.89999999999999991, 0.40000000000000002, - 0.17453292519943295 }, - { 0.34938003933330430, 0.89999999999999991, 0.40000000000000002, - 0.34906585039886590 }, - { 0.52562093533067444, 0.89999999999999991, 0.40000000000000002, - 0.52359877559829882 }, - { 0.70589461324915681, 0.89999999999999991, 0.40000000000000002, - 0.69813170079773179 }, - { 0.89472658511942849, 0.89999999999999991, 0.40000000000000002, - 0.87266462599716477 }, - { 1.0987419542323438, 0.89999999999999991, 0.40000000000000002, - 1.0471975511965976 }, - { 1.3261349565496301, 0.89999999999999991, 0.40000000000000002, - 1.2217304763960306 }, - { 1.5831293909853761, 0.89999999999999991, 0.40000000000000002, - 1.3962634015954636 }, - { 1.8641114227238347, 0.89999999999999991, 0.40000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.40000000000000002. -template <typename Tp> -void test185() -{ - 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(data185) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data185[i].k), Tp(data185[i].nu), - Tp(data185[i].phi)); - const Tp f0 = data185[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, nu=0.50000000000000000. -testcase_ellint_3<double> data186[] = { - { -0.0000000000000000, 0.89999999999999991, 0.50000000000000000, - 0.0000000000000000 }, - { 0.17437497557073336, 0.89999999999999991, 0.50000000000000000, - 0.17453292519943295 }, - { 0.34804093691586013, 0.89999999999999991, 0.50000000000000000, - 0.34906585039886590 }, - { 0.52137576320372903, 0.89999999999999991, 0.50000000000000000, - 0.52359877559829882 }, - { 0.69655163996912262, 0.89999999999999991, 0.50000000000000000, - 0.69813170079773179 }, - { 0.87783188683054236, 0.89999999999999991, 0.50000000000000000, - 0.87266462599716477 }, - { 1.0716015959755183, 0.89999999999999991, 0.50000000000000000, - 1.0471975511965976 }, - { 1.2857636916026749, 0.89999999999999991, 0.50000000000000000, - 1.2217304763960306 }, - { 1.5264263913252358, 0.89999999999999991, 0.50000000000000000, - 1.3962634015954636 }, - { 1.7888013241937859, 0.89999999999999991, 0.50000000000000000, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.50000000000000000. -template <typename Tp> -void test186() -{ - 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(data186) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data186[i].k), Tp(data186[i].nu), - Tp(data186[i].phi)); - const Tp f0 = data186[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, nu=0.59999999999999998. -testcase_ellint_3<double> data187[] = { - { -0.0000000000000000, 0.89999999999999991, 0.59999999999999998, - 0.0000000000000000 }, - { 0.17420100334657815, 0.89999999999999991, 0.59999999999999998, - 0.17453292519943295 }, - { 0.34671975876122157, 0.89999999999999991, 0.59999999999999998, - 0.34906585039886590 }, - { 0.51724631570707957, 0.89999999999999991, 0.59999999999999998, - 0.52359877559829882 }, - { 0.68760879113743034, 0.89999999999999991, 0.59999999999999998, - 0.69813170079773179 }, - { 0.86192157779698364, 0.89999999999999991, 0.59999999999999998, - 0.87266462599716477 }, - { 1.0464279696166352, 0.89999999999999991, 0.59999999999999998, - 1.0471975511965976 }, - { 1.2488156247094004, 0.89999999999999991, 0.59999999999999998, - 1.2217304763960306 }, - { 1.4750988777188470, 0.89999999999999991, 0.59999999999999998, - 1.3962634015954636 }, - { 1.7211781128919521, 0.89999999999999991, 0.59999999999999998, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.59999999999999998. -template <typename Tp> -void test187() -{ - 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(data187) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data187[i].k), Tp(data187[i].nu), - Tp(data187[i].phi)); - const Tp f0 = data187[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, nu=0.69999999999999996. -testcase_ellint_3<double> data188[] = { - { -0.0000000000000000, 0.89999999999999991, 0.69999999999999996, - 0.0000000000000000 }, - { 0.17402765093102210, 0.89999999999999991, 0.69999999999999996, - 0.17453292519943295 }, - { 0.34541608382635131, 0.89999999999999991, 0.69999999999999996, - 0.34906585039886590 }, - { 0.51322715827061693, 0.89999999999999991, 0.69999999999999996, - 0.52359877559829882 }, - { 0.67903717872440283, 0.89999999999999991, 0.69999999999999996, - 0.69813170079773179 }, - { 0.84690113601682671, 0.89999999999999991, 0.69999999999999996, - 0.87266462599716477 }, - { 1.0229914311548416, 0.89999999999999991, 0.69999999999999996, - 1.0471975511965976 }, - { 1.2148329639709381, 0.89999999999999991, 0.69999999999999996, - 1.2217304763960306 }, - { 1.4283586501307799, 0.89999999999999991, 0.69999999999999996, - 1.3962634015954636 }, - { 1.6600480747670936, 0.89999999999999991, 0.69999999999999996, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.69999999999999996. -template <typename Tp> -void test188() -{ - 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(data188) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data188[i].k), Tp(data188[i].nu), - Tp(data188[i].phi)); - const Tp f0 = data188[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, nu=0.80000000000000004. -testcase_ellint_3<double> data189[] = { - { -0.0000000000000000, 0.89999999999999991, 0.80000000000000004, - 0.0000000000000000 }, - { 0.17385491439925149, 0.89999999999999991, 0.80000000000000004, - 0.17453292519943295 }, - { 0.34412950523113928, 0.89999999999999991, 0.80000000000000004, - 0.34906585039886590 }, - { 0.50931321668729601, 0.89999999999999991, 0.80000000000000004, - 0.52359877559829882 }, - { 0.67081081392296327, 0.89999999999999991, 0.80000000000000004, - 0.69813170079773179 }, - { 0.83268846097293259, 0.89999999999999991, 0.80000000000000004, - 0.87266462599716477 }, - { 1.0010985015814025, 0.89999999999999991, 0.80000000000000004, - 1.0471975511965976 }, - { 1.1834394045489678, 0.89999999999999991, 0.80000000000000004, - 1.2217304763960306 }, - { 1.3855695891683182, 0.89999999999999991, 0.80000000000000004, - 1.3962634015954636 }, - { 1.6044591960982200, 0.89999999999999991, 0.80000000000000004, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.80000000000000004. -template <typename Tp> -void test189() -{ - 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(data189) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data189[i].k), Tp(data189[i].nu), - Tp(data189[i].phi)); - const Tp f0 = data189[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, nu=0.90000000000000002. -testcase_ellint_3<double> data190[] = { - { -0.0000000000000000, 0.89999999999999991, 0.90000000000000002, - 0.0000000000000000 }, - { 0.17368278986240138, 0.89999999999999991, 0.90000000000000002, - 0.17453292519943295 }, - { 0.34285962963961397, 0.89999999999999991, 0.90000000000000002, - 0.34906585039886590 }, - { 0.50549974644993312, 0.89999999999999991, 0.90000000000000002, - 0.52359877559829882 }, - { 0.66290623857720876, 0.89999999999999991, 0.90000000000000002, - 0.69813170079773179 }, - { 0.81921183128847164, 0.89999999999999991, 0.90000000000000002, - 0.87266462599716477 }, - { 0.98058481956066368, 0.89999999999999991, 0.90000000000000002, - 1.0471975511965976 }, - { 1.1543223520473569, 0.89999999999999991, 0.90000000000000002, - 1.2217304763960306 }, - { 1.3462119782292934, 0.89999999999999991, 0.90000000000000002, - 1.3962634015954636 }, - { 1.5536420236310944, 0.89999999999999991, 0.90000000000000002, - 1.5707963267948966 }, -}; - -// Test function for k=0.89999999999999991, nu=0.90000000000000002. -template <typename Tp> -void test190() -{ - 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(data190) - / sizeof(testcase_ellint_3<double>); - for (unsigned int i = 0; i < num_datum; ++i) - { - const Tp f = std::tr1::ellint_3(Tp(data190[i].k), Tp(data190[i].nu), - Tp(data190[i].phi)); - const Tp f0 = data190[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)); -} +// max(|f - f_Boost|): 4.4408920985006262e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 7.7782721357365268e-16 +// mean(f - f_Boost): 8.9928064994637676e-16 +// variance(f - f_Boost): 1.5485199571025344e-30 +// stddev(f - f_Boost): 1.2443954183066307e-15 +const testcase_ellint_3<double> +data180[10] = +{ + { 0.0000000000000000, 0.80000000000000004, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17672267223433513, 0.80000000000000004, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36727835537196063, 0.80000000000000004, 0.90000000000000002, + 0.34906585039886590 }, + { 0.58934569363716649, 0.80000000000000004, 0.90000000000000002, + 0.52359877559829882 }, + { 0.87032723471138851, 0.80000000000000004, 0.90000000000000002, + 0.69813170079773179 }, + { 1.2588676111323349, 0.80000000000000004, 0.90000000000000002, + 0.87266462599716477 }, + { 1.8498731900660019, 0.80000000000000004, 0.90000000000000002, + 1.0471975511965976 }, + { 2.8368381299300420, 0.80000000000000004, 0.90000000000000002, + 1.2217304763960306 }, + { 4.5674844191654058, 0.80000000000000004, 0.90000000000000002, + 1.3962634015954636 }, + { 7.2263259298637115, 0.80000000000000004, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler180 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.0000000000000000. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.3381508715713360e-16 +// mean(f - f_Boost): 5.8286708792820721e-17 +// variance(f - f_Boost): 4.1942474344433133e-34 +// stddev(f - f_Boost): 2.0479861900030756e-17 +const testcase_ellint_3<double> +data181[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.0000000000000000, + 0.0000000000000000 }, + { 0.17525427376115027, 0.90000000000000013, 0.0000000000000000, + 0.17453292519943295 }, + { 0.35492464591297446, 0.90000000000000013, 0.0000000000000000, + 0.34906585039886590 }, + { 0.54388221416157123, 0.90000000000000013, 0.0000000000000000, + 0.52359877559829882 }, + { 0.74797400423532512, 0.90000000000000013, 0.0000000000000000, + 0.69813170079773179 }, + { 0.97463898451966446, 0.90000000000000013, 0.0000000000000000, + 0.87266462599716477 }, + { 1.2334463254523440, 0.90000000000000013, 0.0000000000000000, + 1.0471975511965976 }, + { 1.5355247765594915, 0.90000000000000013, 0.0000000000000000, + 1.2217304763960306 }, + { 1.8882928567775128, 0.90000000000000013, 0.0000000000000000, + 1.3962634015954636 }, + { 2.2805491384227707, 0.90000000000000013, 0.0000000000000000, + 1.5707963267948966 }, +}; +const double toler181 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.10000000000000001. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.1500594295134815e-16 +// mean(f - f_Boost): 9.1593399531575410e-17 +// variance(f - f_Boost): 1.0357223256482469e-33 +// stddev(f - f_Boost): 3.2182640128619758e-17 +const testcase_ellint_3<double> +data182[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.10000000000000001, + 0.0000000000000000 }, + { 0.17543204932716244, 0.90000000000000013, 0.10000000000000001, + 0.17453292519943295 }, + { 0.35636022898551184, 0.90000000000000013, 0.10000000000000001, + 0.34906585039886590 }, + { 0.54880278898382595, 0.90000000000000013, 0.10000000000000001, + 0.52359877559829882 }, + { 0.75988834774529268, 0.90000000000000013, 0.10000000000000001, + 0.69813170079773179 }, + { 0.99853303003568117, 0.90000000000000013, 0.10000000000000001, + 0.87266462599716477 }, + { 1.2759958823999022, 0.90000000000000013, 0.10000000000000001, + 1.0471975511965976 }, + { 1.6051187364639401, 0.90000000000000013, 0.10000000000000001, + 1.2217304763960306 }, + { 1.9941406879519474, 0.90000000000000013, 0.10000000000000001, + 1.3962634015954636 }, + { 2.4295011187834890, 0.90000000000000013, 0.10000000000000001, + 1.5707963267948966 }, +}; +const double toler182 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.20000000000000001. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.9533518431433547e-16 +// mean(f - f_Boost): 1.0269562977782698e-16 +// variance(f - f_Boost): 1.4388836606733082e-32 +// stddev(f - f_Boost): 1.1995347684303728e-16 +const testcase_ellint_3<double> +data183[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.20000000000000001, + 0.0000000000000000 }, + { 0.17561047321968409, 0.90000000000000013, 0.20000000000000001, + 0.17453292519943295 }, + { 0.35781659944356109, 0.90000000000000013, 0.20000000000000001, + 0.34906585039886590 }, + { 0.55388150905215283, 0.90000000000000013, 0.20000000000000001, + 0.52359877559829882 }, + { 0.77246874123251441, 0.90000000000000013, 0.20000000000000001, + 0.69813170079773179 }, + { 1.0244466254771925, 0.90000000000000013, 0.20000000000000001, + 0.87266462599716477 }, + { 1.3234824077640801, 0.90000000000000013, 0.20000000000000001, + 1.0471975511965976 }, + { 1.6849848968804240, 0.90000000000000013, 0.20000000000000001, + 1.2217304763960306 }, + { 2.1185749045502278, 0.90000000000000013, 0.20000000000000001, + 1.3962634015954636 }, + { 2.6076835743348417, 0.90000000000000013, 0.20000000000000001, + 1.5707963267948966 }, +}; +const double toler183 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.30000000000000004. +// max(|f - f_Boost|): 6.6613381477509392e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 3.9712691025502371e-16 +// mean(f - f_Boost): 6.9388939039072284e-17 +// variance(f - f_Boost): 5.9442282234173945e-34 +// stddev(f - f_Boost): 2.4380787976227090e-17 +const testcase_ellint_3<double> +data184[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.30000000000000004, + 0.0000000000000000 }, + { 0.17578954966746221, 0.90000000000000013, 0.30000000000000004, + 0.17453292519943295 }, + { 0.35929429810867447, 0.90000000000000013, 0.30000000000000004, + 0.34906585039886590 }, + { 0.55912757154240822, 0.90000000000000013, 0.30000000000000004, + 0.52359877559829882 }, + { 0.78578314722025389, 0.90000000000000013, 0.30000000000000004, + 0.69813170079773179 }, + { 1.0526941001131365, 0.90000000000000013, 0.30000000000000004, + 0.87266462599716477 }, + { 1.3769682234538601, 0.90000000000000013, 0.30000000000000004, + 1.0471975511965976 }, + { 1.7779437432911240, 0.90000000000000013, 0.30000000000000004, + 1.2217304763960306 }, + { 2.2676509341813635, 0.90000000000000013, 0.30000000000000004, + 1.3962634015954636 }, + { 2.8256506968858517, 0.90000000000000013, 0.30000000000000004, + 1.5707963267948966 }, +}; +const double toler184 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.40000000000000002. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.7042235432234642e-16 +// mean(f - f_Boost): 1.8041124150158794e-16 +// variance(f - f_Boost): 8.5834655546147173e-33 +// stddev(f - f_Boost): 9.2646994309662939e-17 +const testcase_ellint_3<double> +data185[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.40000000000000002, + 0.0000000000000000 }, + { 0.17596928293938452, 0.90000000000000013, 0.40000000000000002, + 0.17453292519943295 }, + { 0.36079388642472821, 0.90000000000000013, 0.40000000000000002, + 0.34906585039886590 }, + { 0.56455096667115612, 0.90000000000000013, 0.40000000000000002, + 0.52359877559829882 }, + { 0.79990996997869435, 0.90000000000000013, 0.40000000000000002, + 0.69813170079773179 }, + { 1.0836647913872215, 0.90000000000000013, 0.40000000000000002, + 0.87266462599716477 }, + { 1.4378726836091849, 0.90000000000000013, 0.40000000000000002, + 1.0471975511965976 }, + { 1.8880446720682853, 0.90000000000000013, 0.40000000000000002, + 1.2217304763960306 }, + { 2.4505848932025232, 0.90000000000000013, 0.40000000000000002, + 1.3962634015954636 }, + { 3.1000689868578624, 0.90000000000000013, 0.40000000000000002, + 1.5707963267948966 }, +}; +const double toler185 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.50000000000000000. +// max(|f - f_Boost|): 8.8817841970012523e-16 at index 7 +// max(|f - f_Boost| / |f_Boost|): 4.3939646155354115e-16 +// mean(f - f_Boost): 1.5820678100908481e-16 +// variance(f - f_Boost): 1.0089970755557622e-32 +// stddev(f - f_Boost): 1.0044884646205561e-16 +const testcase_ellint_3<double> +data186[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.50000000000000000, + 0.0000000000000000 }, + { 0.17614967734498183, 0.90000000000000013, 0.50000000000000000, + 0.17453292519943295 }, + { 0.36231594750319435, 0.90000000000000013, 0.50000000000000000, + 0.34906585039886590 }, + { 0.57016256984349567, 0.90000000000000013, 0.50000000000000000, + 0.52359877559829882 }, + { 0.81494025918293422, 0.90000000000000013, 0.50000000000000000, + 0.69813170079773179 }, + { 1.1178482279283477, 0.90000000000000013, 0.50000000000000000, + 0.87266462599716477 }, + { 1.5081455873012106, 0.90000000000000013, 0.50000000000000000, + 1.0471975511965976 }, + { 2.0213599730863998, 0.90000000000000013, 0.50000000000000000, + 1.2217304763960306 }, + { 2.6822467012926832, 0.90000000000000013, 0.50000000000000000, + 1.3962634015954636 }, + { 3.4591069002104686, 0.90000000000000013, 0.50000000000000000, + 1.5707963267948966 }, +}; +const double toler186 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.60000000000000009. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 4.4914274070443813e-16 +// mean(f - f_Boost): 3.4694469519536142e-16 +// variance(f - f_Boost): 2.5224926888894056e-31 +// stddev(f - f_Boost): 5.0224423231027804e-16 +const testcase_ellint_3<double> +data187[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.60000000000000009, + 0.0000000000000000 }, + { 0.17633073723493825, 0.90000000000000013, 0.60000000000000009, + 0.17453292519943295 }, + { 0.36386108723492810, 0.90000000000000013, 0.60000000000000009, + 0.34906585039886590 }, + { 0.57597424744716241, 0.90000000000000013, 0.60000000000000009, + 0.52359877559829882 }, + { 0.83098051948501150, 0.90000000000000013, 0.60000000000000009, + 0.69813170079773179 }, + { 1.1558706545698916, 0.90000000000000013, 0.60000000000000009, + 0.87266462599716477 }, + { 1.5905576379415669, 0.90000000000000013, 0.60000000000000009, + 1.0471975511965976 }, + { 2.1875186010215084, 0.90000000000000013, 0.60000000000000009, + 1.2217304763960306 }, + { 2.9885767771316853, 0.90000000000000013, 0.60000000000000009, + 1.3962634015954636 }, + { 3.9549939883570238, 0.90000000000000013, 0.60000000000000009, + 1.5707963267948966 }, +}; +const double toler187 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.70000000000000007. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 9 +// max(|f - f_Boost| / |f_Boost|): 5.5442489886293633e-16 +// mean(f - f_Boost): 4.3576253716537392e-16 +// variance(f - f_Boost): 2.2187568928205130e-31 +// stddev(f - f_Boost): 4.7103682370070737e-16 +const testcase_ellint_3<double> +data188[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.70000000000000007, + 0.0000000000000000 }, + { 0.17651246700160939, 0.90000000000000013, 0.70000000000000007, + 0.17453292519943295 }, + { 0.36542993547358982, 0.90000000000000013, 0.70000000000000007, + 0.34906585039886590 }, + { 0.58199897877674867, 0.90000000000000013, 0.70000000000000007, + 0.52359877559829882 }, + { 0.84815633587352857, 0.90000000000000013, 0.70000000000000007, + 0.69813170079773179 }, + { 1.1985495623872375, 0.90000000000000013, 0.70000000000000007, + 0.87266462599716477 }, + { 1.6892158134027691, 0.90000000000000013, 0.70000000000000007, + 1.0471975511965976 }, + { 2.4029722191094236, 0.90000000000000013, 0.70000000000000007, + 1.2217304763960306 }, + { 3.4201084941340061, 0.90000000000000013, 0.70000000000000007, + 1.3962634015954636 }, + { 4.6985482312992444, 0.90000000000000013, 0.70000000000000007, + 1.5707963267948966 }, +}; +const double toler188 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.80000000000000004. +// max(|f - f_Boost|): 1.7763568394002505e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.9362432595976420e-16 +// mean(f - f_Boost): 3.0531133177191805e-16 +// variance(f - f_Boost): 1.1508025840536076e-32 +// stddev(f - f_Boost): 1.0727546709539920e-16 +const testcase_ellint_3<double> +data189[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.80000000000000004, + 0.0000000000000000 }, + { 0.17669487107954862, 0.90000000000000013, 0.80000000000000004, + 0.17453292519943295 }, + { 0.36702314729628421, 0.90000000000000013, 0.80000000000000004, + 0.34906585039886590 }, + { 0.58825099711365492, 0.90000000000000013, 0.80000000000000004, + 0.52359877559829882 }, + { 0.86661711422209031, 0.90000000000000013, 0.80000000000000004, + 0.69813170079773179 }, + { 1.2469779109884802, 0.90000000000000013, 0.80000000000000004, + 0.87266462599716477 }, + { 1.8105469760531578, 0.90000000000000013, 0.80000000000000004, + 1.0471975511965976 }, + { 2.6989505165893752, 0.90000000000000013, 0.80000000000000004, + 1.2217304763960306 }, + { 4.0935213267757433, 0.90000000000000013, 0.80000000000000004, + 1.3962634015954636 }, + { 5.9820740813645727, 0.90000000000000013, 0.80000000000000004, + 1.5707963267948966 }, +}; +const double toler189 = 2.5000000000000020e-13; + +// Test data for k=0.90000000000000013, nu=0.90000000000000002. +// max(|f - f_Boost|): 2.6645352591003757e-15 at index 8 +// max(|f - f_Boost| / |f_Boost|): 4.9577148062669782e-16 +// mean(f - f_Boost): 5.9119376061289588e-16 +// variance(f - f_Boost): 1.7340883003959522e-31 +// stddev(f - f_Boost): 4.1642385863395872e-16 +const testcase_ellint_3<double> +data190[10] = +{ + { 0.0000000000000000, 0.90000000000000013, 0.90000000000000002, + 0.0000000000000000 }, + { 0.17687795394604169, 0.90000000000000013, 0.90000000000000002, + 0.17453292519943295 }, + { 0.36864140434751286, 0.90000000000000013, 0.90000000000000002, + 0.34906585039886590 }, + { 0.59474595366817051, 0.90000000000000013, 0.90000000000000002, + 0.52359877559829882 }, + { 0.88654237226056665, 0.90000000000000013, 0.90000000000000002, + 0.69813170079773179 }, + { 1.3026595810616726, 0.90000000000000013, 0.90000000000000002, + 0.87266462599716477 }, + { 1.9653635459278080, 0.90000000000000013, 0.90000000000000002, + 1.0471975511965976 }, + { 3.1451407527189468, 0.90000000000000013, 0.90000000000000002, + 1.2217304763960306 }, + { 5.3745230680316132, 0.90000000000000013, 0.90000000000000002, + 1.3962634015954636 }, + { 8.9942562031858717, 0.90000000000000013, 0.90000000000000002, + 1.5707963267948966 }, +}; +const double toler190 = 2.5000000000000020e-13; + +template<typename Ret, unsigned int Num> + void + test(const testcase_ellint_3<Ret> (&data)[Num], Ret toler) + { + bool test __attribute__((unused)) = true; + const Ret eps = std::numeric_limits<Ret>::epsilon(); + Ret max_abs_diff = -Ret(1); + Ret max_abs_frac = -Ret(1); + unsigned int num_datum = Num; + for (unsigned int i = 0; i < num_datum; ++i) + { + const Ret f = std::tr1::ellint_3(data[i].k, data[i].nu, + data[i].phi); + const Ret f0 = data[i].f0; + const Ret diff = f - f0; + if (std::abs(diff) > max_abs_diff) + max_abs_diff = std::abs(diff); + if (std::abs(f0) > Ret(10) * eps + && std::abs(f) > Ret(10) * eps) + { + const Ret frac = diff / f0; + if (std::abs(frac) > max_abs_frac) + max_abs_frac = std::abs(frac); + } + } + VERIFY(max_abs_frac < toler); + } -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>(); - test020<double>(); - test021<double>(); - test022<double>(); - test023<double>(); - test024<double>(); - test025<double>(); - test026<double>(); - test027<double>(); - test028<double>(); - test029<double>(); - test030<double>(); - test031<double>(); - test032<double>(); - test033<double>(); - test034<double>(); - test035<double>(); - test036<double>(); - test037<double>(); - test038<double>(); - test039<double>(); - test040<double>(); - test041<double>(); - test042<double>(); - test043<double>(); - test044<double>(); - test045<double>(); - test046<double>(); - test047<double>(); - test048<double>(); - test049<double>(); - test050<double>(); - test051<double>(); - test052<double>(); - test053<double>(); - test054<double>(); - test055<double>(); - test056<double>(); - test057<double>(); - test058<double>(); - test059<double>(); - test060<double>(); - test061<double>(); - test062<double>(); - test063<double>(); - test064<double>(); - test065<double>(); - test066<double>(); - test067<double>(); - test068<double>(); - test069<double>(); - test070<double>(); - test071<double>(); - test072<double>(); - test073<double>(); - test074<double>(); - test075<double>(); - test076<double>(); - test077<double>(); - test078<double>(); - test079<double>(); - test080<double>(); - test081<double>(); - test082<double>(); - test083<double>(); - test084<double>(); - test085<double>(); - test086<double>(); - test087<double>(); - test088<double>(); - test089<double>(); - test090<double>(); - test091<double>(); - test092<double>(); - test093<double>(); - test094<double>(); - test095<double>(); - test096<double>(); - test097<double>(); - test098<double>(); - test099<double>(); - test100<double>(); - test101<double>(); - test102<double>(); - test103<double>(); - test104<double>(); - test105<double>(); - test106<double>(); - test107<double>(); - test108<double>(); - test109<double>(); - test110<double>(); - test111<double>(); - test112<double>(); - test113<double>(); - test114<double>(); - test115<double>(); - test116<double>(); - test117<double>(); - test118<double>(); - test119<double>(); - test120<double>(); - test121<double>(); - test122<double>(); - test123<double>(); - test124<double>(); - test125<double>(); - test126<double>(); - test127<double>(); - test128<double>(); - test129<double>(); - test130<double>(); - test131<double>(); - test132<double>(); - test133<double>(); - test134<double>(); - test135<double>(); - test136<double>(); - test137<double>(); - test138<double>(); - test139<double>(); - test140<double>(); - test141<double>(); - test142<double>(); - test143<double>(); - test144<double>(); - test145<double>(); - test146<double>(); - test147<double>(); - test148<double>(); - test149<double>(); - test150<double>(); - test151<double>(); - test152<double>(); - test153<double>(); - test154<double>(); - test155<double>(); - test156<double>(); - test157<double>(); - test158<double>(); - test159<double>(); - test160<double>(); - test161<double>(); - test162<double>(); - test163<double>(); - test164<double>(); - test165<double>(); - test166<double>(); - test167<double>(); - test168<double>(); - test169<double>(); - test170<double>(); - test171<double>(); - test172<double>(); - test173<double>(); - test174<double>(); - test175<double>(); - test176<double>(); - test177<double>(); - test178<double>(); - test179<double>(); - test180<double>(); - test181<double>(); - test182<double>(); - test183<double>(); - test184<double>(); - test185<double>(); - test186<double>(); - test187<double>(); - test188<double>(); - test189<double>(); - test190<double>(); +int +main() +{ + test(data001, toler001); + test(data002, toler002); + test(data003, toler003); + test(data004, toler004); + test(data005, toler005); + test(data006, toler006); + test(data007, toler007); + test(data008, toler008); + test(data009, toler009); + test(data010, toler010); + test(data011, toler011); + test(data012, toler012); + test(data013, toler013); + test(data014, toler014); + test(data015, toler015); + test(data016, toler016); + test(data017, toler017); + test(data018, toler018); + test(data019, toler019); + test(data020, toler020); + test(data021, toler021); + test(data022, toler022); + test(data023, toler023); + test(data024, toler024); + test(data025, toler025); + test(data026, toler026); + test(data027, toler027); + test(data028, toler028); + test(data029, toler029); + test(data030, toler030); + test(data031, toler031); + test(data032, toler032); + test(data033, toler033); + test(data034, toler034); + test(data035, toler035); + test(data036, toler036); + test(data037, toler037); + test(data038, toler038); + test(data039, toler039); + test(data040, toler040); + test(data041, toler041); + test(data042, toler042); + test(data043, toler043); + test(data044, toler044); + test(data045, toler045); + test(data046, toler046); + test(data047, toler047); + test(data048, toler048); + test(data049, toler049); + test(data050, toler050); + test(data051, toler051); + test(data052, toler052); + test(data053, toler053); + test(data054, toler054); + test(data055, toler055); + test(data056, toler056); + test(data057, toler057); + test(data058, toler058); + test(data059, toler059); + test(data060, toler060); + test(data061, toler061); + test(data062, toler062); + test(data063, toler063); + test(data064, toler064); + test(data065, toler065); + test(data066, toler066); + test(data067, toler067); + test(data068, toler068); + test(data069, toler069); + test(data070, toler070); + test(data071, toler071); + test(data072, toler072); + test(data073, toler073); + test(data074, toler074); + test(data075, toler075); + test(data076, toler076); + test(data077, toler077); + test(data078, toler078); + test(data079, toler079); + test(data080, toler080); + test(data081, toler081); + test(data082, toler082); + test(data083, toler083); + test(data084, toler084); + test(data085, toler085); + test(data086, toler086); + test(data087, toler087); + test(data088, toler088); + test(data089, toler089); + test(data090, toler090); + test(data091, toler091); + test(data092, toler092); + test(data093, toler093); + test(data094, toler094); + test(data095, toler095); + test(data096, toler096); + test(data097, toler097); + test(data098, toler098); + test(data099, toler099); + test(data100, toler100); + test(data101, toler101); + test(data102, toler102); + test(data103, toler103); + test(data104, toler104); + test(data105, toler105); + test(data106, toler106); + test(data107, toler107); + test(data108, toler108); + test(data109, toler109); + test(data110, toler110); + test(data111, toler111); + test(data112, toler112); + test(data113, toler113); + test(data114, toler114); + test(data115, toler115); + test(data116, toler116); + test(data117, toler117); + test(data118, toler118); + test(data119, toler119); + test(data120, toler120); + test(data121, toler121); + test(data122, toler122); + test(data123, toler123); + test(data124, toler124); + test(data125, toler125); + test(data126, toler126); + test(data127, toler127); + test(data128, toler128); + test(data129, toler129); + test(data130, toler130); + test(data131, toler131); + test(data132, toler132); + test(data133, toler133); + test(data134, toler134); + test(data135, toler135); + test(data136, toler136); + test(data137, toler137); + test(data138, toler138); + test(data139, toler139); + test(data140, toler140); + test(data141, toler141); + test(data142, toler142); + test(data143, toler143); + test(data144, toler144); + test(data145, toler145); + test(data146, toler146); + test(data147, toler147); + test(data148, toler148); + test(data149, toler149); + test(data150, toler150); + test(data151, toler151); + test(data152, toler152); + test(data153, toler153); + test(data154, toler154); + test(data155, toler155); + test(data156, toler156); + test(data157, toler157); + test(data158, toler158); + test(data159, toler159); + test(data160, toler160); + test(data161, toler161); + test(data162, toler162); + test(data163, toler163); + test(data164, toler164); + test(data165, toler165); + test(data166, toler166); + test(data167, toler167); + test(data168, toler168); + test(data169, toler169); + test(data170, toler170); + test(data171, toler171); + test(data172, toler172); + test(data173, toler173); + test(data174, toler174); + test(data175, toler175); + test(data176, toler176); + test(data177, toler177); + test(data178, toler178); + test(data179, toler179); + test(data180, toler180); + test(data181, toler181); + test(data182, toler182); + test(data183, toler183); + test(data184, toler184); + test(data185, toler185); + test(data186, toler186); + test(data187, toler187); + test(data188, toler188); + test(data189, toler189); + test(data190, toler190); return 0; } |