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test_Li6.cpp
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#define DOCTEST_CONFIG_IMPLEMENT_WITH_MAIN 1
#include "doctest.h"
#include "alt.h"
#include "c_wrappers.h"
#include "fortran_wrappers.h"
#include "Li6.hpp"
#include "read_data.hpp"
#include "test.hpp"
#include <cmath>
#include <limits>
#include <utility>
std::complex<double> poly_Li6(std::complex<double> z) {
double re{}, im{};
cli6_c(std::real(z), std::imag(z), &re, &im);
return { re, im };
}
#ifdef ENABLE_FORTRAN
std::complex<double> poly_Li6_fortran(std::complex<double> z) {
const double re = std::real(z);
const double im = std::imag(z);
double res_re{}, res_im{};
cli6_fortran(&re, &im, &res_re, &res_im);
return { res_re, res_im };
}
#endif
std::complex<long double> poly_Li6(std::complex<long double> z) {
long double re{}, im{};
cli6l_c(std::real(z), std::imag(z), &re, &im);
return { re, im };
}
TEST_CASE("test_special_values")
{
using polylogarithm::Li6;
const double eps = std::pow(10.0, -std::numeric_limits<double>::digits10);
const double zeta6 = 1.0173430619844491397145179297909;
const std::complex<double> zero(0.0, 0.0);
const std::complex<double> one(1.0, 0.0);
const std::complex<double> mone(-1.0, 0.0);
const std::complex<double> half(0.5, 0.0);
CHECK_CLOSE_COMPLEX(Li6(zero), 0, eps);
CHECK_CLOSE_COMPLEX(Li6(one), zeta6, eps);
CHECK_CLOSE_COMPLEX(Li6(mone), -31.*zeta6/32., eps);
CHECK_CLOSE_COMPLEX(Li6(half), 0.5040953978039886, eps);
}
// tests signbit for 0.0 and -0.0 arguments
TEST_CASE("test_signed_zero")
{
// skip test if platform does not supprt signed zero
if (!has_signed_zero()) {
return;
}
using polylogarithm::Li6;
const double pz64 = 0.0, nz64 = -0.0;
const long double pz128 = 0.0L, nz128 = -0.0L;
// complex Li6
CHECK( std::signbit(std::real(Li6(std::complex<double>(nz64, nz64)))));
CHECK( std::signbit(std::imag(Li6(std::complex<double>(nz64, nz64)))));
CHECK(!std::signbit(std::real(Li6(std::complex<double>(pz64, nz64)))));
CHECK( std::signbit(std::imag(Li6(std::complex<double>(pz64, nz64)))));
CHECK( std::signbit(std::real(Li6(std::complex<double>(nz64, pz64)))));
CHECK(!std::signbit(std::imag(Li6(std::complex<double>(nz64, pz64)))));
CHECK(!std::signbit(std::real(Li6(std::complex<double>(pz64, pz64)))));
CHECK(!std::signbit(std::imag(Li6(std::complex<double>(pz64, pz64)))));
CHECK( std::signbit(std::real(poly_Li6(std::complex<double>(nz64, nz64)))));
CHECK( std::signbit(std::imag(poly_Li6(std::complex<double>(nz64, nz64)))));
CHECK(!std::signbit(std::real(poly_Li6(std::complex<double>(pz64, nz64)))));
CHECK( std::signbit(std::imag(poly_Li6(std::complex<double>(pz64, nz64)))));
CHECK( std::signbit(std::real(poly_Li6(std::complex<double>(nz64, pz64)))));
CHECK(!std::signbit(std::imag(poly_Li6(std::complex<double>(nz64, pz64)))));
CHECK(!std::signbit(std::real(poly_Li6(std::complex<double>(pz64, pz64)))));
CHECK(!std::signbit(std::imag(poly_Li6(std::complex<double>(pz64, pz64)))));
#ifdef ENABLE_FORTRAN
CHECK( std::signbit(std::real(poly_Li6_fortran(std::complex<double>(nz64, nz64)))));
CHECK( std::signbit(std::imag(poly_Li6_fortran(std::complex<double>(nz64, nz64)))));
CHECK(!std::signbit(std::real(poly_Li6_fortran(std::complex<double>(pz64, nz64)))));
CHECK( std::signbit(std::imag(poly_Li6_fortran(std::complex<double>(pz64, nz64)))));
CHECK( std::signbit(std::real(poly_Li6_fortran(std::complex<double>(nz64, pz64)))));
CHECK(!std::signbit(std::imag(poly_Li6_fortran(std::complex<double>(nz64, pz64)))));
CHECK(!std::signbit(std::real(poly_Li6_fortran(std::complex<double>(pz64, pz64)))));
CHECK(!std::signbit(std::imag(poly_Li6_fortran(std::complex<double>(pz64, pz64)))));
#endif
CHECK( std::signbit(std::real(Li6(std::complex<long double>(nz128, nz128)))));
CHECK( std::signbit(std::imag(Li6(std::complex<long double>(nz128, nz128)))));
CHECK(!std::signbit(std::real(Li6(std::complex<long double>(pz128, nz128)))));
CHECK( std::signbit(std::imag(Li6(std::complex<long double>(pz128, nz128)))));
CHECK( std::signbit(std::real(Li6(std::complex<long double>(nz128, pz128)))));
CHECK(!std::signbit(std::imag(Li6(std::complex<long double>(nz128, pz128)))));
CHECK(!std::signbit(std::real(Li6(std::complex<long double>(pz128, pz128)))));
CHECK(!std::signbit(std::imag(Li6(std::complex<long double>(pz128, pz128)))));
CHECK( std::signbit(std::real(poly_Li6(std::complex<long double>(nz128, nz128)))));
CHECK( std::signbit(std::imag(poly_Li6(std::complex<long double>(nz128, nz128)))));
CHECK(!std::signbit(std::real(poly_Li6(std::complex<long double>(pz128, nz128)))));
CHECK( std::signbit(std::imag(poly_Li6(std::complex<long double>(pz128, nz128)))));
CHECK( std::signbit(std::real(poly_Li6(std::complex<long double>(nz128, pz128)))));
CHECK(!std::signbit(std::imag(poly_Li6(std::complex<long double>(nz128, pz128)))));
CHECK(!std::signbit(std::real(poly_Li6(std::complex<long double>(pz128, pz128)))));
CHECK(!std::signbit(std::imag(poly_Li6(std::complex<long double>(pz128, pz128)))));
}
template<typename T>
struct Data {
std::complex<T> z;
std::complex<T> li_expected;
T eps;
};
TEST_CASE("test_overflow")
{
if (!has_inf()) {
return;
}
using polylogarithm::Li6;
const double eps64 = std::pow(10.0, -std::numeric_limits<double>::digits10);
const long double eps128 = std::pow(10.0L, -std::numeric_limits<long double>::digits10);
const Data<double> data64[] = {
{{1e300, 1.0}, {-1.5086876165613597e14, 4.11768711823317e12}, 2*eps64},
{{1.0, 1e300}, {-1.5090387516918862e14, 2058950021167.7976}, eps64}
};
for (const auto& d : data64) {
CHECK_CLOSE_COMPLEX(Li6(d.z), d.li_expected, d.eps);
CHECK_CLOSE_COMPLEX(poly_Li6(d.z), d.li_expected, d.eps);
#ifdef ENABLE_FORTRAN
CHECK_CLOSE_COMPLEX(poly_Li6_fortran(d.z), d.li_expected, d.eps);
#endif
}
if (std::numeric_limits<long double>::max_exponent10 >= 4000) {
const Data<long double> data128[] = {
{{1e4000L, 1.0L}, {-8.478540098238822566033321355282680660651e20L, 1.7351899625805641348387419061716509476e18L}, eps128}
};
for (const auto& d : data128) {
CHECK_CLOSE_COMPLEX(Li6(d.z), d.li_expected, d.eps);
CHECK_CLOSE_COMPLEX(poly_Li6(d.z), d.li_expected, d.eps);
}
}
}
TEST_CASE("test_fixed_values")
{
const auto eps64 = std::pow(10.0 , -std::numeric_limits<double>::digits10);
const auto eps128 = std::pow(10.0L, -std::numeric_limits<long double>::digits10);
const std::string filename(std::string(TEST_DATA_DIR) + PATH_SEPARATOR + "Li6.txt");
const auto fixed_values = polylogarithm::test::read_from_file<long double>(filename);
for (auto v: fixed_values) {
const auto z128 = v.first;
const auto z64 = to<double>(z128);
const auto li128_expected = v.second;
const auto li64_expected = to<double>(li128_expected);
const auto li64_cmpl = polylogarithm::Li6(z64);
const auto li128_cmpl = polylogarithm::Li6(z128);
const auto li64_cmpl_c = poly_Li6(z64);
#ifdef ENABLE_FORTRAN
const auto li64_cmpl_f = poly_Li6_fortran(z64);
#endif
const auto li128_cmpl_c = poly_Li6(z128);
INFO("z(128) = " << z128);
INFO("Li4(64) cmpl = " << li64_expected << " (expected)");
INFO("Li4(64) cmpl = " << li64_cmpl << " (polylogarithm C++)");
INFO("Li4(64) cmpl = " << li64_cmpl_c << " (polylogarithm C)");
#ifdef ENABLE_FORTRAN
INFO("Li4(64) cmpl = " << li64_cmpl_f << " (polylogarithm Fortran)");
#endif
INFO("Li4(128) cmpl = " << li128_expected << " (expected)");
INFO("Li4(128) cmpl = " << li128_cmpl << " (polylogarithm C++)");
INFO("Li4(128) cmpl = " << li128_cmpl_c << " (polylogarithm C)");
CHECK_CLOSE_COMPLEX(li64_cmpl , li64_expected , 2*eps64);
CHECK_CLOSE_COMPLEX(li64_cmpl_c , li64_expected , 2*eps64);
#ifdef ENABLE_FORTRAN
CHECK_CLOSE_COMPLEX(li64_cmpl_f , li64_expected , 3*eps64);
#endif
CHECK_CLOSE_COMPLEX(li128_cmpl , li128_expected, 2*eps128);
CHECK_CLOSE_COMPLEX(li128_cmpl_c, li128_expected, 2*eps128);
}
}