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/*
* Copyright Nick Thompson, 2019
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#include "math_unit_test.hpp"
#include <numeric>
#include <utility>
#include <random>
#include <cmath>
#include <boost/math/tools/test_value.hpp>
#include <boost/core/demangle.hpp>
#include <boost/math/tools/agm.hpp>
#if __has_include(<stdfloat>)
# include <stdfloat>
#endif
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
using boost::math::tools::agm;
using std::sqrt;
template<class Real>
void test_gauss_constant()
{
// http://oeis.org/A014549/constant
Real G_expected = BOOST_MATH_TEST_VALUE(Real, 0.83462684167407318628142973279904680899399301349034700244982737010368199270952641186969116035127532412906785);
Real G_computed = 1/agm(sqrt(Real(2)), Real(1));
if(!CHECK_ULP_CLOSE(G_expected, G_computed, 2)) {
std::cerr << " Gauss constant not computed correctly.\n";
}
}
template<typename Real>
void test_scaling()
{
Real a = 2;
Real g = 1;
Real scale = 7;
Real expected = agm(scale*a, scale*g);
Real computed = scale*agm(a, g);
if(!CHECK_ULP_CLOSE(expected, computed, 2)) {
std::cerr << " Scaling property agm(kx,ky) = k*agm(x, y) is violated.\n";
}
expected = 0;
computed = agm(a, Real(0));
if(!CHECK_ULP_CLOSE(expected, computed, 0)) {
std::cerr << " agm(a, 0) != 0.\n";
}
computed = agm(Real(0), Real(0));
if(!CHECK_ULP_CLOSE(expected, computed, 0)) {
std::cerr << " agm(0, 0) != 0.\n";
}
expected = 1;
computed = agm(Real(1), Real(1));
if(!CHECK_ULP_CLOSE(expected, computed, 0)) {
std::cerr << " agm(1, 1) != 1.\n";
}
expected = 7;
computed = agm(Real(7), Real(7));
if(!CHECK_ULP_CLOSE(expected, computed, 0)) {
std::cerr << " agm(7, 7) != 1.\n";
}
// Properties I found at: https://mathworld.wolfram.com/Arithmetic-GeometricMean.html
// agm(x,y) = agm((x+y)/2, sqrt(xy))
expected = agm(Real(3), Real(1));
computed = agm(Real(2), sqrt(Real(3)));
if(!CHECK_ULP_CLOSE(expected, computed, 0)) {
std::cerr << " agm(x, y) != agm((x+y)/2, sqrt(xy)).\n";
}
//computed = agm(std::numeric_limits<Real>::infinity(), Real(7));
//std::cout << "Computed at infinity = " << computed << "\n";
for (Real x = 0; x < 1; x += Real(1)/128) {
expected = agm(Real(1), sqrt(1-x*x));
computed = agm(1+x, 1-x);
if(!CHECK_ULP_CLOSE(expected, computed, 0)) {
std::cerr << " agm(1, sqrt(1-x^2) != agm(1+x,1-x).\n";
}
}
}
int main()
{
#ifdef __STDCPP_FLOAT32_T__
test_gauss_constant<std::float32_t>();
test_scaling<std::float32_t>();
#else
test_gauss_constant<float>();
test_scaling<float>();
#endif
#ifdef __STDCPP_FLOAT64_T__
test_scaling<std::float64_t>();
test_gauss_constant<std::float64_t>();
#else
test_scaling<double>();
test_gauss_constant<double>();
#endif
test_scaling<long double>();
test_gauss_constant<long double>();
#ifdef BOOST_HAS_FLOAT128
test_gauss_constant<float128>();
test_scaling<float128>();
#endif
return boost::math::test::report_errors();
}
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