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/*
* Copyright Nick Thompson, 2020
* 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 <boost/math/tools/centered_continued_fraction.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/core/demangle.hpp>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
using boost::math::tools::centered_continued_fraction;
using boost::multiprecision::cpp_bin_float_100;
using boost::math::constants::pi;
template<class Real>
void test_integral()
{
for (int64_t i = -20; i < 20; ++i) {
Real ii = i;
auto cfrac = centered_continued_fraction<Real>(ii);
auto const & a = cfrac.partial_denominators();
CHECK_EQUAL(size_t(1), a.size());
CHECK_EQUAL(i, a.front());
}
}
template<class Real>
void test_halves()
{
for (int64_t i = 0; i < 20; ++i) {
// std::round rounds 0.5 up if i > 0, and rounds down if i < 0.
// Should we care? These representations are not unique anyway;
// In any case, this behavior agrees with Maple.
Real x = i + Real(1)/Real(2);
auto cfrac = centered_continued_fraction<Real>(x);
auto const & a = cfrac.partial_denominators();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(i + 1, a.front());
CHECK_EQUAL(int64_t(-2), a.back());
}
// We'll also test quarters; why not?
for (int64_t i = -20; i < 20; ++i) {
Real x = i + Real(1)/Real(4);
auto cfrac = centered_continued_fraction<Real>(x);
auto const & a = cfrac.partial_denominators();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(i, a.front());
CHECK_EQUAL(int64_t(4), a.back());
}
for (int64_t i = -20; i < 20; ++i) {
Real x = i + Real(1)/Real(8);
auto cfrac = centered_continued_fraction<Real>(x);
auto const & a = cfrac.partial_denominators();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(i, a.front());
CHECK_EQUAL(int64_t(8), a.back());
}
for (int64_t i = -20; i < 20; ++i) {
Real x = i + Real(3)/Real(4);
auto cfrac = centered_continued_fraction<Real>(x);
auto const & a = cfrac.partial_denominators();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(i+1, a.front());
CHECK_EQUAL(int64_t(-4), a[1]);
}
for (int64_t i = -20; i < 20; ++i) {
Real x = i + Real(7)/Real(8);
auto cfrac = centered_continued_fraction<Real>(x);
auto const & a = cfrac.partial_denominators();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(i + 1, a.front());
CHECK_EQUAL(int64_t(-8), a[1]);
}
}
template<typename Real>
void test_simple()
{
std::cout << "Testing rational numbers on type " << boost::core::demangle(typeid(Real).name()) << "\n";
{
Real x = Real(649)/200;
// ContinuedFraction[649/200] = [3; 4, 12, 4]
auto cfrac = centered_continued_fraction(x);
auto const & a = cfrac.partial_denominators();
CHECK_EQUAL(size_t(4), a.size());
CHECK_EQUAL(int64_t(3), a[0]);
CHECK_EQUAL(int64_t(4), a[1]);
CHECK_EQUAL(int64_t(12), a[2]);
CHECK_EQUAL(int64_t(4), a[3]);
}
{
Real x = Real(415)/Real(93);
// [4; 2, 6, 7]:
auto cfrac = centered_continued_fraction(x);
auto const & a = cfrac.partial_denominators();
CHECK_EQUAL(size_t(4), a.size());
CHECK_EQUAL(int64_t(4), a[0]);
CHECK_EQUAL(int64_t(2), a[1]);
CHECK_EQUAL(int64_t(6), a[2]);
CHECK_EQUAL(int64_t(7), a[3]);
}
}
template<typename Real>
void test_khinchin()
{
using std::sqrt;
auto rt_cfrac = centered_continued_fraction(sqrt(static_cast<Real>(2)));
Real K0 = rt_cfrac.khinchin_geometric_mean();
CHECK_ULP_CLOSE(Real(2), K0, 10);
}
int main()
{
test_integral<float>();
test_integral<double>();
test_integral<long double>();
test_integral<cpp_bin_float_100>();
test_halves<float>();
test_halves<double>();
test_halves<long double>();
test_halves<cpp_bin_float_100>();
test_simple<float>();
test_simple<double>();
test_simple<long double>();
test_simple<cpp_bin_float_100>();
test_khinchin<cpp_bin_float_100>();
#ifdef BOOST_HAS_FLOAT128
test_integral<float128>();
test_halves<float128>();
test_simple<float128>();
test_khinchin<float128>();
#endif
return boost::math::test::report_errors();
}
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