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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/engel_expansion.hpp>
#include <boost/core/demangle.hpp>
#include <boost/math/constants/constants.hpp>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
#include <boost/multiprecision/cpp_bin_float.hpp>
using boost::math::tools::engel_expansion;
using boost::multiprecision::cpp_bin_float_100;
using boost::math::constants::pi;
template<class Real>
void test_rationals()
{
for (int64_t i = 1; i < 20; ++i)
{
Real x = Real(1)/Real(i);
auto engel = engel_expansion<Real>(x);
auto const & a = engel.digits();
CHECK_EQUAL(size_t(1), a.size());
CHECK_EQUAL(i, a.front());
}
Real x = Real(3)/Real(8);
auto engel = engel_expansion<Real>(x);
auto const & a = engel.digits();
if (!CHECK_EQUAL(size_t(2), a.size())) {
std::cerr << " Wrong number of digits for x = 3/8 on type " << boost::core::demangle(typeid(Real).name()) << "\n";
std::cerr << " engel = " << engel << "\n";
}
CHECK_EQUAL(int64_t(3), a.front());
CHECK_EQUAL(int64_t(8), a.back());
}
template<typename Real>
void test_well_known()
{
std::cout << "Testing well-known Engel expansions on type " << boost::core::demangle(typeid(Real).name()) << "\n";
using boost::math::constants::pi;
using boost::math::constants::e;
auto engel = engel_expansion(pi<Real>());
// See: http://oeis.org/A006784/list
std::vector<int64_t> expected{1,1,1,8,8,17,19,300,1991,2492,7236,10586,34588,
63403,70637,1236467,5417668,5515697,5633167,
7458122,9637848,9805775,41840855,58408380,
213130873,424342175,2366457522,4109464489,
21846713216,27803071890,31804388758,32651669133};
auto a = engel.digits();
// The last digit might be off somewhat, so don't test it:
size_t n = (std::min)(a.size() - 1, expected.size());
for(size_t i = 0; i < n; ++i)
{
if (!CHECK_EQUAL(expected[i], a[i]))
{
std::cerr << " Engel expansion of pi differs from expected at digit " << i << " of " << a.size() - 1 << "\n";
}
}
// The Engel expansion of e is {1, 1, 2, 3, 4, 5, 6, ...}
engel = engel_expansion(e<Real>());
a = engel.digits();
CHECK_EQUAL(int64_t(1), a.front());
int64_t m = a.size() - 1;
for (int64_t i = 1; i < m; ++i)
{
CHECK_EQUAL(i, a[i]);
}
}
int main()
{
test_rationals<float>();
test_rationals<double>();
test_rationals<long double>();
test_rationals<cpp_bin_float_100>();
test_well_known<float>();
test_well_known<double>();
test_well_known<long double>();
test_well_known<cpp_bin_float_100>();
#ifdef BOOST_HAS_FLOAT128
test_rationals<float128>();
test_well_known<float128>();
#endif
return boost::math::test::report_errors();
}
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