98 lines
3.1 KiB
C++
98 lines
3.1 KiB
C++
/*
|
|
* 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/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();
|
|
}
|