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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/luroth_expansion.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
using boost::math::tools::luroth_expansion;
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 luroth = luroth_expansion<Real>(ii);
auto const & a = luroth.digits();
CHECK_EQUAL(size_t(1), a.size());
CHECK_EQUAL(i, a.front());
}
}
template<class Real>
void test_halves()
{
// x = n + 1/k => lur(x) = ((n; k - 1))
// Note that this is a bit different that Kalpazidou (examine the half-open interval of definition carefully).
// One way to examine this definition is correct for rationals (it never happens for irrationals)
// is to consider i + 1/3. If you follow Kalpazidou, then you get ((i, 3, 0)); a zero digit!
// That's bad since it destroys uniqueness and also breaks the computation of the geometric mean.
for (int64_t i = -20; i < 20; ++i) {
Real x = i + Real(1)/Real(2);
auto luroth = luroth_expansion<Real>(x);
auto const & a = luroth.digits();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(i, a.front());
CHECK_EQUAL(int64_t(1), a.back());
}
for (int64_t i = -20; i < 20; ++i) {
Real x = i + Real(1)/Real(4);
auto luroth = luroth_expansion<Real>(x);
auto const & a = luroth.digits();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(i, a.front());
CHECK_EQUAL(int64_t(3), a.back());
}
for (int64_t i = -20; i < 20; ++i) {
Real x = i + Real(1)/Real(8);
auto luroth = luroth_expansion<Real>(x);
auto const & a = luroth.digits();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(i, a.front());
CHECK_EQUAL(int64_t(7), a.back());
}
// 1/3 is a pain because it's not representable:
Real x = Real(1)/Real(3);
auto luroth = luroth_expansion<Real>(x);
auto const & a = luroth.digits();
CHECK_EQUAL(size_t(2), a.size());
CHECK_EQUAL(int64_t(0), a.front());
CHECK_EQUAL(int64_t(2), a.back());
}
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>();
#ifdef BOOST_HAS_FLOAT128
test_integral<float128>();
test_halves<float128>();
#endif
return boost::math::test::report_errors();
}
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