96 lines
3.0 KiB
C++
96 lines
3.0 KiB
C++
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/*
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* Copyright Nick Thompson, 2020
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* Use, modification and distribution are subject to the
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* Boost Software License, Version 1.0. (See accompanying file
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* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#include "math_unit_test.hpp"
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#include <boost/math/tools/luroth_expansion.hpp>
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#include <boost/math/constants/constants.hpp>
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#ifdef BOOST_HAS_FLOAT128
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#include <boost/multiprecision/float128.hpp>
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using boost::multiprecision::float128;
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#endif
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#include <boost/multiprecision/cpp_bin_float.hpp>
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using boost::math::tools::luroth_expansion;
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using boost::multiprecision::cpp_bin_float_100;
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using boost::math::constants::pi;
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template<class Real>
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void test_integral()
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{
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for (int64_t i = -20; i < 20; ++i) {
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Real ii = i;
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auto luroth = luroth_expansion<Real>(ii);
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auto const & a = luroth.digits();
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CHECK_EQUAL(size_t(1), a.size());
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CHECK_EQUAL(i, a.front());
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}
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}
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template<class Real>
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void test_halves()
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{
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// x = n + 1/k => lur(x) = ((n; k - 1))
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// Note that this is a bit different that Kalpazidou (examine the half-open interval of definition carefully).
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// One way to examine this definition is correct for rationals (it never happens for irrationals)
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// is to consider i + 1/3. If you follow Kalpazidou, then you get ((i, 3, 0)); a zero digit!
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// That's bad since it destroys uniqueness and also breaks the computation of the geometric mean.
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for (int64_t i = -20; i < 20; ++i) {
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Real x = i + Real(1)/Real(2);
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auto luroth = luroth_expansion<Real>(x);
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auto const & a = luroth.digits();
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CHECK_EQUAL(size_t(2), a.size());
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CHECK_EQUAL(i, a.front());
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CHECK_EQUAL(int64_t(1), a.back());
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}
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for (int64_t i = -20; i < 20; ++i) {
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Real x = i + Real(1)/Real(4);
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auto luroth = luroth_expansion<Real>(x);
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auto const & a = luroth.digits();
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CHECK_EQUAL(size_t(2), a.size());
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CHECK_EQUAL(i, a.front());
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CHECK_EQUAL(int64_t(3), a.back());
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}
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for (int64_t i = -20; i < 20; ++i) {
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Real x = i + Real(1)/Real(8);
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auto luroth = luroth_expansion<Real>(x);
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auto const & a = luroth.digits();
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CHECK_EQUAL(size_t(2), a.size());
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CHECK_EQUAL(i, a.front());
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CHECK_EQUAL(int64_t(7), a.back());
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}
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// 1/3 is a pain because it's not representable:
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Real x = Real(1)/Real(3);
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auto luroth = luroth_expansion<Real>(x);
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auto const & a = luroth.digits();
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CHECK_EQUAL(size_t(2), a.size());
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CHECK_EQUAL(int64_t(0), a.front());
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CHECK_EQUAL(int64_t(2), a.back());
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}
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int main()
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{
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test_integral<float>();
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test_integral<double>();
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test_integral<long double>();
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test_integral<cpp_bin_float_100>();
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test_halves<float>();
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test_halves<double>();
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test_halves<long double>();
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test_halves<cpp_bin_float_100>();
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#ifdef BOOST_HAS_FLOAT128
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test_integral<float128>();
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test_halves<float128>();
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#endif
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return boost::math::test::report_errors();
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}
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