ceph/src/boost/libs/math/test/luroth_expansion_test.cpp

   1 /*
   2  * Copyright Nick Thompson, 2020
   3  * Use, modification and distribution are subject to the
   4  * Boost Software License, Version 1.0. (See accompanying file
   5  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   6  */
   7
   8 #include "math_unit_test.hpp"
   9 #include <boost/math/tools/luroth_expansion.hpp>
  10 #include <boost/math/constants/constants.hpp>
  11 #include <boost/multiprecision/cpp_bin_float.hpp>
  12 #ifdef BOOST_HAS_FLOAT128
  13 #include <boost/multiprecision/float128.hpp>
  14 using boost::multiprecision::float128;
  15 #endif
  16
  17 using boost::math::tools::luroth_expansion;
  18 using boost::multiprecision::cpp_bin_float_100;
  19 using boost::math::constants::pi;
  20
  21 template<class Real>
  22 void test_integral()
  23 {
  24     for (int64_t i = -20; i < 20; ++i) {
  25         Real ii = i;
  26         auto luroth = luroth_expansion<Real>(ii);
  27         auto const & a = luroth.digits();
  28         CHECK_EQUAL(size_t(1), a.size());
  29         CHECK_EQUAL(i, a.front());
  30     }
  31 }
  32
  33
  34 template<class Real>
  35 void test_halves()
  36 {
  37     // x = n + 1/k => lur(x) = ((n; k - 1))
  38     // Note that this is a bit different that Kalpazidou (examine the half-open interval of definition carefully).
  39     // One way to examine this definition is correct for rationals (it never happens for irrationals)
  40     // is to consider i + 1/3. If you follow Kalpazidou, then you get ((i, 3, 0)); a zero digit!
  41     // That's bad since it destroys uniqueness and also breaks the computation of the geometric mean.
  42     for (int64_t i = -20; i < 20; ++i) {
  43         Real x = i + Real(1)/Real(2);
  44         auto luroth = luroth_expansion<Real>(x);
  45         auto const & a = luroth.digits();
  46         CHECK_EQUAL(size_t(2), a.size());
  47         CHECK_EQUAL(i, a.front());
  48         CHECK_EQUAL(int64_t(1), a.back());
  49     }
  50
  51     for (int64_t i = -20; i < 20; ++i) {
  52         Real x = i + Real(1)/Real(4);
  53         auto luroth = luroth_expansion<Real>(x);
  54         auto const & a = luroth.digits();
  55         CHECK_EQUAL(size_t(2), a.size());
  56         CHECK_EQUAL(i, a.front());
  57         CHECK_EQUAL(int64_t(3), a.back());
  58     }
  59
  60     for (int64_t i = -20; i < 20; ++i) {
  61         Real x = i + Real(1)/Real(8);
  62         auto luroth = luroth_expansion<Real>(x);
  63         auto const & a = luroth.digits();
  64         CHECK_EQUAL(size_t(2), a.size());
  65         CHECK_EQUAL(i, a.front());
  66         CHECK_EQUAL(int64_t(7), a.back());
  67     }
  68     // 1/3 is a pain because it's not representable:
  69     Real x = Real(1)/Real(3);
  70     auto luroth = luroth_expansion<Real>(x);
  71     auto const & a = luroth.digits();
  72     CHECK_EQUAL(size_t(2), a.size());
  73     CHECK_EQUAL(int64_t(0), a.front());
  74     CHECK_EQUAL(int64_t(2), a.back());
  75 }
  76
  77
  78 int main()
  79 {
  80     test_integral<float>();
  81     test_integral<double>();
  82     test_integral<long double>();
  83     test_integral<cpp_bin_float_100>();
  84
  85     test_halves<float>();
  86     test_halves<double>();
  87     test_halves<long double>();
  88     test_halves<cpp_bin_float_100>();
  89
  90     #ifdef BOOST_HAS_FLOAT128
  91     test_integral<float128>();
  92     test_halves<float128>();
  93     #endif
  94     return boost::math::test::report_errors();
  95 }