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multiprecision/test/test_mpfi.cpp

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///////////////////////////////////////////////////////////////
// Copyright 2012 John Maddock. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
#ifdef _MSC_VER
#define _SCL_SECURE_NO_WARNINGS
#endif
#include "test.hpp"
#include <boost/multiprecision/mpfi.hpp>
#include <boost/multiprecision/random.hpp>
using namespace boost::multiprecision;
using namespace boost::random;
void test_exp()
{
std::cout << "Testing exp\n";
mpfr_float_50 val = 1.25;
for (unsigned i = 0; i < 2000; ++i)
{
mpfr_float_100 a(val);
mpfr_float_100 b = exp(a);
mpfi_float_50 in = val;
in = exp(in);
BOOST_CHECK((boost::math::isfinite)(in));
BOOST_CHECK(lower(in) <= b);
BOOST_CHECK(upper(in) >= b);
b = log(a);
in = val;
in = log(in);
BOOST_CHECK((boost::math::isfinite)(in));
BOOST_CHECK(lower(in) <= b);
BOOST_CHECK(upper(in) >= b);
val *= 1.01;
}
val = 1;
for (unsigned i = 0; i < 2000; ++i)
{
mpfr_float_100 a(val);
mpfr_float_100 b = exp(a);
mpfi_float_50 in = val;
in = exp(in);
BOOST_CHECK((boost::math::isfinite)(in));
BOOST_CHECK(lower(in) <= b);
BOOST_CHECK(upper(in) >= b);
b = log(a);
in = val;
in = log(in);
BOOST_CHECK((boost::math::isfinite)(in));
BOOST_CHECK(lower(in) <= b);
BOOST_CHECK(upper(in) >= b);
val /= 1.01;
}
}
void test_pow()
{
std::cout << "Testing pow function\n";
mt19937 gen;
uniform_real_distribution<mpfr_float_50> dist1(0, 400);
for (unsigned i = 0; i < 5000; ++i)
{
mpfr_float_50 base, p;
base = dist1(gen);
p = dist1(gen);
mpfr_float_100 a, b, r;
a = base;
b = p;
r = pow(a, b);
mpfi_float_50 ai, bi, ri;
ai = base;
bi = p;
ri = pow(ai, bi);
BOOST_CHECK((boost::math::isfinite)(ri));
BOOST_CHECK(lower(ri) <= r);
BOOST_CHECK(upper(ri) >= r);
}
}
void test_trig()
{
std::cout << "Testing trig functions\n";
mt19937 gen;
uniform_real_distribution<mpfr_float_50> dist1(-1.57079632679, 1.57079632679);
uniform_real_distribution<mpfr_float_50> dist2(-1, 1);
for (unsigned i = 0; i < 5000; ++i)
{
mpfr_float_50 val;
val = dist1(gen);
mpfr_float_100 a = val;
mpfr_float_100 b = sin(a);
mpfi_float_50 a2 = val;
mpfi_float_50 b2 = sin(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
b = cos(a);
b2 = cos(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
b = tan(a);
b2 = tan(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
}
for (unsigned i = 0; i < 5000; ++i)
{
mpfr_float_50 val;
val = dist2(gen);
mpfr_float_100 a = val;
mpfr_float_100 b = asin(a);
mpfi_float_50 a2 = val;
mpfi_float_50 b2 = asin(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
b = acos(a);
b2 = acos(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
b = atan(a);
b2 = atan(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
}
}
void test_hyp()
{
std::cout << "Testing hyperbolic trig functions\n";
mt19937 gen;
uniform_real_distribution<mpfr_float_50> dist1(-10, 10);
uniform_real_distribution<mpfr_float_50> dist2(-1, 1);
for (unsigned i = 0; i < 5000; ++i)
{
mpfr_float_50 val;
val = dist1(gen);
mpfr_float_100 a = val;
mpfr_float_100 b = sinh(a);
mpfi_float_50 a2 = val;
mpfi_float_50 b2 = sinh(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
b = cosh(a);
b2 = cosh(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
b = tanh(a);
b2 = tanh(a2);
BOOST_CHECK((boost::math::isfinite)(b2));
BOOST_CHECK(lower(b2) <= b);
BOOST_CHECK(upper(b2) >= b);
}
}
void test_intervals()
{
mpfi_float_50 a(1, 2);
mpfi_float_50 b(1.5, 2.5);
BOOST_CHECK_EQUAL(lower(a), 1);
BOOST_CHECK_EQUAL(upper(a), 2);
BOOST_CHECK_EQUAL(median(a), 1.5);
BOOST_CHECK_EQUAL(width(a), 1);
mpfi_float_50 r = intersect(a, b);
BOOST_CHECK_EQUAL(lower(r), 1.5);
BOOST_CHECK_EQUAL(upper(r), 2);
r = hull(a, b);
BOOST_CHECK_EQUAL(lower(r), 1);
BOOST_CHECK_EQUAL(upper(r), 2.5);
BOOST_CHECK(overlap(a, b));
BOOST_CHECK(in(mpfr_float_50(1.5), a));
BOOST_CHECK(in(mpfr_float_50(1), a));
BOOST_CHECK(in(mpfr_float_50(2), a));
BOOST_CHECK(!zero_in(a));
b = mpfi_float_50(1.5, 1.75);
BOOST_CHECK(subset(b, a));
BOOST_CHECK(proper_subset(b, a));
BOOST_CHECK(!empty(a));
BOOST_CHECK(!singleton(a));
b = mpfi_float_50(5, 6);
r = intersect(a, b);
BOOST_CHECK(empty(r));
}
#ifdef TEST_SPECIAL
#include "math/table_type.hpp"
#include <boost/math/special_functions.hpp>
#define T mpfi_float_50
typedef number<mpfi_float_backend<25> > mpfi_float_25;
void test_log1p_expm1()
{
#include "../../math/test/log1p_expm1_data.ipp"
std::cout << std::setprecision(std::numeric_limits<mpfi_float_25>::max_digits10);
std::cout << "Testing log1p and expm1\n";
for (unsigned i = 0; i < log1p_expm1_data.size(); ++i)
{
mpfi_float_25 in(log1p_expm1_data[i][0]);
mpfi_float_25 out = boost::math::log1p(in);
mpfi_float_25 expected(log1p_expm1_data[i][1]);
if (!subset(expected, out))
{
std::cout << in << std::endl;
std::cout << out << std::endl;
std::cout << expected << std::endl;
BOOST_CHECK(lower(out) <= lower(expected));
BOOST_CHECK(upper(out) >= upper(expected));
}
out = boost::math::expm1(in);
expected = mpfi_float_25(log1p_expm1_data[i][2]);
if (!subset(expected, out))
{
std::cout << in << std::endl;
std::cout << out << std::endl;
std::cout << expected << std::endl;
BOOST_CHECK(lower(out) <= lower(expected));
BOOST_CHECK(upper(out) >= upper(expected));
}
}
}
void test_bessel()
{
#include "../../math/test/bessel_i_int_data.ipp"
#include "../../math/test/bessel_i_data.ipp"
std::cout << std::setprecision(std::numeric_limits<mpfi_float_25>::max_digits10);
std::cout << "Testing Bessel Functions\n";
for (unsigned i = 0; i < bessel_i_int_data.size(); ++i)
{
int v = boost::lexical_cast<int>(static_cast<const char*>(bessel_i_int_data[i][0]));
mpfi_float_25 in(bessel_i_int_data[i][1]);
mpfi_float_25 out = boost::math::cyl_bessel_i(v, in);
mpfi_float_25 expected(bessel_i_int_data[i][2]);
if (!subset(expected, out))
{
std::cout << in << std::endl;
std::cout << out << std::endl;
std::cout << expected << std::endl;
BOOST_CHECK(lower(out) <= lower(expected));
BOOST_CHECK(upper(out) >= upper(expected));
}
}
}
#endif
int main()
{
#ifdef TEST_SPECIAL
test_log1p_expm1();
test_bessel();
#endif
test_intervals();
test_exp();
test_pow();
test_trig();
test_hyp();
return boost::report_errors();
}
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