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nest-open-source / nest-cam / 4320010 / boost / 62d1066a6d52d5ac4e10c106f0eab14c820be0ce / . / boost / libs / multiprecision / test / test_arithmetic.hpp
blob: d787f938db4a77842015f884159d15ddfe5c4a0f [file] [log] [blame]
///////////////////////////////////////////////////////////////
// Copyright 2012 John Maddock. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
#ifdef TEST_VLD
#include <vld.h>
#endif
#include <boost/math/special_functions/pow.hpp>
#include <boost/math/common_factor_rt.hpp>
#include "test.hpp"
template <class T>
struct is_boost_rational : public boost::mpl::false_{};
#ifdef BOOST_MSVC
// warning C4127: conditional expression is constant
#pragma warning(disable:4127)
#endif
template <class Target, class Source>
Target checked_lexical_cast(const Source& val)
{
try
{
return boost::lexical_cast<Target>(val);
}
catch(...)
{
std::cerr << "Error in lexical cast\nSource type = " << typeid(Source).name() << " \"" << val << "\"\n";
std::cerr << "Target type = " << typeid(Target).name() << std::endl;
throw;
}
}
bool isfloat(float){ return true; }
bool isfloat(double){ return true; }
bool isfloat(long double){ return true; }
template <class T> bool isfloat(T){ return false; }
namespace detail{
template<class tag, class Arg1, class Arg2, class Arg3, class Arg4>
typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type
abs(boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4> const& v)
{
typedef typename boost::multiprecision::detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type result_type;
return v < 0 ? result_type(-v) : result_type(v);
}
}
template <class T>
struct is_twos_complement_integer : public boost::mpl::true_ {};
template <class T>
struct related_type
{
typedef T type;
};
template <class Real, class Val>
void test_comparisons(Val, Val, const boost::mpl::false_)
{}
int normalize_compare_result(int r)
{
return r > 0 ? 1 : r < 0 ? -1 : 0;
}
template <class Real, class Val>
void test_comparisons(Val a, Val b, const boost::mpl::true_)
{
Real r1(a);
Real r2(b);
Real z(1);
int cr = a < b ? -1 : a > b ? 1 : 0;
BOOST_CHECK_EQUAL(r1 == r2, a == b);
BOOST_CHECK_EQUAL(r1 != r2, a != b);
BOOST_CHECK_EQUAL(r1 <= r2, a <= b);
BOOST_CHECK_EQUAL(r1 < r2, a < b);
BOOST_CHECK_EQUAL(r1 >= r2, a >= b);
BOOST_CHECK_EQUAL(r1 > r2, a > b);
BOOST_CHECK_EQUAL(r1 == b, a == b);
BOOST_CHECK_EQUAL(r1 != b, a != b);
BOOST_CHECK_EQUAL(r1 <= b, a <= b);
BOOST_CHECK_EQUAL(r1 < b, a < b);
BOOST_CHECK_EQUAL(r1 >= b, a >= b);
BOOST_CHECK_EQUAL(r1 > b, a > b);
BOOST_CHECK_EQUAL(a == r2, a == b);
BOOST_CHECK_EQUAL(a != r2, a != b);
BOOST_CHECK_EQUAL(a <= r2, a <= b);
BOOST_CHECK_EQUAL(a < r2, a < b);
BOOST_CHECK_EQUAL(a >= r2, a >= b);
BOOST_CHECK_EQUAL(a > r2, a > b);
BOOST_CHECK_EQUAL(r1*z == r2, a == b);
BOOST_CHECK_EQUAL(r1*z != r2, a != b);
BOOST_CHECK_EQUAL(r1*z <= r2, a <= b);
BOOST_CHECK_EQUAL(r1*z < r2, a < b);
BOOST_CHECK_EQUAL(r1*z >= r2, a >= b);
BOOST_CHECK_EQUAL(r1*z > r2, a > b);
BOOST_CHECK_EQUAL(r1 == r2*z, a == b);
BOOST_CHECK_EQUAL(r1 != r2*z, a != b);
BOOST_CHECK_EQUAL(r1 <= r2*z, a <= b);
BOOST_CHECK_EQUAL(r1 < r2*z, a < b);
BOOST_CHECK_EQUAL(r1 >= r2*z, a >= b);
BOOST_CHECK_EQUAL(r1 > r2*z, a > b);
BOOST_CHECK_EQUAL(r1*z == r2*z, a == b);
BOOST_CHECK_EQUAL(r1*z != r2*z, a != b);
BOOST_CHECK_EQUAL(r1*z <= r2*z, a <= b);
BOOST_CHECK_EQUAL(r1*z < r2*z, a < b);
BOOST_CHECK_EQUAL(r1*z >= r2*z, a >= b);
BOOST_CHECK_EQUAL(r1*z > r2*z, a > b);
BOOST_CHECK_EQUAL(r1*z == b, a == b);
BOOST_CHECK_EQUAL(r1*z != b, a != b);
BOOST_CHECK_EQUAL(r1*z <= b, a <= b);
BOOST_CHECK_EQUAL(r1*z < b, a < b);
BOOST_CHECK_EQUAL(r1*z >= b, a >= b);
BOOST_CHECK_EQUAL(r1*z > b, a > b);
BOOST_CHECK_EQUAL(a == r2*z, a == b);
BOOST_CHECK_EQUAL(a != r2*z, a != b);
BOOST_CHECK_EQUAL(a <= r2*z, a <= b);
BOOST_CHECK_EQUAL(a < r2*z, a < b);
BOOST_CHECK_EQUAL(a >= r2*z, a >= b);
BOOST_CHECK_EQUAL(a > r2*z, a > b);
BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(r2)), cr);
BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(r1)), -cr);
BOOST_CHECK_EQUAL(normalize_compare_result(r1.compare(b)), cr);
BOOST_CHECK_EQUAL(normalize_compare_result(r2.compare(a)), -cr);
}
template <class Real, class Exp>
void test_conditional(Real v, Exp e)
{
//
// Verify that Exp is usable in Boolean contexts, and has the same value as v:
//
if(e)
{
BOOST_CHECK(v);
}
else
{
BOOST_CHECK(!v);
}
if(!e)
{
BOOST_CHECK(!v);
}
else
{
BOOST_CHECK(v);
}
}
template <class Real>
void test_complement(Real a, Real b, Real c, const boost::mpl::true_&)
{
int i = 1020304;
int j = 56789123;
int sign_mask = ~0;
if(std::numeric_limits<Real>::is_signed)
{
BOOST_CHECK_EQUAL(~a , (~i & sign_mask));
c = a & ~b;
BOOST_CHECK_EQUAL(c , (i & (~j & sign_mask)));
c = ~(a | b);
BOOST_CHECK_EQUAL(c , (~(i | j) & sign_mask));
}
else
{
BOOST_CHECK_EQUAL((~a & a) , 0);
}
}
template <class Real>
void test_complement(Real, Real, Real, const boost::mpl::false_&)
{
}
template <class Real, class T>
void test_integer_ops(const T&){}
template <class Real>
void test_rational(const boost::mpl::true_&)
{
Real a(2);
a /= 3;
BOOST_CHECK_EQUAL(numerator(a) , 2);
BOOST_CHECK_EQUAL(denominator(a) , 3);
Real b(4);
b /= 6;
BOOST_CHECK_EQUAL(a , b);
//
// Check IO code:
//
std::stringstream ss;
ss << a;
ss >> b;
BOOST_CHECK_EQUAL(a, b);
}
template <class Real>
void test_rational(const boost::mpl::false_&)
{
Real a(2);
a /= 3;
BOOST_CHECK_EQUAL(numerator(a) , 2);
BOOST_CHECK_EQUAL(denominator(a) , 3);
Real b(4);
b /= 6;
BOOST_CHECK_EQUAL(a , b);
BOOST_CHECK_THROW(Real(a / 0), std::overflow_error);
BOOST_CHECK_THROW(Real("3.14"), std::runtime_error);
b = Real("2/3");
BOOST_CHECK_EQUAL(a, b);
//
// Check IO code:
//
std::stringstream ss;
ss << a;
ss >> b;
BOOST_CHECK_EQUAL(a, b);
}
template <class Real>
void test_integer_ops(const boost::mpl::int_<boost::multiprecision::number_kind_rational>&)
{
test_rational<Real>(is_boost_rational<Real>());
}
template <class Real>
void test_signed_integer_ops(const boost::mpl::true_&)
{
Real a(20);
Real b(7);
Real c(5);
BOOST_CHECK_EQUAL(-a % c , 0);
BOOST_CHECK_EQUAL(-a % b , -20 % 7);
BOOST_CHECK_EQUAL(-a % -b , -20 % -7);
BOOST_CHECK_EQUAL(a % -b , 20 % -7);
BOOST_CHECK_EQUAL(-a % 7 , -20 % 7);
BOOST_CHECK_EQUAL(-a % -7 , -20 % -7);
BOOST_CHECK_EQUAL(a % -7 , 20 % -7);
BOOST_CHECK_EQUAL(-a % 7u , -20 % 7);
BOOST_CHECK_EQUAL(-a % a , 0);
BOOST_CHECK_EQUAL(-a % 5 , 0);
BOOST_CHECK_EQUAL(-a % -5 , 0);
BOOST_CHECK_EQUAL(a % -5 , 0);
b = -b;
BOOST_CHECK_EQUAL(a % b , 20 % -7);
a = -a;
BOOST_CHECK_EQUAL(a % b , -20 % -7);
BOOST_CHECK_EQUAL(a % -7 , -20 % -7);
b = 7;
BOOST_CHECK_EQUAL(a % b , -20 % 7);
BOOST_CHECK_EQUAL(a % 7 , -20 % 7);
BOOST_CHECK_EQUAL(a % 7u , -20 % 7);
a = 20;
a %= b;
BOOST_CHECK_EQUAL(a , 20 % 7);
a = -20;
a %= b;
BOOST_CHECK_EQUAL(a , -20 % 7);
a = 20;
a %= -b;
BOOST_CHECK_EQUAL(a , 20 % -7);
a = -20;
a %= -b;
BOOST_CHECK_EQUAL(a , -20 % -7);
a = 5;
a %= b - a;
BOOST_CHECK_EQUAL(a , 5 % (7-5));
a = -20;
a %= 7;
BOOST_CHECK_EQUAL(a , -20 % 7);
a = 20;
a %= -7;
BOOST_CHECK_EQUAL(a , 20 % -7);
a = -20;
a %= -7;
BOOST_CHECK_EQUAL(a , -20 % -7);
#ifndef BOOST_NO_LONG_LONG
a = -20;
a %= 7uLL;
BOOST_CHECK_EQUAL(a , -20 % 7);
a = 20;
a %= -7LL;
BOOST_CHECK_EQUAL(a , 20 % -7);
a = -20;
a %= -7LL;
BOOST_CHECK_EQUAL(a , -20 % -7);
#endif
a = 400;
b = 45;
BOOST_CHECK_EQUAL(gcd(a, -45) , boost::math::gcd(400, 45));
BOOST_CHECK_EQUAL(lcm(a, -45) , boost::math::lcm(400, 45));
BOOST_CHECK_EQUAL(gcd(-400, b) , boost::math::gcd(400, 45));
BOOST_CHECK_EQUAL(lcm(-400, b) , boost::math::lcm(400, 45));
a = -20;
BOOST_CHECK_EQUAL(abs(a) , 20);
BOOST_CHECK_EQUAL(abs(-a) , 20);
BOOST_CHECK_EQUAL(abs(+a) , 20);
a = 20;
BOOST_CHECK_EQUAL(abs(a) , 20);
BOOST_CHECK_EQUAL(abs(-a) , 20);
BOOST_CHECK_EQUAL(abs(+a) , 20);
a = -400;
b = 45;
BOOST_CHECK_EQUAL(gcd(a, b) , boost::math::gcd(-400, 45));
BOOST_CHECK_EQUAL(lcm(a, b) , boost::math::lcm(-400, 45));
BOOST_CHECK_EQUAL(gcd(a, 45) , boost::math::gcd(-400, 45));
BOOST_CHECK_EQUAL(lcm(a, 45) , boost::math::lcm(-400, 45));
BOOST_CHECK_EQUAL(gcd(-400, b) , boost::math::gcd(-400, 45));
BOOST_CHECK_EQUAL(lcm(-400, b) , boost::math::lcm(-400, 45));
Real r;
divide_qr(a, b, c, r);
BOOST_CHECK_EQUAL(c , a / b);
BOOST_CHECK_EQUAL(r , a % b);
BOOST_CHECK_EQUAL(integer_modulus(a, 57) , abs(a % 57));
b = -57;
divide_qr(a, b, c, r);
BOOST_CHECK_EQUAL(c , a / b);
BOOST_CHECK_EQUAL(r , a % b);
BOOST_CHECK_EQUAL(integer_modulus(a, -57) , abs(a % -57));
a = 458;
divide_qr(a, b, c, r);
BOOST_CHECK_EQUAL(c , a / b);
BOOST_CHECK_EQUAL(r , a % b);
BOOST_CHECK_EQUAL(integer_modulus(a, -57) , abs(a % -57));
}
template <class Real>
void test_signed_integer_ops(const boost::mpl::false_&)
{
}
template <class Real>
void test_integer_ops(const boost::mpl::int_<boost::multiprecision::number_kind_integer>&)
{
test_signed_integer_ops<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
Real a(20);
Real b(7);
Real c(5);
BOOST_CHECK_EQUAL(a % b , 20 % 7);
BOOST_CHECK_EQUAL(a % 7 , 20 % 7);
BOOST_CHECK_EQUAL(a % 7u , 20 % 7);
BOOST_CHECK_EQUAL(a % a , 0);
BOOST_CHECK_EQUAL(a % c , 0);
BOOST_CHECK_EQUAL(a % 5 , 0);
a = a % (b + 0);
BOOST_CHECK_EQUAL(a , 20 % 7);
a = 20;
c = (a + 2) % (a - 1);
BOOST_CHECK_EQUAL(c , 22 % 19);
c = 5;
a = b % (a - 15);
BOOST_CHECK_EQUAL(a , 7 % 5);
a = 20;
a = 20;
a %= 7;
BOOST_CHECK_EQUAL(a , 20 % 7);
#ifndef BOOST_NO_LONG_LONG
a = 20;
a %= 7uLL;
BOOST_CHECK_EQUAL(a , 20 % 7);
#endif
a = 20;
BOOST_CHECK_EQUAL(++a , 21);
BOOST_CHECK_EQUAL(--a , 20);
BOOST_CHECK_EQUAL(a++ , 20);
BOOST_CHECK_EQUAL(a , 21);
BOOST_CHECK_EQUAL(a-- , 21);
BOOST_CHECK_EQUAL(a , 20);
a = 2000;
a <<= 20;
BOOST_CHECK_EQUAL(a , 2000L << 20);
a >>= 20;
BOOST_CHECK_EQUAL(a , 2000);
a <<= 20u;
BOOST_CHECK_EQUAL(a , 2000L << 20);
a >>= 20u;
BOOST_CHECK_EQUAL(a , 2000);
BOOST_CHECK_THROW(a <<= -20, std::out_of_range);
BOOST_CHECK_THROW(a >>= -20, std::out_of_range);
BOOST_CHECK_THROW(Real(a << -20), std::out_of_range);
BOOST_CHECK_THROW(Real(a >> -20), std::out_of_range);
#ifndef BOOST_NO_LONG_LONG
if(sizeof(long long) > sizeof(std::size_t))
{
// extreme values should trigger an exception:
BOOST_CHECK_THROW(a >>= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
BOOST_CHECK_THROW(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
BOOST_CHECK_THROW(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
BOOST_CHECK_THROW(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
BOOST_CHECK_THROW(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
BOOST_CHECK_THROW(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2)), std::out_of_range);
// Unless they fit within range:
a = 2000L;
BOOST_CHECK_EQUAL((a <<= 20uLL) , (2000L << 20));
a = 2000;
BOOST_CHECK_EQUAL((a <<= 20LL) , (2000L << 20));
BOOST_CHECK_THROW(Real(a >> (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
BOOST_CHECK_THROW(Real(a <<= (1uLL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
BOOST_CHECK_THROW(Real(a >>= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
BOOST_CHECK_THROW(Real(a <<= -(1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
BOOST_CHECK_THROW(Real(a >>= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
BOOST_CHECK_THROW(Real(a <<= (1LL << (sizeof(long long) * CHAR_BIT - 2))), std::out_of_range);
// Unless they fit within range:
a = 2000L;
BOOST_CHECK_EQUAL(Real(a << 20uLL) , (2000L << 20));
a = 2000;
BOOST_CHECK_EQUAL(Real(a << 20LL) , (2000L << 20));
}
#endif
a = 20;
b = a << 20;
BOOST_CHECK_EQUAL(b , (20 << 20));
b = a >> 2;
BOOST_CHECK_EQUAL(b , (20 >> 2));
b = (a + 2) << 10;
BOOST_CHECK_EQUAL(b , (22 << 10));
b = (a + 3) >> 3;
BOOST_CHECK_EQUAL(b , (23 >> 3));
//
// Bit fiddling:
//
int i = 1020304;
int j = 56789123;
int k = 4523187;
a = i;
b = j;
c = a;
c &= b;
BOOST_CHECK_EQUAL(c , (i & j));
c = a;
c &= j;
BOOST_CHECK_EQUAL(c , (i & j));
c = a;
c &= a + b;
BOOST_CHECK_EQUAL(c , (i & (i + j)));
BOOST_CHECK_EQUAL((a & b) , (i & j));
c = k;
a = a & (b + k);
BOOST_CHECK_EQUAL(a , (i & (j + k)));
a = i;
a = (b + k) & a;
BOOST_CHECK_EQUAL(a , (i & (j + k)));
a = i;
c = a & b & k;
BOOST_CHECK_EQUAL(c , (i&j&k));
c = a;
c &= (c+b);
BOOST_CHECK_EQUAL(c , (i & (i+j)));
c = a & (b | 1);
BOOST_CHECK_EQUAL(c , (i & (j | 1)));
test_complement<Real>(a, b, c, typename is_twos_complement_integer<Real>::type());
a = i;
b = j;
c = a;
c |= b;
BOOST_CHECK_EQUAL(c , (i | j));
c = a;
c |= j;
BOOST_CHECK_EQUAL(c , (i | j));
c = a;
c |= a + b;
BOOST_CHECK_EQUAL(c , (i | (i + j)));
BOOST_CHECK_EQUAL((a | b) , (i | j));
c = k;
a = a | (b + k);
BOOST_CHECK_EQUAL(a , (i | (j + k)));
a = i;
a = (b + k) | a;
BOOST_CHECK_EQUAL(a , (i | (j + k)));
a = i;
c = a | b | k;
BOOST_CHECK_EQUAL(c , (i|j|k));
c = a;
c |= (c + b);
BOOST_CHECK_EQUAL(c , (i | (i+j)));
c = a | (b | 1);
BOOST_CHECK_EQUAL(c , (i | (j | 1)));
a = i;
b = j;
c = a;
c ^= b;
BOOST_CHECK_EQUAL(c , (i ^ j));
c = a;
c ^= j;
BOOST_CHECK_EQUAL(c , (i ^ j));
c = a;
c ^= a + b;
BOOST_CHECK_EQUAL(c , (i ^ (i + j)));
BOOST_CHECK_EQUAL((a ^ b) , (i ^ j));
c = k;
a = a ^ (b + k);
BOOST_CHECK_EQUAL(a , (i ^ (j + k)));
a = i;
a = (b + k) ^ a;
BOOST_CHECK_EQUAL(a , (i ^ (j + k)));
a = i;
c = a ^ b ^ k;
BOOST_CHECK_EQUAL(c , (i^j^k));
c = a;
c ^= (c + b);
BOOST_CHECK_EQUAL(c , (i ^ (i+j)));
c = a ^ (b | 1);
BOOST_CHECK_EQUAL(c , (i ^ (j | 1)));
a = i;
b = j;
c = k;
//
// Non-member functions:
//
a = 400;
b = 45;
BOOST_CHECK_EQUAL(gcd(a, b) , boost::math::gcd(400, 45));
BOOST_CHECK_EQUAL(lcm(a, b) , boost::math::lcm(400, 45));
BOOST_CHECK_EQUAL(gcd(a, 45) , boost::math::gcd(400, 45));
BOOST_CHECK_EQUAL(lcm(a, 45) , boost::math::lcm(400, 45));
BOOST_CHECK_EQUAL(gcd(a, 45u) , boost::math::gcd(400, 45));
BOOST_CHECK_EQUAL(lcm(a, 45u) , boost::math::lcm(400, 45));
BOOST_CHECK_EQUAL(gcd(400, b) , boost::math::gcd(400, 45));
BOOST_CHECK_EQUAL(lcm(400, b) , boost::math::lcm(400, 45));
BOOST_CHECK_EQUAL(gcd(400u, b) , boost::math::gcd(400, 45));
BOOST_CHECK_EQUAL(lcm(400u, b) , boost::math::lcm(400, 45));
//
// Conditionals involving 2 arg functions:
//
test_conditional(Real(gcd(a, b)), gcd(a, b));
Real r;
divide_qr(a, b, c, r);
BOOST_CHECK_EQUAL(c , a / b);
BOOST_CHECK_EQUAL(r , a % b);
divide_qr(a + 0, b, c, r);
BOOST_CHECK_EQUAL(c , a / b);
BOOST_CHECK_EQUAL(r , a % b);
divide_qr(a, b+0, c, r);
BOOST_CHECK_EQUAL(c , a / b);
BOOST_CHECK_EQUAL(r , a % b);
divide_qr(a+0, b+0, c, r);
BOOST_CHECK_EQUAL(c , a / b);
BOOST_CHECK_EQUAL(r , a % b);
BOOST_CHECK_EQUAL(integer_modulus(a, 57) , a % 57);
for(unsigned i = 0; i < 20; ++i)
{
if(std::numeric_limits<Real>::is_specialized && (!std::numeric_limits<Real>::is_bounded || ((int)i * 17 < std::numeric_limits<Real>::digits)))
{
BOOST_CHECK_EQUAL(lsb(Real(1) << (i * 17)) , i * 17);
BOOST_CHECK_EQUAL(msb(Real(1) << (i * 17)) , i * 17);
BOOST_CHECK(bit_test(Real(1) << (i * 17), i * 17));
BOOST_CHECK(!bit_test(Real(1) << (i * 17), i * 17 + 1));
if(i)
{
BOOST_CHECK(!bit_test(Real(1) << (i * 17), i * 17 - 1));
}
Real zero(0);
BOOST_CHECK(bit_test(bit_set(zero, i * 17), i * 17));
zero = 0;
BOOST_CHECK_EQUAL(bit_flip(zero, i*17) , Real(1) << i * 17);
zero = Real(1) << i * 17;
BOOST_CHECK_EQUAL(bit_flip(zero, i * 17) , 0);
zero = Real(1) << i * 17;
BOOST_CHECK_EQUAL(bit_unset(zero, i * 17) , 0);
}
}
//
// pow, powm:
//
BOOST_CHECK_EQUAL(pow(Real(3), 4) , 81);
BOOST_CHECK_EQUAL(pow(Real(3) + Real(0), 4) , 81);
BOOST_CHECK_EQUAL(powm(Real(3), Real(4), Real(13)) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3), Real(4), 13) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3), Real(4), Real(13) + 0) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, Real(13)) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, 13) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3), Real(4) + 0, Real(13) + 0) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, Real(13)) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, 13) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3), 4 + 0, Real(13) + 0) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), Real(13)) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), 13) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4), Real(13) + 0) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, Real(13)) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, 13) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, Real(4) + 0, Real(13) + 0) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, Real(13)) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, 13) , 81 % 13);
BOOST_CHECK_EQUAL(powm(Real(3) + 0, 4 + 0, Real(13) + 0) , 81 % 13);
//
// Conditionals involving 3 arg functions:
//
test_conditional(Real(powm(Real(3), Real(4), Real(13))), powm(Real(3), Real(4), Real(13)));
//
// Things that are expected errors:
//
BOOST_CHECK_THROW(Real("3.14"), std::runtime_error);
BOOST_CHECK_THROW(Real("3L"), std::runtime_error);
BOOST_CHECK_THROW(Real(Real(20) / 0u), std::overflow_error);
//
// Extra tests added for full coverage:
//
a = 20;
b = 7;
c = 20 % b;
BOOST_CHECK_EQUAL(c , (20 % 7));
c = 20 % (b + 0);
BOOST_CHECK_EQUAL(c , (20 % 7));
c = a & 10;
BOOST_CHECK_EQUAL(c , (20 & 10));
c = 10 & a;
BOOST_CHECK_EQUAL(c , (20 & 10));
c = (a + 0) & (b + 0);
BOOST_CHECK_EQUAL(c , (20 & 7));
c = 10 & (a + 0);
BOOST_CHECK_EQUAL(c , (20 & 10));
c = 10 | a;
BOOST_CHECK_EQUAL(c , (20 | 10));
c = (a + 0) | (b + 0);
BOOST_CHECK(c == (20 | 7))
c = 20 | (b + 0);
BOOST_CHECK_EQUAL(c , (20 | 7));
c = a ^ 7;
BOOST_CHECK_EQUAL(c , (20 ^ 7));
c = 20 ^ b;
BOOST_CHECK_EQUAL(c , (20 ^ 7));
c = (a + 0) ^ (b + 0);
BOOST_CHECK_EQUAL(c , (20 ^ 7));
c = 20 ^ (b + 0);
BOOST_CHECK_EQUAL(c , (20 ^ 7));
}
template <class Real, class T>
void test_float_funcs(const T&){}
template <class Real>
void test_float_funcs(const boost::mpl::true_&)
{
if(boost::multiprecision::is_interval_number<Real>::value)
return;
//
// Test variable reuse in function calls, see https://svn.boost.org/trac/boost/ticket/8326
//
Real a(2), b(10);
a = pow(a, b);
BOOST_CHECK_EQUAL(a, 1024);
a = 2;
b = pow(a, b);
BOOST_CHECK_EQUAL(b, 1024);
b = 10;
a = pow(a, 10);
BOOST_CHECK_EQUAL(a, 1024);
a = -2;
a = abs(a);
BOOST_CHECK_EQUAL(a, 2);
a = -2;
a = fabs(a);
BOOST_CHECK_EQUAL(a, 2);
a = 2.5;
a = floor(a);
BOOST_CHECK_EQUAL(a, 2);
a = 2.5;
a = ceil(a);
BOOST_CHECK_EQUAL(a, 3);
a = 2.5;
a = trunc(a);
BOOST_CHECK_EQUAL(a, 2);
a = 2.25;
a = round(a);
BOOST_CHECK_EQUAL(a, 2);
a = 2;
a = ldexp(a, 1);
BOOST_CHECK_EQUAL(a, 4);
int i;
a = frexp(a, &i);
BOOST_CHECK_EQUAL(a, 0.5);
Real tol = std::numeric_limits<Real>::epsilon() * 3;
a = 4;
a = sqrt(a);
BOOST_CHECK_CLOSE_FRACTION(a, 2, tol);
a = 3;
a = exp(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(exp(Real(3))), tol);
a = 3;
a = log(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(log(Real(3))), tol);
a = 3;
a = log10(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(log10(Real(3))), tol);
a = 0.5;
a = sin(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(sin(Real(0.5))), tol);
a = 0.5;
a = cos(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(cos(Real(0.5))), tol);
a = 0.5;
a = tan(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(tan(Real(0.5))), tol);
a = 0.5;
a = asin(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(asin(Real(0.5))), tol);
a = 0.5;
a = acos(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(acos(Real(0.5))), tol);
a = 0.5;
a = atan(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(atan(Real(0.5))), tol);
a = 0.5;
a = sinh(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(sinh(Real(0.5))), tol);
a = 0.5;
a = cosh(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(cosh(Real(0.5))), tol);
a = 0.5;
a = tanh(a);
BOOST_CHECK_CLOSE_FRACTION(a, Real(tanh(Real(0.5))), tol);
a = 4;
b = 2;
a = fmod(a, b);
BOOST_CHECK_CLOSE_FRACTION(a, Real(fmod(Real(4), Real(2))), tol);
a = 4;
b = fmod(a, b);
BOOST_CHECK_CLOSE_FRACTION(b, Real(fmod(Real(4), Real(2))), tol);
b = 2;
a = atan2(a, b);
BOOST_CHECK_CLOSE_FRACTION(a, Real(atan2(Real(4), Real(2))), tol);
a = 4;
b = atan2(a, b);
BOOST_CHECK_CLOSE_FRACTION(b, Real(atan2(Real(4), Real(2))), tol);
}
template <class Real, class T>
void test_float_ops(const T&){}
template <class Real>
void test_float_ops(const boost::mpl::int_<boost::multiprecision::number_kind_floating_point>&)
{
BOOST_CHECK_EQUAL(abs(Real(2)) , 2);
BOOST_CHECK_EQUAL(abs(Real(-2)) , 2);
BOOST_CHECK_EQUAL(fabs(Real(2)) , 2);
BOOST_CHECK_EQUAL(fabs(Real(-2)) , 2);
BOOST_CHECK_EQUAL(floor(Real(5) / 2) , 2);
BOOST_CHECK_EQUAL(ceil(Real(5) / 2) , 3);
BOOST_CHECK_EQUAL(floor(Real(-5) / 2) , -3);
BOOST_CHECK_EQUAL(ceil(Real(-5) / 2) , -2);
BOOST_CHECK_EQUAL(trunc(Real(5) / 2) , 2);
BOOST_CHECK_EQUAL(trunc(Real(-5) / 2) , -2);
//
// ldexp and frexp, these pretty much have to be implemented by each backend:
//
BOOST_CHECK_EQUAL(ldexp(Real(2), 5) , 64);
BOOST_CHECK_EQUAL(ldexp(Real(2), -5) , Real(2) / 32);
Real v(512);
int exponent;
Real r = frexp(v, &exponent);
BOOST_CHECK_EQUAL(r , 0.5);
BOOST_CHECK_EQUAL(exponent , 10);
BOOST_CHECK_EQUAL(v , 512);
v = 1 / v;
r = frexp(v, &exponent);
BOOST_CHECK_EQUAL(r , 0.5);
BOOST_CHECK_EQUAL(exponent , -8);
typedef typename Real::backend_type::exponent_type e_type;
BOOST_CHECK_EQUAL(ldexp(Real(2), e_type(5)) , 64);
BOOST_CHECK_EQUAL(ldexp(Real(2), e_type(-5)) , Real(2) / 32);
v = 512;
e_type exp2;
r = frexp(v, &exp2);
BOOST_CHECK_EQUAL(r , 0.5);
BOOST_CHECK_EQUAL(exp2 , 10);
BOOST_CHECK_EQUAL(v , 512);
v = 1 / v;
r = frexp(v, &exp2);
BOOST_CHECK_EQUAL(r , 0.5);
BOOST_CHECK_EQUAL(exp2 , -8);
//
// scalbn and logb, these are the same as ldexp and frexp unless the radix is
// something other than 2:
//
if(std::numeric_limits<Real>::is_specialized && std::numeric_limits<Real>::radix)
{
BOOST_CHECK_EQUAL(scalbn(Real(2), 5), 2 * pow(double(std::numeric_limits<Real>::radix), 5));
BOOST_CHECK_EQUAL(scalbn(Real(2), -5), Real(2) / pow(double(std::numeric_limits<Real>::radix), 5));
Real v(512);
int exponent;
Real r;
exponent = ilogb(v);
r = scalbn(v, -exponent);
BOOST_CHECK(r >= 1);
BOOST_CHECK(r < std::numeric_limits<Real>::radix);
BOOST_CHECK_EQUAL(exponent, logb(v));
BOOST_CHECK_EQUAL(v, scalbn(r, exponent));
v = 1 / v;
exponent = ilogb(v);
r = scalbn(v, -exponent);
BOOST_CHECK(r >= 1);
BOOST_CHECK(r < std::numeric_limits<Real>::radix);
BOOST_CHECK_EQUAL(exponent, logb(v));
BOOST_CHECK_EQUAL(v, scalbn(r, exponent));
}
//
// pow and exponent:
//
v = 3.25;
r = pow(v, 0);
BOOST_CHECK_EQUAL(r , 1);
r = pow(v, 1);
BOOST_CHECK_EQUAL(r , 3.25);
r = pow(v, 2);
BOOST_CHECK_EQUAL(r , boost::math::pow<2>(3.25));
r = pow(v, 3);
BOOST_CHECK_EQUAL(r , boost::math::pow<3>(3.25));
r = pow(v, 4);
BOOST_CHECK_EQUAL(r , boost::math::pow<4>(3.25));
r = pow(v, 5);
BOOST_CHECK_EQUAL(r , boost::math::pow<5>(3.25));
r = pow(v, 6);
BOOST_CHECK_EQUAL(r , boost::math::pow<6>(3.25));
r = pow(v, 25);
BOOST_CHECK_EQUAL(r , boost::math::pow<25>(Real(3.25)));
//
// Things that are expected errors:
//
BOOST_CHECK_THROW(Real("3.14L"), std::runtime_error);
if(std::numeric_limits<Real>::is_specialized)
{
if(std::numeric_limits<Real>::has_infinity)
{
BOOST_CHECK((boost::math::isinf)(Real(20) / 0u));
}
else
{
BOOST_CHECK_THROW(Real(Real(20) / 0u), std::overflow_error);
}
}
test_float_funcs<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_specialized>());
}
template <class T>
struct lexical_cast_target_type
{
typedef typename boost::mpl::if_<
boost::is_signed<T>,
boost::intmax_t,
typename boost::mpl::if_<
boost::is_unsigned<T>,
boost::uintmax_t,
T
>::type
>::type type;
};
template <class Real, class Num>
void test_negative_mixed_minmax(boost::mpl::true_ const&)
{
if(!std::numeric_limits<Real>::is_bounded || (std::numeric_limits<Real>::digits >= std::numeric_limits<Num>::digits))
{
Real mx1((std::numeric_limits<Num>::max)() - 1);
++mx1;
Real mx2((std::numeric_limits<Num>::max)());
BOOST_CHECK_EQUAL(mx1, mx2);
mx1 = (std::numeric_limits<Num>::max)() - 1;
++mx1;
mx2 = (std::numeric_limits<Num>::max)();
BOOST_CHECK_EQUAL(mx1, mx2);
if(!std::numeric_limits<Real>::is_bounded || (std::numeric_limits<Real>::digits > std::numeric_limits<Num>::digits))
{
Real mx3((std::numeric_limits<Num>::min)() + 1);
--mx3;
Real mx4((std::numeric_limits<Num>::min)());
BOOST_CHECK_EQUAL(mx3, mx4);
mx3 = (std::numeric_limits<Num>::min)() + 1;
--mx3;
mx4 = (std::numeric_limits<Num>::min)();
BOOST_CHECK_EQUAL(mx3, mx4);
}
}
}
template <class Real, class Num>
void test_negative_mixed_minmax(boost::mpl::false_ const&)
{
}
template <class Real, class Num>
void test_negative_mixed(boost::mpl::true_ const&)
{
typedef typename lexical_cast_target_type<Num>::type target_type;
typedef typename boost::mpl::if_<
boost::is_convertible<Num, Real>,
typename boost::mpl::if_c<boost::is_integral<Num>::value && (sizeof(Num) < sizeof(int)), int, Num>::type,
Real
>::type cast_type;
typedef typename boost::mpl::if_<
boost::is_convertible<Num, Real>,
Num,
Real
>::type simple_cast_type;
std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl;
static const int left_shift = std::numeric_limits<Num>::digits - 1;
Num n1 = -static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
Num n2 = -1;
Num n3 = 0;
Num n4 = -20;
Num n5 = -8;
test_comparisons<Real>(n1, n2, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n1, n3, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n3, n1, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n2, n1, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n1, n1, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n3, n3, boost::is_convertible<Num, Real>());
// Default construct:
BOOST_CHECK_EQUAL(Real(n1) , static_cast<cast_type>(n1));
BOOST_CHECK_EQUAL(Real(n2) , static_cast<cast_type>(n2));
BOOST_CHECK_EQUAL(Real(n3) , static_cast<cast_type>(n3));
BOOST_CHECK_EQUAL(Real(n4) , static_cast<cast_type>(n4));
BOOST_CHECK_EQUAL(static_cast<cast_type>(n1) , Real(n1));
BOOST_CHECK_EQUAL(static_cast<cast_type>(n2) , Real(n2));
BOOST_CHECK_EQUAL(static_cast<cast_type>(n3) , Real(n3));
BOOST_CHECK_EQUAL(static_cast<cast_type>(n4) , Real(n4));
BOOST_CHECK_EQUAL(Real(n1).template convert_to<Num>() , n1);
BOOST_CHECK_EQUAL(Real(n2).template convert_to<Num>() , n2);
BOOST_CHECK_EQUAL(Real(n3).template convert_to<Num>() , n3);
BOOST_CHECK_EQUAL(Real(n4).template convert_to<Num>() , n4);
#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1)) , n1);
BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2)) , n2);
BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3)) , n3);
BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4)) , n4);
#endif
#if defined(TEST_MPFR)
Num tol = 10 * std::numeric_limits<Num>::epsilon();
#else
Num tol = 0;
#endif
std::ios_base::fmtflags f = boost::is_floating_point<Num>::value ? std::ios_base::scientific : std::ios_base::fmtflags(0);
int digits_to_print = boost::is_floating_point<Num>::value && std::numeric_limits<Num>::is_specialized
? std::numeric_limits<Num>::digits10 + 5 : 0;
if(std::numeric_limits<target_type>::digits <= std::numeric_limits<Real>::digits)
{
BOOST_CHECK_CLOSE(n1, checked_lexical_cast<target_type>(Real(n1).str(digits_to_print, f)), tol);
}
BOOST_CHECK_CLOSE(n2, checked_lexical_cast<target_type>(Real(n2).str(digits_to_print, f)), 0);
BOOST_CHECK_CLOSE(n3, checked_lexical_cast<target_type>(Real(n3).str(digits_to_print, f)), 0);
BOOST_CHECK_CLOSE(n4, checked_lexical_cast<target_type>(Real(n4).str(digits_to_print, f)), 0);
// Assignment:
Real r(0);
BOOST_CHECK(r != static_cast<cast_type>(n1));
r = static_cast<simple_cast_type>(n1);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n1));
r = static_cast<simple_cast_type>(n2);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2));
r = static_cast<simple_cast_type>(n3);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n3));
r = static_cast<simple_cast_type>(n4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4));
// Addition:
r = static_cast<simple_cast_type>(n2);
BOOST_CHECK_EQUAL(r + static_cast<simple_cast_type>(n4) , static_cast<cast_type>(n2 + n4));
BOOST_CHECK_EQUAL(Real(r + static_cast<simple_cast_type>(n4)) , static_cast<cast_type>(n2 + n4));
r += static_cast<simple_cast_type>(n4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2 + n4));
// subtraction:
r = static_cast<simple_cast_type>(n4);
BOOST_CHECK_EQUAL(r - static_cast<simple_cast_type>(n5) , static_cast<cast_type>(n4 - n5));
BOOST_CHECK_EQUAL(Real(r - static_cast<simple_cast_type>(n5)) , static_cast<cast_type>(n4 - n5));
r -= static_cast<simple_cast_type>(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5));
// Multiplication:
r = static_cast<simple_cast_type>(n2);
BOOST_CHECK_EQUAL(r * static_cast<simple_cast_type>(n4) , static_cast<cast_type>(n2 * n4));
BOOST_CHECK_EQUAL(Real(r * static_cast<simple_cast_type>(n4)) , static_cast<cast_type>(n2 * n4));
r *= static_cast<simple_cast_type>(n4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2 * n4));
// Division:
r = static_cast<simple_cast_type>(n1);
BOOST_CHECK_EQUAL(r / static_cast<simple_cast_type>(n5) , static_cast<cast_type>(n1 / n5));
BOOST_CHECK_EQUAL(Real(r / static_cast<simple_cast_type>(n5)) , static_cast<cast_type>(n1 / n5));
r /= static_cast<simple_cast_type>(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n1 / n5));
//
// Extra cases for full coverage:
//
r = Real(n4) + static_cast<simple_cast_type>(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 + n5));
r = static_cast<simple_cast_type>(n4) + Real(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 + n5));
r = Real(n4) - static_cast<simple_cast_type>(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5));
r = static_cast<simple_cast_type>(n4) - Real(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5));
r = static_cast<simple_cast_type>(n4) * Real(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 * n5));
r = static_cast<cast_type>(4 * n4) / Real(4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4));
Real a, b, c;
a = 20;
b = 30;
c = -a + b;
BOOST_CHECK_EQUAL(c , 10);
c = b + -a;
BOOST_CHECK_EQUAL(c , 10);
n4 = 30;
c = -a + static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , 10);
c = static_cast<cast_type>(n4) + -a;
BOOST_CHECK_EQUAL(c , 10);
c = -a + -b;
BOOST_CHECK_EQUAL(c , -50);
n4 = 4;
c = -(a + b) + static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , -50+4);
n4 = 50;
c = (a + b) - static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , 0);
c = (a + b) - static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , 0);
c = a - -(b + static_cast<cast_type>(n4));
BOOST_CHECK_EQUAL(c , 20 - -(30 + 50));
c = -(b + static_cast<cast_type>(n4)) - a;
BOOST_CHECK_EQUAL(c , -(30 + 50) - 20);
c = a - -b;
BOOST_CHECK_EQUAL(c , 50);
c = -a - b;
BOOST_CHECK_EQUAL(c , -50);
c = -a - static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , -20 - 50);
c = static_cast<cast_type>(n4) - -a;
BOOST_CHECK_EQUAL(c , 50 + 20);
c = -(a + b) - Real(n4);
BOOST_CHECK_EQUAL(c , -(20 + 30) - 50);
c = static_cast<cast_type>(n4) - (a + b);
BOOST_CHECK_EQUAL(c , 0);
c = (a + b) * static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , 50 * 50);
c = static_cast<cast_type>(n4) * (a + b);
BOOST_CHECK_EQUAL(c , 50 * 50);
c = a * -(b + static_cast<cast_type>(n4));
BOOST_CHECK_EQUAL(c , 20 * -(30 + 50));
c = -(b + static_cast<cast_type>(n4)) * a;
BOOST_CHECK_EQUAL(c , 20 * -(30 + 50));
c = a * -b;
BOOST_CHECK_EQUAL(c , 20 * -30);
c = -a * b;
BOOST_CHECK_EQUAL(c , 20 * -30);
c = -a * static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , -20 * 50);
c = static_cast<cast_type>(n4) * -a;
BOOST_CHECK_EQUAL(c , -20 * 50);
c = -(a + b) + a;
BOOST_CHECK(-50 + 20);
c = static_cast<cast_type>(n4) - (a + b);
BOOST_CHECK_EQUAL(c , 0);
Real d = 10;
c = (a + b) / d;
BOOST_CHECK_EQUAL(c , 5);
c = (a + b) / (d + 0);
BOOST_CHECK_EQUAL(c , 5);
c = (a + b) / static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , 1);
c = static_cast<cast_type>(n4) / (a + b);
BOOST_CHECK_EQUAL(c , 1);
d = 50;
c = d / -(a + b);
BOOST_CHECK_EQUAL(c , -1);
c = -(a + b) / d;
BOOST_CHECK_EQUAL(c , -1);
d = 2;
c = a / -d;
BOOST_CHECK_EQUAL(c , 20 / -2);
c = -a / d;
BOOST_CHECK_EQUAL(c , 20 / -2);
d = 50;
c = -d / static_cast<cast_type>(n4);
BOOST_CHECK_EQUAL(c , -1);
c = static_cast<cast_type>(n4) / -d;
BOOST_CHECK_EQUAL(c , -1);
c = static_cast<cast_type>(n4) + a;
BOOST_CHECK_EQUAL(c , 70);
c = static_cast<cast_type>(n4) - a;
BOOST_CHECK_EQUAL(c , 30);
c = static_cast<cast_type>(n4) * a;
BOOST_CHECK_EQUAL(c , 50 * 20);
n1 = -2;
n2 = -3;
n3 = -4;
a = static_cast<cast_type>(n1);
b = static_cast<cast_type>(n2);
c = static_cast<cast_type>(n3);
d = a + b * c;
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = static_cast<cast_type>(n1) + b * c;
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = a + static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = a + b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = static_cast<cast_type>(n1) + static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = static_cast<cast_type>(n1) + b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
a += static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(a , -2 + -3 * -4);
a = static_cast<cast_type>(n1);
a += b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(a , -2 + -3 * -4);
a = static_cast<cast_type>(n1);
d = b * c + a;
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = b * c + static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = static_cast<cast_type>(n2) * c + a;
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = b * static_cast<cast_type>(n3) + a;
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = static_cast<cast_type>(n2) * c + static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
d = b * static_cast<cast_type>(n3) + static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , -2 + -3 * -4);
a = -20;
d = a - b * c;
BOOST_CHECK_EQUAL(d , -20 - -3 * -4);
n1 = -20;
d = static_cast<cast_type>(n1) - b * c;
BOOST_CHECK_EQUAL(d , -20 - -3 * -4);
d = a - static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(d , -20 - -3 * -4);
d = a - b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(d , -20 - -3 * -4);
d = static_cast<cast_type>(n1) - static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(d , -20 - -3 * -4);
d = static_cast<cast_type>(n1) - b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(d , -20 - -3 * -4);
a -= static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(a , -20 - -3 * -4);
a = static_cast<cast_type>(n1);
a -= b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(a , -20 - -3 * -4);
a = -2;
d = b * c - a;
BOOST_CHECK_EQUAL(d , -3 * -4 - -2);
n1 = -2;
d = b * c - static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , -3 * -4 - -2);
d = static_cast<cast_type>(n2) * c - a;
BOOST_CHECK_EQUAL(d , -3 * -4 - -2);
d = b * static_cast<cast_type>(n3) - a;
BOOST_CHECK_EQUAL(d , -3 * -4 - -2);
d = static_cast<cast_type>(n2) * c - static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , -3 * -4 - -2);
d = b * static_cast<cast_type>(n3) - static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , -3 * -4 - -2);
//
// Conversion from min and max values:
//
test_negative_mixed_minmax<Real, Num>(boost::mpl::bool_<std::numeric_limits<Real>::is_integer && std::numeric_limits<Num>::is_integer>());
}
template <class Real, class Num>
void test_negative_mixed(boost::mpl::false_ const&)
{
}
template <class Real, class Num>
void test_mixed(const boost::mpl::false_&)
{
}
template <class Real, class Num>
void test_mixed(const boost::mpl::true_&)
{
typedef typename lexical_cast_target_type<Num>::type target_type;
typedef typename boost::mpl::if_<
boost::is_convertible<Num, Real>,
typename boost::mpl::if_c<boost::is_integral<Num>::value && (sizeof(Num) < sizeof(int)), int, Num>::type,
Real
>::type cast_type;
typedef typename boost::mpl::if_<
boost::is_convertible<Num, Real>,
Num,
Real
>::type simple_cast_type;
if(std::numeric_limits<Real>::is_specialized && std::numeric_limits<Real>::is_bounded && std::numeric_limits<Real>::digits < std::numeric_limits<Num>::digits)
return;
std::cout << "Testing mixed arithmetic with type: " << typeid(Real).name() << " and " << typeid(Num).name() << std::endl;
static const int left_shift = std::numeric_limits<Num>::digits - 1;
Num n1 = static_cast<Num>(1uLL << ((left_shift < 63) && (left_shift > 0) ? left_shift : 10));
Num n2 = 1;
Num n3 = 0;
Num n4 = 20;
Num n5 = 8;
test_comparisons<Real>(n1, n2, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n1, n3, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n1, n1, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n3, n1, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n2, n1, boost::is_convertible<Num, Real>());
test_comparisons<Real>(n3, n3, boost::is_convertible<Num, Real>());
// Default construct:
BOOST_CHECK_EQUAL(Real(n1) , static_cast<cast_type>(n1));
BOOST_CHECK_EQUAL(Real(n2) , static_cast<cast_type>(n2));
BOOST_CHECK_EQUAL(Real(n3) , static_cast<cast_type>(n3));
BOOST_CHECK_EQUAL(Real(n4) , static_cast<cast_type>(n4));
BOOST_CHECK_EQUAL(Real(n1).template convert_to<Num>() , n1);
BOOST_CHECK_EQUAL(Real(n2).template convert_to<Num>() , n2);
BOOST_CHECK_EQUAL(Real(n3).template convert_to<Num>() , n3);
BOOST_CHECK_EQUAL(Real(n4).template convert_to<Num>() , n4);
#ifndef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
BOOST_CHECK_EQUAL(static_cast<Num>(Real(n1)) , n1);
BOOST_CHECK_EQUAL(static_cast<Num>(Real(n2)) , n2);
BOOST_CHECK_EQUAL(static_cast<Num>(Real(n3)) , n3);
BOOST_CHECK_EQUAL(static_cast<Num>(Real(n4)) , n4);
#endif
BOOST_CHECK_EQUAL(static_cast<cast_type>(n1) , Real(n1));
BOOST_CHECK_EQUAL(static_cast<cast_type>(n2) , Real(n2));
BOOST_CHECK_EQUAL(static_cast<cast_type>(n3) , Real(n3));
BOOST_CHECK_EQUAL(static_cast<cast_type>(n4) , Real(n4));
#if defined(TEST_MPFR)
Num tol = 10 * std::numeric_limits<Num>::epsilon();
#else
Num tol = 0;
#endif
std::ios_base::fmtflags f = boost::is_floating_point<Num>::value ? std::ios_base::scientific : std::ios_base::fmtflags(0);
int digits_to_print = boost::is_floating_point<Num>::value && std::numeric_limits<Num>::is_specialized
? std::numeric_limits<Num>::digits10 + 5 : 0;
if(std::numeric_limits<target_type>::digits <= std::numeric_limits<Real>::digits)
{
BOOST_CHECK_CLOSE(n1, checked_lexical_cast<target_type>(Real(n1).str(digits_to_print, f)), tol);
}
BOOST_CHECK_CLOSE(n2, checked_lexical_cast<target_type>(Real(n2).str(digits_to_print, f)), 0);
BOOST_CHECK_CLOSE(n3, checked_lexical_cast<target_type>(Real(n3).str(digits_to_print, f)), 0);
BOOST_CHECK_CLOSE(n4, checked_lexical_cast<target_type>(Real(n4).str(digits_to_print, f)), 0);
// Assignment:
Real r(0);
BOOST_CHECK(r != static_cast<cast_type>(n1));
r = static_cast<simple_cast_type>(n1);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n1));
r = static_cast<simple_cast_type>(n2);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2));
r = static_cast<simple_cast_type>(n3);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n3));
r = static_cast<simple_cast_type>(n4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4));
// Addition:
r = static_cast<simple_cast_type>(n2);
BOOST_CHECK_EQUAL(r + static_cast<simple_cast_type>(n4) , static_cast<cast_type>(n2 + n4));
BOOST_CHECK_EQUAL(Real(r + static_cast<simple_cast_type>(n4)) , static_cast<cast_type>(n2 + n4));
r += static_cast<simple_cast_type>(n4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2 + n4));
// subtraction:
r = static_cast<simple_cast_type>(n4);
BOOST_CHECK_EQUAL(r - static_cast<simple_cast_type>(n5) , static_cast<cast_type>(n4 - n5));
BOOST_CHECK_EQUAL(Real(r - static_cast<simple_cast_type>(n5)) , static_cast<cast_type>(n4 - n5));
r -= static_cast<simple_cast_type>(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5));
// Multiplication:
r = static_cast<simple_cast_type>(n2);
BOOST_CHECK_EQUAL(r * static_cast<simple_cast_type>(n4) , static_cast<cast_type>(n2 * n4));
BOOST_CHECK_EQUAL(Real(r * static_cast<simple_cast_type>(n4)) , static_cast<cast_type>(n2 * n4));
r *= static_cast<simple_cast_type>(n4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n2 * n4));
// Division:
r = static_cast<simple_cast_type>(n1);
BOOST_CHECK_EQUAL(r / static_cast<simple_cast_type>(n5) , static_cast<cast_type>(n1 / n5));
BOOST_CHECK_EQUAL(Real(r / static_cast<simple_cast_type>(n5)) , static_cast<cast_type>(n1 / n5));
r /= static_cast<simple_cast_type>(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n1 / n5));
//
// special cases for full coverage:
//
r = static_cast<simple_cast_type>(n5) + Real(n4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 + n5));
r = static_cast<simple_cast_type>(n4) - Real(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 - n5));
r = static_cast<simple_cast_type>(n4) * Real(n5);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4 * n5));
r = static_cast<cast_type>(4 * n4) / Real(4);
BOOST_CHECK_EQUAL(r , static_cast<cast_type>(n4));
typedef boost::mpl::bool_<
(!std::numeric_limits<Num>::is_specialized || std::numeric_limits<Num>::is_signed)
&& (!std::numeric_limits<Real>::is_specialized || std::numeric_limits<Real>::is_signed)> signed_tag;
test_negative_mixed<Real, Num>(signed_tag());
n1 = 2;
n2 = 3;
n3 = 4;
Real a(n1), b(n2), c(n3), d;
d = a + b * c;
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = static_cast<cast_type>(n1) + b * c;
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = a + static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = a + b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = static_cast<cast_type>(n1) + static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = static_cast<cast_type>(n1) + b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
a += static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(a , 2 + 3 * 4);
a = static_cast<cast_type>(n1);
a += b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(a , 2 + 3 * 4);
a = static_cast<cast_type>(n1);
d = b * c + a;
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = b * c + static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = static_cast<cast_type>(n2) * c + a;
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = b * static_cast<cast_type>(n3) + a;
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = static_cast<cast_type>(n2) * c + static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
d = b * static_cast<cast_type>(n3) + static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , 2 + 3 * 4);
a = 20;
d = a - b * c;
BOOST_CHECK_EQUAL(d , 20 - 3 * 4);
n1 = 20;
d = static_cast<cast_type>(n1) - b * c;
BOOST_CHECK_EQUAL(d , 20 - 3 * 4);
d = a - static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(d , 20 - 3 * 4);
d = a - b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(d , 20 - 3 * 4);
d = static_cast<cast_type>(n1) - static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(d , 20 - 3 * 4);
d = static_cast<cast_type>(n1) - b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(d , 20 - 3 * 4);
a -= static_cast<cast_type>(n2) * c;
BOOST_CHECK_EQUAL(a , 20 - 3 * 4);
a = static_cast<cast_type>(n1);
a -= b * static_cast<cast_type>(n3);
BOOST_CHECK_EQUAL(a , 20 - 3 * 4);
a = 2;
d = b * c - a;
BOOST_CHECK_EQUAL(d , 3 * 4 - 2);
n1 = 2;
d = b * c - static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , 3 * 4 - 2);
d = static_cast<cast_type>(n2) * c - a;
BOOST_CHECK_EQUAL(d , 3 * 4 - 2);
d = b * static_cast<cast_type>(n3) - a;
BOOST_CHECK_EQUAL(d , 3 * 4 - a);
d = static_cast<cast_type>(n2) * c - static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , 3 * 4 - 2);
d = b * static_cast<cast_type>(n3) - static_cast<cast_type>(n1);
BOOST_CHECK_EQUAL(d , 3 * 4 - 2);
}
template <class Real>
void test_members(Real)
{
//
// Test sign and zero functions:
//
Real a = 20;
Real b = 30;
BOOST_CHECK(a.sign() > 0);
BOOST_CHECK(!a.is_zero());
if(std::numeric_limits<Real>::is_signed)
{
a = -20;
BOOST_CHECK(a.sign() < 0);
BOOST_CHECK(!a.is_zero());
}
a = 0;
BOOST_CHECK_EQUAL(a.sign() , 0);
BOOST_CHECK(a.is_zero());
a = 20;
b = 30;
a.swap(b);
BOOST_CHECK_EQUAL(a , 30);
BOOST_CHECK_EQUAL(b , 20);
}
template <class Real>
void test_members(boost::rational<Real>)
{
}
template <class Real>
void test_signed_ops(const boost::mpl::true_&)
{
Real a(8);
Real b(64);
Real c(500);
Real d(1024);
Real ac;
BOOST_CHECK_EQUAL(-a , -8);
ac = a;
ac = ac - b;
BOOST_CHECK_EQUAL(ac , 8 - 64);
ac = a;
ac -= a + b;
BOOST_CHECK_EQUAL(ac , -64);
ac = a;
ac -= b - a;
BOOST_CHECK_EQUAL(ac , 16 - 64);
ac = -a;
BOOST_CHECK_EQUAL(ac , -8);
ac = a;
ac -= -a;
BOOST_CHECK_EQUAL(ac , 16);
ac = a;
ac += -a;
BOOST_CHECK_EQUAL(ac , 0);
ac = b;
ac /= -a;
BOOST_CHECK_EQUAL(ac , -8);
ac = a;
ac *= -a;
BOOST_CHECK_EQUAL(ac , -64);
ac = a + -b;
BOOST_CHECK_EQUAL(ac , 8 - 64);
ac = -a + b;
BOOST_CHECK_EQUAL(ac , -8+64);
ac = -a + -b;
BOOST_CHECK_EQUAL(ac , -72);
ac = a + - + -b; // lots of unary operators!!
BOOST_CHECK_EQUAL(ac , 72);
test_conditional(Real(-a), -a);
}
template <class Real>
void test_signed_ops(const boost::mpl::false_&)
{
}
template <class Real>
void test()
{
#if !defined(NO_MIXED_OPS) && !defined(SLOW_COMPILER)
boost::multiprecision::is_number<Real> tag;
test_mixed<Real, unsigned char>(tag);
test_mixed<Real, signed char>(tag);
test_mixed<Real, char>(tag);
test_mixed<Real, short>(tag);
test_mixed<Real, unsigned short>(tag);
test_mixed<Real, int>(tag);
test_mixed<Real, unsigned int>(tag);
test_mixed<Real, long>(tag);
test_mixed<Real, unsigned long>(tag);
#ifdef BOOST_HAS_LONG_LONG
test_mixed<Real, long long>(tag);
test_mixed<Real, unsigned long long>(tag);
#endif
test_mixed<Real, float>(tag);
test_mixed<Real, double>(tag);
test_mixed<Real, long double>(tag);
typedef typename related_type<Real>::type related_type;
boost::mpl::bool_<boost::multiprecision::is_number<Real>::value && !boost::is_same<related_type, Real>::value> tag2;
test_mixed<Real, related_type>(tag2);
#endif
//
// Integer only functions:
//
test_integer_ops<Real>(typename boost::multiprecision::number_category<Real>::type());
//
// Real number only functions:
//
test_float_ops<Real>(typename boost::multiprecision::number_category<Real>::type());
//
// Test basic arithmetic:
//
Real a(8);
Real b(64);
Real c(500);
Real d(1024);
BOOST_CHECK_EQUAL(a + b , 72);
a += b;
BOOST_CHECK_EQUAL(a , 72);
BOOST_CHECK_EQUAL(a - b , 8);
a -= b;
BOOST_CHECK_EQUAL(a , 8);
BOOST_CHECK_EQUAL(a * b , 8*64L);
a *= b;
BOOST_CHECK_EQUAL(a , 8*64L);
BOOST_CHECK_EQUAL(a / b , 8);
a /= b;
BOOST_CHECK_EQUAL(a , 8);
Real ac(a);
BOOST_CHECK_EQUAL(ac , a);
ac = a * c;
BOOST_CHECK_EQUAL(ac , 8*500L);
ac = 8*500L;
ac = ac + b + c;
BOOST_CHECK_EQUAL(ac , 8*500L+64+500);
ac = a;
ac = b + c + ac;
BOOST_CHECK_EQUAL(ac , 8+64+500);
ac = ac - b + c;
BOOST_CHECK_EQUAL(ac , 8+64+500-64+500);
ac = a;
ac = b + c - ac;
BOOST_CHECK_EQUAL(ac , -8+64+500);
ac = a;
ac = ac * b;
BOOST_CHECK_EQUAL(ac , 8*64);
ac = a;
ac *= b * ac;
BOOST_CHECK_EQUAL(ac , 8*8*64);
ac = b;
ac = ac / a;
BOOST_CHECK_EQUAL(ac , 64/8);
ac = b;
ac /= ac / a;
BOOST_CHECK_EQUAL(ac , 64 / (64/8));
ac = a;
ac = b + ac * a;
BOOST_CHECK_EQUAL(ac , 64 * 2);
ac = a;
ac = b - ac * a;
BOOST_CHECK_EQUAL(ac , 0);
ac = a;
ac = b * (ac + a);
BOOST_CHECK_EQUAL(ac , 64 * (16));
ac = a;
ac = b / (ac * 1);
BOOST_CHECK_EQUAL(ac , 64 / 8);
ac = a;
ac = ac + b;
BOOST_CHECK_EQUAL(ac , 8 + 64);
ac = a;
ac = a + ac;
BOOST_CHECK_EQUAL(ac , 16);
ac = a;
ac = a - ac;
BOOST_CHECK_EQUAL(ac , 0);
ac = a;
ac += a + b;
BOOST_CHECK_EQUAL(ac , 80);
ac = a;
ac += b + a;
BOOST_CHECK_EQUAL(ac , 80);
ac = +a;
BOOST_CHECK_EQUAL(ac , 8);
ac = 8;
ac = a * ac;
BOOST_CHECK_EQUAL(ac , 8*8);
ac = a;
ac = a;
ac += +a;
BOOST_CHECK_EQUAL(ac , 16);
ac = a;
ac += b - a;
BOOST_CHECK_EQUAL(ac , 8 + 64-8);
ac = a;
ac += b*c;
BOOST_CHECK_EQUAL(ac , 8 + 64 * 500);
ac = a;
ac = a;
ac -= +a;
BOOST_CHECK_EQUAL(ac , 0);
ac = a;
if(std::numeric_limits<Real>::is_signed || is_twos_complement_integer<Real>::value)
{
ac = a;
ac -= c - b;
BOOST_CHECK_EQUAL(ac , 8 - (500-64));
ac = a;
ac -= b*c;
BOOST_CHECK_EQUAL(ac , 8 - 500*64);
}
ac = a;
ac += ac * b;
BOOST_CHECK_EQUAL(ac , 8 + 8 * 64);
if(std::numeric_limits<Real>::is_signed || is_twos_complement_integer<Real>::value)
{
ac = a;
ac -= ac * b;
BOOST_CHECK_EQUAL(ac , 8 - 8 * 64);
}
ac = a * 8;
ac *= +a;
BOOST_CHECK_EQUAL(ac , 64 * 8);
ac = a;
ac *= b * c;
BOOST_CHECK_EQUAL(ac , 8 * 64 * 500);
ac = a;
ac *= b / a;
BOOST_CHECK_EQUAL(ac , 8 * 64 / 8);
ac = a;
ac *= b + c;
BOOST_CHECK_EQUAL(ac , 8 * (64 + 500));
ac = b;
ac /= +a;
BOOST_CHECK_EQUAL(ac , 8);
ac = b;
ac /= b / a;
BOOST_CHECK_EQUAL(ac , 64 / (64/8));
ac = b;
ac /= a + Real(0);
BOOST_CHECK_EQUAL(ac , 8);
//
// simple tests with immediate values, these calls can be optimised in many backends:
//
ac = a + b;
BOOST_CHECK_EQUAL(ac , 72);
ac = a + +b;
BOOST_CHECK_EQUAL(ac , 72);
ac = +a + b;
BOOST_CHECK_EQUAL(ac , 72);
ac = +a + +b;
BOOST_CHECK_EQUAL(ac , 72);
ac = a;
ac = b / ac;
BOOST_CHECK_EQUAL(ac , b / a);
//
// Comparisons:
//
BOOST_CHECK_EQUAL((a == b) , false);
BOOST_CHECK_EQUAL((a != b) , true);
BOOST_CHECK_EQUAL((a <= b) , true);
BOOST_CHECK_EQUAL((a < b) , true);
BOOST_CHECK_EQUAL((a >= b) , false);
BOOST_CHECK_EQUAL((a > b) , false);
BOOST_CHECK_EQUAL((a+b == b) , false);
BOOST_CHECK_EQUAL((a+b != b) , true);
BOOST_CHECK_EQUAL((a+b >= b) , true);
BOOST_CHECK_EQUAL((a+b > b) , true);
BOOST_CHECK_EQUAL((a+b <= b) , false);
BOOST_CHECK_EQUAL((a+b < b) , false);
BOOST_CHECK_EQUAL((a == b+a) , false);
BOOST_CHECK_EQUAL((a != b+a) , true);
BOOST_CHECK_EQUAL((a <= b+a) , true);
BOOST_CHECK_EQUAL((a < b+a) , true);
BOOST_CHECK_EQUAL((a >= b+a) , false);
BOOST_CHECK_EQUAL((a > b+a) , false);
BOOST_CHECK_EQUAL((a+b == b+a) , true);
BOOST_CHECK_EQUAL((a+b != b+a) , false);
BOOST_CHECK_EQUAL((a+b <= b+a) , true);
BOOST_CHECK_EQUAL((a+b < b+a) , false);
BOOST_CHECK_EQUAL((a+b >= b+a) , true);
BOOST_CHECK_EQUAL((a+b > b+a) , false);
BOOST_CHECK_EQUAL((8 == b+a) , false);
BOOST_CHECK_EQUAL((8 != b+a) , true);
BOOST_CHECK_EQUAL((8 <= b+a) , true);
BOOST_CHECK_EQUAL((8 < b+a) , true);
BOOST_CHECK_EQUAL((8 >= b+a) , false);
BOOST_CHECK_EQUAL((8 > b+a) , false);
BOOST_CHECK_EQUAL((800 == b+a) , false);
BOOST_CHECK_EQUAL((800 != b+a) , true);
BOOST_CHECK_EQUAL((800 >= b+a) , true);
BOOST_CHECK_EQUAL((800 > b+a) , true);
BOOST_CHECK_EQUAL((800 <= b+a) , false);
BOOST_CHECK_EQUAL((800 < b+a) , false);
BOOST_CHECK_EQUAL((72 == b+a) , true);
BOOST_CHECK_EQUAL((72 != b+a) , false);
BOOST_CHECK_EQUAL((72 <= b+a) , true);
BOOST_CHECK_EQUAL((72 < b+a) , false);
BOOST_CHECK_EQUAL((72 >= b+a) , true);
BOOST_CHECK_EQUAL((72 > b+a) , false);
test_members(a);
//
// Use in Boolean context:
//
a = 0;
if(a)
{
BOOST_ERROR("Unexpected non-zero result");
}
if(!a){}
else
{
BOOST_ERROR("Unexpected zero result");
}
b = 2;
if(!b)
{
BOOST_ERROR("Unexpected zero result");
}
if(b){}
else
{
BOOST_ERROR("Unexpected non-zero result");
}
if(a && b)
{
BOOST_ERROR("Unexpected zero result");
}
if(!(a || b))
{
BOOST_ERROR("Unexpected zero result");
}
if(a + b){}
else
{
BOOST_ERROR("Unexpected zero result");
}
if(b - 2)
{
BOOST_ERROR("Unexpected non-zero result");
}
//
// Test iostreams:
//
std::stringstream ss;
a = 20;
b = 2;
ss << a;
ss >> c;
BOOST_CHECK_EQUAL(a , c);
ss.clear();
ss << a + b;
ss >> c;
BOOST_CHECK_EQUAL(c , 22);
BOOST_CHECK_EQUAL(c , a + b);
//
// More cases for complete code coverage:
//
a = 20;
b = 30;
swap(a, b);
BOOST_CHECK_EQUAL(a , 30);
BOOST_CHECK_EQUAL(b , 20);
a = 20;
b = 30;
std::swap(a, b);
BOOST_CHECK_EQUAL(a , 30);
BOOST_CHECK_EQUAL(b , 20);
a = 20;
b = 30;
a = a + b * 2;
BOOST_CHECK_EQUAL(a , 20 + 30 * 2);
a = 100;
a = a - b * 2;
BOOST_CHECK_EQUAL(a , 100 - 30 * 2);
a = 20;
a = a * (b + 2);
BOOST_CHECK_EQUAL(a , 20 * (32));
a = 20;
a = (b + 2) * a;
BOOST_CHECK_EQUAL(a , 20 * (32));
a = 90;
b = 2;
a = a / (b + 0);
BOOST_CHECK_EQUAL(a , 45);
a = 20;
b = 30;
c = (a * b) + 22;
BOOST_CHECK_EQUAL(c , 20 * 30 + 22);
c = 22 + (a * b);
BOOST_CHECK_EQUAL(c , 20 * 30 + 22);
c = 10;
ac = a + b * c;
BOOST_CHECK_EQUAL(ac , 20 + 30 * 10);
ac = b * c + a;
BOOST_CHECK_EQUAL(ac , 20 + 30 * 10);
a = a + b * c;
BOOST_CHECK_EQUAL(a , 20 + 30 * 10);
a = 20;
b = a + b * c;
BOOST_CHECK_EQUAL(b , 20 + 30 * 10);
b = 30;
c = a + b * c;
BOOST_CHECK_EQUAL(c , 20 + 30 * 10);
c = 10;
c = a + b / c;
BOOST_CHECK_EQUAL(c , 20 + 30 / 10);
//
// Test conditionals:
//
a = 20;
test_conditional(a, +a);
test_conditional(a, (a + 0));
test_signed_ops<Real>(boost::mpl::bool_<std::numeric_limits<Real>::is_signed>());
//
// Test move:
//
#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
Real m(static_cast<Real&&>(a));
BOOST_CHECK_EQUAL(m, 20);
// Move from already moved from object:
Real m2(static_cast<Real&&>(a));
// assign from moved from object
// (may result in "a" being left in valid state as implementation artifact):
c = static_cast<Real&&>(a);
// assignment to moved-from objects:
c = static_cast<Real&&>(m);
BOOST_CHECK_EQUAL(c, 20);
m2 = c;
BOOST_CHECK_EQUAL(c, 20);
// Destructor of "a" checks destruction of moved-from-object...
Real m3(static_cast<Real&&>(a));
#endif
}