e1d4e035fa
2010-10-18 Paolo Carlini <paolo.carlini@oracle.com> PR libstdc++/45866 * include/std/ratio (ratio<>::type): Add. (ratio_add<>::num, ratio_add<>::den, ratio_subtract<>::num, ratio_subtract<>::den, ratio_multiply<>::num, ratio_multiply<>::den, ratio_divide<>::num, ratio_divide<>::den): Likewise. * testsuite/20_util/ratio/operations/45866.cc: New. From-SVN: r165649
349 lines
10 KiB
C++
349 lines
10 KiB
C++
// ratio -*- C++ -*-
|
|
|
|
// Copyright (C) 2008, 2009, 2010 Free Software Foundation, Inc.
|
|
//
|
|
// This file is part of the GNU ISO C++ Library. This library is free
|
|
// software; you can redistribute it and/or modify it under the
|
|
// terms of the GNU General Public License as published by the
|
|
// Free Software Foundation; either version 3, or (at your option)
|
|
// any later version.
|
|
|
|
// This library is distributed in the hope that it will be useful,
|
|
// but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
// GNU General Public License for more details.
|
|
|
|
// Under Section 7 of GPL version 3, you are granted additional
|
|
// permissions described in the GCC Runtime Library Exception, version
|
|
// 3.1, as published by the Free Software Foundation.
|
|
|
|
// You should have received a copy of the GNU General Public License and
|
|
// a copy of the GCC Runtime Library Exception along with this program;
|
|
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
|
|
// <http://www.gnu.org/licenses/>.
|
|
|
|
/** @file ratio
|
|
* This is a Standard C++ Library header.
|
|
*/
|
|
|
|
#ifndef _GLIBCXX_RATIO
|
|
#define _GLIBCXX_RATIO 1
|
|
|
|
#pragma GCC system_header
|
|
|
|
#ifndef __GXX_EXPERIMENTAL_CXX0X__
|
|
# include <bits/c++0x_warning.h>
|
|
#else
|
|
|
|
#include <type_traits>
|
|
#include <cstdint>
|
|
|
|
#ifdef _GLIBCXX_USE_C99_STDINT_TR1
|
|
|
|
namespace std
|
|
{
|
|
/**
|
|
* @defgroup ratio Rational Arithmetic
|
|
* @ingroup utilities
|
|
*
|
|
* Compile time representation of finite rational numbers.
|
|
* @{
|
|
*/
|
|
|
|
template<intmax_t _Pn>
|
|
struct __static_sign
|
|
: integral_constant<intmax_t, (_Pn < 0) ? -1 : 1>
|
|
{ };
|
|
|
|
template<intmax_t _Pn>
|
|
struct __static_abs
|
|
: integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value>
|
|
{ };
|
|
|
|
template<intmax_t _Pn, intmax_t _Qn>
|
|
struct __static_gcd;
|
|
|
|
template<intmax_t _Pn, intmax_t _Qn>
|
|
struct __static_gcd
|
|
: __static_gcd<_Qn, (_Pn % _Qn)>
|
|
{ };
|
|
|
|
template<intmax_t _Pn>
|
|
struct __static_gcd<_Pn, 0>
|
|
: integral_constant<intmax_t, __static_abs<_Pn>::value>
|
|
{ };
|
|
|
|
template<intmax_t _Qn>
|
|
struct __static_gcd<0, _Qn>
|
|
: integral_constant<intmax_t, __static_abs<_Qn>::value>
|
|
{ };
|
|
|
|
// Let c = 2^(half # of bits in an intmax_t)
|
|
// then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0
|
|
// The multiplication of N and M becomes,
|
|
// N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0
|
|
// Multiplication is safe if each term and the sum of the terms
|
|
// is representable by intmax_t.
|
|
template<intmax_t _Pn, intmax_t _Qn>
|
|
struct __safe_multiply
|
|
{
|
|
private:
|
|
static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);
|
|
|
|
static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;
|
|
static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;
|
|
static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;
|
|
static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;
|
|
|
|
static_assert(__a1 == 0 || __b1 == 0,
|
|
"overflow in multiplication");
|
|
static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
|
|
"overflow in multiplication");
|
|
static_assert(__b0 * __a0 <= __INTMAX_MAX__,
|
|
"overflow in multiplication");
|
|
static_assert((__a0 * __b1 + __b0 * __a1) * __c <=
|
|
__INTMAX_MAX__ - __b0 * __a0, "overflow in multiplication");
|
|
|
|
public:
|
|
static const intmax_t value = _Pn * _Qn;
|
|
};
|
|
|
|
// Helpers for __safe_add
|
|
template<intmax_t _Pn, intmax_t _Qn, bool>
|
|
struct __add_overflow_check_impl
|
|
: integral_constant<bool, (_Pn <= __INTMAX_MAX__ - _Qn)>
|
|
{ };
|
|
|
|
template<intmax_t _Pn, intmax_t _Qn>
|
|
struct __add_overflow_check_impl<_Pn, _Qn, false>
|
|
: integral_constant<bool, (_Pn >= -__INTMAX_MAX__ - _Qn)>
|
|
{ };
|
|
|
|
template<intmax_t _Pn, intmax_t _Qn>
|
|
struct __add_overflow_check
|
|
: __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
|
|
{ };
|
|
|
|
template<intmax_t _Pn, intmax_t _Qn>
|
|
struct __safe_add
|
|
{
|
|
static_assert(__add_overflow_check<_Pn, _Qn>::value != 0,
|
|
"overflow in addition");
|
|
|
|
static const intmax_t value = _Pn + _Qn;
|
|
};
|
|
|
|
/**
|
|
* @brief Provides compile-time rational arithmetic.
|
|
*
|
|
* This class template represents any finite rational number with a
|
|
* numerator and denominator representable by compile-time constants of
|
|
* type intmax_t. The ratio is simplified when instantiated.
|
|
*
|
|
* For example:
|
|
* @code
|
|
* std::ratio<7,-21>::num == -1;
|
|
* std::ratio<7,-21>::den == 3;
|
|
* @endcode
|
|
*
|
|
*/
|
|
template<intmax_t _Num, intmax_t _Den = 1>
|
|
struct ratio
|
|
{
|
|
static_assert(_Den != 0, "denominator cannot be zero");
|
|
static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
|
|
"out of range");
|
|
|
|
// Note: sign(N) * abs(N) == N
|
|
static const intmax_t num =
|
|
_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
|
|
|
|
static const intmax_t den =
|
|
__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
|
|
|
|
typedef ratio<num, den> type;
|
|
};
|
|
|
|
template<intmax_t _Num, intmax_t _Den>
|
|
const intmax_t ratio<_Num, _Den>::num;
|
|
|
|
template<intmax_t _Num, intmax_t _Den>
|
|
const intmax_t ratio<_Num, _Den>::den;
|
|
|
|
/// ratio_add
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_add
|
|
{
|
|
private:
|
|
static const intmax_t __gcd =
|
|
__static_gcd<_R1::den, _R2::den>::value;
|
|
|
|
public:
|
|
typedef ratio<
|
|
__safe_add<
|
|
__safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
|
|
__safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value,
|
|
__safe_multiply<_R1::den, (_R2::den / __gcd)>::value> type;
|
|
|
|
static const intmax_t num = type::num;
|
|
static const intmax_t den = type::den;
|
|
};
|
|
|
|
template<typename _R1, typename _R2>
|
|
const intmax_t ratio_add<_R1, _R2>::num;
|
|
|
|
template<typename _R1, typename _R2>
|
|
const intmax_t ratio_add<_R1, _R2>::den;
|
|
|
|
/// ratio_subtract
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_subtract
|
|
{
|
|
typedef typename ratio_add<
|
|
_R1,
|
|
ratio<-_R2::num, _R2::den>>::type type;
|
|
|
|
static const intmax_t num = type::num;
|
|
static const intmax_t den = type::den;
|
|
};
|
|
|
|
template<typename _R1, typename _R2>
|
|
const intmax_t ratio_subtract<_R1, _R2>::num;
|
|
|
|
template<typename _R1, typename _R2>
|
|
const intmax_t ratio_subtract<_R1, _R2>::den;
|
|
|
|
/// ratio_multiply
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_multiply
|
|
{
|
|
private:
|
|
static const intmax_t __gcd1 =
|
|
__static_gcd<_R1::num, _R2::den>::value;
|
|
static const intmax_t __gcd2 =
|
|
__static_gcd<_R2::num, _R1::den>::value;
|
|
|
|
public:
|
|
typedef ratio<
|
|
__safe_multiply<(_R1::num / __gcd1),
|
|
(_R2::num / __gcd2)>::value,
|
|
__safe_multiply<(_R1::den / __gcd2),
|
|
(_R2::den / __gcd1)>::value> type;
|
|
|
|
static const intmax_t num = type::num;
|
|
static const intmax_t den = type::den;
|
|
};
|
|
|
|
template<typename _R1, typename _R2>
|
|
const intmax_t ratio_multiply<_R1, _R2>::num;
|
|
|
|
template<typename _R1, typename _R2>
|
|
const intmax_t ratio_multiply<_R1, _R2>::den;
|
|
|
|
/// ratio_divide
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_divide
|
|
{
|
|
static_assert(_R2::num != 0, "division by 0");
|
|
|
|
typedef typename ratio_multiply<
|
|
_R1,
|
|
ratio<_R2::den, _R2::num>>::type type;
|
|
|
|
static const intmax_t num = type::num;
|
|
static const intmax_t den = type::den;
|
|
};
|
|
|
|
template<typename _R1, typename _R2>
|
|
const intmax_t ratio_divide<_R1, _R2>::num;
|
|
|
|
template<typename _R1, typename _R2>
|
|
const intmax_t ratio_divide<_R1, _R2>::den;
|
|
|
|
/// ratio_equal
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_equal
|
|
: integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
|
|
{ };
|
|
|
|
/// ratio_not_equal
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_not_equal
|
|
: integral_constant<bool, !ratio_equal<_R1, _R2>::value>
|
|
{ };
|
|
|
|
template<typename _R1>
|
|
struct __ratio_less_impl_1
|
|
: integral_constant<bool, _R1::num < _R1::den>
|
|
{ };
|
|
|
|
template<typename _R1, typename _R2,
|
|
bool = (_R1::num == 0 || _R2::num == 0
|
|
|| (__static_sign<_R1::num>::value
|
|
!= __static_sign<_R2::num>::value)),
|
|
bool = (__static_sign<_R1::num>::value == -1
|
|
&& __static_sign<_R2::num>::value == -1)>
|
|
struct __ratio_less_impl
|
|
: __ratio_less_impl_1<typename ratio_divide<_R1, _R2>::type>::type
|
|
{ };
|
|
|
|
template<typename _R1, typename _R2>
|
|
struct __ratio_less_impl<_R1, _R2, true, false>
|
|
: integral_constant<bool, _R1::num < _R2::num>
|
|
{ };
|
|
|
|
template<typename _R1, typename _R2>
|
|
struct __ratio_less_impl<_R1, _R2, false, true>
|
|
: __ratio_less_impl_1<typename ratio_divide<_R2, _R1>::type>::type
|
|
{ };
|
|
|
|
/// ratio_less
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_less
|
|
: __ratio_less_impl<_R1, _R2>::type
|
|
{ };
|
|
|
|
/// ratio_less_equal
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_less_equal
|
|
: integral_constant<bool, !ratio_less<_R2, _R1>::value>
|
|
{ };
|
|
|
|
/// ratio_greater
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_greater
|
|
: integral_constant<bool, ratio_less<_R2, _R1>::value>
|
|
{ };
|
|
|
|
/// ratio_greater_equal
|
|
template<typename _R1, typename _R2>
|
|
struct ratio_greater_equal
|
|
: integral_constant<bool, !ratio_less<_R1, _R2>::value>
|
|
{ };
|
|
|
|
typedef ratio<1, 1000000000000000000> atto;
|
|
typedef ratio<1, 1000000000000000> femto;
|
|
typedef ratio<1, 1000000000000> pico;
|
|
typedef ratio<1, 1000000000> nano;
|
|
typedef ratio<1, 1000000> micro;
|
|
typedef ratio<1, 1000> milli;
|
|
typedef ratio<1, 100> centi;
|
|
typedef ratio<1, 10> deci;
|
|
typedef ratio< 10, 1> deca;
|
|
typedef ratio< 100, 1> hecto;
|
|
typedef ratio< 1000, 1> kilo;
|
|
typedef ratio< 1000000, 1> mega;
|
|
typedef ratio< 1000000000, 1> giga;
|
|
typedef ratio< 1000000000000, 1> tera;
|
|
typedef ratio< 1000000000000000, 1> peta;
|
|
typedef ratio< 1000000000000000000, 1> exa;
|
|
|
|
// @} group ratio
|
|
}
|
|
|
|
#endif //_GLIBCXX_USE_C99_STDINT_TR1
|
|
|
|
#endif //__GXX_EXPERIMENTAL_CXX0X__
|
|
|
|
#endif //_GLIBCXX_RATIO
|