0,0 → 1,538 |
// ratio -*- C++ -*- |
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// Copyright (C) 2008-2015 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. |
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// 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. |
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// 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. |
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// 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/>. |
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/** @file include/ratio |
* This is a Standard C++ Library header. |
*/ |
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#ifndef _GLIBCXX_RATIO |
#define _GLIBCXX_RATIO 1 |
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#pragma GCC system_header |
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#if __cplusplus < 201103L |
# include <bits/c++0x_warning.h> |
#else |
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#include <type_traits> |
#include <cstdint> |
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#ifdef _GLIBCXX_USE_C99_STDINT_TR1 |
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namespace std _GLIBCXX_VISIBILITY(default) |
{ |
_GLIBCXX_BEGIN_NAMESPACE_VERSION |
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/** |
* @defgroup ratio Rational Arithmetic |
* @ingroup utilities |
* |
* Compile time representation of finite rational numbers. |
* @{ |
*/ |
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template<intmax_t _Pn> |
struct __static_sign |
: integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> |
{ }; |
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template<intmax_t _Pn> |
struct __static_abs |
: integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> |
{ }; |
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template<intmax_t _Pn, intmax_t _Qn> |
struct __static_gcd |
: __static_gcd<_Qn, (_Pn % _Qn)> |
{ }; |
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template<intmax_t _Pn> |
struct __static_gcd<_Pn, 0> |
: integral_constant<intmax_t, __static_abs<_Pn>::value> |
{ }; |
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template<intmax_t _Qn> |
struct __static_gcd<0, _Qn> |
: integral_constant<intmax_t, __static_abs<_Qn>::value> |
{ }; |
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// 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); |
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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; |
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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"); |
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public: |
static const intmax_t value = _Pn * _Qn; |
}; |
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// Some double-precision utilities, where numbers are represented as |
// __hi*2^(8*sizeof(uintmax_t)) + __lo. |
template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> |
struct __big_less |
: integral_constant<bool, (__hi1 < __hi2 |
|| (__hi1 == __hi2 && __lo1 < __lo2))> |
{ }; |
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template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> |
struct __big_add |
{ |
static constexpr uintmax_t __lo = __lo1 + __lo2; |
static constexpr uintmax_t __hi = (__hi1 + __hi2 + |
(__lo1 + __lo2 < __lo1)); // carry |
}; |
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// Subtract a number from a bigger one. |
template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> |
struct __big_sub |
{ |
static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, |
"Internal library error"); |
static constexpr uintmax_t __lo = __lo1 - __lo2; |
static constexpr uintmax_t __hi = (__hi1 - __hi2 - |
(__lo1 < __lo2)); // carry |
}; |
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// Same principle as __safe_multiply. |
template<uintmax_t __x, uintmax_t __y> |
struct __big_mul |
{ |
private: |
static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); |
static constexpr uintmax_t __x0 = __x % __c; |
static constexpr uintmax_t __x1 = __x / __c; |
static constexpr uintmax_t __y0 = __y % __c; |
static constexpr uintmax_t __y1 = __y / __c; |
static constexpr uintmax_t __x0y0 = __x0 * __y0; |
static constexpr uintmax_t __x0y1 = __x0 * __y1; |
static constexpr uintmax_t __x1y0 = __x1 * __y0; |
static constexpr uintmax_t __x1y1 = __x1 * __y1; |
static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... |
static constexpr uintmax_t __mix_lo = __mix * __c; |
static constexpr uintmax_t __mix_hi |
= __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here |
typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; |
public: |
static constexpr uintmax_t __hi = _Res::__hi; |
static constexpr uintmax_t __lo = _Res::__lo; |
}; |
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// Adapted from __udiv_qrnnd_c in longlong.h |
// This version assumes that the high bit of __d is 1. |
template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> |
struct __big_div_impl |
{ |
private: |
static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), |
"Internal library error"); |
static_assert(__n1 < __d, "Internal library error"); |
static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); |
static constexpr uintmax_t __d1 = __d / __c; |
static constexpr uintmax_t __d0 = __d % __c; |
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static constexpr uintmax_t __q1x = __n1 / __d1; |
static constexpr uintmax_t __r1x = __n1 % __d1; |
static constexpr uintmax_t __m = __q1x * __d0; |
static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; |
static constexpr uintmax_t __r1z = __r1y + __d; |
static constexpr uintmax_t __r1 |
= ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) |
? (__r1z + __d) : __r1z : __r1y) - __m; |
static constexpr uintmax_t __q1 |
= __q1x - ((__r1y < __m) |
? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); |
static constexpr uintmax_t __q0x = __r1 / __d1; |
static constexpr uintmax_t __r0x = __r1 % __d1; |
static constexpr uintmax_t __n = __q0x * __d0; |
static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; |
static constexpr uintmax_t __r0z = __r0y + __d; |
static constexpr uintmax_t __r0 |
= ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) |
? (__r0z + __d) : __r0z : __r0y) - __n; |
static constexpr uintmax_t __q0 |
= __q0x - ((__r0y < __n) ? ((__r0z >= __d) |
&& (__r0z < __n)) ? 2 : 1 : 0); |
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public: |
static constexpr uintmax_t __quot = __q1 * __c + __q0; |
static constexpr uintmax_t __rem = __r0; |
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private: |
typedef __big_mul<__quot, __d> _Prod; |
typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; |
static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, |
"Internal library error"); |
}; |
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template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> |
struct __big_div |
{ |
private: |
static_assert(__d != 0, "Internal library error"); |
static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), |
"This library calls __builtin_clzll on uintmax_t, which " |
"is unsafe on your platform. Please complain to " |
"http://gcc.gnu.org/bugzilla/"); |
static constexpr int __shift = __builtin_clzll(__d); |
static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; |
static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; |
static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; |
static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; |
static constexpr uintmax_t __new_d = __d * __c1; |
static constexpr uintmax_t __new_n0 = __n0 * __c1; |
static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; |
static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; |
static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; |
typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; |
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public: |
static constexpr uintmax_t __quot_hi = __n1 / __d; |
static constexpr uintmax_t __quot_lo = _Res::__quot; |
static constexpr uintmax_t __rem = _Res::__rem / __c1; |
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private: |
typedef __big_mul<__quot_lo, __d> _P0; |
typedef __big_mul<__quot_hi, __d> _P1; |
typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; |
// No overflow. |
static_assert(_P1::__hi == 0, "Internal library error"); |
static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); |
// Matches the input data. |
static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, |
"Internal library error"); |
static_assert(__rem < __d, "Internal library error"); |
}; |
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/** |
* @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"); |
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// Note: sign(N) * abs(N) == N |
static constexpr intmax_t num = |
_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; |
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static constexpr intmax_t den = |
__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; |
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typedef ratio<num, den> type; |
}; |
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template<intmax_t _Num, intmax_t _Den> |
constexpr intmax_t ratio<_Num, _Den>::num; |
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template<intmax_t _Num, intmax_t _Den> |
constexpr intmax_t ratio<_Num, _Den>::den; |
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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; |
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public: |
typedef ratio< |
__safe_multiply<(_R1::num / __gcd1), |
(_R2::num / __gcd2)>::value, |
__safe_multiply<(_R1::den / __gcd2), |
(_R2::den / __gcd1)>::value> type; |
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static constexpr intmax_t num = type::num; |
static constexpr intmax_t den = type::den; |
}; |
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template<typename _R1, typename _R2> |
constexpr intmax_t __ratio_multiply<_R1, _R2>::num; |
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template<typename _R1, typename _R2> |
constexpr intmax_t __ratio_multiply<_R1, _R2>::den; |
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/// ratio_multiply |
template<typename _R1, typename _R2> |
using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; |
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template<typename _R1, typename _R2> |
struct __ratio_divide |
{ |
static_assert(_R2::num != 0, "division by 0"); |
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typedef typename __ratio_multiply< |
_R1, |
ratio<_R2::den, _R2::num>>::type type; |
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static constexpr intmax_t num = type::num; |
static constexpr intmax_t den = type::den; |
}; |
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template<typename _R1, typename _R2> |
constexpr intmax_t __ratio_divide<_R1, _R2>::num; |
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template<typename _R1, typename _R2> |
constexpr intmax_t __ratio_divide<_R1, _R2>::den; |
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/// ratio_divide |
template<typename _R1, typename _R2> |
using ratio_divide = typename __ratio_divide<_R1, _R2>::type; |
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/// ratio_equal |
template<typename _R1, typename _R2> |
struct ratio_equal |
: integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> |
{ }; |
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/// ratio_not_equal |
template<typename _R1, typename _R2> |
struct ratio_not_equal |
: integral_constant<bool, !ratio_equal<_R1, _R2>::value> |
{ }; |
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// Both numbers are positive. |
template<typename _R1, typename _R2, |
typename _Left = __big_mul<_R1::num,_R2::den>, |
typename _Right = __big_mul<_R2::num,_R1::den> > |
struct __ratio_less_impl_1 |
: integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, |
_Right::__hi, _Right::__lo>::value> |
{ }; |
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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<_R1, _R2>::type |
{ }; |
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template<typename _R1, typename _R2> |
struct __ratio_less_impl<_R1, _R2, true, false> |
: integral_constant<bool, _R1::num < _R2::num> |
{ }; |
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template<typename _R1, typename _R2> |
struct __ratio_less_impl<_R1, _R2, false, true> |
: __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, |
ratio<-_R1::num, _R1::den> >::type |
{ }; |
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/// ratio_less |
template<typename _R1, typename _R2> |
struct ratio_less |
: __ratio_less_impl<_R1, _R2>::type |
{ }; |
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/// ratio_less_equal |
template<typename _R1, typename _R2> |
struct ratio_less_equal |
: integral_constant<bool, !ratio_less<_R2, _R1>::value> |
{ }; |
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/// ratio_greater |
template<typename _R1, typename _R2> |
struct ratio_greater |
: integral_constant<bool, ratio_less<_R2, _R1>::value> |
{ }; |
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/// ratio_greater_equal |
template<typename _R1, typename _R2> |
struct ratio_greater_equal |
: integral_constant<bool, !ratio_less<_R1, _R2>::value> |
{ }; |
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template<typename _R1, typename _R2, |
bool = (_R1::num >= 0), |
bool = (_R2::num >= 0), |
bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, |
ratio<__static_abs<_R2::num>::value, _R2::den> >::value> |
struct __ratio_add_impl |
{ |
private: |
typedef typename __ratio_add_impl< |
ratio<-_R1::num, _R1::den>, |
ratio<-_R2::num, _R2::den> >::type __t; |
public: |
typedef ratio<-__t::num, __t::den> type; |
}; |
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// True addition of nonnegative numbers. |
template<typename _R1, typename _R2, bool __b> |
struct __ratio_add_impl<_R1, _R2, true, true, __b> |
{ |
private: |
static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; |
static constexpr uintmax_t __d2 = _R2::den / __g; |
typedef __big_mul<_R1::den, __d2> __d; |
typedef __big_mul<_R1::num, _R2::den / __g> __x; |
typedef __big_mul<_R2::num, _R1::den / __g> __y; |
typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; |
static_assert(__n::__hi >= __x::__hi, "Internal library error"); |
typedef __big_div<__n::__hi, __n::__lo, __g> __ng; |
static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; |
typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; |
static_assert(__n_final::__rem == 0, "Internal library error"); |
static_assert(__n_final::__quot_hi == 0 && |
__n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); |
typedef __big_mul<_R1::den / __g2, __d2> __d_final; |
static_assert(__d_final::__hi == 0 && |
__d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); |
public: |
typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; |
}; |
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template<typename _R1, typename _R2> |
struct __ratio_add_impl<_R1, _R2, false, true, true> |
: __ratio_add_impl<_R2, _R1> |
{ }; |
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// True subtraction of nonnegative numbers yielding a nonnegative result. |
template<typename _R1, typename _R2> |
struct __ratio_add_impl<_R1, _R2, true, false, false> |
{ |
private: |
static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; |
static constexpr uintmax_t __d2 = _R2::den / __g; |
typedef __big_mul<_R1::den, __d2> __d; |
typedef __big_mul<_R1::num, _R2::den / __g> __x; |
typedef __big_mul<-_R2::num, _R1::den / __g> __y; |
typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; |
typedef __big_div<__n::__hi, __n::__lo, __g> __ng; |
static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; |
typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; |
static_assert(__n_final::__rem == 0, "Internal library error"); |
static_assert(__n_final::__quot_hi == 0 && |
__n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); |
typedef __big_mul<_R1::den / __g2, __d2> __d_final; |
static_assert(__d_final::__hi == 0 && |
__d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); |
public: |
typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; |
}; |
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template<typename _R1, typename _R2> |
struct __ratio_add |
{ |
typedef typename __ratio_add_impl<_R1, _R2>::type type; |
static constexpr intmax_t num = type::num; |
static constexpr intmax_t den = type::den; |
}; |
|
template<typename _R1, typename _R2> |
constexpr intmax_t __ratio_add<_R1, _R2>::num; |
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template<typename _R1, typename _R2> |
constexpr intmax_t __ratio_add<_R1, _R2>::den; |
|
/// ratio_add |
template<typename _R1, typename _R2> |
using ratio_add = typename __ratio_add<_R1, _R2>::type; |
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template<typename _R1, typename _R2> |
struct __ratio_subtract |
{ |
typedef typename __ratio_add< |
_R1, |
ratio<-_R2::num, _R2::den>>::type type; |
|
static constexpr intmax_t num = type::num; |
static constexpr intmax_t den = type::den; |
}; |
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template<typename _R1, typename _R2> |
constexpr intmax_t __ratio_subtract<_R1, _R2>::num; |
|
template<typename _R1, typename _R2> |
constexpr intmax_t __ratio_subtract<_R1, _R2>::den; |
|
/// ratio_subtract |
template<typename _R1, typename _R2> |
using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; |
|
|
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; |
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// @} group ratio |
_GLIBCXX_END_NAMESPACE_VERSION |
} // namespace |
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#endif //_GLIBCXX_USE_C99_STDINT_TR1 |
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#endif // C++11 |
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#endif //_GLIBCXX_RATIO |