// ratio -*- C++ -*-
// Copyright (C) 2008, 2009, 2010, 2011 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 include/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 _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/**
* @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 constexpr intmax_t num =
_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
static constexpr intmax_t den =
__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
typedef ratio<num, den> type;
};
template<intmax_t _Num, intmax_t _Den>
constexpr intmax_t ratio<_Num, _Den>::num;
template<intmax_t _Num, intmax_t _Den>
constexpr intmax_t ratio<_Num, _Den>::den;
/// ratio_add
template<typename _R1, typename _R2>
struct ratio_add
{
private:
static constexpr intmax_t __gcd =
__static_gcd<_R1::den, _R2::den>::value;
static constexpr intmax_t __n = __safe_add<
__safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
__safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value;
// The new numerator may have common factors with the denominator,
// but they have to also be factors of __gcd.
static constexpr intmax_t __gcd2 = __static_gcd<__n, __gcd>::value;
public:
typedef ratio<__n / __gcd2,
__safe_multiply<_R1::den / __gcd2, _R2::den / __gcd>::value> 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;
template<typename _R1, typename _R2>
constexpr 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 constexpr intmax_t num = type::num;
static constexpr intmax_t den = type::den;
};
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_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 constexpr intmax_t num = type::num;
static constexpr intmax_t den = type::den;
};
template<typename _R1, typename _R2>
constexpr intmax_t ratio_multiply<_R1, _R2>::num;
template<typename _R1, typename _R2>
constexpr 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 constexpr intmax_t num = type::num;
static constexpr intmax_t den = type::den;
};
template<typename _R1, typename _R2>
constexpr intmax_t ratio_divide<_R1, _R2>::num;
template<typename _R1, typename _R2>
constexpr 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>
{ };
// 0 <= _Ri < 1
// If one is 0, conclude
// Otherwise, x < y iff 1/y < 1/x
template<typename _R1, typename _R2>
struct __ratio_less_impl_2;
// _Ri > 0
// Compare the integral parts, and remove them if they are equal
template<typename _R1, typename _R2, intmax_t __q1 = _R1::num / _R1::den,
intmax_t __q2 = _R2::num / _R2::den, bool __eq = (__q1 == __q2)>
struct __ratio_less_impl_1
: __ratio_less_impl_2<ratio<_R1::num % _R1::den, _R1::den>,
ratio<_R2::num % _R2::den, _R2::den> >::type
{ };
template<typename _R1, typename _R2, intmax_t __q1, intmax_t __q2>
struct __ratio_less_impl_1<_R1, _R2, __q1, __q2, false>
: integral_constant<bool, (__q1 < __q2) >
{ };
template<typename _R1, typename _R2>
struct __ratio_less_impl_2
: __ratio_less_impl_1<ratio<_R2::den, _R2::num>,
ratio<_R1::den, _R1::num> >::type
{ };
template<intmax_t __d1, typename _R2>
struct __ratio_less_impl_2<ratio<0, __d1>, _R2>
: integral_constant<bool, true>
{ };
template<typename _R1, intmax_t __d2>
struct __ratio_less_impl_2<_R1, ratio<0, __d2> >
: integral_constant<bool, false>
{ };
template<intmax_t __d1, intmax_t __d2>
struct __ratio_less_impl_2<ratio<0, __d1>, ratio<0, __d2> >
: integral_constant<bool, false>
{ };
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
{ };
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<ratio<-_R2::num, _R2::den>,
ratio<-_R1::num, _R1::den> >::type
{ };
/// ratio_less
// using a continued fraction expansion
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
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace
#endif //_GLIBCXX_USE_C99_STDINT_TR1
#endif //__GXX_EXPERIMENTAL_CXX0X__
#endif //_GLIBCXX_RATIO