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// ratio -*- C++ -*- |
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|
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// Copyright (C) 2008-2021 Free Software Foundation, Inc. |
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// |
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// This file is part of the GNU ISO C++ Library. This library is free |
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// software; you can redistribute it and/or modify it under the |
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// terms of the GNU General Public License as published by the |
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// Free Software Foundation; either version 3, or (at your option) |
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// any later version. |
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|
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// This library is distributed in the hope that it will be useful, |
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// but WITHOUT ANY WARRANTY; without even the implied warranty of |
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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// GNU General Public License for more details. |
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|
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// Under Section 7 of GPL version 3, you are granted additional |
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// permissions described in the GCC Runtime Library Exception, version |
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// 3.1, as published by the Free Software Foundation. |
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|
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// You should have received a copy of the GNU General Public License and |
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// a copy of the GCC Runtime Library Exception along with this program; |
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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see |
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// <http://www.gnu.org/licenses/>. |
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|
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/** @file include/ratio |
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* This is a Standard C++ Library header. |
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* @ingroup ratio |
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*/ |
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|
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#ifndef _GLIBCXX_RATIO |
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#define _GLIBCXX_RATIO 1 |
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|
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#pragma GCC system_header |
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|
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#if __cplusplus < 201103L |
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# include <bits/c++0x_warning.h> |
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#else |
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|
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#include <type_traits> |
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#include <cstdint> // intmax_t, uintmax_t |
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|
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namespace std _GLIBCXX_VISIBILITY(default) |
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{ |
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_GLIBCXX_BEGIN_NAMESPACE_VERSION |
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|
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/** |
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* @defgroup ratio Rational Arithmetic |
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* @ingroup utilities |
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* |
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* Compile time representation of finite rational numbers. |
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* @{ |
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*/ |
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|
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/// @cond undocumented |
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|
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template<intmax_t _Pn> |
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struct __static_sign |
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: integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> |
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{ }; |
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|
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template<intmax_t _Pn> |
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struct __static_abs |
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: integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> |
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{ }; |
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|
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template<intmax_t _Pn, intmax_t _Qn> |
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struct __static_gcd |
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: __static_gcd<_Qn, (_Pn % _Qn)> |
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{ }; |
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|
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template<intmax_t _Pn> |
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struct __static_gcd<_Pn, 0> |
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: integral_constant<intmax_t, __static_abs<_Pn>::value> |
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{ }; |
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|
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template<intmax_t _Qn> |
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struct __static_gcd<0, _Qn> |
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: integral_constant<intmax_t, __static_abs<_Qn>::value> |
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{ }; |
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|
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// Let c = 2^(half # of bits in an intmax_t) |
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// then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0 |
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// The multiplication of N and M becomes, |
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// N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0 |
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// Multiplication is safe if each term and the sum of the terms |
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// is representable by intmax_t. |
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template<intmax_t _Pn, intmax_t _Qn> |
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struct __safe_multiply |
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{ |
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private: |
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static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); |
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|
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static const uintmax_t __a0 = __static_abs<_Pn>::value % __c; |
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static const uintmax_t __a1 = __static_abs<_Pn>::value / __c; |
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static const uintmax_t __b0 = __static_abs<_Qn>::value % __c; |
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static const uintmax_t __b1 = __static_abs<_Qn>::value / __c; |
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|
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static_assert(__a1 == 0 || __b1 == 0, |
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"overflow in multiplication"); |
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static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), |
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"overflow in multiplication"); |
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static_assert(__b0 * __a0 <= __INTMAX_MAX__, |
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"overflow in multiplication"); |
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static_assert((__a0 * __b1 + __b0 * __a1) * __c |
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<= __INTMAX_MAX__ - __b0 * __a0, |
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"overflow in multiplication"); |
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|
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public: |
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static const intmax_t value = _Pn * _Qn; |
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}; |
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|
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// Some double-precision utilities, where numbers are represented as |
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// __hi*2^(8*sizeof(uintmax_t)) + __lo. |
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template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> |
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struct __big_less |
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: integral_constant<bool, (__hi1 < __hi2 |
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|| (__hi1 == __hi2 && __lo1 < __lo2))> |
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{ }; |
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|
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template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> |
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struct __big_add |
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{ |
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static constexpr uintmax_t __lo = __lo1 + __lo2; |
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static constexpr uintmax_t __hi = (__hi1 + __hi2 + |
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(__lo1 + __lo2 < __lo1)); // carry |
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}; |
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|
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// Subtract a number from a bigger one. |
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template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> |
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struct __big_sub |
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{ |
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static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, |
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"Internal library error"); |
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static constexpr uintmax_t __lo = __lo1 - __lo2; |
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static constexpr uintmax_t __hi = (__hi1 - __hi2 - |
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(__lo1 < __lo2)); // carry |
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}; |
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|
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// Same principle as __safe_multiply. |
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template<uintmax_t __x, uintmax_t __y> |
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struct __big_mul |
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{ |
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private: |
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static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); |
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static constexpr uintmax_t __x0 = __x % __c; |
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static constexpr uintmax_t __x1 = __x / __c; |
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static constexpr uintmax_t __y0 = __y % __c; |
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static constexpr uintmax_t __y1 = __y / __c; |
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static constexpr uintmax_t __x0y0 = __x0 * __y0; |
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static constexpr uintmax_t __x0y1 = __x0 * __y1; |
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static constexpr uintmax_t __x1y0 = __x1 * __y0; |
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static constexpr uintmax_t __x1y1 = __x1 * __y1; |
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static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... |
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static constexpr uintmax_t __mix_lo = __mix * __c; |
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static constexpr uintmax_t __mix_hi |
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= __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here |
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typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; |
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public: |
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static constexpr uintmax_t __hi = _Res::__hi; |
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static constexpr uintmax_t __lo = _Res::__lo; |
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}; |
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|
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// Adapted from __udiv_qrnnd_c in longlong.h |
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// This version assumes that the high bit of __d is 1. |
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template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> |
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struct __big_div_impl |
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{ |
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private: |
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static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), |
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"Internal library error"); |
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static_assert(__n1 < __d, "Internal library error"); |
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static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); |
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static constexpr uintmax_t __d1 = __d / __c; |
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static constexpr uintmax_t __d0 = __d % __c; |
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|
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static constexpr uintmax_t __q1x = __n1 / __d1; |
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static constexpr uintmax_t __r1x = __n1 % __d1; |
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static constexpr uintmax_t __m = __q1x * __d0; |
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static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; |
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static constexpr uintmax_t __r1z = __r1y + __d; |
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static constexpr uintmax_t __r1 |
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= ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) |
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? (__r1z + __d) : __r1z : __r1y) - __m; |
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static constexpr uintmax_t __q1 |
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= __q1x - ((__r1y < __m) |
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? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); |
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static constexpr uintmax_t __q0x = __r1 / __d1; |
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static constexpr uintmax_t __r0x = __r1 % __d1; |
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static constexpr uintmax_t __n = __q0x * __d0; |
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static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; |
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static constexpr uintmax_t __r0z = __r0y + __d; |
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static constexpr uintmax_t __r0 |
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= ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) |
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? (__r0z + __d) : __r0z : __r0y) - __n; |
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static constexpr uintmax_t __q0 |
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= __q0x - ((__r0y < __n) ? ((__r0z >= __d) |
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&& (__r0z < __n)) ? 2 : 1 : 0); |
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|
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public: |
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static constexpr uintmax_t __quot = __q1 * __c + __q0; |
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static constexpr uintmax_t __rem = __r0; |
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|
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private: |
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typedef __big_mul<__quot, __d> _Prod; |
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typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; |
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static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, |
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"Internal library error"); |
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}; |
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|
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template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> |
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struct __big_div |
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{ |
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private: |
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static_assert(__d != 0, "Internal library error"); |
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static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), |
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"This library calls __builtin_clzll on uintmax_t, which " |
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"is unsafe on your platform. Please complain to " |
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"http://gcc.gnu.org/bugzilla/"); |
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static constexpr int __shift = __builtin_clzll(__d); |
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static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; |
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static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; |
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static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; |
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static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; |
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static constexpr uintmax_t __new_d = __d * __c1; |
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static constexpr uintmax_t __new_n0 = __n0 * __c1; |
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static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; |
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static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; |
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static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; |
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typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; |
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|
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public: |
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static constexpr uintmax_t __quot_hi = __n1 / __d; |
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static constexpr uintmax_t __quot_lo = _Res::__quot; |
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static constexpr uintmax_t __rem = _Res::__rem / __c1; |
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|
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private: |
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typedef __big_mul<__quot_lo, __d> _P0; |
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typedef __big_mul<__quot_hi, __d> _P1; |
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typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; |
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// No overflow. |
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static_assert(_P1::__hi == 0, "Internal library error"); |
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static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); |
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// Matches the input data. |
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static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, |
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"Internal library error"); |
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static_assert(__rem < __d, "Internal library error"); |
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}; |
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|
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/// @endcond |
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|
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/** |
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* @brief Provides compile-time rational arithmetic. |
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* |
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* This class template represents any finite rational number with a |
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* numerator and denominator representable by compile-time constants of |
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* type intmax_t. The ratio is simplified when instantiated. |
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* |
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* For example: |
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* @code |
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* std::ratio<7,-21>::num == -1; |
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* std::ratio<7,-21>::den == 3; |
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* @endcode |
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* |
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*/ |
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template<intmax_t _Num, intmax_t _Den = 1> |
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struct ratio |
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{ |
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static_assert(_Den != 0, "denominator cannot be zero"); |
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static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__, |
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"out of range"); |
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|
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// Note: sign(N) * abs(N) == N |
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static constexpr intmax_t num = |
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_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; |
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|
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static constexpr intmax_t den = |
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__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; |
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|
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typedef ratio<num, den> type; |
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}; |
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|
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template<intmax_t _Num, intmax_t _Den> |
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constexpr intmax_t ratio<_Num, _Den>::num; |
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|
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template<intmax_t _Num, intmax_t _Den> |
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constexpr intmax_t ratio<_Num, _Den>::den; |
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|
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/// @cond undocumented |
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|
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template<typename _R1, typename _R2> |
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struct __ratio_multiply |
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{ |
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private: |
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static const intmax_t __gcd1 = |
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__static_gcd<_R1::num, _R2::den>::value; |
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static const intmax_t __gcd2 = |
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__static_gcd<_R2::num, _R1::den>::value; |
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|
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public: |
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typedef ratio< |
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__safe_multiply<(_R1::num / __gcd1), |
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(_R2::num / __gcd2)>::value, |
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__safe_multiply<(_R1::den / __gcd2), |
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(_R2::den / __gcd1)>::value> type; |
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|
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static constexpr intmax_t num = type::num; |
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static constexpr intmax_t den = type::den; |
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}; |
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|
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template<typename _R1, typename _R2> |
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constexpr intmax_t __ratio_multiply<_R1, _R2>::num; |
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|
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template<typename _R1, typename _R2> |
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constexpr intmax_t __ratio_multiply<_R1, _R2>::den; |
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|
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/// @endcond |
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|
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/// ratio_multiply |
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template<typename _R1, typename _R2> |
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using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; |
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|
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/// @cond undocumented |
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|
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template<typename _R1, typename _R2> |
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struct __ratio_divide |
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{ |
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static_assert(_R2::num != 0, "division by 0"); |
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|
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typedef typename __ratio_multiply< |
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_R1, |
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ratio<_R2::den, _R2::num>>::type type; |
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|
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static constexpr intmax_t num = type::num; |
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static constexpr intmax_t den = type::den; |
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}; |
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|
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template<typename _R1, typename _R2> |
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constexpr intmax_t __ratio_divide<_R1, _R2>::num; |
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|
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template<typename _R1, typename _R2> |
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constexpr intmax_t __ratio_divide<_R1, _R2>::den; |
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|
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/// @endcond |
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|
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/// ratio_divide |
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template<typename _R1, typename _R2> |
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using ratio_divide = typename __ratio_divide<_R1, _R2>::type; |
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|
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/// ratio_equal |
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template<typename _R1, typename _R2> |
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struct ratio_equal |
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: integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> |
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{ }; |
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|
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/// ratio_not_equal |
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template<typename _R1, typename _R2> |
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struct ratio_not_equal |
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: integral_constant<bool, !ratio_equal<_R1, _R2>::value> |
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{ }; |
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|
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/// @cond undocumented |
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|
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// Both numbers are positive. |
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template<typename _R1, typename _R2, |
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typename _Left = __big_mul<_R1::num,_R2::den>, |
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typename _Right = __big_mul<_R2::num,_R1::den> > |
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struct __ratio_less_impl_1 |
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: integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, |
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_Right::__hi, _Right::__lo>::value> |
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{ }; |
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|
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template<typename _R1, typename _R2, |
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bool = (_R1::num == 0 || _R2::num == 0 |
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|| (__static_sign<_R1::num>::value |
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!= __static_sign<_R2::num>::value)), |
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bool = (__static_sign<_R1::num>::value == -1 |
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&& __static_sign<_R2::num>::value == -1)> |
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struct __ratio_less_impl |
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: __ratio_less_impl_1<_R1, _R2>::type |
| 380 |
{ }; |
| 381 |
|
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template<typename _R1, typename _R2> |
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struct __ratio_less_impl<_R1, _R2, true, false> |
| 384 |
: integral_constant<bool, _R1::num < _R2::num> |
| 385 |
{ }; |
| 386 |
|
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template<typename _R1, typename _R2> |
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struct __ratio_less_impl<_R1, _R2, false, true> |
| 389 |
: __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, |
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ratio<-_R1::num, _R1::den> >::type |
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{ }; |
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|
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/// @endcond |
| 394 |
|
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/// ratio_less |
| 396 |
template<typename _R1, typename _R2> |
| 397 |
struct ratio_less |
| 398 |
: __ratio_less_impl<_R1, _R2>::type |
| 399 |
{ }; |
| 400 |
|
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/// ratio_less_equal |
| 402 |
template<typename _R1, typename _R2> |
| 403 |
struct ratio_less_equal |
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: integral_constant<bool, !ratio_less<_R2, _R1>::value> |
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{ }; |
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|
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/// ratio_greater |
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template<typename _R1, typename _R2> |
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struct ratio_greater |
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: integral_constant<bool, ratio_less<_R2, _R1>::value> |
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{ }; |
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|
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/// ratio_greater_equal |
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template<typename _R1, typename _R2> |
| 415 |
struct ratio_greater_equal |
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: integral_constant<bool, !ratio_less<_R1, _R2>::value> |
| 417 |
{ }; |
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|
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#if __cplusplus > 201402L |
| 420 |
template <typename _R1, typename _R2> |
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inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; |
| 422 |
template <typename _R1, typename _R2> |
| 423 |
inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; |
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template <typename _R1, typename _R2> |
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inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; |
| 426 |
template <typename _R1, typename _R2> |
| 427 |
inline constexpr bool ratio_less_equal_v = |
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ratio_less_equal<_R1, _R2>::value; |
| 429 |
template <typename _R1, typename _R2> |
| 430 |
inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; |
| 431 |
template <typename _R1, typename _R2> |
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inline constexpr bool ratio_greater_equal_v |
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= ratio_greater_equal<_R1, _R2>::value; |
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#endif // C++17 |
| 435 |
|
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/// @cond undocumented |
| 437 |
|
| 438 |
template<typename _R1, typename _R2, |
| 439 |
bool = (_R1::num >= 0), |
| 440 |
bool = (_R2::num >= 0), |
| 441 |
bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, |
| 442 |
ratio<__static_abs<_R2::num>::value, _R2::den> >::value> |
| 443 |
struct __ratio_add_impl |
| 444 |
{ |
| 445 |
private: |
| 446 |
typedef typename __ratio_add_impl< |
| 447 |
ratio<-_R1::num, _R1::den>, |
| 448 |
ratio<-_R2::num, _R2::den> >::type __t; |
| 449 |
public: |
| 450 |
typedef ratio<-__t::num, __t::den> type; |
| 451 |
}; |
| 452 |
|
| 453 |
// True addition of nonnegative numbers. |
| 454 |
template<typename _R1, typename _R2, bool __b> |
| 455 |
struct __ratio_add_impl<_R1, _R2, true, true, __b> |
| 456 |
{ |
| 457 |
private: |
| 458 |
static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; |
| 459 |
static constexpr uintmax_t __d2 = _R2::den / __g; |
| 460 |
typedef __big_mul<_R1::den, __d2> __d; |
| 461 |
typedef __big_mul<_R1::num, _R2::den / __g> __x; |
| 462 |
typedef __big_mul<_R2::num, _R1::den / __g> __y; |
| 463 |
typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; |
| 464 |
static_assert(__n::__hi >= __x::__hi, "Internal library error"); |
| 465 |
typedef __big_div<__n::__hi, __n::__lo, __g> __ng; |
| 466 |
static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; |
| 467 |
typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; |
| 468 |
static_assert(__n_final::__rem == 0, "Internal library error"); |
| 469 |
static_assert(__n_final::__quot_hi == 0 && |
| 470 |
__n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); |
| 471 |
typedef __big_mul<_R1::den / __g2, __d2> __d_final; |
| 472 |
static_assert(__d_final::__hi == 0 && |
| 473 |
__d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); |
| 474 |
public: |
| 475 |
typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; |
| 476 |
}; |
| 477 |
|
| 478 |
template<typename _R1, typename _R2> |
| 479 |
struct __ratio_add_impl<_R1, _R2, false, true, true> |
| 480 |
: __ratio_add_impl<_R2, _R1> |
| 481 |
{ }; |
| 482 |
|
| 483 |
// True subtraction of nonnegative numbers yielding a nonnegative result. |
| 484 |
template<typename _R1, typename _R2> |
| 485 |
struct __ratio_add_impl<_R1, _R2, true, false, false> |
| 486 |
{ |
| 487 |
private: |
| 488 |
static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; |
| 489 |
static constexpr uintmax_t __d2 = _R2::den / __g; |
| 490 |
typedef __big_mul<_R1::den, __d2> __d; |
| 491 |
typedef __big_mul<_R1::num, _R2::den / __g> __x; |
| 492 |
typedef __big_mul<-_R2::num, _R1::den / __g> __y; |
| 493 |
typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; |
| 494 |
typedef __big_div<__n::__hi, __n::__lo, __g> __ng; |
| 495 |
static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; |
| 496 |
typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; |
| 497 |
static_assert(__n_final::__rem == 0, "Internal library error"); |
| 498 |
static_assert(__n_final::__quot_hi == 0 && |
| 499 |
__n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); |
| 500 |
typedef __big_mul<_R1::den / __g2, __d2> __d_final; |
| 501 |
static_assert(__d_final::__hi == 0 && |
| 502 |
__d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); |
| 503 |
public: |
| 504 |
typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; |
| 505 |
}; |
| 506 |
|
| 507 |
template<typename _R1, typename _R2> |
| 508 |
struct __ratio_add |
| 509 |
{ |
| 510 |
typedef typename __ratio_add_impl<_R1, _R2>::type type; |
| 511 |
static constexpr intmax_t num = type::num; |
| 512 |
static constexpr intmax_t den = type::den; |
| 513 |
}; |
| 514 |
|
| 515 |
template<typename _R1, typename _R2> |
| 516 |
constexpr intmax_t __ratio_add<_R1, _R2>::num; |
| 517 |
|
| 518 |
template<typename _R1, typename _R2> |
| 519 |
constexpr intmax_t __ratio_add<_R1, _R2>::den; |
| 520 |
|
| 521 |
/// @endcond |
| 522 |
|
| 523 |
/// ratio_add |
| 524 |
template<typename _R1, typename _R2> |
| 525 |
using ratio_add = typename __ratio_add<_R1, _R2>::type; |
| 526 |
|
| 527 |
/// @cond undocumented |
| 528 |
|
| 529 |
template<typename _R1, typename _R2> |
| 530 |
struct __ratio_subtract |
| 531 |
{ |
| 532 |
typedef typename __ratio_add< |
| 533 |
_R1, |
| 534 |
ratio<-_R2::num, _R2::den>>::type type; |
| 535 |
|
| 536 |
static constexpr intmax_t num = type::num; |
| 537 |
static constexpr intmax_t den = type::den; |
| 538 |
}; |
| 539 |
|
| 540 |
template<typename _R1, typename _R2> |
| 541 |
constexpr intmax_t __ratio_subtract<_R1, _R2>::num; |
| 542 |
|
| 543 |
template<typename _R1, typename _R2> |
| 544 |
constexpr intmax_t __ratio_subtract<_R1, _R2>::den; |
| 545 |
|
| 546 |
/// @endcond |
| 547 |
|
| 548 |
/// ratio_subtract |
| 549 |
template<typename _R1, typename _R2> |
| 550 |
using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; |
| 551 |
|
| 552 |
|
| 553 |
typedef ratio<1, 1000000000000000000> atto; |
| 554 |
typedef ratio<1, 1000000000000000> femto; |
| 555 |
typedef ratio<1, 1000000000000> pico; |
| 556 |
typedef ratio<1, 1000000000> nano; |
| 557 |
typedef ratio<1, 1000000> micro; |
| 558 |
typedef ratio<1, 1000> milli; |
| 559 |
typedef ratio<1, 100> centi; |
| 560 |
typedef ratio<1, 10> deci; |
| 561 |
typedef ratio< 10, 1> deca; |
| 562 |
typedef ratio< 100, 1> hecto; |
| 563 |
typedef ratio< 1000, 1> kilo; |
| 564 |
typedef ratio< 1000000, 1> mega; |
| 565 |
typedef ratio< 1000000000, 1> giga; |
| 566 |
typedef ratio< 1000000000000, 1> tera; |
| 567 |
typedef ratio< 1000000000000000, 1> peta; |
| 568 |
typedef ratio< 1000000000000000000, 1> exa; |
| 569 |
|
| 570 |
/// @} group ratio |
| 571 |
_GLIBCXX_END_NAMESPACE_VERSION |
| 572 |
} // namespace |
| 573 |
|
| 574 |
#endif // C++11 |
| 575 |
|
| 576 |
#endif //_GLIBCXX_RATIO |
