539 lines
19 KiB
C++
539 lines
19 KiB
C++
// ratio -*- C++ -*-
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// Copyright (C) 2008-2013 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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// 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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// 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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// 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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/** @file include/ratio
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* This is a Standard C++ Library header.
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*/
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#ifndef _GLIBCXX_RATIO
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#define _GLIBCXX_RATIO 1
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#pragma GCC system_header
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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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#include <type_traits>
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#include <cstdint>
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#ifdef _GLIBCXX_USE_C99_STDINT_TR1
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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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* @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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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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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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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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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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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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// 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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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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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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public:
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static const intmax_t value = _Pn * _Qn;
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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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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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// 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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// 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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// 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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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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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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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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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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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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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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* @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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// 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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static constexpr intmax_t den =
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__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
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typedef ratio<num, den> type;
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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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template<intmax_t _Num, intmax_t _Den>
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constexpr intmax_t ratio<_Num, _Den>::den;
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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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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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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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template<typename _R1, typename _R2>
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constexpr intmax_t __ratio_multiply<_R1, _R2>::num;
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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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/// 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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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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typedef typename __ratio_multiply<
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_R1,
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ratio<_R2::den, _R2::num>>::type type;
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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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template<typename _R1, typename _R2>
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constexpr intmax_t __ratio_divide<_R1, _R2>::num;
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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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/// 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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/// 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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/// 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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// 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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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
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{ };
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template<typename _R1, typename _R2>
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struct __ratio_less_impl<_R1, _R2, true, false>
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: integral_constant<bool, _R1::num < _R2::num>
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{ };
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template<typename _R1, typename _R2>
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struct __ratio_less_impl<_R1, _R2, false, true>
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: __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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/// ratio_less
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template<typename _R1, typename _R2>
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struct ratio_less
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: __ratio_less_impl<_R1, _R2>::type
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{ };
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/// ratio_less_equal
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template<typename _R1, typename _R2>
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struct ratio_less_equal
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: integral_constant<bool, !ratio_less<_R2, _R1>::value>
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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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/// ratio_greater_equal
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template<typename _R1, typename _R2>
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struct ratio_greater_equal
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: integral_constant<bool, !ratio_less<_R1, _R2>::value>
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{ };
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template<typename _R1, typename _R2,
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bool = (_R1::num >= 0),
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bool = (_R2::num >= 0),
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bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>,
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ratio<__static_abs<_R2::num>::value, _R2::den> >::value>
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struct __ratio_add_impl
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{
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private:
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typedef typename __ratio_add_impl<
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ratio<-_R1::num, _R1::den>,
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ratio<-_R2::num, _R2::den> >::type __t;
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public:
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typedef ratio<-__t::num, __t::den> type;
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};
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// True addition of nonnegative numbers.
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template<typename _R1, typename _R2, bool __b>
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struct __ratio_add_impl<_R1, _R2, true, true, __b>
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{
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private:
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static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value;
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static constexpr uintmax_t __d2 = _R2::den / __g;
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typedef __big_mul<_R1::den, __d2> __d;
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typedef __big_mul<_R1::num, _R2::den / __g> __x;
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typedef __big_mul<_R2::num, _R1::den / __g> __y;
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typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n;
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static_assert(__n::__hi >= __x::__hi, "Internal library error");
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typedef __big_div<__n::__hi, __n::__lo, __g> __ng;
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static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value;
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typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final;
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static_assert(__n_final::__rem == 0, "Internal library error");
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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;
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|
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;
|
|
};
|
|
|
|
template<typename _R1, typename _R2>
|
|
struct __ratio_add_impl<_R1, _R2, false, true, true>
|
|
: __ratio_add_impl<_R2, _R1>
|
|
{ };
|
|
|
|
// 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;
|
|
};
|
|
|
|
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;
|
|
|
|
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;
|
|
|
|
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_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;
|
|
|
|
// @} group ratio
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace
|
|
|
|
#endif //_GLIBCXX_USE_C99_STDINT_TR1
|
|
|
|
#endif // C++11
|
|
|
|
#endif //_GLIBCXX_RATIO
|