// ratio -*- C++ -*-
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// ratio -*- C++ -*-
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// Copyright (C) 2008, 2009, 2010 Free Software Foundation, Inc.
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// Copyright (C) 2008, 2009, 2010 Free Software Foundation, Inc.
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//
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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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// 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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// 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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// 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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// Free Software Foundation; either version 3, or (at your option)
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// any later version.
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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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// 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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// 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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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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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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// 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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// 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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// 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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// 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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// 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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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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// .
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// .
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/** @file ratio
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/** @file ratio
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* This is a Standard C++ Library header.
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* This is a Standard C++ Library header.
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*/
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*/
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#ifndef _GLIBCXX_RATIO
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#ifndef _GLIBCXX_RATIO
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#define _GLIBCXX_RATIO 1
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#define _GLIBCXX_RATIO 1
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#pragma GCC system_header
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#pragma GCC system_header
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#ifndef __GXX_EXPERIMENTAL_CXX0X__
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#ifndef __GXX_EXPERIMENTAL_CXX0X__
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# include
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# include
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#else
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#else
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#include
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#include
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#include
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#include
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#ifdef _GLIBCXX_USE_C99_STDINT_TR1
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#ifdef _GLIBCXX_USE_C99_STDINT_TR1
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namespace std
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namespace std
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{
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{
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/**
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/**
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* @defgroup ratio Rational Arithmetic
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* @defgroup ratio Rational Arithmetic
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* @ingroup utilities
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* @ingroup utilities
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*
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*
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* Compile time representation of finite rational numbers.
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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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*/
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template
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template
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struct __static_sign
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struct __static_sign
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: integral_constant
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: integral_constant
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{ };
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{ };
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template
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template
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struct __static_abs
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struct __static_abs
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: integral_constant::value>
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: integral_constant::value>
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{ };
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{ };
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template
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template
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struct __static_gcd;
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struct __static_gcd;
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template
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template
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struct __static_gcd
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struct __static_gcd
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: __static_gcd<_Qn, (_Pn % _Qn)>
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: __static_gcd<_Qn, (_Pn % _Qn)>
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{ };
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{ };
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template
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template
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struct __static_gcd<_Pn, 0>
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struct __static_gcd<_Pn, 0>
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: integral_constant::value>
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: integral_constant::value>
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{ };
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{ };
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template
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template
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struct __static_gcd<0, _Qn>
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struct __static_gcd<0, _Qn>
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: integral_constant::value>
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: integral_constant::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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// 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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// 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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// 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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// 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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// 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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// is representable by intmax_t.
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template
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template
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struct __safe_multiply
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struct __safe_multiply
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{
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{
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private:
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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 __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 __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 __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 __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 const uintmax_t __b1 = __static_abs<_Qn>::value / __c;
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static_assert(__a1 == 0 || __b1 == 0,
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static_assert(__a1 == 0 || __b1 == 0,
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"overflow in multiplication");
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"overflow in multiplication");
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static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
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static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
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"overflow in multiplication");
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"overflow in multiplication");
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static_assert(__b0 * __a0 <= __INTMAX_MAX__,
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static_assert(__b0 * __a0 <= __INTMAX_MAX__,
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"overflow in multiplication");
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"overflow in multiplication");
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static_assert((__a0 * __b1 + __b0 * __a1) * __c <=
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static_assert((__a0 * __b1 + __b0 * __a1) * __c <=
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__INTMAX_MAX__ - __b0 * __a0, "overflow in multiplication");
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__INTMAX_MAX__ - __b0 * __a0, "overflow in multiplication");
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public:
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public:
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static const intmax_t value = _Pn * _Qn;
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static const intmax_t value = _Pn * _Qn;
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};
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};
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// Helpers for __safe_add
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// Helpers for __safe_add
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template
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template
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struct __add_overflow_check_impl
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struct __add_overflow_check_impl
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: integral_constant
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: integral_constant
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{ };
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{ };
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template
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template
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struct __add_overflow_check_impl<_Pn, _Qn, false>
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struct __add_overflow_check_impl<_Pn, _Qn, false>
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: integral_constant= -__INTMAX_MAX__ - _Qn)>
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: integral_constant= -__INTMAX_MAX__ - _Qn)>
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{ };
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{ };
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template
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template
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struct __add_overflow_check
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struct __add_overflow_check
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: __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
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: __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
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{ };
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{ };
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template
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template
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struct __safe_add
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struct __safe_add
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{
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{
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static_assert(__add_overflow_check<_Pn, _Qn>::value != 0,
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static_assert(__add_overflow_check<_Pn, _Qn>::value != 0,
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"overflow in addition");
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"overflow in addition");
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static const intmax_t value = _Pn + _Qn;
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static const intmax_t value = _Pn + _Qn;
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};
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};
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/**
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/**
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* @brief Provides compile-time rational arithmetic.
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* @brief Provides compile-time rational arithmetic.
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*
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*
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* This class template represents any finite rational number with a
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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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* 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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* type intmax_t. The ratio is simplified when instantiated.
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*
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*
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* For example:
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* For example:
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* @code
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* @code
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* std::ratio<7,-21>::num == -1;
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* std::ratio<7,-21>::num == -1;
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* std::ratio<7,-21>::den == 3;
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* std::ratio<7,-21>::den == 3;
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* @endcode
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* @endcode
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*
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*
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*/
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*/
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template
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template
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struct ratio
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struct ratio
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{
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{
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static_assert(_Den != 0, "denominator cannot be zero");
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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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static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
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"out of range");
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"out of range");
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// Note: sign(N) * abs(N) == N
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// Note: sign(N) * abs(N) == N
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static const intmax_t num =
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static const intmax_t num =
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_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
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_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
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static const intmax_t den =
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static const intmax_t den =
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__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
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__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
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};
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};
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template
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template
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const intmax_t ratio<_Num, _Den>::num;
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const intmax_t ratio<_Num, _Den>::num;
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template
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template
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const intmax_t ratio<_Num, _Den>::den;
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const intmax_t ratio<_Num, _Den>::den;
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/// ratio_add
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/// ratio_add
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template
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template
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struct ratio_add
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struct ratio_add
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{
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{
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private:
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private:
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static const intmax_t __gcd =
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static const intmax_t __gcd =
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__static_gcd<_R1::den, _R2::den>::value;
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__static_gcd<_R1::den, _R2::den>::value;
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public:
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public:
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typedef ratio<
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typedef ratio<
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__safe_add<
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__safe_add<
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__safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
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__safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
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__safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value,
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__safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value,
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__safe_multiply<_R1::den, (_R2::den / __gcd)>::value> type;
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__safe_multiply<_R1::den, (_R2::den / __gcd)>::value> type;
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};
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};
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/// ratio_subtract
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/// ratio_subtract
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template
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template
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struct ratio_subtract
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struct ratio_subtract
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{
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{
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typedef typename ratio_add<
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typedef typename ratio_add<
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_R1,
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_R1,
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ratio<-_R2::num, _R2::den>>::type type;
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ratio<-_R2::num, _R2::den>>::type type;
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};
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};
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/// ratio_multiply
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/// ratio_multiply
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template
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template
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struct ratio_multiply
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struct ratio_multiply
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{
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{
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private:
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private:
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static const intmax_t __gcd1 =
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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_gcd<_R1::num, _R2::den>::value;
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static const intmax_t __gcd2 =
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static const intmax_t __gcd2 =
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__static_gcd<_R2::num, _R1::den>::value;
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__static_gcd<_R2::num, _R1::den>::value;
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public:
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public:
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typedef ratio<
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typedef ratio<
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__safe_multiply<(_R1::num / __gcd1),
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__safe_multiply<(_R1::num / __gcd1),
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(_R2::num / __gcd2)>::value,
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(_R2::num / __gcd2)>::value,
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__safe_multiply<(_R1::den / __gcd2),
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__safe_multiply<(_R1::den / __gcd2),
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(_R2::den / __gcd1)>::value> type;
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(_R2::den / __gcd1)>::value> type;
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};
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};
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/// ratio_divide
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/// ratio_divide
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template
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template
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struct ratio_divide
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struct ratio_divide
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{
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{
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static_assert(_R2::num != 0, "division by 0");
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static_assert(_R2::num != 0, "division by 0");
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typedef typename ratio_multiply<
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typedef typename ratio_multiply<
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_R1,
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_R1,
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ratio<_R2::den, _R2::num>>::type type;
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ratio<_R2::den, _R2::num>>::type type;
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};
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};
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/// ratio_equal
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/// ratio_equal
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template
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template
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struct ratio_equal
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struct ratio_equal
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: integral_constant
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: integral_constant
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{ };
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{ };
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/// ratio_not_equal
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/// ratio_not_equal
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template
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template
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struct ratio_not_equal
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struct ratio_not_equal
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: integral_constant::value>
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: integral_constant::value>
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{ };
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{ };
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template
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template
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struct __ratio_less_simple_impl
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struct __ratio_less_simple_impl
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: integral_constant
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: integral_constant
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(__safe_multiply<_R1::num, _R2::den>::value
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(__safe_multiply<_R1::num, _R2::den>::value
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< __safe_multiply<_R2::num, _R1::den>::value)>
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< __safe_multiply<_R2::num, _R1::den>::value)>
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{ };
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{ };
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// If the denominators are equal or the signs differ, we can just compare
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// If the denominators are equal or the signs differ, we can just compare
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// numerators, otherwise fallback to the simple cross-multiply method.
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// numerators, otherwise fallback to the simple cross-multiply method.
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template
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template
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struct __ratio_less_impl
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struct __ratio_less_impl
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: conditional<(_R1::den == _R2::den
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: conditional<(_R1::den == _R2::den
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|| (__static_sign<_R1::num>::value
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|| (__static_sign<_R1::num>::value
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!= __static_sign<_R2::num>::value)),
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!= __static_sign<_R2::num>::value)),
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integral_constant,
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integral_constant,
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__ratio_less_simple_impl<_R1, _R2>>::type
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__ratio_less_simple_impl<_R1, _R2>>::type
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{ };
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{ };
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/// ratio_less
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/// ratio_less
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template
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template
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struct ratio_less
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struct ratio_less
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: __ratio_less_impl<_R1, _R2>::type
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: __ratio_less_impl<_R1, _R2>::type
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{ };
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{ };
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/// ratio_less_equal
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/// ratio_less_equal
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template
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template
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struct ratio_less_equal
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struct ratio_less_equal
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: integral_constant::value>
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: integral_constant::value>
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{ };
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{ };
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/// ratio_greater
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/// ratio_greater
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template
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template
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struct ratio_greater
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struct ratio_greater
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: integral_constant::value>
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: integral_constant::value>
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{ };
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{ };
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/// ratio_greater_equal
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/// ratio_greater_equal
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template
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template
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struct ratio_greater_equal
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struct ratio_greater_equal
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: integral_constant::value>
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: integral_constant::value>
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{ };
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{ };
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typedef ratio<1, 1000000000000000000> atto;
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typedef ratio<1, 1000000000000000000> atto;
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typedef ratio<1, 1000000000000000> femto;
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typedef ratio<1, 1000000000000000> femto;
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typedef ratio<1, 1000000000000> pico;
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typedef ratio<1, 1000000000000> pico;
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typedef ratio<1, 1000000000> nano;
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typedef ratio<1, 1000000000> nano;
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typedef ratio<1, 1000000> micro;
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typedef ratio<1, 1000000> micro;
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typedef ratio<1, 1000> milli;
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typedef ratio<1, 1000> milli;
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typedef ratio<1, 100> centi;
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typedef ratio<1, 100> centi;
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typedef ratio<1, 10> deci;
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typedef ratio<1, 10> deci;
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typedef ratio< 10, 1> deca;
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typedef ratio< 10, 1> deca;
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typedef ratio< 100, 1> hecto;
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typedef ratio< 100, 1> hecto;
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typedef ratio< 1000, 1> kilo;
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typedef ratio< 1000, 1> kilo;
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typedef ratio< 1000000, 1> mega;
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typedef ratio< 1000000, 1> mega;
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typedef ratio< 1000000000, 1> giga;
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typedef ratio< 1000000000, 1> giga;
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typedef ratio< 1000000000000, 1> tera;
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typedef ratio< 1000000000000, 1> tera;
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typedef ratio< 1000000000000000, 1> peta;
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typedef ratio< 1000000000000000, 1> peta;
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typedef ratio< 1000000000000000000, 1> exa;
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typedef ratio< 1000000000000000000, 1> exa;
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// @} group ratio
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// @} group ratio
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}
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}
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#endif //_GLIBCXX_USE_C99_STDINT_TR1
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#endif //_GLIBCXX_USE_C99_STDINT_TR1
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#endif //__GXX_EXPERIMENTAL_CXX0X__
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#endif //__GXX_EXPERIMENTAL_CXX0X__
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#endif //_GLIBCXX_RATIO
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#endif //_GLIBCXX_RATIO
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