534 lines
16 KiB
Plaintext
534 lines
16 KiB
Plaintext
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// -*- C++ -*-
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//===---------------------------- ratio -----------------------------------===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file is dual licensed under the MIT and the University of Illinois Open
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// Source Licenses. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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#ifndef _LIBCPP_RATIO
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#define _LIBCPP_RATIO
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/*
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ratio synopsis
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namespace std
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{
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template <intmax_t N, intmax_t D = 1>
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class ratio
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{
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public:
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static constexpr intmax_t num;
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static constexpr intmax_t den;
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typedef ratio<num, den> type;
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};
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// ratio arithmetic
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template <class R1, class R2> using ratio_add = ...;
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template <class R1, class R2> using ratio_subtract = ...;
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template <class R1, class R2> using ratio_multiply = ...;
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template <class R1, class R2> using ratio_divide = ...;
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// ratio comparison
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template <class R1, class R2> struct ratio_equal;
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template <class R1, class R2> struct ratio_not_equal;
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template <class R1, class R2> struct ratio_less;
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template <class R1, class R2> struct ratio_less_equal;
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template <class R1, class R2> struct ratio_greater;
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template <class R1, class R2> struct ratio_greater_equal;
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// convenience SI typedefs
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typedef ratio<1, 1000000000000000000000000> yocto; // not supported
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typedef ratio<1, 1000000000000000000000> zepto; // not supported
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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, 1000000000000> pico;
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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, 1000> milli;
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typedef ratio<1, 100> centi;
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typedef ratio<1, 10> deci;
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typedef ratio< 10, 1> deca;
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typedef ratio< 100, 1> hecto;
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typedef ratio< 1000, 1> kilo;
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typedef ratio< 1000000, 1> mega;
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typedef ratio< 1000000000, 1> giga;
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typedef ratio< 1000000000000, 1> tera;
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typedef ratio< 1000000000000000, 1> peta;
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typedef ratio< 1000000000000000000, 1> exa;
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typedef ratio< 1000000000000000000000, 1> zetta; // not supported
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typedef ratio<1000000000000000000000000, 1> yotta; // not supported
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// 20.11.5, ratio comparison
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template <class R1, class R2> inline constexpr bool ratio_equal_v
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= ratio_equal<R1, R2>::value; // C++17
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template <class R1, class R2> inline constexpr bool ratio_not_equal_v
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= ratio_not_equal<R1, R2>::value; // C++17
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template <class R1, class R2> inline constexpr bool ratio_less_v
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= ratio_less<R1, R2>::value; // C++17
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template <class R1, class R2> inline constexpr bool ratio_less_equal_v
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= ratio_less_equal<R1, R2>::value; // C++17
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template <class R1, class R2> inline constexpr bool ratio_greater_v
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= ratio_greater<R1, R2>::value; // C++17
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template <class R1, class R2> inline constexpr bool ratio_greater_equal_v
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= ratio_greater_equal<R1, R2>::value; // C++17
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}
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*/
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#include <__config>
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#include <cstdint>
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#include <climits>
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#include <type_traits>
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#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
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#pragma GCC system_header
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#endif
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_LIBCPP_PUSH_MACROS
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#include <__undef_macros>
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_LIBCPP_BEGIN_NAMESPACE_STD
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// __static_gcd
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template <intmax_t _Xp, intmax_t _Yp>
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struct __static_gcd
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{
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static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value;
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};
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template <intmax_t _Xp>
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struct __static_gcd<_Xp, 0>
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{
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static const intmax_t value = _Xp;
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};
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template <>
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struct __static_gcd<0, 0>
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{
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static const intmax_t value = 1;
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};
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// __static_lcm
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template <intmax_t _Xp, intmax_t _Yp>
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struct __static_lcm
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{
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static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp;
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};
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template <intmax_t _Xp>
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struct __static_abs
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{
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static const intmax_t value = _Xp < 0 ? -_Xp : _Xp;
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};
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template <intmax_t _Xp>
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struct __static_sign
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{
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static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1);
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};
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template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
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class __ll_add;
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template <intmax_t _Xp, intmax_t _Yp>
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class __ll_add<_Xp, _Yp, 1>
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{
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static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
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static const intmax_t max = -min;
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static_assert(_Xp <= max - _Yp, "overflow in __ll_add");
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public:
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static const intmax_t value = _Xp + _Yp;
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};
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template <intmax_t _Xp, intmax_t _Yp>
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class __ll_add<_Xp, _Yp, 0>
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{
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public:
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static const intmax_t value = _Xp;
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};
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template <intmax_t _Xp, intmax_t _Yp>
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class __ll_add<_Xp, _Yp, -1>
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{
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static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
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static const intmax_t max = -min;
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static_assert(min - _Yp <= _Xp, "overflow in __ll_add");
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public:
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static const intmax_t value = _Xp + _Yp;
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};
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template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
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class __ll_sub;
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template <intmax_t _Xp, intmax_t _Yp>
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class __ll_sub<_Xp, _Yp, 1>
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{
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static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
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static const intmax_t max = -min;
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static_assert(min + _Yp <= _Xp, "overflow in __ll_sub");
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public:
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static const intmax_t value = _Xp - _Yp;
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};
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template <intmax_t _Xp, intmax_t _Yp>
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class __ll_sub<_Xp, _Yp, 0>
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{
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public:
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static const intmax_t value = _Xp;
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};
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template <intmax_t _Xp, intmax_t _Yp>
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class __ll_sub<_Xp, _Yp, -1>
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{
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static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
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static const intmax_t max = -min;
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static_assert(_Xp <= max + _Yp, "overflow in __ll_sub");
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public:
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static const intmax_t value = _Xp - _Yp;
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};
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template <intmax_t _Xp, intmax_t _Yp>
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class __ll_mul
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{
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static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
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static const intmax_t min = nan + 1;
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static const intmax_t max = -min;
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static const intmax_t __a_x = __static_abs<_Xp>::value;
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static const intmax_t __a_y = __static_abs<_Yp>::value;
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static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul");
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public:
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static const intmax_t value = _Xp * _Yp;
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};
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template <intmax_t _Yp>
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class __ll_mul<0, _Yp>
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{
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public:
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static const intmax_t value = 0;
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};
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template <intmax_t _Xp>
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class __ll_mul<_Xp, 0>
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{
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public:
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static const intmax_t value = 0;
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};
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template <>
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class __ll_mul<0, 0>
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{
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public:
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static const intmax_t value = 0;
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};
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// Not actually used but left here in case needed in future maintenance
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template <intmax_t _Xp, intmax_t _Yp>
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class __ll_div
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{
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static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
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static const intmax_t min = nan + 1;
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static const intmax_t max = -min;
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static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div");
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public:
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static const intmax_t value = _Xp / _Yp;
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};
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template <intmax_t _Num, intmax_t _Den = 1>
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class _LIBCPP_TEMPLATE_VIS ratio
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{
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static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range");
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static_assert(_Den != 0, "ratio divide by 0");
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static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range");
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static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value;
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static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value;
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static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value;
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static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value;
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public:
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static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd;
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static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd;
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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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_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num;
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template <intmax_t _Num, intmax_t _Den>
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_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den;
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template <class _Tp> struct __is_ratio : false_type {};
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template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {};
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typedef ratio<1LL, 1000000000000000000LL> atto;
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typedef ratio<1LL, 1000000000000000LL> femto;
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typedef ratio<1LL, 1000000000000LL> pico;
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typedef ratio<1LL, 1000000000LL> nano;
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typedef ratio<1LL, 1000000LL> micro;
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typedef ratio<1LL, 1000LL> milli;
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typedef ratio<1LL, 100LL> centi;
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typedef ratio<1LL, 10LL> deci;
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typedef ratio< 10LL, 1LL> deca;
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typedef ratio< 100LL, 1LL> hecto;
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typedef ratio< 1000LL, 1LL> kilo;
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typedef ratio< 1000000LL, 1LL> mega;
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typedef ratio< 1000000000LL, 1LL> giga;
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typedef ratio< 1000000000000LL, 1LL> tera;
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typedef ratio< 1000000000000000LL, 1LL> peta;
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typedef ratio<1000000000000000000LL, 1LL> exa;
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template <class _R1, class _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 __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value;
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static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value;
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public:
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typedef typename ratio
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<
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__ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value,
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__ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value
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>::type type;
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};
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#ifndef _LIBCPP_CXX03_LANG
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template <class _R1, class _R2> using ratio_multiply
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= typename __ratio_multiply<_R1, _R2>::type;
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#else // _LIBCPP_CXX03_LANG
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template <class _R1, class _R2>
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struct _LIBCPP_TEMPLATE_VIS ratio_multiply
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: public __ratio_multiply<_R1, _R2>::type {};
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#endif // _LIBCPP_CXX03_LANG
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template <class _R1, class _R2>
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struct __ratio_divide
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{
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private:
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static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
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static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
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public:
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typedef typename ratio
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<
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__ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
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__ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
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>::type type;
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};
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#ifndef _LIBCPP_CXX03_LANG
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template <class _R1, class _R2> using ratio_divide
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= typename __ratio_divide<_R1, _R2>::type;
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#else // _LIBCPP_CXX03_LANG
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template <class _R1, class _R2>
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struct _LIBCPP_TEMPLATE_VIS ratio_divide
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: public __ratio_divide<_R1, _R2>::type {};
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#endif // _LIBCPP_CXX03_LANG
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template <class _R1, class _R2>
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struct __ratio_add
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{
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private:
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static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
|
||
|
|
static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
|
||
|
|
public:
|
||
|
|
typedef typename ratio_multiply
|
||
|
|
<
|
||
|
|
ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,
|
||
|
|
ratio
|
||
|
|
<
|
||
|
|
__ll_add
|
||
|
|
<
|
||
|
|
__ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
|
||
|
|
__ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
|
||
|
|
>::value,
|
||
|
|
_R2::den
|
||
|
|
>
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
|
||
|
|
#ifndef _LIBCPP_CXX03_LANG
|
||
|
|
|
||
|
|
template <class _R1, class _R2> using ratio_add
|
||
|
|
= typename __ratio_add<_R1, _R2>::type;
|
||
|
|
|
||
|
|
#else // _LIBCPP_CXX03_LANG
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct _LIBCPP_TEMPLATE_VIS ratio_add
|
||
|
|
: public __ratio_add<_R1, _R2>::type {};
|
||
|
|
|
||
|
|
#endif // _LIBCPP_CXX03_LANG
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct __ratio_subtract
|
||
|
|
{
|
||
|
|
private:
|
||
|
|
static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value;
|
||
|
|
static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value;
|
||
|
|
public:
|
||
|
|
typedef typename ratio_multiply
|
||
|
|
<
|
||
|
|
ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,
|
||
|
|
ratio
|
||
|
|
<
|
||
|
|
__ll_sub
|
||
|
|
<
|
||
|
|
__ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
|
||
|
|
__ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value
|
||
|
|
>::value,
|
||
|
|
_R2::den
|
||
|
|
>
|
||
|
|
>::type type;
|
||
|
|
};
|
||
|
|
|
||
|
|
#ifndef _LIBCPP_CXX03_LANG
|
||
|
|
|
||
|
|
template <class _R1, class _R2> using ratio_subtract
|
||
|
|
= typename __ratio_subtract<_R1, _R2>::type;
|
||
|
|
|
||
|
|
#else // _LIBCPP_CXX03_LANG
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct _LIBCPP_TEMPLATE_VIS ratio_subtract
|
||
|
|
: public __ratio_subtract<_R1, _R2>::type {};
|
||
|
|
|
||
|
|
#endif // _LIBCPP_CXX03_LANG
|
||
|
|
|
||
|
|
// ratio_equal
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct _LIBCPP_TEMPLATE_VIS ratio_equal
|
||
|
|
: public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {};
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct _LIBCPP_TEMPLATE_VIS ratio_not_equal
|
||
|
|
: public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {};
|
||
|
|
|
||
|
|
// ratio_less
|
||
|
|
|
||
|
|
template <class _R1, class _R2, bool _Odd = false,
|
||
|
|
intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den,
|
||
|
|
intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den>
|
||
|
|
struct __ratio_less1
|
||
|
|
{
|
||
|
|
static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class _R1, class _R2, bool _Odd, intmax_t _Qp>
|
||
|
|
struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0>
|
||
|
|
{
|
||
|
|
static const bool value = false;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2>
|
||
|
|
struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2>
|
||
|
|
{
|
||
|
|
static const bool value = !_Odd;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1>
|
||
|
|
struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0>
|
||
|
|
{
|
||
|
|
static const bool value = _Odd;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1,
|
||
|
|
intmax_t _M2>
|
||
|
|
struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2>
|
||
|
|
{
|
||
|
|
static const bool value = __ratio_less1<ratio<_R1::den, _M1>,
|
||
|
|
ratio<_R2::den, _M2>, !_Odd>::value;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value,
|
||
|
|
intmax_t _S2 = __static_sign<_R2::num>::value>
|
||
|
|
struct __ratio_less
|
||
|
|
{
|
||
|
|
static const bool value = _S1 < _S2;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct __ratio_less<_R1, _R2, 1LL, 1LL>
|
||
|
|
{
|
||
|
|
static const bool value = __ratio_less1<_R1, _R2>::value;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct __ratio_less<_R1, _R2, -1LL, -1LL>
|
||
|
|
{
|
||
|
|
static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct _LIBCPP_TEMPLATE_VIS ratio_less
|
||
|
|
: public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {};
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct _LIBCPP_TEMPLATE_VIS ratio_less_equal
|
||
|
|
: public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {};
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct _LIBCPP_TEMPLATE_VIS ratio_greater
|
||
|
|
: public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {};
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal
|
||
|
|
: public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {};
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
struct __ratio_gcd
|
||
|
|
{
|
||
|
|
typedef ratio<__static_gcd<_R1::num, _R2::num>::value,
|
||
|
|
__static_lcm<_R1::den, _R2::den>::value> type;
|
||
|
|
};
|
||
|
|
|
||
|
|
#if _LIBCPP_STD_VER > 14 && !defined(_LIBCPP_HAS_NO_VARIABLE_TEMPLATES)
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_equal_v
|
||
|
|
= ratio_equal<_R1, _R2>::value;
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_not_equal_v
|
||
|
|
= ratio_not_equal<_R1, _R2>::value;
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_less_v
|
||
|
|
= ratio_less<_R1, _R2>::value;
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_less_equal_v
|
||
|
|
= ratio_less_equal<_R1, _R2>::value;
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_greater_v
|
||
|
|
= ratio_greater<_R1, _R2>::value;
|
||
|
|
|
||
|
|
template <class _R1, class _R2>
|
||
|
|
_LIBCPP_INLINE_VAR _LIBCPP_CONSTEXPR bool ratio_greater_equal_v
|
||
|
|
= ratio_greater_equal<_R1, _R2>::value;
|
||
|
|
#endif
|
||
|
|
|
||
|
|
_LIBCPP_END_NAMESPACE_STD
|
||
|
|
|
||
|
|
_LIBCPP_POP_MACROS
|
||
|
|
|
||
|
|
#endif // _LIBCPP_RATIO
|