include/ratio - LeafOS-Project/android_external_libcxx - Gitiles

 // -*- C++ -*-
 //===---------------------------- ratio -----------------------------------===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is dual licensed under the MIT and the University of Illinois Open
 // Source Licenses. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//

 #ifndef _LIBCPP_RATIO
 #define _LIBCPP_RATIO

 /*
     ratio synopsis

 namespace std
 {

 template <intmax_t N, intmax_t D = 1>
 class ratio
 {
 public:
     static constexpr intmax_t num;
     static constexpr intmax_t den;
     typedef ratio<num, den> type;
 };

 // ratio arithmetic
 template <class R1, class R2> using ratio_add = ...;
 template <class R1, class R2> using ratio_subtract = ...;
 template <class R1, class R2> using ratio_multiply = ...;
 template <class R1, class R2> using ratio_divide = ...;

 // ratio comparison
 template <class R1, class R2> struct ratio_equal;
 template <class R1, class R2> struct ratio_not_equal;
 template <class R1, class R2> struct ratio_less;
 template <class R1, class R2> struct ratio_less_equal;
 template <class R1, class R2> struct ratio_greater;
 template <class R1, class R2> struct ratio_greater_equal;

 // convenience SI typedefs
 typedef ratio<1, 1000000000000000000000000> yocto;  // not supported
 typedef ratio<1,    1000000000000000000000> zepto;  // not supported
 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;
 typedef ratio<   1000000000000000000000, 1> zetta;  // not supported
 typedef ratio<1000000000000000000000000, 1> yotta;  // not supported

   // 20.11.5, ratio comparison
   template <class R1, class R2> constexpr bool ratio_equal_v
     = ratio_equal<R1, R2>::value;                                       // C++17
   template <class R1, class R2> constexpr bool ratio_not_equal_v
     = ratio_not_equal<R1, R2>::value;                                   // C++17
   template <class R1, class R2> constexpr bool ratio_less_v
     = ratio_less<R1, R2>::value;                                        // C++17
   template <class R1, class R2> constexpr bool ratio_less_equal_v
     = ratio_less_equal<R1, R2>::value;                                  // C++17
   template <class R1, class R2> constexpr bool ratio_greater_v
     = ratio_greater<R1, R2>::value;                                     // C++17
   template <class R1, class R2> constexpr bool ratio_greater_equal_v
     = ratio_greater_equal<R1, R2>::value;                               // C++17
 }
 */

 #include <__config>
 #include <cstdint>
 #include <climits>
 #include <type_traits>

 #include <__undef_min_max>

 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif

 _LIBCPP_BEGIN_NAMESPACE_STD

 // __static_gcd

 template <intmax_t _Xp, intmax_t _Yp>
 struct __static_gcd
 {
     static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value;
 };

 template <intmax_t _Xp>
 struct __static_gcd<_Xp, 0>
 {
     static const intmax_t value = _Xp;
 };

 template <>
 struct __static_gcd<0, 0>
 {
     static const intmax_t value = 1;
 };

 // __static_lcm

 template <intmax_t _Xp, intmax_t _Yp>
 struct __static_lcm
 {
     static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp;
 };

 template <intmax_t _Xp>
 struct __static_abs
 {
     static const intmax_t value = _Xp < 0 ? -_Xp : _Xp;
 };

 template <intmax_t _Xp>
 struct __static_sign
 {
     static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1);
 };

 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
 class __ll_add;

 template <intmax_t _Xp, intmax_t _Yp>
 class __ll_add<_Xp, _Yp, 1>
 {
     static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
     static const intmax_t max = -min;

     static_assert(_Xp <= max - _Yp, "overflow in __ll_add");
 public:
     static const intmax_t value = _Xp + _Yp;
 };

 template <intmax_t _Xp, intmax_t _Yp>
 class __ll_add<_Xp, _Yp, 0>
 {
 public:
     static const intmax_t value = _Xp;
 };

 template <intmax_t _Xp, intmax_t _Yp>
 class __ll_add<_Xp, _Yp, -1>
 {
     static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
     static const intmax_t max = -min;

     static_assert(min - _Yp <= _Xp, "overflow in __ll_add");
 public:
     static const intmax_t value = _Xp + _Yp;
 };

 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
 class __ll_sub;

 template <intmax_t _Xp, intmax_t _Yp>
 class __ll_sub<_Xp, _Yp, 1>
 {
     static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
     static const intmax_t max = -min;

     static_assert(min + _Yp <= _Xp, "overflow in __ll_sub");
 public:
     static const intmax_t value = _Xp - _Yp;
 };

 template <intmax_t _Xp, intmax_t _Yp>
 class __ll_sub<_Xp, _Yp, 0>
 {
 public:
     static const intmax_t value = _Xp;
 };

 template <intmax_t _Xp, intmax_t _Yp>
 class __ll_sub<_Xp, _Yp, -1>
 {
     static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
     static const intmax_t max = -min;

     static_assert(_Xp <= max + _Yp, "overflow in __ll_sub");
 public:
     static const intmax_t value = _Xp - _Yp;
 };

 template <intmax_t _Xp, intmax_t _Yp>
 class __ll_mul
 {
     static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
     static const intmax_t min = nan + 1;
     static const intmax_t max = -min;
     static const intmax_t __a_x = __static_abs<_Xp>::value;
     static const intmax_t __a_y = __static_abs<_Yp>::value;

     static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul");
 public:
     static const intmax_t value = _Xp * _Yp;
 };

 template <intmax_t _Yp>
 class __ll_mul<0, _Yp>
 {
 public:
     static const intmax_t value = 0;
 };

 template <intmax_t _Xp>
 class __ll_mul<_Xp, 0>
 {
 public:
     static const intmax_t value = 0;
 };

 template <>
 class __ll_mul<0, 0>
 {
 public:
     static const intmax_t value = 0;
 };

 // Not actually used but left here in case needed in future maintenance
 template <intmax_t _Xp, intmax_t _Yp>
 class __ll_div
 {
     static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
     static const intmax_t min = nan + 1;
     static const intmax_t max = -min;

     static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div");
 public:
     static const intmax_t value = _Xp / _Yp;
 };

 template <intmax_t _Num, intmax_t _Den = 1>
 class _LIBCPP_TYPE_VIS_ONLY ratio
 {
     static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range");
     static_assert(_Den != 0, "ratio divide by 0");
     static_assert(__static_abs<_Den>::value >  0, "ratio denominator is out of range");
     static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value;
     static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value;
     static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value;
     static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value;
 public:
     static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd;
     static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd;

     typedef ratio<num, den> type;
 };

 template <intmax_t _Num, intmax_t _Den>
 _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num;

 template <intmax_t _Num, intmax_t _Den>
 _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den;

 template <class _Tp>                    struct __is_ratio                     : false_type {};
 template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type  {};

 typedef ratio<1LL, 1000000000000000000LL> atto;
 typedef ratio<1LL,    1000000000000000LL> femto;
 typedef ratio<1LL,       1000000000000LL> pico;
 typedef ratio<1LL,          1000000000LL> nano;
 typedef ratio<1LL,             1000000LL> micro;
 typedef ratio<1LL,                1000LL> milli;
 typedef ratio<1LL,                 100LL> centi;
 typedef ratio<1LL,                  10LL> deci;
 typedef ratio<                 10LL, 1LL> deca;
 typedef ratio<                100LL, 1LL> hecto;
 typedef ratio<               1000LL, 1LL> kilo;
 typedef ratio<            1000000LL, 1LL> mega;
 typedef ratio<         1000000000LL, 1LL> giga;
 typedef ratio<      1000000000000LL, 1LL> tera;
 typedef ratio<   1000000000000000LL, 1LL> peta;
 typedef ratio<1000000000000000000LL, 1LL> exa;

 template <class _R1, class _R2>
 struct __ratio_multiply
 {
 private:
     static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value;
     static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value;
 public:
     typedef typename ratio
         <
             __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value,
             __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value
         >::type type;
 };

 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2> using ratio_multiply
                                     = typename __ratio_multiply<_R1, _R2>::type;

 #else  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY ratio_multiply
     : public __ratio_multiply<_R1, _R2>::type {};

 #endif  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2>
 struct __ratio_divide
 {
 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
         <
             __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
         >::type type;
 };

 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2> using ratio_divide
                                       = typename __ratio_divide<_R1, _R2>::type;

 #else  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY ratio_divide
     : public __ratio_divide<_R1, _R2>::type {};

 #endif  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2>
 struct __ratio_add
 {
 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_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_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2> using ratio_add
                                          = typename __ratio_add<_R1, _R2>::type;

 #else  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY ratio_add
     : public __ratio_add<_R1, _R2>::type {};

 #endif  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 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_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2> using ratio_subtract
                                     = typename __ratio_subtract<_R1, _R2>::type;

 #else  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY ratio_subtract
     : public __ratio_subtract<_R1, _R2>::type {};

 #endif  // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

 // ratio_equal

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY ratio_equal
     : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {};

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY 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_TYPE_VIS_ONLY ratio_less
     : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {};

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY ratio_less_equal
     : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {};

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY ratio_greater
     : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {};

 template <class _R1, class _R2>
 struct _LIBCPP_TYPE_VIS_ONLY 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_CONSTEXPR bool ratio_equal_v
     = ratio_equal<_R1, _R2>::value;

 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_not_equal_v
     = ratio_not_equal<_R1, _R2>::value;

 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_v
     = ratio_less<_R1, _R2>::value;

 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_equal_v
     = ratio_less_equal<_R1, _R2>::value;

 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_v
     = ratio_greater<_R1, _R2>::value;

 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_equal_v
     = ratio_greater_equal<_R1, _R2>::value;
 #endif

 _LIBCPP_END_NAMESPACE_STD

 #endif  // _LIBCPP_RATIO
	// -- C++ --
	//===---------------------------- ratio -----------------------------------===//
	//
	// The LLVM Compiler Infrastructure
	//
	// This file is dual licensed under the MIT and the University of Illinois Open
	// Source Licenses. See LICENSE.TXT for details.
	//
	//===----------------------------------------------------------------------===//

	#ifndef _LIBCPP_RATIO
	#define _LIBCPP_RATIO

	/*
	ratio synopsis

	namespace std
	{

	template <intmax_t N, intmax_t D = 1>
	class ratio
	{
	public:
	static constexpr intmax_t num;
	static constexpr intmax_t den;
	typedef ratio<num, den> type;
	};

	// ratio arithmetic
	template <class R1, class R2> using ratio_add = ...;
	template <class R1, class R2> using ratio_subtract = ...;
	template <class R1, class R2> using ratio_multiply = ...;
	template <class R1, class R2> using ratio_divide = ...;

	// ratio comparison
	template <class R1, class R2> struct ratio_equal;
	template <class R1, class R2> struct ratio_not_equal;
	template <class R1, class R2> struct ratio_less;
	template <class R1, class R2> struct ratio_less_equal;
	template <class R1, class R2> struct ratio_greater;
	template <class R1, class R2> struct ratio_greater_equal;

	// convenience SI typedefs
	typedef ratio<1, 1000000000000000000000000> yocto; // not supported
	typedef ratio<1, 1000000000000000000000> zepto; // not supported
	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;
	typedef ratio< 1000000000000000000000, 1> zetta; // not supported
	typedef ratio<1000000000000000000000000, 1> yotta; // not supported

	// 20.11.5, ratio comparison
	template <class R1, class R2> constexpr bool ratio_equal_v
	= ratio_equal<R1, R2>::value; // C++17
	template <class R1, class R2> constexpr bool ratio_not_equal_v
	= ratio_not_equal<R1, R2>::value; // C++17
	template <class R1, class R2> constexpr bool ratio_less_v
	= ratio_less<R1, R2>::value; // C++17
	template <class R1, class R2> constexpr bool ratio_less_equal_v
	= ratio_less_equal<R1, R2>::value; // C++17
	template <class R1, class R2> constexpr bool ratio_greater_v
	= ratio_greater<R1, R2>::value; // C++17
	template <class R1, class R2> constexpr bool ratio_greater_equal_v
	= ratio_greater_equal<R1, R2>::value; // C++17
	}
	*/

	#include <__config>
	#include <cstdint>
	#include <climits>
	#include <type_traits>

	#include <__undef_min_max>

	#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
	#pragma GCC system_header
	#endif

	_LIBCPP_BEGIN_NAMESPACE_STD

	// __static_gcd

	template <intmax_t _Xp, intmax_t _Yp>
	struct __static_gcd
	{
	static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value;
	};

	template <intmax_t _Xp>
	struct __static_gcd<_Xp, 0>
	{
	static const intmax_t value = _Xp;
	};

	template <>
	struct __static_gcd<0, 0>
	{
	static const intmax_t value = 1;
	};

	// __static_lcm

	template <intmax_t _Xp, intmax_t _Yp>
	struct __static_lcm
	{
	static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp;
	};

	template <intmax_t _Xp>
	struct __static_abs
	{
	static const intmax_t value = _Xp < 0 ? -_Xp : _Xp;
	};

	template <intmax_t _Xp>
	struct __static_sign
	{
	static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1);
	};

	template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
	class __ll_add;

	template <intmax_t _Xp, intmax_t _Yp>
	class __ll_add<_Xp, _Yp, 1>
	{
	static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
	static const intmax_t max = -min;

	static_assert(_Xp <= max - _Yp, "overflow in __ll_add");
	public:
	static const intmax_t value = _Xp + _Yp;
	};

	template <intmax_t _Xp, intmax_t _Yp>
	class __ll_add<_Xp, _Yp, 0>
	{
	public:
	static const intmax_t value = _Xp;
	};

	template <intmax_t _Xp, intmax_t _Yp>
	class __ll_add<_Xp, _Yp, -1>
	{
	static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
	static const intmax_t max = -min;

	static_assert(min - _Yp <= _Xp, "overflow in __ll_add");
	public:
	static const intmax_t value = _Xp + _Yp;
	};

	template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
	class __ll_sub;

	template <intmax_t _Xp, intmax_t _Yp>
	class __ll_sub<_Xp, _Yp, 1>
	{
	static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
	static const intmax_t max = -min;

	static_assert(min + _Yp <= _Xp, "overflow in __ll_sub");
	public:
	static const intmax_t value = _Xp - _Yp;
	};

	template <intmax_t _Xp, intmax_t _Yp>
	class __ll_sub<_Xp, _Yp, 0>
	{
	public:
	static const intmax_t value = _Xp;
	};

	template <intmax_t _Xp, intmax_t _Yp>
	class __ll_sub<_Xp, _Yp, -1>
	{
	static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
	static const intmax_t max = -min;

	static_assert(_Xp <= max + _Yp, "overflow in __ll_sub");
	public:
	static const intmax_t value = _Xp - _Yp;
	};

	template <intmax_t _Xp, intmax_t _Yp>
	class __ll_mul
	{
	static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
	static const intmax_t min = nan + 1;
	static const intmax_t max = -min;
	static const intmax_t __a_x = __static_abs<_Xp>::value;
	static const intmax_t __a_y = __static_abs<_Yp>::value;

	static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul");
	public:
	static const intmax_t value = _Xp * _Yp;
	};

	template <intmax_t _Yp>
	class __ll_mul<0, _Yp>
	{
	public:
	static const intmax_t value = 0;
	};

	template <intmax_t _Xp>
	class __ll_mul<_Xp, 0>
	{
	public:
	static const intmax_t value = 0;
	};

	template <>
	class __ll_mul<0, 0>
	{
	public:
	static const intmax_t value = 0;
	};

	// Not actually used but left here in case needed in future maintenance
	template <intmax_t _Xp, intmax_t _Yp>
	class __ll_div
	{
	static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
	static const intmax_t min = nan + 1;
	static const intmax_t max = -min;

	static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div");
	public:
	static const intmax_t value = _Xp / _Yp;
	};

	template <intmax_t _Num, intmax_t _Den = 1>
	class _LIBCPP_TYPE_VIS_ONLY ratio
	{
	static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range");
	static_assert(_Den != 0, "ratio divide by 0");
	static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range");
	static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value;
	static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value;
	static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value;
	static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value;
	public:
	static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd;
	static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd;

	typedef ratio<num, den> type;
	};

	template <intmax_t _Num, intmax_t _Den>
	_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num;

	template <intmax_t _Num, intmax_t _Den>
	_LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den;

	template <class _Tp> struct __is_ratio : false_type {};
	template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {};

	typedef ratio<1LL, 1000000000000000000LL> atto;
	typedef ratio<1LL, 1000000000000000LL> femto;
	typedef ratio<1LL, 1000000000000LL> pico;
	typedef ratio<1LL, 1000000000LL> nano;
	typedef ratio<1LL, 1000000LL> micro;
	typedef ratio<1LL, 1000LL> milli;
	typedef ratio<1LL, 100LL> centi;
	typedef ratio<1LL, 10LL> deci;
	typedef ratio< 10LL, 1LL> deca;
	typedef ratio< 100LL, 1LL> hecto;
	typedef ratio< 1000LL, 1LL> kilo;
	typedef ratio< 1000000LL, 1LL> mega;
	typedef ratio< 1000000000LL, 1LL> giga;
	typedef ratio< 1000000000000LL, 1LL> tera;
	typedef ratio< 1000000000000000LL, 1LL> peta;
	typedef ratio<1000000000000000000LL, 1LL> exa;

	template <class _R1, class _R2>
	struct __ratio_multiply
	{
	private:
	static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value;
	static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value;
	public:
	typedef typename ratio
	<
	__ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value,
	__ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value
	>::type type;
	};

	#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2> using ratio_multiply
	= typename __ratio_multiply<_R1, _R2>::type;

	#else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY ratio_multiply
	: public __ratio_multiply<_R1, _R2>::type {};

	#endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2>
	struct __ratio_divide
	{
	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
	<
	__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
	>::type type;
	};

	#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2> using ratio_divide
	= typename __ratio_divide<_R1, _R2>::type;

	#else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY ratio_divide
	: public __ratio_divide<_R1, _R2>::type {};

	#endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2>
	struct __ratio_add
	{
	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_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_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2> using ratio_add
	= typename __ratio_add<_R1, _R2>::type;

	#else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY ratio_add
	: public __ratio_add<_R1, _R2>::type {};

	#endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	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_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2> using ratio_subtract
	= typename __ratio_subtract<_R1, _R2>::type;

	#else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY ratio_subtract
	: public __ratio_subtract<_R1, _R2>::type {};

	#endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES

	// ratio_equal

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY ratio_equal
	: public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {};

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY 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_TYPE_VIS_ONLY ratio_less
	: public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {};

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY ratio_less_equal
	: public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {};

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY ratio_greater
	: public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {};

	template <class _R1, class _R2>
	struct _LIBCPP_TYPE_VIS_ONLY 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_CONSTEXPR bool ratio_equal_v
	= ratio_equal<_R1, _R2>::value;

	template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_not_equal_v
	= ratio_not_equal<_R1, _R2>::value;

	template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_v
	= ratio_less<_R1, _R2>::value;

	template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_equal_v
	= ratio_less_equal<_R1, _R2>::value;

	template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_v
	= ratio_greater<_R1, _R2>::value;

	template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_equal_v
	= ratio_greater_equal<_R1, _R2>::value;
	#endif

	_LIBCPP_END_NAMESPACE_STD

	#endif // _LIBCPP_RATIO