#ifndef _LIBCPP_RATIO
#define _LIBCPP_RATIO
#include <__config>
#include <__type_traits/integral_constant.h>
#include <climits>
#include <cstdint>
#include <version>
#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
# pragma GCC system_header
#endif
_LIBCPP_PUSH_MACROS
#include <__undef_macros>
_LIBCPP_BEGIN_NAMESPACE_STD
template <intmax_t _Xp, intmax_t _Yp>
struct __static_gcd { … };
__static_gcd<_Xp, 0>;
template <>
struct __static_gcd<0, 0> { … };
template <intmax_t _Xp, intmax_t _Yp>
struct __static_lcm { … };
template <intmax_t _Xp>
struct __static_abs { … };
template <intmax_t _Xp>
struct __static_sign { … };
template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
class __ll_add;
__ll_add<_Xp, _Yp, 1>;
__ll_add<_Xp, _Yp, 0>;
__ll_add<_Xp, _Yp, -1>;
template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value>
class __ll_sub;
__ll_sub<_Xp, _Yp, 1>;
__ll_sub<_Xp, _Yp, 0>;
__ll_sub<_Xp, _Yp, -1>;
template <intmax_t _Xp, intmax_t _Yp>
class __ll_mul { … };
__ll_mul<0, _Yp>;
__ll_mul<_Xp, 0>;
template <>
class __ll_mul<0, 0> { … };
template <intmax_t _Xp, intmax_t _Yp>
class __ll_div { … };
template <intmax_t _Num, intmax_t _Den = 1>
class _LIBCPP_TEMPLATE_VIS ratio { … };
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 { … };
__is_ratio<ratio<_Num, _Den>>;
atto;
femto;
pico;
nano;
micro;
milli;
centi;
deci;
deca;
hecto;
kilo;
mega;
giga;
tera;
peta;
exa;
template <class _R1, class _R2>
struct __ratio_multiply { … };
#ifndef _LIBCPP_CXX03_LANG
ratio_multiply;
#else
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_multiply : public __ratio_multiply<_R1, _R2>::type {};
#endif
template <class _R1, class _R2>
struct __ratio_divide { … };
#ifndef _LIBCPP_CXX03_LANG
ratio_divide;
#else
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_divide : public __ratio_divide<_R1, _R2>::type {};
#endif
template <class _R1, class _R2>
struct __ratio_add { … };
#ifndef _LIBCPP_CXX03_LANG
ratio_add;
#else
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_add : public __ratio_add<_R1, _R2>::type {};
#endif
template <class _R1, class _R2>
struct __ratio_subtract { … };
#ifndef _LIBCPP_CXX03_LANG
ratio_subtract;
#else
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_subtract : public __ratio_subtract<_R1, _R2>::type {};
#endif
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_equal : _BoolConstant<(_R1::num == _R2::num && _R1::den == _R2::den)> { … };
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_not_equal : _BoolConstant<!ratio_equal<_R1, _R2>::value> { … };
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 { … };
__ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0>;
__ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2>;
__ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0>;
__ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2>;
template <class _R1,
class _R2,
intmax_t _S1 = __static_sign<_R1::num>::value,
intmax_t _S2 = __static_sign<_R2::num>::value>
struct __ratio_less { … };
__ratio_less<_R1, _R2, 1LL, 1LL>;
__ratio_less<_R1, _R2, -1LL, -1LL>;
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_less : _BoolConstant<__ratio_less<_R1, _R2>::value> { … };
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_less_equal : _BoolConstant<!ratio_less<_R2, _R1>::value> { … };
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_greater : _BoolConstant<ratio_less<_R2, _R1>::value> { … };
template <class _R1, class _R2>
struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal : _BoolConstant<!ratio_less<_R1, _R2>::value> { … };
template <class _R1, class _R2>
struct __ratio_gcd { … };
#if _LIBCPP_STD_VER >= 17
ratio_equal_v;
ratio_not_equal_v;
ratio_less_v;
ratio_less_equal_v;
ratio_greater_v;
ratio_greater_equal_v;
#endif
_LIBCPP_END_NAMESPACE_STD
_LIBCPP_POP_MACROS
#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20
# include <type_traits>
#endif
#endif