| // -*- C++ -*- |
| //===---------------------------- ratio -----------------------------------===// |
| // |
| // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| // See https://llvm.org/LICENSE.txt for license information. |
| // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| // |
| //===----------------------------------------------------------------------===// |
| |
| #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> inline constexpr bool ratio_equal_v |
| = ratio_equal<R1, R2>::value; // C++17 |
| template <class R1, class R2> inline constexpr bool ratio_not_equal_v |
| = ratio_not_equal<R1, R2>::value; // C++17 |
| template <class R1, class R2> inline constexpr bool ratio_less_v |
| = ratio_less<R1, R2>::value; // C++17 |
| template <class R1, class R2> inline constexpr bool ratio_less_equal_v |
| = ratio_less_equal<R1, R2>::value; // C++17 |
| template <class R1, class R2> inline constexpr bool ratio_greater_v |
| = ratio_greater<R1, R2>::value; // C++17 |
| template <class R1, class R2> inline constexpr bool ratio_greater_equal_v |
| = ratio_greater_equal<R1, R2>::value; // C++17 |
| } |
| */ |
| |
| #include <__config> |
| #include <climits> |
| #include <cstdint> |
| #include <type_traits> |
| |
| #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) |
| #pragma GCC system_header |
| #endif |
| |
| _LIBCPP_PUSH_MACROS |
| #include <__undef_macros> |
| |
| |
| _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_TEMPLATE_VIS 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_CXX03_LANG |
| |
| template <class _R1, class _R2> using ratio_multiply |
| = typename __ratio_multiply<_R1, _R2>::type; |
| |
| #else // _LIBCPP_CXX03_LANG |
| |
| template <class _R1, class _R2> |
| struct _LIBCPP_TEMPLATE_VIS ratio_multiply |
| : public __ratio_multiply<_R1, _R2>::type {}; |
| |
| #endif // _LIBCPP_CXX03_LANG |
| |
| 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_CXX03_LANG |
| |
| template <class _R1, class _R2> using ratio_divide |
| = typename __ratio_divide<_R1, _R2>::type; |
| |
| #else // _LIBCPP_CXX03_LANG |
| |
| template <class _R1, class _R2> |
| struct _LIBCPP_TEMPLATE_VIS ratio_divide |
| : public __ratio_divide<_R1, _R2>::type {}; |
| |
| #endif // _LIBCPP_CXX03_LANG |
| |
| 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_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 |
| template <class _R1, class _R2> |
| inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value; |
| |
| template <class _R1, class _R2> |
| inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value; |
| |
| template <class _R1, class _R2> |
| inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value; |
| |
| template <class _R1, class _R2> |
| inline constexpr bool ratio_less_equal_v = ratio_less_equal<_R1, _R2>::value; |
| |
| template <class _R1, class _R2> |
| inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value; |
| |
| template <class _R1, class _R2> |
| inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value; |
| #endif |
| |
| _LIBCPP_END_NAMESPACE_STD |
| |
| _LIBCPP_POP_MACROS |
| |
| #endif // _LIBCPP_RATIO |