LCOM1920-T02G10

// -*- 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

}

*/

#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;

};

_LIBCPP_END_NAMESPACE_STD

#endif  // _LIBCPP_RATIO