STL/stl/inc/ratio

// ratio standard header (core)

// Copyright (c) Microsoft Corporation.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception

#pragma once
#ifndef _RATIO_
#define _RATIO_
#include <yvals_core.h>
#if _STL_COMPILER_PREPROCESSOR
#include <stdint.h>
#include <type_traits>

#pragma pack(push, _CRT_PACKING)
#pragma warning(push, _STL_WARNING_LEVEL)
#pragma warning(disable : _STL_DISABLED_WARNINGS)
_STL_DISABLE_CLANG_WARNINGS
#pragma push_macro("new")
#undef new

_STD_BEGIN
// STRUCT TEMPLATE _Abs
template <intmax_t _Val>
struct _Abs : integral_constant<intmax_t, (_Val < 0 ? -_Val : _Val)> { // computes absolute value of _Val
};

// STRUCT TEMPLATE _Safe_mult
template <intmax_t _Ax, intmax_t _Bx, bool _Sfinae = false,
    bool _Good = (_Abs<_Ax>::value <= INTMAX_MAX / (_Bx == 0 ? 1 : _Abs<_Bx>::value))>
struct _Safe_mult : integral_constant<intmax_t, _Ax * _Bx> { // computes _Ax * _Bx without overflow
};

template <intmax_t _Ax, intmax_t _Bx, bool _Sfinae>
struct _Safe_mult<_Ax, _Bx, _Sfinae, false> { // _Ax * _Bx would overflow
    static_assert(_Sfinae, "integer arithmetic overflow");
};

// STRUCT TEMPLATE _Sign_of
template <intmax_t _Val>
struct _Sign_of : integral_constant<intmax_t, (_Val < 0 ? -1 : 1)> { // computes sign of _Val
};

// STRUCT TEMPLATE _Safe_add
template <intmax_t _Ax, intmax_t _Bx, bool _Good, bool _Also_good>
struct _Safe_addX : integral_constant<intmax_t, _Ax + _Bx> { // computes _Ax + _Bx without overflow
};

template <intmax_t _Ax, intmax_t _Bx>
struct _Safe_addX<_Ax, _Bx, false, false> { // _Ax + _Bx would overflow
    static_assert(_Always_false<_Safe_addX>, "integer arithmetic overflow");
};

template <intmax_t _Ax, intmax_t _Bx>
struct _Safe_add
    : _Safe_addX<_Ax, _Bx, _Sign_of<_Ax>::value != _Sign_of<_Bx>::value,
          (_Abs<_Ax>::value <= INTMAX_MAX - _Abs<_Bx>::value)>::type { // computes _Ax + _Bx, forbids overflow
};

// STRUCT TEMPLATE _Gcd
template <intmax_t _Ax, intmax_t _Bx>
struct _GcdX : _GcdX<_Bx, _Ax % _Bx>::type { // computes greatest common divisor of _Ax and _Bx
};

template <intmax_t _Ax>
struct _GcdX<_Ax, 0> : integral_constant<intmax_t, _Ax> { // computes greatest common divisor of _Ax and 0
};

template <intmax_t _Ax, intmax_t _Bx>
struct _Gcd
    : _GcdX<_Abs<_Ax>::value, _Abs<_Bx>::value>::type { // computes greatest common divisor of abs(_Ax) and abs(_Bx)
};

template <>
struct _Gcd<0, 0> : integral_constant<intmax_t, 1> // contrary to mathematical convention
{ // avoids division by 0 in ratio_less
};

// STRUCT TEMPLATE ratio
template <intmax_t _Nx, intmax_t _Dx = 1>
struct ratio { // holds the ratio of _Nx to _Dx
    static_assert(_Dx != 0, "zero denominator");
    static_assert(-INTMAX_MAX <= _Nx, "numerator too negative");
    static_assert(-INTMAX_MAX <= _Dx, "denominator too negative");

    static constexpr intmax_t num =
        _Sign_of<_Nx>::value * _Sign_of<_Dx>::value * _Abs<_Nx>::value / _Gcd<_Nx, _Dx>::value;

    static constexpr intmax_t den = _Abs<_Dx>::value / _Gcd<_Nx, _Dx>::value;

    using type = ratio<num, den>;
};

// VARIABLE TEMPLATE _Is_ratio_v
template <class _Ty>
_INLINE_VAR constexpr bool _Is_ratio_v = false; // test for ratio type

template <intmax_t _R1, intmax_t _R2>
_INLINE_VAR constexpr bool _Is_ratio_v<ratio<_R1, _R2>> = true;

// ALIAS TEMPLATE ratio_add
template <class _R1, class _R2>
struct _Ratio_add { // add two ratios
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_add<R1, R2> requires R1 and R2 to be ratio<>s.");

    static constexpr intmax_t _N1 = _R1::num;
    static constexpr intmax_t _D1 = _R1::den;
    static constexpr intmax_t _N2 = _R2::num;
    static constexpr intmax_t _D2 = _R2::den;

    static constexpr intmax_t _Gx = _Gcd<_D1, _D2>::value;

    // typename ratio<>::type is necessary here
    using type = typename ratio<_Safe_add<_Safe_mult<_N1, _D2 / _Gx>::value, _Safe_mult<_N2, _D1 / _Gx>::value>::value,
        _Safe_mult<_D1, _D2 / _Gx>::value>::type;
};

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

// ALIAS TEMPLATE ratio_subtract
template <class _R1, class _R2>
struct _Ratio_subtract { // subtract two ratios
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_subtract<R1, R2> requires R1 and R2 to be ratio<>s.");

    static constexpr intmax_t _N2 = _R2::num;
    static constexpr intmax_t _D2 = _R2::den;

    using type = ratio_add<_R1, ratio<-_N2, _D2>>;
};

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

// ALIAS TEMPLATE ratio_multiply
template <class _R1, class _R2>
struct _Ratio_multiply { // multiply two ratios
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_multiply<R1, R2> requires R1 and R2 to be ratio<>s.");

    static constexpr intmax_t _N1 = _R1::num;
    static constexpr intmax_t _D1 = _R1::den;
    static constexpr intmax_t _N2 = _R2::num;
    static constexpr intmax_t _D2 = _R2::den;

    static constexpr intmax_t _Gx = _Gcd<_N1, _D2>::value;
    static constexpr intmax_t _Gy = _Gcd<_N2, _D1>::value;

    using _Num = _Safe_mult<_N1 / _Gx, _N2 / _Gy, true>;
    using _Den = _Safe_mult<_D1 / _Gy, _D2 / _Gx, true>;
};

template <class _R1, class _R2, bool _Sfinae = true, class = void>
struct _Ratio_multiply_sfinae { // detect overflow during multiplication
    static_assert(_Sfinae, "integer arithmetic overflow");
};

template <class _R1, class _R2, bool _Sfinae>
struct _Ratio_multiply_sfinae<_R1, _R2, _Sfinae,
    void_t<typename _Ratio_multiply<_R1, _R2>::_Num::type,
        typename _Ratio_multiply<_R1, _R2>::_Den::type>> { // typename ratio<>::type is unnecessary here
    using type = ratio<_Ratio_multiply<_R1, _R2>::_Num::value, _Ratio_multiply<_R1, _R2>::_Den::value>;
};

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

// ALIAS TEMPLATE ratio_divide
template <class _R1, class _R2>
struct _Ratio_divide { // divide two ratios
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_divide<R1, R2> requires R1 and R2 to be ratio<>s.");

    static constexpr intmax_t _N2 = _R2::num;
    static constexpr intmax_t _D2 = _R2::den;

    using _R2_inverse = ratio<_D2, _N2>;
};

template <class _R1, class _R2, bool _Sfinae = true>
using _Ratio_divide_sfinae =
    typename _Ratio_multiply_sfinae<_R1, typename _Ratio_divide<_R1, _R2>::_R2_inverse, _Sfinae>::type;

template <class _R1, class _R2>
using ratio_divide = _Ratio_divide_sfinae<_R1, _R2, false>;

// STRUCT TEMPLATE ratio_equal
template <class _R1, class _R2>
struct ratio_equal : bool_constant<_R1::num == _R2::num && _R1::den == _R2::den> { // tests if ratio == ratio
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_equal<R1, R2> requires R1 and R2 to be ratio<>s.");
};

template <class _R1, class _R2>
_INLINE_VAR constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value;

// STRUCT TEMPLATE ratio_not_equal
template <class _R1, class _R2>
struct ratio_not_equal : bool_constant<!ratio_equal_v<_R1, _R2>> { // tests if ratio != ratio
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_not_equal<R1, R2> requires R1 and R2 to be ratio<>s.");
};

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

// STRUCT TEMPLATE ratio_less
struct _Big_uint128 {
    uint64_t _Upper;
    uint64_t _Lower;

    constexpr bool operator<(const _Big_uint128 _Rhs) const noexcept {
        if (_Upper != _Rhs._Upper) {
            return _Upper < _Rhs._Upper;
        }

        return _Lower < _Rhs._Lower;
    }
};

constexpr _Big_uint128 _Big_multiply(const uint64_t _Lfactor,
    const uint64_t _Rfactor) noexcept { // multiply two 64-bit integers into a 128-bit integer, Knuth's algorithm M
    const uint64_t _Llow  = _Lfactor & 0xFFFF'FFFFULL;
    const uint64_t _Lhigh = _Lfactor >> 32;
    const uint64_t _Rlow  = _Rfactor & 0xFFFF'FFFFULL;
    const uint64_t _Rhigh = _Rfactor >> 32;

    uint64_t _Temp          = _Llow * _Rlow;
    const uint64_t _Lower32 = _Temp & 0xFFFF'FFFFULL;
    uint64_t _Carry         = _Temp >> 32;

    _Temp                     = _Llow * _Rhigh + _Carry;
    const uint64_t _Mid_lower = _Temp & 0xFFFF'FFFFULL;
    const uint64_t _Mid_upper = _Temp >> 32;

    _Temp  = _Lhigh * _Rlow + _Mid_lower;
    _Carry = _Temp >> 32;

    return {_Lhigh * _Rhigh + _Mid_upper + _Carry, (_Temp << 32) + _Lower32};
}

constexpr bool _Ratio_less(const int64_t _N1, const int64_t _D1, const int64_t _N2, const int64_t _D2) noexcept {
    if (_N1 >= 0 && _N2 >= 0) {
        return _Big_multiply(static_cast<uint64_t>(_N1), static_cast<uint64_t>(_D2))
               < _Big_multiply(static_cast<uint64_t>(_N2), static_cast<uint64_t>(_D1));
    }

    if (_N1 < 0 && _N2 < 0) {
        return _Big_multiply(static_cast<uint64_t>(-_N2), static_cast<uint64_t>(_D1))
               < _Big_multiply(static_cast<uint64_t>(-_N1), static_cast<uint64_t>(_D2));
    }

    return _N1 < _N2;
}

template <class _R1, class _R2>
struct ratio_less : bool_constant<_Ratio_less(_R1::num, _R1::den, _R2::num, _R2::den)> { // tests if ratio < ratio
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_less<R1, R2> requires R1 and R2 to be ratio<>s.");
};

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

// STRUCT TEMPLATE ratio_less_equal
template <class _R1, class _R2>
struct ratio_less_equal : bool_constant<!ratio_less_v<_R2, _R1>> { // tests if ratio <= ratio
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_less_equal<R1, R2> requires R1 and R2 to be ratio<>s.");
};

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

// STRUCT TEMPLATE ratio_greater
template <class _R1, class _R2>
struct ratio_greater : ratio_less<_R2, _R1>::type { // tests if ratio > ratio
    static_assert(_Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_greater<R1, R2> requires R1 and R2 to be ratio<>s.");
};

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

// STRUCT TEMPLATE ratio_greater_equal
template <class _R1, class _R2>
struct ratio_greater_equal : bool_constant<!ratio_less_v<_R1, _R2>> { // tests if ratio >= ratio
    static_assert(
        _Is_ratio_v<_R1> && _Is_ratio_v<_R2>, "ratio_greater_equal<R1, R2> requires R1 and R2 to be ratio<>s.");
};

template <class _R1, class _R2>
_INLINE_VAR constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value;

// SI TYPEDEFS
using atto  = ratio<1, 1000000000000000000LL>;
using femto = ratio<1, 1000000000000000LL>;
using pico  = ratio<1, 1000000000000LL>;
using nano  = ratio<1, 1000000000>;
using micro = ratio<1, 1000000>;
using milli = ratio<1, 1000>;
using centi = ratio<1, 100>;
using deci  = ratio<1, 10>;
using deca  = ratio<10, 1>;
using hecto = ratio<100, 1>;
using kilo  = ratio<1000, 1>;
using mega  = ratio<1000000, 1>;
using giga  = ratio<1000000000, 1>;
using tera  = ratio<1000000000000LL, 1>;
using peta  = ratio<1000000000000000LL, 1>;
using exa   = ratio<1000000000000000000LL, 1>;
_STD_END
#pragma pop_macro("new")
_STL_RESTORE_CLANG_WARNINGS
#pragma warning(pop)
#pragma pack(pop)
#endif // _STL_COMPILER_PREPROCESSOR
#endif // _RATIO_