rational.h

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/*
Copyright (c) 2026 MrXie1109
 
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#pragma once
#include <cstdint>
#include <cmath>
#include <cstdlib>
#include <iostream>
#include <type_traits>
#include "csexc.h"
 
namespace console
{
    template <class T>
    class BasicRational
    {
        static_assert(std::is_integral<T>::value &&
                          std::is_signed<T>::value,
                      "T must be signed integral type"); 
 
        T num; 
        T den; 

        static T gcd(T a, T b)
        {
            a = std::abs(a);
            b = std::abs(b);
            while (b != 0)
            {
                T temp = b;
                b = a % b;
                a = temp;
            }
            return a;
        }

        void reduce()
        {
            if (den == 0)
            {
                throw domain_error("Denominator cannot be zero");
            }
            if (den < 0)
            {
                num = -num;
                den = -den;
            }
            T g = gcd(num, den);
            num /= g;
            den /= g;
        }
 
    public:
        constexpr BasicRational() : num(0), den(1) {}

        constexpr BasicRational(T n) : num(n), den(1) {}

        BasicRational(T n, T d) : num(n), den(d) { reduce(); }

        T numerator() const { return num; }

        T denominator() const { return den; }

        template <class U>
        explicit operator U() const { return U(num) / den; }

        friend BasicRational operator+(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return BasicRational(lhs.num * rhs.den + rhs.num * lhs.den,
                                 lhs.den * rhs.den);
        }

        friend BasicRational operator-(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return BasicRational(lhs.num * rhs.den - rhs.num * lhs.den,
                                 lhs.den * rhs.den);
        }

        friend BasicRational operator*(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return BasicRational(lhs.num * rhs.num, lhs.den * rhs.den);
        }

        friend BasicRational operator/(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            if (rhs.num == 0)
                throw domain_error("Division by zero");
            return BasicRational(lhs.num * rhs.den, lhs.den * rhs.num);
        }

        BasicRational &operator+=(const BasicRational &other)
        {
            *this = *this + other;
            return *this;
        }

        BasicRational &operator-=(const BasicRational &other)
        {
            *this = *this - other;
            return *this;
        }

        BasicRational &operator*=(const BasicRational &other)
        {
            *this = *this * other;
            return *this;
        }

        BasicRational &operator/=(const BasicRational &other)
        {
            *this = *this / other;
            return *this;
        }

        BasicRational operator-() const { return BasicRational(-num, den); }

        BasicRational operator+() const { return *this; }

        friend bool operator==(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return lhs.num == rhs.num && lhs.den == rhs.den;
        }

        friend bool operator!=(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return !(lhs == rhs);
        }

        friend bool operator<(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return lhs.num * rhs.den < rhs.num * lhs.den;
        }

        friend bool operator>(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return rhs < lhs;
        }

        friend bool operator<=(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return !(lhs > rhs);
        }

        friend bool operator>=(
            const BasicRational &lhs, const BasicRational &rhs)
        {
            return !(lhs < rhs);
        }

        friend std::ostream &operator<<(std::ostream &os, const BasicRational &r)
        {
            os << intmax_t(r.num);
            if (r.den != 1)
                os << '/' << intmax_t(r.den);
            return os;
        }

        friend std::istream &operator>>(std::istream &is, BasicRational &r)
        {
            intmax_t n, d;
            char slash;
            is >> n;
            if (is >> std::ws, is.peek() == '/')
            {
                is >> slash >> d;
                r = BasicRational(intmax_t(n), intmax_t(d));
            }
            else
                r = BasicRational(intmax_t(n));
            return is;
        }
    };
 
    using Rational = BasicRational<intmax_t>;   
    using Rational_8 = BasicRational<int8_t>;   
    using Rational_16 = BasicRational<int16_t>; 
    using Rational_32 = BasicRational<int32_t>; 
    using Rational_64 = BasicRational<int64_t>; 
}