rational.h

Go to the documentation of this file.

 
/*
Copyright (c) 2026 MrXie1109
 
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
 
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
 
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
 
#pragma once
#include <cmath>
#include <cstdint>
#include <cstdlib>
#include <iostream>
#include <ostream>
#include <type_traits>
 
#include "../core/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 DomainError("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 DomainError("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);
        }

        template <class CharT, class Traits>
        friend std::basic_ostream<CharT, Traits> &operator<<(
            std::basic_ostream<CharT, Traits> &os, const BasicRational &r) {
            os << intmax_t(r.num);
            if (r.den != 1) os << '/' << intmax_t(r.den);
            return os;
        }

        template <class CharT, class Traits>
        friend std::basic_istream<CharT, Traits> &
        operator>>(std::basic_istream<CharT, Traits> &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>;  
}