CircleFraction.cs

using System;

namespace RT.Coordinates
{
    /// <summary>Encapsulates a rational number between 0 and 1 that represents a fraction of a circle.</summary>
    public struct CircleFraction : IEquatable<CircleFraction>, IComparable<CircleFraction>
    {
        /// <summary>Numerator.</summary>
        public int Numerator { get; private set; }
        /// <summary>Denominator.</summary>
        public int Denominator { get; private set; }

        /// <summary>Constructor.</summary>
        public CircleFraction(int numerator, int denominator)
        {
            if (numerator % denominator == 0)
            {
                Numerator = 0;
                Denominator = 1;
            }
            else
            {
                var divisor = gcd(Math.Abs(numerator), Math.Abs(denominator));
                Denominator = denominator / divisor;
                var num = numerator / divisor;
                Numerator = (num % Denominator + Denominator) % Denominator;
            }
        }

        /// <summary>Represents the value 0 (zero).</summary>
        public static readonly CircleFraction Zero = new CircleFraction(0, 1);

        private static int gcd(int a, int b)
        {
            while (a != 0 && b != 0)
            {
                if (a > b)
                    a %= b;
                else
                    b %= a;
            }

            return a | b;
        }

        /// <summary>Addition operator.</summary>
        public static CircleFraction operator +(CircleFraction a, CircleFraction b) => new CircleFraction(a.Numerator * b.Denominator + b.Numerator * a.Denominator, a.Denominator * b.Denominator);
        /// <summary>Subtraction operator.</summary>
        public static CircleFraction operator -(CircleFraction a, CircleFraction b) => new CircleFraction(a.Numerator * b.Denominator - b.Numerator * a.Denominator, a.Denominator * b.Denominator);
        /// <summary>Multiplication operator.</summary>
        public static CircleFraction operator *(CircleFraction a, CircleFraction b) => new CircleFraction(a.Numerator * b.Numerator, a.Denominator * b.Denominator);
        /// <summary>Division operator.</summary>
        public static CircleFraction operator /(CircleFraction a, CircleFraction b) => new CircleFraction(a.Numerator * b.Denominator, a.Denominator * b.Numerator);
        /// <summary>Less-than comparison operator.</summary>
        public static bool operator <(CircleFraction a, CircleFraction b) => a.Numerator * b.Denominator < b.Numerator * a.Denominator;
        /// <summary>Greater-than comparison operator.</summary>
        public static bool operator >(CircleFraction a, CircleFraction b) => a.Numerator * b.Denominator > b.Numerator * a.Denominator;
        /// <summary>Less-than-or-equal-to comparison operator.</summary>
        public static bool operator <=(CircleFraction a, CircleFraction b) => a.Numerator * b.Denominator <= b.Numerator * a.Denominator;
        /// <summary>Greater-than-or-equal-to comparison operator.</summary>
        public static bool operator >=(CircleFraction a, CircleFraction b) => a.Numerator * b.Denominator >= b.Numerator * a.Denominator;
        /// <summary>Equality comparison operator.</summary>
        public static bool operator ==(CircleFraction a, CircleFraction b) => a.Numerator * b.Denominator == b.Numerator * a.Denominator;
        /// <summary>Inequality comparison operator.</summary>
        public static bool operator !=(CircleFraction a, CircleFraction b) => a.Numerator * b.Denominator != b.Numerator * a.Denominator;
        /// <summary>
        ///     Determines whether the current value is strictly between <paramref name="min"/> and <paramref name="max"/>
        ///     (exclusive).</summary>
        public bool IsStrictlyBetween(CircleFraction min, CircleFraction max) => max > min ? (this > min && this < max) : (this > min || this < max);
        /// <summary>
        ///     Determines whether the current value is between <paramref name="min"/> and <paramref name="max"/> (inclusive).</summary>
        public bool IsBetweenInclusive(CircleFraction min, CircleFraction max) => max > min ? (this >= min && this <= max) : (this >= min || this <= max);

        /// <summary>Addition operator.</summary>
        public static double operator +(CircleFraction a, double b) => b + ((double) a.Numerator / a.Denominator);
        /// <summary>Addition operator.</summary>
        public static double operator +(double b, CircleFraction a) => b + ((double) a.Numerator / a.Denominator);
        /// <summary>Subtraction operator.</summary>
        public static double operator -(CircleFraction a, double b) => ((double) a.Numerator / a.Denominator) - b;
        /// <summary>Subtraction operator.</summary>
        public static double operator -(double b, CircleFraction a) => b - ((double) a.Numerator / a.Denominator);
        /// <summary>Multiplication operator.</summary>
        public static double operator *(CircleFraction a, double b) => b * a.Numerator / a.Denominator;
        /// <summary>Multiplication operator.</summary>
        public static double operator *(double b, CircleFraction a) => b * a.Numerator / a.Denominator;
        /// <summary>Division operator.</summary>
        public static double operator /(CircleFraction a, double b) => (double) a.Numerator / a.Denominator / b;
        /// <summary>Division operator.</summary>
        public static double operator /(double b, CircleFraction a) => b * a.Denominator / a.Numerator;

        /// <inheritdoc/>
        public int CompareTo(CircleFraction other) => (Numerator * other.Denominator).CompareTo(other.Numerator * Denominator);
        /// <inheritdoc/>
        public bool Equals(CircleFraction other) => other.Numerator == Numerator && other.Denominator == Denominator;
        /// <inheritdoc/>
        public override bool Equals(object obj) => obj is CircleFraction other && other.Numerator == Numerator && other.Denominator == Denominator;
        /// <inheritdoc/>
        public override int GetHashCode() => unchecked(Numerator * 28935701 + Denominator);
        /// <inheritdoc/>
        public override readonly string ToString() => $"{Numerator}/{Denominator}";
    }
}