using System;
using System.Numerics;

namespace Algorithms.ModularArithmetic
{
    /// <summary>
    /// Modular multiplicative inverse: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse.
    /// </summary>
    public static class ModularMultiplicativeInverse
    {
        /// <summary>
        ///     Computes the modular multiplicative inverse of a in Z/nZ, if there is any (i.e. if a and n are coprime).
        /// </summary>
        /// <param name="a">The number a, of which to compute the multiplicative inverse.</param>
        /// <param name="n">The modulus n.</param>
        /// <returns>The multiplicative inverse of a in Z/nZ, a value in the interval [0, n).</returns>
        /// <exception cref="ArithmeticException">If there exists no multiplicative inverse of a in Z/nZ.</exception>
        public static long Compute(long a, long n)
        {
            var eeaResult = ExtendedEuclideanAlgorithm.Compute(a, n);

            // Check if there is an inverse:
            if (eeaResult.gcd != 1)
            {
                throw new ArithmeticException($"{a} is not invertible in Z/{n}Z.");
            }

            // Make sure, inverseOfA (i.e. the bezout coefficient of a) is in the interval [0, n).
            var inverseOfA = eeaResult.bezoutA;
            if (inverseOfA < 0)
            {
                inverseOfA += n;
            }

            return inverseOfA;
        }

        /// <summary>
        ///     Computes the modular multiplicative inverse of a in Z/nZ, if there is any (i.e. if a and n are coprime).
        /// </summary>
        /// <param name="a">The number a, of which to compute the multiplicative inverse.</param>
        /// <param name="n">The modulus n.</param>
        /// <returns>The multiplicative inverse of a in Z/nZ, a value in the interval [0, n).</returns>
        /// <exception cref="ArithmeticException">If there exists no multiplicative inverse of a in Z/nZ.</exception>
        public static BigInteger Compute(BigInteger a, BigInteger n)
        {
            var eeaResult = ExtendedEuclideanAlgorithm.Compute(a, n);

            // Check if there is an inverse:
            if (eeaResult.gcd != 1)
            {
                throw new ArithmeticException($"{a} is not invertible in Z/{n}Z.");
            }

            // Make sure, inverseOfA (i.e. the bezout coefficient of a) is in the interval [0, n).
            var inverseOfA = eeaResult.bezoutA;
            if (inverseOfA < 0)
            {
                inverseOfA += n;
            }

            return inverseOfA;
        }
    }
}