using System;
using System.Numerics;

namespace Algorithms.Numeric
{
    /// <summary>
    /// https://en.wikipedia.org/wiki/Miller-Rabin_primality_test
    /// The Miller–Rabin primality test or Rabin–Miller primality test is a probabilistic primality test:
    /// an algorithm which determines whether a given number is likely to be prime,
    /// similar to the Fermat primality test and the Solovay–Strassen primality test.
    /// It is of historical significance in the search for a polynomial-time deterministic primality test.
    /// Its probabilistic variant remains widely used in practice, as one of the simplest and fastest tests known.
    /// </summary>
    public static class MillerRabinPrimalityChecker
    {
        /// <summary>
        ///     Run the probabilistic primality test.
        ///     </summary>
        /// <param name="n">Number to check.</param>
        /// <param name="rounds">Number of rounds, the parameter determines the accuracy of the test, recommended value is Log2(n).</param>
        /// <param name="seed">Seed for random number generator.</param>
        /// <returns>True if is a highly likely prime number; False otherwise.</returns>
        /// <exception cref="ArgumentException">Error: number should be more than 3.</exception>
        public static bool IsProbablyPrimeNumber(BigInteger n, BigInteger rounds, int? seed = null)
        {
            Random rand = seed is null
                ? new()
                : new(seed.Value);
            return IsProbablyPrimeNumber(n, rounds, rand);
        }

        private static bool IsProbablyPrimeNumber(BigInteger n, BigInteger rounds, Random rand)
        {
            if (n <= 3)
            {
                throw new ArgumentException($"{nameof(n)} should be more than 3");
            }

            // Input #1: n > 3, an odd integer to be tested for primality
            // Input #2: k, the number of rounds of testing to perform, recommended k = Log2(n)
            // Output:   false = “composite”
            //           true  = “probably prime”

            // write n as 2r·d + 1 with d odd(by factoring out powers of 2 from n − 1)
            BigInteger r = 0;
            BigInteger d = n - 1;
            while (d % 2 == 0)
            {
                r++;
                d /= 2;
            }

            // as there is no native random function for BigInteger we suppose a random int number is sufficient
            int nMaxValue = (n > int.MaxValue) ? int.MaxValue : (int)n;
            BigInteger a = rand.Next(2, nMaxValue - 2); // ; pick a random integer a in the range[2, n − 2]

            while (rounds > 0)
            {
                rounds--;
                var x = BigInteger.ModPow(a, d, n);
                if (x == 1 || x == (n - 1))
                {
                    continue;
                }

                BigInteger tempr = r - 1;
                while (tempr > 0 && (x != n - 1))
                {
                    tempr--;
                    x = BigInteger.ModPow(x, 2, n);
                }

                if (x == n - 1)
                {
                    continue;
                }

                return false;
            }

            return true;
        }
    }
}