FixedIntXPrimality.cs

Fixed BigInteger Primality

using System;
using System.Numerics;
using System.Threading;
public class FixedIntXPrimality
{
    private readonly FixedBigInteger _twoSixtyFourPlusIntMax = new FixedBigInteger("18446744073709551616", 64);
    private readonly uint[]          _w0                     = {2};
    private readonly uint[]          _w1                     = {2, 3};
    private readonly uint[]          _w10                    = {2, 3, 5, 7, 11, 13, 17, 19, 23};
    private readonly uint[]          _w11                    = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};
    private readonly uint[]          _w12                    = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41};
    private readonly uint[]          _w2                     = {31, 73};
    private readonly uint[]          _w3                     = {2, 3, 5};
    private readonly uint[]          _w4                     = {2, 3, 5, 7};
    private readonly uint[]          _w5                     = {2, 7, 61};
    private readonly uint[]          _w6                     = {2, 13, 23, 1662803};
    private readonly uint[]          _w7                     = {2, 3, 5, 7, 11};
    private readonly uint[]          _w8                     = {2, 3, 5, 7, 11, 13};
    private readonly uint[]          _w9                     = {2, 3, 5, 7, 11, 13, 17};
    private readonly int[] LowPrimes =
    {
        2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
        157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313,
        317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491,
        499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677,
        683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881,
        883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
    };
    private int                                  _bitWidth;
    private FixedBigIntegerRandomNumberGenerator _rng;
    public  int                                  CandidateTried;
    public FixedIntXPrimality(int bitWidth)
    {
        _bitWidth     = bitWidth;
        _rng          = new FixedBigIntegerRandomNumberGenerator(_bitWidth);
        _rng.OddsOnly = true;
        _rng.Unsigned = true;
    }
    public void ResetBitWidth(int bitWidth)
    {
        _bitWidth     = bitWidth;
        _rng          = new FixedBigIntegerRandomNumberGenerator(_bitWidth);
        _rng.OddsOnly = true;
        _rng.Unsigned = true;
    }
    private bool TrialDivision(FixedBigInteger candidate)
    {
        for (var i = 0; i < LowPrimes.Length; i++)
        {
            var p = LowPrimes[i];
            if (i < p)
            {
                if (candidate % p != 0)
                    continue;
                return false;
            }
            break;
        }
        return true;
    }
    private static bool PrimeCheckM10LD(FixedBigInteger n)
    {
        var d1 = (int) (n % 10);
        return d1 == 1 || d1 == 3 || d1 == 7 || d1 == 9;
    }
    private static bool PrimeCheckM6(FixedBigInteger n)
    {
        var d1 = (int) (n % 6);
        return d1 == 1 || d1 == 5;
    }
    public bool IsPrime(uint bi)
    {
        return IsPrime((FixedBigInteger) bi);
    }
    public bool IsPrime(int bi)
    {
        bi = Math.Abs(bi);
        return IsPrime((FixedBigInteger) bi);
    }
    public bool IsPrime(short bi)
    {
        bi = Math.Abs(bi);
        return IsPrime((FixedBigInteger) bi);
    }
    public bool IsPrime(ushort bi)
    {
        return IsPrime((FixedBigInteger) bi);
    }
    public bool IsPrime(byte bi)
    {
        return IsPrime((FixedBigInteger) bi);
    }
    public bool IsPrime(sbyte bi)
    {
        bi = Math.Abs(bi);
        return IsPrime((FixedBigInteger) bi);
    }
    private bool CheckLowPrimes(FixedBigInteger val)
    {
        foreach (var v in LowPrimes)
            if (val == v)
                return true;
        return false;
    }
    public bool IsPrime(FixedBigInteger candidate)
    {
        if (candidate == 1)
            return false;
        if (candidate == 2 || candidate == 3 || candidate == 5)
            return true;
        if (candidate <= 1000)
            return CheckLowPrimes(candidate);
        if (!PrimeCheckM10LD(candidate))
            return false;
        if (!PrimeCheckM6(candidate))
            return false;
        if (!TrialDivision(candidate))
            return false;
        if (candidate < 2047)
        {
            if (!MillerRabin(candidate, _w0))
                return false;
        }
        else if (candidate > 2047 && candidate <= 1373653)
        {
            if (!MillerRabin(candidate, _w1))
                return false;
        }
        else if (candidate > 1373653 && candidate <= 9080191)
        {
            if (!MillerRabin(candidate, _w2))
                return false;
        }
        else if (candidate > 9080191 && candidate <= 25326001)
        {
            if (!MillerRabin(candidate, _w3))
                return false;
        }
        else if (candidate > 25326001 && candidate <= 3215031751)
        {
            if (!MillerRabin(candidate, _w4))
                return false;
        }
        else if (candidate > 3215031751 && candidate <= 4759123141)
        {
            if (!MillerRabin(candidate, _w5))
                return false;
        }
        else if (candidate > 4759123141 && candidate <= 1122004669633)
        {
            if (!MillerRabin(candidate, _w6))
                return false;
        }
        else if (candidate > 1122004669633 && candidate <= 2152302898747)
        {
            if (!MillerRabin(candidate, _w7))
                return false;
        }
        else if (candidate > 2152302898747 && candidate <= 3474749660383)
        {
            if (!MillerRabin(candidate, _w8))
                return false;
        }
        else if (candidate > 3474749660383 && candidate <= 341550071728321)
        {
            if (!MillerRabin(candidate, _w9))
                return false;
        }
        else if (candidate > 341550071728321 && candidate <= 3825123056546413051)
        {
            if (!MillerRabin(candidate, _w10))
                return false;
        }
        else if (candidate > 3825123056546413051 && candidate < _twoSixtyFourPlusIntMax)
        {
            if (!MillerRabin(candidate, _w11))
                return false;
        }
        else if (candidate > _twoSixtyFourPlusIntMax)
        {
            if (!MillerRabin(candidate, _w12))
                return false;
        }
        return true;
    }
    private bool MillerRabin(FixedBigInteger candidate, uint[] w)
    {
        var s = 0;
        var d = candidate - FixedBigInteger.One;
        while ((d & 1) == 0)
        {
            d >>= 1;
            s++;
        }
        if (s == 0)
            return false;
        var nmo = candidate - FixedBigInteger.One;
        for (var i = 0; i < w.Length; ++i)
        {
            var x = BigInteger.ModPow(w[i], (BigInteger) d, (BigInteger) candidate);
            if (x == 1 || x == nmo)
                continue;
            for (var r = 1; r < s; ++r)
            {
                x = BigInteger.ModPow(x, 2, (BigInteger) candidate);
                if (x == 1)
                    return false;
                if (x == nmo)
                    break;
            }
            if (x == nmo)
                continue;
            return false;
        }
        return true;
    }
    public FixedBigInteger GetPrimeNumber(bool fixedWidth = false)
    {
        var bw = 0;
        if (!fixedWidth)
        {
            var MaxBytes = _bitWidth >> 3;
            var bwb      = new byte[2];
            _rng.GetBytes(bwb);
            bw = bwb[0] % MaxBytes + 1;
            if (bw < 1)
                bw = 1;
        }
        else
        {
            bw = _bitWidth >> 3;
        }
        var buffer = new byte[bw];
        var n      = new FixedBigInteger(0, 0);
        CandidateTried = 0;
        var btrd = new Thread(() =>
        {
            while (true)
            {
                CandidateTried++;
                _rng.GetBytes(buffer);
                n = new FixedBigInteger(buffer, _bitWidth) | 1;
                if (n == 1)
                    continue;
                if (n > n.MaxValue)
                    continue;
                if (IsPrime(n))
                    break;
            }
        }) {Priority = ThreadPriority.Highest};
        btrd.Start();
        btrd.Join();
        return n;
    }
}