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;
}
}