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Program.cs
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Program.cs
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//#define _DEBUG
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Numerics;
using System.Threading;
using System.Threading.Tasks;
using static System.Console;
#pragma warning disable IDE0011,IDE0040,IDE0045,IDE0048,IDE1006,IDE1005,IDE1017,CS0219,CS01682
/*
* IDE0011 Add braces to 'if' statement
* IDE0040 Accessibility modifiers
* IDE0045 'if' statement can be simplified
* IDE0048 Add parantheses for clarity
* IDE1006 Suppress Naming Rule Violation IDE1006
* IDE1005 Delegate invocation can be simplified
* IDE1017 Object initialization can be simplified
* CS0168 The variable 'var' is declared but never used.
* CS0219 The variable 'variable' is assigned but its value is never used
*/
namespace RSABigInt
{
class MyBigInteger_Class
{
private const uint ARRAY_SIZE = 0x166e0e21;
//private const uint ARRAY_SIZE = Int32.MaxValue;
private const ulong LIMIT = Int32.MaxValue;
private Random _randObj;
private uint[] primes;
private uint[] factor_base; //
private uint[,] matrix; // 2-dimensional matrix
private struct smooth_num
{
public BigInteger Q_of_x;
public BigInteger x;
public uint[] exponents;
};
private smooth_num[] Qx;
// constructor
public MyBigInteger_Class()
{
_randObj = new Random((int)DateTime.Now.Ticks);
primes = new uint[ARRAY_SIZE]; // 131072 elements --- 0x18000000 = 1.5GB array
factor_base = new uint[ARRAY_SIZE];
prime_sieve(LIMIT>>8);
}
public void prime_sieve(ulong n)
{
int p;
primes.Initialize();
Stopwatch sw = new Stopwatch();
sw.Start();
primes[0] = 2;
for (p = 0; primes[p] < n;)
{
for (uint i = primes[p]*primes[p]; i < n; i += primes[p])
primes[i] = 1;
primes[p+1] = primes[p++] + 1;
while (primes[p] < n && primes[primes[p]] == 1)
//find next prime (where s[p]==0)
primes[p]++;
}
Array.Resize(ref primes, p);
sw.Stop();
#if _DEBUG
for (p = 0; primes[p] != 1; p++)
;
WriteLine($"primes[{p}] = {primes[p]}");
string strElapsed;
if (sw.ElapsedMilliseconds <= 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", sw.Elapsed.Seconds);
WriteLine("prime_sieve time took: {0}", strElapsed);
#endif
}
BigInteger InverseMod(BigInteger x, BigInteger n)
{
if (x.IsEven && n.IsEven) //if both inputs are even, then inverse doesn't exist
return BigInteger.Zero;
BigInteger eg_u = x;
BigInteger eg_v = n;
BigInteger eg_A = BigInteger.One;
BigInteger eg_B = BigInteger.Zero;
BigInteger eg_C = BigInteger.Zero;
BigInteger eg_D = BigInteger.One;
for (; ; )
{
while (eg_u.IsEven) //while eg_u is even
{
eg_u /= 2;
if (eg_A.IsEven && eg_B.IsEven) //if eg_A==eg_B==0 are even
{
eg_A /= 2;
eg_B /= 2;
}
else
{
eg_A += n;
eg_A /= 2;
eg_B -= x;
eg_B /= 2;
}
} // while
while (eg_v.IsEven) //while eg_v is even
{
eg_v /= 2;
if (eg_C.IsEven && eg_D.IsEven) //if eg_C==eg_D==0 mod 2
{
eg_C /= 2;
eg_D /= 2;
}
else
{
eg_C += n;
eg_C /= 2;
eg_D -= x;
eg_D /= 2;
}
} // while
if (eg_v <= eg_u) //eg_v <= eg_u
{
eg_u -= eg_v;
eg_A -= eg_C;
eg_B -= eg_D;
}
else
{ //eg_v > eg_u
eg_v -= eg_u;
eg_C -= eg_A;
eg_D -= eg_B;
}
if (eg_u == BigInteger.Zero)
{
if (eg_C.Sign == -1) //make sure answer is non-negative
eg_C += n;
x = eg_C;
if (eg_v != BigInteger.One) //if GCD_(x,n)!=1, then there is no inverse
x = BigInteger.Zero;
return x;
}
} // for
}
public BigInteger RandPrime(int size)
{
BigInteger rnd = BigInteger.Zero;
BigInteger rem = BigInteger.Zero;
BigInteger a = new BigInteger(2);
Stopwatch sw = new Stopwatch();
sw.Start();
rnd = BigInteger.Zero;
for (int i = 0; i < size; i++)
{
rnd <<= 16;
rnd += _randObj.Next();
}
rnd |= 1;
bool b_TrialDiv = false;
while (!(b_TrialDiv))
{
foreach (uint p in primes)
{
if (rnd % p == 0 && p != 1)
{
#if _DEBUG
WriteLine($"{p,10:N0}");
#endif
rnd += 2;
break;
}
//Write($"{p,10:N0}\r");
b_TrialDiv = primes[primes.Length - 1] == p;
}
}
#if _DEBUG
WriteLine();
#endif
if (b_TrialDiv)
while (!rem.IsOne)
{
rem = BigInteger.ModPow(a, rnd - 1, rnd);
rnd += 2;
}
sw.Stop();
#if _DEBUG
string strElapsed;
if (sw.ElapsedMilliseconds < 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", (float)sw.Elapsed.Milliseconds / 1000);
WriteLine($"RandPrime({size})\nElapsed time: {strElapsed}\n");
#endif
return rnd;
}
public BigInteger TwinPrime(int size)
{
BigInteger twin = RandPrime(size);
bool found = false;
do
{
twin += 2;
found = MillerRabin(twin, 2) && MillerRabin(twin + 2, 2);
} while (!found);
return twin;
}
public BigInteger PrimeTriplet(int size)
{
BigInteger triple = RandPrime(size);
bool found = false;
do
{
if (MillerRabin(triple, 2))
{
found = (MillerRabin(triple + 2, 2) || MillerRabin(triple + 4, 2))
&& MillerRabin(triple + 6, 2);
}
if (!found)
triple += 2;
} while (!found);
return triple;
}
public BigInteger SquareRoot(BigInteger n)
{
BigInteger d = n >> 1, q, _d;
Stopwatch sw = new Stopwatch();
sw.Start();
//Newton's Method
do
{
q = n / d + d;
_d = d;
q >>= 1;
d = q;
} while (_d > q);
sw.Stop();
#if _DEBUG
string strElapsed;
if (sw.ElapsedMilliseconds <= 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", sw.Elapsed.Seconds);
WriteLine($"\nSquareRoot({n})\nElapsed time: {strElapsed}\n");
#endif
return q;
}
public BigInteger Factorial(int n)
{
BigInteger fact = BigInteger.One;
Stopwatch sw = new Stopwatch();
sw.Start();
for (int i = 2; i <= n; i++)
fact *= i;
sw.Stop();
#if _DEBUG
string strElapsed;
if (sw.ElapsedMilliseconds <= 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", sw.Elapsed.Seconds);
WriteLine("\nFactorial() Elapsed time: {0}\n", strElapsed);
#endif
return fact;
}
public BigInteger Fibonacci(int n)
{
BigInteger Fn = BigInteger.Zero;
BigInteger Fn_plus_one = BigInteger.One;
Stopwatch sw = new Stopwatch();
sw.Start();
for (int i = 1; i < n; i++)
{
BigInteger fib_temp = Fn_plus_one;
Fn_plus_one += Fn;
Fn = fib_temp;
}
sw.Stop();
#if _DEBUG
string strElapsed;
if (sw.ElapsedMilliseconds <= 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", sw.Elapsed.Seconds);
WriteLine("\nFactorial() Elapsed time: {0}\n", strElapsed);
#endif
return Fn_plus_one;
}
uint[] GetPrimeFactors(BigInteger N)
{
uint [] factor_expos = new uint[factor_base.Length];
for (uint i=0; i<factor_base.Length; i++)
{
uint j = 0;
for (j = 0; (N % factor_base[i]) == 0; j++)
N /= factor_base[i];
factor_expos[i] = j;
}
if (N == 1)
return factor_expos;
else
return null;
}
void Factor_Base(BigInteger N)
{
int j = 0;
for (int i = 0; i < primes.Length; i++)
if (Legendre(N, primes[i]) == 1)
{
//Write(factor_base[j] + "\t ");
factor_base[j++] = primes[i];
}
Array.Resize(ref factor_base, j);
WriteLine($"Factor base: {j} primes.\n");
}
public void Smooth_Numbers(BigInteger N1)
{
BigInteger sqrt_N1 = SquareRoot(N1);
BigInteger i = sqrt_N1 + 1;
BigInteger j = sqrt_N1 - 1;
// Collect smooth numbers
Factor_Base(N1);
uint N_smooths = (uint)(factor_base.Length * 1.01d);
if ((N_smooths & 1) == 1)
N_smooths++; // make it even
Qx = new smooth_num[N_smooths];
Qx.Initialize();
long k = -1;
Stopwatch sw = new Stopwatch();
sw.Start();
Task[] smooth = new Task[2];
smooth[0] = Task.Run(() =>
{
while (k < N_smooths-1)
{
BigInteger sm = i * i - N1;
uint[] expo1 = GetPrimeFactors(sm);
if (expo1 != null)
{
Interlocked.Increment(ref k);
Qx[k].Q_of_x = sm;
Qx[k].x = i;
Qx[k].exponents = expo1;
Write(k.ToString() + " smooth numbers\r");
}
i++;
/*
sm = N1 - j * j;
expo1 = GetPrimeFactors(sm);
if (expo1 != null)
{
Qx[k].Q_of_x = sm;
Qx[k].x = j;
Qx[k].exponents = expo1;
Interlocked.Increment(ref k);
Write(k.ToString() + " smooth numbers\r");
}
j--;
*/
}
});
smooth[1] = Task.Run(() =>
{
while (k < N_smooths-1)
{
BigInteger sm = N1 - j * j;
uint[] expo1 = GetPrimeFactors(sm);
if (expo1 != null)
{
Interlocked.Increment(ref k);
Qx[k].Q_of_x = sm;
Qx[k].x = j;
Qx[k].exponents = expo1;
Write(k.ToString() + " smooth numbers\r");
}
j--;
}
});
Task.WaitAll(smooth);
#if _DEBUG
sw.Stop();
string strElapsed;
if (sw.ElapsedMilliseconds <= 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", sw.Elapsed.Seconds);
WriteLine("Collected {k} smooth numbers.\nElapsed time: {strElapsed}\n");
#endif
//WriteLine("{0}\t{1}", i - sqrt_N1, sqrt_N1 - j);
}
int Legendre(BigInteger n, uint p)
{
BigInteger p1, l;
// assumes p is an odd prime
p1 = (p-1)/2;
l = BigInteger.ModPow(n, p1, p);
if (l == 1)
return 1;
if (l == 0)
return 0;
else
return -1;
}
bool MillerRabin(BigInteger n, int k)
{
int[] base_primes = { 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};
BigInteger r = n - 1;
int s = 0;
for (int i = 1; i < base_primes.Length; i++ )
if (n % base_primes[i] == 0)
return false;
while (r.IsEven)
{
s++;
r >>= 1;
}
if (k < 1) k = 1;
if (k > 54) k = 54;
for (int round = 0; round < k; round++)
{
BigInteger x = BigInteger.ModPow(base_primes[round], r, n);
for (int i = 0; i < s; i++)
{
x = (x * x) % n;
if (x.IsOne)
break;
}
if (!x.IsOne && x != n - 1)
return false;
}
return true;
}
public void PrimeTriplet_Test()
{
for (BigInteger X = PrimeTriplet(10); ; X += 2)
if (MillerRabin(X, 2) && MillerRabin(X + 6, 2))
if (MillerRabin(X + 2, 2))
WriteLine("{0}\n{1}\n{2}\n", X.ToString(), (X + 2).ToString(), (X + 6).ToString());
else
if (MillerRabin(X + 4, 2))
WriteLine("{0}\n{1}\n{2}\n", X.ToString(), (X + 4).ToString(), (X + 6).ToString());
}
public void print_time(TextWriter F)
{
DateTime dt = DateTime.Now;
string str_dt = String.Format("[{0} {1}]", dt.ToLongDateString(), dt.ToLongTimeString());
WriteLine("{0}", str_dt);
F.WriteLine(str_dt);
}
public void TwinPrime_Test()
{
BigInteger P = RandPrime(2);
try
{
FileStream F_TP = new FileStream(@".\twin_primes.txt", FileMode.Append);
using (StreamWriter writer = new StreamWriter(F_TP))
{
DateTime dt = DateTime.Now;
int f = 0;
//for (BigInteger X = P; DateTime.Now < dt.AddHours(4.0d); X += 2)
for (BigInteger X = P; DateTime.Now < dt.AddMinutes(5.0d); X += 2)
{
switch (f)
{
case 0:
Write("[|]\r");
break;
case 1:
Write("[/]\r");
break;
case 2:
Write("[-]\r");
break;
case 3:
Write("[\\]\r");
break;
}
f++; f %= 4;
if (MillerRabin(X, 3) && MillerRabin(X + 2, 3))
{
//WriteLine("[{0} {1}]", DateTime.Now.ToLongDateString(), DateTime.Now.ToLongTimeString());
print_time(writer);
WriteLine("{0}\n{1}\n", X.ToString(), (X + 2).ToString());
// output to file
writer.WriteLine(X.ToString());
writer.WriteLine((X + 2).ToString());
writer.WriteLine();
writer.FlushAsync();
}
}
}
F_TP.Close();
}
catch
{
WriteLine("File opening failed.\n");
return;
}
}
public void Mersenne(int limit)
{
BigInteger Pow2Sub1, rem;
string strPow2Sub1;
//for (int i = 0, x = 2; i < primes.Length; i++)
int x = 2;
Parallel.For(0, primes.Length, (int i) =>
{
Pow2Sub1 = new BigInteger(1) << (int)primes[i];
Pow2Sub1--;
//sw.Restart();
rem = BigInteger.ModPow(3, Pow2Sub1 - 1, Pow2Sub1); // really trivial primality test?
if (rem.IsOne)
{
//sw.Stop();
strPow2Sub1 = Pow2Sub1.ToString();
if (x < 10)
WriteLine("M[{0}] = {1}", primes[i], strPow2Sub1);
else
WriteLine("M[{0}] = {1}...{2}", primes[i], strPow2Sub1.Substring(0, 12), strPow2Sub1.Substring(strPow2Sub1.Length - 12, 12));
x++;
//WriteLine("elapsed time: {0} ms\n", sw.ElapsedMilliseconds);
}
});
}
public void Mersenne2(int limit)
{
BigInteger Pow2Sub1;
//bool isMprime;
string strPow2Sub1;
Dictionary<int, Stopwatch> SW_dict = new Dictionary<int, Stopwatch>();
CancellationTokenSource cancellationSource = new CancellationTokenSource();
ParallelOptions parallelOptions = new ParallelOptions()
{
CancellationToken = cancellationSource.Token
};
int Mcount = 1;
Parallel.For(0, primes.Length, parallelOptions, (i, loopState) =>
//for (int i = 0, Mcount = 1; i < primes.Length; i++)
{
int tid = Thread.CurrentThread.ManagedThreadId;
if (!SW_dict.ContainsKey(tid)) // add a new Stopwatch instance if one doesn't already exist in SW_dict
SW_dict.Add(tid, new Stopwatch());
SW_dict.TryGetValue(tid, out var sw); // retrieve instance of Stopwatch for this thread id.
sw.Start();
bool isMprime = LucasLehmer(primes[i]);
if (isMprime)
{
sw.Stop();
Pow2Sub1 = BigInteger.Pow(2, (int)primes[i]) - 1;
strPow2Sub1 = Pow2Sub1.ToString();
// This increment isn't obvious! Number of Mersenne primes found so far
Interlocked.Increment(ref Mcount);
if (Mcount < 10)
WriteLine("M[{0}] = {1}", primes[i], strPow2Sub1);
else
WriteLine("M[{0}] = {1}...{2}", primes[i], strPow2Sub1.Substring(0, 12), strPow2Sub1.Substring(strPow2Sub1.Length - 12, 12));
if (sw.ElapsedMilliseconds < 1000)
WriteLine("elapsed time: {0} ms\n", sw.ElapsedMilliseconds);
else
WriteLine("elapsed time: {0:F1} s\n", sw.Elapsed.Seconds);
sw.Restart();
}
if (limit < Mcount)
{
//break;
loopState.Stop();
}
}); // Parallel.For
}
// Use LucasLehmer to determine if 2^n-1 is prime
bool LucasLehmer(uint n)
{
BigInteger seed = 4;
BigInteger div = (new BigInteger(1) << (int)n) - 1; // div = 2^n - 1
for (int i = 3; i <= n; i++)
{
seed = (seed * seed - 2) % div;
}
return (seed == 0);
}
public void RSA_Numbers()
{
BigInteger P = RandPrime(10);
BigInteger Q = PrimeTriplet(10);
BigInteger N = P * Q;
BigInteger e = new BigInteger(65537);
BigInteger phiN = (P - 1) * (Q - 1);
//WriteLine("GCD({0}, \n {1}) = {2}\n", phiN.ToString(), N, BigInteger.GreatestCommonDivisor(phiN, N));
BigInteger d = InverseMod(e, phiN);
WriteLine("RSA_Numbers()\n");
WriteLine("P = {0}", P.ToString());
WriteLine("Q = {0}", Q.ToString());
WriteLine("N = {0}", N.ToString());
WriteLine("e = {0}", e.ToString());
WriteLine("d = {0}", d.ToString());
BigInteger enc = BigInteger.ModPow(3126225153, e, N);
BigInteger dP = d % (P - 1);
BigInteger dQ = d % (Q - 1);
BigInteger invQ = InverseMod(Q, P);
// Chinese remainder
BigInteger m1 = BigInteger.ModPow(enc, dP, P);
BigInteger m2 = BigInteger.ModPow(enc, dQ, Q);
BigInteger h = invQ * (m1 - m2);
if (h.Sign < 0)
h = -h;
h %= P;
//BigInteger dec = m2 + h * Q;
BigInteger dec = BigInteger.ModPow(enc, d, N);
WriteLine("enc = {0}", enc.ToString());
WriteLine("dec = {0}\n", dec.ToString());
}
public void ModPow_Misc_Stuff()
{
BigInteger N = RandPrime(70);
double Temp = BigInteger.Log10(N);
int nbrPrimes = (int)Math.Exp(Math.Sqrt(Temp * Math.Log(Temp)) * 0.318);
BigInteger T1 = BigInteger.Pow(new BigInteger(2), 1048576); // 315653 digit number!
T1 = (new BigInteger(1) << 9689) - 1;
double LogT1 = BigInteger.Log10(T1);
T1 = BigInteger.Pow(new BigInteger(2), 16777216); // 5050446 decimal digits! (wolframalpha.com)
#if !_DEBUG && false
int len_T1 = T1.ToString().Length; // DON'T evaluate this in DEBUG or RELEASE mode.
#endif
T1 = (new BigInteger(1) << 9689) - 1;
LogT1 = BigInteger.Log10(T1);
//StreamWriter file1 = new StreamWriter("output.txt", false);
//file1.WriteLine(T1.ToString());
//file1.Close();
Stopwatch sw = new Stopwatch();
sw.Start();
BigInteger T2 = BigInteger.ModPow(new BigInteger(13), T1 - 1, T1);
sw.Stop();
WriteLine("ModPow time: {0} ms\n", sw.ElapsedMilliseconds); // ModPow time: 12453 ms
double LogT2 = BigInteger.Log10(T2);
BigInteger sqrt2 = SquareRoot(BigInteger.Parse("2" + new String('0', 10000)));
WriteLine($"sqrt(2) = {sqrt2}\n");
int n = 13017; //7921; // 1789; // 3607;
WriteLine("fact({1}) = {0}\n", Factorial(n), n);
WriteLine("fibonacci({1}) = {0}\n", Fibonacci(n), n);
}
BigInteger g (BigInteger x, BigInteger n, int a)
{
BigInteger x_ = x * x + a;
return BigInteger.Remainder(x_, n);
}
Int64 gx (Int64 x, Int64 n, Int64 a)
{
return (x * x + a) % n;
}
BigInteger Pollard_Rho(BigInteger n, int a)
{
BigInteger x_fixed = 2;
int cycle_size = 2, count = 1;
BigInteger x = 2;
BigInteger h = 1;
BigInteger x_;
while (h == 1) {
count = 1;
while (count <= cycle_size && h == 1) {
//x = g(x, n, a);
x_ = x * x + a;
x = BigInteger.Remainder(x_, n);
//x = gx(Int64.Parse(x.ToString()), Int64.Parse(n.ToString()), a);
//WriteLine("x = {0}", (x-x_fixed).ToString());
count++;
h = BigInteger.GreatestCommonDivisor(x - x_fixed, n);
//WriteLine("h = {0}", h.ToString());
}
if (h != 1)
break;
cycle_size *= 2;
WriteLine("cycle_size = {0,-8}\tx = {1}", cycle_size, x);
x_fixed = x;
}
WriteLine($"count = {count}\n");
return h;
}
public void Pollard_Rho_Test()
{
BigInteger N1;
// msieve factorized this 250-bit number in ~3mins.
//N1 = BigInteger.Parse("923177721865685175285240199236472361656683591279028656230171797690188269779");
N1 = BigInteger.Parse("20000000000000000672000000000000002907");
//N1 = BigInteger.Parse("1152656570285234495703667671274025629"); // Time: 2358867 ms Time: 1873793 ms
// (Time: 502594 ms Time: 430157 ms - command-line Debug\RSABigInt.exe)
//N1 = BigInteger.Parse("43272494503935639032000984197"); // Time: 28926 ms - command-line
//N1 = BigInteger.Parse("462717344089999398416479"); // Time: 988 ms (Time: 873 ms - command-line)
//N1 = BigInteger.Parse("12923855417829126637"); // 20-digits - i.e. GE than 64-bits.
//N1 = BigInteger.Parse("3369738766071892021");
//N1 = BigInteger.Parse("139078421707568423");
//N1 = BigInteger.Parse("87256236345731407");
//N1 = BigInteger.Parse("4607863703200169");
//N1 = BigInteger.Parse("373463523233483");
//N1 = BigInteger.Parse("135723676817");
//N1 = new BigInteger(21530071);
//N1 = new BigInteger(12546257);
const int a = 1;
Stopwatch sw = new Stopwatch();
WriteLine("Pollard_Rho_Test()");
sw.Start();
BigInteger P1 = Pollard_Rho(N1, a);
sw.Stop();
BigInteger Q1 = N1 / P1;
WriteLine("Pollard_Rho({0}, {3}) = {1} x {2}", N1, P1, Q1, a);
WriteLine("Time: {0} ms\n", sw.ElapsedMilliseconds);
}
void Process_Matrix()
{
Stopwatch sw = new Stopwatch();
sw.Start();
matrix = new uint[factor_base.Length*2, factor_base.Length*3];
for (uint i = 0; i < Qx.Length; i++)
{
for (uint j = 0; j < Qx[i].exponents.Length; j++)
matrix[i, j] = Qx[i].exponents[j] & 1; // Transpose values as well: rows become the prime exponents mod 2
matrix[i, Qx[i].exponents.Length + i] = 1; // set identity column value = 1
}
sw.Stop();
#if _DEBUG
string strElapsed;
if (sw.ElapsedMilliseconds <= 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", (float)sw.Elapsed.Milliseconds / 1000);
string strValue = $"Process_Matrix() Elapsed time: {strElapsed}\n";
WriteLine(strValue);
#endif
}
void Gauss_Elimination()
{
uint row_adds = 0, row_swaps = 0;
Stopwatch sw = new Stopwatch();
CancellationTokenSource cancellationSource = new CancellationTokenSource();
ParallelOptions parallelOptions = new ParallelOptions()
{
CancellationToken = cancellationSource.Token
};
sw.Start();
ParallelLoopResult res = Parallel.For(0, matrix.GetLength(0), parallelOptions, (p, loopState) =>
//for (uint p = 0; p < matrix.GetLength(0); p++) // number of rows
{
// find pivot row and swap
for (long i = p + 1; i < matrix.GetLength(0); i++) //
{
if (matrix[i, p] > matrix[p, p])
{
#if _DEBUG
WriteLine("Swap rows: {0} and {1}", p, i);
#endif
row_swaps++;
for (uint j = 0; j < matrix.GetLength(1); j++) // length of the 2nd dimension / number of columns
{
uint t = matrix[i, j];
matrix[i, j] = matrix[p, j];
matrix[p, j] = t;
}
}
if (matrix[i, p] == 1) // Add these rows if value in pivot column is 1
{
#if _DEBUG
WriteLine("Add row: {0} to row: {1}", p, i);
#endif
row_adds++;
for (int j = 0; j < matrix.GetLength(1); j++)
{
matrix[i, j] ^= matrix[p, j];
}
}
} // for i
}); // Parallel.For p
sw.Stop();
#if _DEBUG
SquareRoot(BigInteger.Parse("2" + new String('0', 10000)));
string strElapsed;
if (sw.ElapsedMilliseconds <= 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", (float)sw.Elapsed.Milliseconds / 1000);
string strValue = $"Row adds: {row_adds}\nRow swaps: {row_swaps}\nElapsed time: {strElapsed}\n";
WriteLine(strValue);
#endif
}
void Dump_Matrix()
{
for (uint i = 0; i < matrix.GetLength(0); i++) // number of rows
{
Write("{0,3}: ", i);
for (uint j = 0; j < matrix.GetLength(1); j++) // number of columns
Write("{0} ", matrix[i, j]);
WriteLine();
}
}
ParallelLoopResult function()
{
ParallelLoopResult para_res = new ParallelLoopResult();
return para_res;
}
void Calculate_Factors(BigInteger N1)
{
//for (uint i = (uint)matrix.GetLength(0) - 1; i >= 0; i--) // number of rows
CancellationTokenSource cancellationSource = new CancellationTokenSource();
ParallelOptions parallelOptions = new ParallelOptions()
{
CancellationToken = cancellationSource.Token
};
Stopwatch sw = new Stopwatch();
sw.Start();
DateTime dt0 = DateTime.Now;
//ParallelAlgorithms.SpeculativeFor(fromInclusive: 0, toExclusive: matrix.GetLength(0) - 1, options: parallelOptions, body: () =>
try
{
ParallelLoopResult res = Parallel.For(0, matrix.GetLength(0) - 1, parallelOptions, (i, loopState) =>
{
bool bNonNullFound = false;
for (uint j = 0; j < factor_base.Length; j++)
if (matrix[i, j] != 0) // test for null vector
{
bNonNullFound = true;
break;
//loopState.Stop();
}
if (!bNonNullFound)
{
// calculate smooth number from exponents, should be a perfect square
BigInteger x = 1, y = 1;
for (int j = factor_base.Length; j < matrix.GetLength(1); j++)
if (matrix[i, j] == 1)
{
x *= Qx[j - factor_base.Length].x;
y *= Qx[j - factor_base.Length].Q_of_x;
}
y = x - SquareRoot(y);
BigInteger P = BigInteger.GreatestCommonDivisor(N1, y);
if (P > 1 && P != N1)
{
BigInteger Q = N1 / P;
WriteLine("\nFactors: {0}, {1}\n", P.ToString(), Q.ToString());
loopState.Stop();
cancellationSource.Cancel();
}
}
} ); // ParallelFor(...)
}
catch (OperationCanceledException ex)
{
WriteLine("Caught exception: {0}\n", ex.Message);
WriteLine("\nOperation cancelled, done.");
}
finally
{
cancellationSource.Dispose();
}
DateTime dt1 = DateTime.Now;
sw.Stop();
#if _DEBUG
string strElapsed;
if (sw.ElapsedMilliseconds <= 1000)
strElapsed = String.Format("{0} ms", sw.ElapsedMilliseconds);
else
strElapsed = String.Format("{0:F1} s", sw.Elapsed.Seconds);
WriteLine($"Calculate_Factors({N1})\nElapsed time: {strElapsed}");
WriteLine($"dt1 - dt0 = {dt1.Subtract(dt0).Seconds} s\n");
#endif
} // CalculateFactors
void Calculate_Factors_Task(BigInteger N1)
{
CancellationTokenSource cancellationSource = new CancellationTokenSource();
Task[] sqrtTasks = new Task[matrix.GetLength(0)];
Stopwatch sw = new Stopwatch();
sw.Start();