private SievePolynomial GetDefaultPolynomial(BigInteger n)
{
var m = new IntegerSquareRoot().Sqrt(n);
var ainv = new Dictionary <long, long>();
foreach (var p in _factorBase)
{
ainv.Add(p, 1);
}
var firstSln = new Dictionary <long, long>();
var secondSln = new Dictionary <long, long>();
for (int i = 0; i < _factorBase.Length; i++)
{
var p = _factorBase[i];
firstSln[p] = (long)(ainv[p] * (_sqrtN[p] - m) % p);
secondSln[p] = (long)(ainv[p] * (-_sqrtN[p] - m) % p);
}
return(new SievePolynomial()
{
A = 1,
B = m,
C = (m * m - n),
FirstRoot = firstSln,
SecondRoot = secondSln,
InvA = ainv
});
}
static BigInteger TrialDivision(BigInteger n)
{
var sqrtN = new IntegerSquareRoot().Sqrt(n);
if (n % 2 == 0)
{
return(2);
}
for (BigInteger i = 3; i < sqrtN; i += 2)
{
if (n % i == 0)
{
return(i);
}
}
return(1);
}
private void Init(BigInteger n)
{
if (_autoInit)
{
_primeBound = (long)(12 * BigInteger.Log10(n) * BigInteger.Log10(n));
_factorBase = BuildFactorBase(n);
_sieveBound = (_factorBase.Length) * 60;
_kerSize = 10;
}
else
{
_factorBase = BuildFactorBase(n);
}
_logp = _factorBase.Select(x => Math.Log10(x)).ToArray();
var sqrt = new IntegerSquareRoot();
_thresh = BigInteger.Log10((_sieveBound * sqrt.Sqrt(2 * n)) >> 1) * 0.735;
_partial = new Dictionary <BigInteger, int>();
Console.WriteLine("Prime bound:" + _primeBound);
Console.WriteLine("Sieve size:" + _sieveBound);
Console.WriteLine("Factorbase size:" + _factorBase.Length);
}
public BigInteger FindFactor()
{
var timer = new Stopwatch();
timer.Start();
_polyInfo = _generator.GeneratePolynomial();
Console.WriteLine(_number.Value());
Console.WriteLine("f(x)=" + _polyInfo.Polynomial);
Console.WriteLine("Root=" + _polyInfo.Root);
var rootFinder = new GcdRootFinder();
var algFbBuilder = new AlgebraicFactorbaseBuilder(_polyInfo.Polynomial, rootFinder, _algebraicPrimeBound);
var rationalFbBuilder = new RationalFactorbaseBuilder(_polyInfo.Root, _rationalPrimeBound);
var quadraticCharFbBuilder = new QuadraticCharactersBuilder(_polyInfo.Polynomial, rootFinder, _algebraicPrimeBound, _quadraticCharFbSize);
var rationalFb = rationalFbBuilder.Build();
var quadraticCharFb = quadraticCharFbBuilder.Build();
var algFb = algFbBuilder.Build();
var sieve = new LogSieve();
Console.WriteLine("\nRational factorbase size: " + rationalFb.Elements.Count);
Console.WriteLine("Algebraic factorbase size: " + algFb.Elements.Count);
Console.WriteLine("Quadratic characters factorbase size: " + quadraticCharFb.Elements.Count);
Console.WriteLine("Init time: " + timer.Elapsed);
timer.Reset();
timer.Start();
var pairs =
sieve.Sieve(
(algFb.Elements.Count + rationalFb.Elements.Count + quadraticCharFb.Elements.Count + _kerDim + 1),
new SieveOptions(_sieveSize, -_sieveSize, algFb, rationalFb, _polyInfo.Polynomial, _polyInfo.Root));
Console.WriteLine();
Console.WriteLine(pairs.Count + " relations collected.");
Console.WriteLine("Sieve time: " + timer.Elapsed);
timer.Reset();
timer.Start();
var matrixBuilder = new MatrixBuilder();
var matrix = matrixBuilder.Build(pairs, rationalFb, algFb, quadraticCharFb, _polyInfo.Root, _polyInfo.Polynomial);
var matrixSolver = new GaussianEliminationOverGf2();
//Console.WriteLine("{0}x{1} matrix builded. ",matrix.ColumnsCount,matrix.RowsCount);
var solutions = matrixSolver.Solve(matrix);
// var solutions =matrix.Solve();
Console.WriteLine();
Console.WriteLine("Linear algebra time: " + timer.Elapsed);
Console.WriteLine("{0} solution computed. ", solutions.Count);
timer.Reset();
timer.Start();
var polyMath = new PolynomialMath(-1);
var df = new PolynomialDerivative().Derivative(_polyInfo.Polynomial);
var sqrDf = polyMath.Mul(df, df);
var solutionsCheked = -1;
foreach (var solution in solutions)
{
timer.Reset();
timer.Start();
var sqr = new Polynomial(new BigInteger[] { 1 });
BigInteger sqrtNorm = 1;
BigInteger x = 1;
for (int i = 0; i < solution.Length; i++)
{
if (solution[i] == 1)
{
var tmp = new Polynomial(new BigInteger[] { pairs[i].Item1, pairs[i].Item2 });
x *= pairs[i].Item1 + _polyInfo.Root * pairs[i].Item2;
sqr = polyMath.Rem(polyMath.Mul(tmp, sqr), _polyInfo.Polynomial);
var normCalculator = new FirstDegreeElementsNormCalculator(_polyInfo.Polynomial, pairs[i].Item2);
sqrtNorm *= normCalculator.CalculateNorm(pairs[i].Item1);
}
}
x *= sqrDf.Value(_polyInfo.Root);
if (x < 0)
{
throw new Exception();
}
sqr = polyMath.Rem(polyMath.Mul(sqrDf, sqr), _polyInfo.Polynomial);
var integerSqrt = new IntegerSquareRoot();
var sqrtX = integerSqrt.Sqrt(x);
if (sqrtX * sqrtX != x)
{
if (sqrtX * sqrtX != x)
{
if (sqrtX * sqrtX != x)
{
throw new Exception();
}
}
}
var algSqrt = new AlgebraicSqrt();
sqrtNorm = BigInteger.Abs(sqrtNorm);
var tmpNorm = sqrtNorm;
sqrtNorm = integerSqrt.Sqrt(BigInteger.Abs(sqrtNorm));
timer.Stop();
Console.WriteLine(timer.Elapsed + " Умножение");
if (sqrtNorm * sqrtNorm != tmpNorm)
{
if (sqrtNorm * sqrtNorm != tmpNorm)
{
if (sqrtNorm * sqrtNorm != tmpNorm)
{
throw new Exception();
}
}
}
timer.Reset();
timer.Start();
var sqrt = algSqrt.Sqrt(sqr, _polyInfo.Polynomial, df, sqrtNorm);
timer.Stop();
Console.WriteLine(timer.Elapsed + " Квадратный корень");
if (algSqrt.DontExist)
{
Console.Write("\r{0}/{1} solutions cheked. (BAD SQRT) ", ++solutionsCheked, solutions.Count);
continue;
}
var sqrtY = sqrt.Value(_polyInfo.Root);
var check = polyMath.Rem(polyMath.Mul(sqrt, sqrt), _polyInfo.Polynomial);
if (check != sqr)
{
var primes = new EratosthenesSieve().GetPrimes(5, 10000);
int i;
for (i = 0; i < primes.Length; i++)
{
if (!algSqrt.IsSqr(sqr, _polyInfo.Polynomial, primes[i]))
{
break;
}
}
if (i == primes.Length)
{
throw new Exception();
}
Console.Write("\r{0}/{1} solutions cheked. (BAD SQRT) ", ++solutionsCheked, solutions.Count);
continue;
}
if ((sqrtY * sqrtY - sqrtX * sqrtX) % _number.Value() != 0)
{
throw new Exception();
}
var factor = BigInteger.GreatestCommonDivisor(sqrtX - sqrtY, _number.Value());
if (factor > 1 && factor < _number.Value())
{
Console.Write("\r{0}/{1} solutions cheked ", ++solutionsCheked, solutions.Count);
return(factor);
}
Console.Write("\r{0}/{1} solutions cheked. (BAD SOLUTION)", ++solutionsCheked, solutions.Count);
}
Console.Write("\r{0}/{1} solutions cheked. ", solutionsCheked, solutions.Count);
return(1);
}
public void IntegerSqrt_Test(int number, object expected)
{
Assert.AreEqual(expected, IntegerSquareRoot.SqrtApproximation(number));
}
private List <SievePolynomial> GeneratePolynomials(BigInteger n)
{
var result = new List <SievePolynomial>();
var sqrt = new IntegerSquareRoot();
var sizeBound = sqrt.Sqrt(2 * n) / _sieveBound;
var primes = new List <long>();
BigInteger a = 1;
var aFactorsBound = Math.Exp(BigInteger.Log(sizeBound) / 13);
var indexes = new HashSet <int>();
while (a < sizeBound && _polyIndex < _factorBase.Length)
{
if (_factorBase[_polyIndex] < aFactorsBound)
{
_polyIndex++;
continue;
}
indexes.Add(_polyIndex);
var p = _factorBase[_polyIndex++];
a *= p;
primes.Add(p);
}
var inv = new ModularInverse();
var B = new BigInteger[primes.Count];
var Bainv = new Dictionary <long, Dictionary <int, long> >();
for (int i = 0; i < primes.Count; i++)
{
var q = primes[i];
var aq = a / q;
var gamma = _sqrtN[q] * inv.Inverse(aq, q);
if (gamma > q / 2)
{
gamma = q - gamma;
}
B[i] = aq * gamma;
}
var ainv = new Dictionary <long, long>();
BigInteger b = 0;
for (int i = 0; i < B.Length; i++)
{
b += B[i];
}
var firstSln = new Dictionary <long, long>();
var secondSln = new Dictionary <long, long>();
for (int i = 0; i < _factorBase.Length; i++)
{
if (indexes.Contains(i))
{
continue;
}
var p = _factorBase[i];
ainv.Add(p, (long)inv.Inverse(a, p));
Bainv[p] = new Dictionary <int, long>();
for (int j = 0; j < primes.Count; j++)
{
Bainv[p][j] = (long)(2 * B[j] * ainv[p] % p);
}
firstSln[p] = (long)(ainv[p] * (_sqrtN[p] - b) % p);
secondSln[p] = (long)(ainv[p] * (-_sqrtN[p] - b) % p);
}
if (primes.Count == 0)
{
return(null);
}
result.Add(new SievePolynomial()
{
A = a, B = b, C = (b * b - n) / a, FirstRoot = firstSln, SecondRoot = secondSln, InvA = ainv, MinFactorA = primes[0], MaxFactorA = primes[primes.Count - 1]
});
var polyCount = Math.Pow(2, primes.Count - 1) - 1;
for (int i = 1; i <= polyCount; i++)
{
var v = 1;
for (; (i & (0x1 << (v - 1))) == 0; v++)
{
}
var tmp = (long)Math.Ceiling(i / Math.Pow(2, v));
if (tmp % 2 == 0)
{
b = b + 2 * B[v];
}
else
{
b = b - 2 * B[v];
}
firstSln = new Dictionary <long, long>();
secondSln = new Dictionary <long, long>();
for (var k = 0; k < _factorBase.Length; k++)
{
if (indexes.Contains(k))
{
continue;
}
var p = _factorBase[k];
firstSln[p] = (long)(ainv[p] * (_sqrtN[p] - b) % p);
secondSln[p] = (long)(ainv[p] * (-_sqrtN[p] - b) % p);
}
result.Add(new SievePolynomial()
{
A = a, B = b, C = (b * b - n) / a, FirstRoot = firstSln, SecondRoot = secondSln, InvA = ainv, MinFactorA = primes[0], MaxFactorA = primes[primes.Count - 1]
});
}
_polyIndex += 3 - primes.Count;
return(result);
}
