private List <SmoothPair> Sieve(SievePolynomial sievePolynomial, BigInteger n)
{
var result = new List <SmoothPair>();
var sieveArray = new BigInteger[2 * _sieveBound];
for (int j = 0; j < sieveArray.Length; j++)
{
var x = j > _sieveBound ? _sieveBound - j : j;
var t = sievePolynomial.A * x * x + 2 * sievePolynomial.B * x + sievePolynomial.C;
sieveArray[j] = t;
}
var i = 0;
foreach (var p in _factorBase)
{
//Need skip small primes
if (p == 7621)
{
i++;
i--;
}
if (sievePolynomial.A % p == 0)
{
continue;
}
var logp = _logp[i];
var root1 = sievePolynomial.FirstRoot[p];
var root2 = sievePolynomial.SecondRoot[p];
if (root1 < 0)
{
root1 += p;
}
if (root2 < 0)
{
root2 += p;
}
long x = 0;
while (x < _sieveBound)
{
if (x + root1 < _sieveBound)
{
if (sieveArray[x + root1] % p != 0)
{
throw new Exception();
}
while (sieveArray[x + root1] % p == 0)
{
sieveArray[x + root1] /= p;
}
}
if (x + root2 < _sieveBound && root1 != root2)
{
if (sieveArray[x + root2] % p != 0)
{
throw new Exception();
}
while (sieveArray[x + root2] % p == 0)
{
sieveArray[x + root2] /= p;
}
}
if (x != 0)
{
if (sieveArray[x - root1 + _sieveBound] % p != 0 || sieveArray[x - root2 + _sieveBound] % p != 0)
{
throw new Exception();
}
while (sieveArray[x - root1 + _sieveBound] % p == 0)
{
sieveArray[x - root1 + _sieveBound] /= p;
}
while (sieveArray[x - root2 + _sieveBound] % p == 0 && root1 != root2)
{
sieveArray[x - root2 + _sieveBound] /= p;
}
}
x += p;
}
i += 1;
}
i = 0;
foreach (var value in sieveArray)
{
if (value == 1 || value == -1)
{
var x = i > _sieveBound ? _sieveBound - i : i;
var vector = new Dictionary <long, int>();
var t = sievePolynomial.A * x + sievePolynomial.B;
var polyValue = t * t - n;
if (polyValue < 0)
{
vector.Add(-1, 1);
polyValue = -polyValue;
}
else
{
vector.Add(-1, 0);
}
foreach (var p in _factorBase)
{
while (polyValue % p == 0)
{
if (vector.ContainsKey(p))
{
vector[p]++;
}
else
{
vector.Add(p, 1);
}
polyValue = (polyValue / p);
}
}
if (polyValue == 1)
{
var xVal = sievePolynomial.A * x + sievePolynomial.B;
result.Add(new SmoothPair(xVal, vector));
}
}
i++;
}
return(result);
}
private List <SmoothPair> LogSieve(SievePolynomial sievePolynomial, BigInteger n)
{
var result = new List <SmoothPair>();
double[] sieveArray = new double[2 * _sieveBound];
var i = 0;
for (; i < _factorBase.Length; i++)
{
var p = _factorBase[i];
if (sievePolynomial.A % p == 0)
{
continue;
}
var logp = _logp[i];
var root1 = sievePolynomial.FirstRoot[p];
var root2 = sievePolynomial.SecondRoot[p];
if (root1 < 0)
{
root1 += p;
}
if (root2 < 0)
{
root2 += p;
}
long x = 0;
while (x < _sieveBound)
{
if (x + root1 < _sieveBound)
{
sieveArray[x + root1] += logp;
}
if (x + root2 < _sieveBound)
{
sieveArray[x + root2] += logp;
}
if (x != 0)
{
sieveArray[x - root1 + _sieveBound] += logp;
sieveArray[x - root2 + _sieveBound] += logp;
}
x += p;
}
}
i = 0;
foreach (var value in sieveArray)
{
if (value > _thresh)
{
BigInteger x = i > _sieveBound ? _sieveBound - i : i;
var vector = new Dictionary <long, int>();
var t = sievePolynomial.A * x + sievePolynomial.B;
var polyValue = t * t - n;
if (polyValue < 0)
{
vector.Add(-1, 1);
polyValue = -polyValue;
}
else
{
vector.Add(-1, 0);
}
foreach (var p in _factorBase)
{
while (polyValue % p == 0)
{
if (vector.ContainsKey(p))
{
vector[p]++;
}
else
{
vector.Add(p, 1);
}
polyValue = (polyValue / p);
}
}
var xVal = sievePolynomial.A * x + sievePolynomial.B;
if (polyValue == 1)
{
result.Add(new SmoothPair(xVal, vector));
}
}
i++;
}
return(result);
}