private XInt RecFactorial(int n)
{
if (n < 2)
{
return(XInt.One);
}
return(XInt.Pow(this.RecFactorial(n / 2), 2) * this.Swing(n));
}
private XInt RecFactorial3(int n)
{
if (n < 2)
{
return(XInt.One);
}
var recFact = this.RecFactorial3(n / 2);
var sqrFact = XInt.Pow(recFact, 2);
var swing = n < Smallswing
? SmallOddSwing3[n]
: this.swingDelegate3.EndInvoke(this.results3[--this.taskCounter3]);
return(sqrFact * swing);
}
private XInt OddFactorial(int n)
{
XInt oddFact;
if (n < Smallfact)
{
oddFact = SmallOddFactorial[n];
}
else
{
var sqrOddFact = this.OddFactorial(n / 2);
var ndiv4 = n / 4;
var oddFactNd4 = ndiv4 < Smallfact
? SmallOddFactorial[ndiv4]
: this.oddFactNdiv4;
oddFact = XInt.Pow(sqrOddFact, 2) * OddSwing(n, oddFactNd4);
}
this.oddFactNdiv4 = this.oddFactNdiv2;
this.oddFactNdiv2 = oddFact;
return(oddFact);
}
private XInt NestedSquare(int len)
{
if (len == 0)
{
return(XInt.One);
}
var i = 0;
var mult = this.multiList[0];
while (mult > 1)
{
if ((mult & 1) == 1) // is mult odd ?
{
this.primeList[len++] = this.primeList[i];
}
this.multiList[i++] = mult >> 1;
mult = this.multiList[i];
}
return(XMath.Product(this.primeList, i, len - i)
* XInt.Pow(this.NestedSquare(i), 2));
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
var rootN = XMath.FloorSqrt(n);
var log2N = XMath.FloorLog2(n);
var section = new XInt[log2N + 1];
for (var i = 0; i < section.Length; i++)
{
section[i] = XInt.One;
}
var sieve = new PrimeSieve(n);
var primes = sieve.GetPrimeCollection(3, rootN);
foreach (var prime in primes)
{
int k = 0, m = 0, q = n;
do
{
m += q /= prime;
} while (q >= 1);
while (m > 0)
{
if ((m & 1) == 1)
{
section[k] *= prime;
}
m = m / 2;
k++;
}
}
var j = 2;
var low = n;
while (low != rootN)
{
var high = low;
low = n / j++;
if (low < rootN)
{
low = rootN;
}
var primorial = sieve.GetPrimorial(low + 1, high);
if (primorial != XInt.One)
{
int k = 0, m = j - 2;
while (m > 0)
{
if ((m & 1) == 1)
{
section[k] *= primorial;
}
m = m / 2;
k++;
}
}
}
var factorial = section[log2N];
for (var i = log2N - 1; i >= 0; --i)
{
factorial = XInt.Pow(factorial, 2) * section[i];
}
var exp2N = n - XMath.BitCount(n);
return(factorial << exp2N);
}
