private XInt OddFactorial(int n)
{
if (n < Smallfact)
{
return(SmallOddFactorial[n]);
}
var sqrOddFact = this.OddFactorial(n / 2);
XInt oddFact;
if (n < Smallswing)
{
oddFact = XInt.Pow(sqrOddFact, 2) * SmallOddSwing[n];
}
else
{
var ndiv4 = n / 4;
var oddFactNd4 = ndiv4 < Smallfact ? SmallOddFactorial[ndiv4] : this.oddFactNdiv4;
this.oddSwingTask = Task.Factory.StartNew <XInt>(() => OddSwing(n, oddFactNd4));
sqrOddFact = XInt.Pow(sqrOddFact, 2);
oddFact = sqrOddFact * this.oddSwingTask.Result;
}
this.oddFactNdiv4 = this.oddFactNdiv2;
this.oddFactNdiv2 = oddFact;
return(oddFact);
}
private XInt RecFactorial(int n)
{
if (n < 2)
{
return(XInt.One);
}
return(XInt.Pow(this.RecFactorial(n / 2), 2) * Swing(n));
}
private XInt OddFactorial(uint n)
{
if (n < SmallOddFactorial.Length)
{
return(new XInt(SmallOddFactorial[n]));
}
return(XInt.Pow(this.OddFactorial(n / 2), 2) * this.OddSwing(n));
}
private XInt RecFactorial(int n)
{
if (n < 2)
{
return(XInt.One);
}
//-- Not commutative!!
return(this.Swing(n) * XInt.Pow(this.RecFactorial(n / 2), 2));
}
private XInt RecFactorial(int n)
{
if (n < 2)
{
return(XInt.One);
}
if ((n & 1) == 1)
{
return(this.RecFactorial(n - 1) * n);
}
return(this.MiddleBinomial(n) * XInt.Pow(this.RecFactorial(n / 2), 2));
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
var log2N = XMath.FloorLog2(n);
var j = log2N;
var hN = n;
this.primeList = new int[log2N][];
this.listLength = new int[log2N];
this.bound = new int[log2N];
this.tower = new int[log2N + 1];
while (true)
{
this.tower[j] = hN;
if (hN == 1)
{
break;
}
this.bound[--j] = hN / 3;
var pLen = hN < 4 ? 6 : (int)(2.0 * (XMath.FloorSqrt(hN)
+ (double)hN / (XMath.Log2(hN) - 1)));
this.primeList[j] = new int[pLen];
hN >>= 1;
}
this.tower[0] = 2;
this.PrimeFactors(n);
var init = this.listLength[0] == 0 ? 1 : 3;
var oddFactorial = new XInt(init);
var results = new XInt[log2N];
Parallel.For(1, log2N, i =>
results[i] = XMath.Product(this.primeList[i], 0, this.listLength[i])
);
for (var i = 1; i < log2N; i++)
{
oddFactorial = XInt.Pow(oddFactorial, 2);
oddFactorial = oddFactorial * results[i];
}
return(oddFactorial << (n - XMath.BitCount(n)));
}
private XInt RecFactorial(int n)
{
if (n < 2)
{
return(XInt.One);
}
var recFact = this.RecFactorial(n / 2);
var sqrFact = XInt.Pow(recFact, 2);
var swing = n < Smallswing
? SmallOddSwing[n]
: this.swingDelegate.EndInvoke(this.results[--this.taskCounter]);
return(sqrFact * swing);
}
private XInt RepeatedSquare(int len, int k)
{
if (len == 0)
{
return(XInt.One);
}
int i = 0, 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];
}
var p = XMath.Product(this.primeList, i, len - i);
return(XInt.Pow(p, k) * this.RepeatedSquare(i, 2 * k));
}
private XInt MiddleBinomial(int n) // assuming n = 2k
{
if (n < 50)
{
return(new XInt(Binomial[n / 2]));
}
int k = n / 2, pc = 0, pp = 0;
var rootN = XMath.FloorSqrt(n);
var bigPrimes = this.sieve.GetPrimorial(k + 1, n);
var smallPrimes = this.sieve.GetPrimorial(k / 2 + 1, n / 3);
var primes = this.sieve.GetPrimeCollection(rootN + 1, n / 5);
var primeList = new int[primes.NumberOfPrimes];
foreach (var prime in primes.Where(prime => (n / prime & 1) == 1))
{
primeList[pc++] = prime;
}
var prodPrimes = XMath.Product(primeList, 0, pc);
primes = this.sieve.GetPrimeCollection(1, rootN);
var primePowers = new XInt[primes.NumberOfPrimes];
var exp = 0;
foreach (var prime in primes.Where(prime => (exp = ExpSum(prime, n)) > 0))
{
primePowers[pp++] = XInt.Pow(prime, exp);
}
var powerPrimes = XMath.Product(primePowers, 0, pp);
return(bigPrimes * smallPrimes * prodPrimes * powerPrimes);
}
