private XInt Swing(int n)
{
if (n < 33)
{
return(SmallOddSwing[n]);
}
var count = 0;
var rootN = XMath.FloorSqrt(n);
var j = 1;
var prod = XInt.One;
int high;
while (true)
{
high = n / j++;
var low = n / j++;
if (low < rootN)
{
low = rootN;
}
if (high - low < 32)
{
break;
}
var primorial = this.GetPrimorial(low + 1, high);
prod *= primorial;
}
var primes = this.sieve.GetPrimeCollection(3, high);
foreach (var prime in primes)
{
int q = n, p = 1;
while ((q /= prime) > 0)
{
if ((q & 1) == 1)
{
p *= prime;
}
}
if (p > 1)
{
this.primeList[count++] = p;
}
}
return(prod * XMath.Product(this.primeList, 0, count));
}
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)));
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
this.cache = new Dictionary <int, CachedPrimorial>();
this.sieve = new PrimeSieve(n);
var pLen = (int)(2.0 * (XMath.FloorSqrt(n)
+ (double)n / (XMath.Log2(n) - 1)));
this.primeList = new int[pLen];
var exp2 = n - XMath.BitCount(n);
return(this.RecFactorial(n) << exp2);
}
private XInt Swing(int n)
{
if (n < 33)
{
return(SmallOddSwing[n]);
}
var primorial = Task.Factory.StartNew(() => this.sieve.GetPrimorial(n / 2 + 1, n));
var count = 0;
var rootN = XMath.FloorSqrt(n);
var aPrimes = this.sieve.GetPrimeCollection(3, rootN);
var bPrimes = this.sieve.GetPrimeCollection(rootN + 1, n / 3);
var piN = aPrimes.NumberOfPrimes + bPrimes.NumberOfPrimes;
var primeList = new int[piN];
foreach (var prime in aPrimes)
{
int q = n, p = 1;
while ((q /= prime) > 0)
{
if ((q & 1) == 1)
{
p *= prime;
}
}
if (p > 1)
{
primeList[count++] = p;
}
}
foreach (var prime in bPrimes.Where(prime => ((n / prime) & 1) == 1))
{
primeList[count++] = prime;
}
var primeProduct = XMath.Product(primeList, 0, count);
return(primeProduct * primorial.Result);
}
private static XInt Swing(PrimeSieve sieve, int n)
{
var primorial = Task.Factory.StartNew <XInt>(() => sieve.GetPrimorial(n / 2 + 1, n));
var count = 0;
var rootN = XMath.FloorSqrt(n);
var aPrimes = sieve.GetPrimeCollection(3, rootN);
var bPrimes = sieve.GetPrimeCollection(rootN + 1, n / 3);
var primeList = new int[aPrimes.NumberOfPrimes + bPrimes.NumberOfPrimes];
foreach (var prime in aPrimes)
{
int q = n, p = 1;
while ((q /= prime) > 0)
{
if ((q & 1) == 1)
{
p *= prime;
}
}
if (p > 1)
{
primeList[count++] = p;
}
}
foreach (var prime in bPrimes.Where(prime => ((n / prime) & 1) == 1))
{
primeList[count++] = prime;
}
var primeProduct = XMath.Product(primeList, 0, count);
return(primeProduct * primorial.Result);
}
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);
}