void DoTest(Candidate cand, int n, bool showFullValue, bool verbose)
{
this.watch.Reset();
this.watch.Start();
XInt nFact = cand.GetValue(n);
this.watch.Stop();
int checksum = nFact.GetHashCode();
var ms = this.watch.ElapsedMilliseconds;
var eddms = XMath.ExactDecimalDigitsPerMillisecond(n, ms);
var res = new Result(cand, ms, checksum, eddms);
cand.Performance[n] = res;
if (verbose)
{
this.winsole.WriteRed(string.Format(
// "\nSUMMARY: Computed the factorial "
"\n{0}! = {1}\nAlgorithm used: {2}\nCheckSum: <{3:X}>\nComputation in {4:D} ms.\nDecimal digits per ms {5}.\n",
n, XMath.AsymptFactorial(n), cand.Name, checksum, ms, eddms));
}
if (showFullValue)
{
this.winsole.Write(nl + "Now converting to string. Note: It takes longer to convert than to compute!" + nl + nl);
this.winsole.WriteLine(nFact.ToString());
}
}
public void SanityCheck(int length)
{
bool ok = true;
for (int n = 0; n < length; n++)
{
XInt r = Candidate.Reference.GetValue(n);
foreach (Candidate cand in Candidate.Sanity)
{
XInt t = cand.GetValue(n);
if (!t.Equals(r))
{
this.winsole.WriteLine(string.Format(
"\n{0}({1}) failed!", cand.Name.Trim(), n));
ok = false;
}
}
if ((n % 10) == 0)
{
this.winsole.WriteFlush(" . ");
}
if ((n % 150) == 149)
{
this.winsole.WriteLine();
}
}
this.winsole.Write("\nWell, some values will" + (ok ? " " : " not ") +
"give correct results " + (ok ? ";-)\n" : "~:(\n"));
}
private XInt RecFactorial(int n)
{
if (n < 2)
{
return(XInt.One);
}
return(XInt.Pow(this.RecFactorial(n / 2), 2) * this.Swing(n));
}
static XInt OddSwing(int n, XInt oddFactNdiv4)
{
if (n < Smallswing) return SmallOddSwing[n];
var len = (n - 1) / 4;
if ((n % 4) != 2) len++;
var high = n - ((n + 1) & 1);
return Product(high, len) / oddFactNdiv4;
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new ArithmeticException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
this.oddFactNdiv4 = this.oddFactNdiv2 = XInt.One;
return(this.OddFactorial(n) << (n - XMath.BitCount(n)));
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new ArithmeticException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
this.oddFactNdiv4 = this.oddFactNdiv2 = XInt.One;
return this.OddFactorial(n) << (n - XMath.BitCount(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);
}
static XInt OddSwing(int n, XInt oddFactNdiv4)
{
if (n < Smallswing)
{
return(SmallOddSwing[n]);
}
var len = (n - 1) / 4;
if ((n % 4) != 2)
{
len++;
}
var high = n - ((n + 1) & 1);
return(Product(high, len) / oddFactNdiv4);
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
this.sieve = new PrimeSieve(n);
var log2N = XMath.FloorLog2(n);
var source = new int[log2N];
int h = 0, shift = 0, length = 0;
// -- It is more efficient to add the big intervals
// -- first and the small ones later! Is it?
while (h != n)
{
shift += h;
h = n >> log2N--;
if (h > 2)
{
source[length++] = h;
}
}
var results = new XInt[length];
Parallel.For(0, length, currentIndex =>
results[currentIndex] = this.Swing(source[currentIndex])
);
XInt p = XInt.One, r = XInt.One, rl = XInt.One;
for (var i = 0; i < length; i++)
{
var t = rl * results[i];
p = p * t;
rl = r;
r = r * p;
}
return(r << shift);
}
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);
}
public XInt Factorial(int n)
{
if (n < 20) { return XMath.Factorial(n); }
this.sieve = new PrimeSieve(n);
var log2N = XMath.FloorLog2(n);
var source = new int[log2N];
int h = 0, shift = 0, length = 0;
// -- It is more efficient to add the big intervals
// -- first and the small ones later! Is it?
while (h != n)
{
shift += h;
h = n >> log2N--;
if (h > 2) { source[length++] = h; }
}
var results = new XInt[length];
Parallel.For(0, length, currentIndex =>
results[currentIndex] = this.Swing(source[currentIndex])
);
XInt p = XInt.One, r = XInt.One, rl = XInt.One;
for (var i = 0; i < length; i++)
{
var t = rl * results[i];
p = p * t;
rl = r;
r = r * p;
}
return r << shift;
}
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;
}
private static XInt BigRecProduct(XInt[] s, int n, int m)
{
if (n > m)
{
return XInt.One;
}
if (n == m)
{
return s[n];
}
int k = (n + m) >> 1;
return BigRecProduct(s, n, k) * BigRecProduct(s, k + 1, m);
}
public static XInt Product(XInt[] a, int start, int len)
{
int n = len - 1;
if (len > ParallelThreshold)
{
var task = Task.Factory.StartNew<XInt>(() =>
{
return BigRecProduct(a, start + n / 2 + 1, start + n);
});
var left = BigRecProduct(a, start, start + n / 2);
return left * task.Result;
}
return BigRecProduct(a, start, n);
}
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;
}
public static XInt Product(XInt[] a)
{
return BigRecProduct(a, 0, a.Length - 1);
}
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);
}