public Rational(XInt _num, XInt _den)
{
// If (and only if) the arithmetic supports a
// *real* fast Gcd this would lead to a speed up:
this.num = _num;
this.den = _den;
}
public Rational(long _num, long _den)
{
long g = Gcd(_num, _den);
this.num = new XInt(_num / g);
this.den = new XInt(_den / g);
}
// assuming n = 2k
private XInt MiddleBinomial(int n)
{
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;
}
private static XInt Swing(int n)
{
int z;
switch (n % 4)
{
case 1: z = n / 2 + 1; break;
case 2: z = 2; break;
case 3: z = 2 * (n / 2 + 2); break;
default: z = 1; break;
}
var b = new XInt(z);
z = 2 * (n - ((n + 1) & 1));
for (var i = 1; i <= n / 4; i++, z -= 4)
{
b = (b * z) / i;
}
return(b);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 2)
{
return(XInt.One);
}
long h = n / 2;
var q = h * h;
var r = (n & 1) == 1 ? 2 * q * n : 2 * q;
var f = new XInt(r);
for (var d = 1; d < n - 2; d += 2)
{
f *= q -= d;
}
return(f);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 2) return XInt.One;
var p = XInt.One;
var r = XInt.One;
this.currentN = XInt.One;
int h = 0, shift = 0, high = 1;
var log2N = XMath.FloorLog2(n);
while (h != n)
{
shift += h;
h = n >> log2N--;
var len = high;
high = (h - 1) | 1;
len = (high - len) / 2;
if (len > 0)
{
p *= this.Product(len);
r *= p;
}
}
return r << shift;
}
public Rational(long _num, long _den)
{
long cd = Gcd(_den, _num);
this.num = new XInt(_num / cd);
this.den = new XInt(_den / cd);
}
private XInt Product(int n)
{
var m = n / 2;
if (m == 0) return this.currentN += 2;
if (n == 2) return (this.currentN += 2) * (this.currentN += 2);
return this.Product(n - m) * this.Product(m);
}
private XInt Swing(long n)
{
var s = this.gN - 1 + ((n - this.gN + 1) % 4);
bool oddN = (this.gN & 1) != 1;
for (; this.gN <= s; this.gN++)
{
if (oddN = !oddN) this.f *= this.gN;
else this.f = (this.f * 4) / this.gN;
}
if (oddN) for (; this.gN <= n; this.gN += 4)
{
var m = ((this.gN + 1) * (this.gN + 3)) << 1;
var d = (this.gN * (this.gN + 2)) >> 3;
this.f = (this.f * m) / d;
}
else for (; this.gN <= n; this.gN += 4)
{
var m = (this.gN * (this.gN + 2)) << 1;
var d = ((this.gN + 1) * (this.gN + 3)) >> 3;
this.f = (this.f * m) / d;
}
return this.f;
}
static XInt Swing(int n)
{
var w = XInt.One;
if (n > 1)
{
n = n + 2;
var s = new XInt[n + 1];
s[0] = s[1] = XInt.Zero;
s[2] = w;
for (var m = 3; m <= n; m++)
{
s[m] = s[m - 2];
for (var k = m; k >= 2; k--)
{
s[k] += s[k - 2];
if ((k & 1) == 1) // if k is odd
{
s[k] += s[k - 1];
}
}
}
w = s[n];
}
return(w);
}
static public XInt Product(long[] seq, int start, int len)
{
if (len <= ThresholdProductSerial)
{
var rprod = new XInt(seq[start]);
for (var i = start + 1; i < start + len; i++)
{
rprod *= seq[i];
}
return(rprod);
}
else
{
var halfLen = len / 2;
var rprod = XInt.Zero;
var lprod = XInt.Zero;
Parallel.Invoke(
() => { rprod = Product(seq, start, halfLen); },
() => { lprod = Product(seq, start + halfLen, len - halfLen); }
);
return(lprod * rprod);
}
}
static XInt Swing(int n)
{
var w = XInt.One;
if (n > 1)
{
n = n + 2;
var s = new XInt[n + 1];
s[0] = s[1] = XInt.Zero;
s[2] = w;
for (var m = 3; m <= n; m++)
{
s[m] = s[m - 2];
for (var k = m; k >= 2; k--)
{
s[k] += s[k - 2];
if ((k & 1) == 1) // if k is odd
{
s[k] += s[k - 1];
}
}
}
w = s[n];
}
return w;
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
int r = n % 8, s = n / 8 + 1;
var rf = (long)(new int[] { 1, 1, 2, 6, 24, 120, 720, 5040 })[r];
if (n < 8)
{
return rf;
}
var factors = new XInt[s];
factors[s - 1] = rf;
Parallel.For(0, s - 1, i =>
{
factors[i] = CPpoly(i * 8 + r + 1);
});
return XMath.Product(factors, 0, s);
}
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);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 2)
{
return XInt.One;
}
long h = n / 2;
var q = h * h;
var r = (n & 1) == 1 ? 2 * q * n : 2 * q;
var f = new XInt(r);
for (var d = 1; d < n - 2; d += 2)
{
f *= q -= d;
}
return f;
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
var s = new XInt[n + 1];
s[0] = XInt.One;
for (var m = 1; m <= n; m++)
{
s[m] = XInt.Zero;
for (var k = m; k >= 1; k--)
{
for (var i = 1; i <= k; i++)
{
s[i] += s[i - 1];
}
}
}
return(s[n]);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
int r = n % 8, s = n / 8 + 1;
var rf = (long)(new int[] { 1, 1, 2, 6, 24, 120, 720, 5040 })[r];
if (n < 8)
{
return(rf);
}
var factors = new XInt[s];
factors[s - 1] = rf;
Parallel.For(0, s - 1, i =>
{
factors[i] = CPpoly(i * 8 + r + 1);
});
return(XMath.Product(factors, 0, s));
}
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);
}
return(XInt.Pow(this.RecFactorial(n / 2), 2) * Swing(n));
}
static XInt OddSwing(int n, XInt oddFactNdiv4)
{
var len = (n - 1) / 4;
if ((n % 4) != 2) len++;
//-- if type(n, odd) then high = n else high = n-1.
var high = n - ((n + 1) & 1);
return Product(high, len) / oddFactNdiv4;
}
public Rational(XInt _num, XInt _den)
{
// If (and only if) the arithmetic supports a
// *real* fast Gcd this would lead to a speed up:
// XInt cd = XInt.Gcd(_num, _den);
// num = new XInt(_num / cd);
// den = new XInt(_den / cd);
this.num = _num;
this.den = _den;
}
private XInt RecFactorial(int n)
{
if (n < 2)
{
return(XInt.One);
}
//-- Not commutative!!
return(this.Swing(n) * XInt.Pow(this.RecFactorial(n / 2), 2));
}
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));
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
this.gN = 1;
this.f = XInt.One;
return this.RecFactorial(n);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
this.gN = 1;
this.f = XInt.One;
return(this.RecFactorial(n));
}
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)));
}
static XInt OddSwing(int n, XInt oddFactNdiv4)
{
var len = (n - 1) / 4;
if ((n % 4) != 2)
{
len++;
}
//-- if type(n, odd) then high = n else high = n-1.
var high = n - ((n + 1) & 1);
return(Product(high, len) / oddFactNdiv4);
}
private XInt Product(int n)
{
var m = n / 2;
if (m == 0)
{
return(this.currentN += 2);
}
if (n == 2)
{
return((this.currentN += 2) * (this.currentN += 2));
}
return(this.Product(n - m) * this.Product(m));
}
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);
}
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));
}
XInt IFactorialFunction.Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 2)
{
return(XInt.One);
}
var log2N = XMath.FloorLog2(n);
ProductDelegate prodDelegate = Product;
var results = new IAsyncResult[log2N];
int high = n, low = n >> 1, shift = low, taskCounter = 0;
// -- It is more efficient to add the big intervals
// -- first and the small ones later!
while ((low + 1) < high)
{
results[taskCounter++] = prodDelegate.BeginInvoke(low + 1, high, null, null);
high = low;
low >>= 1;
shift += low;
}
XInt p = XInt.One, r = XInt.One;
while (--taskCounter >= 0)
{
var I = Task.Factory.StartNew(() => r * p);
var t = p * prodDelegate.EndInvoke(results[taskCounter]);
r = I.Result;
p = t;
}
return((r * p) << shift);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 7)
{
return (XInt)(new int[] { 1, 1, 2, 6, 24, 120, 720 })[n];
}
int i = 1, loop = n / 2;
var f = new XInt[loop + (n & 1)];
f[0] = loop;
if ((n & 1) == 1)
{
f[loop] = n;
}
XInt s = loop, t;
for (var inc = loop - 1; inc > 0; inc--)
{
s += inc;
t = s;
while (t.IsEven())
{
loop++;
t /= 2;
}
f[i++] = t;
}
return SplitProduct(f) << loop;
}
private XInt Swing(long n)
{
var s = this.gN - 1 + ((n - this.gN + 1) % 4);
bool oddN = (this.gN & 1) != 1;
for (; this.gN <= s; this.gN++)
{
if (oddN = !oddN)
{
this.f *= this.gN;
}
else
{
this.f = (this.f * 4) / this.gN;
}
}
if (oddN)
{
for (; this.gN <= n; this.gN += 4)
{
var m = ((this.gN + 1) * (this.gN + 3)) << 1;
var d = (this.gN * (this.gN + 2)) >> 3;
this.f = (this.f * m) / d;
}
}
else
{
for (; this.gN <= n; this.gN += 4)
{
var m = (this.gN * (this.gN + 2)) << 1;
var d = ((this.gN + 1) * (this.gN + 3)) >> 3;
this.f = (this.f * m) / d;
}
}
return(this.f);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 7)
{
return((XInt)(new int[] { 1, 1, 2, 6, 24, 120, 720 })[n]);
}
int i = 1, loop = n / 2;
var f = new XInt[loop + (n & 1)];
f[0] = loop;
if ((n & 1) == 1)
{
f[loop] = n;
}
XInt s = loop, t;
for (var inc = loop - 1; inc > 0; inc--)
{
s += inc;
t = s;
while (t.IsEven())
{
loop++;
t /= 2;
}
f[i++] = t;
}
return(SplitProduct(f) << loop);
}
private static XInt Swing(int n)
{
int z;
switch (n % 4)
{
case 1: z = n / 2 + 1; break;
case 2: z = 2; break;
case 3: z = 2 * (n / 2 + 2); break;
default: z = 1; break;
}
var b = new XInt(z);
z = 2 * (n - ((n + 1) & 1));
for (var i = 1; i <= n / 4; i++, z -= 4)
{
b = (b * z) / i;
}
return b;
}
public XInt Factorial(int n)
{
if (n < 20)
{
return(XMath.Factorial(n));
}
this.sieve = new PrimeSieve(n);
var log2N = XMath.FloorLog2(n);
SwingDelegate swingDelegate = this.Swing;
var results = new IAsyncResult[log2N];
int h = 0, shift = 0, taskCounter = 0;
// -- It is more efficient to add the big intervals
// -- first and the small ones later!
while (h != n)
{
shift += h;
h = n >> log2N--;
if (h > 2)
{
results[taskCounter++] = swingDelegate.BeginInvoke(h, null, null);
}
}
XInt p = XInt.One, r = XInt.One, rl = XInt.One;
for (var i = 0; i < taskCounter; i++)
{
var t = rl * swingDelegate.EndInvoke(results[i]);
p = p * t;
rl = r;
r = r * p;
}
return(r << shift);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
if (n < 2)
{
return(XInt.One);
}
var p = XInt.One;
var r = XInt.One;
this.currentN = XInt.One;
int h = 0, shift = 0, high = 1;
var log2N = XMath.FloorLog2(n);
while (h != n)
{
shift += h;
h = n >> log2N--;
var len = high;
high = (h - 1) | 1;
len = (high - len) / 2;
if (len > 0)
{
p *= this.Product(len);
r *= p;
}
}
return(r << shift);
}
public XInt Factorial(int n)
{
if (n < 0)
{
throw new System.ArgumentOutOfRangeException(
this.Name + ": " + nameof(n) + " >= 0 required, but was " + n);
}
var s = new XInt[n + 1];
s[0] = XInt.One;
for (var m = 1; m <= n; m++)
{
s[m] = XInt.Zero;
for (var k = m; k >= 1; k--)
{
for (var i = 1; i <= k; i++)
{
s[i] += s[i - 1];
}
}
}
return s[n];
}
private static XInt CPpoly(XInt x)
{
// Implemented after Fredrik Johansson's arb-function
// rising_fmprb_ui_bsplit_eight (please speak aloud).
// x(x+1)...(x+7) = (28+98x+63x^2+14x^3+x^4)^2-16(7+2x)^2
// t = x^2, v = x^3, u = x^4
var t = x * x;
var v = x * t;
var u = t * t;
// u = (28 + 98x + 63x^2 + 14x^3 + x^4)^2
u += v * 14u;
u += t * 63u;
u += x * 98u;
u += 28;
u *= u;
// 16 (7+2x)^2 = 784 + 448x + 64x^2
u -= 784u;
u -= x * 448u;
u -= t << 6;
return(u);
}
private static XInt CPpoly(XInt x)
{
// Implemented after Fredrik Johansson's arb-function
// rising_fmprb_ui_bsplit_eight (please speak aloud).
// x(x+1)...(x+7) = (28+98x+63x^2+14x^3+x^4)^2-16(7+2x)^2
// t = x^2, v = x^3, u = x^4
var t = x * x;
var v = x * t;
var u = t * t;
// u = (28 + 98x + 63x^2 + 14x^3 + x^4)^2
u += v * 14u;
u += t * 63u;
u += x * 98u;
u += 28;
u *= u;
// 16 (7+2x)^2 = 784 + 448x + 64x^2
u -= 784u;
u -= x * 448u;
u -= t << 6;
return u ;
}
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);
}
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));
}
public readonly XInt Value; // class { get; set; }
public CachedPrimorial(int highBound, XInt val)
{
this.High = highBound;
this.Value = val;
}
public Rational(XInt _num, XInt _den)
{
// If (and only if) the arithmetic supports a
// *real* fast Gcd this would lead to a speed up:
this.num = _num;
this.den = _den;
}
readonly XInt num; // Numerator
#endregion Fields
#region Constructors
public Rational(long _num, long _den)
{
long g = Gcd(_num, _den);
this.num = new XInt(_num / g);
this.den = new XInt(_den / g);
}
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;
}
public Rational(XInt _num, XInt _den)
{
// If (and only if) the arithmetic supports a
// *real* fast Gcd this would lead to a speed up:
// XInt cd = XInt.Gcd(_num, _den);
// num = new XInt(_num / cd);
// den = new XInt(_den / cd);
this.num = _num;
this.den = _den;
}
readonly XInt num; // Numerator
#endregion Fields
#region Constructors
public Rational(long _num, long _den)
{
long cd = Gcd(_den, _num);
this.num = new XInt(_num / cd);
this.den = new XInt(_den / cd);
}
public readonly XInt Value; // class { get; set; }
#endregion Fields
#region Constructors
public CachedPrimorial(int highBound, XInt val)
{
this.High = highBound;
this.Value = val;
}
static public XInt Product(long[] seq, int start, int len)
{
if (len <= ThresholdProductSerial)
{
var rprod = new XInt(seq[start]);
for (var i = start + 1; i < start + len; i++)
{
rprod *= seq[i];
}
return rprod;
}
else
{
var halfLen = len / 2;
var rprod = XInt.Zero;
var lprod = XInt.Zero;
Parallel.Invoke(
() => { rprod = Product(seq, start, halfLen); },
() => { lprod = Product(seq, start + halfLen, len - halfLen); }
);
return lprod * rprod;
}
}
