/// <summary>
/// Gamma function of the specified value.
/// </summary>
public static double Function(double x)
{
double[] P =
{
1.60119522476751861407E-4,
1.19135147006586384913E-3,
1.04213797561761569935E-2,
4.76367800457137231464E-2,
2.07448227648435975150E-1,
4.94214826801497100753E-1,
9.99999999999999996796E-1
};
double[] Q =
{
-2.31581873324120129819E-5,
5.39605580493303397842E-4,
-4.45641913851797240494E-3,
1.18139785222060435552E-2,
3.58236398605498653373E-2,
-2.34591795718243348568E-1,
7.14304917030273074085E-2,
1.00000000000000000320E0
};
double p, z;
double q = Math.Abs(x);
if (q > 33.0)
{
if (x < 0.0)
{
p = Math.Floor(q);
if (p == q)
{
throw new OverflowException();
}
z = q - p;
if (z > 0.5)
{
p += 1.0;
z = q - p;
}
z = q * Math.Sin(Math.PI * z);
if (z == 0.0)
{
throw new OverflowException();
}
z = Math.Abs(z);
z = Math.PI / (z * Stirling(q));
return(-z);
}
return(Stirling(x));
}
z = 1.0;
while (x >= 3.0)
{
x -= 1.0;
z *= x;
}
while (x < 0.0)
{
if (x == 0.0)
{
throw new ArithmeticException();
}
if (x > -1.0E-9)
{
return(z / ((1.0 + 0.5772156649015329 * x) * x));
}
z /= x;
x += 1.0;
}
while (x < 2.0)
{
if (x == 0.0)
{
throw new ArithmeticException();
}
if (x < 1.0E-9)
{
return(z / ((1.0 + 0.5772156649015329 * x) * x));
}
z /= x;
x += 1.0;
}
if ((x == 2.0) || (x == 3.0))
{
return(z);
}
x -= 2.0;
p = Special.Polevl(x, P, 6);
q = Special.Polevl(x, Q, 7);
return(z * p / q);
}
/// <summary>
/// Natural logarithm of the gamma function.
/// </summary>
public static double Log(double x)
{
if (x == 0)
{
return(Double.PositiveInfinity);
}
double p, q, w, z;
double[] A =
{
8.11614167470508450300E-4,
-5.95061904284301438324E-4,
7.93650340457716943945E-4,
-2.77777777730099687205E-3,
8.33333333333331927722E-2
};
double[] B =
{
-1.37825152569120859100E3,
-3.88016315134637840924E4,
-3.31612992738871184744E5,
-1.16237097492762307383E6,
-1.72173700820839662146E6,
-8.53555664245765465627E5
};
double[] C =
{
-3.51815701436523470549E2,
-1.70642106651881159223E4,
-2.20528590553854454839E5,
-1.13933444367982507207E6,
-2.53252307177582951285E6,
-2.01889141433532773231E6
};
if (x < -34.0)
{
q = -x;
w = Log(q);
p = Math.Floor(q);
if (p == q)
{
throw new OverflowException();
}
z = q - p;
if (z > 0.5)
{
p += 1.0;
z = p - q;
}
z = q * Math.Sin(Math.PI * z);
if (z == 0.0)
{
throw new OverflowException();
}
z = Constants.LogPI - Math.Log(z) - w;
return(z);
}
if (x < 13.0)
{
z = 1.0;
while (x >= 3.0)
{
x -= 1.0;
z *= x;
}
while (x < 2.0)
{
if (x == 0.0)
{
throw new OverflowException();
}
z /= x;
x += 1.0;
}
if (z < 0.0)
{
z = -z;
}
if (x == 2.0)
{
return(Math.Log(z));
}
x -= 2.0;
p = x * Special.Polevl(x, B, 5) / Special.P1evl(x, C, 6);
return(Math.Log(z) + p);
}
if (x > 2.556348e305)
{
throw new OverflowException();
}
q = (x - 0.5) * Math.Log(x) - x + 0.91893853320467274178;
if (x > 1.0e8)
{
return(q);
}
p = 1.0 / (x * x);
if (x >= 1000.0)
{
q += ((7.9365079365079365079365e-4 * p
- 2.7777777777777777777778e-3) * p
+ 0.0833333333333333333333) / x;
}
else
{
q += Special.Polevl(p, A, 4) / x;
}
return(q);
}
