/// <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); }