Author: celestin
Date: Tue Oct 2 06:09:03 2012
New Revision: 1392751
URL: http://svn.apache.org/viewvc?rev=1392751&view=rev
Log:
User's guide for special functions now reports accuracy of
Gamma.gamma(double).
Modified:
commons/proper/math/trunk/src/site/apt/userguide/special.apt
Modified: commons/proper/math/trunk/src/site/apt/userguide/special.apt
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/site/apt/userguide/special.apt?rev=1392751&r1=1392750&r2=1392751&view=diff
==============================================================================
--- commons/proper/math/trunk/src/site/apt/userguide/special.apt (original)
+++ commons/proper/math/trunk/src/site/apt/userguide/special.apt Tue Oct 2
06:09:03 2012
@@ -42,7 +42,33 @@
Class {{{../apidocs/org/apache/commons/math3/special/Gamma.html}<<<Gamma>>>}}
contains several useful functions involving the Gamma Function.
-** 5.3.1 Log Gamma
+** Gamma
+
+ <<<Gamma.gamma(x)>>> computes the Gamma function, \u0393(x),
+ (see {{{http://mathworld.wolfram.com/GammaFunction.html}MathWorld}},
+ {{{http://dlmf.nist.gov/5}DLMF}}). The accuracy of the Commons-Math
+ implementation is assessed by comparaison with high precision values computed
+ with the {{{http://maxima.sourceforge.net/}Maxima}} Computer Algebra System.
+
+*---------------+----------------------------------------+-----------------+----------------+
+|| Interval || Values tested || Average error ||
Maximum error |
+*---------------+----------------------------------------+-----------------+----------------+
+| (-5.0, -4.0) | <<<k / 1024, k = -5119, ..., -4097>>> | 0.49 ulps |
3.0 ulps |
+*---------------+----------------------------------------+-----------------+----------------+
+| (-4.0, -3.0) | <<<k / 1024, k = -4095, ..., -3073>>> | 0.36 ulps |
2.0 ulps |
+*---------------+----------------------------------------+-----------------+----------------+
+| (-3.0, -2.0) | <<<k / 1024, k = -3071, ..., -2049>>> | 0.41 ulps |
2.0 ulps |
+*---------------+----------------------------------------+-----------------+----------------+
+| (-2.0, -1.0) | <<<k / 1024, k = -2047, ..., -1025>>> | 0.37 ulps |
2.0 ulps |
+*---------------+----------------------------------------+-----------------+----------------+
+| (-1.0, 0.0) | <<<k / 1024, k = -1023, ..., -1>>> | 0.46 ulps |
2.0 ulps |
+*---------------+----------------------------------------+-----------------+----------------+
+| (0.0, 8.0] | <<<k / 1024, k = 1, ..., 8192>>> | 0.33 ulps |
2.0 ulps |
+*---------------+----------------------------------------+-----------------+----------------+
+| (8.0, 141.0] | <<<k / 64, k = 513, ..., 9024>>> | 1.32 ulps |
7.0 ulps |
+*---------------+----------------------------------------+-----------------+----------------+
+
+** Log Gamma
<<<Gamma.logGamma(x)>>> computes the natural logarithm of the Gamma function,
log \u0393(x), for x > 0
@@ -63,7 +89,7 @@
| [8933.439345993791, 1.75555970201398e+305] | <<<2**(k / 8), k = 105, ...,
8112>>> | 0.35 ulps | 2.0 ulps |
*---------------------------------------------+---------------------------------------+-----------------+----------------+
-** 5.3.2 Regularized Gamma
+** Regularized Gamma
<<<Gamma.regularizedGammaP(a, x)>>> computes the value of the regularized
Gamma function, P(a, x)
