[oct-scm] [oct-git]OCT: A portable Lisp implementation for quad-double precision floats branch master updated. 08d254374188f97026d114451bba5d839dbdad11

[Raymond Toy]

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- Log -----------------------------------------------------------------
commit 08d254374188f97026d114451bba5d839dbdad11
Author: Raymond Toy <toy.raymond at gmail.com>
Date:   Mon Mar 28 22:54:32 2011 -0400

    Make INCOMPLETE-GAMMA-TAIL more accurate.
    
    o Use the new continued fraction for the incomplete-gamma when the
      argument z is close enough to the negative real axis.

diff --git a/qd-gamma.lisp b/qd-gamma.lisp
index e020a91..7048b80 100644
--- a/qd-gamma.lisp
+++ b/qd-gamma.lisp
@@ -372,8 +372,15 @@
 	(if (and (> (abs z) (abs (- a 1)))
 		(not (minusp (realpart z))))
 	    (cf-incomplete-gamma-tail a z)
-	    (- (gamma a) (incomplete-gamma a z)))
-	(cf-incomplete-gamma-tail a z))))
+	    (- (gamma a) (cf-incomplete-gamma a z)))
+	;; If the argument is close enough to the negative real axis,
+	;; the continued fraction for the tail is not very accurate.
+	;; Use the incomplete gamma function to evaluate in this
+	;; region.  (Arbitrarily selected the region to be a sector.
+	;; But what is the correct size of this sector?)
+	(if (<= (phase z) 3.1)
+	    (cf-incomplete-gamma-tail a z)
+	    (- (gamma a) (cf-incomplete-gamma a z))))))
 
 (defun incomplete-gamma (a z)
   "Incomplete gamma function defined by:

-----------------------------------------------------------------------

Summary of changes:
 qd-gamma.lisp |   11 +++++++++--
 1 files changed, 9 insertions(+), 2 deletions(-)


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OCT:  A portable Lisp implementation for quad-double precision floats