[Maxima-commits] Maxima, A Computer Algebra System branch master updated. 5.28.0-2-g4a7a591

[Raymond T. <rt...@us...>]

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- Log -----------------------------------------------------------------
commit 4a7a591d0f09b0729a7d13042529ca96aed4891c
Author: Raymond Toy <toy...@gm...>
Date:   Fri Aug 17 09:54:32 2012 -0700

    Fix Bug 3440046: elliptic_f(0.5,1) signals error
    
    src/ellipt.lisp:
    o Don't call elliptic_kc unless we have to.
    o Signal errors if we try to compute more than one period for
      elliptic_f(x,1), since elliptic_f(%pi/2,1) is infinity.
    
    tests/rtest16.mac:
    o Add test for elliptic_f(0.5,1)
    o Add tests for elliptic_f(2.0,1);

diff --git a/src/ellipt.lisp b/src/ellipt.lisp
index dd014f9..7bd05d1 100644
--- a/src/ellipt.lisp
+++ b/src/ellipt.lisp
@@ -1261,8 +1261,10 @@ first kind:
     ;; F(z|m) = F(z - pi*round(Re(z)/pi)|m) + 2*round(Re(z)/pi)*K(m)
     (let ((period (round (realpart phi-arg) pi)))
       (add (base (- phi-arg (* pi period)) m-arg)
-	   (mul (mul 2 period)
-		(elliptic-k m-arg))))))
+	   (if (zerop period)
+	       0
+	       (mul (mul 2 period)
+		    (elliptic-k m-arg)))))))
 
 ;; Complete elliptic integral of the first kind
 (defun elliptic-k (m)
@@ -1284,6 +1286,9 @@ first kind:
 	((= m 0)
 	 ;; A&S 17.4.19
 	 (float (/ pi 2)))
+	((= m 1)
+	 (maxima::merror
+	  (intl:gettext "elliptic_kc: elliptic_kc(1) is undefined.")))
 	(t
 	 (let ((k (sqrt m)))
 	   (to (bigfloat::bf-rf 0.0 (* (- 1 k)
@@ -2075,14 +2080,20 @@ first kind:
 ;; elliptic_f(phi,m) = sin(phi)*rf(cos(phi)^2, 1-m*sin(phi)^2,1)
 (defun bf-elliptic-f (phi m)
   (flet ((base (phi m)
-	   (let ((s (sin phi))
-		 (c (cos phi)))
-	     (* s (bf-rf (* c c) (- 1 (* m s s)) 1)))))
+	   (cond ((= m 1)
+		  ;; F(z|1) = log(tan(z/2+%pi/4))
+		  (log (tan (+ (/ phi 2) (/ (%pi phi) 4)))))
+		 (t
+		  (let ((s (sin phi))
+			(c (cos phi)))
+		    (* s (bf-rf (* c c) (- 1 (* m s s)) 1)))))))
     ;; Handle periodicity (see elliptic-f)
     (let* ((bfpi (%pi phi))
 	   (period (round (realpart phi) bfpi)))
       (+ (base (- phi (* bfpi period)) m)
-	 (* 2 period (bf-elliptic-k m))))))
+	 (if (zerop period)
+	     0
+	     (* 2 period (bf-elliptic-k m)))))))
 
 ;; elliptic_kc(k) = rf(0, 1-k^2,1)
 ;;
@@ -2094,6 +2105,9 @@ first kind:
 	 (if (maxima::$bfloatp m)
 	     (maxima::$bfloat (maxima::div 'maxima::$%pi 2))
 	     (float (/ pi 2) 1e0)))
+	((= m 1)
+	 (maxima::merror
+	  (intl:gettext "elliptic_kc: elliptic_kc(1) is undefined.")))
 	(t
 	 (bf-rf 0 (- 1 m) 1))))
 
diff --git a/tests/rtest16.mac b/tests/rtest16.mac
index 2f5506b..9267ea6 100644
--- a/tests/rtest16.mac
+++ b/tests/rtest16.mac
@@ -2282,4 +2282,20 @@ polarform((a+1)/2 - a/2 - 0.5);
 polarform((a+1)/2 - a/2 - 0.5b0);
 0.0b0$
 
+/*
+ * ID: 3440046: elliptic_f(0.5,1) signals error
+ *
+ * Add a few more tests for invalid values.
+ */
+closeto(elliptic_f(0.5,1)-elliptic_f(1/2,1), 1e-15);
+true;
+
+closeto(elliptic_f(0.5b0,1) - bfloat(elliptic_f(1/2,1)), 1b-16);
+true;
+
+errcatch(elliptic_f(2.0,1));
+[];
+
+errcatch(elliptic_f(2b0,1));
+[];
 

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

Summary of changes:
 src/ellipt.lisp   |   26 ++++++++++++++++++++------
 tests/rtest16.mac |   16 ++++++++++++++++
 2 files changed, 36 insertions(+), 6 deletions(-)


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