[pure-lang-svn] SF.net SVN: pure-lang:[576] pure/trunk/lib/math.pure

[<ag...@us...>]

Revision: 576
          http://pure-lang.svn.sourceforge.net/pure-lang/?rev=576&view=rev
Author:   agraef
Date:     2008-08-23 10:27:31 +0000 (Sat, 23 Aug 2008)

Log Message:
-----------
Fix broken complex sqrt, minor cosmetic changes in complex trig and hyperbolic functions.

Modified Paths:
--------------
    pure/trunk/lib/math.pure

Modified: pure/trunk/lib/math.pure
===================================================================
--- pure/trunk/lib/math.pure	2008-08-22 20:24:48 UTC (rev 575)
+++ pure/trunk/lib/math.pure	2008-08-23 10:27:31 UTC (rev 576)
@@ -183,8 +183,8 @@
 
 /* Complex sqrt. */
 
-sqrt (x+:y)	= sqrt ((r+x)/2) +: sqrt ((r-x)/2)
-		  when r = sqrt (x*x+y*y) end;
+sqrt (x+:y)	= sqrt r*(cos t +: sin t)
+		  when r = sqrt (x*x+y*y); t = atan2 y x/2 end;
 sqrt (r<:t)	= sqrt r <: t/2;
 
 /* Complex exponential and logarithms. */
@@ -215,9 +215,7 @@
 acos z@(x+:y)	|
 acos z@(r<:t)	= -i*ln (z+sqrt (z*z-1));
 atan z@(x+:y)	|
-atan z@(r<:t)	= 0.0 +: inf if z==i;
-		= 0.0 +: -inf if z==-i;
-		= -i*0.5*ln ((1+i*z)/(1-i*z));
+atan z@(r<:t)	= (ln (1+i*z)-ln (1-i*z))/(2*i);
 
 /* Complex hyperbolic functions. */
 
@@ -233,10 +231,11 @@
 asinh z@(r<:t)	= ln (z+sqrt (z*z+1));
 acosh z@(x+:y)	|
 acosh z@(r<:t)	= ln (z+sqrt (z*z-1));
+// Alternative definition (Kahan).
+// acosh z@(x+:y)	|
+// acosh z@(r<:t)	= 2*ln (sqrt ((z+1)/2)+sqrt ((z-1)/2));
 atanh z@(x+:y)	|
-atanh z@(r<:t)	= inf +: 0.0 if z==1;
-		= -inf +: 0.0 if z==-1;
-		= ln ((1+z)/(1-z))/2;
+atanh z@(r<:t)	= (ln (1+z)-ln (1-z))/2;
 
 /* Complex arithmetic. */
 


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