[pure-lang-svn] SF.net SVN: pure-lang: [350] pure/trunk/lib/math.pure

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

Revision: 350
          http://pure-lang.svn.sourceforge.net/pure-lang/?rev=350&view=rev
Author:   agraef
Date:     2008-07-01 06:19:05 -0700 (Tue, 01 Jul 2008)

Log Message:
-----------
Overhaul of complex powers.

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

Modified: pure/trunk/lib/math.pure
===================================================================
--- pure/trunk/lib/math.pure	2008-07-01 11:22:42 UTC (rev 349)
+++ pure/trunk/lib/math.pure	2008-07-01 13:19:05 UTC (rev 350)
@@ -279,16 +279,6 @@
 (x1+:y1) / (x2+:y2)	= (x1*x2+y1*y2 +: y1*x2-x1*y2) / (x2*x2+y2*y2);
 (r1<:t1) / (r2<:t2)	= r1/r2 <: t1-t2;
 
-z1@(x1+:y1)^z2@(x2+:y2)	= exp (ln z1*z2) if z1!=0;
-			= 0.0+:0.0 if z2!=0;
-			= 1.0+:0.0 otherwise;
-z1@(r1<:t1)^z2@(r2<:t2)	= exp (ln z1*z2) if z1!=0;
-			= 0.0<:0.0 if z2!=0;
-			= 1.0<:0.0 otherwise;
-
-// Complex powers of negative reals.
-x1::double^x2::double	= exp (ln x1*x2) if x1<0;
-
 /* Mixed rect/polar and polar/rect forms always return a rect result. */
 
 z1@(x1+:y1)+z2@(r2<:t2)	= z1 + rect z2;
@@ -303,9 +293,6 @@
 z1@(x1+:y1)/z2@(r2<:t2)	= z1 / rect z2;
 z1@(r1<:t1)/z2@(x2+:y2)	= rect z1 / z2;
 
-z1@(x1+:y1)^z2@(r2<:t2)	= z1 ^ rect z2;
-z1@(r1<:t1)^z2@(x2+:y2)	= rect z1 ^ z2;
-
 /* Mixed complex/real and real/complex forms yield a rect or polar result,
    depending on what the complex input was. */
 
@@ -329,11 +316,24 @@
 (r1<:t1)/x2	= r1/x2 <: t1;
 x1/(r2<:t2)	= x1/r2 <: -t2;
 
+/* Complex powers. */
+
+// These are computed most easily if the 1st operand is in polar form.
+// FIXME: Deal with special cases like 0^0. These always give nan now.
+z1@(x1+:y1)^z2@(x2+:y2)	= polar z1^z2;
+z1@(x1+:y1)^z2@(r2<:t2)	= polar z1^rect z2;
+(r1<:t1)^z2@(x2+:y2)	|
+(r1<:t1)^z2@(r2<:t2)	= exp (ln r1*z2)*exp((0+:t1)*z2);
+
+// Mixed complex/real cases.
 z1@(x1+:y1)^x2	= z1 ^ (x2+:0);
 x1^z2@(x2+:y2)	= (x1+:0) ^ z2;
 (r1<:t1)^x2	= r1^x2 <: t1*x2;
 x1^z2@(r2<:t2)	= (x1<:0) ^ z2;
 
+// Complex powers of negative reals.
+x1::double^x2::double	= exp (ln x1*x2) if x1<0;
+
 /* Equality. */
 
 (x1+:y1) == (x2+:y2)	= x1==x2 && y1==y2;


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