[pure-lang-svn] SF.net SVN: pure-lang:[583] pure/trunk/lib/math.pure
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[pure-lang-svn] SF.net SVN: pure-lang:[583] pure/trunk/lib/math.pure
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From: <ag...@us...> - 2008-08-23 20:50:12
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Revision: 583
http://pure-lang.svn.sourceforge.net/pure-lang/?rev=583&view=rev
Author: agraef
Date: 2008-08-23 20:50:22 +0000 (Sat, 23 Aug 2008)
Log Message:
-----------
Add type guards to rational operations.
Modified Paths:
--------------
pure/trunk/lib/math.pure
Modified: pure/trunk/lib/math.pure
===================================================================
--- pure/trunk/lib/math.pure 2008-08-23 12:56:48 UTC (rev 582)
+++ pure/trunk/lib/math.pure 2008-08-23 20:50:22 UTC (rev 583)
@@ -349,8 +349,10 @@
// rational operands
(x1%y1)%(x2%y2) = (x1*y2)%(y1*x2);
-(x1%y1)%x2 = x1%(y1*x2);
-x1%(x2%y2) = (x1*y2)%x2;
+(x1%y1)%x2::int |
+(x1%y1)%x2::bigint = x1%(y1*x2);
+x1::int%(x2%y2) |
+x1::bigint%(x2%y2) = (x1*y2)%x2;
// complex operands (these must both use the same representation, otherwise
// the result won't be exact)
@@ -358,15 +360,19 @@
z1@(_<:_)%z2@(_+:_) = z1/z2;
(x1+:y1)%(x2+:y2) = (x1*x2+y1*y2)%d +: (y1*x2-x1*y2)%d
when d = x2*x2+y2*y2 end;
-(x1+:y1)%x2 = (x1*x2)%d +: (y1*x2)%d when d = x2*x2 end;
-x1%(x2+:y2) = (x1*x2)%d +: (-x1*y2)%d when d = x2*x2+y2*y2 end;
(r1<:t1)%(r2<:t2) = r1%r2 <: t1-t2;
-(r1<:t1)%x2 = r1%x2 <: t1;
-x1%(r2<:t2) = x1%r2 <: -t2;
+// mixed complex/real cases
+(x1+:y1)%x2 = (x1*x2)%d +: (y1*x2)%d
+ when d = x2*x2 end if realp x2;
+x1%(x2+:y2) = (x1*x2)%d +: (-x1*y2)%d
+ when d = x2*x2+y2*y2 end if realp x1;
+(r1<:t1)%x2 = r1%x2 <: t1 if realp x2;
+x1%(r2<:t2) = x1%r2 <: -t2 if realp x1;
+
// fall back to ordinary inexact division in all other cases
-x::double%y |
-x%y::double = x/y;
+x::double%y = x/y if numberp y;
+x%y::double = x/y if numberp x;
/* Conversions. */
@@ -484,24 +490,37 @@
(x1%y1)-(x2%y2) = (x1*y2-x2*y1) % (y1*y2);
(x1%y1)*(x2%y2) = (x1*x2) % (y1*y2);
-(x1%y1)+x2 = (x1+x2*y1) % y1;
-(x1%y1)-x2 = (x1-x2*y1) % y1;
-(x1%y1)*x2 = (x1*x2) % y1;
+(x1%y1)+x2::int |
+(x1%y1)+x2::bigint = (x1+x2*y1) % y1;
+(x1%y1)-x2::int |
+(x1%y1)-x2::bigint = (x1-x2*y1) % y1;
+(x1%y1)*x2::int |
+(x1%y1)*x2::bigint = (x1*x2) % y1;
-x1+(x2%y2) = (x1*y2+x2) % y2;
-x1-(x2%y2) = (x1*y2-x2) % y2;
-x1*(x2%y2) = (x1*x2) % y2;
+x1::int+(x2%y2) |
+x1::bigint+(x2%y2) = (x1*y2+x2) % y2;
+x1::int-(x2%y2) |
+x1::bigint-(x2%y2) = (x1*y2-x2) % y2;
+x1::int*(x2%y2) |
+x1::bigint*(x2%y2) = (x1*x2) % y2;
-/* / and ^ yield inexact results. */
+/* Fallback rules. */
-(x1%y1)/(x2%y2) = (x1*y2) / (y1*x2);
+// / and ^ always yield inexact results.
+(x1%y1)/(x2%y2) = (x1/y1) / (x2/y2);
(x1%y1)^(x2%y2) = (x1/y1) ^ (x2/y2);
-(x1%y1)/x2 = x1 / (y1*x2);
-(x1%y1)^x2 = (x1/y1) ^ x2;
+(x1%y1)+x2 = (x1/y1)+x2 if numberp x2;
+(x1%y1)-x2 = (x1/y1)-x2 if numberp x2;
+(x1%y1)*x2 = (x1/y1)*x2 if numberp x2;
+(x1%y1)/x2 = (x1/y1)/x2 if numberp x2;
+(x1%y1)^x2 = (x1/y1)^x2 if numberp x2;
-x1/(x2%y2) = (x1*y2) / x2;
-x1^(x2%y2) = x1 ^ (x2/y2);
+x1+(x2%y2) = x1+(x2/y2) if numberp x1;
+x1-(x2%y2) = x1-(x2/y2) if numberp x1;
+x1*(x2%y2) = x1*(x2/y2) if numberp x1;
+x1/(x2%y2) = x1/(x2/y2) if numberp x1;
+x1^(x2%y2) = x1^(x2/y2) if numberp x1;
/* Comparisons. */
@@ -512,19 +531,19 @@
x1%y1 > x2%y2 = x1*y2 > x2*y1;
x1%y1 >= x2%y2 = x1*y2 >= x2*y1;
-x1%y1 == x2 = x1 == x2*y1;
-x1%y1 != x2 = x1 != x2*y1;
-x1%y1 < x2 = x1 < x2*y1;
-x1%y1 <= x2 = x1 <= x2*y1;
-x1%y1 > x2 = x1 > x2*y1;
-x1%y1 >= x2 = x1 >= x2*y1;
+x1%y1 == x2 = x1 == x2*y1 if numberp x2;
+x1%y1 != x2 = x1 != x2*y1 if numberp x2;
+x1%y1 < x2 = x1 < x2*y1 if realp x2;
+x1%y1 <= x2 = x1 <= x2*y1 if realp x2;
+x1%y1 > x2 = x1 > x2*y1 if realp x2;
+x1%y1 >= x2 = x1 >= x2*y1 if realp x2;
-x1 == x2%y2 = x1*y2 == x2;
-x1 != x2%y2 = x1*y2 != x2;
-x1 < x2%y2 = x1*y2 < x2;
-x1 <= x2%y2 = x1*y2 <= x2;
-x1 > x2%y2 = x1*y2 > x2;
-x1 >= x2%y2 = x1*y2 >= x2;
+x1 == x2%y2 = x1*y2 == x2 if numberp x2;
+x1 != x2%y2 = x1*y2 != x2 if numberp x2;
+x1 < x2%y2 = x1*y2 < x2 if realp x2;
+x1 <= x2%y2 = x1*y2 <= x2 if realp x2;
+x1 > x2%y2 = x1*y2 > x2 if realp x2;
+x1 >= x2%y2 = x1*y2 >= x2 if realp x2;
/* Additional number predicates. */
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