! Copyright (c) 2007 Samuel Tardieu
! See http://factorcode.org/license.txt for BSD license.
-USING: kernel math math.ranges namespaces sequences vars math.algebra ;
+USING: kernel math math.ranges namespaces sequences vars ;
IN: math.algebra
<PRIVATE
-VARS: r-1 u-1 v-1 r u v ;
+! The traditional name for the first variable is "r", but we want to avoid
+! a redefinition of "r>" and ">r", so we chose to use "s" instead.
+
+VARS: s-1 u-1 v-1 s u v ;
: init ( a b -- )
- >r >r-1 0 >u 1 >u-1 1 >v 0 >v-1 ;
+ >s >s-1 0 >u 1 >u-1 1 >v 0 >v-1 ;
: advance ( r u v -- )
- v> >v-1 >v u> >u-1 >u r> >r-1 >r ; inline
+ v> >v-1 >v u> >u-1 >u s> >s-1 >s ; inline
: step ( -- )
- r-1> r> 2dup /mod drop [ * - ] keep u-1> over u> * - v-1> rot v> * -
+ s-1> s> 2dup /mod drop [ * - ] keep u-1> over u> * - v-1> rot v> * -
advance ;
PRIVATE>
! Extended Euclidian: http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
: ext-euclidian ( a b -- gcd u v )
- [ init [ r> 0 > ] [ step ] [ ] while r-1> u-1> v-1> ] with-scope ; foldable
+ [ init [ s> 0 > ] [ step ] [ ] while s-1> u-1> v-1> ] with-scope ; foldable
! Inverse a in ring Z/bZ
: ring-inverse ( a b -- i )