35 lines
963 B
Factor
35 lines
963 B
Factor
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! Copyright (c) 2007 Samuel Tardieu
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.ranges namespaces sequences vars math.algebra ;
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IN: math.algebra
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<PRIVATE
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VARS: r-1 u-1 v-1 r u v ;
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: init ( a b -- )
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>r >r-1 0 >u 1 >u-1 1 >v 0 >v-1 ;
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: advance ( r u v -- )
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v> >v-1 >v u> >u-1 >u r> >r-1 >r ; inline
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: step ( -- )
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r-1> r> 2dup /mod drop [ * - ] keep u-1> over u> * - v-1> rot v> * -
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advance ;
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PRIVATE>
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! Extended Euclidian: http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
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: ext-euclidian ( a b -- gcd u v )
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[ init [ r> 0 > ] [ step ] [ ] while r-1> u-1> v-1> ] with-scope ; foldable
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! Inverse a in ring Z/bZ
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: ring-inverse ( a b -- i )
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[ ext-euclidian drop nip ] keep rem ; foldable
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! Chinese remainder: http://en.wikipedia.org/wiki/Chinese_remainder_theorem
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: chinese-remainder ( aseq nseq -- x )
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dup product
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[ [ over / [ ext-euclidian ] keep * 2nip * ] curry 2map sum ] keep rem ;
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foldable
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