2004-08-26 22:21:17 -04:00
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! :folding=indent:collapseFolds=0:
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! $Id$
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!
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! Copyright (C) 2004 Slava Pestov.
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!
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! Redistribution and use in source and binary forms, with or without
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! modification, are permitted provided that the following conditions are met:
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!
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! 1. Redistributions of source code must retain the above copyright notice,
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! this list of conditions and the following disclaimer.
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!
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! 2. Redistributions in binary form must reproduce the above copyright notice,
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! this list of conditions and the following disclaimer in the documentation
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! and/or other materials provided with the distribution.
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!
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! THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
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! INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
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! FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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! DEVELOPERS AND CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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! SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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! PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
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! OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
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! WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
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! OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
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! ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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IN: math
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USE: combinators
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2004-09-19 00:33:40 -04:00
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USE: errors
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2004-08-26 22:21:17 -04:00
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USE: kernel
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USE: stack
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2004-09-19 00:33:40 -04:00
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USE: vectors
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USE: words
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2004-08-26 22:21:17 -04:00
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2004-09-19 00:33:40 -04:00
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: (gcd) ( x y -- z ) dup 0 = [ drop ] [ tuck mod (gcd) ] ifte ;
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: gcd ( x y -- z ) abs swap abs 2dup < [ swap ] when (gcd) ;
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: reduce ( x y -- x' y' )
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dup 0 < [ swap neg swap neg ] when 2dup gcd tuck /i >r /i r> ;
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: ratio ( x y -- x/y ) reduce fraction> ;
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: 2>fraction ( a/b c/d -- a b c d ) >r >fraction r> >fraction ;
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: ratio= ( a/b c/d -- ? ) 2>fraction 2= ;
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: ratio-scale ( a/b c/d -- a*d b*c ) 2>fraction -rot * >r * r> ;
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: ratio+d ( a/b c/d -- b*d ) denominator swap denominator * ;
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: ratio+ ( x y -- x+y ) 2dup ratio-scale + -rot ratio+d ratio ;
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: ratio- ( x y -- x-y ) 2dup ratio-scale - -rot ratio+d ratio ;
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: ratio* ( x y -- x*y ) 2>fraction swapd * >r * r> ratio ;
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: ratio/ ( x y -- x/y ) ratio-scale ratio ;
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: ratio/f ( x y -- x/y ) ratio-scale /f ;
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: ratio< ( x y -- ? ) ratio-scale < ;
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: ratio<= ( x y -- ? ) ratio-scale <= ;
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: ratio> ( x y -- ? ) ratio-scale > ;
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: ratio>= ( x y -- ? ) ratio-scale >= ;
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: 2>rect ( x y -- x:re x:im y:re y:im ) >r >rect r> >rect ;
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: complex= ( x y -- ? ) 2>rect 2= ;
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: complex+ ( x y -- x+y ) 2>rect swapd + >r + r> rect> ;
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: complex- ( x y -- x-y ) 2>rect swapd - >r - r> rect> ;
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: complex*re ( x y -- zx:re * y:re x:im * r:im )
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2>rect swapd * >r * r> ;
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: complex*im ( x y -- x:re * y:im x:im * y:re )
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2>rect >r * swap r> * ;
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: complex* ( x y -- x*y )
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2dup complex*re - -rot complex*im + rect> ;
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: abs^2 ( x -- y ) >rect sq swap sq + ;
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: (complex/) ( x y -- r i m )
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#! r = x:re * y:re + x:im * y:im
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#! i = x:im * y:re - x:re * y:im
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#! m = y:re * y:re + y:im * y:im
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dup abs^2 >r 2dup complex*re + -rot complex*im - r> ;
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: complex/ ( x y -- x/y )
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(complex/) tuck / >r / r> rect> ;
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: complex/f ( x y -- x/y )
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(complex/) tuck /f >r /f r> rect> ;
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: no-method ( -- )
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"No applicable method" throw ;
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: (not-=) ( x y -- f )
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2drop f ;
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: number= ( x y -- ? )
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{
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fixnum=
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(not-=)
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(not-=)
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(not-=)
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ratio=
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complex=
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(not-=)
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(not-=)
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(not-=)
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(not-=)
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(not-=)
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(not-=)
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(not-=)
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bignum=
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float=
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(not-=)
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2004-09-19 17:39:28 -04:00
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(not-=)
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: + ( x y -- x+y )
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{
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fixnum+
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no-method
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no-method
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no-method
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ratio+
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complex+
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum+
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float+
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: - ( x y -- x-y )
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{
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fixnum-
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no-method
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no-method
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no-method
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ratio-
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complex-
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum-
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float-
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: * ( x y -- x*y )
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{
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fixnum*
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no-method
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no-method
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no-method
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ratio*
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complex*
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum*
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float*
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: / ( x y -- x/y )
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{
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ratio
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no-method
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no-method
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no-method
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ratio/
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complex/
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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ratio
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float/f
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: /i ( x y -- x/y )
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{
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fixnum/i
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum/i
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no-method
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: /f ( x y -- x/y )
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{
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fixnum/f
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no-method
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no-method
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no-method
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ratio/f
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complex/f
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum/f
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float/f
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: mod ( x y -- x%y )
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{
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fixnum-mod
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum-mod
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no-method
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: /mod ( x y -- x/y x%y )
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{
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fixnum/mod
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum/mod
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no-method
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: bitand ( x y -- x&y )
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{
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fixnum-bitand
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum-bitand
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no-method
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: bitor ( x y -- x|y )
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{
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fixnum-bitor
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum-bitor
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no-method
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: bitxor ( x y -- x^y )
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{
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fixnum-bitxor
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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no-method
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bignum-bitxor
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no-method
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no-method
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2004-09-19 17:39:28 -04:00
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no-method
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2004-09-19 00:33:40 -04:00
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} 2generic ;
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: bitnot ( x -- ~x )
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{
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[ fixnum-bitnot ]
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[ no-method ]
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[ no-method ]
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[ no-method ]
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[ no-method ]
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[ no-method ]
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[ no-method ]
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[ no-method ]
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|
|
|
[ no-method ]
|
|
|
|
|
[ no-method ]
|
|
|
|
|
[ no-method ]
|
|
|
|
|
[ no-method ]
|
|
|
|
|
[ no-method ]
|
|
|
|
|
[ bignum-bitnot ]
|
|
|
|
|
[ no-method ]
|
|
|
|
|
[ no-method ]
|
2004-09-19 17:39:28 -04:00
|
|
|
[ no-method ]
|
2004-09-19 00:33:40 -04:00
|
|
|
} generic ;
|
|
|
|
|
|
|
|
|
|
: shift ( x n -- x<<n )
|
|
|
|
|
{
|
|
|
|
|
fixnum-shift
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
bignum-shift
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
2004-09-19 17:39:28 -04:00
|
|
|
no-method
|
2004-09-19 00:33:40 -04:00
|
|
|
} 2generic ;
|
|
|
|
|
|
|
|
|
|
: < ( x y -- ? )
|
|
|
|
|
{
|
|
|
|
|
fixnum<
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
ratio<
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
bignum<
|
|
|
|
|
float<
|
|
|
|
|
no-method
|
2004-09-19 17:39:28 -04:00
|
|
|
no-method
|
2004-09-19 00:33:40 -04:00
|
|
|
} 2generic ;
|
|
|
|
|
|
|
|
|
|
: <= ( x y -- ? )
|
|
|
|
|
{
|
|
|
|
|
fixnum<=
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
ratio<=
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
bignum<=
|
|
|
|
|
float<=
|
|
|
|
|
no-method
|
2004-09-19 17:39:28 -04:00
|
|
|
no-method
|
2004-09-19 00:33:40 -04:00
|
|
|
} 2generic ;
|
|
|
|
|
|
|
|
|
|
: > ( x y -- ? )
|
|
|
|
|
{
|
|
|
|
|
fixnum>
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
ratio>
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
bignum>
|
|
|
|
|
float>
|
|
|
|
|
no-method
|
2004-09-19 17:39:28 -04:00
|
|
|
no-method
|
2004-09-19 00:33:40 -04:00
|
|
|
} 2generic ;
|
|
|
|
|
|
|
|
|
|
: >= ( x y -- ? )
|
|
|
|
|
{
|
|
|
|
|
fixnum>=
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
ratio>=
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
no-method
|
|
|
|
|
bignum>=
|
|
|
|
|
float>=
|
|
|
|
|
no-method
|
2004-09-19 17:39:28 -04:00
|
|
|
no-method
|
2004-09-19 00:33:40 -04:00
|
|
|
} 2generic ;
|
