factor/core/math/integers/integers.factor

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4.2 KiB
Factor

! Copyright (C) 2004, 2009 Slava Pestov.
! Copyright (C) 2008, Doug Coleman.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel kernel.private sequences
sequences.private math math.private combinators ;
IN: math.integers.private
: fixnum-min ( x y -- z ) [ fixnum< ] most ; foldable
: fixnum-max ( x y -- z ) [ fixnum> ] most ; foldable
M: integer numerator ; inline
M: integer denominator drop 1 ; inline
M: fixnum >fixnum ; inline
M: fixnum >bignum fixnum>bignum ; inline
M: fixnum >integer ; inline
M: fixnum hashcode* nip ; inline
M: fixnum equal? over bignum? [ >bignum bignum= ] [ 2drop f ] if ; inline
M: fixnum number= eq? ; inline
M: fixnum < fixnum< ; inline
M: fixnum <= fixnum<= ; inline
M: fixnum > fixnum> ; inline
M: fixnum >= fixnum>= ; inline
M: fixnum u< fixnum< ; inline
M: fixnum u<= fixnum<= ; inline
M: fixnum u> fixnum> ; inline
M: fixnum u>= fixnum>= ; inline
M: fixnum + fixnum+ ; inline
M: fixnum - fixnum- ; inline
M: fixnum * fixnum* ; inline
M: fixnum /i fixnum/i ; inline
DEFER: bignum/f
CONSTANT: bignum/f-threshold HEX: 20,0000,0000,0000
: fixnum/f ( m n -- m/n )
[ >float ] bi@ float/f ; inline
M: fixnum /f
2dup [ abs bignum/f-threshold >= ] either?
[ bignum/f ] [ fixnum/f ] if ; inline
M: fixnum mod fixnum-mod ; inline
M: fixnum /mod fixnum/mod ; inline
M: fixnum bitand fixnum-bitand ; inline
M: fixnum bitor fixnum-bitor ; inline
M: fixnum bitxor fixnum-bitxor ; inline
M: fixnum shift >fixnum fixnum-shift ; inline
M: fixnum bitnot fixnum-bitnot ; inline
M: fixnum bit? neg shift 1 bitand 0 > ; inline
: fixnum-log2 ( x -- n )
0 swap [ dup 1 eq? ] [ [ 1 + ] [ 2/ ] bi* ] until drop ;
M: fixnum (log2) fixnum-log2 ; inline
M: bignum >fixnum bignum>fixnum ; inline
M: bignum >bignum ; inline
M: bignum hashcode* nip >fixnum ;
M: bignum equal?
over bignum? [ bignum= ] [
swap dup fixnum? [ >bignum bignum= ] [ 2drop f ] if
] if ; inline
M: bignum number= bignum= ; inline
M: bignum < bignum< ; inline
M: bignum <= bignum<= ; inline
M: bignum > bignum> ; inline
M: bignum >= bignum>= ; inline
M: bignum u< bignum< ; inline
M: bignum u<= bignum<= ; inline
M: bignum u> bignum> ; inline
M: bignum u>= bignum>= ; inline
M: bignum + bignum+ ; inline
M: bignum - bignum- ; inline
M: bignum * bignum* ; inline
M: bignum /i bignum/i ; inline
M: bignum mod bignum-mod ; inline
M: bignum /mod bignum/mod ; inline
M: bignum bitand bignum-bitand ; inline
M: bignum bitor bignum-bitor ; inline
M: bignum bitxor bignum-bitxor ; inline
M: bignum shift >fixnum bignum-shift ; inline
M: bignum bitnot bignum-bitnot ; inline
M: bignum bit? bignum-bit? ; inline
M: bignum (log2) bignum-log2 ; inline
! Converting ratios to floats. Based on FLOAT-RATIO from
! sbcl/src/code/float.lisp, which has the following license:
! "The software is in the public domain and is
! provided with absolutely no warranty."
! First step: pre-scaling
: twos ( x -- y ) dup 1 - bitxor log2 ; inline
: scale-denonimator ( den -- scaled-den scale' )
dup twos neg [ shift ] keep ; inline
: pre-scale ( num den -- scale shifted-num scaled-den )
2dup [ log2 ] bi@ -
[ neg 54 + shift ] [ [ scale-denonimator ] dip + ] bi-curry bi*
-rot ; inline
! Second step: loop
: shift-mantissa ( scale mantissa -- scale' mantissa' )
[ 1 + ] [ 2/ ] bi* ; inline
: /f-loop ( scale mantissa den -- scale' fraction-and-guard rem )
[ 2dup /i log2 53 > ]
[ [ shift-mantissa ] dip ]
while /mod ; inline
! Third step: post-scaling
: unscaled-float ( mantissa -- n )
52 2^ 1 - bitand 1022 52 shift bitor bits>double ; inline
: scale-float ( scale mantissa -- float' )
[ dup 0 < [ neg 2^ recip ] [ 2^ ] if ] dip * ; inline
: post-scale ( scale mantissa -- n )
2/ dup log2 52 > [ shift-mantissa ] when
unscaled-float scale-float ; inline
! Main word
: /f-abs ( m n -- f )
over zero? [
2drop 0.0
] [
[
drop 1/0.
] [
pre-scale
/f-loop over odd?
[ zero? [ 1 + ] unless ] [ drop ] if
post-scale
] if-zero
] if ; inline
: bignum/f ( m n -- f )
[ [ abs ] bi@ /f-abs ] [ [ 0 < ] bi@ xor ] 2bi [ neg ] when ;
M: bignum /f ( m n -- f )
bignum/f ;