-! Copyright (C) 2004, 2008 Slava Pestov.
+! Copyright (C) 2004, 2010 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 ;
+USING: kernel kernel.private sequences sequences.private math
+math.private math.order combinators ;
IN: math.integers.private
-M: integer numerator ;
-M: integer denominator drop 1 ;
+: fixnum-min ( x y -- z ) [ fixnum< ] most ; foldable
+: fixnum-max ( x y -- z ) [ fixnum> ] most ; foldable
-M: fixnum >fixnum ;
-M: fixnum >bignum fixnum>bignum ;
-M: fixnum >integer ;
+M: integer numerator ; inline
+M: integer denominator drop 1 ; inline
-M: fixnum hashcode* nip ;
-M: fixnum equal? over bignum? [ >bignum bignum= ] [ 2drop f ] if ;
-M: fixnum number= eq? ;
+M: fixnum >fixnum ; inline
+M: fixnum >bignum fixnum>bignum ; inline
+M: fixnum >integer ; inline
+M: fixnum >float fixnum>float ; inline
-M: fixnum < fixnum< ;
-M: fixnum <= fixnum<= ;
-M: fixnum > fixnum> ;
-M: fixnum >= fixnum>= ;
+M: fixnum hashcode* nip ; inline
+M: fixnum equal? over bignum? [ >bignum bignum= ] [ 2drop f ] if ; inline
+M: fixnum number= eq? ; inline
-M: fixnum + fixnum+ ;
-M: fixnum - fixnum- ;
-M: fixnum * fixnum* ;
-M: fixnum /i fixnum/i ;
-M: fixnum /f [ >float ] dip >float float/f ;
+M: fixnum < fixnum< ; inline
+M: fixnum <= fixnum<= ; inline
+M: fixnum > fixnum> ; inline
+M: fixnum >= fixnum>= ; inline
-M: fixnum mod fixnum-mod ;
+M: fixnum u< fixnum< ; inline
+M: fixnum u<= fixnum<= ; inline
+M: fixnum u> fixnum> ; inline
+M: fixnum u>= fixnum>= ; inline
-M: fixnum /mod fixnum/mod ;
+M: fixnum min over fixnum? [ fixnum-min ] [ call-next-method ] if ; inline
+M: fixnum max over fixnum? [ fixnum-max ] [ call-next-method ] if ; inline
-M: fixnum bitand fixnum-bitand ;
-M: fixnum bitor fixnum-bitor ;
-M: fixnum bitxor fixnum-bitxor ;
-M: fixnum shift >fixnum fixnum-shift ;
+M: fixnum + fixnum+ ; inline
+M: fixnum - fixnum- ; inline
+M: fixnum * fixnum* ; inline
+M: fixnum /i fixnum/i ; inline
-M: fixnum bitnot fixnum-bitnot ;
+M: fixnum mod fixnum-mod ; inline
-M: fixnum bit? neg shift 1 bitand 0 > ;
+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
+
+: fixnum-bit? ( n m -- b )
+ neg shift 1 bitand 0 > ; inline
+
+M: fixnum bit? fixnum-bit? ; inline
: fixnum-log2 ( x -- n )
- 0 swap [ dup 1 eq? ] [ [ 1+ ] [ 2/ ] bi* ] until drop ;
+ 0 swap [ dup 1 eq? ] [ [ 1 + ] [ 2/ ] bi* ] until drop ;
-M: fixnum (log2) fixnum-log2 ;
+M: fixnum (log2) fixnum-log2 ; inline
-M: bignum >fixnum bignum>fixnum ;
-M: bignum >bignum ;
+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 ;
+ ] if ; inline
+
+M: bignum number= bignum= ; inline
-M: bignum number= bignum= ;
+M: bignum < bignum< ; inline
+M: bignum <= bignum<= ; inline
+M: bignum > bignum> ; inline
+M: bignum >= bignum>= ; inline
-M: bignum < bignum< ;
-M: bignum <= bignum<= ;
-M: bignum > bignum> ;
-M: bignum >= bignum>= ;
+M: bignum u< bignum< ; inline
+M: bignum u<= bignum<= ; inline
+M: bignum u> bignum> ; inline
+M: bignum u>= bignum>= ; inline
-M: bignum + bignum+ ;
-M: bignum - bignum- ;
-M: bignum * bignum* ;
-M: bignum /i bignum/i ;
-M: bignum mod bignum-mod ;
+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 ;
+M: bignum /mod bignum/mod ; inline
-M: bignum bitand bignum-bitand ;
-M: bignum bitor bignum-bitor ;
-M: bignum bitxor bignum-bitxor ;
-M: bignum shift >fixnum bignum-shift ;
+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 ;
-M: bignum bit? bignum-bit? ;
-M: bignum (log2) bignum-log2 ;
+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:
! provided with absolutely no warranty."
! First step: pre-scaling
-: twos ( x -- y ) dup 1- bitxor log2 ; inline
+: 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 )
+: pre-scale ( num den -- mantissa den' scale )
2dup [ log2 ] bi@ -
- [ neg 54 + shift ] [ [ scale-denonimator ] dip + ] bi-curry bi*
- -rot ; inline
+ [ neg 54 + shift ] [ [ scale-denonimator ] dip + ] bi-curry bi* ; 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
+: /f-loop ( mantissa den scale -- fraction-and-guard rem scale' )
+ [ 2over /i log2 53 > ]
+ [ [ 2/ ] [ ] [ 1 + ] tri* ] while
+ [ /mod ] dip ; 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
+: scale-float ( mantissa scale -- float' )
+ {
+ { [ dup 1024 > ] [ 2drop 1/0. ] }
+ { [ dup -1023 < ] [ 1021 + shift bits>double ] }
+ [ [ 52 2^ 1 - bitand ] dip 1022 + 52 shift bitor bits>double ]
+ } cond ; inline
+
+: post-scale ( mantissa scale -- n )
+ [ 2/ ] dip over log2 52 > [ [ 2/ ] [ 1 + ] bi* ] when
+ scale-float ; inline
+
+: round-to-nearest ( fraction-and-guard rem -- fraction-and-guard' )
+ over odd?
+ [ zero? [ dup zero? [ 1 + ] unless ] [ 1 + ] if ] [ drop ] if ;
+ inline
! Main word
: /f-abs ( m n -- f )
- over zero? [
- 2drop 0.0
- ] [
- dup zero? [
- 2drop 1/0.
- ] [
+ over zero? [ nip zero? 0/0. 0.0 ? ] [
+ [ drop 1/0. ] [
pre-scale
- /f-loop over odd?
- [ zero? [ 1+ ] unless ] [ drop ] if
+ /f-loop
+ [ round-to-nearest ] dip
post-scale
- ] if
+ ] if-zero
] if ; inline
-M: bignum /f ( m n -- f )
- [ [ abs ] bi@ /f-abs ] [ [ 0 < ] bi@ xor ] 2bi [ neg ] when ;
+: bignum/f ( m n -- f )
+ [ [ abs ] bi@ /f-abs ] [ [ 0 < ] bi@ xor ] 2bi [ neg ] when ; inline
+
+M: bignum /f ( m n -- f ) { bignum bignum } declare bignum/f ;
+
+CONSTANT: bignum/f-threshold 0x20,0000,0000,0000
+
+: fixnum/f ( m n -- m/n )
+ [ >float ] bi@ float/f ; inline
+
+M: fixnum /f
+ { fixnum fixnum } declare
+ 2dup [ abs bignum/f-threshold >= ] either?
+ [ bignum/f ] [ fixnum/f ] if ; inline
+
+: bignum>float ( bignum -- float )
+ { bignum } declare 1 >bignum bignum/f ;
+
+M: bignum >float bignum>float ; inline
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