! Copyright (C) 2003, 2009 Slava Pestov, Joe Groff.
! See http://factorcode.org/license.txt for BSD license.
-USING: kernel ;
+USING: kernel kernel.private ;
IN: math
+BUILTIN: fixnum ;
+BUILTIN: bignum ;
+BUILTIN: float ;
+
+PRIMITIVE: bits>double ( n -- x )
+PRIMITIVE: bits>float ( n -- x )
+PRIMITIVE: double>bits ( x -- n )
+PRIMITIVE: float>bits ( x -- n )
+
+<PRIVATE
+PRIMITIVE: bignum* ( x y -- z )
+PRIMITIVE: bignum+ ( x y -- z )
+PRIMITIVE: bignum- ( x y -- z )
+PRIMITIVE: bignum-bit? ( x n -- ? )
+PRIMITIVE: bignum-bitand ( x y -- z )
+PRIMITIVE: bignum-bitnot ( x -- y )
+PRIMITIVE: bignum-bitor ( x y -- z )
+PRIMITIVE: bignum-bitxor ( x y -- z )
+PRIMITIVE: bignum-gcd ( x y -- z )
+PRIMITIVE: bignum-log2 ( x -- n )
+PRIMITIVE: bignum-mod ( x y -- z )
+PRIMITIVE: bignum-shift ( x y -- z )
+PRIMITIVE: bignum/i ( x y -- z )
+PRIMITIVE: bignum/mod ( x y -- z w )
+PRIMITIVE: bignum< ( x y -- ? )
+PRIMITIVE: bignum<= ( x y -- ? )
+PRIMITIVE: bignum= ( x y -- ? )
+PRIMITIVE: bignum> ( x y -- ? )
+PRIMITIVE: bignum>= ( x y -- ? )
+PRIMITIVE: bignum>fixnum ( x -- y )
+PRIMITIVE: bignum>fixnum-strict ( x -- y )
+PRIMITIVE: both-fixnums? ( x y -- ? )
+PRIMITIVE: fixnum* ( x y -- z )
+PRIMITIVE: fixnum*fast ( x y -- z )
+PRIMITIVE: fixnum+ ( x y -- z )
+PRIMITIVE: fixnum+fast ( x y -- z )
+PRIMITIVE: fixnum- ( x y -- z )
+PRIMITIVE: fixnum-bitand ( x y -- z )
+PRIMITIVE: fixnum-bitnot ( x -- y )
+PRIMITIVE: fixnum-bitor ( x y -- z )
+PRIMITIVE: fixnum-bitxor ( x y -- z )
+PRIMITIVE: fixnum-fast ( x y -- z )
+PRIMITIVE: fixnum-mod ( x y -- z )
+PRIMITIVE: fixnum-shift ( x y -- z )
+PRIMITIVE: fixnum-shift-fast ( x y -- z )
+PRIMITIVE: fixnum/i ( x y -- z )
+PRIMITIVE: fixnum/i-fast ( x y -- z )
+PRIMITIVE: fixnum/mod ( x y -- z w )
+PRIMITIVE: fixnum/mod-fast ( x y -- z w )
+PRIMITIVE: fixnum< ( x y -- ? )
+PRIMITIVE: fixnum<= ( x y -- z )
+PRIMITIVE: fixnum> ( x y -- ? )
+PRIMITIVE: fixnum>= ( x y -- ? )
+PRIMITIVE: fixnum>bignum ( x -- y )
+PRIMITIVE: fixnum>float ( x -- y )
+PRIMITIVE: float* ( x y -- z )
+PRIMITIVE: float+ ( x y -- z )
+PRIMITIVE: float- ( x y -- z )
+PRIMITIVE: float-u< ( x y -- ? )
+PRIMITIVE: float-u<= ( x y -- ? )
+PRIMITIVE: float-u> ( x y -- ? )
+PRIMITIVE: float-u>= ( x y -- ? )
+PRIMITIVE: float/f ( x y -- z )
+PRIMITIVE: float< ( x y -- ? )
+PRIMITIVE: float<= ( x y -- ? )
+PRIMITIVE: float= ( x y -- ? )
+PRIMITIVE: float> ( x y -- ? )
+PRIMITIVE: float>= ( x y -- ? )
+PRIMITIVE: float>bignum ( x -- y )
+PRIMITIVE: float>fixnum ( x -- y )
+PRIVATE>
+
GENERIC: >fixnum ( x -- n ) foldable
GENERIC: >bignum ( x -- n ) foldable
GENERIC: >integer ( x -- n ) foldable
GENERIC: numerator ( a/b -- a )
GENERIC: denominator ( a/b -- b )
+GENERIC: >fraction ( a/b -- a b )
GENERIC: real-part ( z -- x )
GENERIC: imaginary-part ( z -- y )
MATH: bitand ( x y -- z ) foldable
MATH: bitor ( x y -- z ) foldable
MATH: bitxor ( x y -- z ) foldable
-GENERIC# shift 1 ( x n -- y ) foldable
+GENERIC#: shift 1 ( x n -- y ) foldable
GENERIC: bitnot ( x -- y ) foldable
-GENERIC# bit? 1 ( x n -- ? ) foldable
+GENERIC#: bit? 1 ( x n -- ? ) foldable
GENERIC: abs ( x -- y ) foldable
PRIVATE>
-ERROR: out-of-fixnum-range n ;
+: recursive-hashcode ( n obj quot -- code )
+ pick 0 <= [ 3drop 0 ] [ [ 1 - ] 2dip call ] if ; inline
ERROR: log2-expects-positive x ;
dup 0 <= [ log2-expects-positive ] [ (log2) ] if ; inline
: zero? ( x -- ? ) 0 number= ; inline
-
-! the following lines are necessary because the "-1 shift"
-! definition doesn't (yet) compile as nicely...
-GENERIC: 2/ ( x -- y ) foldable
-M: bignum 2/ -1 bignum-shift ; inline
-M: fixnum 2/ -1 fixnum-shift ; inline
-
+: 2/ ( x -- y ) -1 shift ; inline
: sq ( x -- y ) dup * ; inline
: neg ( x -- -x ) -1 * ; inline
: sgn ( x -- n ) dup 0 < [ drop -1 ] [ 0 > 1 0 ? ] if ; inline
: even? ( n -- ? ) 1 bitand zero? ; inline
: odd? ( n -- ? ) 1 bitand 1 number= ; inline
-GENERIC: neg? ( x -- -x )
+GENERIC: neg? ( x -- ? )
: if-zero ( ..a n quot1: ( ..a -- ..b ) quot2: ( ..a n -- ..b ) -- ..b )
[ dup zero? ] [ [ drop ] prepose ] [ ] tri* if ; inline
-: when-zero ( ..a n quot: ( ..a -- ..b ) -- ..b ) [ ] if-zero ; inline
+: when-zero ( ... n quot: ( ... -- ... x ) -- ... x ) [ ] if-zero ; inline
+
+: unless-zero ( ... n quot: ( ... n -- ... ) -- ... ) [ ] swap if-zero ; inline
-: unless-zero ( ..a n quot: ( ..a -- ..b ) -- ..b ) [ ] swap if-zero ; inline
+: until-zero ( ... n quot: ( ... x -- ... y ) -- ... ) [ dup zero? ] swap until drop ; inline
UNION: integer fixnum bignum ;
-TUPLE: ratio { numerator integer read-only } { denominator integer read-only } ;
+TUPLE: ratio
+ { numerator integer read-only }
+ { denominator integer read-only } ;
UNION: rational integer ratio ;
UNION: real rational float ;
-TUPLE: complex { real real read-only } { imaginary real read-only } ;
+TUPLE: complex
+ { real real read-only }
+ { imaginary real read-only } ;
UNION: number real complex ;
M: number recip 1 swap / ; inline
+: rect> ( x y -- z )
+ ! Note: an imaginary 0.0 should still create a complex
+ dup 0 = [ drop ] [ complex boa ] if ; inline
+
+GENERIC: >rect ( z -- x y )
+
+M: real >rect 0 ; inline
+
+M: complex >rect [ real-part ] [ imaginary-part ] bi ; inline
+
+<PRIVATE
+
+: (gcd) ( b a x y -- a d )
+ swap [
+ nip
+ ] [
+ [ /mod [ over * swapd - ] dip ] keep (gcd)
+ ] if-zero ; inline recursive
+
+PRIVATE>
+
+: gcd ( x y -- a d )
+ [ 0 1 ] 2dip (gcd) dup 0 < [ neg ] when ; inline
+
+MATH: simple-gcd ( x y -- d ) foldable
+
+<PRIVATE
+
+: fixnum-gcd ( x y -- d ) { fixnum fixnum } declare gcd nip ;
+
+PRIVATE>
+
+M: fixnum simple-gcd fixnum-gcd ; inline
+
+M: bignum simple-gcd bignum-gcd ; inline
+
: fp-bitwise= ( x y -- ? ) [ double>bits ] same? ; inline
GENERIC: fp-special? ( x -- ? )
: align ( m w -- n )
1 - [ + ] keep bitnot bitand ; inline
-<PRIVATE
-
-: iterate-prep ( n quot -- i n quot ) [ 0 ] 2dip ; inline
-
-: if-iterate? ( i n true false -- ) [ 2over < ] 2dip if ; inline
-
-: iterate-step ( i n quot -- i n quot )
- #! Apply quot to i, keep i and quot, hide n.
- [ nip call ] 3keep ; inline
-
-: iterate-next ( i n quot -- i' n quot ) [ 1 + ] 2dip ; inline
-
-PRIVATE>
-
-: (each-integer) ( ... i n quot: ( ... i -- ... ) -- ... )
- [ iterate-step iterate-next (each-integer) ]
- [ 3drop ] if-iterate? ; inline recursive
-
-: (find-integer) ( ... i n quot: ( ... i -- ... ? ) -- ... i )
- [
- iterate-step
- [ [ ] ] 2dip
- [ iterate-next (find-integer) ] 2curry bi-curry if
- ] [ 3drop f ] if-iterate? ; inline recursive
-
-: (all-integers?) ( ... i n quot: ( ... i -- ... ? ) -- ... ? )
- [
- iterate-step
- [ iterate-next (all-integers?) ] 3curry
- [ f ] if
- ] [ 3drop t ] if-iterate? ; inline recursive
+: each-integer-from ( ... i n quot: ( ... i -- ... ) -- ... )
+ 2over < [
+ [ nip call ] 3keep
+ [ 1 + ] 2dip each-integer-from
+ ] [
+ 3drop
+ ] if ; inline recursive
: each-integer ( ... n quot: ( ... i -- ... ) -- ... )
- iterate-prep (each-integer) ; inline
+ [ 0 ] 2dip each-integer-from ; inline
: times ( ... n quot: ( ... -- ... ) -- ... )
[ drop ] prepose each-integer ; inline
-: find-integer ( ... n quot: ( ... i -- ... ? ) -- ... i )
- iterate-prep (find-integer) ; inline
+: find-integer-from ( ... i n quot: ( ... i -- ... ? ) -- ... i/f )
+ 2over < [
+ [ nip call ] 3keep roll
+ [ 2drop ]
+ [ [ 1 + ] 2dip find-integer-from ] if
+ ] [
+ 3drop f
+ ] if ; inline recursive
-: all-integers? ( ... n quot: ( ... i -- ... ? ) -- ... ? )
- iterate-prep (all-integers?) ; inline
+: find-integer ( ... n quot: ( ... i -- ... ? ) -- ... i/f )
+ [ 0 ] 2dip find-integer-from ; inline
-: find-last-integer ( ... n quot: ( ... i -- ... ? ) -- ... i )
+: find-last-integer ( ... n quot: ( ... i -- ... ? ) -- ... i/f )
over 0 < [
2drop f
] [
[ 1 - ] dip find-last-integer
] if
] if ; inline recursive
+
+: all-integers-from? ( ... i n quot: ( ... i -- ... ? ) -- ... ? )
+ 2over < [
+ [ nip call ] 3keep roll
+ [ [ 1 + ] 2dip all-integers-from? ]
+ [ 3drop f ] if
+ ] [
+ 3drop t
+ ] if ; inline recursive
+
+: all-integers? ( ... n quot: ( ... i -- ... ? ) -- ... ? )
+ [ 0 ] 2dip all-integers-from? ; inline
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