1 ! Copyright (C) 2003, 2009 Slava Pestov.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: kernel math.private ;
6 GENERIC: >fixnum ( x -- n ) foldable
7 GENERIC: >bignum ( x -- n ) foldable
8 GENERIC: >integer ( x -- n ) foldable
9 GENERIC: >float ( x -- y ) foldable
11 GENERIC: numerator ( a/b -- a )
12 GENERIC: denominator ( a/b -- b )
14 GENERIC: real-part ( z -- x )
15 GENERIC: imaginary-part ( z -- y )
17 MATH: number= ( x y -- ? ) foldable
19 M: object number= 2drop f ;
21 MATH: < ( x y -- ? ) foldable
22 MATH: <= ( x y -- ? ) foldable
23 MATH: > ( x y -- ? ) foldable
24 MATH: >= ( x y -- ? ) foldable
26 MATH: + ( x y -- z ) foldable
27 MATH: - ( x y -- z ) foldable
28 MATH: * ( x y -- z ) foldable
29 MATH: / ( x y -- z ) foldable
30 MATH: /f ( x y -- z ) foldable
31 MATH: /i ( x y -- z ) foldable
32 MATH: mod ( x y -- z ) foldable
34 MATH: /mod ( x y -- z w ) foldable
36 MATH: bitand ( x y -- z ) foldable
37 MATH: bitor ( x y -- z ) foldable
38 MATH: bitxor ( x y -- z ) foldable
39 GENERIC# shift 1 ( x n -- y ) foldable
40 GENERIC: bitnot ( x -- y ) foldable
41 GENERIC# bit? 1 ( x n -- ? ) foldable
43 GENERIC: abs ( x -- y ) foldable
47 GENERIC: (log2) ( x -- n ) foldable
51 ERROR: log2-expects-positive x ;
60 : zero? ( x -- ? ) 0 number= ; inline
61 : 2/ ( x -- y ) -1 shift ; inline
62 : sq ( x -- y ) dup * ; inline
63 : neg ( x -- -x ) -1 * ; inline
64 : recip ( x -- y ) 1 swap / ; inline
65 : sgn ( x -- n ) dup 0 < [ drop -1 ] [ 0 > 1 0 ? ] if ; inline
66 : ?1+ ( x -- y ) [ 1 + ] [ 0 ] if* ; inline
67 : rem ( x y -- z ) abs [ mod ] [ + ] [ mod ] tri ; foldable
68 : 2^ ( n -- 2^n ) 1 swap shift ; inline
69 : even? ( n -- ? ) 1 bitand zero? ;
70 : odd? ( n -- ? ) 1 bitand 1 number= ;
72 : if-zero ( n quot1 quot2 -- )
73 [ dup zero? ] [ [ drop ] prepose ] [ ] tri* if ; inline
75 : when-zero ( n quot -- ) [ ] if-zero ; inline
77 : unless-zero ( n quot -- ) [ ] swap if-zero ; inline
79 UNION: integer fixnum bignum ;
81 TUPLE: ratio { numerator integer read-only } { denominator integer read-only } ;
83 UNION: rational integer ratio ;
85 UNION: real rational float ;
87 TUPLE: complex { real real read-only } { imaginary real read-only } ;
89 UNION: number real complex ;
91 : fp-bitwise= ( x y -- ? ) [ double>bits ] bi@ = ; inline
93 GENERIC: fp-special? ( x -- ? )
94 GENERIC: fp-nan? ( x -- ? )
95 GENERIC: fp-qnan? ( x -- ? )
96 GENERIC: fp-snan? ( x -- ? )
97 GENERIC: fp-infinity? ( x -- ? )
98 GENERIC: fp-nan-payload ( x -- bits )
100 M: object fp-special?
108 M: object fp-infinity?
110 M: object fp-nan-payload
114 double>bits -52 shift HEX: 7ff [ bitand ] keep = ;
116 M: float fp-nan-payload
117 double>bits HEX: fffffffffffff bitand ; foldable flushable
120 dup fp-special? [ fp-nan-payload zero? not ] [ drop f ] if ;
123 dup fp-nan? [ fp-nan-payload HEX: 8000000000000 bitand zero? not ] [ drop f ] if ;
126 dup fp-nan? [ fp-nan-payload HEX: 8000000000000 bitand zero? ] [ drop f ] if ;
128 M: float fp-infinity?
129 dup fp-special? [ fp-nan-payload zero? ] [ drop f ] if ;
131 : <fp-nan> ( payload -- nan )
132 HEX: 7ff0000000000000 bitor bits>double ; foldable flushable
134 : next-float ( m -- n )
136 dup -0.0 double>bits > [ 1 - bits>double ] [ ! negative non-zero
137 dup -0.0 double>bits = [ drop 0.0 ] [ ! negative zero
138 1 + bits>double ! positive
140 ] if ; foldable flushable
142 : prev-float ( m -- n )
144 dup -0.0 double>bits >= [ 1 + bits>double ] [ ! negative
145 dup 0.0 double>bits = [ drop -0.0 ] [ ! positive zero
146 1 - bits>double ! positive non-zero
148 ] if ; foldable flushable
150 : next-power-of-2 ( m -- n )
151 dup 2 <= [ drop 2 ] [ 1 - log2 1 + 2^ ] if ; inline
153 : power-of-2? ( n -- ? )
154 dup 0 <= [ drop f ] [ dup 1 - bitand zero? ] if ; foldable
157 1 - [ + ] keep bitnot bitand ; inline
161 : iterate-prep ( n quot -- i n quot ) [ 0 ] 2dip ; inline
163 : if-iterate? ( i n true false -- ) [ 2over < ] 2dip if ; inline
165 : iterate-step ( i n quot -- i n quot )
166 #! Apply quot to i, keep i and quot, hide n.
167 [ nip call ] 3keep ; inline
169 : iterate-next ( i n quot -- i' n quot ) [ 1 + ] 2dip ; inline
173 : (each-integer) ( i n quot: ( i -- ) -- )
174 [ iterate-step iterate-next (each-integer) ]
175 [ 3drop ] if-iterate? ; inline recursive
177 : (find-integer) ( i n quot: ( i -- ? ) -- i )
180 [ 2drop ] [ iterate-next (find-integer) ] if
181 ] [ 3drop f ] if-iterate? ; inline recursive
183 : (all-integers?) ( i n quot: ( i -- ? ) -- ? )
186 [ iterate-next (all-integers?) ] [ 3drop f ] if
187 ] [ 3drop t ] if-iterate? ; inline recursive
189 : each-integer ( n quot -- )
190 iterate-prep (each-integer) ; inline
192 : times ( n quot -- )
193 [ drop ] prepose each-integer ; inline
195 : find-integer ( n quot -- i )
196 iterate-prep (find-integer) ; inline
198 : all-integers? ( n quot -- ? )
199 iterate-prep (all-integers?) ; inline
201 : find-last-integer ( n quot: ( i -- ? ) -- i )
208 [ 1 - ] dip find-last-integer
210 ] if ; inline recursive