1 ;;;; This file contains macro-like source transformations which
2 ;;;; convert uses of certain functions into the canonical form desired
3 ;;;; within the compiler. FIXME: and other IR1 transforms and stuff.
5 ;;;; This software is part of the SBCL system. See the README file for
8 ;;;; This software is derived from the CMU CL system, which was
9 ;;;; written at Carnegie Mellon University and released into the
10 ;;;; public domain. The software is in the public domain and is
11 ;;;; provided with absolutely no warranty. See the COPYING and CREDITS
12 ;;;; files for more information.
16 ;;; Convert into an IF so that IF optimizations will eliminate redundant
18 (define-source-transform not
(x) `(if ,x nil t
))
19 (define-source-transform null
(x) `(if ,x nil t
))
21 ;;; ENDP is just NULL with a LIST assertion. The assertion will be
22 ;;; optimized away when SAFETY optimization is low; hopefully that
23 ;;; is consistent with ANSI's "should return an error".
24 (define-source-transform endp
(x) `(null (the list
,x
)))
26 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
27 ;;; returns the first value of its argument. Ditto for VALUES with one
29 (define-source-transform identity
(x) `(prog1 ,x
))
30 (define-source-transform values
(x) `(prog1 ,x
))
32 ;;; Bind the value and make a closure that returns it.
33 (define-source-transform constantly
(value)
34 (with-unique-names (rest n-value
)
35 `(let ((,n-value
,value
))
37 (declare (ignore ,rest
))
40 ;;; If the function has a known number of arguments, then return a
41 ;;; lambda with the appropriate fixed number of args. If the
42 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
43 ;;; MV optimization figure things out.
44 (deftransform complement
((fun) * * :node node
)
46 (multiple-value-bind (min max
)
47 (fun-type-nargs (lvar-type fun
))
49 ((and min
(eql min max
))
50 (let ((dums (make-gensym-list min
)))
51 `#'(lambda ,dums
(not (funcall fun
,@dums
)))))
52 ((awhen (node-lvar node
)
53 (let ((dest (lvar-dest it
)))
54 (and (combination-p dest
)
55 (eq (combination-fun dest
) it
))))
56 '#'(lambda (&rest args
)
57 (not (apply fun args
))))
59 (give-up-ir1-transform
60 "The function doesn't have a fixed argument count.")))))
64 ;;; Translate CxR into CAR/CDR combos.
65 (defun source-transform-cxr (form)
66 (if (/= (length form
) 2)
68 (let* ((name (car form
))
72 (leaf (leaf-source-name name
))))))
73 (do ((i (- (length string
) 2) (1- i
))
75 `(,(ecase (char string i
)
81 ;;; Make source transforms to turn CxR forms into combinations of CAR
82 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
84 (/show0
"about to set CxR source transforms")
85 (loop for i of-type index from
2 upto
4 do
86 ;; Iterate over BUF = all names CxR where x = an I-element
87 ;; string of #\A or #\D characters.
88 (let ((buf (make-string (+ 2 i
))))
89 (setf (aref buf
0) #\C
90 (aref buf
(1+ i
)) #\R
)
91 (dotimes (j (ash 2 i
))
92 (declare (type index j
))
94 (declare (type index k
))
95 (setf (aref buf
(1+ k
))
96 (if (logbitp k j
) #\A
#\D
)))
97 (setf (info :function
:source-transform
(intern buf
))
98 #'source-transform-cxr
))))
99 (/show0
"done setting CxR source transforms")
101 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
102 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
103 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
105 (define-source-transform first
(x) `(car ,x
))
106 (define-source-transform rest
(x) `(cdr ,x
))
107 (define-source-transform second
(x) `(cadr ,x
))
108 (define-source-transform third
(x) `(caddr ,x
))
109 (define-source-transform fourth
(x) `(cadddr ,x
))
110 (define-source-transform fifth
(x) `(nth 4 ,x
))
111 (define-source-transform sixth
(x) `(nth 5 ,x
))
112 (define-source-transform seventh
(x) `(nth 6 ,x
))
113 (define-source-transform eighth
(x) `(nth 7 ,x
))
114 (define-source-transform ninth
(x) `(nth 8 ,x
))
115 (define-source-transform tenth
(x) `(nth 9 ,x
))
117 ;;; LIST with one arg is an extremely common operation (at least inside
118 ;;; SBCL itself); translate it to CONS to take advantage of common
119 ;;; allocation routines.
120 (define-source-transform list
(&rest args
)
122 (1 `(cons ,(first args
) nil
))
125 ;;; And similarly for LIST*.
126 (define-source-transform list
* (arg &rest others
)
127 (cond ((not others
) arg
)
128 ((not (cdr others
)) `(cons ,arg
,(car others
)))
131 (defoptimizer (list* derive-type
) ((arg &rest args
))
133 (specifier-type 'cons
)
136 ;;; Translate RPLACx to LET and SETF.
137 (define-source-transform rplaca
(x y
)
142 (define-source-transform rplacd
(x y
)
148 (define-source-transform nth
(n l
) `(car (nthcdr ,n
,l
)))
150 (deftransform last
((list &optional n
) (t &optional t
))
151 (let ((c (constant-lvar-p n
)))
153 (and c
(eql 1 (lvar-value n
))))
155 ((and c
(eql 0 (lvar-value n
)))
158 (let ((type (lvar-type n
)))
159 (cond ((csubtypep type
(specifier-type 'fixnum
))
160 '(%lastn
/fixnum list n
))
161 ((csubtypep type
(specifier-type 'bignum
))
162 '(%lastn
/bignum list n
))
164 (give-up-ir1-transform "second argument type too vague"))))))))
166 (define-source-transform gethash
(&rest args
)
168 (2 `(sb!impl
::gethash3
,@args nil
))
169 (3 `(sb!impl
::gethash3
,@args
))
171 (define-source-transform get
(&rest args
)
173 (2 `(sb!impl
::get2
,@args
))
174 (3 `(sb!impl
::get3
,@args
))
177 (defvar *default-nthcdr-open-code-limit
* 6)
178 (defvar *extreme-nthcdr-open-code-limit
* 20)
180 (deftransform nthcdr
((n l
) (unsigned-byte t
) * :node node
)
181 "convert NTHCDR to CAxxR"
182 (unless (constant-lvar-p n
)
183 (give-up-ir1-transform))
184 (let ((n (lvar-value n
)))
186 (if (policy node
(and (= speed
3) (= space
0)))
187 *extreme-nthcdr-open-code-limit
*
188 *default-nthcdr-open-code-limit
*))
189 (give-up-ir1-transform))
194 `(cdr ,(frob (1- n
))))))
197 ;;;; arithmetic and numerology
199 (define-source-transform plusp
(x) `(> ,x
0))
200 (define-source-transform minusp
(x) `(< ,x
0))
201 (define-source-transform zerop
(x) `(= ,x
0))
203 (define-source-transform 1+ (x) `(+ ,x
1))
204 (define-source-transform 1-
(x) `(- ,x
1))
206 (define-source-transform oddp
(x) `(logtest ,x
1))
207 (define-source-transform evenp
(x) `(not (logtest ,x
1)))
209 ;;; Note that all the integer division functions are available for
210 ;;; inline expansion.
212 (macrolet ((deffrob (fun)
213 `(define-source-transform ,fun
(x &optional
(y nil y-p
))
220 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
222 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
225 ;;; This used to be a source transform (hence the lack of restrictions
226 ;;; on the argument types), but we make it a regular transform so that
227 ;;; the VM has a chance to see the bare LOGTEST and potentiall choose
228 ;;; to implement it differently. --njf, 06-02-2006
229 (deftransform logtest
((x y
) * *)
230 `(not (zerop (logand x y
))))
232 (deftransform logbitp
233 ((index integer
) (unsigned-byte (or (signed-byte #.sb
!vm
:n-word-bits
)
234 (unsigned-byte #.sb
!vm
:n-word-bits
))))
235 `(if (>= index
#.sb
!vm
:n-word-bits
)
237 (not (zerop (logand integer
(ash 1 index
))))))
239 (define-source-transform byte
(size position
)
240 `(cons ,size
,position
))
241 (define-source-transform byte-size
(spec) `(car ,spec
))
242 (define-source-transform byte-position
(spec) `(cdr ,spec
))
243 (define-source-transform ldb-test
(bytespec integer
)
244 `(not (zerop (mask-field ,bytespec
,integer
))))
246 ;;; With the ratio and complex accessors, we pick off the "identity"
247 ;;; case, and use a primitive to handle the cell access case.
248 (define-source-transform numerator
(num)
249 (once-only ((n-num `(the rational
,num
)))
253 (define-source-transform denominator
(num)
254 (once-only ((n-num `(the rational
,num
)))
256 (%denominator
,n-num
)
259 ;;;; interval arithmetic for computing bounds
261 ;;;; This is a set of routines for operating on intervals. It
262 ;;;; implements a simple interval arithmetic package. Although SBCL
263 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
264 ;;;; for two reasons:
266 ;;;; 1. This package is simpler than NUMERIC-TYPE.
268 ;;;; 2. It makes debugging much easier because you can just strip
269 ;;;; out these routines and test them independently of SBCL. (This is a
272 ;;;; One disadvantage is a probable increase in consing because we
273 ;;;; have to create these new interval structures even though
274 ;;;; numeric-type has everything we want to know. Reason 2 wins for
277 ;;; Support operations that mimic real arithmetic comparison
278 ;;; operators, but imposing a total order on the floating points such
279 ;;; that negative zeros are strictly less than positive zeros.
280 (macrolet ((def (name op
)
283 (if (and (floatp x
) (floatp y
) (zerop x
) (zerop y
))
284 (,op
(float-sign x
) (float-sign y
))
286 (def signed-zero-
>= >=)
287 (def signed-zero-
> >)
288 (def signed-zero-
= =)
289 (def signed-zero-
< <)
290 (def signed-zero-
<= <=))
292 ;;; The basic interval type. It can handle open and closed intervals.
293 ;;; A bound is open if it is a list containing a number, just like
294 ;;; Lisp says. NIL means unbounded.
295 (defstruct (interval (:constructor %make-interval
)
299 (defun make-interval (&key low high
)
300 (labels ((normalize-bound (val)
303 (float-infinity-p val
))
304 ;; Handle infinities.
308 ;; Handle any closed bounds.
311 ;; We have an open bound. Normalize the numeric
312 ;; bound. If the normalized bound is still a number
313 ;; (not nil), keep the bound open. Otherwise, the
314 ;; bound is really unbounded, so drop the openness.
315 (let ((new-val (normalize-bound (first val
))))
317 ;; The bound exists, so keep it open still.
320 (error "unknown bound type in MAKE-INTERVAL")))))
321 (%make-interval
:low
(normalize-bound low
)
322 :high
(normalize-bound high
))))
324 ;;; Given a number X, create a form suitable as a bound for an
325 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
326 #!-sb-fluid
(declaim (inline set-bound
))
327 (defun set-bound (x open-p
)
328 (if (and x open-p
) (list x
) x
))
330 ;;; Apply the function F to a bound X. If X is an open bound, then
331 ;;; the result will be open. IF X is NIL, the result is NIL.
332 (defun bound-func (f x
)
333 (declare (type function f
))
335 (with-float-traps-masked (:underflow
:overflow
:inexact
:divide-by-zero
)
336 ;; With these traps masked, we might get things like infinity
337 ;; or negative infinity returned. Check for this and return
338 ;; NIL to indicate unbounded.
339 (let ((y (funcall f
(type-bound-number x
))))
341 (float-infinity-p y
))
343 (set-bound y
(consp x
)))))))
345 (defun safe-double-coercion-p (x)
346 (or (typep x
'double-float
)
347 (<= most-negative-double-float x most-positive-double-float
)))
349 (defun safe-single-coercion-p (x)
350 (or (typep x
'single-float
)
351 ;; Fix for bug 420, and related issues: during type derivation we often
352 ;; end up deriving types for both
354 ;; (some-op <int> <single>)
356 ;; (some-op (coerce <int> 'single-float) <single>)
358 ;; or other equivalent transformed forms. The problem with this is that
359 ;; on some platforms like x86 (+ <int> <single>) is on the machine level
362 ;; (coerce (+ (coerce <int> 'double-float)
363 ;; (coerce <single> 'double-float))
366 ;; so if the result of (coerce <int> 'single-float) is not exact, the
367 ;; derived types for the transformed forms will have an empty
368 ;; intersection -- which in turn means that the compiler will conclude
369 ;; that the call never returns, and all hell breaks lose when it *does*
370 ;; return at runtime. (This affects not just +, but other operators are
372 (and (not (typep x
`(or (integer * (,most-negative-exactly-single-float-fixnum
))
373 (integer (,most-positive-exactly-single-float-fixnum
) *))))
374 (<= most-negative-single-float x most-positive-single-float
))))
376 ;;; Apply a binary operator OP to two bounds X and Y. The result is
377 ;;; NIL if either is NIL. Otherwise bound is computed and the result
378 ;;; is open if either X or Y is open.
380 ;;; FIXME: only used in this file, not needed in target runtime
382 ;;; ANSI contaigon specifies coercion to floating point if one of the
383 ;;; arguments is floating point. Here we should check to be sure that
384 ;;; the other argument is within the bounds of that floating point
387 (defmacro safely-binop
(op x y
)
389 ((typep ,x
'double-float
)
390 (when (safe-double-coercion-p ,y
)
392 ((typep ,y
'double-float
)
393 (when (safe-double-coercion-p ,x
)
395 ((typep ,x
'single-float
)
396 (when (safe-single-coercion-p ,y
)
398 ((typep ,y
'single-float
)
399 (when (safe-single-coercion-p ,x
)
403 (defmacro bound-binop
(op x y
)
405 (with-float-traps-masked (:underflow
:overflow
:inexact
:divide-by-zero
)
406 (set-bound (safely-binop ,op
(type-bound-number ,x
)
407 (type-bound-number ,y
))
408 (or (consp ,x
) (consp ,y
))))))
410 (defun coerce-for-bound (val type
)
412 (list (coerce-for-bound (car val
) type
))
414 ((subtypep type
'double-float
)
415 (if (<= most-negative-double-float val most-positive-double-float
)
417 ((or (subtypep type
'single-float
) (subtypep type
'float
))
418 ;; coerce to float returns a single-float
419 (if (<= most-negative-single-float val most-positive-single-float
)
421 (t (coerce val type
)))))
423 (defun coerce-and-truncate-floats (val type
)
426 (list (coerce-and-truncate-floats (car val
) type
))
428 ((subtypep type
'double-float
)
429 (if (<= most-negative-double-float val most-positive-double-float
)
431 (if (< val most-negative-double-float
)
432 most-negative-double-float most-positive-double-float
)))
433 ((or (subtypep type
'single-float
) (subtypep type
'float
))
434 ;; coerce to float returns a single-float
435 (if (<= most-negative-single-float val most-positive-single-float
)
437 (if (< val most-negative-single-float
)
438 most-negative-single-float most-positive-single-float
)))
439 (t (coerce val type
))))))
441 ;;; Convert a numeric-type object to an interval object.
442 (defun numeric-type->interval
(x)
443 (declare (type numeric-type x
))
444 (make-interval :low
(numeric-type-low x
)
445 :high
(numeric-type-high x
)))
447 (defun type-approximate-interval (type)
448 (declare (type ctype type
))
449 (let ((types (prepare-arg-for-derive-type type
))
452 (let ((type (if (member-type-p type
)
453 (convert-member-type type
)
455 (unless (numeric-type-p type
)
456 (return-from type-approximate-interval nil
))
457 (let ((interval (numeric-type->interval type
)))
460 (interval-approximate-union result interval
)
464 (defun copy-interval-limit (limit)
469 (defun copy-interval (x)
470 (declare (type interval x
))
471 (make-interval :low
(copy-interval-limit (interval-low x
))
472 :high
(copy-interval-limit (interval-high x
))))
474 ;;; Given a point P contained in the interval X, split X into two
475 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
476 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
477 ;;; contains P. You can specify both to be T or NIL.
478 (defun interval-split (p x
&optional close-lower close-upper
)
479 (declare (type number p
)
481 (list (make-interval :low
(copy-interval-limit (interval-low x
))
482 :high
(if close-lower p
(list p
)))
483 (make-interval :low
(if close-upper
(list p
) p
)
484 :high
(copy-interval-limit (interval-high x
)))))
486 ;;; Return the closure of the interval. That is, convert open bounds
487 ;;; to closed bounds.
488 (defun interval-closure (x)
489 (declare (type interval x
))
490 (make-interval :low
(type-bound-number (interval-low x
))
491 :high
(type-bound-number (interval-high x
))))
493 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
494 ;;; '-. Otherwise return NIL.
495 (defun interval-range-info (x &optional
(point 0))
496 (declare (type interval x
))
497 (let ((lo (interval-low x
))
498 (hi (interval-high x
)))
499 (cond ((and lo
(signed-zero->= (type-bound-number lo
) point
))
501 ((and hi
(signed-zero->= point
(type-bound-number hi
)))
506 ;;; Test to see whether the interval X is bounded. HOW determines the
507 ;;; test, and should be either ABOVE, BELOW, or BOTH.
508 (defun interval-bounded-p (x how
)
509 (declare (type interval x
))
516 (and (interval-low x
) (interval-high x
)))))
518 ;;; See whether the interval X contains the number P, taking into
519 ;;; account that the interval might not be closed.
520 (defun interval-contains-p (p x
)
521 (declare (type number p
)
523 ;; Does the interval X contain the number P? This would be a lot
524 ;; easier if all intervals were closed!
525 (let ((lo (interval-low x
))
526 (hi (interval-high x
)))
528 ;; The interval is bounded
529 (if (and (signed-zero-<= (type-bound-number lo
) p
)
530 (signed-zero-<= p
(type-bound-number hi
)))
531 ;; P is definitely in the closure of the interval.
532 ;; We just need to check the end points now.
533 (cond ((signed-zero-= p
(type-bound-number lo
))
535 ((signed-zero-= p
(type-bound-number hi
))
540 ;; Interval with upper bound
541 (if (signed-zero-< p
(type-bound-number hi
))
543 (and (numberp hi
) (signed-zero-= p hi
))))
545 ;; Interval with lower bound
546 (if (signed-zero-> p
(type-bound-number lo
))
548 (and (numberp lo
) (signed-zero-= p lo
))))
550 ;; Interval with no bounds
553 ;;; Determine whether two intervals X and Y intersect. Return T if so.
554 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
555 ;;; were closed. Otherwise the intervals are treated as they are.
557 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
558 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
559 ;;; is T, then they do intersect because we use the closure of X = [0,
560 ;;; 1] and Y = [1, 2] to determine intersection.
561 (defun interval-intersect-p (x y
&optional closed-intervals-p
)
562 (declare (type interval x y
))
563 (and (interval-intersection/difference
(if closed-intervals-p
566 (if closed-intervals-p
571 ;;; Are the two intervals adjacent? That is, is there a number
572 ;;; between the two intervals that is not an element of either
573 ;;; interval? If so, they are not adjacent. For example [0, 1) and
574 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
575 ;;; between both intervals.
576 (defun interval-adjacent-p (x y
)
577 (declare (type interval x y
))
578 (flet ((adjacent (lo hi
)
579 ;; Check to see whether lo and hi are adjacent. If either is
580 ;; nil, they can't be adjacent.
581 (when (and lo hi
(= (type-bound-number lo
) (type-bound-number hi
)))
582 ;; The bounds are equal. They are adjacent if one of
583 ;; them is closed (a number). If both are open (consp),
584 ;; then there is a number that lies between them.
585 (or (numberp lo
) (numberp hi
)))))
586 (or (adjacent (interval-low y
) (interval-high x
))
587 (adjacent (interval-low x
) (interval-high y
)))))
589 ;;; Compute the intersection and difference between two intervals.
590 ;;; Two values are returned: the intersection and the difference.
592 ;;; Let the two intervals be X and Y, and let I and D be the two
593 ;;; values returned by this function. Then I = X intersect Y. If I
594 ;;; is NIL (the empty set), then D is X union Y, represented as the
595 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
596 ;;; - I, which is a list of two intervals.
598 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
599 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
600 (defun interval-intersection/difference
(x y
)
601 (declare (type interval x y
))
602 (let ((x-lo (interval-low x
))
603 (x-hi (interval-high x
))
604 (y-lo (interval-low y
))
605 (y-hi (interval-high y
)))
608 ;; If p is an open bound, make it closed. If p is a closed
609 ;; bound, make it open.
613 (test-number (p int bound
)
614 ;; Test whether P is in the interval.
615 (let ((pn (type-bound-number p
)))
616 (when (interval-contains-p pn
(interval-closure int
))
617 ;; Check for endpoints.
618 (let* ((lo (interval-low int
))
619 (hi (interval-high int
))
620 (lon (type-bound-number lo
))
621 (hin (type-bound-number hi
)))
623 ;; Interval may be a point.
624 ((and lon hin
(= lon hin pn
))
625 (and (numberp p
) (numberp lo
) (numberp hi
)))
626 ;; Point matches the low end.
627 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
628 ;; (P [P,?} => TRUE P) [P,?} => FALSE
629 ;; (P (P,?} => TRUE P) (P,?} => FALSE
630 ((and lon
(= pn lon
))
631 (or (and (numberp p
) (numberp lo
))
632 (and (consp p
) (eq :low bound
))))
633 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
634 ;; P) {?,P] => TRUE (P {?,P] => FALSE
635 ;; P) {?,P) => TRUE (P {?,P) => FALSE
636 ((and hin
(= pn hin
))
637 (or (and (numberp p
) (numberp hi
))
638 (and (consp p
) (eq :high bound
))))
639 ;; Not an endpoint, all is well.
642 (test-lower-bound (p int
)
643 ;; P is a lower bound of an interval.
645 (test-number p int
:low
)
646 (not (interval-bounded-p int
'below
))))
647 (test-upper-bound (p int
)
648 ;; P is an upper bound of an interval.
650 (test-number p int
:high
)
651 (not (interval-bounded-p int
'above
)))))
652 (let ((x-lo-in-y (test-lower-bound x-lo y
))
653 (x-hi-in-y (test-upper-bound x-hi y
))
654 (y-lo-in-x (test-lower-bound y-lo x
))
655 (y-hi-in-x (test-upper-bound y-hi x
)))
656 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x
)
657 ;; Intervals intersect. Let's compute the intersection
658 ;; and the difference.
659 (multiple-value-bind (lo left-lo left-hi
)
660 (cond (x-lo-in-y (values x-lo y-lo
(opposite-bound x-lo
)))
661 (y-lo-in-x (values y-lo x-lo
(opposite-bound y-lo
))))
662 (multiple-value-bind (hi right-lo right-hi
)
664 (values x-hi
(opposite-bound x-hi
) y-hi
))
666 (values y-hi
(opposite-bound y-hi
) x-hi
)))
667 (values (make-interval :low lo
:high hi
)
668 (list (make-interval :low left-lo
670 (make-interval :low right-lo
673 (values nil
(list x y
))))))))
675 ;;; If intervals X and Y intersect, return a new interval that is the
676 ;;; union of the two. If they do not intersect, return NIL.
677 (defun interval-merge-pair (x y
)
678 (declare (type interval x y
))
679 ;; If x and y intersect or are adjacent, create the union.
680 ;; Otherwise return nil
681 (when (or (interval-intersect-p x y
)
682 (interval-adjacent-p x y
))
683 (flet ((select-bound (x1 x2 min-op max-op
)
684 (let ((x1-val (type-bound-number x1
))
685 (x2-val (type-bound-number x2
)))
687 ;; Both bounds are finite. Select the right one.
688 (cond ((funcall min-op x1-val x2-val
)
689 ;; x1 is definitely better.
691 ((funcall max-op x1-val x2-val
)
692 ;; x2 is definitely better.
695 ;; Bounds are equal. Select either
696 ;; value and make it open only if
698 (set-bound x1-val
(and (consp x1
) (consp x2
))))))
700 ;; At least one bound is not finite. The
701 ;; non-finite bound always wins.
703 (let* ((x-lo (copy-interval-limit (interval-low x
)))
704 (x-hi (copy-interval-limit (interval-high x
)))
705 (y-lo (copy-interval-limit (interval-low y
)))
706 (y-hi (copy-interval-limit (interval-high y
))))
707 (make-interval :low
(select-bound x-lo y-lo
#'< #'>)
708 :high
(select-bound x-hi y-hi
#'> #'<))))))
710 ;;; return the minimal interval, containing X and Y
711 (defun interval-approximate-union (x y
)
712 (cond ((interval-merge-pair x y
))
714 (make-interval :low
(copy-interval-limit (interval-low x
))
715 :high
(copy-interval-limit (interval-high y
))))
717 (make-interval :low
(copy-interval-limit (interval-low y
))
718 :high
(copy-interval-limit (interval-high x
))))))
720 ;;; basic arithmetic operations on intervals. We probably should do
721 ;;; true interval arithmetic here, but it's complicated because we
722 ;;; have float and integer types and bounds can be open or closed.
724 ;;; the negative of an interval
725 (defun interval-neg (x)
726 (declare (type interval x
))
727 (make-interval :low
(bound-func #'-
(interval-high x
))
728 :high
(bound-func #'-
(interval-low x
))))
730 ;;; Add two intervals.
731 (defun interval-add (x y
)
732 (declare (type interval x y
))
733 (make-interval :low
(bound-binop + (interval-low x
) (interval-low y
))
734 :high
(bound-binop + (interval-high x
) (interval-high y
))))
736 ;;; Subtract two intervals.
737 (defun interval-sub (x y
)
738 (declare (type interval x y
))
739 (make-interval :low
(bound-binop -
(interval-low x
) (interval-high y
))
740 :high
(bound-binop -
(interval-high x
) (interval-low y
))))
742 ;;; Multiply two intervals.
743 (defun interval-mul (x y
)
744 (declare (type interval x y
))
745 (flet ((bound-mul (x y
)
746 (cond ((or (null x
) (null y
))
747 ;; Multiply by infinity is infinity
749 ((or (and (numberp x
) (zerop x
))
750 (and (numberp y
) (zerop y
)))
751 ;; Multiply by closed zero is special. The result
752 ;; is always a closed bound. But don't replace this
753 ;; with zero; we want the multiplication to produce
754 ;; the correct signed zero, if needed. Use SIGNUM
755 ;; to avoid trying to multiply huge bignums with 0.0.
756 (* (signum (type-bound-number x
)) (signum (type-bound-number y
))))
757 ((or (and (floatp x
) (float-infinity-p x
))
758 (and (floatp y
) (float-infinity-p y
)))
759 ;; Infinity times anything is infinity
762 ;; General multiply. The result is open if either is open.
763 (bound-binop * x y
)))))
764 (let ((x-range (interval-range-info x
))
765 (y-range (interval-range-info y
)))
766 (cond ((null x-range
)
767 ;; Split x into two and multiply each separately
768 (destructuring-bind (x- x
+) (interval-split 0 x t t
)
769 (interval-merge-pair (interval-mul x- y
)
770 (interval-mul x
+ y
))))
772 ;; Split y into two and multiply each separately
773 (destructuring-bind (y- y
+) (interval-split 0 y t t
)
774 (interval-merge-pair (interval-mul x y-
)
775 (interval-mul x y
+))))
777 (interval-neg (interval-mul (interval-neg x
) y
)))
779 (interval-neg (interval-mul x
(interval-neg y
))))
780 ((and (eq x-range
'+) (eq y-range
'+))
781 ;; If we are here, X and Y are both positive.
783 :low
(bound-mul (interval-low x
) (interval-low y
))
784 :high
(bound-mul (interval-high x
) (interval-high y
))))
786 (bug "excluded case in INTERVAL-MUL"))))))
788 ;;; Divide two intervals.
789 (defun interval-div (top bot
)
790 (declare (type interval top bot
))
791 (flet ((bound-div (x y y-low-p
)
794 ;; Divide by infinity means result is 0. However,
795 ;; we need to watch out for the sign of the result,
796 ;; to correctly handle signed zeros. We also need
797 ;; to watch out for positive or negative infinity.
798 (if (floatp (type-bound-number x
))
800 (- (float-sign (type-bound-number x
) 0.0))
801 (float-sign (type-bound-number x
) 0.0))
803 ((zerop (type-bound-number y
))
804 ;; Divide by zero means result is infinity
806 ((and (numberp x
) (zerop x
))
807 ;; Zero divided by anything is zero.
810 (bound-binop / x y
)))))
811 (let ((top-range (interval-range-info top
))
812 (bot-range (interval-range-info bot
)))
813 (cond ((null bot-range
)
814 ;; The denominator contains zero, so anything goes!
815 (make-interval :low nil
:high nil
))
817 ;; Denominator is negative so flip the sign, compute the
818 ;; result, and flip it back.
819 (interval-neg (interval-div top
(interval-neg bot
))))
821 ;; Split top into two positive and negative parts, and
822 ;; divide each separately
823 (destructuring-bind (top- top
+) (interval-split 0 top t t
)
824 (interval-merge-pair (interval-div top- bot
)
825 (interval-div top
+ bot
))))
827 ;; Top is negative so flip the sign, divide, and flip the
828 ;; sign of the result.
829 (interval-neg (interval-div (interval-neg top
) bot
)))
830 ((and (eq top-range
'+) (eq bot-range
'+))
833 :low
(bound-div (interval-low top
) (interval-high bot
) t
)
834 :high
(bound-div (interval-high top
) (interval-low bot
) nil
)))
836 (bug "excluded case in INTERVAL-DIV"))))))
838 ;;; Apply the function F to the interval X. If X = [a, b], then the
839 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
840 ;;; result makes sense. It will if F is monotonic increasing (or
842 (defun interval-func (f x
)
843 (declare (type function f
)
845 (let ((lo (bound-func f
(interval-low x
)))
846 (hi (bound-func f
(interval-high x
))))
847 (make-interval :low lo
:high hi
)))
849 ;;; Return T if X < Y. That is every number in the interval X is
850 ;;; always less than any number in the interval Y.
851 (defun interval-< (x y
)
852 (declare (type interval x y
))
853 ;; X < Y only if X is bounded above, Y is bounded below, and they
855 (when (and (interval-bounded-p x
'above
)
856 (interval-bounded-p y
'below
))
857 ;; Intervals are bounded in the appropriate way. Make sure they
859 (let ((left (interval-high x
))
860 (right (interval-low y
)))
861 (cond ((> (type-bound-number left
)
862 (type-bound-number right
))
863 ;; The intervals definitely overlap, so result is NIL.
865 ((< (type-bound-number left
)
866 (type-bound-number right
))
867 ;; The intervals definitely don't touch, so result is T.
870 ;; Limits are equal. Check for open or closed bounds.
871 ;; Don't overlap if one or the other are open.
872 (or (consp left
) (consp right
)))))))
874 ;;; Return T if X >= Y. That is, every number in the interval X is
875 ;;; always greater than any number in the interval Y.
876 (defun interval->= (x y
)
877 (declare (type interval x y
))
878 ;; X >= Y if lower bound of X >= upper bound of Y
879 (when (and (interval-bounded-p x
'below
)
880 (interval-bounded-p y
'above
))
881 (>= (type-bound-number (interval-low x
))
882 (type-bound-number (interval-high y
)))))
884 ;;; Return T if X = Y.
885 (defun interval-= (x y
)
886 (declare (type interval x y
))
887 (and (interval-bounded-p x
'both
)
888 (interval-bounded-p y
'both
)
892 ;; Open intervals cannot be =
893 (return-from interval-
= nil
))))
894 ;; Both intervals refer to the same point
895 (= (bound (interval-high x
)) (bound (interval-low x
))
896 (bound (interval-high y
)) (bound (interval-low y
))))))
898 ;;; Return T if X /= Y
899 (defun interval-/= (x y
)
900 (not (interval-intersect-p x y
)))
902 ;;; Return an interval that is the absolute value of X. Thus, if
903 ;;; X = [-1 10], the result is [0, 10].
904 (defun interval-abs (x)
905 (declare (type interval x
))
906 (case (interval-range-info x
)
912 (destructuring-bind (x- x
+) (interval-split 0 x t t
)
913 (interval-merge-pair (interval-neg x-
) x
+)))))
915 ;;; Compute the square of an interval.
916 (defun interval-sqr (x)
917 (declare (type interval x
))
918 (interval-func (lambda (x) (* x x
))
921 ;;;; numeric DERIVE-TYPE methods
923 ;;; a utility for defining derive-type methods of integer operations. If
924 ;;; the types of both X and Y are integer types, then we compute a new
925 ;;; integer type with bounds determined Fun when applied to X and Y.
926 ;;; Otherwise, we use NUMERIC-CONTAGION.
927 (defun derive-integer-type-aux (x y fun
)
928 (declare (type function fun
))
929 (if (and (numeric-type-p x
) (numeric-type-p y
)
930 (eq (numeric-type-class x
) 'integer
)
931 (eq (numeric-type-class y
) 'integer
)
932 (eq (numeric-type-complexp x
) :real
)
933 (eq (numeric-type-complexp y
) :real
))
934 (multiple-value-bind (low high
) (funcall fun x y
)
935 (make-numeric-type :class
'integer
939 (numeric-contagion x y
)))
941 (defun derive-integer-type (x y fun
)
942 (declare (type lvar x y
) (type function fun
))
943 (let ((x (lvar-type x
))
945 (derive-integer-type-aux x y fun
)))
947 ;;; simple utility to flatten a list
948 (defun flatten-list (x)
949 (labels ((flatten-and-append (tree list
)
950 (cond ((null tree
) list
)
951 ((atom tree
) (cons tree list
))
952 (t (flatten-and-append
953 (car tree
) (flatten-and-append (cdr tree
) list
))))))
954 (flatten-and-append x nil
)))
956 ;;; Take some type of lvar and massage it so that we get a list of the
957 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
959 (defun prepare-arg-for-derive-type (arg)
960 (flet ((listify (arg)
965 (union-type-types arg
))
968 (unless (eq arg
*empty-type
*)
969 ;; Make sure all args are some type of numeric-type. For member
970 ;; types, convert the list of members into a union of equivalent
971 ;; single-element member-type's.
972 (let ((new-args nil
))
973 (dolist (arg (listify arg
))
974 (if (member-type-p arg
)
975 ;; Run down the list of members and convert to a list of
977 (mapc-member-type-members
979 (push (if (numberp member
)
980 (make-member-type :members
(list member
))
984 (push arg new-args
)))
985 (unless (member *empty-type
* new-args
)
988 ;;; Convert from the standard type convention for which -0.0 and 0.0
989 ;;; are equal to an intermediate convention for which they are
990 ;;; considered different which is more natural for some of the
992 (defun convert-numeric-type (type)
993 (declare (type numeric-type type
))
994 ;;; Only convert real float interval delimiters types.
995 (if (eq (numeric-type-complexp type
) :real
)
996 (let* ((lo (numeric-type-low type
))
997 (lo-val (type-bound-number lo
))
998 (lo-float-zero-p (and lo
(floatp lo-val
) (= lo-val
0.0)))
999 (hi (numeric-type-high type
))
1000 (hi-val (type-bound-number hi
))
1001 (hi-float-zero-p (and hi
(floatp hi-val
) (= hi-val
0.0))))
1002 (if (or lo-float-zero-p hi-float-zero-p
)
1004 :class
(numeric-type-class type
)
1005 :format
(numeric-type-format type
)
1007 :low
(if lo-float-zero-p
1009 (list (float 0.0 lo-val
))
1010 (float (load-time-value (make-unportable-float :single-float-negative-zero
)) lo-val
))
1012 :high
(if hi-float-zero-p
1014 (list (float (load-time-value (make-unportable-float :single-float-negative-zero
)) hi-val
))
1021 ;;; Convert back from the intermediate convention for which -0.0 and
1022 ;;; 0.0 are considered different to the standard type convention for
1023 ;;; which and equal.
1024 (defun convert-back-numeric-type (type)
1025 (declare (type numeric-type type
))
1026 ;;; Only convert real float interval delimiters types.
1027 (if (eq (numeric-type-complexp type
) :real
)
1028 (let* ((lo (numeric-type-low type
))
1029 (lo-val (type-bound-number lo
))
1031 (and lo
(floatp lo-val
) (= lo-val
0.0)
1032 (float-sign lo-val
)))
1033 (hi (numeric-type-high type
))
1034 (hi-val (type-bound-number hi
))
1036 (and hi
(floatp hi-val
) (= hi-val
0.0)
1037 (float-sign hi-val
))))
1039 ;; (float +0.0 +0.0) => (member 0.0)
1040 ;; (float -0.0 -0.0) => (member -0.0)
1041 ((and lo-float-zero-p hi-float-zero-p
)
1042 ;; shouldn't have exclusive bounds here..
1043 (aver (and (not (consp lo
)) (not (consp hi
))))
1044 (if (= lo-float-zero-p hi-float-zero-p
)
1045 ;; (float +0.0 +0.0) => (member 0.0)
1046 ;; (float -0.0 -0.0) => (member -0.0)
1047 (specifier-type `(member ,lo-val
))
1048 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1049 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1050 (make-numeric-type :class
(numeric-type-class type
)
1051 :format
(numeric-type-format type
)
1057 ;; (float -0.0 x) => (float 0.0 x)
1058 ((and (not (consp lo
)) (minusp lo-float-zero-p
))
1059 (make-numeric-type :class
(numeric-type-class type
)
1060 :format
(numeric-type-format type
)
1062 :low
(float 0.0 lo-val
)
1064 ;; (float (+0.0) x) => (float (0.0) x)
1065 ((and (consp lo
) (plusp lo-float-zero-p
))
1066 (make-numeric-type :class
(numeric-type-class type
)
1067 :format
(numeric-type-format type
)
1069 :low
(list (float 0.0 lo-val
))
1072 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1073 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1074 (list (make-member-type :members
(list (float 0.0 lo-val
)))
1075 (make-numeric-type :class
(numeric-type-class type
)
1076 :format
(numeric-type-format type
)
1078 :low
(list (float 0.0 lo-val
))
1082 ;; (float x +0.0) => (float x 0.0)
1083 ((and (not (consp hi
)) (plusp hi-float-zero-p
))
1084 (make-numeric-type :class
(numeric-type-class type
)
1085 :format
(numeric-type-format type
)
1088 :high
(float 0.0 hi-val
)))
1089 ;; (float x (-0.0)) => (float x (0.0))
1090 ((and (consp hi
) (minusp hi-float-zero-p
))
1091 (make-numeric-type :class
(numeric-type-class type
)
1092 :format
(numeric-type-format type
)
1095 :high
(list (float 0.0 hi-val
))))
1097 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1098 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1099 (list (make-member-type :members
(list (float (load-time-value (make-unportable-float :single-float-negative-zero
)) hi-val
)))
1100 (make-numeric-type :class
(numeric-type-class type
)
1101 :format
(numeric-type-format type
)
1104 :high
(list (float 0.0 hi-val
)))))))
1110 ;;; Convert back a possible list of numeric types.
1111 (defun convert-back-numeric-type-list (type-list)
1114 (let ((results '()))
1115 (dolist (type type-list
)
1116 (if (numeric-type-p type
)
1117 (let ((result (convert-back-numeric-type type
)))
1119 (setf results
(append results result
))
1120 (push result results
)))
1121 (push type results
)))
1124 (convert-back-numeric-type type-list
))
1126 (convert-back-numeric-type-list (union-type-types type-list
)))
1130 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
1131 ;;; belong in the kernel's type logic, invoked always, instead of in
1132 ;;; the compiler, invoked only during some type optimizations. (In
1133 ;;; fact, as of 0.pre8.100 or so they probably are, under
1134 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
1136 ;;; Take a list of types and return a canonical type specifier,
1137 ;;; combining any MEMBER types together. If both positive and negative
1138 ;;; MEMBER types are present they are converted to a float type.
1139 ;;; XXX This would be far simpler if the type-union methods could handle
1140 ;;; member/number unions.
1141 (defun make-canonical-union-type (type-list)
1142 (let ((xset (alloc-xset))
1145 (dolist (type type-list
)
1146 (cond ((member-type-p type
)
1147 (mapc-member-type-members
1149 (if (fp-zero-p member
)
1150 (unless (member member fp-zeroes
)
1151 (pushnew member fp-zeroes
))
1152 (add-to-xset member xset
)))
1155 (push type misc-types
))))
1156 (if (and (xset-empty-p xset
) (not fp-zeroes
))
1157 (apply #'type-union misc-types
)
1158 (apply #'type-union
(make-member-type :xset xset
:fp-zeroes fp-zeroes
) misc-types
))))
1160 ;;; Convert a member type with a single member to a numeric type.
1161 (defun convert-member-type (arg)
1162 (let* ((members (member-type-members arg
))
1163 (member (first members
))
1164 (member-type (type-of member
)))
1165 (aver (not (rest members
)))
1166 (specifier-type (cond ((typep member
'integer
)
1167 `(integer ,member
,member
))
1168 ((memq member-type
'(short-float single-float
1169 double-float long-float
))
1170 `(,member-type
,member
,member
))
1174 ;;; This is used in defoptimizers for computing the resulting type of
1177 ;;; Given the lvar ARG, derive the resulting type using the
1178 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1179 ;;; "atomic" lvar type like numeric-type or member-type (containing
1180 ;;; just one element). It should return the resulting type, which can
1181 ;;; be a list of types.
1183 ;;; For the case of member types, if a MEMBER-FUN is given it is
1184 ;;; called to compute the result otherwise the member type is first
1185 ;;; converted to a numeric type and the DERIVE-FUN is called.
1186 (defun one-arg-derive-type (arg derive-fun member-fun
1187 &optional
(convert-type t
))
1188 (declare (type function derive-fun
)
1189 (type (or null function
) member-fun
))
1190 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg
))))
1196 (with-float-traps-masked
1197 (:underflow
:overflow
:divide-by-zero
)
1199 `(eql ,(funcall member-fun
1200 (first (member-type-members x
))))))
1201 ;; Otherwise convert to a numeric type.
1202 (let ((result-type-list
1203 (funcall derive-fun
(convert-member-type x
))))
1205 (convert-back-numeric-type-list result-type-list
)
1206 result-type-list
))))
1209 (convert-back-numeric-type-list
1210 (funcall derive-fun
(convert-numeric-type x
)))
1211 (funcall derive-fun x
)))
1213 *universal-type
*))))
1214 ;; Run down the list of args and derive the type of each one,
1215 ;; saving all of the results in a list.
1216 (let ((results nil
))
1217 (dolist (arg arg-list
)
1218 (let ((result (deriver arg
)))
1220 (setf results
(append results result
))
1221 (push result results
))))
1223 (make-canonical-union-type results
)
1224 (first results
)))))))
1226 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1227 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1228 ;;; original args and a third which is T to indicate if the two args
1229 ;;; really represent the same lvar. This is useful for deriving the
1230 ;;; type of things like (* x x), which should always be positive. If
1231 ;;; we didn't do this, we wouldn't be able to tell.
1232 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1233 &optional
(convert-type t
))
1234 (declare (type function derive-fun fun
))
1235 (flet ((deriver (x y same-arg
)
1236 (cond ((and (member-type-p x
) (member-type-p y
))
1237 (let* ((x (first (member-type-members x
)))
1238 (y (first (member-type-members y
)))
1239 (result (ignore-errors
1240 (with-float-traps-masked
1241 (:underflow
:overflow
:divide-by-zero
1243 (funcall fun x y
)))))
1244 (cond ((null result
) *empty-type
*)
1245 ((and (floatp result
) (float-nan-p result
))
1246 (make-numeric-type :class
'float
1247 :format
(type-of result
)
1250 (specifier-type `(eql ,result
))))))
1251 ((and (member-type-p x
) (numeric-type-p y
))
1252 (let* ((x (convert-member-type x
))
1253 (y (if convert-type
(convert-numeric-type y
) y
))
1254 (result (funcall derive-fun x y same-arg
)))
1256 (convert-back-numeric-type-list result
)
1258 ((and (numeric-type-p x
) (member-type-p y
))
1259 (let* ((x (if convert-type
(convert-numeric-type x
) x
))
1260 (y (convert-member-type y
))
1261 (result (funcall derive-fun x y same-arg
)))
1263 (convert-back-numeric-type-list result
)
1265 ((and (numeric-type-p x
) (numeric-type-p y
))
1266 (let* ((x (if convert-type
(convert-numeric-type x
) x
))
1267 (y (if convert-type
(convert-numeric-type y
) y
))
1268 (result (funcall derive-fun x y same-arg
)))
1270 (convert-back-numeric-type-list result
)
1273 *universal-type
*))))
1274 (let ((same-arg (same-leaf-ref-p arg1 arg2
))
1275 (a1 (prepare-arg-for-derive-type (lvar-type arg1
)))
1276 (a2 (prepare-arg-for-derive-type (lvar-type arg2
))))
1278 (let ((results nil
))
1280 ;; Since the args are the same LVARs, just run down the
1283 (let ((result (deriver x x same-arg
)))
1285 (setf results
(append results result
))
1286 (push result results
))))
1287 ;; Try all pairwise combinations.
1290 (let ((result (or (deriver x y same-arg
)
1291 (numeric-contagion x y
))))
1293 (setf results
(append results result
))
1294 (push result results
))))))
1296 (make-canonical-union-type results
)
1297 (first results
)))))))
1299 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1301 (defoptimizer (+ derive-type
) ((x y
))
1302 (derive-integer-type
1309 (values (frob (numeric-type-low x
) (numeric-type-low y
))
1310 (frob (numeric-type-high x
) (numeric-type-high y
)))))))
1312 (defoptimizer (- derive-type
) ((x y
))
1313 (derive-integer-type
1320 (values (frob (numeric-type-low x
) (numeric-type-high y
))
1321 (frob (numeric-type-high x
) (numeric-type-low y
)))))))
1323 (defoptimizer (* derive-type
) ((x y
))
1324 (derive-integer-type
1327 (let ((x-low (numeric-type-low x
))
1328 (x-high (numeric-type-high x
))
1329 (y-low (numeric-type-low y
))
1330 (y-high (numeric-type-high y
)))
1331 (cond ((not (and x-low y-low
))
1333 ((or (minusp x-low
) (minusp y-low
))
1334 (if (and x-high y-high
)
1335 (let ((max (* (max (abs x-low
) (abs x-high
))
1336 (max (abs y-low
) (abs y-high
)))))
1337 (values (- max
) max
))
1340 (values (* x-low y-low
)
1341 (if (and x-high y-high
)
1345 (defoptimizer (/ derive-type
) ((x y
))
1346 (numeric-contagion (lvar-type x
) (lvar-type y
)))
1350 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1352 (defun +-derive-type-aux
(x y same-arg
)
1353 (if (and (numeric-type-real-p x
)
1354 (numeric-type-real-p y
))
1357 (let ((x-int (numeric-type->interval x
)))
1358 (interval-add x-int x-int
))
1359 (interval-add (numeric-type->interval x
)
1360 (numeric-type->interval y
))))
1361 (result-type (numeric-contagion x y
)))
1362 ;; If the result type is a float, we need to be sure to coerce
1363 ;; the bounds into the correct type.
1364 (when (eq (numeric-type-class result-type
) 'float
)
1365 (setf result
(interval-func
1367 (coerce-for-bound x
(or (numeric-type-format result-type
)
1371 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1372 (eq (numeric-type-class y
) 'integer
))
1373 ;; The sum of integers is always an integer.
1375 (numeric-type-class result-type
))
1376 :format
(numeric-type-format result-type
)
1377 :low
(interval-low result
)
1378 :high
(interval-high result
)))
1379 ;; general contagion
1380 (numeric-contagion x y
)))
1382 (defoptimizer (+ derive-type
) ((x y
))
1383 (two-arg-derive-type x y
#'+-derive-type-aux
#'+))
1385 (defun --derive-type-aux (x y same-arg
)
1386 (if (and (numeric-type-real-p x
)
1387 (numeric-type-real-p y
))
1389 ;; (- X X) is always 0.
1391 (make-interval :low
0 :high
0)
1392 (interval-sub (numeric-type->interval x
)
1393 (numeric-type->interval y
))))
1394 (result-type (numeric-contagion x y
)))
1395 ;; If the result type is a float, we need to be sure to coerce
1396 ;; the bounds into the correct type.
1397 (when (eq (numeric-type-class result-type
) 'float
)
1398 (setf result
(interval-func
1400 (coerce-for-bound x
(or (numeric-type-format result-type
)
1404 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1405 (eq (numeric-type-class y
) 'integer
))
1406 ;; The difference of integers is always an integer.
1408 (numeric-type-class result-type
))
1409 :format
(numeric-type-format result-type
)
1410 :low
(interval-low result
)
1411 :high
(interval-high result
)))
1412 ;; general contagion
1413 (numeric-contagion x y
)))
1415 (defoptimizer (- derive-type
) ((x y
))
1416 (two-arg-derive-type x y
#'--derive-type-aux
#'-
))
1418 (defun *-derive-type-aux
(x y same-arg
)
1419 (if (and (numeric-type-real-p x
)
1420 (numeric-type-real-p y
))
1422 ;; (* X X) is always positive, so take care to do it right.
1424 (interval-sqr (numeric-type->interval x
))
1425 (interval-mul (numeric-type->interval x
)
1426 (numeric-type->interval y
))))
1427 (result-type (numeric-contagion x y
)))
1428 ;; If the result type is a float, we need to be sure to coerce
1429 ;; the bounds into the correct type.
1430 (when (eq (numeric-type-class result-type
) 'float
)
1431 (setf result
(interval-func
1433 (coerce-for-bound x
(or (numeric-type-format result-type
)
1437 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1438 (eq (numeric-type-class y
) 'integer
))
1439 ;; The product of integers is always an integer.
1441 (numeric-type-class result-type
))
1442 :format
(numeric-type-format result-type
)
1443 :low
(interval-low result
)
1444 :high
(interval-high result
)))
1445 (numeric-contagion x y
)))
1447 (defoptimizer (* derive-type
) ((x y
))
1448 (two-arg-derive-type x y
#'*-derive-type-aux
#'*))
1450 (defun /-derive-type-aux
(x y same-arg
)
1451 (if (and (numeric-type-real-p x
)
1452 (numeric-type-real-p y
))
1454 ;; (/ X X) is always 1, except if X can contain 0. In
1455 ;; that case, we shouldn't optimize the division away
1456 ;; because we want 0/0 to signal an error.
1458 (not (interval-contains-p
1459 0 (interval-closure (numeric-type->interval y
)))))
1460 (make-interval :low
1 :high
1)
1461 (interval-div (numeric-type->interval x
)
1462 (numeric-type->interval y
))))
1463 (result-type (numeric-contagion x y
)))
1464 ;; If the result type is a float, we need to be sure to coerce
1465 ;; the bounds into the correct type.
1466 (when (eq (numeric-type-class result-type
) 'float
)
1467 (setf result
(interval-func
1469 (coerce-for-bound x
(or (numeric-type-format result-type
)
1472 (make-numeric-type :class
(numeric-type-class result-type
)
1473 :format
(numeric-type-format result-type
)
1474 :low
(interval-low result
)
1475 :high
(interval-high result
)))
1476 (numeric-contagion x y
)))
1478 (defoptimizer (/ derive-type
) ((x y
))
1479 (two-arg-derive-type x y
#'/-derive-type-aux
#'/))
1483 (defun ash-derive-type-aux (n-type shift same-arg
)
1484 (declare (ignore same-arg
))
1485 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1486 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1487 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1488 ;; two bignums yielding zero) and it's hard to avoid that
1489 ;; calculation in here.
1490 #+(and cmu sb-xc-host
)
1491 (when (and (or (typep (numeric-type-low n-type
) 'bignum
)
1492 (typep (numeric-type-high n-type
) 'bignum
))
1493 (or (typep (numeric-type-low shift
) 'bignum
)
1494 (typep (numeric-type-high shift
) 'bignum
)))
1495 (return-from ash-derive-type-aux
*universal-type
*))
1496 (flet ((ash-outer (n s
)
1497 (when (and (fixnump s
)
1499 (> s sb
!xc
:most-negative-fixnum
))
1501 ;; KLUDGE: The bare 64's here should be related to
1502 ;; symbolic machine word size values somehow.
1505 (if (and (fixnump s
)
1506 (> s sb
!xc
:most-negative-fixnum
))
1508 (if (minusp n
) -
1 0))))
1509 (or (and (csubtypep n-type
(specifier-type 'integer
))
1510 (csubtypep shift
(specifier-type 'integer
))
1511 (let ((n-low (numeric-type-low n-type
))
1512 (n-high (numeric-type-high n-type
))
1513 (s-low (numeric-type-low shift
))
1514 (s-high (numeric-type-high shift
)))
1515 (make-numeric-type :class
'integer
:complexp
:real
1518 (ash-outer n-low s-high
)
1519 (ash-inner n-low s-low
)))
1522 (ash-inner n-high s-low
)
1523 (ash-outer n-high s-high
))))))
1526 (defoptimizer (ash derive-type
) ((n shift
))
1527 (two-arg-derive-type n shift
#'ash-derive-type-aux
#'ash
))
1529 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1530 (macrolet ((frob (fun)
1531 `#'(lambda (type type2
)
1532 (declare (ignore type2
))
1533 (let ((lo (numeric-type-low type
))
1534 (hi (numeric-type-high type
)))
1535 (values (if hi
(,fun hi
) nil
) (if lo
(,fun lo
) nil
))))))
1537 (defoptimizer (%negate derive-type
) ((num))
1538 (derive-integer-type num num
(frob -
))))
1540 (defun lognot-derive-type-aux (int)
1541 (derive-integer-type-aux int int
1542 (lambda (type type2
)
1543 (declare (ignore type2
))
1544 (let ((lo (numeric-type-low type
))
1545 (hi (numeric-type-high type
)))
1546 (values (if hi
(lognot hi
) nil
)
1547 (if lo
(lognot lo
) nil
)
1548 (numeric-type-class type
)
1549 (numeric-type-format type
))))))
1551 (defoptimizer (lognot derive-type
) ((int))
1552 (lognot-derive-type-aux (lvar-type int
)))
1554 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1555 (defoptimizer (%negate derive-type
) ((num))
1556 (flet ((negate-bound (b)
1558 (set-bound (- (type-bound-number b
))
1560 (one-arg-derive-type num
1562 (modified-numeric-type
1564 :low
(negate-bound (numeric-type-high type
))
1565 :high
(negate-bound (numeric-type-low type
))))
1568 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1569 (defoptimizer (abs derive-type
) ((num))
1570 (let ((type (lvar-type num
)))
1571 (if (and (numeric-type-p type
)
1572 (eq (numeric-type-class type
) 'integer
)
1573 (eq (numeric-type-complexp type
) :real
))
1574 (let ((lo (numeric-type-low type
))
1575 (hi (numeric-type-high type
)))
1576 (make-numeric-type :class
'integer
:complexp
:real
1577 :low
(cond ((and hi
(minusp hi
))
1583 :high
(if (and hi lo
)
1584 (max (abs hi
) (abs lo
))
1586 (numeric-contagion type type
))))
1588 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1589 (defun abs-derive-type-aux (type)
1590 (cond ((eq (numeric-type-complexp type
) :complex
)
1591 ;; The absolute value of a complex number is always a
1592 ;; non-negative float.
1593 (let* ((format (case (numeric-type-class type
)
1594 ((integer rational
) 'single-float
)
1595 (t (numeric-type-format type
))))
1596 (bound-format (or format
'float
)))
1597 (make-numeric-type :class
'float
1600 :low
(coerce 0 bound-format
)
1603 ;; The absolute value of a real number is a non-negative real
1604 ;; of the same type.
1605 (let* ((abs-bnd (interval-abs (numeric-type->interval type
)))
1606 (class (numeric-type-class type
))
1607 (format (numeric-type-format type
))
1608 (bound-type (or format class
'real
)))
1613 :low
(coerce-and-truncate-floats (interval-low abs-bnd
) bound-type
)
1614 :high
(coerce-and-truncate-floats
1615 (interval-high abs-bnd
) bound-type
))))))
1617 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1618 (defoptimizer (abs derive-type
) ((num))
1619 (one-arg-derive-type num
#'abs-derive-type-aux
#'abs
))
1621 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1622 (defoptimizer (truncate derive-type
) ((number divisor
))
1623 (let ((number-type (lvar-type number
))
1624 (divisor-type (lvar-type divisor
))
1625 (integer-type (specifier-type 'integer
)))
1626 (if (and (numeric-type-p number-type
)
1627 (csubtypep number-type integer-type
)
1628 (numeric-type-p divisor-type
)
1629 (csubtypep divisor-type integer-type
))
1630 (let ((number-low (numeric-type-low number-type
))
1631 (number-high (numeric-type-high number-type
))
1632 (divisor-low (numeric-type-low divisor-type
))
1633 (divisor-high (numeric-type-high divisor-type
)))
1634 (values-specifier-type
1635 `(values ,(integer-truncate-derive-type number-low number-high
1636 divisor-low divisor-high
)
1637 ,(integer-rem-derive-type number-low number-high
1638 divisor-low divisor-high
))))
1641 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1644 (defun rem-result-type (number-type divisor-type
)
1645 ;; Figure out what the remainder type is. The remainder is an
1646 ;; integer if both args are integers; a rational if both args are
1647 ;; rational; and a float otherwise.
1648 (cond ((and (csubtypep number-type
(specifier-type 'integer
))
1649 (csubtypep divisor-type
(specifier-type 'integer
)))
1651 ((and (csubtypep number-type
(specifier-type 'rational
))
1652 (csubtypep divisor-type
(specifier-type 'rational
)))
1654 ((and (csubtypep number-type
(specifier-type 'float
))
1655 (csubtypep divisor-type
(specifier-type 'float
)))
1656 ;; Both are floats so the result is also a float, of
1657 ;; the largest type.
1658 (or (float-format-max (numeric-type-format number-type
)
1659 (numeric-type-format divisor-type
))
1661 ((and (csubtypep number-type
(specifier-type 'float
))
1662 (csubtypep divisor-type
(specifier-type 'rational
)))
1663 ;; One of the arguments is a float and the other is a
1664 ;; rational. The remainder is a float of the same
1666 (or (numeric-type-format number-type
) 'float
))
1667 ((and (csubtypep divisor-type
(specifier-type 'float
))
1668 (csubtypep number-type
(specifier-type 'rational
)))
1669 ;; One of the arguments is a float and the other is a
1670 ;; rational. The remainder is a float of the same
1672 (or (numeric-type-format divisor-type
) 'float
))
1674 ;; Some unhandled combination. This usually means both args
1675 ;; are REAL so the result is a REAL.
1678 (defun truncate-derive-type-quot (number-type divisor-type
)
1679 (let* ((rem-type (rem-result-type number-type divisor-type
))
1680 (number-interval (numeric-type->interval number-type
))
1681 (divisor-interval (numeric-type->interval divisor-type
)))
1682 ;;(declare (type (member '(integer rational float)) rem-type))
1683 ;; We have real numbers now.
1684 (cond ((eq rem-type
'integer
)
1685 ;; Since the remainder type is INTEGER, both args are
1687 (let* ((res (integer-truncate-derive-type
1688 (interval-low number-interval
)
1689 (interval-high number-interval
)
1690 (interval-low divisor-interval
)
1691 (interval-high divisor-interval
))))
1692 (specifier-type (if (listp res
) res
'integer
))))
1694 (let ((quot (truncate-quotient-bound
1695 (interval-div number-interval
1696 divisor-interval
))))
1697 (specifier-type `(integer ,(or (interval-low quot
) '*)
1698 ,(or (interval-high quot
) '*))))))))
1700 (defun truncate-derive-type-rem (number-type divisor-type
)
1701 (let* ((rem-type (rem-result-type number-type divisor-type
))
1702 (number-interval (numeric-type->interval number-type
))
1703 (divisor-interval (numeric-type->interval divisor-type
))
1704 (rem (truncate-rem-bound number-interval divisor-interval
)))
1705 ;;(declare (type (member '(integer rational float)) rem-type))
1706 ;; We have real numbers now.
1707 (cond ((eq rem-type
'integer
)
1708 ;; Since the remainder type is INTEGER, both args are
1710 (specifier-type `(,rem-type
,(or (interval-low rem
) '*)
1711 ,(or (interval-high rem
) '*))))
1713 (multiple-value-bind (class format
)
1716 (values 'integer nil
))
1718 (values 'rational nil
))
1719 ((or single-float double-float
#!+long-float long-float
)
1720 (values 'float rem-type
))
1722 (values 'float nil
))
1725 (when (member rem-type
'(float single-float double-float
1726 #!+long-float long-float
))
1727 (setf rem
(interval-func #'(lambda (x)
1728 (coerce-for-bound x rem-type
))
1730 (make-numeric-type :class class
1732 :low
(interval-low rem
)
1733 :high
(interval-high rem
)))))))
1735 (defun truncate-derive-type-quot-aux (num div same-arg
)
1736 (declare (ignore same-arg
))
1737 (if (and (numeric-type-real-p num
)
1738 (numeric-type-real-p div
))
1739 (truncate-derive-type-quot num div
)
1742 (defun truncate-derive-type-rem-aux (num div same-arg
)
1743 (declare (ignore same-arg
))
1744 (if (and (numeric-type-real-p num
)
1745 (numeric-type-real-p div
))
1746 (truncate-derive-type-rem num div
)
1749 (defoptimizer (truncate derive-type
) ((number divisor
))
1750 (let ((quot (two-arg-derive-type number divisor
1751 #'truncate-derive-type-quot-aux
#'truncate
))
1752 (rem (two-arg-derive-type number divisor
1753 #'truncate-derive-type-rem-aux
#'rem
)))
1754 (when (and quot rem
)
1755 (make-values-type :required
(list quot rem
)))))
1757 (defun ftruncate-derive-type-quot (number-type divisor-type
)
1758 ;; The bounds are the same as for truncate. However, the first
1759 ;; result is a float of some type. We need to determine what that
1760 ;; type is. Basically it's the more contagious of the two types.
1761 (let ((q-type (truncate-derive-type-quot number-type divisor-type
))
1762 (res-type (numeric-contagion number-type divisor-type
)))
1763 (make-numeric-type :class
'float
1764 :format
(numeric-type-format res-type
)
1765 :low
(numeric-type-low q-type
)
1766 :high
(numeric-type-high q-type
))))
1768 (defun ftruncate-derive-type-quot-aux (n d same-arg
)
1769 (declare (ignore same-arg
))
1770 (if (and (numeric-type-real-p n
)
1771 (numeric-type-real-p d
))
1772 (ftruncate-derive-type-quot n d
)
1775 (defoptimizer (ftruncate derive-type
) ((number divisor
))
1777 (two-arg-derive-type number divisor
1778 #'ftruncate-derive-type-quot-aux
#'ftruncate
))
1779 (rem (two-arg-derive-type number divisor
1780 #'truncate-derive-type-rem-aux
#'rem
)))
1781 (when (and quot rem
)
1782 (make-values-type :required
(list quot rem
)))))
1784 (defun %unary-truncate-derive-type-aux
(number)
1785 (truncate-derive-type-quot number
(specifier-type '(integer 1 1))))
1787 (defoptimizer (%unary-truncate derive-type
) ((number))
1788 (one-arg-derive-type number
1789 #'%unary-truncate-derive-type-aux
1792 (defoptimizer (%unary-truncate
/single-float derive-type
) ((number))
1793 (one-arg-derive-type number
1794 #'%unary-truncate-derive-type-aux
1797 (defoptimizer (%unary-truncate
/double-float derive-type
) ((number))
1798 (one-arg-derive-type number
1799 #'%unary-truncate-derive-type-aux
1802 (defoptimizer (%unary-ftruncate derive-type
) ((number))
1803 (let ((divisor (specifier-type '(integer 1 1))))
1804 (one-arg-derive-type number
1806 (ftruncate-derive-type-quot-aux n divisor nil
))
1807 #'%unary-ftruncate
)))
1809 (defoptimizer (%unary-round derive-type
) ((number))
1810 (one-arg-derive-type number
1813 (unless (numeric-type-real-p n
)
1814 (return *empty-type
*))
1815 (let* ((interval (numeric-type->interval n
))
1816 (low (interval-low interval
))
1817 (high (interval-high interval
)))
1819 (setf low
(car low
)))
1821 (setf high
(car high
)))
1831 ;;; Define optimizers for FLOOR and CEILING.
1833 ((def (name q-name r-name
)
1834 (let ((q-aux (symbolicate q-name
"-AUX"))
1835 (r-aux (symbolicate r-name
"-AUX")))
1837 ;; Compute type of quotient (first) result.
1838 (defun ,q-aux
(number-type divisor-type
)
1839 (let* ((number-interval
1840 (numeric-type->interval number-type
))
1842 (numeric-type->interval divisor-type
))
1843 (quot (,q-name
(interval-div number-interval
1844 divisor-interval
))))
1845 (specifier-type `(integer ,(or (interval-low quot
) '*)
1846 ,(or (interval-high quot
) '*)))))
1847 ;; Compute type of remainder.
1848 (defun ,r-aux
(number-type divisor-type
)
1849 (let* ((divisor-interval
1850 (numeric-type->interval divisor-type
))
1851 (rem (,r-name divisor-interval
))
1852 (result-type (rem-result-type number-type divisor-type
)))
1853 (multiple-value-bind (class format
)
1856 (values 'integer nil
))
1858 (values 'rational nil
))
1859 ((or single-float double-float
#!+long-float long-float
)
1860 (values 'float result-type
))
1862 (values 'float nil
))
1865 (when (member result-type
'(float single-float double-float
1866 #!+long-float long-float
))
1867 ;; Make sure that the limits on the interval have
1869 (setf rem
(interval-func (lambda (x)
1870 (coerce-for-bound x result-type
))
1872 (make-numeric-type :class class
1874 :low
(interval-low rem
)
1875 :high
(interval-high rem
)))))
1876 ;; the optimizer itself
1877 (defoptimizer (,name derive-type
) ((number divisor
))
1878 (flet ((derive-q (n d same-arg
)
1879 (declare (ignore same-arg
))
1880 (if (and (numeric-type-real-p n
)
1881 (numeric-type-real-p d
))
1884 (derive-r (n d same-arg
)
1885 (declare (ignore same-arg
))
1886 (if (and (numeric-type-real-p n
)
1887 (numeric-type-real-p d
))
1890 (let ((quot (two-arg-derive-type
1891 number divisor
#'derive-q
#',name
))
1892 (rem (two-arg-derive-type
1893 number divisor
#'derive-r
#'mod
)))
1894 (when (and quot rem
)
1895 (make-values-type :required
(list quot rem
))))))))))
1897 (def floor floor-quotient-bound floor-rem-bound
)
1898 (def ceiling ceiling-quotient-bound ceiling-rem-bound
))
1900 ;;; Define optimizers for FFLOOR and FCEILING
1901 (macrolet ((def (name q-name r-name
)
1902 (let ((q-aux (symbolicate "F" q-name
"-AUX"))
1903 (r-aux (symbolicate r-name
"-AUX")))
1905 ;; Compute type of quotient (first) result.
1906 (defun ,q-aux
(number-type divisor-type
)
1907 (let* ((number-interval
1908 (numeric-type->interval number-type
))
1910 (numeric-type->interval divisor-type
))
1911 (quot (,q-name
(interval-div number-interval
1913 (res-type (numeric-contagion number-type
1916 :class
(numeric-type-class res-type
)
1917 :format
(numeric-type-format res-type
)
1918 :low
(interval-low quot
)
1919 :high
(interval-high quot
))))
1921 (defoptimizer (,name derive-type
) ((number divisor
))
1922 (flet ((derive-q (n d same-arg
)
1923 (declare (ignore same-arg
))
1924 (if (and (numeric-type-real-p n
)
1925 (numeric-type-real-p d
))
1928 (derive-r (n d same-arg
)
1929 (declare (ignore same-arg
))
1930 (if (and (numeric-type-real-p n
)
1931 (numeric-type-real-p d
))
1934 (let ((quot (two-arg-derive-type
1935 number divisor
#'derive-q
#',name
))
1936 (rem (two-arg-derive-type
1937 number divisor
#'derive-r
#'mod
)))
1938 (when (and quot rem
)
1939 (make-values-type :required
(list quot rem
))))))))))
1941 (def ffloor floor-quotient-bound floor-rem-bound
)
1942 (def fceiling ceiling-quotient-bound ceiling-rem-bound
))
1944 ;;; functions to compute the bounds on the quotient and remainder for
1945 ;;; the FLOOR function
1946 (defun floor-quotient-bound (quot)
1947 ;; Take the floor of the quotient and then massage it into what we
1949 (let ((lo (interval-low quot
))
1950 (hi (interval-high quot
)))
1951 ;; Take the floor of the lower bound. The result is always a
1952 ;; closed lower bound.
1954 (floor (type-bound-number lo
))
1956 ;; For the upper bound, we need to be careful.
1959 ;; An open bound. We need to be careful here because
1960 ;; the floor of '(10.0) is 9, but the floor of
1962 (multiple-value-bind (q r
) (floor (first hi
))
1967 ;; A closed bound, so the answer is obvious.
1971 (make-interval :low lo
:high hi
)))
1972 (defun floor-rem-bound (div)
1973 ;; The remainder depends only on the divisor. Try to get the
1974 ;; correct sign for the remainder if we can.
1975 (case (interval-range-info div
)
1977 ;; The divisor is always positive.
1978 (let ((rem (interval-abs div
)))
1979 (setf (interval-low rem
) 0)
1980 (when (and (numberp (interval-high rem
))
1981 (not (zerop (interval-high rem
))))
1982 ;; The remainder never contains the upper bound. However,
1983 ;; watch out for the case where the high limit is zero!
1984 (setf (interval-high rem
) (list (interval-high rem
))))
1987 ;; The divisor is always negative.
1988 (let ((rem (interval-neg (interval-abs div
))))
1989 (setf (interval-high rem
) 0)
1990 (when (numberp (interval-low rem
))
1991 ;; The remainder never contains the lower bound.
1992 (setf (interval-low rem
) (list (interval-low rem
))))
1995 ;; The divisor can be positive or negative. All bets off. The
1996 ;; magnitude of remainder is the maximum value of the divisor.
1997 (let ((limit (type-bound-number (interval-high (interval-abs div
)))))
1998 ;; The bound never reaches the limit, so make the interval open.
1999 (make-interval :low
(if limit
2002 :high
(list limit
))))))
2004 (floor-quotient-bound (make-interval :low
0.3 :high
10.3))
2005 => #S
(INTERVAL :LOW
0 :HIGH
10)
2006 (floor-quotient-bound (make-interval :low
0.3 :high
'(10.3
)))
2007 => #S
(INTERVAL :LOW
0 :HIGH
10)
2008 (floor-quotient-bound (make-interval :low
0.3 :high
10))
2009 => #S
(INTERVAL :LOW
0 :HIGH
10)
2010 (floor-quotient-bound (make-interval :low
0.3 :high
'(10)))
2011 => #S
(INTERVAL :LOW
0 :HIGH
9)
2012 (floor-quotient-bound (make-interval :low
'(0.3
) :high
10.3))
2013 => #S
(INTERVAL :LOW
0 :HIGH
10)
2014 (floor-quotient-bound (make-interval :low
'(0.0
) :high
10.3))
2015 => #S
(INTERVAL :LOW
0 :HIGH
10)
2016 (floor-quotient-bound (make-interval :low
'(-1.3
) :high
10.3))
2017 => #S
(INTERVAL :LOW -
2 :HIGH
10)
2018 (floor-quotient-bound (make-interval :low
'(-1.0
) :high
10.3))
2019 => #S
(INTERVAL :LOW -
1 :HIGH
10)
2020 (floor-quotient-bound (make-interval :low -
1.0 :high
10.3))
2021 => #S
(INTERVAL :LOW -
1 :HIGH
10)
2023 (floor-rem-bound (make-interval :low
0.3 :high
10.3))
2024 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
2025 (floor-rem-bound (make-interval :low
0.3 :high
'(10.3
)))
2026 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
2027 (floor-rem-bound (make-interval :low -
10 :high -
2.3))
2028 #S
(INTERVAL :LOW
(-10) :HIGH
0)
2029 (floor-rem-bound (make-interval :low
0.3 :high
10))
2030 => #S
(INTERVAL :LOW
0 :HIGH
'(10))
2031 (floor-rem-bound (make-interval :low
'(-1.3
) :high
10.3))
2032 => #S
(INTERVAL :LOW
'(-10.3
) :HIGH
'(10.3
))
2033 (floor-rem-bound (make-interval :low
'(-20.3
) :high
10.3))
2034 => #S
(INTERVAL :LOW
(-20.3
) :HIGH
(20.3
))
2037 ;;; same functions for CEILING
2038 (defun ceiling-quotient-bound (quot)
2039 ;; Take the ceiling of the quotient and then massage it into what we
2041 (let ((lo (interval-low quot
))
2042 (hi (interval-high quot
)))
2043 ;; Take the ceiling of the upper bound. The result is always a
2044 ;; closed upper bound.
2046 (ceiling (type-bound-number hi
))
2048 ;; For the lower bound, we need to be careful.
2051 ;; An open bound. We need to be careful here because
2052 ;; the ceiling of '(10.0) is 11, but the ceiling of
2054 (multiple-value-bind (q r
) (ceiling (first lo
))
2059 ;; A closed bound, so the answer is obvious.
2063 (make-interval :low lo
:high hi
)))
2064 (defun ceiling-rem-bound (div)
2065 ;; The remainder depends only on the divisor. Try to get the
2066 ;; correct sign for the remainder if we can.
2067 (case (interval-range-info div
)
2069 ;; Divisor is always positive. The remainder is negative.
2070 (let ((rem (interval-neg (interval-abs div
))))
2071 (setf (interval-high rem
) 0)
2072 (when (and (numberp (interval-low rem
))
2073 (not (zerop (interval-low rem
))))
2074 ;; The remainder never contains the upper bound. However,
2075 ;; watch out for the case when the upper bound is zero!
2076 (setf (interval-low rem
) (list (interval-low rem
))))
2079 ;; Divisor is always negative. The remainder is positive
2080 (let ((rem (interval-abs div
)))
2081 (setf (interval-low rem
) 0)
2082 (when (numberp (interval-high rem
))
2083 ;; The remainder never contains the lower bound.
2084 (setf (interval-high rem
) (list (interval-high rem
))))
2087 ;; The divisor can be positive or negative. All bets off. The
2088 ;; magnitude of remainder is the maximum value of the divisor.
2089 (let ((limit (type-bound-number (interval-high (interval-abs div
)))))
2090 ;; The bound never reaches the limit, so make the interval open.
2091 (make-interval :low
(if limit
2094 :high
(list limit
))))))
2097 (ceiling-quotient-bound (make-interval :low
0.3 :high
10.3))
2098 => #S
(INTERVAL :LOW
1 :HIGH
11)
2099 (ceiling-quotient-bound (make-interval :low
0.3 :high
'(10.3
)))
2100 => #S
(INTERVAL :LOW
1 :HIGH
11)
2101 (ceiling-quotient-bound (make-interval :low
0.3 :high
10))
2102 => #S
(INTERVAL :LOW
1 :HIGH
10)
2103 (ceiling-quotient-bound (make-interval :low
0.3 :high
'(10)))
2104 => #S
(INTERVAL :LOW
1 :HIGH
10)
2105 (ceiling-quotient-bound (make-interval :low
'(0.3
) :high
10.3))
2106 => #S
(INTERVAL :LOW
1 :HIGH
11)
2107 (ceiling-quotient-bound (make-interval :low
'(0.0
) :high
10.3))
2108 => #S
(INTERVAL :LOW
1 :HIGH
11)
2109 (ceiling-quotient-bound (make-interval :low
'(-1.3
) :high
10.3))
2110 => #S
(INTERVAL :LOW -
1 :HIGH
11)
2111 (ceiling-quotient-bound (make-interval :low
'(-1.0
) :high
10.3))
2112 => #S
(INTERVAL :LOW
0 :HIGH
11)
2113 (ceiling-quotient-bound (make-interval :low -
1.0 :high
10.3))
2114 => #S
(INTERVAL :LOW -
1 :HIGH
11)
2116 (ceiling-rem-bound (make-interval :low
0.3 :high
10.3))
2117 => #S
(INTERVAL :LOW
(-10.3
) :HIGH
0)
2118 (ceiling-rem-bound (make-interval :low
0.3 :high
'(10.3
)))
2119 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
2120 (ceiling-rem-bound (make-interval :low -
10 :high -
2.3))
2121 => #S
(INTERVAL :LOW
0 :HIGH
(10))
2122 (ceiling-rem-bound (make-interval :low
0.3 :high
10))
2123 => #S
(INTERVAL :LOW
(-10) :HIGH
0)
2124 (ceiling-rem-bound (make-interval :low
'(-1.3
) :high
10.3))
2125 => #S
(INTERVAL :LOW
(-10.3
) :HIGH
(10.3
))
2126 (ceiling-rem-bound (make-interval :low
'(-20.3
) :high
10.3))
2127 => #S
(INTERVAL :LOW
(-20.3
) :HIGH
(20.3
))
2130 (defun truncate-quotient-bound (quot)
2131 ;; For positive quotients, truncate is exactly like floor. For
2132 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2133 ;; it's the union of the two pieces.
2134 (case (interval-range-info quot
)
2137 (floor-quotient-bound quot
))
2139 ;; just like CEILING
2140 (ceiling-quotient-bound quot
))
2142 ;; Split the interval into positive and negative pieces, compute
2143 ;; the result for each piece and put them back together.
2144 (destructuring-bind (neg pos
) (interval-split 0 quot t t
)
2145 (interval-merge-pair (ceiling-quotient-bound neg
)
2146 (floor-quotient-bound pos
))))))
2148 (defun truncate-rem-bound (num div
)
2149 ;; This is significantly more complicated than FLOOR or CEILING. We
2150 ;; need both the number and the divisor to determine the range. The
2151 ;; basic idea is to split the ranges of NUM and DEN into positive
2152 ;; and negative pieces and deal with each of the four possibilities
2154 (case (interval-range-info num
)
2156 (case (interval-range-info div
)
2158 (floor-rem-bound div
))
2160 (ceiling-rem-bound div
))
2162 (destructuring-bind (neg pos
) (interval-split 0 div t t
)
2163 (interval-merge-pair (truncate-rem-bound num neg
)
2164 (truncate-rem-bound num pos
))))))
2166 (case (interval-range-info div
)
2168 (ceiling-rem-bound div
))
2170 (floor-rem-bound div
))
2172 (destructuring-bind (neg pos
) (interval-split 0 div t t
)
2173 (interval-merge-pair (truncate-rem-bound num neg
)
2174 (truncate-rem-bound num pos
))))))
2176 (destructuring-bind (neg pos
) (interval-split 0 num t t
)
2177 (interval-merge-pair (truncate-rem-bound neg div
)
2178 (truncate-rem-bound pos div
))))))
2181 ;;; Derive useful information about the range. Returns three values:
2182 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2183 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2184 ;;; - The abs of the maximal value if there is one, or nil if it is
2186 (defun numeric-range-info (low high
)
2187 (cond ((and low
(not (minusp low
)))
2188 (values '+ low high
))
2189 ((and high
(not (plusp high
)))
2190 (values '-
(- high
) (if low
(- low
) nil
)))
2192 (values nil
0 (and low high
(max (- low
) high
))))))
2194 (defun integer-truncate-derive-type
2195 (number-low number-high divisor-low divisor-high
)
2196 ;; The result cannot be larger in magnitude than the number, but the
2197 ;; sign might change. If we can determine the sign of either the
2198 ;; number or the divisor, we can eliminate some of the cases.
2199 (multiple-value-bind (number-sign number-min number-max
)
2200 (numeric-range-info number-low number-high
)
2201 (multiple-value-bind (divisor-sign divisor-min divisor-max
)
2202 (numeric-range-info divisor-low divisor-high
)
2203 (when (and divisor-max
(zerop divisor-max
))
2204 ;; We've got a problem: guaranteed division by zero.
2205 (return-from integer-truncate-derive-type t
))
2206 (when (zerop divisor-min
)
2207 ;; We'll assume that they aren't going to divide by zero.
2209 (cond ((and number-sign divisor-sign
)
2210 ;; We know the sign of both.
2211 (if (eq number-sign divisor-sign
)
2212 ;; Same sign, so the result will be positive.
2213 `(integer ,(if divisor-max
2214 (truncate number-min divisor-max
)
2217 (truncate number-max divisor-min
)
2219 ;; Different signs, the result will be negative.
2220 `(integer ,(if number-max
2221 (- (truncate number-max divisor-min
))
2224 (- (truncate number-min divisor-max
))
2226 ((eq divisor-sign
'+)
2227 ;; The divisor is positive. Therefore, the number will just
2228 ;; become closer to zero.
2229 `(integer ,(if number-low
2230 (truncate number-low divisor-min
)
2233 (truncate number-high divisor-min
)
2235 ((eq divisor-sign
'-
)
2236 ;; The divisor is negative. Therefore, the absolute value of
2237 ;; the number will become closer to zero, but the sign will also
2239 `(integer ,(if number-high
2240 (- (truncate number-high divisor-min
))
2243 (- (truncate number-low divisor-min
))
2245 ;; The divisor could be either positive or negative.
2247 ;; The number we are dividing has a bound. Divide that by the
2248 ;; smallest posible divisor.
2249 (let ((bound (truncate number-max divisor-min
)))
2250 `(integer ,(- bound
) ,bound
)))
2252 ;; The number we are dividing is unbounded, so we can't tell
2253 ;; anything about the result.
2256 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2257 (defun integer-rem-derive-type
2258 (number-low number-high divisor-low divisor-high
)
2259 (if (and divisor-low divisor-high
)
2260 ;; We know the range of the divisor, and the remainder must be
2261 ;; smaller than the divisor. We can tell the sign of the
2262 ;; remainer if we know the sign of the number.
2263 (let ((divisor-max (1- (max (abs divisor-low
) (abs divisor-high
)))))
2264 `(integer ,(if (or (null number-low
)
2265 (minusp number-low
))
2268 ,(if (or (null number-high
)
2269 (plusp number-high
))
2272 ;; The divisor is potentially either very positive or very
2273 ;; negative. Therefore, the remainer is unbounded, but we might
2274 ;; be able to tell something about the sign from the number.
2275 `(integer ,(if (and number-low
(not (minusp number-low
)))
2276 ;; The number we are dividing is positive.
2277 ;; Therefore, the remainder must be positive.
2280 ,(if (and number-high
(not (plusp number-high
)))
2281 ;; The number we are dividing is negative.
2282 ;; Therefore, the remainder must be negative.
2286 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2287 (defoptimizer (random derive-type
) ((bound &optional state
))
2288 (let ((type (lvar-type bound
)))
2289 (when (numeric-type-p type
)
2290 (let ((class (numeric-type-class type
))
2291 (high (numeric-type-high type
))
2292 (format (numeric-type-format type
)))
2296 :low
(coerce 0 (or format class
'real
))
2297 :high
(cond ((not high
) nil
)
2298 ((eq class
'integer
) (max (1- high
) 0))
2299 ((or (consp high
) (zerop high
)) high
)
2302 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2303 (defun random-derive-type-aux (type)
2304 (let ((class (numeric-type-class type
))
2305 (high (numeric-type-high type
))
2306 (format (numeric-type-format type
)))
2310 :low
(coerce 0 (or format class
'real
))
2311 :high
(cond ((not high
) nil
)
2312 ((eq class
'integer
) (max (1- high
) 0))
2313 ((or (consp high
) (zerop high
)) high
)
2316 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2317 (defoptimizer (random derive-type
) ((bound &optional state
))
2318 (one-arg-derive-type bound
#'random-derive-type-aux nil
))
2320 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2322 ;;; Return the maximum number of bits an integer of the supplied type
2323 ;;; can take up, or NIL if it is unbounded. The second (third) value
2324 ;;; is T if the integer can be positive (negative) and NIL if not.
2325 ;;; Zero counts as positive.
2326 (defun integer-type-length (type)
2327 (if (numeric-type-p type
)
2328 (let ((min (numeric-type-low type
))
2329 (max (numeric-type-high type
)))
2330 (values (and min max
(max (integer-length min
) (integer-length max
)))
2331 (or (null max
) (not (minusp max
)))
2332 (or (null min
) (minusp min
))))
2335 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2336 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2337 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2338 ;;; versions in CMUCL, from which these functions copy liberally.
2340 (defun logand-derive-unsigned-low-bound (x y
)
2341 (let ((a (numeric-type-low x
))
2342 (b (numeric-type-high x
))
2343 (c (numeric-type-low y
))
2344 (d (numeric-type-high y
)))
2345 (loop for m
= (ash 1 (integer-length (lognor a c
))) then
(ash m -
1)
2347 (unless (zerop (logand m
(lognot a
) (lognot c
)))
2348 (let ((temp (logandc2 (logior a m
) (1- m
))))
2352 (setf temp
(logandc2 (logior c m
) (1- m
)))
2356 finally
(return (logand a c
)))))
2358 (defun logand-derive-unsigned-high-bound (x y
)
2359 (let ((a (numeric-type-low x
))
2360 (b (numeric-type-high x
))
2361 (c (numeric-type-low y
))
2362 (d (numeric-type-high y
)))
2363 (loop for m
= (ash 1 (integer-length (logxor b d
))) then
(ash m -
1)
2366 ((not (zerop (logand b
(lognot d
) m
)))
2367 (let ((temp (logior (logandc2 b m
) (1- m
))))
2371 ((not (zerop (logand (lognot b
) d m
)))
2372 (let ((temp (logior (logandc2 d m
) (1- m
))))
2376 finally
(return (logand b d
)))))
2378 (defun logand-derive-type-aux (x y
&optional same-leaf
)
2380 (return-from logand-derive-type-aux x
))
2381 (multiple-value-bind (x-len x-pos x-neg
) (integer-type-length x
)
2382 (declare (ignore x-pos
))
2383 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2384 (declare (ignore y-pos
))
2386 ;; X must be positive.
2388 ;; They must both be positive.
2389 (cond ((and (null x-len
) (null y-len
))
2390 (specifier-type 'unsigned-byte
))
2392 (specifier-type `(unsigned-byte* ,y-len
)))
2394 (specifier-type `(unsigned-byte* ,x-len
)))
2396 (let ((low (logand-derive-unsigned-low-bound x y
))
2397 (high (logand-derive-unsigned-high-bound x y
)))
2398 (specifier-type `(integer ,low
,high
)))))
2399 ;; X is positive, but Y might be negative.
2401 (specifier-type 'unsigned-byte
))
2403 (specifier-type `(unsigned-byte* ,x-len
)))))
2404 ;; X might be negative.
2406 ;; Y must be positive.
2408 (specifier-type 'unsigned-byte
))
2409 (t (specifier-type `(unsigned-byte* ,y-len
))))
2410 ;; Either might be negative.
2411 (if (and x-len y-len
)
2412 ;; The result is bounded.
2413 (specifier-type `(signed-byte ,(1+ (max x-len y-len
))))
2414 ;; We can't tell squat about the result.
2415 (specifier-type 'integer
)))))))
2417 (defun logior-derive-unsigned-low-bound (x y
)
2418 (let ((a (numeric-type-low x
))
2419 (b (numeric-type-high x
))
2420 (c (numeric-type-low y
))
2421 (d (numeric-type-high y
)))
2422 (loop for m
= (ash 1 (integer-length (logxor a c
))) then
(ash m -
1)
2425 ((not (zerop (logandc2 (logand c m
) a
)))
2426 (let ((temp (logand (logior a m
) (1+ (lognot m
)))))
2430 ((not (zerop (logandc2 (logand a m
) c
)))
2431 (let ((temp (logand (logior c m
) (1+ (lognot m
)))))
2435 finally
(return (logior a c
)))))
2437 (defun logior-derive-unsigned-high-bound (x y
)
2438 (let ((a (numeric-type-low x
))
2439 (b (numeric-type-high x
))
2440 (c (numeric-type-low y
))
2441 (d (numeric-type-high y
)))
2442 (loop for m
= (ash 1 (integer-length (logand b d
))) then
(ash m -
1)
2444 (unless (zerop (logand b d m
))
2445 (let ((temp (logior (- b m
) (1- m
))))
2449 (setf temp
(logior (- d m
) (1- m
)))
2453 finally
(return (logior b d
)))))
2455 (defun logior-derive-type-aux (x y
&optional same-leaf
)
2457 (return-from logior-derive-type-aux x
))
2458 (multiple-value-bind (x-len x-pos x-neg
) (integer-type-length x
)
2459 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2461 ((and (not x-neg
) (not y-neg
))
2462 ;; Both are positive.
2463 (if (and x-len y-len
)
2464 (let ((low (logior-derive-unsigned-low-bound x y
))
2465 (high (logior-derive-unsigned-high-bound x y
)))
2466 (specifier-type `(integer ,low
,high
)))
2467 (specifier-type `(unsigned-byte* *))))
2469 ;; X must be negative.
2471 ;; Both are negative. The result is going to be negative
2472 ;; and be the same length or shorter than the smaller.
2473 (if (and x-len y-len
)
2475 (specifier-type `(integer ,(ash -
1 (min x-len y-len
)) -
1))
2477 (specifier-type '(integer * -
1)))
2478 ;; X is negative, but we don't know about Y. The result
2479 ;; will be negative, but no more negative than X.
2481 `(integer ,(or (numeric-type-low x
) '*)
2484 ;; X might be either positive or negative.
2486 ;; But Y is negative. The result will be negative.
2488 `(integer ,(or (numeric-type-low y
) '*)
2490 ;; We don't know squat about either. It won't get any bigger.
2491 (if (and x-len y-len
)
2493 (specifier-type `(signed-byte ,(1+ (max x-len y-len
))))
2495 (specifier-type 'integer
))))))))
2497 (defun logxor-derive-unsigned-low-bound (x y
)
2498 (let ((a (numeric-type-low x
))
2499 (b (numeric-type-high x
))
2500 (c (numeric-type-low y
))
2501 (d (numeric-type-high y
)))
2502 (loop for m
= (ash 1 (integer-length (logxor a c
))) then
(ash m -
1)
2505 ((not (zerop (logandc2 (logand c m
) a
)))
2506 (let ((temp (logand (logior a m
)
2510 ((not (zerop (logandc2 (logand a m
) c
)))
2511 (let ((temp (logand (logior c m
)
2515 finally
(return (logxor a c
)))))
2517 (defun logxor-derive-unsigned-high-bound (x y
)
2518 (let ((a (numeric-type-low x
))
2519 (b (numeric-type-high x
))
2520 (c (numeric-type-low y
))
2521 (d (numeric-type-high y
)))
2522 (loop for m
= (ash 1 (integer-length (logand b d
))) then
(ash m -
1)
2524 (unless (zerop (logand b d m
))
2525 (let ((temp (logior (- b m
) (1- m
))))
2527 ((>= temp a
) (setf b temp
))
2528 (t (let ((temp (logior (- d m
) (1- m
))))
2531 finally
(return (logxor b d
)))))
2533 (defun logxor-derive-type-aux (x y
&optional same-leaf
)
2535 (return-from logxor-derive-type-aux
(specifier-type '(eql 0))))
2536 (multiple-value-bind (x-len x-pos x-neg
) (integer-type-length x
)
2537 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2539 ((and (not x-neg
) (not y-neg
))
2540 ;; Both are positive
2541 (if (and x-len y-len
)
2542 (let ((low (logxor-derive-unsigned-low-bound x y
))
2543 (high (logxor-derive-unsigned-high-bound x y
)))
2544 (specifier-type `(integer ,low
,high
)))
2545 (specifier-type '(unsigned-byte* *))))
2546 ((and (not x-pos
) (not y-pos
))
2547 ;; Both are negative. The result will be positive, and as long
2549 (specifier-type `(unsigned-byte* ,(if (and x-len y-len
)
2552 ((or (and (not x-pos
) (not y-neg
))
2553 (and (not y-pos
) (not x-neg
)))
2554 ;; Either X is negative and Y is positive or vice-versa. The
2555 ;; result will be negative.
2556 (specifier-type `(integer ,(if (and x-len y-len
)
2557 (ash -
1 (max x-len y-len
))
2560 ;; We can't tell what the sign of the result is going to be.
2561 ;; All we know is that we don't create new bits.
2563 (specifier-type `(signed-byte ,(1+ (max x-len y-len
)))))
2565 (specifier-type 'integer
))))))
2567 (macrolet ((deffrob (logfun)
2568 (let ((fun-aux (symbolicate logfun
"-DERIVE-TYPE-AUX")))
2569 `(defoptimizer (,logfun derive-type
) ((x y
))
2570 (two-arg-derive-type x y
#',fun-aux
#',logfun
)))))
2575 (defoptimizer (logeqv derive-type
) ((x y
))
2576 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2577 (lognot-derive-type-aux
2578 (logxor-derive-type-aux x y same-leaf
)))
2580 (defoptimizer (lognand derive-type
) ((x y
))
2581 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2582 (lognot-derive-type-aux
2583 (logand-derive-type-aux x y same-leaf
)))
2585 (defoptimizer (lognor derive-type
) ((x y
))
2586 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2587 (lognot-derive-type-aux
2588 (logior-derive-type-aux x y same-leaf
)))
2590 (defoptimizer (logandc1 derive-type
) ((x y
))
2591 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2593 (specifier-type '(eql 0))
2594 (logand-derive-type-aux
2595 (lognot-derive-type-aux x
) y nil
)))
2597 (defoptimizer (logandc2 derive-type
) ((x y
))
2598 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2600 (specifier-type '(eql 0))
2601 (logand-derive-type-aux
2602 x
(lognot-derive-type-aux y
) nil
)))
2604 (defoptimizer (logorc1 derive-type
) ((x y
))
2605 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2607 (specifier-type '(eql -
1))
2608 (logior-derive-type-aux
2609 (lognot-derive-type-aux x
) y nil
)))
2611 (defoptimizer (logorc2 derive-type
) ((x y
))
2612 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2614 (specifier-type '(eql -
1))
2615 (logior-derive-type-aux
2616 x
(lognot-derive-type-aux y
) nil
)))
2619 ;;;; miscellaneous derive-type methods
2621 (defoptimizer (integer-length derive-type
) ((x))
2622 (let ((x-type (lvar-type x
)))
2623 (when (numeric-type-p x-type
)
2624 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2625 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2626 ;; careful about LO or HI being NIL, though. Also, if 0 is
2627 ;; contained in X, the lower bound is obviously 0.
2628 (flet ((null-or-min (a b
)
2629 (and a b
(min (integer-length a
)
2630 (integer-length b
))))
2632 (and a b
(max (integer-length a
)
2633 (integer-length b
)))))
2634 (let* ((min (numeric-type-low x-type
))
2635 (max (numeric-type-high x-type
))
2636 (min-len (null-or-min min max
))
2637 (max-len (null-or-max min max
)))
2638 (when (ctypep 0 x-type
)
2640 (specifier-type `(integer ,(or min-len
'*) ,(or max-len
'*))))))))
2642 (defoptimizer (isqrt derive-type
) ((x))
2643 (let ((x-type (lvar-type x
)))
2644 (when (numeric-type-p x-type
)
2645 (let* ((lo (numeric-type-low x-type
))
2646 (hi (numeric-type-high x-type
))
2647 (lo-res (if lo
(isqrt lo
) '*))
2648 (hi-res (if hi
(isqrt hi
) '*)))
2649 (specifier-type `(integer ,lo-res
,hi-res
))))))
2651 (defoptimizer (char-code derive-type
) ((char))
2652 (let ((type (type-intersection (lvar-type char
) (specifier-type 'character
))))
2653 (cond ((member-type-p type
)
2656 ,@(loop for member in
(member-type-members type
)
2657 when
(characterp member
)
2658 collect
(char-code member
)))))
2659 ((sb!kernel
::character-set-type-p type
)
2662 ,@(loop for
(low . high
)
2663 in
(character-set-type-pairs type
)
2664 collect
`(integer ,low
,high
)))))
2665 ((csubtypep type
(specifier-type 'base-char
))
2667 `(mod ,base-char-code-limit
)))
2670 `(mod ,char-code-limit
))))))
2672 (defoptimizer (code-char derive-type
) ((code))
2673 (let ((type (lvar-type code
)))
2674 ;; FIXME: unions of integral ranges? It ought to be easier to do
2675 ;; this, given that CHARACTER-SET is basically an integral range
2676 ;; type. -- CSR, 2004-10-04
2677 (when (numeric-type-p type
)
2678 (let* ((lo (numeric-type-low type
))
2679 (hi (numeric-type-high type
))
2680 (type (specifier-type `(character-set ((,lo .
,hi
))))))
2682 ;; KLUDGE: when running on the host, we lose a slight amount
2683 ;; of precision so that we don't have to "unparse" types
2684 ;; that formally we can't, such as (CHARACTER-SET ((0
2685 ;; . 0))). -- CSR, 2004-10-06
2687 ((csubtypep type
(specifier-type 'standard-char
)) type
)
2689 ((csubtypep type
(specifier-type 'base-char
))
2690 (specifier-type 'base-char
))
2692 ((csubtypep type
(specifier-type 'extended-char
))
2693 (specifier-type 'extended-char
))
2694 (t #+sb-xc-host
(specifier-type 'character
)
2695 #-sb-xc-host type
))))))
2697 (defoptimizer (values derive-type
) ((&rest values
))
2698 (make-values-type :required
(mapcar #'lvar-type values
)))
2700 (defun signum-derive-type-aux (type)
2701 (if (eq (numeric-type-complexp type
) :complex
)
2702 (let* ((format (case (numeric-type-class type
)
2703 ((integer rational
) 'single-float
)
2704 (t (numeric-type-format type
))))
2705 (bound-format (or format
'float
)))
2706 (make-numeric-type :class
'float
2709 :low
(coerce -
1 bound-format
)
2710 :high
(coerce 1 bound-format
)))
2711 (let* ((interval (numeric-type->interval type
))
2712 (range-info (interval-range-info interval
))
2713 (contains-0-p (interval-contains-p 0 interval
))
2714 (class (numeric-type-class type
))
2715 (format (numeric-type-format type
))
2716 (one (coerce 1 (or format class
'real
)))
2717 (zero (coerce 0 (or format class
'real
)))
2718 (minus-one (coerce -
1 (or format class
'real
)))
2719 (plus (make-numeric-type :class class
:format format
2720 :low one
:high one
))
2721 (minus (make-numeric-type :class class
:format format
2722 :low minus-one
:high minus-one
))
2723 ;; KLUDGE: here we have a fairly horrible hack to deal
2724 ;; with the schizophrenia in the type derivation engine.
2725 ;; The problem is that the type derivers reinterpret
2726 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2727 ;; 0d0) within the derivation mechanism doesn't include
2728 ;; -0d0. Ugh. So force it in here, instead.
2729 (zero (make-numeric-type :class class
:format format
2730 :low
(- zero
) :high zero
)))
2732 (+ (if contains-0-p
(type-union plus zero
) plus
))
2733 (- (if contains-0-p
(type-union minus zero
) minus
))
2734 (t (type-union minus zero plus
))))))
2736 (defoptimizer (signum derive-type
) ((num))
2737 (one-arg-derive-type num
#'signum-derive-type-aux nil
))
2739 ;;;; byte operations
2741 ;;;; We try to turn byte operations into simple logical operations.
2742 ;;;; First, we convert byte specifiers into separate size and position
2743 ;;;; arguments passed to internal %FOO functions. We then attempt to
2744 ;;;; transform the %FOO functions into boolean operations when the
2745 ;;;; size and position are constant and the operands are fixnums.
2747 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2748 ;; expressions that evaluate to the SIZE and POSITION of
2749 ;; the byte-specifier form SPEC. We may wrap a let around
2750 ;; the result of the body to bind some variables.
2752 ;; If the spec is a BYTE form, then bind the vars to the
2753 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2754 ;; and BYTE-POSITION. The goal of this transformation is to
2755 ;; avoid consing up byte specifiers and then immediately
2756 ;; throwing them away.
2757 (with-byte-specifier ((size-var pos-var spec
) &body body
)
2758 (once-only ((spec `(macroexpand ,spec
))
2760 `(if (and (consp ,spec
)
2761 (eq (car ,spec
) 'byte
)
2762 (= (length ,spec
) 3))
2763 (let ((,size-var
(second ,spec
))
2764 (,pos-var
(third ,spec
)))
2766 (let ((,size-var
`(byte-size ,,temp
))
2767 (,pos-var
`(byte-position ,,temp
)))
2768 `(let ((,,temp
,,spec
))
2771 (define-source-transform ldb
(spec int
)
2772 (with-byte-specifier (size pos spec
)
2773 `(%ldb
,size
,pos
,int
)))
2775 (define-source-transform dpb
(newbyte spec int
)
2776 (with-byte-specifier (size pos spec
)
2777 `(%dpb
,newbyte
,size
,pos
,int
)))
2779 (define-source-transform mask-field
(spec int
)
2780 (with-byte-specifier (size pos spec
)
2781 `(%mask-field
,size
,pos
,int
)))
2783 (define-source-transform deposit-field
(newbyte spec int
)
2784 (with-byte-specifier (size pos spec
)
2785 `(%deposit-field
,newbyte
,size
,pos
,int
))))
2787 (defoptimizer (%ldb derive-type
) ((size posn num
))
2788 (let ((size (lvar-type size
)))
2789 (if (and (numeric-type-p size
)
2790 (csubtypep size
(specifier-type 'integer
)))
2791 (let ((size-high (numeric-type-high size
)))
2792 (if (and size-high
(<= size-high sb
!vm
:n-word-bits
))
2793 (specifier-type `(unsigned-byte* ,size-high
))
2794 (specifier-type 'unsigned-byte
)))
2797 (defoptimizer (%mask-field derive-type
) ((size posn num
))
2798 (let ((size (lvar-type size
))
2799 (posn (lvar-type posn
)))
2800 (if (and (numeric-type-p size
)
2801 (csubtypep size
(specifier-type 'integer
))
2802 (numeric-type-p posn
)
2803 (csubtypep posn
(specifier-type 'integer
)))
2804 (let ((size-high (numeric-type-high size
))
2805 (posn-high (numeric-type-high posn
)))
2806 (if (and size-high posn-high
2807 (<= (+ size-high posn-high
) sb
!vm
:n-word-bits
))
2808 (specifier-type `(unsigned-byte* ,(+ size-high posn-high
)))
2809 (specifier-type 'unsigned-byte
)))
2812 (defun %deposit-field-derive-type-aux
(size posn int
)
2813 (let ((size (lvar-type size
))
2814 (posn (lvar-type posn
))
2815 (int (lvar-type int
)))
2816 (when (and (numeric-type-p size
)
2817 (numeric-type-p posn
)
2818 (numeric-type-p int
))
2819 (let ((size-high (numeric-type-high size
))
2820 (posn-high (numeric-type-high posn
))
2821 (high (numeric-type-high int
))
2822 (low (numeric-type-low int
)))
2823 (when (and size-high posn-high high low
2824 ;; KLUDGE: we need this cutoff here, otherwise we
2825 ;; will merrily derive the type of %DPB as
2826 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2827 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2828 ;; 1073741822))), with hilarious consequences. We
2829 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2830 ;; over a reasonable amount of shifting, even on
2831 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2832 ;; machine integers are 64-bits. -- CSR,
2834 (<= (+ size-high posn-high
) (* 4 sb
!vm
:n-word-bits
)))
2835 (let ((raw-bit-count (max (integer-length high
)
2836 (integer-length low
)
2837 (+ size-high posn-high
))))
2840 `(signed-byte ,(1+ raw-bit-count
))
2841 `(unsigned-byte* ,raw-bit-count
)))))))))
2843 (defoptimizer (%dpb derive-type
) ((newbyte size posn int
))
2844 (%deposit-field-derive-type-aux size posn int
))
2846 (defoptimizer (%deposit-field derive-type
) ((newbyte size posn int
))
2847 (%deposit-field-derive-type-aux size posn int
))
2849 (deftransform %ldb
((size posn int
)
2850 (fixnum fixnum integer
)
2851 (unsigned-byte #.sb
!vm
:n-word-bits
))
2852 "convert to inline logical operations"
2853 `(logand (ash int
(- posn
))
2854 (ash ,(1- (ash 1 sb
!vm
:n-word-bits
))
2855 (- size
,sb
!vm
:n-word-bits
))))
2857 (deftransform %mask-field
((size posn int
)
2858 (fixnum fixnum integer
)
2859 (unsigned-byte #.sb
!vm
:n-word-bits
))
2860 "convert to inline logical operations"
2862 (ash (ash ,(1- (ash 1 sb
!vm
:n-word-bits
))
2863 (- size
,sb
!vm
:n-word-bits
))
2866 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2867 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2868 ;;; as the result type, as that would allow result types that cover
2869 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2870 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2872 (deftransform %dpb
((new size posn int
)
2874 (unsigned-byte #.sb
!vm
:n-word-bits
))
2875 "convert to inline logical operations"
2876 `(let ((mask (ldb (byte size
0) -
1)))
2877 (logior (ash (logand new mask
) posn
)
2878 (logand int
(lognot (ash mask posn
))))))
2880 (deftransform %dpb
((new size posn int
)
2882 (signed-byte #.sb
!vm
:n-word-bits
))
2883 "convert to inline logical operations"
2884 `(let ((mask (ldb (byte size
0) -
1)))
2885 (logior (ash (logand new mask
) posn
)
2886 (logand int
(lognot (ash mask posn
))))))
2888 (deftransform %deposit-field
((new size posn int
)
2890 (unsigned-byte #.sb
!vm
:n-word-bits
))
2891 "convert to inline logical operations"
2892 `(let ((mask (ash (ldb (byte size
0) -
1) posn
)))
2893 (logior (logand new mask
)
2894 (logand int
(lognot mask
)))))
2896 (deftransform %deposit-field
((new size posn int
)
2898 (signed-byte #.sb
!vm
:n-word-bits
))
2899 "convert to inline logical operations"
2900 `(let ((mask (ash (ldb (byte size
0) -
1) posn
)))
2901 (logior (logand new mask
)
2902 (logand int
(lognot mask
)))))
2904 (defoptimizer (mask-signed-field derive-type
) ((size x
))
2905 (let ((size (lvar-type size
)))
2906 (if (numeric-type-p size
)
2907 (let ((size-high (numeric-type-high size
)))
2908 (if (and size-high
(<= 1 size-high sb
!vm
:n-word-bits
))
2909 (specifier-type `(signed-byte ,size-high
))
2914 ;;; Modular functions
2916 ;;; (ldb (byte s 0) (foo x y ...)) =
2917 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2919 ;;; and similar for other arguments.
2921 (defun make-modular-fun-type-deriver (prototype kind width signedp
)
2922 (declare (ignore kind
))
2924 (binding* ((info (info :function
:info prototype
) :exit-if-null
)
2925 (fun (fun-info-derive-type info
) :exit-if-null
)
2926 (mask-type (specifier-type
2928 ((nil) (let ((mask (1- (ash 1 width
))))
2929 `(integer ,mask
,mask
)))
2930 ((t) `(signed-byte ,width
))))))
2932 (let ((res (funcall fun call
)))
2934 (if (eq signedp nil
)
2935 (logand-derive-type-aux res mask-type
))))))
2938 (binding* ((info (info :function
:info prototype
) :exit-if-null
)
2939 (fun (fun-info-derive-type info
) :exit-if-null
)
2940 (res (funcall fun call
) :exit-if-null
)
2941 (mask-type (specifier-type
2943 ((nil) (let ((mask (1- (ash 1 width
))))
2944 `(integer ,mask
,mask
)))
2945 ((t) `(signed-byte ,width
))))))
2946 (if (eq signedp nil
)
2947 (logand-derive-type-aux res mask-type
)))))
2949 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2951 ;;; For good functions, we just recursively cut arguments; their
2952 ;;; "goodness" means that the result will not increase (in the
2953 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2954 ;;; replaced with the version, cutting its result to WIDTH or more
2955 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2956 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2957 ;;; arguments (maybe to a different width) and returning the name of a
2958 ;;; modular version, if it exists, or NIL. If we have changed
2959 ;;; anything, we need to flush old derived types, because they have
2960 ;;; nothing in common with the new code.
2961 (defun cut-to-width (lvar kind width signedp
)
2962 (declare (type lvar lvar
) (type (integer 0) width
))
2963 (let ((type (specifier-type (if (zerop width
)
2966 ((nil) 'unsigned-byte
)
2969 (labels ((reoptimize-node (node name
)
2970 (setf (node-derived-type node
)
2972 (info :function
:type name
)))
2973 (setf (lvar-%derived-type
(node-lvar node
)) nil
)
2974 (setf (node-reoptimize node
) t
)
2975 (setf (block-reoptimize (node-block node
)) t
)
2976 (reoptimize-component (node-component node
) :maybe
))
2977 (cut-node (node &aux did-something
)
2978 (when (and (not (block-delete-p (node-block node
)))
2979 (combination-p node
)
2980 (eq (basic-combination-kind node
) :known
))
2981 (let* ((fun-ref (lvar-use (combination-fun node
)))
2982 (fun-name (leaf-source-name (ref-leaf fun-ref
)))
2983 (modular-fun (find-modular-version fun-name kind signedp width
)))
2984 (when (and modular-fun
2985 (not (and (eq fun-name
'logand
)
2987 (single-value-type (node-derived-type node
))
2989 (binding* ((name (etypecase modular-fun
2990 ((eql :good
) fun-name
)
2992 (modular-fun-info-name modular-fun
))
2994 (funcall modular-fun node width
)))
2996 (unless (eql modular-fun
:good
)
2997 (setq did-something t
)
3000 (find-free-fun name
"in a strange place"))
3001 (setf (combination-kind node
) :full
))
3002 (unless (functionp modular-fun
)
3003 (dolist (arg (basic-combination-args node
))
3004 (when (cut-lvar arg
)
3005 (setq did-something t
))))
3007 (reoptimize-node node name
))
3009 (cut-lvar (lvar &aux did-something
)
3010 (do-uses (node lvar
)
3011 (when (cut-node node
)
3012 (setq did-something t
)))
3016 (defun best-modular-version (width signedp
)
3017 ;; 1. exact width-matched :untagged
3018 ;; 2. >/>= width-matched :tagged
3019 ;; 3. >/>= width-matched :untagged
3020 (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class
*))
3021 (uswidths (modular-class-widths *untagged-signed-modular-class
*))
3022 (uwidths (merge 'list uuwidths uswidths
#'< :key
#'car
))
3023 (twidths (modular-class-widths *tagged-modular-class
*)))
3024 (let ((exact (find (cons width signedp
) uwidths
:test
#'equal
)))
3026 (return-from best-modular-version
(values width
:untagged signedp
))))
3027 (flet ((inexact-match (w)
3029 ((eq signedp
(cdr w
)) (<= width
(car w
)))
3030 ((eq signedp nil
) (< width
(car w
))))))
3031 (let ((tgt (find-if #'inexact-match twidths
)))
3033 (return-from best-modular-version
3034 (values (car tgt
) :tagged
(cdr tgt
)))))
3035 (let ((ugt (find-if #'inexact-match uwidths
)))
3037 (return-from best-modular-version
3038 (values (car ugt
) :untagged
(cdr ugt
))))))))
3040 (defoptimizer (logand optimizer
) ((x y
) node
)
3041 (let ((result-type (single-value-type (node-derived-type node
))))
3042 (when (numeric-type-p result-type
)
3043 (let ((low (numeric-type-low result-type
))
3044 (high (numeric-type-high result-type
)))
3045 (when (and (numberp low
)
3048 (let ((width (integer-length high
)))
3049 (multiple-value-bind (w kind signedp
)
3050 (best-modular-version width nil
)
3052 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP).
3053 (cut-to-width x kind width signedp
)
3054 (cut-to-width y kind width signedp
)
3055 nil
; After fixing above, replace with T.
3058 (defoptimizer (mask-signed-field optimizer
) ((width x
) node
)
3059 (let ((result-type (single-value-type (node-derived-type node
))))
3060 (when (numeric-type-p result-type
)
3061 (let ((low (numeric-type-low result-type
))
3062 (high (numeric-type-high result-type
)))
3063 (when (and (numberp low
) (numberp high
))
3064 (let ((width (max (integer-length high
) (integer-length low
))))
3065 (multiple-value-bind (w kind
)
3066 (best-modular-version width t
)
3068 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH T).
3069 (cut-to-width x kind width t
)
3070 nil
; After fixing above, replace with T.
3073 ;;; miscellanous numeric transforms
3075 ;;; If a constant appears as the first arg, swap the args.
3076 (deftransform commutative-arg-swap
((x y
) * * :defun-only t
:node node
)
3077 (if (and (constant-lvar-p x
)
3078 (not (constant-lvar-p y
)))
3079 `(,(lvar-fun-name (basic-combination-fun node
))
3082 (give-up-ir1-transform)))
3084 (dolist (x '(= char
= + * logior logand logxor
))
3085 (%deftransform x
'(function * *) #'commutative-arg-swap
3086 "place constant arg last"))
3088 ;;; Handle the case of a constant BOOLE-CODE.
3089 (deftransform boole
((op x y
) * *)
3090 "convert to inline logical operations"
3091 (unless (constant-lvar-p op
)
3092 (give-up-ir1-transform "BOOLE code is not a constant."))
3093 (let ((control (lvar-value op
)))
3095 (#.sb
!xc
:boole-clr
0)
3096 (#.sb
!xc
:boole-set -
1)
3097 (#.sb
!xc
:boole-1
'x
)
3098 (#.sb
!xc
:boole-2
'y
)
3099 (#.sb
!xc
:boole-c1
'(lognot x
))
3100 (#.sb
!xc
:boole-c2
'(lognot y
))
3101 (#.sb
!xc
:boole-and
'(logand x y
))
3102 (#.sb
!xc
:boole-ior
'(logior x y
))
3103 (#.sb
!xc
:boole-xor
'(logxor x y
))
3104 (#.sb
!xc
:boole-eqv
'(logeqv x y
))
3105 (#.sb
!xc
:boole-nand
'(lognand x y
))
3106 (#.sb
!xc
:boole-nor
'(lognor x y
))
3107 (#.sb
!xc
:boole-andc1
'(logandc1 x y
))
3108 (#.sb
!xc
:boole-andc2
'(logandc2 x y
))
3109 (#.sb
!xc
:boole-orc1
'(logorc1 x y
))
3110 (#.sb
!xc
:boole-orc2
'(logorc2 x y
))
3112 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
3115 ;;;; converting special case multiply/divide to shifts
3117 ;;; If arg is a constant power of two, turn * into a shift.
3118 (deftransform * ((x y
) (integer integer
) *)
3119 "convert x*2^k to shift"
3120 (unless (constant-lvar-p y
)
3121 (give-up-ir1-transform))
3122 (let* ((y (lvar-value y
))
3124 (len (1- (integer-length y-abs
))))
3125 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3126 (give-up-ir1-transform))
3131 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3132 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3134 (flet ((frob (y ceil-p
)
3135 (unless (constant-lvar-p y
)
3136 (give-up-ir1-transform))
3137 (let* ((y (lvar-value y
))
3139 (len (1- (integer-length y-abs
))))
3140 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3141 (give-up-ir1-transform))
3142 (let ((shift (- len
))
3144 (delta (if ceil-p
(* (signum y
) (1- y-abs
)) 0)))
3145 `(let ((x (+ x
,delta
)))
3147 `(values (ash (- x
) ,shift
)
3148 (- (- (logand (- x
) ,mask
)) ,delta
))
3149 `(values (ash x
,shift
)
3150 (- (logand x
,mask
) ,delta
))))))))
3151 (deftransform floor
((x y
) (integer integer
) *)
3152 "convert division by 2^k to shift"
3154 (deftransform ceiling
((x y
) (integer integer
) *)
3155 "convert division by 2^k to shift"
3158 ;;; Do the same for MOD.
3159 (deftransform mod
((x y
) (integer integer
) *)
3160 "convert remainder mod 2^k to LOGAND"
3161 (unless (constant-lvar-p y
)
3162 (give-up-ir1-transform))
3163 (let* ((y (lvar-value y
))
3165 (len (1- (integer-length y-abs
))))
3166 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3167 (give-up-ir1-transform))
3168 (let ((mask (1- y-abs
)))
3170 `(- (logand (- x
) ,mask
))
3171 `(logand x
,mask
)))))
3173 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3174 (deftransform truncate
((x y
) (integer integer
))
3175 "convert division by 2^k to shift"
3176 (unless (constant-lvar-p y
)
3177 (give-up-ir1-transform))
3178 (let* ((y (lvar-value y
))
3180 (len (1- (integer-length y-abs
))))
3181 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3182 (give-up-ir1-transform))
3183 (let* ((shift (- len
))
3186 (values ,(if (minusp y
)
3188 `(- (ash (- x
) ,shift
)))
3189 (- (logand (- x
) ,mask
)))
3190 (values ,(if (minusp y
)
3191 `(ash (- ,mask x
) ,shift
)
3193 (logand x
,mask
))))))
3195 ;;; And the same for REM.
3196 (deftransform rem
((x y
) (integer integer
) *)
3197 "convert remainder mod 2^k to LOGAND"
3198 (unless (constant-lvar-p y
)
3199 (give-up-ir1-transform))
3200 (let* ((y (lvar-value y
))
3202 (len (1- (integer-length y-abs
))))
3203 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3204 (give-up-ir1-transform))
3205 (let ((mask (1- y-abs
)))
3207 (- (logand (- x
) ,mask
))
3208 (logand x
,mask
)))))
3210 ;;;; arithmetic and logical identity operation elimination
3212 ;;; Flush calls to various arith functions that convert to the
3213 ;;; identity function or a constant.
3214 (macrolet ((def (name identity result
)
3215 `(deftransform ,name
((x y
) (* (constant-arg (member ,identity
))) *)
3216 "fold identity operations"
3223 (def logxor -
1 (lognot x
))
3226 (deftransform logand
((x y
) (* (constant-arg t
)) *)
3227 "fold identity operation"
3228 (let ((y (lvar-value y
)))
3229 (unless (and (plusp y
)
3230 (= y
(1- (ash 1 (integer-length y
)))))
3231 (give-up-ir1-transform))
3232 (unless (csubtypep (lvar-type x
)
3233 (specifier-type `(integer 0 ,y
)))
3234 (give-up-ir1-transform))
3237 (deftransform mask-signed-field
((size x
) ((constant-arg t
) *) *)
3238 "fold identity operation"
3239 (let ((size (lvar-value size
)))
3240 (unless (csubtypep (lvar-type x
) (specifier-type `(signed-byte ,size
)))
3241 (give-up-ir1-transform))
3244 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3245 ;;; (* 0 -4.0) is -0.0.
3246 (deftransform -
((x y
) ((constant-arg (member 0)) rational
) *)
3247 "convert (- 0 x) to negate"
3249 (deftransform * ((x y
) (rational (constant-arg (member 0))) *)
3250 "convert (* x 0) to 0"
3253 ;;; Return T if in an arithmetic op including lvars X and Y, the
3254 ;;; result type is not affected by the type of X. That is, Y is at
3255 ;;; least as contagious as X.
3257 (defun not-more-contagious (x y
)
3258 (declare (type continuation x y
))
3259 (let ((x (lvar-type x
))
3261 (values (type= (numeric-contagion x y
)
3262 (numeric-contagion y y
)))))
3263 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3264 ;;; XXX needs more work as valid transforms are missed; some cases are
3265 ;;; specific to particular transform functions so the use of this
3266 ;;; function may need a re-think.
3267 (defun not-more-contagious (x y
)
3268 (declare (type lvar x y
))
3269 (flet ((simple-numeric-type (num)
3270 (and (numeric-type-p num
)
3271 ;; Return non-NIL if NUM is integer, rational, or a float
3272 ;; of some type (but not FLOAT)
3273 (case (numeric-type-class num
)
3277 (numeric-type-format num
))
3280 (let ((x (lvar-type x
))
3282 (if (and (simple-numeric-type x
)
3283 (simple-numeric-type y
))
3284 (values (type= (numeric-contagion x y
)
3285 (numeric-contagion y y
)))))))
3287 (def!type exact-number
()
3288 '(or rational
(complex rational
)))
3292 ;;; Only safely applicable for exact numbers. For floating-point
3293 ;;; x, one would have to first show that neither x or y are signed
3294 ;;; 0s, and that x isn't an SNaN.
3295 (deftransform + ((x y
) (exact-number (constant-arg (eql 0))) *)
3300 (deftransform -
((x y
) (exact-number (constant-arg (eql 0))) *)
3304 ;;; Fold (OP x +/-1)
3306 ;;; %NEGATE might not always signal correctly.
3308 ((def (name result minus-result
)
3309 `(deftransform ,name
((x y
)
3310 (exact-number (constant-arg (member 1 -
1))))
3311 "fold identity operations"
3312 (if (minusp (lvar-value y
)) ',minus-result
',result
))))
3313 (def * x
(%negate x
))
3314 (def / x
(%negate x
))
3315 (def expt x
(/ 1 x
)))
3317 ;;; Fold (expt x n) into multiplications for small integral values of
3318 ;;; N; convert (expt x 1/2) to sqrt.
3319 (deftransform expt
((x y
) (t (constant-arg real
)) *)
3320 "recode as multiplication or sqrt"
3321 (let ((val (lvar-value y
)))
3322 ;; If Y would cause the result to be promoted to the same type as
3323 ;; Y, we give up. If not, then the result will be the same type
3324 ;; as X, so we can replace the exponentiation with simple
3325 ;; multiplication and division for small integral powers.
3326 (unless (not-more-contagious y x
)
3327 (give-up-ir1-transform))
3329 (let ((x-type (lvar-type x
)))
3330 (cond ((csubtypep x-type
(specifier-type '(or rational
3331 (complex rational
))))
3333 ((csubtypep x-type
(specifier-type 'real
))
3337 ((csubtypep x-type
(specifier-type 'complex
))
3338 ;; both parts are float
3340 (t (give-up-ir1-transform)))))
3341 ((= val
2) '(* x x
))
3342 ((= val -
2) '(/ (* x x
)))
3343 ((= val
3) '(* x x x
))
3344 ((= val -
3) '(/ (* x x x
)))
3345 ((= val
1/2) '(sqrt x
))
3346 ((= val -
1/2) '(/ (sqrt x
)))
3347 (t (give-up-ir1-transform)))))
3349 (deftransform expt
((x y
) ((constant-arg (member -
1 -
1.0 -
1.0d0
)) integer
) *)
3350 "recode as an ODDP check"
3351 (let ((val (lvar-value x
)))
3353 '(- 1 (* 2 (logand 1 y
)))
3358 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3359 ;;; transformations?
3360 ;;; Perhaps we should have to prove that the denominator is nonzero before
3361 ;;; doing them? -- WHN 19990917
3362 (macrolet ((def (name)
3363 `(deftransform ,name
((x y
) ((constant-arg (integer 0 0)) integer
)
3370 (macrolet ((def (name)
3371 `(deftransform ,name
((x y
) ((constant-arg (integer 0 0)) integer
)
3380 ;;;; character operations
3382 (deftransform char-equal
((a b
) (base-char base-char
))
3384 '(let* ((ac (char-code a
))
3386 (sum (logxor ac bc
)))
3388 (when (eql sum
#x20
)
3389 (let ((sum (+ ac bc
)))
3390 (or (and (> sum
161) (< sum
213))
3391 (and (> sum
415) (< sum
461))
3392 (and (> sum
463) (< sum
477))))))))
3394 (deftransform char-upcase
((x) (base-char))
3396 '(let ((n-code (char-code x
)))
3397 (if (or (and (> n-code
#o140
) ; Octal 141 is #\a.
3398 (< n-code
#o173
)) ; Octal 172 is #\z.
3399 (and (> n-code
#o337
)
3401 (and (> n-code
#o367
)
3403 (code-char (logxor #x20 n-code
))
3406 (deftransform char-downcase
((x) (base-char))
3408 '(let ((n-code (char-code x
)))
3409 (if (or (and (> n-code
64) ; 65 is #\A.
3410 (< n-code
91)) ; 90 is #\Z.
3415 (code-char (logxor #x20 n-code
))
3418 ;;;; equality predicate transforms
3420 ;;; Return true if X and Y are lvars whose only use is a
3421 ;;; reference to the same leaf, and the value of the leaf cannot
3423 (defun same-leaf-ref-p (x y
)
3424 (declare (type lvar x y
))
3425 (let ((x-use (principal-lvar-use x
))
3426 (y-use (principal-lvar-use y
)))
3429 (eq (ref-leaf x-use
) (ref-leaf y-use
))
3430 (constant-reference-p x-use
))))
3432 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3433 ;;; if there is no intersection between the types of the arguments,
3434 ;;; then the result is definitely false.
3435 (deftransform simple-equality-transform
((x y
) * *
3438 ((same-leaf-ref-p x y
) t
)
3439 ((not (types-equal-or-intersect (lvar-type x
) (lvar-type y
)))
3441 (t (give-up-ir1-transform))))
3444 `(%deftransform
',x
'(function * *) #'simple-equality-transform
)))
3448 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3449 ;;; try to convert to a type-specific predicate or EQ:
3450 ;;; -- If both args are characters, convert to CHAR=. This is better than
3451 ;;; just converting to EQ, since CHAR= may have special compilation
3452 ;;; strategies for non-standard representations, etc.
3453 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3454 ;;; constant and if so, put X second. Doing this results in better
3455 ;;; code from the backend, since the backend assumes that any constant
3456 ;;; argument comes second.
3457 ;;; -- If either arg is definitely not a number or a fixnum, then we
3458 ;;; can compare with EQ.
3459 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3460 ;;; is constant then we put it second. If X is a subtype of Y, we put
3461 ;;; it second. These rules make it easier for the back end to match
3462 ;;; these interesting cases.
3463 (deftransform eql
((x y
) * * :node node
)
3464 "convert to simpler equality predicate"
3465 (let ((x-type (lvar-type x
))
3466 (y-type (lvar-type y
))
3467 (char-type (specifier-type 'character
)))
3468 (flet ((fixnum-type-p (type)
3469 (csubtypep type
(specifier-type 'fixnum
))))
3471 ((same-leaf-ref-p x y
) t
)
3472 ((not (types-equal-or-intersect x-type y-type
))
3474 ((and (csubtypep x-type char-type
)
3475 (csubtypep y-type char-type
))
3477 ((or (fixnum-type-p x-type
) (fixnum-type-p y-type
))
3478 (commutative-arg-swap node
))
3479 ((or (eq-comparable-type-p x-type
) (eq-comparable-type-p y-type
))
3481 ((and (not (constant-lvar-p y
))
3482 (or (constant-lvar-p x
)
3483 (and (csubtypep x-type y-type
)
3484 (not (csubtypep y-type x-type
)))))
3487 (give-up-ir1-transform))))))
3489 ;;; similarly to the EQL transform above, we attempt to constant-fold
3490 ;;; or convert to a simpler predicate: mostly we have to be careful
3491 ;;; with strings and bit-vectors.
3492 (deftransform equal
((x y
) * *)
3493 "convert to simpler equality predicate"
3494 (let ((x-type (lvar-type x
))
3495 (y-type (lvar-type y
))
3496 (string-type (specifier-type 'string
))
3497 (bit-vector-type (specifier-type 'bit-vector
)))
3499 ((same-leaf-ref-p x y
) t
)
3500 ((and (csubtypep x-type string-type
)
3501 (csubtypep y-type string-type
))
3503 ((and (csubtypep x-type bit-vector-type
)
3504 (csubtypep y-type bit-vector-type
))
3505 '(bit-vector-= x y
))
3506 ;; if at least one is not a string, and at least one is not a
3507 ;; bit-vector, then we can reason from types.
3508 ((and (not (and (types-equal-or-intersect x-type string-type
)
3509 (types-equal-or-intersect y-type string-type
)))
3510 (not (and (types-equal-or-intersect x-type bit-vector-type
)
3511 (types-equal-or-intersect y-type bit-vector-type
)))
3512 (not (types-equal-or-intersect x-type y-type
)))
3514 (t (give-up-ir1-transform)))))
3516 ;;; Convert to EQL if both args are rational and complexp is specified
3517 ;;; and the same for both.
3518 (deftransform = ((x y
) (number number
) *)
3520 (let ((x-type (lvar-type x
))
3521 (y-type (lvar-type y
)))
3522 (cond ((or (and (csubtypep x-type
(specifier-type 'float
))
3523 (csubtypep y-type
(specifier-type 'float
)))
3524 (and (csubtypep x-type
(specifier-type '(complex float
)))
3525 (csubtypep y-type
(specifier-type '(complex float
))))
3526 #!+complex-float-vops
3527 (and (csubtypep x-type
(specifier-type '(or single-float
(complex single-float
))))
3528 (csubtypep y-type
(specifier-type '(or single-float
(complex single-float
)))))
3529 #!+complex-float-vops
3530 (and (csubtypep x-type
(specifier-type '(or double-float
(complex double-float
))))
3531 (csubtypep y-type
(specifier-type '(or double-float
(complex double-float
))))))
3532 ;; They are both floats. Leave as = so that -0.0 is
3533 ;; handled correctly.
3534 (give-up-ir1-transform))
3535 ((or (and (csubtypep x-type
(specifier-type 'rational
))
3536 (csubtypep y-type
(specifier-type 'rational
)))
3537 (and (csubtypep x-type
3538 (specifier-type '(complex rational
)))
3540 (specifier-type '(complex rational
)))))
3541 ;; They are both rationals and complexp is the same.
3545 (give-up-ir1-transform
3546 "The operands might not be the same type.")))))
3548 (defun maybe-float-lvar-p (lvar)
3549 (neq *empty-type
* (type-intersection (specifier-type 'float
)
3552 (flet ((maybe-invert (node op inverted x y
)
3553 ;; Don't invert if either argument can be a float (NaNs)
3555 ((or (maybe-float-lvar-p x
) (maybe-float-lvar-p y
))
3556 (delay-ir1-transform node
:constraint
)
3557 `(or (,op x y
) (= x y
)))
3559 `(if (,inverted x y
) nil t
)))))
3560 (deftransform >= ((x y
) (number number
) * :node node
)
3561 "invert or open code"
3562 (maybe-invert node
'> '< x y
))
3563 (deftransform <= ((x y
) (number number
) * :node node
)
3564 "invert or open code"
3565 (maybe-invert node
'< '> x y
)))
3567 ;;; See whether we can statically determine (< X Y) using type
3568 ;;; information. If X's high bound is < Y's low, then X < Y.
3569 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3570 ;;; NIL). If not, at least make sure any constant arg is second.
3571 (macrolet ((def (name inverse reflexive-p surely-true surely-false
)
3572 `(deftransform ,name
((x y
))
3573 "optimize using intervals"
3574 (if (and (same-leaf-ref-p x y
)
3575 ;; For non-reflexive functions we don't need
3576 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3577 ;; but with reflexive ones we don't know...
3579 '((and (not (maybe-float-lvar-p x
))
3580 (not (maybe-float-lvar-p y
))))))
3582 (let ((ix (or (type-approximate-interval (lvar-type x
))
3583 (give-up-ir1-transform)))
3584 (iy (or (type-approximate-interval (lvar-type y
))
3585 (give-up-ir1-transform))))
3590 ((and (constant-lvar-p x
)
3591 (not (constant-lvar-p y
)))
3594 (give-up-ir1-transform))))))))
3595 (def = = t
(interval-= ix iy
) (interval-/= ix iy
))
3596 (def /= /= nil
(interval-/= ix iy
) (interval-= ix iy
))
3597 (def < > nil
(interval-< ix iy
) (interval->= ix iy
))
3598 (def > < nil
(interval-< iy ix
) (interval->= iy ix
))
3599 (def <= >= t
(interval->= iy ix
) (interval-< iy ix
))
3600 (def >= <= t
(interval->= ix iy
) (interval-< ix iy
)))
3602 (defun ir1-transform-char< (x y first second inverse
)
3604 ((same-leaf-ref-p x y
) nil
)
3605 ;; If we had interval representation of character types, as we
3606 ;; might eventually have to to support 2^21 characters, then here
3607 ;; we could do some compile-time computation as in transforms for
3608 ;; < above. -- CSR, 2003-07-01
3609 ((and (constant-lvar-p first
)
3610 (not (constant-lvar-p second
)))
3612 (t (give-up-ir1-transform))))
3614 (deftransform char
< ((x y
) (character character
) *)
3615 (ir1-transform-char< x y x y
'char
>))
3617 (deftransform char
> ((x y
) (character character
) *)
3618 (ir1-transform-char< y x x y
'char
<))
3620 ;;;; converting N-arg comparisons
3622 ;;;; We convert calls to N-arg comparison functions such as < into
3623 ;;;; two-arg calls. This transformation is enabled for all such
3624 ;;;; comparisons in this file. If any of these predicates are not
3625 ;;;; open-coded, then the transformation should be removed at some
3626 ;;;; point to avoid pessimization.
3628 ;;; This function is used for source transformation of N-arg
3629 ;;; comparison functions other than inequality. We deal both with
3630 ;;; converting to two-arg calls and inverting the sense of the test,
3631 ;;; if necessary. If the call has two args, then we pass or return a
3632 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3633 ;;; then we transform to code that returns true. Otherwise, we bind
3634 ;;; all the arguments and expand into a bunch of IFs.
3635 (defun multi-compare (predicate args not-p type
&optional force-two-arg-p
)
3636 (let ((nargs (length args
)))
3637 (cond ((< nargs
1) (values nil t
))
3638 ((= nargs
1) `(progn (the ,type
,@args
) t
))
3641 `(if (,predicate
,(first args
) ,(second args
)) nil t
)
3643 `(,predicate
,(first args
) ,(second args
))
3646 (do* ((i (1- nargs
) (1- i
))
3648 (current (gensym) (gensym))
3649 (vars (list current
) (cons current vars
))
3651 `(if (,predicate
,current
,last
)
3653 `(if (,predicate
,current
,last
)
3656 `((lambda ,vars
(declare (type ,type
,@vars
)) ,result
)
3659 (define-source-transform = (&rest args
) (multi-compare '= args nil
'number
))
3660 (define-source-transform < (&rest args
) (multi-compare '< args nil
'real
))
3661 (define-source-transform > (&rest args
) (multi-compare '> args nil
'real
))
3662 ;;; We cannot do the inversion for >= and <= here, since both
3663 ;;; (< NaN X) and (> NaN X)
3664 ;;; are false, and we don't have type-inforation available yet. The
3665 ;;; deftransforms for two-argument versions of >= and <= takes care of
3666 ;;; the inversion to > and < when possible.
3667 (define-source-transform <= (&rest args
) (multi-compare '<= args nil
'real
))
3668 (define-source-transform >= (&rest args
) (multi-compare '>= args nil
'real
))
3670 (define-source-transform char
= (&rest args
) (multi-compare 'char
= args nil
3672 (define-source-transform char
< (&rest args
) (multi-compare 'char
< args nil
3674 (define-source-transform char
> (&rest args
) (multi-compare 'char
> args nil
3676 (define-source-transform char
<= (&rest args
) (multi-compare 'char
> args t
3678 (define-source-transform char
>= (&rest args
) (multi-compare 'char
< args t
3681 (define-source-transform char-equal
(&rest args
)
3682 (multi-compare 'sb
!impl
::two-arg-char-equal args nil
'character t
))
3683 (define-source-transform char-lessp
(&rest args
)
3684 (multi-compare 'sb
!impl
::two-arg-char-lessp args nil
'character t
))
3685 (define-source-transform char-greaterp
(&rest args
)
3686 (multi-compare 'sb
!impl
::two-arg-char-greaterp args nil
'character t
))
3687 (define-source-transform char-not-greaterp
(&rest args
)
3688 (multi-compare 'sb
!impl
::two-arg-char-greaterp args t
'character t
))
3689 (define-source-transform char-not-lessp
(&rest args
)
3690 (multi-compare 'sb
!impl
::two-arg-char-lessp args t
'character t
))
3692 ;;; This function does source transformation of N-arg inequality
3693 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3694 ;;; arg cases. If there are more than two args, then we expand into
3695 ;;; the appropriate n^2 comparisons only when speed is important.
3696 (declaim (ftype (function (symbol list t
) *) multi-not-equal
))
3697 (defun multi-not-equal (predicate args type
)
3698 (let ((nargs (length args
)))
3699 (cond ((< nargs
1) (values nil t
))
3700 ((= nargs
1) `(progn (the ,type
,@args
) t
))
3702 `(if (,predicate
,(first args
) ,(second args
)) nil t
))
3703 ((not (policy *lexenv
*
3704 (and (>= speed space
)
3705 (>= speed compilation-speed
))))
3708 (let ((vars (make-gensym-list nargs
)))
3709 (do ((var vars next
)
3710 (next (cdr vars
) (cdr next
))
3713 `((lambda ,vars
(declare (type ,type
,@vars
)) ,result
)
3715 (let ((v1 (first var
)))
3717 (setq result
`(if (,predicate
,v1
,v2
) nil
,result
))))))))))
3719 (define-source-transform /= (&rest args
)
3720 (multi-not-equal '= args
'number
))
3721 (define-source-transform char
/= (&rest args
)
3722 (multi-not-equal 'char
= args
'character
))
3723 (define-source-transform char-not-equal
(&rest args
)
3724 (multi-not-equal 'char-equal args
'character
))
3726 ;;; Expand MAX and MIN into the obvious comparisons.
3727 (define-source-transform max
(arg0 &rest rest
)
3728 (once-only ((arg0 arg0
))
3730 `(values (the real
,arg0
))
3731 `(let ((maxrest (max ,@rest
)))
3732 (if (>= ,arg0 maxrest
) ,arg0 maxrest
)))))
3733 (define-source-transform min
(arg0 &rest rest
)
3734 (once-only ((arg0 arg0
))
3736 `(values (the real
,arg0
))
3737 `(let ((minrest (min ,@rest
)))
3738 (if (<= ,arg0 minrest
) ,arg0 minrest
)))))
3740 ;;;; converting N-arg arithmetic functions
3742 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3743 ;;;; versions, and degenerate cases are flushed.
3745 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3746 (declaim (ftype (function (symbol t list
) list
) associate-args
))
3747 (defun associate-args (function first-arg more-args
)
3748 (let ((next (rest more-args
))
3749 (arg (first more-args
)))
3751 `(,function
,first-arg
,arg
)
3752 (associate-args function
`(,function
,first-arg
,arg
) next
))))
3754 ;;; Do source transformations for transitive functions such as +.
3755 ;;; One-arg cases are replaced with the arg and zero arg cases with
3756 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3757 ;;; ensure (with THE) that the argument in one-argument calls is.
3758 (defun source-transform-transitive (fun args identity
3759 &optional one-arg-result-type
)
3760 (declare (symbol fun
) (list args
))
3763 (1 (if one-arg-result-type
3764 `(values (the ,one-arg-result-type
,(first args
)))
3765 `(values ,(first args
))))
3768 (associate-args fun
(first args
) (rest args
)))))
3770 (define-source-transform + (&rest args
)
3771 (source-transform-transitive '+ args
0 'number
))
3772 (define-source-transform * (&rest args
)
3773 (source-transform-transitive '* args
1 'number
))
3774 (define-source-transform logior
(&rest args
)
3775 (source-transform-transitive 'logior args
0 'integer
))
3776 (define-source-transform logxor
(&rest args
)
3777 (source-transform-transitive 'logxor args
0 'integer
))
3778 (define-source-transform logand
(&rest args
)
3779 (source-transform-transitive 'logand args -
1 'integer
))
3780 (define-source-transform logeqv
(&rest args
)
3781 (source-transform-transitive 'logeqv args -
1 'integer
))
3783 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3784 ;;; because when they are given one argument, they return its absolute
3787 (define-source-transform gcd
(&rest args
)
3790 (1 `(abs (the integer
,(first args
))))
3792 (t (associate-args 'gcd
(first args
) (rest args
)))))
3794 (define-source-transform lcm
(&rest args
)
3797 (1 `(abs (the integer
,(first args
))))
3799 (t (associate-args 'lcm
(first args
) (rest args
)))))
3801 ;;; Do source transformations for intransitive n-arg functions such as
3802 ;;; /. With one arg, we form the inverse. With two args we pass.
3803 ;;; Otherwise we associate into two-arg calls.
3804 (declaim (ftype (function (symbol list t
)
3805 (values list
&optional
(member nil t
)))
3806 source-transform-intransitive
))
3807 (defun source-transform-intransitive (function args inverse
)
3809 ((0 2) (values nil t
))
3810 (1 `(,@inverse
,(first args
)))
3811 (t (associate-args function
(first args
) (rest args
)))))
3813 (define-source-transform -
(&rest args
)
3814 (source-transform-intransitive '- args
'(%negate
)))
3815 (define-source-transform / (&rest args
)
3816 (source-transform-intransitive '/ args
'(/ 1)))
3818 ;;;; transforming APPLY
3820 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3821 ;;; only needs to understand one kind of variable-argument call. It is
3822 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3823 (define-source-transform apply
(fun arg
&rest more-args
)
3824 (let ((args (cons arg more-args
)))
3825 `(multiple-value-call ,fun
3826 ,@(mapcar (lambda (x)
3829 (values-list ,(car (last args
))))))
3831 ;;;; transforming FORMAT
3833 ;;;; If the control string is a compile-time constant, then replace it
3834 ;;;; with a use of the FORMATTER macro so that the control string is
3835 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3836 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3837 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3839 ;;; for compile-time argument count checking.
3841 ;;; FIXME II: In some cases, type information could be correlated; for
3842 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3843 ;;; of a corresponding argument is known and does not intersect the
3844 ;;; list type, a warning could be signalled.
3845 (defun check-format-args (string args fun
)
3846 (declare (type string string
))
3847 (unless (typep string
'simple-string
)
3848 (setq string
(coerce string
'simple-string
)))
3849 (multiple-value-bind (min max
)
3850 (handler-case (sb!format
:%compiler-walk-format-string string args
)
3851 (sb!format
:format-error
(c)
3852 (compiler-warn "~A" c
)))
3854 (let ((nargs (length args
)))
3857 (warn 'format-too-few-args-warning
3859 "Too few arguments (~D) to ~S ~S: requires at least ~D."
3860 :format-arguments
(list nargs fun string min
)))
3862 (warn 'format-too-many-args-warning
3864 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3865 :format-arguments
(list nargs fun string max
))))))))
3867 (defoptimizer (format optimizer
) ((dest control
&rest args
))
3868 (when (constant-lvar-p control
)
3869 (let ((x (lvar-value control
)))
3871 (check-format-args x args
'format
)))))
3873 ;;; We disable this transform in the cross-compiler to save memory in
3874 ;;; the target image; most of the uses of FORMAT in the compiler are for
3875 ;;; error messages, and those don't need to be particularly fast.
3877 (deftransform format
((dest control
&rest args
) (t simple-string
&rest t
) *
3878 :policy
(>= speed space
))
3879 (unless (constant-lvar-p control
)
3880 (give-up-ir1-transform "The control string is not a constant."))
3881 (let ((arg-names (make-gensym-list (length args
))))
3882 `(lambda (dest control
,@arg-names
)
3883 (declare (ignore control
))
3884 (format dest
(formatter ,(lvar-value control
)) ,@arg-names
))))
3886 (deftransform format
((stream control
&rest args
) (stream function
&rest t
))
3887 (let ((arg-names (make-gensym-list (length args
))))
3888 `(lambda (stream control
,@arg-names
)
3889 (funcall control stream
,@arg-names
)
3892 (deftransform format
((tee control
&rest args
) ((member t
) function
&rest t
))
3893 (let ((arg-names (make-gensym-list (length args
))))
3894 `(lambda (tee control
,@arg-names
)
3895 (declare (ignore tee
))
3896 (funcall control
*standard-output
* ,@arg-names
)
3899 (deftransform pathname
((pathspec) (pathname) *)
3902 (deftransform pathname
((pathspec) (string) *)
3903 '(values (parse-namestring pathspec
)))
3907 `(defoptimizer (,name optimizer
) ((control &rest args
))
3908 (when (constant-lvar-p control
)
3909 (let ((x (lvar-value control
)))
3911 (check-format-args x args
',name
)))))))
3914 #+sb-xc-host
; Only we should be using these
3917 (def compiler-error
)
3919 (def compiler-style-warn
)
3920 (def compiler-notify
)
3921 (def maybe-compiler-notify
)
3924 (defoptimizer (cerror optimizer
) ((report control
&rest args
))
3925 (when (and (constant-lvar-p control
)
3926 (constant-lvar-p report
))
3927 (let ((x (lvar-value control
))
3928 (y (lvar-value report
)))
3929 (when (and (stringp x
) (stringp y
))
3930 (multiple-value-bind (min1 max1
)
3932 (sb!format
:%compiler-walk-format-string x args
)
3933 (sb!format
:format-error
(c)
3934 (compiler-warn "~A" c
)))
3936 (multiple-value-bind (min2 max2
)
3938 (sb!format
:%compiler-walk-format-string y args
)
3939 (sb!format
:format-error
(c)
3940 (compiler-warn "~A" c
)))
3942 (let ((nargs (length args
)))
3944 ((< nargs
(min min1 min2
))
3945 (warn 'format-too-few-args-warning
3947 "Too few arguments (~D) to ~S ~S ~S: ~
3948 requires at least ~D."
3950 (list nargs
'cerror y x
(min min1 min2
))))
3951 ((> nargs
(max max1 max2
))
3952 (warn 'format-too-many-args-warning
3954 "Too many arguments (~D) to ~S ~S ~S: ~
3957 (list nargs
'cerror y x
(max max1 max2
))))))))))))))
3959 (defoptimizer (coerce derive-type
) ((value type
))
3961 ((constant-lvar-p type
)
3962 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3963 ;; but dealing with the niggle that complex canonicalization gets
3964 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3966 (let* ((specifier (lvar-value type
))
3967 (result-typeoid (careful-specifier-type specifier
)))
3969 ((null result-typeoid
) nil
)
3970 ((csubtypep result-typeoid
(specifier-type 'number
))
3971 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3972 ;; Rule of Canonical Representation for Complex Rationals,
3973 ;; which is a truly nasty delivery to field.
3975 ((csubtypep result-typeoid
(specifier-type 'real
))
3976 ;; cleverness required here: it would be nice to deduce
3977 ;; that something of type (INTEGER 2 3) coerced to type
3978 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3979 ;; FLOAT gets its own clause because it's implemented as
3980 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3983 ((and (numeric-type-p result-typeoid
)
3984 (eq (numeric-type-complexp result-typeoid
) :real
))
3985 ;; FIXME: is this clause (a) necessary or (b) useful?
3987 ((or (csubtypep result-typeoid
3988 (specifier-type '(complex single-float
)))
3989 (csubtypep result-typeoid
3990 (specifier-type '(complex double-float
)))
3992 (csubtypep result-typeoid
3993 (specifier-type '(complex long-float
))))
3994 ;; float complex types are never canonicalized.
3997 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3998 ;; probably just a COMPLEX or equivalent. So, in that
3999 ;; case, we will return a complex or an object of the
4000 ;; provided type if it's rational:
4001 (type-union result-typeoid
4002 (type-intersection (lvar-type value
)
4003 (specifier-type 'rational
))))))
4004 (t result-typeoid
))))
4006 ;; OK, the result-type argument isn't constant. However, there
4007 ;; are common uses where we can still do better than just
4008 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
4009 ;; where Y is of a known type. See messages on cmucl-imp
4010 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
4011 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
4012 ;; the basis that it's unlikely that other uses are both
4013 ;; time-critical and get to this branch of the COND (non-constant
4014 ;; second argument to COERCE). -- CSR, 2002-12-16
4015 (let ((value-type (lvar-type value
))
4016 (type-type (lvar-type type
)))
4018 ((good-cons-type-p (cons-type)
4019 ;; Make sure the cons-type we're looking at is something
4020 ;; we're prepared to handle which is basically something
4021 ;; that array-element-type can return.
4022 (or (and (member-type-p cons-type
)
4023 (eql 1 (member-type-size cons-type
))
4024 (null (first (member-type-members cons-type
))))
4025 (let ((car-type (cons-type-car-type cons-type
)))
4026 (and (member-type-p car-type
)
4027 (eql 1 (member-type-members car-type
))
4028 (let ((elt (first (member-type-members car-type
))))
4032 (numberp (first elt
)))))
4033 (good-cons-type-p (cons-type-cdr-type cons-type
))))))
4034 (unconsify-type (good-cons-type)
4035 ;; Convert the "printed" respresentation of a cons
4036 ;; specifier into a type specifier. That is, the
4037 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
4038 ;; NULL)) is converted to (SIGNED-BYTE 16).
4039 (cond ((or (null good-cons-type
)
4040 (eq good-cons-type
'null
))
4042 ((and (eq (first good-cons-type
) 'cons
)
4043 (eq (first (second good-cons-type
)) 'member
))
4044 `(,(second (second good-cons-type
))
4045 ,@(unconsify-type (caddr good-cons-type
))))))
4046 (coerceable-p (part)
4047 ;; Can the value be coerced to the given type? Coerce is
4048 ;; complicated, so we don't handle every possible case
4049 ;; here---just the most common and easiest cases:
4051 ;; * Any REAL can be coerced to a FLOAT type.
4052 ;; * Any NUMBER can be coerced to a (COMPLEX
4053 ;; SINGLE/DOUBLE-FLOAT).
4055 ;; FIXME I: we should also be able to deal with characters
4058 ;; FIXME II: I'm not sure that anything is necessary
4059 ;; here, at least while COMPLEX is not a specialized
4060 ;; array element type in the system. Reasoning: if
4061 ;; something cannot be coerced to the requested type, an
4062 ;; error will be raised (and so any downstream compiled
4063 ;; code on the assumption of the returned type is
4064 ;; unreachable). If something can, then it will be of
4065 ;; the requested type, because (by assumption) COMPLEX
4066 ;; (and other difficult types like (COMPLEX INTEGER)
4067 ;; aren't specialized types.
4068 (let ((coerced-type (careful-specifier-type part
)))
4070 (or (and (csubtypep coerced-type
(specifier-type 'float
))
4071 (csubtypep value-type
(specifier-type 'real
)))
4072 (and (csubtypep coerced-type
4073 (specifier-type `(or (complex single-float
)
4074 (complex double-float
))))
4075 (csubtypep value-type
(specifier-type 'number
)))))))
4076 (process-types (type)
4077 ;; FIXME: This needs some work because we should be able
4078 ;; to derive the resulting type better than just the
4079 ;; type arg of coerce. That is, if X is (INTEGER 10
4080 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
4081 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
4083 (cond ((member-type-p type
)
4086 (mapc-member-type-members
4088 (if (coerceable-p member
)
4089 (push member members
)
4090 (return-from punt
*universal-type
*)))
4092 (specifier-type `(or ,@members
)))))
4093 ((and (cons-type-p type
)
4094 (good-cons-type-p type
))
4095 (let ((c-type (unconsify-type (type-specifier type
))))
4096 (if (coerceable-p c-type
)
4097 (specifier-type c-type
)
4100 *universal-type
*))))
4101 (cond ((union-type-p type-type
)
4102 (apply #'type-union
(mapcar #'process-types
4103 (union-type-types type-type
))))
4104 ((or (member-type-p type-type
)
4105 (cons-type-p type-type
))
4106 (process-types type-type
))
4108 *universal-type
*)))))))
4110 (defoptimizer (compile derive-type
) ((nameoid function
))
4111 (when (csubtypep (lvar-type nameoid
)
4112 (specifier-type 'null
))
4113 (values-specifier-type '(values function boolean boolean
))))
4115 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
4116 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
4117 ;;; optimizer, above).
4118 (defoptimizer (array-element-type derive-type
) ((array))
4119 (let ((array-type (lvar-type array
)))
4120 (labels ((consify (list)
4123 `(cons (eql ,(car list
)) ,(consify (rest list
)))))
4124 (get-element-type (a)
4126 (type-specifier (array-type-specialized-element-type a
))))
4127 (cond ((eq element-type
'*)
4128 (specifier-type 'type-specifier
))
4129 ((symbolp element-type
)
4130 (make-member-type :members
(list element-type
)))
4131 ((consp element-type
)
4132 (specifier-type (consify element-type
)))
4134 (error "can't understand type ~S~%" element-type
))))))
4135 (labels ((recurse (type)
4136 (cond ((array-type-p type
)
4137 (get-element-type type
))
4138 ((union-type-p type
)
4140 (mapcar #'recurse
(union-type-types type
))))
4142 *universal-type
*))))
4143 (recurse array-type
)))))
4145 (define-source-transform sb
!impl
::sort-vector
(vector start end predicate key
)
4146 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4147 ;; isn't really related to the CMU CL code, since instead of trying
4148 ;; to generalize the CMU CL code to allow START and END values, this
4149 ;; code has been written from scratch following Chapter 7 of
4150 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4151 `(macrolet ((%index
(x) `(truly-the index
,x
))
4152 (%parent
(i) `(ash ,i -
1))
4153 (%left
(i) `(%index
(ash ,i
1)))
4154 (%right
(i) `(%index
(1+ (ash ,i
1))))
4157 (left (%left i
) (%left i
)))
4158 ((> left current-heap-size
))
4159 (declare (type index i left
))
4160 (let* ((i-elt (%elt i
))
4161 (i-key (funcall keyfun i-elt
))
4162 (left-elt (%elt left
))
4163 (left-key (funcall keyfun left-elt
)))
4164 (multiple-value-bind (large large-elt large-key
)
4165 (if (funcall ,',predicate i-key left-key
)
4166 (values left left-elt left-key
)
4167 (values i i-elt i-key
))
4168 (let ((right (%right i
)))
4169 (multiple-value-bind (largest largest-elt
)
4170 (if (> right current-heap-size
)
4171 (values large large-elt
)
4172 (let* ((right-elt (%elt right
))
4173 (right-key (funcall keyfun right-elt
)))
4174 (if (funcall ,',predicate large-key right-key
)
4175 (values right right-elt
)
4176 (values large large-elt
))))
4177 (cond ((= largest i
)
4180 (setf (%elt i
) largest-elt
4181 (%elt largest
) i-elt
4183 (%sort-vector
(keyfun &optional
(vtype 'vector
))
4184 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4185 ;; trouble getting type inference to
4186 ;; propagate all the way through this
4187 ;; tangled mess of inlining. The TRULY-THE
4188 ;; here works around that. -- WHN
4190 `(aref (truly-the ,',vtype
,',',vector
)
4191 (%index
(+ (%index
,i
) start-1
)))))
4192 (let (;; Heaps prefer 1-based addressing.
4193 (start-1 (1- ,',start
))
4194 (current-heap-size (- ,',end
,',start
))
4196 (declare (type (integer -
1 #.
(1- sb
!xc
:most-positive-fixnum
))
4198 (declare (type index current-heap-size
))
4199 (declare (type function keyfun
))
4200 (loop for i of-type index
4201 from
(ash current-heap-size -
1) downto
1 do
4204 (when (< current-heap-size
2)
4206 (rotatef (%elt
1) (%elt current-heap-size
))
4207 (decf current-heap-size
)
4209 (if (typep ,vector
'simple-vector
)
4210 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4211 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4213 ;; Special-casing the KEY=NIL case lets us avoid some
4215 (%sort-vector
#'identity simple-vector
)
4216 (%sort-vector
,key simple-vector
))
4217 ;; It's hard to anticipate many speed-critical applications for
4218 ;; sorting vector types other than (VECTOR T), so we just lump
4219 ;; them all together in one slow dynamically typed mess.
4221 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4222 (%sort-vector
(or ,key
#'identity
))))))
4224 ;;;; debuggers' little helpers
4226 ;;; for debugging when transforms are behaving mysteriously,
4227 ;;; e.g. when debugging a problem with an ASH transform
4228 ;;; (defun foo (&optional s)
4229 ;;; (sb-c::/report-lvar s "S outside WHEN")
4230 ;;; (when (and (integerp s) (> s 3))
4231 ;;; (sb-c::/report-lvar s "S inside WHEN")
4232 ;;; (let ((bound (ash 1 (1- s))))
4233 ;;; (sb-c::/report-lvar bound "BOUND")
4234 ;;; (let ((x (- bound))
4236 ;;; (sb-c::/report-lvar x "X")
4237 ;;; (sb-c::/report-lvar x "Y"))
4238 ;;; `(integer ,(- bound) ,(1- bound)))))
4239 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4240 ;;; and the function doesn't do anything at all.)
4243 (defknown /report-lvar
(t t
) null
)
4244 (deftransform /report-lvar
((x message
) (t t
))
4245 (format t
"~%/in /REPORT-LVAR~%")
4246 (format t
"/(LVAR-TYPE X)=~S~%" (lvar-type x
))
4247 (when (constant-lvar-p x
)
4248 (format t
"/(LVAR-VALUE X)=~S~%" (lvar-value x
)))
4249 (format t
"/MESSAGE=~S~%" (lvar-value message
))
4250 (give-up-ir1-transform "not a real transform"))
4251 (defun /report-lvar
(x message
)
4252 (declare (ignore x message
))))
4255 ;;;; Transforms for internal compiler utilities
4257 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4258 ;;; checking that it's still valid at run-time.
4259 (deftransform policy-quality
((policy quality-name
)
4261 (unless (and (constant-lvar-p quality-name
)
4262 (policy-quality-name-p (lvar-value quality-name
)))
4263 (give-up-ir1-transform))
4264 '(%policy-quality policy quality-name
))