1 ;;;; This file contains macro-like source transformations which
2 ;;;; convert uses of certain functions into the canonical form desired
3 ;;;; within the compiler. ### 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 (def-source-transform not (x) `(if ,x nil t))
19 (def-source-transform null (x) `(if ,x nil t))
21 ;;; ENDP is just NULL with a LIST assertion.
22 (def-source-transform endp (x) `(null (the list ,x)))
23 ;;; FIXME: Is THE LIST a strong enough assertion for ANSI's "should
24 ;;; return an error"? (THE LIST is optimized away when safety is low;
25 ;;; does that satisfy the spec?)
27 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
28 ;;; returns the first value of its argument. Ditto for VALUES with one
30 (def-source-transform identity (x) `(prog1 ,x))
31 (def-source-transform values (x) `(prog1 ,x))
33 ;;; Bind the values and make a closure that returns them.
34 (def-source-transform constantly (value &rest values)
35 (let ((temps (make-gensym-list (1+ (length values))))
37 `(let ,(loop for temp in temps and
38 value in (list* value values)
39 collect `(,temp ,value))
40 #'(lambda (&rest ,dum)
41 (declare (ignore ,dum))
44 ;;; If the function has a known number of arguments, then return a
45 ;;; lambda with the appropriate fixed number of args. If the
46 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
47 ;;; MV optimization figure things out.
48 (deftransform complement ((fun) * * :node node :when :both)
50 (multiple-value-bind (min max)
51 (function-type-nargs (continuation-type fun))
53 ((and min (eql min max))
54 (let ((dums (make-gensym-list min)))
55 `#'(lambda ,dums (not (funcall fun ,@dums)))))
56 ((let* ((cont (node-cont node))
57 (dest (continuation-dest cont)))
58 (and (combination-p dest)
59 (eq (combination-fun dest) cont)))
60 '#'(lambda (&rest args)
61 (not (apply fun args))))
63 (give-up-ir1-transform
64 "The function doesn't have a fixed argument count.")))))
68 ;;; Translate CxxR into CAR/CDR combos.
70 (defun source-transform-cxr (form)
71 (if (or (byte-compiling) (/= (length form) 2))
73 (let ((name (symbol-name (car form))))
74 (do ((i (- (length name) 2) (1- i))
76 `(,(ecase (char name i)
83 (b '(1 0) (cons i b)))
85 (dotimes (j (ash 1 i))
86 (setf (info :function :source-transform
87 (intern (format nil "C~{~:[A~;D~]~}R"
88 (mapcar #'(lambda (x) (logbitp x j)) b))))
89 #'source-transform-cxr)))
91 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
92 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
93 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
95 (def-source-transform first (x) `(car ,x))
96 (def-source-transform rest (x) `(cdr ,x))
97 (def-source-transform second (x) `(cadr ,x))
98 (def-source-transform third (x) `(caddr ,x))
99 (def-source-transform fourth (x) `(cadddr ,x))
100 (def-source-transform fifth (x) `(nth 4 ,x))
101 (def-source-transform sixth (x) `(nth 5 ,x))
102 (def-source-transform seventh (x) `(nth 6 ,x))
103 (def-source-transform eighth (x) `(nth 7 ,x))
104 (def-source-transform ninth (x) `(nth 8 ,x))
105 (def-source-transform tenth (x) `(nth 9 ,x))
107 ;;; Translate RPLACx to LET and SETF.
108 (def-source-transform rplaca (x y)
113 (def-source-transform rplacd (x y)
119 (def-source-transform nth (n l) `(car (nthcdr ,n ,l)))
121 (defvar *default-nthcdr-open-code-limit* 6)
122 (defvar *extreme-nthcdr-open-code-limit* 20)
124 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
125 "convert NTHCDR to CAxxR"
126 (unless (constant-continuation-p n)
127 (give-up-ir1-transform))
128 (let ((n (continuation-value n)))
130 (if (policy node (= speed 3) (= space 0))
131 *extreme-nthcdr-open-code-limit*
132 *default-nthcdr-open-code-limit*))
133 (give-up-ir1-transform))
138 `(cdr ,(frob (1- n))))))
141 ;;; MNA: cons compound-type patch
142 ;;; FIXIT: all commented out
144 ; ;;;; CONS assessor derive type optimizers.
146 ; (defoptimizer (car derive-type) ((cons))
147 ; (let ((type (continuation-type cons)))
148 ; (cond ((eq type (specifier-type 'null))
149 ; (specifier-type 'null))
150 ; ((cons-type-p type)
151 ; (cons-type-car-type type)))))
153 ; (defoptimizer (cdr derive-type) ((cons))
154 ; (let ((type (continuation-type cons)))
155 ; (cond ((eq type (specifier-type 'null))
156 ; (specifier-type 'null))
157 ; ((cons-type-p type)
158 ; (cons-type-cdr-type type)))))
161 ;;;; arithmetic and numerology
163 (def-source-transform plusp (x) `(> ,x 0))
164 (def-source-transform minusp (x) `(< ,x 0))
165 (def-source-transform zerop (x) `(= ,x 0))
167 (def-source-transform 1+ (x) `(+ ,x 1))
168 (def-source-transform 1- (x) `(- ,x 1))
170 (def-source-transform oddp (x) `(not (zerop (logand ,x 1))))
171 (def-source-transform evenp (x) `(zerop (logand ,x 1)))
173 ;;; Note that all the integer division functions are available for
174 ;;; inline expansion.
176 ;;; FIXME: DEF-FROB instead of FROB
177 (macrolet ((frob (fun)
178 `(def-source-transform ,fun (x &optional (y nil y-p))
185 #!+propagate-float-type
187 #!+propagate-float-type
190 (def-source-transform lognand (x y) `(lognot (logand ,x ,y)))
191 (def-source-transform lognor (x y) `(lognot (logior ,x ,y)))
192 (def-source-transform logandc1 (x y) `(logand (lognot ,x) ,y))
193 (def-source-transform logandc2 (x y) `(logand ,x (lognot ,y)))
194 (def-source-transform logorc1 (x y) `(logior (lognot ,x) ,y))
195 (def-source-transform logorc2 (x y) `(logior ,x (lognot ,y)))
196 (def-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
197 (def-source-transform logbitp (index integer)
198 `(not (zerop (logand (ash 1 ,index) ,integer))))
199 (def-source-transform byte (size position) `(cons ,size ,position))
200 (def-source-transform byte-size (spec) `(car ,spec))
201 (def-source-transform byte-position (spec) `(cdr ,spec))
202 (def-source-transform ldb-test (bytespec integer)
203 `(not (zerop (mask-field ,bytespec ,integer))))
205 ;;; With the ratio and complex accessors, we pick off the "identity"
206 ;;; case, and use a primitive to handle the cell access case.
207 (def-source-transform numerator (num)
208 (once-only ((n-num `(the rational ,num)))
212 (def-source-transform denominator (num)
213 (once-only ((n-num `(the rational ,num)))
215 (%denominator ,n-num)
218 ;;;; Interval arithmetic for computing bounds
219 ;;;; (toy@rtp.ericsson.se)
221 ;;;; This is a set of routines for operating on intervals. It
222 ;;;; implements a simple interval arithmetic package. Although SBCL
223 ;;;; has an interval type in numeric-type, we choose to use our own
224 ;;;; for two reasons:
226 ;;;; 1. This package is simpler than numeric-type
228 ;;;; 2. It makes debugging much easier because you can just strip
229 ;;;; out these routines and test them independently of SBCL. (a
232 ;;;; One disadvantage is a probable increase in consing because we
233 ;;;; have to create these new interval structures even though
234 ;;;; numeric-type has everything we want to know. Reason 2 wins for
237 #-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
239 #!+propagate-float-type
242 ;;; The basic interval type. It can handle open and closed intervals.
243 ;;; A bound is open if it is a list containing a number, just like
244 ;;; Lisp says. NIL means unbounded.
246 (:constructor %make-interval))
249 (defun make-interval (&key low high)
250 (labels ((normalize-bound (val)
251 (cond ((and (floatp val)
252 (float-infinity-p val))
257 ;; Handle any closed bounds
260 ;; We have an open bound. Normalize the numeric
261 ;; bound. If the normalized bound is still a number
262 ;; (not nil), keep the bound open. Otherwise, the
263 ;; bound is really unbounded, so drop the openness.
264 (let ((new-val (normalize-bound (first val))))
266 ;; Bound exists, so keep it open still
269 (error "Unknown bound type in make-interval!")))))
270 (%make-interval :low (normalize-bound low)
271 :high (normalize-bound high))))
273 #!-sb-fluid (declaim (inline bound-value set-bound))
275 ;;; Extract the numeric value of a bound. Return NIL, if X is NIL.
276 (defun bound-value (x)
277 (if (consp x) (car x) x))
279 ;;; Given a number X, create a form suitable as a bound for an
280 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
281 (defun set-bound (x open-p)
282 (if (and x open-p) (list x) x))
284 ;;; Apply the function F to a bound X. If X is an open bound, then
285 ;;; the result will be open. IF X is NIL, the result is NIL.
286 (defun bound-func (f x)
288 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
289 ;; With these traps masked, we might get things like infinity
290 ;; or negative infinity returned. Check for this and return
291 ;; NIL to indicate unbounded.
292 (let ((y (funcall f (bound-value x))))
294 (float-infinity-p y))
296 (set-bound (funcall f (bound-value x)) (consp x)))))))
298 ;;; Apply a binary operator OP to two bounds X and Y. The result is
299 ;;; NIL if either is NIL. Otherwise bound is computed and the result
300 ;;; is open if either X or Y is open.
302 ;;; FIXME: only used in this file, not needed in target runtime
303 (defmacro bound-binop (op x y)
305 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
306 (set-bound (,op (bound-value ,x)
308 (or (consp ,x) (consp ,y))))))
310 ;;; NUMERIC-TYPE->INTERVAL
312 ;;; Convert a numeric-type object to an interval object.
314 (defun numeric-type->interval (x)
315 (declare (type numeric-type x))
316 (make-interval :low (numeric-type-low x)
317 :high (numeric-type-high x)))
319 (defun copy-interval-limit (limit)
324 (defun copy-interval (x)
325 (declare (type interval x))
326 (make-interval :low (copy-interval-limit (interval-low x))
327 :high (copy-interval-limit (interval-high x))))
331 ;;; Given a point P contained in the interval X, split X into two
332 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
333 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
334 ;;; contains P. You can specify both to be T or NIL.
335 (defun interval-split (p x &optional close-lower close-upper)
336 (declare (type number p)
338 (list (make-interval :low (copy-interval-limit (interval-low x))
339 :high (if close-lower p (list p)))
340 (make-interval :low (if close-upper (list p) p)
341 :high (copy-interval-limit (interval-high x)))))
345 ;;; Return the closure of the interval. That is, convert open bounds
346 ;;; to closed bounds.
347 (defun interval-closure (x)
348 (declare (type interval x))
349 (make-interval :low (bound-value (interval-low x))
350 :high (bound-value (interval-high x))))
352 (defun signed-zero->= (x y)
356 (>= (float-sign (float x))
357 (float-sign (float y))))))
359 ;;; INTERVAL-RANGE-INFO
361 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
362 ;;; '-. Otherwise return NIL.
364 (defun interval-range-info (x &optional (point 0))
365 (declare (type interval x))
366 (let ((lo (interval-low x))
367 (hi (interval-high x)))
368 (cond ((and lo (signed-zero->= (bound-value lo) point))
370 ((and hi (signed-zero->= point (bound-value hi)))
374 (defun interval-range-info (x &optional (point 0))
375 (declare (type interval x))
376 (labels ((signed->= (x y)
377 (if (and (zerop x) (zerop y) (floatp x) (floatp y))
378 (>= (float-sign x) (float-sign y))
380 (let ((lo (interval-low x))
381 (hi (interval-high x)))
382 (cond ((and lo (signed->= (bound-value lo) point))
384 ((and hi (signed->= point (bound-value hi)))
389 ;;; INTERVAL-BOUNDED-P
391 ;;; Test to see whether the interval X is bounded. HOW determines the
392 ;;; test, and should be either ABOVE, BELOW, or BOTH.
393 (defun interval-bounded-p (x how)
394 (declare (type interval x))
401 (and (interval-low x) (interval-high x)))))
403 ;;; Signed zero comparison functions. Use these functions if we need
404 ;;; to distinguish between signed zeroes.
406 (defun signed-zero-< (x y)
410 (< (float-sign (float x))
411 (float-sign (float y))))))
412 (defun signed-zero-> (x y)
416 (> (float-sign (float x))
417 (float-sign (float y))))))
419 (defun signed-zero-= (x y)
422 (= (float-sign (float x))
423 (float-sign (float y)))))
425 (defun signed-zero-<= (x y)
429 (<= (float-sign (float x))
430 (float-sign (float y))))))
432 ;;; INTERVAL-CONTAINS-P
434 ;;; See whether the interval X contains the number P, taking into account
435 ;;; that the interval might not be closed.
436 (defun interval-contains-p (p x)
437 (declare (type number p)
439 ;; Does the interval X contain the number P? This would be a lot
440 ;; easier if all intervals were closed!
441 (let ((lo (interval-low x))
442 (hi (interval-high x)))
444 ;; The interval is bounded
445 (if (and (signed-zero-<= (bound-value lo) p)
446 (signed-zero-<= p (bound-value hi)))
447 ;; P is definitely in the closure of the interval.
448 ;; We just need to check the end points now.
449 (cond ((signed-zero-= p (bound-value lo))
451 ((signed-zero-= p (bound-value hi))
456 ;; Interval with upper bound
457 (if (signed-zero-< p (bound-value hi))
459 (and (numberp hi) (signed-zero-= p hi))))
461 ;; Interval with lower bound
462 (if (signed-zero-> p (bound-value lo))
464 (and (numberp lo) (signed-zero-= p lo))))
466 ;; Interval with no bounds
469 ;;; INTERVAL-INTERSECT-P
471 ;;; Determine if two intervals X and Y intersect. Return T if so. If
472 ;;; CLOSED-INTERVALS-P is T, the treat the intervals as if they were
473 ;;; closed. Otherwise the intervals are treated as they are.
475 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
476 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
477 ;;; is T, then they do intersect because we use the closure of X = [0,
478 ;;; 1] and Y = [1, 2] to determine intersection.
479 (defun interval-intersect-p (x y &optional closed-intervals-p)
480 (declare (type interval x y))
481 (multiple-value-bind (intersect diff)
482 (interval-intersection/difference (if closed-intervals-p
485 (if closed-intervals-p
488 (declare (ignore diff))
491 ;;; Are the two intervals adjacent? That is, is there a number
492 ;;; between the two intervals that is not an element of either
493 ;;; interval? If so, they are not adjacent. For example [0, 1) and
494 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
495 ;;; between both intervals.
496 (defun interval-adjacent-p (x y)
497 (declare (type interval x y))
498 (flet ((adjacent (lo hi)
499 ;; Check to see whether lo and hi are adjacent. If either is
500 ;; nil, they can't be adjacent.
501 (when (and lo hi (= (bound-value lo) (bound-value hi)))
502 ;; The bounds are equal. They are adjacent if one of
503 ;; them is closed (a number). If both are open (consp),
504 ;; then there is a number that lies between them.
505 (or (numberp lo) (numberp hi)))))
506 (or (adjacent (interval-low y) (interval-high x))
507 (adjacent (interval-low x) (interval-high y)))))
509 ;;; INTERVAL-INTERSECTION/DIFFERENCE
511 ;;; Compute the intersection and difference between two intervals.
512 ;;; Two values are returned: the intersection and the difference.
514 ;;; Let the two intervals be X and Y, and let I and D be the two
515 ;;; values returned by this function. Then I = X intersect Y. If I
516 ;;; is NIL (the empty set), then D is X union Y, represented as the
517 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
518 ;;; - I, which is a list of two intervals.
520 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
521 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
522 (defun interval-intersection/difference (x y)
523 (declare (type interval x y))
524 (let ((x-lo (interval-low x))
525 (x-hi (interval-high x))
526 (y-lo (interval-low y))
527 (y-hi (interval-high y)))
530 ;; If p is an open bound, make it closed. If p is a closed
531 ;; bound, make it open.
536 ;; Test whether P is in the interval.
537 (when (interval-contains-p (bound-value p)
538 (interval-closure int))
539 (let ((lo (interval-low int))
540 (hi (interval-high int)))
541 ;; Check for endpoints
542 (cond ((and lo (= (bound-value p) (bound-value lo)))
543 (not (and (consp p) (numberp lo))))
544 ((and hi (= (bound-value p) (bound-value hi)))
545 (not (and (numberp p) (consp hi))))
547 (test-lower-bound (p int)
548 ;; P is a lower bound of an interval.
551 (not (interval-bounded-p int 'below))))
552 (test-upper-bound (p int)
553 ;; P is an upper bound of an interval
556 (not (interval-bounded-p int 'above)))))
557 (let ((x-lo-in-y (test-lower-bound x-lo y))
558 (x-hi-in-y (test-upper-bound x-hi y))
559 (y-lo-in-x (test-lower-bound y-lo x))
560 (y-hi-in-x (test-upper-bound y-hi x)))
561 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
562 ;; Intervals intersect. Let's compute the intersection
563 ;; and the difference.
564 (multiple-value-bind (lo left-lo left-hi)
565 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
566 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
567 (multiple-value-bind (hi right-lo right-hi)
569 (values x-hi (opposite-bound x-hi) y-hi))
571 (values y-hi (opposite-bound y-hi) x-hi)))
572 (values (make-interval :low lo :high hi)
573 (list (make-interval :low left-lo :high left-hi)
574 (make-interval :low right-lo :high right-hi))))))
576 (values nil (list x y))))))))
578 ;;; INTERVAL-MERGE-PAIR
580 ;;; If intervals X and Y intersect, return a new interval that is the
581 ;;; union of the two. If they do not intersect, return NIL.
582 (defun interval-merge-pair (x y)
583 (declare (type interval x y))
584 ;; If x and y intersect or are adjacent, create the union.
585 ;; Otherwise return nil
586 (when (or (interval-intersect-p x y)
587 (interval-adjacent-p x y))
588 (flet ((select-bound (x1 x2 min-op max-op)
589 (let ((x1-val (bound-value x1))
590 (x2-val (bound-value x2)))
592 ;; Both bounds are finite. Select the right one.
593 (cond ((funcall min-op x1-val x2-val)
594 ;; x1 definitely better
596 ((funcall max-op x1-val x2-val)
597 ;; x2 definitely better
600 ;; Bounds are equal. Select either
601 ;; value and make it open only if
603 (set-bound x1-val (and (consp x1) (consp x2))))))
605 ;; At least one bound is not finite. The
606 ;; non-finite bound always wins.
608 (let* ((x-lo (copy-interval-limit (interval-low x)))
609 (x-hi (copy-interval-limit (interval-high x)))
610 (y-lo (copy-interval-limit (interval-low y)))
611 (y-hi (copy-interval-limit (interval-high y))))
612 (make-interval :low (select-bound x-lo y-lo #'< #'>)
613 :high (select-bound x-hi y-hi #'> #'<))))))
615 ;;; Basic arithmetic operations on intervals. We probably should do
616 ;;; true interval arithmetic here, but it's complicated because we
617 ;;; have float and integer types and bounds can be open or closed.
621 ;;; The negative of an interval
622 (defun interval-neg (x)
623 (declare (type interval x))
624 (make-interval :low (bound-func #'- (interval-high x))
625 :high (bound-func #'- (interval-low x))))
629 ;;; Add two intervals
630 (defun interval-add (x y)
631 (declare (type interval x y))
632 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
633 :high (bound-binop + (interval-high x) (interval-high y))))
637 ;;; Subtract two intervals
638 (defun interval-sub (x y)
639 (declare (type interval x y))
640 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
641 :high (bound-binop - (interval-high x) (interval-low y))))
645 ;;; Multiply two intervals
646 (defun interval-mul (x y)
647 (declare (type interval x y))
648 (flet ((bound-mul (x y)
649 (cond ((or (null x) (null y))
650 ;; Multiply by infinity is infinity
652 ((or (and (numberp x) (zerop x))
653 (and (numberp y) (zerop y)))
654 ;; Multiply by closed zero is special. The result
655 ;; is always a closed bound. But don't replace this
656 ;; with zero; we want the multiplication to produce
657 ;; the correct signed zero, if needed.
658 (* (bound-value x) (bound-value y)))
659 ((or (and (floatp x) (float-infinity-p x))
660 (and (floatp y) (float-infinity-p y)))
661 ;; Infinity times anything is infinity
664 ;; General multiply. The result is open if either is open.
665 (bound-binop * x y)))))
666 (let ((x-range (interval-range-info x))
667 (y-range (interval-range-info y)))
668 (cond ((null x-range)
669 ;; Split x into two and multiply each separately
670 (destructuring-bind (x- x+) (interval-split 0 x t t)
671 (interval-merge-pair (interval-mul x- y)
672 (interval-mul x+ y))))
674 ;; Split y into two and multiply each separately
675 (destructuring-bind (y- y+) (interval-split 0 y t t)
676 (interval-merge-pair (interval-mul x y-)
677 (interval-mul x y+))))
679 (interval-neg (interval-mul (interval-neg x) y)))
681 (interval-neg (interval-mul x (interval-neg y))))
682 ((and (eq x-range '+) (eq y-range '+))
683 ;; If we are here, X and Y are both positive
684 (make-interval :low (bound-mul (interval-low x) (interval-low y))
685 :high (bound-mul (interval-high x) (interval-high y))))
687 (error "This shouldn't happen!"))))))
691 ;;; Divide two intervals.
692 (defun interval-div (top bot)
693 (declare (type interval top bot))
694 (flet ((bound-div (x y y-low-p)
697 ;; Divide by infinity means result is 0. However,
698 ;; we need to watch out for the sign of the result,
699 ;; to correctly handle signed zeros. We also need
700 ;; to watch out for positive or negative infinity.
701 (if (floatp (bound-value x))
703 (- (float-sign (bound-value x) 0.0))
704 (float-sign (bound-value x) 0.0))
706 ((zerop (bound-value y))
707 ;; Divide by zero means result is infinity
709 ((and (numberp x) (zerop x))
710 ;; Zero divided by anything is zero.
713 (bound-binop / x y)))))
714 (let ((top-range (interval-range-info top))
715 (bot-range (interval-range-info bot)))
716 (cond ((null bot-range)
717 ;; The denominator contains zero, so anything goes!
718 (make-interval :low nil :high nil))
720 ;; Denominator is negative so flip the sign, compute the
721 ;; result, and flip it back.
722 (interval-neg (interval-div top (interval-neg bot))))
724 ;; Split top into two positive and negative parts, and
725 ;; divide each separately
726 (destructuring-bind (top- top+) (interval-split 0 top t t)
727 (interval-merge-pair (interval-div top- bot)
728 (interval-div top+ bot))))
730 ;; Top is negative so flip the sign, divide, and flip the
731 ;; sign of the result.
732 (interval-neg (interval-div (interval-neg top) bot)))
733 ((and (eq top-range '+) (eq bot-range '+))
735 (make-interval :low (bound-div (interval-low top) (interval-high bot) t)
736 :high (bound-div (interval-high top) (interval-low bot) nil)))
738 (error "This shouldn't happen!"))))))
742 ;;; Apply the function F to the interval X. If X = [a, b], then the
743 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
744 ;;; result makes sense. It will if F is monotonic increasing (or
746 (defun interval-func (f x)
747 (declare (type interval x))
748 (let ((lo (bound-func f (interval-low x)))
749 (hi (bound-func f (interval-high x))))
750 (make-interval :low lo :high hi)))
754 ;;; Return T if X < Y. That is every number in the interval X is
755 ;;; always less than any number in the interval Y.
756 (defun interval-< (x y)
757 (declare (type interval x y))
758 ;; X < Y only if X is bounded above, Y is bounded below, and they
760 (when (and (interval-bounded-p x 'above)
761 (interval-bounded-p y 'below))
762 ;; Intervals are bounded in the appropriate way. Make sure they
764 (let ((left (interval-high x))
765 (right (interval-low y)))
766 (cond ((> (bound-value left)
768 ;; Definitely overlap so result is NIL
770 ((< (bound-value left)
772 ;; Definitely don't touch, so result is T
775 ;; Limits are equal. Check for open or closed bounds.
776 ;; Don't overlap if one or the other are open.
777 (or (consp left) (consp right)))))))
781 ;;; Return T if X >= Y. That is, every number in the interval X is
782 ;;; always greater than any number in the interval Y.
783 (defun interval->= (x y)
784 (declare (type interval x y))
785 ;; X >= Y if lower bound of X >= upper bound of Y
786 (when (and (interval-bounded-p x 'below)
787 (interval-bounded-p y 'above))
788 (>= (bound-value (interval-low x)) (bound-value (interval-high y)))))
792 ;;; Return an interval that is the absolute value of X. Thus, if X =
793 ;;; [-1 10], the result is [0, 10].
794 (defun interval-abs (x)
795 (declare (type interval x))
796 (case (interval-range-info x)
802 (destructuring-bind (x- x+) (interval-split 0 x t t)
803 (interval-merge-pair (interval-neg x-) x+)))))
807 ;;; Compute the square of an interval.
808 (defun interval-sqr (x)
809 (declare (type interval x))
810 (interval-func #'(lambda (x) (* x x))
814 ;;;; numeric derive-type methods
816 ;;; Utility for defining derive-type methods of integer operations. If the
817 ;;; types of both X and Y are integer types, then we compute a new integer type
818 ;;; with bounds determined Fun when applied to X and Y. Otherwise, we use
819 ;;; Numeric-Contagion.
820 (defun derive-integer-type (x y fun)
821 (declare (type continuation x y) (type function fun))
822 (let ((x (continuation-type x))
823 (y (continuation-type y)))
824 (if (and (numeric-type-p x) (numeric-type-p y)
825 (eq (numeric-type-class x) 'integer)
826 (eq (numeric-type-class y) 'integer)
827 (eq (numeric-type-complexp x) :real)
828 (eq (numeric-type-complexp y) :real))
829 (multiple-value-bind (low high) (funcall fun x y)
830 (make-numeric-type :class 'integer
834 (numeric-contagion x y))))
836 #!+(or propagate-float-type propagate-fun-type)
839 ;; Simple utility to flatten a list
840 (defun flatten-list (x)
841 (labels ((flatten-helper (x r);; 'r' is the stuff to the 'right'.
845 (t (flatten-helper (car x)
846 (flatten-helper (cdr x) r))))))
847 (flatten-helper x nil)))
849 ;;; Take some type of continuation and massage it so that we get a
850 ;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
851 ;;; to indicate failure.
852 (defun prepare-arg-for-derive-type (arg)
853 (flet ((listify (arg)
858 (union-type-types arg))
861 (unless (eq arg *empty-type*)
862 ;; Make sure all args are some type of numeric-type. For member
863 ;; types, convert the list of members into a union of equivalent
864 ;; single-element member-type's.
865 (let ((new-args nil))
866 (dolist (arg (listify arg))
867 (if (member-type-p arg)
868 ;; Run down the list of members and convert to a list of
870 (dolist (member (member-type-members arg))
871 (push (if (numberp member)
872 (make-member-type :members (list member))
875 (push arg new-args)))
876 (unless (member *empty-type* new-args)
879 ;;; Convert from the standard type convention for which -0.0 and 0.0
880 ;;; and equal to an intermediate convention for which they are
881 ;;; considered different which is more natural for some of the
883 #!-negative-zero-is-not-zero
884 (defun convert-numeric-type (type)
885 (declare (type numeric-type type))
886 ;;; Only convert real float interval delimiters types.
887 (if (eq (numeric-type-complexp type) :real)
888 (let* ((lo (numeric-type-low type))
889 (lo-val (bound-value lo))
890 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
891 (hi (numeric-type-high type))
892 (hi-val (bound-value hi))
893 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
894 (if (or lo-float-zero-p hi-float-zero-p)
896 :class (numeric-type-class type)
897 :format (numeric-type-format type)
899 :low (if lo-float-zero-p
901 (list (float 0.0 lo-val))
904 :high (if hi-float-zero-p
906 (list (float -0.0 hi-val))
913 ;;; Convert back from the intermediate convention for which -0.0 and
914 ;;; 0.0 are considered different to the standard type convention for
916 #!-negative-zero-is-not-zero
917 (defun convert-back-numeric-type (type)
918 (declare (type numeric-type type))
919 ;;; Only convert real float interval delimiters types.
920 (if (eq (numeric-type-complexp type) :real)
921 (let* ((lo (numeric-type-low type))
922 (lo-val (bound-value lo))
924 (and lo (floatp lo-val) (= lo-val 0.0)
925 (float-sign lo-val)))
926 (hi (numeric-type-high type))
927 (hi-val (bound-value hi))
929 (and hi (floatp hi-val) (= hi-val 0.0)
930 (float-sign hi-val))))
932 ;; (float +0.0 +0.0) => (member 0.0)
933 ;; (float -0.0 -0.0) => (member -0.0)
934 ((and lo-float-zero-p hi-float-zero-p)
935 ;; Shouldn't have exclusive bounds here.
936 (assert (and (not (consp lo)) (not (consp hi))))
937 (if (= lo-float-zero-p hi-float-zero-p)
938 ;; (float +0.0 +0.0) => (member 0.0)
939 ;; (float -0.0 -0.0) => (member -0.0)
940 (specifier-type `(member ,lo-val))
941 ;; (float -0.0 +0.0) => (float 0.0 0.0)
942 ;; (float +0.0 -0.0) => (float 0.0 0.0)
943 (make-numeric-type :class (numeric-type-class type)
944 :format (numeric-type-format type)
950 ;; (float -0.0 x) => (float 0.0 x)
951 ((and (not (consp lo)) (minusp lo-float-zero-p))
952 (make-numeric-type :class (numeric-type-class type)
953 :format (numeric-type-format type)
955 :low (float 0.0 lo-val)
957 ;; (float (+0.0) x) => (float (0.0) x)
958 ((and (consp lo) (plusp lo-float-zero-p))
959 (make-numeric-type :class (numeric-type-class type)
960 :format (numeric-type-format type)
962 :low (list (float 0.0 lo-val))
965 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
966 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
967 (list (make-member-type :members (list (float 0.0 lo-val)))
968 (make-numeric-type :class (numeric-type-class type)
969 :format (numeric-type-format type)
971 :low (list (float 0.0 lo-val))
975 ;; (float x +0.0) => (float x 0.0)
976 ((and (not (consp hi)) (plusp hi-float-zero-p))
977 (make-numeric-type :class (numeric-type-class type)
978 :format (numeric-type-format type)
981 :high (float 0.0 hi-val)))
982 ;; (float x (-0.0)) => (float x (0.0))
983 ((and (consp hi) (minusp hi-float-zero-p))
984 (make-numeric-type :class (numeric-type-class type)
985 :format (numeric-type-format type)
988 :high (list (float 0.0 hi-val))))
990 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
991 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
992 (list (make-member-type :members (list (float -0.0 hi-val)))
993 (make-numeric-type :class (numeric-type-class type)
994 :format (numeric-type-format type)
997 :high (list (float 0.0 hi-val)))))))
1003 ;;; Convert back a possible list of numeric types.
1004 #!-negative-zero-is-not-zero
1005 (defun convert-back-numeric-type-list (type-list)
1008 (let ((results '()))
1009 (dolist (type type-list)
1010 (if (numeric-type-p type)
1011 (let ((result (convert-back-numeric-type type)))
1013 (setf results (append results result))
1014 (push result results)))
1015 (push type results)))
1018 (convert-back-numeric-type type-list))
1020 (convert-back-numeric-type-list (union-type-types type-list)))
1024 ;;; Make-Canonical-Union-Type
1026 ;;; Take a list of types and return a canonical type specifier,
1027 ;;; combining any members types together. If both positive and
1028 ;;; negative members types are present they are converted to a float
1029 ;;; type. X This would be far simpler if the type-union methods could
1030 ;;; handle member/number unions.
1031 (defun make-canonical-union-type (type-list)
1034 (dolist (type type-list)
1035 (if (member-type-p type)
1036 (setf members (union members (member-type-members type)))
1037 (push type misc-types)))
1039 (when (null (set-difference '(-0l0 0l0) members))
1040 #!-negative-zero-is-not-zero
1041 (push (specifier-type '(long-float 0l0 0l0)) misc-types)
1042 #!+negative-zero-is-not-zero
1043 (push (specifier-type '(long-float -0l0 0l0)) misc-types)
1044 (setf members (set-difference members '(-0l0 0l0))))
1045 (when (null (set-difference '(-0d0 0d0) members))
1046 #!-negative-zero-is-not-zero
1047 (push (specifier-type '(double-float 0d0 0d0)) misc-types)
1048 #!+negative-zero-is-not-zero
1049 (push (specifier-type '(double-float -0d0 0d0)) misc-types)
1050 (setf members (set-difference members '(-0d0 0d0))))
1051 (when (null (set-difference '(-0f0 0f0) members))
1052 #!-negative-zero-is-not-zero
1053 (push (specifier-type '(single-float 0f0 0f0)) misc-types)
1054 #!+negative-zero-is-not-zero
1055 (push (specifier-type '(single-float -0f0 0f0)) misc-types)
1056 (setf members (set-difference members '(-0f0 0f0))))
1057 (cond ((null members)
1058 (let ((res (first misc-types)))
1059 (dolist (type (rest misc-types))
1060 (setq res (type-union res type)))
1063 (make-member-type :members members))
1065 (let ((res (first misc-types)))
1066 (dolist (type (rest misc-types))
1067 (setq res (type-union res type)))
1068 (dolist (type members)
1069 (setq res (type-union
1070 res (make-member-type :members (list type)))))
1073 ;;; Convert-Member-Type
1075 ;;; Convert a member type with a single member to a numeric type.
1076 (defun convert-member-type (arg)
1077 (let* ((members (member-type-members arg))
1078 (member (first members))
1079 (member-type (type-of member)))
1080 (assert (not (rest members)))
1081 (specifier-type `(,(if (subtypep member-type 'integer)
1086 ;;; ONE-ARG-DERIVE-TYPE
1088 ;;; This is used in defoptimizers for computing the resulting type of
1091 ;;; Given the continuation ARG, derive the resulting type using the
1092 ;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
1093 ;;; "atomic" continuation type like numeric-type or member-type
1094 ;;; (containing just one element). It should return the resulting
1095 ;;; type, which can be a list of types.
1097 ;;; For the case of member types, if a member-fcn is given it is
1098 ;;; called to compute the result otherwise the member type is first
1099 ;;; converted to a numeric type and the derive-fcn is call.
1100 (defun one-arg-derive-type (arg derive-fcn member-fcn
1101 &optional (convert-type t))
1102 (declare (type function derive-fcn)
1103 (type (or null function) member-fcn)
1104 #!+negative-zero-is-not-zero (ignore convert-type))
1105 (let ((arg-list (prepare-arg-for-derive-type (continuation-type arg))))
1111 (with-float-traps-masked
1112 (:underflow :overflow :divide-by-zero)
1116 (first (member-type-members x))))))
1117 ;; Otherwise convert to a numeric type.
1118 (let ((result-type-list
1119 (funcall derive-fcn (convert-member-type x))))
1120 #!-negative-zero-is-not-zero
1122 (convert-back-numeric-type-list result-type-list)
1124 #!+negative-zero-is-not-zero
1127 #!-negative-zero-is-not-zero
1129 (convert-back-numeric-type-list
1130 (funcall derive-fcn (convert-numeric-type x)))
1131 (funcall derive-fcn x))
1132 #!+negative-zero-is-not-zero
1133 (funcall derive-fcn x))
1135 *universal-type*))))
1136 ;; Run down the list of args and derive the type of each one,
1137 ;; saving all of the results in a list.
1138 (let ((results nil))
1139 (dolist (arg arg-list)
1140 (let ((result (deriver arg)))
1142 (setf results (append results result))
1143 (push result results))))
1145 (make-canonical-union-type results)
1146 (first results)))))))
1148 ;;; TWO-ARG-DERIVE-TYPE
1150 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1151 ;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
1152 ;;; original args and a third which is T to indicate if the two args
1153 ;;; really represent the same continuation. This is useful for
1154 ;;; deriving the type of things like (* x x), which should always be
1155 ;;; positive. If we didn't do this, we wouldn't be able to tell.
1156 (defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
1157 &optional (convert-type t))
1158 #!+negative-zero-is-not-zero
1159 (declare (ignore convert-type))
1160 (flet (#!-negative-zero-is-not-zero
1161 (deriver (x y same-arg)
1162 (cond ((and (member-type-p x) (member-type-p y))
1163 (let* ((x (first (member-type-members x)))
1164 (y (first (member-type-members y)))
1165 (result (with-float-traps-masked
1166 (:underflow :overflow :divide-by-zero
1168 (funcall fcn x y))))
1169 (cond ((null result))
1170 ((and (floatp result) (float-nan-p result))
1173 :format (type-of result)
1176 (make-member-type :members (list result))))))
1177 ((and (member-type-p x) (numeric-type-p y))
1178 (let* ((x (convert-member-type x))
1179 (y (if convert-type (convert-numeric-type y) y))
1180 (result (funcall derive-fcn x y same-arg)))
1182 (convert-back-numeric-type-list result)
1184 ((and (numeric-type-p x) (member-type-p y))
1185 (let* ((x (if convert-type (convert-numeric-type x) x))
1186 (y (convert-member-type y))
1187 (result (funcall derive-fcn x y same-arg)))
1189 (convert-back-numeric-type-list result)
1191 ((and (numeric-type-p x) (numeric-type-p y))
1192 (let* ((x (if convert-type (convert-numeric-type x) x))
1193 (y (if convert-type (convert-numeric-type y) y))
1194 (result (funcall derive-fcn x y same-arg)))
1196 (convert-back-numeric-type-list result)
1200 #!+negative-zero-is-not-zero
1201 (deriver (x y same-arg)
1202 (cond ((and (member-type-p x) (member-type-p y))
1203 (let* ((x (first (member-type-members x)))
1204 (y (first (member-type-members y)))
1205 (result (with-float-traps-masked
1206 (:underflow :overflow :divide-by-zero)
1207 (funcall fcn x y))))
1209 (make-member-type :members (list result)))))
1210 ((and (member-type-p x) (numeric-type-p y))
1211 (let ((x (convert-member-type x)))
1212 (funcall derive-fcn x y same-arg)))
1213 ((and (numeric-type-p x) (member-type-p y))
1214 (let ((y (convert-member-type y)))
1215 (funcall derive-fcn x y same-arg)))
1216 ((and (numeric-type-p x) (numeric-type-p y))
1217 (funcall derive-fcn x y same-arg))
1219 *universal-type*))))
1220 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1221 (a1 (prepare-arg-for-derive-type (continuation-type arg1)))
1222 (a2 (prepare-arg-for-derive-type (continuation-type arg2))))
1224 (let ((results nil))
1226 ;; Since the args are the same continuation, just run
1229 (let ((result (deriver x x same-arg)))
1231 (setf results (append results result))
1232 (push result results))))
1233 ;; Try all pairwise combinations.
1236 (let ((result (or (deriver x y same-arg)
1237 (numeric-contagion x y))))
1239 (setf results (append results result))
1240 (push result results))))))
1242 (make-canonical-union-type results)
1243 (first results)))))))
1247 #!-propagate-float-type
1249 (defoptimizer (+ derive-type) ((x y))
1250 (derive-integer-type
1257 (values (frob (numeric-type-low x) (numeric-type-low y))
1258 (frob (numeric-type-high x) (numeric-type-high y)))))))
1260 (defoptimizer (- derive-type) ((x y))
1261 (derive-integer-type
1268 (values (frob (numeric-type-low x) (numeric-type-high y))
1269 (frob (numeric-type-high x) (numeric-type-low y)))))))
1271 (defoptimizer (* derive-type) ((x y))
1272 (derive-integer-type
1275 (let ((x-low (numeric-type-low x))
1276 (x-high (numeric-type-high x))
1277 (y-low (numeric-type-low y))
1278 (y-high (numeric-type-high y)))
1279 (cond ((not (and x-low y-low))
1281 ((or (minusp x-low) (minusp y-low))
1282 (if (and x-high y-high)
1283 (let ((max (* (max (abs x-low) (abs x-high))
1284 (max (abs y-low) (abs y-high)))))
1285 (values (- max) max))
1288 (values (* x-low y-low)
1289 (if (and x-high y-high)
1293 (defoptimizer (/ derive-type) ((x y))
1294 (numeric-contagion (continuation-type x) (continuation-type y)))
1298 #!+propagate-float-type
1300 (defun +-derive-type-aux (x y same-arg)
1301 (if (and (numeric-type-real-p x)
1302 (numeric-type-real-p y))
1305 (let ((x-int (numeric-type->interval x)))
1306 (interval-add x-int x-int))
1307 (interval-add (numeric-type->interval x)
1308 (numeric-type->interval y))))
1309 (result-type (numeric-contagion x y)))
1310 ;; If the result type is a float, we need to be sure to coerce
1311 ;; the bounds into the correct type.
1312 (when (eq (numeric-type-class result-type) 'float)
1313 (setf result (interval-func
1315 (coerce x (or (numeric-type-format result-type)
1319 :class (if (and (eq (numeric-type-class x) 'integer)
1320 (eq (numeric-type-class y) 'integer))
1321 ;; The sum of integers is always an integer
1323 (numeric-type-class result-type))
1324 :format (numeric-type-format result-type)
1325 :low (interval-low result)
1326 :high (interval-high result)))
1327 ;; General contagion
1328 (numeric-contagion x y)))
1330 (defoptimizer (+ derive-type) ((x y))
1331 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1333 (defun --derive-type-aux (x y same-arg)
1334 (if (and (numeric-type-real-p x)
1335 (numeric-type-real-p y))
1337 ;; (- x x) is always 0.
1339 (make-interval :low 0 :high 0)
1340 (interval-sub (numeric-type->interval x)
1341 (numeric-type->interval y))))
1342 (result-type (numeric-contagion x y)))
1343 ;; If the result type is a float, we need to be sure to coerce
1344 ;; the bounds into the correct type.
1345 (when (eq (numeric-type-class result-type) 'float)
1346 (setf result (interval-func
1348 (coerce x (or (numeric-type-format result-type)
1352 :class (if (and (eq (numeric-type-class x) 'integer)
1353 (eq (numeric-type-class y) 'integer))
1354 ;; The difference of integers is always an integer
1356 (numeric-type-class result-type))
1357 :format (numeric-type-format result-type)
1358 :low (interval-low result)
1359 :high (interval-high result)))
1360 ;; General contagion
1361 (numeric-contagion x y)))
1363 (defoptimizer (- derive-type) ((x y))
1364 (two-arg-derive-type x y #'--derive-type-aux #'-))
1366 (defun *-derive-type-aux (x y same-arg)
1367 (if (and (numeric-type-real-p x)
1368 (numeric-type-real-p y))
1370 ;; (* x x) is always positive, so take care to do it
1373 (interval-sqr (numeric-type->interval x))
1374 (interval-mul (numeric-type->interval x)
1375 (numeric-type->interval y))))
1376 (result-type (numeric-contagion x y)))
1377 ;; If the result type is a float, we need to be sure to coerce
1378 ;; the bounds into the correct type.
1379 (when (eq (numeric-type-class result-type) 'float)
1380 (setf result (interval-func
1382 (coerce x (or (numeric-type-format result-type)
1386 :class (if (and (eq (numeric-type-class x) 'integer)
1387 (eq (numeric-type-class y) 'integer))
1388 ;; The product of integers is always an integer
1390 (numeric-type-class result-type))
1391 :format (numeric-type-format result-type)
1392 :low (interval-low result)
1393 :high (interval-high result)))
1394 (numeric-contagion x y)))
1396 (defoptimizer (* derive-type) ((x y))
1397 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1399 (defun /-derive-type-aux (x y same-arg)
1400 (if (and (numeric-type-real-p x)
1401 (numeric-type-real-p y))
1403 ;; (/ x x) is always 1, except if x can contain 0. In
1404 ;; that case, we shouldn't optimize the division away
1405 ;; because we want 0/0 to signal an error.
1407 (not (interval-contains-p
1408 0 (interval-closure (numeric-type->interval y)))))
1409 (make-interval :low 1 :high 1)
1410 (interval-div (numeric-type->interval x)
1411 (numeric-type->interval y))))
1412 (result-type (numeric-contagion x y)))
1413 ;; If the result type is a float, we need to be sure to coerce
1414 ;; the bounds into the correct type.
1415 (when (eq (numeric-type-class result-type) 'float)
1416 (setf result (interval-func
1418 (coerce x (or (numeric-type-format result-type)
1421 (make-numeric-type :class (numeric-type-class result-type)
1422 :format (numeric-type-format result-type)
1423 :low (interval-low result)
1424 :high (interval-high result)))
1425 (numeric-contagion x y)))
1427 (defoptimizer (/ derive-type) ((x y))
1428 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1432 ;;; KLUDGE: All this ASH optimization is suppressed under CMU CL
1433 ;;; because as of version 2.4.6 for Debian, CMU CL blows up on (ASH
1434 ;;; 1000000000 -100000000000) (i.e. ASH of two bignums yielding zero)
1435 ;;; and it's hard to avoid that calculation in here.
1436 #-(and cmu sb-xc-host)
1438 #!-propagate-fun-type
1439 (defoptimizer (ash derive-type) ((n shift))
1440 (or (let ((n-type (continuation-type n)))
1441 (when (numeric-type-p n-type)
1442 (let ((n-low (numeric-type-low n-type))
1443 (n-high (numeric-type-high n-type)))
1444 (if (constant-continuation-p shift)
1445 (let ((shift (continuation-value shift)))
1446 (make-numeric-type :class 'integer
1448 :low (when n-low (ash n-low shift))
1449 :high (when n-high (ash n-high shift))))
1450 (let ((s-type (continuation-type shift)))
1451 (when (numeric-type-p s-type)
1452 (let ((s-low (numeric-type-low s-type))
1453 (s-high (numeric-type-high s-type)))
1454 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1455 (make-numeric-type :class 'integer
1458 (min (ash n-low s-high)
1461 (max (ash n-high s-high)
1462 (ash n-high s-low))))
1463 (make-numeric-type :class 'integer
1464 :complexp :real)))))))))
1466 #!+propagate-fun-type
1467 (defun ash-derive-type-aux (n-type shift same-arg)
1468 (declare (ignore same-arg))
1469 (or (and (csubtypep n-type (specifier-type 'integer))
1470 (csubtypep shift (specifier-type 'integer))
1471 (let ((n-low (numeric-type-low n-type))
1472 (n-high (numeric-type-high n-type))
1473 (s-low (numeric-type-low shift))
1474 (s-high (numeric-type-high shift)))
1475 ;; KLUDGE: The bare 64's here should be related to
1476 ;; symbolic machine word size values somehow.
1477 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1478 (make-numeric-type :class 'integer :complexp :real
1480 (min (ash n-low s-high)
1483 (max (ash n-high s-high)
1484 (ash n-high s-low))))
1485 (make-numeric-type :class 'integer
1488 #!+propagate-fun-type
1489 (defoptimizer (ash derive-type) ((n shift))
1490 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1493 #!-propagate-float-type
1494 (macrolet ((frob (fun)
1495 `#'(lambda (type type2)
1496 (declare (ignore type2))
1497 (let ((lo (numeric-type-low type))
1498 (hi (numeric-type-high type)))
1499 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1501 (defoptimizer (%negate derive-type) ((num))
1502 (derive-integer-type num num (frob -)))
1504 (defoptimizer (lognot derive-type) ((int))
1505 (derive-integer-type int int (frob lognot))))
1507 #!+propagate-float-type
1508 (defoptimizer (lognot derive-type) ((int))
1509 (derive-integer-type int int
1510 #'(lambda (type type2)
1511 (declare (ignore type2))
1512 (let ((lo (numeric-type-low type))
1513 (hi (numeric-type-high type)))
1514 (values (if hi (lognot hi) nil)
1515 (if lo (lognot lo) nil)
1516 (numeric-type-class type)
1517 (numeric-type-format type))))))
1519 #!+propagate-float-type
1520 (defoptimizer (%negate derive-type) ((num))
1521 (flet ((negate-bound (b)
1522 (set-bound (- (bound-value b)) (consp b))))
1523 (one-arg-derive-type num
1525 (let ((lo (numeric-type-low type))
1526 (hi (numeric-type-high type))
1527 (result (copy-numeric-type type)))
1528 (setf (numeric-type-low result)
1529 (if hi (negate-bound hi) nil))
1530 (setf (numeric-type-high result)
1531 (if lo (negate-bound lo) nil))
1535 #!-propagate-float-type
1536 (defoptimizer (abs derive-type) ((num))
1537 (let ((type (continuation-type num)))
1538 (if (and (numeric-type-p type)
1539 (eq (numeric-type-class type) 'integer)
1540 (eq (numeric-type-complexp type) :real))
1541 (let ((lo (numeric-type-low type))
1542 (hi (numeric-type-high type)))
1543 (make-numeric-type :class 'integer :complexp :real
1544 :low (cond ((and hi (minusp hi))
1550 :high (if (and hi lo)
1551 (max (abs hi) (abs lo))
1553 (numeric-contagion type type))))
1555 #!+propagate-float-type
1556 (defun abs-derive-type-aux (type)
1557 (cond ((eq (numeric-type-complexp type) :complex)
1558 ;; The absolute value of a complex number is always a
1559 ;; non-negative float.
1560 (let* ((format (case (numeric-type-class type)
1561 ((integer rational) 'single-float)
1562 (t (numeric-type-format type))))
1563 (bound-format (or format 'float)))
1564 (make-numeric-type :class 'float
1567 :low (coerce 0 bound-format)
1570 ;; The absolute value of a real number is a non-negative real
1571 ;; of the same type.
1572 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1573 (class (numeric-type-class type))
1574 (format (numeric-type-format type))
1575 (bound-type (or format class 'real)))
1580 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1581 :high (coerce-numeric-bound
1582 (interval-high abs-bnd) bound-type))))))
1584 #!+propagate-float-type
1585 (defoptimizer (abs derive-type) ((num))
1586 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1588 #!-propagate-float-type
1589 (defoptimizer (truncate derive-type) ((number divisor))
1590 (let ((number-type (continuation-type number))
1591 (divisor-type (continuation-type divisor))
1592 (integer-type (specifier-type 'integer)))
1593 (if (and (numeric-type-p number-type)
1594 (csubtypep number-type integer-type)
1595 (numeric-type-p divisor-type)
1596 (csubtypep divisor-type integer-type))
1597 (let ((number-low (numeric-type-low number-type))
1598 (number-high (numeric-type-high number-type))
1599 (divisor-low (numeric-type-low divisor-type))
1600 (divisor-high (numeric-type-high divisor-type)))
1601 (values-specifier-type
1602 `(values ,(integer-truncate-derive-type number-low number-high
1603 divisor-low divisor-high)
1604 ,(integer-rem-derive-type number-low number-high
1605 divisor-low divisor-high))))
1608 #-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
1610 #!+propagate-float-type
1613 (defun rem-result-type (number-type divisor-type)
1614 ;; Figure out what the remainder type is. The remainder is an
1615 ;; integer if both args are integers; a rational if both args are
1616 ;; rational; and a float otherwise.
1617 (cond ((and (csubtypep number-type (specifier-type 'integer))
1618 (csubtypep divisor-type (specifier-type 'integer)))
1620 ((and (csubtypep number-type (specifier-type 'rational))
1621 (csubtypep divisor-type (specifier-type 'rational)))
1623 ((and (csubtypep number-type (specifier-type 'float))
1624 (csubtypep divisor-type (specifier-type 'float)))
1625 ;; Both are floats so the result is also a float, of
1626 ;; the largest type.
1627 (or (float-format-max (numeric-type-format number-type)
1628 (numeric-type-format divisor-type))
1630 ((and (csubtypep number-type (specifier-type 'float))
1631 (csubtypep divisor-type (specifier-type 'rational)))
1632 ;; One of the arguments is a float and the other is a
1633 ;; rational. The remainder is a float of the same
1635 (or (numeric-type-format number-type) 'float))
1636 ((and (csubtypep divisor-type (specifier-type 'float))
1637 (csubtypep number-type (specifier-type 'rational)))
1638 ;; One of the arguments is a float and the other is a
1639 ;; rational. The remainder is a float of the same
1641 (or (numeric-type-format divisor-type) 'float))
1643 ;; Some unhandled combination. This usually means both args
1644 ;; are REAL so the result is a REAL.
1647 (defun truncate-derive-type-quot (number-type divisor-type)
1648 (let* ((rem-type (rem-result-type number-type divisor-type))
1649 (number-interval (numeric-type->interval number-type))
1650 (divisor-interval (numeric-type->interval divisor-type)))
1651 ;;(declare (type (member '(integer rational float)) rem-type))
1652 ;; We have real numbers now.
1653 (cond ((eq rem-type 'integer)
1654 ;; Since the remainder type is INTEGER, both args are
1656 (let* ((res (integer-truncate-derive-type
1657 (interval-low number-interval)
1658 (interval-high number-interval)
1659 (interval-low divisor-interval)
1660 (interval-high divisor-interval))))
1661 (specifier-type (if (listp res) res 'integer))))
1663 (let ((quot (truncate-quotient-bound
1664 (interval-div number-interval
1665 divisor-interval))))
1666 (specifier-type `(integer ,(or (interval-low quot) '*)
1667 ,(or (interval-high quot) '*))))))))
1669 (defun truncate-derive-type-rem (number-type divisor-type)
1670 (let* ((rem-type (rem-result-type number-type divisor-type))
1671 (number-interval (numeric-type->interval number-type))
1672 (divisor-interval (numeric-type->interval divisor-type))
1673 (rem (truncate-rem-bound number-interval divisor-interval)))
1674 ;;(declare (type (member '(integer rational float)) rem-type))
1675 ;; We have real numbers now.
1676 (cond ((eq rem-type 'integer)
1677 ;; Since the remainder type is INTEGER, both args are
1679 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1680 ,(or (interval-high rem) '*))))
1682 (multiple-value-bind (class format)
1685 (values 'integer nil))
1687 (values 'rational nil))
1688 ((or single-float double-float #!+long-float long-float)
1689 (values 'float rem-type))
1691 (values 'float nil))
1694 (when (member rem-type '(float single-float double-float
1695 #!+long-float long-float))
1696 (setf rem (interval-func #'(lambda (x)
1697 (coerce x rem-type))
1699 (make-numeric-type :class class
1701 :low (interval-low rem)
1702 :high (interval-high rem)))))))
1704 (defun truncate-derive-type-quot-aux (num div same-arg)
1705 (declare (ignore same-arg))
1706 (if (and (numeric-type-real-p num)
1707 (numeric-type-real-p div))
1708 (truncate-derive-type-quot num div)
1711 (defun truncate-derive-type-rem-aux (num div same-arg)
1712 (declare (ignore same-arg))
1713 (if (and (numeric-type-real-p num)
1714 (numeric-type-real-p div))
1715 (truncate-derive-type-rem num div)
1718 (defoptimizer (truncate derive-type) ((number divisor))
1719 (let ((quot (two-arg-derive-type number divisor
1720 #'truncate-derive-type-quot-aux #'truncate))
1721 (rem (two-arg-derive-type number divisor
1722 #'truncate-derive-type-rem-aux #'rem)))
1723 (when (and quot rem)
1724 (make-values-type :required (list quot rem)))))
1726 (defun ftruncate-derive-type-quot (number-type divisor-type)
1727 ;; The bounds are the same as for truncate. However, the first
1728 ;; result is a float of some type. We need to determine what that
1729 ;; type is. Basically it's the more contagious of the two types.
1730 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1731 (res-type (numeric-contagion number-type divisor-type)))
1732 (make-numeric-type :class 'float
1733 :format (numeric-type-format res-type)
1734 :low (numeric-type-low q-type)
1735 :high (numeric-type-high q-type))))
1737 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1738 (declare (ignore same-arg))
1739 (if (and (numeric-type-real-p n)
1740 (numeric-type-real-p d))
1741 (ftruncate-derive-type-quot n d)
1744 (defoptimizer (ftruncate derive-type) ((number divisor))
1746 (two-arg-derive-type number divisor
1747 #'ftruncate-derive-type-quot-aux #'ftruncate))
1748 (rem (two-arg-derive-type number divisor
1749 #'truncate-derive-type-rem-aux #'rem)))
1750 (when (and quot rem)
1751 (make-values-type :required (list quot rem)))))
1753 (defun %unary-truncate-derive-type-aux (number)
1754 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1756 (defoptimizer (%unary-truncate derive-type) ((number))
1757 (one-arg-derive-type number
1758 #'%unary-truncate-derive-type-aux
1761 ;;; Define optimizers for FLOOR and CEILING.
1763 ((frob-opt (name q-name r-name)
1764 (let ((q-aux (symbolicate q-name "-AUX"))
1765 (r-aux (symbolicate r-name "-AUX")))
1767 ;; Compute type of quotient (first) result
1768 (defun ,q-aux (number-type divisor-type)
1769 (let* ((number-interval
1770 (numeric-type->interval number-type))
1772 (numeric-type->interval divisor-type))
1773 (quot (,q-name (interval-div number-interval
1774 divisor-interval))))
1775 (specifier-type `(integer ,(or (interval-low quot) '*)
1776 ,(or (interval-high quot) '*)))))
1777 ;; Compute type of remainder
1778 (defun ,r-aux (number-type divisor-type)
1779 (let* ((divisor-interval
1780 (numeric-type->interval divisor-type))
1781 (rem (,r-name divisor-interval))
1782 (result-type (rem-result-type number-type divisor-type)))
1783 (multiple-value-bind (class format)
1786 (values 'integer nil))
1788 (values 'rational nil))
1789 ((or single-float double-float #!+long-float long-float)
1790 (values 'float result-type))
1792 (values 'float nil))
1795 (when (member result-type '(float single-float double-float
1796 #!+long-float long-float))
1797 ;; Make sure the limits on the interval have
1799 (setf rem (interval-func #'(lambda (x)
1800 (coerce x result-type))
1802 (make-numeric-type :class class
1804 :low (interval-low rem)
1805 :high (interval-high rem)))))
1806 ;; The optimizer itself
1807 (defoptimizer (,name derive-type) ((number divisor))
1808 (flet ((derive-q (n d same-arg)
1809 (declare (ignore same-arg))
1810 (if (and (numeric-type-real-p n)
1811 (numeric-type-real-p d))
1814 (derive-r (n d same-arg)
1815 (declare (ignore same-arg))
1816 (if (and (numeric-type-real-p n)
1817 (numeric-type-real-p d))
1820 (let ((quot (two-arg-derive-type
1821 number divisor #'derive-q #',name))
1822 (rem (two-arg-derive-type
1823 number divisor #'derive-r #'mod)))
1824 (when (and quot rem)
1825 (make-values-type :required (list quot rem))))))
1828 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1829 (frob-opt floor floor-quotient-bound floor-rem-bound)
1830 (frob-opt ceiling ceiling-quotient-bound ceiling-rem-bound))
1832 ;;; Define optimizers for FFLOOR and FCEILING
1834 ((frob-opt (name q-name r-name)
1835 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1836 (r-aux (symbolicate r-name "-AUX")))
1838 ;; Compute type of quotient (first) result
1839 (defun ,q-aux (number-type divisor-type)
1840 (let* ((number-interval
1841 (numeric-type->interval number-type))
1843 (numeric-type->interval divisor-type))
1844 (quot (,q-name (interval-div number-interval
1846 (res-type (numeric-contagion number-type divisor-type)))
1848 :class (numeric-type-class res-type)
1849 :format (numeric-type-format res-type)
1850 :low (interval-low quot)
1851 :high (interval-high quot))))
1853 (defoptimizer (,name derive-type) ((number divisor))
1854 (flet ((derive-q (n d same-arg)
1855 (declare (ignore same-arg))
1856 (if (and (numeric-type-real-p n)
1857 (numeric-type-real-p d))
1860 (derive-r (n d same-arg)
1861 (declare (ignore same-arg))
1862 (if (and (numeric-type-real-p n)
1863 (numeric-type-real-p d))
1866 (let ((quot (two-arg-derive-type
1867 number divisor #'derive-q #',name))
1868 (rem (two-arg-derive-type
1869 number divisor #'derive-r #'mod)))
1870 (when (and quot rem)
1871 (make-values-type :required (list quot rem))))))))))
1873 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1874 (frob-opt ffloor floor-quotient-bound floor-rem-bound)
1875 (frob-opt fceiling ceiling-quotient-bound ceiling-rem-bound))
1877 ;;; Functions to compute the bounds on the quotient and remainder for
1878 ;;; the FLOOR function.
1879 (defun floor-quotient-bound (quot)
1880 ;; Take the floor of the quotient and then massage it into what we
1882 (let ((lo (interval-low quot))
1883 (hi (interval-high quot)))
1884 ;; Take the floor of the lower bound. The result is always a
1885 ;; closed lower bound.
1887 (floor (bound-value lo))
1889 ;; For the upper bound, we need to be careful
1892 ;; An open bound. We need to be careful here because
1893 ;; the floor of '(10.0) is 9, but the floor of
1895 (multiple-value-bind (q r) (floor (first hi))
1900 ;; A closed bound, so the answer is obvious.
1904 (make-interval :low lo :high hi)))
1905 (defun floor-rem-bound (div)
1906 ;; The remainder depends only on the divisor. Try to get the
1907 ;; correct sign for the remainder if we can.
1908 (case (interval-range-info div)
1910 ;; Divisor is always positive.
1911 (let ((rem (interval-abs div)))
1912 (setf (interval-low rem) 0)
1913 (when (and (numberp (interval-high rem))
1914 (not (zerop (interval-high rem))))
1915 ;; The remainder never contains the upper bound. However,
1916 ;; watch out for the case where the high limit is zero!
1917 (setf (interval-high rem) (list (interval-high rem))))
1920 ;; Divisor is always negative
1921 (let ((rem (interval-neg (interval-abs div))))
1922 (setf (interval-high rem) 0)
1923 (when (numberp (interval-low rem))
1924 ;; The remainder never contains the lower bound.
1925 (setf (interval-low rem) (list (interval-low rem))))
1928 ;; The divisor can be positive or negative. All bets off.
1929 ;; The magnitude of remainder is the maximum value of the
1931 (let ((limit (bound-value (interval-high (interval-abs div)))))
1932 ;; The bound never reaches the limit, so make the interval open
1933 (make-interval :low (if limit
1936 :high (list limit))))))
1938 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1939 => #S(INTERVAL :LOW 0 :HIGH 10)
1940 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1941 => #S(INTERVAL :LOW 0 :HIGH 10)
1942 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1943 => #S(INTERVAL :LOW 0 :HIGH 10)
1944 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1945 => #S(INTERVAL :LOW 0 :HIGH 9)
1946 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1947 => #S(INTERVAL :LOW 0 :HIGH 10)
1948 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1949 => #S(INTERVAL :LOW 0 :HIGH 10)
1950 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1951 => #S(INTERVAL :LOW -2 :HIGH 10)
1952 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1953 => #S(INTERVAL :LOW -1 :HIGH 10)
1954 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1955 => #S(INTERVAL :LOW -1 :HIGH 10)
1957 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1958 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1959 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1960 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1961 (floor-rem-bound (make-interval :low -10 :high -2.3))
1962 #S(INTERVAL :LOW (-10) :HIGH 0)
1963 (floor-rem-bound (make-interval :low 0.3 :high 10))
1964 => #S(INTERVAL :LOW 0 :HIGH '(10))
1965 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1966 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1967 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1968 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1971 ;;; same functions for CEILING
1972 (defun ceiling-quotient-bound (quot)
1973 ;; Take the ceiling of the quotient and then massage it into what we
1975 (let ((lo (interval-low quot))
1976 (hi (interval-high quot)))
1977 ;; Take the ceiling of the upper bound. The result is always a
1978 ;; closed upper bound.
1980 (ceiling (bound-value hi))
1982 ;; For the lower bound, we need to be careful
1985 ;; An open bound. We need to be careful here because
1986 ;; the ceiling of '(10.0) is 11, but the ceiling of
1988 (multiple-value-bind (q r) (ceiling (first lo))
1993 ;; A closed bound, so the answer is obvious.
1997 (make-interval :low lo :high hi)))
1998 (defun ceiling-rem-bound (div)
1999 ;; The remainder depends only on the divisor. Try to get the
2000 ;; correct sign for the remainder if we can.
2002 (case (interval-range-info div)
2004 ;; Divisor is always positive. The remainder is negative.
2005 (let ((rem (interval-neg (interval-abs div))))
2006 (setf (interval-high rem) 0)
2007 (when (and (numberp (interval-low rem))
2008 (not (zerop (interval-low rem))))
2009 ;; The remainder never contains the upper bound. However,
2010 ;; watch out for the case when the upper bound is zero!
2011 (setf (interval-low rem) (list (interval-low rem))))
2014 ;; Divisor is always negative. The remainder is positive
2015 (let ((rem (interval-abs div)))
2016 (setf (interval-low rem) 0)
2017 (when (numberp (interval-high rem))
2018 ;; The remainder never contains the lower bound.
2019 (setf (interval-high rem) (list (interval-high rem))))
2022 ;; The divisor can be positive or negative. All bets off.
2023 ;; The magnitude of remainder is the maximum value of the
2025 (let ((limit (bound-value (interval-high (interval-abs div)))))
2026 ;; The bound never reaches the limit, so make the interval open
2027 (make-interval :low (if limit
2030 :high (list limit))))))
2033 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2034 => #S(INTERVAL :LOW 1 :HIGH 11)
2035 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2036 => #S(INTERVAL :LOW 1 :HIGH 11)
2037 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2038 => #S(INTERVAL :LOW 1 :HIGH 10)
2039 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2040 => #S(INTERVAL :LOW 1 :HIGH 10)
2041 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2042 => #S(INTERVAL :LOW 1 :HIGH 11)
2043 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2044 => #S(INTERVAL :LOW 1 :HIGH 11)
2045 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2046 => #S(INTERVAL :LOW -1 :HIGH 11)
2047 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2048 => #S(INTERVAL :LOW 0 :HIGH 11)
2049 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2050 => #S(INTERVAL :LOW -1 :HIGH 11)
2052 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2053 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2054 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2055 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2056 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2057 => #S(INTERVAL :LOW 0 :HIGH (10))
2058 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2059 => #S(INTERVAL :LOW (-10) :HIGH 0)
2060 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2061 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2062 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2063 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2066 (defun truncate-quotient-bound (quot)
2067 ;; For positive quotients, truncate is exactly like floor. For
2068 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2069 ;; it's the union of the two pieces.
2070 (case (interval-range-info quot)
2073 (floor-quotient-bound quot))
2075 ;; Just like ceiling
2076 (ceiling-quotient-bound quot))
2078 ;; Split the interval into positive and negative pieces, compute
2079 ;; the result for each piece and put them back together.
2080 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2081 (interval-merge-pair (ceiling-quotient-bound neg)
2082 (floor-quotient-bound pos))))))
2084 (defun truncate-rem-bound (num div)
2085 ;; This is significantly more complicated than floor or ceiling. We
2086 ;; need both the number and the divisor to determine the range. The
2087 ;; basic idea is to split the ranges of num and den into positive
2088 ;; and negative pieces and deal with each of the four possibilities
2090 (case (interval-range-info num)
2092 (case (interval-range-info div)
2094 (floor-rem-bound div))
2096 (ceiling-rem-bound div))
2098 (destructuring-bind (neg pos) (interval-split 0 div t t)
2099 (interval-merge-pair (truncate-rem-bound num neg)
2100 (truncate-rem-bound num pos))))))
2102 (case (interval-range-info div)
2104 (ceiling-rem-bound div))
2106 (floor-rem-bound div))
2108 (destructuring-bind (neg pos) (interval-split 0 div t t)
2109 (interval-merge-pair (truncate-rem-bound num neg)
2110 (truncate-rem-bound num pos))))))
2112 (destructuring-bind (neg pos) (interval-split 0 num t t)
2113 (interval-merge-pair (truncate-rem-bound neg div)
2114 (truncate-rem-bound pos div))))))
2117 ;;; Derive useful information about the range. Returns three values:
2118 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2119 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2120 ;;; - The abs of the maximal value if there is one, or nil if it is
2122 (defun numeric-range-info (low high)
2123 (cond ((and low (not (minusp low)))
2124 (values '+ low high))
2125 ((and high (not (plusp high)))
2126 (values '- (- high) (if low (- low) nil)))
2128 (values nil 0 (and low high (max (- low) high))))))
2130 (defun integer-truncate-derive-type
2131 (number-low number-high divisor-low divisor-high)
2132 ;; The result cannot be larger in magnitude than the number, but the sign
2133 ;; might change. If we can determine the sign of either the number or
2134 ;; the divisor, we can eliminate some of the cases.
2135 (multiple-value-bind (number-sign number-min number-max)
2136 (numeric-range-info number-low number-high)
2137 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2138 (numeric-range-info divisor-low divisor-high)
2139 (when (and divisor-max (zerop divisor-max))
2140 ;; We've got a problem: guaranteed division by zero.
2141 (return-from integer-truncate-derive-type t))
2142 (when (zerop divisor-min)
2143 ;; We'll assume that they aren't going to divide by zero.
2145 (cond ((and number-sign divisor-sign)
2146 ;; We know the sign of both.
2147 (if (eq number-sign divisor-sign)
2148 ;; Same sign, so the result will be positive.
2149 `(integer ,(if divisor-max
2150 (truncate number-min divisor-max)
2153 (truncate number-max divisor-min)
2155 ;; Different signs, the result will be negative.
2156 `(integer ,(if number-max
2157 (- (truncate number-max divisor-min))
2160 (- (truncate number-min divisor-max))
2162 ((eq divisor-sign '+)
2163 ;; The divisor is positive. Therefore, the number will just
2164 ;; become closer to zero.
2165 `(integer ,(if number-low
2166 (truncate number-low divisor-min)
2169 (truncate number-high divisor-min)
2171 ((eq divisor-sign '-)
2172 ;; The divisor is negative. Therefore, the absolute value of
2173 ;; the number will become closer to zero, but the sign will also
2175 `(integer ,(if number-high
2176 (- (truncate number-high divisor-min))
2179 (- (truncate number-low divisor-min))
2181 ;; The divisor could be either positive or negative.
2183 ;; The number we are dividing has a bound. Divide that by the
2184 ;; smallest posible divisor.
2185 (let ((bound (truncate number-max divisor-min)))
2186 `(integer ,(- bound) ,bound)))
2188 ;; The number we are dividing is unbounded, so we can't tell
2189 ;; anything about the result.
2192 #!-propagate-float-type
2193 (defun integer-rem-derive-type
2194 (number-low number-high divisor-low divisor-high)
2195 (if (and divisor-low divisor-high)
2196 ;; We know the range of the divisor, and the remainder must be smaller
2197 ;; than the divisor. We can tell the sign of the remainer if we know
2198 ;; the sign of the number.
2199 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2200 `(integer ,(if (or (null number-low)
2201 (minusp number-low))
2204 ,(if (or (null number-high)
2205 (plusp number-high))
2208 ;; The divisor is potentially either very positive or very negative.
2209 ;; Therefore, the remainer is unbounded, but we might be able to tell
2210 ;; something about the sign from the number.
2211 `(integer ,(if (and number-low (not (minusp number-low)))
2212 ;; The number we are dividing is positive. Therefore,
2213 ;; the remainder must be positive.
2216 ,(if (and number-high (not (plusp number-high)))
2217 ;; The number we are dividing is negative. Therefore,
2218 ;; the remainder must be negative.
2222 #!-propagate-float-type
2223 (defoptimizer (random derive-type) ((bound &optional state))
2224 (let ((type (continuation-type bound)))
2225 (when (numeric-type-p type)
2226 (let ((class (numeric-type-class type))
2227 (high (numeric-type-high type))
2228 (format (numeric-type-format type)))
2232 :low (coerce 0 (or format class 'real))
2233 :high (cond ((not high) nil)
2234 ((eq class 'integer) (max (1- high) 0))
2235 ((or (consp high) (zerop high)) high)
2238 #!+propagate-float-type
2239 (defun random-derive-type-aux (type)
2240 (let ((class (numeric-type-class type))
2241 (high (numeric-type-high type))
2242 (format (numeric-type-format type)))
2246 :low (coerce 0 (or format class 'real))
2247 :high (cond ((not high) nil)
2248 ((eq class 'integer) (max (1- high) 0))
2249 ((or (consp high) (zerop high)) high)
2252 #!+propagate-float-type
2253 (defoptimizer (random derive-type) ((bound &optional state))
2254 (one-arg-derive-type bound #'random-derive-type-aux nil))
2256 ;;;; logical derive-type methods
2258 ;;; Return the maximum number of bits an integer of the supplied type can take
2259 ;;; up, or NIL if it is unbounded. The second (third) value is T if the
2260 ;;; integer can be positive (negative) and NIL if not. Zero counts as
2262 (defun integer-type-length (type)
2263 (if (numeric-type-p type)
2264 (let ((min (numeric-type-low type))
2265 (max (numeric-type-high type)))
2266 (values (and min max (max (integer-length min) (integer-length max)))
2267 (or (null max) (not (minusp max)))
2268 (or (null min) (minusp min))))
2271 #!-propagate-fun-type
2273 (defoptimizer (logand derive-type) ((x y))
2274 (multiple-value-bind (x-len x-pos x-neg)
2275 (integer-type-length (continuation-type x))
2276 (declare (ignore x-pos))
2277 (multiple-value-bind (y-len y-pos y-neg)
2278 (integer-type-length (continuation-type y))
2279 (declare (ignore y-pos))
2281 ;; X must be positive.
2283 ;; The must both be positive.
2284 (cond ((or (null x-len) (null y-len))
2285 (specifier-type 'unsigned-byte))
2286 ((or (zerop x-len) (zerop y-len))
2287 (specifier-type '(integer 0 0)))
2289 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2290 ;; X is positive, but Y might be negative.
2292 (specifier-type 'unsigned-byte))
2294 (specifier-type '(integer 0 0)))
2296 (specifier-type `(unsigned-byte ,x-len)))))
2297 ;; X might be negative.
2299 ;; Y must be positive.
2301 (specifier-type 'unsigned-byte))
2303 (specifier-type '(integer 0 0)))
2306 `(unsigned-byte ,y-len))))
2307 ;; Either might be negative.
2308 (if (and x-len y-len)
2309 ;; The result is bounded.
2310 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2311 ;; We can't tell squat about the result.
2312 (specifier-type 'integer)))))))
2314 (defoptimizer (logior derive-type) ((x y))
2315 (multiple-value-bind (x-len x-pos x-neg)
2316 (integer-type-length (continuation-type x))
2317 (multiple-value-bind (y-len y-pos y-neg)
2318 (integer-type-length (continuation-type y))
2320 ((and (not x-neg) (not y-neg))
2321 ;; Both are positive.
2322 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2326 ;; X must be negative.
2328 ;; Both are negative. The result is going to be negative and be
2329 ;; the same length or shorter than the smaller.
2330 (if (and x-len y-len)
2332 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2334 (specifier-type '(integer * -1)))
2335 ;; X is negative, but we don't know about Y. The result will be
2336 ;; negative, but no more negative than X.
2338 `(integer ,(or (numeric-type-low (continuation-type x)) '*)
2341 ;; X might be either positive or negative.
2343 ;; But Y is negative. The result will be negative.
2345 `(integer ,(or (numeric-type-low (continuation-type y)) '*)
2347 ;; We don't know squat about either. It won't get any bigger.
2348 (if (and x-len y-len)
2350 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2352 (specifier-type 'integer))))))))
2354 (defoptimizer (logxor derive-type) ((x y))
2355 (multiple-value-bind (x-len x-pos x-neg)
2356 (integer-type-length (continuation-type x))
2357 (multiple-value-bind (y-len y-pos y-neg)
2358 (integer-type-length (continuation-type y))
2360 ((or (and (not x-neg) (not y-neg))
2361 (and (not x-pos) (not y-pos)))
2362 ;; Either both are negative or both are positive. The result will be
2363 ;; positive, and as long as the longer.
2364 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2367 ((or (and (not x-pos) (not y-neg))
2368 (and (not y-neg) (not y-pos)))
2369 ;; Either X is negative and Y is positive of vice-verca. The result
2370 ;; will be negative.
2371 (specifier-type `(integer ,(if (and x-len y-len)
2372 (ash -1 (max x-len y-len))
2375 ;; We can't tell what the sign of the result is going to be. All we
2376 ;; know is that we don't create new bits.
2378 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2380 (specifier-type 'integer))))))
2384 #!+propagate-fun-type
2386 (defun logand-derive-type-aux (x y &optional same-leaf)
2387 (declare (ignore same-leaf))
2388 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2389 (declare (ignore x-pos))
2390 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2391 (declare (ignore y-pos))
2393 ;; X must be positive.
2395 ;; The must both be positive.
2396 (cond ((or (null x-len) (null y-len))
2397 (specifier-type 'unsigned-byte))
2398 ((or (zerop x-len) (zerop y-len))
2399 (specifier-type '(integer 0 0)))
2401 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2402 ;; X is positive, but Y might be negative.
2404 (specifier-type 'unsigned-byte))
2406 (specifier-type '(integer 0 0)))
2408 (specifier-type `(unsigned-byte ,x-len)))))
2409 ;; X might be negative.
2411 ;; Y must be positive.
2413 (specifier-type 'unsigned-byte))
2415 (specifier-type '(integer 0 0)))
2418 `(unsigned-byte ,y-len))))
2419 ;; Either might be negative.
2420 (if (and x-len y-len)
2421 ;; The result is bounded.
2422 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2423 ;; We can't tell squat about the result.
2424 (specifier-type 'integer)))))))
2426 (defun logior-derive-type-aux (x y &optional same-leaf)
2427 (declare (ignore same-leaf))
2428 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2429 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2431 ((and (not x-neg) (not y-neg))
2432 ;; Both are positive.
2433 (if (and x-len y-len (zerop x-len) (zerop y-len))
2434 (specifier-type '(integer 0 0))
2435 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2439 ;; X must be negative.
2441 ;; Both are negative. The result is going to be negative and be
2442 ;; the same length or shorter than the smaller.
2443 (if (and x-len y-len)
2445 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2447 (specifier-type '(integer * -1)))
2448 ;; X is negative, but we don't know about Y. The result will be
2449 ;; negative, but no more negative than X.
2451 `(integer ,(or (numeric-type-low x) '*)
2454 ;; X might be either positive or negative.
2456 ;; But Y is negative. The result will be negative.
2458 `(integer ,(or (numeric-type-low y) '*)
2460 ;; We don't know squat about either. It won't get any bigger.
2461 (if (and x-len y-len)
2463 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2465 (specifier-type 'integer))))))))
2467 (defun logxor-derive-type-aux (x y &optional same-leaf)
2468 (declare (ignore same-leaf))
2469 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2470 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2472 ((or (and (not x-neg) (not y-neg))
2473 (and (not x-pos) (not y-pos)))
2474 ;; Either both are negative or both are positive. The result will be
2475 ;; positive, and as long as the longer.
2476 (if (and x-len y-len (zerop x-len) (zerop y-len))
2477 (specifier-type '(integer 0 0))
2478 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2481 ((or (and (not x-pos) (not y-neg))
2482 (and (not y-neg) (not y-pos)))
2483 ;; Either X is negative and Y is positive of vice-verca. The result
2484 ;; will be negative.
2485 (specifier-type `(integer ,(if (and x-len y-len)
2486 (ash -1 (max x-len y-len))
2489 ;; We can't tell what the sign of the result is going to be. All we
2490 ;; know is that we don't create new bits.
2492 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2494 (specifier-type 'integer))))))
2496 (macrolet ((frob (logfcn)
2497 (let ((fcn-aux (symbolicate logfcn "-DERIVE-TYPE-AUX")))
2498 `(defoptimizer (,logfcn derive-type) ((x y))
2499 (two-arg-derive-type x y #',fcn-aux #',logfcn)))))
2500 ;; FIXME: DEF-FROB, not just FROB
2505 ;; MNA: defoptimizer for integer-length patch
2506 (defoptimizer (integer-length derive-type) ((x))
2507 (let ((x-type (continuation-type x)))
2508 (when (and (numeric-type-p x-type)
2509 (csubtypep x-type (specifier-type 'integer)))
2510 ;; If the X is of type (INTEGER LO HI), then the integer-length
2511 ;; of X is (INTEGER (min lo hi) (max lo hi), basically. Be
2512 ;; careful about LO or HI being NIL, though. Also, if 0 is
2513 ;; contained in X, the lower bound is obviously 0.
2514 (flet ((null-or-min (a b)
2515 (and a b (min (integer-length a)
2516 (integer-length b))))
2518 (and a b (max (integer-length a)
2519 (integer-length b)))))
2520 (let* ((min (numeric-type-low x-type))
2521 (max (numeric-type-high x-type))
2522 (min-len (null-or-min min max))
2523 (max-len (null-or-max min max)))
2524 (when (ctypep 0 x-type)
2526 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2529 ;;;; miscellaneous derive-type methods
2531 (defoptimizer (code-char derive-type) ((code))
2532 (specifier-type 'base-char))
2534 (defoptimizer (values derive-type) ((&rest values))
2535 (values-specifier-type
2536 `(values ,@(mapcar #'(lambda (x)
2537 (type-specifier (continuation-type x)))
2540 ;;;; byte operations
2542 ;;;; We try to turn byte operations into simple logical operations. First, we
2543 ;;;; convert byte specifiers into separate size and position arguments passed
2544 ;;;; to internal %FOO functions. We then attempt to transform the %FOO
2545 ;;;; functions into boolean operations when the size and position are constant
2546 ;;;; and the operands are fixnums.
2548 (macrolet (;; Evaluate body with Size-Var and Pos-Var bound to expressions that
2549 ;; evaluate to the Size and Position of the byte-specifier form
2550 ;; Spec. We may wrap a let around the result of the body to bind
2553 ;; If the spec is a Byte form, then bind the vars to the subforms.
2554 ;; otherwise, evaluate Spec and use the Byte-Size and Byte-Position.
2555 ;; The goal of this transformation is to avoid consing up byte
2556 ;; specifiers and then immediately throwing them away.
2557 (with-byte-specifier ((size-var pos-var spec) &body body)
2558 (once-only ((spec `(macroexpand ,spec))
2560 `(if (and (consp ,spec)
2561 (eq (car ,spec) 'byte)
2562 (= (length ,spec) 3))
2563 (let ((,size-var (second ,spec))
2564 (,pos-var (third ,spec)))
2566 (let ((,size-var `(byte-size ,,temp))
2567 (,pos-var `(byte-position ,,temp)))
2568 `(let ((,,temp ,,spec))
2571 (def-source-transform ldb (spec int)
2572 (with-byte-specifier (size pos spec)
2573 `(%ldb ,size ,pos ,int)))
2575 (def-source-transform dpb (newbyte spec int)
2576 (with-byte-specifier (size pos spec)
2577 `(%dpb ,newbyte ,size ,pos ,int)))
2579 (def-source-transform mask-field (spec int)
2580 (with-byte-specifier (size pos spec)
2581 `(%mask-field ,size ,pos ,int)))
2583 (def-source-transform deposit-field (newbyte spec int)
2584 (with-byte-specifier (size pos spec)
2585 `(%deposit-field ,newbyte ,size ,pos ,int))))
2587 (defoptimizer (%ldb derive-type) ((size posn num))
2588 (let ((size (continuation-type size)))
2589 (if (and (numeric-type-p size)
2590 (csubtypep size (specifier-type 'integer)))
2591 (let ((size-high (numeric-type-high size)))
2592 (if (and size-high (<= size-high sb!vm:word-bits))
2593 (specifier-type `(unsigned-byte ,size-high))
2594 (specifier-type 'unsigned-byte)))
2597 (defoptimizer (%mask-field derive-type) ((size posn num))
2598 (let ((size (continuation-type size))
2599 (posn (continuation-type posn)))
2600 (if (and (numeric-type-p size)
2601 (csubtypep size (specifier-type 'integer))
2602 (numeric-type-p posn)
2603 (csubtypep posn (specifier-type 'integer)))
2604 (let ((size-high (numeric-type-high size))
2605 (posn-high (numeric-type-high posn)))
2606 (if (and size-high posn-high
2607 (<= (+ size-high posn-high) sb!vm:word-bits))
2608 (specifier-type `(unsigned-byte ,(+ size-high posn-high)))
2609 (specifier-type 'unsigned-byte)))
2612 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2613 (let ((size (continuation-type size))
2614 (posn (continuation-type posn))
2615 (int (continuation-type int)))
2616 (if (and (numeric-type-p size)
2617 (csubtypep size (specifier-type 'integer))
2618 (numeric-type-p posn)
2619 (csubtypep posn (specifier-type 'integer))
2620 (numeric-type-p int)
2621 (csubtypep int (specifier-type 'integer)))
2622 (let ((size-high (numeric-type-high size))
2623 (posn-high (numeric-type-high posn))
2624 (high (numeric-type-high int))
2625 (low (numeric-type-low int)))
2626 (if (and size-high posn-high high low
2627 (<= (+ size-high posn-high) sb!vm:word-bits))
2629 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2630 (max (integer-length high)
2631 (integer-length low)
2632 (+ size-high posn-high))))
2636 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2637 (let ((size (continuation-type size))
2638 (posn (continuation-type posn))
2639 (int (continuation-type int)))
2640 (if (and (numeric-type-p size)
2641 (csubtypep size (specifier-type 'integer))
2642 (numeric-type-p posn)
2643 (csubtypep posn (specifier-type 'integer))
2644 (numeric-type-p int)
2645 (csubtypep int (specifier-type 'integer)))
2646 (let ((size-high (numeric-type-high size))
2647 (posn-high (numeric-type-high posn))
2648 (high (numeric-type-high int))
2649 (low (numeric-type-low int)))
2650 (if (and size-high posn-high high low
2651 (<= (+ size-high posn-high) sb!vm:word-bits))
2653 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2654 (max (integer-length high)
2655 (integer-length low)
2656 (+ size-high posn-high))))
2660 (deftransform %ldb ((size posn int)
2661 (fixnum fixnum integer)
2662 (unsigned-byte #.sb!vm:word-bits))
2663 "convert to inline logical ops"
2664 `(logand (ash int (- posn))
2665 (ash ,(1- (ash 1 sb!vm:word-bits))
2666 (- size ,sb!vm:word-bits))))
2668 (deftransform %mask-field ((size posn int)
2669 (fixnum fixnum integer)
2670 (unsigned-byte #.sb!vm:word-bits))
2671 "convert to inline logical ops"
2673 (ash (ash ,(1- (ash 1 sb!vm:word-bits))
2674 (- size ,sb!vm:word-bits))
2677 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2678 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2679 ;;; as the result type, as that would allow result types
2680 ;;; that cover the range -2^(n-1) .. 1-2^n, instead of allowing result types
2681 ;;; of (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2683 (deftransform %dpb ((new size posn int)
2685 (unsigned-byte #.sb!vm:word-bits))
2686 "convert to inline logical ops"
2687 `(let ((mask (ldb (byte size 0) -1)))
2688 (logior (ash (logand new mask) posn)
2689 (logand int (lognot (ash mask posn))))))
2691 (deftransform %dpb ((new size posn int)
2693 (signed-byte #.sb!vm:word-bits))
2694 "convert to inline logical ops"
2695 `(let ((mask (ldb (byte size 0) -1)))
2696 (logior (ash (logand new mask) posn)
2697 (logand int (lognot (ash mask posn))))))
2699 (deftransform %deposit-field ((new size posn int)
2701 (unsigned-byte #.sb!vm:word-bits))
2702 "convert to inline logical ops"
2703 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2704 (logior (logand new mask)
2705 (logand int (lognot mask)))))
2707 (deftransform %deposit-field ((new size posn int)
2709 (signed-byte #.sb!vm:word-bits))
2710 "convert to inline logical ops"
2711 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2712 (logior (logand new mask)
2713 (logand int (lognot mask)))))
2715 ;;; miscellanous numeric transforms
2717 ;;; If a constant appears as the first arg, swap the args.
2718 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2719 (if (and (constant-continuation-p x)
2720 (not (constant-continuation-p y)))
2721 `(,(continuation-function-name (basic-combination-fun node))
2723 ,(continuation-value x))
2724 (give-up-ir1-transform)))
2726 (dolist (x '(= char= + * logior logand logxor))
2727 (%deftransform x '(function * *) #'commutative-arg-swap
2728 "place constant arg last."))
2730 ;;; Handle the case of a constant BOOLE-CODE.
2731 (deftransform boole ((op x y) * * :when :both)
2732 "convert to inline logical ops"
2733 (unless (constant-continuation-p op)
2734 (give-up-ir1-transform "BOOLE code is not a constant."))
2735 (let ((control (continuation-value op)))
2741 (#.boole-c1 '(lognot x))
2742 (#.boole-c2 '(lognot y))
2743 (#.boole-and '(logand x y))
2744 (#.boole-ior '(logior x y))
2745 (#.boole-xor '(logxor x y))
2746 (#.boole-eqv '(logeqv x y))
2747 (#.boole-nand '(lognand x y))
2748 (#.boole-nor '(lognor x y))
2749 (#.boole-andc1 '(logandc1 x y))
2750 (#.boole-andc2 '(logandc2 x y))
2751 (#.boole-orc1 '(logorc1 x y))
2752 (#.boole-orc2 '(logorc2 x y))
2754 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2757 ;;;; converting special case multiply/divide to shifts
2759 ;;; If arg is a constant power of two, turn * into a shift.
2760 (deftransform * ((x y) (integer integer) * :when :both)
2761 "convert x*2^k to shift"
2762 (unless (constant-continuation-p y)
2763 (give-up-ir1-transform))
2764 (let* ((y (continuation-value y))
2766 (len (1- (integer-length y-abs))))
2767 (unless (= y-abs (ash 1 len))
2768 (give-up-ir1-transform))
2773 ;;; If both arguments and the result are (unsigned-byte 32), try to come up
2774 ;;; with a ``better'' multiplication using multiplier recoding. There are two
2775 ;;; different ways the multiplier can be recoded. The more obvious is to shift
2776 ;;; X by the correct amount for each bit set in Y and to sum the results. But
2777 ;;; if there is a string of bits that are all set, you can add X shifted by
2778 ;;; one more then the bit position of the first set bit and subtract X shifted
2779 ;;; by the bit position of the last set bit. We can't use this second method
2780 ;;; when the high order bit is bit 31 because shifting by 32 doesn't work
2782 (deftransform * ((x y)
2783 ((unsigned-byte 32) (unsigned-byte 32))
2785 "recode as shift and add"
2786 (unless (constant-continuation-p y)
2787 (give-up-ir1-transform))
2788 (let ((y (continuation-value y))
2791 (labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x))
2796 `(+ ,result ,(tub32 next-factor))
2798 (declare (inline add))
2799 (dotimes (bitpos 32)
2801 (when (not (logbitp bitpos y))
2802 (add (if (= (1+ first-one) bitpos)
2803 ;; There is only a single bit in the string.
2805 ;; There are at least two.
2806 `(- ,(tub32 `(ash x ,bitpos))
2807 ,(tub32 `(ash x ,first-one)))))
2808 (setf first-one nil))
2809 (when (logbitp bitpos y)
2810 (setf first-one bitpos))))
2812 (cond ((= first-one 31))
2816 (add `(- ,(tub32 '(ash x 31)) ,(tub32 `(ash x ,first-one))))))
2820 ;;; If arg is a constant power of two, turn FLOOR into a shift and mask.
2821 ;;; If CEILING, add in (1- (ABS Y)) and then do FLOOR.
2822 (flet ((frob (y ceil-p)
2823 (unless (constant-continuation-p y)
2824 (give-up-ir1-transform))
2825 (let* ((y (continuation-value y))
2827 (len (1- (integer-length y-abs))))
2828 (unless (= y-abs (ash 1 len))
2829 (give-up-ir1-transform))
2830 (let ((shift (- len))
2832 `(let ,(when ceil-p `((x (+ x ,(1- y-abs)))))
2834 `(values (ash (- x) ,shift)
2835 (- (logand (- x) ,mask)))
2836 `(values (ash x ,shift)
2837 (logand x ,mask))))))))
2838 (deftransform floor ((x y) (integer integer) *)
2839 "convert division by 2^k to shift"
2841 (deftransform ceiling ((x y) (integer integer) *)
2842 "convert division by 2^k to shift"
2845 ;;; Do the same for MOD.
2846 (deftransform mod ((x y) (integer integer) * :when :both)
2847 "convert remainder mod 2^k to LOGAND"
2848 (unless (constant-continuation-p y)
2849 (give-up-ir1-transform))
2850 (let* ((y (continuation-value y))
2852 (len (1- (integer-length y-abs))))
2853 (unless (= y-abs (ash 1 len))
2854 (give-up-ir1-transform))
2855 (let ((mask (1- y-abs)))
2857 `(- (logand (- x) ,mask))
2858 `(logand x ,mask)))))
2860 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2861 (deftransform truncate ((x y) (integer integer))
2862 "convert division by 2^k to shift"
2863 (unless (constant-continuation-p y)
2864 (give-up-ir1-transform))
2865 (let* ((y (continuation-value y))
2867 (len (1- (integer-length y-abs))))
2868 (unless (= y-abs (ash 1 len))
2869 (give-up-ir1-transform))
2870 (let* ((shift (- len))
2873 (values ,(if (minusp y)
2875 `(- (ash (- x) ,shift)))
2876 (- (logand (- x) ,mask)))
2877 (values ,(if (minusp y)
2878 `(- (ash (- x) ,shift))
2880 (logand x ,mask))))))
2882 ;;; And the same for REM.
2883 (deftransform rem ((x y) (integer integer) * :when :both)
2884 "convert remainder mod 2^k to LOGAND"
2885 (unless (constant-continuation-p y)
2886 (give-up-ir1-transform))
2887 (let* ((y (continuation-value y))
2889 (len (1- (integer-length y-abs))))
2890 (unless (= y-abs (ash 1 len))
2891 (give-up-ir1-transform))
2892 (let ((mask (1- y-abs)))
2894 (- (logand (- x) ,mask))
2895 (logand x ,mask)))))
2897 ;;;; arithmetic and logical identity operation elimination
2899 ;;;; Flush calls to various arith functions that convert to the identity
2900 ;;;; function or a constant.
2902 (dolist (stuff '((ash 0 x)
2907 (logxor -1 (lognot x))
2909 (destructuring-bind (name identity result) stuff
2910 (deftransform name ((x y) `(* (constant-argument (member ,identity))) '*
2911 :eval-name t :when :both)
2912 "fold identity operations"
2915 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2916 ;;; (* 0 -4.0) is -0.0.
2917 (deftransform - ((x y) ((constant-argument (member 0)) rational) *
2919 "convert (- 0 x) to negate"
2921 (deftransform * ((x y) (rational (constant-argument (member 0))) *
2923 "convert (* x 0) to 0."
2926 ;;; Return T if in an arithmetic op including continuations X and Y, the
2927 ;;; result type is not affected by the type of X. That is, Y is at least as
2928 ;;; contagious as X.
2930 (defun not-more-contagious (x y)
2931 (declare (type continuation x y))
2932 (let ((x (continuation-type x))
2933 (y (continuation-type y)))
2934 (values (type= (numeric-contagion x y)
2935 (numeric-contagion y y)))))
2936 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2937 ;;; needs more work as valid transforms are missed; some cases are
2938 ;;; specific to particular transform functions so the use of this
2939 ;;; function may need a re-think.
2940 (defun not-more-contagious (x y)
2941 (declare (type continuation x y))
2942 (flet ((simple-numeric-type (num)
2943 (and (numeric-type-p num)
2944 ;; Return non-NIL if NUM is integer, rational, or a float
2945 ;; of some type (but not FLOAT)
2946 (case (numeric-type-class num)
2950 (numeric-type-format num))
2953 (let ((x (continuation-type x))
2954 (y (continuation-type y)))
2955 (if (and (simple-numeric-type x)
2956 (simple-numeric-type y))
2957 (values (type= (numeric-contagion x y)
2958 (numeric-contagion y y)))))))
2962 ;;; If y is not constant, not zerop, or is contagious, or a
2963 ;;; positive float +0.0 then give up.
2964 (deftransform + ((x y) (t (constant-argument t)) * :when :both)
2966 (let ((val (continuation-value y)))
2967 (unless (and (zerop val)
2968 (not (and (floatp val) (plusp (float-sign val))))
2969 (not-more-contagious y x))
2970 (give-up-ir1-transform)))
2975 ;;; If y is not constant, not zerop, or is contagious, or a
2976 ;;; negative float -0.0 then give up.
2977 (deftransform - ((x y) (t (constant-argument t)) * :when :both)
2979 (let ((val (continuation-value y)))
2980 (unless (and (zerop val)
2981 (not (and (floatp val) (minusp (float-sign val))))
2982 (not-more-contagious y x))
2983 (give-up-ir1-transform)))
2986 ;;; Fold (OP x +/-1)
2987 (dolist (stuff '((* x (%negate x))
2990 (destructuring-bind (name result minus-result) stuff
2991 (deftransform name ((x y) '(t (constant-argument real)) '* :eval-name t
2993 "fold identity operations"
2994 (let ((val (continuation-value y)))
2995 (unless (and (= (abs val) 1)
2996 (not-more-contagious y x))
2997 (give-up-ir1-transform))
2998 (if (minusp val) minus-result result)))))
3000 ;;; Fold (expt x n) into multiplications for small integral values of
3001 ;;; N; convert (expt x 1/2) to sqrt.
3002 (deftransform expt ((x y) (t (constant-argument real)) *)
3003 "recode as multiplication or sqrt"
3004 (let ((val (continuation-value y)))
3005 ;; If Y would cause the result to be promoted to the same type as
3006 ;; Y, we give up. If not, then the result will be the same type
3007 ;; as X, so we can replace the exponentiation with simple
3008 ;; multiplication and division for small integral powers.
3009 (unless (not-more-contagious y x)
3010 (give-up-ir1-transform))
3011 (cond ((zerop val) '(float 1 x))
3012 ((= val 2) '(* x x))
3013 ((= val -2) '(/ (* x x)))
3014 ((= val 3) '(* x x x))
3015 ((= val -3) '(/ (* x x x)))
3016 ((= val 1/2) '(sqrt x))
3017 ((= val -1/2) '(/ (sqrt x)))
3018 (t (give-up-ir1-transform)))))
3020 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3021 ;;; transformations?
3022 ;;; Perhaps we should have to prove that the denominator is nonzero before
3023 ;;; doing them? (Also the DOLIST over macro calls is weird. Perhaps
3024 ;;; just FROB?) -- WHN 19990917
3025 (dolist (name '(ash /))
3026 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3027 :eval-name t :when :both)
3030 (dolist (name '(truncate round floor ceiling))
3031 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3032 :eval-name t :when :both)
3036 ;;;; character operations
3038 (deftransform char-equal ((a b) (base-char base-char))
3040 '(let* ((ac (char-code a))
3042 (sum (logxor ac bc)))
3044 (when (eql sum #x20)
3045 (let ((sum (+ ac bc)))
3046 (and (> sum 161) (< sum 213)))))))
3048 (deftransform char-upcase ((x) (base-char))
3050 '(let ((n-code (char-code x)))
3051 (if (and (> n-code #o140) ; Octal 141 is #\a.
3052 (< n-code #o173)) ; Octal 172 is #\z.
3053 (code-char (logxor #x20 n-code))
3056 (deftransform char-downcase ((x) (base-char))
3058 '(let ((n-code (char-code x)))
3059 (if (and (> n-code 64) ; 65 is #\A.
3060 (< n-code 91)) ; 90 is #\Z.
3061 (code-char (logxor #x20 n-code))
3064 ;;;; equality predicate transforms
3066 ;;; Return true if X and Y are continuations whose only use is a reference
3067 ;;; to the same leaf, and the value of the leaf cannot change.
3068 (defun same-leaf-ref-p (x y)
3069 (declare (type continuation x y))
3070 (let ((x-use (continuation-use x))
3071 (y-use (continuation-use y)))
3074 (eq (ref-leaf x-use) (ref-leaf y-use))
3075 (constant-reference-p x-use))))
3077 ;;; If X and Y are the same leaf, then the result is true. Otherwise, if
3078 ;;; there is no intersection between the types of the arguments, then the
3079 ;;; result is definitely false.
3080 (deftransform simple-equality-transform ((x y) * * :defun-only t
3082 (cond ((same-leaf-ref-p x y)
3084 ((not (types-intersect (continuation-type x) (continuation-type y)))
3087 (give-up-ir1-transform))))
3089 (dolist (x '(eq char= equal))
3090 (%deftransform x '(function * *) #'simple-equality-transform))
3092 ;;; Similar to SIMPLE-EQUALITY-PREDICATE, except that we also try to convert
3093 ;;; to a type-specific predicate or EQ:
3094 ;;; -- If both args are characters, convert to CHAR=. This is better than just
3095 ;;; converting to EQ, since CHAR= may have special compilation strategies
3096 ;;; for non-standard representations, etc.
3097 ;;; -- If either arg is definitely not a number, then we can compare with EQ.
3098 ;;; -- Otherwise, we try to put the arg we know more about second. If X is
3099 ;;; constant then we put it second. If X is a subtype of Y, we put it
3100 ;;; second. These rules make it easier for the back end to match these
3101 ;;; interesting cases.
3102 ;;; -- If Y is a fixnum, then we quietly pass because the back end can handle
3103 ;;; that case, otherwise give an efficency note.
3104 (deftransform eql ((x y) * * :when :both)
3105 "convert to simpler equality predicate"
3106 (let ((x-type (continuation-type x))
3107 (y-type (continuation-type y))
3108 (char-type (specifier-type 'character))
3109 (number-type (specifier-type 'number)))
3110 (cond ((same-leaf-ref-p x y)
3112 ((not (types-intersect x-type y-type))
3114 ((and (csubtypep x-type char-type)
3115 (csubtypep y-type char-type))
3117 ((or (not (types-intersect x-type number-type))
3118 (not (types-intersect y-type number-type)))
3120 ((and (not (constant-continuation-p y))
3121 (or (constant-continuation-p x)
3122 (and (csubtypep x-type y-type)
3123 (not (csubtypep y-type x-type)))))
3126 (give-up-ir1-transform)))))
3128 ;;; Convert to EQL if both args are rational and complexp is specified
3129 ;;; and the same for both.
3130 (deftransform = ((x y) * * :when :both)
3132 (let ((x-type (continuation-type x))
3133 (y-type (continuation-type y)))
3134 (if (and (csubtypep x-type (specifier-type 'number))
3135 (csubtypep y-type (specifier-type 'number)))
3136 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3137 (csubtypep y-type (specifier-type 'float)))
3138 (and (csubtypep x-type (specifier-type '(complex float)))
3139 (csubtypep y-type (specifier-type '(complex float)))))
3140 ;; They are both floats. Leave as = so that -0.0 is
3141 ;; handled correctly.
3142 (give-up-ir1-transform))
3143 ((or (and (csubtypep x-type (specifier-type 'rational))
3144 (csubtypep y-type (specifier-type 'rational)))
3145 (and (csubtypep x-type (specifier-type '(complex rational)))
3146 (csubtypep y-type (specifier-type '(complex rational)))))
3147 ;; They are both rationals and complexp is the same. Convert
3151 (give-up-ir1-transform
3152 "The operands might not be the same type.")))
3153 (give-up-ir1-transform
3154 "The operands might not be the same type."))))
3156 ;;; If Cont's type is a numeric type, then return the type, otherwise
3157 ;;; GIVE-UP-IR1-TRANSFORM.
3158 (defun numeric-type-or-lose (cont)
3159 (declare (type continuation cont))
3160 (let ((res (continuation-type cont)))
3161 (unless (numeric-type-p res) (give-up-ir1-transform))
3164 ;;; See whether we can statically determine (< X Y) using type information.
3165 ;;; If X's high bound is < Y's low, then X < Y. Similarly, if X's low is >=
3166 ;;; to Y's high, the X >= Y (so return NIL). If not, at least make sure any
3167 ;;; constant arg is second.
3169 ;;; KLUDGE: Why should constant argument be second? It would be nice to find
3170 ;;; out and explain. -- WHN 19990917
3171 #!-propagate-float-type
3172 (defun ir1-transform-< (x y first second inverse)
3173 (if (same-leaf-ref-p x y)
3175 (let* ((x-type (numeric-type-or-lose x))
3176 (x-lo (numeric-type-low x-type))
3177 (x-hi (numeric-type-high x-type))
3178 (y-type (numeric-type-or-lose y))
3179 (y-lo (numeric-type-low y-type))
3180 (y-hi (numeric-type-high y-type)))
3181 (cond ((and x-hi y-lo (< x-hi y-lo))
3183 ((and y-hi x-lo (>= x-lo y-hi))
3185 ((and (constant-continuation-p first)
3186 (not (constant-continuation-p second)))
3189 (give-up-ir1-transform))))))
3190 #!+propagate-float-type
3191 (defun ir1-transform-< (x y first second inverse)
3192 (if (same-leaf-ref-p x y)
3194 (let ((xi (numeric-type->interval (numeric-type-or-lose x)))
3195 (yi (numeric-type->interval (numeric-type-or-lose y))))
3196 (cond ((interval-< xi yi)
3198 ((interval->= xi yi)
3200 ((and (constant-continuation-p first)
3201 (not (constant-continuation-p second)))
3204 (give-up-ir1-transform))))))
3206 (deftransform < ((x y) (integer integer) * :when :both)
3207 (ir1-transform-< x y x y '>))
3209 (deftransform > ((x y) (integer integer) * :when :both)
3210 (ir1-transform-< y x x y '<))
3212 #!+propagate-float-type
3213 (deftransform < ((x y) (float float) * :when :both)
3214 (ir1-transform-< x y x y '>))
3216 #!+propagate-float-type
3217 (deftransform > ((x y) (float float) * :when :both)
3218 (ir1-transform-< y x x y '<))
3220 ;;;; converting N-arg comparisons
3222 ;;;; We convert calls to N-arg comparison functions such as < into
3223 ;;;; two-arg calls. This transformation is enabled for all such
3224 ;;;; comparisons in this file. If any of these predicates are not
3225 ;;;; open-coded, then the transformation should be removed at some
3226 ;;;; point to avoid pessimization.
3228 ;;; This function is used for source transformation of N-arg
3229 ;;; comparison functions other than inequality. We deal both with
3230 ;;; converting to two-arg calls and inverting the sense of the test,
3231 ;;; if necessary. If the call has two args, then we pass or return a
3232 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3233 ;;; then we transform to code that returns true. Otherwise, we bind
3234 ;;; all the arguments and expand into a bunch of IFs.
3235 (declaim (ftype (function (symbol list boolean) *) multi-compare))
3236 (defun multi-compare (predicate args not-p)
3237 (let ((nargs (length args)))
3238 (cond ((< nargs 1) (values nil t))
3239 ((= nargs 1) `(progn ,@args t))
3242 `(if (,predicate ,(first args) ,(second args)) nil t)
3245 (do* ((i (1- nargs) (1- i))
3247 (current (gensym) (gensym))
3248 (vars (list current) (cons current vars))
3249 (result 't (if not-p
3250 `(if (,predicate ,current ,last)
3252 `(if (,predicate ,current ,last)
3255 `((lambda ,vars ,result) . ,args)))))))
3257 (def-source-transform = (&rest args) (multi-compare '= args nil))
3258 (def-source-transform < (&rest args) (multi-compare '< args nil))
3259 (def-source-transform > (&rest args) (multi-compare '> args nil))
3260 (def-source-transform <= (&rest args) (multi-compare '> args t))
3261 (def-source-transform >= (&rest args) (multi-compare '< args t))
3263 (def-source-transform char= (&rest args) (multi-compare 'char= args nil))
3264 (def-source-transform char< (&rest args) (multi-compare 'char< args nil))
3265 (def-source-transform char> (&rest args) (multi-compare 'char> args nil))
3266 (def-source-transform char<= (&rest args) (multi-compare 'char> args t))
3267 (def-source-transform char>= (&rest args) (multi-compare 'char< args t))
3269 (def-source-transform char-equal (&rest args) (multi-compare 'char-equal args nil))
3270 (def-source-transform char-lessp (&rest args) (multi-compare 'char-lessp args nil))
3271 (def-source-transform char-greaterp (&rest args) (multi-compare 'char-greaterp args nil))
3272 (def-source-transform char-not-greaterp (&rest args) (multi-compare 'char-greaterp args t))
3273 (def-source-transform char-not-lessp (&rest args) (multi-compare 'char-lessp args t))
3275 ;;; This function does source transformation of N-arg inequality
3276 ;;; functions such as /=. This is similar to Multi-Compare in the <3
3277 ;;; arg cases. If there are more than two args, then we expand into
3278 ;;; the appropriate n^2 comparisons only when speed is important.
3279 (declaim (ftype (function (symbol list) *) multi-not-equal))
3280 (defun multi-not-equal (predicate args)
3281 (let ((nargs (length args)))
3282 (cond ((< nargs 1) (values nil t))
3283 ((= nargs 1) `(progn ,@args t))
3285 `(if (,predicate ,(first args) ,(second args)) nil t))
3286 ((not (policy nil (>= speed space) (>= speed cspeed)))
3289 (let ((vars (make-gensym-list nargs)))
3290 (do ((var vars next)
3291 (next (cdr vars) (cdr next))
3294 `((lambda ,vars ,result) . ,args))
3295 (let ((v1 (first var)))
3297 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3299 (def-source-transform /= (&rest args) (multi-not-equal '= args))
3300 (def-source-transform char/= (&rest args) (multi-not-equal 'char= args))
3301 (def-source-transform char-not-equal (&rest args) (multi-not-equal 'char-equal args))
3303 ;;; Expand MAX and MIN into the obvious comparisons.
3304 (def-source-transform max (arg &rest more-args)
3305 (if (null more-args)
3307 (once-only ((arg1 arg)
3308 (arg2 `(max ,@more-args)))
3309 `(if (> ,arg1 ,arg2)
3311 (def-source-transform min (arg &rest more-args)
3312 (if (null more-args)
3314 (once-only ((arg1 arg)
3315 (arg2 `(min ,@more-args)))
3316 `(if (< ,arg1 ,arg2)
3319 ;;;; converting N-arg arithmetic functions
3321 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3322 ;;;; versions, and degenerate cases are flushed.
3324 ;;; Left-associate First-Arg and More-Args using Function.
3325 (declaim (ftype (function (symbol t list) list) associate-arguments))
3326 (defun associate-arguments (function first-arg more-args)
3327 (let ((next (rest more-args))
3328 (arg (first more-args)))
3330 `(,function ,first-arg ,arg)
3331 (associate-arguments function `(,function ,first-arg ,arg) next))))
3333 ;;; Do source transformations for transitive functions such as +.
3334 ;;; One-arg cases are replaced with the arg and zero arg cases with
3335 ;;; the identity. If Leaf-Fun is true, then replace two-arg calls with
3336 ;;; a call to that function.
3337 (defun source-transform-transitive (fun args identity &optional leaf-fun)
3338 (declare (symbol fun leaf-fun) (list args))
3341 (1 `(values ,(first args)))
3343 `(,leaf-fun ,(first args) ,(second args))
3346 (associate-arguments fun (first args) (rest args)))))
3348 (def-source-transform + (&rest args) (source-transform-transitive '+ args 0))
3349 (def-source-transform * (&rest args) (source-transform-transitive '* args 1))
3350 (def-source-transform logior (&rest args) (source-transform-transitive 'logior args 0))
3351 (def-source-transform logxor (&rest args) (source-transform-transitive 'logxor args 0))
3352 (def-source-transform logand (&rest args) (source-transform-transitive 'logand args -1))
3354 (def-source-transform logeqv (&rest args)
3355 (if (evenp (length args))
3356 `(lognot (logxor ,@args))
3359 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3360 ;;; because when they are given one argument, they return its absolute
3363 (def-source-transform gcd (&rest args)
3366 (1 `(abs (the integer ,(first args))))
3368 (t (associate-arguments 'gcd (first args) (rest args)))))
3370 (def-source-transform lcm (&rest args)
3373 (1 `(abs (the integer ,(first args))))
3375 (t (associate-arguments 'lcm (first args) (rest args)))))
3377 ;;; Do source transformations for intransitive n-arg functions such as
3378 ;;; /. With one arg, we form the inverse. With two args we pass.
3379 ;;; Otherwise we associate into two-arg calls.
3380 (declaim (ftype (function (symbol list t) list) source-transform-intransitive))
3381 (defun source-transform-intransitive (function args inverse)
3383 ((0 2) (values nil t))
3384 (1 `(,@inverse ,(first args)))
3385 (t (associate-arguments function (first args) (rest args)))))
3387 (def-source-transform - (&rest args)
3388 (source-transform-intransitive '- args '(%negate)))
3389 (def-source-transform / (&rest args)
3390 (source-transform-intransitive '/ args '(/ 1)))
3394 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3395 ;;; only needs to understand one kind of variable-argument call. It is
3396 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3397 (def-source-transform apply (fun arg &rest more-args)
3398 (let ((args (cons arg more-args)))
3399 `(multiple-value-call ,fun
3400 ,@(mapcar #'(lambda (x)
3403 (values-list ,(car (last args))))))
3407 ;;;; If the control string is a compile-time constant, then replace it
3408 ;;;; with a use of the FORMATTER macro so that the control string is
3409 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3410 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3411 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3413 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3414 :policy (> speed space))
3415 (unless (constant-continuation-p control)
3416 (give-up-ir1-transform "The control string is not a constant."))
3417 (let ((arg-names (make-gensym-list (length args))))
3418 `(lambda (dest control ,@arg-names)
3419 (declare (ignore control))
3420 (format dest (formatter ,(continuation-value control)) ,@arg-names))))
3422 (deftransform format ((stream control &rest args) (stream function &rest t) *
3423 :policy (> speed space))
3424 (let ((arg-names (make-gensym-list (length args))))
3425 `(lambda (stream control ,@arg-names)
3426 (funcall control stream ,@arg-names)
3429 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3430 :policy (> speed space))
3431 (let ((arg-names (make-gensym-list (length args))))
3432 `(lambda (tee control ,@arg-names)
3433 (declare (ignore tee))
3434 (funcall control *standard-output* ,@arg-names)