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. The assertion will be
22 ;;; optimized away when SAFETY optimization is low; hopefully that
23 ;;; is consistent with ANSI's "should return an error".
24 (def-source-transform endp (x) `(null (the list ,x)))
26 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
27 ;;; returns the first value of its argument. Ditto for VALUES with one
29 (def-source-transform identity (x) `(prog1 ,x))
30 (def-source-transform values (x) `(prog1 ,x))
32 ;;; Bind the values and make a closure that returns them.
33 (def-source-transform constantly (value)
34 (let ((rest (gensym "CONSTANTLY-REST-")))
35 `(lambda (&rest ,rest)
36 (declare (ignore ,rest))
39 ;;; If the function has a known number of arguments, then return a
40 ;;; lambda with the appropriate fixed number of args. If the
41 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
42 ;;; MV optimization figure things out.
43 (deftransform complement ((fun) * * :node node :when :both)
45 (multiple-value-bind (min max)
46 (function-type-nargs (continuation-type fun))
48 ((and min (eql min max))
49 (let ((dums (make-gensym-list min)))
50 `#'(lambda ,dums (not (funcall fun ,@dums)))))
51 ((let* ((cont (node-cont node))
52 (dest (continuation-dest cont)))
53 (and (combination-p dest)
54 (eq (combination-fun dest) cont)))
55 '#'(lambda (&rest args)
56 (not (apply fun args))))
58 (give-up-ir1-transform
59 "The function doesn't have a fixed argument count.")))))
63 ;;; Translate CxxR into CAR/CDR combos.
65 (defun source-transform-cxr (form)
66 (if (or (byte-compiling) (/= (length form) 2))
68 (let ((name (symbol-name (car form))))
69 (do ((i (- (length name) 2) (1- i))
71 `(,(ecase (char name i)
78 (b '(1 0) (cons i b)))
80 (dotimes (j (ash 1 i))
81 (setf (info :function :source-transform
82 (intern (format nil "C~{~:[A~;D~]~}R"
83 (mapcar #'(lambda (x) (logbitp x j)) b))))
84 #'source-transform-cxr)))
86 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
87 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
88 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
90 (def-source-transform first (x) `(car ,x))
91 (def-source-transform rest (x) `(cdr ,x))
92 (def-source-transform second (x) `(cadr ,x))
93 (def-source-transform third (x) `(caddr ,x))
94 (def-source-transform fourth (x) `(cadddr ,x))
95 (def-source-transform fifth (x) `(nth 4 ,x))
96 (def-source-transform sixth (x) `(nth 5 ,x))
97 (def-source-transform seventh (x) `(nth 6 ,x))
98 (def-source-transform eighth (x) `(nth 7 ,x))
99 (def-source-transform ninth (x) `(nth 8 ,x))
100 (def-source-transform tenth (x) `(nth 9 ,x))
102 ;;; Translate RPLACx to LET and SETF.
103 (def-source-transform rplaca (x y)
108 (def-source-transform rplacd (x y)
114 (def-source-transform nth (n l) `(car (nthcdr ,n ,l)))
116 (defvar *default-nthcdr-open-code-limit* 6)
117 (defvar *extreme-nthcdr-open-code-limit* 20)
119 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
120 "convert NTHCDR to CAxxR"
121 (unless (constant-continuation-p n)
122 (give-up-ir1-transform))
123 (let ((n (continuation-value n)))
125 (if (policy node (and (= speed 3) (= space 0)))
126 *extreme-nthcdr-open-code-limit*
127 *default-nthcdr-open-code-limit*))
128 (give-up-ir1-transform))
133 `(cdr ,(frob (1- n))))))
136 ;;;; arithmetic and numerology
138 (def-source-transform plusp (x) `(> ,x 0))
139 (def-source-transform minusp (x) `(< ,x 0))
140 (def-source-transform zerop (x) `(= ,x 0))
142 (def-source-transform 1+ (x) `(+ ,x 1))
143 (def-source-transform 1- (x) `(- ,x 1))
145 (def-source-transform oddp (x) `(not (zerop (logand ,x 1))))
146 (def-source-transform evenp (x) `(zerop (logand ,x 1)))
148 ;;; Note that all the integer division functions are available for
149 ;;; inline expansion.
151 ;;; FIXME: DEF-FROB instead of FROB
152 (macrolet ((frob (fun)
153 `(def-source-transform ,fun (x &optional (y nil y-p))
160 #!+propagate-float-type
162 #!+propagate-float-type
165 (def-source-transform lognand (x y) `(lognot (logand ,x ,y)))
166 (def-source-transform lognor (x y) `(lognot (logior ,x ,y)))
167 (def-source-transform logandc1 (x y) `(logand (lognot ,x) ,y))
168 (def-source-transform logandc2 (x y) `(logand ,x (lognot ,y)))
169 (def-source-transform logorc1 (x y) `(logior (lognot ,x) ,y))
170 (def-source-transform logorc2 (x y) `(logior ,x (lognot ,y)))
171 (def-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
172 (def-source-transform logbitp (index integer)
173 `(not (zerop (logand (ash 1 ,index) ,integer))))
174 (def-source-transform byte (size position) `(cons ,size ,position))
175 (def-source-transform byte-size (spec) `(car ,spec))
176 (def-source-transform byte-position (spec) `(cdr ,spec))
177 (def-source-transform ldb-test (bytespec integer)
178 `(not (zerop (mask-field ,bytespec ,integer))))
180 ;;; With the ratio and complex accessors, we pick off the "identity"
181 ;;; case, and use a primitive to handle the cell access case.
182 (def-source-transform numerator (num)
183 (once-only ((n-num `(the rational ,num)))
187 (def-source-transform denominator (num)
188 (once-only ((n-num `(the rational ,num)))
190 (%denominator ,n-num)
193 ;;;; Interval arithmetic for computing bounds
194 ;;;; (toy@rtp.ericsson.se)
196 ;;;; This is a set of routines for operating on intervals. It
197 ;;;; implements a simple interval arithmetic package. Although SBCL
198 ;;;; has an interval type in numeric-type, we choose to use our own
199 ;;;; for two reasons:
201 ;;;; 1. This package is simpler than numeric-type
203 ;;;; 2. It makes debugging much easier because you can just strip
204 ;;;; out these routines and test them independently of SBCL. (a
207 ;;;; One disadvantage is a probable increase in consing because we
208 ;;;; have to create these new interval structures even though
209 ;;;; numeric-type has everything we want to know. Reason 2 wins for
212 #-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
214 #!+propagate-float-type
217 ;;; The basic interval type. It can handle open and closed intervals.
218 ;;; A bound is open if it is a list containing a number, just like
219 ;;; Lisp says. NIL means unbounded.
221 (:constructor %make-interval))
224 (defun make-interval (&key low high)
225 (labels ((normalize-bound (val)
226 (cond ((and (floatp val)
227 (float-infinity-p val))
232 ;; Handle any closed bounds
235 ;; We have an open bound. Normalize the numeric
236 ;; bound. If the normalized bound is still a number
237 ;; (not nil), keep the bound open. Otherwise, the
238 ;; bound is really unbounded, so drop the openness.
239 (let ((new-val (normalize-bound (first val))))
241 ;; Bound exists, so keep it open still
244 (error "Unknown bound type in make-interval!")))))
245 (%make-interval :low (normalize-bound low)
246 :high (normalize-bound high))))
248 #!-sb-fluid (declaim (inline bound-value set-bound))
250 ;;; Extract the numeric value of a bound. Return NIL, if X is NIL.
251 (defun bound-value (x)
252 (if (consp x) (car x) x))
254 ;;; Given a number X, create a form suitable as a bound for an
255 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
256 (defun set-bound (x open-p)
257 (if (and x open-p) (list x) x))
259 ;;; Apply the function F to a bound X. If X is an open bound, then
260 ;;; the result will be open. IF X is NIL, the result is NIL.
261 (defun bound-func (f x)
263 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
264 ;; With these traps masked, we might get things like infinity
265 ;; or negative infinity returned. Check for this and return
266 ;; NIL to indicate unbounded.
267 (let ((y (funcall f (bound-value x))))
269 (float-infinity-p y))
271 (set-bound (funcall f (bound-value x)) (consp x)))))))
273 ;;; Apply a binary operator OP to two bounds X and Y. The result is
274 ;;; NIL if either is NIL. Otherwise bound is computed and the result
275 ;;; is open if either X or Y is open.
277 ;;; FIXME: only used in this file, not needed in target runtime
278 (defmacro bound-binop (op x y)
280 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
281 (set-bound (,op (bound-value ,x)
283 (or (consp ,x) (consp ,y))))))
285 ;;; NUMERIC-TYPE->INTERVAL
287 ;;; Convert a numeric-type object to an interval object.
289 (defun numeric-type->interval (x)
290 (declare (type numeric-type x))
291 (make-interval :low (numeric-type-low x)
292 :high (numeric-type-high x)))
294 (defun copy-interval-limit (limit)
299 (defun copy-interval (x)
300 (declare (type interval x))
301 (make-interval :low (copy-interval-limit (interval-low x))
302 :high (copy-interval-limit (interval-high x))))
306 ;;; Given a point P contained in the interval X, split X into two
307 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
308 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
309 ;;; contains P. You can specify both to be T or NIL.
310 (defun interval-split (p x &optional close-lower close-upper)
311 (declare (type number p)
313 (list (make-interval :low (copy-interval-limit (interval-low x))
314 :high (if close-lower p (list p)))
315 (make-interval :low (if close-upper (list p) p)
316 :high (copy-interval-limit (interval-high x)))))
320 ;;; Return the closure of the interval. That is, convert open bounds
321 ;;; to closed bounds.
322 (defun interval-closure (x)
323 (declare (type interval x))
324 (make-interval :low (bound-value (interval-low x))
325 :high (bound-value (interval-high x))))
327 (defun signed-zero->= (x y)
331 (>= (float-sign (float x))
332 (float-sign (float y))))))
334 ;;; INTERVAL-RANGE-INFO
336 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
337 ;;; '-. Otherwise return NIL.
339 (defun interval-range-info (x &optional (point 0))
340 (declare (type interval x))
341 (let ((lo (interval-low x))
342 (hi (interval-high x)))
343 (cond ((and lo (signed-zero->= (bound-value lo) point))
345 ((and hi (signed-zero->= point (bound-value hi)))
349 (defun interval-range-info (x &optional (point 0))
350 (declare (type interval x))
351 (labels ((signed->= (x y)
352 (if (and (zerop x) (zerop y) (floatp x) (floatp y))
353 (>= (float-sign x) (float-sign y))
355 (let ((lo (interval-low x))
356 (hi (interval-high x)))
357 (cond ((and lo (signed->= (bound-value lo) point))
359 ((and hi (signed->= point (bound-value hi)))
364 ;;; INTERVAL-BOUNDED-P
366 ;;; Test to see whether the interval X is bounded. HOW determines the
367 ;;; test, and should be either ABOVE, BELOW, or BOTH.
368 (defun interval-bounded-p (x how)
369 (declare (type interval x))
376 (and (interval-low x) (interval-high x)))))
378 ;;; Signed zero comparison functions. Use these functions if we need
379 ;;; to distinguish between signed zeroes.
381 (defun signed-zero-< (x y)
385 (< (float-sign (float x))
386 (float-sign (float y))))))
387 (defun signed-zero-> (x y)
391 (> (float-sign (float x))
392 (float-sign (float y))))))
394 (defun signed-zero-= (x y)
397 (= (float-sign (float x))
398 (float-sign (float y)))))
400 (defun signed-zero-<= (x y)
404 (<= (float-sign (float x))
405 (float-sign (float y))))))
407 ;;; INTERVAL-CONTAINS-P
409 ;;; See whether the interval X contains the number P, taking into account
410 ;;; that the interval might not be closed.
411 (defun interval-contains-p (p x)
412 (declare (type number p)
414 ;; Does the interval X contain the number P? This would be a lot
415 ;; easier if all intervals were closed!
416 (let ((lo (interval-low x))
417 (hi (interval-high x)))
419 ;; The interval is bounded
420 (if (and (signed-zero-<= (bound-value lo) p)
421 (signed-zero-<= p (bound-value hi)))
422 ;; P is definitely in the closure of the interval.
423 ;; We just need to check the end points now.
424 (cond ((signed-zero-= p (bound-value lo))
426 ((signed-zero-= p (bound-value hi))
431 ;; Interval with upper bound
432 (if (signed-zero-< p (bound-value hi))
434 (and (numberp hi) (signed-zero-= p hi))))
436 ;; Interval with lower bound
437 (if (signed-zero-> p (bound-value lo))
439 (and (numberp lo) (signed-zero-= p lo))))
441 ;; Interval with no bounds
444 ;;; INTERVAL-INTERSECT-P
446 ;;; Determine if two intervals X and Y intersect. Return T if so. If
447 ;;; CLOSED-INTERVALS-P is T, the treat the intervals as if they were
448 ;;; closed. Otherwise the intervals are treated as they are.
450 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
451 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
452 ;;; is T, then they do intersect because we use the closure of X = [0,
453 ;;; 1] and Y = [1, 2] to determine intersection.
454 (defun interval-intersect-p (x y &optional closed-intervals-p)
455 (declare (type interval x y))
456 (multiple-value-bind (intersect diff)
457 (interval-intersection/difference (if closed-intervals-p
460 (if closed-intervals-p
463 (declare (ignore diff))
466 ;;; Are the two intervals adjacent? That is, is there a number
467 ;;; between the two intervals that is not an element of either
468 ;;; interval? If so, they are not adjacent. For example [0, 1) and
469 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
470 ;;; between both intervals.
471 (defun interval-adjacent-p (x y)
472 (declare (type interval x y))
473 (flet ((adjacent (lo hi)
474 ;; Check to see whether lo and hi are adjacent. If either is
475 ;; nil, they can't be adjacent.
476 (when (and lo hi (= (bound-value lo) (bound-value hi)))
477 ;; The bounds are equal. They are adjacent if one of
478 ;; them is closed (a number). If both are open (consp),
479 ;; then there is a number that lies between them.
480 (or (numberp lo) (numberp hi)))))
481 (or (adjacent (interval-low y) (interval-high x))
482 (adjacent (interval-low x) (interval-high y)))))
484 ;;; INTERVAL-INTERSECTION/DIFFERENCE
486 ;;; Compute the intersection and difference between two intervals.
487 ;;; Two values are returned: the intersection and the difference.
489 ;;; Let the two intervals be X and Y, and let I and D be the two
490 ;;; values returned by this function. Then I = X intersect Y. If I
491 ;;; is NIL (the empty set), then D is X union Y, represented as the
492 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
493 ;;; - I, which is a list of two intervals.
495 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
496 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
497 (defun interval-intersection/difference (x y)
498 (declare (type interval x y))
499 (let ((x-lo (interval-low x))
500 (x-hi (interval-high x))
501 (y-lo (interval-low y))
502 (y-hi (interval-high y)))
505 ;; If p is an open bound, make it closed. If p is a closed
506 ;; bound, make it open.
511 ;; Test whether P is in the interval.
512 (when (interval-contains-p (bound-value p)
513 (interval-closure int))
514 (let ((lo (interval-low int))
515 (hi (interval-high int)))
516 ;; Check for endpoints
517 (cond ((and lo (= (bound-value p) (bound-value lo)))
518 (not (and (consp p) (numberp lo))))
519 ((and hi (= (bound-value p) (bound-value hi)))
520 (not (and (numberp p) (consp hi))))
522 (test-lower-bound (p int)
523 ;; P is a lower bound of an interval.
526 (not (interval-bounded-p int 'below))))
527 (test-upper-bound (p int)
528 ;; P is an upper bound of an interval
531 (not (interval-bounded-p int 'above)))))
532 (let ((x-lo-in-y (test-lower-bound x-lo y))
533 (x-hi-in-y (test-upper-bound x-hi y))
534 (y-lo-in-x (test-lower-bound y-lo x))
535 (y-hi-in-x (test-upper-bound y-hi x)))
536 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
537 ;; Intervals intersect. Let's compute the intersection
538 ;; and the difference.
539 (multiple-value-bind (lo left-lo left-hi)
540 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
541 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
542 (multiple-value-bind (hi right-lo right-hi)
544 (values x-hi (opposite-bound x-hi) y-hi))
546 (values y-hi (opposite-bound y-hi) x-hi)))
547 (values (make-interval :low lo :high hi)
548 (list (make-interval :low left-lo :high left-hi)
549 (make-interval :low right-lo :high right-hi))))))
551 (values nil (list x y))))))))
553 ;;; INTERVAL-MERGE-PAIR
555 ;;; If intervals X and Y intersect, return a new interval that is the
556 ;;; union of the two. If they do not intersect, return NIL.
557 (defun interval-merge-pair (x y)
558 (declare (type interval x y))
559 ;; If x and y intersect or are adjacent, create the union.
560 ;; Otherwise return nil
561 (when (or (interval-intersect-p x y)
562 (interval-adjacent-p x y))
563 (flet ((select-bound (x1 x2 min-op max-op)
564 (let ((x1-val (bound-value x1))
565 (x2-val (bound-value x2)))
567 ;; Both bounds are finite. Select the right one.
568 (cond ((funcall min-op x1-val x2-val)
569 ;; x1 definitely better
571 ((funcall max-op x1-val x2-val)
572 ;; x2 definitely better
575 ;; Bounds are equal. Select either
576 ;; value and make it open only if
578 (set-bound x1-val (and (consp x1) (consp x2))))))
580 ;; At least one bound is not finite. The
581 ;; non-finite bound always wins.
583 (let* ((x-lo (copy-interval-limit (interval-low x)))
584 (x-hi (copy-interval-limit (interval-high x)))
585 (y-lo (copy-interval-limit (interval-low y)))
586 (y-hi (copy-interval-limit (interval-high y))))
587 (make-interval :low (select-bound x-lo y-lo #'< #'>)
588 :high (select-bound x-hi y-hi #'> #'<))))))
590 ;;; Basic arithmetic operations on intervals. We probably should do
591 ;;; true interval arithmetic here, but it's complicated because we
592 ;;; have float and integer types and bounds can be open or closed.
596 ;;; The negative of an interval
597 (defun interval-neg (x)
598 (declare (type interval x))
599 (make-interval :low (bound-func #'- (interval-high x))
600 :high (bound-func #'- (interval-low x))))
604 ;;; Add two intervals
605 (defun interval-add (x y)
606 (declare (type interval x y))
607 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
608 :high (bound-binop + (interval-high x) (interval-high y))))
612 ;;; Subtract two intervals
613 (defun interval-sub (x y)
614 (declare (type interval x y))
615 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
616 :high (bound-binop - (interval-high x) (interval-low y))))
620 ;;; Multiply two intervals
621 (defun interval-mul (x y)
622 (declare (type interval x y))
623 (flet ((bound-mul (x y)
624 (cond ((or (null x) (null y))
625 ;; Multiply by infinity is infinity
627 ((or (and (numberp x) (zerop x))
628 (and (numberp y) (zerop y)))
629 ;; Multiply by closed zero is special. The result
630 ;; is always a closed bound. But don't replace this
631 ;; with zero; we want the multiplication to produce
632 ;; the correct signed zero, if needed.
633 (* (bound-value x) (bound-value y)))
634 ((or (and (floatp x) (float-infinity-p x))
635 (and (floatp y) (float-infinity-p y)))
636 ;; Infinity times anything is infinity
639 ;; General multiply. The result is open if either is open.
640 (bound-binop * x y)))))
641 (let ((x-range (interval-range-info x))
642 (y-range (interval-range-info y)))
643 (cond ((null x-range)
644 ;; Split x into two and multiply each separately
645 (destructuring-bind (x- x+) (interval-split 0 x t t)
646 (interval-merge-pair (interval-mul x- y)
647 (interval-mul x+ y))))
649 ;; Split y into two and multiply each separately
650 (destructuring-bind (y- y+) (interval-split 0 y t t)
651 (interval-merge-pair (interval-mul x y-)
652 (interval-mul x y+))))
654 (interval-neg (interval-mul (interval-neg x) y)))
656 (interval-neg (interval-mul x (interval-neg y))))
657 ((and (eq x-range '+) (eq y-range '+))
658 ;; If we are here, X and Y are both positive
659 (make-interval :low (bound-mul (interval-low x) (interval-low y))
660 :high (bound-mul (interval-high x) (interval-high y))))
662 (error "This shouldn't happen!"))))))
666 ;;; Divide two intervals.
667 (defun interval-div (top bot)
668 (declare (type interval top bot))
669 (flet ((bound-div (x y y-low-p)
672 ;; Divide by infinity means result is 0. However,
673 ;; we need to watch out for the sign of the result,
674 ;; to correctly handle signed zeros. We also need
675 ;; to watch out for positive or negative infinity.
676 (if (floatp (bound-value x))
678 (- (float-sign (bound-value x) 0.0))
679 (float-sign (bound-value x) 0.0))
681 ((zerop (bound-value y))
682 ;; Divide by zero means result is infinity
684 ((and (numberp x) (zerop x))
685 ;; Zero divided by anything is zero.
688 (bound-binop / x y)))))
689 (let ((top-range (interval-range-info top))
690 (bot-range (interval-range-info bot)))
691 (cond ((null bot-range)
692 ;; The denominator contains zero, so anything goes!
693 (make-interval :low nil :high nil))
695 ;; Denominator is negative so flip the sign, compute the
696 ;; result, and flip it back.
697 (interval-neg (interval-div top (interval-neg bot))))
699 ;; Split top into two positive and negative parts, and
700 ;; divide each separately
701 (destructuring-bind (top- top+) (interval-split 0 top t t)
702 (interval-merge-pair (interval-div top- bot)
703 (interval-div top+ bot))))
705 ;; Top is negative so flip the sign, divide, and flip the
706 ;; sign of the result.
707 (interval-neg (interval-div (interval-neg top) bot)))
708 ((and (eq top-range '+) (eq bot-range '+))
710 (make-interval :low (bound-div (interval-low top) (interval-high bot) t)
711 :high (bound-div (interval-high top) (interval-low bot) nil)))
713 (error "This shouldn't happen!"))))))
717 ;;; Apply the function F to the interval X. If X = [a, b], then the
718 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
719 ;;; result makes sense. It will if F is monotonic increasing (or
721 (defun interval-func (f x)
722 (declare (type interval x))
723 (let ((lo (bound-func f (interval-low x)))
724 (hi (bound-func f (interval-high x))))
725 (make-interval :low lo :high hi)))
729 ;;; Return T if X < Y. That is every number in the interval X is
730 ;;; always less than any number in the interval Y.
731 (defun interval-< (x y)
732 (declare (type interval x y))
733 ;; X < Y only if X is bounded above, Y is bounded below, and they
735 (when (and (interval-bounded-p x 'above)
736 (interval-bounded-p y 'below))
737 ;; Intervals are bounded in the appropriate way. Make sure they
739 (let ((left (interval-high x))
740 (right (interval-low y)))
741 (cond ((> (bound-value left)
743 ;; Definitely overlap so result is NIL
745 ((< (bound-value left)
747 ;; Definitely don't touch, so result is T
750 ;; Limits are equal. Check for open or closed bounds.
751 ;; Don't overlap if one or the other are open.
752 (or (consp left) (consp right)))))))
756 ;;; Return T if X >= Y. That is, every number in the interval X is
757 ;;; always greater than any number in the interval Y.
758 (defun interval->= (x y)
759 (declare (type interval x y))
760 ;; X >= Y if lower bound of X >= upper bound of Y
761 (when (and (interval-bounded-p x 'below)
762 (interval-bounded-p y 'above))
763 (>= (bound-value (interval-low x)) (bound-value (interval-high y)))))
767 ;;; Return an interval that is the absolute value of X. Thus, if X =
768 ;;; [-1 10], the result is [0, 10].
769 (defun interval-abs (x)
770 (declare (type interval x))
771 (case (interval-range-info x)
777 (destructuring-bind (x- x+) (interval-split 0 x t t)
778 (interval-merge-pair (interval-neg x-) x+)))))
782 ;;; Compute the square of an interval.
783 (defun interval-sqr (x)
784 (declare (type interval x))
785 (interval-func #'(lambda (x) (* x x))
789 ;;;; numeric derive-type methods
791 ;;; Utility for defining derive-type methods of integer operations. If the
792 ;;; types of both X and Y are integer types, then we compute a new integer type
793 ;;; with bounds determined Fun when applied to X and Y. Otherwise, we use
794 ;;; Numeric-Contagion.
795 (defun derive-integer-type (x y fun)
796 (declare (type continuation x y) (type function fun))
797 (let ((x (continuation-type x))
798 (y (continuation-type y)))
799 (if (and (numeric-type-p x) (numeric-type-p y)
800 (eq (numeric-type-class x) 'integer)
801 (eq (numeric-type-class y) 'integer)
802 (eq (numeric-type-complexp x) :real)
803 (eq (numeric-type-complexp y) :real))
804 (multiple-value-bind (low high) (funcall fun x y)
805 (make-numeric-type :class 'integer
809 (numeric-contagion x y))))
811 #!+(or propagate-float-type propagate-fun-type)
814 ;; Simple utility to flatten a list
815 (defun flatten-list (x)
816 (labels ((flatten-helper (x r);; 'r' is the stuff to the 'right'.
820 (t (flatten-helper (car x)
821 (flatten-helper (cdr x) r))))))
822 (flatten-helper x nil)))
824 ;;; Take some type of continuation and massage it so that we get a
825 ;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
826 ;;; to indicate failure.
827 (defun prepare-arg-for-derive-type (arg)
828 (flet ((listify (arg)
833 (union-type-types arg))
836 (unless (eq arg *empty-type*)
837 ;; Make sure all args are some type of numeric-type. For member
838 ;; types, convert the list of members into a union of equivalent
839 ;; single-element member-type's.
840 (let ((new-args nil))
841 (dolist (arg (listify arg))
842 (if (member-type-p arg)
843 ;; Run down the list of members and convert to a list of
845 (dolist (member (member-type-members arg))
846 (push (if (numberp member)
847 (make-member-type :members (list member))
850 (push arg new-args)))
851 (unless (member *empty-type* new-args)
854 ;;; Convert from the standard type convention for which -0.0 and 0.0
855 ;;; and equal to an intermediate convention for which they are
856 ;;; considered different which is more natural for some of the
858 #!-negative-zero-is-not-zero
859 (defun convert-numeric-type (type)
860 (declare (type numeric-type type))
861 ;;; Only convert real float interval delimiters types.
862 (if (eq (numeric-type-complexp type) :real)
863 (let* ((lo (numeric-type-low type))
864 (lo-val (bound-value lo))
865 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
866 (hi (numeric-type-high type))
867 (hi-val (bound-value hi))
868 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
869 (if (or lo-float-zero-p hi-float-zero-p)
871 :class (numeric-type-class type)
872 :format (numeric-type-format type)
874 :low (if lo-float-zero-p
876 (list (float 0.0 lo-val))
879 :high (if hi-float-zero-p
881 (list (float -0.0 hi-val))
888 ;;; Convert back from the intermediate convention for which -0.0 and
889 ;;; 0.0 are considered different to the standard type convention for
891 #!-negative-zero-is-not-zero
892 (defun convert-back-numeric-type (type)
893 (declare (type numeric-type type))
894 ;;; Only convert real float interval delimiters types.
895 (if (eq (numeric-type-complexp type) :real)
896 (let* ((lo (numeric-type-low type))
897 (lo-val (bound-value lo))
899 (and lo (floatp lo-val) (= lo-val 0.0)
900 (float-sign lo-val)))
901 (hi (numeric-type-high type))
902 (hi-val (bound-value hi))
904 (and hi (floatp hi-val) (= hi-val 0.0)
905 (float-sign hi-val))))
907 ;; (float +0.0 +0.0) => (member 0.0)
908 ;; (float -0.0 -0.0) => (member -0.0)
909 ((and lo-float-zero-p hi-float-zero-p)
910 ;; Shouldn't have exclusive bounds here.
911 (assert (and (not (consp lo)) (not (consp hi))))
912 (if (= lo-float-zero-p hi-float-zero-p)
913 ;; (float +0.0 +0.0) => (member 0.0)
914 ;; (float -0.0 -0.0) => (member -0.0)
915 (specifier-type `(member ,lo-val))
916 ;; (float -0.0 +0.0) => (float 0.0 0.0)
917 ;; (float +0.0 -0.0) => (float 0.0 0.0)
918 (make-numeric-type :class (numeric-type-class type)
919 :format (numeric-type-format type)
925 ;; (float -0.0 x) => (float 0.0 x)
926 ((and (not (consp lo)) (minusp lo-float-zero-p))
927 (make-numeric-type :class (numeric-type-class type)
928 :format (numeric-type-format type)
930 :low (float 0.0 lo-val)
932 ;; (float (+0.0) x) => (float (0.0) x)
933 ((and (consp lo) (plusp lo-float-zero-p))
934 (make-numeric-type :class (numeric-type-class type)
935 :format (numeric-type-format type)
937 :low (list (float 0.0 lo-val))
940 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
941 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
942 (list (make-member-type :members (list (float 0.0 lo-val)))
943 (make-numeric-type :class (numeric-type-class type)
944 :format (numeric-type-format type)
946 :low (list (float 0.0 lo-val))
950 ;; (float x +0.0) => (float x 0.0)
951 ((and (not (consp hi)) (plusp hi-float-zero-p))
952 (make-numeric-type :class (numeric-type-class type)
953 :format (numeric-type-format type)
956 :high (float 0.0 hi-val)))
957 ;; (float x (-0.0)) => (float x (0.0))
958 ((and (consp hi) (minusp hi-float-zero-p))
959 (make-numeric-type :class (numeric-type-class type)
960 :format (numeric-type-format type)
963 :high (list (float 0.0 hi-val))))
965 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
966 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
967 (list (make-member-type :members (list (float -0.0 hi-val)))
968 (make-numeric-type :class (numeric-type-class type)
969 :format (numeric-type-format type)
972 :high (list (float 0.0 hi-val)))))))
978 ;;; Convert back a possible list of numeric types.
979 #!-negative-zero-is-not-zero
980 (defun convert-back-numeric-type-list (type-list)
984 (dolist (type type-list)
985 (if (numeric-type-p type)
986 (let ((result (convert-back-numeric-type type)))
988 (setf results (append results result))
989 (push result results)))
990 (push type results)))
993 (convert-back-numeric-type type-list))
995 (convert-back-numeric-type-list (union-type-types type-list)))
999 ;;; Make-Canonical-Union-Type
1001 ;;; Take a list of types and return a canonical type specifier,
1002 ;;; combining any members types together. If both positive and
1003 ;;; negative members types are present they are converted to a float
1004 ;;; type. X This would be far simpler if the type-union methods could
1005 ;;; handle member/number unions.
1006 (defun make-canonical-union-type (type-list)
1009 (dolist (type type-list)
1010 (if (member-type-p type)
1011 (setf members (union members (member-type-members type)))
1012 (push type misc-types)))
1014 (when (null (set-difference '(-0l0 0l0) members))
1015 #!-negative-zero-is-not-zero
1016 (push (specifier-type '(long-float 0l0 0l0)) misc-types)
1017 #!+negative-zero-is-not-zero
1018 (push (specifier-type '(long-float -0l0 0l0)) misc-types)
1019 (setf members (set-difference members '(-0l0 0l0))))
1020 (when (null (set-difference '(-0d0 0d0) members))
1021 #!-negative-zero-is-not-zero
1022 (push (specifier-type '(double-float 0d0 0d0)) misc-types)
1023 #!+negative-zero-is-not-zero
1024 (push (specifier-type '(double-float -0d0 0d0)) misc-types)
1025 (setf members (set-difference members '(-0d0 0d0))))
1026 (when (null (set-difference '(-0f0 0f0) members))
1027 #!-negative-zero-is-not-zero
1028 (push (specifier-type '(single-float 0f0 0f0)) misc-types)
1029 #!+negative-zero-is-not-zero
1030 (push (specifier-type '(single-float -0f0 0f0)) misc-types)
1031 (setf members (set-difference members '(-0f0 0f0))))
1032 (cond ((null members)
1033 (let ((res (first misc-types)))
1034 (dolist (type (rest misc-types))
1035 (setq res (type-union res type)))
1038 (make-member-type :members members))
1040 (let ((res (first misc-types)))
1041 (dolist (type (rest misc-types))
1042 (setq res (type-union res type)))
1043 (dolist (type members)
1044 (setq res (type-union
1045 res (make-member-type :members (list type)))))
1048 ;;; Convert-Member-Type
1050 ;;; Convert a member type with a single member to a numeric type.
1051 (defun convert-member-type (arg)
1052 (let* ((members (member-type-members arg))
1053 (member (first members))
1054 (member-type (type-of member)))
1055 (assert (not (rest members)))
1056 (specifier-type `(,(if (subtypep member-type 'integer)
1061 ;;; ONE-ARG-DERIVE-TYPE
1063 ;;; This is used in defoptimizers for computing the resulting type of
1066 ;;; Given the continuation ARG, derive the resulting type using the
1067 ;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
1068 ;;; "atomic" continuation type like numeric-type or member-type
1069 ;;; (containing just one element). It should return the resulting
1070 ;;; type, which can be a list of types.
1072 ;;; For the case of member types, if a member-fcn is given it is
1073 ;;; called to compute the result otherwise the member type is first
1074 ;;; converted to a numeric type and the derive-fcn is call.
1075 (defun one-arg-derive-type (arg derive-fcn member-fcn
1076 &optional (convert-type t))
1077 (declare (type function derive-fcn)
1078 (type (or null function) member-fcn)
1079 #!+negative-zero-is-not-zero (ignore convert-type))
1080 (let ((arg-list (prepare-arg-for-derive-type (continuation-type arg))))
1086 (with-float-traps-masked
1087 (:underflow :overflow :divide-by-zero)
1091 (first (member-type-members x))))))
1092 ;; Otherwise convert to a numeric type.
1093 (let ((result-type-list
1094 (funcall derive-fcn (convert-member-type x))))
1095 #!-negative-zero-is-not-zero
1097 (convert-back-numeric-type-list result-type-list)
1099 #!+negative-zero-is-not-zero
1102 #!-negative-zero-is-not-zero
1104 (convert-back-numeric-type-list
1105 (funcall derive-fcn (convert-numeric-type x)))
1106 (funcall derive-fcn x))
1107 #!+negative-zero-is-not-zero
1108 (funcall derive-fcn x))
1110 *universal-type*))))
1111 ;; Run down the list of args and derive the type of each one,
1112 ;; saving all of the results in a list.
1113 (let ((results nil))
1114 (dolist (arg arg-list)
1115 (let ((result (deriver arg)))
1117 (setf results (append results result))
1118 (push result results))))
1120 (make-canonical-union-type results)
1121 (first results)))))))
1123 ;;; TWO-ARG-DERIVE-TYPE
1125 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1126 ;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
1127 ;;; original args and a third which is T to indicate if the two args
1128 ;;; really represent the same continuation. This is useful for
1129 ;;; deriving the type of things like (* x x), which should always be
1130 ;;; positive. If we didn't do this, we wouldn't be able to tell.
1131 (defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
1132 &optional (convert-type t))
1133 #!+negative-zero-is-not-zero
1134 (declare (ignore convert-type))
1135 (flet (#!-negative-zero-is-not-zero
1136 (deriver (x y same-arg)
1137 (cond ((and (member-type-p x) (member-type-p y))
1138 (let* ((x (first (member-type-members x)))
1139 (y (first (member-type-members y)))
1140 (result (with-float-traps-masked
1141 (:underflow :overflow :divide-by-zero
1143 (funcall fcn x y))))
1144 (cond ((null result))
1145 ((and (floatp result) (float-nan-p result))
1148 :format (type-of result)
1151 (make-member-type :members (list result))))))
1152 ((and (member-type-p x) (numeric-type-p y))
1153 (let* ((x (convert-member-type x))
1154 (y (if convert-type (convert-numeric-type y) y))
1155 (result (funcall derive-fcn x y same-arg)))
1157 (convert-back-numeric-type-list result)
1159 ((and (numeric-type-p x) (member-type-p y))
1160 (let* ((x (if convert-type (convert-numeric-type x) x))
1161 (y (convert-member-type y))
1162 (result (funcall derive-fcn x y same-arg)))
1164 (convert-back-numeric-type-list result)
1166 ((and (numeric-type-p x) (numeric-type-p y))
1167 (let* ((x (if convert-type (convert-numeric-type x) x))
1168 (y (if convert-type (convert-numeric-type y) y))
1169 (result (funcall derive-fcn x y same-arg)))
1171 (convert-back-numeric-type-list result)
1175 #!+negative-zero-is-not-zero
1176 (deriver (x y same-arg)
1177 (cond ((and (member-type-p x) (member-type-p y))
1178 (let* ((x (first (member-type-members x)))
1179 (y (first (member-type-members y)))
1180 (result (with-float-traps-masked
1181 (:underflow :overflow :divide-by-zero)
1182 (funcall fcn x y))))
1184 (make-member-type :members (list result)))))
1185 ((and (member-type-p x) (numeric-type-p y))
1186 (let ((x (convert-member-type x)))
1187 (funcall derive-fcn x y same-arg)))
1188 ((and (numeric-type-p x) (member-type-p y))
1189 (let ((y (convert-member-type y)))
1190 (funcall derive-fcn x y same-arg)))
1191 ((and (numeric-type-p x) (numeric-type-p y))
1192 (funcall derive-fcn x y same-arg))
1194 *universal-type*))))
1195 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1196 (a1 (prepare-arg-for-derive-type (continuation-type arg1)))
1197 (a2 (prepare-arg-for-derive-type (continuation-type arg2))))
1199 (let ((results nil))
1201 ;; Since the args are the same continuation, just run
1204 (let ((result (deriver x x same-arg)))
1206 (setf results (append results result))
1207 (push result results))))
1208 ;; Try all pairwise combinations.
1211 (let ((result (or (deriver x y same-arg)
1212 (numeric-contagion x y))))
1214 (setf results (append results result))
1215 (push result results))))))
1217 (make-canonical-union-type results)
1218 (first results)))))))
1222 #!-propagate-float-type
1224 (defoptimizer (+ derive-type) ((x y))
1225 (derive-integer-type
1232 (values (frob (numeric-type-low x) (numeric-type-low y))
1233 (frob (numeric-type-high x) (numeric-type-high y)))))))
1235 (defoptimizer (- derive-type) ((x y))
1236 (derive-integer-type
1243 (values (frob (numeric-type-low x) (numeric-type-high y))
1244 (frob (numeric-type-high x) (numeric-type-low y)))))))
1246 (defoptimizer (* derive-type) ((x y))
1247 (derive-integer-type
1250 (let ((x-low (numeric-type-low x))
1251 (x-high (numeric-type-high x))
1252 (y-low (numeric-type-low y))
1253 (y-high (numeric-type-high y)))
1254 (cond ((not (and x-low y-low))
1256 ((or (minusp x-low) (minusp y-low))
1257 (if (and x-high y-high)
1258 (let ((max (* (max (abs x-low) (abs x-high))
1259 (max (abs y-low) (abs y-high)))))
1260 (values (- max) max))
1263 (values (* x-low y-low)
1264 (if (and x-high y-high)
1268 (defoptimizer (/ derive-type) ((x y))
1269 (numeric-contagion (continuation-type x) (continuation-type y)))
1273 #!+propagate-float-type
1275 (defun +-derive-type-aux (x y same-arg)
1276 (if (and (numeric-type-real-p x)
1277 (numeric-type-real-p y))
1280 (let ((x-int (numeric-type->interval x)))
1281 (interval-add x-int x-int))
1282 (interval-add (numeric-type->interval x)
1283 (numeric-type->interval y))))
1284 (result-type (numeric-contagion x y)))
1285 ;; If the result type is a float, we need to be sure to coerce
1286 ;; the bounds into the correct type.
1287 (when (eq (numeric-type-class result-type) 'float)
1288 (setf result (interval-func
1290 (coerce x (or (numeric-type-format result-type)
1294 :class (if (and (eq (numeric-type-class x) 'integer)
1295 (eq (numeric-type-class y) 'integer))
1296 ;; The sum of integers is always an integer
1298 (numeric-type-class result-type))
1299 :format (numeric-type-format result-type)
1300 :low (interval-low result)
1301 :high (interval-high result)))
1302 ;; General contagion
1303 (numeric-contagion x y)))
1305 (defoptimizer (+ derive-type) ((x y))
1306 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1308 (defun --derive-type-aux (x y same-arg)
1309 (if (and (numeric-type-real-p x)
1310 (numeric-type-real-p y))
1312 ;; (- x x) is always 0.
1314 (make-interval :low 0 :high 0)
1315 (interval-sub (numeric-type->interval x)
1316 (numeric-type->interval y))))
1317 (result-type (numeric-contagion x y)))
1318 ;; If the result type is a float, we need to be sure to coerce
1319 ;; the bounds into the correct type.
1320 (when (eq (numeric-type-class result-type) 'float)
1321 (setf result (interval-func
1323 (coerce x (or (numeric-type-format result-type)
1327 :class (if (and (eq (numeric-type-class x) 'integer)
1328 (eq (numeric-type-class y) 'integer))
1329 ;; The difference of integers is always an integer
1331 (numeric-type-class result-type))
1332 :format (numeric-type-format result-type)
1333 :low (interval-low result)
1334 :high (interval-high result)))
1335 ;; General contagion
1336 (numeric-contagion x y)))
1338 (defoptimizer (- derive-type) ((x y))
1339 (two-arg-derive-type x y #'--derive-type-aux #'-))
1341 (defun *-derive-type-aux (x y same-arg)
1342 (if (and (numeric-type-real-p x)
1343 (numeric-type-real-p y))
1345 ;; (* x x) is always positive, so take care to do it
1348 (interval-sqr (numeric-type->interval x))
1349 (interval-mul (numeric-type->interval x)
1350 (numeric-type->interval y))))
1351 (result-type (numeric-contagion x y)))
1352 ;; If the result type is a float, we need to be sure to coerce
1353 ;; the bounds into the correct type.
1354 (when (eq (numeric-type-class result-type) 'float)
1355 (setf result (interval-func
1357 (coerce x (or (numeric-type-format result-type)
1361 :class (if (and (eq (numeric-type-class x) 'integer)
1362 (eq (numeric-type-class y) 'integer))
1363 ;; The product of integers is always an integer
1365 (numeric-type-class result-type))
1366 :format (numeric-type-format result-type)
1367 :low (interval-low result)
1368 :high (interval-high result)))
1369 (numeric-contagion x y)))
1371 (defoptimizer (* derive-type) ((x y))
1372 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1374 (defun /-derive-type-aux (x y same-arg)
1375 (if (and (numeric-type-real-p x)
1376 (numeric-type-real-p y))
1378 ;; (/ x x) is always 1, except if x can contain 0. In
1379 ;; that case, we shouldn't optimize the division away
1380 ;; because we want 0/0 to signal an error.
1382 (not (interval-contains-p
1383 0 (interval-closure (numeric-type->interval y)))))
1384 (make-interval :low 1 :high 1)
1385 (interval-div (numeric-type->interval x)
1386 (numeric-type->interval y))))
1387 (result-type (numeric-contagion x y)))
1388 ;; If the result type is a float, we need to be sure to coerce
1389 ;; the bounds into the correct type.
1390 (when (eq (numeric-type-class result-type) 'float)
1391 (setf result (interval-func
1393 (coerce x (or (numeric-type-format result-type)
1396 (make-numeric-type :class (numeric-type-class result-type)
1397 :format (numeric-type-format result-type)
1398 :low (interval-low result)
1399 :high (interval-high result)))
1400 (numeric-contagion x y)))
1402 (defoptimizer (/ derive-type) ((x y))
1403 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1407 ;;; KLUDGE: All this ASH optimization is suppressed under CMU CL
1408 ;;; because as of version 2.4.6 for Debian, CMU CL blows up on (ASH
1409 ;;; 1000000000 -100000000000) (i.e. ASH of two bignums yielding zero)
1410 ;;; and it's hard to avoid that calculation in here.
1411 #-(and cmu sb-xc-host)
1413 #!-propagate-fun-type
1414 (defoptimizer (ash derive-type) ((n shift))
1415 (or (let ((n-type (continuation-type n)))
1416 (when (numeric-type-p n-type)
1417 (let ((n-low (numeric-type-low n-type))
1418 (n-high (numeric-type-high n-type)))
1419 (if (constant-continuation-p shift)
1420 (let ((shift (continuation-value shift)))
1421 (make-numeric-type :class 'integer
1423 :low (when n-low (ash n-low shift))
1424 :high (when n-high (ash n-high shift))))
1425 (let ((s-type (continuation-type shift)))
1426 (when (numeric-type-p s-type)
1427 (let ((s-low (numeric-type-low s-type))
1428 (s-high (numeric-type-high s-type)))
1429 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1430 (make-numeric-type :class 'integer
1433 (min (ash n-low s-high)
1436 (max (ash n-high s-high)
1437 (ash n-high s-low))))
1438 (make-numeric-type :class 'integer
1439 :complexp :real)))))))))
1441 #!+propagate-fun-type
1442 (defun ash-derive-type-aux (n-type shift same-arg)
1443 (declare (ignore same-arg))
1444 (or (and (csubtypep n-type (specifier-type 'integer))
1445 (csubtypep shift (specifier-type 'integer))
1446 (let ((n-low (numeric-type-low n-type))
1447 (n-high (numeric-type-high n-type))
1448 (s-low (numeric-type-low shift))
1449 (s-high (numeric-type-high shift)))
1450 ;; KLUDGE: The bare 64's here should be related to
1451 ;; symbolic machine word size values somehow.
1452 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1453 (make-numeric-type :class 'integer :complexp :real
1455 (min (ash n-low s-high)
1458 (max (ash n-high s-high)
1459 (ash n-high s-low))))
1460 (make-numeric-type :class 'integer
1463 #!+propagate-fun-type
1464 (defoptimizer (ash derive-type) ((n shift))
1465 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1468 #!-propagate-float-type
1469 (macrolet ((frob (fun)
1470 `#'(lambda (type type2)
1471 (declare (ignore type2))
1472 (let ((lo (numeric-type-low type))
1473 (hi (numeric-type-high type)))
1474 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1476 (defoptimizer (%negate derive-type) ((num))
1477 (derive-integer-type num num (frob -)))
1479 (defoptimizer (lognot derive-type) ((int))
1480 (derive-integer-type int int (frob lognot))))
1482 #!+propagate-float-type
1483 (defoptimizer (lognot derive-type) ((int))
1484 (derive-integer-type int int
1485 #'(lambda (type type2)
1486 (declare (ignore type2))
1487 (let ((lo (numeric-type-low type))
1488 (hi (numeric-type-high type)))
1489 (values (if hi (lognot hi) nil)
1490 (if lo (lognot lo) nil)
1491 (numeric-type-class type)
1492 (numeric-type-format type))))))
1494 #!+propagate-float-type
1495 (defoptimizer (%negate derive-type) ((num))
1496 (flet ((negate-bound (b)
1497 (set-bound (- (bound-value b)) (consp b))))
1498 (one-arg-derive-type num
1500 (let ((lo (numeric-type-low type))
1501 (hi (numeric-type-high type))
1502 (result (copy-numeric-type type)))
1503 (setf (numeric-type-low result)
1504 (if hi (negate-bound hi) nil))
1505 (setf (numeric-type-high result)
1506 (if lo (negate-bound lo) nil))
1510 #!-propagate-float-type
1511 (defoptimizer (abs derive-type) ((num))
1512 (let ((type (continuation-type num)))
1513 (if (and (numeric-type-p type)
1514 (eq (numeric-type-class type) 'integer)
1515 (eq (numeric-type-complexp type) :real))
1516 (let ((lo (numeric-type-low type))
1517 (hi (numeric-type-high type)))
1518 (make-numeric-type :class 'integer :complexp :real
1519 :low (cond ((and hi (minusp hi))
1525 :high (if (and hi lo)
1526 (max (abs hi) (abs lo))
1528 (numeric-contagion type type))))
1530 #!+propagate-float-type
1531 (defun abs-derive-type-aux (type)
1532 (cond ((eq (numeric-type-complexp type) :complex)
1533 ;; The absolute value of a complex number is always a
1534 ;; non-negative float.
1535 (let* ((format (case (numeric-type-class type)
1536 ((integer rational) 'single-float)
1537 (t (numeric-type-format type))))
1538 (bound-format (or format 'float)))
1539 (make-numeric-type :class 'float
1542 :low (coerce 0 bound-format)
1545 ;; The absolute value of a real number is a non-negative real
1546 ;; of the same type.
1547 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1548 (class (numeric-type-class type))
1549 (format (numeric-type-format type))
1550 (bound-type (or format class 'real)))
1555 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1556 :high (coerce-numeric-bound
1557 (interval-high abs-bnd) bound-type))))))
1559 #!+propagate-float-type
1560 (defoptimizer (abs derive-type) ((num))
1561 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1563 #!-propagate-float-type
1564 (defoptimizer (truncate derive-type) ((number divisor))
1565 (let ((number-type (continuation-type number))
1566 (divisor-type (continuation-type divisor))
1567 (integer-type (specifier-type 'integer)))
1568 (if (and (numeric-type-p number-type)
1569 (csubtypep number-type integer-type)
1570 (numeric-type-p divisor-type)
1571 (csubtypep divisor-type integer-type))
1572 (let ((number-low (numeric-type-low number-type))
1573 (number-high (numeric-type-high number-type))
1574 (divisor-low (numeric-type-low divisor-type))
1575 (divisor-high (numeric-type-high divisor-type)))
1576 (values-specifier-type
1577 `(values ,(integer-truncate-derive-type number-low number-high
1578 divisor-low divisor-high)
1579 ,(integer-rem-derive-type number-low number-high
1580 divisor-low divisor-high))))
1583 #-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
1585 #!+propagate-float-type
1588 (defun rem-result-type (number-type divisor-type)
1589 ;; Figure out what the remainder type is. The remainder is an
1590 ;; integer if both args are integers; a rational if both args are
1591 ;; rational; and a float otherwise.
1592 (cond ((and (csubtypep number-type (specifier-type 'integer))
1593 (csubtypep divisor-type (specifier-type 'integer)))
1595 ((and (csubtypep number-type (specifier-type 'rational))
1596 (csubtypep divisor-type (specifier-type 'rational)))
1598 ((and (csubtypep number-type (specifier-type 'float))
1599 (csubtypep divisor-type (specifier-type 'float)))
1600 ;; Both are floats so the result is also a float, of
1601 ;; the largest type.
1602 (or (float-format-max (numeric-type-format number-type)
1603 (numeric-type-format divisor-type))
1605 ((and (csubtypep number-type (specifier-type 'float))
1606 (csubtypep divisor-type (specifier-type 'rational)))
1607 ;; One of the arguments is a float and the other is a
1608 ;; rational. The remainder is a float of the same
1610 (or (numeric-type-format number-type) 'float))
1611 ((and (csubtypep divisor-type (specifier-type 'float))
1612 (csubtypep number-type (specifier-type 'rational)))
1613 ;; One of the arguments is a float and the other is a
1614 ;; rational. The remainder is a float of the same
1616 (or (numeric-type-format divisor-type) 'float))
1618 ;; Some unhandled combination. This usually means both args
1619 ;; are REAL so the result is a REAL.
1622 (defun truncate-derive-type-quot (number-type divisor-type)
1623 (let* ((rem-type (rem-result-type number-type divisor-type))
1624 (number-interval (numeric-type->interval number-type))
1625 (divisor-interval (numeric-type->interval divisor-type)))
1626 ;;(declare (type (member '(integer rational float)) rem-type))
1627 ;; We have real numbers now.
1628 (cond ((eq rem-type 'integer)
1629 ;; Since the remainder type is INTEGER, both args are
1631 (let* ((res (integer-truncate-derive-type
1632 (interval-low number-interval)
1633 (interval-high number-interval)
1634 (interval-low divisor-interval)
1635 (interval-high divisor-interval))))
1636 (specifier-type (if (listp res) res 'integer))))
1638 (let ((quot (truncate-quotient-bound
1639 (interval-div number-interval
1640 divisor-interval))))
1641 (specifier-type `(integer ,(or (interval-low quot) '*)
1642 ,(or (interval-high quot) '*))))))))
1644 (defun truncate-derive-type-rem (number-type divisor-type)
1645 (let* ((rem-type (rem-result-type number-type divisor-type))
1646 (number-interval (numeric-type->interval number-type))
1647 (divisor-interval (numeric-type->interval divisor-type))
1648 (rem (truncate-rem-bound number-interval divisor-interval)))
1649 ;;(declare (type (member '(integer rational float)) rem-type))
1650 ;; We have real numbers now.
1651 (cond ((eq rem-type 'integer)
1652 ;; Since the remainder type is INTEGER, both args are
1654 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1655 ,(or (interval-high rem) '*))))
1657 (multiple-value-bind (class format)
1660 (values 'integer nil))
1662 (values 'rational nil))
1663 ((or single-float double-float #!+long-float long-float)
1664 (values 'float rem-type))
1666 (values 'float nil))
1669 (when (member rem-type '(float single-float double-float
1670 #!+long-float long-float))
1671 (setf rem (interval-func #'(lambda (x)
1672 (coerce x rem-type))
1674 (make-numeric-type :class class
1676 :low (interval-low rem)
1677 :high (interval-high rem)))))))
1679 (defun truncate-derive-type-quot-aux (num div same-arg)
1680 (declare (ignore same-arg))
1681 (if (and (numeric-type-real-p num)
1682 (numeric-type-real-p div))
1683 (truncate-derive-type-quot num div)
1686 (defun truncate-derive-type-rem-aux (num div same-arg)
1687 (declare (ignore same-arg))
1688 (if (and (numeric-type-real-p num)
1689 (numeric-type-real-p div))
1690 (truncate-derive-type-rem num div)
1693 (defoptimizer (truncate derive-type) ((number divisor))
1694 (let ((quot (two-arg-derive-type number divisor
1695 #'truncate-derive-type-quot-aux #'truncate))
1696 (rem (two-arg-derive-type number divisor
1697 #'truncate-derive-type-rem-aux #'rem)))
1698 (when (and quot rem)
1699 (make-values-type :required (list quot rem)))))
1701 (defun ftruncate-derive-type-quot (number-type divisor-type)
1702 ;; The bounds are the same as for truncate. However, the first
1703 ;; result is a float of some type. We need to determine what that
1704 ;; type is. Basically it's the more contagious of the two types.
1705 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1706 (res-type (numeric-contagion number-type divisor-type)))
1707 (make-numeric-type :class 'float
1708 :format (numeric-type-format res-type)
1709 :low (numeric-type-low q-type)
1710 :high (numeric-type-high q-type))))
1712 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1713 (declare (ignore same-arg))
1714 (if (and (numeric-type-real-p n)
1715 (numeric-type-real-p d))
1716 (ftruncate-derive-type-quot n d)
1719 (defoptimizer (ftruncate derive-type) ((number divisor))
1721 (two-arg-derive-type number divisor
1722 #'ftruncate-derive-type-quot-aux #'ftruncate))
1723 (rem (two-arg-derive-type number divisor
1724 #'truncate-derive-type-rem-aux #'rem)))
1725 (when (and quot rem)
1726 (make-values-type :required (list quot rem)))))
1728 (defun %unary-truncate-derive-type-aux (number)
1729 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1731 (defoptimizer (%unary-truncate derive-type) ((number))
1732 (one-arg-derive-type number
1733 #'%unary-truncate-derive-type-aux
1736 ;;; Define optimizers for FLOOR and CEILING.
1738 ((frob-opt (name q-name r-name)
1739 (let ((q-aux (symbolicate q-name "-AUX"))
1740 (r-aux (symbolicate r-name "-AUX")))
1742 ;; Compute type of quotient (first) result
1743 (defun ,q-aux (number-type divisor-type)
1744 (let* ((number-interval
1745 (numeric-type->interval number-type))
1747 (numeric-type->interval divisor-type))
1748 (quot (,q-name (interval-div number-interval
1749 divisor-interval))))
1750 (specifier-type `(integer ,(or (interval-low quot) '*)
1751 ,(or (interval-high quot) '*)))))
1752 ;; Compute type of remainder
1753 (defun ,r-aux (number-type divisor-type)
1754 (let* ((divisor-interval
1755 (numeric-type->interval divisor-type))
1756 (rem (,r-name divisor-interval))
1757 (result-type (rem-result-type number-type divisor-type)))
1758 (multiple-value-bind (class format)
1761 (values 'integer nil))
1763 (values 'rational nil))
1764 ((or single-float double-float #!+long-float long-float)
1765 (values 'float result-type))
1767 (values 'float nil))
1770 (when (member result-type '(float single-float double-float
1771 #!+long-float long-float))
1772 ;; Make sure the limits on the interval have
1774 (setf rem (interval-func #'(lambda (x)
1775 (coerce x result-type))
1777 (make-numeric-type :class class
1779 :low (interval-low rem)
1780 :high (interval-high rem)))))
1781 ;; The optimizer itself
1782 (defoptimizer (,name derive-type) ((number divisor))
1783 (flet ((derive-q (n d same-arg)
1784 (declare (ignore same-arg))
1785 (if (and (numeric-type-real-p n)
1786 (numeric-type-real-p d))
1789 (derive-r (n d same-arg)
1790 (declare (ignore same-arg))
1791 (if (and (numeric-type-real-p n)
1792 (numeric-type-real-p d))
1795 (let ((quot (two-arg-derive-type
1796 number divisor #'derive-q #',name))
1797 (rem (two-arg-derive-type
1798 number divisor #'derive-r #'mod)))
1799 (when (and quot rem)
1800 (make-values-type :required (list quot rem))))))
1803 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1804 (frob-opt floor floor-quotient-bound floor-rem-bound)
1805 (frob-opt ceiling ceiling-quotient-bound ceiling-rem-bound))
1807 ;;; Define optimizers for FFLOOR and FCEILING
1809 ((frob-opt (name q-name r-name)
1810 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1811 (r-aux (symbolicate r-name "-AUX")))
1813 ;; Compute type of quotient (first) result
1814 (defun ,q-aux (number-type divisor-type)
1815 (let* ((number-interval
1816 (numeric-type->interval number-type))
1818 (numeric-type->interval divisor-type))
1819 (quot (,q-name (interval-div number-interval
1821 (res-type (numeric-contagion number-type divisor-type)))
1823 :class (numeric-type-class res-type)
1824 :format (numeric-type-format res-type)
1825 :low (interval-low quot)
1826 :high (interval-high quot))))
1828 (defoptimizer (,name derive-type) ((number divisor))
1829 (flet ((derive-q (n d same-arg)
1830 (declare (ignore same-arg))
1831 (if (and (numeric-type-real-p n)
1832 (numeric-type-real-p d))
1835 (derive-r (n d same-arg)
1836 (declare (ignore same-arg))
1837 (if (and (numeric-type-real-p n)
1838 (numeric-type-real-p d))
1841 (let ((quot (two-arg-derive-type
1842 number divisor #'derive-q #',name))
1843 (rem (two-arg-derive-type
1844 number divisor #'derive-r #'mod)))
1845 (when (and quot rem)
1846 (make-values-type :required (list quot rem))))))))))
1848 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1849 (frob-opt ffloor floor-quotient-bound floor-rem-bound)
1850 (frob-opt fceiling ceiling-quotient-bound ceiling-rem-bound))
1852 ;;; Functions to compute the bounds on the quotient and remainder for
1853 ;;; the FLOOR function.
1854 (defun floor-quotient-bound (quot)
1855 ;; Take the floor of the quotient and then massage it into what we
1857 (let ((lo (interval-low quot))
1858 (hi (interval-high quot)))
1859 ;; Take the floor of the lower bound. The result is always a
1860 ;; closed lower bound.
1862 (floor (bound-value lo))
1864 ;; For the upper bound, we need to be careful
1867 ;; An open bound. We need to be careful here because
1868 ;; the floor of '(10.0) is 9, but the floor of
1870 (multiple-value-bind (q r) (floor (first hi))
1875 ;; A closed bound, so the answer is obvious.
1879 (make-interval :low lo :high hi)))
1880 (defun floor-rem-bound (div)
1881 ;; The remainder depends only on the divisor. Try to get the
1882 ;; correct sign for the remainder if we can.
1883 (case (interval-range-info div)
1885 ;; Divisor is always positive.
1886 (let ((rem (interval-abs div)))
1887 (setf (interval-low rem) 0)
1888 (when (and (numberp (interval-high rem))
1889 (not (zerop (interval-high rem))))
1890 ;; The remainder never contains the upper bound. However,
1891 ;; watch out for the case where the high limit is zero!
1892 (setf (interval-high rem) (list (interval-high rem))))
1895 ;; Divisor is always negative
1896 (let ((rem (interval-neg (interval-abs div))))
1897 (setf (interval-high rem) 0)
1898 (when (numberp (interval-low rem))
1899 ;; The remainder never contains the lower bound.
1900 (setf (interval-low rem) (list (interval-low rem))))
1903 ;; The divisor can be positive or negative. All bets off.
1904 ;; The magnitude of remainder is the maximum value of the
1906 (let ((limit (bound-value (interval-high (interval-abs div)))))
1907 ;; The bound never reaches the limit, so make the interval open
1908 (make-interval :low (if limit
1911 :high (list limit))))))
1913 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1914 => #S(INTERVAL :LOW 0 :HIGH 10)
1915 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1916 => #S(INTERVAL :LOW 0 :HIGH 10)
1917 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1918 => #S(INTERVAL :LOW 0 :HIGH 10)
1919 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1920 => #S(INTERVAL :LOW 0 :HIGH 9)
1921 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1922 => #S(INTERVAL :LOW 0 :HIGH 10)
1923 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1924 => #S(INTERVAL :LOW 0 :HIGH 10)
1925 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1926 => #S(INTERVAL :LOW -2 :HIGH 10)
1927 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1928 => #S(INTERVAL :LOW -1 :HIGH 10)
1929 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1930 => #S(INTERVAL :LOW -1 :HIGH 10)
1932 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1933 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1934 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1935 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1936 (floor-rem-bound (make-interval :low -10 :high -2.3))
1937 #S(INTERVAL :LOW (-10) :HIGH 0)
1938 (floor-rem-bound (make-interval :low 0.3 :high 10))
1939 => #S(INTERVAL :LOW 0 :HIGH '(10))
1940 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1941 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1942 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1943 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1946 ;;; same functions for CEILING
1947 (defun ceiling-quotient-bound (quot)
1948 ;; Take the ceiling of the quotient and then massage it into what we
1950 (let ((lo (interval-low quot))
1951 (hi (interval-high quot)))
1952 ;; Take the ceiling of the upper bound. The result is always a
1953 ;; closed upper bound.
1955 (ceiling (bound-value hi))
1957 ;; For the lower bound, we need to be careful
1960 ;; An open bound. We need to be careful here because
1961 ;; the ceiling of '(10.0) is 11, but the ceiling of
1963 (multiple-value-bind (q r) (ceiling (first lo))
1968 ;; A closed bound, so the answer is obvious.
1972 (make-interval :low lo :high hi)))
1973 (defun ceiling-rem-bound (div)
1974 ;; The remainder depends only on the divisor. Try to get the
1975 ;; correct sign for the remainder if we can.
1977 (case (interval-range-info div)
1979 ;; Divisor is always positive. The remainder is negative.
1980 (let ((rem (interval-neg (interval-abs div))))
1981 (setf (interval-high rem) 0)
1982 (when (and (numberp (interval-low rem))
1983 (not (zerop (interval-low rem))))
1984 ;; The remainder never contains the upper bound. However,
1985 ;; watch out for the case when the upper bound is zero!
1986 (setf (interval-low rem) (list (interval-low rem))))
1989 ;; Divisor is always negative. The remainder is positive
1990 (let ((rem (interval-abs div)))
1991 (setf (interval-low rem) 0)
1992 (when (numberp (interval-high rem))
1993 ;; The remainder never contains the lower bound.
1994 (setf (interval-high rem) (list (interval-high rem))))
1997 ;; The divisor can be positive or negative. All bets off.
1998 ;; The magnitude of remainder is the maximum value of the
2000 (let ((limit (bound-value (interval-high (interval-abs div)))))
2001 ;; The bound never reaches the limit, so make the interval open
2002 (make-interval :low (if limit
2005 :high (list limit))))))
2008 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2009 => #S(INTERVAL :LOW 1 :HIGH 11)
2010 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2011 => #S(INTERVAL :LOW 1 :HIGH 11)
2012 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2013 => #S(INTERVAL :LOW 1 :HIGH 10)
2014 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2015 => #S(INTERVAL :LOW 1 :HIGH 10)
2016 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2017 => #S(INTERVAL :LOW 1 :HIGH 11)
2018 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2019 => #S(INTERVAL :LOW 1 :HIGH 11)
2020 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2021 => #S(INTERVAL :LOW -1 :HIGH 11)
2022 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2023 => #S(INTERVAL :LOW 0 :HIGH 11)
2024 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2025 => #S(INTERVAL :LOW -1 :HIGH 11)
2027 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2028 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2029 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2030 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2031 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2032 => #S(INTERVAL :LOW 0 :HIGH (10))
2033 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2034 => #S(INTERVAL :LOW (-10) :HIGH 0)
2035 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2036 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2037 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2038 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2041 (defun truncate-quotient-bound (quot)
2042 ;; For positive quotients, truncate is exactly like floor. For
2043 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2044 ;; it's the union of the two pieces.
2045 (case (interval-range-info quot)
2048 (floor-quotient-bound quot))
2050 ;; Just like ceiling
2051 (ceiling-quotient-bound quot))
2053 ;; Split the interval into positive and negative pieces, compute
2054 ;; the result for each piece and put them back together.
2055 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2056 (interval-merge-pair (ceiling-quotient-bound neg)
2057 (floor-quotient-bound pos))))))
2059 (defun truncate-rem-bound (num div)
2060 ;; This is significantly more complicated than floor or ceiling. We
2061 ;; need both the number and the divisor to determine the range. The
2062 ;; basic idea is to split the ranges of num and den into positive
2063 ;; and negative pieces and deal with each of the four possibilities
2065 (case (interval-range-info num)
2067 (case (interval-range-info div)
2069 (floor-rem-bound div))
2071 (ceiling-rem-bound div))
2073 (destructuring-bind (neg pos) (interval-split 0 div t t)
2074 (interval-merge-pair (truncate-rem-bound num neg)
2075 (truncate-rem-bound num pos))))))
2077 (case (interval-range-info div)
2079 (ceiling-rem-bound div))
2081 (floor-rem-bound div))
2083 (destructuring-bind (neg pos) (interval-split 0 div t t)
2084 (interval-merge-pair (truncate-rem-bound num neg)
2085 (truncate-rem-bound num pos))))))
2087 (destructuring-bind (neg pos) (interval-split 0 num t t)
2088 (interval-merge-pair (truncate-rem-bound neg div)
2089 (truncate-rem-bound pos div))))))
2092 ;;; Derive useful information about the range. Returns three values:
2093 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2094 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2095 ;;; - The abs of the maximal value if there is one, or nil if it is
2097 (defun numeric-range-info (low high)
2098 (cond ((and low (not (minusp low)))
2099 (values '+ low high))
2100 ((and high (not (plusp high)))
2101 (values '- (- high) (if low (- low) nil)))
2103 (values nil 0 (and low high (max (- low) high))))))
2105 (defun integer-truncate-derive-type
2106 (number-low number-high divisor-low divisor-high)
2107 ;; The result cannot be larger in magnitude than the number, but the sign
2108 ;; might change. If we can determine the sign of either the number or
2109 ;; the divisor, we can eliminate some of the cases.
2110 (multiple-value-bind (number-sign number-min number-max)
2111 (numeric-range-info number-low number-high)
2112 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2113 (numeric-range-info divisor-low divisor-high)
2114 (when (and divisor-max (zerop divisor-max))
2115 ;; We've got a problem: guaranteed division by zero.
2116 (return-from integer-truncate-derive-type t))
2117 (when (zerop divisor-min)
2118 ;; We'll assume that they aren't going to divide by zero.
2120 (cond ((and number-sign divisor-sign)
2121 ;; We know the sign of both.
2122 (if (eq number-sign divisor-sign)
2123 ;; Same sign, so the result will be positive.
2124 `(integer ,(if divisor-max
2125 (truncate number-min divisor-max)
2128 (truncate number-max divisor-min)
2130 ;; Different signs, the result will be negative.
2131 `(integer ,(if number-max
2132 (- (truncate number-max divisor-min))
2135 (- (truncate number-min divisor-max))
2137 ((eq divisor-sign '+)
2138 ;; The divisor is positive. Therefore, the number will just
2139 ;; become closer to zero.
2140 `(integer ,(if number-low
2141 (truncate number-low divisor-min)
2144 (truncate number-high divisor-min)
2146 ((eq divisor-sign '-)
2147 ;; The divisor is negative. Therefore, the absolute value of
2148 ;; the number will become closer to zero, but the sign will also
2150 `(integer ,(if number-high
2151 (- (truncate number-high divisor-min))
2154 (- (truncate number-low divisor-min))
2156 ;; The divisor could be either positive or negative.
2158 ;; The number we are dividing has a bound. Divide that by the
2159 ;; smallest posible divisor.
2160 (let ((bound (truncate number-max divisor-min)))
2161 `(integer ,(- bound) ,bound)))
2163 ;; The number we are dividing is unbounded, so we can't tell
2164 ;; anything about the result.
2167 #!-propagate-float-type
2168 (defun integer-rem-derive-type
2169 (number-low number-high divisor-low divisor-high)
2170 (if (and divisor-low divisor-high)
2171 ;; We know the range of the divisor, and the remainder must be smaller
2172 ;; than the divisor. We can tell the sign of the remainer if we know
2173 ;; the sign of the number.
2174 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2175 `(integer ,(if (or (null number-low)
2176 (minusp number-low))
2179 ,(if (or (null number-high)
2180 (plusp number-high))
2183 ;; The divisor is potentially either very positive or very negative.
2184 ;; Therefore, the remainer is unbounded, but we might be able to tell
2185 ;; something about the sign from the number.
2186 `(integer ,(if (and number-low (not (minusp number-low)))
2187 ;; The number we are dividing is positive. Therefore,
2188 ;; the remainder must be positive.
2191 ,(if (and number-high (not (plusp number-high)))
2192 ;; The number we are dividing is negative. Therefore,
2193 ;; the remainder must be negative.
2197 #!-propagate-float-type
2198 (defoptimizer (random derive-type) ((bound &optional state))
2199 (let ((type (continuation-type bound)))
2200 (when (numeric-type-p type)
2201 (let ((class (numeric-type-class type))
2202 (high (numeric-type-high type))
2203 (format (numeric-type-format type)))
2207 :low (coerce 0 (or format class 'real))
2208 :high (cond ((not high) nil)
2209 ((eq class 'integer) (max (1- high) 0))
2210 ((or (consp high) (zerop high)) high)
2213 #!+propagate-float-type
2214 (defun random-derive-type-aux (type)
2215 (let ((class (numeric-type-class type))
2216 (high (numeric-type-high type))
2217 (format (numeric-type-format type)))
2221 :low (coerce 0 (or format class 'real))
2222 :high (cond ((not high) nil)
2223 ((eq class 'integer) (max (1- high) 0))
2224 ((or (consp high) (zerop high)) high)
2227 #!+propagate-float-type
2228 (defoptimizer (random derive-type) ((bound &optional state))
2229 (one-arg-derive-type bound #'random-derive-type-aux nil))
2231 ;;;; logical derive-type methods
2233 ;;; Return the maximum number of bits an integer of the supplied type can take
2234 ;;; up, or NIL if it is unbounded. The second (third) value is T if the
2235 ;;; integer can be positive (negative) and NIL if not. Zero counts as
2237 (defun integer-type-length (type)
2238 (if (numeric-type-p type)
2239 (let ((min (numeric-type-low type))
2240 (max (numeric-type-high type)))
2241 (values (and min max (max (integer-length min) (integer-length max)))
2242 (or (null max) (not (minusp max)))
2243 (or (null min) (minusp min))))
2246 #!-propagate-fun-type
2248 (defoptimizer (logand derive-type) ((x y))
2249 (multiple-value-bind (x-len x-pos x-neg)
2250 (integer-type-length (continuation-type x))
2251 (declare (ignore x-pos))
2252 (multiple-value-bind (y-len y-pos y-neg)
2253 (integer-type-length (continuation-type y))
2254 (declare (ignore y-pos))
2256 ;; X must be positive.
2258 ;; The must both be positive.
2259 (cond ((or (null x-len) (null y-len))
2260 (specifier-type 'unsigned-byte))
2261 ((or (zerop x-len) (zerop y-len))
2262 (specifier-type '(integer 0 0)))
2264 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2265 ;; X is positive, but Y might be negative.
2267 (specifier-type 'unsigned-byte))
2269 (specifier-type '(integer 0 0)))
2271 (specifier-type `(unsigned-byte ,x-len)))))
2272 ;; X might be negative.
2274 ;; Y must be positive.
2276 (specifier-type 'unsigned-byte))
2278 (specifier-type '(integer 0 0)))
2281 `(unsigned-byte ,y-len))))
2282 ;; Either might be negative.
2283 (if (and x-len y-len)
2284 ;; The result is bounded.
2285 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2286 ;; We can't tell squat about the result.
2287 (specifier-type 'integer)))))))
2289 (defoptimizer (logior derive-type) ((x y))
2290 (multiple-value-bind (x-len x-pos x-neg)
2291 (integer-type-length (continuation-type x))
2292 (multiple-value-bind (y-len y-pos y-neg)
2293 (integer-type-length (continuation-type y))
2295 ((and (not x-neg) (not y-neg))
2296 ;; Both are positive.
2297 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2301 ;; X must be negative.
2303 ;; Both are negative. The result is going to be negative and be
2304 ;; the same length or shorter than the smaller.
2305 (if (and x-len y-len)
2307 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2309 (specifier-type '(integer * -1)))
2310 ;; X is negative, but we don't know about Y. The result will be
2311 ;; negative, but no more negative than X.
2313 `(integer ,(or (numeric-type-low (continuation-type x)) '*)
2316 ;; X might be either positive or negative.
2318 ;; But Y is negative. The result will be negative.
2320 `(integer ,(or (numeric-type-low (continuation-type y)) '*)
2322 ;; We don't know squat about either. It won't get any bigger.
2323 (if (and x-len y-len)
2325 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2327 (specifier-type 'integer))))))))
2329 (defoptimizer (logxor derive-type) ((x y))
2330 (multiple-value-bind (x-len x-pos x-neg)
2331 (integer-type-length (continuation-type x))
2332 (multiple-value-bind (y-len y-pos y-neg)
2333 (integer-type-length (continuation-type y))
2335 ((or (and (not x-neg) (not y-neg))
2336 (and (not x-pos) (not y-pos)))
2337 ;; Either both are negative or both are positive. The result will be
2338 ;; positive, and as long as the longer.
2339 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2342 ((or (and (not x-pos) (not y-neg))
2343 (and (not y-neg) (not y-pos)))
2344 ;; Either X is negative and Y is positive of vice-verca. The result
2345 ;; will be negative.
2346 (specifier-type `(integer ,(if (and x-len y-len)
2347 (ash -1 (max x-len y-len))
2350 ;; We can't tell what the sign of the result is going to be. All we
2351 ;; know is that we don't create new bits.
2353 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2355 (specifier-type 'integer))))))
2359 #!+propagate-fun-type
2361 (defun logand-derive-type-aux (x y &optional same-leaf)
2362 (declare (ignore same-leaf))
2363 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2364 (declare (ignore x-pos))
2365 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2366 (declare (ignore y-pos))
2368 ;; X must be positive.
2370 ;; The must both be positive.
2371 (cond ((or (null x-len) (null y-len))
2372 (specifier-type 'unsigned-byte))
2373 ((or (zerop x-len) (zerop y-len))
2374 (specifier-type '(integer 0 0)))
2376 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2377 ;; X is positive, but Y might be negative.
2379 (specifier-type 'unsigned-byte))
2381 (specifier-type '(integer 0 0)))
2383 (specifier-type `(unsigned-byte ,x-len)))))
2384 ;; X might be negative.
2386 ;; Y must be positive.
2388 (specifier-type 'unsigned-byte))
2390 (specifier-type '(integer 0 0)))
2393 `(unsigned-byte ,y-len))))
2394 ;; Either might be negative.
2395 (if (and x-len y-len)
2396 ;; The result is bounded.
2397 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2398 ;; We can't tell squat about the result.
2399 (specifier-type 'integer)))))))
2401 (defun logior-derive-type-aux (x y &optional same-leaf)
2402 (declare (ignore same-leaf))
2403 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2404 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2406 ((and (not x-neg) (not y-neg))
2407 ;; Both are positive.
2408 (if (and x-len y-len (zerop x-len) (zerop y-len))
2409 (specifier-type '(integer 0 0))
2410 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2414 ;; X must be negative.
2416 ;; Both are negative. The result is going to be negative and be
2417 ;; the same length or shorter than the smaller.
2418 (if (and x-len y-len)
2420 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2422 (specifier-type '(integer * -1)))
2423 ;; X is negative, but we don't know about Y. The result will be
2424 ;; negative, but no more negative than X.
2426 `(integer ,(or (numeric-type-low x) '*)
2429 ;; X might be either positive or negative.
2431 ;; But Y is negative. The result will be negative.
2433 `(integer ,(or (numeric-type-low y) '*)
2435 ;; We don't know squat about either. It won't get any bigger.
2436 (if (and x-len y-len)
2438 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2440 (specifier-type 'integer))))))))
2442 (defun logxor-derive-type-aux (x y &optional same-leaf)
2443 (declare (ignore same-leaf))
2444 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2445 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2447 ((or (and (not x-neg) (not y-neg))
2448 (and (not x-pos) (not y-pos)))
2449 ;; Either both are negative or both are positive. The result will be
2450 ;; positive, and as long as the longer.
2451 (if (and x-len y-len (zerop x-len) (zerop y-len))
2452 (specifier-type '(integer 0 0))
2453 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2456 ((or (and (not x-pos) (not y-neg))
2457 (and (not y-neg) (not y-pos)))
2458 ;; Either X is negative and Y is positive of vice-verca. The result
2459 ;; will be negative.
2460 (specifier-type `(integer ,(if (and x-len y-len)
2461 (ash -1 (max x-len y-len))
2464 ;; We can't tell what the sign of the result is going to be. All we
2465 ;; know is that we don't create new bits.
2467 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2469 (specifier-type 'integer))))))
2471 (macrolet ((frob (logfcn)
2472 (let ((fcn-aux (symbolicate logfcn "-DERIVE-TYPE-AUX")))
2473 `(defoptimizer (,logfcn derive-type) ((x y))
2474 (two-arg-derive-type x y #',fcn-aux #',logfcn)))))
2475 ;; FIXME: DEF-FROB, not just FROB
2480 (defoptimizer (integer-length derive-type) ((x))
2481 (let ((x-type (continuation-type x)))
2482 (when (and (numeric-type-p x-type)
2483 (csubtypep x-type (specifier-type 'integer)))
2484 ;; If the X is of type (INTEGER LO HI), then the integer-length
2485 ;; of X is (INTEGER (min lo hi) (max lo hi), basically. Be
2486 ;; careful about LO or HI being NIL, though. Also, if 0 is
2487 ;; contained in X, the lower bound is obviously 0.
2488 (flet ((null-or-min (a b)
2489 (and a b (min (integer-length a)
2490 (integer-length b))))
2492 (and a b (max (integer-length a)
2493 (integer-length b)))))
2494 (let* ((min (numeric-type-low x-type))
2495 (max (numeric-type-high x-type))
2496 (min-len (null-or-min min max))
2497 (max-len (null-or-max min max)))
2498 (when (ctypep 0 x-type)
2500 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2503 ;;;; miscellaneous derive-type methods
2505 (defoptimizer (code-char derive-type) ((code))
2506 (specifier-type 'base-char))
2508 (defoptimizer (values derive-type) ((&rest values))
2509 (values-specifier-type
2510 `(values ,@(mapcar #'(lambda (x)
2511 (type-specifier (continuation-type x)))
2514 ;;;; byte operations
2516 ;;;; We try to turn byte operations into simple logical operations. First, we
2517 ;;;; convert byte specifiers into separate size and position arguments passed
2518 ;;;; to internal %FOO functions. We then attempt to transform the %FOO
2519 ;;;; functions into boolean operations when the size and position are constant
2520 ;;;; and the operands are fixnums.
2522 (macrolet (;; Evaluate body with Size-Var and Pos-Var bound to expressions that
2523 ;; evaluate to the Size and Position of the byte-specifier form
2524 ;; Spec. We may wrap a let around the result of the body to bind
2527 ;; If the spec is a Byte form, then bind the vars to the subforms.
2528 ;; otherwise, evaluate Spec and use the Byte-Size and Byte-Position.
2529 ;; The goal of this transformation is to avoid consing up byte
2530 ;; specifiers and then immediately throwing them away.
2531 (with-byte-specifier ((size-var pos-var spec) &body body)
2532 (once-only ((spec `(macroexpand ,spec))
2534 `(if (and (consp ,spec)
2535 (eq (car ,spec) 'byte)
2536 (= (length ,spec) 3))
2537 (let ((,size-var (second ,spec))
2538 (,pos-var (third ,spec)))
2540 (let ((,size-var `(byte-size ,,temp))
2541 (,pos-var `(byte-position ,,temp)))
2542 `(let ((,,temp ,,spec))
2545 (def-source-transform ldb (spec int)
2546 (with-byte-specifier (size pos spec)
2547 `(%ldb ,size ,pos ,int)))
2549 (def-source-transform dpb (newbyte spec int)
2550 (with-byte-specifier (size pos spec)
2551 `(%dpb ,newbyte ,size ,pos ,int)))
2553 (def-source-transform mask-field (spec int)
2554 (with-byte-specifier (size pos spec)
2555 `(%mask-field ,size ,pos ,int)))
2557 (def-source-transform deposit-field (newbyte spec int)
2558 (with-byte-specifier (size pos spec)
2559 `(%deposit-field ,newbyte ,size ,pos ,int))))
2561 (defoptimizer (%ldb derive-type) ((size posn num))
2562 (let ((size (continuation-type size)))
2563 (if (and (numeric-type-p size)
2564 (csubtypep size (specifier-type 'integer)))
2565 (let ((size-high (numeric-type-high size)))
2566 (if (and size-high (<= size-high sb!vm:word-bits))
2567 (specifier-type `(unsigned-byte ,size-high))
2568 (specifier-type 'unsigned-byte)))
2571 (defoptimizer (%mask-field derive-type) ((size posn num))
2572 (let ((size (continuation-type size))
2573 (posn (continuation-type posn)))
2574 (if (and (numeric-type-p size)
2575 (csubtypep size (specifier-type 'integer))
2576 (numeric-type-p posn)
2577 (csubtypep posn (specifier-type 'integer)))
2578 (let ((size-high (numeric-type-high size))
2579 (posn-high (numeric-type-high posn)))
2580 (if (and size-high posn-high
2581 (<= (+ size-high posn-high) sb!vm:word-bits))
2582 (specifier-type `(unsigned-byte ,(+ size-high posn-high)))
2583 (specifier-type 'unsigned-byte)))
2586 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2587 (let ((size (continuation-type size))
2588 (posn (continuation-type posn))
2589 (int (continuation-type int)))
2590 (if (and (numeric-type-p size)
2591 (csubtypep size (specifier-type 'integer))
2592 (numeric-type-p posn)
2593 (csubtypep posn (specifier-type 'integer))
2594 (numeric-type-p int)
2595 (csubtypep int (specifier-type 'integer)))
2596 (let ((size-high (numeric-type-high size))
2597 (posn-high (numeric-type-high posn))
2598 (high (numeric-type-high int))
2599 (low (numeric-type-low int)))
2600 (if (and size-high posn-high high low
2601 (<= (+ size-high posn-high) sb!vm:word-bits))
2603 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2604 (max (integer-length high)
2605 (integer-length low)
2606 (+ size-high posn-high))))
2610 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2611 (let ((size (continuation-type size))
2612 (posn (continuation-type posn))
2613 (int (continuation-type int)))
2614 (if (and (numeric-type-p size)
2615 (csubtypep size (specifier-type 'integer))
2616 (numeric-type-p posn)
2617 (csubtypep posn (specifier-type 'integer))
2618 (numeric-type-p int)
2619 (csubtypep int (specifier-type 'integer)))
2620 (let ((size-high (numeric-type-high size))
2621 (posn-high (numeric-type-high posn))
2622 (high (numeric-type-high int))
2623 (low (numeric-type-low int)))
2624 (if (and size-high posn-high high low
2625 (<= (+ size-high posn-high) sb!vm:word-bits))
2627 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2628 (max (integer-length high)
2629 (integer-length low)
2630 (+ size-high posn-high))))
2634 (deftransform %ldb ((size posn int)
2635 (fixnum fixnum integer)
2636 (unsigned-byte #.sb!vm:word-bits))
2637 "convert to inline logical ops"
2638 `(logand (ash int (- posn))
2639 (ash ,(1- (ash 1 sb!vm:word-bits))
2640 (- size ,sb!vm:word-bits))))
2642 (deftransform %mask-field ((size posn int)
2643 (fixnum fixnum integer)
2644 (unsigned-byte #.sb!vm:word-bits))
2645 "convert to inline logical ops"
2647 (ash (ash ,(1- (ash 1 sb!vm:word-bits))
2648 (- size ,sb!vm:word-bits))
2651 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2652 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2653 ;;; as the result type, as that would allow result types
2654 ;;; that cover the range -2^(n-1) .. 1-2^n, instead of allowing result types
2655 ;;; of (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2657 (deftransform %dpb ((new size posn int)
2659 (unsigned-byte #.sb!vm:word-bits))
2660 "convert to inline logical ops"
2661 `(let ((mask (ldb (byte size 0) -1)))
2662 (logior (ash (logand new mask) posn)
2663 (logand int (lognot (ash mask posn))))))
2665 (deftransform %dpb ((new size posn int)
2667 (signed-byte #.sb!vm:word-bits))
2668 "convert to inline logical ops"
2669 `(let ((mask (ldb (byte size 0) -1)))
2670 (logior (ash (logand new mask) posn)
2671 (logand int (lognot (ash mask posn))))))
2673 (deftransform %deposit-field ((new size posn int)
2675 (unsigned-byte #.sb!vm:word-bits))
2676 "convert to inline logical ops"
2677 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2678 (logior (logand new mask)
2679 (logand int (lognot mask)))))
2681 (deftransform %deposit-field ((new size posn int)
2683 (signed-byte #.sb!vm:word-bits))
2684 "convert to inline logical ops"
2685 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2686 (logior (logand new mask)
2687 (logand int (lognot mask)))))
2689 ;;; miscellanous numeric transforms
2691 ;;; If a constant appears as the first arg, swap the args.
2692 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2693 (if (and (constant-continuation-p x)
2694 (not (constant-continuation-p y)))
2695 `(,(continuation-function-name (basic-combination-fun node))
2697 ,(continuation-value x))
2698 (give-up-ir1-transform)))
2700 (dolist (x '(= char= + * logior logand logxor))
2701 (%deftransform x '(function * *) #'commutative-arg-swap
2702 "place constant arg last."))
2704 ;;; Handle the case of a constant BOOLE-CODE.
2705 (deftransform boole ((op x y) * * :when :both)
2706 "convert to inline logical ops"
2707 (unless (constant-continuation-p op)
2708 (give-up-ir1-transform "BOOLE code is not a constant."))
2709 (let ((control (continuation-value op)))
2715 (#.boole-c1 '(lognot x))
2716 (#.boole-c2 '(lognot y))
2717 (#.boole-and '(logand x y))
2718 (#.boole-ior '(logior x y))
2719 (#.boole-xor '(logxor x y))
2720 (#.boole-eqv '(logeqv x y))
2721 (#.boole-nand '(lognand x y))
2722 (#.boole-nor '(lognor x y))
2723 (#.boole-andc1 '(logandc1 x y))
2724 (#.boole-andc2 '(logandc2 x y))
2725 (#.boole-orc1 '(logorc1 x y))
2726 (#.boole-orc2 '(logorc2 x y))
2728 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2731 ;;;; converting special case multiply/divide to shifts
2733 ;;; If arg is a constant power of two, turn * into a shift.
2734 (deftransform * ((x y) (integer integer) * :when :both)
2735 "convert x*2^k to shift"
2736 (unless (constant-continuation-p y)
2737 (give-up-ir1-transform))
2738 (let* ((y (continuation-value y))
2740 (len (1- (integer-length y-abs))))
2741 (unless (= y-abs (ash 1 len))
2742 (give-up-ir1-transform))
2747 ;;; If both arguments and the result are (unsigned-byte 32), try to come up
2748 ;;; with a ``better'' multiplication using multiplier recoding. There are two
2749 ;;; different ways the multiplier can be recoded. The more obvious is to shift
2750 ;;; X by the correct amount for each bit set in Y and to sum the results. But
2751 ;;; if there is a string of bits that are all set, you can add X shifted by
2752 ;;; one more then the bit position of the first set bit and subtract X shifted
2753 ;;; by the bit position of the last set bit. We can't use this second method
2754 ;;; when the high order bit is bit 31 because shifting by 32 doesn't work
2756 (deftransform * ((x y)
2757 ((unsigned-byte 32) (unsigned-byte 32))
2759 "recode as shift and add"
2760 (unless (constant-continuation-p y)
2761 (give-up-ir1-transform))
2762 (let ((y (continuation-value y))
2765 (labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x))
2770 `(+ ,result ,(tub32 next-factor))
2772 (declare (inline add))
2773 (dotimes (bitpos 32)
2775 (when (not (logbitp bitpos y))
2776 (add (if (= (1+ first-one) bitpos)
2777 ;; There is only a single bit in the string.
2779 ;; There are at least two.
2780 `(- ,(tub32 `(ash x ,bitpos))
2781 ,(tub32 `(ash x ,first-one)))))
2782 (setf first-one nil))
2783 (when (logbitp bitpos y)
2784 (setf first-one bitpos))))
2786 (cond ((= first-one 31))
2790 (add `(- ,(tub32 '(ash x 31)) ,(tub32 `(ash x ,first-one))))))
2794 ;;; If arg is a constant power of two, turn FLOOR into a shift and mask.
2795 ;;; If CEILING, add in (1- (ABS Y)) and then do FLOOR.
2796 (flet ((frob (y ceil-p)
2797 (unless (constant-continuation-p y)
2798 (give-up-ir1-transform))
2799 (let* ((y (continuation-value y))
2801 (len (1- (integer-length y-abs))))
2802 (unless (= y-abs (ash 1 len))
2803 (give-up-ir1-transform))
2804 (let ((shift (- len))
2806 `(let ,(when ceil-p `((x (+ x ,(1- y-abs)))))
2808 `(values (ash (- x) ,shift)
2809 (- (logand (- x) ,mask)))
2810 `(values (ash x ,shift)
2811 (logand x ,mask))))))))
2812 (deftransform floor ((x y) (integer integer) *)
2813 "convert division by 2^k to shift"
2815 (deftransform ceiling ((x y) (integer integer) *)
2816 "convert division by 2^k to shift"
2819 ;;; Do the same for MOD.
2820 (deftransform mod ((x y) (integer integer) * :when :both)
2821 "convert remainder mod 2^k to LOGAND"
2822 (unless (constant-continuation-p y)
2823 (give-up-ir1-transform))
2824 (let* ((y (continuation-value y))
2826 (len (1- (integer-length y-abs))))
2827 (unless (= y-abs (ash 1 len))
2828 (give-up-ir1-transform))
2829 (let ((mask (1- y-abs)))
2831 `(- (logand (- x) ,mask))
2832 `(logand x ,mask)))))
2834 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2835 (deftransform truncate ((x y) (integer integer))
2836 "convert division by 2^k to shift"
2837 (unless (constant-continuation-p y)
2838 (give-up-ir1-transform))
2839 (let* ((y (continuation-value y))
2841 (len (1- (integer-length y-abs))))
2842 (unless (= y-abs (ash 1 len))
2843 (give-up-ir1-transform))
2844 (let* ((shift (- len))
2847 (values ,(if (minusp y)
2849 `(- (ash (- x) ,shift)))
2850 (- (logand (- x) ,mask)))
2851 (values ,(if (minusp y)
2852 `(- (ash (- x) ,shift))
2854 (logand x ,mask))))))
2856 ;;; And the same for REM.
2857 (deftransform rem ((x y) (integer integer) * :when :both)
2858 "convert remainder mod 2^k to LOGAND"
2859 (unless (constant-continuation-p y)
2860 (give-up-ir1-transform))
2861 (let* ((y (continuation-value y))
2863 (len (1- (integer-length y-abs))))
2864 (unless (= y-abs (ash 1 len))
2865 (give-up-ir1-transform))
2866 (let ((mask (1- y-abs)))
2868 (- (logand (- x) ,mask))
2869 (logand x ,mask)))))
2871 ;;;; arithmetic and logical identity operation elimination
2873 ;;;; Flush calls to various arith functions that convert to the identity
2874 ;;;; function or a constant.
2876 (dolist (stuff '((ash 0 x)
2881 (logxor -1 (lognot x))
2883 (destructuring-bind (name identity result) stuff
2884 (deftransform name ((x y) `(* (constant-argument (member ,identity))) '*
2885 :eval-name t :when :both)
2886 "fold identity operations"
2889 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2890 ;;; (* 0 -4.0) is -0.0.
2891 (deftransform - ((x y) ((constant-argument (member 0)) rational) *
2893 "convert (- 0 x) to negate"
2895 (deftransform * ((x y) (rational (constant-argument (member 0))) *
2897 "convert (* x 0) to 0."
2900 ;;; Return T if in an arithmetic op including continuations X and Y, the
2901 ;;; result type is not affected by the type of X. That is, Y is at least as
2902 ;;; contagious as X.
2904 (defun not-more-contagious (x y)
2905 (declare (type continuation x y))
2906 (let ((x (continuation-type x))
2907 (y (continuation-type y)))
2908 (values (type= (numeric-contagion x y)
2909 (numeric-contagion y y)))))
2910 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2911 ;;; needs more work as valid transforms are missed; some cases are
2912 ;;; specific to particular transform functions so the use of this
2913 ;;; function may need a re-think.
2914 (defun not-more-contagious (x y)
2915 (declare (type continuation x y))
2916 (flet ((simple-numeric-type (num)
2917 (and (numeric-type-p num)
2918 ;; Return non-NIL if NUM is integer, rational, or a float
2919 ;; of some type (but not FLOAT)
2920 (case (numeric-type-class num)
2924 (numeric-type-format num))
2927 (let ((x (continuation-type x))
2928 (y (continuation-type y)))
2929 (if (and (simple-numeric-type x)
2930 (simple-numeric-type y))
2931 (values (type= (numeric-contagion x y)
2932 (numeric-contagion y y)))))))
2936 ;;; If y is not constant, not zerop, or is contagious, or a
2937 ;;; positive float +0.0 then give up.
2938 (deftransform + ((x y) (t (constant-argument t)) * :when :both)
2940 (let ((val (continuation-value y)))
2941 (unless (and (zerop val)
2942 (not (and (floatp val) (plusp (float-sign val))))
2943 (not-more-contagious y x))
2944 (give-up-ir1-transform)))
2949 ;;; If y is not constant, not zerop, or is contagious, or a
2950 ;;; negative float -0.0 then give up.
2951 (deftransform - ((x y) (t (constant-argument t)) * :when :both)
2953 (let ((val (continuation-value y)))
2954 (unless (and (zerop val)
2955 (not (and (floatp val) (minusp (float-sign val))))
2956 (not-more-contagious y x))
2957 (give-up-ir1-transform)))
2960 ;;; Fold (OP x +/-1)
2961 (dolist (stuff '((* x (%negate x))
2964 (destructuring-bind (name result minus-result) stuff
2965 (deftransform name ((x y) '(t (constant-argument real)) '* :eval-name t
2967 "fold identity operations"
2968 (let ((val (continuation-value y)))
2969 (unless (and (= (abs val) 1)
2970 (not-more-contagious y x))
2971 (give-up-ir1-transform))
2972 (if (minusp val) minus-result result)))))
2974 ;;; Fold (expt x n) into multiplications for small integral values of
2975 ;;; N; convert (expt x 1/2) to sqrt.
2976 (deftransform expt ((x y) (t (constant-argument real)) *)
2977 "recode as multiplication or sqrt"
2978 (let ((val (continuation-value y)))
2979 ;; If Y would cause the result to be promoted to the same type as
2980 ;; Y, we give up. If not, then the result will be the same type
2981 ;; as X, so we can replace the exponentiation with simple
2982 ;; multiplication and division for small integral powers.
2983 (unless (not-more-contagious y x)
2984 (give-up-ir1-transform))
2985 (cond ((zerop val) '(float 1 x))
2986 ((= val 2) '(* x x))
2987 ((= val -2) '(/ (* x x)))
2988 ((= val 3) '(* x x x))
2989 ((= val -3) '(/ (* x x x)))
2990 ((= val 1/2) '(sqrt x))
2991 ((= val -1/2) '(/ (sqrt x)))
2992 (t (give-up-ir1-transform)))))
2994 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
2995 ;;; transformations?
2996 ;;; Perhaps we should have to prove that the denominator is nonzero before
2997 ;;; doing them? (Also the DOLIST over macro calls is weird. Perhaps
2998 ;;; just FROB?) -- WHN 19990917
3000 ;;; FIXME: What gives with the single quotes in the argument lists
3001 ;;; for DEFTRANSFORMs here? Does that work? Is it needed? Why?
3002 (dolist (name '(ash /))
3003 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3004 :eval-name t :when :both)
3007 (dolist (name '(truncate round floor ceiling))
3008 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3009 :eval-name t :when :both)
3013 ;;;; character operations
3015 (deftransform char-equal ((a b) (base-char base-char))
3017 '(let* ((ac (char-code a))
3019 (sum (logxor ac bc)))
3021 (when (eql sum #x20)
3022 (let ((sum (+ ac bc)))
3023 (and (> sum 161) (< sum 213)))))))
3025 (deftransform char-upcase ((x) (base-char))
3027 '(let ((n-code (char-code x)))
3028 (if (and (> n-code #o140) ; Octal 141 is #\a.
3029 (< n-code #o173)) ; Octal 172 is #\z.
3030 (code-char (logxor #x20 n-code))
3033 (deftransform char-downcase ((x) (base-char))
3035 '(let ((n-code (char-code x)))
3036 (if (and (> n-code 64) ; 65 is #\A.
3037 (< n-code 91)) ; 90 is #\Z.
3038 (code-char (logxor #x20 n-code))
3041 ;;;; equality predicate transforms
3043 ;;; Return true if X and Y are continuations whose only use is a reference
3044 ;;; to the same leaf, and the value of the leaf cannot change.
3045 (defun same-leaf-ref-p (x y)
3046 (declare (type continuation x y))
3047 (let ((x-use (continuation-use x))
3048 (y-use (continuation-use y)))
3051 (eq (ref-leaf x-use) (ref-leaf y-use))
3052 (constant-reference-p x-use))))
3054 ;;; If X and Y are the same leaf, then the result is true. Otherwise, if
3055 ;;; there is no intersection between the types of the arguments, then the
3056 ;;; result is definitely false.
3057 (deftransform simple-equality-transform ((x y) * * :defun-only t
3059 (cond ((same-leaf-ref-p x y)
3061 ((not (types-intersect (continuation-type x) (continuation-type y)))
3064 (give-up-ir1-transform))))
3066 (dolist (x '(eq char= equal))
3067 (%deftransform x '(function * *) #'simple-equality-transform))
3069 ;;; Similar to SIMPLE-EQUALITY-PREDICATE, except that we also try to convert
3070 ;;; to a type-specific predicate or EQ:
3071 ;;; -- If both args are characters, convert to CHAR=. This is better than just
3072 ;;; converting to EQ, since CHAR= may have special compilation strategies
3073 ;;; for non-standard representations, etc.
3074 ;;; -- If either arg is definitely not a number, then we can compare with EQ.
3075 ;;; -- Otherwise, we try to put the arg we know more about second. If X is
3076 ;;; constant then we put it second. If X is a subtype of Y, we put it
3077 ;;; second. These rules make it easier for the back end to match these
3078 ;;; interesting cases.
3079 ;;; -- If Y is a fixnum, then we quietly pass because the back end can handle
3080 ;;; that case, otherwise give an efficency note.
3081 (deftransform eql ((x y) * * :when :both)
3082 "convert to simpler equality predicate"
3083 (let ((x-type (continuation-type x))
3084 (y-type (continuation-type y))
3085 (char-type (specifier-type 'character))
3086 (number-type (specifier-type 'number)))
3087 (cond ((same-leaf-ref-p x y)
3089 ((not (types-intersect x-type y-type))
3091 ((and (csubtypep x-type char-type)
3092 (csubtypep y-type char-type))
3094 ((or (not (types-intersect x-type number-type))
3095 (not (types-intersect y-type number-type)))
3097 ((and (not (constant-continuation-p y))
3098 (or (constant-continuation-p x)
3099 (and (csubtypep x-type y-type)
3100 (not (csubtypep y-type x-type)))))
3103 (give-up-ir1-transform)))))
3105 ;;; Convert to EQL if both args are rational and complexp is specified
3106 ;;; and the same for both.
3107 (deftransform = ((x y) * * :when :both)
3109 (let ((x-type (continuation-type x))
3110 (y-type (continuation-type y)))
3111 (if (and (csubtypep x-type (specifier-type 'number))
3112 (csubtypep y-type (specifier-type 'number)))
3113 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3114 (csubtypep y-type (specifier-type 'float)))
3115 (and (csubtypep x-type (specifier-type '(complex float)))
3116 (csubtypep y-type (specifier-type '(complex float)))))
3117 ;; They are both floats. Leave as = so that -0.0 is
3118 ;; handled correctly.
3119 (give-up-ir1-transform))
3120 ((or (and (csubtypep x-type (specifier-type 'rational))
3121 (csubtypep y-type (specifier-type 'rational)))
3122 (and (csubtypep x-type (specifier-type '(complex rational)))
3123 (csubtypep y-type (specifier-type '(complex rational)))))
3124 ;; They are both rationals and complexp is the same. Convert
3128 (give-up-ir1-transform
3129 "The operands might not be the same type.")))
3130 (give-up-ir1-transform
3131 "The operands might not be the same type."))))
3133 ;;; If Cont's type is a numeric type, then return the type, otherwise
3134 ;;; GIVE-UP-IR1-TRANSFORM.
3135 (defun numeric-type-or-lose (cont)
3136 (declare (type continuation cont))
3137 (let ((res (continuation-type cont)))
3138 (unless (numeric-type-p res) (give-up-ir1-transform))
3141 ;;; See whether we can statically determine (< X Y) using type information.
3142 ;;; If X's high bound is < Y's low, then X < Y. Similarly, if X's low is >=
3143 ;;; to Y's high, the X >= Y (so return NIL). If not, at least make sure any
3144 ;;; constant arg is second.
3146 ;;; KLUDGE: Why should constant argument be second? It would be nice to find
3147 ;;; out and explain. -- WHN 19990917
3148 #!-propagate-float-type
3149 (defun ir1-transform-< (x y first second inverse)
3150 (if (same-leaf-ref-p x y)
3152 (let* ((x-type (numeric-type-or-lose x))
3153 (x-lo (numeric-type-low x-type))
3154 (x-hi (numeric-type-high x-type))
3155 (y-type (numeric-type-or-lose y))
3156 (y-lo (numeric-type-low y-type))
3157 (y-hi (numeric-type-high y-type)))
3158 (cond ((and x-hi y-lo (< x-hi y-lo))
3160 ((and y-hi x-lo (>= x-lo y-hi))
3162 ((and (constant-continuation-p first)
3163 (not (constant-continuation-p second)))
3166 (give-up-ir1-transform))))))
3167 #!+propagate-float-type
3168 (defun ir1-transform-< (x y first second inverse)
3169 (if (same-leaf-ref-p x y)
3171 (let ((xi (numeric-type->interval (numeric-type-or-lose x)))
3172 (yi (numeric-type->interval (numeric-type-or-lose y))))
3173 (cond ((interval-< xi yi)
3175 ((interval->= xi yi)
3177 ((and (constant-continuation-p first)
3178 (not (constant-continuation-p second)))
3181 (give-up-ir1-transform))))))
3183 (deftransform < ((x y) (integer integer) * :when :both)
3184 (ir1-transform-< x y x y '>))
3186 (deftransform > ((x y) (integer integer) * :when :both)
3187 (ir1-transform-< y x x y '<))
3189 #!+propagate-float-type
3190 (deftransform < ((x y) (float float) * :when :both)
3191 (ir1-transform-< x y x y '>))
3193 #!+propagate-float-type
3194 (deftransform > ((x y) (float float) * :when :both)
3195 (ir1-transform-< y x x y '<))
3197 ;;;; converting N-arg comparisons
3199 ;;;; We convert calls to N-arg comparison functions such as < into
3200 ;;;; two-arg calls. This transformation is enabled for all such
3201 ;;;; comparisons in this file. If any of these predicates are not
3202 ;;;; open-coded, then the transformation should be removed at some
3203 ;;;; point to avoid pessimization.
3205 ;;; This function is used for source transformation of N-arg
3206 ;;; comparison functions other than inequality. We deal both with
3207 ;;; converting to two-arg calls and inverting the sense of the test,
3208 ;;; if necessary. If the call has two args, then we pass or return a
3209 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3210 ;;; then we transform to code that returns true. Otherwise, we bind
3211 ;;; all the arguments and expand into a bunch of IFs.
3212 (declaim (ftype (function (symbol list boolean) *) multi-compare))
3213 (defun multi-compare (predicate args not-p)
3214 (let ((nargs (length args)))
3215 (cond ((< nargs 1) (values nil t))
3216 ((= nargs 1) `(progn ,@args t))
3219 `(if (,predicate ,(first args) ,(second args)) nil t)
3222 (do* ((i (1- nargs) (1- i))
3224 (current (gensym) (gensym))
3225 (vars (list current) (cons current vars))
3226 (result 't (if not-p
3227 `(if (,predicate ,current ,last)
3229 `(if (,predicate ,current ,last)
3232 `((lambda ,vars ,result) . ,args)))))))
3234 (def-source-transform = (&rest args) (multi-compare '= args nil))
3235 (def-source-transform < (&rest args) (multi-compare '< args nil))
3236 (def-source-transform > (&rest args) (multi-compare '> args nil))
3237 (def-source-transform <= (&rest args) (multi-compare '> args t))
3238 (def-source-transform >= (&rest args) (multi-compare '< args t))
3240 (def-source-transform char= (&rest args) (multi-compare 'char= args nil))
3241 (def-source-transform char< (&rest args) (multi-compare 'char< args nil))
3242 (def-source-transform char> (&rest args) (multi-compare 'char> args nil))
3243 (def-source-transform char<= (&rest args) (multi-compare 'char> args t))
3244 (def-source-transform char>= (&rest args) (multi-compare 'char< args t))
3246 (def-source-transform char-equal (&rest args) (multi-compare 'char-equal args nil))
3247 (def-source-transform char-lessp (&rest args) (multi-compare 'char-lessp args nil))
3248 (def-source-transform char-greaterp (&rest args) (multi-compare 'char-greaterp args nil))
3249 (def-source-transform char-not-greaterp (&rest args) (multi-compare 'char-greaterp args t))
3250 (def-source-transform char-not-lessp (&rest args) (multi-compare 'char-lessp args t))
3252 ;;; This function does source transformation of N-arg inequality
3253 ;;; functions such as /=. This is similar to Multi-Compare in the <3
3254 ;;; arg cases. If there are more than two args, then we expand into
3255 ;;; the appropriate n^2 comparisons only when speed is important.
3256 (declaim (ftype (function (symbol list) *) multi-not-equal))
3257 (defun multi-not-equal (predicate args)
3258 (let ((nargs (length args)))
3259 (cond ((< nargs 1) (values nil t))
3260 ((= nargs 1) `(progn ,@args t))
3262 `(if (,predicate ,(first args) ,(second args)) nil t))
3263 ((not (policy nil (and (>= speed space)
3264 (>= speed compilation-speed))))
3267 (let ((vars (make-gensym-list nargs)))
3268 (do ((var vars next)
3269 (next (cdr vars) (cdr next))
3272 `((lambda ,vars ,result) . ,args))
3273 (let ((v1 (first var)))
3275 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3277 (def-source-transform /= (&rest args) (multi-not-equal '= args))
3278 (def-source-transform char/= (&rest args) (multi-not-equal 'char= args))
3279 (def-source-transform char-not-equal (&rest args) (multi-not-equal 'char-equal args))
3281 ;;; Expand MAX and MIN into the obvious comparisons.
3282 (def-source-transform max (arg &rest more-args)
3283 (if (null more-args)
3285 (once-only ((arg1 arg)
3286 (arg2 `(max ,@more-args)))
3287 `(if (> ,arg1 ,arg2)
3289 (def-source-transform min (arg &rest more-args)
3290 (if (null more-args)
3292 (once-only ((arg1 arg)
3293 (arg2 `(min ,@more-args)))
3294 `(if (< ,arg1 ,arg2)
3297 ;;;; converting N-arg arithmetic functions
3299 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3300 ;;;; versions, and degenerate cases are flushed.
3302 ;;; Left-associate First-Arg and More-Args using Function.
3303 (declaim (ftype (function (symbol t list) list) associate-arguments))
3304 (defun associate-arguments (function first-arg more-args)
3305 (let ((next (rest more-args))
3306 (arg (first more-args)))
3308 `(,function ,first-arg ,arg)
3309 (associate-arguments function `(,function ,first-arg ,arg) next))))
3311 ;;; Do source transformations for transitive functions such as +.
3312 ;;; One-arg cases are replaced with the arg and zero arg cases with
3313 ;;; the identity. If Leaf-Fun is true, then replace two-arg calls with
3314 ;;; a call to that function.
3315 (defun source-transform-transitive (fun args identity &optional leaf-fun)
3316 (declare (symbol fun leaf-fun) (list args))
3319 (1 `(values ,(first args)))
3321 `(,leaf-fun ,(first args) ,(second args))
3324 (associate-arguments fun (first args) (rest args)))))
3326 (def-source-transform + (&rest args) (source-transform-transitive '+ args 0))
3327 (def-source-transform * (&rest args) (source-transform-transitive '* args 1))
3328 (def-source-transform logior (&rest args) (source-transform-transitive 'logior args 0))
3329 (def-source-transform logxor (&rest args) (source-transform-transitive 'logxor args 0))
3330 (def-source-transform logand (&rest args) (source-transform-transitive 'logand args -1))
3332 (def-source-transform logeqv (&rest args)
3333 (if (evenp (length args))
3334 `(lognot (logxor ,@args))
3337 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3338 ;;; because when they are given one argument, they return its absolute
3341 (def-source-transform gcd (&rest args)
3344 (1 `(abs (the integer ,(first args))))
3346 (t (associate-arguments 'gcd (first args) (rest args)))))
3348 (def-source-transform lcm (&rest args)
3351 (1 `(abs (the integer ,(first args))))
3353 (t (associate-arguments 'lcm (first args) (rest args)))))
3355 ;;; Do source transformations for intransitive n-arg functions such as
3356 ;;; /. With one arg, we form the inverse. With two args we pass.
3357 ;;; Otherwise we associate into two-arg calls.
3358 (declaim (ftype (function (symbol list t) list) source-transform-intransitive))
3359 (defun source-transform-intransitive (function args inverse)
3361 ((0 2) (values nil t))
3362 (1 `(,@inverse ,(first args)))
3363 (t (associate-arguments function (first args) (rest args)))))
3365 (def-source-transform - (&rest args)
3366 (source-transform-intransitive '- args '(%negate)))
3367 (def-source-transform / (&rest args)
3368 (source-transform-intransitive '/ args '(/ 1)))
3372 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3373 ;;; only needs to understand one kind of variable-argument call. It is
3374 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3375 (def-source-transform apply (fun arg &rest more-args)
3376 (let ((args (cons arg more-args)))
3377 `(multiple-value-call ,fun
3378 ,@(mapcar #'(lambda (x)
3381 (values-list ,(car (last args))))))
3385 ;;;; If the control string is a compile-time constant, then replace it
3386 ;;;; with a use of the FORMATTER macro so that the control string is
3387 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3388 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3389 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3391 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3392 :policy (> speed space))
3393 (unless (constant-continuation-p control)
3394 (give-up-ir1-transform "The control string is not a constant."))
3395 (let ((arg-names (make-gensym-list (length args))))
3396 `(lambda (dest control ,@arg-names)
3397 (declare (ignore control))
3398 (format dest (formatter ,(continuation-value control)) ,@arg-names))))
3400 (deftransform format ((stream control &rest args) (stream function &rest t) *
3401 :policy (> speed space))
3402 (let ((arg-names (make-gensym-list (length args))))
3403 `(lambda (stream control ,@arg-names)
3404 (funcall control stream ,@arg-names)
3407 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3408 :policy (> speed space))
3409 (let ((arg-names (make-gensym-list (length args))))
3410 `(lambda (tee control ,@arg-names)
3411 (declare (ignore tee))
3412 (funcall control *standard-output* ,@arg-names)