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.
220 (defstruct (interval (: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 ;;; Convert a numeric-type object to an interval object.
286 (defun numeric-type->interval (x)
287 (declare (type numeric-type x))
288 (make-interval :low (numeric-type-low x)
289 :high (numeric-type-high x)))
291 (defun copy-interval-limit (limit)
296 (defun copy-interval (x)
297 (declare (type interval x))
298 (make-interval :low (copy-interval-limit (interval-low x))
299 :high (copy-interval-limit (interval-high x))))
301 ;;; Given a point P contained in the interval X, split X into two
302 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
303 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
304 ;;; contains P. You can specify both to be T or NIL.
305 (defun interval-split (p x &optional close-lower close-upper)
306 (declare (type number p)
308 (list (make-interval :low (copy-interval-limit (interval-low x))
309 :high (if close-lower p (list p)))
310 (make-interval :low (if close-upper (list p) p)
311 :high (copy-interval-limit (interval-high x)))))
313 ;;; Return the closure of the interval. That is, convert open bounds
314 ;;; to closed bounds.
315 (defun interval-closure (x)
316 (declare (type interval x))
317 (make-interval :low (bound-value (interval-low x))
318 :high (bound-value (interval-high x))))
320 (defun signed-zero->= (x y)
324 (>= (float-sign (float x))
325 (float-sign (float y))))))
327 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
328 ;;; '-. Otherwise return NIL.
330 (defun interval-range-info (x &optional (point 0))
331 (declare (type interval x))
332 (let ((lo (interval-low x))
333 (hi (interval-high x)))
334 (cond ((and lo (signed-zero->= (bound-value lo) point))
336 ((and hi (signed-zero->= point (bound-value hi)))
340 (defun interval-range-info (x &optional (point 0))
341 (declare (type interval x))
342 (labels ((signed->= (x y)
343 (if (and (zerop x) (zerop y) (floatp x) (floatp y))
344 (>= (float-sign x) (float-sign y))
346 (let ((lo (interval-low x))
347 (hi (interval-high x)))
348 (cond ((and lo (signed->= (bound-value lo) point))
350 ((and hi (signed->= point (bound-value hi)))
355 ;;; Test to see whether the interval X is bounded. HOW determines the
356 ;;; test, and should be either ABOVE, BELOW, or BOTH.
357 (defun interval-bounded-p (x how)
358 (declare (type interval x))
365 (and (interval-low x) (interval-high x)))))
367 ;;; signed zero comparison functions. Use these functions if we need
368 ;;; to distinguish between signed zeroes.
369 (defun signed-zero-< (x y)
373 (< (float-sign (float x))
374 (float-sign (float y))))))
375 (defun signed-zero-> (x y)
379 (> (float-sign (float x))
380 (float-sign (float y))))))
381 (defun signed-zero-= (x y)
384 (= (float-sign (float x))
385 (float-sign (float y)))))
386 (defun signed-zero-<= (x y)
390 (<= (float-sign (float x))
391 (float-sign (float y))))))
393 ;;; See whether the interval X contains the number P, taking into
394 ;;; account that the interval might not be closed.
395 (defun interval-contains-p (p x)
396 (declare (type number p)
398 ;; Does the interval X contain the number P? This would be a lot
399 ;; easier if all intervals were closed!
400 (let ((lo (interval-low x))
401 (hi (interval-high x)))
403 ;; The interval is bounded
404 (if (and (signed-zero-<= (bound-value lo) p)
405 (signed-zero-<= p (bound-value hi)))
406 ;; P is definitely in the closure of the interval.
407 ;; We just need to check the end points now.
408 (cond ((signed-zero-= p (bound-value lo))
410 ((signed-zero-= p (bound-value hi))
415 ;; Interval with upper bound
416 (if (signed-zero-< p (bound-value hi))
418 (and (numberp hi) (signed-zero-= p hi))))
420 ;; Interval with lower bound
421 (if (signed-zero-> p (bound-value lo))
423 (and (numberp lo) (signed-zero-= p lo))))
425 ;; Interval with no bounds
428 ;;; Determine if two intervals X and Y intersect. Return T if so. If
429 ;;; CLOSED-INTERVALS-P is T, the treat the intervals as if they were
430 ;;; closed. Otherwise the intervals are treated as they are.
432 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
433 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
434 ;;; is T, then they do intersect because we use the closure of X = [0,
435 ;;; 1] and Y = [1, 2] to determine intersection.
436 (defun interval-intersect-p (x y &optional closed-intervals-p)
437 (declare (type interval x y))
438 (multiple-value-bind (intersect diff)
439 (interval-intersection/difference (if closed-intervals-p
442 (if closed-intervals-p
445 (declare (ignore diff))
448 ;;; Are the two intervals adjacent? That is, is there a number
449 ;;; between the two intervals that is not an element of either
450 ;;; interval? If so, they are not adjacent. For example [0, 1) and
451 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
452 ;;; between both intervals.
453 (defun interval-adjacent-p (x y)
454 (declare (type interval x y))
455 (flet ((adjacent (lo hi)
456 ;; Check to see whether lo and hi are adjacent. If either is
457 ;; nil, they can't be adjacent.
458 (when (and lo hi (= (bound-value lo) (bound-value hi)))
459 ;; The bounds are equal. They are adjacent if one of
460 ;; them is closed (a number). If both are open (consp),
461 ;; then there is a number that lies between them.
462 (or (numberp lo) (numberp hi)))))
463 (or (adjacent (interval-low y) (interval-high x))
464 (adjacent (interval-low x) (interval-high y)))))
466 ;;; Compute the intersection and difference between two intervals.
467 ;;; Two values are returned: the intersection and the difference.
469 ;;; Let the two intervals be X and Y, and let I and D be the two
470 ;;; values returned by this function. Then I = X intersect Y. If I
471 ;;; is NIL (the empty set), then D is X union Y, represented as the
472 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
473 ;;; - I, which is a list of two intervals.
475 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
476 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
477 (defun interval-intersection/difference (x y)
478 (declare (type interval x y))
479 (let ((x-lo (interval-low x))
480 (x-hi (interval-high x))
481 (y-lo (interval-low y))
482 (y-hi (interval-high y)))
485 ;; If p is an open bound, make it closed. If p is a closed
486 ;; bound, make it open.
491 ;; Test whether P is in the interval.
492 (when (interval-contains-p (bound-value p)
493 (interval-closure int))
494 (let ((lo (interval-low int))
495 (hi (interval-high int)))
496 ;; Check for endpoints
497 (cond ((and lo (= (bound-value p) (bound-value lo)))
498 (not (and (consp p) (numberp lo))))
499 ((and hi (= (bound-value p) (bound-value hi)))
500 (not (and (numberp p) (consp hi))))
502 (test-lower-bound (p int)
503 ;; P is a lower bound of an interval.
506 (not (interval-bounded-p int 'below))))
507 (test-upper-bound (p int)
508 ;; P is an upper bound of an interval
511 (not (interval-bounded-p int 'above)))))
512 (let ((x-lo-in-y (test-lower-bound x-lo y))
513 (x-hi-in-y (test-upper-bound x-hi y))
514 (y-lo-in-x (test-lower-bound y-lo x))
515 (y-hi-in-x (test-upper-bound y-hi x)))
516 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
517 ;; Intervals intersect. Let's compute the intersection
518 ;; and the difference.
519 (multiple-value-bind (lo left-lo left-hi)
520 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
521 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
522 (multiple-value-bind (hi right-lo right-hi)
524 (values x-hi (opposite-bound x-hi) y-hi))
526 (values y-hi (opposite-bound y-hi) x-hi)))
527 (values (make-interval :low lo :high hi)
528 (list (make-interval :low left-lo
530 (make-interval :low right-lo
533 (values nil (list x y))))))))
535 ;;; If intervals X and Y intersect, return a new interval that is the
536 ;;; union of the two. If they do not intersect, return NIL.
537 (defun interval-merge-pair (x y)
538 (declare (type interval x y))
539 ;; If x and y intersect or are adjacent, create the union.
540 ;; Otherwise return nil
541 (when (or (interval-intersect-p x y)
542 (interval-adjacent-p x y))
543 (flet ((select-bound (x1 x2 min-op max-op)
544 (let ((x1-val (bound-value x1))
545 (x2-val (bound-value x2)))
547 ;; Both bounds are finite. Select the right one.
548 (cond ((funcall min-op x1-val x2-val)
549 ;; x1 definitely better
551 ((funcall max-op x1-val x2-val)
552 ;; x2 definitely better
555 ;; Bounds are equal. Select either
556 ;; value and make it open only if
558 (set-bound x1-val (and (consp x1) (consp x2))))))
560 ;; At least one bound is not finite. The
561 ;; non-finite bound always wins.
563 (let* ((x-lo (copy-interval-limit (interval-low x)))
564 (x-hi (copy-interval-limit (interval-high x)))
565 (y-lo (copy-interval-limit (interval-low y)))
566 (y-hi (copy-interval-limit (interval-high y))))
567 (make-interval :low (select-bound x-lo y-lo #'< #'>)
568 :high (select-bound x-hi y-hi #'> #'<))))))
570 ;;; basic arithmetic operations on intervals. We probably should do
571 ;;; true interval arithmetic here, but it's complicated because we
572 ;;; have float and integer types and bounds can be open or closed.
574 ;;; The negative of an interval
575 (defun interval-neg (x)
576 (declare (type interval x))
577 (make-interval :low (bound-func #'- (interval-high x))
578 :high (bound-func #'- (interval-low x))))
580 ;;; Add two intervals
581 (defun interval-add (x y)
582 (declare (type interval x y))
583 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
584 :high (bound-binop + (interval-high x) (interval-high y))))
586 ;;; Subtract two intervals
587 (defun interval-sub (x y)
588 (declare (type interval x y))
589 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
590 :high (bound-binop - (interval-high x) (interval-low y))))
592 ;;; Multiply two intervals
593 (defun interval-mul (x y)
594 (declare (type interval x y))
595 (flet ((bound-mul (x y)
596 (cond ((or (null x) (null y))
597 ;; Multiply by infinity is infinity
599 ((or (and (numberp x) (zerop x))
600 (and (numberp y) (zerop y)))
601 ;; Multiply by closed zero is special. The result
602 ;; is always a closed bound. But don't replace this
603 ;; with zero; we want the multiplication to produce
604 ;; the correct signed zero, if needed.
605 (* (bound-value x) (bound-value y)))
606 ((or (and (floatp x) (float-infinity-p x))
607 (and (floatp y) (float-infinity-p y)))
608 ;; Infinity times anything is infinity
611 ;; General multiply. The result is open if either is open.
612 (bound-binop * x y)))))
613 (let ((x-range (interval-range-info x))
614 (y-range (interval-range-info y)))
615 (cond ((null x-range)
616 ;; Split x into two and multiply each separately
617 (destructuring-bind (x- x+) (interval-split 0 x t t)
618 (interval-merge-pair (interval-mul x- y)
619 (interval-mul x+ y))))
621 ;; Split y into two and multiply each separately
622 (destructuring-bind (y- y+) (interval-split 0 y t t)
623 (interval-merge-pair (interval-mul x y-)
624 (interval-mul x y+))))
626 (interval-neg (interval-mul (interval-neg x) y)))
628 (interval-neg (interval-mul x (interval-neg y))))
629 ((and (eq x-range '+) (eq y-range '+))
630 ;; If we are here, X and Y are both positive
631 (make-interval :low (bound-mul (interval-low x) (interval-low y))
632 :high (bound-mul (interval-high x) (interval-high y))))
634 (error "This shouldn't happen!"))))))
636 ;;; Divide two intervals.
637 (defun interval-div (top bot)
638 (declare (type interval top bot))
639 (flet ((bound-div (x y y-low-p)
642 ;; Divide by infinity means result is 0. However,
643 ;; we need to watch out for the sign of the result,
644 ;; to correctly handle signed zeros. We also need
645 ;; to watch out for positive or negative infinity.
646 (if (floatp (bound-value x))
648 (- (float-sign (bound-value x) 0.0))
649 (float-sign (bound-value x) 0.0))
651 ((zerop (bound-value y))
652 ;; Divide by zero means result is infinity
654 ((and (numberp x) (zerop x))
655 ;; Zero divided by anything is zero.
658 (bound-binop / x y)))))
659 (let ((top-range (interval-range-info top))
660 (bot-range (interval-range-info bot)))
661 (cond ((null bot-range)
662 ;; The denominator contains zero, so anything goes!
663 (make-interval :low nil :high nil))
665 ;; Denominator is negative so flip the sign, compute the
666 ;; result, and flip it back.
667 (interval-neg (interval-div top (interval-neg bot))))
669 ;; Split top into two positive and negative parts, and
670 ;; divide each separately
671 (destructuring-bind (top- top+) (interval-split 0 top t t)
672 (interval-merge-pair (interval-div top- bot)
673 (interval-div top+ bot))))
675 ;; Top is negative so flip the sign, divide, and flip the
676 ;; sign of the result.
677 (interval-neg (interval-div (interval-neg top) bot)))
678 ((and (eq top-range '+) (eq bot-range '+))
680 (make-interval :low (bound-div (interval-low top) (interval-high bot) t)
681 :high (bound-div (interval-high top) (interval-low bot) nil)))
683 (error "This shouldn't happen!"))))))
685 ;;; Apply the function F to the interval X. If X = [a, b], then the
686 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
687 ;;; result makes sense. It will if F is monotonic increasing (or
689 (defun interval-func (f x)
690 (declare (type interval x))
691 (let ((lo (bound-func f (interval-low x)))
692 (hi (bound-func f (interval-high x))))
693 (make-interval :low lo :high hi)))
695 ;;; Return T if X < Y. That is every number in the interval X is
696 ;;; always less than any number in the interval Y.
697 (defun interval-< (x y)
698 (declare (type interval x y))
699 ;; X < Y only if X is bounded above, Y is bounded below, and they
701 (when (and (interval-bounded-p x 'above)
702 (interval-bounded-p y 'below))
703 ;; Intervals are bounded in the appropriate way. Make sure they
705 (let ((left (interval-high x))
706 (right (interval-low y)))
707 (cond ((> (bound-value left)
709 ;; Definitely overlap so result is NIL
711 ((< (bound-value left)
713 ;; Definitely don't touch, so result is T
716 ;; Limits are equal. Check for open or closed bounds.
717 ;; Don't overlap if one or the other are open.
718 (or (consp left) (consp right)))))))
720 ;;; Return T if X >= Y. That is, every number in the interval X is
721 ;;; always greater than any number in the interval Y.
722 (defun interval->= (x y)
723 (declare (type interval x y))
724 ;; X >= Y if lower bound of X >= upper bound of Y
725 (when (and (interval-bounded-p x 'below)
726 (interval-bounded-p y 'above))
727 (>= (bound-value (interval-low x)) (bound-value (interval-high y)))))
729 ;;; Return an interval that is the absolute value of X. Thus, if
730 ;;; X = [-1 10], the result is [0, 10].
731 (defun interval-abs (x)
732 (declare (type interval x))
733 (case (interval-range-info x)
739 (destructuring-bind (x- x+) (interval-split 0 x t t)
740 (interval-merge-pair (interval-neg x-) x+)))))
742 ;;; Compute the square of an interval.
743 (defun interval-sqr (x)
744 (declare (type interval x))
745 (interval-func #'(lambda (x) (* x x))
749 ;;;; numeric derive-type methods
751 ;;; a utility for defining derive-type methods of integer operations. If
752 ;;; the types of both X and Y are integer types, then we compute a new
753 ;;; integer type with bounds determined Fun when applied to X and Y.
754 ;;; Otherwise, we use Numeric-Contagion.
755 (defun derive-integer-type (x y fun)
756 (declare (type continuation x y) (type function fun))
757 (let ((x (continuation-type x))
758 (y (continuation-type y)))
759 (if (and (numeric-type-p x) (numeric-type-p y)
760 (eq (numeric-type-class x) 'integer)
761 (eq (numeric-type-class y) 'integer)
762 (eq (numeric-type-complexp x) :real)
763 (eq (numeric-type-complexp y) :real))
764 (multiple-value-bind (low high) (funcall fun x y)
765 (make-numeric-type :class 'integer
769 (numeric-contagion x y))))
771 #!+(or propagate-float-type propagate-fun-type)
774 ;;; simple utility to flatten a list
775 (defun flatten-list (x)
776 (labels ((flatten-helper (x r);; 'r' is the stuff to the 'right'.
780 (t (flatten-helper (car x)
781 (flatten-helper (cdr x) r))))))
782 (flatten-helper x nil)))
784 ;;; Take some type of continuation and massage it so that we get a
785 ;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
786 ;;; to indicate failure.
787 (defun prepare-arg-for-derive-type (arg)
788 (flet ((listify (arg)
793 (union-type-types arg))
796 (unless (eq arg *empty-type*)
797 ;; Make sure all args are some type of numeric-type. For member
798 ;; types, convert the list of members into a union of equivalent
799 ;; single-element member-type's.
800 (let ((new-args nil))
801 (dolist (arg (listify arg))
802 (if (member-type-p arg)
803 ;; Run down the list of members and convert to a list of
805 (dolist (member (member-type-members arg))
806 (push (if (numberp member)
807 (make-member-type :members (list member))
810 (push arg new-args)))
811 (unless (member *empty-type* new-args)
814 ;;; Convert from the standard type convention for which -0.0 and 0.0
815 ;;; and equal to an intermediate convention for which they are
816 ;;; considered different which is more natural for some of the
818 #!-negative-zero-is-not-zero
819 (defun convert-numeric-type (type)
820 (declare (type numeric-type type))
821 ;;; Only convert real float interval delimiters types.
822 (if (eq (numeric-type-complexp type) :real)
823 (let* ((lo (numeric-type-low type))
824 (lo-val (bound-value lo))
825 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
826 (hi (numeric-type-high type))
827 (hi-val (bound-value hi))
828 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
829 (if (or lo-float-zero-p hi-float-zero-p)
831 :class (numeric-type-class type)
832 :format (numeric-type-format type)
834 :low (if lo-float-zero-p
836 (list (float 0.0 lo-val))
839 :high (if hi-float-zero-p
841 (list (float -0.0 hi-val))
848 ;;; Convert back from the intermediate convention for which -0.0 and
849 ;;; 0.0 are considered different to the standard type convention for
851 #!-negative-zero-is-not-zero
852 (defun convert-back-numeric-type (type)
853 (declare (type numeric-type type))
854 ;;; Only convert real float interval delimiters types.
855 (if (eq (numeric-type-complexp type) :real)
856 (let* ((lo (numeric-type-low type))
857 (lo-val (bound-value lo))
859 (and lo (floatp lo-val) (= lo-val 0.0)
860 (float-sign lo-val)))
861 (hi (numeric-type-high type))
862 (hi-val (bound-value hi))
864 (and hi (floatp hi-val) (= hi-val 0.0)
865 (float-sign hi-val))))
867 ;; (float +0.0 +0.0) => (member 0.0)
868 ;; (float -0.0 -0.0) => (member -0.0)
869 ((and lo-float-zero-p hi-float-zero-p)
870 ;; shouldn't have exclusive bounds here..
871 (aver (and (not (consp lo)) (not (consp hi))))
872 (if (= lo-float-zero-p hi-float-zero-p)
873 ;; (float +0.0 +0.0) => (member 0.0)
874 ;; (float -0.0 -0.0) => (member -0.0)
875 (specifier-type `(member ,lo-val))
876 ;; (float -0.0 +0.0) => (float 0.0 0.0)
877 ;; (float +0.0 -0.0) => (float 0.0 0.0)
878 (make-numeric-type :class (numeric-type-class type)
879 :format (numeric-type-format type)
885 ;; (float -0.0 x) => (float 0.0 x)
886 ((and (not (consp lo)) (minusp lo-float-zero-p))
887 (make-numeric-type :class (numeric-type-class type)
888 :format (numeric-type-format type)
890 :low (float 0.0 lo-val)
892 ;; (float (+0.0) x) => (float (0.0) x)
893 ((and (consp lo) (plusp lo-float-zero-p))
894 (make-numeric-type :class (numeric-type-class type)
895 :format (numeric-type-format type)
897 :low (list (float 0.0 lo-val))
900 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
901 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
902 (list (make-member-type :members (list (float 0.0 lo-val)))
903 (make-numeric-type :class (numeric-type-class type)
904 :format (numeric-type-format type)
906 :low (list (float 0.0 lo-val))
910 ;; (float x +0.0) => (float x 0.0)
911 ((and (not (consp hi)) (plusp hi-float-zero-p))
912 (make-numeric-type :class (numeric-type-class type)
913 :format (numeric-type-format type)
916 :high (float 0.0 hi-val)))
917 ;; (float x (-0.0)) => (float x (0.0))
918 ((and (consp hi) (minusp hi-float-zero-p))
919 (make-numeric-type :class (numeric-type-class type)
920 :format (numeric-type-format type)
923 :high (list (float 0.0 hi-val))))
925 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
926 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
927 (list (make-member-type :members (list (float -0.0 hi-val)))
928 (make-numeric-type :class (numeric-type-class type)
929 :format (numeric-type-format type)
932 :high (list (float 0.0 hi-val)))))))
938 ;;; Convert back a possible list of numeric types.
939 #!-negative-zero-is-not-zero
940 (defun convert-back-numeric-type-list (type-list)
944 (dolist (type type-list)
945 (if (numeric-type-p type)
946 (let ((result (convert-back-numeric-type type)))
948 (setf results (append results result))
949 (push result results)))
950 (push type results)))
953 (convert-back-numeric-type type-list))
955 (convert-back-numeric-type-list (union-type-types type-list)))
959 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
960 ;;; belong in the kernel's type logic, invoked always, instead of in
961 ;;; the compiler, invoked only during some type optimizations.
963 ;;; Take a list of types and return a canonical type specifier,
964 ;;; combining any MEMBER types together. If both positive and negative
965 ;;; MEMBER types are present they are converted to a float type.
966 ;;; XXX This would be far simpler if the type-union methods could handle
967 ;;; member/number unions.
968 (defun make-canonical-union-type (type-list)
971 (dolist (type type-list)
972 (if (member-type-p type)
973 (setf members (union members (member-type-members type)))
974 (push type misc-types)))
976 (when (null (set-difference '(-0l0 0l0) members))
977 #!-negative-zero-is-not-zero
978 (push (specifier-type '(long-float 0l0 0l0)) misc-types)
979 #!+negative-zero-is-not-zero
980 (push (specifier-type '(long-float -0l0 0l0)) misc-types)
981 (setf members (set-difference members '(-0l0 0l0))))
982 (when (null (set-difference '(-0d0 0d0) members))
983 #!-negative-zero-is-not-zero
984 (push (specifier-type '(double-float 0d0 0d0)) misc-types)
985 #!+negative-zero-is-not-zero
986 (push (specifier-type '(double-float -0d0 0d0)) misc-types)
987 (setf members (set-difference members '(-0d0 0d0))))
988 (when (null (set-difference '(-0f0 0f0) members))
989 #!-negative-zero-is-not-zero
990 (push (specifier-type '(single-float 0f0 0f0)) misc-types)
991 #!+negative-zero-is-not-zero
992 (push (specifier-type '(single-float -0f0 0f0)) misc-types)
993 (setf members (set-difference members '(-0f0 0f0))))
995 (apply #'type-union (make-member-type :members members) misc-types)
996 (apply #'type-union misc-types))))
998 ;;; Convert a member type with a single member to a numeric type.
999 (defun convert-member-type (arg)
1000 (let* ((members (member-type-members arg))
1001 (member (first members))
1002 (member-type (type-of member)))
1003 (aver (not (rest members)))
1004 (specifier-type `(,(if (subtypep member-type 'integer)
1009 ;;; This is used in defoptimizers for computing the resulting type of
1012 ;;; Given the continuation ARG, derive the resulting type using the
1013 ;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
1014 ;;; "atomic" continuation type like numeric-type or member-type
1015 ;;; (containing just one element). It should return the resulting
1016 ;;; type, which can be a list of types.
1018 ;;; For the case of member types, if a member-fcn is given it is
1019 ;;; called to compute the result otherwise the member type is first
1020 ;;; converted to a numeric type and the derive-fcn is call.
1021 (defun one-arg-derive-type (arg derive-fcn member-fcn
1022 &optional (convert-type t))
1023 (declare (type function derive-fcn)
1024 (type (or null function) member-fcn)
1025 #!+negative-zero-is-not-zero (ignore convert-type))
1026 (let ((arg-list (prepare-arg-for-derive-type (continuation-type arg))))
1032 (with-float-traps-masked
1033 (:underflow :overflow :divide-by-zero)
1037 (first (member-type-members x))))))
1038 ;; Otherwise convert to a numeric type.
1039 (let ((result-type-list
1040 (funcall derive-fcn (convert-member-type x))))
1041 #!-negative-zero-is-not-zero
1043 (convert-back-numeric-type-list result-type-list)
1045 #!+negative-zero-is-not-zero
1048 #!-negative-zero-is-not-zero
1050 (convert-back-numeric-type-list
1051 (funcall derive-fcn (convert-numeric-type x)))
1052 (funcall derive-fcn x))
1053 #!+negative-zero-is-not-zero
1054 (funcall derive-fcn x))
1056 *universal-type*))))
1057 ;; Run down the list of args and derive the type of each one,
1058 ;; saving all of the results in a list.
1059 (let ((results nil))
1060 (dolist (arg arg-list)
1061 (let ((result (deriver arg)))
1063 (setf results (append results result))
1064 (push result results))))
1066 (make-canonical-union-type results)
1067 (first results)))))))
1069 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1070 ;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
1071 ;;; original args and a third which is T to indicate if the two args
1072 ;;; really represent the same continuation. This is useful for
1073 ;;; deriving the type of things like (* x x), which should always be
1074 ;;; positive. If we didn't do this, we wouldn't be able to tell.
1075 (defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
1076 &optional (convert-type t))
1077 #!+negative-zero-is-not-zero
1078 (declare (ignore convert-type))
1079 (flet (#!-negative-zero-is-not-zero
1080 (deriver (x y same-arg)
1081 (cond ((and (member-type-p x) (member-type-p y))
1082 (let* ((x (first (member-type-members x)))
1083 (y (first (member-type-members y)))
1084 (result (with-float-traps-masked
1085 (:underflow :overflow :divide-by-zero
1087 (funcall fcn x y))))
1088 (cond ((null result))
1089 ((and (floatp result) (float-nan-p result))
1092 :format (type-of result)
1095 (make-member-type :members (list result))))))
1096 ((and (member-type-p x) (numeric-type-p y))
1097 (let* ((x (convert-member-type x))
1098 (y (if convert-type (convert-numeric-type y) y))
1099 (result (funcall derive-fcn x y same-arg)))
1101 (convert-back-numeric-type-list result)
1103 ((and (numeric-type-p x) (member-type-p y))
1104 (let* ((x (if convert-type (convert-numeric-type x) x))
1105 (y (convert-member-type y))
1106 (result (funcall derive-fcn x y same-arg)))
1108 (convert-back-numeric-type-list result)
1110 ((and (numeric-type-p x) (numeric-type-p y))
1111 (let* ((x (if convert-type (convert-numeric-type x) x))
1112 (y (if convert-type (convert-numeric-type y) y))
1113 (result (funcall derive-fcn x y same-arg)))
1115 (convert-back-numeric-type-list result)
1119 #!+negative-zero-is-not-zero
1120 (deriver (x y same-arg)
1121 (cond ((and (member-type-p x) (member-type-p y))
1122 (let* ((x (first (member-type-members x)))
1123 (y (first (member-type-members y)))
1124 (result (with-float-traps-masked
1125 (:underflow :overflow :divide-by-zero)
1126 (funcall fcn x y))))
1128 (make-member-type :members (list result)))))
1129 ((and (member-type-p x) (numeric-type-p y))
1130 (let ((x (convert-member-type x)))
1131 (funcall derive-fcn x y same-arg)))
1132 ((and (numeric-type-p x) (member-type-p y))
1133 (let ((y (convert-member-type y)))
1134 (funcall derive-fcn x y same-arg)))
1135 ((and (numeric-type-p x) (numeric-type-p y))
1136 (funcall derive-fcn x y same-arg))
1138 *universal-type*))))
1139 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1140 (a1 (prepare-arg-for-derive-type (continuation-type arg1)))
1141 (a2 (prepare-arg-for-derive-type (continuation-type arg2))))
1143 (let ((results nil))
1145 ;; Since the args are the same continuation, just run
1148 (let ((result (deriver x x same-arg)))
1150 (setf results (append results result))
1151 (push result results))))
1152 ;; Try all pairwise combinations.
1155 (let ((result (or (deriver x y same-arg)
1156 (numeric-contagion x y))))
1158 (setf results (append results result))
1159 (push result results))))))
1161 (make-canonical-union-type results)
1162 (first results)))))))
1166 #!-propagate-float-type
1168 (defoptimizer (+ derive-type) ((x y))
1169 (derive-integer-type
1176 (values (frob (numeric-type-low x) (numeric-type-low y))
1177 (frob (numeric-type-high x) (numeric-type-high y)))))))
1179 (defoptimizer (- derive-type) ((x y))
1180 (derive-integer-type
1187 (values (frob (numeric-type-low x) (numeric-type-high y))
1188 (frob (numeric-type-high x) (numeric-type-low y)))))))
1190 (defoptimizer (* derive-type) ((x y))
1191 (derive-integer-type
1194 (let ((x-low (numeric-type-low x))
1195 (x-high (numeric-type-high x))
1196 (y-low (numeric-type-low y))
1197 (y-high (numeric-type-high y)))
1198 (cond ((not (and x-low y-low))
1200 ((or (minusp x-low) (minusp y-low))
1201 (if (and x-high y-high)
1202 (let ((max (* (max (abs x-low) (abs x-high))
1203 (max (abs y-low) (abs y-high)))))
1204 (values (- max) max))
1207 (values (* x-low y-low)
1208 (if (and x-high y-high)
1212 (defoptimizer (/ derive-type) ((x y))
1213 (numeric-contagion (continuation-type x) (continuation-type y)))
1217 #!+propagate-float-type
1219 (defun +-derive-type-aux (x y same-arg)
1220 (if (and (numeric-type-real-p x)
1221 (numeric-type-real-p y))
1224 (let ((x-int (numeric-type->interval x)))
1225 (interval-add x-int x-int))
1226 (interval-add (numeric-type->interval x)
1227 (numeric-type->interval y))))
1228 (result-type (numeric-contagion x y)))
1229 ;; If the result type is a float, we need to be sure to coerce
1230 ;; the bounds into the correct type.
1231 (when (eq (numeric-type-class result-type) 'float)
1232 (setf result (interval-func
1234 (coerce x (or (numeric-type-format result-type)
1238 :class (if (and (eq (numeric-type-class x) 'integer)
1239 (eq (numeric-type-class y) 'integer))
1240 ;; The sum of integers is always an integer
1242 (numeric-type-class result-type))
1243 :format (numeric-type-format result-type)
1244 :low (interval-low result)
1245 :high (interval-high result)))
1246 ;; General contagion
1247 (numeric-contagion x y)))
1249 (defoptimizer (+ derive-type) ((x y))
1250 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1252 (defun --derive-type-aux (x y same-arg)
1253 (if (and (numeric-type-real-p x)
1254 (numeric-type-real-p y))
1256 ;; (- x x) is always 0.
1258 (make-interval :low 0 :high 0)
1259 (interval-sub (numeric-type->interval x)
1260 (numeric-type->interval y))))
1261 (result-type (numeric-contagion x y)))
1262 ;; If the result type is a float, we need to be sure to coerce
1263 ;; the bounds into the correct type.
1264 (when (eq (numeric-type-class result-type) 'float)
1265 (setf result (interval-func
1267 (coerce x (or (numeric-type-format result-type)
1271 :class (if (and (eq (numeric-type-class x) 'integer)
1272 (eq (numeric-type-class y) 'integer))
1273 ;; The difference of integers is always an integer
1275 (numeric-type-class result-type))
1276 :format (numeric-type-format result-type)
1277 :low (interval-low result)
1278 :high (interval-high result)))
1279 ;; General contagion
1280 (numeric-contagion x y)))
1282 (defoptimizer (- derive-type) ((x y))
1283 (two-arg-derive-type x y #'--derive-type-aux #'-))
1285 (defun *-derive-type-aux (x y same-arg)
1286 (if (and (numeric-type-real-p x)
1287 (numeric-type-real-p y))
1289 ;; (* x x) is always positive, so take care to do it
1292 (interval-sqr (numeric-type->interval x))
1293 (interval-mul (numeric-type->interval x)
1294 (numeric-type->interval y))))
1295 (result-type (numeric-contagion x y)))
1296 ;; If the result type is a float, we need to be sure to coerce
1297 ;; the bounds into the correct type.
1298 (when (eq (numeric-type-class result-type) 'float)
1299 (setf result (interval-func
1301 (coerce x (or (numeric-type-format result-type)
1305 :class (if (and (eq (numeric-type-class x) 'integer)
1306 (eq (numeric-type-class y) 'integer))
1307 ;; The product of integers is always an integer.
1309 (numeric-type-class result-type))
1310 :format (numeric-type-format result-type)
1311 :low (interval-low result)
1312 :high (interval-high result)))
1313 (numeric-contagion x y)))
1315 (defoptimizer (* derive-type) ((x y))
1316 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1318 (defun /-derive-type-aux (x y same-arg)
1319 (if (and (numeric-type-real-p x)
1320 (numeric-type-real-p y))
1322 ;; (/ X X) is always 1, except if X can contain 0. In
1323 ;; that case, we shouldn't optimize the division away
1324 ;; because we want 0/0 to signal an error.
1326 (not (interval-contains-p
1327 0 (interval-closure (numeric-type->interval y)))))
1328 (make-interval :low 1 :high 1)
1329 (interval-div (numeric-type->interval x)
1330 (numeric-type->interval y))))
1331 (result-type (numeric-contagion x y)))
1332 ;; If the result type is a float, we need to be sure to coerce
1333 ;; the bounds into the correct type.
1334 (when (eq (numeric-type-class result-type) 'float)
1335 (setf result (interval-func
1337 (coerce x (or (numeric-type-format result-type)
1340 (make-numeric-type :class (numeric-type-class result-type)
1341 :format (numeric-type-format result-type)
1342 :low (interval-low result)
1343 :high (interval-high result)))
1344 (numeric-contagion x y)))
1346 (defoptimizer (/ derive-type) ((x y))
1347 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1352 ;;; KLUDGE: All this ASH optimization is suppressed under CMU CL
1353 ;;; because as of version 2.4.6 for Debian, CMU CL blows up on (ASH
1354 ;;; 1000000000 -100000000000) (i.e. ASH of two bignums yielding zero)
1355 ;;; and it's hard to avoid that calculation in here.
1356 #-(and cmu sb-xc-host)
1358 #!-propagate-fun-type
1359 (defoptimizer (ash derive-type) ((n shift))
1360 ;; Large resulting bounds are easy to generate but are not
1361 ;; particularly useful, so an open outer bound is returned for a
1362 ;; shift greater than 64 - the largest word size of any of the ports.
1363 ;; Large negative shifts are also problematic as the ASH
1364 ;; implementation only accepts shifts greater than
1365 ;; MOST-NEGATIVE-FIXNUM. These issues are handled by two local
1367 ;; ASH-OUTER: Perform the shift when within an acceptable range,
1368 ;; otherwise return an open bound.
1369 ;; ASH-INNER: Perform the shift when within range, limited to a
1370 ;; maximum of 64, otherwise returns the inner limit.
1372 ;; FIXME: The magic number 64 should be given a mnemonic name as a
1373 ;; symbolic constant -- perhaps +MAX-REGISTER-SIZE+. And perhaps is
1374 ;; should become an architecture-specific SB!VM:+MAX-REGISTER-SIZE+
1375 ;; instead of trying to have a single magic number which covers
1376 ;; all possible ports.
1377 (flet ((ash-outer (n s)
1378 (when (and (fixnump s)
1380 (> s sb!vm:*target-most-negative-fixnum*))
1383 (if (and (fixnump s)
1384 (> s sb!vm:*target-most-negative-fixnum*))
1386 (if (minusp n) -1 0))))
1387 (or (let ((n-type (continuation-type n)))
1388 (when (numeric-type-p n-type)
1389 (let ((n-low (numeric-type-low n-type))
1390 (n-high (numeric-type-high n-type)))
1391 (if (constant-continuation-p shift)
1392 (let ((shift (continuation-value shift)))
1393 (make-numeric-type :class 'integer
1395 :low (when n-low (ash n-low shift))
1396 :high (when n-high (ash n-high shift))))
1397 (let ((s-type (continuation-type shift)))
1398 (when (numeric-type-p s-type)
1399 (let* ((s-low (numeric-type-low s-type))
1400 (s-high (numeric-type-high s-type))
1401 (low-slot (when n-low
1403 (ash-outer n-low s-high)
1404 (ash-inner n-low s-low))))
1405 (high-slot (when n-high
1407 (ash-inner n-high s-low)
1408 (ash-outer n-high s-high)))))
1409 (make-numeric-type :class 'integer
1412 :high high-slot))))))))
1414 (or (let ((n-type (continuation-type n)))
1415 (when (numeric-type-p n-type)
1416 (let ((n-low (numeric-type-low n-type))
1417 (n-high (numeric-type-high n-type)))
1418 (if (constant-continuation-p shift)
1419 (let ((shift (continuation-value shift)))
1420 (make-numeric-type :class 'integer
1422 :low (when n-low (ash n-low shift))
1423 :high (when n-high (ash n-high shift))))
1424 (let ((s-type (continuation-type shift)))
1425 (when (numeric-type-p s-type)
1426 (let ((s-low (numeric-type-low s-type))
1427 (s-high (numeric-type-high s-type)))
1428 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1429 (make-numeric-type :class 'integer
1432 (min (ash n-low s-high)
1435 (max (ash n-high s-high)
1436 (ash n-high s-low))))
1437 (make-numeric-type :class 'integer
1438 :complexp :real)))))))))
1441 #!+propagate-fun-type
1442 (defun ash-derive-type-aux (n-type shift same-arg)
1443 (declare (ignore same-arg))
1444 (flet ((ash-outer (n s)
1445 (when (and (fixnump s)
1447 (> s sb!vm:*target-most-negative-fixnum*))
1449 ;; KLUDGE: The bare 64's here should be related to
1450 ;; symbolic machine word size values somehow.
1453 (if (and (fixnump s)
1454 (> s sb!vm:*target-most-negative-fixnum*))
1456 (if (minusp n) -1 0))))
1457 (or (and (csubtypep n-type (specifier-type 'integer))
1458 (csubtypep shift (specifier-type 'integer))
1459 (let ((n-low (numeric-type-low n-type))
1460 (n-high (numeric-type-high n-type))
1461 (s-low (numeric-type-low shift))
1462 (s-high (numeric-type-high shift)))
1463 (make-numeric-type :class 'integer :complexp :real
1466 (ash-outer n-low s-high)
1467 (ash-inner n-low s-low)))
1470 (ash-inner n-high s-low)
1471 (ash-outer n-high s-high))))))
1474 #!+propagate-fun-type
1475 (defoptimizer (ash derive-type) ((n shift))
1476 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1479 #!-propagate-float-type
1480 (macrolet ((frob (fun)
1481 `#'(lambda (type type2)
1482 (declare (ignore type2))
1483 (let ((lo (numeric-type-low type))
1484 (hi (numeric-type-high type)))
1485 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1487 (defoptimizer (%negate derive-type) ((num))
1488 (derive-integer-type num num (frob -)))
1490 (defoptimizer (lognot derive-type) ((int))
1491 (derive-integer-type int int (frob lognot))))
1493 #!+propagate-float-type
1494 (defoptimizer (lognot derive-type) ((int))
1495 (derive-integer-type int int
1496 (lambda (type type2)
1497 (declare (ignore type2))
1498 (let ((lo (numeric-type-low type))
1499 (hi (numeric-type-high type)))
1500 (values (if hi (lognot hi) nil)
1501 (if lo (lognot lo) nil)
1502 (numeric-type-class type)
1503 (numeric-type-format type))))))
1505 #!+propagate-float-type
1506 (defoptimizer (%negate derive-type) ((num))
1507 (flet ((negate-bound (b)
1508 (set-bound (- (bound-value b)) (consp b))))
1509 (one-arg-derive-type num
1511 (let ((lo (numeric-type-low type))
1512 (hi (numeric-type-high type))
1513 (result (copy-numeric-type type)))
1514 (setf (numeric-type-low result)
1515 (if hi (negate-bound hi) nil))
1516 (setf (numeric-type-high result)
1517 (if lo (negate-bound lo) nil))
1521 #!-propagate-float-type
1522 (defoptimizer (abs derive-type) ((num))
1523 (let ((type (continuation-type num)))
1524 (if (and (numeric-type-p type)
1525 (eq (numeric-type-class type) 'integer)
1526 (eq (numeric-type-complexp type) :real))
1527 (let ((lo (numeric-type-low type))
1528 (hi (numeric-type-high type)))
1529 (make-numeric-type :class 'integer :complexp :real
1530 :low (cond ((and hi (minusp hi))
1536 :high (if (and hi lo)
1537 (max (abs hi) (abs lo))
1539 (numeric-contagion type type))))
1541 #!+propagate-float-type
1542 (defun abs-derive-type-aux (type)
1543 (cond ((eq (numeric-type-complexp type) :complex)
1544 ;; The absolute value of a complex number is always a
1545 ;; non-negative float.
1546 (let* ((format (case (numeric-type-class type)
1547 ((integer rational) 'single-float)
1548 (t (numeric-type-format type))))
1549 (bound-format (or format 'float)))
1550 (make-numeric-type :class 'float
1553 :low (coerce 0 bound-format)
1556 ;; The absolute value of a real number is a non-negative real
1557 ;; of the same type.
1558 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1559 (class (numeric-type-class type))
1560 (format (numeric-type-format type))
1561 (bound-type (or format class 'real)))
1566 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1567 :high (coerce-numeric-bound
1568 (interval-high abs-bnd) bound-type))))))
1570 #!+propagate-float-type
1571 (defoptimizer (abs derive-type) ((num))
1572 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1574 #!-propagate-float-type
1575 (defoptimizer (truncate derive-type) ((number divisor))
1576 (let ((number-type (continuation-type number))
1577 (divisor-type (continuation-type divisor))
1578 (integer-type (specifier-type 'integer)))
1579 (if (and (numeric-type-p number-type)
1580 (csubtypep number-type integer-type)
1581 (numeric-type-p divisor-type)
1582 (csubtypep divisor-type integer-type))
1583 (let ((number-low (numeric-type-low number-type))
1584 (number-high (numeric-type-high number-type))
1585 (divisor-low (numeric-type-low divisor-type))
1586 (divisor-high (numeric-type-high divisor-type)))
1587 (values-specifier-type
1588 `(values ,(integer-truncate-derive-type number-low number-high
1589 divisor-low divisor-high)
1590 ,(integer-rem-derive-type number-low number-high
1591 divisor-low divisor-high))))
1594 #-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
1596 #!+propagate-float-type
1599 (defun rem-result-type (number-type divisor-type)
1600 ;; Figure out what the remainder type is. The remainder is an
1601 ;; integer if both args are integers; a rational if both args are
1602 ;; rational; and a float otherwise.
1603 (cond ((and (csubtypep number-type (specifier-type 'integer))
1604 (csubtypep divisor-type (specifier-type 'integer)))
1606 ((and (csubtypep number-type (specifier-type 'rational))
1607 (csubtypep divisor-type (specifier-type 'rational)))
1609 ((and (csubtypep number-type (specifier-type 'float))
1610 (csubtypep divisor-type (specifier-type 'float)))
1611 ;; Both are floats so the result is also a float, of
1612 ;; the largest type.
1613 (or (float-format-max (numeric-type-format number-type)
1614 (numeric-type-format divisor-type))
1616 ((and (csubtypep number-type (specifier-type 'float))
1617 (csubtypep divisor-type (specifier-type 'rational)))
1618 ;; One of the arguments is a float and the other is a
1619 ;; rational. The remainder is a float of the same
1621 (or (numeric-type-format number-type) 'float))
1622 ((and (csubtypep divisor-type (specifier-type 'float))
1623 (csubtypep number-type (specifier-type 'rational)))
1624 ;; One of the arguments is a float and the other is a
1625 ;; rational. The remainder is a float of the same
1627 (or (numeric-type-format divisor-type) 'float))
1629 ;; Some unhandled combination. This usually means both args
1630 ;; are REAL so the result is a REAL.
1633 (defun truncate-derive-type-quot (number-type divisor-type)
1634 (let* ((rem-type (rem-result-type number-type divisor-type))
1635 (number-interval (numeric-type->interval number-type))
1636 (divisor-interval (numeric-type->interval divisor-type)))
1637 ;;(declare (type (member '(integer rational float)) rem-type))
1638 ;; We have real numbers now.
1639 (cond ((eq rem-type 'integer)
1640 ;; Since the remainder type is INTEGER, both args are
1642 (let* ((res (integer-truncate-derive-type
1643 (interval-low number-interval)
1644 (interval-high number-interval)
1645 (interval-low divisor-interval)
1646 (interval-high divisor-interval))))
1647 (specifier-type (if (listp res) res 'integer))))
1649 (let ((quot (truncate-quotient-bound
1650 (interval-div number-interval
1651 divisor-interval))))
1652 (specifier-type `(integer ,(or (interval-low quot) '*)
1653 ,(or (interval-high quot) '*))))))))
1655 (defun truncate-derive-type-rem (number-type divisor-type)
1656 (let* ((rem-type (rem-result-type number-type divisor-type))
1657 (number-interval (numeric-type->interval number-type))
1658 (divisor-interval (numeric-type->interval divisor-type))
1659 (rem (truncate-rem-bound number-interval divisor-interval)))
1660 ;;(declare (type (member '(integer rational float)) rem-type))
1661 ;; We have real numbers now.
1662 (cond ((eq rem-type 'integer)
1663 ;; Since the remainder type is INTEGER, both args are
1665 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1666 ,(or (interval-high rem) '*))))
1668 (multiple-value-bind (class format)
1671 (values 'integer nil))
1673 (values 'rational nil))
1674 ((or single-float double-float #!+long-float long-float)
1675 (values 'float rem-type))
1677 (values 'float nil))
1680 (when (member rem-type '(float single-float double-float
1681 #!+long-float long-float))
1682 (setf rem (interval-func #'(lambda (x)
1683 (coerce x rem-type))
1685 (make-numeric-type :class class
1687 :low (interval-low rem)
1688 :high (interval-high rem)))))))
1690 (defun truncate-derive-type-quot-aux (num div same-arg)
1691 (declare (ignore same-arg))
1692 (if (and (numeric-type-real-p num)
1693 (numeric-type-real-p div))
1694 (truncate-derive-type-quot num div)
1697 (defun truncate-derive-type-rem-aux (num div same-arg)
1698 (declare (ignore same-arg))
1699 (if (and (numeric-type-real-p num)
1700 (numeric-type-real-p div))
1701 (truncate-derive-type-rem num div)
1704 (defoptimizer (truncate derive-type) ((number divisor))
1705 (let ((quot (two-arg-derive-type number divisor
1706 #'truncate-derive-type-quot-aux #'truncate))
1707 (rem (two-arg-derive-type number divisor
1708 #'truncate-derive-type-rem-aux #'rem)))
1709 (when (and quot rem)
1710 (make-values-type :required (list quot rem)))))
1712 (defun ftruncate-derive-type-quot (number-type divisor-type)
1713 ;; The bounds are the same as for truncate. However, the first
1714 ;; result is a float of some type. We need to determine what that
1715 ;; type is. Basically it's the more contagious of the two types.
1716 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1717 (res-type (numeric-contagion number-type divisor-type)))
1718 (make-numeric-type :class 'float
1719 :format (numeric-type-format res-type)
1720 :low (numeric-type-low q-type)
1721 :high (numeric-type-high q-type))))
1723 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1724 (declare (ignore same-arg))
1725 (if (and (numeric-type-real-p n)
1726 (numeric-type-real-p d))
1727 (ftruncate-derive-type-quot n d)
1730 (defoptimizer (ftruncate derive-type) ((number divisor))
1732 (two-arg-derive-type number divisor
1733 #'ftruncate-derive-type-quot-aux #'ftruncate))
1734 (rem (two-arg-derive-type number divisor
1735 #'truncate-derive-type-rem-aux #'rem)))
1736 (when (and quot rem)
1737 (make-values-type :required (list quot rem)))))
1739 (defun %unary-truncate-derive-type-aux (number)
1740 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1742 (defoptimizer (%unary-truncate derive-type) ((number))
1743 (one-arg-derive-type number
1744 #'%unary-truncate-derive-type-aux
1747 ;;; Define optimizers for FLOOR and CEILING.
1749 ((frob-opt (name q-name r-name)
1750 (let ((q-aux (symbolicate q-name "-AUX"))
1751 (r-aux (symbolicate r-name "-AUX")))
1753 ;; Compute type of quotient (first) result
1754 (defun ,q-aux (number-type divisor-type)
1755 (let* ((number-interval
1756 (numeric-type->interval number-type))
1758 (numeric-type->interval divisor-type))
1759 (quot (,q-name (interval-div number-interval
1760 divisor-interval))))
1761 (specifier-type `(integer ,(or (interval-low quot) '*)
1762 ,(or (interval-high quot) '*)))))
1763 ;; Compute type of remainder
1764 (defun ,r-aux (number-type divisor-type)
1765 (let* ((divisor-interval
1766 (numeric-type->interval divisor-type))
1767 (rem (,r-name divisor-interval))
1768 (result-type (rem-result-type number-type divisor-type)))
1769 (multiple-value-bind (class format)
1772 (values 'integer nil))
1774 (values 'rational nil))
1775 ((or single-float double-float #!+long-float long-float)
1776 (values 'float result-type))
1778 (values 'float nil))
1781 (when (member result-type '(float single-float double-float
1782 #!+long-float long-float))
1783 ;; Make sure the limits on the interval have
1785 (setf rem (interval-func #'(lambda (x)
1786 (coerce x result-type))
1788 (make-numeric-type :class class
1790 :low (interval-low rem)
1791 :high (interval-high rem)))))
1792 ;; The optimizer itself
1793 (defoptimizer (,name derive-type) ((number divisor))
1794 (flet ((derive-q (n d same-arg)
1795 (declare (ignore same-arg))
1796 (if (and (numeric-type-real-p n)
1797 (numeric-type-real-p d))
1800 (derive-r (n d same-arg)
1801 (declare (ignore same-arg))
1802 (if (and (numeric-type-real-p n)
1803 (numeric-type-real-p d))
1806 (let ((quot (two-arg-derive-type
1807 number divisor #'derive-q #',name))
1808 (rem (two-arg-derive-type
1809 number divisor #'derive-r #'mod)))
1810 (when (and quot rem)
1811 (make-values-type :required (list quot rem))))))
1814 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1815 (frob-opt floor floor-quotient-bound floor-rem-bound)
1816 (frob-opt ceiling ceiling-quotient-bound ceiling-rem-bound))
1818 ;;; Define optimizers for FFLOOR and FCEILING
1820 ((frob-opt (name q-name r-name)
1821 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1822 (r-aux (symbolicate r-name "-AUX")))
1824 ;; Compute type of quotient (first) result
1825 (defun ,q-aux (number-type divisor-type)
1826 (let* ((number-interval
1827 (numeric-type->interval number-type))
1829 (numeric-type->interval divisor-type))
1830 (quot (,q-name (interval-div number-interval
1832 (res-type (numeric-contagion number-type divisor-type)))
1834 :class (numeric-type-class res-type)
1835 :format (numeric-type-format res-type)
1836 :low (interval-low quot)
1837 :high (interval-high quot))))
1839 (defoptimizer (,name derive-type) ((number divisor))
1840 (flet ((derive-q (n d same-arg)
1841 (declare (ignore same-arg))
1842 (if (and (numeric-type-real-p n)
1843 (numeric-type-real-p d))
1846 (derive-r (n d same-arg)
1847 (declare (ignore same-arg))
1848 (if (and (numeric-type-real-p n)
1849 (numeric-type-real-p d))
1852 (let ((quot (two-arg-derive-type
1853 number divisor #'derive-q #',name))
1854 (rem (two-arg-derive-type
1855 number divisor #'derive-r #'mod)))
1856 (when (and quot rem)
1857 (make-values-type :required (list quot rem))))))))))
1859 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1860 (frob-opt ffloor floor-quotient-bound floor-rem-bound)
1861 (frob-opt fceiling ceiling-quotient-bound ceiling-rem-bound))
1863 ;;; functions to compute the bounds on the quotient and remainder for
1864 ;;; the FLOOR function
1865 (defun floor-quotient-bound (quot)
1866 ;; Take the floor of the quotient and then massage it into what we
1868 (let ((lo (interval-low quot))
1869 (hi (interval-high quot)))
1870 ;; Take the floor of the lower bound. The result is always a
1871 ;; closed lower bound.
1873 (floor (bound-value lo))
1875 ;; For the upper bound, we need to be careful
1878 ;; An open bound. We need to be careful here because
1879 ;; the floor of '(10.0) is 9, but the floor of
1881 (multiple-value-bind (q r) (floor (first hi))
1886 ;; A closed bound, so the answer is obvious.
1890 (make-interval :low lo :high hi)))
1891 (defun floor-rem-bound (div)
1892 ;; The remainder depends only on the divisor. Try to get the
1893 ;; correct sign for the remainder if we can.
1894 (case (interval-range-info div)
1896 ;; Divisor is always positive.
1897 (let ((rem (interval-abs div)))
1898 (setf (interval-low rem) 0)
1899 (when (and (numberp (interval-high rem))
1900 (not (zerop (interval-high rem))))
1901 ;; The remainder never contains the upper bound. However,
1902 ;; watch out for the case where the high limit is zero!
1903 (setf (interval-high rem) (list (interval-high rem))))
1906 ;; Divisor is always negative
1907 (let ((rem (interval-neg (interval-abs div))))
1908 (setf (interval-high rem) 0)
1909 (when (numberp (interval-low rem))
1910 ;; The remainder never contains the lower bound.
1911 (setf (interval-low rem) (list (interval-low rem))))
1914 ;; The divisor can be positive or negative. All bets off.
1915 ;; The magnitude of remainder is the maximum value of the
1917 (let ((limit (bound-value (interval-high (interval-abs div)))))
1918 ;; The bound never reaches the limit, so make the interval open
1919 (make-interval :low (if limit
1922 :high (list limit))))))
1924 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1925 => #S(INTERVAL :LOW 0 :HIGH 10)
1926 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1927 => #S(INTERVAL :LOW 0 :HIGH 10)
1928 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1929 => #S(INTERVAL :LOW 0 :HIGH 10)
1930 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1931 => #S(INTERVAL :LOW 0 :HIGH 9)
1932 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1933 => #S(INTERVAL :LOW 0 :HIGH 10)
1934 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1935 => #S(INTERVAL :LOW 0 :HIGH 10)
1936 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1937 => #S(INTERVAL :LOW -2 :HIGH 10)
1938 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1939 => #S(INTERVAL :LOW -1 :HIGH 10)
1940 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1941 => #S(INTERVAL :LOW -1 :HIGH 10)
1943 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1944 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1945 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1946 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1947 (floor-rem-bound (make-interval :low -10 :high -2.3))
1948 #S(INTERVAL :LOW (-10) :HIGH 0)
1949 (floor-rem-bound (make-interval :low 0.3 :high 10))
1950 => #S(INTERVAL :LOW 0 :HIGH '(10))
1951 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1952 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1953 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1954 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1957 ;;; same functions for CEILING
1958 (defun ceiling-quotient-bound (quot)
1959 ;; Take the ceiling of the quotient and then massage it into what we
1961 (let ((lo (interval-low quot))
1962 (hi (interval-high quot)))
1963 ;; Take the ceiling of the upper bound. The result is always a
1964 ;; closed upper bound.
1966 (ceiling (bound-value hi))
1968 ;; For the lower bound, we need to be careful
1971 ;; An open bound. We need to be careful here because
1972 ;; the ceiling of '(10.0) is 11, but the ceiling of
1974 (multiple-value-bind (q r) (ceiling (first lo))
1979 ;; A closed bound, so the answer is obvious.
1983 (make-interval :low lo :high hi)))
1984 (defun ceiling-rem-bound (div)
1985 ;; The remainder depends only on the divisor. Try to get the
1986 ;; correct sign for the remainder if we can.
1988 (case (interval-range-info div)
1990 ;; Divisor is always positive. The remainder is negative.
1991 (let ((rem (interval-neg (interval-abs div))))
1992 (setf (interval-high rem) 0)
1993 (when (and (numberp (interval-low rem))
1994 (not (zerop (interval-low rem))))
1995 ;; The remainder never contains the upper bound. However,
1996 ;; watch out for the case when the upper bound is zero!
1997 (setf (interval-low rem) (list (interval-low rem))))
2000 ;; Divisor is always negative. The remainder is positive
2001 (let ((rem (interval-abs div)))
2002 (setf (interval-low rem) 0)
2003 (when (numberp (interval-high rem))
2004 ;; The remainder never contains the lower bound.
2005 (setf (interval-high rem) (list (interval-high rem))))
2008 ;; The divisor can be positive or negative. All bets off.
2009 ;; The magnitude of remainder is the maximum value of the
2011 (let ((limit (bound-value (interval-high (interval-abs div)))))
2012 ;; The bound never reaches the limit, so make the interval open
2013 (make-interval :low (if limit
2016 :high (list limit))))))
2019 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2020 => #S(INTERVAL :LOW 1 :HIGH 11)
2021 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2022 => #S(INTERVAL :LOW 1 :HIGH 11)
2023 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2024 => #S(INTERVAL :LOW 1 :HIGH 10)
2025 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2026 => #S(INTERVAL :LOW 1 :HIGH 10)
2027 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2028 => #S(INTERVAL :LOW 1 :HIGH 11)
2029 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2030 => #S(INTERVAL :LOW 1 :HIGH 11)
2031 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2032 => #S(INTERVAL :LOW -1 :HIGH 11)
2033 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2034 => #S(INTERVAL :LOW 0 :HIGH 11)
2035 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2036 => #S(INTERVAL :LOW -1 :HIGH 11)
2038 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2039 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2040 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2041 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2042 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2043 => #S(INTERVAL :LOW 0 :HIGH (10))
2044 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2045 => #S(INTERVAL :LOW (-10) :HIGH 0)
2046 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2047 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2048 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2049 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2052 (defun truncate-quotient-bound (quot)
2053 ;; For positive quotients, truncate is exactly like floor. For
2054 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2055 ;; it's the union of the two pieces.
2056 (case (interval-range-info quot)
2059 (floor-quotient-bound quot))
2061 ;; Just like ceiling
2062 (ceiling-quotient-bound quot))
2064 ;; Split the interval into positive and negative pieces, compute
2065 ;; the result for each piece and put them back together.
2066 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2067 (interval-merge-pair (ceiling-quotient-bound neg)
2068 (floor-quotient-bound pos))))))
2070 (defun truncate-rem-bound (num div)
2071 ;; This is significantly more complicated than floor or ceiling. We
2072 ;; need both the number and the divisor to determine the range. The
2073 ;; basic idea is to split the ranges of num and den into positive
2074 ;; and negative pieces and deal with each of the four possibilities
2076 (case (interval-range-info num)
2078 (case (interval-range-info div)
2080 (floor-rem-bound div))
2082 (ceiling-rem-bound div))
2084 (destructuring-bind (neg pos) (interval-split 0 div t t)
2085 (interval-merge-pair (truncate-rem-bound num neg)
2086 (truncate-rem-bound num pos))))))
2088 (case (interval-range-info div)
2090 (ceiling-rem-bound div))
2092 (floor-rem-bound div))
2094 (destructuring-bind (neg pos) (interval-split 0 div t t)
2095 (interval-merge-pair (truncate-rem-bound num neg)
2096 (truncate-rem-bound num pos))))))
2098 (destructuring-bind (neg pos) (interval-split 0 num t t)
2099 (interval-merge-pair (truncate-rem-bound neg div)
2100 (truncate-rem-bound pos div))))))
2103 ;;; Derive useful information about the range. Returns three values:
2104 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2105 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2106 ;;; - The abs of the maximal value if there is one, or nil if it is
2108 (defun numeric-range-info (low high)
2109 (cond ((and low (not (minusp low)))
2110 (values '+ low high))
2111 ((and high (not (plusp high)))
2112 (values '- (- high) (if low (- low) nil)))
2114 (values nil 0 (and low high (max (- low) high))))))
2116 (defun integer-truncate-derive-type
2117 (number-low number-high divisor-low divisor-high)
2118 ;; The result cannot be larger in magnitude than the number, but the sign
2119 ;; might change. If we can determine the sign of either the number or
2120 ;; the divisor, we can eliminate some of the cases.
2121 (multiple-value-bind (number-sign number-min number-max)
2122 (numeric-range-info number-low number-high)
2123 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2124 (numeric-range-info divisor-low divisor-high)
2125 (when (and divisor-max (zerop divisor-max))
2126 ;; We've got a problem: guaranteed division by zero.
2127 (return-from integer-truncate-derive-type t))
2128 (when (zerop divisor-min)
2129 ;; We'll assume that they aren't going to divide by zero.
2131 (cond ((and number-sign divisor-sign)
2132 ;; We know the sign of both.
2133 (if (eq number-sign divisor-sign)
2134 ;; Same sign, so the result will be positive.
2135 `(integer ,(if divisor-max
2136 (truncate number-min divisor-max)
2139 (truncate number-max divisor-min)
2141 ;; Different signs, the result will be negative.
2142 `(integer ,(if number-max
2143 (- (truncate number-max divisor-min))
2146 (- (truncate number-min divisor-max))
2148 ((eq divisor-sign '+)
2149 ;; The divisor is positive. Therefore, the number will just
2150 ;; become closer to zero.
2151 `(integer ,(if number-low
2152 (truncate number-low divisor-min)
2155 (truncate number-high divisor-min)
2157 ((eq divisor-sign '-)
2158 ;; The divisor is negative. Therefore, the absolute value of
2159 ;; the number will become closer to zero, but the sign will also
2161 `(integer ,(if number-high
2162 (- (truncate number-high divisor-min))
2165 (- (truncate number-low divisor-min))
2167 ;; The divisor could be either positive or negative.
2169 ;; The number we are dividing has a bound. Divide that by the
2170 ;; smallest posible divisor.
2171 (let ((bound (truncate number-max divisor-min)))
2172 `(integer ,(- bound) ,bound)))
2174 ;; The number we are dividing is unbounded, so we can't tell
2175 ;; anything about the result.
2178 #!-propagate-float-type
2179 (defun integer-rem-derive-type
2180 (number-low number-high divisor-low divisor-high)
2181 (if (and divisor-low divisor-high)
2182 ;; We know the range of the divisor, and the remainder must be smaller
2183 ;; than the divisor. We can tell the sign of the remainer if we know
2184 ;; the sign of the number.
2185 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2186 `(integer ,(if (or (null number-low)
2187 (minusp number-low))
2190 ,(if (or (null number-high)
2191 (plusp number-high))
2194 ;; The divisor is potentially either very positive or very negative.
2195 ;; Therefore, the remainer is unbounded, but we might be able to tell
2196 ;; something about the sign from the number.
2197 `(integer ,(if (and number-low (not (minusp number-low)))
2198 ;; The number we are dividing is positive. Therefore,
2199 ;; the remainder must be positive.
2202 ,(if (and number-high (not (plusp number-high)))
2203 ;; The number we are dividing is negative. Therefore,
2204 ;; the remainder must be negative.
2208 #!-propagate-float-type
2209 (defoptimizer (random derive-type) ((bound &optional state))
2210 (let ((type (continuation-type bound)))
2211 (when (numeric-type-p type)
2212 (let ((class (numeric-type-class type))
2213 (high (numeric-type-high type))
2214 (format (numeric-type-format type)))
2218 :low (coerce 0 (or format class 'real))
2219 :high (cond ((not high) nil)
2220 ((eq class 'integer) (max (1- high) 0))
2221 ((or (consp high) (zerop high)) high)
2224 #!+propagate-float-type
2225 (defun random-derive-type-aux (type)
2226 (let ((class (numeric-type-class type))
2227 (high (numeric-type-high type))
2228 (format (numeric-type-format type)))
2232 :low (coerce 0 (or format class 'real))
2233 :high (cond ((not high) nil)
2234 ((eq class 'integer) (max (1- high) 0))
2235 ((or (consp high) (zerop high)) high)
2238 #!+propagate-float-type
2239 (defoptimizer (random derive-type) ((bound &optional state))
2240 (one-arg-derive-type bound #'random-derive-type-aux nil))
2242 ;;;; logical derive-type methods
2244 ;;; Return the maximum number of bits an integer of the supplied type can take
2245 ;;; up, or NIL if it is unbounded. The second (third) value is T if the
2246 ;;; integer can be positive (negative) and NIL if not. Zero counts as
2248 (defun integer-type-length (type)
2249 (if (numeric-type-p type)
2250 (let ((min (numeric-type-low type))
2251 (max (numeric-type-high type)))
2252 (values (and min max (max (integer-length min) (integer-length max)))
2253 (or (null max) (not (minusp max)))
2254 (or (null min) (minusp min))))
2257 #!-propagate-fun-type
2259 (defoptimizer (logand derive-type) ((x y))
2260 (multiple-value-bind (x-len x-pos x-neg)
2261 (integer-type-length (continuation-type x))
2262 (declare (ignore x-pos))
2263 (multiple-value-bind (y-len y-pos y-neg)
2264 (integer-type-length (continuation-type y))
2265 (declare (ignore y-pos))
2267 ;; X must be positive.
2269 ;; The must both be positive.
2270 (cond ((or (null x-len) (null y-len))
2271 (specifier-type 'unsigned-byte))
2272 ((or (zerop x-len) (zerop y-len))
2273 (specifier-type '(integer 0 0)))
2275 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2276 ;; X is positive, but Y might be negative.
2278 (specifier-type 'unsigned-byte))
2280 (specifier-type '(integer 0 0)))
2282 (specifier-type `(unsigned-byte ,x-len)))))
2283 ;; X might be negative.
2285 ;; Y must be positive.
2287 (specifier-type 'unsigned-byte))
2289 (specifier-type '(integer 0 0)))
2292 `(unsigned-byte ,y-len))))
2293 ;; Either might be negative.
2294 (if (and x-len y-len)
2295 ;; The result is bounded.
2296 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2297 ;; We can't tell squat about the result.
2298 (specifier-type 'integer)))))))
2300 (defoptimizer (logior derive-type) ((x y))
2301 (multiple-value-bind (x-len x-pos x-neg)
2302 (integer-type-length (continuation-type x))
2303 (multiple-value-bind (y-len y-pos y-neg)
2304 (integer-type-length (continuation-type y))
2306 ((and (not x-neg) (not y-neg))
2307 ;; Both are positive.
2308 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2312 ;; X must be negative.
2314 ;; Both are negative. The result is going to be negative and be
2315 ;; the same length or shorter than the smaller.
2316 (if (and x-len y-len)
2318 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2320 (specifier-type '(integer * -1)))
2321 ;; X is negative, but we don't know about Y. The result will be
2322 ;; negative, but no more negative than X.
2324 `(integer ,(or (numeric-type-low (continuation-type x)) '*)
2327 ;; X might be either positive or negative.
2329 ;; But Y is negative. The result will be negative.
2331 `(integer ,(or (numeric-type-low (continuation-type y)) '*)
2333 ;; We don't know squat about either. It won't get any bigger.
2334 (if (and x-len y-len)
2336 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2338 (specifier-type 'integer))))))))
2340 (defoptimizer (logxor derive-type) ((x y))
2341 (multiple-value-bind (x-len x-pos x-neg)
2342 (integer-type-length (continuation-type x))
2343 (multiple-value-bind (y-len y-pos y-neg)
2344 (integer-type-length (continuation-type y))
2346 ((or (and (not x-neg) (not y-neg))
2347 (and (not x-pos) (not y-pos)))
2348 ;; Either both are negative or both are positive. The result will be
2349 ;; positive, and as long as the longer.
2350 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2353 ((or (and (not x-pos) (not y-neg))
2354 (and (not y-neg) (not y-pos)))
2355 ;; Either X is negative and Y is positive of vice-verca. The result
2356 ;; will be negative.
2357 (specifier-type `(integer ,(if (and x-len y-len)
2358 (ash -1 (max x-len y-len))
2361 ;; We can't tell what the sign of the result is going to be. All we
2362 ;; know is that we don't create new bits.
2364 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2366 (specifier-type 'integer))))))
2370 #!+propagate-fun-type
2372 (defun logand-derive-type-aux (x y &optional same-leaf)
2373 (declare (ignore same-leaf))
2374 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2375 (declare (ignore x-pos))
2376 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2377 (declare (ignore y-pos))
2379 ;; X must be positive.
2381 ;; The must both be positive.
2382 (cond ((or (null x-len) (null y-len))
2383 (specifier-type 'unsigned-byte))
2384 ((or (zerop x-len) (zerop y-len))
2385 (specifier-type '(integer 0 0)))
2387 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2388 ;; X is positive, but Y might be negative.
2390 (specifier-type 'unsigned-byte))
2392 (specifier-type '(integer 0 0)))
2394 (specifier-type `(unsigned-byte ,x-len)))))
2395 ;; X might be negative.
2397 ;; Y must be positive.
2399 (specifier-type 'unsigned-byte))
2401 (specifier-type '(integer 0 0)))
2404 `(unsigned-byte ,y-len))))
2405 ;; Either might be negative.
2406 (if (and x-len y-len)
2407 ;; The result is bounded.
2408 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2409 ;; We can't tell squat about the result.
2410 (specifier-type 'integer)))))))
2412 (defun logior-derive-type-aux (x y &optional same-leaf)
2413 (declare (ignore same-leaf))
2414 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2415 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2417 ((and (not x-neg) (not y-neg))
2418 ;; Both are positive.
2419 (if (and x-len y-len (zerop x-len) (zerop y-len))
2420 (specifier-type '(integer 0 0))
2421 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2425 ;; X must be negative.
2427 ;; Both are negative. The result is going to be negative and be
2428 ;; the same length or shorter than the smaller.
2429 (if (and x-len y-len)
2431 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2433 (specifier-type '(integer * -1)))
2434 ;; X is negative, but we don't know about Y. The result will be
2435 ;; negative, but no more negative than X.
2437 `(integer ,(or (numeric-type-low x) '*)
2440 ;; X might be either positive or negative.
2442 ;; But Y is negative. The result will be negative.
2444 `(integer ,(or (numeric-type-low y) '*)
2446 ;; We don't know squat about either. It won't get any bigger.
2447 (if (and x-len y-len)
2449 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2451 (specifier-type 'integer))))))))
2453 (defun logxor-derive-type-aux (x y &optional same-leaf)
2454 (declare (ignore same-leaf))
2455 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2456 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2458 ((or (and (not x-neg) (not y-neg))
2459 (and (not x-pos) (not y-pos)))
2460 ;; Either both are negative or both are positive. The result will be
2461 ;; positive, and as long as the longer.
2462 (if (and x-len y-len (zerop x-len) (zerop y-len))
2463 (specifier-type '(integer 0 0))
2464 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2467 ((or (and (not x-pos) (not y-neg))
2468 (and (not y-neg) (not y-pos)))
2469 ;; Either X is negative and Y is positive of vice-verca. The result
2470 ;; will be negative.
2471 (specifier-type `(integer ,(if (and x-len y-len)
2472 (ash -1 (max x-len y-len))
2475 ;; We can't tell what the sign of the result is going to be. All we
2476 ;; know is that we don't create new bits.
2478 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2480 (specifier-type 'integer))))))
2482 (macrolet ((frob (logfcn)
2483 (let ((fcn-aux (symbolicate logfcn "-DERIVE-TYPE-AUX")))
2484 `(defoptimizer (,logfcn derive-type) ((x y))
2485 (two-arg-derive-type x y #',fcn-aux #',logfcn)))))
2486 ;; FIXME: DEF-FROB, not just FROB
2491 (defoptimizer (integer-length derive-type) ((x))
2492 (let ((x-type (continuation-type x)))
2493 (when (and (numeric-type-p x-type)
2494 (csubtypep x-type (specifier-type 'integer)))
2495 ;; If the X is of type (INTEGER LO HI), then the integer-length
2496 ;; of X is (INTEGER (min lo hi) (max lo hi), basically. Be
2497 ;; careful about LO or HI being NIL, though. Also, if 0 is
2498 ;; contained in X, the lower bound is obviously 0.
2499 (flet ((null-or-min (a b)
2500 (and a b (min (integer-length a)
2501 (integer-length b))))
2503 (and a b (max (integer-length a)
2504 (integer-length b)))))
2505 (let* ((min (numeric-type-low x-type))
2506 (max (numeric-type-high x-type))
2507 (min-len (null-or-min min max))
2508 (max-len (null-or-max min max)))
2509 (when (ctypep 0 x-type)
2511 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2514 ;;;; miscellaneous derive-type methods
2516 (defoptimizer (code-char derive-type) ((code))
2517 (specifier-type 'base-char))
2519 (defoptimizer (values derive-type) ((&rest values))
2520 (values-specifier-type
2521 `(values ,@(mapcar #'(lambda (x)
2522 (type-specifier (continuation-type x)))
2525 ;;;; byte operations
2527 ;;;; We try to turn byte operations into simple logical operations. First, we
2528 ;;;; convert byte specifiers into separate size and position arguments passed
2529 ;;;; to internal %FOO functions. We then attempt to transform the %FOO
2530 ;;;; functions into boolean operations when the size and position are constant
2531 ;;;; and the operands are fixnums.
2533 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to expressions that
2534 ;; evaluate to the SIZE and POSITION of the byte-specifier form
2535 ;; SPEC. We may wrap a let around the result of the body to bind
2538 ;; If the spec is a BYTE form, then bind the vars to the subforms.
2539 ;; otherwise, evaluate SPEC and use the BYTE-SIZE and BYTE-POSITION.
2540 ;; The goal of this transformation is to avoid consing up byte
2541 ;; specifiers and then immediately throwing them away.
2542 (with-byte-specifier ((size-var pos-var spec) &body body)
2543 (once-only ((spec `(macroexpand ,spec))
2545 `(if (and (consp ,spec)
2546 (eq (car ,spec) 'byte)
2547 (= (length ,spec) 3))
2548 (let ((,size-var (second ,spec))
2549 (,pos-var (third ,spec)))
2551 (let ((,size-var `(byte-size ,,temp))
2552 (,pos-var `(byte-position ,,temp)))
2553 `(let ((,,temp ,,spec))
2556 (def-source-transform ldb (spec int)
2557 (with-byte-specifier (size pos spec)
2558 `(%ldb ,size ,pos ,int)))
2560 (def-source-transform dpb (newbyte spec int)
2561 (with-byte-specifier (size pos spec)
2562 `(%dpb ,newbyte ,size ,pos ,int)))
2564 (def-source-transform mask-field (spec int)
2565 (with-byte-specifier (size pos spec)
2566 `(%mask-field ,size ,pos ,int)))
2568 (def-source-transform deposit-field (newbyte spec int)
2569 (with-byte-specifier (size pos spec)
2570 `(%deposit-field ,newbyte ,size ,pos ,int))))
2572 (defoptimizer (%ldb derive-type) ((size posn num))
2573 (let ((size (continuation-type size)))
2574 (if (and (numeric-type-p size)
2575 (csubtypep size (specifier-type 'integer)))
2576 (let ((size-high (numeric-type-high size)))
2577 (if (and size-high (<= size-high sb!vm:word-bits))
2578 (specifier-type `(unsigned-byte ,size-high))
2579 (specifier-type 'unsigned-byte)))
2582 (defoptimizer (%mask-field derive-type) ((size posn num))
2583 (let ((size (continuation-type size))
2584 (posn (continuation-type posn)))
2585 (if (and (numeric-type-p size)
2586 (csubtypep size (specifier-type 'integer))
2587 (numeric-type-p posn)
2588 (csubtypep posn (specifier-type 'integer)))
2589 (let ((size-high (numeric-type-high size))
2590 (posn-high (numeric-type-high posn)))
2591 (if (and size-high posn-high
2592 (<= (+ size-high posn-high) sb!vm:word-bits))
2593 (specifier-type `(unsigned-byte ,(+ size-high posn-high)))
2594 (specifier-type 'unsigned-byte)))
2597 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2598 (let ((size (continuation-type size))
2599 (posn (continuation-type posn))
2600 (int (continuation-type int)))
2601 (if (and (numeric-type-p size)
2602 (csubtypep size (specifier-type 'integer))
2603 (numeric-type-p posn)
2604 (csubtypep posn (specifier-type 'integer))
2605 (numeric-type-p int)
2606 (csubtypep int (specifier-type 'integer)))
2607 (let ((size-high (numeric-type-high size))
2608 (posn-high (numeric-type-high posn))
2609 (high (numeric-type-high int))
2610 (low (numeric-type-low int)))
2611 (if (and size-high posn-high high low
2612 (<= (+ size-high posn-high) sb!vm:word-bits))
2614 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2615 (max (integer-length high)
2616 (integer-length low)
2617 (+ size-high posn-high))))
2621 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2622 (let ((size (continuation-type size))
2623 (posn (continuation-type posn))
2624 (int (continuation-type int)))
2625 (if (and (numeric-type-p size)
2626 (csubtypep size (specifier-type 'integer))
2627 (numeric-type-p posn)
2628 (csubtypep posn (specifier-type 'integer))
2629 (numeric-type-p int)
2630 (csubtypep int (specifier-type 'integer)))
2631 (let ((size-high (numeric-type-high size))
2632 (posn-high (numeric-type-high posn))
2633 (high (numeric-type-high int))
2634 (low (numeric-type-low int)))
2635 (if (and size-high posn-high high low
2636 (<= (+ size-high posn-high) sb!vm:word-bits))
2638 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2639 (max (integer-length high)
2640 (integer-length low)
2641 (+ size-high posn-high))))
2645 (deftransform %ldb ((size posn int)
2646 (fixnum fixnum integer)
2647 (unsigned-byte #.sb!vm:word-bits))
2648 "convert to inline logical operations"
2649 `(logand (ash int (- posn))
2650 (ash ,(1- (ash 1 sb!vm:word-bits))
2651 (- size ,sb!vm:word-bits))))
2653 (deftransform %mask-field ((size posn int)
2654 (fixnum fixnum integer)
2655 (unsigned-byte #.sb!vm:word-bits))
2656 "convert to inline logical operations"
2658 (ash (ash ,(1- (ash 1 sb!vm:word-bits))
2659 (- size ,sb!vm:word-bits))
2662 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2663 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2664 ;;; as the result type, as that would allow result types
2665 ;;; that cover the range -2^(n-1) .. 1-2^n, instead of allowing result types
2666 ;;; of (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2668 (deftransform %dpb ((new size posn int)
2670 (unsigned-byte #.sb!vm:word-bits))
2671 "convert to inline logical operations"
2672 `(let ((mask (ldb (byte size 0) -1)))
2673 (logior (ash (logand new mask) posn)
2674 (logand int (lognot (ash mask posn))))))
2676 (deftransform %dpb ((new size posn int)
2678 (signed-byte #.sb!vm:word-bits))
2679 "convert to inline logical operations"
2680 `(let ((mask (ldb (byte size 0) -1)))
2681 (logior (ash (logand new mask) posn)
2682 (logand int (lognot (ash mask posn))))))
2684 (deftransform %deposit-field ((new size posn int)
2686 (unsigned-byte #.sb!vm:word-bits))
2687 "convert to inline logical operations"
2688 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2689 (logior (logand new mask)
2690 (logand int (lognot mask)))))
2692 (deftransform %deposit-field ((new size posn int)
2694 (signed-byte #.sb!vm:word-bits))
2695 "convert to inline logical operations"
2696 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2697 (logior (logand new mask)
2698 (logand int (lognot mask)))))
2700 ;;; miscellanous numeric transforms
2702 ;;; If a constant appears as the first arg, swap the args.
2703 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2704 (if (and (constant-continuation-p x)
2705 (not (constant-continuation-p y)))
2706 `(,(continuation-function-name (basic-combination-fun node))
2708 ,(continuation-value x))
2709 (give-up-ir1-transform)))
2711 (dolist (x '(= char= + * logior logand logxor))
2712 (%deftransform x '(function * *) #'commutative-arg-swap
2713 "place constant arg last."))
2715 ;;; Handle the case of a constant BOOLE-CODE.
2716 (deftransform boole ((op x y) * * :when :both)
2717 "convert to inline logical operations"
2718 (unless (constant-continuation-p op)
2719 (give-up-ir1-transform "BOOLE code is not a constant."))
2720 (let ((control (continuation-value op)))
2726 (#.boole-c1 '(lognot x))
2727 (#.boole-c2 '(lognot y))
2728 (#.boole-and '(logand x y))
2729 (#.boole-ior '(logior x y))
2730 (#.boole-xor '(logxor x y))
2731 (#.boole-eqv '(logeqv x y))
2732 (#.boole-nand '(lognand x y))
2733 (#.boole-nor '(lognor x y))
2734 (#.boole-andc1 '(logandc1 x y))
2735 (#.boole-andc2 '(logandc2 x y))
2736 (#.boole-orc1 '(logorc1 x y))
2737 (#.boole-orc2 '(logorc2 x y))
2739 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2742 ;;;; converting special case multiply/divide to shifts
2744 ;;; If arg is a constant power of two, turn * into a shift.
2745 (deftransform * ((x y) (integer integer) * :when :both)
2746 "convert x*2^k to shift"
2747 (unless (constant-continuation-p y)
2748 (give-up-ir1-transform))
2749 (let* ((y (continuation-value y))
2751 (len (1- (integer-length y-abs))))
2752 (unless (= y-abs (ash 1 len))
2753 (give-up-ir1-transform))
2758 ;;; If both arguments and the result are (unsigned-byte 32), try to come up
2759 ;;; with a ``better'' multiplication using multiplier recoding. There are two
2760 ;;; different ways the multiplier can be recoded. The more obvious is to shift
2761 ;;; X by the correct amount for each bit set in Y and to sum the results. But
2762 ;;; if there is a string of bits that are all set, you can add X shifted by
2763 ;;; one more then the bit position of the first set bit and subtract X shifted
2764 ;;; by the bit position of the last set bit. We can't use this second method
2765 ;;; when the high order bit is bit 31 because shifting by 32 doesn't work
2767 (deftransform * ((x y)
2768 ((unsigned-byte 32) (unsigned-byte 32))
2770 "recode as shift and add"
2771 (unless (constant-continuation-p y)
2772 (give-up-ir1-transform))
2773 (let ((y (continuation-value y))
2776 (labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x))
2781 `(+ ,result ,(tub32 next-factor))
2783 (declare (inline add))
2784 (dotimes (bitpos 32)
2786 (when (not (logbitp bitpos y))
2787 (add (if (= (1+ first-one) bitpos)
2788 ;; There is only a single bit in the string.
2790 ;; There are at least two.
2791 `(- ,(tub32 `(ash x ,bitpos))
2792 ,(tub32 `(ash x ,first-one)))))
2793 (setf first-one nil))
2794 (when (logbitp bitpos y)
2795 (setf first-one bitpos))))
2797 (cond ((= first-one 31))
2801 (add `(- ,(tub32 '(ash x 31)) ,(tub32 `(ash x ,first-one))))))
2805 ;;; If arg is a constant power of two, turn FLOOR into a shift and mask.
2806 ;;; If CEILING, add in (1- (ABS Y)) and then do FLOOR.
2807 (flet ((frob (y ceil-p)
2808 (unless (constant-continuation-p y)
2809 (give-up-ir1-transform))
2810 (let* ((y (continuation-value y))
2812 (len (1- (integer-length y-abs))))
2813 (unless (= y-abs (ash 1 len))
2814 (give-up-ir1-transform))
2815 (let ((shift (- len))
2817 `(let ,(when ceil-p `((x (+ x ,(1- y-abs)))))
2819 `(values (ash (- x) ,shift)
2820 (- (logand (- x) ,mask)))
2821 `(values (ash x ,shift)
2822 (logand x ,mask))))))))
2823 (deftransform floor ((x y) (integer integer) *)
2824 "convert division by 2^k to shift"
2826 (deftransform ceiling ((x y) (integer integer) *)
2827 "convert division by 2^k to shift"
2830 ;;; Do the same for MOD.
2831 (deftransform mod ((x y) (integer integer) * :when :both)
2832 "convert remainder mod 2^k to LOGAND"
2833 (unless (constant-continuation-p y)
2834 (give-up-ir1-transform))
2835 (let* ((y (continuation-value y))
2837 (len (1- (integer-length y-abs))))
2838 (unless (= y-abs (ash 1 len))
2839 (give-up-ir1-transform))
2840 (let ((mask (1- y-abs)))
2842 `(- (logand (- x) ,mask))
2843 `(logand x ,mask)))))
2845 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2846 (deftransform truncate ((x y) (integer integer))
2847 "convert division by 2^k to shift"
2848 (unless (constant-continuation-p y)
2849 (give-up-ir1-transform))
2850 (let* ((y (continuation-value y))
2852 (len (1- (integer-length y-abs))))
2853 (unless (= y-abs (ash 1 len))
2854 (give-up-ir1-transform))
2855 (let* ((shift (- len))
2858 (values ,(if (minusp y)
2860 `(- (ash (- x) ,shift)))
2861 (- (logand (- x) ,mask)))
2862 (values ,(if (minusp y)
2863 `(- (ash (- x) ,shift))
2865 (logand x ,mask))))))
2867 ;;; And the same for REM.
2868 (deftransform rem ((x y) (integer integer) * :when :both)
2869 "convert remainder mod 2^k to LOGAND"
2870 (unless (constant-continuation-p y)
2871 (give-up-ir1-transform))
2872 (let* ((y (continuation-value y))
2874 (len (1- (integer-length y-abs))))
2875 (unless (= y-abs (ash 1 len))
2876 (give-up-ir1-transform))
2877 (let ((mask (1- y-abs)))
2879 (- (logand (- x) ,mask))
2880 (logand x ,mask)))))
2882 ;;;; arithmetic and logical identity operation elimination
2884 ;;;; Flush calls to various arith functions that convert to the identity
2885 ;;;; function or a constant.
2887 (dolist (stuff '((ash 0 x)
2892 (logxor -1 (lognot x))
2894 (destructuring-bind (name identity result) stuff
2895 (deftransform name ((x y) `(* (constant-argument (member ,identity))) '*
2896 :eval-name t :when :both)
2897 "fold identity operations"
2900 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2901 ;;; (* 0 -4.0) is -0.0.
2902 (deftransform - ((x y) ((constant-argument (member 0)) rational) *
2904 "convert (- 0 x) to negate"
2906 (deftransform * ((x y) (rational (constant-argument (member 0))) *
2908 "convert (* x 0) to 0."
2911 ;;; Return T if in an arithmetic op including continuations X and Y, the
2912 ;;; result type is not affected by the type of X. That is, Y is at least as
2913 ;;; contagious as X.
2915 (defun not-more-contagious (x y)
2916 (declare (type continuation x y))
2917 (let ((x (continuation-type x))
2918 (y (continuation-type y)))
2919 (values (type= (numeric-contagion x y)
2920 (numeric-contagion y y)))))
2921 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2922 ;;; needs more work as valid transforms are missed; some cases are
2923 ;;; specific to particular transform functions so the use of this
2924 ;;; function may need a re-think.
2925 (defun not-more-contagious (x y)
2926 (declare (type continuation x y))
2927 (flet ((simple-numeric-type (num)
2928 (and (numeric-type-p num)
2929 ;; Return non-NIL if NUM is integer, rational, or a float
2930 ;; of some type (but not FLOAT)
2931 (case (numeric-type-class num)
2935 (numeric-type-format num))
2938 (let ((x (continuation-type x))
2939 (y (continuation-type y)))
2940 (if (and (simple-numeric-type x)
2941 (simple-numeric-type y))
2942 (values (type= (numeric-contagion x y)
2943 (numeric-contagion y y)))))))
2947 ;;; If y is not constant, not zerop, or is contagious, or a
2948 ;;; positive float +0.0 then give up.
2949 (deftransform + ((x y) (t (constant-argument t)) * :when :both)
2951 (let ((val (continuation-value y)))
2952 (unless (and (zerop val)
2953 (not (and (floatp val) (plusp (float-sign val))))
2954 (not-more-contagious y x))
2955 (give-up-ir1-transform)))
2960 ;;; If y is not constant, not zerop, or is contagious, or a
2961 ;;; negative float -0.0 then give up.
2962 (deftransform - ((x y) (t (constant-argument t)) * :when :both)
2964 (let ((val (continuation-value y)))
2965 (unless (and (zerop val)
2966 (not (and (floatp val) (minusp (float-sign val))))
2967 (not-more-contagious y x))
2968 (give-up-ir1-transform)))
2971 ;;; Fold (OP x +/-1)
2972 (dolist (stuff '((* x (%negate x))
2975 (destructuring-bind (name result minus-result) stuff
2976 (deftransform name ((x y) '(t (constant-argument real)) '* :eval-name t
2978 "fold identity operations"
2979 (let ((val (continuation-value y)))
2980 (unless (and (= (abs val) 1)
2981 (not-more-contagious y x))
2982 (give-up-ir1-transform))
2983 (if (minusp val) minus-result result)))))
2985 ;;; Fold (expt x n) into multiplications for small integral values of
2986 ;;; N; convert (expt x 1/2) to sqrt.
2987 (deftransform expt ((x y) (t (constant-argument real)) *)
2988 "recode as multiplication or sqrt"
2989 (let ((val (continuation-value y)))
2990 ;; If Y would cause the result to be promoted to the same type as
2991 ;; Y, we give up. If not, then the result will be the same type
2992 ;; as X, so we can replace the exponentiation with simple
2993 ;; multiplication and division for small integral powers.
2994 (unless (not-more-contagious y x)
2995 (give-up-ir1-transform))
2996 (cond ((zerop val) '(float 1 x))
2997 ((= val 2) '(* x x))
2998 ((= val -2) '(/ (* x x)))
2999 ((= val 3) '(* x x x))
3000 ((= val -3) '(/ (* x x x)))
3001 ((= val 1/2) '(sqrt x))
3002 ((= val -1/2) '(/ (sqrt x)))
3003 (t (give-up-ir1-transform)))))
3005 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3006 ;;; transformations?
3007 ;;; Perhaps we should have to prove that the denominator is nonzero before
3008 ;;; doing them? (Also the DOLIST over macro calls is weird. Perhaps
3009 ;;; just FROB?) -- WHN 19990917
3011 ;;; FIXME: What gives with the single quotes in the argument lists
3012 ;;; for DEFTRANSFORMs here? Does that work? Is it needed? Why?
3013 (dolist (name '(ash /))
3014 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3015 :eval-name t :when :both)
3018 (dolist (name '(truncate round floor ceiling))
3019 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3020 :eval-name t :when :both)
3024 ;;;; character operations
3026 (deftransform char-equal ((a b) (base-char base-char))
3028 '(let* ((ac (char-code a))
3030 (sum (logxor ac bc)))
3032 (when (eql sum #x20)
3033 (let ((sum (+ ac bc)))
3034 (and (> sum 161) (< sum 213)))))))
3036 (deftransform char-upcase ((x) (base-char))
3038 '(let ((n-code (char-code x)))
3039 (if (and (> n-code #o140) ; Octal 141 is #\a.
3040 (< n-code #o173)) ; Octal 172 is #\z.
3041 (code-char (logxor #x20 n-code))
3044 (deftransform char-downcase ((x) (base-char))
3046 '(let ((n-code (char-code x)))
3047 (if (and (> n-code 64) ; 65 is #\A.
3048 (< n-code 91)) ; 90 is #\Z.
3049 (code-char (logxor #x20 n-code))
3052 ;;;; equality predicate transforms
3054 ;;; Return true if X and Y are continuations whose only use is a reference
3055 ;;; to the same leaf, and the value of the leaf cannot change.
3056 (defun same-leaf-ref-p (x y)
3057 (declare (type continuation x y))
3058 (let ((x-use (continuation-use x))
3059 (y-use (continuation-use y)))
3062 (eq (ref-leaf x-use) (ref-leaf y-use))
3063 (constant-reference-p x-use))))
3065 ;;; If X and Y are the same leaf, then the result is true. Otherwise, if
3066 ;;; there is no intersection between the types of the arguments, then the
3067 ;;; result is definitely false.
3068 (deftransform simple-equality-transform ((x y) * *
3071 (cond ((same-leaf-ref-p x y)
3073 ((not (types-intersect (continuation-type x) (continuation-type y)))
3076 (give-up-ir1-transform))))
3078 (dolist (x '(eq char= equal))
3079 (%deftransform x '(function * *) #'simple-equality-transform))
3081 ;;; Similar to SIMPLE-EQUALITY-PREDICATE, except that we also try to
3082 ;;; convert to a type-specific predicate or EQ:
3083 ;;; -- If both args are characters, convert to CHAR=. This is better than
3084 ;;; just converting to EQ, since CHAR= may have special compilation
3085 ;;; strategies for non-standard representations, etc.
3086 ;;; -- If either arg is definitely not a number, then we can compare
3088 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3089 ;;; is constant then we put it second. If X is a subtype of Y, we put
3090 ;;; it second. These rules make it easier for the back end to match
3091 ;;; these interesting cases.
3092 ;;; -- If Y is a fixnum, then we quietly pass because the back end can
3093 ;;; handle that case, otherwise give an efficency note.
3094 (deftransform eql ((x y) * * :when :both)
3095 "convert to simpler equality predicate"
3096 (let ((x-type (continuation-type x))
3097 (y-type (continuation-type y))
3098 (char-type (specifier-type 'character))
3099 (number-type (specifier-type 'number)))
3100 (cond ((same-leaf-ref-p x y)
3102 ((not (types-intersect x-type y-type))
3104 ((and (csubtypep x-type char-type)
3105 (csubtypep y-type char-type))
3107 ((or (not (types-intersect x-type number-type))
3108 (not (types-intersect y-type number-type)))
3110 ((and (not (constant-continuation-p y))
3111 (or (constant-continuation-p x)
3112 (and (csubtypep x-type y-type)
3113 (not (csubtypep y-type x-type)))))
3116 (give-up-ir1-transform)))))
3118 ;;; Convert to EQL if both args are rational and complexp is specified
3119 ;;; and the same for both.
3120 (deftransform = ((x y) * * :when :both)
3122 (let ((x-type (continuation-type x))
3123 (y-type (continuation-type y)))
3124 (if (and (csubtypep x-type (specifier-type 'number))
3125 (csubtypep y-type (specifier-type 'number)))
3126 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3127 (csubtypep y-type (specifier-type 'float)))
3128 (and (csubtypep x-type (specifier-type '(complex float)))
3129 (csubtypep y-type (specifier-type '(complex float)))))
3130 ;; They are both floats. Leave as = so that -0.0 is
3131 ;; handled correctly.
3132 (give-up-ir1-transform))
3133 ((or (and (csubtypep x-type (specifier-type 'rational))
3134 (csubtypep y-type (specifier-type 'rational)))
3135 (and (csubtypep x-type (specifier-type '(complex rational)))
3136 (csubtypep y-type (specifier-type '(complex rational)))))
3137 ;; They are both rationals and complexp is the same. Convert
3141 (give-up-ir1-transform
3142 "The operands might not be the same type.")))
3143 (give-up-ir1-transform
3144 "The operands might not be the same type."))))
3146 ;;; If Cont's type is a numeric type, then return the type, otherwise
3147 ;;; GIVE-UP-IR1-TRANSFORM.
3148 (defun numeric-type-or-lose (cont)
3149 (declare (type continuation cont))
3150 (let ((res (continuation-type cont)))
3151 (unless (numeric-type-p res) (give-up-ir1-transform))
3154 ;;; See whether we can statically determine (< X Y) using type information.
3155 ;;; If X's high bound is < Y's low, then X < Y. Similarly, if X's low is >=
3156 ;;; to Y's high, the X >= Y (so return NIL). If not, at least make sure any
3157 ;;; constant arg is second.
3159 ;;; KLUDGE: Why should constant argument be second? It would be nice to find
3160 ;;; out and explain. -- WHN 19990917
3161 #!-propagate-float-type
3162 (defun ir1-transform-< (x y first second inverse)
3163 (if (same-leaf-ref-p x y)
3165 (let* ((x-type (numeric-type-or-lose x))
3166 (x-lo (numeric-type-low x-type))
3167 (x-hi (numeric-type-high x-type))
3168 (y-type (numeric-type-or-lose y))
3169 (y-lo (numeric-type-low y-type))
3170 (y-hi (numeric-type-high y-type)))
3171 (cond ((and x-hi y-lo (< x-hi y-lo))
3173 ((and y-hi x-lo (>= x-lo y-hi))
3175 ((and (constant-continuation-p first)
3176 (not (constant-continuation-p second)))
3179 (give-up-ir1-transform))))))
3180 #!+propagate-float-type
3181 (defun ir1-transform-< (x y first second inverse)
3182 (if (same-leaf-ref-p x y)
3184 (let ((xi (numeric-type->interval (numeric-type-or-lose x)))
3185 (yi (numeric-type->interval (numeric-type-or-lose y))))
3186 (cond ((interval-< xi yi)
3188 ((interval->= xi yi)
3190 ((and (constant-continuation-p first)
3191 (not (constant-continuation-p second)))
3194 (give-up-ir1-transform))))))
3196 (deftransform < ((x y) (integer integer) * :when :both)
3197 (ir1-transform-< x y x y '>))
3199 (deftransform > ((x y) (integer integer) * :when :both)
3200 (ir1-transform-< y x x y '<))
3202 #!+propagate-float-type
3203 (deftransform < ((x y) (float float) * :when :both)
3204 (ir1-transform-< x y x y '>))
3206 #!+propagate-float-type
3207 (deftransform > ((x y) (float float) * :when :both)
3208 (ir1-transform-< y x x y '<))
3210 ;;;; converting N-arg comparisons
3212 ;;;; We convert calls to N-arg comparison functions such as < into
3213 ;;;; two-arg calls. This transformation is enabled for all such
3214 ;;;; comparisons in this file. If any of these predicates are not
3215 ;;;; open-coded, then the transformation should be removed at some
3216 ;;;; point to avoid pessimization.
3218 ;;; This function is used for source transformation of N-arg
3219 ;;; comparison functions other than inequality. We deal both with
3220 ;;; converting to two-arg calls and inverting the sense of the test,
3221 ;;; if necessary. If the call has two args, then we pass or return a
3222 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3223 ;;; then we transform to code that returns true. Otherwise, we bind
3224 ;;; all the arguments and expand into a bunch of IFs.
3225 (declaim (ftype (function (symbol list boolean) *) multi-compare))
3226 (defun multi-compare (predicate args not-p)
3227 (let ((nargs (length args)))
3228 (cond ((< nargs 1) (values nil t))
3229 ((= nargs 1) `(progn ,@args t))
3232 `(if (,predicate ,(first args) ,(second args)) nil t)
3235 (do* ((i (1- nargs) (1- i))
3237 (current (gensym) (gensym))
3238 (vars (list current) (cons current vars))
3239 (result 't (if not-p
3240 `(if (,predicate ,current ,last)
3242 `(if (,predicate ,current ,last)
3245 `((lambda ,vars ,result) . ,args)))))))
3247 (def-source-transform = (&rest args) (multi-compare '= args nil))
3248 (def-source-transform < (&rest args) (multi-compare '< args nil))
3249 (def-source-transform > (&rest args) (multi-compare '> args nil))
3250 (def-source-transform <= (&rest args) (multi-compare '> args t))
3251 (def-source-transform >= (&rest args) (multi-compare '< args t))
3253 (def-source-transform char= (&rest args) (multi-compare 'char= args nil))
3254 (def-source-transform char< (&rest args) (multi-compare 'char< args nil))
3255 (def-source-transform char> (&rest args) (multi-compare 'char> args nil))
3256 (def-source-transform char<= (&rest args) (multi-compare 'char> args t))
3257 (def-source-transform char>= (&rest args) (multi-compare 'char< args t))
3259 (def-source-transform char-equal (&rest args) (multi-compare 'char-equal args nil))
3260 (def-source-transform char-lessp (&rest args) (multi-compare 'char-lessp args nil))
3261 (def-source-transform char-greaterp (&rest args)
3262 (multi-compare 'char-greaterp args nil))
3263 (def-source-transform char-not-greaterp (&rest args)
3264 (multi-compare 'char-greaterp args t))
3265 (def-source-transform char-not-lessp (&rest args) (multi-compare 'char-lessp args t))
3267 ;;; This function does source transformation of N-arg inequality
3268 ;;; functions such as /=. This is similar to Multi-Compare in the <3
3269 ;;; arg cases. If there are more than two args, then we expand into
3270 ;;; the appropriate n^2 comparisons only when speed is important.
3271 (declaim (ftype (function (symbol list) *) multi-not-equal))
3272 (defun multi-not-equal (predicate args)
3273 (let ((nargs (length args)))
3274 (cond ((< nargs 1) (values nil t))
3275 ((= nargs 1) `(progn ,@args t))
3277 `(if (,predicate ,(first args) ,(second args)) nil t))
3278 ((not (policy nil (and (>= speed space)
3279 (>= speed compilation-speed))))
3282 (let ((vars (make-gensym-list nargs)))
3283 (do ((var vars next)
3284 (next (cdr vars) (cdr next))
3287 `((lambda ,vars ,result) . ,args))
3288 (let ((v1 (first var)))
3290 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3292 (def-source-transform /= (&rest args) (multi-not-equal '= args))
3293 (def-source-transform char/= (&rest args) (multi-not-equal 'char= args))
3294 (def-source-transform char-not-equal (&rest args) (multi-not-equal 'char-equal args))
3296 ;;; Expand MAX and MIN into the obvious comparisons.
3297 (def-source-transform max (arg &rest more-args)
3298 (if (null more-args)
3300 (once-only ((arg1 arg)
3301 (arg2 `(max ,@more-args)))
3302 `(if (> ,arg1 ,arg2)
3304 (def-source-transform min (arg &rest more-args)
3305 (if (null more-args)
3307 (once-only ((arg1 arg)
3308 (arg2 `(min ,@more-args)))
3309 `(if (< ,arg1 ,arg2)
3312 ;;;; converting N-arg arithmetic functions
3314 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3315 ;;;; versions, and degenerate cases are flushed.
3317 ;;; Left-associate First-Arg and More-Args using Function.
3318 (declaim (ftype (function (symbol t list) list) associate-arguments))
3319 (defun associate-arguments (function first-arg more-args)
3320 (let ((next (rest more-args))
3321 (arg (first more-args)))
3323 `(,function ,first-arg ,arg)
3324 (associate-arguments function `(,function ,first-arg ,arg) next))))
3326 ;;; Do source transformations for transitive functions such as +.
3327 ;;; One-arg cases are replaced with the arg and zero arg cases with
3328 ;;; the identity. If LEAF-FUN is true, then replace two-arg calls with
3329 ;;; a call to that function.
3330 (defun source-transform-transitive (fun args identity &optional leaf-fun)
3331 (declare (symbol fun leaf-fun) (list args))
3334 (1 `(values ,(first args)))
3336 `(,leaf-fun ,(first args) ,(second args))
3339 (associate-arguments fun (first args) (rest args)))))
3341 (def-source-transform + (&rest args) (source-transform-transitive '+ args 0))
3342 (def-source-transform * (&rest args) (source-transform-transitive '* args 1))
3343 (def-source-transform logior (&rest args)
3344 (source-transform-transitive 'logior args 0))
3345 (def-source-transform logxor (&rest args)
3346 (source-transform-transitive 'logxor args 0))
3347 (def-source-transform logand (&rest args)
3348 (source-transform-transitive 'logand args -1))
3350 (def-source-transform logeqv (&rest args)
3351 (if (evenp (length args))
3352 `(lognot (logxor ,@args))
3355 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3356 ;;; because when they are given one argument, they return its absolute
3359 (def-source-transform gcd (&rest args)
3362 (1 `(abs (the integer ,(first args))))
3364 (t (associate-arguments 'gcd (first args) (rest args)))))
3366 (def-source-transform lcm (&rest args)
3369 (1 `(abs (the integer ,(first args))))
3371 (t (associate-arguments 'lcm (first args) (rest args)))))
3373 ;;; Do source transformations for intransitive n-arg functions such as
3374 ;;; /. With one arg, we form the inverse. With two args we pass.
3375 ;;; Otherwise we associate into two-arg calls.
3376 (declaim (ftype (function (symbol list t) list) source-transform-intransitive))
3377 (defun source-transform-intransitive (function args inverse)
3379 ((0 2) (values nil t))
3380 (1 `(,@inverse ,(first args)))
3381 (t (associate-arguments function (first args) (rest args)))))
3383 (def-source-transform - (&rest args)
3384 (source-transform-intransitive '- args '(%negate)))
3385 (def-source-transform / (&rest args)
3386 (source-transform-intransitive '/ args '(/ 1)))
3388 ;;;; transforming APPLY
3390 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3391 ;;; only needs to understand one kind of variable-argument call. It is
3392 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3393 (def-source-transform apply (fun arg &rest more-args)
3394 (let ((args (cons arg more-args)))
3395 `(multiple-value-call ,fun
3396 ,@(mapcar #'(lambda (x)
3399 (values-list ,(car (last args))))))
3401 ;;;; transforming FORMAT
3403 ;;;; If the control string is a compile-time constant, then replace it
3404 ;;;; with a use of the FORMATTER macro so that the control string is
3405 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3406 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3407 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3409 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3410 :policy (> speed space))
3411 (unless (constant-continuation-p control)
3412 (give-up-ir1-transform "The control string is not a constant."))
3413 (let ((arg-names (make-gensym-list (length args))))
3414 `(lambda (dest control ,@arg-names)
3415 (declare (ignore control))
3416 (format dest (formatter ,(continuation-value control)) ,@arg-names))))
3418 (deftransform format ((stream control &rest args) (stream function &rest t) *
3419 :policy (> speed space))
3420 (let ((arg-names (make-gensym-list (length args))))
3421 `(lambda (stream control ,@arg-names)
3422 (funcall control stream ,@arg-names)
3425 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3426 :policy (> speed space))
3427 (let ((arg-names (make-gensym-list (length args))))
3428 `(lambda (tee control ,@arg-names)
3429 (declare (ignore tee))
3430 (funcall control *standard-output* ,@arg-names)