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.
19 ;;; Convert into an IF so that IF optimizations will eliminate redundant
21 (def-source-transform not (x) `(if ,x nil t))
22 (def-source-transform null (x) `(if ,x nil t))
24 ;;; ENDP is just NULL with a LIST assertion.
25 (def-source-transform endp (x) `(null (the list ,x)))
26 ;;; FIXME: Is THE LIST a strong enough assertion for ANSI's "should
27 ;;; return an error"? (THE LIST is optimized away when safety is low;
28 ;;; does that satisfy the spec?)
30 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
31 ;;; returns the first value of its argument. Ditto for VALUES with one
33 (def-source-transform identity (x) `(prog1 ,x))
34 (def-source-transform values (x) `(prog1 ,x))
36 ;;; Bind the values and make a closure that returns them.
37 (def-source-transform constantly (value &rest values)
38 (let ((temps (loop repeat (1+ (length values))
41 `(let ,(loop for temp in temps and
42 value in (list* value values)
43 collect `(,temp ,value))
44 #'(lambda (&rest ,dum)
45 (declare (ignore ,dum))
48 ;;; If the function has a known number of arguments, then return a
49 ;;; lambda with the appropriate fixed number of args. If the
50 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
51 ;;; MV optimization figure things out.
52 (deftransform complement ((fun) * * :node node :when :both)
54 (multiple-value-bind (min max)
55 (function-type-nargs (continuation-type fun))
57 ((and min (eql min max))
58 (let ((dums (loop repeat min collect (gensym))))
59 `#'(lambda ,dums (not (funcall fun ,@dums)))))
60 ((let* ((cont (node-cont node))
61 (dest (continuation-dest cont)))
62 (and (combination-p dest)
63 (eq (combination-fun dest) cont)))
64 '#'(lambda (&rest args)
65 (not (apply fun args))))
67 (give-up-ir1-transform
68 "The function doesn't have a fixed argument count.")))))
72 ;;; Translate CxxR into CAR/CDR combos.
74 (defun source-transform-cxr (form)
75 (if (or (byte-compiling) (/= (length form) 2))
77 (let ((name (symbol-name (car form))))
78 (do ((i (- (length name) 2) (1- i))
80 `(,(ecase (char name i)
87 (b '(1 0) (cons i b)))
89 (dotimes (j (ash 1 i))
90 (setf (info :function :source-transform
91 (intern (format nil "C~{~:[A~;D~]~}R"
92 (mapcar #'(lambda (x) (logbitp x j)) b))))
93 #'source-transform-cxr)))
95 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
96 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
97 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
99 (def-source-transform first (x) `(car ,x))
100 (def-source-transform rest (x) `(cdr ,x))
101 (def-source-transform second (x) `(cadr ,x))
102 (def-source-transform third (x) `(caddr ,x))
103 (def-source-transform fourth (x) `(cadddr ,x))
104 (def-source-transform fifth (x) `(nth 4 ,x))
105 (def-source-transform sixth (x) `(nth 5 ,x))
106 (def-source-transform seventh (x) `(nth 6 ,x))
107 (def-source-transform eighth (x) `(nth 7 ,x))
108 (def-source-transform ninth (x) `(nth 8 ,x))
109 (def-source-transform tenth (x) `(nth 9 ,x))
111 ;;; Translate RPLACx to LET and SETF.
112 (def-source-transform rplaca (x y)
117 (def-source-transform rplacd (x y)
123 (def-source-transform nth (n l) `(car (nthcdr ,n ,l)))
125 (defvar *default-nthcdr-open-code-limit* 6)
126 (defvar *extreme-nthcdr-open-code-limit* 20)
128 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
129 "convert NTHCDR to CAxxR"
130 (unless (constant-continuation-p n)
131 (give-up-ir1-transform))
132 (let ((n (continuation-value n)))
134 (if (policy node (= speed 3) (= space 0))
135 *extreme-nthcdr-open-code-limit*
136 *default-nthcdr-open-code-limit*))
137 (give-up-ir1-transform))
142 `(cdr ,(frob (1- n))))))
145 ;;;; arithmetic and numerology
147 (def-source-transform plusp (x) `(> ,x 0))
148 (def-source-transform minusp (x) `(< ,x 0))
149 (def-source-transform zerop (x) `(= ,x 0))
151 (def-source-transform 1+ (x) `(+ ,x 1))
152 (def-source-transform 1- (x) `(- ,x 1))
154 (def-source-transform oddp (x) `(not (zerop (logand ,x 1))))
155 (def-source-transform evenp (x) `(zerop (logand ,x 1)))
157 ;;; Note that all the integer division functions are available for
158 ;;; inline expansion.
160 ;;; FIXME: DEF-FROB instead of FROB
161 (macrolet ((frob (fun)
162 `(def-source-transform ,fun (x &optional (y nil y-p))
169 #!+propagate-float-type
171 #!+propagate-float-type
174 (def-source-transform lognand (x y) `(lognot (logand ,x ,y)))
175 (def-source-transform lognor (x y) `(lognot (logior ,x ,y)))
176 (def-source-transform logandc1 (x y) `(logand (lognot ,x) ,y))
177 (def-source-transform logandc2 (x y) `(logand ,x (lognot ,y)))
178 (def-source-transform logorc1 (x y) `(logior (lognot ,x) ,y))
179 (def-source-transform logorc2 (x y) `(logior ,x (lognot ,y)))
180 (def-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
181 (def-source-transform logbitp (index integer)
182 `(not (zerop (logand (ash 1 ,index) ,integer))))
183 (def-source-transform byte (size position) `(cons ,size ,position))
184 (def-source-transform byte-size (spec) `(car ,spec))
185 (def-source-transform byte-position (spec) `(cdr ,spec))
186 (def-source-transform ldb-test (bytespec integer)
187 `(not (zerop (mask-field ,bytespec ,integer))))
189 ;;; With the ratio and complex accessors, we pick off the "identity"
190 ;;; case, and use a primitive to handle the cell access case.
191 (def-source-transform numerator (num)
192 (once-only ((n-num `(the rational ,num)))
196 (def-source-transform denominator (num)
197 (once-only ((n-num `(the rational ,num)))
199 (%denominator ,n-num)
202 ;;;; Interval arithmetic for computing bounds
203 ;;;; (toy@rtp.ericsson.se)
205 ;;;; This is a set of routines for operating on intervals. It
206 ;;;; implements a simple interval arithmetic package. Although SBCL
207 ;;;; has an interval type in numeric-type, we choose to use our own
208 ;;;; for two reasons:
210 ;;;; 1. This package is simpler than numeric-type
212 ;;;; 2. It makes debugging much easier because you can just strip
213 ;;;; out these routines and test them independently of SBCL. (a
216 ;;;; One disadvantage is a probable increase in consing because we
217 ;;;; have to create these new interval structures even though
218 ;;;; numeric-type has everything we want to know. Reason 2 wins for
221 #-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
223 #!+propagate-float-type
226 ;;; The basic interval type. It can handle open and closed intervals.
227 ;;; A bound is open if it is a list containing a number, just like
228 ;;; Lisp says. NIL means unbounded.
230 (:constructor %make-interval))
233 (defun make-interval (&key low high)
234 (labels ((normalize-bound (val)
235 (cond ((and (floatp val)
236 (float-infinity-p val))
241 ;; Handle any closed bounds
244 ;; We have an open bound. Normalize the numeric
245 ;; bound. If the normalized bound is still a number
246 ;; (not nil), keep the bound open. Otherwise, the
247 ;; bound is really unbounded, so drop the openness.
248 (let ((new-val (normalize-bound (first val))))
250 ;; Bound exists, so keep it open still
253 (error "Unknown bound type in make-interval!")))))
254 (%make-interval :low (normalize-bound low)
255 :high (normalize-bound high))))
257 #!-sb-fluid (declaim (inline bound-value set-bound))
259 ;;; Extract the numeric value of a bound. Return NIL, if X is NIL.
260 (defun bound-value (x)
261 (if (consp x) (car x) x))
263 ;;; Given a number X, create a form suitable as a bound for an
264 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
265 (defun set-bound (x open-p)
266 (if (and x open-p) (list x) x))
268 ;;; Apply the function F to a bound X. If X is an open bound, then
269 ;;; the result will be open. IF X is NIL, the result is NIL.
270 (defun bound-func (f x)
272 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
273 ;; With these traps masked, we might get things like infinity
274 ;; or negative infinity returned. Check for this and return
275 ;; NIL to indicate unbounded.
276 (let ((y (funcall f (bound-value x))))
278 (float-infinity-p y))
280 (set-bound (funcall f (bound-value x)) (consp x)))))))
282 ;;; Apply a binary operator OP to two bounds X and Y. The result is
283 ;;; NIL if either is NIL. Otherwise bound is computed and the result
284 ;;; is open if either X or Y is open.
286 ;;; FIXME: only used in this file, not needed in target runtime
287 (defmacro bound-binop (op x y)
289 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
290 (set-bound (,op (bound-value ,x)
292 (or (consp ,x) (consp ,y))))))
294 ;;; NUMERIC-TYPE->INTERVAL
296 ;;; Convert a numeric-type object to an interval object.
298 (defun numeric-type->interval (x)
299 (declare (type numeric-type x))
300 (make-interval :low (numeric-type-low x)
301 :high (numeric-type-high x)))
303 (defun copy-interval-limit (limit)
308 (defun copy-interval (x)
309 (declare (type interval x))
310 (make-interval :low (copy-interval-limit (interval-low x))
311 :high (copy-interval-limit (interval-high x))))
315 ;;; Given a point P contained in the interval X, split X into two
316 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
317 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
318 ;;; contains P. You can specify both to be T or NIL.
319 (defun interval-split (p x &optional close-lower close-upper)
320 (declare (type number p)
322 (list (make-interval :low (copy-interval-limit (interval-low x))
323 :high (if close-lower p (list p)))
324 (make-interval :low (if close-upper (list p) p)
325 :high (copy-interval-limit (interval-high x)))))
329 ;;; Return the closure of the interval. That is, convert open bounds
330 ;;; to closed bounds.
331 (defun interval-closure (x)
332 (declare (type interval x))
333 (make-interval :low (bound-value (interval-low x))
334 :high (bound-value (interval-high x))))
336 (defun signed-zero->= (x y)
340 (>= (float-sign (float x))
341 (float-sign (float y))))))
343 ;;; INTERVAL-RANGE-INFO
345 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
346 ;;; '-. Otherwise return NIL.
348 (defun interval-range-info (x &optional (point 0))
349 (declare (type interval x))
350 (let ((lo (interval-low x))
351 (hi (interval-high x)))
352 (cond ((and lo (signed-zero->= (bound-value lo) point))
354 ((and hi (signed-zero->= point (bound-value hi)))
358 (defun interval-range-info (x &optional (point 0))
359 (declare (type interval x))
360 (labels ((signed->= (x y)
361 (if (and (zerop x) (zerop y) (floatp x) (floatp y))
362 (>= (float-sign x) (float-sign y))
364 (let ((lo (interval-low x))
365 (hi (interval-high x)))
366 (cond ((and lo (signed->= (bound-value lo) point))
368 ((and hi (signed->= point (bound-value hi)))
373 ;;; INTERVAL-BOUNDED-P
375 ;;; Test to see whether the interval X is bounded. HOW determines the
376 ;;; test, and should be either ABOVE, BELOW, or BOTH.
377 (defun interval-bounded-p (x how)
378 (declare (type interval x))
385 (and (interval-low x) (interval-high x)))))
387 ;;; Signed zero comparison functions. Use these functions if we need
388 ;;; to distinguish between signed zeroes.
390 (defun signed-zero-< (x y)
394 (< (float-sign (float x))
395 (float-sign (float y))))))
396 (defun signed-zero-> (x y)
400 (> (float-sign (float x))
401 (float-sign (float y))))))
403 (defun signed-zero-= (x y)
406 (= (float-sign (float x))
407 (float-sign (float y)))))
409 (defun signed-zero-<= (x y)
413 (<= (float-sign (float x))
414 (float-sign (float y))))))
416 ;;; INTERVAL-CONTAINS-P
418 ;;; See whether the interval X contains the number P, taking into account
419 ;;; that the interval might not be closed.
420 (defun interval-contains-p (p x)
421 (declare (type number p)
423 ;; Does the interval X contain the number P? This would be a lot
424 ;; easier if all intervals were closed!
425 (let ((lo (interval-low x))
426 (hi (interval-high x)))
428 ;; The interval is bounded
429 (if (and (signed-zero-<= (bound-value lo) p)
430 (signed-zero-<= p (bound-value hi)))
431 ;; P is definitely in the closure of the interval.
432 ;; We just need to check the end points now.
433 (cond ((signed-zero-= p (bound-value lo))
435 ((signed-zero-= p (bound-value hi))
440 ;; Interval with upper bound
441 (if (signed-zero-< p (bound-value hi))
443 (and (numberp hi) (signed-zero-= p hi))))
445 ;; Interval with lower bound
446 (if (signed-zero-> p (bound-value lo))
448 (and (numberp lo) (signed-zero-= p lo))))
450 ;; Interval with no bounds
453 ;;; INTERVAL-INTERSECT-P
455 ;;; Determine if two intervals X and Y intersect. Return T if so. If
456 ;;; CLOSED-INTERVALS-P is T, the treat the intervals as if they were
457 ;;; closed. Otherwise the intervals are treated as they are.
459 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
460 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
461 ;;; is T, then they do intersect because we use the closure of X = [0,
462 ;;; 1] and Y = [1, 2] to determine intersection.
463 (defun interval-intersect-p (x y &optional closed-intervals-p)
464 (declare (type interval x y))
465 (multiple-value-bind (intersect diff)
466 (interval-intersection/difference (if closed-intervals-p
469 (if closed-intervals-p
472 (declare (ignore diff))
475 ;;; Are the two intervals adjacent? That is, is there a number
476 ;;; between the two intervals that is not an element of either
477 ;;; interval? If so, they are not adjacent. For example [0, 1) and
478 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
479 ;;; between both intervals.
480 (defun interval-adjacent-p (x y)
481 (declare (type interval x y))
482 (flet ((adjacent (lo hi)
483 ;; Check to see whether lo and hi are adjacent. If either is
484 ;; nil, they can't be adjacent.
485 (when (and lo hi (= (bound-value lo) (bound-value hi)))
486 ;; The bounds are equal. They are adjacent if one of
487 ;; them is closed (a number). If both are open (consp),
488 ;; then there is a number that lies between them.
489 (or (numberp lo) (numberp hi)))))
490 (or (adjacent (interval-low y) (interval-high x))
491 (adjacent (interval-low x) (interval-high y)))))
493 ;;; INTERVAL-INTERSECTION/DIFFERENCE
495 ;;; Compute the intersection and difference between two intervals.
496 ;;; Two values are returned: the intersection and the difference.
498 ;;; Let the two intervals be X and Y, and let I and D be the two
499 ;;; values returned by this function. Then I = X intersect Y. If I
500 ;;; is NIL (the empty set), then D is X union Y, represented as the
501 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
502 ;;; - I, which is a list of two intervals.
504 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
505 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
506 (defun interval-intersection/difference (x y)
507 (declare (type interval x y))
508 (let ((x-lo (interval-low x))
509 (x-hi (interval-high x))
510 (y-lo (interval-low y))
511 (y-hi (interval-high y)))
514 ;; If p is an open bound, make it closed. If p is a closed
515 ;; bound, make it open.
520 ;; Test whether P is in the interval.
521 (when (interval-contains-p (bound-value p)
522 (interval-closure int))
523 (let ((lo (interval-low int))
524 (hi (interval-high int)))
525 ;; Check for endpoints
526 (cond ((and lo (= (bound-value p) (bound-value lo)))
527 (not (and (consp p) (numberp lo))))
528 ((and hi (= (bound-value p) (bound-value hi)))
529 (not (and (numberp p) (consp hi))))
531 (test-lower-bound (p int)
532 ;; P is a lower bound of an interval.
535 (not (interval-bounded-p int 'below))))
536 (test-upper-bound (p int)
537 ;; P is an upper bound of an interval
540 (not (interval-bounded-p int 'above)))))
541 (let ((x-lo-in-y (test-lower-bound x-lo y))
542 (x-hi-in-y (test-upper-bound x-hi y))
543 (y-lo-in-x (test-lower-bound y-lo x))
544 (y-hi-in-x (test-upper-bound y-hi x)))
545 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
546 ;; Intervals intersect. Let's compute the intersection
547 ;; and the difference.
548 (multiple-value-bind (lo left-lo left-hi)
549 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
550 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
551 (multiple-value-bind (hi right-lo right-hi)
553 (values x-hi (opposite-bound x-hi) y-hi))
555 (values y-hi (opposite-bound y-hi) x-hi)))
556 (values (make-interval :low lo :high hi)
557 (list (make-interval :low left-lo :high left-hi)
558 (make-interval :low right-lo :high right-hi))))))
560 (values nil (list x y))))))))
562 ;;; INTERVAL-MERGE-PAIR
564 ;;; If intervals X and Y intersect, return a new interval that is the
565 ;;; union of the two. If they do not intersect, return NIL.
566 (defun interval-merge-pair (x y)
567 (declare (type interval x y))
568 ;; If x and y intersect or are adjacent, create the union.
569 ;; Otherwise return nil
570 (when (or (interval-intersect-p x y)
571 (interval-adjacent-p x y))
572 (flet ((select-bound (x1 x2 min-op max-op)
573 (let ((x1-val (bound-value x1))
574 (x2-val (bound-value x2)))
576 ;; Both bounds are finite. Select the right one.
577 (cond ((funcall min-op x1-val x2-val)
578 ;; x1 definitely better
580 ((funcall max-op x1-val x2-val)
581 ;; x2 definitely better
584 ;; Bounds are equal. Select either
585 ;; value and make it open only if
587 (set-bound x1-val (and (consp x1) (consp x2))))))
589 ;; At least one bound is not finite. The
590 ;; non-finite bound always wins.
592 (let* ((x-lo (copy-interval-limit (interval-low x)))
593 (x-hi (copy-interval-limit (interval-high x)))
594 (y-lo (copy-interval-limit (interval-low y)))
595 (y-hi (copy-interval-limit (interval-high y))))
596 (make-interval :low (select-bound x-lo y-lo #'< #'>)
597 :high (select-bound x-hi y-hi #'> #'<))))))
599 ;;; Basic arithmetic operations on intervals. We probably should do
600 ;;; true interval arithmetic here, but it's complicated because we
601 ;;; have float and integer types and bounds can be open or closed.
605 ;;; The negative of an interval
606 (defun interval-neg (x)
607 (declare (type interval x))
608 (make-interval :low (bound-func #'- (interval-high x))
609 :high (bound-func #'- (interval-low x))))
613 ;;; Add two intervals
614 (defun interval-add (x y)
615 (declare (type interval x y))
616 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
617 :high (bound-binop + (interval-high x) (interval-high y))))
621 ;;; Subtract two intervals
622 (defun interval-sub (x y)
623 (declare (type interval x y))
624 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
625 :high (bound-binop - (interval-high x) (interval-low y))))
629 ;;; Multiply two intervals
630 (defun interval-mul (x y)
631 (declare (type interval x y))
632 (flet ((bound-mul (x y)
633 (cond ((or (null x) (null y))
634 ;; Multiply by infinity is infinity
636 ((or (and (numberp x) (zerop x))
637 (and (numberp y) (zerop y)))
638 ;; Multiply by closed zero is special. The result
639 ;; is always a closed bound. But don't replace this
640 ;; with zero; we want the multiplication to produce
641 ;; the correct signed zero, if needed.
642 (* (bound-value x) (bound-value y)))
643 ((or (and (floatp x) (float-infinity-p x))
644 (and (floatp y) (float-infinity-p y)))
645 ;; Infinity times anything is infinity
648 ;; General multiply. The result is open if either is open.
649 (bound-binop * x y)))))
650 (let ((x-range (interval-range-info x))
651 (y-range (interval-range-info y)))
652 (cond ((null x-range)
653 ;; Split x into two and multiply each separately
654 (destructuring-bind (x- x+) (interval-split 0 x t t)
655 (interval-merge-pair (interval-mul x- y)
656 (interval-mul x+ y))))
658 ;; Split y into two and multiply each separately
659 (destructuring-bind (y- y+) (interval-split 0 y t t)
660 (interval-merge-pair (interval-mul x y-)
661 (interval-mul x y+))))
663 (interval-neg (interval-mul (interval-neg x) y)))
665 (interval-neg (interval-mul x (interval-neg y))))
666 ((and (eq x-range '+) (eq y-range '+))
667 ;; If we are here, X and Y are both positive
668 (make-interval :low (bound-mul (interval-low x) (interval-low y))
669 :high (bound-mul (interval-high x) (interval-high y))))
671 (error "This shouldn't happen!"))))))
675 ;;; Divide two intervals.
676 (defun interval-div (top bot)
677 (declare (type interval top bot))
678 (flet ((bound-div (x y y-low-p)
681 ;; Divide by infinity means result is 0. However,
682 ;; we need to watch out for the sign of the result,
683 ;; to correctly handle signed zeros. We also need
684 ;; to watch out for positive or negative infinity.
685 (if (floatp (bound-value x))
687 (- (float-sign (bound-value x) 0.0))
688 (float-sign (bound-value x) 0.0))
690 ((zerop (bound-value y))
691 ;; Divide by zero means result is infinity
693 ((and (numberp x) (zerop x))
694 ;; Zero divided by anything is zero.
697 (bound-binop / x y)))))
698 (let ((top-range (interval-range-info top))
699 (bot-range (interval-range-info bot)))
700 (cond ((null bot-range)
701 ;; The denominator contains zero, so anything goes!
702 (make-interval :low nil :high nil))
704 ;; Denominator is negative so flip the sign, compute the
705 ;; result, and flip it back.
706 (interval-neg (interval-div top (interval-neg bot))))
708 ;; Split top into two positive and negative parts, and
709 ;; divide each separately
710 (destructuring-bind (top- top+) (interval-split 0 top t t)
711 (interval-merge-pair (interval-div top- bot)
712 (interval-div top+ bot))))
714 ;; Top is negative so flip the sign, divide, and flip the
715 ;; sign of the result.
716 (interval-neg (interval-div (interval-neg top) bot)))
717 ((and (eq top-range '+) (eq bot-range '+))
719 (make-interval :low (bound-div (interval-low top) (interval-high bot) t)
720 :high (bound-div (interval-high top) (interval-low bot) nil)))
722 (error "This shouldn't happen!"))))))
726 ;;; Apply the function F to the interval X. If X = [a, b], then the
727 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
728 ;;; result makes sense. It will if F is monotonic increasing (or
730 (defun interval-func (f x)
731 (declare (type interval x))
732 (let ((lo (bound-func f (interval-low x)))
733 (hi (bound-func f (interval-high x))))
734 (make-interval :low lo :high hi)))
738 ;;; Return T if X < Y. That is every number in the interval X is
739 ;;; always less than any number in the interval Y.
740 (defun interval-< (x y)
741 (declare (type interval x y))
742 ;; X < Y only if X is bounded above, Y is bounded below, and they
744 (when (and (interval-bounded-p x 'above)
745 (interval-bounded-p y 'below))
746 ;; Intervals are bounded in the appropriate way. Make sure they
748 (let ((left (interval-high x))
749 (right (interval-low y)))
750 (cond ((> (bound-value left)
752 ;; Definitely overlap so result is NIL
754 ((< (bound-value left)
756 ;; Definitely don't touch, so result is T
759 ;; Limits are equal. Check for open or closed bounds.
760 ;; Don't overlap if one or the other are open.
761 (or (consp left) (consp right)))))))
765 ;;; Return T if X >= Y. That is, every number in the interval X is
766 ;;; always greater than any number in the interval Y.
767 (defun interval->= (x y)
768 (declare (type interval x y))
769 ;; X >= Y if lower bound of X >= upper bound of Y
770 (when (and (interval-bounded-p x 'below)
771 (interval-bounded-p y 'above))
772 (>= (bound-value (interval-low x)) (bound-value (interval-high y)))))
776 ;;; Return an interval that is the absolute value of X. Thus, if X =
777 ;;; [-1 10], the result is [0, 10].
778 (defun interval-abs (x)
779 (declare (type interval x))
780 (case (interval-range-info x)
786 (destructuring-bind (x- x+) (interval-split 0 x t t)
787 (interval-merge-pair (interval-neg x-) x+)))))
791 ;;; Compute the square of an interval.
792 (defun interval-sqr (x)
793 (declare (type interval x))
794 (interval-func #'(lambda (x) (* x x))
798 ;;;; numeric derive-type methods
800 ;;; Utility for defining derive-type methods of integer operations. If the
801 ;;; types of both X and Y are integer types, then we compute a new integer type
802 ;;; with bounds determined Fun when applied to X and Y. Otherwise, we use
803 ;;; Numeric-Contagion.
804 (defun derive-integer-type (x y fun)
805 (declare (type continuation x y) (type function fun))
806 (let ((x (continuation-type x))
807 (y (continuation-type y)))
808 (if (and (numeric-type-p x) (numeric-type-p y)
809 (eq (numeric-type-class x) 'integer)
810 (eq (numeric-type-class y) 'integer)
811 (eq (numeric-type-complexp x) :real)
812 (eq (numeric-type-complexp y) :real))
813 (multiple-value-bind (low high) (funcall fun x y)
814 (make-numeric-type :class 'integer
818 (numeric-contagion x y))))
820 #!+(or propagate-float-type propagate-fun-type)
823 ;; Simple utility to flatten a list
824 (defun flatten-list (x)
825 (labels ((flatten-helper (x r);; 'r' is the stuff to the 'right'.
829 (t (flatten-helper (car x)
830 (flatten-helper (cdr x) r))))))
831 (flatten-helper x nil)))
833 ;;; Take some type of continuation and massage it so that we get a
834 ;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
835 ;;; to indicate failure.
836 (defun prepare-arg-for-derive-type (arg)
837 (flet ((listify (arg)
842 (union-type-types arg))
845 (unless (eq arg *empty-type*)
846 ;; Make sure all args are some type of numeric-type. For member
847 ;; types, convert the list of members into a union of equivalent
848 ;; single-element member-type's.
849 (let ((new-args nil))
850 (dolist (arg (listify arg))
851 (if (member-type-p arg)
852 ;; Run down the list of members and convert to a list of
854 (dolist (member (member-type-members arg))
855 (push (if (numberp member)
856 (make-member-type :members (list member))
859 (push arg new-args)))
860 (unless (member *empty-type* new-args)
863 ;;; Convert from the standard type convention for which -0.0 and 0.0
864 ;;; and equal to an intermediate convention for which they are
865 ;;; considered different which is more natural for some of the
867 #!-negative-zero-is-not-zero
868 (defun convert-numeric-type (type)
869 (declare (type numeric-type type))
870 ;;; Only convert real float interval delimiters types.
871 (if (eq (numeric-type-complexp type) :real)
872 (let* ((lo (numeric-type-low type))
873 (lo-val (bound-value lo))
874 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
875 (hi (numeric-type-high type))
876 (hi-val (bound-value hi))
877 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
878 (if (or lo-float-zero-p hi-float-zero-p)
880 :class (numeric-type-class type)
881 :format (numeric-type-format type)
883 :low (if lo-float-zero-p
885 (list (float 0.0 lo-val))
888 :high (if hi-float-zero-p
890 (list (float -0.0 hi-val))
897 ;;; Convert back from the intermediate convention for which -0.0 and
898 ;;; 0.0 are considered different to the standard type convention for
900 #!-negative-zero-is-not-zero
901 (defun convert-back-numeric-type (type)
902 (declare (type numeric-type type))
903 ;;; Only convert real float interval delimiters types.
904 (if (eq (numeric-type-complexp type) :real)
905 (let* ((lo (numeric-type-low type))
906 (lo-val (bound-value lo))
908 (and lo (floatp lo-val) (= lo-val 0.0)
909 (float-sign lo-val)))
910 (hi (numeric-type-high type))
911 (hi-val (bound-value hi))
913 (and hi (floatp hi-val) (= hi-val 0.0)
914 (float-sign hi-val))))
916 ;; (float +0.0 +0.0) => (member 0.0)
917 ;; (float -0.0 -0.0) => (member -0.0)
918 ((and lo-float-zero-p hi-float-zero-p)
919 ;; Shouldn't have exclusive bounds here.
920 (assert (and (not (consp lo)) (not (consp hi))))
921 (if (= lo-float-zero-p hi-float-zero-p)
922 ;; (float +0.0 +0.0) => (member 0.0)
923 ;; (float -0.0 -0.0) => (member -0.0)
924 (specifier-type `(member ,lo-val))
925 ;; (float -0.0 +0.0) => (float 0.0 0.0)
926 ;; (float +0.0 -0.0) => (float 0.0 0.0)
927 (make-numeric-type :class (numeric-type-class type)
928 :format (numeric-type-format type)
934 ;; (float -0.0 x) => (float 0.0 x)
935 ((and (not (consp lo)) (minusp lo-float-zero-p))
936 (make-numeric-type :class (numeric-type-class type)
937 :format (numeric-type-format type)
939 :low (float 0.0 lo-val)
941 ;; (float (+0.0) x) => (float (0.0) x)
942 ((and (consp lo) (plusp lo-float-zero-p))
943 (make-numeric-type :class (numeric-type-class type)
944 :format (numeric-type-format type)
946 :low (list (float 0.0 lo-val))
949 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
950 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
951 (list (make-member-type :members (list (float 0.0 lo-val)))
952 (make-numeric-type :class (numeric-type-class type)
953 :format (numeric-type-format type)
955 :low (list (float 0.0 lo-val))
959 ;; (float x +0.0) => (float x 0.0)
960 ((and (not (consp hi)) (plusp hi-float-zero-p))
961 (make-numeric-type :class (numeric-type-class type)
962 :format (numeric-type-format type)
965 :high (float 0.0 hi-val)))
966 ;; (float x (-0.0)) => (float x (0.0))
967 ((and (consp hi) (minusp hi-float-zero-p))
968 (make-numeric-type :class (numeric-type-class type)
969 :format (numeric-type-format type)
972 :high (list (float 0.0 hi-val))))
974 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
975 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
976 (list (make-member-type :members (list (float -0.0 hi-val)))
977 (make-numeric-type :class (numeric-type-class type)
978 :format (numeric-type-format type)
981 :high (list (float 0.0 hi-val)))))))
987 ;;; Convert back a possible list of numeric types.
988 #!-negative-zero-is-not-zero
989 (defun convert-back-numeric-type-list (type-list)
993 (dolist (type type-list)
994 (if (numeric-type-p type)
995 (let ((result (convert-back-numeric-type type)))
997 (setf results (append results result))
998 (push result results)))
999 (push type results)))
1002 (convert-back-numeric-type type-list))
1004 (convert-back-numeric-type-list (union-type-types type-list)))
1008 ;;; Make-Canonical-Union-Type
1010 ;;; Take a list of types and return a canonical type specifier,
1011 ;;; combining any members types together. If both positive and
1012 ;;; negative members types are present they are converted to a float
1013 ;;; type. X This would be far simpler if the type-union methods could
1014 ;;; handle member/number unions.
1015 (defun make-canonical-union-type (type-list)
1018 (dolist (type type-list)
1019 (if (member-type-p type)
1020 (setf members (union members (member-type-members type)))
1021 (push type misc-types)))
1023 (when (null (set-difference '(-0l0 0l0) members))
1024 #!-negative-zero-is-not-zero
1025 (push (specifier-type '(long-float 0l0 0l0)) misc-types)
1026 #!+negative-zero-is-not-zero
1027 (push (specifier-type '(long-float -0l0 0l0)) misc-types)
1028 (setf members (set-difference members '(-0l0 0l0))))
1029 (when (null (set-difference '(-0d0 0d0) members))
1030 #!-negative-zero-is-not-zero
1031 (push (specifier-type '(double-float 0d0 0d0)) misc-types)
1032 #!+negative-zero-is-not-zero
1033 (push (specifier-type '(double-float -0d0 0d0)) misc-types)
1034 (setf members (set-difference members '(-0d0 0d0))))
1035 (when (null (set-difference '(-0f0 0f0) members))
1036 #!-negative-zero-is-not-zero
1037 (push (specifier-type '(single-float 0f0 0f0)) misc-types)
1038 #!+negative-zero-is-not-zero
1039 (push (specifier-type '(single-float -0f0 0f0)) misc-types)
1040 (setf members (set-difference members '(-0f0 0f0))))
1041 (cond ((null members)
1042 (let ((res (first misc-types)))
1043 (dolist (type (rest misc-types))
1044 (setq res (type-union res type)))
1047 (make-member-type :members members))
1049 (let ((res (first misc-types)))
1050 (dolist (type (rest misc-types))
1051 (setq res (type-union res type)))
1052 (dolist (type members)
1053 (setq res (type-union
1054 res (make-member-type :members (list type)))))
1057 ;;; Convert-Member-Type
1059 ;;; Convert a member type with a single member to a numeric type.
1060 (defun convert-member-type (arg)
1061 (let* ((members (member-type-members arg))
1062 (member (first members))
1063 (member-type (type-of member)))
1064 (assert (not (rest members)))
1065 (specifier-type `(,(if (subtypep member-type 'integer)
1070 ;;; ONE-ARG-DERIVE-TYPE
1072 ;;; This is used in defoptimizers for computing the resulting type of
1075 ;;; Given the continuation ARG, derive the resulting type using the
1076 ;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
1077 ;;; "atomic" continuation type like numeric-type or member-type
1078 ;;; (containing just one element). It should return the resulting
1079 ;;; type, which can be a list of types.
1081 ;;; For the case of member types, if a member-fcn is given it is
1082 ;;; called to compute the result otherwise the member type is first
1083 ;;; converted to a numeric type and the derive-fcn is call.
1084 (defun one-arg-derive-type (arg derive-fcn member-fcn
1085 &optional (convert-type t))
1086 (declare (type function derive-fcn)
1087 (type (or null function) member-fcn)
1088 #!+negative-zero-is-not-zero (ignore convert-type))
1089 (let ((arg-list (prepare-arg-for-derive-type (continuation-type arg))))
1095 (with-float-traps-masked
1096 (:underflow :overflow :divide-by-zero)
1100 (first (member-type-members x))))))
1101 ;; Otherwise convert to a numeric type.
1102 (let ((result-type-list
1103 (funcall derive-fcn (convert-member-type x))))
1104 #!-negative-zero-is-not-zero
1106 (convert-back-numeric-type-list result-type-list)
1108 #!+negative-zero-is-not-zero
1111 #!-negative-zero-is-not-zero
1113 (convert-back-numeric-type-list
1114 (funcall derive-fcn (convert-numeric-type x)))
1115 (funcall derive-fcn x))
1116 #!+negative-zero-is-not-zero
1117 (funcall derive-fcn x))
1119 *universal-type*))))
1120 ;; Run down the list of args and derive the type of each one,
1121 ;; saving all of the results in a list.
1122 (let ((results nil))
1123 (dolist (arg arg-list)
1124 (let ((result (deriver arg)))
1126 (setf results (append results result))
1127 (push result results))))
1129 (make-canonical-union-type results)
1130 (first results)))))))
1132 ;;; TWO-ARG-DERIVE-TYPE
1134 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1135 ;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
1136 ;;; original args and a third which is T to indicate if the two args
1137 ;;; really represent the same continuation. This is useful for
1138 ;;; deriving the type of things like (* x x), which should always be
1139 ;;; positive. If we didn't do this, we wouldn't be able to tell.
1140 (defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
1141 &optional (convert-type t))
1142 #!+negative-zero-is-not-zero
1143 (declare (ignore convert-type))
1144 (flet (#!-negative-zero-is-not-zero
1145 (deriver (x y same-arg)
1146 (cond ((and (member-type-p x) (member-type-p y))
1147 (let* ((x (first (member-type-members x)))
1148 (y (first (member-type-members y)))
1149 (result (with-float-traps-masked
1150 (:underflow :overflow :divide-by-zero
1152 (funcall fcn x y))))
1153 (cond ((null result))
1154 ((and (floatp result) (float-nan-p result))
1157 :format (type-of result)
1160 (make-member-type :members (list result))))))
1161 ((and (member-type-p x) (numeric-type-p y))
1162 (let* ((x (convert-member-type x))
1163 (y (if convert-type (convert-numeric-type y) y))
1164 (result (funcall derive-fcn x y same-arg)))
1166 (convert-back-numeric-type-list result)
1168 ((and (numeric-type-p x) (member-type-p y))
1169 (let* ((x (if convert-type (convert-numeric-type x) x))
1170 (y (convert-member-type y))
1171 (result (funcall derive-fcn x y same-arg)))
1173 (convert-back-numeric-type-list result)
1175 ((and (numeric-type-p x) (numeric-type-p y))
1176 (let* ((x (if convert-type (convert-numeric-type x) x))
1177 (y (if convert-type (convert-numeric-type y) y))
1178 (result (funcall derive-fcn x y same-arg)))
1180 (convert-back-numeric-type-list result)
1184 #!+negative-zero-is-not-zero
1185 (deriver (x y same-arg)
1186 (cond ((and (member-type-p x) (member-type-p y))
1187 (let* ((x (first (member-type-members x)))
1188 (y (first (member-type-members y)))
1189 (result (with-float-traps-masked
1190 (:underflow :overflow :divide-by-zero)
1191 (funcall fcn x y))))
1193 (make-member-type :members (list result)))))
1194 ((and (member-type-p x) (numeric-type-p y))
1195 (let ((x (convert-member-type x)))
1196 (funcall derive-fcn x y same-arg)))
1197 ((and (numeric-type-p x) (member-type-p y))
1198 (let ((y (convert-member-type y)))
1199 (funcall derive-fcn x y same-arg)))
1200 ((and (numeric-type-p x) (numeric-type-p y))
1201 (funcall derive-fcn x y same-arg))
1203 *universal-type*))))
1204 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1205 (a1 (prepare-arg-for-derive-type (continuation-type arg1)))
1206 (a2 (prepare-arg-for-derive-type (continuation-type arg2))))
1208 (let ((results nil))
1210 ;; Since the args are the same continuation, just run
1213 (let ((result (deriver x x same-arg)))
1215 (setf results (append results result))
1216 (push result results))))
1217 ;; Try all pairwise combinations.
1220 (let ((result (or (deriver x y same-arg)
1221 (numeric-contagion x y))))
1223 (setf results (append results result))
1224 (push result results))))))
1226 (make-canonical-union-type results)
1227 (first results)))))))
1231 #!-propagate-float-type
1233 (defoptimizer (+ derive-type) ((x y))
1234 (derive-integer-type
1241 (values (frob (numeric-type-low x) (numeric-type-low y))
1242 (frob (numeric-type-high x) (numeric-type-high y)))))))
1244 (defoptimizer (- derive-type) ((x y))
1245 (derive-integer-type
1252 (values (frob (numeric-type-low x) (numeric-type-high y))
1253 (frob (numeric-type-high x) (numeric-type-low y)))))))
1255 (defoptimizer (* derive-type) ((x y))
1256 (derive-integer-type
1259 (let ((x-low (numeric-type-low x))
1260 (x-high (numeric-type-high x))
1261 (y-low (numeric-type-low y))
1262 (y-high (numeric-type-high y)))
1263 (cond ((not (and x-low y-low))
1265 ((or (minusp x-low) (minusp y-low))
1266 (if (and x-high y-high)
1267 (let ((max (* (max (abs x-low) (abs x-high))
1268 (max (abs y-low) (abs y-high)))))
1269 (values (- max) max))
1272 (values (* x-low y-low)
1273 (if (and x-high y-high)
1277 (defoptimizer (/ derive-type) ((x y))
1278 (numeric-contagion (continuation-type x) (continuation-type y)))
1282 #!+propagate-float-type
1284 (defun +-derive-type-aux (x y same-arg)
1285 (if (and (numeric-type-real-p x)
1286 (numeric-type-real-p y))
1289 (let ((x-int (numeric-type->interval x)))
1290 (interval-add x-int x-int))
1291 (interval-add (numeric-type->interval x)
1292 (numeric-type->interval y))))
1293 (result-type (numeric-contagion x y)))
1294 ;; If the result type is a float, we need to be sure to coerce
1295 ;; the bounds into the correct type.
1296 (when (eq (numeric-type-class result-type) 'float)
1297 (setf result (interval-func
1299 (coerce x (or (numeric-type-format result-type)
1303 :class (if (and (eq (numeric-type-class x) 'integer)
1304 (eq (numeric-type-class y) 'integer))
1305 ;; The sum of integers is always an integer
1307 (numeric-type-class result-type))
1308 :format (numeric-type-format result-type)
1309 :low (interval-low result)
1310 :high (interval-high result)))
1311 ;; General contagion
1312 (numeric-contagion x y)))
1314 (defoptimizer (+ derive-type) ((x y))
1315 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1317 (defun --derive-type-aux (x y same-arg)
1318 (if (and (numeric-type-real-p x)
1319 (numeric-type-real-p y))
1321 ;; (- x x) is always 0.
1323 (make-interval :low 0 :high 0)
1324 (interval-sub (numeric-type->interval x)
1325 (numeric-type->interval y))))
1326 (result-type (numeric-contagion x y)))
1327 ;; If the result type is a float, we need to be sure to coerce
1328 ;; the bounds into the correct type.
1329 (when (eq (numeric-type-class result-type) 'float)
1330 (setf result (interval-func
1332 (coerce x (or (numeric-type-format result-type)
1336 :class (if (and (eq (numeric-type-class x) 'integer)
1337 (eq (numeric-type-class y) 'integer))
1338 ;; The difference of integers is always an integer
1340 (numeric-type-class result-type))
1341 :format (numeric-type-format result-type)
1342 :low (interval-low result)
1343 :high (interval-high result)))
1344 ;; General contagion
1345 (numeric-contagion x y)))
1347 (defoptimizer (- derive-type) ((x y))
1348 (two-arg-derive-type x y #'--derive-type-aux #'-))
1350 (defun *-derive-type-aux (x y same-arg)
1351 (if (and (numeric-type-real-p x)
1352 (numeric-type-real-p y))
1354 ;; (* x x) is always positive, so take care to do it
1357 (interval-sqr (numeric-type->interval x))
1358 (interval-mul (numeric-type->interval x)
1359 (numeric-type->interval y))))
1360 (result-type (numeric-contagion x y)))
1361 ;; If the result type is a float, we need to be sure to coerce
1362 ;; the bounds into the correct type.
1363 (when (eq (numeric-type-class result-type) 'float)
1364 (setf result (interval-func
1366 (coerce x (or (numeric-type-format result-type)
1370 :class (if (and (eq (numeric-type-class x) 'integer)
1371 (eq (numeric-type-class y) 'integer))
1372 ;; The product of integers is always an integer
1374 (numeric-type-class result-type))
1375 :format (numeric-type-format result-type)
1376 :low (interval-low result)
1377 :high (interval-high result)))
1378 (numeric-contagion x y)))
1380 (defoptimizer (* derive-type) ((x y))
1381 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1383 (defun /-derive-type-aux (x y same-arg)
1384 (if (and (numeric-type-real-p x)
1385 (numeric-type-real-p y))
1387 ;; (/ x x) is always 1, except if x can contain 0. In
1388 ;; that case, we shouldn't optimize the division away
1389 ;; because we want 0/0 to signal an error.
1391 (not (interval-contains-p
1392 0 (interval-closure (numeric-type->interval y)))))
1393 (make-interval :low 1 :high 1)
1394 (interval-div (numeric-type->interval x)
1395 (numeric-type->interval y))))
1396 (result-type (numeric-contagion x y)))
1397 ;; If the result type is a float, we need to be sure to coerce
1398 ;; the bounds into the correct type.
1399 (when (eq (numeric-type-class result-type) 'float)
1400 (setf result (interval-func
1402 (coerce x (or (numeric-type-format result-type)
1405 (make-numeric-type :class (numeric-type-class result-type)
1406 :format (numeric-type-format result-type)
1407 :low (interval-low result)
1408 :high (interval-high result)))
1409 (numeric-contagion x y)))
1411 (defoptimizer (/ derive-type) ((x y))
1412 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1416 ;;; KLUDGE: All this ASH optimization is suppressed under CMU CL
1417 ;;; because as of version 2.4.6 for Debian, CMU CL blows up on (ASH
1418 ;;; 1000000000 -100000000000) (i.e. ASH of two bignums yielding zero)
1419 ;;; and it's hard to avoid that calculation in here.
1420 #-(and cmu sb-xc-host)
1422 #!-propagate-fun-type
1423 (defoptimizer (ash derive-type) ((n shift))
1424 (or (let ((n-type (continuation-type n)))
1425 (when (numeric-type-p n-type)
1426 (let ((n-low (numeric-type-low n-type))
1427 (n-high (numeric-type-high n-type)))
1428 (if (constant-continuation-p shift)
1429 (let ((shift (continuation-value shift)))
1430 (make-numeric-type :class 'integer
1432 :low (when n-low (ash n-low shift))
1433 :high (when n-high (ash n-high shift))))
1434 (let ((s-type (continuation-type shift)))
1435 (when (numeric-type-p s-type)
1436 (let ((s-low (numeric-type-low s-type))
1437 (s-high (numeric-type-high s-type)))
1438 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1439 (make-numeric-type :class 'integer
1442 (min (ash n-low s-high)
1445 (max (ash n-high s-high)
1446 (ash n-high s-low))))
1447 (make-numeric-type :class 'integer
1448 :complexp :real)))))))))
1450 #!+propagate-fun-type
1451 (defun ash-derive-type-aux (n-type shift same-arg)
1452 (declare (ignore same-arg))
1453 (or (and (csubtypep n-type (specifier-type 'integer))
1454 (csubtypep shift (specifier-type 'integer))
1455 (let ((n-low (numeric-type-low n-type))
1456 (n-high (numeric-type-high n-type))
1457 (s-low (numeric-type-low shift))
1458 (s-high (numeric-type-high shift)))
1459 ;; KLUDGE: The bare 64's here should be related to
1460 ;; symbolic machine word size values somehow.
1461 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1462 (make-numeric-type :class 'integer :complexp :real
1464 (min (ash n-low s-high)
1467 (max (ash n-high s-high)
1468 (ash n-high s-low))))
1469 (make-numeric-type :class 'integer
1472 #!+propagate-fun-type
1473 (defoptimizer (ash derive-type) ((n shift))
1474 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1477 #!-propagate-float-type
1478 (macrolet ((frob (fun)
1479 `#'(lambda (type type2)
1480 (declare (ignore type2))
1481 (let ((lo (numeric-type-low type))
1482 (hi (numeric-type-high type)))
1483 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1485 (defoptimizer (%negate derive-type) ((num))
1486 (derive-integer-type num num (frob -)))
1488 (defoptimizer (lognot derive-type) ((int))
1489 (derive-integer-type int int (frob lognot))))
1491 #!+propagate-float-type
1492 (defoptimizer (lognot derive-type) ((int))
1493 (derive-integer-type int int
1494 #'(lambda (type type2)
1495 (declare (ignore type2))
1496 (let ((lo (numeric-type-low type))
1497 (hi (numeric-type-high type)))
1498 (values (if hi (lognot hi) nil)
1499 (if lo (lognot lo) nil)
1500 (numeric-type-class type)
1501 (numeric-type-format type))))))
1503 #!+propagate-float-type
1504 (defoptimizer (%negate derive-type) ((num))
1505 (flet ((negate-bound (b)
1506 (set-bound (- (bound-value b)) (consp b))))
1507 (one-arg-derive-type num
1509 (let ((lo (numeric-type-low type))
1510 (hi (numeric-type-high type))
1511 (result (copy-numeric-type type)))
1512 (setf (numeric-type-low result)
1513 (if hi (negate-bound hi) nil))
1514 (setf (numeric-type-high result)
1515 (if lo (negate-bound lo) nil))
1519 #!-propagate-float-type
1520 (defoptimizer (abs derive-type) ((num))
1521 (let ((type (continuation-type num)))
1522 (if (and (numeric-type-p type)
1523 (eq (numeric-type-class type) 'integer)
1524 (eq (numeric-type-complexp type) :real))
1525 (let ((lo (numeric-type-low type))
1526 (hi (numeric-type-high type)))
1527 (make-numeric-type :class 'integer :complexp :real
1528 :low (cond ((and hi (minusp hi))
1534 :high (if (and hi lo)
1535 (max (abs hi) (abs lo))
1537 (numeric-contagion type type))))
1539 #!+propagate-float-type
1540 (defun abs-derive-type-aux (type)
1541 (cond ((eq (numeric-type-complexp type) :complex)
1542 ;; The absolute value of a complex number is always a
1543 ;; non-negative float.
1544 (let* ((format (case (numeric-type-class type)
1545 ((integer rational) 'single-float)
1546 (t (numeric-type-format type))))
1547 (bound-format (or format 'float)))
1548 (make-numeric-type :class 'float
1551 :low (coerce 0 bound-format)
1554 ;; The absolute value of a real number is a non-negative real
1555 ;; of the same type.
1556 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1557 (class (numeric-type-class type))
1558 (format (numeric-type-format type))
1559 (bound-type (or format class 'real)))
1564 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1565 :high (coerce-numeric-bound
1566 (interval-high abs-bnd) bound-type))))))
1568 #!+propagate-float-type
1569 (defoptimizer (abs derive-type) ((num))
1570 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1572 #!-propagate-float-type
1573 (defoptimizer (truncate derive-type) ((number divisor))
1574 (let ((number-type (continuation-type number))
1575 (divisor-type (continuation-type divisor))
1576 (integer-type (specifier-type 'integer)))
1577 (if (and (numeric-type-p number-type)
1578 (csubtypep number-type integer-type)
1579 (numeric-type-p divisor-type)
1580 (csubtypep divisor-type integer-type))
1581 (let ((number-low (numeric-type-low number-type))
1582 (number-high (numeric-type-high number-type))
1583 (divisor-low (numeric-type-low divisor-type))
1584 (divisor-high (numeric-type-high divisor-type)))
1585 (values-specifier-type
1586 `(values ,(integer-truncate-derive-type number-low number-high
1587 divisor-low divisor-high)
1588 ,(integer-rem-derive-type number-low number-high
1589 divisor-low divisor-high))))
1592 #-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
1594 #!+propagate-float-type
1597 (defun rem-result-type (number-type divisor-type)
1598 ;; Figure out what the remainder type is. The remainder is an
1599 ;; integer if both args are integers; a rational if both args are
1600 ;; rational; and a float otherwise.
1601 (cond ((and (csubtypep number-type (specifier-type 'integer))
1602 (csubtypep divisor-type (specifier-type 'integer)))
1604 ((and (csubtypep number-type (specifier-type 'rational))
1605 (csubtypep divisor-type (specifier-type 'rational)))
1607 ((and (csubtypep number-type (specifier-type 'float))
1608 (csubtypep divisor-type (specifier-type 'float)))
1609 ;; Both are floats so the result is also a float, of
1610 ;; the largest type.
1611 (or (float-format-max (numeric-type-format number-type)
1612 (numeric-type-format divisor-type))
1614 ((and (csubtypep number-type (specifier-type 'float))
1615 (csubtypep divisor-type (specifier-type 'rational)))
1616 ;; One of the arguments is a float and the other is a
1617 ;; rational. The remainder is a float of the same
1619 (or (numeric-type-format number-type) 'float))
1620 ((and (csubtypep divisor-type (specifier-type 'float))
1621 (csubtypep number-type (specifier-type 'rational)))
1622 ;; One of the arguments is a float and the other is a
1623 ;; rational. The remainder is a float of the same
1625 (or (numeric-type-format divisor-type) 'float))
1627 ;; Some unhandled combination. This usually means both args
1628 ;; are REAL so the result is a REAL.
1631 (defun truncate-derive-type-quot (number-type divisor-type)
1632 (let* ((rem-type (rem-result-type number-type divisor-type))
1633 (number-interval (numeric-type->interval number-type))
1634 (divisor-interval (numeric-type->interval divisor-type)))
1635 ;;(declare (type (member '(integer rational float)) rem-type))
1636 ;; We have real numbers now.
1637 (cond ((eq rem-type 'integer)
1638 ;; Since the remainder type is INTEGER, both args are
1640 (let* ((res (integer-truncate-derive-type
1641 (interval-low number-interval)
1642 (interval-high number-interval)
1643 (interval-low divisor-interval)
1644 (interval-high divisor-interval))))
1645 (specifier-type (if (listp res) res 'integer))))
1647 (let ((quot (truncate-quotient-bound
1648 (interval-div number-interval
1649 divisor-interval))))
1650 (specifier-type `(integer ,(or (interval-low quot) '*)
1651 ,(or (interval-high quot) '*))))))))
1653 (defun truncate-derive-type-rem (number-type divisor-type)
1654 (let* ((rem-type (rem-result-type number-type divisor-type))
1655 (number-interval (numeric-type->interval number-type))
1656 (divisor-interval (numeric-type->interval divisor-type))
1657 (rem (truncate-rem-bound number-interval divisor-interval)))
1658 ;;(declare (type (member '(integer rational float)) rem-type))
1659 ;; We have real numbers now.
1660 (cond ((eq rem-type 'integer)
1661 ;; Since the remainder type is INTEGER, both args are
1663 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1664 ,(or (interval-high rem) '*))))
1666 (multiple-value-bind (class format)
1669 (values 'integer nil))
1671 (values 'rational nil))
1672 ((or single-float double-float #!+long-float long-float)
1673 (values 'float rem-type))
1675 (values 'float nil))
1678 (when (member rem-type '(float single-float double-float
1679 #!+long-float long-float))
1680 (setf rem (interval-func #'(lambda (x)
1681 (coerce x rem-type))
1683 (make-numeric-type :class class
1685 :low (interval-low rem)
1686 :high (interval-high rem)))))))
1688 (defun truncate-derive-type-quot-aux (num div same-arg)
1689 (declare (ignore same-arg))
1690 (if (and (numeric-type-real-p num)
1691 (numeric-type-real-p div))
1692 (truncate-derive-type-quot num div)
1695 (defun truncate-derive-type-rem-aux (num div same-arg)
1696 (declare (ignore same-arg))
1697 (if (and (numeric-type-real-p num)
1698 (numeric-type-real-p div))
1699 (truncate-derive-type-rem num div)
1702 (defoptimizer (truncate derive-type) ((number divisor))
1703 (let ((quot (two-arg-derive-type number divisor
1704 #'truncate-derive-type-quot-aux #'truncate))
1705 (rem (two-arg-derive-type number divisor
1706 #'truncate-derive-type-rem-aux #'rem)))
1707 (when (and quot rem)
1708 (make-values-type :required (list quot rem)))))
1710 (defun ftruncate-derive-type-quot (number-type divisor-type)
1711 ;; The bounds are the same as for truncate. However, the first
1712 ;; result is a float of some type. We need to determine what that
1713 ;; type is. Basically it's the more contagious of the two types.
1714 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1715 (res-type (numeric-contagion number-type divisor-type)))
1716 (make-numeric-type :class 'float
1717 :format (numeric-type-format res-type)
1718 :low (numeric-type-low q-type)
1719 :high (numeric-type-high q-type))))
1721 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1722 (declare (ignore same-arg))
1723 (if (and (numeric-type-real-p n)
1724 (numeric-type-real-p d))
1725 (ftruncate-derive-type-quot n d)
1728 (defoptimizer (ftruncate derive-type) ((number divisor))
1730 (two-arg-derive-type number divisor
1731 #'ftruncate-derive-type-quot-aux #'ftruncate))
1732 (rem (two-arg-derive-type number divisor
1733 #'truncate-derive-type-rem-aux #'rem)))
1734 (when (and quot rem)
1735 (make-values-type :required (list quot rem)))))
1737 (defun %unary-truncate-derive-type-aux (number)
1738 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1740 (defoptimizer (%unary-truncate derive-type) ((number))
1741 (one-arg-derive-type number
1742 #'%unary-truncate-derive-type-aux
1745 ;;; Define optimizers for FLOOR and CEILING.
1747 ((frob-opt (name q-name r-name)
1748 (let ((q-aux (symbolicate q-name "-AUX"))
1749 (r-aux (symbolicate r-name "-AUX")))
1751 ;; Compute type of quotient (first) result
1752 (defun ,q-aux (number-type divisor-type)
1753 (let* ((number-interval
1754 (numeric-type->interval number-type))
1756 (numeric-type->interval divisor-type))
1757 (quot (,q-name (interval-div number-interval
1758 divisor-interval))))
1759 (specifier-type `(integer ,(or (interval-low quot) '*)
1760 ,(or (interval-high quot) '*)))))
1761 ;; Compute type of remainder
1762 (defun ,r-aux (number-type divisor-type)
1763 (let* ((divisor-interval
1764 (numeric-type->interval divisor-type))
1765 (rem (,r-name divisor-interval))
1766 (result-type (rem-result-type number-type divisor-type)))
1767 (multiple-value-bind (class format)
1770 (values 'integer nil))
1772 (values 'rational nil))
1773 ((or single-float double-float #!+long-float long-float)
1774 (values 'float result-type))
1776 (values 'float nil))
1779 (when (member result-type '(float single-float double-float
1780 #!+long-float long-float))
1781 ;; Make sure the limits on the interval have
1783 (setf rem (interval-func #'(lambda (x)
1784 (coerce x result-type))
1786 (make-numeric-type :class class
1788 :low (interval-low rem)
1789 :high (interval-high rem)))))
1790 ;; The optimizer itself
1791 (defoptimizer (,name derive-type) ((number divisor))
1792 (flet ((derive-q (n d same-arg)
1793 (declare (ignore same-arg))
1794 (if (and (numeric-type-real-p n)
1795 (numeric-type-real-p d))
1798 (derive-r (n d same-arg)
1799 (declare (ignore same-arg))
1800 (if (and (numeric-type-real-p n)
1801 (numeric-type-real-p d))
1804 (let ((quot (two-arg-derive-type
1805 number divisor #'derive-q #',name))
1806 (rem (two-arg-derive-type
1807 number divisor #'derive-r #'mod)))
1808 (when (and quot rem)
1809 (make-values-type :required (list quot rem))))))
1812 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1813 (frob-opt floor floor-quotient-bound floor-rem-bound)
1814 (frob-opt ceiling ceiling-quotient-bound ceiling-rem-bound))
1816 ;;; Define optimizers for FFLOOR and FCEILING
1818 ((frob-opt (name q-name r-name)
1819 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1820 (r-aux (symbolicate r-name "-AUX")))
1822 ;; Compute type of quotient (first) result
1823 (defun ,q-aux (number-type divisor-type)
1824 (let* ((number-interval
1825 (numeric-type->interval number-type))
1827 (numeric-type->interval divisor-type))
1828 (quot (,q-name (interval-div number-interval
1830 (res-type (numeric-contagion number-type divisor-type)))
1832 :class (numeric-type-class res-type)
1833 :format (numeric-type-format res-type)
1834 :low (interval-low quot)
1835 :high (interval-high quot))))
1837 (defoptimizer (,name derive-type) ((number divisor))
1838 (flet ((derive-q (n d same-arg)
1839 (declare (ignore same-arg))
1840 (if (and (numeric-type-real-p n)
1841 (numeric-type-real-p d))
1844 (derive-r (n d same-arg)
1845 (declare (ignore same-arg))
1846 (if (and (numeric-type-real-p n)
1847 (numeric-type-real-p d))
1850 (let ((quot (two-arg-derive-type
1851 number divisor #'derive-q #',name))
1852 (rem (two-arg-derive-type
1853 number divisor #'derive-r #'mod)))
1854 (when (and quot rem)
1855 (make-values-type :required (list quot rem))))))))))
1857 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1858 (frob-opt ffloor floor-quotient-bound floor-rem-bound)
1859 (frob-opt fceiling ceiling-quotient-bound ceiling-rem-bound))
1861 ;;; Functions to compute the bounds on the quotient and remainder for
1862 ;;; the FLOOR function.
1863 (defun floor-quotient-bound (quot)
1864 ;; Take the floor of the quotient and then massage it into what we
1866 (let ((lo (interval-low quot))
1867 (hi (interval-high quot)))
1868 ;; Take the floor of the lower bound. The result is always a
1869 ;; closed lower bound.
1871 (floor (bound-value lo))
1873 ;; For the upper bound, we need to be careful
1876 ;; An open bound. We need to be careful here because
1877 ;; the floor of '(10.0) is 9, but the floor of
1879 (multiple-value-bind (q r) (floor (first hi))
1884 ;; A closed bound, so the answer is obvious.
1888 (make-interval :low lo :high hi)))
1889 (defun floor-rem-bound (div)
1890 ;; The remainder depends only on the divisor. Try to get the
1891 ;; correct sign for the remainder if we can.
1892 (case (interval-range-info div)
1894 ;; Divisor is always positive.
1895 (let ((rem (interval-abs div)))
1896 (setf (interval-low rem) 0)
1897 (when (and (numberp (interval-high rem))
1898 (not (zerop (interval-high rem))))
1899 ;; The remainder never contains the upper bound. However,
1900 ;; watch out for the case where the high limit is zero!
1901 (setf (interval-high rem) (list (interval-high rem))))
1904 ;; Divisor is always negative
1905 (let ((rem (interval-neg (interval-abs div))))
1906 (setf (interval-high rem) 0)
1907 (when (numberp (interval-low rem))
1908 ;; The remainder never contains the lower bound.
1909 (setf (interval-low rem) (list (interval-low rem))))
1912 ;; The divisor can be positive or negative. All bets off.
1913 ;; The magnitude of remainder is the maximum value of the
1915 (let ((limit (bound-value (interval-high (interval-abs div)))))
1916 ;; The bound never reaches the limit, so make the interval open
1917 (make-interval :low (if limit
1920 :high (list limit))))))
1922 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1923 => #S(INTERVAL :LOW 0 :HIGH 10)
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))
1927 => #S(INTERVAL :LOW 0 :HIGH 10)
1928 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1929 => #S(INTERVAL :LOW 0 :HIGH 9)
1930 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1931 => #S(INTERVAL :LOW 0 :HIGH 10)
1932 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1933 => #S(INTERVAL :LOW 0 :HIGH 10)
1934 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1935 => #S(INTERVAL :LOW -2 :HIGH 10)
1936 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1937 => #S(INTERVAL :LOW -1 :HIGH 10)
1938 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1939 => #S(INTERVAL :LOW -1 :HIGH 10)
1941 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1942 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
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 -10 :high -2.3))
1946 #S(INTERVAL :LOW (-10) :HIGH 0)
1947 (floor-rem-bound (make-interval :low 0.3 :high 10))
1948 => #S(INTERVAL :LOW 0 :HIGH '(10))
1949 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1950 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1951 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1952 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1955 ;;; same functions for CEILING
1956 (defun ceiling-quotient-bound (quot)
1957 ;; Take the ceiling of the quotient and then massage it into what we
1959 (let ((lo (interval-low quot))
1960 (hi (interval-high quot)))
1961 ;; Take the ceiling of the upper bound. The result is always a
1962 ;; closed upper bound.
1964 (ceiling (bound-value hi))
1966 ;; For the lower bound, we need to be careful
1969 ;; An open bound. We need to be careful here because
1970 ;; the ceiling of '(10.0) is 11, but the ceiling of
1972 (multiple-value-bind (q r) (ceiling (first lo))
1977 ;; A closed bound, so the answer is obvious.
1981 (make-interval :low lo :high hi)))
1982 (defun ceiling-rem-bound (div)
1983 ;; The remainder depends only on the divisor. Try to get the
1984 ;; correct sign for the remainder if we can.
1986 (case (interval-range-info div)
1988 ;; Divisor is always positive. The remainder is negative.
1989 (let ((rem (interval-neg (interval-abs div))))
1990 (setf (interval-high rem) 0)
1991 (when (and (numberp (interval-low rem))
1992 (not (zerop (interval-low rem))))
1993 ;; The remainder never contains the upper bound. However,
1994 ;; watch out for the case when the upper bound is zero!
1995 (setf (interval-low rem) (list (interval-low rem))))
1998 ;; Divisor is always negative. The remainder is positive
1999 (let ((rem (interval-abs div)))
2000 (setf (interval-low rem) 0)
2001 (when (numberp (interval-high rem))
2002 ;; The remainder never contains the lower bound.
2003 (setf (interval-high rem) (list (interval-high rem))))
2006 ;; The divisor can be positive or negative. All bets off.
2007 ;; The magnitude of remainder is the maximum value of the
2009 (let ((limit (bound-value (interval-high (interval-abs div)))))
2010 ;; The bound never reaches the limit, so make the interval open
2011 (make-interval :low (if limit
2014 :high (list limit))))))
2017 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2018 => #S(INTERVAL :LOW 1 :HIGH 11)
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))
2022 => #S(INTERVAL :LOW 1 :HIGH 10)
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 10.3))
2026 => #S(INTERVAL :LOW 1 :HIGH 11)
2027 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2028 => #S(INTERVAL :LOW 1 :HIGH 11)
2029 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2030 => #S(INTERVAL :LOW -1 :HIGH 11)
2031 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2032 => #S(INTERVAL :LOW 0 :HIGH 11)
2033 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2034 => #S(INTERVAL :LOW -1 :HIGH 11)
2036 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2037 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2038 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2039 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2040 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2041 => #S(INTERVAL :LOW 0 :HIGH (10))
2042 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2043 => #S(INTERVAL :LOW (-10) :HIGH 0)
2044 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2045 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2046 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2047 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2050 (defun truncate-quotient-bound (quot)
2051 ;; For positive quotients, truncate is exactly like floor. For
2052 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2053 ;; it's the union of the two pieces.
2054 (case (interval-range-info quot)
2057 (floor-quotient-bound quot))
2059 ;; Just like ceiling
2060 (ceiling-quotient-bound quot))
2062 ;; Split the interval into positive and negative pieces, compute
2063 ;; the result for each piece and put them back together.
2064 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2065 (interval-merge-pair (ceiling-quotient-bound neg)
2066 (floor-quotient-bound pos))))))
2068 (defun truncate-rem-bound (num div)
2069 ;; This is significantly more complicated than floor or ceiling. We
2070 ;; need both the number and the divisor to determine the range. The
2071 ;; basic idea is to split the ranges of num and den into positive
2072 ;; and negative pieces and deal with each of the four possibilities
2074 (case (interval-range-info num)
2076 (case (interval-range-info div)
2078 (floor-rem-bound div))
2080 (ceiling-rem-bound div))
2082 (destructuring-bind (neg pos) (interval-split 0 div t t)
2083 (interval-merge-pair (truncate-rem-bound num neg)
2084 (truncate-rem-bound num pos))))))
2086 (case (interval-range-info div)
2088 (ceiling-rem-bound div))
2090 (floor-rem-bound div))
2092 (destructuring-bind (neg pos) (interval-split 0 div t t)
2093 (interval-merge-pair (truncate-rem-bound num neg)
2094 (truncate-rem-bound num pos))))))
2096 (destructuring-bind (neg pos) (interval-split 0 num t t)
2097 (interval-merge-pair (truncate-rem-bound neg div)
2098 (truncate-rem-bound pos div))))))
2101 ;;; Derive useful information about the range. Returns three values:
2102 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2103 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2104 ;;; - The abs of the maximal value if there is one, or nil if it is
2106 (defun numeric-range-info (low high)
2107 (cond ((and low (not (minusp low)))
2108 (values '+ low high))
2109 ((and high (not (plusp high)))
2110 (values '- (- high) (if low (- low) nil)))
2112 (values nil 0 (and low high (max (- low) high))))))
2114 (defun integer-truncate-derive-type
2115 (number-low number-high divisor-low divisor-high)
2116 ;; The result cannot be larger in magnitude than the number, but the sign
2117 ;; might change. If we can determine the sign of either the number or
2118 ;; the divisor, we can eliminate some of the cases.
2119 (multiple-value-bind (number-sign number-min number-max)
2120 (numeric-range-info number-low number-high)
2121 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2122 (numeric-range-info divisor-low divisor-high)
2123 (when (and divisor-max (zerop divisor-max))
2124 ;; We've got a problem: guaranteed division by zero.
2125 (return-from integer-truncate-derive-type t))
2126 (when (zerop divisor-min)
2127 ;; We'll assume that they aren't going to divide by zero.
2129 (cond ((and number-sign divisor-sign)
2130 ;; We know the sign of both.
2131 (if (eq number-sign divisor-sign)
2132 ;; Same sign, so the result will be positive.
2133 `(integer ,(if divisor-max
2134 (truncate number-min divisor-max)
2137 (truncate number-max divisor-min)
2139 ;; Different signs, the result will be negative.
2140 `(integer ,(if number-max
2141 (- (truncate number-max divisor-min))
2144 (- (truncate number-min divisor-max))
2146 ((eq divisor-sign '+)
2147 ;; The divisor is positive. Therefore, the number will just
2148 ;; become closer to zero.
2149 `(integer ,(if number-low
2150 (truncate number-low divisor-min)
2153 (truncate number-high divisor-min)
2155 ((eq divisor-sign '-)
2156 ;; The divisor is negative. Therefore, the absolute value of
2157 ;; the number will become closer to zero, but the sign will also
2159 `(integer ,(if number-high
2160 (- (truncate number-high divisor-min))
2163 (- (truncate number-low divisor-min))
2165 ;; The divisor could be either positive or negative.
2167 ;; The number we are dividing has a bound. Divide that by the
2168 ;; smallest posible divisor.
2169 (let ((bound (truncate number-max divisor-min)))
2170 `(integer ,(- bound) ,bound)))
2172 ;; The number we are dividing is unbounded, so we can't tell
2173 ;; anything about the result.
2176 #!-propagate-float-type
2177 (defun integer-rem-derive-type
2178 (number-low number-high divisor-low divisor-high)
2179 (if (and divisor-low divisor-high)
2180 ;; We know the range of the divisor, and the remainder must be smaller
2181 ;; than the divisor. We can tell the sign of the remainer if we know
2182 ;; the sign of the number.
2183 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2184 `(integer ,(if (or (null number-low)
2185 (minusp number-low))
2188 ,(if (or (null number-high)
2189 (plusp number-high))
2192 ;; The divisor is potentially either very positive or very negative.
2193 ;; Therefore, the remainer is unbounded, but we might be able to tell
2194 ;; something about the sign from the number.
2195 `(integer ,(if (and number-low (not (minusp number-low)))
2196 ;; The number we are dividing is positive. Therefore,
2197 ;; the remainder must be positive.
2200 ,(if (and number-high (not (plusp number-high)))
2201 ;; The number we are dividing is negative. Therefore,
2202 ;; the remainder must be negative.
2206 #!-propagate-float-type
2207 (defoptimizer (random derive-type) ((bound &optional state))
2208 (let ((type (continuation-type bound)))
2209 (when (numeric-type-p type)
2210 (let ((class (numeric-type-class type))
2211 (high (numeric-type-high type))
2212 (format (numeric-type-format type)))
2216 :low (coerce 0 (or format class 'real))
2217 :high (cond ((not high) nil)
2218 ((eq class 'integer) (max (1- high) 0))
2219 ((or (consp high) (zerop high)) high)
2222 #!+propagate-float-type
2223 (defun random-derive-type-aux (type)
2224 (let ((class (numeric-type-class type))
2225 (high (numeric-type-high type))
2226 (format (numeric-type-format type)))
2230 :low (coerce 0 (or format class 'real))
2231 :high (cond ((not high) nil)
2232 ((eq class 'integer) (max (1- high) 0))
2233 ((or (consp high) (zerop high)) high)
2236 #!+propagate-float-type
2237 (defoptimizer (random derive-type) ((bound &optional state))
2238 (one-arg-derive-type bound #'random-derive-type-aux nil))
2240 ;;;; logical derive-type methods
2242 ;;; Return the maximum number of bits an integer of the supplied type can take
2243 ;;; up, or NIL if it is unbounded. The second (third) value is T if the
2244 ;;; integer can be positive (negative) and NIL if not. Zero counts as
2246 (defun integer-type-length (type)
2247 (if (numeric-type-p type)
2248 (let ((min (numeric-type-low type))
2249 (max (numeric-type-high type)))
2250 (values (and min max (max (integer-length min) (integer-length max)))
2251 (or (null max) (not (minusp max)))
2252 (or (null min) (minusp min))))
2255 #!-propagate-fun-type
2257 (defoptimizer (logand derive-type) ((x y))
2258 (multiple-value-bind (x-len x-pos x-neg)
2259 (integer-type-length (continuation-type x))
2260 (declare (ignore x-pos))
2261 (multiple-value-bind (y-len y-pos y-neg)
2262 (integer-type-length (continuation-type y))
2263 (declare (ignore y-pos))
2265 ;; X must be positive.
2267 ;; The must both be positive.
2268 (cond ((or (null x-len) (null y-len))
2269 (specifier-type 'unsigned-byte))
2270 ((or (zerop x-len) (zerop y-len))
2271 (specifier-type '(integer 0 0)))
2273 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2274 ;; X is positive, but Y might be negative.
2276 (specifier-type 'unsigned-byte))
2278 (specifier-type '(integer 0 0)))
2280 (specifier-type `(unsigned-byte ,x-len)))))
2281 ;; X might be negative.
2283 ;; Y must be positive.
2285 (specifier-type 'unsigned-byte))
2287 (specifier-type '(integer 0 0)))
2290 `(unsigned-byte ,y-len))))
2291 ;; Either might be negative.
2292 (if (and x-len y-len)
2293 ;; The result is bounded.
2294 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2295 ;; We can't tell squat about the result.
2296 (specifier-type 'integer)))))))
2298 (defoptimizer (logior derive-type) ((x y))
2299 (multiple-value-bind (x-len x-pos x-neg)
2300 (integer-type-length (continuation-type x))
2301 (multiple-value-bind (y-len y-pos y-neg)
2302 (integer-type-length (continuation-type y))
2304 ((and (not x-neg) (not y-neg))
2305 ;; Both are positive.
2306 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2310 ;; X must be negative.
2312 ;; Both are negative. The result is going to be negative and be
2313 ;; the same length or shorter than the smaller.
2314 (if (and x-len y-len)
2316 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2318 (specifier-type '(integer * -1)))
2319 ;; X is negative, but we don't know about Y. The result will be
2320 ;; negative, but no more negative than X.
2322 `(integer ,(or (numeric-type-low (continuation-type x)) '*)
2325 ;; X might be either positive or negative.
2327 ;; But Y is negative. The result will be negative.
2329 `(integer ,(or (numeric-type-low (continuation-type y)) '*)
2331 ;; We don't know squat about either. It won't get any bigger.
2332 (if (and x-len y-len)
2334 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2336 (specifier-type 'integer))))))))
2338 (defoptimizer (logxor derive-type) ((x y))
2339 (multiple-value-bind (x-len x-pos x-neg)
2340 (integer-type-length (continuation-type x))
2341 (multiple-value-bind (y-len y-pos y-neg)
2342 (integer-type-length (continuation-type y))
2344 ((or (and (not x-neg) (not y-neg))
2345 (and (not x-pos) (not y-pos)))
2346 ;; Either both are negative or both are positive. The result will be
2347 ;; positive, and as long as the longer.
2348 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2351 ((or (and (not x-pos) (not y-neg))
2352 (and (not y-neg) (not y-pos)))
2353 ;; Either X is negative and Y is positive of vice-verca. The result
2354 ;; will be negative.
2355 (specifier-type `(integer ,(if (and x-len y-len)
2356 (ash -1 (max x-len y-len))
2359 ;; We can't tell what the sign of the result is going to be. All we
2360 ;; know is that we don't create new bits.
2362 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2364 (specifier-type 'integer))))))
2368 #!+propagate-fun-type
2370 (defun logand-derive-type-aux (x y &optional same-leaf)
2371 (declare (ignore same-leaf))
2372 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2373 (declare (ignore x-pos))
2374 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2375 (declare (ignore y-pos))
2377 ;; X must be positive.
2379 ;; The must both be positive.
2380 (cond ((or (null x-len) (null y-len))
2381 (specifier-type 'unsigned-byte))
2382 ((or (zerop x-len) (zerop y-len))
2383 (specifier-type '(integer 0 0)))
2385 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2386 ;; X is positive, but Y might be negative.
2388 (specifier-type 'unsigned-byte))
2390 (specifier-type '(integer 0 0)))
2392 (specifier-type `(unsigned-byte ,x-len)))))
2393 ;; X might be negative.
2395 ;; Y must be positive.
2397 (specifier-type 'unsigned-byte))
2399 (specifier-type '(integer 0 0)))
2402 `(unsigned-byte ,y-len))))
2403 ;; Either might be negative.
2404 (if (and x-len y-len)
2405 ;; The result is bounded.
2406 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2407 ;; We can't tell squat about the result.
2408 (specifier-type 'integer)))))))
2410 (defun logior-derive-type-aux (x y &optional same-leaf)
2411 (declare (ignore same-leaf))
2412 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2413 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2415 ((and (not x-neg) (not y-neg))
2416 ;; Both are positive.
2417 (if (and x-len y-len (zerop x-len) (zerop y-len))
2418 (specifier-type '(integer 0 0))
2419 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2423 ;; X must be negative.
2425 ;; Both are negative. The result is going to be negative and be
2426 ;; the same length or shorter than the smaller.
2427 (if (and x-len y-len)
2429 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2431 (specifier-type '(integer * -1)))
2432 ;; X is negative, but we don't know about Y. The result will be
2433 ;; negative, but no more negative than X.
2435 `(integer ,(or (numeric-type-low x) '*)
2438 ;; X might be either positive or negative.
2440 ;; But Y is negative. The result will be negative.
2442 `(integer ,(or (numeric-type-low y) '*)
2444 ;; We don't know squat about either. It won't get any bigger.
2445 (if (and x-len y-len)
2447 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2449 (specifier-type 'integer))))))))
2451 (defun logxor-derive-type-aux (x y &optional same-leaf)
2452 (declare (ignore same-leaf))
2453 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2454 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2456 ((or (and (not x-neg) (not y-neg))
2457 (and (not x-pos) (not y-pos)))
2458 ;; Either both are negative or both are positive. The result will be
2459 ;; positive, and as long as the longer.
2460 (if (and x-len y-len (zerop x-len) (zerop y-len))
2461 (specifier-type '(integer 0 0))
2462 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2465 ((or (and (not x-pos) (not y-neg))
2466 (and (not y-neg) (not y-pos)))
2467 ;; Either X is negative and Y is positive of vice-verca. The result
2468 ;; will be negative.
2469 (specifier-type `(integer ,(if (and x-len y-len)
2470 (ash -1 (max x-len y-len))
2473 ;; We can't tell what the sign of the result is going to be. All we
2474 ;; know is that we don't create new bits.
2476 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2478 (specifier-type 'integer))))))
2480 (macrolet ((frob (logfcn)
2481 (let ((fcn-aux (symbolicate logfcn "-DERIVE-TYPE-AUX")))
2482 `(defoptimizer (,logfcn derive-type) ((x y))
2483 (two-arg-derive-type x y #',fcn-aux #',logfcn)))))
2484 ;; FIXME: DEF-FROB, not just FROB
2491 ;;;; miscellaneous derive-type methods
2493 (defoptimizer (code-char derive-type) ((code))
2494 (specifier-type 'base-char))
2496 (defoptimizer (values derive-type) ((&rest values))
2497 (values-specifier-type
2498 `(values ,@(mapcar #'(lambda (x)
2499 (type-specifier (continuation-type x)))
2502 ;;;; byte operations
2504 ;;;; We try to turn byte operations into simple logical operations. First, we
2505 ;;;; convert byte specifiers into separate size and position arguments passed
2506 ;;;; to internal %FOO functions. We then attempt to transform the %FOO
2507 ;;;; functions into boolean operations when the size and position are constant
2508 ;;;; and the operands are fixnums.
2510 (macrolet (;; Evaluate body with Size-Var and Pos-Var bound to expressions that
2511 ;; evaluate to the Size and Position of the byte-specifier form
2512 ;; Spec. We may wrap a let around the result of the body to bind
2515 ;; If the spec is a Byte form, then bind the vars to the subforms.
2516 ;; otherwise, evaluate Spec and use the Byte-Size and Byte-Position.
2517 ;; The goal of this transformation is to avoid consing up byte
2518 ;; specifiers and then immediately throwing them away.
2519 (with-byte-specifier ((size-var pos-var spec) &body body)
2520 (once-only ((spec `(macroexpand ,spec))
2522 `(if (and (consp ,spec)
2523 (eq (car ,spec) 'byte)
2524 (= (length ,spec) 3))
2525 (let ((,size-var (second ,spec))
2526 (,pos-var (third ,spec)))
2528 (let ((,size-var `(byte-size ,,temp))
2529 (,pos-var `(byte-position ,,temp)))
2530 `(let ((,,temp ,,spec))
2533 (def-source-transform ldb (spec int)
2534 (with-byte-specifier (size pos spec)
2535 `(%ldb ,size ,pos ,int)))
2537 (def-source-transform dpb (newbyte spec int)
2538 (with-byte-specifier (size pos spec)
2539 `(%dpb ,newbyte ,size ,pos ,int)))
2541 (def-source-transform mask-field (spec int)
2542 (with-byte-specifier (size pos spec)
2543 `(%mask-field ,size ,pos ,int)))
2545 (def-source-transform deposit-field (newbyte spec int)
2546 (with-byte-specifier (size pos spec)
2547 `(%deposit-field ,newbyte ,size ,pos ,int))))
2549 (defoptimizer (%ldb derive-type) ((size posn num))
2550 (let ((size (continuation-type size)))
2551 (if (and (numeric-type-p size)
2552 (csubtypep size (specifier-type 'integer)))
2553 (let ((size-high (numeric-type-high size)))
2554 (if (and size-high (<= size-high sb!vm:word-bits))
2555 (specifier-type `(unsigned-byte ,size-high))
2556 (specifier-type 'unsigned-byte)))
2559 (defoptimizer (%mask-field derive-type) ((size posn num))
2560 (let ((size (continuation-type size))
2561 (posn (continuation-type posn)))
2562 (if (and (numeric-type-p size)
2563 (csubtypep size (specifier-type 'integer))
2564 (numeric-type-p posn)
2565 (csubtypep posn (specifier-type 'integer)))
2566 (let ((size-high (numeric-type-high size))
2567 (posn-high (numeric-type-high posn)))
2568 (if (and size-high posn-high
2569 (<= (+ size-high posn-high) sb!vm:word-bits))
2570 (specifier-type `(unsigned-byte ,(+ size-high posn-high)))
2571 (specifier-type 'unsigned-byte)))
2574 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2575 (let ((size (continuation-type size))
2576 (posn (continuation-type posn))
2577 (int (continuation-type int)))
2578 (if (and (numeric-type-p size)
2579 (csubtypep size (specifier-type 'integer))
2580 (numeric-type-p posn)
2581 (csubtypep posn (specifier-type 'integer))
2582 (numeric-type-p int)
2583 (csubtypep int (specifier-type 'integer)))
2584 (let ((size-high (numeric-type-high size))
2585 (posn-high (numeric-type-high posn))
2586 (high (numeric-type-high int))
2587 (low (numeric-type-low int)))
2588 (if (and size-high posn-high high low
2589 (<= (+ size-high posn-high) sb!vm:word-bits))
2591 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2592 (max (integer-length high)
2593 (integer-length low)
2594 (+ size-high posn-high))))
2598 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2599 (let ((size (continuation-type size))
2600 (posn (continuation-type posn))
2601 (int (continuation-type int)))
2602 (if (and (numeric-type-p size)
2603 (csubtypep size (specifier-type 'integer))
2604 (numeric-type-p posn)
2605 (csubtypep posn (specifier-type 'integer))
2606 (numeric-type-p int)
2607 (csubtypep int (specifier-type 'integer)))
2608 (let ((size-high (numeric-type-high size))
2609 (posn-high (numeric-type-high posn))
2610 (high (numeric-type-high int))
2611 (low (numeric-type-low int)))
2612 (if (and size-high posn-high high low
2613 (<= (+ size-high posn-high) sb!vm:word-bits))
2615 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2616 (max (integer-length high)
2617 (integer-length low)
2618 (+ size-high posn-high))))
2622 (deftransform %ldb ((size posn int)
2623 (fixnum fixnum integer)
2624 (unsigned-byte #.sb!vm:word-bits))
2625 "convert to inline logical ops"
2626 `(logand (ash int (- posn))
2627 (ash ,(1- (ash 1 sb!vm:word-bits))
2628 (- size ,sb!vm:word-bits))))
2630 (deftransform %mask-field ((size posn int)
2631 (fixnum fixnum integer)
2632 (unsigned-byte #.sb!vm:word-bits))
2633 "convert to inline logical ops"
2635 (ash (ash ,(1- (ash 1 sb!vm:word-bits))
2636 (- size ,sb!vm:word-bits))
2639 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2640 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2641 ;;; as the result type, as that would allow result types
2642 ;;; that cover the range -2^(n-1) .. 1-2^n, instead of allowing result types
2643 ;;; of (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2645 (deftransform %dpb ((new size posn int)
2647 (unsigned-byte #.sb!vm:word-bits))
2648 "convert to inline logical ops"
2649 `(let ((mask (ldb (byte size 0) -1)))
2650 (logior (ash (logand new mask) posn)
2651 (logand int (lognot (ash mask posn))))))
2653 (deftransform %dpb ((new size posn int)
2655 (signed-byte #.sb!vm:word-bits))
2656 "convert to inline logical ops"
2657 `(let ((mask (ldb (byte size 0) -1)))
2658 (logior (ash (logand new mask) posn)
2659 (logand int (lognot (ash mask posn))))))
2661 (deftransform %deposit-field ((new size posn int)
2663 (unsigned-byte #.sb!vm:word-bits))
2664 "convert to inline logical ops"
2665 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2666 (logior (logand new mask)
2667 (logand int (lognot mask)))))
2669 (deftransform %deposit-field ((new size posn int)
2671 (signed-byte #.sb!vm:word-bits))
2672 "convert to inline logical ops"
2673 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2674 (logior (logand new mask)
2675 (logand int (lognot mask)))))
2677 ;;; miscellanous numeric transforms
2679 ;;; If a constant appears as the first arg, swap the args.
2680 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2681 (if (and (constant-continuation-p x)
2682 (not (constant-continuation-p y)))
2683 `(,(continuation-function-name (basic-combination-fun node))
2685 ,(continuation-value x))
2686 (give-up-ir1-transform)))
2688 (dolist (x '(= char= + * logior logand logxor))
2689 (%deftransform x '(function * *) #'commutative-arg-swap
2690 "place constant arg last."))
2692 ;;; Handle the case of a constant BOOLE-CODE.
2693 (deftransform boole ((op x y) * * :when :both)
2694 "convert to inline logical ops"
2695 (unless (constant-continuation-p op)
2696 (give-up-ir1-transform "BOOLE code is not a constant."))
2697 (let ((control (continuation-value op)))
2703 (#.boole-c1 '(lognot x))
2704 (#.boole-c2 '(lognot y))
2705 (#.boole-and '(logand x y))
2706 (#.boole-ior '(logior x y))
2707 (#.boole-xor '(logxor x y))
2708 (#.boole-eqv '(logeqv x y))
2709 (#.boole-nand '(lognand x y))
2710 (#.boole-nor '(lognor x y))
2711 (#.boole-andc1 '(logandc1 x y))
2712 (#.boole-andc2 '(logandc2 x y))
2713 (#.boole-orc1 '(logorc1 x y))
2714 (#.boole-orc2 '(logorc2 x y))
2716 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2719 ;;;; converting special case multiply/divide to shifts
2721 ;;; If arg is a constant power of two, turn * into a shift.
2722 (deftransform * ((x y) (integer integer) * :when :both)
2723 "convert x*2^k to shift"
2724 (unless (constant-continuation-p y)
2725 (give-up-ir1-transform))
2726 (let* ((y (continuation-value y))
2728 (len (1- (integer-length y-abs))))
2729 (unless (= y-abs (ash 1 len))
2730 (give-up-ir1-transform))
2735 ;;; If both arguments and the result are (unsigned-byte 32), try to come up
2736 ;;; with a ``better'' multiplication using multiplier recoding. There are two
2737 ;;; different ways the multiplier can be recoded. The more obvious is to shift
2738 ;;; X by the correct amount for each bit set in Y and to sum the results. But
2739 ;;; if there is a string of bits that are all set, you can add X shifted by
2740 ;;; one more then the bit position of the first set bit and subtract X shifted
2741 ;;; by the bit position of the last set bit. We can't use this second method
2742 ;;; when the high order bit is bit 31 because shifting by 32 doesn't work
2744 (deftransform * ((x y)
2745 ((unsigned-byte 32) (unsigned-byte 32))
2747 "recode as shift and add"
2748 (unless (constant-continuation-p y)
2749 (give-up-ir1-transform))
2750 (let ((y (continuation-value y))
2753 (labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x))
2758 `(+ ,result ,(tub32 next-factor))
2760 (declare (inline add))
2761 (dotimes (bitpos 32)
2763 (when (not (logbitp bitpos y))
2764 (add (if (= (1+ first-one) bitpos)
2765 ;; There is only a single bit in the string.
2767 ;; There are at least two.
2768 `(- ,(tub32 `(ash x ,bitpos))
2769 ,(tub32 `(ash x ,first-one)))))
2770 (setf first-one nil))
2771 (when (logbitp bitpos y)
2772 (setf first-one bitpos))))
2774 (cond ((= first-one 31))
2778 (add `(- ,(tub32 '(ash x 31)) ,(tub32 `(ash x ,first-one))))))
2782 ;;; If arg is a constant power of two, turn FLOOR into a shift and mask.
2783 ;;; If CEILING, add in (1- (ABS Y)) and then do FLOOR.
2784 (flet ((frob (y ceil-p)
2785 (unless (constant-continuation-p y)
2786 (give-up-ir1-transform))
2787 (let* ((y (continuation-value y))
2789 (len (1- (integer-length y-abs))))
2790 (unless (= y-abs (ash 1 len))
2791 (give-up-ir1-transform))
2792 (let ((shift (- len))
2794 `(let ,(when ceil-p `((x (+ x ,(1- y-abs)))))
2796 `(values (ash (- x) ,shift)
2797 (- (logand (- x) ,mask)))
2798 `(values (ash x ,shift)
2799 (logand x ,mask))))))))
2800 (deftransform floor ((x y) (integer integer) *)
2801 "convert division by 2^k to shift"
2803 (deftransform ceiling ((x y) (integer integer) *)
2804 "convert division by 2^k to shift"
2807 ;;; Do the same for MOD.
2808 (deftransform mod ((x y) (integer integer) * :when :both)
2809 "convert remainder mod 2^k to LOGAND"
2810 (unless (constant-continuation-p y)
2811 (give-up-ir1-transform))
2812 (let* ((y (continuation-value y))
2814 (len (1- (integer-length y-abs))))
2815 (unless (= y-abs (ash 1 len))
2816 (give-up-ir1-transform))
2817 (let ((mask (1- y-abs)))
2819 `(- (logand (- x) ,mask))
2820 `(logand x ,mask)))))
2822 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2823 (deftransform truncate ((x y) (integer integer))
2824 "convert division by 2^k to shift"
2825 (unless (constant-continuation-p y)
2826 (give-up-ir1-transform))
2827 (let* ((y (continuation-value y))
2829 (len (1- (integer-length y-abs))))
2830 (unless (= y-abs (ash 1 len))
2831 (give-up-ir1-transform))
2832 (let* ((shift (- len))
2835 (values ,(if (minusp y)
2837 `(- (ash (- x) ,shift)))
2838 (- (logand (- x) ,mask)))
2839 (values ,(if (minusp y)
2840 `(- (ash (- x) ,shift))
2842 (logand x ,mask))))))
2844 ;;; And the same for REM.
2845 (deftransform rem ((x y) (integer integer) * :when :both)
2846 "convert remainder mod 2^k to LOGAND"
2847 (unless (constant-continuation-p y)
2848 (give-up-ir1-transform))
2849 (let* ((y (continuation-value y))
2851 (len (1- (integer-length y-abs))))
2852 (unless (= y-abs (ash 1 len))
2853 (give-up-ir1-transform))
2854 (let ((mask (1- y-abs)))
2856 (- (logand (- x) ,mask))
2857 (logand x ,mask)))))
2859 ;;;; arithmetic and logical identity operation elimination
2861 ;;;; Flush calls to various arith functions that convert to the identity
2862 ;;;; function or a constant.
2864 (dolist (stuff '((ash 0 x)
2869 (logxor -1 (lognot x))
2871 (destructuring-bind (name identity result) stuff
2872 (deftransform name ((x y) `(* (constant-argument (member ,identity))) '*
2873 :eval-name t :when :both)
2874 "fold identity operations"
2877 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2878 ;;; (* 0 -4.0) is -0.0.
2879 (deftransform - ((x y) ((constant-argument (member 0)) rational) *
2881 "convert (- 0 x) to negate"
2883 (deftransform * ((x y) (rational (constant-argument (member 0))) *
2885 "convert (* x 0) to 0."
2888 ;;; Return T if in an arithmetic op including continuations X and Y, the
2889 ;;; result type is not affected by the type of X. That is, Y is at least as
2890 ;;; contagious as X.
2892 (defun not-more-contagious (x y)
2893 (declare (type continuation x y))
2894 (let ((x (continuation-type x))
2895 (y (continuation-type y)))
2896 (values (type= (numeric-contagion x y)
2897 (numeric-contagion y y)))))
2898 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2899 ;;; needs more work as valid transforms are missed; some cases are
2900 ;;; specific to particular transform functions so the use of this
2901 ;;; function may need a re-think.
2902 (defun not-more-contagious (x y)
2903 (declare (type continuation x y))
2904 (flet ((simple-numeric-type (num)
2905 (and (numeric-type-p num)
2906 ;; Return non-NIL if NUM is integer, rational, or a float
2907 ;; of some type (but not FLOAT)
2908 (case (numeric-type-class num)
2912 (numeric-type-format num))
2915 (let ((x (continuation-type x))
2916 (y (continuation-type y)))
2917 (if (and (simple-numeric-type x)
2918 (simple-numeric-type y))
2919 (values (type= (numeric-contagion x y)
2920 (numeric-contagion y y)))))))
2924 ;;; If y is not constant, not zerop, or is contagious, or a
2925 ;;; positive float +0.0 then give up.
2926 (deftransform + ((x y) (t (constant-argument t)) * :when :both)
2928 (let ((val (continuation-value y)))
2929 (unless (and (zerop val)
2930 (not (and (floatp val) (plusp (float-sign val))))
2931 (not-more-contagious y x))
2932 (give-up-ir1-transform)))
2937 ;;; If y is not constant, not zerop, or is contagious, or a
2938 ;;; negative float -0.0 then give up.
2939 (deftransform - ((x y) (t (constant-argument t)) * :when :both)
2941 (let ((val (continuation-value y)))
2942 (unless (and (zerop val)
2943 (not (and (floatp val) (minusp (float-sign val))))
2944 (not-more-contagious y x))
2945 (give-up-ir1-transform)))
2948 ;;; Fold (OP x +/-1)
2949 (dolist (stuff '((* x (%negate x))
2952 (destructuring-bind (name result minus-result) stuff
2953 (deftransform name ((x y) '(t (constant-argument real)) '* :eval-name t
2955 "fold identity operations"
2956 (let ((val (continuation-value y)))
2957 (unless (and (= (abs val) 1)
2958 (not-more-contagious y x))
2959 (give-up-ir1-transform))
2960 (if (minusp val) minus-result result)))))
2962 ;;; Fold (expt x n) into multiplications for small integral values of
2963 ;;; N; convert (expt x 1/2) to sqrt.
2964 (deftransform expt ((x y) (t (constant-argument real)) *)
2965 "recode as multiplication or sqrt"
2966 (let ((val (continuation-value y)))
2967 ;; If Y would cause the result to be promoted to the same type as
2968 ;; Y, we give up. If not, then the result will be the same type
2969 ;; as X, so we can replace the exponentiation with simple
2970 ;; multiplication and division for small integral powers.
2971 (unless (not-more-contagious y x)
2972 (give-up-ir1-transform))
2973 (cond ((zerop val) '(float 1 x))
2974 ((= val 2) '(* x x))
2975 ((= val -2) '(/ (* x x)))
2976 ((= val 3) '(* x x x))
2977 ((= val -3) '(/ (* x x x)))
2978 ((= val 1/2) '(sqrt x))
2979 ((= val -1/2) '(/ (sqrt x)))
2980 (t (give-up-ir1-transform)))))
2982 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
2983 ;;; transformations?
2984 ;;; Perhaps we should have to prove that the denominator is nonzero before
2985 ;;; doing them? (Also the DOLIST over macro calls is weird. Perhaps
2986 ;;; just FROB?) -- WHN 19990917
2987 (dolist (name '(ash /))
2988 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
2989 :eval-name t :when :both)
2992 (dolist (name '(truncate round floor ceiling))
2993 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
2994 :eval-name t :when :both)
2998 ;;;; character operations
3000 (deftransform char-equal ((a b) (base-char base-char))
3002 '(let* ((ac (char-code a))
3004 (sum (logxor ac bc)))
3006 (when (eql sum #x20)
3007 (let ((sum (+ ac bc)))
3008 (and (> sum 161) (< sum 213)))))))
3010 (deftransform char-upcase ((x) (base-char))
3012 '(let ((n-code (char-code x)))
3013 (if (and (> n-code #o140) ; Octal 141 is #\a.
3014 (< n-code #o173)) ; Octal 172 is #\z.
3015 (code-char (logxor #x20 n-code))
3018 (deftransform char-downcase ((x) (base-char))
3020 '(let ((n-code (char-code x)))
3021 (if (and (> n-code 64) ; 65 is #\A.
3022 (< n-code 91)) ; 90 is #\Z.
3023 (code-char (logxor #x20 n-code))
3026 ;;;; equality predicate transforms
3028 ;;; Return true if X and Y are continuations whose only use is a reference
3029 ;;; to the same leaf, and the value of the leaf cannot change.
3030 (defun same-leaf-ref-p (x y)
3031 (declare (type continuation x y))
3032 (let ((x-use (continuation-use x))
3033 (y-use (continuation-use y)))
3036 (eq (ref-leaf x-use) (ref-leaf y-use))
3037 (constant-reference-p x-use))))
3039 ;;; If X and Y are the same leaf, then the result is true. Otherwise, if
3040 ;;; there is no intersection between the types of the arguments, then the
3041 ;;; result is definitely false.
3042 (deftransform simple-equality-transform ((x y) * * :defun-only t
3044 (cond ((same-leaf-ref-p x y)
3046 ((not (types-intersect (continuation-type x) (continuation-type y)))
3049 (give-up-ir1-transform))))
3051 (dolist (x '(eq char= equal))
3052 (%deftransform x '(function * *) #'simple-equality-transform))
3054 ;;; Similar to SIMPLE-EQUALITY-PREDICATE, except that we also try to convert
3055 ;;; to a type-specific predicate or EQ:
3056 ;;; -- If both args are characters, convert to CHAR=. This is better than just
3057 ;;; converting to EQ, since CHAR= may have special compilation strategies
3058 ;;; for non-standard representations, etc.
3059 ;;; -- If either arg is definitely not a number, then we can compare with EQ.
3060 ;;; -- Otherwise, we try to put the arg we know more about second. If X is
3061 ;;; constant then we put it second. If X is a subtype of Y, we put it
3062 ;;; second. These rules make it easier for the back end to match these
3063 ;;; interesting cases.
3064 ;;; -- If Y is a fixnum, then we quietly pass because the back end can handle
3065 ;;; that case, otherwise give an efficency note.
3066 (deftransform eql ((x y) * * :when :both)
3067 "convert to simpler equality predicate"
3068 (let ((x-type (continuation-type x))
3069 (y-type (continuation-type y))
3070 (char-type (specifier-type 'character))
3071 (number-type (specifier-type 'number)))
3072 (cond ((same-leaf-ref-p x y)
3074 ((not (types-intersect x-type y-type))
3076 ((and (csubtypep x-type char-type)
3077 (csubtypep y-type char-type))
3079 ((or (not (types-intersect x-type number-type))
3080 (not (types-intersect y-type number-type)))
3082 ((and (not (constant-continuation-p y))
3083 (or (constant-continuation-p x)
3084 (and (csubtypep x-type y-type)
3085 (not (csubtypep y-type x-type)))))
3088 (give-up-ir1-transform)))))
3090 ;;; Convert to EQL if both args are rational and complexp is specified
3091 ;;; and the same for both.
3092 (deftransform = ((x y) * * :when :both)
3094 (let ((x-type (continuation-type x))
3095 (y-type (continuation-type y)))
3096 (if (and (csubtypep x-type (specifier-type 'number))
3097 (csubtypep y-type (specifier-type 'number)))
3098 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3099 (csubtypep y-type (specifier-type 'float)))
3100 (and (csubtypep x-type (specifier-type '(complex float)))
3101 (csubtypep y-type (specifier-type '(complex float)))))
3102 ;; They are both floats. Leave as = so that -0.0 is
3103 ;; handled correctly.
3104 (give-up-ir1-transform))
3105 ((or (and (csubtypep x-type (specifier-type 'rational))
3106 (csubtypep y-type (specifier-type 'rational)))
3107 (and (csubtypep x-type (specifier-type '(complex rational)))
3108 (csubtypep y-type (specifier-type '(complex rational)))))
3109 ;; They are both rationals and complexp is the same. Convert
3113 (give-up-ir1-transform
3114 "The operands might not be the same type.")))
3115 (give-up-ir1-transform
3116 "The operands might not be the same type."))))
3118 ;;; If Cont's type is a numeric type, then return the type, otherwise
3119 ;;; GIVE-UP-IR1-TRANSFORM.
3120 (defun numeric-type-or-lose (cont)
3121 (declare (type continuation cont))
3122 (let ((res (continuation-type cont)))
3123 (unless (numeric-type-p res) (give-up-ir1-transform))
3126 ;;; See whether we can statically determine (< X Y) using type information.
3127 ;;; If X's high bound is < Y's low, then X < Y. Similarly, if X's low is >=
3128 ;;; to Y's high, the X >= Y (so return NIL). If not, at least make sure any
3129 ;;; constant arg is second.
3131 ;;; KLUDGE: Why should constant argument be second? It would be nice to find
3132 ;;; out and explain. -- WHN 19990917
3133 #!-propagate-float-type
3134 (defun ir1-transform-< (x y first second inverse)
3135 (if (same-leaf-ref-p x y)
3137 (let* ((x-type (numeric-type-or-lose x))
3138 (x-lo (numeric-type-low x-type))
3139 (x-hi (numeric-type-high x-type))
3140 (y-type (numeric-type-or-lose y))
3141 (y-lo (numeric-type-low y-type))
3142 (y-hi (numeric-type-high y-type)))
3143 (cond ((and x-hi y-lo (< x-hi y-lo))
3145 ((and y-hi x-lo (>= x-lo y-hi))
3147 ((and (constant-continuation-p first)
3148 (not (constant-continuation-p second)))
3151 (give-up-ir1-transform))))))
3152 #!+propagate-float-type
3153 (defun ir1-transform-< (x y first second inverse)
3154 (if (same-leaf-ref-p x y)
3156 (let ((xi (numeric-type->interval (numeric-type-or-lose x)))
3157 (yi (numeric-type->interval (numeric-type-or-lose y))))
3158 (cond ((interval-< xi yi)
3160 ((interval->= xi yi)
3162 ((and (constant-continuation-p first)
3163 (not (constant-continuation-p second)))
3166 (give-up-ir1-transform))))))
3168 (deftransform < ((x y) (integer integer) * :when :both)
3169 (ir1-transform-< x y x y '>))
3171 (deftransform > ((x y) (integer integer) * :when :both)
3172 (ir1-transform-< y x x y '<))
3174 #!+propagate-float-type
3175 (deftransform < ((x y) (float float) * :when :both)
3176 (ir1-transform-< x y x y '>))
3178 #!+propagate-float-type
3179 (deftransform > ((x y) (float float) * :when :both)
3180 (ir1-transform-< y x x y '<))
3182 ;;;; converting N-arg comparisons
3184 ;;;; We convert calls to N-arg comparison functions such as < into
3185 ;;;; two-arg calls. This transformation is enabled for all such
3186 ;;;; comparisons in this file. If any of these predicates are not
3187 ;;;; open-coded, then the transformation should be removed at some
3188 ;;;; point to avoid pessimization.
3190 ;;; This function is used for source transformation of N-arg
3191 ;;; comparison functions other than inequality. We deal both with
3192 ;;; converting to two-arg calls and inverting the sense of the test,
3193 ;;; if necessary. If the call has two args, then we pass or return a
3194 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3195 ;;; then we transform to code that returns true. Otherwise, we bind
3196 ;;; all the arguments and expand into a bunch of IFs.
3197 (declaim (ftype (function (symbol list boolean) *) multi-compare))
3198 (defun multi-compare (predicate args not-p)
3199 (let ((nargs (length args)))
3200 (cond ((< nargs 1) (values nil t))
3201 ((= nargs 1) `(progn ,@args t))
3204 `(if (,predicate ,(first args) ,(second args)) nil t)
3207 (do* ((i (1- nargs) (1- i))
3209 (current (gensym) (gensym))
3210 (vars (list current) (cons current vars))
3211 (result 't (if not-p
3212 `(if (,predicate ,current ,last)
3214 `(if (,predicate ,current ,last)
3217 `((lambda ,vars ,result) . ,args)))))))
3219 (def-source-transform = (&rest args) (multi-compare '= args nil))
3220 (def-source-transform < (&rest args) (multi-compare '< args nil))
3221 (def-source-transform > (&rest args) (multi-compare '> args nil))
3222 (def-source-transform <= (&rest args) (multi-compare '> args t))
3223 (def-source-transform >= (&rest args) (multi-compare '< args t))
3225 (def-source-transform char= (&rest args) (multi-compare 'char= args nil))
3226 (def-source-transform char< (&rest args) (multi-compare 'char< args nil))
3227 (def-source-transform char> (&rest args) (multi-compare 'char> args nil))
3228 (def-source-transform char<= (&rest args) (multi-compare 'char> args t))
3229 (def-source-transform char>= (&rest args) (multi-compare 'char< args t))
3231 (def-source-transform char-equal (&rest args) (multi-compare 'char-equal args nil))
3232 (def-source-transform char-lessp (&rest args) (multi-compare 'char-lessp args nil))
3233 (def-source-transform char-greaterp (&rest args) (multi-compare 'char-greaterp args nil))
3234 (def-source-transform char-not-greaterp (&rest args) (multi-compare 'char-greaterp args t))
3235 (def-source-transform char-not-lessp (&rest args) (multi-compare 'char-lessp args t))
3237 ;;; This function does source transformation of N-arg inequality
3238 ;;; functions such as /=. This is similar to Multi-Compare in the <3
3239 ;;; arg cases. If there are more than two args, then we expand into
3240 ;;; the appropriate n^2 comparisons only when speed is important.
3241 (declaim (ftype (function (symbol list) *) multi-not-equal))
3242 (defun multi-not-equal (predicate args)
3243 (let ((nargs (length args)))
3244 (cond ((< nargs 1) (values nil t))
3245 ((= nargs 1) `(progn ,@args t))
3247 `(if (,predicate ,(first args) ,(second args)) nil t))
3248 ((not (policy nil (>= speed space) (>= speed cspeed)))
3252 (dotimes (i nargs) (vars (gensym)))
3253 (do ((var (vars) next)
3254 (next (cdr (vars)) (cdr next))
3257 `((lambda ,(vars) ,result) . ,args))
3258 (let ((v1 (first var)))
3260 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3262 (def-source-transform /= (&rest args) (multi-not-equal '= args))
3263 (def-source-transform char/= (&rest args) (multi-not-equal 'char= args))
3264 (def-source-transform char-not-equal (&rest args) (multi-not-equal 'char-equal args))
3266 ;;; Expand MAX and MIN into the obvious comparisons.
3267 (def-source-transform max (arg &rest more-args)
3268 (if (null more-args)
3270 (once-only ((arg1 arg)
3271 (arg2 `(max ,@more-args)))
3272 `(if (> ,arg1 ,arg2)
3274 (def-source-transform min (arg &rest more-args)
3275 (if (null more-args)
3277 (once-only ((arg1 arg)
3278 (arg2 `(min ,@more-args)))
3279 `(if (< ,arg1 ,arg2)
3282 ;;;; converting N-arg arithmetic functions
3284 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3285 ;;;; versions, and degenerate cases are flushed.
3287 ;;; Left-associate First-Arg and More-Args using Function.
3288 (declaim (ftype (function (symbol t list) list) associate-arguments))
3289 (defun associate-arguments (function first-arg more-args)
3290 (let ((next (rest more-args))
3291 (arg (first more-args)))
3293 `(,function ,first-arg ,arg)
3294 (associate-arguments function `(,function ,first-arg ,arg) next))))
3296 ;;; Do source transformations for transitive functions such as +.
3297 ;;; One-arg cases are replaced with the arg and zero arg cases with
3298 ;;; the identity. If Leaf-Fun is true, then replace two-arg calls with
3299 ;;; a call to that function.
3300 (defun source-transform-transitive (fun args identity &optional leaf-fun)
3301 (declare (symbol fun leaf-fun) (list args))
3304 (1 `(values ,(first args)))
3306 `(,leaf-fun ,(first args) ,(second args))
3309 (associate-arguments fun (first args) (rest args)))))
3311 (def-source-transform + (&rest args) (source-transform-transitive '+ args 0))
3312 (def-source-transform * (&rest args) (source-transform-transitive '* args 1))
3313 (def-source-transform logior (&rest args) (source-transform-transitive 'logior args 0))
3314 (def-source-transform logxor (&rest args) (source-transform-transitive 'logxor args 0))
3315 (def-source-transform logand (&rest args) (source-transform-transitive 'logand args -1))
3317 (def-source-transform logeqv (&rest args)
3318 (if (evenp (length args))
3319 `(lognot (logxor ,@args))
3322 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3323 ;;; because when they are given one argument, they return its absolute
3326 (def-source-transform gcd (&rest args)
3329 (1 `(abs (the integer ,(first args))))
3331 (t (associate-arguments 'gcd (first args) (rest args)))))
3333 (def-source-transform lcm (&rest args)
3336 (1 `(abs (the integer ,(first args))))
3338 (t (associate-arguments 'lcm (first args) (rest args)))))
3340 ;;; Do source transformations for intransitive n-arg functions such as
3341 ;;; /. With one arg, we form the inverse. With two args we pass.
3342 ;;; Otherwise we associate into two-arg calls.
3343 (declaim (ftype (function (symbol list t) list) source-transform-intransitive))
3344 (defun source-transform-intransitive (function args inverse)
3346 ((0 2) (values nil t))
3347 (1 `(,@inverse ,(first args)))
3348 (t (associate-arguments function (first args) (rest args)))))
3350 (def-source-transform - (&rest args)
3351 (source-transform-intransitive '- args '(%negate)))
3352 (def-source-transform / (&rest args)
3353 (source-transform-intransitive '/ args '(/ 1)))
3357 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3358 ;;; only needs to understand one kind of variable-argument call. It is
3359 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3360 (def-source-transform apply (fun arg &rest more-args)
3361 (let ((args (cons arg more-args)))
3362 `(multiple-value-call ,fun
3363 ,@(mapcar #'(lambda (x)
3366 (values-list ,(car (last args))))))
3370 ;;;; If the control string is a compile-time constant, then replace it
3371 ;;;; with a use of the FORMATTER macro so that the control string is
3372 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3373 ;;;; or T and the control string is a function (i.e. formatter), then
3374 ;;;; convert the call to format to just a funcall of that function.
3376 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3377 :policy (> speed space))
3378 (unless (constant-continuation-p control)
3379 (give-up-ir1-transform "The control string is not a constant."))
3380 (let ((arg-names (mapcar #'(lambda (x) (declare (ignore x)) (gensym)) args)))
3381 `(lambda (dest control ,@arg-names)
3382 (declare (ignore control))
3383 (format dest (formatter ,(continuation-value control)) ,@arg-names))))
3385 (deftransform format ((stream control &rest args) (stream function &rest t) *
3386 :policy (> speed space))
3387 (let ((arg-names (mapcar #'(lambda (x) (declare (ignore x)) (gensym)) args)))
3388 `(lambda (stream control ,@arg-names)
3389 (funcall control stream ,@arg-names)
3392 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3393 :policy (> speed space))
3394 (let ((arg-names (mapcar #'(lambda (x) (declare (ignore x)) (gensym)) args)))
3395 `(lambda (tee control ,@arg-names)
3396 (declare (ignore tee))
3397 (funcall control *standard-output* ,@arg-names)