1 ;;;; This file contains macro-like source transformations which
2 ;;;; convert uses of certain functions into the canonical form desired
3 ;;;; within the compiler. ### and other IR1 transforms and stuff.
5 ;;;; This software is part of the SBCL system. See the README file for
8 ;;;; This software is derived from the CMU CL system, which was
9 ;;;; written at Carnegie Mellon University and released into the
10 ;;;; public domain. The software is in the public domain and is
11 ;;;; provided with absolutely no warranty. See the COPYING and CREDITS
12 ;;;; files for more information.
16 ;;; Convert into an IF so that IF optimizations will eliminate redundant
18 (def-source-transform not (x) `(if ,x nil t))
19 (def-source-transform null (x) `(if ,x nil t))
21 ;;; ENDP is just NULL with a LIST assertion. The assertion will be
22 ;;; optimized away when SAFETY optimization is low; hopefully that
23 ;;; is consistent with ANSI's "should return an error".
24 (def-source-transform endp (x) `(null (the list ,x)))
26 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
27 ;;; returns the first value of its argument. Ditto for VALUES with one
29 (def-source-transform identity (x) `(prog1 ,x))
30 (def-source-transform values (x) `(prog1 ,x))
32 ;;; Bind the values and make a closure that returns them.
33 (def-source-transform constantly (value)
34 (let ((rest (gensym "CONSTANTLY-REST-")))
35 `(lambda (&rest ,rest)
36 (declare (ignore ,rest))
39 ;;; If the function has a known number of arguments, then return a
40 ;;; lambda with the appropriate fixed number of args. If the
41 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
42 ;;; MV optimization figure things out.
43 (deftransform complement ((fun) * * :node node :when :both)
45 (multiple-value-bind (min max)
46 (function-type-nargs (continuation-type fun))
48 ((and min (eql min max))
49 (let ((dums (make-gensym-list min)))
50 `#'(lambda ,dums (not (funcall fun ,@dums)))))
51 ((let* ((cont (node-cont node))
52 (dest (continuation-dest cont)))
53 (and (combination-p dest)
54 (eq (combination-fun dest) cont)))
55 '#'(lambda (&rest args)
56 (not (apply fun args))))
58 (give-up-ir1-transform
59 "The function doesn't have a fixed argument count.")))))
63 ;;; Translate CxR into CAR/CDR combos.
64 (defun source-transform-cxr (form)
65 (if (or (byte-compiling) (/= (length form) 2))
67 (let ((name (symbol-name (car form))))
68 (do ((i (- (length name) 2) (1- i))
70 `(,(ecase (char name i)
76 ;;; Make source transforms to turn CxR forms into combinations of CAR
77 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
79 (/show0 "about to set CxR source transforms")
80 (loop for i of-type index from 2 upto 4 do
81 ;; Iterate over BUF = all names CxR where x = an I-element
82 ;; string of #\A or #\D characters.
83 (let ((buf (make-string (+ 2 i))))
84 (setf (aref buf 0) #\C
85 (aref buf (1+ i)) #\R)
86 (dotimes (j (ash 2 i))
87 (declare (type index j))
89 (declare (type index k))
90 (setf (aref buf (1+ k))
91 (if (logbitp k j) #\A #\D)))
92 (setf (info :function :source-transform (intern buf))
93 #'source-transform-cxr))))
94 (/show0 "done setting CxR source transforms")
96 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
97 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
98 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
100 (def-source-transform first (x) `(car ,x))
101 (def-source-transform rest (x) `(cdr ,x))
102 (def-source-transform second (x) `(cadr ,x))
103 (def-source-transform third (x) `(caddr ,x))
104 (def-source-transform fourth (x) `(cadddr ,x))
105 (def-source-transform fifth (x) `(nth 4 ,x))
106 (def-source-transform sixth (x) `(nth 5 ,x))
107 (def-source-transform seventh (x) `(nth 6 ,x))
108 (def-source-transform eighth (x) `(nth 7 ,x))
109 (def-source-transform ninth (x) `(nth 8 ,x))
110 (def-source-transform tenth (x) `(nth 9 ,x))
112 ;;; Translate RPLACx to LET and SETF.
113 (def-source-transform rplaca (x y)
118 (def-source-transform rplacd (x y)
124 (def-source-transform nth (n l) `(car (nthcdr ,n ,l)))
126 (defvar *default-nthcdr-open-code-limit* 6)
127 (defvar *extreme-nthcdr-open-code-limit* 20)
129 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
130 "convert NTHCDR to CAxxR"
131 (unless (constant-continuation-p n)
132 (give-up-ir1-transform))
133 (let ((n (continuation-value n)))
135 (if (policy node (and (= speed 3) (= space 0)))
136 *extreme-nthcdr-open-code-limit*
137 *default-nthcdr-open-code-limit*))
138 (give-up-ir1-transform))
143 `(cdr ,(frob (1- n))))))
146 ;;;; arithmetic and numerology
148 (def-source-transform plusp (x) `(> ,x 0))
149 (def-source-transform minusp (x) `(< ,x 0))
150 (def-source-transform zerop (x) `(= ,x 0))
152 (def-source-transform 1+ (x) `(+ ,x 1))
153 (def-source-transform 1- (x) `(- ,x 1))
155 (def-source-transform oddp (x) `(not (zerop (logand ,x 1))))
156 (def-source-transform evenp (x) `(zerop (logand ,x 1)))
158 ;;; Note that all the integer division functions are available for
159 ;;; inline expansion.
161 ;;; FIXME: DEF-FROB instead of FROB
162 (macrolet ((frob (fun)
163 `(def-source-transform ,fun (x &optional (y nil y-p))
170 #!+sb-propagate-float-type
172 #!+sb-propagate-float-type
175 (def-source-transform lognand (x y) `(lognot (logand ,x ,y)))
176 (def-source-transform lognor (x y) `(lognot (logior ,x ,y)))
177 (def-source-transform logandc1 (x y) `(logand (lognot ,x) ,y))
178 (def-source-transform logandc2 (x y) `(logand ,x (lognot ,y)))
179 (def-source-transform logorc1 (x y) `(logior (lognot ,x) ,y))
180 (def-source-transform logorc2 (x y) `(logior ,x (lognot ,y)))
181 (def-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
182 (def-source-transform logbitp (index integer)
183 `(not (zerop (logand (ash 1 ,index) ,integer))))
184 (def-source-transform byte (size position) `(cons ,size ,position))
185 (def-source-transform byte-size (spec) `(car ,spec))
186 (def-source-transform byte-position (spec) `(cdr ,spec))
187 (def-source-transform ldb-test (bytespec integer)
188 `(not (zerop (mask-field ,bytespec ,integer))))
190 ;;; With the ratio and complex accessors, we pick off the "identity"
191 ;;; case, and use a primitive to handle the cell access case.
192 (def-source-transform numerator (num)
193 (once-only ((n-num `(the rational ,num)))
197 (def-source-transform denominator (num)
198 (once-only ((n-num `(the rational ,num)))
200 (%denominator ,n-num)
203 ;;;; interval arithmetic for computing bounds
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. (This is 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-propagate-float-type
224 ;;; The basic interval type. It can handle open and closed intervals.
225 ;;; A bound is open if it is a list containing a number, just like
226 ;;; Lisp says. NIL means unbounded.
227 (defstruct (interval (:constructor %make-interval)
231 (defun make-interval (&key low high)
232 (labels ((normalize-bound (val)
233 (cond ((and (floatp val)
234 (float-infinity-p val))
235 ;; Handle infinities.
239 ;; Handle any closed bounds.
242 ;; We have an open bound. Normalize the numeric
243 ;; bound. If the normalized bound is still a number
244 ;; (not nil), keep the bound open. Otherwise, the
245 ;; bound is really unbounded, so drop the openness.
246 (let ((new-val (normalize-bound (first val))))
248 ;; The bound exists, so keep it open still.
251 (error "Unknown bound type in make-interval!")))))
252 (%make-interval :low (normalize-bound low)
253 :high (normalize-bound high))))
255 ;;; Given a number X, create a form suitable as a bound for an
256 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
257 #!-sb-fluid (declaim (inline set-bound))
258 (defun set-bound (x open-p)
259 (if (and x open-p) (list x) x))
261 ;;; Apply the function F to a bound X. If X is an open bound, then
262 ;;; the result will be open. IF X is NIL, the result is NIL.
263 (defun bound-func (f x)
265 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
266 ;; With these traps masked, we might get things like infinity
267 ;; or negative infinity returned. Check for this and return
268 ;; NIL to indicate unbounded.
269 (let ((y (funcall f (type-bound-number x))))
271 (float-infinity-p y))
273 (set-bound (funcall f (type-bound-number x)) (consp x)))))))
275 ;;; Apply a binary operator OP to two bounds X and Y. The result is
276 ;;; NIL if either is NIL. Otherwise bound is computed and the result
277 ;;; is open if either X or Y is open.
279 ;;; FIXME: only used in this file, not needed in target runtime
280 (defmacro bound-binop (op x y)
282 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
283 (set-bound (,op (type-bound-number ,x)
284 (type-bound-number ,y))
285 (or (consp ,x) (consp ,y))))))
287 ;;; Convert a numeric-type object to an interval object.
288 (defun numeric-type->interval (x)
289 (declare (type numeric-type x))
290 (make-interval :low (numeric-type-low x)
291 :high (numeric-type-high x)))
293 (defun copy-interval-limit (limit)
298 (defun copy-interval (x)
299 (declare (type interval x))
300 (make-interval :low (copy-interval-limit (interval-low x))
301 :high (copy-interval-limit (interval-high x))))
303 ;;; Given a point P contained in the interval X, split X into two
304 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
305 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
306 ;;; contains P. You can specify both to be T or NIL.
307 (defun interval-split (p x &optional close-lower close-upper)
308 (declare (type number p)
310 (list (make-interval :low (copy-interval-limit (interval-low x))
311 :high (if close-lower p (list p)))
312 (make-interval :low (if close-upper (list p) p)
313 :high (copy-interval-limit (interval-high x)))))
315 ;;; Return the closure of the interval. That is, convert open bounds
316 ;;; to closed bounds.
317 (defun interval-closure (x)
318 (declare (type interval x))
319 (make-interval :low (type-bound-number (interval-low x))
320 :high (type-bound-number (interval-high x))))
322 (defun signed-zero->= (x y)
326 (>= (float-sign (float x))
327 (float-sign (float y))))))
329 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
330 ;;; '-. Otherwise return NIL.
332 (defun interval-range-info (x &optional (point 0))
333 (declare (type interval x))
334 (let ((lo (interval-low x))
335 (hi (interval-high x)))
336 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
338 ((and hi (signed-zero->= point (type-bound-number hi)))
342 (defun interval-range-info (x &optional (point 0))
343 (declare (type interval x))
344 (labels ((signed->= (x y)
345 (if (and (zerop x) (zerop y) (floatp x) (floatp y))
346 (>= (float-sign x) (float-sign y))
348 (let ((lo (interval-low x))
349 (hi (interval-high x)))
350 (cond ((and lo (signed->= (type-bound-number lo) point))
352 ((and hi (signed->= point (type-bound-number hi)))
357 ;;; Test to see whether the interval X is bounded. HOW determines the
358 ;;; test, and should be either ABOVE, BELOW, or BOTH.
359 (defun interval-bounded-p (x how)
360 (declare (type interval x))
367 (and (interval-low x) (interval-high x)))))
369 ;;; signed zero comparison functions. Use these functions if we need
370 ;;; to distinguish between signed zeroes.
371 (defun signed-zero-< (x y)
375 (< (float-sign (float x))
376 (float-sign (float y))))))
377 (defun signed-zero-> (x y)
381 (> (float-sign (float x))
382 (float-sign (float y))))))
383 (defun signed-zero-= (x y)
386 (= (float-sign (float x))
387 (float-sign (float y)))))
388 (defun signed-zero-<= (x y)
392 (<= (float-sign (float x))
393 (float-sign (float y))))))
395 ;;; See whether the interval X contains the number P, taking into
396 ;;; account that the interval might not be closed.
397 (defun interval-contains-p (p x)
398 (declare (type number p)
400 ;; Does the interval X contain the number P? This would be a lot
401 ;; easier if all intervals were closed!
402 (let ((lo (interval-low x))
403 (hi (interval-high x)))
405 ;; The interval is bounded
406 (if (and (signed-zero-<= (type-bound-number lo) p)
407 (signed-zero-<= p (type-bound-number hi)))
408 ;; P is definitely in the closure of the interval.
409 ;; We just need to check the end points now.
410 (cond ((signed-zero-= p (type-bound-number lo))
412 ((signed-zero-= p (type-bound-number hi))
417 ;; Interval with upper bound
418 (if (signed-zero-< p (type-bound-number hi))
420 (and (numberp hi) (signed-zero-= p hi))))
422 ;; Interval with lower bound
423 (if (signed-zero-> p (type-bound-number lo))
425 (and (numberp lo) (signed-zero-= p lo))))
427 ;; Interval with no bounds
430 ;;; Determine whether two intervals X and Y intersect. Return T if so.
431 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
432 ;;; were closed. Otherwise the intervals are treated as they are.
434 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
435 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
436 ;;; is T, then they do intersect because we use the closure of X = [0,
437 ;;; 1] and Y = [1, 2] to determine intersection.
438 (defun interval-intersect-p (x y &optional closed-intervals-p)
439 (declare (type interval x y))
440 (multiple-value-bind (intersect diff)
441 (interval-intersection/difference (if closed-intervals-p
444 (if closed-intervals-p
447 (declare (ignore diff))
450 ;;; Are the two intervals adjacent? That is, is there a number
451 ;;; between the two intervals that is not an element of either
452 ;;; interval? If so, they are not adjacent. For example [0, 1) and
453 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
454 ;;; between both intervals.
455 (defun interval-adjacent-p (x y)
456 (declare (type interval x y))
457 (flet ((adjacent (lo hi)
458 ;; Check to see whether lo and hi are adjacent. If either is
459 ;; nil, they can't be adjacent.
460 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
461 ;; The bounds are equal. They are adjacent if one of
462 ;; them is closed (a number). If both are open (consp),
463 ;; then there is a number that lies between them.
464 (or (numberp lo) (numberp hi)))))
465 (or (adjacent (interval-low y) (interval-high x))
466 (adjacent (interval-low x) (interval-high y)))))
468 ;;; Compute the intersection and difference between two intervals.
469 ;;; Two values are returned: the intersection and the difference.
471 ;;; Let the two intervals be X and Y, and let I and D be the two
472 ;;; values returned by this function. Then I = X intersect Y. If I
473 ;;; is NIL (the empty set), then D is X union Y, represented as the
474 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
475 ;;; - I, which is a list of two intervals.
477 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
478 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
479 (defun interval-intersection/difference (x y)
480 (declare (type interval x y))
481 (let ((x-lo (interval-low x))
482 (x-hi (interval-high x))
483 (y-lo (interval-low y))
484 (y-hi (interval-high y)))
487 ;; If p is an open bound, make it closed. If p is a closed
488 ;; bound, make it open.
493 ;; Test whether P is in the interval.
494 (when (interval-contains-p (type-bound-number p)
495 (interval-closure int))
496 (let ((lo (interval-low int))
497 (hi (interval-high int)))
498 ;; Check for endpoints.
499 (cond ((and lo (= (type-bound-number p) (type-bound-number lo)))
500 (not (and (consp p) (numberp lo))))
501 ((and hi (= (type-bound-number p) (type-bound-number hi)))
502 (not (and (numberp p) (consp hi))))
504 (test-lower-bound (p int)
505 ;; P is a lower bound of an interval.
508 (not (interval-bounded-p int 'below))))
509 (test-upper-bound (p int)
510 ;; P is an upper bound of an interval.
513 (not (interval-bounded-p int 'above)))))
514 (let ((x-lo-in-y (test-lower-bound x-lo y))
515 (x-hi-in-y (test-upper-bound x-hi y))
516 (y-lo-in-x (test-lower-bound y-lo x))
517 (y-hi-in-x (test-upper-bound y-hi x)))
518 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
519 ;; Intervals intersect. Let's compute the intersection
520 ;; and the difference.
521 (multiple-value-bind (lo left-lo left-hi)
522 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
523 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
524 (multiple-value-bind (hi right-lo right-hi)
526 (values x-hi (opposite-bound x-hi) y-hi))
528 (values y-hi (opposite-bound y-hi) x-hi)))
529 (values (make-interval :low lo :high hi)
530 (list (make-interval :low left-lo
532 (make-interval :low right-lo
535 (values nil (list x y))))))))
537 ;;; If intervals X and Y intersect, return a new interval that is the
538 ;;; union of the two. If they do not intersect, return NIL.
539 (defun interval-merge-pair (x y)
540 (declare (type interval x y))
541 ;; If x and y intersect or are adjacent, create the union.
542 ;; Otherwise return nil
543 (when (or (interval-intersect-p x y)
544 (interval-adjacent-p x y))
545 (flet ((select-bound (x1 x2 min-op max-op)
546 (let ((x1-val (type-bound-number x1))
547 (x2-val (type-bound-number x2)))
549 ;; Both bounds are finite. Select the right one.
550 (cond ((funcall min-op x1-val x2-val)
551 ;; x1 is definitely better.
553 ((funcall max-op x1-val x2-val)
554 ;; x2 is definitely better.
557 ;; Bounds are equal. Select either
558 ;; value and make it open only if
560 (set-bound x1-val (and (consp x1) (consp x2))))))
562 ;; At least one bound is not finite. The
563 ;; non-finite bound always wins.
565 (let* ((x-lo (copy-interval-limit (interval-low x)))
566 (x-hi (copy-interval-limit (interval-high x)))
567 (y-lo (copy-interval-limit (interval-low y)))
568 (y-hi (copy-interval-limit (interval-high y))))
569 (make-interval :low (select-bound x-lo y-lo #'< #'>)
570 :high (select-bound x-hi y-hi #'> #'<))))))
572 ;;; basic arithmetic operations on intervals. We probably should do
573 ;;; true interval arithmetic here, but it's complicated because we
574 ;;; have float and integer types and bounds can be open or closed.
576 ;;; the negative of an interval
577 (defun interval-neg (x)
578 (declare (type interval x))
579 (make-interval :low (bound-func #'- (interval-high x))
580 :high (bound-func #'- (interval-low x))))
582 ;;; Add two intervals.
583 (defun interval-add (x y)
584 (declare (type interval x y))
585 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
586 :high (bound-binop + (interval-high x) (interval-high y))))
588 ;;; Subtract two intervals.
589 (defun interval-sub (x y)
590 (declare (type interval x y))
591 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
592 :high (bound-binop - (interval-high x) (interval-low y))))
594 ;;; Multiply two intervals.
595 (defun interval-mul (x y)
596 (declare (type interval x y))
597 (flet ((bound-mul (x y)
598 (cond ((or (null x) (null y))
599 ;; Multiply by infinity is infinity
601 ((or (and (numberp x) (zerop x))
602 (and (numberp y) (zerop y)))
603 ;; Multiply by closed zero is special. The result
604 ;; is always a closed bound. But don't replace this
605 ;; with zero; we want the multiplication to produce
606 ;; the correct signed zero, if needed.
607 (* (type-bound-number x) (type-bound-number y)))
608 ((or (and (floatp x) (float-infinity-p x))
609 (and (floatp y) (float-infinity-p y)))
610 ;; Infinity times anything is infinity
613 ;; General multiply. The result is open if either is open.
614 (bound-binop * x y)))))
615 (let ((x-range (interval-range-info x))
616 (y-range (interval-range-info y)))
617 (cond ((null x-range)
618 ;; Split x into two and multiply each separately
619 (destructuring-bind (x- x+) (interval-split 0 x t t)
620 (interval-merge-pair (interval-mul x- y)
621 (interval-mul x+ y))))
623 ;; Split y into two and multiply each separately
624 (destructuring-bind (y- y+) (interval-split 0 y t t)
625 (interval-merge-pair (interval-mul x y-)
626 (interval-mul x y+))))
628 (interval-neg (interval-mul (interval-neg x) y)))
630 (interval-neg (interval-mul x (interval-neg y))))
631 ((and (eq x-range '+) (eq y-range '+))
632 ;; If we are here, X and Y are both positive
633 (make-interval :low (bound-mul (interval-low x) (interval-low y))
634 :high (bound-mul (interval-high x) (interval-high y))))
636 (error "This shouldn't happen!"))))))
638 ;;; Divide two intervals.
639 (defun interval-div (top bot)
640 (declare (type interval top bot))
641 (flet ((bound-div (x y y-low-p)
644 ;; Divide by infinity means result is 0. However,
645 ;; we need to watch out for the sign of the result,
646 ;; to correctly handle signed zeros. We also need
647 ;; to watch out for positive or negative infinity.
648 (if (floatp (type-bound-number x))
650 (- (float-sign (type-bound-number x) 0.0))
651 (float-sign (type-bound-number x) 0.0))
653 ((zerop (type-bound-number y))
654 ;; Divide by zero means result is infinity
656 ((and (numberp x) (zerop x))
657 ;; Zero divided by anything is zero.
660 (bound-binop / x y)))))
661 (let ((top-range (interval-range-info top))
662 (bot-range (interval-range-info bot)))
663 (cond ((null bot-range)
664 ;; The denominator contains zero, so anything goes!
665 (make-interval :low nil :high nil))
667 ;; Denominator is negative so flip the sign, compute the
668 ;; result, and flip it back.
669 (interval-neg (interval-div top (interval-neg bot))))
671 ;; Split top into two positive and negative parts, and
672 ;; divide each separately
673 (destructuring-bind (top- top+) (interval-split 0 top t t)
674 (interval-merge-pair (interval-div top- bot)
675 (interval-div top+ bot))))
677 ;; Top is negative so flip the sign, divide, and flip the
678 ;; sign of the result.
679 (interval-neg (interval-div (interval-neg top) bot)))
680 ((and (eq top-range '+) (eq bot-range '+))
682 (make-interval :low (bound-div (interval-low top) (interval-high bot) t)
683 :high (bound-div (interval-high top) (interval-low bot) nil)))
685 (error "This shouldn't happen!"))))))
687 ;;; Apply the function F to the interval X. If X = [a, b], then the
688 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
689 ;;; result makes sense. It will if F is monotonic increasing (or
691 (defun interval-func (f x)
692 (declare (type interval x))
693 (let ((lo (bound-func f (interval-low x)))
694 (hi (bound-func f (interval-high x))))
695 (make-interval :low lo :high hi)))
697 ;;; Return T if X < Y. That is every number in the interval X is
698 ;;; always less than any number in the interval Y.
699 (defun interval-< (x y)
700 (declare (type interval x y))
701 ;; X < Y only if X is bounded above, Y is bounded below, and they
703 (when (and (interval-bounded-p x 'above)
704 (interval-bounded-p y 'below))
705 ;; Intervals are bounded in the appropriate way. Make sure they
707 (let ((left (interval-high x))
708 (right (interval-low y)))
709 (cond ((> (type-bound-number left)
710 (type-bound-number right))
711 ;; The intervals definitely overlap, so result is NIL.
713 ((< (type-bound-number left)
714 (type-bound-number right))
715 ;; The intervals definitely don't touch, so result is T.
718 ;; Limits are equal. Check for open or closed bounds.
719 ;; Don't overlap if one or the other are open.
720 (or (consp left) (consp right)))))))
722 ;;; Return T if X >= Y. That is, every number in the interval X is
723 ;;; always greater than any number in the interval Y.
724 (defun interval->= (x y)
725 (declare (type interval x y))
726 ;; X >= Y if lower bound of X >= upper bound of Y
727 (when (and (interval-bounded-p x 'below)
728 (interval-bounded-p y 'above))
729 (>= (type-bound-number (interval-low x))
730 (type-bound-number (interval-high y)))))
732 ;;; Return an interval that is the absolute value of X. Thus, if
733 ;;; X = [-1 10], the result is [0, 10].
734 (defun interval-abs (x)
735 (declare (type interval x))
736 (case (interval-range-info x)
742 (destructuring-bind (x- x+) (interval-split 0 x t t)
743 (interval-merge-pair (interval-neg x-) x+)))))
745 ;;; Compute the square of an interval.
746 (defun interval-sqr (x)
747 (declare (type interval x))
748 (interval-func #'(lambda (x) (* x x))
752 ;;;; numeric DERIVE-TYPE methods
754 ;;; a utility for defining derive-type methods of integer operations. If
755 ;;; the types of both X and Y are integer types, then we compute a new
756 ;;; integer type with bounds determined Fun when applied to X and Y.
757 ;;; Otherwise, we use Numeric-Contagion.
758 (defun derive-integer-type (x y fun)
759 (declare (type continuation x y) (type function fun))
760 (let ((x (continuation-type x))
761 (y (continuation-type y)))
762 (if (and (numeric-type-p x) (numeric-type-p y)
763 (eq (numeric-type-class x) 'integer)
764 (eq (numeric-type-class y) 'integer)
765 (eq (numeric-type-complexp x) :real)
766 (eq (numeric-type-complexp y) :real))
767 (multiple-value-bind (low high) (funcall fun x y)
768 (make-numeric-type :class 'integer
772 (numeric-contagion x y))))
774 #!+(or sb-propagate-float-type sb-propagate-fun-type)
777 ;;; simple utility to flatten a list
778 (defun flatten-list (x)
779 (labels ((flatten-helper (x r);; 'r' is the stuff to the 'right'.
783 (t (flatten-helper (car x)
784 (flatten-helper (cdr x) r))))))
785 (flatten-helper x nil)))
787 ;;; Take some type of continuation and massage it so that we get a
788 ;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
789 ;;; to indicate failure.
790 (defun prepare-arg-for-derive-type (arg)
791 (flet ((listify (arg)
796 (union-type-types arg))
799 (unless (eq arg *empty-type*)
800 ;; Make sure all args are some type of numeric-type. For member
801 ;; types, convert the list of members into a union of equivalent
802 ;; single-element member-type's.
803 (let ((new-args nil))
804 (dolist (arg (listify arg))
805 (if (member-type-p arg)
806 ;; Run down the list of members and convert to a list of
808 (dolist (member (member-type-members arg))
809 (push (if (numberp member)
810 (make-member-type :members (list member))
813 (push arg new-args)))
814 (unless (member *empty-type* new-args)
817 ;;; Convert from the standard type convention for which -0.0 and 0.0
818 ;;; are equal to an intermediate convention for which they are
819 ;;; considered different which is more natural for some of the
821 #!-negative-zero-is-not-zero
822 (defun convert-numeric-type (type)
823 (declare (type numeric-type type))
824 ;;; Only convert real float interval delimiters types.
825 (if (eq (numeric-type-complexp type) :real)
826 (let* ((lo (numeric-type-low type))
827 (lo-val (type-bound-number lo))
828 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
829 (hi (numeric-type-high type))
830 (hi-val (type-bound-number hi))
831 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
832 (if (or lo-float-zero-p hi-float-zero-p)
834 :class (numeric-type-class type)
835 :format (numeric-type-format type)
837 :low (if lo-float-zero-p
839 (list (float 0.0 lo-val))
842 :high (if hi-float-zero-p
844 (list (float -0.0 hi-val))
851 ;;; Convert back from the intermediate convention for which -0.0 and
852 ;;; 0.0 are considered different to the standard type convention for
854 #!-negative-zero-is-not-zero
855 (defun convert-back-numeric-type (type)
856 (declare (type numeric-type type))
857 ;;; Only convert real float interval delimiters types.
858 (if (eq (numeric-type-complexp type) :real)
859 (let* ((lo (numeric-type-low type))
860 (lo-val (type-bound-number lo))
862 (and lo (floatp lo-val) (= lo-val 0.0)
863 (float-sign lo-val)))
864 (hi (numeric-type-high type))
865 (hi-val (type-bound-number hi))
867 (and hi (floatp hi-val) (= hi-val 0.0)
868 (float-sign hi-val))))
870 ;; (float +0.0 +0.0) => (member 0.0)
871 ;; (float -0.0 -0.0) => (member -0.0)
872 ((and lo-float-zero-p hi-float-zero-p)
873 ;; shouldn't have exclusive bounds here..
874 (aver (and (not (consp lo)) (not (consp hi))))
875 (if (= lo-float-zero-p hi-float-zero-p)
876 ;; (float +0.0 +0.0) => (member 0.0)
877 ;; (float -0.0 -0.0) => (member -0.0)
878 (specifier-type `(member ,lo-val))
879 ;; (float -0.0 +0.0) => (float 0.0 0.0)
880 ;; (float +0.0 -0.0) => (float 0.0 0.0)
881 (make-numeric-type :class (numeric-type-class type)
882 :format (numeric-type-format type)
888 ;; (float -0.0 x) => (float 0.0 x)
889 ((and (not (consp lo)) (minusp lo-float-zero-p))
890 (make-numeric-type :class (numeric-type-class type)
891 :format (numeric-type-format type)
893 :low (float 0.0 lo-val)
895 ;; (float (+0.0) x) => (float (0.0) x)
896 ((and (consp lo) (plusp lo-float-zero-p))
897 (make-numeric-type :class (numeric-type-class type)
898 :format (numeric-type-format type)
900 :low (list (float 0.0 lo-val))
903 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
904 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
905 (list (make-member-type :members (list (float 0.0 lo-val)))
906 (make-numeric-type :class (numeric-type-class type)
907 :format (numeric-type-format type)
909 :low (list (float 0.0 lo-val))
913 ;; (float x +0.0) => (float x 0.0)
914 ((and (not (consp hi)) (plusp hi-float-zero-p))
915 (make-numeric-type :class (numeric-type-class type)
916 :format (numeric-type-format type)
919 :high (float 0.0 hi-val)))
920 ;; (float x (-0.0)) => (float x (0.0))
921 ((and (consp hi) (minusp hi-float-zero-p))
922 (make-numeric-type :class (numeric-type-class type)
923 :format (numeric-type-format type)
926 :high (list (float 0.0 hi-val))))
928 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
929 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
930 (list (make-member-type :members (list (float -0.0 hi-val)))
931 (make-numeric-type :class (numeric-type-class type)
932 :format (numeric-type-format type)
935 :high (list (float 0.0 hi-val)))))))
941 ;;; Convert back a possible list of numeric types.
942 #!-negative-zero-is-not-zero
943 (defun convert-back-numeric-type-list (type-list)
947 (dolist (type type-list)
948 (if (numeric-type-p type)
949 (let ((result (convert-back-numeric-type type)))
951 (setf results (append results result))
952 (push result results)))
953 (push type results)))
956 (convert-back-numeric-type type-list))
958 (convert-back-numeric-type-list (union-type-types type-list)))
962 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
963 ;;; belong in the kernel's type logic, invoked always, instead of in
964 ;;; the compiler, invoked only during some type optimizations.
966 ;;; Take a list of types and return a canonical type specifier,
967 ;;; combining any MEMBER types together. If both positive and negative
968 ;;; MEMBER types are present they are converted to a float type.
969 ;;; XXX This would be far simpler if the type-union methods could handle
970 ;;; member/number unions.
971 (defun make-canonical-union-type (type-list)
974 (dolist (type type-list)
975 (if (member-type-p type)
976 (setf members (union members (member-type-members type)))
977 (push type misc-types)))
979 (when (null (set-difference '(-0l0 0l0) members))
980 #!-negative-zero-is-not-zero
981 (push (specifier-type '(long-float 0l0 0l0)) misc-types)
982 #!+negative-zero-is-not-zero
983 (push (specifier-type '(long-float -0l0 0l0)) misc-types)
984 (setf members (set-difference members '(-0l0 0l0))))
985 (when (null (set-difference '(-0d0 0d0) members))
986 #!-negative-zero-is-not-zero
987 (push (specifier-type '(double-float 0d0 0d0)) misc-types)
988 #!+negative-zero-is-not-zero
989 (push (specifier-type '(double-float -0d0 0d0)) misc-types)
990 (setf members (set-difference members '(-0d0 0d0))))
991 (when (null (set-difference '(-0f0 0f0) members))
992 #!-negative-zero-is-not-zero
993 (push (specifier-type '(single-float 0f0 0f0)) misc-types)
994 #!+negative-zero-is-not-zero
995 (push (specifier-type '(single-float -0f0 0f0)) misc-types)
996 (setf members (set-difference members '(-0f0 0f0))))
998 (apply #'type-union (make-member-type :members members) misc-types)
999 (apply #'type-union misc-types))))
1001 ;;; Convert a member type with a single member to a numeric type.
1002 (defun convert-member-type (arg)
1003 (let* ((members (member-type-members arg))
1004 (member (first members))
1005 (member-type (type-of member)))
1006 (aver (not (rest members)))
1007 (specifier-type `(,(if (subtypep member-type 'integer)
1012 ;;; This is used in defoptimizers for computing the resulting type of
1015 ;;; Given the continuation ARG, derive the resulting type using the
1016 ;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
1017 ;;; "atomic" continuation type like numeric-type or member-type
1018 ;;; (containing just one element). It should return the resulting
1019 ;;; type, which can be a list of types.
1021 ;;; For the case of member types, if a member-fcn is given it is
1022 ;;; called to compute the result otherwise the member type is first
1023 ;;; converted to a numeric type and the derive-fcn is call.
1024 (defun one-arg-derive-type (arg derive-fcn member-fcn
1025 &optional (convert-type t))
1026 (declare (type function derive-fcn)
1027 (type (or null function) member-fcn)
1028 #!+negative-zero-is-not-zero (ignore convert-type))
1029 (let ((arg-list (prepare-arg-for-derive-type (continuation-type arg))))
1035 (with-float-traps-masked
1036 (:underflow :overflow :divide-by-zero)
1040 (first (member-type-members x))))))
1041 ;; Otherwise convert to a numeric type.
1042 (let ((result-type-list
1043 (funcall derive-fcn (convert-member-type x))))
1044 #!-negative-zero-is-not-zero
1046 (convert-back-numeric-type-list result-type-list)
1048 #!+negative-zero-is-not-zero
1051 #!-negative-zero-is-not-zero
1053 (convert-back-numeric-type-list
1054 (funcall derive-fcn (convert-numeric-type x)))
1055 (funcall derive-fcn x))
1056 #!+negative-zero-is-not-zero
1057 (funcall derive-fcn x))
1059 *universal-type*))))
1060 ;; Run down the list of args and derive the type of each one,
1061 ;; saving all of the results in a list.
1062 (let ((results nil))
1063 (dolist (arg arg-list)
1064 (let ((result (deriver arg)))
1066 (setf results (append results result))
1067 (push result results))))
1069 (make-canonical-union-type results)
1070 (first results)))))))
1072 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1073 ;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
1074 ;;; original args and a third which is T to indicate if the two args
1075 ;;; really represent the same continuation. This is useful for
1076 ;;; deriving the type of things like (* x x), which should always be
1077 ;;; positive. If we didn't do this, we wouldn't be able to tell.
1078 (defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
1079 &optional (convert-type t))
1080 #!+negative-zero-is-not-zero
1081 (declare (ignore convert-type))
1082 (flet (#!-negative-zero-is-not-zero
1083 (deriver (x y same-arg)
1084 (cond ((and (member-type-p x) (member-type-p y))
1085 (let* ((x (first (member-type-members x)))
1086 (y (first (member-type-members y)))
1087 (result (with-float-traps-masked
1088 (:underflow :overflow :divide-by-zero
1090 (funcall fcn x y))))
1091 (cond ((null result))
1092 ((and (floatp result) (float-nan-p result))
1093 (make-numeric-type :class 'float
1094 :format (type-of result)
1097 (make-member-type :members (list result))))))
1098 ((and (member-type-p x) (numeric-type-p y))
1099 (let* ((x (convert-member-type x))
1100 (y (if convert-type (convert-numeric-type y) y))
1101 (result (funcall derive-fcn x y same-arg)))
1103 (convert-back-numeric-type-list result)
1105 ((and (numeric-type-p x) (member-type-p y))
1106 (let* ((x (if convert-type (convert-numeric-type x) x))
1107 (y (convert-member-type y))
1108 (result (funcall derive-fcn x y same-arg)))
1110 (convert-back-numeric-type-list result)
1112 ((and (numeric-type-p x) (numeric-type-p y))
1113 (let* ((x (if convert-type (convert-numeric-type x) x))
1114 (y (if convert-type (convert-numeric-type y) y))
1115 (result (funcall derive-fcn x y same-arg)))
1117 (convert-back-numeric-type-list result)
1121 #!+negative-zero-is-not-zero
1122 (deriver (x y same-arg)
1123 (cond ((and (member-type-p x) (member-type-p y))
1124 (let* ((x (first (member-type-members x)))
1125 (y (first (member-type-members y)))
1126 (result (with-float-traps-masked
1127 (:underflow :overflow :divide-by-zero)
1128 (funcall fcn x y))))
1130 (make-member-type :members (list result)))))
1131 ((and (member-type-p x) (numeric-type-p y))
1132 (let ((x (convert-member-type x)))
1133 (funcall derive-fcn x y same-arg)))
1134 ((and (numeric-type-p x) (member-type-p y))
1135 (let ((y (convert-member-type y)))
1136 (funcall derive-fcn x y same-arg)))
1137 ((and (numeric-type-p x) (numeric-type-p y))
1138 (funcall derive-fcn x y same-arg))
1140 *universal-type*))))
1141 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1142 (a1 (prepare-arg-for-derive-type (continuation-type arg1)))
1143 (a2 (prepare-arg-for-derive-type (continuation-type arg2))))
1145 (let ((results nil))
1147 ;; Since the args are the same continuation, just run
1150 (let ((result (deriver x x same-arg)))
1152 (setf results (append results result))
1153 (push result results))))
1154 ;; Try all pairwise combinations.
1157 (let ((result (or (deriver x y same-arg)
1158 (numeric-contagion x y))))
1160 (setf results (append results result))
1161 (push result results))))))
1163 (make-canonical-union-type results)
1164 (first results)))))))
1168 #!-sb-propagate-float-type
1170 (defoptimizer (+ derive-type) ((x y))
1171 (derive-integer-type
1178 (values (frob (numeric-type-low x) (numeric-type-low y))
1179 (frob (numeric-type-high x) (numeric-type-high y)))))))
1181 (defoptimizer (- derive-type) ((x y))
1182 (derive-integer-type
1189 (values (frob (numeric-type-low x) (numeric-type-high y))
1190 (frob (numeric-type-high x) (numeric-type-low y)))))))
1192 (defoptimizer (* derive-type) ((x y))
1193 (derive-integer-type
1196 (let ((x-low (numeric-type-low x))
1197 (x-high (numeric-type-high x))
1198 (y-low (numeric-type-low y))
1199 (y-high (numeric-type-high y)))
1200 (cond ((not (and x-low y-low))
1202 ((or (minusp x-low) (minusp y-low))
1203 (if (and x-high y-high)
1204 (let ((max (* (max (abs x-low) (abs x-high))
1205 (max (abs y-low) (abs y-high)))))
1206 (values (- max) max))
1209 (values (* x-low y-low)
1210 (if (and x-high y-high)
1214 (defoptimizer (/ derive-type) ((x y))
1215 (numeric-contagion (continuation-type x) (continuation-type y)))
1219 #!+sb-propagate-float-type
1221 (defun +-derive-type-aux (x y same-arg)
1222 (if (and (numeric-type-real-p x)
1223 (numeric-type-real-p y))
1226 (let ((x-int (numeric-type->interval x)))
1227 (interval-add x-int x-int))
1228 (interval-add (numeric-type->interval x)
1229 (numeric-type->interval y))))
1230 (result-type (numeric-contagion x y)))
1231 ;; If the result type is a float, we need to be sure to coerce
1232 ;; the bounds into the correct type.
1233 (when (eq (numeric-type-class result-type) 'float)
1234 (setf result (interval-func
1236 (coerce x (or (numeric-type-format result-type)
1240 :class (if (and (eq (numeric-type-class x) 'integer)
1241 (eq (numeric-type-class y) 'integer))
1242 ;; The sum of integers is always an integer.
1244 (numeric-type-class result-type))
1245 :format (numeric-type-format result-type)
1246 :low (interval-low result)
1247 :high (interval-high result)))
1248 ;; general contagion
1249 (numeric-contagion x y)))
1251 (defoptimizer (+ derive-type) ((x y))
1252 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1254 (defun --derive-type-aux (x y same-arg)
1255 (if (and (numeric-type-real-p x)
1256 (numeric-type-real-p y))
1258 ;; (- X X) is always 0.
1260 (make-interval :low 0 :high 0)
1261 (interval-sub (numeric-type->interval x)
1262 (numeric-type->interval y))))
1263 (result-type (numeric-contagion x y)))
1264 ;; If the result type is a float, we need to be sure to coerce
1265 ;; the bounds into the correct type.
1266 (when (eq (numeric-type-class result-type) 'float)
1267 (setf result (interval-func
1269 (coerce x (or (numeric-type-format result-type)
1273 :class (if (and (eq (numeric-type-class x) 'integer)
1274 (eq (numeric-type-class y) 'integer))
1275 ;; The difference of integers is always an integer.
1277 (numeric-type-class result-type))
1278 :format (numeric-type-format result-type)
1279 :low (interval-low result)
1280 :high (interval-high result)))
1281 ;; general contagion
1282 (numeric-contagion x y)))
1284 (defoptimizer (- derive-type) ((x y))
1285 (two-arg-derive-type x y #'--derive-type-aux #'-))
1287 (defun *-derive-type-aux (x y same-arg)
1288 (if (and (numeric-type-real-p x)
1289 (numeric-type-real-p y))
1291 ;; (* X X) is always positive, so take care to do it right.
1293 (interval-sqr (numeric-type->interval x))
1294 (interval-mul (numeric-type->interval x)
1295 (numeric-type->interval y))))
1296 (result-type (numeric-contagion x y)))
1297 ;; If the result type is a float, we need to be sure to coerce
1298 ;; the bounds into the correct type.
1299 (when (eq (numeric-type-class result-type) 'float)
1300 (setf result (interval-func
1302 (coerce x (or (numeric-type-format result-type)
1306 :class (if (and (eq (numeric-type-class x) 'integer)
1307 (eq (numeric-type-class y) 'integer))
1308 ;; The product of integers is always an integer.
1310 (numeric-type-class result-type))
1311 :format (numeric-type-format result-type)
1312 :low (interval-low result)
1313 :high (interval-high result)))
1314 (numeric-contagion x y)))
1316 (defoptimizer (* derive-type) ((x y))
1317 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1319 (defun /-derive-type-aux (x y same-arg)
1320 (if (and (numeric-type-real-p x)
1321 (numeric-type-real-p y))
1323 ;; (/ X X) is always 1, except if X can contain 0. In
1324 ;; that case, we shouldn't optimize the division away
1325 ;; because we want 0/0 to signal an error.
1327 (not (interval-contains-p
1328 0 (interval-closure (numeric-type->interval y)))))
1329 (make-interval :low 1 :high 1)
1330 (interval-div (numeric-type->interval x)
1331 (numeric-type->interval y))))
1332 (result-type (numeric-contagion x y)))
1333 ;; If the result type is a float, we need to be sure to coerce
1334 ;; the bounds into the correct type.
1335 (when (eq (numeric-type-class result-type) 'float)
1336 (setf result (interval-func
1338 (coerce x (or (numeric-type-format result-type)
1341 (make-numeric-type :class (numeric-type-class result-type)
1342 :format (numeric-type-format result-type)
1343 :low (interval-low result)
1344 :high (interval-high result)))
1345 (numeric-contagion x y)))
1347 (defoptimizer (/ derive-type) ((x y))
1348 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1353 ;;; KLUDGE: All this ASH optimization is suppressed under CMU CL
1354 ;;; because as of version 2.4.6 for Debian, CMU CL blows up on (ASH
1355 ;;; 1000000000 -100000000000) (i.e. ASH of two bignums yielding zero)
1356 ;;; and it's hard to avoid that calculation in here.
1357 #-(and cmu sb-xc-host)
1359 #!-sb-propagate-fun-type
1360 (defoptimizer (ash derive-type) ((n shift))
1361 ;; Large resulting bounds are easy to generate but are not
1362 ;; particularly useful, so an open outer bound is returned for a
1363 ;; shift greater than 64 - the largest word size of any of the ports.
1364 ;; Large negative shifts are also problematic as the ASH
1365 ;; implementation only accepts shifts greater than
1366 ;; MOST-NEGATIVE-FIXNUM. These issues are handled by two local
1368 ;; ASH-OUTER: Perform the shift when within an acceptable range,
1369 ;; otherwise return an open bound.
1370 ;; ASH-INNER: Perform the shift when within range, limited to a
1371 ;; maximum of 64, otherwise returns the inner limit.
1373 ;; FIXME: The magic number 64 should be given a mnemonic name as a
1374 ;; symbolic constant -- perhaps +MAX-REGISTER-SIZE+. And perhaps is
1375 ;; should become an architecture-specific SB!VM:+MAX-REGISTER-SIZE+
1376 ;; instead of trying to have a single magic number which covers
1377 ;; all possible ports.
1378 (flet ((ash-outer (n s)
1379 (when (and (fixnump s)
1381 (> s sb!vm:*target-most-negative-fixnum*))
1384 (if (and (fixnump s)
1385 (> s sb!vm:*target-most-negative-fixnum*))
1387 (if (minusp n) -1 0))))
1388 (or (let ((n-type (continuation-type n)))
1389 (when (numeric-type-p n-type)
1390 (let ((n-low (numeric-type-low n-type))
1391 (n-high (numeric-type-high n-type)))
1392 (if (constant-continuation-p shift)
1393 (let ((shift (continuation-value shift)))
1394 (make-numeric-type :class 'integer
1396 :low (when n-low (ash n-low shift))
1397 :high (when n-high (ash n-high shift))))
1398 (let ((s-type (continuation-type shift)))
1399 (when (numeric-type-p s-type)
1400 (let* ((s-low (numeric-type-low s-type))
1401 (s-high (numeric-type-high s-type))
1402 (low-slot (when n-low
1404 (ash-outer n-low s-high)
1405 (ash-inner n-low s-low))))
1406 (high-slot (when n-high
1408 (ash-inner n-high s-low)
1409 (ash-outer n-high s-high)))))
1410 (make-numeric-type :class 'integer
1413 :high high-slot))))))))
1415 (or (let ((n-type (continuation-type n)))
1416 (when (numeric-type-p n-type)
1417 (let ((n-low (numeric-type-low n-type))
1418 (n-high (numeric-type-high n-type)))
1419 (if (constant-continuation-p shift)
1420 (let ((shift (continuation-value shift)))
1421 (make-numeric-type :class 'integer
1423 :low (when n-low (ash n-low shift))
1424 :high (when n-high (ash n-high shift))))
1425 (let ((s-type (continuation-type shift)))
1426 (when (numeric-type-p s-type)
1427 (let ((s-low (numeric-type-low s-type))
1428 (s-high (numeric-type-high s-type)))
1429 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1430 (make-numeric-type :class 'integer
1433 (min (ash n-low s-high)
1436 (max (ash n-high s-high)
1437 (ash n-high s-low))))
1438 (make-numeric-type :class 'integer
1439 :complexp :real)))))))))
1442 #!+sb-propagate-fun-type
1443 (defun ash-derive-type-aux (n-type shift same-arg)
1444 (declare (ignore same-arg))
1445 (flet ((ash-outer (n s)
1446 (when (and (fixnump s)
1448 (> s sb!vm:*target-most-negative-fixnum*))
1450 ;; KLUDGE: The bare 64's here should be related to
1451 ;; symbolic machine word size values somehow.
1454 (if (and (fixnump s)
1455 (> s sb!vm:*target-most-negative-fixnum*))
1457 (if (minusp n) -1 0))))
1458 (or (and (csubtypep n-type (specifier-type 'integer))
1459 (csubtypep shift (specifier-type 'integer))
1460 (let ((n-low (numeric-type-low n-type))
1461 (n-high (numeric-type-high n-type))
1462 (s-low (numeric-type-low shift))
1463 (s-high (numeric-type-high shift)))
1464 (make-numeric-type :class 'integer :complexp :real
1467 (ash-outer n-low s-high)
1468 (ash-inner n-low s-low)))
1471 (ash-inner n-high s-low)
1472 (ash-outer n-high s-high))))))
1475 #!+sb-propagate-fun-type
1476 (defoptimizer (ash derive-type) ((n shift))
1477 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1480 #!-sb-propagate-float-type
1481 (macrolet ((frob (fun)
1482 `#'(lambda (type type2)
1483 (declare (ignore type2))
1484 (let ((lo (numeric-type-low type))
1485 (hi (numeric-type-high type)))
1486 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1488 (defoptimizer (%negate derive-type) ((num))
1489 (derive-integer-type num num (frob -)))
1491 (defoptimizer (lognot derive-type) ((int))
1492 (derive-integer-type int int (frob lognot))))
1494 #!+sb-propagate-float-type
1495 (defoptimizer (lognot derive-type) ((int))
1496 (derive-integer-type int int
1497 (lambda (type type2)
1498 (declare (ignore type2))
1499 (let ((lo (numeric-type-low type))
1500 (hi (numeric-type-high type)))
1501 (values (if hi (lognot hi) nil)
1502 (if lo (lognot lo) nil)
1503 (numeric-type-class type)
1504 (numeric-type-format type))))))
1506 #!+sb-propagate-float-type
1507 (defoptimizer (%negate derive-type) ((num))
1508 (flet ((negate-bound (b)
1510 (set-bound (- (type-bound-number b))
1512 (one-arg-derive-type num
1514 (modified-numeric-type
1516 :low (negate-bound (numeric-type-high type))
1517 :high (negate-bound (numeric-type-low type))))
1520 #!-sb-propagate-float-type
1521 (defoptimizer (abs derive-type) ((num))
1522 (let ((type (continuation-type num)))
1523 (if (and (numeric-type-p type)
1524 (eq (numeric-type-class type) 'integer)
1525 (eq (numeric-type-complexp type) :real))
1526 (let ((lo (numeric-type-low type))
1527 (hi (numeric-type-high type)))
1528 (make-numeric-type :class 'integer :complexp :real
1529 :low (cond ((and hi (minusp hi))
1535 :high (if (and hi lo)
1536 (max (abs hi) (abs lo))
1538 (numeric-contagion type type))))
1540 #!+sb-propagate-float-type
1541 (defun abs-derive-type-aux (type)
1542 (cond ((eq (numeric-type-complexp type) :complex)
1543 ;; The absolute value of a complex number is always a
1544 ;; non-negative float.
1545 (let* ((format (case (numeric-type-class type)
1546 ((integer rational) 'single-float)
1547 (t (numeric-type-format type))))
1548 (bound-format (or format 'float)))
1549 (make-numeric-type :class 'float
1552 :low (coerce 0 bound-format)
1555 ;; The absolute value of a real number is a non-negative real
1556 ;; of the same type.
1557 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1558 (class (numeric-type-class type))
1559 (format (numeric-type-format type))
1560 (bound-type (or format class 'real)))
1565 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1566 :high (coerce-numeric-bound
1567 (interval-high abs-bnd) bound-type))))))
1569 #!+sb-propagate-float-type
1570 (defoptimizer (abs derive-type) ((num))
1571 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1573 #!-sb-propagate-float-type
1574 (defoptimizer (truncate derive-type) ((number divisor))
1575 (let ((number-type (continuation-type number))
1576 (divisor-type (continuation-type divisor))
1577 (integer-type (specifier-type 'integer)))
1578 (if (and (numeric-type-p number-type)
1579 (csubtypep number-type integer-type)
1580 (numeric-type-p divisor-type)
1581 (csubtypep divisor-type integer-type))
1582 (let ((number-low (numeric-type-low number-type))
1583 (number-high (numeric-type-high number-type))
1584 (divisor-low (numeric-type-low divisor-type))
1585 (divisor-high (numeric-type-high divisor-type)))
1586 (values-specifier-type
1587 `(values ,(integer-truncate-derive-type number-low number-high
1588 divisor-low divisor-high)
1589 ,(integer-rem-derive-type number-low number-high
1590 divisor-low divisor-high))))
1593 #!+sb-propagate-float-type
1596 (defun rem-result-type (number-type divisor-type)
1597 ;; Figure out what the remainder type is. The remainder is an
1598 ;; integer if both args are integers; a rational if both args are
1599 ;; rational; and a float otherwise.
1600 (cond ((and (csubtypep number-type (specifier-type 'integer))
1601 (csubtypep divisor-type (specifier-type 'integer)))
1603 ((and (csubtypep number-type (specifier-type 'rational))
1604 (csubtypep divisor-type (specifier-type 'rational)))
1606 ((and (csubtypep number-type (specifier-type 'float))
1607 (csubtypep divisor-type (specifier-type 'float)))
1608 ;; Both are floats so the result is also a float, of
1609 ;; the largest type.
1610 (or (float-format-max (numeric-type-format number-type)
1611 (numeric-type-format divisor-type))
1613 ((and (csubtypep number-type (specifier-type 'float))
1614 (csubtypep divisor-type (specifier-type 'rational)))
1615 ;; One of the arguments is a float and the other is a
1616 ;; rational. The remainder is a float of the same
1618 (or (numeric-type-format number-type) 'float))
1619 ((and (csubtypep divisor-type (specifier-type 'float))
1620 (csubtypep number-type (specifier-type 'rational)))
1621 ;; One of the arguments is a float and the other is a
1622 ;; rational. The remainder is a float of the same
1624 (or (numeric-type-format divisor-type) 'float))
1626 ;; Some unhandled combination. This usually means both args
1627 ;; are REAL so the result is a REAL.
1630 (defun truncate-derive-type-quot (number-type divisor-type)
1631 (let* ((rem-type (rem-result-type number-type divisor-type))
1632 (number-interval (numeric-type->interval number-type))
1633 (divisor-interval (numeric-type->interval divisor-type)))
1634 ;;(declare (type (member '(integer rational float)) rem-type))
1635 ;; We have real numbers now.
1636 (cond ((eq rem-type 'integer)
1637 ;; Since the remainder type is INTEGER, both args are
1639 (let* ((res (integer-truncate-derive-type
1640 (interval-low number-interval)
1641 (interval-high number-interval)
1642 (interval-low divisor-interval)
1643 (interval-high divisor-interval))))
1644 (specifier-type (if (listp res) res 'integer))))
1646 (let ((quot (truncate-quotient-bound
1647 (interval-div number-interval
1648 divisor-interval))))
1649 (specifier-type `(integer ,(or (interval-low quot) '*)
1650 ,(or (interval-high quot) '*))))))))
1652 (defun truncate-derive-type-rem (number-type divisor-type)
1653 (let* ((rem-type (rem-result-type number-type divisor-type))
1654 (number-interval (numeric-type->interval number-type))
1655 (divisor-interval (numeric-type->interval divisor-type))
1656 (rem (truncate-rem-bound number-interval divisor-interval)))
1657 ;;(declare (type (member '(integer rational float)) rem-type))
1658 ;; We have real numbers now.
1659 (cond ((eq rem-type 'integer)
1660 ;; Since the remainder type is INTEGER, both args are
1662 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1663 ,(or (interval-high rem) '*))))
1665 (multiple-value-bind (class format)
1668 (values 'integer nil))
1670 (values 'rational nil))
1671 ((or single-float double-float #!+long-float long-float)
1672 (values 'float rem-type))
1674 (values 'float nil))
1677 (when (member rem-type '(float single-float double-float
1678 #!+long-float long-float))
1679 (setf rem (interval-func #'(lambda (x)
1680 (coerce x rem-type))
1682 (make-numeric-type :class class
1684 :low (interval-low rem)
1685 :high (interval-high rem)))))))
1687 (defun truncate-derive-type-quot-aux (num div same-arg)
1688 (declare (ignore same-arg))
1689 (if (and (numeric-type-real-p num)
1690 (numeric-type-real-p div))
1691 (truncate-derive-type-quot num div)
1694 (defun truncate-derive-type-rem-aux (num div same-arg)
1695 (declare (ignore same-arg))
1696 (if (and (numeric-type-real-p num)
1697 (numeric-type-real-p div))
1698 (truncate-derive-type-rem num div)
1701 (defoptimizer (truncate derive-type) ((number divisor))
1702 (let ((quot (two-arg-derive-type number divisor
1703 #'truncate-derive-type-quot-aux #'truncate))
1704 (rem (two-arg-derive-type number divisor
1705 #'truncate-derive-type-rem-aux #'rem)))
1706 (when (and quot rem)
1707 (make-values-type :required (list quot rem)))))
1709 (defun ftruncate-derive-type-quot (number-type divisor-type)
1710 ;; The bounds are the same as for truncate. However, the first
1711 ;; result is a float of some type. We need to determine what that
1712 ;; type is. Basically it's the more contagious of the two types.
1713 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1714 (res-type (numeric-contagion number-type divisor-type)))
1715 (make-numeric-type :class 'float
1716 :format (numeric-type-format res-type)
1717 :low (numeric-type-low q-type)
1718 :high (numeric-type-high q-type))))
1720 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1721 (declare (ignore same-arg))
1722 (if (and (numeric-type-real-p n)
1723 (numeric-type-real-p d))
1724 (ftruncate-derive-type-quot n d)
1727 (defoptimizer (ftruncate derive-type) ((number divisor))
1729 (two-arg-derive-type number divisor
1730 #'ftruncate-derive-type-quot-aux #'ftruncate))
1731 (rem (two-arg-derive-type number divisor
1732 #'truncate-derive-type-rem-aux #'rem)))
1733 (when (and quot rem)
1734 (make-values-type :required (list quot rem)))))
1736 (defun %unary-truncate-derive-type-aux (number)
1737 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1739 (defoptimizer (%unary-truncate derive-type) ((number))
1740 (one-arg-derive-type number
1741 #'%unary-truncate-derive-type-aux
1744 ;;; Define optimizers for FLOOR and CEILING.
1746 ((frob-opt (name q-name r-name)
1747 (let ((q-aux (symbolicate q-name "-AUX"))
1748 (r-aux (symbolicate r-name "-AUX")))
1750 ;; Compute type of quotient (first) result.
1751 (defun ,q-aux (number-type divisor-type)
1752 (let* ((number-interval
1753 (numeric-type->interval number-type))
1755 (numeric-type->interval divisor-type))
1756 (quot (,q-name (interval-div number-interval
1757 divisor-interval))))
1758 (specifier-type `(integer ,(or (interval-low quot) '*)
1759 ,(or (interval-high quot) '*)))))
1760 ;; Compute type of remainder.
1761 (defun ,r-aux (number-type divisor-type)
1762 (let* ((divisor-interval
1763 (numeric-type->interval divisor-type))
1764 (rem (,r-name divisor-interval))
1765 (result-type (rem-result-type number-type divisor-type)))
1766 (multiple-value-bind (class format)
1769 (values 'integer nil))
1771 (values 'rational nil))
1772 ((or single-float double-float #!+long-float long-float)
1773 (values 'float result-type))
1775 (values 'float nil))
1778 (when (member result-type '(float single-float double-float
1779 #!+long-float long-float))
1780 ;; Make sure that the limits on the interval have
1782 (setf rem (interval-func (lambda (x)
1783 (coerce x result-type))
1785 (make-numeric-type :class class
1787 :low (interval-low rem)
1788 :high (interval-high rem)))))
1789 ;; the optimizer itself
1790 (defoptimizer (,name derive-type) ((number divisor))
1791 (flet ((derive-q (n d same-arg)
1792 (declare (ignore same-arg))
1793 (if (and (numeric-type-real-p n)
1794 (numeric-type-real-p d))
1797 (derive-r (n d same-arg)
1798 (declare (ignore same-arg))
1799 (if (and (numeric-type-real-p n)
1800 (numeric-type-real-p d))
1803 (let ((quot (two-arg-derive-type
1804 number divisor #'derive-q #',name))
1805 (rem (two-arg-derive-type
1806 number divisor #'derive-r #'mod)))
1807 (when (and quot rem)
1808 (make-values-type :required (list quot rem))))))))))
1810 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1811 (frob-opt floor floor-quotient-bound floor-rem-bound)
1812 (frob-opt ceiling ceiling-quotient-bound ceiling-rem-bound))
1814 ;;; Define optimizers for FFLOOR and FCEILING
1816 ((frob-opt (name q-name r-name)
1817 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1818 (r-aux (symbolicate r-name "-AUX")))
1820 ;; Compute type of quotient (first) result.
1821 (defun ,q-aux (number-type divisor-type)
1822 (let* ((number-interval
1823 (numeric-type->interval number-type))
1825 (numeric-type->interval divisor-type))
1826 (quot (,q-name (interval-div number-interval
1828 (res-type (numeric-contagion number-type divisor-type)))
1830 :class (numeric-type-class res-type)
1831 :format (numeric-type-format res-type)
1832 :low (interval-low quot)
1833 :high (interval-high quot))))
1835 (defoptimizer (,name derive-type) ((number divisor))
1836 (flet ((derive-q (n d same-arg)
1837 (declare (ignore same-arg))
1838 (if (and (numeric-type-real-p n)
1839 (numeric-type-real-p d))
1842 (derive-r (n d same-arg)
1843 (declare (ignore same-arg))
1844 (if (and (numeric-type-real-p n)
1845 (numeric-type-real-p d))
1848 (let ((quot (two-arg-derive-type
1849 number divisor #'derive-q #',name))
1850 (rem (two-arg-derive-type
1851 number divisor #'derive-r #'mod)))
1852 (when (and quot rem)
1853 (make-values-type :required (list quot rem))))))))))
1855 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1856 (frob-opt ffloor floor-quotient-bound floor-rem-bound)
1857 (frob-opt fceiling ceiling-quotient-bound ceiling-rem-bound))
1859 ;;; functions to compute the bounds on the quotient and remainder for
1860 ;;; the FLOOR function
1861 (defun floor-quotient-bound (quot)
1862 ;; Take the floor of the quotient and then massage it into what we
1864 (let ((lo (interval-low quot))
1865 (hi (interval-high quot)))
1866 ;; Take the floor of the lower bound. The result is always a
1867 ;; closed lower bound.
1869 (floor (type-bound-number lo))
1871 ;; For the upper bound, we need to be careful.
1874 ;; An open bound. We need to be careful here because
1875 ;; the floor of '(10.0) is 9, but the floor of
1877 (multiple-value-bind (q r) (floor (first hi))
1882 ;; A closed bound, so the answer is obvious.
1886 (make-interval :low lo :high hi)))
1887 (defun floor-rem-bound (div)
1888 ;; The remainder depends only on the divisor. Try to get the
1889 ;; correct sign for the remainder if we can.
1890 (case (interval-range-info div)
1892 ;; The divisor is always positive.
1893 (let ((rem (interval-abs div)))
1894 (setf (interval-low rem) 0)
1895 (when (and (numberp (interval-high rem))
1896 (not (zerop (interval-high rem))))
1897 ;; The remainder never contains the upper bound. However,
1898 ;; watch out for the case where the high limit is zero!
1899 (setf (interval-high rem) (list (interval-high rem))))
1902 ;; The divisor is always negative.
1903 (let ((rem (interval-neg (interval-abs div))))
1904 (setf (interval-high rem) 0)
1905 (when (numberp (interval-low rem))
1906 ;; The remainder never contains the lower bound.
1907 (setf (interval-low rem) (list (interval-low rem))))
1910 ;; The divisor can be positive or negative. All bets off. The
1911 ;; magnitude of remainder is the maximum value of the divisor.
1912 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1913 ;; The bound never reaches the limit, so make the interval open.
1914 (make-interval :low (if limit
1917 :high (list limit))))))
1919 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1920 => #S(INTERVAL :LOW 0 :HIGH 10)
1921 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1922 => #S(INTERVAL :LOW 0 :HIGH 10)
1923 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1924 => #S(INTERVAL :LOW 0 :HIGH 10)
1925 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1926 => #S(INTERVAL :LOW 0 :HIGH 9)
1927 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1928 => #S(INTERVAL :LOW 0 :HIGH 10)
1929 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1930 => #S(INTERVAL :LOW 0 :HIGH 10)
1931 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1932 => #S(INTERVAL :LOW -2 :HIGH 10)
1933 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1934 => #S(INTERVAL :LOW -1 :HIGH 10)
1935 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1936 => #S(INTERVAL :LOW -1 :HIGH 10)
1938 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1939 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1940 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1941 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1942 (floor-rem-bound (make-interval :low -10 :high -2.3))
1943 #S(INTERVAL :LOW (-10) :HIGH 0)
1944 (floor-rem-bound (make-interval :low 0.3 :high 10))
1945 => #S(INTERVAL :LOW 0 :HIGH '(10))
1946 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1947 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1948 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1949 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1952 ;;; same functions for CEILING
1953 (defun ceiling-quotient-bound (quot)
1954 ;; Take the ceiling of the quotient and then massage it into what we
1956 (let ((lo (interval-low quot))
1957 (hi (interval-high quot)))
1958 ;; Take the ceiling of the upper bound. The result is always a
1959 ;; closed upper bound.
1961 (ceiling (type-bound-number hi))
1963 ;; For the lower bound, we need to be careful.
1966 ;; An open bound. We need to be careful here because
1967 ;; the ceiling of '(10.0) is 11, but the ceiling of
1969 (multiple-value-bind (q r) (ceiling (first lo))
1974 ;; A closed bound, so the answer is obvious.
1978 (make-interval :low lo :high hi)))
1979 (defun ceiling-rem-bound (div)
1980 ;; The remainder depends only on the divisor. Try to get the
1981 ;; correct sign for the remainder if we can.
1982 (case (interval-range-info div)
1984 ;; Divisor is always positive. The remainder is negative.
1985 (let ((rem (interval-neg (interval-abs div))))
1986 (setf (interval-high rem) 0)
1987 (when (and (numberp (interval-low rem))
1988 (not (zerop (interval-low rem))))
1989 ;; The remainder never contains the upper bound. However,
1990 ;; watch out for the case when the upper bound is zero!
1991 (setf (interval-low rem) (list (interval-low rem))))
1994 ;; Divisor is always negative. The remainder is positive
1995 (let ((rem (interval-abs div)))
1996 (setf (interval-low rem) 0)
1997 (when (numberp (interval-high rem))
1998 ;; The remainder never contains the lower bound.
1999 (setf (interval-high rem) (list (interval-high rem))))
2002 ;; The divisor can be positive or negative. All bets off. The
2003 ;; magnitude of remainder is the maximum value of the divisor.
2004 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2005 ;; The bound never reaches the limit, so make the interval open.
2006 (make-interval :low (if limit
2009 :high (list limit))))))
2012 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2013 => #S(INTERVAL :LOW 1 :HIGH 11)
2014 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2015 => #S(INTERVAL :LOW 1 :HIGH 11)
2016 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2017 => #S(INTERVAL :LOW 1 :HIGH 10)
2018 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2019 => #S(INTERVAL :LOW 1 :HIGH 10)
2020 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2021 => #S(INTERVAL :LOW 1 :HIGH 11)
2022 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2023 => #S(INTERVAL :LOW 1 :HIGH 11)
2024 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2025 => #S(INTERVAL :LOW -1 :HIGH 11)
2026 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2027 => #S(INTERVAL :LOW 0 :HIGH 11)
2028 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2029 => #S(INTERVAL :LOW -1 :HIGH 11)
2031 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2032 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2033 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2034 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2035 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2036 => #S(INTERVAL :LOW 0 :HIGH (10))
2037 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2038 => #S(INTERVAL :LOW (-10) :HIGH 0)
2039 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2040 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2041 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2042 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2045 (defun truncate-quotient-bound (quot)
2046 ;; For positive quotients, truncate is exactly like floor. For
2047 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2048 ;; it's the union of the two pieces.
2049 (case (interval-range-info quot)
2052 (floor-quotient-bound quot))
2054 ;; just like CEILING
2055 (ceiling-quotient-bound quot))
2057 ;; Split the interval into positive and negative pieces, compute
2058 ;; the result for each piece and put them back together.
2059 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2060 (interval-merge-pair (ceiling-quotient-bound neg)
2061 (floor-quotient-bound pos))))))
2063 (defun truncate-rem-bound (num div)
2064 ;; This is significantly more complicated than FLOOR or CEILING. We
2065 ;; need both the number and the divisor to determine the range. The
2066 ;; basic idea is to split the ranges of NUM and DEN into positive
2067 ;; and negative pieces and deal with each of the four possibilities
2069 (case (interval-range-info num)
2071 (case (interval-range-info div)
2073 (floor-rem-bound div))
2075 (ceiling-rem-bound div))
2077 (destructuring-bind (neg pos) (interval-split 0 div t t)
2078 (interval-merge-pair (truncate-rem-bound num neg)
2079 (truncate-rem-bound num pos))))))
2081 (case (interval-range-info div)
2083 (ceiling-rem-bound div))
2085 (floor-rem-bound div))
2087 (destructuring-bind (neg pos) (interval-split 0 div t t)
2088 (interval-merge-pair (truncate-rem-bound num neg)
2089 (truncate-rem-bound num pos))))))
2091 (destructuring-bind (neg pos) (interval-split 0 num t t)
2092 (interval-merge-pair (truncate-rem-bound neg div)
2093 (truncate-rem-bound pos div))))))
2096 ;;; Derive useful information about the range. Returns three values:
2097 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2098 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2099 ;;; - The abs of the maximal value if there is one, or nil if it is
2101 (defun numeric-range-info (low high)
2102 (cond ((and low (not (minusp low)))
2103 (values '+ low high))
2104 ((and high (not (plusp high)))
2105 (values '- (- high) (if low (- low) nil)))
2107 (values nil 0 (and low high (max (- low) high))))))
2109 (defun integer-truncate-derive-type
2110 (number-low number-high divisor-low divisor-high)
2111 ;; The result cannot be larger in magnitude than the number, but the
2112 ;; sign might change. If we can determine the sign of either the
2113 ;; number or the divisor, we can eliminate some of the cases.
2114 (multiple-value-bind (number-sign number-min number-max)
2115 (numeric-range-info number-low number-high)
2116 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2117 (numeric-range-info divisor-low divisor-high)
2118 (when (and divisor-max (zerop divisor-max))
2119 ;; We've got a problem: guaranteed division by zero.
2120 (return-from integer-truncate-derive-type t))
2121 (when (zerop divisor-min)
2122 ;; We'll assume that they aren't going to divide by zero.
2124 (cond ((and number-sign divisor-sign)
2125 ;; We know the sign of both.
2126 (if (eq number-sign divisor-sign)
2127 ;; Same sign, so the result will be positive.
2128 `(integer ,(if divisor-max
2129 (truncate number-min divisor-max)
2132 (truncate number-max divisor-min)
2134 ;; Different signs, the result will be negative.
2135 `(integer ,(if number-max
2136 (- (truncate number-max divisor-min))
2139 (- (truncate number-min divisor-max))
2141 ((eq divisor-sign '+)
2142 ;; The divisor is positive. Therefore, the number will just
2143 ;; become closer to zero.
2144 `(integer ,(if number-low
2145 (truncate number-low divisor-min)
2148 (truncate number-high divisor-min)
2150 ((eq divisor-sign '-)
2151 ;; The divisor is negative. Therefore, the absolute value of
2152 ;; the number will become closer to zero, but the sign will also
2154 `(integer ,(if number-high
2155 (- (truncate number-high divisor-min))
2158 (- (truncate number-low divisor-min))
2160 ;; The divisor could be either positive or negative.
2162 ;; The number we are dividing has a bound. Divide that by the
2163 ;; smallest posible divisor.
2164 (let ((bound (truncate number-max divisor-min)))
2165 `(integer ,(- bound) ,bound)))
2167 ;; The number we are dividing is unbounded, so we can't tell
2168 ;; anything about the result.
2171 #!-sb-propagate-float-type
2172 (defun integer-rem-derive-type
2173 (number-low number-high divisor-low divisor-high)
2174 (if (and divisor-low divisor-high)
2175 ;; We know the range of the divisor, and the remainder must be
2176 ;; smaller than the divisor. We can tell the sign of the
2177 ;; remainer if we know the sign of the number.
2178 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2179 `(integer ,(if (or (null number-low)
2180 (minusp number-low))
2183 ,(if (or (null number-high)
2184 (plusp number-high))
2187 ;; The divisor is potentially either very positive or very
2188 ;; negative. Therefore, the remainer is unbounded, but we might
2189 ;; be able to tell something about the sign from the number.
2190 `(integer ,(if (and number-low (not (minusp number-low)))
2191 ;; The number we are dividing is positive.
2192 ;; Therefore, the remainder must be positive.
2195 ,(if (and number-high (not (plusp number-high)))
2196 ;; The number we are dividing is negative.
2197 ;; Therefore, the remainder must be negative.
2201 #!-sb-propagate-float-type
2202 (defoptimizer (random derive-type) ((bound &optional state))
2203 (let ((type (continuation-type bound)))
2204 (when (numeric-type-p type)
2205 (let ((class (numeric-type-class type))
2206 (high (numeric-type-high type))
2207 (format (numeric-type-format type)))
2211 :low (coerce 0 (or format class 'real))
2212 :high (cond ((not high) nil)
2213 ((eq class 'integer) (max (1- high) 0))
2214 ((or (consp high) (zerop high)) high)
2217 #!+sb-propagate-float-type
2218 (defun random-derive-type-aux (type)
2219 (let ((class (numeric-type-class type))
2220 (high (numeric-type-high type))
2221 (format (numeric-type-format type)))
2225 :low (coerce 0 (or format class 'real))
2226 :high (cond ((not high) nil)
2227 ((eq class 'integer) (max (1- high) 0))
2228 ((or (consp high) (zerop high)) high)
2231 #!+sb-propagate-float-type
2232 (defoptimizer (random derive-type) ((bound &optional state))
2233 (one-arg-derive-type bound #'random-derive-type-aux nil))
2235 ;;;; logical derive-type methods
2237 ;;; Return the maximum number of bits an integer of the supplied type
2238 ;;; can take up, or NIL if it is unbounded. The second (third) value
2239 ;;; is T if the integer can be positive (negative) and NIL if not.
2240 ;;; Zero counts as positive.
2241 (defun integer-type-length (type)
2242 (if (numeric-type-p type)
2243 (let ((min (numeric-type-low type))
2244 (max (numeric-type-high type)))
2245 (values (and min max (max (integer-length min) (integer-length max)))
2246 (or (null max) (not (minusp max)))
2247 (or (null min) (minusp min))))
2250 #!-sb-propagate-fun-type
2253 (defoptimizer (logand derive-type) ((x y))
2254 (multiple-value-bind (x-len x-pos x-neg)
2255 (integer-type-length (continuation-type x))
2256 (declare (ignore x-pos))
2257 (multiple-value-bind (y-len y-pos y-neg)
2258 (integer-type-length (continuation-type y))
2259 (declare (ignore y-pos))
2261 ;; X must be positive.
2263 ;; The must both be positive.
2264 (cond ((or (null x-len) (null y-len))
2265 (specifier-type 'unsigned-byte))
2266 ((or (zerop x-len) (zerop y-len))
2267 (specifier-type '(integer 0 0)))
2269 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2270 ;; X is positive, but Y might be negative.
2272 (specifier-type 'unsigned-byte))
2274 (specifier-type '(integer 0 0)))
2276 (specifier-type `(unsigned-byte ,x-len)))))
2277 ;; X might be negative.
2279 ;; Y must be positive.
2281 (specifier-type 'unsigned-byte))
2283 (specifier-type '(integer 0 0)))
2286 `(unsigned-byte ,y-len))))
2287 ;; Either might be negative.
2288 (if (and x-len y-len)
2289 ;; The result is bounded.
2290 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2291 ;; We can't tell squat about the result.
2292 (specifier-type 'integer)))))))
2294 (defoptimizer (logior derive-type) ((x y))
2295 (multiple-value-bind (x-len x-pos x-neg)
2296 (integer-type-length (continuation-type x))
2297 (multiple-value-bind (y-len y-pos y-neg)
2298 (integer-type-length (continuation-type y))
2300 ((and (not x-neg) (not y-neg))
2301 ;; Both are positive.
2302 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2306 ;; X must be negative.
2308 ;; Both are negative. The result is going to be negative and be
2309 ;; the same length or shorter than the smaller.
2310 (if (and x-len y-len)
2312 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2314 (specifier-type '(integer * -1)))
2315 ;; X is negative, but we don't know about Y. The result will be
2316 ;; negative, but no more negative than X.
2318 `(integer ,(or (numeric-type-low (continuation-type x)) '*)
2321 ;; X might be either positive or negative.
2323 ;; But Y is negative. The result will be negative.
2325 `(integer ,(or (numeric-type-low (continuation-type y)) '*)
2327 ;; We don't know squat about either. It won't get any bigger.
2328 (if (and x-len y-len)
2330 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2332 (specifier-type 'integer))))))))
2334 (defoptimizer (logxor derive-type) ((x y))
2335 (multiple-value-bind (x-len x-pos x-neg)
2336 (integer-type-length (continuation-type x))
2337 (multiple-value-bind (y-len y-pos y-neg)
2338 (integer-type-length (continuation-type y))
2340 ((or (and (not x-neg) (not y-neg))
2341 (and (not x-pos) (not y-pos)))
2342 ;; Either both are negative or both are positive. The result
2343 ;; will be positive, and as long as the longer.
2344 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2347 ((or (and (not x-pos) (not y-neg))
2348 (and (not y-neg) (not y-pos)))
2349 ;; Either X is negative and Y is positive of vice-versa. The
2350 ;; result will be negative.
2351 (specifier-type `(integer ,(if (and x-len y-len)
2352 (ash -1 (max x-len y-len))
2355 ;; We can't tell what the sign of the result is going to be.
2356 ;; All we know is that we don't create new bits.
2358 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2360 (specifier-type 'integer))))))
2364 #!+sb-propagate-fun-type
2367 (defun logand-derive-type-aux (x y &optional same-leaf)
2368 (declare (ignore same-leaf))
2369 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2370 (declare (ignore x-pos))
2371 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2372 (declare (ignore y-pos))
2374 ;; X must be positive.
2376 ;; They must both be positive.
2377 (cond ((or (null x-len) (null y-len))
2378 (specifier-type 'unsigned-byte))
2379 ((or (zerop x-len) (zerop y-len))
2380 (specifier-type '(integer 0 0)))
2382 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2383 ;; X is positive, but Y might be negative.
2385 (specifier-type 'unsigned-byte))
2387 (specifier-type '(integer 0 0)))
2389 (specifier-type `(unsigned-byte ,x-len)))))
2390 ;; X might be negative.
2392 ;; Y must be positive.
2394 (specifier-type 'unsigned-byte))
2396 (specifier-type '(integer 0 0)))
2399 `(unsigned-byte ,y-len))))
2400 ;; Either might be negative.
2401 (if (and x-len y-len)
2402 ;; The result is bounded.
2403 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2404 ;; We can't tell squat about the result.
2405 (specifier-type 'integer)))))))
2407 (defun logior-derive-type-aux (x y &optional same-leaf)
2408 (declare (ignore same-leaf))
2409 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2410 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2412 ((and (not x-neg) (not y-neg))
2413 ;; Both are positive.
2414 (if (and x-len y-len (zerop x-len) (zerop y-len))
2415 (specifier-type '(integer 0 0))
2416 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2420 ;; X must be negative.
2422 ;; Both are negative. The result is going to be negative
2423 ;; and be the same length or shorter than the smaller.
2424 (if (and x-len y-len)
2426 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2428 (specifier-type '(integer * -1)))
2429 ;; X is negative, but we don't know about Y. The result
2430 ;; will be negative, but no more negative than X.
2432 `(integer ,(or (numeric-type-low x) '*)
2435 ;; X might be either positive or negative.
2437 ;; But Y is negative. The result will be negative.
2439 `(integer ,(or (numeric-type-low y) '*)
2441 ;; We don't know squat about either. It won't get any bigger.
2442 (if (and x-len y-len)
2444 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2446 (specifier-type 'integer))))))))
2448 (defun logxor-derive-type-aux (x y &optional same-leaf)
2449 (declare (ignore same-leaf))
2450 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2451 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2453 ((or (and (not x-neg) (not y-neg))
2454 (and (not x-pos) (not y-pos)))
2455 ;; Either both are negative or both are positive. The result
2456 ;; will be positive, and as long as the longer.
2457 (if (and x-len y-len (zerop x-len) (zerop y-len))
2458 (specifier-type '(integer 0 0))
2459 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2462 ((or (and (not x-pos) (not y-neg))
2463 (and (not y-neg) (not y-pos)))
2464 ;; Either X is negative and Y is positive of vice-verca. The
2465 ;; result will be negative.
2466 (specifier-type `(integer ,(if (and x-len y-len)
2467 (ash -1 (max x-len y-len))
2470 ;; We can't tell what the sign of the result is going to be.
2471 ;; All we know is that we don't create new bits.
2473 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2475 (specifier-type 'integer))))))
2477 (macrolet ((frob (logfcn)
2478 (let ((fcn-aux (symbolicate logfcn "-DERIVE-TYPE-AUX")))
2479 `(defoptimizer (,logfcn derive-type) ((x y))
2480 (two-arg-derive-type x y #',fcn-aux #',logfcn)))))
2481 ;; FIXME: DEF-FROB, not just FROB
2486 (defoptimizer (integer-length derive-type) ((x))
2487 (let ((x-type (continuation-type x)))
2488 (when (and (numeric-type-p x-type)
2489 (csubtypep x-type (specifier-type 'integer)))
2490 ;; If the X is of type (INTEGER LO HI), then the integer-length
2491 ;; of X is (INTEGER (min lo hi) (max lo hi), basically. Be
2492 ;; careful about LO or HI being NIL, though. Also, if 0 is
2493 ;; contained in X, the lower bound is obviously 0.
2494 (flet ((null-or-min (a b)
2495 (and a b (min (integer-length a)
2496 (integer-length b))))
2498 (and a b (max (integer-length a)
2499 (integer-length b)))))
2500 (let* ((min (numeric-type-low x-type))
2501 (max (numeric-type-high x-type))
2502 (min-len (null-or-min min max))
2503 (max-len (null-or-max min max)))
2504 (when (ctypep 0 x-type)
2506 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2509 ;;;; miscellaneous derive-type methods
2511 (defoptimizer (code-char derive-type) ((code))
2512 (specifier-type 'base-char))
2514 (defoptimizer (values derive-type) ((&rest values))
2515 (values-specifier-type
2516 `(values ,@(mapcar #'(lambda (x)
2517 (type-specifier (continuation-type x)))
2520 ;;;; byte operations
2522 ;;;; We try to turn byte operations into simple logical operations.
2523 ;;;; First, we convert byte specifiers into separate size and position
2524 ;;;; arguments passed to internal %FOO functions. We then attempt to
2525 ;;;; transform the %FOO functions into boolean operations when the
2526 ;;;; size and position are constant and the operands are fixnums.
2528 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2529 ;; expressions that evaluate to the SIZE and POSITION of
2530 ;; the byte-specifier form SPEC. We may wrap a let around
2531 ;; the result of the body to bind some variables.
2533 ;; If the spec is a BYTE form, then bind the vars to the
2534 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2535 ;; and BYTE-POSITION. The goal of this transformation is to
2536 ;; avoid consing up byte specifiers and then immediately
2537 ;; throwing them away.
2538 (with-byte-specifier ((size-var pos-var spec) &body body)
2539 (once-only ((spec `(macroexpand ,spec))
2541 `(if (and (consp ,spec)
2542 (eq (car ,spec) 'byte)
2543 (= (length ,spec) 3))
2544 (let ((,size-var (second ,spec))
2545 (,pos-var (third ,spec)))
2547 (let ((,size-var `(byte-size ,,temp))
2548 (,pos-var `(byte-position ,,temp)))
2549 `(let ((,,temp ,,spec))
2552 (def-source-transform ldb (spec int)
2553 (with-byte-specifier (size pos spec)
2554 `(%ldb ,size ,pos ,int)))
2556 (def-source-transform dpb (newbyte spec int)
2557 (with-byte-specifier (size pos spec)
2558 `(%dpb ,newbyte ,size ,pos ,int)))
2560 (def-source-transform mask-field (spec int)
2561 (with-byte-specifier (size pos spec)
2562 `(%mask-field ,size ,pos ,int)))
2564 (def-source-transform deposit-field (newbyte spec int)
2565 (with-byte-specifier (size pos spec)
2566 `(%deposit-field ,newbyte ,size ,pos ,int))))
2568 (defoptimizer (%ldb derive-type) ((size posn num))
2569 (let ((size (continuation-type size)))
2570 (if (and (numeric-type-p size)
2571 (csubtypep size (specifier-type 'integer)))
2572 (let ((size-high (numeric-type-high size)))
2573 (if (and size-high (<= size-high sb!vm:word-bits))
2574 (specifier-type `(unsigned-byte ,size-high))
2575 (specifier-type 'unsigned-byte)))
2578 (defoptimizer (%mask-field derive-type) ((size posn num))
2579 (let ((size (continuation-type size))
2580 (posn (continuation-type posn)))
2581 (if (and (numeric-type-p size)
2582 (csubtypep size (specifier-type 'integer))
2583 (numeric-type-p posn)
2584 (csubtypep posn (specifier-type 'integer)))
2585 (let ((size-high (numeric-type-high size))
2586 (posn-high (numeric-type-high posn)))
2587 (if (and size-high posn-high
2588 (<= (+ size-high posn-high) sb!vm:word-bits))
2589 (specifier-type `(unsigned-byte ,(+ size-high posn-high)))
2590 (specifier-type 'unsigned-byte)))
2593 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2594 (let ((size (continuation-type size))
2595 (posn (continuation-type posn))
2596 (int (continuation-type int)))
2597 (if (and (numeric-type-p size)
2598 (csubtypep size (specifier-type 'integer))
2599 (numeric-type-p posn)
2600 (csubtypep posn (specifier-type 'integer))
2601 (numeric-type-p int)
2602 (csubtypep int (specifier-type 'integer)))
2603 (let ((size-high (numeric-type-high size))
2604 (posn-high (numeric-type-high posn))
2605 (high (numeric-type-high int))
2606 (low (numeric-type-low int)))
2607 (if (and size-high posn-high high low
2608 (<= (+ size-high posn-high) sb!vm:word-bits))
2610 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2611 (max (integer-length high)
2612 (integer-length low)
2613 (+ size-high posn-high))))
2617 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2618 (let ((size (continuation-type size))
2619 (posn (continuation-type posn))
2620 (int (continuation-type int)))
2621 (if (and (numeric-type-p size)
2622 (csubtypep size (specifier-type 'integer))
2623 (numeric-type-p posn)
2624 (csubtypep posn (specifier-type 'integer))
2625 (numeric-type-p int)
2626 (csubtypep int (specifier-type 'integer)))
2627 (let ((size-high (numeric-type-high size))
2628 (posn-high (numeric-type-high posn))
2629 (high (numeric-type-high int))
2630 (low (numeric-type-low int)))
2631 (if (and size-high posn-high high low
2632 (<= (+ size-high posn-high) sb!vm:word-bits))
2634 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2635 (max (integer-length high)
2636 (integer-length low)
2637 (+ size-high posn-high))))
2641 (deftransform %ldb ((size posn int)
2642 (fixnum fixnum integer)
2643 (unsigned-byte #.sb!vm:word-bits))
2644 "convert to inline logical operations"
2645 `(logand (ash int (- posn))
2646 (ash ,(1- (ash 1 sb!vm:word-bits))
2647 (- size ,sb!vm:word-bits))))
2649 (deftransform %mask-field ((size posn int)
2650 (fixnum fixnum integer)
2651 (unsigned-byte #.sb!vm:word-bits))
2652 "convert to inline logical operations"
2654 (ash (ash ,(1- (ash 1 sb!vm:word-bits))
2655 (- size ,sb!vm:word-bits))
2658 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2659 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2660 ;;; as the result type, as that would allow result types that cover
2661 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2662 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2664 (deftransform %dpb ((new size posn int)
2666 (unsigned-byte #.sb!vm:word-bits))
2667 "convert to inline logical operations"
2668 `(let ((mask (ldb (byte size 0) -1)))
2669 (logior (ash (logand new mask) posn)
2670 (logand int (lognot (ash mask posn))))))
2672 (deftransform %dpb ((new size posn int)
2674 (signed-byte #.sb!vm:word-bits))
2675 "convert to inline logical operations"
2676 `(let ((mask (ldb (byte size 0) -1)))
2677 (logior (ash (logand new mask) posn)
2678 (logand int (lognot (ash mask posn))))))
2680 (deftransform %deposit-field ((new size posn int)
2682 (unsigned-byte #.sb!vm:word-bits))
2683 "convert to inline logical operations"
2684 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2685 (logior (logand new mask)
2686 (logand int (lognot mask)))))
2688 (deftransform %deposit-field ((new size posn int)
2690 (signed-byte #.sb!vm:word-bits))
2691 "convert to inline logical operations"
2692 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2693 (logior (logand new mask)
2694 (logand int (lognot mask)))))
2696 ;;; miscellanous numeric transforms
2698 ;;; If a constant appears as the first arg, swap the args.
2699 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2700 (if (and (constant-continuation-p x)
2701 (not (constant-continuation-p y)))
2702 `(,(continuation-function-name (basic-combination-fun node))
2704 ,(continuation-value x))
2705 (give-up-ir1-transform)))
2707 (dolist (x '(= char= + * logior logand logxor))
2708 (%deftransform x '(function * *) #'commutative-arg-swap
2709 "place constant arg last."))
2711 ;;; Handle the case of a constant BOOLE-CODE.
2712 (deftransform boole ((op x y) * * :when :both)
2713 "convert to inline logical operations"
2714 (unless (constant-continuation-p op)
2715 (give-up-ir1-transform "BOOLE code is not a constant."))
2716 (let ((control (continuation-value op)))
2722 (#.boole-c1 '(lognot x))
2723 (#.boole-c2 '(lognot y))
2724 (#.boole-and '(logand x y))
2725 (#.boole-ior '(logior x y))
2726 (#.boole-xor '(logxor x y))
2727 (#.boole-eqv '(logeqv x y))
2728 (#.boole-nand '(lognand x y))
2729 (#.boole-nor '(lognor x y))
2730 (#.boole-andc1 '(logandc1 x y))
2731 (#.boole-andc2 '(logandc2 x y))
2732 (#.boole-orc1 '(logorc1 x y))
2733 (#.boole-orc2 '(logorc2 x y))
2735 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2738 ;;;; converting special case multiply/divide to shifts
2740 ;;; If arg is a constant power of two, turn * into a shift.
2741 (deftransform * ((x y) (integer integer) * :when :both)
2742 "convert x*2^k to shift"
2743 (unless (constant-continuation-p y)
2744 (give-up-ir1-transform))
2745 (let* ((y (continuation-value y))
2747 (len (1- (integer-length y-abs))))
2748 (unless (= y-abs (ash 1 len))
2749 (give-up-ir1-transform))
2754 ;;; If both arguments and the result are (UNSIGNED-BYTE 32), try to
2755 ;;; come up with a ``better'' multiplication using multiplier
2756 ;;; recoding. There are two different ways the multiplier can be
2757 ;;; recoded. The more obvious is to shift X by the correct amount for
2758 ;;; each bit set in Y and to sum the results. But if there is a string
2759 ;;; of bits that are all set, you can add X shifted by one more then
2760 ;;; the bit position of the first set bit and subtract X shifted by
2761 ;;; the bit position of the last set bit. We can't use this second
2762 ;;; method when the high order bit is bit 31 because shifting by 32
2763 ;;; doesn't work too well.
2764 (deftransform * ((x y)
2765 ((unsigned-byte 32) (unsigned-byte 32))
2767 "recode as shift and add"
2768 (unless (constant-continuation-p y)
2769 (give-up-ir1-transform))
2770 (let ((y (continuation-value y))
2773 (labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x))
2778 `(+ ,result ,(tub32 next-factor))
2780 (declare (inline add))
2781 (dotimes (bitpos 32)
2783 (when (not (logbitp bitpos y))
2784 (add (if (= (1+ first-one) bitpos)
2785 ;; There is only a single bit in the string.
2787 ;; There are at least two.
2788 `(- ,(tub32 `(ash x ,bitpos))
2789 ,(tub32 `(ash x ,first-one)))))
2790 (setf first-one nil))
2791 (when (logbitp bitpos y)
2792 (setf first-one bitpos))))
2794 (cond ((= first-one 31))
2798 (add `(- ,(tub32 '(ash x 31)) ,(tub32 `(ash x ,first-one))))))
2802 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2803 ;;; mask. If CEILING, add in (1- (ABS Y)) and then do FLOOR.
2804 (flet ((frob (y ceil-p)
2805 (unless (constant-continuation-p y)
2806 (give-up-ir1-transform))
2807 (let* ((y (continuation-value y))
2809 (len (1- (integer-length y-abs))))
2810 (unless (= y-abs (ash 1 len))
2811 (give-up-ir1-transform))
2812 (let ((shift (- len))
2814 `(let ,(when ceil-p `((x (+ x ,(1- y-abs)))))
2816 `(values (ash (- x) ,shift)
2817 (- (logand (- x) ,mask)))
2818 `(values (ash x ,shift)
2819 (logand x ,mask))))))))
2820 (deftransform floor ((x y) (integer integer) *)
2821 "convert division by 2^k to shift"
2823 (deftransform ceiling ((x y) (integer integer) *)
2824 "convert division by 2^k to shift"
2827 ;;; Do the same for MOD.
2828 (deftransform mod ((x y) (integer integer) * :when :both)
2829 "convert remainder mod 2^k to LOGAND"
2830 (unless (constant-continuation-p y)
2831 (give-up-ir1-transform))
2832 (let* ((y (continuation-value y))
2834 (len (1- (integer-length y-abs))))
2835 (unless (= y-abs (ash 1 len))
2836 (give-up-ir1-transform))
2837 (let ((mask (1- y-abs)))
2839 `(- (logand (- x) ,mask))
2840 `(logand x ,mask)))))
2842 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2843 (deftransform truncate ((x y) (integer integer))
2844 "convert division by 2^k to shift"
2845 (unless (constant-continuation-p y)
2846 (give-up-ir1-transform))
2847 (let* ((y (continuation-value y))
2849 (len (1- (integer-length y-abs))))
2850 (unless (= y-abs (ash 1 len))
2851 (give-up-ir1-transform))
2852 (let* ((shift (- len))
2855 (values ,(if (minusp y)
2857 `(- (ash (- x) ,shift)))
2858 (- (logand (- x) ,mask)))
2859 (values ,(if (minusp y)
2860 `(- (ash (- x) ,shift))
2862 (logand x ,mask))))))
2864 ;;; And the same for REM.
2865 (deftransform rem ((x y) (integer integer) * :when :both)
2866 "convert remainder mod 2^k to LOGAND"
2867 (unless (constant-continuation-p y)
2868 (give-up-ir1-transform))
2869 (let* ((y (continuation-value y))
2871 (len (1- (integer-length y-abs))))
2872 (unless (= y-abs (ash 1 len))
2873 (give-up-ir1-transform))
2874 (let ((mask (1- y-abs)))
2876 (- (logand (- x) ,mask))
2877 (logand x ,mask)))))
2879 ;;;; arithmetic and logical identity operation elimination
2881 ;;;; Flush calls to various arith functions that convert to the
2882 ;;;; identity function or a constant.
2884 (dolist (stuff '((ash 0 x)
2889 (logxor -1 (lognot x))
2891 (destructuring-bind (name identity result) stuff
2892 (deftransform name ((x y) `(* (constant-argument (member ,identity))) '*
2893 :eval-name t :when :both)
2894 "fold identity operations"
2897 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2898 ;;; (* 0 -4.0) is -0.0.
2899 (deftransform - ((x y) ((constant-argument (member 0)) rational) *
2901 "convert (- 0 x) to negate"
2903 (deftransform * ((x y) (rational (constant-argument (member 0))) *
2905 "convert (* x 0) to 0."
2908 ;;; Return T if in an arithmetic op including continuations X and Y,
2909 ;;; the result type is not affected by the type of X. That is, Y is at
2910 ;;; least as contagious as X.
2912 (defun not-more-contagious (x y)
2913 (declare (type continuation x y))
2914 (let ((x (continuation-type x))
2915 (y (continuation-type y)))
2916 (values (type= (numeric-contagion x y)
2917 (numeric-contagion y y)))))
2918 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2919 ;;; XXX needs more work as valid transforms are missed; some cases are
2920 ;;; specific to particular transform functions so the use of this
2921 ;;; function may need a re-think.
2922 (defun not-more-contagious (x y)
2923 (declare (type continuation x y))
2924 (flet ((simple-numeric-type (num)
2925 (and (numeric-type-p num)
2926 ;; Return non-NIL if NUM is integer, rational, or a float
2927 ;; of some type (but not FLOAT)
2928 (case (numeric-type-class num)
2932 (numeric-type-format num))
2935 (let ((x (continuation-type x))
2936 (y (continuation-type y)))
2937 (if (and (simple-numeric-type x)
2938 (simple-numeric-type y))
2939 (values (type= (numeric-contagion x y)
2940 (numeric-contagion y y)))))))
2944 ;;; If y is not constant, not zerop, or is contagious, or a positive
2945 ;;; float +0.0 then give up.
2946 (deftransform + ((x y) (t (constant-argument t)) * :when :both)
2948 (let ((val (continuation-value y)))
2949 (unless (and (zerop val)
2950 (not (and (floatp val) (plusp (float-sign val))))
2951 (not-more-contagious y x))
2952 (give-up-ir1-transform)))
2957 ;;; If y is not constant, not zerop, or is contagious, or a negative
2958 ;;; float -0.0 then give up.
2959 (deftransform - ((x y) (t (constant-argument t)) * :when :both)
2961 (let ((val (continuation-value y)))
2962 (unless (and (zerop val)
2963 (not (and (floatp val) (minusp (float-sign val))))
2964 (not-more-contagious y x))
2965 (give-up-ir1-transform)))
2968 ;;; Fold (OP x +/-1)
2969 (dolist (stuff '((* x (%negate x))
2972 (destructuring-bind (name result minus-result) stuff
2973 (deftransform name ((x y) '(t (constant-argument real)) '* :eval-name t
2975 "fold identity operations"
2976 (let ((val (continuation-value y)))
2977 (unless (and (= (abs val) 1)
2978 (not-more-contagious y x))
2979 (give-up-ir1-transform))
2980 (if (minusp val) minus-result result)))))
2982 ;;; Fold (expt x n) into multiplications for small integral values of
2983 ;;; N; convert (expt x 1/2) to sqrt.
2984 (deftransform expt ((x y) (t (constant-argument real)) *)
2985 "recode as multiplication or sqrt"
2986 (let ((val (continuation-value y)))
2987 ;; If Y would cause the result to be promoted to the same type as
2988 ;; Y, we give up. If not, then the result will be the same type
2989 ;; as X, so we can replace the exponentiation with simple
2990 ;; multiplication and division for small integral powers.
2991 (unless (not-more-contagious y x)
2992 (give-up-ir1-transform))
2993 (cond ((zerop val) '(float 1 x))
2994 ((= val 2) '(* x x))
2995 ((= val -2) '(/ (* x x)))
2996 ((= val 3) '(* x x x))
2997 ((= val -3) '(/ (* x x x)))
2998 ((= val 1/2) '(sqrt x))
2999 ((= val -1/2) '(/ (sqrt x)))
3000 (t (give-up-ir1-transform)))))
3002 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3003 ;;; transformations?
3004 ;;; Perhaps we should have to prove that the denominator is nonzero before
3005 ;;; doing them? (Also the DOLIST over macro calls is weird. Perhaps
3006 ;;; just FROB?) -- WHN 19990917
3008 ;;; FIXME: What gives with the single quotes in the argument lists
3009 ;;; for DEFTRANSFORMs here? Does that work? Is it needed? Why?
3010 (dolist (name '(ash /))
3011 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3012 :eval-name t :when :both)
3015 (dolist (name '(truncate round floor ceiling))
3016 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3017 :eval-name t :when :both)
3021 ;;;; character operations
3023 (deftransform char-equal ((a b) (base-char base-char))
3025 '(let* ((ac (char-code a))
3027 (sum (logxor ac bc)))
3029 (when (eql sum #x20)
3030 (let ((sum (+ ac bc)))
3031 (and (> sum 161) (< sum 213)))))))
3033 (deftransform char-upcase ((x) (base-char))
3035 '(let ((n-code (char-code x)))
3036 (if (and (> n-code #o140) ; Octal 141 is #\a.
3037 (< n-code #o173)) ; Octal 172 is #\z.
3038 (code-char (logxor #x20 n-code))
3041 (deftransform char-downcase ((x) (base-char))
3043 '(let ((n-code (char-code x)))
3044 (if (and (> n-code 64) ; 65 is #\A.
3045 (< n-code 91)) ; 90 is #\Z.
3046 (code-char (logxor #x20 n-code))
3049 ;;;; equality predicate transforms
3051 ;;; Return true if X and Y are continuations whose only use is a
3052 ;;; reference to the same leaf, and the value of the leaf cannot
3054 (defun same-leaf-ref-p (x y)
3055 (declare (type continuation x y))
3056 (let ((x-use (continuation-use x))
3057 (y-use (continuation-use y)))
3060 (eq (ref-leaf x-use) (ref-leaf y-use))
3061 (constant-reference-p x-use))))
3063 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3064 ;;; if there is no intersection between the types of the arguments,
3065 ;;; then the result is definitely false.
3066 (deftransform simple-equality-transform ((x y) * *
3069 (cond ((same-leaf-ref-p x y)
3071 ((not (types-equal-or-intersect (continuation-type x)
3072 (continuation-type y)))
3075 (give-up-ir1-transform))))
3077 (dolist (x '(eq char= equal))
3078 (%deftransform x '(function * *) #'simple-equality-transform))
3080 ;;; Similar to SIMPLE-EQUALITY-PREDICATE, except that we also try to
3081 ;;; convert to a type-specific predicate or EQ:
3082 ;;; -- If both args are characters, convert to CHAR=. This is better than
3083 ;;; just converting to EQ, since CHAR= may have special compilation
3084 ;;; strategies for non-standard representations, etc.
3085 ;;; -- If either arg is definitely not a number, then we can compare
3087 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3088 ;;; is constant then we put it second. If X is a subtype of Y, we put
3089 ;;; it second. These rules make it easier for the back end to match
3090 ;;; these interesting cases.
3091 ;;; -- If Y is a fixnum, then we quietly pass because the back end can
3092 ;;; handle that case, otherwise give an efficency note.
3093 (deftransform eql ((x y) * * :when :both)
3094 "convert to simpler equality predicate"
3095 (let ((x-type (continuation-type x))
3096 (y-type (continuation-type y))
3097 (char-type (specifier-type 'character))
3098 (number-type (specifier-type 'number)))
3099 (cond ((same-leaf-ref-p x y)
3101 ((not (types-equal-or-intersect x-type y-type))
3103 ((and (csubtypep x-type char-type)
3104 (csubtypep y-type char-type))
3106 ((or (not (types-equal-or-intersect x-type number-type))
3107 (not (types-equal-or-intersect y-type number-type)))
3109 ((and (not (constant-continuation-p y))
3110 (or (constant-continuation-p x)
3111 (and (csubtypep x-type y-type)
3112 (not (csubtypep y-type x-type)))))
3115 (give-up-ir1-transform)))))
3117 ;;; Convert to EQL if both args are rational and complexp is specified
3118 ;;; and the same for both.
3119 (deftransform = ((x y) * * :when :both)
3121 (let ((x-type (continuation-type x))
3122 (y-type (continuation-type y)))
3123 (if (and (csubtypep x-type (specifier-type 'number))
3124 (csubtypep y-type (specifier-type 'number)))
3125 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3126 (csubtypep y-type (specifier-type 'float)))
3127 (and (csubtypep x-type (specifier-type '(complex float)))
3128 (csubtypep y-type (specifier-type '(complex float)))))
3129 ;; They are both floats. Leave as = so that -0.0 is
3130 ;; handled correctly.
3131 (give-up-ir1-transform))
3132 ((or (and (csubtypep x-type (specifier-type 'rational))
3133 (csubtypep y-type (specifier-type 'rational)))
3134 (and (csubtypep x-type
3135 (specifier-type '(complex rational)))
3137 (specifier-type '(complex rational)))))
3138 ;; They are both rationals and complexp is the same.
3142 (give-up-ir1-transform
3143 "The operands might not be the same type.")))
3144 (give-up-ir1-transform
3145 "The operands might not be the same type."))))
3147 ;;; If CONT's type is a numeric type, then return the type, otherwise
3148 ;;; GIVE-UP-IR1-TRANSFORM.
3149 (defun numeric-type-or-lose (cont)
3150 (declare (type continuation cont))
3151 (let ((res (continuation-type cont)))
3152 (unless (numeric-type-p res) (give-up-ir1-transform))
3155 ;;; See whether we can statically determine (< X Y) using type
3156 ;;; information. If X's high bound is < Y's low, then X < Y.
3157 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3158 ;;; NIL). If not, at least make sure any constant arg is second.
3160 ;;; FIXME: Why should constant argument be second? It would be nice to
3161 ;;; find out and explain.
3162 #!-sb-propagate-float-type
3163 (defun ir1-transform-< (x y first second inverse)
3164 (if (same-leaf-ref-p x y)
3166 (let* ((x-type (numeric-type-or-lose x))
3167 (x-lo (numeric-type-low x-type))
3168 (x-hi (numeric-type-high x-type))
3169 (y-type (numeric-type-or-lose y))
3170 (y-lo (numeric-type-low y-type))
3171 (y-hi (numeric-type-high y-type)))
3172 (cond ((and x-hi y-lo (< x-hi y-lo))
3174 ((and y-hi x-lo (>= x-lo y-hi))
3176 ((and (constant-continuation-p first)
3177 (not (constant-continuation-p second)))
3180 (give-up-ir1-transform))))))
3181 #!+sb-propagate-float-type
3182 (defun ir1-transform-< (x y first second inverse)
3183 (if (same-leaf-ref-p x y)
3185 (let ((xi (numeric-type->interval (numeric-type-or-lose x)))
3186 (yi (numeric-type->interval (numeric-type-or-lose y))))
3187 (cond ((interval-< xi yi)
3189 ((interval->= xi yi)
3191 ((and (constant-continuation-p first)
3192 (not (constant-continuation-p second)))
3195 (give-up-ir1-transform))))))
3197 (deftransform < ((x y) (integer integer) * :when :both)
3198 (ir1-transform-< x y x y '>))
3200 (deftransform > ((x y) (integer integer) * :when :both)
3201 (ir1-transform-< y x x y '<))
3203 #!+sb-propagate-float-type
3204 (deftransform < ((x y) (float float) * :when :both)
3205 (ir1-transform-< x y x y '>))
3207 #!+sb-propagate-float-type
3208 (deftransform > ((x y) (float float) * :when :both)
3209 (ir1-transform-< y x x y '<))
3211 ;;;; converting N-arg comparisons
3213 ;;;; We convert calls to N-arg comparison functions such as < into
3214 ;;;; two-arg calls. This transformation is enabled for all such
3215 ;;;; comparisons in this file. If any of these predicates are not
3216 ;;;; open-coded, then the transformation should be removed at some
3217 ;;;; point to avoid pessimization.
3219 ;;; This function is used for source transformation of N-arg
3220 ;;; comparison functions other than inequality. We deal both with
3221 ;;; converting to two-arg calls and inverting the sense of the test,
3222 ;;; if necessary. If the call has two args, then we pass or return a
3223 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3224 ;;; then we transform to code that returns true. Otherwise, we bind
3225 ;;; all the arguments and expand into a bunch of IFs.
3226 (declaim (ftype (function (symbol list boolean) *) multi-compare))
3227 (defun multi-compare (predicate args not-p)
3228 (let ((nargs (length args)))
3229 (cond ((< nargs 1) (values nil t))
3230 ((= nargs 1) `(progn ,@args t))
3233 `(if (,predicate ,(first args) ,(second args)) nil t)
3236 (do* ((i (1- nargs) (1- i))
3238 (current (gensym) (gensym))
3239 (vars (list current) (cons current vars))
3241 `(if (,predicate ,current ,last)
3243 `(if (,predicate ,current ,last)
3246 `((lambda ,vars ,result) . ,args)))))))
3248 (def-source-transform = (&rest args) (multi-compare '= args nil))
3249 (def-source-transform < (&rest args) (multi-compare '< args nil))
3250 (def-source-transform > (&rest args) (multi-compare '> args nil))
3251 (def-source-transform <= (&rest args) (multi-compare '> args t))
3252 (def-source-transform >= (&rest args) (multi-compare '< args t))
3254 (def-source-transform char= (&rest args) (multi-compare 'char= args nil))
3255 (def-source-transform char< (&rest args) (multi-compare 'char< args nil))
3256 (def-source-transform char> (&rest args) (multi-compare 'char> args nil))
3257 (def-source-transform char<= (&rest args) (multi-compare 'char> args t))
3258 (def-source-transform char>= (&rest args) (multi-compare 'char< args t))
3260 (def-source-transform char-equal (&rest args)
3261 (multi-compare 'char-equal args nil))
3262 (def-source-transform char-lessp (&rest args)
3263 (multi-compare 'char-lessp args nil))
3264 (def-source-transform char-greaterp (&rest args)
3265 (multi-compare 'char-greaterp args nil))
3266 (def-source-transform char-not-greaterp (&rest args)
3267 (multi-compare 'char-greaterp args t))
3268 (def-source-transform char-not-lessp (&rest args)
3269 (multi-compare 'char-lessp args t))
3271 ;;; This function does source transformation of N-arg inequality
3272 ;;; functions such as /=. This is similar to Multi-Compare in the <3
3273 ;;; arg cases. If there are more than two args, then we expand into
3274 ;;; the appropriate n^2 comparisons only when speed is important.
3275 (declaim (ftype (function (symbol list) *) multi-not-equal))
3276 (defun multi-not-equal (predicate args)
3277 (let ((nargs (length args)))
3278 (cond ((< nargs 1) (values nil t))
3279 ((= nargs 1) `(progn ,@args t))
3281 `(if (,predicate ,(first args) ,(second args)) nil t))
3282 ((not (policy *lexenv*
3283 (and (>= speed space)
3284 (>= speed compilation-speed))))
3287 (let ((vars (make-gensym-list nargs)))
3288 (do ((var vars next)
3289 (next (cdr vars) (cdr next))
3292 `((lambda ,vars ,result) . ,args))
3293 (let ((v1 (first var)))
3295 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3297 (def-source-transform /= (&rest args) (multi-not-equal '= args))
3298 (def-source-transform char/= (&rest args) (multi-not-equal 'char= args))
3299 (def-source-transform char-not-equal (&rest args)
3300 (multi-not-equal 'char-equal args))
3302 ;;; Expand MAX and MIN into the obvious comparisons.
3303 (def-source-transform max (arg &rest more-args)
3304 (if (null more-args)
3306 (once-only ((arg1 arg)
3307 (arg2 `(max ,@more-args)))
3308 `(if (> ,arg1 ,arg2)
3310 (def-source-transform min (arg &rest more-args)
3311 (if (null more-args)
3313 (once-only ((arg1 arg)
3314 (arg2 `(min ,@more-args)))
3315 `(if (< ,arg1 ,arg2)
3318 ;;;; converting N-arg arithmetic functions
3320 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3321 ;;;; versions, and degenerate cases are flushed.
3323 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3324 (declaim (ftype (function (symbol t list) list) associate-arguments))
3325 (defun associate-arguments (function first-arg more-args)
3326 (let ((next (rest more-args))
3327 (arg (first more-args)))
3329 `(,function ,first-arg ,arg)
3330 (associate-arguments function `(,function ,first-arg ,arg) next))))
3332 ;;; Do source transformations for transitive functions such as +.
3333 ;;; One-arg cases are replaced with the arg and zero arg cases with
3334 ;;; the identity. If LEAF-FUN is true, then replace two-arg calls with
3335 ;;; a call to that function.
3336 (defun source-transform-transitive (fun args identity &optional leaf-fun)
3337 (declare (symbol fun leaf-fun) (list args))
3340 (1 `(values ,(first args)))
3342 `(,leaf-fun ,(first args) ,(second args))
3345 (associate-arguments fun (first args) (rest args)))))
3347 (def-source-transform + (&rest args) (source-transform-transitive '+ args 0))
3348 (def-source-transform * (&rest args) (source-transform-transitive '* args 1))
3349 (def-source-transform logior (&rest args)
3350 (source-transform-transitive 'logior args 0))
3351 (def-source-transform logxor (&rest args)
3352 (source-transform-transitive 'logxor args 0))
3353 (def-source-transform logand (&rest args)
3354 (source-transform-transitive 'logand args -1))
3356 (def-source-transform logeqv (&rest args)
3357 (if (evenp (length args))
3358 `(lognot (logxor ,@args))
3361 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3362 ;;; because when they are given one argument, they return its absolute
3365 (def-source-transform gcd (&rest args)
3368 (1 `(abs (the integer ,(first args))))
3370 (t (associate-arguments 'gcd (first args) (rest args)))))
3372 (def-source-transform lcm (&rest args)
3375 (1 `(abs (the integer ,(first args))))
3377 (t (associate-arguments 'lcm (first args) (rest args)))))
3379 ;;; Do source transformations for intransitive n-arg functions such as
3380 ;;; /. With one arg, we form the inverse. With two args we pass.
3381 ;;; Otherwise we associate into two-arg calls.
3382 (declaim (ftype (function (symbol list t) list) source-transform-intransitive))
3383 (defun source-transform-intransitive (function args inverse)
3385 ((0 2) (values nil t))
3386 (1 `(,@inverse ,(first args)))
3387 (t (associate-arguments function (first args) (rest args)))))
3389 (def-source-transform - (&rest args)
3390 (source-transform-intransitive '- args '(%negate)))
3391 (def-source-transform / (&rest args)
3392 (source-transform-intransitive '/ args '(/ 1)))
3394 ;;;; transforming APPLY
3396 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3397 ;;; only needs to understand one kind of variable-argument call. It is
3398 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3399 (def-source-transform apply (fun arg &rest more-args)
3400 (let ((args (cons arg more-args)))
3401 `(multiple-value-call ,fun
3402 ,@(mapcar #'(lambda (x)
3405 (values-list ,(car (last args))))))
3407 ;;;; transforming FORMAT
3409 ;;;; If the control string is a compile-time constant, then replace it
3410 ;;;; with a use of the FORMATTER macro so that the control string is
3411 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3412 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3413 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3415 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3416 :policy (> speed space))
3417 (unless (constant-continuation-p control)
3418 (give-up-ir1-transform "The control string is not a constant."))
3419 (let ((arg-names (make-gensym-list (length args))))
3420 `(lambda (dest control ,@arg-names)
3421 (declare (ignore control))
3422 (format dest (formatter ,(continuation-value control)) ,@arg-names))))
3424 (deftransform format ((stream control &rest args) (stream function &rest t) *
3425 :policy (> speed space))
3426 (let ((arg-names (make-gensym-list (length args))))
3427 `(lambda (stream control ,@arg-names)
3428 (funcall control stream ,@arg-names)
3431 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3432 :policy (> speed space))
3433 (let ((arg-names (make-gensym-list (length args))))
3434 `(lambda (tee control ,@arg-names)
3435 (declare (ignore tee))
3436 (funcall control *standard-output* ,@arg-names)
3439 (defoptimizer (coerce derive-type) ((value type))
3440 (let ((value-type (continuation-type value))
3441 (type-type (continuation-type type)))
3442 #!+sb-show (format t "~&coerce-derive-type value-type ~A type-type ~A~%"
3443 value-type type-type)
3445 ((good-cons-type-p (cons-type)
3446 ;; Make sure the cons-type we're looking at is something
3447 ;; we're prepared to handle which is basically something
3448 ;; that array-element-type can return.
3449 (or (and (member-type-p cons-type)
3450 (null (rest (member-type-members cons-type)))
3451 (null (first (member-type-members cons-type))))
3452 (let ((car-type (cons-type-car-type cons-type)))
3453 (and (member-type-p car-type)
3454 (null (rest (member-type-members car-type)))
3455 (or (symbolp (first (member-type-members car-type)))
3456 (numberp (first (member-type-members car-type)))
3457 (and (listp (first (member-type-members car-type)))
3458 (numberp (first (first (member-type-members
3460 (good-cons-type-p (cons-type-cdr-type cons-type))))))
3461 (unconsify-type (good-cons-type)
3462 ;; Convert the "printed" respresentation of a cons
3463 ;; specifier into a type specifier. That is, the specifier
3464 ;; (cons (eql signed-byte) (cons (eql 16) null)) is
3465 ;; converted to (signed-byte 16).
3466 (cond ((or (null good-cons-type)
3467 (eq good-cons-type 'null))
3469 ((and (eq (first good-cons-type) 'cons)
3470 (eq (first (second good-cons-type)) 'member))
3471 `(,(second (second good-cons-type))
3472 ,@(unconsify-type (caddr good-cons-type))))))
3473 (coerceable-p (c-type)
3474 ;; Can the value be coerced to the given type? Coerce is
3475 ;; complicated, so we don't handle every possible case
3476 ;; here---just the most common and easiest cases:
3478 ;; o Any real can be coerced to a float type.
3479 ;; o Any number can be coerced to a complex single/double-float.
3480 ;; o An integer can be coerced to an integer.
3481 (let ((coerced-type c-type))
3482 (or (and (subtypep coerced-type 'float)
3483 (csubtypep value-type (specifier-type 'real)))
3484 (and (subtypep coerced-type
3485 '(or (complex single-float)
3486 (complex double-float)))
3487 (csubtypep value-type (specifier-type 'number)))
3488 (and (subtypep coerced-type 'integer)
3489 (csubtypep value-type (specifier-type 'integer))))))
3490 (process-types (type)
3492 ;; This needs some work because we should be able to derive
3493 ;; the resulting type better than just the type arg of
3494 ;; coerce. That is, if x is (integer 10 20), the (coerce x
3495 ;; 'double-float) should say (double-float 10d0 20d0)
3496 ;; instead of just double-float.
3497 (cond ((member-type-p type)
3498 (let ((members (member-type-members type)))
3499 (if (every #'coerceable-p members)
3500 (specifier-type `(or ,@members))
3502 ((and (cons-type-p type)
3503 (good-cons-type-p type))
3504 (let ((c-type (unconsify-type (type-specifier type))))
3505 (if (coerceable-p c-type)
3506 (specifier-type c-type)
3509 *universal-type*))))
3510 (cond ((union-type-p type-type)
3511 (apply #'type-union (mapcar #'process-types
3512 (union-type-types type-type))))
3513 ((or (member-type-p type-type)
3514 (cons-type-p type-type))
3515 (process-types type-type))
3517 *universal-type*)))))
3519 (defoptimizer (array-element-type derive-type) ((array))
3520 (let* ((array-type (continuation-type array)))
3522 (format t "~& defoptimizer array-elt-derive-type - array-element-type ~~
3524 (labels ((consify (list)
3527 `(cons (eql ,(car list)) ,(consify (rest list)))))
3528 (get-element-type (a)
3529 (let ((element-type (type-specifier
3530 (array-type-specialized-element-type a))))
3531 (cond ((symbolp element-type)
3532 (make-member-type :members (list element-type)))
3533 ((consp element-type)
3534 (specifier-type (consify element-type)))
3536 (error "Can't grok type ~A~%" element-type))))))
3537 (cond ((array-type-p array-type)
3538 (get-element-type array-type))
3539 ((union-type-p array-type)
3541 (mapcar #'get-element-type (union-type-types array-type))))
3543 *universal-type*)))))
3545 ;;;; debuggers' little helpers
3547 ;;; for debugging when transforms are behaving mysteriously,
3548 ;;; e.g. when debugging a problem with an ASH transform
3549 ;;; (defun foo (&optional s)
3550 ;;; (sb-c::/report-continuation s "S outside WHEN")
3551 ;;; (when (and (integerp s) (> s 3))
3552 ;;; (sb-c::/report-continuation s "S inside WHEN")
3553 ;;; (let ((bound (ash 1 (1- s))))
3554 ;;; (sb-c::/report-continuation bound "BOUND")
3555 ;;; (let ((x (- bound))
3557 ;;; (sb-c::/report-continuation x "X")
3558 ;;; (sb-c::/report-continuation x "Y"))
3559 ;;; `(integer ,(- bound) ,(1- bound)))))
3560 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
3561 ;;; and the function doesn't do anything at all.)
3564 (defknown /report-continuation (t t) null)
3565 (deftransform /report-continuation ((x message) (t t))
3566 (format t "~%/in /REPORT-CONTINUATION~%")
3567 (format t "/(CONTINUATION-TYPE X)=~S~%" (continuation-type x))
3568 (when (constant-continuation-p x)
3569 (format t "/(CONTINUATION-VALUE X)=~S~%" (continuation-value x)))
3570 (format t "/MESSAGE=~S~%" (continuation-value message))
3571 (give-up-ir1-transform "not a real transform"))
3572 (defun /report-continuation (&rest rest)
3573 (declare (ignore rest))))