1 ;;;; This file contains macro-like source transformations which
2 ;;;; convert uses of certain functions into the canonical form desired
3 ;;;; within the compiler. ### and other IR1 transforms and stuff.
5 ;;;; This software is part of the SBCL system. See the README file for
8 ;;;; This software is derived from the CMU CL system, which was
9 ;;;; written at Carnegie Mellon University and released into the
10 ;;;; public domain. The software is in the public domain and is
11 ;;;; provided with absolutely no warranty. See the COPYING and CREDITS
12 ;;;; files for more information.
16 ;;; Convert into an IF so that IF optimizations will eliminate redundant
18 (def-source-transform not (x) `(if ,x nil t))
19 (def-source-transform null (x) `(if ,x nil t))
21 ;;; ENDP is just NULL with a LIST assertion. The assertion will be
22 ;;; optimized away when SAFETY optimization is low; hopefully that
23 ;;; is consistent with ANSI's "should return an error".
24 (def-source-transform endp (x) `(null (the list ,x)))
26 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
27 ;;; returns the first value of its argument. Ditto for VALUES with one
29 (def-source-transform identity (x) `(prog1 ,x))
30 (def-source-transform values (x) `(prog1 ,x))
32 ;;; Bind the values and make a closure that returns them.
33 (def-source-transform constantly (value)
34 (let ((rest (gensym "CONSTANTLY-REST-")))
35 `(lambda (&rest ,rest)
36 (declare (ignore ,rest))
39 ;;; If the function has a known number of arguments, then return a
40 ;;; lambda with the appropriate fixed number of args. If the
41 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
42 ;;; MV optimization figure things out.
43 (deftransform complement ((fun) * * :node node :when :both)
45 (multiple-value-bind (min max)
46 (function-type-nargs (continuation-type fun))
48 ((and min (eql min max))
49 (let ((dums (make-gensym-list min)))
50 `#'(lambda ,dums (not (funcall fun ,@dums)))))
51 ((let* ((cont (node-cont node))
52 (dest (continuation-dest cont)))
53 (and (combination-p dest)
54 (eq (combination-fun dest) cont)))
55 '#'(lambda (&rest args)
56 (not (apply fun args))))
58 (give-up-ir1-transform
59 "The function doesn't have a fixed argument count.")))))
63 ;;; Translate CxxR into CAR/CDR combos.
65 (defun source-transform-cxr (form)
66 (if (or (byte-compiling) (/= (length form) 2))
68 (let ((name (symbol-name (car form))))
69 (do ((i (- (length name) 2) (1- i))
71 `(,(ecase (char name i)
78 (b '(1 0) (cons i b)))
80 (dotimes (j (ash 1 i))
81 (setf (info :function :source-transform
82 (intern (format nil "C~{~:[A~;D~]~}R"
83 (mapcar #'(lambda (x) (logbitp x j)) b))))
84 #'source-transform-cxr)))
86 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
87 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
88 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
90 (def-source-transform first (x) `(car ,x))
91 (def-source-transform rest (x) `(cdr ,x))
92 (def-source-transform second (x) `(cadr ,x))
93 (def-source-transform third (x) `(caddr ,x))
94 (def-source-transform fourth (x) `(cadddr ,x))
95 (def-source-transform fifth (x) `(nth 4 ,x))
96 (def-source-transform sixth (x) `(nth 5 ,x))
97 (def-source-transform seventh (x) `(nth 6 ,x))
98 (def-source-transform eighth (x) `(nth 7 ,x))
99 (def-source-transform ninth (x) `(nth 8 ,x))
100 (def-source-transform tenth (x) `(nth 9 ,x))
102 ;;; Translate RPLACx to LET and SETF.
103 (def-source-transform rplaca (x y)
108 (def-source-transform rplacd (x y)
114 (def-source-transform nth (n l) `(car (nthcdr ,n ,l)))
116 (defvar *default-nthcdr-open-code-limit* 6)
117 (defvar *extreme-nthcdr-open-code-limit* 20)
119 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
120 "convert NTHCDR to CAxxR"
121 (unless (constant-continuation-p n)
122 (give-up-ir1-transform))
123 (let ((n (continuation-value n)))
125 (if (policy node (and (= speed 3) (= space 0)))
126 *extreme-nthcdr-open-code-limit*
127 *default-nthcdr-open-code-limit*))
128 (give-up-ir1-transform))
133 `(cdr ,(frob (1- n))))))
136 ;;;; arithmetic and numerology
138 (def-source-transform plusp (x) `(> ,x 0))
139 (def-source-transform minusp (x) `(< ,x 0))
140 (def-source-transform zerop (x) `(= ,x 0))
142 (def-source-transform 1+ (x) `(+ ,x 1))
143 (def-source-transform 1- (x) `(- ,x 1))
145 (def-source-transform oddp (x) `(not (zerop (logand ,x 1))))
146 (def-source-transform evenp (x) `(zerop (logand ,x 1)))
148 ;;; Note that all the integer division functions are available for
149 ;;; inline expansion.
151 ;;; FIXME: DEF-FROB instead of FROB
152 (macrolet ((frob (fun)
153 `(def-source-transform ,fun (x &optional (y nil y-p))
160 #!+propagate-float-type
162 #!+propagate-float-type
165 (def-source-transform lognand (x y) `(lognot (logand ,x ,y)))
166 (def-source-transform lognor (x y) `(lognot (logior ,x ,y)))
167 (def-source-transform logandc1 (x y) `(logand (lognot ,x) ,y))
168 (def-source-transform logandc2 (x y) `(logand ,x (lognot ,y)))
169 (def-source-transform logorc1 (x y) `(logior (lognot ,x) ,y))
170 (def-source-transform logorc2 (x y) `(logior ,x (lognot ,y)))
171 (def-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
172 (def-source-transform logbitp (index integer)
173 `(not (zerop (logand (ash 1 ,index) ,integer))))
174 (def-source-transform byte (size position) `(cons ,size ,position))
175 (def-source-transform byte-size (spec) `(car ,spec))
176 (def-source-transform byte-position (spec) `(cdr ,spec))
177 (def-source-transform ldb-test (bytespec integer)
178 `(not (zerop (mask-field ,bytespec ,integer))))
180 ;;; With the ratio and complex accessors, we pick off the "identity"
181 ;;; case, and use a primitive to handle the cell access case.
182 (def-source-transform numerator (num)
183 (once-only ((n-num `(the rational ,num)))
187 (def-source-transform denominator (num)
188 (once-only ((n-num `(the rational ,num)))
190 (%denominator ,n-num)
193 ;;;; interval arithmetic for computing bounds
195 ;;;; This is a set of routines for operating on intervals. It
196 ;;;; implements a simple interval arithmetic package. Although SBCL
197 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
198 ;;;; for two reasons:
200 ;;;; 1. This package is simpler than NUMERIC-TYPE.
202 ;;;; 2. It makes debugging much easier because you can just strip
203 ;;;; out these routines and test them independently of SBCL. (This is a
206 ;;;; One disadvantage is a probable increase in consing because we
207 ;;;; have to create these new interval structures even though
208 ;;;; numeric-type has everything we want to know. Reason 2 wins for
211 #-sb-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
213 #!+propagate-float-type
216 ;;; The basic interval type. It can handle open and closed intervals.
217 ;;; A bound is open if it is a list containing a number, just like
218 ;;; Lisp says. NIL means unbounded.
219 (defstruct (interval (:constructor %make-interval)
223 (defun make-interval (&key low high)
224 (labels ((normalize-bound (val)
225 (cond ((and (floatp val)
226 (float-infinity-p val))
227 ;; Handle infinities.
231 ;; Handle any closed bounds.
234 ;; We have an open bound. Normalize the numeric
235 ;; bound. If the normalized bound is still a number
236 ;; (not nil), keep the bound open. Otherwise, the
237 ;; bound is really unbounded, so drop the openness.
238 (let ((new-val (normalize-bound (first val))))
240 ;; The bound exists, so keep it open still.
243 (error "Unknown bound type in make-interval!")))))
244 (%make-interval :low (normalize-bound low)
245 :high (normalize-bound high))))
247 #!-sb-fluid (declaim (inline bound-value set-bound))
249 ;;; Extract the numeric value of a bound. Return NIL, if X is NIL.
250 (defun bound-value (x)
251 (if (consp x) (car x) x))
253 ;;; Given a number X, create a form suitable as a bound for an
254 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
255 (defun set-bound (x open-p)
256 (if (and x open-p) (list x) x))
258 ;;; Apply the function F to a bound X. If X is an open bound, then
259 ;;; the result will be open. IF X is NIL, the result is NIL.
260 (defun bound-func (f x)
262 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
263 ;; With these traps masked, we might get things like infinity
264 ;; or negative infinity returned. Check for this and return
265 ;; NIL to indicate unbounded.
266 (let ((y (funcall f (bound-value x))))
268 (float-infinity-p y))
270 (set-bound (funcall f (bound-value x)) (consp x)))))))
272 ;;; Apply a binary operator OP to two bounds X and Y. The result is
273 ;;; NIL if either is NIL. Otherwise bound is computed and the result
274 ;;; is open if either X or Y is open.
276 ;;; FIXME: only used in this file, not needed in target runtime
277 (defmacro bound-binop (op x y)
279 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
280 (set-bound (,op (bound-value ,x)
282 (or (consp ,x) (consp ,y))))))
284 ;;; Convert a numeric-type object to an interval object.
285 (defun numeric-type->interval (x)
286 (declare (type numeric-type x))
287 (make-interval :low (numeric-type-low x)
288 :high (numeric-type-high x)))
290 (defun copy-interval-limit (limit)
295 (defun copy-interval (x)
296 (declare (type interval x))
297 (make-interval :low (copy-interval-limit (interval-low x))
298 :high (copy-interval-limit (interval-high x))))
300 ;;; Given a point P contained in the interval X, split X into two
301 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
302 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
303 ;;; contains P. You can specify both to be T or NIL.
304 (defun interval-split (p x &optional close-lower close-upper)
305 (declare (type number p)
307 (list (make-interval :low (copy-interval-limit (interval-low x))
308 :high (if close-lower p (list p)))
309 (make-interval :low (if close-upper (list p) p)
310 :high (copy-interval-limit (interval-high x)))))
312 ;;; Return the closure of the interval. That is, convert open bounds
313 ;;; to closed bounds.
314 (defun interval-closure (x)
315 (declare (type interval x))
316 (make-interval :low (bound-value (interval-low x))
317 :high (bound-value (interval-high x))))
319 (defun signed-zero->= (x y)
323 (>= (float-sign (float x))
324 (float-sign (float y))))))
326 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
327 ;;; '-. Otherwise return NIL.
329 (defun interval-range-info (x &optional (point 0))
330 (declare (type interval x))
331 (let ((lo (interval-low x))
332 (hi (interval-high x)))
333 (cond ((and lo (signed-zero->= (bound-value lo) point))
335 ((and hi (signed-zero->= point (bound-value hi)))
339 (defun interval-range-info (x &optional (point 0))
340 (declare (type interval x))
341 (labels ((signed->= (x y)
342 (if (and (zerop x) (zerop y) (floatp x) (floatp y))
343 (>= (float-sign x) (float-sign y))
345 (let ((lo (interval-low x))
346 (hi (interval-high x)))
347 (cond ((and lo (signed->= (bound-value lo) point))
349 ((and hi (signed->= point (bound-value hi)))
354 ;;; Test to see whether the interval X is bounded. HOW determines the
355 ;;; test, and should be either ABOVE, BELOW, or BOTH.
356 (defun interval-bounded-p (x how)
357 (declare (type interval x))
364 (and (interval-low x) (interval-high x)))))
366 ;;; signed zero comparison functions. Use these functions if we need
367 ;;; to distinguish between signed zeroes.
368 (defun signed-zero-< (x y)
372 (< (float-sign (float x))
373 (float-sign (float y))))))
374 (defun signed-zero-> (x y)
378 (> (float-sign (float x))
379 (float-sign (float y))))))
380 (defun signed-zero-= (x y)
383 (= (float-sign (float x))
384 (float-sign (float y)))))
385 (defun signed-zero-<= (x y)
389 (<= (float-sign (float x))
390 (float-sign (float y))))))
392 ;;; See whether the interval X contains the number P, taking into
393 ;;; account that the interval might not be closed.
394 (defun interval-contains-p (p x)
395 (declare (type number p)
397 ;; Does the interval X contain the number P? This would be a lot
398 ;; easier if all intervals were closed!
399 (let ((lo (interval-low x))
400 (hi (interval-high x)))
402 ;; The interval is bounded
403 (if (and (signed-zero-<= (bound-value lo) p)
404 (signed-zero-<= p (bound-value hi)))
405 ;; P is definitely in the closure of the interval.
406 ;; We just need to check the end points now.
407 (cond ((signed-zero-= p (bound-value lo))
409 ((signed-zero-= p (bound-value hi))
414 ;; Interval with upper bound
415 (if (signed-zero-< p (bound-value hi))
417 (and (numberp hi) (signed-zero-= p hi))))
419 ;; Interval with lower bound
420 (if (signed-zero-> p (bound-value lo))
422 (and (numberp lo) (signed-zero-= p lo))))
424 ;; Interval with no bounds
427 ;;; Determine whether two intervals X and Y intersect. Return T if so.
428 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
429 ;;; were closed. Otherwise the intervals are treated as they are.
431 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
432 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
433 ;;; is T, then they do intersect because we use the closure of X = [0,
434 ;;; 1] and Y = [1, 2] to determine intersection.
435 (defun interval-intersect-p (x y &optional closed-intervals-p)
436 (declare (type interval x y))
437 (multiple-value-bind (intersect diff)
438 (interval-intersection/difference (if closed-intervals-p
441 (if closed-intervals-p
444 (declare (ignore diff))
447 ;;; Are the two intervals adjacent? That is, is there a number
448 ;;; between the two intervals that is not an element of either
449 ;;; interval? If so, they are not adjacent. For example [0, 1) and
450 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
451 ;;; between both intervals.
452 (defun interval-adjacent-p (x y)
453 (declare (type interval x y))
454 (flet ((adjacent (lo hi)
455 ;; Check to see whether lo and hi are adjacent. If either is
456 ;; nil, they can't be adjacent.
457 (when (and lo hi (= (bound-value lo) (bound-value hi)))
458 ;; The bounds are equal. They are adjacent if one of
459 ;; them is closed (a number). If both are open (consp),
460 ;; then there is a number that lies between them.
461 (or (numberp lo) (numberp hi)))))
462 (or (adjacent (interval-low y) (interval-high x))
463 (adjacent (interval-low x) (interval-high y)))))
465 ;;; Compute the intersection and difference between two intervals.
466 ;;; Two values are returned: the intersection and the difference.
468 ;;; Let the two intervals be X and Y, and let I and D be the two
469 ;;; values returned by this function. Then I = X intersect Y. If I
470 ;;; is NIL (the empty set), then D is X union Y, represented as the
471 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
472 ;;; - I, which is a list of two intervals.
474 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
475 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
476 (defun interval-intersection/difference (x y)
477 (declare (type interval x y))
478 (let ((x-lo (interval-low x))
479 (x-hi (interval-high x))
480 (y-lo (interval-low y))
481 (y-hi (interval-high y)))
484 ;; If p is an open bound, make it closed. If p is a closed
485 ;; bound, make it open.
490 ;; Test whether P is in the interval.
491 (when (interval-contains-p (bound-value p)
492 (interval-closure int))
493 (let ((lo (interval-low int))
494 (hi (interval-high int)))
495 ;; Check for endpoints.
496 (cond ((and lo (= (bound-value p) (bound-value lo)))
497 (not (and (consp p) (numberp lo))))
498 ((and hi (= (bound-value p) (bound-value hi)))
499 (not (and (numberp p) (consp hi))))
501 (test-lower-bound (p int)
502 ;; P is a lower bound of an interval.
505 (not (interval-bounded-p int 'below))))
506 (test-upper-bound (p int)
507 ;; P is an upper bound of an interval.
510 (not (interval-bounded-p int 'above)))))
511 (let ((x-lo-in-y (test-lower-bound x-lo y))
512 (x-hi-in-y (test-upper-bound x-hi y))
513 (y-lo-in-x (test-lower-bound y-lo x))
514 (y-hi-in-x (test-upper-bound y-hi x)))
515 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
516 ;; Intervals intersect. Let's compute the intersection
517 ;; and the difference.
518 (multiple-value-bind (lo left-lo left-hi)
519 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
520 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
521 (multiple-value-bind (hi right-lo right-hi)
523 (values x-hi (opposite-bound x-hi) y-hi))
525 (values y-hi (opposite-bound y-hi) x-hi)))
526 (values (make-interval :low lo :high hi)
527 (list (make-interval :low left-lo
529 (make-interval :low right-lo
532 (values nil (list x y))))))))
534 ;;; If intervals X and Y intersect, return a new interval that is the
535 ;;; union of the two. If they do not intersect, return NIL.
536 (defun interval-merge-pair (x y)
537 (declare (type interval x y))
538 ;; If x and y intersect or are adjacent, create the union.
539 ;; Otherwise return nil
540 (when (or (interval-intersect-p x y)
541 (interval-adjacent-p x y))
542 (flet ((select-bound (x1 x2 min-op max-op)
543 (let ((x1-val (bound-value x1))
544 (x2-val (bound-value x2)))
546 ;; Both bounds are finite. Select the right one.
547 (cond ((funcall min-op x1-val x2-val)
548 ;; x1 is definitely better.
550 ((funcall max-op x1-val x2-val)
551 ;; x2 is definitely better.
554 ;; Bounds are equal. Select either
555 ;; value and make it open only if
557 (set-bound x1-val (and (consp x1) (consp x2))))))
559 ;; At least one bound is not finite. The
560 ;; non-finite bound always wins.
562 (let* ((x-lo (copy-interval-limit (interval-low x)))
563 (x-hi (copy-interval-limit (interval-high x)))
564 (y-lo (copy-interval-limit (interval-low y)))
565 (y-hi (copy-interval-limit (interval-high y))))
566 (make-interval :low (select-bound x-lo y-lo #'< #'>)
567 :high (select-bound x-hi y-hi #'> #'<))))))
569 ;;; basic arithmetic operations on intervals. We probably should do
570 ;;; true interval arithmetic here, but it's complicated because we
571 ;;; have float and integer types and bounds can be open or closed.
573 ;;; the negative of an interval
574 (defun interval-neg (x)
575 (declare (type interval x))
576 (make-interval :low (bound-func #'- (interval-high x))
577 :high (bound-func #'- (interval-low x))))
579 ;;; Add two intervals.
580 (defun interval-add (x y)
581 (declare (type interval x y))
582 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
583 :high (bound-binop + (interval-high x) (interval-high y))))
585 ;;; Subtract two intervals.
586 (defun interval-sub (x y)
587 (declare (type interval x y))
588 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
589 :high (bound-binop - (interval-high x) (interval-low y))))
591 ;;; Multiply two intervals.
592 (defun interval-mul (x y)
593 (declare (type interval x y))
594 (flet ((bound-mul (x y)
595 (cond ((or (null x) (null y))
596 ;; Multiply by infinity is infinity
598 ((or (and (numberp x) (zerop x))
599 (and (numberp y) (zerop y)))
600 ;; Multiply by closed zero is special. The result
601 ;; is always a closed bound. But don't replace this
602 ;; with zero; we want the multiplication to produce
603 ;; the correct signed zero, if needed.
604 (* (bound-value x) (bound-value y)))
605 ((or (and (floatp x) (float-infinity-p x))
606 (and (floatp y) (float-infinity-p y)))
607 ;; Infinity times anything is infinity
610 ;; General multiply. The result is open if either is open.
611 (bound-binop * x y)))))
612 (let ((x-range (interval-range-info x))
613 (y-range (interval-range-info y)))
614 (cond ((null x-range)
615 ;; Split x into two and multiply each separately
616 (destructuring-bind (x- x+) (interval-split 0 x t t)
617 (interval-merge-pair (interval-mul x- y)
618 (interval-mul x+ y))))
620 ;; Split y into two and multiply each separately
621 (destructuring-bind (y- y+) (interval-split 0 y t t)
622 (interval-merge-pair (interval-mul x y-)
623 (interval-mul x y+))))
625 (interval-neg (interval-mul (interval-neg x) y)))
627 (interval-neg (interval-mul x (interval-neg y))))
628 ((and (eq x-range '+) (eq y-range '+))
629 ;; If we are here, X and Y are both positive
630 (make-interval :low (bound-mul (interval-low x) (interval-low y))
631 :high (bound-mul (interval-high x) (interval-high y))))
633 (error "This shouldn't happen!"))))))
635 ;;; Divide two intervals.
636 (defun interval-div (top bot)
637 (declare (type interval top bot))
638 (flet ((bound-div (x y y-low-p)
641 ;; Divide by infinity means result is 0. However,
642 ;; we need to watch out for the sign of the result,
643 ;; to correctly handle signed zeros. We also need
644 ;; to watch out for positive or negative infinity.
645 (if (floatp (bound-value x))
647 (- (float-sign (bound-value x) 0.0))
648 (float-sign (bound-value x) 0.0))
650 ((zerop (bound-value y))
651 ;; Divide by zero means result is infinity
653 ((and (numberp x) (zerop x))
654 ;; Zero divided by anything is zero.
657 (bound-binop / x y)))))
658 (let ((top-range (interval-range-info top))
659 (bot-range (interval-range-info bot)))
660 (cond ((null bot-range)
661 ;; The denominator contains zero, so anything goes!
662 (make-interval :low nil :high nil))
664 ;; Denominator is negative so flip the sign, compute the
665 ;; result, and flip it back.
666 (interval-neg (interval-div top (interval-neg bot))))
668 ;; Split top into two positive and negative parts, and
669 ;; divide each separately
670 (destructuring-bind (top- top+) (interval-split 0 top t t)
671 (interval-merge-pair (interval-div top- bot)
672 (interval-div top+ bot))))
674 ;; Top is negative so flip the sign, divide, and flip the
675 ;; sign of the result.
676 (interval-neg (interval-div (interval-neg top) bot)))
677 ((and (eq top-range '+) (eq bot-range '+))
679 (make-interval :low (bound-div (interval-low top) (interval-high bot) t)
680 :high (bound-div (interval-high top) (interval-low bot) nil)))
682 (error "This shouldn't happen!"))))))
684 ;;; Apply the function F to the interval X. If X = [a, b], then the
685 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
686 ;;; result makes sense. It will if F is monotonic increasing (or
688 (defun interval-func (f x)
689 (declare (type interval x))
690 (let ((lo (bound-func f (interval-low x)))
691 (hi (bound-func f (interval-high x))))
692 (make-interval :low lo :high hi)))
694 ;;; Return T if X < Y. That is every number in the interval X is
695 ;;; always less than any number in the interval Y.
696 (defun interval-< (x y)
697 (declare (type interval x y))
698 ;; X < Y only if X is bounded above, Y is bounded below, and they
700 (when (and (interval-bounded-p x 'above)
701 (interval-bounded-p y 'below))
702 ;; Intervals are bounded in the appropriate way. Make sure they
704 (let ((left (interval-high x))
705 (right (interval-low y)))
706 (cond ((> (bound-value left)
708 ;; Definitely overlap so result is NIL
710 ((< (bound-value left)
712 ;; Definitely don't touch, so result is T
715 ;; Limits are equal. Check for open or closed bounds.
716 ;; Don't overlap if one or the other are open.
717 (or (consp left) (consp right)))))))
719 ;;; Return T if X >= Y. That is, every number in the interval X is
720 ;;; always greater than any number in the interval Y.
721 (defun interval->= (x y)
722 (declare (type interval x y))
723 ;; X >= Y if lower bound of X >= upper bound of Y
724 (when (and (interval-bounded-p x 'below)
725 (interval-bounded-p y 'above))
726 (>= (bound-value (interval-low x)) (bound-value (interval-high y)))))
728 ;;; Return an interval that is the absolute value of X. Thus, if
729 ;;; X = [-1 10], the result is [0, 10].
730 (defun interval-abs (x)
731 (declare (type interval x))
732 (case (interval-range-info x)
738 (destructuring-bind (x- x+) (interval-split 0 x t t)
739 (interval-merge-pair (interval-neg x-) x+)))))
741 ;;; Compute the square of an interval.
742 (defun interval-sqr (x)
743 (declare (type interval x))
744 (interval-func #'(lambda (x) (* x x))
748 ;;;; numeric DERIVE-TYPE methods
750 ;;; a utility for defining derive-type methods of integer operations. If
751 ;;; the types of both X and Y are integer types, then we compute a new
752 ;;; integer type with bounds determined Fun when applied to X and Y.
753 ;;; Otherwise, we use Numeric-Contagion.
754 (defun derive-integer-type (x y fun)
755 (declare (type continuation x y) (type function fun))
756 (let ((x (continuation-type x))
757 (y (continuation-type y)))
758 (if (and (numeric-type-p x) (numeric-type-p y)
759 (eq (numeric-type-class x) 'integer)
760 (eq (numeric-type-class y) 'integer)
761 (eq (numeric-type-complexp x) :real)
762 (eq (numeric-type-complexp y) :real))
763 (multiple-value-bind (low high) (funcall fun x y)
764 (make-numeric-type :class 'integer
768 (numeric-contagion x y))))
770 #!+(or propagate-float-type propagate-fun-type)
773 ;;; simple utility to flatten a list
774 (defun flatten-list (x)
775 (labels ((flatten-helper (x r);; 'r' is the stuff to the 'right'.
779 (t (flatten-helper (car x)
780 (flatten-helper (cdr x) r))))))
781 (flatten-helper x nil)))
783 ;;; Take some type of continuation and massage it so that we get a
784 ;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
785 ;;; to indicate failure.
786 (defun prepare-arg-for-derive-type (arg)
787 (flet ((listify (arg)
792 (union-type-types arg))
795 (unless (eq arg *empty-type*)
796 ;; Make sure all args are some type of numeric-type. For member
797 ;; types, convert the list of members into a union of equivalent
798 ;; single-element member-type's.
799 (let ((new-args nil))
800 (dolist (arg (listify arg))
801 (if (member-type-p arg)
802 ;; Run down the list of members and convert to a list of
804 (dolist (member (member-type-members arg))
805 (push (if (numberp member)
806 (make-member-type :members (list member))
809 (push arg new-args)))
810 (unless (member *empty-type* new-args)
813 ;;; Convert from the standard type convention for which -0.0 and 0.0
814 ;;; and equal to an intermediate convention for which they are
815 ;;; considered different which is more natural for some of the
817 #!-negative-zero-is-not-zero
818 (defun convert-numeric-type (type)
819 (declare (type numeric-type type))
820 ;;; Only convert real float interval delimiters types.
821 (if (eq (numeric-type-complexp type) :real)
822 (let* ((lo (numeric-type-low type))
823 (lo-val (bound-value lo))
824 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
825 (hi (numeric-type-high type))
826 (hi-val (bound-value hi))
827 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
828 (if (or lo-float-zero-p hi-float-zero-p)
830 :class (numeric-type-class type)
831 :format (numeric-type-format type)
833 :low (if lo-float-zero-p
835 (list (float 0.0 lo-val))
838 :high (if hi-float-zero-p
840 (list (float -0.0 hi-val))
847 ;;; Convert back from the intermediate convention for which -0.0 and
848 ;;; 0.0 are considered different to the standard type convention for
850 #!-negative-zero-is-not-zero
851 (defun convert-back-numeric-type (type)
852 (declare (type numeric-type type))
853 ;;; Only convert real float interval delimiters types.
854 (if (eq (numeric-type-complexp type) :real)
855 (let* ((lo (numeric-type-low type))
856 (lo-val (bound-value lo))
858 (and lo (floatp lo-val) (= lo-val 0.0)
859 (float-sign lo-val)))
860 (hi (numeric-type-high type))
861 (hi-val (bound-value hi))
863 (and hi (floatp hi-val) (= hi-val 0.0)
864 (float-sign hi-val))))
866 ;; (float +0.0 +0.0) => (member 0.0)
867 ;; (float -0.0 -0.0) => (member -0.0)
868 ((and lo-float-zero-p hi-float-zero-p)
869 ;; shouldn't have exclusive bounds here..
870 (aver (and (not (consp lo)) (not (consp hi))))
871 (if (= lo-float-zero-p hi-float-zero-p)
872 ;; (float +0.0 +0.0) => (member 0.0)
873 ;; (float -0.0 -0.0) => (member -0.0)
874 (specifier-type `(member ,lo-val))
875 ;; (float -0.0 +0.0) => (float 0.0 0.0)
876 ;; (float +0.0 -0.0) => (float 0.0 0.0)
877 (make-numeric-type :class (numeric-type-class type)
878 :format (numeric-type-format type)
884 ;; (float -0.0 x) => (float 0.0 x)
885 ((and (not (consp lo)) (minusp lo-float-zero-p))
886 (make-numeric-type :class (numeric-type-class type)
887 :format (numeric-type-format type)
889 :low (float 0.0 lo-val)
891 ;; (float (+0.0) x) => (float (0.0) x)
892 ((and (consp lo) (plusp lo-float-zero-p))
893 (make-numeric-type :class (numeric-type-class type)
894 :format (numeric-type-format type)
896 :low (list (float 0.0 lo-val))
899 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
900 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
901 (list (make-member-type :members (list (float 0.0 lo-val)))
902 (make-numeric-type :class (numeric-type-class type)
903 :format (numeric-type-format type)
905 :low (list (float 0.0 lo-val))
909 ;; (float x +0.0) => (float x 0.0)
910 ((and (not (consp hi)) (plusp hi-float-zero-p))
911 (make-numeric-type :class (numeric-type-class type)
912 :format (numeric-type-format type)
915 :high (float 0.0 hi-val)))
916 ;; (float x (-0.0)) => (float x (0.0))
917 ((and (consp hi) (minusp hi-float-zero-p))
918 (make-numeric-type :class (numeric-type-class type)
919 :format (numeric-type-format type)
922 :high (list (float 0.0 hi-val))))
924 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
925 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
926 (list (make-member-type :members (list (float -0.0 hi-val)))
927 (make-numeric-type :class (numeric-type-class type)
928 :format (numeric-type-format type)
931 :high (list (float 0.0 hi-val)))))))
937 ;;; Convert back a possible list of numeric types.
938 #!-negative-zero-is-not-zero
939 (defun convert-back-numeric-type-list (type-list)
943 (dolist (type type-list)
944 (if (numeric-type-p type)
945 (let ((result (convert-back-numeric-type type)))
947 (setf results (append results result))
948 (push result results)))
949 (push type results)))
952 (convert-back-numeric-type type-list))
954 (convert-back-numeric-type-list (union-type-types type-list)))
958 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
959 ;;; belong in the kernel's type logic, invoked always, instead of in
960 ;;; the compiler, invoked only during some type optimizations.
962 ;;; Take a list of types and return a canonical type specifier,
963 ;;; combining any MEMBER types together. If both positive and negative
964 ;;; MEMBER types are present they are converted to a float type.
965 ;;; XXX This would be far simpler if the type-union methods could handle
966 ;;; member/number unions.
967 (defun make-canonical-union-type (type-list)
970 (dolist (type type-list)
971 (if (member-type-p type)
972 (setf members (union members (member-type-members type)))
973 (push type misc-types)))
975 (when (null (set-difference '(-0l0 0l0) members))
976 #!-negative-zero-is-not-zero
977 (push (specifier-type '(long-float 0l0 0l0)) misc-types)
978 #!+negative-zero-is-not-zero
979 (push (specifier-type '(long-float -0l0 0l0)) misc-types)
980 (setf members (set-difference members '(-0l0 0l0))))
981 (when (null (set-difference '(-0d0 0d0) members))
982 #!-negative-zero-is-not-zero
983 (push (specifier-type '(double-float 0d0 0d0)) misc-types)
984 #!+negative-zero-is-not-zero
985 (push (specifier-type '(double-float -0d0 0d0)) misc-types)
986 (setf members (set-difference members '(-0d0 0d0))))
987 (when (null (set-difference '(-0f0 0f0) members))
988 #!-negative-zero-is-not-zero
989 (push (specifier-type '(single-float 0f0 0f0)) misc-types)
990 #!+negative-zero-is-not-zero
991 (push (specifier-type '(single-float -0f0 0f0)) misc-types)
992 (setf members (set-difference members '(-0f0 0f0))))
994 (apply #'type-union (make-member-type :members members) misc-types)
995 (apply #'type-union misc-types))))
997 ;;; Convert a member type with a single member to a numeric type.
998 (defun convert-member-type (arg)
999 (let* ((members (member-type-members arg))
1000 (member (first members))
1001 (member-type (type-of member)))
1002 (aver (not (rest members)))
1003 (specifier-type `(,(if (subtypep member-type 'integer)
1008 ;;; This is used in defoptimizers for computing the resulting type of
1011 ;;; Given the continuation ARG, derive the resulting type using the
1012 ;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
1013 ;;; "atomic" continuation type like numeric-type or member-type
1014 ;;; (containing just one element). It should return the resulting
1015 ;;; type, which can be a list of types.
1017 ;;; For the case of member types, if a member-fcn is given it is
1018 ;;; called to compute the result otherwise the member type is first
1019 ;;; converted to a numeric type and the derive-fcn is call.
1020 (defun one-arg-derive-type (arg derive-fcn member-fcn
1021 &optional (convert-type t))
1022 (declare (type function derive-fcn)
1023 (type (or null function) member-fcn)
1024 #!+negative-zero-is-not-zero (ignore convert-type))
1025 (let ((arg-list (prepare-arg-for-derive-type (continuation-type arg))))
1031 (with-float-traps-masked
1032 (:underflow :overflow :divide-by-zero)
1036 (first (member-type-members x))))))
1037 ;; Otherwise convert to a numeric type.
1038 (let ((result-type-list
1039 (funcall derive-fcn (convert-member-type x))))
1040 #!-negative-zero-is-not-zero
1042 (convert-back-numeric-type-list result-type-list)
1044 #!+negative-zero-is-not-zero
1047 #!-negative-zero-is-not-zero
1049 (convert-back-numeric-type-list
1050 (funcall derive-fcn (convert-numeric-type x)))
1051 (funcall derive-fcn x))
1052 #!+negative-zero-is-not-zero
1053 (funcall derive-fcn x))
1055 *universal-type*))))
1056 ;; Run down the list of args and derive the type of each one,
1057 ;; saving all of the results in a list.
1058 (let ((results nil))
1059 (dolist (arg arg-list)
1060 (let ((result (deriver arg)))
1062 (setf results (append results result))
1063 (push result results))))
1065 (make-canonical-union-type results)
1066 (first results)))))))
1068 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1069 ;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
1070 ;;; original args and a third which is T to indicate if the two args
1071 ;;; really represent the same continuation. This is useful for
1072 ;;; deriving the type of things like (* x x), which should always be
1073 ;;; positive. If we didn't do this, we wouldn't be able to tell.
1074 (defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
1075 &optional (convert-type t))
1076 #!+negative-zero-is-not-zero
1077 (declare (ignore convert-type))
1078 (flet (#!-negative-zero-is-not-zero
1079 (deriver (x y same-arg)
1080 (cond ((and (member-type-p x) (member-type-p y))
1081 (let* ((x (first (member-type-members x)))
1082 (y (first (member-type-members y)))
1083 (result (with-float-traps-masked
1084 (:underflow :overflow :divide-by-zero
1086 (funcall fcn x y))))
1087 (cond ((null result))
1088 ((and (floatp result) (float-nan-p result))
1091 :format (type-of result)
1094 (make-member-type :members (list result))))))
1095 ((and (member-type-p x) (numeric-type-p y))
1096 (let* ((x (convert-member-type x))
1097 (y (if convert-type (convert-numeric-type y) y))
1098 (result (funcall derive-fcn x y same-arg)))
1100 (convert-back-numeric-type-list result)
1102 ((and (numeric-type-p x) (member-type-p y))
1103 (let* ((x (if convert-type (convert-numeric-type x) x))
1104 (y (convert-member-type y))
1105 (result (funcall derive-fcn x y same-arg)))
1107 (convert-back-numeric-type-list result)
1109 ((and (numeric-type-p x) (numeric-type-p y))
1110 (let* ((x (if convert-type (convert-numeric-type x) x))
1111 (y (if convert-type (convert-numeric-type y) y))
1112 (result (funcall derive-fcn x y same-arg)))
1114 (convert-back-numeric-type-list result)
1118 #!+negative-zero-is-not-zero
1119 (deriver (x y same-arg)
1120 (cond ((and (member-type-p x) (member-type-p y))
1121 (let* ((x (first (member-type-members x)))
1122 (y (first (member-type-members y)))
1123 (result (with-float-traps-masked
1124 (:underflow :overflow :divide-by-zero)
1125 (funcall fcn x y))))
1127 (make-member-type :members (list result)))))
1128 ((and (member-type-p x) (numeric-type-p y))
1129 (let ((x (convert-member-type x)))
1130 (funcall derive-fcn x y same-arg)))
1131 ((and (numeric-type-p x) (member-type-p y))
1132 (let ((y (convert-member-type y)))
1133 (funcall derive-fcn x y same-arg)))
1134 ((and (numeric-type-p x) (numeric-type-p y))
1135 (funcall derive-fcn x y same-arg))
1137 *universal-type*))))
1138 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1139 (a1 (prepare-arg-for-derive-type (continuation-type arg1)))
1140 (a2 (prepare-arg-for-derive-type (continuation-type arg2))))
1142 (let ((results nil))
1144 ;; Since the args are the same continuation, just run
1147 (let ((result (deriver x x same-arg)))
1149 (setf results (append results result))
1150 (push result results))))
1151 ;; Try all pairwise combinations.
1154 (let ((result (or (deriver x y same-arg)
1155 (numeric-contagion x y))))
1157 (setf results (append results result))
1158 (push result results))))))
1160 (make-canonical-union-type results)
1161 (first results)))))))
1165 #!-propagate-float-type
1167 (defoptimizer (+ derive-type) ((x y))
1168 (derive-integer-type
1175 (values (frob (numeric-type-low x) (numeric-type-low y))
1176 (frob (numeric-type-high x) (numeric-type-high y)))))))
1178 (defoptimizer (- derive-type) ((x y))
1179 (derive-integer-type
1186 (values (frob (numeric-type-low x) (numeric-type-high y))
1187 (frob (numeric-type-high x) (numeric-type-low y)))))))
1189 (defoptimizer (* derive-type) ((x y))
1190 (derive-integer-type
1193 (let ((x-low (numeric-type-low x))
1194 (x-high (numeric-type-high x))
1195 (y-low (numeric-type-low y))
1196 (y-high (numeric-type-high y)))
1197 (cond ((not (and x-low y-low))
1199 ((or (minusp x-low) (minusp y-low))
1200 (if (and x-high y-high)
1201 (let ((max (* (max (abs x-low) (abs x-high))
1202 (max (abs y-low) (abs y-high)))))
1203 (values (- max) max))
1206 (values (* x-low y-low)
1207 (if (and x-high y-high)
1211 (defoptimizer (/ derive-type) ((x y))
1212 (numeric-contagion (continuation-type x) (continuation-type y)))
1216 #!+propagate-float-type
1218 (defun +-derive-type-aux (x y same-arg)
1219 (if (and (numeric-type-real-p x)
1220 (numeric-type-real-p y))
1223 (let ((x-int (numeric-type->interval x)))
1224 (interval-add x-int x-int))
1225 (interval-add (numeric-type->interval x)
1226 (numeric-type->interval y))))
1227 (result-type (numeric-contagion x y)))
1228 ;; If the result type is a float, we need to be sure to coerce
1229 ;; the bounds into the correct type.
1230 (when (eq (numeric-type-class result-type) 'float)
1231 (setf result (interval-func
1233 (coerce x (or (numeric-type-format result-type)
1237 :class (if (and (eq (numeric-type-class x) 'integer)
1238 (eq (numeric-type-class y) 'integer))
1239 ;; The sum of integers is always an integer
1241 (numeric-type-class result-type))
1242 :format (numeric-type-format result-type)
1243 :low (interval-low result)
1244 :high (interval-high result)))
1245 ;; General contagion
1246 (numeric-contagion x y)))
1248 (defoptimizer (+ derive-type) ((x y))
1249 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1251 (defun --derive-type-aux (x y same-arg)
1252 (if (and (numeric-type-real-p x)
1253 (numeric-type-real-p y))
1255 ;; (- X X) is always 0.
1257 (make-interval :low 0 :high 0)
1258 (interval-sub (numeric-type->interval x)
1259 (numeric-type->interval y))))
1260 (result-type (numeric-contagion x y)))
1261 ;; If the result type is a float, we need to be sure to coerce
1262 ;; the bounds into the correct type.
1263 (when (eq (numeric-type-class result-type) 'float)
1264 (setf result (interval-func
1266 (coerce x (or (numeric-type-format result-type)
1270 :class (if (and (eq (numeric-type-class x) 'integer)
1271 (eq (numeric-type-class y) 'integer))
1272 ;; The difference of integers is always an integer.
1274 (numeric-type-class result-type))
1275 :format (numeric-type-format result-type)
1276 :low (interval-low result)
1277 :high (interval-high result)))
1278 ;; general contagion
1279 (numeric-contagion x y)))
1281 (defoptimizer (- derive-type) ((x y))
1282 (two-arg-derive-type x y #'--derive-type-aux #'-))
1284 (defun *-derive-type-aux (x y same-arg)
1285 (if (and (numeric-type-real-p x)
1286 (numeric-type-real-p y))
1288 ;; (* x x) is always positive, so take care to do it
1291 (interval-sqr (numeric-type->interval x))
1292 (interval-mul (numeric-type->interval x)
1293 (numeric-type->interval y))))
1294 (result-type (numeric-contagion x y)))
1295 ;; If the result type is a float, we need to be sure to coerce
1296 ;; the bounds into the correct type.
1297 (when (eq (numeric-type-class result-type) 'float)
1298 (setf result (interval-func
1300 (coerce x (or (numeric-type-format result-type)
1304 :class (if (and (eq (numeric-type-class x) 'integer)
1305 (eq (numeric-type-class y) 'integer))
1306 ;; The product of integers is always an integer.
1308 (numeric-type-class result-type))
1309 :format (numeric-type-format result-type)
1310 :low (interval-low result)
1311 :high (interval-high result)))
1312 (numeric-contagion x y)))
1314 (defoptimizer (* derive-type) ((x y))
1315 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1317 (defun /-derive-type-aux (x y same-arg)
1318 (if (and (numeric-type-real-p x)
1319 (numeric-type-real-p y))
1321 ;; (/ X X) is always 1, except if X can contain 0. In
1322 ;; that case, we shouldn't optimize the division away
1323 ;; because we want 0/0 to signal an error.
1325 (not (interval-contains-p
1326 0 (interval-closure (numeric-type->interval y)))))
1327 (make-interval :low 1 :high 1)
1328 (interval-div (numeric-type->interval x)
1329 (numeric-type->interval y))))
1330 (result-type (numeric-contagion x y)))
1331 ;; If the result type is a float, we need to be sure to coerce
1332 ;; the bounds into the correct type.
1333 (when (eq (numeric-type-class result-type) 'float)
1334 (setf result (interval-func
1336 (coerce x (or (numeric-type-format result-type)
1339 (make-numeric-type :class (numeric-type-class result-type)
1340 :format (numeric-type-format result-type)
1341 :low (interval-low result)
1342 :high (interval-high result)))
1343 (numeric-contagion x y)))
1345 (defoptimizer (/ derive-type) ((x y))
1346 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1351 ;;; KLUDGE: All this ASH optimization is suppressed under CMU CL
1352 ;;; because as of version 2.4.6 for Debian, CMU CL blows up on (ASH
1353 ;;; 1000000000 -100000000000) (i.e. ASH of two bignums yielding zero)
1354 ;;; and it's hard to avoid that calculation in here.
1355 #-(and cmu sb-xc-host)
1357 #!-propagate-fun-type
1358 (defoptimizer (ash derive-type) ((n shift))
1359 ;; Large resulting bounds are easy to generate but are not
1360 ;; particularly useful, so an open outer bound is returned for a
1361 ;; shift greater than 64 - the largest word size of any of the ports.
1362 ;; Large negative shifts are also problematic as the ASH
1363 ;; implementation only accepts shifts greater than
1364 ;; MOST-NEGATIVE-FIXNUM. These issues are handled by two local
1366 ;; ASH-OUTER: Perform the shift when within an acceptable range,
1367 ;; otherwise return an open bound.
1368 ;; ASH-INNER: Perform the shift when within range, limited to a
1369 ;; maximum of 64, otherwise returns the inner limit.
1371 ;; FIXME: The magic number 64 should be given a mnemonic name as a
1372 ;; symbolic constant -- perhaps +MAX-REGISTER-SIZE+. And perhaps is
1373 ;; should become an architecture-specific SB!VM:+MAX-REGISTER-SIZE+
1374 ;; instead of trying to have a single magic number which covers
1375 ;; all possible ports.
1376 (flet ((ash-outer (n s)
1377 (when (and (fixnump s)
1379 (> s sb!vm:*target-most-negative-fixnum*))
1382 (if (and (fixnump s)
1383 (> s sb!vm:*target-most-negative-fixnum*))
1385 (if (minusp n) -1 0))))
1386 (or (let ((n-type (continuation-type n)))
1387 (when (numeric-type-p n-type)
1388 (let ((n-low (numeric-type-low n-type))
1389 (n-high (numeric-type-high n-type)))
1390 (if (constant-continuation-p shift)
1391 (let ((shift (continuation-value shift)))
1392 (make-numeric-type :class 'integer
1394 :low (when n-low (ash n-low shift))
1395 :high (when n-high (ash n-high shift))))
1396 (let ((s-type (continuation-type shift)))
1397 (when (numeric-type-p s-type)
1398 (let* ((s-low (numeric-type-low s-type))
1399 (s-high (numeric-type-high s-type))
1400 (low-slot (when n-low
1402 (ash-outer n-low s-high)
1403 (ash-inner n-low s-low))))
1404 (high-slot (when n-high
1406 (ash-inner n-high s-low)
1407 (ash-outer n-high s-high)))))
1408 (make-numeric-type :class 'integer
1411 :high high-slot))))))))
1413 (or (let ((n-type (continuation-type n)))
1414 (when (numeric-type-p n-type)
1415 (let ((n-low (numeric-type-low n-type))
1416 (n-high (numeric-type-high n-type)))
1417 (if (constant-continuation-p shift)
1418 (let ((shift (continuation-value shift)))
1419 (make-numeric-type :class 'integer
1421 :low (when n-low (ash n-low shift))
1422 :high (when n-high (ash n-high shift))))
1423 (let ((s-type (continuation-type shift)))
1424 (when (numeric-type-p s-type)
1425 (let ((s-low (numeric-type-low s-type))
1426 (s-high (numeric-type-high s-type)))
1427 (if (and s-low s-high (<= s-low 64) (<= s-high 64))
1428 (make-numeric-type :class 'integer
1431 (min (ash n-low s-high)
1434 (max (ash n-high s-high)
1435 (ash n-high s-low))))
1436 (make-numeric-type :class 'integer
1437 :complexp :real)))))))))
1440 #!+propagate-fun-type
1441 (defun ash-derive-type-aux (n-type shift same-arg)
1442 (declare (ignore same-arg))
1443 (flet ((ash-outer (n s)
1444 (when (and (fixnump s)
1446 (> s sb!vm:*target-most-negative-fixnum*))
1448 ;; KLUDGE: The bare 64's here should be related to
1449 ;; symbolic machine word size values somehow.
1452 (if (and (fixnump s)
1453 (> s sb!vm:*target-most-negative-fixnum*))
1455 (if (minusp n) -1 0))))
1456 (or (and (csubtypep n-type (specifier-type 'integer))
1457 (csubtypep shift (specifier-type 'integer))
1458 (let ((n-low (numeric-type-low n-type))
1459 (n-high (numeric-type-high n-type))
1460 (s-low (numeric-type-low shift))
1461 (s-high (numeric-type-high shift)))
1462 (make-numeric-type :class 'integer :complexp :real
1465 (ash-outer n-low s-high)
1466 (ash-inner n-low s-low)))
1469 (ash-inner n-high s-low)
1470 (ash-outer n-high s-high))))))
1473 #!+propagate-fun-type
1474 (defoptimizer (ash derive-type) ((n shift))
1475 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1478 #!-propagate-float-type
1479 (macrolet ((frob (fun)
1480 `#'(lambda (type type2)
1481 (declare (ignore type2))
1482 (let ((lo (numeric-type-low type))
1483 (hi (numeric-type-high type)))
1484 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1486 (defoptimizer (%negate derive-type) ((num))
1487 (derive-integer-type num num (frob -)))
1489 (defoptimizer (lognot derive-type) ((int))
1490 (derive-integer-type int int (frob lognot))))
1492 #!+propagate-float-type
1493 (defoptimizer (lognot derive-type) ((int))
1494 (derive-integer-type int int
1495 (lambda (type type2)
1496 (declare (ignore type2))
1497 (let ((lo (numeric-type-low type))
1498 (hi (numeric-type-high type)))
1499 (values (if hi (lognot hi) nil)
1500 (if lo (lognot lo) nil)
1501 (numeric-type-class type)
1502 (numeric-type-format type))))))
1504 #!+propagate-float-type
1505 (defoptimizer (%negate derive-type) ((num))
1506 (flet ((negate-bound (b)
1507 (set-bound (- (bound-value b)) (consp b))))
1508 (one-arg-derive-type num
1510 (let ((lo (numeric-type-low type))
1511 (hi (numeric-type-high type))
1512 (result (copy-numeric-type type)))
1513 (setf (numeric-type-low result)
1514 (if hi (negate-bound hi) nil))
1515 (setf (numeric-type-high result)
1516 (if lo (negate-bound lo) nil))
1520 #!-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 #!+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 #!+propagate-float-type
1570 (defoptimizer (abs derive-type) ((num))
1571 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1573 #!-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-xc-host ;(CROSS-FLOAT-INFINITY-KLUDGE, see base-target-features.lisp-expr)
1595 #!+propagate-float-type
1598 (defun rem-result-type (number-type divisor-type)
1599 ;; Figure out what the remainder type is. The remainder is an
1600 ;; integer if both args are integers; a rational if both args are
1601 ;; rational; and a float otherwise.
1602 (cond ((and (csubtypep number-type (specifier-type 'integer))
1603 (csubtypep divisor-type (specifier-type 'integer)))
1605 ((and (csubtypep number-type (specifier-type 'rational))
1606 (csubtypep divisor-type (specifier-type 'rational)))
1608 ((and (csubtypep number-type (specifier-type 'float))
1609 (csubtypep divisor-type (specifier-type 'float)))
1610 ;; Both are floats so the result is also a float, of
1611 ;; the largest type.
1612 (or (float-format-max (numeric-type-format number-type)
1613 (numeric-type-format divisor-type))
1615 ((and (csubtypep number-type (specifier-type 'float))
1616 (csubtypep divisor-type (specifier-type 'rational)))
1617 ;; One of the arguments is a float and the other is a
1618 ;; rational. The remainder is a float of the same
1620 (or (numeric-type-format number-type) 'float))
1621 ((and (csubtypep divisor-type (specifier-type 'float))
1622 (csubtypep number-type (specifier-type 'rational)))
1623 ;; One of the arguments is a float and the other is a
1624 ;; rational. The remainder is a float of the same
1626 (or (numeric-type-format divisor-type) 'float))
1628 ;; Some unhandled combination. This usually means both args
1629 ;; are REAL so the result is a REAL.
1632 (defun truncate-derive-type-quot (number-type divisor-type)
1633 (let* ((rem-type (rem-result-type number-type divisor-type))
1634 (number-interval (numeric-type->interval number-type))
1635 (divisor-interval (numeric-type->interval divisor-type)))
1636 ;;(declare (type (member '(integer rational float)) rem-type))
1637 ;; We have real numbers now.
1638 (cond ((eq rem-type 'integer)
1639 ;; Since the remainder type is INTEGER, both args are
1641 (let* ((res (integer-truncate-derive-type
1642 (interval-low number-interval)
1643 (interval-high number-interval)
1644 (interval-low divisor-interval)
1645 (interval-high divisor-interval))))
1646 (specifier-type (if (listp res) res 'integer))))
1648 (let ((quot (truncate-quotient-bound
1649 (interval-div number-interval
1650 divisor-interval))))
1651 (specifier-type `(integer ,(or (interval-low quot) '*)
1652 ,(or (interval-high quot) '*))))))))
1654 (defun truncate-derive-type-rem (number-type divisor-type)
1655 (let* ((rem-type (rem-result-type number-type divisor-type))
1656 (number-interval (numeric-type->interval number-type))
1657 (divisor-interval (numeric-type->interval divisor-type))
1658 (rem (truncate-rem-bound number-interval divisor-interval)))
1659 ;;(declare (type (member '(integer rational float)) rem-type))
1660 ;; We have real numbers now.
1661 (cond ((eq rem-type 'integer)
1662 ;; Since the remainder type is INTEGER, both args are
1664 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1665 ,(or (interval-high rem) '*))))
1667 (multiple-value-bind (class format)
1670 (values 'integer nil))
1672 (values 'rational nil))
1673 ((or single-float double-float #!+long-float long-float)
1674 (values 'float rem-type))
1676 (values 'float nil))
1679 (when (member rem-type '(float single-float double-float
1680 #!+long-float long-float))
1681 (setf rem (interval-func #'(lambda (x)
1682 (coerce x rem-type))
1684 (make-numeric-type :class class
1686 :low (interval-low rem)
1687 :high (interval-high rem)))))))
1689 (defun truncate-derive-type-quot-aux (num div same-arg)
1690 (declare (ignore same-arg))
1691 (if (and (numeric-type-real-p num)
1692 (numeric-type-real-p div))
1693 (truncate-derive-type-quot num div)
1696 (defun truncate-derive-type-rem-aux (num div same-arg)
1697 (declare (ignore same-arg))
1698 (if (and (numeric-type-real-p num)
1699 (numeric-type-real-p div))
1700 (truncate-derive-type-rem num div)
1703 (defoptimizer (truncate derive-type) ((number divisor))
1704 (let ((quot (two-arg-derive-type number divisor
1705 #'truncate-derive-type-quot-aux #'truncate))
1706 (rem (two-arg-derive-type number divisor
1707 #'truncate-derive-type-rem-aux #'rem)))
1708 (when (and quot rem)
1709 (make-values-type :required (list quot rem)))))
1711 (defun ftruncate-derive-type-quot (number-type divisor-type)
1712 ;; The bounds are the same as for truncate. However, the first
1713 ;; result is a float of some type. We need to determine what that
1714 ;; type is. Basically it's the more contagious of the two types.
1715 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1716 (res-type (numeric-contagion number-type divisor-type)))
1717 (make-numeric-type :class 'float
1718 :format (numeric-type-format res-type)
1719 :low (numeric-type-low q-type)
1720 :high (numeric-type-high q-type))))
1722 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1723 (declare (ignore same-arg))
1724 (if (and (numeric-type-real-p n)
1725 (numeric-type-real-p d))
1726 (ftruncate-derive-type-quot n d)
1729 (defoptimizer (ftruncate derive-type) ((number divisor))
1731 (two-arg-derive-type number divisor
1732 #'ftruncate-derive-type-quot-aux #'ftruncate))
1733 (rem (two-arg-derive-type number divisor
1734 #'truncate-derive-type-rem-aux #'rem)))
1735 (when (and quot rem)
1736 (make-values-type :required (list quot rem)))))
1738 (defun %unary-truncate-derive-type-aux (number)
1739 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1741 (defoptimizer (%unary-truncate derive-type) ((number))
1742 (one-arg-derive-type number
1743 #'%unary-truncate-derive-type-aux
1746 ;;; Define optimizers for FLOOR and CEILING.
1748 ((frob-opt (name q-name r-name)
1749 (let ((q-aux (symbolicate q-name "-AUX"))
1750 (r-aux (symbolicate r-name "-AUX")))
1752 ;; Compute type of quotient (first) result
1753 (defun ,q-aux (number-type divisor-type)
1754 (let* ((number-interval
1755 (numeric-type->interval number-type))
1757 (numeric-type->interval divisor-type))
1758 (quot (,q-name (interval-div number-interval
1759 divisor-interval))))
1760 (specifier-type `(integer ,(or (interval-low quot) '*)
1761 ,(or (interval-high quot) '*)))))
1762 ;; Compute type of remainder
1763 (defun ,r-aux (number-type divisor-type)
1764 (let* ((divisor-interval
1765 (numeric-type->interval divisor-type))
1766 (rem (,r-name divisor-interval))
1767 (result-type (rem-result-type number-type divisor-type)))
1768 (multiple-value-bind (class format)
1771 (values 'integer nil))
1773 (values 'rational nil))
1774 ((or single-float double-float #!+long-float long-float)
1775 (values 'float result-type))
1777 (values 'float nil))
1780 (when (member result-type '(float single-float double-float
1781 #!+long-float long-float))
1782 ;; Make sure the limits on the interval have
1784 (setf rem (interval-func #'(lambda (x)
1785 (coerce x result-type))
1787 (make-numeric-type :class class
1789 :low (interval-low rem)
1790 :high (interval-high rem)))))
1791 ;; The optimizer itself
1792 (defoptimizer (,name derive-type) ((number divisor))
1793 (flet ((derive-q (n d same-arg)
1794 (declare (ignore same-arg))
1795 (if (and (numeric-type-real-p n)
1796 (numeric-type-real-p d))
1799 (derive-r (n d same-arg)
1800 (declare (ignore same-arg))
1801 (if (and (numeric-type-real-p n)
1802 (numeric-type-real-p d))
1805 (let ((quot (two-arg-derive-type
1806 number divisor #'derive-q #',name))
1807 (rem (two-arg-derive-type
1808 number divisor #'derive-r #'mod)))
1809 (when (and quot rem)
1810 (make-values-type :required (list quot rem))))))
1813 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1814 (frob-opt floor floor-quotient-bound floor-rem-bound)
1815 (frob-opt ceiling ceiling-quotient-bound ceiling-rem-bound))
1817 ;;; Define optimizers for FFLOOR and FCEILING
1819 ((frob-opt (name q-name r-name)
1820 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1821 (r-aux (symbolicate r-name "-AUX")))
1823 ;; Compute type of quotient (first) result
1824 (defun ,q-aux (number-type divisor-type)
1825 (let* ((number-interval
1826 (numeric-type->interval number-type))
1828 (numeric-type->interval divisor-type))
1829 (quot (,q-name (interval-div number-interval
1831 (res-type (numeric-contagion number-type divisor-type)))
1833 :class (numeric-type-class res-type)
1834 :format (numeric-type-format res-type)
1835 :low (interval-low quot)
1836 :high (interval-high quot))))
1838 (defoptimizer (,name derive-type) ((number divisor))
1839 (flet ((derive-q (n d same-arg)
1840 (declare (ignore same-arg))
1841 (if (and (numeric-type-real-p n)
1842 (numeric-type-real-p d))
1845 (derive-r (n d same-arg)
1846 (declare (ignore same-arg))
1847 (if (and (numeric-type-real-p n)
1848 (numeric-type-real-p d))
1851 (let ((quot (two-arg-derive-type
1852 number divisor #'derive-q #',name))
1853 (rem (two-arg-derive-type
1854 number divisor #'derive-r #'mod)))
1855 (when (and quot rem)
1856 (make-values-type :required (list quot rem))))))))))
1858 ;; FIXME: DEF-FROB-OPT, not just FROB-OPT
1859 (frob-opt ffloor floor-quotient-bound floor-rem-bound)
1860 (frob-opt fceiling ceiling-quotient-bound ceiling-rem-bound))
1862 ;;; functions to compute the bounds on the quotient and remainder for
1863 ;;; the FLOOR function
1864 (defun floor-quotient-bound (quot)
1865 ;; Take the floor of the quotient and then massage it into what we
1867 (let ((lo (interval-low quot))
1868 (hi (interval-high quot)))
1869 ;; Take the floor of the lower bound. The result is always a
1870 ;; closed lower bound.
1872 (floor (bound-value lo))
1874 ;; For the upper bound, we need to be careful
1877 ;; An open bound. We need to be careful here because
1878 ;; the floor of '(10.0) is 9, but the floor of
1880 (multiple-value-bind (q r) (floor (first hi))
1885 ;; A closed bound, so the answer is obvious.
1889 (make-interval :low lo :high hi)))
1890 (defun floor-rem-bound (div)
1891 ;; The remainder depends only on the divisor. Try to get the
1892 ;; correct sign for the remainder if we can.
1893 (case (interval-range-info div)
1895 ;; Divisor is always positive.
1896 (let ((rem (interval-abs div)))
1897 (setf (interval-low rem) 0)
1898 (when (and (numberp (interval-high rem))
1899 (not (zerop (interval-high rem))))
1900 ;; The remainder never contains the upper bound. However,
1901 ;; watch out for the case where the high limit is zero!
1902 (setf (interval-high rem) (list (interval-high rem))))
1905 ;; Divisor is always negative
1906 (let ((rem (interval-neg (interval-abs div))))
1907 (setf (interval-high rem) 0)
1908 (when (numberp (interval-low rem))
1909 ;; The remainder never contains the lower bound.
1910 (setf (interval-low rem) (list (interval-low rem))))
1913 ;; The divisor can be positive or negative. All bets off.
1914 ;; The magnitude of remainder is the maximum value of the
1916 (let ((limit (bound-value (interval-high (interval-abs div)))))
1917 ;; The bound never reaches the limit, so make the interval open
1918 (make-interval :low (if limit
1921 :high (list limit))))))
1923 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1924 => #S(INTERVAL :LOW 0 :HIGH 10)
1925 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1926 => #S(INTERVAL :LOW 0 :HIGH 10)
1927 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1928 => #S(INTERVAL :LOW 0 :HIGH 10)
1929 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1930 => #S(INTERVAL :LOW 0 :HIGH 9)
1931 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1932 => #S(INTERVAL :LOW 0 :HIGH 10)
1933 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1934 => #S(INTERVAL :LOW 0 :HIGH 10)
1935 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1936 => #S(INTERVAL :LOW -2 :HIGH 10)
1937 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1938 => #S(INTERVAL :LOW -1 :HIGH 10)
1939 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1940 => #S(INTERVAL :LOW -1 :HIGH 10)
1942 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1943 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1944 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1945 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1946 (floor-rem-bound (make-interval :low -10 :high -2.3))
1947 #S(INTERVAL :LOW (-10) :HIGH 0)
1948 (floor-rem-bound (make-interval :low 0.3 :high 10))
1949 => #S(INTERVAL :LOW 0 :HIGH '(10))
1950 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1951 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1952 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1953 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1956 ;;; same functions for CEILING
1957 (defun ceiling-quotient-bound (quot)
1958 ;; Take the ceiling of the quotient and then massage it into what we
1960 (let ((lo (interval-low quot))
1961 (hi (interval-high quot)))
1962 ;; Take the ceiling of the upper bound. The result is always a
1963 ;; closed upper bound.
1965 (ceiling (bound-value hi))
1967 ;; For the lower bound, we need to be careful
1970 ;; An open bound. We need to be careful here because
1971 ;; the ceiling of '(10.0) is 11, but the ceiling of
1973 (multiple-value-bind (q r) (ceiling (first lo))
1978 ;; A closed bound, so the answer is obvious.
1982 (make-interval :low lo :high hi)))
1983 (defun ceiling-rem-bound (div)
1984 ;; The remainder depends only on the divisor. Try to get the
1985 ;; correct sign for the remainder if we can.
1987 (case (interval-range-info div)
1989 ;; Divisor is always positive. The remainder is negative.
1990 (let ((rem (interval-neg (interval-abs div))))
1991 (setf (interval-high rem) 0)
1992 (when (and (numberp (interval-low rem))
1993 (not (zerop (interval-low rem))))
1994 ;; The remainder never contains the upper bound. However,
1995 ;; watch out for the case when the upper bound is zero!
1996 (setf (interval-low rem) (list (interval-low rem))))
1999 ;; Divisor is always negative. The remainder is positive
2000 (let ((rem (interval-abs div)))
2001 (setf (interval-low rem) 0)
2002 (when (numberp (interval-high rem))
2003 ;; The remainder never contains the lower bound.
2004 (setf (interval-high rem) (list (interval-high rem))))
2007 ;; The divisor can be positive or negative. All bets off.
2008 ;; The magnitude of remainder is the maximum value of the
2010 (let ((limit (bound-value (interval-high (interval-abs div)))))
2011 ;; The bound never reaches the limit, so make the interval open
2012 (make-interval :low (if limit
2015 :high (list limit))))))
2018 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2019 => #S(INTERVAL :LOW 1 :HIGH 11)
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 0.3 :high 10))
2023 => #S(INTERVAL :LOW 1 :HIGH 10)
2024 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2025 => #S(INTERVAL :LOW 1 :HIGH 10)
2026 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2027 => #S(INTERVAL :LOW 1 :HIGH 11)
2028 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2029 => #S(INTERVAL :LOW 1 :HIGH 11)
2030 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2031 => #S(INTERVAL :LOW -1 :HIGH 11)
2032 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2033 => #S(INTERVAL :LOW 0 :HIGH 11)
2034 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2035 => #S(INTERVAL :LOW -1 :HIGH 11)
2037 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2038 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2039 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2040 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2041 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2042 => #S(INTERVAL :LOW 0 :HIGH (10))
2043 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2044 => #S(INTERVAL :LOW (-10) :HIGH 0)
2045 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2046 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2047 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2048 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2051 (defun truncate-quotient-bound (quot)
2052 ;; For positive quotients, truncate is exactly like floor. For
2053 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2054 ;; it's the union of the two pieces.
2055 (case (interval-range-info quot)
2058 (floor-quotient-bound quot))
2060 ;; Just like ceiling
2061 (ceiling-quotient-bound quot))
2063 ;; Split the interval into positive and negative pieces, compute
2064 ;; the result for each piece and put them back together.
2065 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2066 (interval-merge-pair (ceiling-quotient-bound neg)
2067 (floor-quotient-bound pos))))))
2069 (defun truncate-rem-bound (num div)
2070 ;; This is significantly more complicated than floor or ceiling. We
2071 ;; need both the number and the divisor to determine the range. The
2072 ;; basic idea is to split the ranges of num and den into positive
2073 ;; and negative pieces and deal with each of the four possibilities
2075 (case (interval-range-info num)
2077 (case (interval-range-info div)
2079 (floor-rem-bound div))
2081 (ceiling-rem-bound div))
2083 (destructuring-bind (neg pos) (interval-split 0 div t t)
2084 (interval-merge-pair (truncate-rem-bound num neg)
2085 (truncate-rem-bound num pos))))))
2087 (case (interval-range-info div)
2089 (ceiling-rem-bound div))
2091 (floor-rem-bound div))
2093 (destructuring-bind (neg pos) (interval-split 0 div t t)
2094 (interval-merge-pair (truncate-rem-bound num neg)
2095 (truncate-rem-bound num pos))))))
2097 (destructuring-bind (neg pos) (interval-split 0 num t t)
2098 (interval-merge-pair (truncate-rem-bound neg div)
2099 (truncate-rem-bound pos div))))))
2102 ;;; Derive useful information about the range. Returns three values:
2103 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2104 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2105 ;;; - The abs of the maximal value if there is one, or nil if it is
2107 (defun numeric-range-info (low high)
2108 (cond ((and low (not (minusp low)))
2109 (values '+ low high))
2110 ((and high (not (plusp high)))
2111 (values '- (- high) (if low (- low) nil)))
2113 (values nil 0 (and low high (max (- low) high))))))
2115 (defun integer-truncate-derive-type
2116 (number-low number-high divisor-low divisor-high)
2117 ;; The result cannot be larger in magnitude than the number, but the sign
2118 ;; might change. If we can determine the sign of either the number or
2119 ;; the divisor, we can eliminate some of the cases.
2120 (multiple-value-bind (number-sign number-min number-max)
2121 (numeric-range-info number-low number-high)
2122 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2123 (numeric-range-info divisor-low divisor-high)
2124 (when (and divisor-max (zerop divisor-max))
2125 ;; We've got a problem: guaranteed division by zero.
2126 (return-from integer-truncate-derive-type t))
2127 (when (zerop divisor-min)
2128 ;; We'll assume that they aren't going to divide by zero.
2130 (cond ((and number-sign divisor-sign)
2131 ;; We know the sign of both.
2132 (if (eq number-sign divisor-sign)
2133 ;; Same sign, so the result will be positive.
2134 `(integer ,(if divisor-max
2135 (truncate number-min divisor-max)
2138 (truncate number-max divisor-min)
2140 ;; Different signs, the result will be negative.
2141 `(integer ,(if number-max
2142 (- (truncate number-max divisor-min))
2145 (- (truncate number-min divisor-max))
2147 ((eq divisor-sign '+)
2148 ;; The divisor is positive. Therefore, the number will just
2149 ;; become closer to zero.
2150 `(integer ,(if number-low
2151 (truncate number-low divisor-min)
2154 (truncate number-high divisor-min)
2156 ((eq divisor-sign '-)
2157 ;; The divisor is negative. Therefore, the absolute value of
2158 ;; the number will become closer to zero, but the sign will also
2160 `(integer ,(if number-high
2161 (- (truncate number-high divisor-min))
2164 (- (truncate number-low divisor-min))
2166 ;; The divisor could be either positive or negative.
2168 ;; The number we are dividing has a bound. Divide that by the
2169 ;; smallest posible divisor.
2170 (let ((bound (truncate number-max divisor-min)))
2171 `(integer ,(- bound) ,bound)))
2173 ;; The number we are dividing is unbounded, so we can't tell
2174 ;; anything about the result.
2177 #!-propagate-float-type
2178 (defun integer-rem-derive-type
2179 (number-low number-high divisor-low divisor-high)
2180 (if (and divisor-low divisor-high)
2181 ;; We know the range of the divisor, and the remainder must be smaller
2182 ;; than the divisor. We can tell the sign of the remainer if we know
2183 ;; the sign of the number.
2184 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2185 `(integer ,(if (or (null number-low)
2186 (minusp number-low))
2189 ,(if (or (null number-high)
2190 (plusp number-high))
2193 ;; The divisor is potentially either very positive or very negative.
2194 ;; Therefore, the remainer is unbounded, but we might be able to tell
2195 ;; something about the sign from the number.
2196 `(integer ,(if (and number-low (not (minusp number-low)))
2197 ;; The number we are dividing is positive. Therefore,
2198 ;; the remainder must be positive.
2201 ,(if (and number-high (not (plusp number-high)))
2202 ;; The number we are dividing is negative. Therefore,
2203 ;; the remainder must be negative.
2207 #!-propagate-float-type
2208 (defoptimizer (random derive-type) ((bound &optional state))
2209 (let ((type (continuation-type bound)))
2210 (when (numeric-type-p type)
2211 (let ((class (numeric-type-class type))
2212 (high (numeric-type-high type))
2213 (format (numeric-type-format type)))
2217 :low (coerce 0 (or format class 'real))
2218 :high (cond ((not high) nil)
2219 ((eq class 'integer) (max (1- high) 0))
2220 ((or (consp high) (zerop high)) high)
2223 #!+propagate-float-type
2224 (defun random-derive-type-aux (type)
2225 (let ((class (numeric-type-class type))
2226 (high (numeric-type-high type))
2227 (format (numeric-type-format type)))
2231 :low (coerce 0 (or format class 'real))
2232 :high (cond ((not high) nil)
2233 ((eq class 'integer) (max (1- high) 0))
2234 ((or (consp high) (zerop high)) high)
2237 #!+propagate-float-type
2238 (defoptimizer (random derive-type) ((bound &optional state))
2239 (one-arg-derive-type bound #'random-derive-type-aux nil))
2241 ;;;; logical derive-type methods
2243 ;;; Return the maximum number of bits an integer of the supplied type can take
2244 ;;; up, or NIL if it is unbounded. The second (third) value is T if the
2245 ;;; integer can be positive (negative) and NIL if not. Zero counts as
2247 (defun integer-type-length (type)
2248 (if (numeric-type-p type)
2249 (let ((min (numeric-type-low type))
2250 (max (numeric-type-high type)))
2251 (values (and min max (max (integer-length min) (integer-length max)))
2252 (or (null max) (not (minusp max)))
2253 (or (null min) (minusp min))))
2256 #!-propagate-fun-type
2258 (defoptimizer (logand derive-type) ((x y))
2259 (multiple-value-bind (x-len x-pos x-neg)
2260 (integer-type-length (continuation-type x))
2261 (declare (ignore x-pos))
2262 (multiple-value-bind (y-len y-pos y-neg)
2263 (integer-type-length (continuation-type y))
2264 (declare (ignore y-pos))
2266 ;; X must be positive.
2268 ;; The must both be positive.
2269 (cond ((or (null x-len) (null y-len))
2270 (specifier-type 'unsigned-byte))
2271 ((or (zerop x-len) (zerop y-len))
2272 (specifier-type '(integer 0 0)))
2274 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2275 ;; X is positive, but Y might be negative.
2277 (specifier-type 'unsigned-byte))
2279 (specifier-type '(integer 0 0)))
2281 (specifier-type `(unsigned-byte ,x-len)))))
2282 ;; X might be negative.
2284 ;; Y must be positive.
2286 (specifier-type 'unsigned-byte))
2288 (specifier-type '(integer 0 0)))
2291 `(unsigned-byte ,y-len))))
2292 ;; Either might be negative.
2293 (if (and x-len y-len)
2294 ;; The result is bounded.
2295 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2296 ;; We can't tell squat about the result.
2297 (specifier-type 'integer)))))))
2299 (defoptimizer (logior derive-type) ((x y))
2300 (multiple-value-bind (x-len x-pos x-neg)
2301 (integer-type-length (continuation-type x))
2302 (multiple-value-bind (y-len y-pos y-neg)
2303 (integer-type-length (continuation-type y))
2305 ((and (not x-neg) (not y-neg))
2306 ;; Both are positive.
2307 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2311 ;; X must be negative.
2313 ;; Both are negative. The result is going to be negative and be
2314 ;; the same length or shorter than the smaller.
2315 (if (and x-len y-len)
2317 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2319 (specifier-type '(integer * -1)))
2320 ;; X is negative, but we don't know about Y. The result will be
2321 ;; negative, but no more negative than X.
2323 `(integer ,(or (numeric-type-low (continuation-type x)) '*)
2326 ;; X might be either positive or negative.
2328 ;; But Y is negative. The result will be negative.
2330 `(integer ,(or (numeric-type-low (continuation-type y)) '*)
2332 ;; We don't know squat about either. It won't get any bigger.
2333 (if (and x-len y-len)
2335 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2337 (specifier-type 'integer))))))))
2339 (defoptimizer (logxor derive-type) ((x y))
2340 (multiple-value-bind (x-len x-pos x-neg)
2341 (integer-type-length (continuation-type x))
2342 (multiple-value-bind (y-len y-pos y-neg)
2343 (integer-type-length (continuation-type y))
2345 ((or (and (not x-neg) (not y-neg))
2346 (and (not x-pos) (not y-pos)))
2347 ;; Either both are negative or both are positive. The result will be
2348 ;; positive, and as long as the longer.
2349 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2352 ((or (and (not x-pos) (not y-neg))
2353 (and (not y-neg) (not y-pos)))
2354 ;; Either X is negative and Y is positive of vice-verca. The result
2355 ;; will be negative.
2356 (specifier-type `(integer ,(if (and x-len y-len)
2357 (ash -1 (max x-len y-len))
2360 ;; We can't tell what the sign of the result is going to be. All we
2361 ;; know is that we don't create new bits.
2363 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2365 (specifier-type 'integer))))))
2369 #!+propagate-fun-type
2371 (defun logand-derive-type-aux (x y &optional same-leaf)
2372 (declare (ignore same-leaf))
2373 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2374 (declare (ignore x-pos))
2375 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2376 (declare (ignore y-pos))
2378 ;; X must be positive.
2380 ;; The must both be positive.
2381 (cond ((or (null x-len) (null y-len))
2382 (specifier-type 'unsigned-byte))
2383 ((or (zerop x-len) (zerop y-len))
2384 (specifier-type '(integer 0 0)))
2386 (specifier-type `(unsigned-byte ,(min x-len y-len)))))
2387 ;; X is positive, but Y might be negative.
2389 (specifier-type 'unsigned-byte))
2391 (specifier-type '(integer 0 0)))
2393 (specifier-type `(unsigned-byte ,x-len)))))
2394 ;; X might be negative.
2396 ;; Y must be positive.
2398 (specifier-type 'unsigned-byte))
2400 (specifier-type '(integer 0 0)))
2403 `(unsigned-byte ,y-len))))
2404 ;; Either might be negative.
2405 (if (and x-len y-len)
2406 ;; The result is bounded.
2407 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2408 ;; We can't tell squat about the result.
2409 (specifier-type 'integer)))))))
2411 (defun logior-derive-type-aux (x y &optional same-leaf)
2412 (declare (ignore same-leaf))
2413 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2414 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2416 ((and (not x-neg) (not y-neg))
2417 ;; Both are positive.
2418 (if (and x-len y-len (zerop x-len) (zerop y-len))
2419 (specifier-type '(integer 0 0))
2420 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2424 ;; X must be negative.
2426 ;; Both are negative. The result is going to be negative and be
2427 ;; the same length or shorter than the smaller.
2428 (if (and x-len y-len)
2430 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2432 (specifier-type '(integer * -1)))
2433 ;; X is negative, but we don't know about Y. The result will be
2434 ;; negative, but no more negative than X.
2436 `(integer ,(or (numeric-type-low x) '*)
2439 ;; X might be either positive or negative.
2441 ;; But Y is negative. The result will be negative.
2443 `(integer ,(or (numeric-type-low y) '*)
2445 ;; We don't know squat about either. It won't get any bigger.
2446 (if (and x-len y-len)
2448 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2450 (specifier-type 'integer))))))))
2452 (defun logxor-derive-type-aux (x y &optional same-leaf)
2453 (declare (ignore same-leaf))
2454 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2455 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2457 ((or (and (not x-neg) (not y-neg))
2458 (and (not x-pos) (not y-pos)))
2459 ;; Either both are negative or both are positive. The result will be
2460 ;; positive, and as long as the longer.
2461 (if (and x-len y-len (zerop x-len) (zerop y-len))
2462 (specifier-type '(integer 0 0))
2463 (specifier-type `(unsigned-byte ,(if (and x-len y-len)
2466 ((or (and (not x-pos) (not y-neg))
2467 (and (not y-neg) (not y-pos)))
2468 ;; Either X is negative and Y is positive of vice-verca. The result
2469 ;; will be negative.
2470 (specifier-type `(integer ,(if (and x-len y-len)
2471 (ash -1 (max x-len y-len))
2474 ;; We can't tell what the sign of the result is going to be. All we
2475 ;; know is that we don't create new bits.
2477 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2479 (specifier-type 'integer))))))
2481 (macrolet ((frob (logfcn)
2482 (let ((fcn-aux (symbolicate logfcn "-DERIVE-TYPE-AUX")))
2483 `(defoptimizer (,logfcn derive-type) ((x y))
2484 (two-arg-derive-type x y #',fcn-aux #',logfcn)))))
2485 ;; FIXME: DEF-FROB, not just FROB
2490 (defoptimizer (integer-length derive-type) ((x))
2491 (let ((x-type (continuation-type x)))
2492 (when (and (numeric-type-p x-type)
2493 (csubtypep x-type (specifier-type 'integer)))
2494 ;; If the X is of type (INTEGER LO HI), then the integer-length
2495 ;; of X is (INTEGER (min lo hi) (max lo hi), basically. Be
2496 ;; careful about LO or HI being NIL, though. Also, if 0 is
2497 ;; contained in X, the lower bound is obviously 0.
2498 (flet ((null-or-min (a b)
2499 (and a b (min (integer-length a)
2500 (integer-length b))))
2502 (and a b (max (integer-length a)
2503 (integer-length b)))))
2504 (let* ((min (numeric-type-low x-type))
2505 (max (numeric-type-high x-type))
2506 (min-len (null-or-min min max))
2507 (max-len (null-or-max min max)))
2508 (when (ctypep 0 x-type)
2510 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2513 ;;;; miscellaneous derive-type methods
2515 (defoptimizer (code-char derive-type) ((code))
2516 (specifier-type 'base-char))
2518 (defoptimizer (values derive-type) ((&rest values))
2519 (values-specifier-type
2520 `(values ,@(mapcar #'(lambda (x)
2521 (type-specifier (continuation-type x)))
2524 ;;;; byte operations
2526 ;;;; We try to turn byte operations into simple logical operations. First, we
2527 ;;;; convert byte specifiers into separate size and position arguments passed
2528 ;;;; to internal %FOO functions. We then attempt to transform the %FOO
2529 ;;;; functions into boolean operations when the size and position are constant
2530 ;;;; and the operands are fixnums.
2532 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to expressions that
2533 ;; evaluate to the SIZE and POSITION of the byte-specifier form
2534 ;; SPEC. We may wrap a let around the result of the body to bind
2537 ;; If the spec is a BYTE form, then bind the vars to the subforms.
2538 ;; otherwise, evaluate SPEC and use the BYTE-SIZE and BYTE-POSITION.
2539 ;; The goal of this transformation is to avoid consing up byte
2540 ;; specifiers and then immediately throwing them away.
2541 (with-byte-specifier ((size-var pos-var spec) &body body)
2542 (once-only ((spec `(macroexpand ,spec))
2544 `(if (and (consp ,spec)
2545 (eq (car ,spec) 'byte)
2546 (= (length ,spec) 3))
2547 (let ((,size-var (second ,spec))
2548 (,pos-var (third ,spec)))
2550 (let ((,size-var `(byte-size ,,temp))
2551 (,pos-var `(byte-position ,,temp)))
2552 `(let ((,,temp ,,spec))
2555 (def-source-transform ldb (spec int)
2556 (with-byte-specifier (size pos spec)
2557 `(%ldb ,size ,pos ,int)))
2559 (def-source-transform dpb (newbyte spec int)
2560 (with-byte-specifier (size pos spec)
2561 `(%dpb ,newbyte ,size ,pos ,int)))
2563 (def-source-transform mask-field (spec int)
2564 (with-byte-specifier (size pos spec)
2565 `(%mask-field ,size ,pos ,int)))
2567 (def-source-transform deposit-field (newbyte spec int)
2568 (with-byte-specifier (size pos spec)
2569 `(%deposit-field ,newbyte ,size ,pos ,int))))
2571 (defoptimizer (%ldb derive-type) ((size posn num))
2572 (let ((size (continuation-type size)))
2573 (if (and (numeric-type-p size)
2574 (csubtypep size (specifier-type 'integer)))
2575 (let ((size-high (numeric-type-high size)))
2576 (if (and size-high (<= size-high sb!vm:word-bits))
2577 (specifier-type `(unsigned-byte ,size-high))
2578 (specifier-type 'unsigned-byte)))
2581 (defoptimizer (%mask-field derive-type) ((size posn num))
2582 (let ((size (continuation-type size))
2583 (posn (continuation-type posn)))
2584 (if (and (numeric-type-p size)
2585 (csubtypep size (specifier-type 'integer))
2586 (numeric-type-p posn)
2587 (csubtypep posn (specifier-type 'integer)))
2588 (let ((size-high (numeric-type-high size))
2589 (posn-high (numeric-type-high posn)))
2590 (if (and size-high posn-high
2591 (<= (+ size-high posn-high) sb!vm:word-bits))
2592 (specifier-type `(unsigned-byte ,(+ size-high posn-high)))
2593 (specifier-type 'unsigned-byte)))
2596 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2597 (let ((size (continuation-type size))
2598 (posn (continuation-type posn))
2599 (int (continuation-type int)))
2600 (if (and (numeric-type-p size)
2601 (csubtypep size (specifier-type 'integer))
2602 (numeric-type-p posn)
2603 (csubtypep posn (specifier-type 'integer))
2604 (numeric-type-p int)
2605 (csubtypep int (specifier-type 'integer)))
2606 (let ((size-high (numeric-type-high size))
2607 (posn-high (numeric-type-high posn))
2608 (high (numeric-type-high int))
2609 (low (numeric-type-low int)))
2610 (if (and size-high posn-high high low
2611 (<= (+ size-high posn-high) sb!vm:word-bits))
2613 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2614 (max (integer-length high)
2615 (integer-length low)
2616 (+ size-high posn-high))))
2620 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2621 (let ((size (continuation-type size))
2622 (posn (continuation-type posn))
2623 (int (continuation-type int)))
2624 (if (and (numeric-type-p size)
2625 (csubtypep size (specifier-type 'integer))
2626 (numeric-type-p posn)
2627 (csubtypep posn (specifier-type 'integer))
2628 (numeric-type-p int)
2629 (csubtypep int (specifier-type 'integer)))
2630 (let ((size-high (numeric-type-high size))
2631 (posn-high (numeric-type-high posn))
2632 (high (numeric-type-high int))
2633 (low (numeric-type-low int)))
2634 (if (and size-high posn-high high low
2635 (<= (+ size-high posn-high) sb!vm:word-bits))
2637 (list (if (minusp low) 'signed-byte 'unsigned-byte)
2638 (max (integer-length high)
2639 (integer-length low)
2640 (+ size-high posn-high))))
2644 (deftransform %ldb ((size posn int)
2645 (fixnum fixnum integer)
2646 (unsigned-byte #.sb!vm:word-bits))
2647 "convert to inline logical operations"
2648 `(logand (ash int (- posn))
2649 (ash ,(1- (ash 1 sb!vm:word-bits))
2650 (- size ,sb!vm:word-bits))))
2652 (deftransform %mask-field ((size posn int)
2653 (fixnum fixnum integer)
2654 (unsigned-byte #.sb!vm:word-bits))
2655 "convert to inline logical operations"
2657 (ash (ash ,(1- (ash 1 sb!vm:word-bits))
2658 (- size ,sb!vm:word-bits))
2661 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2662 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2663 ;;; as the result type, as that would allow result types
2664 ;;; that cover the range -2^(n-1) .. 1-2^n, instead of allowing result types
2665 ;;; of (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2667 (deftransform %dpb ((new size posn int)
2669 (unsigned-byte #.sb!vm:word-bits))
2670 "convert to inline logical operations"
2671 `(let ((mask (ldb (byte size 0) -1)))
2672 (logior (ash (logand new mask) posn)
2673 (logand int (lognot (ash mask posn))))))
2675 (deftransform %dpb ((new size posn int)
2677 (signed-byte #.sb!vm:word-bits))
2678 "convert to inline logical operations"
2679 `(let ((mask (ldb (byte size 0) -1)))
2680 (logior (ash (logand new mask) posn)
2681 (logand int (lognot (ash mask posn))))))
2683 (deftransform %deposit-field ((new size posn int)
2685 (unsigned-byte #.sb!vm:word-bits))
2686 "convert to inline logical operations"
2687 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2688 (logior (logand new mask)
2689 (logand int (lognot mask)))))
2691 (deftransform %deposit-field ((new size posn int)
2693 (signed-byte #.sb!vm:word-bits))
2694 "convert to inline logical operations"
2695 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2696 (logior (logand new mask)
2697 (logand int (lognot mask)))))
2699 ;;; miscellanous numeric transforms
2701 ;;; If a constant appears as the first arg, swap the args.
2702 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2703 (if (and (constant-continuation-p x)
2704 (not (constant-continuation-p y)))
2705 `(,(continuation-function-name (basic-combination-fun node))
2707 ,(continuation-value x))
2708 (give-up-ir1-transform)))
2710 (dolist (x '(= char= + * logior logand logxor))
2711 (%deftransform x '(function * *) #'commutative-arg-swap
2712 "place constant arg last."))
2714 ;;; Handle the case of a constant BOOLE-CODE.
2715 (deftransform boole ((op x y) * * :when :both)
2716 "convert to inline logical operations"
2717 (unless (constant-continuation-p op)
2718 (give-up-ir1-transform "BOOLE code is not a constant."))
2719 (let ((control (continuation-value op)))
2725 (#.boole-c1 '(lognot x))
2726 (#.boole-c2 '(lognot y))
2727 (#.boole-and '(logand x y))
2728 (#.boole-ior '(logior x y))
2729 (#.boole-xor '(logxor x y))
2730 (#.boole-eqv '(logeqv x y))
2731 (#.boole-nand '(lognand x y))
2732 (#.boole-nor '(lognor x y))
2733 (#.boole-andc1 '(logandc1 x y))
2734 (#.boole-andc2 '(logandc2 x y))
2735 (#.boole-orc1 '(logorc1 x y))
2736 (#.boole-orc2 '(logorc2 x y))
2738 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2741 ;;;; converting special case multiply/divide to shifts
2743 ;;; If arg is a constant power of two, turn * into a shift.
2744 (deftransform * ((x y) (integer integer) * :when :both)
2745 "convert x*2^k to shift"
2746 (unless (constant-continuation-p y)
2747 (give-up-ir1-transform))
2748 (let* ((y (continuation-value y))
2750 (len (1- (integer-length y-abs))))
2751 (unless (= y-abs (ash 1 len))
2752 (give-up-ir1-transform))
2757 ;;; If both arguments and the result are (unsigned-byte 32), try to come up
2758 ;;; with a ``better'' multiplication using multiplier recoding. There are two
2759 ;;; different ways the multiplier can be recoded. The more obvious is to shift
2760 ;;; X by the correct amount for each bit set in Y and to sum the results. But
2761 ;;; if there is a string of bits that are all set, you can add X shifted by
2762 ;;; one more then the bit position of the first set bit and subtract X shifted
2763 ;;; by the bit position of the last set bit. We can't use this second method
2764 ;;; when the high order bit is bit 31 because shifting by 32 doesn't work
2766 (deftransform * ((x y)
2767 ((unsigned-byte 32) (unsigned-byte 32))
2769 "recode as shift and add"
2770 (unless (constant-continuation-p y)
2771 (give-up-ir1-transform))
2772 (let ((y (continuation-value y))
2775 (labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x))
2780 `(+ ,result ,(tub32 next-factor))
2782 (declare (inline add))
2783 (dotimes (bitpos 32)
2785 (when (not (logbitp bitpos y))
2786 (add (if (= (1+ first-one) bitpos)
2787 ;; There is only a single bit in the string.
2789 ;; There are at least two.
2790 `(- ,(tub32 `(ash x ,bitpos))
2791 ,(tub32 `(ash x ,first-one)))))
2792 (setf first-one nil))
2793 (when (logbitp bitpos y)
2794 (setf first-one bitpos))))
2796 (cond ((= first-one 31))
2800 (add `(- ,(tub32 '(ash x 31)) ,(tub32 `(ash x ,first-one))))))
2804 ;;; If arg is a constant power of two, turn FLOOR into a shift and mask.
2805 ;;; If CEILING, add in (1- (ABS Y)) and then do FLOOR.
2806 (flet ((frob (y ceil-p)
2807 (unless (constant-continuation-p y)
2808 (give-up-ir1-transform))
2809 (let* ((y (continuation-value y))
2811 (len (1- (integer-length y-abs))))
2812 (unless (= y-abs (ash 1 len))
2813 (give-up-ir1-transform))
2814 (let ((shift (- len))
2816 `(let ,(when ceil-p `((x (+ x ,(1- y-abs)))))
2818 `(values (ash (- x) ,shift)
2819 (- (logand (- x) ,mask)))
2820 `(values (ash x ,shift)
2821 (logand x ,mask))))))))
2822 (deftransform floor ((x y) (integer integer) *)
2823 "convert division by 2^k to shift"
2825 (deftransform ceiling ((x y) (integer integer) *)
2826 "convert division by 2^k to shift"
2829 ;;; Do the same for MOD.
2830 (deftransform mod ((x y) (integer integer) * :when :both)
2831 "convert remainder mod 2^k to LOGAND"
2832 (unless (constant-continuation-p y)
2833 (give-up-ir1-transform))
2834 (let* ((y (continuation-value y))
2836 (len (1- (integer-length y-abs))))
2837 (unless (= y-abs (ash 1 len))
2838 (give-up-ir1-transform))
2839 (let ((mask (1- y-abs)))
2841 `(- (logand (- x) ,mask))
2842 `(logand x ,mask)))))
2844 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2845 (deftransform truncate ((x y) (integer integer))
2846 "convert division by 2^k to shift"
2847 (unless (constant-continuation-p y)
2848 (give-up-ir1-transform))
2849 (let* ((y (continuation-value y))
2851 (len (1- (integer-length y-abs))))
2852 (unless (= y-abs (ash 1 len))
2853 (give-up-ir1-transform))
2854 (let* ((shift (- len))
2857 (values ,(if (minusp y)
2859 `(- (ash (- x) ,shift)))
2860 (- (logand (- x) ,mask)))
2861 (values ,(if (minusp y)
2862 `(- (ash (- x) ,shift))
2864 (logand x ,mask))))))
2866 ;;; And the same for REM.
2867 (deftransform rem ((x y) (integer integer) * :when :both)
2868 "convert remainder mod 2^k to LOGAND"
2869 (unless (constant-continuation-p y)
2870 (give-up-ir1-transform))
2871 (let* ((y (continuation-value y))
2873 (len (1- (integer-length y-abs))))
2874 (unless (= y-abs (ash 1 len))
2875 (give-up-ir1-transform))
2876 (let ((mask (1- y-abs)))
2878 (- (logand (- x) ,mask))
2879 (logand x ,mask)))))
2881 ;;;; arithmetic and logical identity operation elimination
2883 ;;;; Flush calls to various arith functions that convert to the identity
2884 ;;;; function or a constant.
2886 (dolist (stuff '((ash 0 x)
2891 (logxor -1 (lognot x))
2893 (destructuring-bind (name identity result) stuff
2894 (deftransform name ((x y) `(* (constant-argument (member ,identity))) '*
2895 :eval-name t :when :both)
2896 "fold identity operations"
2899 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2900 ;;; (* 0 -4.0) is -0.0.
2901 (deftransform - ((x y) ((constant-argument (member 0)) rational) *
2903 "convert (- 0 x) to negate"
2905 (deftransform * ((x y) (rational (constant-argument (member 0))) *
2907 "convert (* x 0) to 0."
2910 ;;; Return T if in an arithmetic op including continuations X and Y, the
2911 ;;; result type is not affected by the type of X. That is, Y is at least as
2912 ;;; contagious as X.
2914 (defun not-more-contagious (x y)
2915 (declare (type continuation x y))
2916 (let ((x (continuation-type x))
2917 (y (continuation-type y)))
2918 (values (type= (numeric-contagion x y)
2919 (numeric-contagion y y)))))
2920 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2921 ;;; needs more work as valid transforms are missed; some cases are
2922 ;;; specific to particular transform functions so the use of this
2923 ;;; function may need a re-think.
2924 (defun not-more-contagious (x y)
2925 (declare (type continuation x y))
2926 (flet ((simple-numeric-type (num)
2927 (and (numeric-type-p num)
2928 ;; Return non-NIL if NUM is integer, rational, or a float
2929 ;; of some type (but not FLOAT)
2930 (case (numeric-type-class num)
2934 (numeric-type-format num))
2937 (let ((x (continuation-type x))
2938 (y (continuation-type y)))
2939 (if (and (simple-numeric-type x)
2940 (simple-numeric-type y))
2941 (values (type= (numeric-contagion x y)
2942 (numeric-contagion y y)))))))
2946 ;;; If y is not constant, not zerop, or is contagious, or a
2947 ;;; positive float +0.0 then give up.
2948 (deftransform + ((x y) (t (constant-argument t)) * :when :both)
2950 (let ((val (continuation-value y)))
2951 (unless (and (zerop val)
2952 (not (and (floatp val) (plusp (float-sign val))))
2953 (not-more-contagious y x))
2954 (give-up-ir1-transform)))
2959 ;;; If y is not constant, not zerop, or is contagious, or a
2960 ;;; negative float -0.0 then give up.
2961 (deftransform - ((x y) (t (constant-argument t)) * :when :both)
2963 (let ((val (continuation-value y)))
2964 (unless (and (zerop val)
2965 (not (and (floatp val) (minusp (float-sign val))))
2966 (not-more-contagious y x))
2967 (give-up-ir1-transform)))
2970 ;;; Fold (OP x +/-1)
2971 (dolist (stuff '((* x (%negate x))
2974 (destructuring-bind (name result minus-result) stuff
2975 (deftransform name ((x y) '(t (constant-argument real)) '* :eval-name t
2977 "fold identity operations"
2978 (let ((val (continuation-value y)))
2979 (unless (and (= (abs val) 1)
2980 (not-more-contagious y x))
2981 (give-up-ir1-transform))
2982 (if (minusp val) minus-result result)))))
2984 ;;; Fold (expt x n) into multiplications for small integral values of
2985 ;;; N; convert (expt x 1/2) to sqrt.
2986 (deftransform expt ((x y) (t (constant-argument real)) *)
2987 "recode as multiplication or sqrt"
2988 (let ((val (continuation-value y)))
2989 ;; If Y would cause the result to be promoted to the same type as
2990 ;; Y, we give up. If not, then the result will be the same type
2991 ;; as X, so we can replace the exponentiation with simple
2992 ;; multiplication and division for small integral powers.
2993 (unless (not-more-contagious y x)
2994 (give-up-ir1-transform))
2995 (cond ((zerop val) '(float 1 x))
2996 ((= val 2) '(* x x))
2997 ((= val -2) '(/ (* x x)))
2998 ((= val 3) '(* x x x))
2999 ((= val -3) '(/ (* x x x)))
3000 ((= val 1/2) '(sqrt x))
3001 ((= val -1/2) '(/ (sqrt x)))
3002 (t (give-up-ir1-transform)))))
3004 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3005 ;;; transformations?
3006 ;;; Perhaps we should have to prove that the denominator is nonzero before
3007 ;;; doing them? (Also the DOLIST over macro calls is weird. Perhaps
3008 ;;; just FROB?) -- WHN 19990917
3010 ;;; FIXME: What gives with the single quotes in the argument lists
3011 ;;; for DEFTRANSFORMs here? Does that work? Is it needed? Why?
3012 (dolist (name '(ash /))
3013 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3014 :eval-name t :when :both)
3017 (dolist (name '(truncate round floor ceiling))
3018 (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '*
3019 :eval-name t :when :both)
3023 ;;;; character operations
3025 (deftransform char-equal ((a b) (base-char base-char))
3027 '(let* ((ac (char-code a))
3029 (sum (logxor ac bc)))
3031 (when (eql sum #x20)
3032 (let ((sum (+ ac bc)))
3033 (and (> sum 161) (< sum 213)))))))
3035 (deftransform char-upcase ((x) (base-char))
3037 '(let ((n-code (char-code x)))
3038 (if (and (> n-code #o140) ; Octal 141 is #\a.
3039 (< n-code #o173)) ; Octal 172 is #\z.
3040 (code-char (logxor #x20 n-code))
3043 (deftransform char-downcase ((x) (base-char))
3045 '(let ((n-code (char-code x)))
3046 (if (and (> n-code 64) ; 65 is #\A.
3047 (< n-code 91)) ; 90 is #\Z.
3048 (code-char (logxor #x20 n-code))
3051 ;;;; equality predicate transforms
3053 ;;; Return true if X and Y are continuations whose only use is a reference
3054 ;;; to the same leaf, and the value of the leaf cannot change.
3055 (defun same-leaf-ref-p (x y)
3056 (declare (type continuation x y))
3057 (let ((x-use (continuation-use x))
3058 (y-use (continuation-use y)))
3061 (eq (ref-leaf x-use) (ref-leaf y-use))
3062 (constant-reference-p x-use))))
3064 ;;; If X and Y are the same leaf, then the result is true. Otherwise, if
3065 ;;; there is no intersection between the types of the arguments, then the
3066 ;;; result is definitely false.
3067 (deftransform simple-equality-transform ((x y) * *
3070 (cond ((same-leaf-ref-p x y)
3072 ((not (types-intersect (continuation-type x) (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-intersect x-type y-type))
3103 ((and (csubtypep x-type char-type)
3104 (csubtypep y-type char-type))
3106 ((or (not (types-intersect x-type number-type))
3107 (not (types-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 (specifier-type '(complex rational)))
3135 (csubtypep y-type (specifier-type '(complex rational)))))
3136 ;; They are both rationals and complexp is the same. Convert
3140 (give-up-ir1-transform
3141 "The operands might not be the same type.")))
3142 (give-up-ir1-transform
3143 "The operands might not be the same type."))))
3145 ;;; If Cont's type is a numeric type, then return the type, otherwise
3146 ;;; GIVE-UP-IR1-TRANSFORM.
3147 (defun numeric-type-or-lose (cont)
3148 (declare (type continuation cont))
3149 (let ((res (continuation-type cont)))
3150 (unless (numeric-type-p res) (give-up-ir1-transform))
3153 ;;; See whether we can statically determine (< X Y) using type information.
3154 ;;; If X's high bound is < Y's low, then X < Y. Similarly, if X's low is >=
3155 ;;; to Y's high, the X >= Y (so return NIL). If not, at least make sure any
3156 ;;; constant arg is second.
3158 ;;; KLUDGE: Why should constant argument be second? It would be nice to find
3159 ;;; out and explain. -- WHN 19990917
3160 #!-propagate-float-type
3161 (defun ir1-transform-< (x y first second inverse)
3162 (if (same-leaf-ref-p x y)
3164 (let* ((x-type (numeric-type-or-lose x))
3165 (x-lo (numeric-type-low x-type))
3166 (x-hi (numeric-type-high x-type))
3167 (y-type (numeric-type-or-lose y))
3168 (y-lo (numeric-type-low y-type))
3169 (y-hi (numeric-type-high y-type)))
3170 (cond ((and x-hi y-lo (< x-hi y-lo))
3172 ((and y-hi x-lo (>= x-lo y-hi))
3174 ((and (constant-continuation-p first)
3175 (not (constant-continuation-p second)))
3178 (give-up-ir1-transform))))))
3179 #!+propagate-float-type
3180 (defun ir1-transform-< (x y first second inverse)
3181 (if (same-leaf-ref-p x y)
3183 (let ((xi (numeric-type->interval (numeric-type-or-lose x)))
3184 (yi (numeric-type->interval (numeric-type-or-lose y))))
3185 (cond ((interval-< xi yi)
3187 ((interval->= xi yi)
3189 ((and (constant-continuation-p first)
3190 (not (constant-continuation-p second)))
3193 (give-up-ir1-transform))))))
3195 (deftransform < ((x y) (integer integer) * :when :both)
3196 (ir1-transform-< x y x y '>))
3198 (deftransform > ((x y) (integer integer) * :when :both)
3199 (ir1-transform-< y x x y '<))
3201 #!+propagate-float-type
3202 (deftransform < ((x y) (float float) * :when :both)
3203 (ir1-transform-< x y x y '>))
3205 #!+propagate-float-type
3206 (deftransform > ((x y) (float float) * :when :both)
3207 (ir1-transform-< y x x y '<))
3209 ;;;; converting N-arg comparisons
3211 ;;;; We convert calls to N-arg comparison functions such as < into
3212 ;;;; two-arg calls. This transformation is enabled for all such
3213 ;;;; comparisons in this file. If any of these predicates are not
3214 ;;;; open-coded, then the transformation should be removed at some
3215 ;;;; point to avoid pessimization.
3217 ;;; This function is used for source transformation of N-arg
3218 ;;; comparison functions other than inequality. We deal both with
3219 ;;; converting to two-arg calls and inverting the sense of the test,
3220 ;;; if necessary. If the call has two args, then we pass or return a
3221 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3222 ;;; then we transform to code that returns true. Otherwise, we bind
3223 ;;; all the arguments and expand into a bunch of IFs.
3224 (declaim (ftype (function (symbol list boolean) *) multi-compare))
3225 (defun multi-compare (predicate args not-p)
3226 (let ((nargs (length args)))
3227 (cond ((< nargs 1) (values nil t))
3228 ((= nargs 1) `(progn ,@args t))
3231 `(if (,predicate ,(first args) ,(second args)) nil t)
3234 (do* ((i (1- nargs) (1- i))
3236 (current (gensym) (gensym))
3237 (vars (list current) (cons current vars))
3238 (result 't (if not-p
3239 `(if (,predicate ,current ,last)
3241 `(if (,predicate ,current ,last)
3244 `((lambda ,vars ,result) . ,args)))))))
3246 (def-source-transform = (&rest args) (multi-compare '= args nil))
3247 (def-source-transform < (&rest args) (multi-compare '< args nil))
3248 (def-source-transform > (&rest args) (multi-compare '> args nil))
3249 (def-source-transform <= (&rest args) (multi-compare '> args t))
3250 (def-source-transform >= (&rest args) (multi-compare '< args t))
3252 (def-source-transform char= (&rest args) (multi-compare 'char= args nil))
3253 (def-source-transform char< (&rest args) (multi-compare 'char< args nil))
3254 (def-source-transform char> (&rest args) (multi-compare 'char> args nil))
3255 (def-source-transform char<= (&rest args) (multi-compare 'char> args t))
3256 (def-source-transform char>= (&rest args) (multi-compare 'char< args t))
3258 (def-source-transform char-equal (&rest args) (multi-compare 'char-equal args nil))
3259 (def-source-transform char-lessp (&rest args) (multi-compare 'char-lessp args nil))
3260 (def-source-transform char-greaterp (&rest args)
3261 (multi-compare 'char-greaterp args nil))
3262 (def-source-transform char-not-greaterp (&rest args)
3263 (multi-compare 'char-greaterp args t))
3264 (def-source-transform char-not-lessp (&rest args) (multi-compare 'char-lessp args t))
3266 ;;; This function does source transformation of N-arg inequality
3267 ;;; functions such as /=. This is similar to Multi-Compare in the <3
3268 ;;; arg cases. If there are more than two args, then we expand into
3269 ;;; the appropriate n^2 comparisons only when speed is important.
3270 (declaim (ftype (function (symbol list) *) multi-not-equal))
3271 (defun multi-not-equal (predicate args)
3272 (let ((nargs (length args)))
3273 (cond ((< nargs 1) (values nil t))
3274 ((= nargs 1) `(progn ,@args t))
3276 `(if (,predicate ,(first args) ,(second args)) nil t))
3277 ((not (policy nil (and (>= speed space)
3278 (>= speed compilation-speed))))
3281 (let ((vars (make-gensym-list nargs)))
3282 (do ((var vars next)
3283 (next (cdr vars) (cdr next))
3286 `((lambda ,vars ,result) . ,args))
3287 (let ((v1 (first var)))
3289 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3291 (def-source-transform /= (&rest args) (multi-not-equal '= args))
3292 (def-source-transform char/= (&rest args) (multi-not-equal 'char= args))
3293 (def-source-transform char-not-equal (&rest args) (multi-not-equal 'char-equal args))
3295 ;;; Expand MAX and MIN into the obvious comparisons.
3296 (def-source-transform max (arg &rest more-args)
3297 (if (null more-args)
3299 (once-only ((arg1 arg)
3300 (arg2 `(max ,@more-args)))
3301 `(if (> ,arg1 ,arg2)
3303 (def-source-transform min (arg &rest more-args)
3304 (if (null more-args)
3306 (once-only ((arg1 arg)
3307 (arg2 `(min ,@more-args)))
3308 `(if (< ,arg1 ,arg2)
3311 ;;;; converting N-arg arithmetic functions
3313 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3314 ;;;; versions, and degenerate cases are flushed.
3316 ;;; Left-associate First-Arg and More-Args using Function.
3317 (declaim (ftype (function (symbol t list) list) associate-arguments))
3318 (defun associate-arguments (function first-arg more-args)
3319 (let ((next (rest more-args))
3320 (arg (first more-args)))
3322 `(,function ,first-arg ,arg)
3323 (associate-arguments function `(,function ,first-arg ,arg) next))))
3325 ;;; Do source transformations for transitive functions such as +.
3326 ;;; One-arg cases are replaced with the arg and zero arg cases with
3327 ;;; the identity. If LEAF-FUN is true, then replace two-arg calls with
3328 ;;; a call to that function.
3329 (defun source-transform-transitive (fun args identity &optional leaf-fun)
3330 (declare (symbol fun leaf-fun) (list args))
3333 (1 `(values ,(first args)))
3335 `(,leaf-fun ,(first args) ,(second args))
3338 (associate-arguments fun (first args) (rest args)))))
3340 (def-source-transform + (&rest args) (source-transform-transitive '+ args 0))
3341 (def-source-transform * (&rest args) (source-transform-transitive '* args 1))
3342 (def-source-transform logior (&rest args)
3343 (source-transform-transitive 'logior args 0))
3344 (def-source-transform logxor (&rest args)
3345 (source-transform-transitive 'logxor args 0))
3346 (def-source-transform logand (&rest args)
3347 (source-transform-transitive 'logand args -1))
3349 (def-source-transform logeqv (&rest args)
3350 (if (evenp (length args))
3351 `(lognot (logxor ,@args))
3354 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3355 ;;; because when they are given one argument, they return its absolute
3358 (def-source-transform gcd (&rest args)
3361 (1 `(abs (the integer ,(first args))))
3363 (t (associate-arguments 'gcd (first args) (rest args)))))
3365 (def-source-transform lcm (&rest args)
3368 (1 `(abs (the integer ,(first args))))
3370 (t (associate-arguments 'lcm (first args) (rest args)))))
3372 ;;; Do source transformations for intransitive n-arg functions such as
3373 ;;; /. With one arg, we form the inverse. With two args we pass.
3374 ;;; Otherwise we associate into two-arg calls.
3375 (declaim (ftype (function (symbol list t) list) source-transform-intransitive))
3376 (defun source-transform-intransitive (function args inverse)
3378 ((0 2) (values nil t))
3379 (1 `(,@inverse ,(first args)))
3380 (t (associate-arguments function (first args) (rest args)))))
3382 (def-source-transform - (&rest args)
3383 (source-transform-intransitive '- args '(%negate)))
3384 (def-source-transform / (&rest args)
3385 (source-transform-intransitive '/ args '(/ 1)))
3387 ;;;; transforming APPLY
3389 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3390 ;;; only needs to understand one kind of variable-argument call. It is
3391 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3392 (def-source-transform apply (fun arg &rest more-args)
3393 (let ((args (cons arg more-args)))
3394 `(multiple-value-call ,fun
3395 ,@(mapcar #'(lambda (x)
3398 (values-list ,(car (last args))))))
3400 ;;;; transforming FORMAT
3402 ;;;; If the control string is a compile-time constant, then replace it
3403 ;;;; with a use of the FORMATTER macro so that the control string is
3404 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3405 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3406 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3408 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3409 :policy (> speed space))
3410 (unless (constant-continuation-p control)
3411 (give-up-ir1-transform "The control string is not a constant."))
3412 (let ((arg-names (make-gensym-list (length args))))
3413 `(lambda (dest control ,@arg-names)
3414 (declare (ignore control))
3415 (format dest (formatter ,(continuation-value control)) ,@arg-names))))
3417 (deftransform format ((stream control &rest args) (stream function &rest t) *
3418 :policy (> speed space))
3419 (let ((arg-names (make-gensym-list (length args))))
3420 `(lambda (stream control ,@arg-names)
3421 (funcall control stream ,@arg-names)
3424 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3425 :policy (> speed space))
3426 (let ((arg-names (make-gensym-list (length args))))
3427 `(lambda (tee control ,@arg-names)
3428 (declare (ignore tee))
3429 (funcall control *standard-output* ,@arg-names)