1 ;;;; This file contains macro-like source transformations which
2 ;;;; convert uses of certain functions into the canonical form desired
3 ;;;; within the compiler. FIXME: 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 (define-source-transform not (x) `(if ,x nil t))
19 (define-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 (define-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 (define-source-transform identity (x) `(prog1 ,x))
30 (define-source-transform values (x) `(prog1 ,x))
32 ;;; Bind the value and make a closure that returns it.
33 (define-source-transform constantly (value)
34 (with-unique-names (rest n-value)
35 `(let ((,n-value ,value))
37 (declare (ignore ,rest))
40 ;;; If the function has a known number of arguments, then return a
41 ;;; lambda with the appropriate fixed number of args. If the
42 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
43 ;;; MV optimization figure things out.
44 (deftransform complement ((fun) * * :node node)
46 (multiple-value-bind (min max)
47 (fun-type-nargs (lvar-type fun))
49 ((and min (eql min max))
50 (let ((dums (make-gensym-list min)))
51 `#'(lambda ,dums (not (funcall fun ,@dums)))))
52 ((awhen (node-lvar node)
53 (let ((dest (lvar-dest it)))
54 (and (combination-p dest)
55 (eq (combination-fun dest) it))))
56 '#'(lambda (&rest args)
57 (not (apply fun args))))
59 (give-up-ir1-transform
60 "The function doesn't have a fixed argument count.")))))
64 ;;; Translate CxR into CAR/CDR combos.
65 (defun source-transform-cxr (form)
66 (if (/= (length form) 2)
68 (let* ((name (car form))
72 (leaf (leaf-source-name name))))))
73 (do ((i (- (length string) 2) (1- i))
75 `(,(ecase (char string i)
81 ;;; Make source transforms to turn CxR forms into combinations of CAR
82 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
84 (/show0 "about to set CxR source transforms")
85 (loop for i of-type index from 2 upto 4 do
86 ;; Iterate over BUF = all names CxR where x = an I-element
87 ;; string of #\A or #\D characters.
88 (let ((buf (make-string (+ 2 i))))
89 (setf (aref buf 0) #\C
90 (aref buf (1+ i)) #\R)
91 (dotimes (j (ash 2 i))
92 (declare (type index j))
94 (declare (type index k))
95 (setf (aref buf (1+ k))
96 (if (logbitp k j) #\A #\D)))
97 (setf (info :function :source-transform (intern buf))
98 #'source-transform-cxr))))
99 (/show0 "done setting CxR source transforms")
101 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
102 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
103 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
105 (define-source-transform first (x) `(car ,x))
106 (define-source-transform rest (x) `(cdr ,x))
107 (define-source-transform second (x) `(cadr ,x))
108 (define-source-transform third (x) `(caddr ,x))
109 (define-source-transform fourth (x) `(cadddr ,x))
110 (define-source-transform fifth (x) `(nth 4 ,x))
111 (define-source-transform sixth (x) `(nth 5 ,x))
112 (define-source-transform seventh (x) `(nth 6 ,x))
113 (define-source-transform eighth (x) `(nth 7 ,x))
114 (define-source-transform ninth (x) `(nth 8 ,x))
115 (define-source-transform tenth (x) `(nth 9 ,x))
117 ;;; Translate RPLACx to LET and SETF.
118 (define-source-transform rplaca (x y)
123 (define-source-transform rplacd (x y)
129 (define-source-transform nth (n l) `(car (nthcdr ,n ,l)))
131 (define-source-transform last (x) `(sb!impl::last1 ,x))
132 ;; (define-source-transform last (x)
133 ;; `(let* ((x (the list ,x))
135 ;; (do () ((atom r) x)
136 ;; (shiftf x r (cdr r)))))
138 (defvar *default-nthcdr-open-code-limit* 6)
139 (defvar *extreme-nthcdr-open-code-limit* 20)
141 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
142 "convert NTHCDR to CAxxR"
143 (unless (constant-lvar-p n)
144 (give-up-ir1-transform))
145 (let ((n (lvar-value n)))
147 (if (policy node (and (= speed 3) (= space 0)))
148 *extreme-nthcdr-open-code-limit*
149 *default-nthcdr-open-code-limit*))
150 (give-up-ir1-transform))
155 `(cdr ,(frob (1- n))))))
158 ;;;; arithmetic and numerology
160 (define-source-transform plusp (x) `(> ,x 0))
161 (define-source-transform minusp (x) `(< ,x 0))
162 (define-source-transform zerop (x) `(= ,x 0))
164 (define-source-transform 1+ (x) `(+ ,x 1))
165 (define-source-transform 1- (x) `(- ,x 1))
167 (define-source-transform oddp (x) `(not (zerop (logand ,x 1))))
168 (define-source-transform evenp (x) `(zerop (logand ,x 1)))
170 ;;; Note that all the integer division functions are available for
171 ;;; inline expansion.
173 (macrolet ((deffrob (fun)
174 `(define-source-transform ,fun (x &optional (y nil y-p))
181 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
183 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
186 (define-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
188 (deftransform logbitp
189 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
190 (unsigned-byte #.sb!vm:n-word-bits))))
191 `(if (>= index #.sb!vm:n-word-bits)
193 (not (zerop (logand integer (ash 1 index))))))
195 (define-source-transform byte (size position)
196 `(cons ,size ,position))
197 (define-source-transform byte-size (spec) `(car ,spec))
198 (define-source-transform byte-position (spec) `(cdr ,spec))
199 (define-source-transform ldb-test (bytespec integer)
200 `(not (zerop (mask-field ,bytespec ,integer))))
202 ;;; With the ratio and complex accessors, we pick off the "identity"
203 ;;; case, and use a primitive to handle the cell access case.
204 (define-source-transform numerator (num)
205 (once-only ((n-num `(the rational ,num)))
209 (define-source-transform denominator (num)
210 (once-only ((n-num `(the rational ,num)))
212 (%denominator ,n-num)
215 ;;;; interval arithmetic for computing bounds
217 ;;;; This is a set of routines for operating on intervals. It
218 ;;;; implements a simple interval arithmetic package. Although SBCL
219 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
220 ;;;; for two reasons:
222 ;;;; 1. This package is simpler than NUMERIC-TYPE.
224 ;;;; 2. It makes debugging much easier because you can just strip
225 ;;;; out these routines and test them independently of SBCL. (This is a
228 ;;;; One disadvantage is a probable increase in consing because we
229 ;;;; have to create these new interval structures even though
230 ;;;; numeric-type has everything we want to know. Reason 2 wins for
233 ;;; Support operations that mimic real arithmetic comparison
234 ;;; operators, but imposing a total order on the floating points such
235 ;;; that negative zeros are strictly less than positive zeros.
236 (macrolet ((def (name op)
239 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
240 (,op (float-sign x) (float-sign y))
242 (def signed-zero->= >=)
243 (def signed-zero-> >)
244 (def signed-zero-= =)
245 (def signed-zero-< <)
246 (def signed-zero-<= <=))
248 ;;; The basic interval type. It can handle open and closed intervals.
249 ;;; A bound is open if it is a list containing a number, just like
250 ;;; Lisp says. NIL means unbounded.
251 (defstruct (interval (:constructor %make-interval)
255 (defun make-interval (&key low high)
256 (labels ((normalize-bound (val)
259 (float-infinity-p val))
260 ;; Handle infinities.
264 ;; Handle any closed bounds.
267 ;; We have an open bound. Normalize the numeric
268 ;; bound. If the normalized bound is still a number
269 ;; (not nil), keep the bound open. Otherwise, the
270 ;; bound is really unbounded, so drop the openness.
271 (let ((new-val (normalize-bound (first val))))
273 ;; The bound exists, so keep it open still.
276 (error "unknown bound type in MAKE-INTERVAL")))))
277 (%make-interval :low (normalize-bound low)
278 :high (normalize-bound high))))
280 ;;; Given a number X, create a form suitable as a bound for an
281 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
282 #!-sb-fluid (declaim (inline set-bound))
283 (defun set-bound (x open-p)
284 (if (and x open-p) (list x) x))
286 ;;; Apply the function F to a bound X. If X is an open bound, then
287 ;;; the result will be open. IF X is NIL, the result is NIL.
288 (defun bound-func (f x)
289 (declare (type function f))
291 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
292 ;; With these traps masked, we might get things like infinity
293 ;; or negative infinity returned. Check for this and return
294 ;; NIL to indicate unbounded.
295 (let ((y (funcall f (type-bound-number x))))
297 (float-infinity-p y))
299 (set-bound (funcall f (type-bound-number x)) (consp x)))))))
301 ;;; Apply a binary operator OP to two bounds X and Y. The result is
302 ;;; NIL if either is NIL. Otherwise bound is computed and the result
303 ;;; is open if either X or Y is open.
305 ;;; FIXME: only used in this file, not needed in target runtime
306 (defmacro bound-binop (op x y)
308 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
309 (set-bound (,op (type-bound-number ,x)
310 (type-bound-number ,y))
311 (or (consp ,x) (consp ,y))))))
313 ;;; Convert a numeric-type object to an interval object.
314 (defun numeric-type->interval (x)
315 (declare (type numeric-type x))
316 (make-interval :low (numeric-type-low x)
317 :high (numeric-type-high x)))
319 (defun type-approximate-interval (type)
320 (declare (type ctype type))
321 (let ((types (prepare-arg-for-derive-type type))
324 (let ((type (if (member-type-p type)
325 (convert-member-type type)
327 (unless (numeric-type-p type)
328 (return-from type-approximate-interval nil))
329 (let ((interval (numeric-type->interval type)))
332 (interval-approximate-union result interval)
336 (defun copy-interval-limit (limit)
341 (defun copy-interval (x)
342 (declare (type interval x))
343 (make-interval :low (copy-interval-limit (interval-low x))
344 :high (copy-interval-limit (interval-high x))))
346 ;;; Given a point P contained in the interval X, split X into two
347 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
348 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
349 ;;; contains P. You can specify both to be T or NIL.
350 (defun interval-split (p x &optional close-lower close-upper)
351 (declare (type number p)
353 (list (make-interval :low (copy-interval-limit (interval-low x))
354 :high (if close-lower p (list p)))
355 (make-interval :low (if close-upper (list p) p)
356 :high (copy-interval-limit (interval-high x)))))
358 ;;; Return the closure of the interval. That is, convert open bounds
359 ;;; to closed bounds.
360 (defun interval-closure (x)
361 (declare (type interval x))
362 (make-interval :low (type-bound-number (interval-low x))
363 :high (type-bound-number (interval-high x))))
365 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
366 ;;; '-. Otherwise return NIL.
367 (defun interval-range-info (x &optional (point 0))
368 (declare (type interval x))
369 (let ((lo (interval-low x))
370 (hi (interval-high x)))
371 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
373 ((and hi (signed-zero->= point (type-bound-number hi)))
378 ;;; Test to see whether the interval X is bounded. HOW determines the
379 ;;; test, and should be either ABOVE, BELOW, or BOTH.
380 (defun interval-bounded-p (x how)
381 (declare (type interval x))
388 (and (interval-low x) (interval-high x)))))
390 ;;; See whether the interval X contains the number P, taking into
391 ;;; account that the interval might not be closed.
392 (defun interval-contains-p (p x)
393 (declare (type number p)
395 ;; Does the interval X contain the number P? This would be a lot
396 ;; easier if all intervals were closed!
397 (let ((lo (interval-low x))
398 (hi (interval-high x)))
400 ;; The interval is bounded
401 (if (and (signed-zero-<= (type-bound-number lo) p)
402 (signed-zero-<= p (type-bound-number hi)))
403 ;; P is definitely in the closure of the interval.
404 ;; We just need to check the end points now.
405 (cond ((signed-zero-= p (type-bound-number lo))
407 ((signed-zero-= p (type-bound-number hi))
412 ;; Interval with upper bound
413 (if (signed-zero-< p (type-bound-number hi))
415 (and (numberp hi) (signed-zero-= p hi))))
417 ;; Interval with lower bound
418 (if (signed-zero-> p (type-bound-number lo))
420 (and (numberp lo) (signed-zero-= p lo))))
422 ;; Interval with no bounds
425 ;;; Determine whether two intervals X and Y intersect. Return T if so.
426 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
427 ;;; were closed. Otherwise the intervals are treated as they are.
429 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
430 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
431 ;;; is T, then they do intersect because we use the closure of X = [0,
432 ;;; 1] and Y = [1, 2] to determine intersection.
433 (defun interval-intersect-p (x y &optional closed-intervals-p)
434 (declare (type interval x y))
435 (multiple-value-bind (intersect diff)
436 (interval-intersection/difference (if closed-intervals-p
439 (if closed-intervals-p
442 (declare (ignore diff))
445 ;;; Are the two intervals adjacent? That is, is there a number
446 ;;; between the two intervals that is not an element of either
447 ;;; interval? If so, they are not adjacent. For example [0, 1) and
448 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
449 ;;; between both intervals.
450 (defun interval-adjacent-p (x y)
451 (declare (type interval x y))
452 (flet ((adjacent (lo hi)
453 ;; Check to see whether lo and hi are adjacent. If either is
454 ;; nil, they can't be adjacent.
455 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
456 ;; The bounds are equal. They are adjacent if one of
457 ;; them is closed (a number). If both are open (consp),
458 ;; then there is a number that lies between them.
459 (or (numberp lo) (numberp hi)))))
460 (or (adjacent (interval-low y) (interval-high x))
461 (adjacent (interval-low x) (interval-high y)))))
463 ;;; Compute the intersection and difference between two intervals.
464 ;;; Two values are returned: the intersection and the difference.
466 ;;; Let the two intervals be X and Y, and let I and D be the two
467 ;;; values returned by this function. Then I = X intersect Y. If I
468 ;;; is NIL (the empty set), then D is X union Y, represented as the
469 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
470 ;;; - I, which is a list of two intervals.
472 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
473 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
474 (defun interval-intersection/difference (x y)
475 (declare (type interval x y))
476 (let ((x-lo (interval-low x))
477 (x-hi (interval-high x))
478 (y-lo (interval-low y))
479 (y-hi (interval-high y)))
482 ;; If p is an open bound, make it closed. If p is a closed
483 ;; bound, make it open.
488 ;; Test whether P is in the interval.
489 (when (interval-contains-p (type-bound-number p)
490 (interval-closure int))
491 (let ((lo (interval-low int))
492 (hi (interval-high int)))
493 ;; Check for endpoints.
494 (cond ((and lo (= (type-bound-number p) (type-bound-number lo)))
495 (not (and (consp p) (numberp lo))))
496 ((and hi (= (type-bound-number p) (type-bound-number hi)))
497 (not (and (numberp p) (consp hi))))
499 (test-lower-bound (p int)
500 ;; P is a lower bound of an interval.
503 (not (interval-bounded-p int 'below))))
504 (test-upper-bound (p int)
505 ;; P is an upper bound of an interval.
508 (not (interval-bounded-p int 'above)))))
509 (let ((x-lo-in-y (test-lower-bound x-lo y))
510 (x-hi-in-y (test-upper-bound x-hi y))
511 (y-lo-in-x (test-lower-bound y-lo x))
512 (y-hi-in-x (test-upper-bound y-hi x)))
513 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
514 ;; Intervals intersect. Let's compute the intersection
515 ;; and the difference.
516 (multiple-value-bind (lo left-lo left-hi)
517 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
518 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
519 (multiple-value-bind (hi right-lo right-hi)
521 (values x-hi (opposite-bound x-hi) y-hi))
523 (values y-hi (opposite-bound y-hi) x-hi)))
524 (values (make-interval :low lo :high hi)
525 (list (make-interval :low left-lo
527 (make-interval :low right-lo
530 (values nil (list x y))))))))
532 ;;; If intervals X and Y intersect, return a new interval that is the
533 ;;; union of the two. If they do not intersect, return NIL.
534 (defun interval-merge-pair (x y)
535 (declare (type interval x y))
536 ;; If x and y intersect or are adjacent, create the union.
537 ;; Otherwise return nil
538 (when (or (interval-intersect-p x y)
539 (interval-adjacent-p x y))
540 (flet ((select-bound (x1 x2 min-op max-op)
541 (let ((x1-val (type-bound-number x1))
542 (x2-val (type-bound-number x2)))
544 ;; Both bounds are finite. Select the right one.
545 (cond ((funcall min-op x1-val x2-val)
546 ;; x1 is definitely better.
548 ((funcall max-op x1-val x2-val)
549 ;; x2 is definitely better.
552 ;; Bounds are equal. Select either
553 ;; value and make it open only if
555 (set-bound x1-val (and (consp x1) (consp x2))))))
557 ;; At least one bound is not finite. The
558 ;; non-finite bound always wins.
560 (let* ((x-lo (copy-interval-limit (interval-low x)))
561 (x-hi (copy-interval-limit (interval-high x)))
562 (y-lo (copy-interval-limit (interval-low y)))
563 (y-hi (copy-interval-limit (interval-high y))))
564 (make-interval :low (select-bound x-lo y-lo #'< #'>)
565 :high (select-bound x-hi y-hi #'> #'<))))))
567 ;;; return the minimal interval, containing X and Y
568 (defun interval-approximate-union (x y)
569 (cond ((interval-merge-pair x y))
571 (make-interval :low (copy-interval-limit (interval-low x))
572 :high (copy-interval-limit (interval-high y))))
574 (make-interval :low (copy-interval-limit (interval-low y))
575 :high (copy-interval-limit (interval-high x))))))
577 ;;; basic arithmetic operations on intervals. We probably should do
578 ;;; true interval arithmetic here, but it's complicated because we
579 ;;; have float and integer types and bounds can be open or closed.
581 ;;; the negative of an interval
582 (defun interval-neg (x)
583 (declare (type interval x))
584 (make-interval :low (bound-func #'- (interval-high x))
585 :high (bound-func #'- (interval-low x))))
587 ;;; Add two intervals.
588 (defun interval-add (x y)
589 (declare (type interval x y))
590 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
591 :high (bound-binop + (interval-high x) (interval-high y))))
593 ;;; Subtract two intervals.
594 (defun interval-sub (x y)
595 (declare (type interval x y))
596 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
597 :high (bound-binop - (interval-high x) (interval-low y))))
599 ;;; Multiply two intervals.
600 (defun interval-mul (x y)
601 (declare (type interval x y))
602 (flet ((bound-mul (x y)
603 (cond ((or (null x) (null y))
604 ;; Multiply by infinity is infinity
606 ((or (and (numberp x) (zerop x))
607 (and (numberp y) (zerop y)))
608 ;; Multiply by closed zero is special. The result
609 ;; is always a closed bound. But don't replace this
610 ;; with zero; we want the multiplication to produce
611 ;; the correct signed zero, if needed.
612 (* (type-bound-number x) (type-bound-number y)))
613 ((or (and (floatp x) (float-infinity-p x))
614 (and (floatp y) (float-infinity-p y)))
615 ;; Infinity times anything is infinity
618 ;; General multiply. The result is open if either is open.
619 (bound-binop * x y)))))
620 (let ((x-range (interval-range-info x))
621 (y-range (interval-range-info y)))
622 (cond ((null x-range)
623 ;; Split x into two and multiply each separately
624 (destructuring-bind (x- x+) (interval-split 0 x t t)
625 (interval-merge-pair (interval-mul x- y)
626 (interval-mul x+ y))))
628 ;; Split y into two and multiply each separately
629 (destructuring-bind (y- y+) (interval-split 0 y t t)
630 (interval-merge-pair (interval-mul x y-)
631 (interval-mul x y+))))
633 (interval-neg (interval-mul (interval-neg x) y)))
635 (interval-neg (interval-mul x (interval-neg y))))
636 ((and (eq x-range '+) (eq y-range '+))
637 ;; If we are here, X and Y are both positive.
639 :low (bound-mul (interval-low x) (interval-low y))
640 :high (bound-mul (interval-high x) (interval-high y))))
642 (bug "excluded case in INTERVAL-MUL"))))))
644 ;;; Divide two intervals.
645 (defun interval-div (top bot)
646 (declare (type interval top bot))
647 (flet ((bound-div (x y y-low-p)
650 ;; Divide by infinity means result is 0. However,
651 ;; we need to watch out for the sign of the result,
652 ;; to correctly handle signed zeros. We also need
653 ;; to watch out for positive or negative infinity.
654 (if (floatp (type-bound-number x))
656 (- (float-sign (type-bound-number x) 0.0))
657 (float-sign (type-bound-number x) 0.0))
659 ((zerop (type-bound-number y))
660 ;; Divide by zero means result is infinity
662 ((and (numberp x) (zerop x))
663 ;; Zero divided by anything is zero.
666 (bound-binop / x y)))))
667 (let ((top-range (interval-range-info top))
668 (bot-range (interval-range-info bot)))
669 (cond ((null bot-range)
670 ;; The denominator contains zero, so anything goes!
671 (make-interval :low nil :high nil))
673 ;; Denominator is negative so flip the sign, compute the
674 ;; result, and flip it back.
675 (interval-neg (interval-div top (interval-neg bot))))
677 ;; Split top into two positive and negative parts, and
678 ;; divide each separately
679 (destructuring-bind (top- top+) (interval-split 0 top t t)
680 (interval-merge-pair (interval-div top- bot)
681 (interval-div top+ bot))))
683 ;; Top is negative so flip the sign, divide, and flip the
684 ;; sign of the result.
685 (interval-neg (interval-div (interval-neg top) bot)))
686 ((and (eq top-range '+) (eq bot-range '+))
689 :low (bound-div (interval-low top) (interval-high bot) t)
690 :high (bound-div (interval-high top) (interval-low bot) nil)))
692 (bug "excluded case in INTERVAL-DIV"))))))
694 ;;; Apply the function F to the interval X. If X = [a, b], then the
695 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
696 ;;; result makes sense. It will if F is monotonic increasing (or
698 (defun interval-func (f x)
699 (declare (type function f)
701 (let ((lo (bound-func f (interval-low x)))
702 (hi (bound-func f (interval-high x))))
703 (make-interval :low lo :high hi)))
705 ;;; Return T if X < Y. That is every number in the interval X is
706 ;;; always less than any number in the interval Y.
707 (defun interval-< (x y)
708 (declare (type interval x y))
709 ;; X < Y only if X is bounded above, Y is bounded below, and they
711 (when (and (interval-bounded-p x 'above)
712 (interval-bounded-p y 'below))
713 ;; Intervals are bounded in the appropriate way. Make sure they
715 (let ((left (interval-high x))
716 (right (interval-low y)))
717 (cond ((> (type-bound-number left)
718 (type-bound-number right))
719 ;; The intervals definitely overlap, so result is NIL.
721 ((< (type-bound-number left)
722 (type-bound-number right))
723 ;; The intervals definitely don't touch, so result is T.
726 ;; Limits are equal. Check for open or closed bounds.
727 ;; Don't overlap if one or the other are open.
728 (or (consp left) (consp right)))))))
730 ;;; Return T if X >= Y. That is, every number in the interval X is
731 ;;; always greater than any number in the interval Y.
732 (defun interval->= (x y)
733 (declare (type interval x y))
734 ;; X >= Y if lower bound of X >= upper bound of Y
735 (when (and (interval-bounded-p x 'below)
736 (interval-bounded-p y 'above))
737 (>= (type-bound-number (interval-low x))
738 (type-bound-number (interval-high y)))))
740 ;;; Return an interval that is the absolute value of X. Thus, if
741 ;;; X = [-1 10], the result is [0, 10].
742 (defun interval-abs (x)
743 (declare (type interval x))
744 (case (interval-range-info x)
750 (destructuring-bind (x- x+) (interval-split 0 x t t)
751 (interval-merge-pair (interval-neg x-) x+)))))
753 ;;; Compute the square of an interval.
754 (defun interval-sqr (x)
755 (declare (type interval x))
756 (interval-func (lambda (x) (* x x))
759 ;;;; numeric DERIVE-TYPE methods
761 ;;; a utility for defining derive-type methods of integer operations. If
762 ;;; the types of both X and Y are integer types, then we compute a new
763 ;;; integer type with bounds determined Fun when applied to X and Y.
764 ;;; Otherwise, we use NUMERIC-CONTAGION.
765 (defun derive-integer-type-aux (x y fun)
766 (declare (type function fun))
767 (if (and (numeric-type-p x) (numeric-type-p y)
768 (eq (numeric-type-class x) 'integer)
769 (eq (numeric-type-class y) 'integer)
770 (eq (numeric-type-complexp x) :real)
771 (eq (numeric-type-complexp y) :real))
772 (multiple-value-bind (low high) (funcall fun x y)
773 (make-numeric-type :class 'integer
777 (numeric-contagion x y)))
779 (defun derive-integer-type (x y fun)
780 (declare (type lvar x y) (type function fun))
781 (let ((x (lvar-type x))
783 (derive-integer-type-aux x y fun)))
785 ;;; simple utility to flatten a list
786 (defun flatten-list (x)
787 (labels ((flatten-and-append (tree list)
788 (cond ((null tree) list)
789 ((atom tree) (cons tree list))
790 (t (flatten-and-append
791 (car tree) (flatten-and-append (cdr tree) list))))))
792 (flatten-and-append x nil)))
794 ;;; Take some type of lvar and massage it so that we get a list of the
795 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
797 (defun prepare-arg-for-derive-type (arg)
798 (flet ((listify (arg)
803 (union-type-types arg))
806 (unless (eq arg *empty-type*)
807 ;; Make sure all args are some type of numeric-type. For member
808 ;; types, convert the list of members into a union of equivalent
809 ;; single-element member-type's.
810 (let ((new-args nil))
811 (dolist (arg (listify arg))
812 (if (member-type-p arg)
813 ;; Run down the list of members and convert to a list of
815 (dolist (member (member-type-members arg))
816 (push (if (numberp member)
817 (make-member-type :members (list member))
820 (push arg new-args)))
821 (unless (member *empty-type* new-args)
824 ;;; Convert from the standard type convention for which -0.0 and 0.0
825 ;;; are equal to an intermediate convention for which they are
826 ;;; considered different which is more natural for some of the
828 (defun convert-numeric-type (type)
829 (declare (type numeric-type type))
830 ;;; Only convert real float interval delimiters types.
831 (if (eq (numeric-type-complexp type) :real)
832 (let* ((lo (numeric-type-low type))
833 (lo-val (type-bound-number lo))
834 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
835 (hi (numeric-type-high type))
836 (hi-val (type-bound-number hi))
837 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
838 (if (or lo-float-zero-p hi-float-zero-p)
840 :class (numeric-type-class type)
841 :format (numeric-type-format type)
843 :low (if lo-float-zero-p
845 (list (float 0.0 lo-val))
846 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
848 :high (if hi-float-zero-p
850 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
857 ;;; Convert back from the intermediate convention for which -0.0 and
858 ;;; 0.0 are considered different to the standard type convention for
860 (defun convert-back-numeric-type (type)
861 (declare (type numeric-type type))
862 ;;; Only convert real float interval delimiters types.
863 (if (eq (numeric-type-complexp type) :real)
864 (let* ((lo (numeric-type-low type))
865 (lo-val (type-bound-number lo))
867 (and lo (floatp lo-val) (= lo-val 0.0)
868 (float-sign lo-val)))
869 (hi (numeric-type-high type))
870 (hi-val (type-bound-number hi))
872 (and hi (floatp hi-val) (= hi-val 0.0)
873 (float-sign hi-val))))
875 ;; (float +0.0 +0.0) => (member 0.0)
876 ;; (float -0.0 -0.0) => (member -0.0)
877 ((and lo-float-zero-p hi-float-zero-p)
878 ;; shouldn't have exclusive bounds here..
879 (aver (and (not (consp lo)) (not (consp hi))))
880 (if (= lo-float-zero-p hi-float-zero-p)
881 ;; (float +0.0 +0.0) => (member 0.0)
882 ;; (float -0.0 -0.0) => (member -0.0)
883 (specifier-type `(member ,lo-val))
884 ;; (float -0.0 +0.0) => (float 0.0 0.0)
885 ;; (float +0.0 -0.0) => (float 0.0 0.0)
886 (make-numeric-type :class (numeric-type-class type)
887 :format (numeric-type-format type)
893 ;; (float -0.0 x) => (float 0.0 x)
894 ((and (not (consp lo)) (minusp lo-float-zero-p))
895 (make-numeric-type :class (numeric-type-class type)
896 :format (numeric-type-format type)
898 :low (float 0.0 lo-val)
900 ;; (float (+0.0) x) => (float (0.0) x)
901 ((and (consp lo) (plusp lo-float-zero-p))
902 (make-numeric-type :class (numeric-type-class type)
903 :format (numeric-type-format type)
905 :low (list (float 0.0 lo-val))
908 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
909 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
910 (list (make-member-type :members (list (float 0.0 lo-val)))
911 (make-numeric-type :class (numeric-type-class type)
912 :format (numeric-type-format type)
914 :low (list (float 0.0 lo-val))
918 ;; (float x +0.0) => (float x 0.0)
919 ((and (not (consp hi)) (plusp hi-float-zero-p))
920 (make-numeric-type :class (numeric-type-class type)
921 :format (numeric-type-format type)
924 :high (float 0.0 hi-val)))
925 ;; (float x (-0.0)) => (float x (0.0))
926 ((and (consp hi) (minusp hi-float-zero-p))
927 (make-numeric-type :class (numeric-type-class type)
928 :format (numeric-type-format type)
931 :high (list (float 0.0 hi-val))))
933 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
934 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
935 (list (make-member-type :members (list (float -0.0 hi-val)))
936 (make-numeric-type :class (numeric-type-class type)
937 :format (numeric-type-format type)
940 :high (list (float 0.0 hi-val)))))))
946 ;;; Convert back a possible list of numeric types.
947 (defun convert-back-numeric-type-list (type-list)
951 (dolist (type type-list)
952 (if (numeric-type-p type)
953 (let ((result (convert-back-numeric-type type)))
955 (setf results (append results result))
956 (push result results)))
957 (push type results)))
960 (convert-back-numeric-type type-list))
962 (convert-back-numeric-type-list (union-type-types type-list)))
966 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
967 ;;; belong in the kernel's type logic, invoked always, instead of in
968 ;;; the compiler, invoked only during some type optimizations. (In
969 ;;; fact, as of 0.pre8.100 or so they probably are, under
970 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
972 ;;; Take a list of types and return a canonical type specifier,
973 ;;; combining any MEMBER types together. If both positive and negative
974 ;;; MEMBER types are present they are converted to a float type.
975 ;;; XXX This would be far simpler if the type-union methods could handle
976 ;;; member/number unions.
977 (defun make-canonical-union-type (type-list)
980 (dolist (type type-list)
981 (if (member-type-p type)
982 (setf members (union members (member-type-members type)))
983 (push type misc-types)))
985 (when (null (set-difference `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0) members))
986 (push (specifier-type '(long-float 0.0l0 0.0l0)) misc-types)
987 (setf members (set-difference members `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0))))
988 (when (null (set-difference `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0) members))
989 (push (specifier-type '(double-float 0.0d0 0.0d0)) misc-types)
990 (setf members (set-difference members `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0))))
991 (when (null (set-difference `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0) members))
992 (push (specifier-type '(single-float 0.0f0 0.0f0)) misc-types)
993 (setf members (set-difference members `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0))))
995 (apply #'type-union (make-member-type :members members) misc-types)
996 (apply #'type-union misc-types))))
998 ;;; Convert a member type with a single member to a numeric type.
999 (defun convert-member-type (arg)
1000 (let* ((members (member-type-members arg))
1001 (member (first members))
1002 (member-type (type-of member)))
1003 (aver (not (rest members)))
1004 (specifier-type (cond ((typep member 'integer)
1005 `(integer ,member ,member))
1006 ((memq member-type '(short-float single-float
1007 double-float long-float))
1008 `(,member-type ,member ,member))
1012 ;;; This is used in defoptimizers for computing the resulting type of
1015 ;;; Given the lvar ARG, derive the resulting type using the
1016 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1017 ;;; "atomic" lvar type like numeric-type or member-type (containing
1018 ;;; just one element). It should return the resulting type, which can
1019 ;;; be a list of types.
1021 ;;; For the case of member types, if a MEMBER-FUN is given it is
1022 ;;; called to compute the result otherwise the member type is first
1023 ;;; converted to a numeric type and the DERIVE-FUN is called.
1024 (defun one-arg-derive-type (arg derive-fun member-fun
1025 &optional (convert-type t))
1026 (declare (type function derive-fun)
1027 (type (or null function) member-fun))
1028 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1034 (with-float-traps-masked
1035 (:underflow :overflow :divide-by-zero)
1037 `(eql ,(funcall member-fun
1038 (first (member-type-members x))))))
1039 ;; Otherwise convert to a numeric type.
1040 (let ((result-type-list
1041 (funcall derive-fun (convert-member-type x))))
1043 (convert-back-numeric-type-list result-type-list)
1044 result-type-list))))
1047 (convert-back-numeric-type-list
1048 (funcall derive-fun (convert-numeric-type x)))
1049 (funcall derive-fun x)))
1051 *universal-type*))))
1052 ;; Run down the list of args and derive the type of each one,
1053 ;; saving all of the results in a list.
1054 (let ((results nil))
1055 (dolist (arg arg-list)
1056 (let ((result (deriver arg)))
1058 (setf results (append results result))
1059 (push result results))))
1061 (make-canonical-union-type results)
1062 (first results)))))))
1064 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1065 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1066 ;;; original args and a third which is T to indicate if the two args
1067 ;;; really represent the same lvar. This is useful for deriving the
1068 ;;; type of things like (* x x), which should always be positive. If
1069 ;;; we didn't do this, we wouldn't be able to tell.
1070 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1071 &optional (convert-type t))
1072 (declare (type function derive-fun fun))
1073 (flet ((deriver (x y same-arg)
1074 (cond ((and (member-type-p x) (member-type-p y))
1075 (let* ((x (first (member-type-members x)))
1076 (y (first (member-type-members y)))
1077 (result (ignore-errors
1078 (with-float-traps-masked
1079 (:underflow :overflow :divide-by-zero
1081 (funcall fun x y)))))
1082 (cond ((null result) *empty-type*)
1083 ((and (floatp result) (float-nan-p result))
1084 (make-numeric-type :class 'float
1085 :format (type-of result)
1088 (specifier-type `(eql ,result))))))
1089 ((and (member-type-p x) (numeric-type-p y))
1090 (let* ((x (convert-member-type x))
1091 (y (if convert-type (convert-numeric-type y) y))
1092 (result (funcall derive-fun x y same-arg)))
1094 (convert-back-numeric-type-list result)
1096 ((and (numeric-type-p x) (member-type-p y))
1097 (let* ((x (if convert-type (convert-numeric-type x) x))
1098 (y (convert-member-type y))
1099 (result (funcall derive-fun x y same-arg)))
1101 (convert-back-numeric-type-list result)
1103 ((and (numeric-type-p x) (numeric-type-p y))
1104 (let* ((x (if convert-type (convert-numeric-type x) x))
1105 (y (if convert-type (convert-numeric-type y) y))
1106 (result (funcall derive-fun x y same-arg)))
1108 (convert-back-numeric-type-list result)
1111 *universal-type*))))
1112 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1113 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1114 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1116 (let ((results nil))
1118 ;; Since the args are the same LVARs, just run down the
1121 (let ((result (deriver x x same-arg)))
1123 (setf results (append results result))
1124 (push result results))))
1125 ;; Try all pairwise combinations.
1128 (let ((result (or (deriver x y same-arg)
1129 (numeric-contagion x y))))
1131 (setf results (append results result))
1132 (push result results))))))
1134 (make-canonical-union-type results)
1135 (first results)))))))
1137 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1139 (defoptimizer (+ derive-type) ((x y))
1140 (derive-integer-type
1147 (values (frob (numeric-type-low x) (numeric-type-low y))
1148 (frob (numeric-type-high x) (numeric-type-high y)))))))
1150 (defoptimizer (- derive-type) ((x y))
1151 (derive-integer-type
1158 (values (frob (numeric-type-low x) (numeric-type-high y))
1159 (frob (numeric-type-high x) (numeric-type-low y)))))))
1161 (defoptimizer (* derive-type) ((x y))
1162 (derive-integer-type
1165 (let ((x-low (numeric-type-low x))
1166 (x-high (numeric-type-high x))
1167 (y-low (numeric-type-low y))
1168 (y-high (numeric-type-high y)))
1169 (cond ((not (and x-low y-low))
1171 ((or (minusp x-low) (minusp y-low))
1172 (if (and x-high y-high)
1173 (let ((max (* (max (abs x-low) (abs x-high))
1174 (max (abs y-low) (abs y-high)))))
1175 (values (- max) max))
1178 (values (* x-low y-low)
1179 (if (and x-high y-high)
1183 (defoptimizer (/ derive-type) ((x y))
1184 (numeric-contagion (lvar-type x) (lvar-type y)))
1188 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1190 (defun +-derive-type-aux (x y same-arg)
1191 (if (and (numeric-type-real-p x)
1192 (numeric-type-real-p y))
1195 (let ((x-int (numeric-type->interval x)))
1196 (interval-add x-int x-int))
1197 (interval-add (numeric-type->interval x)
1198 (numeric-type->interval y))))
1199 (result-type (numeric-contagion x y)))
1200 ;; If the result type is a float, we need to be sure to coerce
1201 ;; the bounds into the correct type.
1202 (when (eq (numeric-type-class result-type) 'float)
1203 (setf result (interval-func
1205 (coerce x (or (numeric-type-format result-type)
1209 :class (if (and (eq (numeric-type-class x) 'integer)
1210 (eq (numeric-type-class y) 'integer))
1211 ;; The sum of integers is always an integer.
1213 (numeric-type-class result-type))
1214 :format (numeric-type-format result-type)
1215 :low (interval-low result)
1216 :high (interval-high result)))
1217 ;; general contagion
1218 (numeric-contagion x y)))
1220 (defoptimizer (+ derive-type) ((x y))
1221 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1223 (defun --derive-type-aux (x y same-arg)
1224 (if (and (numeric-type-real-p x)
1225 (numeric-type-real-p y))
1227 ;; (- X X) is always 0.
1229 (make-interval :low 0 :high 0)
1230 (interval-sub (numeric-type->interval x)
1231 (numeric-type->interval y))))
1232 (result-type (numeric-contagion x y)))
1233 ;; If the result type is a float, we need to be sure to coerce
1234 ;; the bounds into the correct type.
1235 (when (eq (numeric-type-class result-type) 'float)
1236 (setf result (interval-func
1238 (coerce x (or (numeric-type-format result-type)
1242 :class (if (and (eq (numeric-type-class x) 'integer)
1243 (eq (numeric-type-class y) 'integer))
1244 ;; The difference of integers is always an integer.
1246 (numeric-type-class result-type))
1247 :format (numeric-type-format result-type)
1248 :low (interval-low result)
1249 :high (interval-high result)))
1250 ;; general contagion
1251 (numeric-contagion x y)))
1253 (defoptimizer (- derive-type) ((x y))
1254 (two-arg-derive-type x y #'--derive-type-aux #'-))
1256 (defun *-derive-type-aux (x y same-arg)
1257 (if (and (numeric-type-real-p x)
1258 (numeric-type-real-p y))
1260 ;; (* X X) is always positive, so take care to do it right.
1262 (interval-sqr (numeric-type->interval x))
1263 (interval-mul (numeric-type->interval x)
1264 (numeric-type->interval y))))
1265 (result-type (numeric-contagion x y)))
1266 ;; If the result type is a float, we need to be sure to coerce
1267 ;; the bounds into the correct type.
1268 (when (eq (numeric-type-class result-type) 'float)
1269 (setf result (interval-func
1271 (coerce x (or (numeric-type-format result-type)
1275 :class (if (and (eq (numeric-type-class x) 'integer)
1276 (eq (numeric-type-class y) 'integer))
1277 ;; The product of integers is always an integer.
1279 (numeric-type-class result-type))
1280 :format (numeric-type-format result-type)
1281 :low (interval-low result)
1282 :high (interval-high result)))
1283 (numeric-contagion x y)))
1285 (defoptimizer (* derive-type) ((x y))
1286 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1288 (defun /-derive-type-aux (x y same-arg)
1289 (if (and (numeric-type-real-p x)
1290 (numeric-type-real-p y))
1292 ;; (/ X X) is always 1, except if X can contain 0. In
1293 ;; that case, we shouldn't optimize the division away
1294 ;; because we want 0/0 to signal an error.
1296 (not (interval-contains-p
1297 0 (interval-closure (numeric-type->interval y)))))
1298 (make-interval :low 1 :high 1)
1299 (interval-div (numeric-type->interval x)
1300 (numeric-type->interval y))))
1301 (result-type (numeric-contagion x y)))
1302 ;; If the result type is a float, we need to be sure to coerce
1303 ;; the bounds into the correct type.
1304 (when (eq (numeric-type-class result-type) 'float)
1305 (setf result (interval-func
1307 (coerce x (or (numeric-type-format result-type)
1310 (make-numeric-type :class (numeric-type-class result-type)
1311 :format (numeric-type-format result-type)
1312 :low (interval-low result)
1313 :high (interval-high result)))
1314 (numeric-contagion x y)))
1316 (defoptimizer (/ derive-type) ((x y))
1317 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1321 (defun ash-derive-type-aux (n-type shift same-arg)
1322 (declare (ignore same-arg))
1323 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1324 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1325 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1326 ;; two bignums yielding zero) and it's hard to avoid that
1327 ;; calculation in here.
1328 #+(and cmu sb-xc-host)
1329 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1330 (typep (numeric-type-high n-type) 'bignum))
1331 (or (typep (numeric-type-low shift) 'bignum)
1332 (typep (numeric-type-high shift) 'bignum)))
1333 (return-from ash-derive-type-aux *universal-type*))
1334 (flet ((ash-outer (n s)
1335 (when (and (fixnump s)
1337 (> s sb!xc:most-negative-fixnum))
1339 ;; KLUDGE: The bare 64's here should be related to
1340 ;; symbolic machine word size values somehow.
1343 (if (and (fixnump s)
1344 (> s sb!xc:most-negative-fixnum))
1346 (if (minusp n) -1 0))))
1347 (or (and (csubtypep n-type (specifier-type 'integer))
1348 (csubtypep shift (specifier-type 'integer))
1349 (let ((n-low (numeric-type-low n-type))
1350 (n-high (numeric-type-high n-type))
1351 (s-low (numeric-type-low shift))
1352 (s-high (numeric-type-high shift)))
1353 (make-numeric-type :class 'integer :complexp :real
1356 (ash-outer n-low s-high)
1357 (ash-inner n-low s-low)))
1360 (ash-inner n-high s-low)
1361 (ash-outer n-high s-high))))))
1364 (defoptimizer (ash derive-type) ((n shift))
1365 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1367 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1368 (macrolet ((frob (fun)
1369 `#'(lambda (type type2)
1370 (declare (ignore type2))
1371 (let ((lo (numeric-type-low type))
1372 (hi (numeric-type-high type)))
1373 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1375 (defoptimizer (%negate derive-type) ((num))
1376 (derive-integer-type num num (frob -))))
1378 (defun lognot-derive-type-aux (int)
1379 (derive-integer-type-aux int int
1380 (lambda (type type2)
1381 (declare (ignore type2))
1382 (let ((lo (numeric-type-low type))
1383 (hi (numeric-type-high type)))
1384 (values (if hi (lognot hi) nil)
1385 (if lo (lognot lo) nil)
1386 (numeric-type-class type)
1387 (numeric-type-format type))))))
1389 (defoptimizer (lognot derive-type) ((int))
1390 (lognot-derive-type-aux (lvar-type int)))
1392 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1393 (defoptimizer (%negate derive-type) ((num))
1394 (flet ((negate-bound (b)
1396 (set-bound (- (type-bound-number b))
1398 (one-arg-derive-type num
1400 (modified-numeric-type
1402 :low (negate-bound (numeric-type-high type))
1403 :high (negate-bound (numeric-type-low type))))
1406 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1407 (defoptimizer (abs derive-type) ((num))
1408 (let ((type (lvar-type num)))
1409 (if (and (numeric-type-p type)
1410 (eq (numeric-type-class type) 'integer)
1411 (eq (numeric-type-complexp type) :real))
1412 (let ((lo (numeric-type-low type))
1413 (hi (numeric-type-high type)))
1414 (make-numeric-type :class 'integer :complexp :real
1415 :low (cond ((and hi (minusp hi))
1421 :high (if (and hi lo)
1422 (max (abs hi) (abs lo))
1424 (numeric-contagion type type))))
1426 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1427 (defun abs-derive-type-aux (type)
1428 (cond ((eq (numeric-type-complexp type) :complex)
1429 ;; The absolute value of a complex number is always a
1430 ;; non-negative float.
1431 (let* ((format (case (numeric-type-class type)
1432 ((integer rational) 'single-float)
1433 (t (numeric-type-format type))))
1434 (bound-format (or format 'float)))
1435 (make-numeric-type :class 'float
1438 :low (coerce 0 bound-format)
1441 ;; The absolute value of a real number is a non-negative real
1442 ;; of the same type.
1443 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1444 (class (numeric-type-class type))
1445 (format (numeric-type-format type))
1446 (bound-type (or format class 'real)))
1451 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1452 :high (coerce-numeric-bound
1453 (interval-high abs-bnd) bound-type))))))
1455 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1456 (defoptimizer (abs derive-type) ((num))
1457 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1459 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1460 (defoptimizer (truncate derive-type) ((number divisor))
1461 (let ((number-type (lvar-type number))
1462 (divisor-type (lvar-type divisor))
1463 (integer-type (specifier-type 'integer)))
1464 (if (and (numeric-type-p number-type)
1465 (csubtypep number-type integer-type)
1466 (numeric-type-p divisor-type)
1467 (csubtypep divisor-type integer-type))
1468 (let ((number-low (numeric-type-low number-type))
1469 (number-high (numeric-type-high number-type))
1470 (divisor-low (numeric-type-low divisor-type))
1471 (divisor-high (numeric-type-high divisor-type)))
1472 (values-specifier-type
1473 `(values ,(integer-truncate-derive-type number-low number-high
1474 divisor-low divisor-high)
1475 ,(integer-rem-derive-type number-low number-high
1476 divisor-low divisor-high))))
1479 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1482 (defun rem-result-type (number-type divisor-type)
1483 ;; Figure out what the remainder type is. The remainder is an
1484 ;; integer if both args are integers; a rational if both args are
1485 ;; rational; and a float otherwise.
1486 (cond ((and (csubtypep number-type (specifier-type 'integer))
1487 (csubtypep divisor-type (specifier-type 'integer)))
1489 ((and (csubtypep number-type (specifier-type 'rational))
1490 (csubtypep divisor-type (specifier-type 'rational)))
1492 ((and (csubtypep number-type (specifier-type 'float))
1493 (csubtypep divisor-type (specifier-type 'float)))
1494 ;; Both are floats so the result is also a float, of
1495 ;; the largest type.
1496 (or (float-format-max (numeric-type-format number-type)
1497 (numeric-type-format divisor-type))
1499 ((and (csubtypep number-type (specifier-type 'float))
1500 (csubtypep divisor-type (specifier-type 'rational)))
1501 ;; One of the arguments is a float and the other is a
1502 ;; rational. The remainder is a float of the same
1504 (or (numeric-type-format number-type) 'float))
1505 ((and (csubtypep divisor-type (specifier-type 'float))
1506 (csubtypep number-type (specifier-type 'rational)))
1507 ;; One of the arguments is a float and the other is a
1508 ;; rational. The remainder is a float of the same
1510 (or (numeric-type-format divisor-type) 'float))
1512 ;; Some unhandled combination. This usually means both args
1513 ;; are REAL so the result is a REAL.
1516 (defun truncate-derive-type-quot (number-type divisor-type)
1517 (let* ((rem-type (rem-result-type number-type divisor-type))
1518 (number-interval (numeric-type->interval number-type))
1519 (divisor-interval (numeric-type->interval divisor-type)))
1520 ;;(declare (type (member '(integer rational float)) rem-type))
1521 ;; We have real numbers now.
1522 (cond ((eq rem-type 'integer)
1523 ;; Since the remainder type is INTEGER, both args are
1525 (let* ((res (integer-truncate-derive-type
1526 (interval-low number-interval)
1527 (interval-high number-interval)
1528 (interval-low divisor-interval)
1529 (interval-high divisor-interval))))
1530 (specifier-type (if (listp res) res 'integer))))
1532 (let ((quot (truncate-quotient-bound
1533 (interval-div number-interval
1534 divisor-interval))))
1535 (specifier-type `(integer ,(or (interval-low quot) '*)
1536 ,(or (interval-high quot) '*))))))))
1538 (defun truncate-derive-type-rem (number-type divisor-type)
1539 (let* ((rem-type (rem-result-type number-type divisor-type))
1540 (number-interval (numeric-type->interval number-type))
1541 (divisor-interval (numeric-type->interval divisor-type))
1542 (rem (truncate-rem-bound number-interval divisor-interval)))
1543 ;;(declare (type (member '(integer rational float)) rem-type))
1544 ;; We have real numbers now.
1545 (cond ((eq rem-type 'integer)
1546 ;; Since the remainder type is INTEGER, both args are
1548 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1549 ,(or (interval-high rem) '*))))
1551 (multiple-value-bind (class format)
1554 (values 'integer nil))
1556 (values 'rational nil))
1557 ((or single-float double-float #!+long-float long-float)
1558 (values 'float rem-type))
1560 (values 'float nil))
1563 (when (member rem-type '(float single-float double-float
1564 #!+long-float long-float))
1565 (setf rem (interval-func #'(lambda (x)
1566 (coerce x rem-type))
1568 (make-numeric-type :class class
1570 :low (interval-low rem)
1571 :high (interval-high rem)))))))
1573 (defun truncate-derive-type-quot-aux (num div same-arg)
1574 (declare (ignore same-arg))
1575 (if (and (numeric-type-real-p num)
1576 (numeric-type-real-p div))
1577 (truncate-derive-type-quot num div)
1580 (defun truncate-derive-type-rem-aux (num div same-arg)
1581 (declare (ignore same-arg))
1582 (if (and (numeric-type-real-p num)
1583 (numeric-type-real-p div))
1584 (truncate-derive-type-rem num div)
1587 (defoptimizer (truncate derive-type) ((number divisor))
1588 (let ((quot (two-arg-derive-type number divisor
1589 #'truncate-derive-type-quot-aux #'truncate))
1590 (rem (two-arg-derive-type number divisor
1591 #'truncate-derive-type-rem-aux #'rem)))
1592 (when (and quot rem)
1593 (make-values-type :required (list quot rem)))))
1595 (defun ftruncate-derive-type-quot (number-type divisor-type)
1596 ;; The bounds are the same as for truncate. However, the first
1597 ;; result is a float of some type. We need to determine what that
1598 ;; type is. Basically it's the more contagious of the two types.
1599 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1600 (res-type (numeric-contagion number-type divisor-type)))
1601 (make-numeric-type :class 'float
1602 :format (numeric-type-format res-type)
1603 :low (numeric-type-low q-type)
1604 :high (numeric-type-high q-type))))
1606 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1607 (declare (ignore same-arg))
1608 (if (and (numeric-type-real-p n)
1609 (numeric-type-real-p d))
1610 (ftruncate-derive-type-quot n d)
1613 (defoptimizer (ftruncate derive-type) ((number divisor))
1615 (two-arg-derive-type number divisor
1616 #'ftruncate-derive-type-quot-aux #'ftruncate))
1617 (rem (two-arg-derive-type number divisor
1618 #'truncate-derive-type-rem-aux #'rem)))
1619 (when (and quot rem)
1620 (make-values-type :required (list quot rem)))))
1622 (defun %unary-truncate-derive-type-aux (number)
1623 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1625 (defoptimizer (%unary-truncate derive-type) ((number))
1626 (one-arg-derive-type number
1627 #'%unary-truncate-derive-type-aux
1630 (defoptimizer (%unary-ftruncate derive-type) ((number))
1631 (let ((divisor (specifier-type '(integer 1 1))))
1632 (one-arg-derive-type number
1634 (ftruncate-derive-type-quot-aux n divisor nil))
1635 #'%unary-ftruncate)))
1637 ;;; Define optimizers for FLOOR and CEILING.
1639 ((def (name q-name r-name)
1640 (let ((q-aux (symbolicate q-name "-AUX"))
1641 (r-aux (symbolicate r-name "-AUX")))
1643 ;; Compute type of quotient (first) result.
1644 (defun ,q-aux (number-type divisor-type)
1645 (let* ((number-interval
1646 (numeric-type->interval number-type))
1648 (numeric-type->interval divisor-type))
1649 (quot (,q-name (interval-div number-interval
1650 divisor-interval))))
1651 (specifier-type `(integer ,(or (interval-low quot) '*)
1652 ,(or (interval-high quot) '*)))))
1653 ;; Compute type of remainder.
1654 (defun ,r-aux (number-type divisor-type)
1655 (let* ((divisor-interval
1656 (numeric-type->interval divisor-type))
1657 (rem (,r-name divisor-interval))
1658 (result-type (rem-result-type number-type divisor-type)))
1659 (multiple-value-bind (class format)
1662 (values 'integer nil))
1664 (values 'rational nil))
1665 ((or single-float double-float #!+long-float long-float)
1666 (values 'float result-type))
1668 (values 'float nil))
1671 (when (member result-type '(float single-float double-float
1672 #!+long-float long-float))
1673 ;; Make sure that the limits on the interval have
1675 (setf rem (interval-func (lambda (x)
1676 (coerce x result-type))
1678 (make-numeric-type :class class
1680 :low (interval-low rem)
1681 :high (interval-high rem)))))
1682 ;; the optimizer itself
1683 (defoptimizer (,name derive-type) ((number divisor))
1684 (flet ((derive-q (n d same-arg)
1685 (declare (ignore same-arg))
1686 (if (and (numeric-type-real-p n)
1687 (numeric-type-real-p d))
1690 (derive-r (n d same-arg)
1691 (declare (ignore same-arg))
1692 (if (and (numeric-type-real-p n)
1693 (numeric-type-real-p d))
1696 (let ((quot (two-arg-derive-type
1697 number divisor #'derive-q #',name))
1698 (rem (two-arg-derive-type
1699 number divisor #'derive-r #'mod)))
1700 (when (and quot rem)
1701 (make-values-type :required (list quot rem))))))))))
1703 (def floor floor-quotient-bound floor-rem-bound)
1704 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1706 ;;; Define optimizers for FFLOOR and FCEILING
1707 (macrolet ((def (name q-name r-name)
1708 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1709 (r-aux (symbolicate r-name "-AUX")))
1711 ;; Compute type of quotient (first) result.
1712 (defun ,q-aux (number-type divisor-type)
1713 (let* ((number-interval
1714 (numeric-type->interval number-type))
1716 (numeric-type->interval divisor-type))
1717 (quot (,q-name (interval-div number-interval
1719 (res-type (numeric-contagion number-type
1722 :class (numeric-type-class res-type)
1723 :format (numeric-type-format res-type)
1724 :low (interval-low quot)
1725 :high (interval-high quot))))
1727 (defoptimizer (,name derive-type) ((number divisor))
1728 (flet ((derive-q (n d same-arg)
1729 (declare (ignore same-arg))
1730 (if (and (numeric-type-real-p n)
1731 (numeric-type-real-p d))
1734 (derive-r (n d same-arg)
1735 (declare (ignore same-arg))
1736 (if (and (numeric-type-real-p n)
1737 (numeric-type-real-p d))
1740 (let ((quot (two-arg-derive-type
1741 number divisor #'derive-q #',name))
1742 (rem (two-arg-derive-type
1743 number divisor #'derive-r #'mod)))
1744 (when (and quot rem)
1745 (make-values-type :required (list quot rem))))))))))
1747 (def ffloor floor-quotient-bound floor-rem-bound)
1748 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
1750 ;;; functions to compute the bounds on the quotient and remainder for
1751 ;;; the FLOOR function
1752 (defun floor-quotient-bound (quot)
1753 ;; Take the floor of the quotient and then massage it into what we
1755 (let ((lo (interval-low quot))
1756 (hi (interval-high quot)))
1757 ;; Take the floor of the lower bound. The result is always a
1758 ;; closed lower bound.
1760 (floor (type-bound-number lo))
1762 ;; For the upper bound, we need to be careful.
1765 ;; An open bound. We need to be careful here because
1766 ;; the floor of '(10.0) is 9, but the floor of
1768 (multiple-value-bind (q r) (floor (first hi))
1773 ;; A closed bound, so the answer is obvious.
1777 (make-interval :low lo :high hi)))
1778 (defun floor-rem-bound (div)
1779 ;; The remainder depends only on the divisor. Try to get the
1780 ;; correct sign for the remainder if we can.
1781 (case (interval-range-info div)
1783 ;; The divisor is always positive.
1784 (let ((rem (interval-abs div)))
1785 (setf (interval-low rem) 0)
1786 (when (and (numberp (interval-high rem))
1787 (not (zerop (interval-high rem))))
1788 ;; The remainder never contains the upper bound. However,
1789 ;; watch out for the case where the high limit is zero!
1790 (setf (interval-high rem) (list (interval-high rem))))
1793 ;; The divisor is always negative.
1794 (let ((rem (interval-neg (interval-abs div))))
1795 (setf (interval-high rem) 0)
1796 (when (numberp (interval-low rem))
1797 ;; The remainder never contains the lower bound.
1798 (setf (interval-low rem) (list (interval-low rem))))
1801 ;; The divisor can be positive or negative. All bets off. The
1802 ;; magnitude of remainder is the maximum value of the divisor.
1803 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1804 ;; The bound never reaches the limit, so make the interval open.
1805 (make-interval :low (if limit
1808 :high (list limit))))))
1810 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1811 => #S(INTERVAL :LOW 0 :HIGH 10)
1812 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1813 => #S(INTERVAL :LOW 0 :HIGH 10)
1814 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1815 => #S(INTERVAL :LOW 0 :HIGH 10)
1816 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1817 => #S(INTERVAL :LOW 0 :HIGH 9)
1818 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1819 => #S(INTERVAL :LOW 0 :HIGH 10)
1820 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1821 => #S(INTERVAL :LOW 0 :HIGH 10)
1822 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1823 => #S(INTERVAL :LOW -2 :HIGH 10)
1824 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1825 => #S(INTERVAL :LOW -1 :HIGH 10)
1826 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1827 => #S(INTERVAL :LOW -1 :HIGH 10)
1829 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1830 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1831 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1832 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1833 (floor-rem-bound (make-interval :low -10 :high -2.3))
1834 #S(INTERVAL :LOW (-10) :HIGH 0)
1835 (floor-rem-bound (make-interval :low 0.3 :high 10))
1836 => #S(INTERVAL :LOW 0 :HIGH '(10))
1837 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1838 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1839 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1840 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1843 ;;; same functions for CEILING
1844 (defun ceiling-quotient-bound (quot)
1845 ;; Take the ceiling of the quotient and then massage it into what we
1847 (let ((lo (interval-low quot))
1848 (hi (interval-high quot)))
1849 ;; Take the ceiling of the upper bound. The result is always a
1850 ;; closed upper bound.
1852 (ceiling (type-bound-number hi))
1854 ;; For the lower bound, we need to be careful.
1857 ;; An open bound. We need to be careful here because
1858 ;; the ceiling of '(10.0) is 11, but the ceiling of
1860 (multiple-value-bind (q r) (ceiling (first lo))
1865 ;; A closed bound, so the answer is obvious.
1869 (make-interval :low lo :high hi)))
1870 (defun ceiling-rem-bound (div)
1871 ;; The remainder depends only on the divisor. Try to get the
1872 ;; correct sign for the remainder if we can.
1873 (case (interval-range-info div)
1875 ;; Divisor is always positive. The remainder is negative.
1876 (let ((rem (interval-neg (interval-abs div))))
1877 (setf (interval-high rem) 0)
1878 (when (and (numberp (interval-low rem))
1879 (not (zerop (interval-low rem))))
1880 ;; The remainder never contains the upper bound. However,
1881 ;; watch out for the case when the upper bound is zero!
1882 (setf (interval-low rem) (list (interval-low rem))))
1885 ;; Divisor is always negative. The remainder is positive
1886 (let ((rem (interval-abs div)))
1887 (setf (interval-low rem) 0)
1888 (when (numberp (interval-high rem))
1889 ;; The remainder never contains the lower bound.
1890 (setf (interval-high rem) (list (interval-high rem))))
1893 ;; The divisor can be positive or negative. All bets off. The
1894 ;; magnitude of remainder is the maximum value of the divisor.
1895 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1896 ;; The bound never reaches the limit, so make the interval open.
1897 (make-interval :low (if limit
1900 :high (list limit))))))
1903 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
1904 => #S(INTERVAL :LOW 1 :HIGH 11)
1905 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1906 => #S(INTERVAL :LOW 1 :HIGH 11)
1907 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
1908 => #S(INTERVAL :LOW 1 :HIGH 10)
1909 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
1910 => #S(INTERVAL :LOW 1 :HIGH 10)
1911 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
1912 => #S(INTERVAL :LOW 1 :HIGH 11)
1913 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
1914 => #S(INTERVAL :LOW 1 :HIGH 11)
1915 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1916 => #S(INTERVAL :LOW -1 :HIGH 11)
1917 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1918 => #S(INTERVAL :LOW 0 :HIGH 11)
1919 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
1920 => #S(INTERVAL :LOW -1 :HIGH 11)
1922 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
1923 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
1924 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
1925 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1926 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
1927 => #S(INTERVAL :LOW 0 :HIGH (10))
1928 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
1929 => #S(INTERVAL :LOW (-10) :HIGH 0)
1930 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
1931 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
1932 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
1933 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1936 (defun truncate-quotient-bound (quot)
1937 ;; For positive quotients, truncate is exactly like floor. For
1938 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
1939 ;; it's the union of the two pieces.
1940 (case (interval-range-info quot)
1943 (floor-quotient-bound quot))
1945 ;; just like CEILING
1946 (ceiling-quotient-bound quot))
1948 ;; Split the interval into positive and negative pieces, compute
1949 ;; the result for each piece and put them back together.
1950 (destructuring-bind (neg pos) (interval-split 0 quot t t)
1951 (interval-merge-pair (ceiling-quotient-bound neg)
1952 (floor-quotient-bound pos))))))
1954 (defun truncate-rem-bound (num div)
1955 ;; This is significantly more complicated than FLOOR or CEILING. We
1956 ;; need both the number and the divisor to determine the range. The
1957 ;; basic idea is to split the ranges of NUM and DEN into positive
1958 ;; and negative pieces and deal with each of the four possibilities
1960 (case (interval-range-info num)
1962 (case (interval-range-info div)
1964 (floor-rem-bound div))
1966 (ceiling-rem-bound div))
1968 (destructuring-bind (neg pos) (interval-split 0 div t t)
1969 (interval-merge-pair (truncate-rem-bound num neg)
1970 (truncate-rem-bound num pos))))))
1972 (case (interval-range-info div)
1974 (ceiling-rem-bound div))
1976 (floor-rem-bound div))
1978 (destructuring-bind (neg pos) (interval-split 0 div t t)
1979 (interval-merge-pair (truncate-rem-bound num neg)
1980 (truncate-rem-bound num pos))))))
1982 (destructuring-bind (neg pos) (interval-split 0 num t t)
1983 (interval-merge-pair (truncate-rem-bound neg div)
1984 (truncate-rem-bound pos div))))))
1987 ;;; Derive useful information about the range. Returns three values:
1988 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
1989 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
1990 ;;; - The abs of the maximal value if there is one, or nil if it is
1992 (defun numeric-range-info (low high)
1993 (cond ((and low (not (minusp low)))
1994 (values '+ low high))
1995 ((and high (not (plusp high)))
1996 (values '- (- high) (if low (- low) nil)))
1998 (values nil 0 (and low high (max (- low) high))))))
2000 (defun integer-truncate-derive-type
2001 (number-low number-high divisor-low divisor-high)
2002 ;; The result cannot be larger in magnitude than the number, but the
2003 ;; sign might change. If we can determine the sign of either the
2004 ;; number or the divisor, we can eliminate some of the cases.
2005 (multiple-value-bind (number-sign number-min number-max)
2006 (numeric-range-info number-low number-high)
2007 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2008 (numeric-range-info divisor-low divisor-high)
2009 (when (and divisor-max (zerop divisor-max))
2010 ;; We've got a problem: guaranteed division by zero.
2011 (return-from integer-truncate-derive-type t))
2012 (when (zerop divisor-min)
2013 ;; We'll assume that they aren't going to divide by zero.
2015 (cond ((and number-sign divisor-sign)
2016 ;; We know the sign of both.
2017 (if (eq number-sign divisor-sign)
2018 ;; Same sign, so the result will be positive.
2019 `(integer ,(if divisor-max
2020 (truncate number-min divisor-max)
2023 (truncate number-max divisor-min)
2025 ;; Different signs, the result will be negative.
2026 `(integer ,(if number-max
2027 (- (truncate number-max divisor-min))
2030 (- (truncate number-min divisor-max))
2032 ((eq divisor-sign '+)
2033 ;; The divisor is positive. Therefore, the number will just
2034 ;; become closer to zero.
2035 `(integer ,(if number-low
2036 (truncate number-low divisor-min)
2039 (truncate number-high divisor-min)
2041 ((eq divisor-sign '-)
2042 ;; The divisor is negative. Therefore, the absolute value of
2043 ;; the number will become closer to zero, but the sign will also
2045 `(integer ,(if number-high
2046 (- (truncate number-high divisor-min))
2049 (- (truncate number-low divisor-min))
2051 ;; The divisor could be either positive or negative.
2053 ;; The number we are dividing has a bound. Divide that by the
2054 ;; smallest posible divisor.
2055 (let ((bound (truncate number-max divisor-min)))
2056 `(integer ,(- bound) ,bound)))
2058 ;; The number we are dividing is unbounded, so we can't tell
2059 ;; anything about the result.
2062 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2063 (defun integer-rem-derive-type
2064 (number-low number-high divisor-low divisor-high)
2065 (if (and divisor-low divisor-high)
2066 ;; We know the range of the divisor, and the remainder must be
2067 ;; smaller than the divisor. We can tell the sign of the
2068 ;; remainer if we know the sign of the number.
2069 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2070 `(integer ,(if (or (null number-low)
2071 (minusp number-low))
2074 ,(if (or (null number-high)
2075 (plusp number-high))
2078 ;; The divisor is potentially either very positive or very
2079 ;; negative. Therefore, the remainer is unbounded, but we might
2080 ;; be able to tell something about the sign from the number.
2081 `(integer ,(if (and number-low (not (minusp number-low)))
2082 ;; The number we are dividing is positive.
2083 ;; Therefore, the remainder must be positive.
2086 ,(if (and number-high (not (plusp number-high)))
2087 ;; The number we are dividing is negative.
2088 ;; Therefore, the remainder must be negative.
2092 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2093 (defoptimizer (random derive-type) ((bound &optional state))
2094 (let ((type (lvar-type bound)))
2095 (when (numeric-type-p type)
2096 (let ((class (numeric-type-class type))
2097 (high (numeric-type-high type))
2098 (format (numeric-type-format type)))
2102 :low (coerce 0 (or format class 'real))
2103 :high (cond ((not high) nil)
2104 ((eq class 'integer) (max (1- high) 0))
2105 ((or (consp high) (zerop high)) high)
2108 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2109 (defun random-derive-type-aux (type)
2110 (let ((class (numeric-type-class type))
2111 (high (numeric-type-high type))
2112 (format (numeric-type-format type)))
2116 :low (coerce 0 (or format class 'real))
2117 :high (cond ((not high) nil)
2118 ((eq class 'integer) (max (1- high) 0))
2119 ((or (consp high) (zerop high)) high)
2122 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2123 (defoptimizer (random derive-type) ((bound &optional state))
2124 (one-arg-derive-type bound #'random-derive-type-aux nil))
2126 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2128 ;;; Return the maximum number of bits an integer of the supplied type
2129 ;;; can take up, or NIL if it is unbounded. The second (third) value
2130 ;;; is T if the integer can be positive (negative) and NIL if not.
2131 ;;; Zero counts as positive.
2132 (defun integer-type-length (type)
2133 (if (numeric-type-p type)
2134 (let ((min (numeric-type-low type))
2135 (max (numeric-type-high type)))
2136 (values (and min max (max (integer-length min) (integer-length max)))
2137 (or (null max) (not (minusp max)))
2138 (or (null min) (minusp min))))
2141 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2142 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2143 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2144 ;;; versions in CMUCL, from which these functions copy liberally.
2146 (defun logand-derive-unsigned-low-bound (x y)
2147 (let ((a (numeric-type-low x))
2148 (b (numeric-type-high x))
2149 (c (numeric-type-low y))
2150 (d (numeric-type-high y)))
2151 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2153 (unless (zerop (logand m (lognot a) (lognot c)))
2154 (let ((temp (logandc2 (logior a m) (1- m))))
2158 (setf temp (logandc2 (logior c m) (1- m)))
2162 finally (return (logand a c)))))
2164 (defun logand-derive-unsigned-high-bound (x y)
2165 (let ((a (numeric-type-low x))
2166 (b (numeric-type-high x))
2167 (c (numeric-type-low y))
2168 (d (numeric-type-high y)))
2169 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2172 ((not (zerop (logand b (lognot d) m)))
2173 (let ((temp (logior (logandc2 b m) (1- m))))
2177 ((not (zerop (logand (lognot b) d m)))
2178 (let ((temp (logior (logandc2 d m) (1- m))))
2182 finally (return (logand b d)))))
2184 (defun logand-derive-type-aux (x y &optional same-leaf)
2186 (return-from logand-derive-type-aux x))
2187 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2188 (declare (ignore x-pos))
2189 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2190 (declare (ignore y-pos))
2192 ;; X must be positive.
2194 ;; They must both be positive.
2195 (cond ((and (null x-len) (null y-len))
2196 (specifier-type 'unsigned-byte))
2198 (specifier-type `(unsigned-byte* ,y-len)))
2200 (specifier-type `(unsigned-byte* ,x-len)))
2202 (let ((low (logand-derive-unsigned-low-bound x y))
2203 (high (logand-derive-unsigned-high-bound x y)))
2204 (specifier-type `(integer ,low ,high)))))
2205 ;; X is positive, but Y might be negative.
2207 (specifier-type 'unsigned-byte))
2209 (specifier-type `(unsigned-byte* ,x-len)))))
2210 ;; X might be negative.
2212 ;; Y must be positive.
2214 (specifier-type 'unsigned-byte))
2215 (t (specifier-type `(unsigned-byte* ,y-len))))
2216 ;; Either might be negative.
2217 (if (and x-len y-len)
2218 ;; The result is bounded.
2219 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2220 ;; We can't tell squat about the result.
2221 (specifier-type 'integer)))))))
2223 (defun logior-derive-unsigned-low-bound (x y)
2224 (let ((a (numeric-type-low x))
2225 (b (numeric-type-high x))
2226 (c (numeric-type-low y))
2227 (d (numeric-type-high y)))
2228 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2231 ((not (zerop (logandc2 (logand c m) a)))
2232 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2236 ((not (zerop (logandc2 (logand a m) c)))
2237 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2241 finally (return (logior a c)))))
2243 (defun logior-derive-unsigned-high-bound (x y)
2244 (let ((a (numeric-type-low x))
2245 (b (numeric-type-high x))
2246 (c (numeric-type-low y))
2247 (d (numeric-type-high y)))
2248 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2250 (unless (zerop (logand b d m))
2251 (let ((temp (logior (- b m) (1- m))))
2255 (setf temp (logior (- d m) (1- m)))
2259 finally (return (logior b d)))))
2261 (defun logior-derive-type-aux (x y &optional same-leaf)
2263 (return-from logior-derive-type-aux x))
2264 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2265 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2267 ((and (not x-neg) (not y-neg))
2268 ;; Both are positive.
2269 (if (and x-len y-len)
2270 (let ((low (logior-derive-unsigned-low-bound x y))
2271 (high (logior-derive-unsigned-high-bound x y)))
2272 (specifier-type `(integer ,low ,high)))
2273 (specifier-type `(unsigned-byte* *))))
2275 ;; X must be negative.
2277 ;; Both are negative. The result is going to be negative
2278 ;; and be the same length or shorter than the smaller.
2279 (if (and x-len y-len)
2281 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2283 (specifier-type '(integer * -1)))
2284 ;; X is negative, but we don't know about Y. The result
2285 ;; will be negative, but no more negative than X.
2287 `(integer ,(or (numeric-type-low x) '*)
2290 ;; X might be either positive or negative.
2292 ;; But Y is negative. The result will be negative.
2294 `(integer ,(or (numeric-type-low y) '*)
2296 ;; We don't know squat about either. It won't get any bigger.
2297 (if (and x-len y-len)
2299 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2301 (specifier-type 'integer))))))))
2303 (defun logxor-derive-unsigned-low-bound (x y)
2304 (let ((a (numeric-type-low x))
2305 (b (numeric-type-high x))
2306 (c (numeric-type-low y))
2307 (d (numeric-type-high y)))
2308 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2311 ((not (zerop (logandc2 (logand c m) a)))
2312 (let ((temp (logand (logior a m)
2316 ((not (zerop (logandc2 (logand a m) c)))
2317 (let ((temp (logand (logior c m)
2321 finally (return (logxor a c)))))
2323 (defun logxor-derive-unsigned-high-bound (x y)
2324 (let ((a (numeric-type-low x))
2325 (b (numeric-type-high x))
2326 (c (numeric-type-low y))
2327 (d (numeric-type-high y)))
2328 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2330 (unless (zerop (logand b d m))
2331 (let ((temp (logior (- b m) (1- m))))
2333 ((>= temp a) (setf b temp))
2334 (t (let ((temp (logior (- d m) (1- m))))
2337 finally (return (logxor b d)))))
2339 (defun logxor-derive-type-aux (x y &optional same-leaf)
2341 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2342 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2343 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2345 ((and (not x-neg) (not y-neg))
2346 ;; Both are positive
2347 (if (and x-len y-len)
2348 (let ((low (logxor-derive-unsigned-low-bound x y))
2349 (high (logxor-derive-unsigned-high-bound x y)))
2350 (specifier-type `(integer ,low ,high)))
2351 (specifier-type '(unsigned-byte* *))))
2352 ((and (not x-pos) (not y-pos))
2353 ;; Both are negative. The result will be positive, and as long
2355 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2358 ((or (and (not x-pos) (not y-neg))
2359 (and (not y-pos) (not x-neg)))
2360 ;; Either X is negative and Y is positive or vice-versa. The
2361 ;; result will be negative.
2362 (specifier-type `(integer ,(if (and x-len y-len)
2363 (ash -1 (max x-len y-len))
2366 ;; We can't tell what the sign of the result is going to be.
2367 ;; All we know is that we don't create new bits.
2369 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2371 (specifier-type 'integer))))))
2373 (macrolet ((deffrob (logfun)
2374 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2375 `(defoptimizer (,logfun derive-type) ((x y))
2376 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2381 (defoptimizer (logeqv derive-type) ((x y))
2382 (two-arg-derive-type x y (lambda (x y same-leaf)
2383 (lognot-derive-type-aux
2384 (logxor-derive-type-aux x y same-leaf)))
2386 (defoptimizer (lognand derive-type) ((x y))
2387 (two-arg-derive-type x y (lambda (x y same-leaf)
2388 (lognot-derive-type-aux
2389 (logand-derive-type-aux x y same-leaf)))
2391 (defoptimizer (lognor derive-type) ((x y))
2392 (two-arg-derive-type x y (lambda (x y same-leaf)
2393 (lognot-derive-type-aux
2394 (logior-derive-type-aux x y same-leaf)))
2396 (defoptimizer (logandc1 derive-type) ((x y))
2397 (two-arg-derive-type x y (lambda (x y same-leaf)
2399 (specifier-type '(eql 0))
2400 (logand-derive-type-aux
2401 (lognot-derive-type-aux x) y nil)))
2403 (defoptimizer (logandc2 derive-type) ((x y))
2404 (two-arg-derive-type x y (lambda (x y same-leaf)
2406 (specifier-type '(eql 0))
2407 (logand-derive-type-aux
2408 x (lognot-derive-type-aux y) nil)))
2410 (defoptimizer (logorc1 derive-type) ((x y))
2411 (two-arg-derive-type x y (lambda (x y same-leaf)
2413 (specifier-type '(eql -1))
2414 (logior-derive-type-aux
2415 (lognot-derive-type-aux x) y nil)))
2417 (defoptimizer (logorc2 derive-type) ((x y))
2418 (two-arg-derive-type x y (lambda (x y same-leaf)
2420 (specifier-type '(eql -1))
2421 (logior-derive-type-aux
2422 x (lognot-derive-type-aux y) nil)))
2425 ;;;; miscellaneous derive-type methods
2427 (defoptimizer (integer-length derive-type) ((x))
2428 (let ((x-type (lvar-type x)))
2429 (when (numeric-type-p x-type)
2430 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2431 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2432 ;; careful about LO or HI being NIL, though. Also, if 0 is
2433 ;; contained in X, the lower bound is obviously 0.
2434 (flet ((null-or-min (a b)
2435 (and a b (min (integer-length a)
2436 (integer-length b))))
2438 (and a b (max (integer-length a)
2439 (integer-length b)))))
2440 (let* ((min (numeric-type-low x-type))
2441 (max (numeric-type-high x-type))
2442 (min-len (null-or-min min max))
2443 (max-len (null-or-max min max)))
2444 (when (ctypep 0 x-type)
2446 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2448 (defoptimizer (isqrt derive-type) ((x))
2449 (let ((x-type (lvar-type x)))
2450 (when (numeric-type-p x-type)
2451 (let* ((lo (numeric-type-low x-type))
2452 (hi (numeric-type-high x-type))
2453 (lo-res (if lo (isqrt lo) '*))
2454 (hi-res (if hi (isqrt hi) '*)))
2455 (specifier-type `(integer ,lo-res ,hi-res))))))
2457 (defoptimizer (code-char derive-type) ((code))
2458 (let ((type (lvar-type code)))
2459 ;; FIXME: unions of integral ranges? It ought to be easier to do
2460 ;; this, given that CHARACTER-SET is basically an integral range
2461 ;; type. -- CSR, 2004-10-04
2462 (when (numeric-type-p type)
2463 (let* ((lo (numeric-type-low type))
2464 (hi (numeric-type-high type))
2465 (type (specifier-type `(character-set ((,lo . ,hi))))))
2467 ;; KLUDGE: when running on the host, we lose a slight amount
2468 ;; of precision so that we don't have to "unparse" types
2469 ;; that formally we can't, such as (CHARACTER-SET ((0
2470 ;; . 0))). -- CSR, 2004-10-06
2472 ((csubtypep type (specifier-type 'standard-char)) type)
2474 ((csubtypep type (specifier-type 'base-char))
2475 (specifier-type 'base-char))
2477 ((csubtypep type (specifier-type 'extended-char))
2478 (specifier-type 'extended-char))
2479 (t #+sb-xc-host (specifier-type 'character)
2480 #-sb-xc-host type))))))
2482 (defoptimizer (values derive-type) ((&rest values))
2483 (make-values-type :required (mapcar #'lvar-type values)))
2485 (defun signum-derive-type-aux (type)
2486 (if (eq (numeric-type-complexp type) :complex)
2487 (let* ((format (case (numeric-type-class type)
2488 ((integer rational) 'single-float)
2489 (t (numeric-type-format type))))
2490 (bound-format (or format 'float)))
2491 (make-numeric-type :class 'float
2494 :low (coerce -1 bound-format)
2495 :high (coerce 1 bound-format)))
2496 (let* ((interval (numeric-type->interval type))
2497 (range-info (interval-range-info interval))
2498 (contains-0-p (interval-contains-p 0 interval))
2499 (class (numeric-type-class type))
2500 (format (numeric-type-format type))
2501 (one (coerce 1 (or format class 'real)))
2502 (zero (coerce 0 (or format class 'real)))
2503 (minus-one (coerce -1 (or format class 'real)))
2504 (plus (make-numeric-type :class class :format format
2505 :low one :high one))
2506 (minus (make-numeric-type :class class :format format
2507 :low minus-one :high minus-one))
2508 ;; KLUDGE: here we have a fairly horrible hack to deal
2509 ;; with the schizophrenia in the type derivation engine.
2510 ;; The problem is that the type derivers reinterpret
2511 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2512 ;; 0d0) within the derivation mechanism doesn't include
2513 ;; -0d0. Ugh. So force it in here, instead.
2514 (zero (make-numeric-type :class class :format format
2515 :low (- zero) :high zero)))
2517 (+ (if contains-0-p (type-union plus zero) plus))
2518 (- (if contains-0-p (type-union minus zero) minus))
2519 (t (type-union minus zero plus))))))
2521 (defoptimizer (signum derive-type) ((num))
2522 (one-arg-derive-type num #'signum-derive-type-aux nil))
2524 ;;;; byte operations
2526 ;;;; We try to turn byte operations into simple logical operations.
2527 ;;;; First, we convert byte specifiers into separate size and position
2528 ;;;; arguments passed to internal %FOO functions. We then attempt to
2529 ;;;; transform the %FOO functions into boolean operations when the
2530 ;;;; size and position are constant and the operands are fixnums.
2532 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2533 ;; expressions that evaluate to the SIZE and POSITION of
2534 ;; the byte-specifier form SPEC. We may wrap a let around
2535 ;; the result of the body to bind some variables.
2537 ;; If the spec is a BYTE form, then bind the vars to the
2538 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2539 ;; and BYTE-POSITION. The goal of this transformation is to
2540 ;; avoid consing up byte specifiers and then immediately
2541 ;; throwing them away.
2542 (with-byte-specifier ((size-var pos-var spec) &body body)
2543 (once-only ((spec `(macroexpand ,spec))
2545 `(if (and (consp ,spec)
2546 (eq (car ,spec) 'byte)
2547 (= (length ,spec) 3))
2548 (let ((,size-var (second ,spec))
2549 (,pos-var (third ,spec)))
2551 (let ((,size-var `(byte-size ,,temp))
2552 (,pos-var `(byte-position ,,temp)))
2553 `(let ((,,temp ,,spec))
2556 (define-source-transform ldb (spec int)
2557 (with-byte-specifier (size pos spec)
2558 `(%ldb ,size ,pos ,int)))
2560 (define-source-transform dpb (newbyte spec int)
2561 (with-byte-specifier (size pos spec)
2562 `(%dpb ,newbyte ,size ,pos ,int)))
2564 (define-source-transform mask-field (spec int)
2565 (with-byte-specifier (size pos spec)
2566 `(%mask-field ,size ,pos ,int)))
2568 (define-source-transform deposit-field (newbyte spec int)
2569 (with-byte-specifier (size pos spec)
2570 `(%deposit-field ,newbyte ,size ,pos ,int))))
2572 (defoptimizer (%ldb derive-type) ((size posn num))
2573 (let ((size (lvar-type size)))
2574 (if (and (numeric-type-p size)
2575 (csubtypep size (specifier-type 'integer)))
2576 (let ((size-high (numeric-type-high size)))
2577 (if (and size-high (<= size-high sb!vm:n-word-bits))
2578 (specifier-type `(unsigned-byte* ,size-high))
2579 (specifier-type 'unsigned-byte)))
2582 (defoptimizer (%mask-field derive-type) ((size posn num))
2583 (let ((size (lvar-type size))
2584 (posn (lvar-type posn)))
2585 (if (and (numeric-type-p size)
2586 (csubtypep size (specifier-type 'integer))
2587 (numeric-type-p posn)
2588 (csubtypep posn (specifier-type 'integer)))
2589 (let ((size-high (numeric-type-high size))
2590 (posn-high (numeric-type-high posn)))
2591 (if (and size-high posn-high
2592 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2593 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2594 (specifier-type 'unsigned-byte)))
2597 (defun %deposit-field-derive-type-aux (size posn int)
2598 (let ((size (lvar-type size))
2599 (posn (lvar-type posn))
2600 (int (lvar-type int)))
2601 (when (and (numeric-type-p size)
2602 (numeric-type-p posn)
2603 (numeric-type-p int))
2604 (let ((size-high (numeric-type-high size))
2605 (posn-high (numeric-type-high posn))
2606 (high (numeric-type-high int))
2607 (low (numeric-type-low int)))
2608 (when (and size-high posn-high high low
2609 ;; KLUDGE: we need this cutoff here, otherwise we
2610 ;; will merrily derive the type of %DPB as
2611 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2612 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2613 ;; 1073741822))), with hilarious consequences. We
2614 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2615 ;; over a reasonable amount of shifting, even on
2616 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2617 ;; machine integers are 64-bits. -- CSR,
2619 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2620 (let ((raw-bit-count (max (integer-length high)
2621 (integer-length low)
2622 (+ size-high posn-high))))
2625 `(signed-byte ,(1+ raw-bit-count))
2626 `(unsigned-byte* ,raw-bit-count)))))))))
2628 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2629 (%deposit-field-derive-type-aux size posn int))
2631 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2632 (%deposit-field-derive-type-aux size posn int))
2634 (deftransform %ldb ((size posn int)
2635 (fixnum fixnum integer)
2636 (unsigned-byte #.sb!vm:n-word-bits))
2637 "convert to inline logical operations"
2638 `(logand (ash int (- posn))
2639 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2640 (- size ,sb!vm:n-word-bits))))
2642 (deftransform %mask-field ((size posn int)
2643 (fixnum fixnum integer)
2644 (unsigned-byte #.sb!vm:n-word-bits))
2645 "convert to inline logical operations"
2647 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2648 (- size ,sb!vm:n-word-bits))
2651 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2652 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2653 ;;; as the result type, as that would allow result types that cover
2654 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2655 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2657 (deftransform %dpb ((new size posn int)
2659 (unsigned-byte #.sb!vm:n-word-bits))
2660 "convert to inline logical operations"
2661 `(let ((mask (ldb (byte size 0) -1)))
2662 (logior (ash (logand new mask) posn)
2663 (logand int (lognot (ash mask posn))))))
2665 (deftransform %dpb ((new size posn int)
2667 (signed-byte #.sb!vm:n-word-bits))
2668 "convert to inline logical operations"
2669 `(let ((mask (ldb (byte size 0) -1)))
2670 (logior (ash (logand new mask) posn)
2671 (logand int (lognot (ash mask posn))))))
2673 (deftransform %deposit-field ((new size posn int)
2675 (unsigned-byte #.sb!vm:n-word-bits))
2676 "convert to inline logical operations"
2677 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2678 (logior (logand new mask)
2679 (logand int (lognot mask)))))
2681 (deftransform %deposit-field ((new size posn int)
2683 (signed-byte #.sb!vm:n-word-bits))
2684 "convert to inline logical operations"
2685 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2686 (logior (logand new mask)
2687 (logand int (lognot mask)))))
2689 (defoptimizer (mask-signed-field derive-type) ((size x))
2690 (let ((size (lvar-type size)))
2691 (if (numeric-type-p size)
2692 (let ((size-high (numeric-type-high size)))
2693 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2694 (specifier-type `(signed-byte ,size-high))
2699 ;;; Modular functions
2701 ;;; (ldb (byte s 0) (foo x y ...)) =
2702 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2704 ;;; and similar for other arguments.
2706 (defun make-modular-fun-type-deriver (prototype class width)
2708 (binding* ((info (info :function :info prototype) :exit-if-null)
2709 (fun (fun-info-derive-type info) :exit-if-null)
2710 (mask-type (specifier-type
2712 (:unsigned (let ((mask (1- (ash 1 width))))
2713 `(integer ,mask ,mask)))
2714 (:signed `(signed-byte ,width))))))
2716 (let ((res (funcall fun call)))
2718 (if (eq class :unsigned)
2719 (logand-derive-type-aux res mask-type))))))
2722 (binding* ((info (info :function :info prototype) :exit-if-null)
2723 (fun (fun-info-derive-type info) :exit-if-null)
2724 (res (funcall fun call) :exit-if-null)
2725 (mask-type (specifier-type
2727 (:unsigned (let ((mask (1- (ash 1 width))))
2728 `(integer ,mask ,mask)))
2729 (:signed `(signed-byte ,width))))))
2730 (if (eq class :unsigned)
2731 (logand-derive-type-aux res mask-type)))))
2733 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2735 ;;; For good functions, we just recursively cut arguments; their
2736 ;;; "goodness" means that the result will not increase (in the
2737 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2738 ;;; replaced with the version, cutting its result to WIDTH or more
2739 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2740 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2741 ;;; arguments (maybe to a different width) and returning the name of a
2742 ;;; modular version, if it exists, or NIL. If we have changed
2743 ;;; anything, we need to flush old derived types, because they have
2744 ;;; nothing in common with the new code.
2745 (defun cut-to-width (lvar class width)
2746 (declare (type lvar lvar) (type (integer 0) width))
2747 (let ((type (specifier-type (if (zerop width)
2749 `(,(ecase class (:unsigned 'unsigned-byte)
2750 (:signed 'signed-byte))
2752 (labels ((reoptimize-node (node name)
2753 (setf (node-derived-type node)
2755 (info :function :type name)))
2756 (setf (lvar-%derived-type (node-lvar node)) nil)
2757 (setf (node-reoptimize node) t)
2758 (setf (block-reoptimize (node-block node)) t)
2759 (reoptimize-component (node-component node) :maybe))
2760 (cut-node (node &aux did-something)
2761 (when (and (not (block-delete-p (node-block node)))
2762 (combination-p node)
2763 (eq (basic-combination-kind node) :known))
2764 (let* ((fun-ref (lvar-use (combination-fun node)))
2765 (fun-name (leaf-source-name (ref-leaf fun-ref)))
2766 (modular-fun (find-modular-version fun-name class width)))
2767 (when (and modular-fun
2768 (not (and (eq fun-name 'logand)
2770 (single-value-type (node-derived-type node))
2772 (binding* ((name (etypecase modular-fun
2773 ((eql :good) fun-name)
2775 (modular-fun-info-name modular-fun))
2777 (funcall modular-fun node width)))
2779 (unless (eql modular-fun :good)
2780 (setq did-something t)
2783 (find-free-fun name "in a strange place"))
2784 (setf (combination-kind node) :full))
2785 (unless (functionp modular-fun)
2786 (dolist (arg (basic-combination-args node))
2787 (when (cut-lvar arg)
2788 (setq did-something t))))
2790 (reoptimize-node node name))
2792 (cut-lvar (lvar &aux did-something)
2793 (do-uses (node lvar)
2794 (when (cut-node node)
2795 (setq did-something t)))
2799 (defoptimizer (logand optimizer) ((x y) node)
2800 (let ((result-type (single-value-type (node-derived-type node))))
2801 (when (numeric-type-p result-type)
2802 (let ((low (numeric-type-low result-type))
2803 (high (numeric-type-high result-type)))
2804 (when (and (numberp low)
2807 (let ((width (integer-length high)))
2808 (when (some (lambda (x) (<= width x))
2809 (modular-class-widths *unsigned-modular-class*))
2810 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2811 (cut-to-width x :unsigned width)
2812 (cut-to-width y :unsigned width)
2813 nil ; After fixing above, replace with T.
2816 (defoptimizer (mask-signed-field optimizer) ((width x) node)
2817 (let ((result-type (single-value-type (node-derived-type node))))
2818 (when (numeric-type-p result-type)
2819 (let ((low (numeric-type-low result-type))
2820 (high (numeric-type-high result-type)))
2821 (when (and (numberp low) (numberp high))
2822 (let ((width (max (integer-length high) (integer-length low))))
2823 (when (some (lambda (x) (<= width x))
2824 (modular-class-widths *signed-modular-class*))
2825 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2826 (cut-to-width x :signed width)
2827 nil ; After fixing above, replace with T.
2830 ;;; miscellanous numeric transforms
2832 ;;; If a constant appears as the first arg, swap the args.
2833 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2834 (if (and (constant-lvar-p x)
2835 (not (constant-lvar-p y)))
2836 `(,(lvar-fun-name (basic-combination-fun node))
2839 (give-up-ir1-transform)))
2841 (dolist (x '(= char= + * logior logand logxor))
2842 (%deftransform x '(function * *) #'commutative-arg-swap
2843 "place constant arg last"))
2845 ;;; Handle the case of a constant BOOLE-CODE.
2846 (deftransform boole ((op x y) * *)
2847 "convert to inline logical operations"
2848 (unless (constant-lvar-p op)
2849 (give-up-ir1-transform "BOOLE code is not a constant."))
2850 (let ((control (lvar-value op)))
2852 (#.sb!xc:boole-clr 0)
2853 (#.sb!xc:boole-set -1)
2854 (#.sb!xc:boole-1 'x)
2855 (#.sb!xc:boole-2 'y)
2856 (#.sb!xc:boole-c1 '(lognot x))
2857 (#.sb!xc:boole-c2 '(lognot y))
2858 (#.sb!xc:boole-and '(logand x y))
2859 (#.sb!xc:boole-ior '(logior x y))
2860 (#.sb!xc:boole-xor '(logxor x y))
2861 (#.sb!xc:boole-eqv '(logeqv x y))
2862 (#.sb!xc:boole-nand '(lognand x y))
2863 (#.sb!xc:boole-nor '(lognor x y))
2864 (#.sb!xc:boole-andc1 '(logandc1 x y))
2865 (#.sb!xc:boole-andc2 '(logandc2 x y))
2866 (#.sb!xc:boole-orc1 '(logorc1 x y))
2867 (#.sb!xc:boole-orc2 '(logorc2 x y))
2869 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2872 ;;;; converting special case multiply/divide to shifts
2874 ;;; If arg is a constant power of two, turn * into a shift.
2875 (deftransform * ((x y) (integer integer) *)
2876 "convert x*2^k to shift"
2877 (unless (constant-lvar-p y)
2878 (give-up-ir1-transform))
2879 (let* ((y (lvar-value y))
2881 (len (1- (integer-length y-abs))))
2882 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2883 (give-up-ir1-transform))
2888 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2889 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
2891 (flet ((frob (y ceil-p)
2892 (unless (constant-lvar-p y)
2893 (give-up-ir1-transform))
2894 (let* ((y (lvar-value y))
2896 (len (1- (integer-length y-abs))))
2897 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2898 (give-up-ir1-transform))
2899 (let ((shift (- len))
2901 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
2902 `(let ((x (+ x ,delta)))
2904 `(values (ash (- x) ,shift)
2905 (- (- (logand (- x) ,mask)) ,delta))
2906 `(values (ash x ,shift)
2907 (- (logand x ,mask) ,delta))))))))
2908 (deftransform floor ((x y) (integer integer) *)
2909 "convert division by 2^k to shift"
2911 (deftransform ceiling ((x y) (integer integer) *)
2912 "convert division by 2^k to shift"
2915 ;;; Do the same for MOD.
2916 (deftransform mod ((x y) (integer integer) *)
2917 "convert remainder mod 2^k to LOGAND"
2918 (unless (constant-lvar-p y)
2919 (give-up-ir1-transform))
2920 (let* ((y (lvar-value y))
2922 (len (1- (integer-length y-abs))))
2923 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2924 (give-up-ir1-transform))
2925 (let ((mask (1- y-abs)))
2927 `(- (logand (- x) ,mask))
2928 `(logand x ,mask)))))
2930 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2931 (deftransform truncate ((x y) (integer integer))
2932 "convert division by 2^k to shift"
2933 (unless (constant-lvar-p y)
2934 (give-up-ir1-transform))
2935 (let* ((y (lvar-value y))
2937 (len (1- (integer-length y-abs))))
2938 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2939 (give-up-ir1-transform))
2940 (let* ((shift (- len))
2943 (values ,(if (minusp y)
2945 `(- (ash (- x) ,shift)))
2946 (- (logand (- x) ,mask)))
2947 (values ,(if (minusp y)
2948 `(ash (- ,mask x) ,shift)
2950 (logand x ,mask))))))
2952 ;;; And the same for REM.
2953 (deftransform rem ((x y) (integer integer) *)
2954 "convert remainder mod 2^k to LOGAND"
2955 (unless (constant-lvar-p y)
2956 (give-up-ir1-transform))
2957 (let* ((y (lvar-value y))
2959 (len (1- (integer-length y-abs))))
2960 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2961 (give-up-ir1-transform))
2962 (let ((mask (1- y-abs)))
2964 (- (logand (- x) ,mask))
2965 (logand x ,mask)))))
2967 ;;;; arithmetic and logical identity operation elimination
2969 ;;; Flush calls to various arith functions that convert to the
2970 ;;; identity function or a constant.
2971 (macrolet ((def (name identity result)
2972 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
2973 "fold identity operations"
2980 (def logxor -1 (lognot x))
2983 (deftransform logand ((x y) (* (constant-arg t)) *)
2984 "fold identity operation"
2985 (let ((y (lvar-value y)))
2986 (unless (and (plusp y)
2987 (= y (1- (ash 1 (integer-length y)))))
2988 (give-up-ir1-transform))
2989 (unless (csubtypep (lvar-type x)
2990 (specifier-type `(integer 0 ,y)))
2991 (give-up-ir1-transform))
2994 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
2995 "fold identity operation"
2996 (let ((size (lvar-value size)))
2997 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
2998 (give-up-ir1-transform))
3001 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3002 ;;; (* 0 -4.0) is -0.0.
3003 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3004 "convert (- 0 x) to negate"
3006 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3007 "convert (* x 0) to 0"
3010 ;;; Return T if in an arithmetic op including lvars X and Y, the
3011 ;;; result type is not affected by the type of X. That is, Y is at
3012 ;;; least as contagious as X.
3014 (defun not-more-contagious (x y)
3015 (declare (type continuation x y))
3016 (let ((x (lvar-type x))
3018 (values (type= (numeric-contagion x y)
3019 (numeric-contagion y y)))))
3020 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3021 ;;; XXX needs more work as valid transforms are missed; some cases are
3022 ;;; specific to particular transform functions so the use of this
3023 ;;; function may need a re-think.
3024 (defun not-more-contagious (x y)
3025 (declare (type lvar x y))
3026 (flet ((simple-numeric-type (num)
3027 (and (numeric-type-p num)
3028 ;; Return non-NIL if NUM is integer, rational, or a float
3029 ;; of some type (but not FLOAT)
3030 (case (numeric-type-class num)
3034 (numeric-type-format num))
3037 (let ((x (lvar-type x))
3039 (if (and (simple-numeric-type x)
3040 (simple-numeric-type y))
3041 (values (type= (numeric-contagion x y)
3042 (numeric-contagion y y)))))))
3046 ;;; If y is not constant, not zerop, or is contagious, or a positive
3047 ;;; float +0.0 then give up.
3048 (deftransform + ((x y) (t (constant-arg t)) *)
3050 (let ((val (lvar-value y)))
3051 (unless (and (zerop val)
3052 (not (and (floatp val) (plusp (float-sign val))))
3053 (not-more-contagious y x))
3054 (give-up-ir1-transform)))
3059 ;;; If y is not constant, not zerop, or is contagious, or a negative
3060 ;;; float -0.0 then give up.
3061 (deftransform - ((x y) (t (constant-arg t)) *)
3063 (let ((val (lvar-value y)))
3064 (unless (and (zerop val)
3065 (not (and (floatp val) (minusp (float-sign val))))
3066 (not-more-contagious y x))
3067 (give-up-ir1-transform)))
3070 ;;; Fold (OP x +/-1)
3071 (macrolet ((def (name result minus-result)
3072 `(deftransform ,name ((x y) (t (constant-arg real)) *)
3073 "fold identity operations"
3074 (let ((val (lvar-value y)))
3075 (unless (and (= (abs val) 1)
3076 (not-more-contagious y x))
3077 (give-up-ir1-transform))
3078 (if (minusp val) ',minus-result ',result)))))
3079 (def * x (%negate x))
3080 (def / x (%negate x))
3081 (def expt x (/ 1 x)))
3083 ;;; Fold (expt x n) into multiplications for small integral values of
3084 ;;; N; convert (expt x 1/2) to sqrt.
3085 (deftransform expt ((x y) (t (constant-arg real)) *)
3086 "recode as multiplication or sqrt"
3087 (let ((val (lvar-value y)))
3088 ;; If Y would cause the result to be promoted to the same type as
3089 ;; Y, we give up. If not, then the result will be the same type
3090 ;; as X, so we can replace the exponentiation with simple
3091 ;; multiplication and division for small integral powers.
3092 (unless (not-more-contagious y x)
3093 (give-up-ir1-transform))
3095 (let ((x-type (lvar-type x)))
3096 (cond ((csubtypep x-type (specifier-type '(or rational
3097 (complex rational))))
3099 ((csubtypep x-type (specifier-type 'real))
3103 ((csubtypep x-type (specifier-type 'complex))
3104 ;; both parts are float
3106 (t (give-up-ir1-transform)))))
3107 ((= val 2) '(* x x))
3108 ((= val -2) '(/ (* x x)))
3109 ((= val 3) '(* x x x))
3110 ((= val -3) '(/ (* x x x)))
3111 ((= val 1/2) '(sqrt x))
3112 ((= val -1/2) '(/ (sqrt x)))
3113 (t (give-up-ir1-transform)))))
3115 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3116 ;;; transformations?
3117 ;;; Perhaps we should have to prove that the denominator is nonzero before
3118 ;;; doing them? -- WHN 19990917
3119 (macrolet ((def (name)
3120 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3127 (macrolet ((def (name)
3128 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3137 ;;;; character operations
3139 (deftransform char-equal ((a b) (base-char base-char))
3141 '(let* ((ac (char-code a))
3143 (sum (logxor ac bc)))
3145 (when (eql sum #x20)
3146 (let ((sum (+ ac bc)))
3147 (or (and (> sum 161) (< sum 213))
3148 (and (> sum 415) (< sum 461))
3149 (and (> sum 463) (< sum 477))))))))
3151 (deftransform char-upcase ((x) (base-char))
3153 '(let ((n-code (char-code x)))
3154 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3155 (< n-code #o173)) ; Octal 172 is #\z.
3156 (and (> n-code #o337)
3158 (and (> n-code #o367)
3160 (code-char (logxor #x20 n-code))
3163 (deftransform char-downcase ((x) (base-char))
3165 '(let ((n-code (char-code x)))
3166 (if (or (and (> n-code 64) ; 65 is #\A.
3167 (< n-code 91)) ; 90 is #\Z.
3172 (code-char (logxor #x20 n-code))
3175 ;;;; equality predicate transforms
3177 ;;; Return true if X and Y are lvars whose only use is a
3178 ;;; reference to the same leaf, and the value of the leaf cannot
3180 (defun same-leaf-ref-p (x y)
3181 (declare (type lvar x y))
3182 (let ((x-use (principal-lvar-use x))
3183 (y-use (principal-lvar-use y)))
3186 (eq (ref-leaf x-use) (ref-leaf y-use))
3187 (constant-reference-p x-use))))
3189 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3190 ;;; if there is no intersection between the types of the arguments,
3191 ;;; then the result is definitely false.
3192 (deftransform simple-equality-transform ((x y) * *
3195 ((same-leaf-ref-p x y) t)
3196 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3198 (t (give-up-ir1-transform))))
3201 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3205 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3206 ;;; try to convert to a type-specific predicate or EQ:
3207 ;;; -- If both args are characters, convert to CHAR=. This is better than
3208 ;;; just converting to EQ, since CHAR= may have special compilation
3209 ;;; strategies for non-standard representations, etc.
3210 ;;; -- If either arg is definitely a fixnum we punt and let the backend
3212 ;;; -- If either arg is definitely not a number or a fixnum, then we
3213 ;;; can compare with EQ.
3214 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3215 ;;; is constant then we put it second. If X is a subtype of Y, we put
3216 ;;; it second. These rules make it easier for the back end to match
3217 ;;; these interesting cases.
3218 (deftransform eql ((x y) * *)
3219 "convert to simpler equality predicate"
3220 (let ((x-type (lvar-type x))
3221 (y-type (lvar-type y))
3222 (char-type (specifier-type 'character)))
3223 (flet ((simple-type-p (type)
3224 (csubtypep type (specifier-type '(or fixnum (not number)))))
3225 (fixnum-type-p (type)
3226 (csubtypep type (specifier-type 'fixnum))))
3228 ((same-leaf-ref-p x y) t)
3229 ((not (types-equal-or-intersect x-type y-type))
3231 ((and (csubtypep x-type char-type)
3232 (csubtypep y-type char-type))
3234 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3235 (give-up-ir1-transform))
3236 ((or (simple-type-p x-type) (simple-type-p y-type))
3238 ((and (not (constant-lvar-p y))
3239 (or (constant-lvar-p x)
3240 (and (csubtypep x-type y-type)
3241 (not (csubtypep y-type x-type)))))
3244 (give-up-ir1-transform))))))
3246 ;;; similarly to the EQL transform above, we attempt to constant-fold
3247 ;;; or convert to a simpler predicate: mostly we have to be careful
3248 ;;; with strings and bit-vectors.
3249 (deftransform equal ((x y) * *)
3250 "convert to simpler equality predicate"
3251 (let ((x-type (lvar-type x))
3252 (y-type (lvar-type y))
3253 (string-type (specifier-type 'string))
3254 (bit-vector-type (specifier-type 'bit-vector)))
3256 ((same-leaf-ref-p x y) t)
3257 ((and (csubtypep x-type string-type)
3258 (csubtypep y-type string-type))
3260 ((and (csubtypep x-type bit-vector-type)
3261 (csubtypep y-type bit-vector-type))
3262 '(bit-vector-= x y))
3263 ;; if at least one is not a string, and at least one is not a
3264 ;; bit-vector, then we can reason from types.
3265 ((and (not (and (types-equal-or-intersect x-type string-type)
3266 (types-equal-or-intersect y-type string-type)))
3267 (not (and (types-equal-or-intersect x-type bit-vector-type)
3268 (types-equal-or-intersect y-type bit-vector-type)))
3269 (not (types-equal-or-intersect x-type y-type)))
3271 (t (give-up-ir1-transform)))))
3273 ;;; Convert to EQL if both args are rational and complexp is specified
3274 ;;; and the same for both.
3275 (deftransform = ((x y) * *)
3277 (let ((x-type (lvar-type x))
3278 (y-type (lvar-type y)))
3279 (if (and (csubtypep x-type (specifier-type 'number))
3280 (csubtypep y-type (specifier-type 'number)))
3281 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3282 (csubtypep y-type (specifier-type 'float)))
3283 (and (csubtypep x-type (specifier-type '(complex float)))
3284 (csubtypep y-type (specifier-type '(complex float)))))
3285 ;; They are both floats. Leave as = so that -0.0 is
3286 ;; handled correctly.
3287 (give-up-ir1-transform))
3288 ((or (and (csubtypep x-type (specifier-type 'rational))
3289 (csubtypep y-type (specifier-type 'rational)))
3290 (and (csubtypep x-type
3291 (specifier-type '(complex rational)))
3293 (specifier-type '(complex rational)))))
3294 ;; They are both rationals and complexp is the same.
3298 (give-up-ir1-transform
3299 "The operands might not be the same type.")))
3300 (give-up-ir1-transform
3301 "The operands might not be the same type."))))
3303 ;;; If LVAR's type is a numeric type, then return the type, otherwise
3304 ;;; GIVE-UP-IR1-TRANSFORM.
3305 (defun numeric-type-or-lose (lvar)
3306 (declare (type lvar lvar))
3307 (let ((res (lvar-type lvar)))
3308 (unless (numeric-type-p res) (give-up-ir1-transform))
3311 ;;; See whether we can statically determine (< X Y) using type
3312 ;;; information. If X's high bound is < Y's low, then X < Y.
3313 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3314 ;;; NIL). If not, at least make sure any constant arg is second.
3315 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3316 `(deftransform ,name ((x y))
3317 (if (same-leaf-ref-p x y)
3319 (let ((ix (or (type-approximate-interval (lvar-type x))
3320 (give-up-ir1-transform)))
3321 (iy (or (type-approximate-interval (lvar-type y))
3322 (give-up-ir1-transform))))
3327 ((and (constant-lvar-p x)
3328 (not (constant-lvar-p y)))
3331 (give-up-ir1-transform))))))))
3332 (def < > nil (interval-< ix iy) (interval->= ix iy))
3333 (def > < nil (interval-< iy ix) (interval->= iy ix))
3334 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3335 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3337 (defun ir1-transform-char< (x y first second inverse)
3339 ((same-leaf-ref-p x y) nil)
3340 ;; If we had interval representation of character types, as we
3341 ;; might eventually have to to support 2^21 characters, then here
3342 ;; we could do some compile-time computation as in transforms for
3343 ;; < above. -- CSR, 2003-07-01
3344 ((and (constant-lvar-p first)
3345 (not (constant-lvar-p second)))
3347 (t (give-up-ir1-transform))))
3349 (deftransform char< ((x y) (character character) *)
3350 (ir1-transform-char< x y x y 'char>))
3352 (deftransform char> ((x y) (character character) *)
3353 (ir1-transform-char< y x x y 'char<))
3355 ;;;; converting N-arg comparisons
3357 ;;;; We convert calls to N-arg comparison functions such as < into
3358 ;;;; two-arg calls. This transformation is enabled for all such
3359 ;;;; comparisons in this file. If any of these predicates are not
3360 ;;;; open-coded, then the transformation should be removed at some
3361 ;;;; point to avoid pessimization.
3363 ;;; This function is used for source transformation of N-arg
3364 ;;; comparison functions other than inequality. We deal both with
3365 ;;; converting to two-arg calls and inverting the sense of the test,
3366 ;;; if necessary. If the call has two args, then we pass or return a
3367 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3368 ;;; then we transform to code that returns true. Otherwise, we bind
3369 ;;; all the arguments and expand into a bunch of IFs.
3370 (declaim (ftype (function (symbol list boolean t) *) multi-compare))
3371 (defun multi-compare (predicate args not-p type)
3372 (let ((nargs (length args)))
3373 (cond ((< nargs 1) (values nil t))
3374 ((= nargs 1) `(progn (the ,type ,@args) t))
3377 `(if (,predicate ,(first args) ,(second args)) nil t)
3380 (do* ((i (1- nargs) (1- i))
3382 (current (gensym) (gensym))
3383 (vars (list current) (cons current vars))
3385 `(if (,predicate ,current ,last)
3387 `(if (,predicate ,current ,last)
3390 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3393 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3394 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3395 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3396 (define-source-transform <= (&rest args) (multi-compare '> args t 'real))
3397 (define-source-transform >= (&rest args) (multi-compare '< args t 'real))
3399 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3401 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3403 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3405 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3407 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3410 (define-source-transform char-equal (&rest args)
3411 (multi-compare 'char-equal args nil 'character))
3412 (define-source-transform char-lessp (&rest args)
3413 (multi-compare 'char-lessp args nil 'character))
3414 (define-source-transform char-greaterp (&rest args)
3415 (multi-compare 'char-greaterp args nil 'character))
3416 (define-source-transform char-not-greaterp (&rest args)
3417 (multi-compare 'char-greaterp args t 'character))
3418 (define-source-transform char-not-lessp (&rest args)
3419 (multi-compare 'char-lessp args t 'character))
3421 ;;; This function does source transformation of N-arg inequality
3422 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3423 ;;; arg cases. If there are more than two args, then we expand into
3424 ;;; the appropriate n^2 comparisons only when speed is important.
3425 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3426 (defun multi-not-equal (predicate args type)
3427 (let ((nargs (length args)))
3428 (cond ((< nargs 1) (values nil t))
3429 ((= nargs 1) `(progn (the ,type ,@args) t))
3431 `(if (,predicate ,(first args) ,(second args)) nil t))
3432 ((not (policy *lexenv*
3433 (and (>= speed space)
3434 (>= speed compilation-speed))))
3437 (let ((vars (make-gensym-list nargs)))
3438 (do ((var vars next)
3439 (next (cdr vars) (cdr next))
3442 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3444 (let ((v1 (first var)))
3446 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3448 (define-source-transform /= (&rest args)
3449 (multi-not-equal '= args 'number))
3450 (define-source-transform char/= (&rest args)
3451 (multi-not-equal 'char= args 'character))
3452 (define-source-transform char-not-equal (&rest args)
3453 (multi-not-equal 'char-equal args 'character))
3455 ;;; Expand MAX and MIN into the obvious comparisons.
3456 (define-source-transform max (arg0 &rest rest)
3457 (once-only ((arg0 arg0))
3459 `(values (the real ,arg0))
3460 `(let ((maxrest (max ,@rest)))
3461 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3462 (define-source-transform min (arg0 &rest rest)
3463 (once-only ((arg0 arg0))
3465 `(values (the real ,arg0))
3466 `(let ((minrest (min ,@rest)))
3467 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3469 ;;;; converting N-arg arithmetic functions
3471 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3472 ;;;; versions, and degenerate cases are flushed.
3474 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3475 (declaim (ftype (function (symbol t list) list) associate-args))
3476 (defun associate-args (function first-arg more-args)
3477 (let ((next (rest more-args))
3478 (arg (first more-args)))
3480 `(,function ,first-arg ,arg)
3481 (associate-args function `(,function ,first-arg ,arg) next))))
3483 ;;; Do source transformations for transitive functions such as +.
3484 ;;; One-arg cases are replaced with the arg and zero arg cases with
3485 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3486 ;;; ensure (with THE) that the argument in one-argument calls is.
3487 (defun source-transform-transitive (fun args identity
3488 &optional one-arg-result-type)
3489 (declare (symbol fun) (list args))
3492 (1 (if one-arg-result-type
3493 `(values (the ,one-arg-result-type ,(first args)))
3494 `(values ,(first args))))
3497 (associate-args fun (first args) (rest args)))))
3499 (define-source-transform + (&rest args)
3500 (source-transform-transitive '+ args 0 'number))
3501 (define-source-transform * (&rest args)
3502 (source-transform-transitive '* args 1 'number))
3503 (define-source-transform logior (&rest args)
3504 (source-transform-transitive 'logior args 0 'integer))
3505 (define-source-transform logxor (&rest args)
3506 (source-transform-transitive 'logxor args 0 'integer))
3507 (define-source-transform logand (&rest args)
3508 (source-transform-transitive 'logand args -1 'integer))
3509 (define-source-transform logeqv (&rest args)
3510 (source-transform-transitive 'logeqv args -1 'integer))
3512 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3513 ;;; because when they are given one argument, they return its absolute
3516 (define-source-transform gcd (&rest args)
3519 (1 `(abs (the integer ,(first args))))
3521 (t (associate-args 'gcd (first args) (rest args)))))
3523 (define-source-transform lcm (&rest args)
3526 (1 `(abs (the integer ,(first args))))
3528 (t (associate-args 'lcm (first args) (rest args)))))
3530 ;;; Do source transformations for intransitive n-arg functions such as
3531 ;;; /. With one arg, we form the inverse. With two args we pass.
3532 ;;; Otherwise we associate into two-arg calls.
3533 (declaim (ftype (function (symbol list t)
3534 (values list &optional (member nil t)))
3535 source-transform-intransitive))
3536 (defun source-transform-intransitive (function args inverse)
3538 ((0 2) (values nil t))
3539 (1 `(,@inverse ,(first args)))
3540 (t (associate-args function (first args) (rest args)))))
3542 (define-source-transform - (&rest args)
3543 (source-transform-intransitive '- args '(%negate)))
3544 (define-source-transform / (&rest args)
3545 (source-transform-intransitive '/ args '(/ 1)))
3547 ;;;; transforming APPLY
3549 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3550 ;;; only needs to understand one kind of variable-argument call. It is
3551 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3552 (define-source-transform apply (fun arg &rest more-args)
3553 (let ((args (cons arg more-args)))
3554 `(multiple-value-call ,fun
3555 ,@(mapcar (lambda (x)
3558 (values-list ,(car (last args))))))
3560 ;;;; transforming FORMAT
3562 ;;;; If the control string is a compile-time constant, then replace it
3563 ;;;; with a use of the FORMATTER macro so that the control string is
3564 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3565 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3566 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3568 ;;; for compile-time argument count checking.
3570 ;;; FIXME II: In some cases, type information could be correlated; for
3571 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3572 ;;; of a corresponding argument is known and does not intersect the
3573 ;;; list type, a warning could be signalled.
3574 (defun check-format-args (string args fun)
3575 (declare (type string string))
3576 (unless (typep string 'simple-string)
3577 (setq string (coerce string 'simple-string)))
3578 (multiple-value-bind (min max)
3579 (handler-case (sb!format:%compiler-walk-format-string string args)
3580 (sb!format:format-error (c)
3581 (compiler-warn "~A" c)))
3583 (let ((nargs (length args)))
3586 (warn 'format-too-few-args-warning
3588 "Too few arguments (~D) to ~S ~S: requires at least ~D."
3589 :format-arguments (list nargs fun string min)))
3591 (warn 'format-too-many-args-warning
3593 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3594 :format-arguments (list nargs fun string max))))))))
3596 (defoptimizer (format optimizer) ((dest control &rest args))
3597 (when (constant-lvar-p control)
3598 (let ((x (lvar-value control)))
3600 (check-format-args x args 'format)))))
3602 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3603 :policy (> speed space))
3604 (unless (constant-lvar-p control)
3605 (give-up-ir1-transform "The control string is not a constant."))
3606 (let ((arg-names (make-gensym-list (length args))))
3607 `(lambda (dest control ,@arg-names)
3608 (declare (ignore control))
3609 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
3611 (deftransform format ((stream control &rest args) (stream function &rest t) *
3612 :policy (> speed space))
3613 (let ((arg-names (make-gensym-list (length args))))
3614 `(lambda (stream control ,@arg-names)
3615 (funcall control stream ,@arg-names)
3618 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3619 :policy (> speed space))
3620 (let ((arg-names (make-gensym-list (length args))))
3621 `(lambda (tee control ,@arg-names)
3622 (declare (ignore tee))
3623 (funcall control *standard-output* ,@arg-names)
3628 `(defoptimizer (,name optimizer) ((control &rest args))
3629 (when (constant-lvar-p control)
3630 (let ((x (lvar-value control)))
3632 (check-format-args x args ',name)))))))
3635 #+sb-xc-host ; Only we should be using these
3638 (def compiler-abort)
3639 (def compiler-error)
3641 (def compiler-style-warn)
3642 (def compiler-notify)
3643 (def maybe-compiler-notify)
3646 (defoptimizer (cerror optimizer) ((report control &rest args))
3647 (when (and (constant-lvar-p control)
3648 (constant-lvar-p report))
3649 (let ((x (lvar-value control))
3650 (y (lvar-value report)))
3651 (when (and (stringp x) (stringp y))
3652 (multiple-value-bind (min1 max1)
3654 (sb!format:%compiler-walk-format-string x args)
3655 (sb!format:format-error (c)
3656 (compiler-warn "~A" c)))
3658 (multiple-value-bind (min2 max2)
3660 (sb!format:%compiler-walk-format-string y args)
3661 (sb!format:format-error (c)
3662 (compiler-warn "~A" c)))
3664 (let ((nargs (length args)))
3666 ((< nargs (min min1 min2))
3667 (warn 'format-too-few-args-warning
3669 "Too few arguments (~D) to ~S ~S ~S: ~
3670 requires at least ~D."
3672 (list nargs 'cerror y x (min min1 min2))))
3673 ((> nargs (max max1 max2))
3674 (warn 'format-too-many-args-warning
3676 "Too many arguments (~D) to ~S ~S ~S: ~
3679 (list nargs 'cerror y x (max max1 max2))))))))))))))
3681 (defoptimizer (coerce derive-type) ((value type))
3683 ((constant-lvar-p type)
3684 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3685 ;; but dealing with the niggle that complex canonicalization gets
3686 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3688 (let* ((specifier (lvar-value type))
3689 (result-typeoid (careful-specifier-type specifier)))
3691 ((null result-typeoid) nil)
3692 ((csubtypep result-typeoid (specifier-type 'number))
3693 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3694 ;; Rule of Canonical Representation for Complex Rationals,
3695 ;; which is a truly nasty delivery to field.
3697 ((csubtypep result-typeoid (specifier-type 'real))
3698 ;; cleverness required here: it would be nice to deduce
3699 ;; that something of type (INTEGER 2 3) coerced to type
3700 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3701 ;; FLOAT gets its own clause because it's implemented as
3702 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3705 ((and (numeric-type-p result-typeoid)
3706 (eq (numeric-type-complexp result-typeoid) :real))
3707 ;; FIXME: is this clause (a) necessary or (b) useful?
3709 ((or (csubtypep result-typeoid
3710 (specifier-type '(complex single-float)))
3711 (csubtypep result-typeoid
3712 (specifier-type '(complex double-float)))
3714 (csubtypep result-typeoid
3715 (specifier-type '(complex long-float))))
3716 ;; float complex types are never canonicalized.
3719 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3720 ;; probably just a COMPLEX or equivalent. So, in that
3721 ;; case, we will return a complex or an object of the
3722 ;; provided type if it's rational:
3723 (type-union result-typeoid
3724 (type-intersection (lvar-type value)
3725 (specifier-type 'rational))))))
3726 (t result-typeoid))))
3728 ;; OK, the result-type argument isn't constant. However, there
3729 ;; are common uses where we can still do better than just
3730 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3731 ;; where Y is of a known type. See messages on cmucl-imp
3732 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3733 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3734 ;; the basis that it's unlikely that other uses are both
3735 ;; time-critical and get to this branch of the COND (non-constant
3736 ;; second argument to COERCE). -- CSR, 2002-12-16
3737 (let ((value-type (lvar-type value))
3738 (type-type (lvar-type type)))
3740 ((good-cons-type-p (cons-type)
3741 ;; Make sure the cons-type we're looking at is something
3742 ;; we're prepared to handle which is basically something
3743 ;; that array-element-type can return.
3744 (or (and (member-type-p cons-type)
3745 (null (rest (member-type-members cons-type)))
3746 (null (first (member-type-members cons-type))))
3747 (let ((car-type (cons-type-car-type cons-type)))
3748 (and (member-type-p car-type)
3749 (null (rest (member-type-members car-type)))
3750 (or (symbolp (first (member-type-members car-type)))
3751 (numberp (first (member-type-members car-type)))
3752 (and (listp (first (member-type-members
3754 (numberp (first (first (member-type-members
3756 (good-cons-type-p (cons-type-cdr-type cons-type))))))
3757 (unconsify-type (good-cons-type)
3758 ;; Convert the "printed" respresentation of a cons
3759 ;; specifier into a type specifier. That is, the
3760 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3761 ;; NULL)) is converted to (SIGNED-BYTE 16).
3762 (cond ((or (null good-cons-type)
3763 (eq good-cons-type 'null))
3765 ((and (eq (first good-cons-type) 'cons)
3766 (eq (first (second good-cons-type)) 'member))
3767 `(,(second (second good-cons-type))
3768 ,@(unconsify-type (caddr good-cons-type))))))
3769 (coerceable-p (c-type)
3770 ;; Can the value be coerced to the given type? Coerce is
3771 ;; complicated, so we don't handle every possible case
3772 ;; here---just the most common and easiest cases:
3774 ;; * Any REAL can be coerced to a FLOAT type.
3775 ;; * Any NUMBER can be coerced to a (COMPLEX
3776 ;; SINGLE/DOUBLE-FLOAT).
3778 ;; FIXME I: we should also be able to deal with characters
3781 ;; FIXME II: I'm not sure that anything is necessary
3782 ;; here, at least while COMPLEX is not a specialized
3783 ;; array element type in the system. Reasoning: if
3784 ;; something cannot be coerced to the requested type, an
3785 ;; error will be raised (and so any downstream compiled
3786 ;; code on the assumption of the returned type is
3787 ;; unreachable). If something can, then it will be of
3788 ;; the requested type, because (by assumption) COMPLEX
3789 ;; (and other difficult types like (COMPLEX INTEGER)
3790 ;; aren't specialized types.
3791 (let ((coerced-type c-type))
3792 (or (and (subtypep coerced-type 'float)
3793 (csubtypep value-type (specifier-type 'real)))
3794 (and (subtypep coerced-type
3795 '(or (complex single-float)
3796 (complex double-float)))
3797 (csubtypep value-type (specifier-type 'number))))))
3798 (process-types (type)
3799 ;; FIXME: This needs some work because we should be able
3800 ;; to derive the resulting type better than just the
3801 ;; type arg of coerce. That is, if X is (INTEGER 10
3802 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3803 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3805 (cond ((member-type-p type)
3806 (let ((members (member-type-members type)))
3807 (if (every #'coerceable-p members)
3808 (specifier-type `(or ,@members))
3810 ((and (cons-type-p type)
3811 (good-cons-type-p type))
3812 (let ((c-type (unconsify-type (type-specifier type))))
3813 (if (coerceable-p c-type)
3814 (specifier-type c-type)
3817 *universal-type*))))
3818 (cond ((union-type-p type-type)
3819 (apply #'type-union (mapcar #'process-types
3820 (union-type-types type-type))))
3821 ((or (member-type-p type-type)
3822 (cons-type-p type-type))
3823 (process-types type-type))
3825 *universal-type*)))))))
3827 (defoptimizer (compile derive-type) ((nameoid function))
3828 (when (csubtypep (lvar-type nameoid)
3829 (specifier-type 'null))
3830 (values-specifier-type '(values function boolean boolean))))
3832 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3833 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3834 ;;; optimizer, above).
3835 (defoptimizer (array-element-type derive-type) ((array))
3836 (let ((array-type (lvar-type array)))
3837 (labels ((consify (list)
3840 `(cons (eql ,(car list)) ,(consify (rest list)))))
3841 (get-element-type (a)
3843 (type-specifier (array-type-specialized-element-type a))))
3844 (cond ((eq element-type '*)
3845 (specifier-type 'type-specifier))
3846 ((symbolp element-type)
3847 (make-member-type :members (list element-type)))
3848 ((consp element-type)
3849 (specifier-type (consify element-type)))
3851 (error "can't understand type ~S~%" element-type))))))
3852 (cond ((array-type-p array-type)
3853 (get-element-type array-type))
3854 ((union-type-p array-type)
3856 (mapcar #'get-element-type (union-type-types array-type))))
3858 *universal-type*)))))
3860 ;;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3861 ;;; isn't really related to the CMU CL code, since instead of trying
3862 ;;; to generalize the CMU CL code to allow START and END values, this
3863 ;;; code has been written from scratch following Chapter 7 of
3864 ;;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3865 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
3866 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3867 ;; isn't really related to the CMU CL code, since instead of trying
3868 ;; to generalize the CMU CL code to allow START and END values, this
3869 ;; code has been written from scratch following Chapter 7 of
3870 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3871 `(macrolet ((%index (x) `(truly-the index ,x))
3872 (%parent (i) `(ash ,i -1))
3873 (%left (i) `(%index (ash ,i 1)))
3874 (%right (i) `(%index (1+ (ash ,i 1))))
3877 (left (%left i) (%left i)))
3878 ((> left current-heap-size))
3879 (declare (type index i left))
3880 (let* ((i-elt (%elt i))
3881 (i-key (funcall keyfun i-elt))
3882 (left-elt (%elt left))
3883 (left-key (funcall keyfun left-elt)))
3884 (multiple-value-bind (large large-elt large-key)
3885 (if (funcall ,',predicate i-key left-key)
3886 (values left left-elt left-key)
3887 (values i i-elt i-key))
3888 (let ((right (%right i)))
3889 (multiple-value-bind (largest largest-elt)
3890 (if (> right current-heap-size)
3891 (values large large-elt)
3892 (let* ((right-elt (%elt right))
3893 (right-key (funcall keyfun right-elt)))
3894 (if (funcall ,',predicate large-key right-key)
3895 (values right right-elt)
3896 (values large large-elt))))
3897 (cond ((= largest i)
3900 (setf (%elt i) largest-elt
3901 (%elt largest) i-elt
3903 (%sort-vector (keyfun &optional (vtype 'vector))
3904 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
3905 ;; trouble getting type inference to
3906 ;; propagate all the way through this
3907 ;; tangled mess of inlining. The TRULY-THE
3908 ;; here works around that. -- WHN
3910 `(aref (truly-the ,',vtype ,',',vector)
3911 (%index (+ (%index ,i) start-1)))))
3912 (let (;; Heaps prefer 1-based addressing.
3913 (start-1 (1- ,',start))
3914 (current-heap-size (- ,',end ,',start))
3916 (declare (type (integer -1 #.(1- most-positive-fixnum))
3918 (declare (type index current-heap-size))
3919 (declare (type function keyfun))
3920 (loop for i of-type index
3921 from (ash current-heap-size -1) downto 1 do
3924 (when (< current-heap-size 2)
3926 (rotatef (%elt 1) (%elt current-heap-size))
3927 (decf current-heap-size)
3929 (if (typep ,vector 'simple-vector)
3930 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
3931 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
3933 ;; Special-casing the KEY=NIL case lets us avoid some
3935 (%sort-vector #'identity simple-vector)
3936 (%sort-vector ,key simple-vector))
3937 ;; It's hard to anticipate many speed-critical applications for
3938 ;; sorting vector types other than (VECTOR T), so we just lump
3939 ;; them all together in one slow dynamically typed mess.
3941 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
3942 (%sort-vector (or ,key #'identity))))))
3944 ;;;; debuggers' little helpers
3946 ;;; for debugging when transforms are behaving mysteriously,
3947 ;;; e.g. when debugging a problem with an ASH transform
3948 ;;; (defun foo (&optional s)
3949 ;;; (sb-c::/report-lvar s "S outside WHEN")
3950 ;;; (when (and (integerp s) (> s 3))
3951 ;;; (sb-c::/report-lvar s "S inside WHEN")
3952 ;;; (let ((bound (ash 1 (1- s))))
3953 ;;; (sb-c::/report-lvar bound "BOUND")
3954 ;;; (let ((x (- bound))
3956 ;;; (sb-c::/report-lvar x "X")
3957 ;;; (sb-c::/report-lvar x "Y"))
3958 ;;; `(integer ,(- bound) ,(1- bound)))))
3959 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
3960 ;;; and the function doesn't do anything at all.)
3963 (defknown /report-lvar (t t) null)
3964 (deftransform /report-lvar ((x message) (t t))
3965 (format t "~%/in /REPORT-LVAR~%")
3966 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
3967 (when (constant-lvar-p x)
3968 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
3969 (format t "/MESSAGE=~S~%" (lvar-value message))
3970 (give-up-ir1-transform "not a real transform"))
3971 (defun /report-lvar (x message)
3972 (declare (ignore x message))))