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 gethash (&rest args)
134 (2 `(sb!impl::gethash2 ,@args))
135 (3 `(sb!impl::gethash3 ,@args))
137 (define-source-transform get (&rest args)
139 (2 `(sb!impl::get2 ,@args))
140 (3 `(sb!impl::get3 ,@args))
143 (defvar *default-nthcdr-open-code-limit* 6)
144 (defvar *extreme-nthcdr-open-code-limit* 20)
146 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
147 "convert NTHCDR to CAxxR"
148 (unless (constant-lvar-p n)
149 (give-up-ir1-transform))
150 (let ((n (lvar-value n)))
152 (if (policy node (and (= speed 3) (= space 0)))
153 *extreme-nthcdr-open-code-limit*
154 *default-nthcdr-open-code-limit*))
155 (give-up-ir1-transform))
160 `(cdr ,(frob (1- n))))))
163 ;;;; arithmetic and numerology
165 (define-source-transform plusp (x) `(> ,x 0))
166 (define-source-transform minusp (x) `(< ,x 0))
167 (define-source-transform zerop (x) `(= ,x 0))
169 (define-source-transform 1+ (x) `(+ ,x 1))
170 (define-source-transform 1- (x) `(- ,x 1))
172 (define-source-transform oddp (x) `(not (zerop (logand ,x 1))))
173 (define-source-transform evenp (x) `(zerop (logand ,x 1)))
175 ;;; Note that all the integer division functions are available for
176 ;;; inline expansion.
178 (macrolet ((deffrob (fun)
179 `(define-source-transform ,fun (x &optional (y nil y-p))
186 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
188 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
191 (define-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
193 (deftransform logbitp
194 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
195 (unsigned-byte #.sb!vm:n-word-bits))))
196 `(if (>= index #.sb!vm:n-word-bits)
198 (not (zerop (logand integer (ash 1 index))))))
200 (define-source-transform byte (size position)
201 `(cons ,size ,position))
202 (define-source-transform byte-size (spec) `(car ,spec))
203 (define-source-transform byte-position (spec) `(cdr ,spec))
204 (define-source-transform ldb-test (bytespec integer)
205 `(not (zerop (mask-field ,bytespec ,integer))))
207 ;;; With the ratio and complex accessors, we pick off the "identity"
208 ;;; case, and use a primitive to handle the cell access case.
209 (define-source-transform numerator (num)
210 (once-only ((n-num `(the rational ,num)))
214 (define-source-transform denominator (num)
215 (once-only ((n-num `(the rational ,num)))
217 (%denominator ,n-num)
220 ;;;; interval arithmetic for computing bounds
222 ;;;; This is a set of routines for operating on intervals. It
223 ;;;; implements a simple interval arithmetic package. Although SBCL
224 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
225 ;;;; for two reasons:
227 ;;;; 1. This package is simpler than NUMERIC-TYPE.
229 ;;;; 2. It makes debugging much easier because you can just strip
230 ;;;; out these routines and test them independently of SBCL. (This is a
233 ;;;; One disadvantage is a probable increase in consing because we
234 ;;;; have to create these new interval structures even though
235 ;;;; numeric-type has everything we want to know. Reason 2 wins for
238 ;;; Support operations that mimic real arithmetic comparison
239 ;;; operators, but imposing a total order on the floating points such
240 ;;; that negative zeros are strictly less than positive zeros.
241 (macrolet ((def (name op)
244 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
245 (,op (float-sign x) (float-sign y))
247 (def signed-zero->= >=)
248 (def signed-zero-> >)
249 (def signed-zero-= =)
250 (def signed-zero-< <)
251 (def signed-zero-<= <=))
253 ;;; The basic interval type. It can handle open and closed intervals.
254 ;;; A bound is open if it is a list containing a number, just like
255 ;;; Lisp says. NIL means unbounded.
256 (defstruct (interval (:constructor %make-interval)
260 (defun make-interval (&key low high)
261 (labels ((normalize-bound (val)
264 (float-infinity-p val))
265 ;; Handle infinities.
269 ;; Handle any closed bounds.
272 ;; We have an open bound. Normalize the numeric
273 ;; bound. If the normalized bound is still a number
274 ;; (not nil), keep the bound open. Otherwise, the
275 ;; bound is really unbounded, so drop the openness.
276 (let ((new-val (normalize-bound (first val))))
278 ;; The bound exists, so keep it open still.
281 (error "unknown bound type in MAKE-INTERVAL")))))
282 (%make-interval :low (normalize-bound low)
283 :high (normalize-bound high))))
285 ;;; Given a number X, create a form suitable as a bound for an
286 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
287 #!-sb-fluid (declaim (inline set-bound))
288 (defun set-bound (x open-p)
289 (if (and x open-p) (list x) x))
291 ;;; Apply the function F to a bound X. If X is an open bound, then
292 ;;; the result will be open. IF X is NIL, the result is NIL.
293 (defun bound-func (f x)
294 (declare (type function f))
296 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
297 ;; With these traps masked, we might get things like infinity
298 ;; or negative infinity returned. Check for this and return
299 ;; NIL to indicate unbounded.
300 (let ((y (funcall f (type-bound-number x))))
302 (float-infinity-p y))
304 (set-bound (funcall f (type-bound-number x)) (consp x)))))))
306 ;;; Apply a binary operator OP to two bounds X and Y. The result is
307 ;;; NIL if either is NIL. Otherwise bound is computed and the result
308 ;;; is open if either X or Y is open.
310 ;;; FIXME: only used in this file, not needed in target runtime
311 (defmacro bound-binop (op x y)
313 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
314 (set-bound (,op (type-bound-number ,x)
315 (type-bound-number ,y))
316 (or (consp ,x) (consp ,y))))))
318 ;;; Convert a numeric-type object to an interval object.
319 (defun numeric-type->interval (x)
320 (declare (type numeric-type x))
321 (make-interval :low (numeric-type-low x)
322 :high (numeric-type-high x)))
324 (defun type-approximate-interval (type)
325 (declare (type ctype type))
326 (let ((types (prepare-arg-for-derive-type type))
329 (let ((type (if (member-type-p type)
330 (convert-member-type type)
332 (unless (numeric-type-p type)
333 (return-from type-approximate-interval nil))
334 (let ((interval (numeric-type->interval type)))
337 (interval-approximate-union result interval)
341 (defun copy-interval-limit (limit)
346 (defun copy-interval (x)
347 (declare (type interval x))
348 (make-interval :low (copy-interval-limit (interval-low x))
349 :high (copy-interval-limit (interval-high x))))
351 ;;; Given a point P contained in the interval X, split X into two
352 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
353 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
354 ;;; contains P. You can specify both to be T or NIL.
355 (defun interval-split (p x &optional close-lower close-upper)
356 (declare (type number p)
358 (list (make-interval :low (copy-interval-limit (interval-low x))
359 :high (if close-lower p (list p)))
360 (make-interval :low (if close-upper (list p) p)
361 :high (copy-interval-limit (interval-high x)))))
363 ;;; Return the closure of the interval. That is, convert open bounds
364 ;;; to closed bounds.
365 (defun interval-closure (x)
366 (declare (type interval x))
367 (make-interval :low (type-bound-number (interval-low x))
368 :high (type-bound-number (interval-high x))))
370 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
371 ;;; '-. Otherwise return NIL.
372 (defun interval-range-info (x &optional (point 0))
373 (declare (type interval x))
374 (let ((lo (interval-low x))
375 (hi (interval-high x)))
376 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
378 ((and hi (signed-zero->= point (type-bound-number hi)))
383 ;;; Test to see whether the interval X is bounded. HOW determines the
384 ;;; test, and should be either ABOVE, BELOW, or BOTH.
385 (defun interval-bounded-p (x how)
386 (declare (type interval x))
393 (and (interval-low x) (interval-high x)))))
395 ;;; See whether the interval X contains the number P, taking into
396 ;;; account that the interval might not be closed.
397 (defun interval-contains-p (p x)
398 (declare (type number p)
400 ;; Does the interval X contain the number P? This would be a lot
401 ;; easier if all intervals were closed!
402 (let ((lo (interval-low x))
403 (hi (interval-high x)))
405 ;; The interval is bounded
406 (if (and (signed-zero-<= (type-bound-number lo) p)
407 (signed-zero-<= p (type-bound-number hi)))
408 ;; P is definitely in the closure of the interval.
409 ;; We just need to check the end points now.
410 (cond ((signed-zero-= p (type-bound-number lo))
412 ((signed-zero-= p (type-bound-number hi))
417 ;; Interval with upper bound
418 (if (signed-zero-< p (type-bound-number hi))
420 (and (numberp hi) (signed-zero-= p hi))))
422 ;; Interval with lower bound
423 (if (signed-zero-> p (type-bound-number lo))
425 (and (numberp lo) (signed-zero-= p lo))))
427 ;; Interval with no bounds
430 ;;; Determine whether two intervals X and Y intersect. Return T if so.
431 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
432 ;;; were closed. Otherwise the intervals are treated as they are.
434 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
435 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
436 ;;; is T, then they do intersect because we use the closure of X = [0,
437 ;;; 1] and Y = [1, 2] to determine intersection.
438 (defun interval-intersect-p (x y &optional closed-intervals-p)
439 (declare (type interval x y))
440 (multiple-value-bind (intersect diff)
441 (interval-intersection/difference (if closed-intervals-p
444 (if closed-intervals-p
447 (declare (ignore diff))
450 ;;; Are the two intervals adjacent? That is, is there a number
451 ;;; between the two intervals that is not an element of either
452 ;;; interval? If so, they are not adjacent. For example [0, 1) and
453 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
454 ;;; between both intervals.
455 (defun interval-adjacent-p (x y)
456 (declare (type interval x y))
457 (flet ((adjacent (lo hi)
458 ;; Check to see whether lo and hi are adjacent. If either is
459 ;; nil, they can't be adjacent.
460 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
461 ;; The bounds are equal. They are adjacent if one of
462 ;; them is closed (a number). If both are open (consp),
463 ;; then there is a number that lies between them.
464 (or (numberp lo) (numberp hi)))))
465 (or (adjacent (interval-low y) (interval-high x))
466 (adjacent (interval-low x) (interval-high y)))))
468 ;;; Compute the intersection and difference between two intervals.
469 ;;; Two values are returned: the intersection and the difference.
471 ;;; Let the two intervals be X and Y, and let I and D be the two
472 ;;; values returned by this function. Then I = X intersect Y. If I
473 ;;; is NIL (the empty set), then D is X union Y, represented as the
474 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
475 ;;; - I, which is a list of two intervals.
477 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
478 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
479 (defun interval-intersection/difference (x y)
480 (declare (type interval x y))
481 (let ((x-lo (interval-low x))
482 (x-hi (interval-high x))
483 (y-lo (interval-low y))
484 (y-hi (interval-high y)))
487 ;; If p is an open bound, make it closed. If p is a closed
488 ;; bound, make it open.
493 ;; Test whether P is in the interval.
494 (when (interval-contains-p (type-bound-number p)
495 (interval-closure int))
496 (let ((lo (interval-low int))
497 (hi (interval-high int)))
498 ;; Check for endpoints.
499 (cond ((and lo (= (type-bound-number p) (type-bound-number lo)))
500 (not (and (consp p) (numberp lo))))
501 ((and hi (= (type-bound-number p) (type-bound-number hi)))
502 (not (and (numberp p) (consp hi))))
504 (test-lower-bound (p int)
505 ;; P is a lower bound of an interval.
508 (not (interval-bounded-p int 'below))))
509 (test-upper-bound (p int)
510 ;; P is an upper bound of an interval.
513 (not (interval-bounded-p int 'above)))))
514 (let ((x-lo-in-y (test-lower-bound x-lo y))
515 (x-hi-in-y (test-upper-bound x-hi y))
516 (y-lo-in-x (test-lower-bound y-lo x))
517 (y-hi-in-x (test-upper-bound y-hi x)))
518 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
519 ;; Intervals intersect. Let's compute the intersection
520 ;; and the difference.
521 (multiple-value-bind (lo left-lo left-hi)
522 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
523 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
524 (multiple-value-bind (hi right-lo right-hi)
526 (values x-hi (opposite-bound x-hi) y-hi))
528 (values y-hi (opposite-bound y-hi) x-hi)))
529 (values (make-interval :low lo :high hi)
530 (list (make-interval :low left-lo
532 (make-interval :low right-lo
535 (values nil (list x y))))))))
537 ;;; If intervals X and Y intersect, return a new interval that is the
538 ;;; union of the two. If they do not intersect, return NIL.
539 (defun interval-merge-pair (x y)
540 (declare (type interval x y))
541 ;; If x and y intersect or are adjacent, create the union.
542 ;; Otherwise return nil
543 (when (or (interval-intersect-p x y)
544 (interval-adjacent-p x y))
545 (flet ((select-bound (x1 x2 min-op max-op)
546 (let ((x1-val (type-bound-number x1))
547 (x2-val (type-bound-number x2)))
549 ;; Both bounds are finite. Select the right one.
550 (cond ((funcall min-op x1-val x2-val)
551 ;; x1 is definitely better.
553 ((funcall max-op x1-val x2-val)
554 ;; x2 is definitely better.
557 ;; Bounds are equal. Select either
558 ;; value and make it open only if
560 (set-bound x1-val (and (consp x1) (consp x2))))))
562 ;; At least one bound is not finite. The
563 ;; non-finite bound always wins.
565 (let* ((x-lo (copy-interval-limit (interval-low x)))
566 (x-hi (copy-interval-limit (interval-high x)))
567 (y-lo (copy-interval-limit (interval-low y)))
568 (y-hi (copy-interval-limit (interval-high y))))
569 (make-interval :low (select-bound x-lo y-lo #'< #'>)
570 :high (select-bound x-hi y-hi #'> #'<))))))
572 ;;; return the minimal interval, containing X and Y
573 (defun interval-approximate-union (x y)
574 (cond ((interval-merge-pair x y))
576 (make-interval :low (copy-interval-limit (interval-low x))
577 :high (copy-interval-limit (interval-high y))))
579 (make-interval :low (copy-interval-limit (interval-low y))
580 :high (copy-interval-limit (interval-high x))))))
582 ;;; basic arithmetic operations on intervals. We probably should do
583 ;;; true interval arithmetic here, but it's complicated because we
584 ;;; have float and integer types and bounds can be open or closed.
586 ;;; the negative of an interval
587 (defun interval-neg (x)
588 (declare (type interval x))
589 (make-interval :low (bound-func #'- (interval-high x))
590 :high (bound-func #'- (interval-low x))))
592 ;;; Add two intervals.
593 (defun interval-add (x y)
594 (declare (type interval x y))
595 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
596 :high (bound-binop + (interval-high x) (interval-high y))))
598 ;;; Subtract two intervals.
599 (defun interval-sub (x y)
600 (declare (type interval x y))
601 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
602 :high (bound-binop - (interval-high x) (interval-low y))))
604 ;;; Multiply two intervals.
605 (defun interval-mul (x y)
606 (declare (type interval x y))
607 (flet ((bound-mul (x y)
608 (cond ((or (null x) (null y))
609 ;; Multiply by infinity is infinity
611 ((or (and (numberp x) (zerop x))
612 (and (numberp y) (zerop y)))
613 ;; Multiply by closed zero is special. The result
614 ;; is always a closed bound. But don't replace this
615 ;; with zero; we want the multiplication to produce
616 ;; the correct signed zero, if needed.
617 (* (type-bound-number x) (type-bound-number y)))
618 ((or (and (floatp x) (float-infinity-p x))
619 (and (floatp y) (float-infinity-p y)))
620 ;; Infinity times anything is infinity
623 ;; General multiply. The result is open if either is open.
624 (bound-binop * x y)))))
625 (let ((x-range (interval-range-info x))
626 (y-range (interval-range-info y)))
627 (cond ((null x-range)
628 ;; Split x into two and multiply each separately
629 (destructuring-bind (x- x+) (interval-split 0 x t t)
630 (interval-merge-pair (interval-mul x- y)
631 (interval-mul x+ y))))
633 ;; Split y into two and multiply each separately
634 (destructuring-bind (y- y+) (interval-split 0 y t t)
635 (interval-merge-pair (interval-mul x y-)
636 (interval-mul x y+))))
638 (interval-neg (interval-mul (interval-neg x) y)))
640 (interval-neg (interval-mul x (interval-neg y))))
641 ((and (eq x-range '+) (eq y-range '+))
642 ;; If we are here, X and Y are both positive.
644 :low (bound-mul (interval-low x) (interval-low y))
645 :high (bound-mul (interval-high x) (interval-high y))))
647 (bug "excluded case in INTERVAL-MUL"))))))
649 ;;; Divide two intervals.
650 (defun interval-div (top bot)
651 (declare (type interval top bot))
652 (flet ((bound-div (x y y-low-p)
655 ;; Divide by infinity means result is 0. However,
656 ;; we need to watch out for the sign of the result,
657 ;; to correctly handle signed zeros. We also need
658 ;; to watch out for positive or negative infinity.
659 (if (floatp (type-bound-number x))
661 (- (float-sign (type-bound-number x) 0.0))
662 (float-sign (type-bound-number x) 0.0))
664 ((zerop (type-bound-number y))
665 ;; Divide by zero means result is infinity
667 ((and (numberp x) (zerop x))
668 ;; Zero divided by anything is zero.
671 (bound-binop / x y)))))
672 (let ((top-range (interval-range-info top))
673 (bot-range (interval-range-info bot)))
674 (cond ((null bot-range)
675 ;; The denominator contains zero, so anything goes!
676 (make-interval :low nil :high nil))
678 ;; Denominator is negative so flip the sign, compute the
679 ;; result, and flip it back.
680 (interval-neg (interval-div top (interval-neg bot))))
682 ;; Split top into two positive and negative parts, and
683 ;; divide each separately
684 (destructuring-bind (top- top+) (interval-split 0 top t t)
685 (interval-merge-pair (interval-div top- bot)
686 (interval-div top+ bot))))
688 ;; Top is negative so flip the sign, divide, and flip the
689 ;; sign of the result.
690 (interval-neg (interval-div (interval-neg top) bot)))
691 ((and (eq top-range '+) (eq bot-range '+))
694 :low (bound-div (interval-low top) (interval-high bot) t)
695 :high (bound-div (interval-high top) (interval-low bot) nil)))
697 (bug "excluded case in INTERVAL-DIV"))))))
699 ;;; Apply the function F to the interval X. If X = [a, b], then the
700 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
701 ;;; result makes sense. It will if F is monotonic increasing (or
703 (defun interval-func (f x)
704 (declare (type function f)
706 (let ((lo (bound-func f (interval-low x)))
707 (hi (bound-func f (interval-high x))))
708 (make-interval :low lo :high hi)))
710 ;;; Return T if X < Y. That is every number in the interval X is
711 ;;; always less than any number in the interval Y.
712 (defun interval-< (x y)
713 (declare (type interval x y))
714 ;; X < Y only if X is bounded above, Y is bounded below, and they
716 (when (and (interval-bounded-p x 'above)
717 (interval-bounded-p y 'below))
718 ;; Intervals are bounded in the appropriate way. Make sure they
720 (let ((left (interval-high x))
721 (right (interval-low y)))
722 (cond ((> (type-bound-number left)
723 (type-bound-number right))
724 ;; The intervals definitely overlap, so result is NIL.
726 ((< (type-bound-number left)
727 (type-bound-number right))
728 ;; The intervals definitely don't touch, so result is T.
731 ;; Limits are equal. Check for open or closed bounds.
732 ;; Don't overlap if one or the other are open.
733 (or (consp left) (consp right)))))))
735 ;;; Return T if X >= Y. That is, every number in the interval X is
736 ;;; always greater than any number in the interval Y.
737 (defun interval->= (x y)
738 (declare (type interval x y))
739 ;; X >= Y if lower bound of X >= upper bound of Y
740 (when (and (interval-bounded-p x 'below)
741 (interval-bounded-p y 'above))
742 (>= (type-bound-number (interval-low x))
743 (type-bound-number (interval-high y)))))
745 ;;; Return an interval that is the absolute value of X. Thus, if
746 ;;; X = [-1 10], the result is [0, 10].
747 (defun interval-abs (x)
748 (declare (type interval x))
749 (case (interval-range-info x)
755 (destructuring-bind (x- x+) (interval-split 0 x t t)
756 (interval-merge-pair (interval-neg x-) x+)))))
758 ;;; Compute the square of an interval.
759 (defun interval-sqr (x)
760 (declare (type interval x))
761 (interval-func (lambda (x) (* x x))
764 ;;;; numeric DERIVE-TYPE methods
766 ;;; a utility for defining derive-type methods of integer operations. If
767 ;;; the types of both X and Y are integer types, then we compute a new
768 ;;; integer type with bounds determined Fun when applied to X and Y.
769 ;;; Otherwise, we use NUMERIC-CONTAGION.
770 (defun derive-integer-type-aux (x y fun)
771 (declare (type function fun))
772 (if (and (numeric-type-p x) (numeric-type-p y)
773 (eq (numeric-type-class x) 'integer)
774 (eq (numeric-type-class y) 'integer)
775 (eq (numeric-type-complexp x) :real)
776 (eq (numeric-type-complexp y) :real))
777 (multiple-value-bind (low high) (funcall fun x y)
778 (make-numeric-type :class 'integer
782 (numeric-contagion x y)))
784 (defun derive-integer-type (x y fun)
785 (declare (type lvar x y) (type function fun))
786 (let ((x (lvar-type x))
788 (derive-integer-type-aux x y fun)))
790 ;;; simple utility to flatten a list
791 (defun flatten-list (x)
792 (labels ((flatten-and-append (tree list)
793 (cond ((null tree) list)
794 ((atom tree) (cons tree list))
795 (t (flatten-and-append
796 (car tree) (flatten-and-append (cdr tree) list))))))
797 (flatten-and-append x nil)))
799 ;;; Take some type of lvar and massage it so that we get a list of the
800 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
802 (defun prepare-arg-for-derive-type (arg)
803 (flet ((listify (arg)
808 (union-type-types arg))
811 (unless (eq arg *empty-type*)
812 ;; Make sure all args are some type of numeric-type. For member
813 ;; types, convert the list of members into a union of equivalent
814 ;; single-element member-type's.
815 (let ((new-args nil))
816 (dolist (arg (listify arg))
817 (if (member-type-p arg)
818 ;; Run down the list of members and convert to a list of
820 (dolist (member (member-type-members arg))
821 (push (if (numberp member)
822 (make-member-type :members (list member))
825 (push arg new-args)))
826 (unless (member *empty-type* new-args)
829 ;;; Convert from the standard type convention for which -0.0 and 0.0
830 ;;; are equal to an intermediate convention for which they are
831 ;;; considered different which is more natural for some of the
833 (defun convert-numeric-type (type)
834 (declare (type numeric-type type))
835 ;;; Only convert real float interval delimiters types.
836 (if (eq (numeric-type-complexp type) :real)
837 (let* ((lo (numeric-type-low type))
838 (lo-val (type-bound-number lo))
839 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
840 (hi (numeric-type-high type))
841 (hi-val (type-bound-number hi))
842 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
843 (if (or lo-float-zero-p hi-float-zero-p)
845 :class (numeric-type-class type)
846 :format (numeric-type-format type)
848 :low (if lo-float-zero-p
850 (list (float 0.0 lo-val))
851 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
853 :high (if hi-float-zero-p
855 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
862 ;;; Convert back from the intermediate convention for which -0.0 and
863 ;;; 0.0 are considered different to the standard type convention for
865 (defun convert-back-numeric-type (type)
866 (declare (type numeric-type type))
867 ;;; Only convert real float interval delimiters types.
868 (if (eq (numeric-type-complexp type) :real)
869 (let* ((lo (numeric-type-low type))
870 (lo-val (type-bound-number lo))
872 (and lo (floatp lo-val) (= lo-val 0.0)
873 (float-sign lo-val)))
874 (hi (numeric-type-high type))
875 (hi-val (type-bound-number hi))
877 (and hi (floatp hi-val) (= hi-val 0.0)
878 (float-sign hi-val))))
880 ;; (float +0.0 +0.0) => (member 0.0)
881 ;; (float -0.0 -0.0) => (member -0.0)
882 ((and lo-float-zero-p hi-float-zero-p)
883 ;; shouldn't have exclusive bounds here..
884 (aver (and (not (consp lo)) (not (consp hi))))
885 (if (= lo-float-zero-p hi-float-zero-p)
886 ;; (float +0.0 +0.0) => (member 0.0)
887 ;; (float -0.0 -0.0) => (member -0.0)
888 (specifier-type `(member ,lo-val))
889 ;; (float -0.0 +0.0) => (float 0.0 0.0)
890 ;; (float +0.0 -0.0) => (float 0.0 0.0)
891 (make-numeric-type :class (numeric-type-class type)
892 :format (numeric-type-format type)
898 ;; (float -0.0 x) => (float 0.0 x)
899 ((and (not (consp lo)) (minusp lo-float-zero-p))
900 (make-numeric-type :class (numeric-type-class type)
901 :format (numeric-type-format type)
903 :low (float 0.0 lo-val)
905 ;; (float (+0.0) x) => (float (0.0) x)
906 ((and (consp lo) (plusp lo-float-zero-p))
907 (make-numeric-type :class (numeric-type-class type)
908 :format (numeric-type-format type)
910 :low (list (float 0.0 lo-val))
913 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
914 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
915 (list (make-member-type :members (list (float 0.0 lo-val)))
916 (make-numeric-type :class (numeric-type-class type)
917 :format (numeric-type-format type)
919 :low (list (float 0.0 lo-val))
923 ;; (float x +0.0) => (float x 0.0)
924 ((and (not (consp hi)) (plusp hi-float-zero-p))
925 (make-numeric-type :class (numeric-type-class type)
926 :format (numeric-type-format type)
929 :high (float 0.0 hi-val)))
930 ;; (float x (-0.0)) => (float x (0.0))
931 ((and (consp hi) (minusp hi-float-zero-p))
932 (make-numeric-type :class (numeric-type-class type)
933 :format (numeric-type-format type)
936 :high (list (float 0.0 hi-val))))
938 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
939 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
940 (list (make-member-type :members (list (float -0.0 hi-val)))
941 (make-numeric-type :class (numeric-type-class type)
942 :format (numeric-type-format type)
945 :high (list (float 0.0 hi-val)))))))
951 ;;; Convert back a possible list of numeric types.
952 (defun convert-back-numeric-type-list (type-list)
956 (dolist (type type-list)
957 (if (numeric-type-p type)
958 (let ((result (convert-back-numeric-type type)))
960 (setf results (append results result))
961 (push result results)))
962 (push type results)))
965 (convert-back-numeric-type type-list))
967 (convert-back-numeric-type-list (union-type-types type-list)))
971 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
972 ;;; belong in the kernel's type logic, invoked always, instead of in
973 ;;; the compiler, invoked only during some type optimizations. (In
974 ;;; fact, as of 0.pre8.100 or so they probably are, under
975 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
977 ;;; Take a list of types and return a canonical type specifier,
978 ;;; combining any MEMBER types together. If both positive and negative
979 ;;; MEMBER types are present they are converted to a float type.
980 ;;; XXX This would be far simpler if the type-union methods could handle
981 ;;; member/number unions.
982 (defun make-canonical-union-type (type-list)
985 (dolist (type type-list)
986 (if (member-type-p type)
987 (setf members (union members (member-type-members type)))
988 (push type misc-types)))
990 (when (null (set-difference `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0) members))
991 (push (specifier-type '(long-float 0.0l0 0.0l0)) misc-types)
992 (setf members (set-difference members `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0))))
993 (when (null (set-difference `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0) members))
994 (push (specifier-type '(double-float 0.0d0 0.0d0)) misc-types)
995 (setf members (set-difference members `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0))))
996 (when (null (set-difference `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0) members))
997 (push (specifier-type '(single-float 0.0f0 0.0f0)) misc-types)
998 (setf members (set-difference members `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0))))
1000 (apply #'type-union (make-member-type :members members) misc-types)
1001 (apply #'type-union misc-types))))
1003 ;;; Convert a member type with a single member to a numeric type.
1004 (defun convert-member-type (arg)
1005 (let* ((members (member-type-members arg))
1006 (member (first members))
1007 (member-type (type-of member)))
1008 (aver (not (rest members)))
1009 (specifier-type (cond ((typep member 'integer)
1010 `(integer ,member ,member))
1011 ((memq member-type '(short-float single-float
1012 double-float long-float))
1013 `(,member-type ,member ,member))
1017 ;;; This is used in defoptimizers for computing the resulting type of
1020 ;;; Given the lvar ARG, derive the resulting type using the
1021 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1022 ;;; "atomic" lvar type like numeric-type or member-type (containing
1023 ;;; just one element). It should return the resulting type, which can
1024 ;;; be a list of types.
1026 ;;; For the case of member types, if a MEMBER-FUN is given it is
1027 ;;; called to compute the result otherwise the member type is first
1028 ;;; converted to a numeric type and the DERIVE-FUN is called.
1029 (defun one-arg-derive-type (arg derive-fun member-fun
1030 &optional (convert-type t))
1031 (declare (type function derive-fun)
1032 (type (or null function) member-fun))
1033 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1039 (with-float-traps-masked
1040 (:underflow :overflow :divide-by-zero)
1042 `(eql ,(funcall member-fun
1043 (first (member-type-members x))))))
1044 ;; Otherwise convert to a numeric type.
1045 (let ((result-type-list
1046 (funcall derive-fun (convert-member-type x))))
1048 (convert-back-numeric-type-list result-type-list)
1049 result-type-list))))
1052 (convert-back-numeric-type-list
1053 (funcall derive-fun (convert-numeric-type x)))
1054 (funcall derive-fun x)))
1056 *universal-type*))))
1057 ;; Run down the list of args and derive the type of each one,
1058 ;; saving all of the results in a list.
1059 (let ((results nil))
1060 (dolist (arg arg-list)
1061 (let ((result (deriver arg)))
1063 (setf results (append results result))
1064 (push result results))))
1066 (make-canonical-union-type results)
1067 (first results)))))))
1069 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1070 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1071 ;;; original args and a third which is T to indicate if the two args
1072 ;;; really represent the same lvar. This is useful for deriving the
1073 ;;; type of things like (* x x), which should always be positive. If
1074 ;;; we didn't do this, we wouldn't be able to tell.
1075 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1076 &optional (convert-type t))
1077 (declare (type function derive-fun fun))
1078 (flet ((deriver (x y same-arg)
1079 (cond ((and (member-type-p x) (member-type-p y))
1080 (let* ((x (first (member-type-members x)))
1081 (y (first (member-type-members y)))
1082 (result (ignore-errors
1083 (with-float-traps-masked
1084 (:underflow :overflow :divide-by-zero
1086 (funcall fun x y)))))
1087 (cond ((null result) *empty-type*)
1088 ((and (floatp result) (float-nan-p result))
1089 (make-numeric-type :class 'float
1090 :format (type-of result)
1093 (specifier-type `(eql ,result))))))
1094 ((and (member-type-p x) (numeric-type-p y))
1095 (let* ((x (convert-member-type x))
1096 (y (if convert-type (convert-numeric-type y) y))
1097 (result (funcall derive-fun x y same-arg)))
1099 (convert-back-numeric-type-list result)
1101 ((and (numeric-type-p x) (member-type-p y))
1102 (let* ((x (if convert-type (convert-numeric-type x) x))
1103 (y (convert-member-type y))
1104 (result (funcall derive-fun x y same-arg)))
1106 (convert-back-numeric-type-list result)
1108 ((and (numeric-type-p x) (numeric-type-p y))
1109 (let* ((x (if convert-type (convert-numeric-type x) x))
1110 (y (if convert-type (convert-numeric-type y) y))
1111 (result (funcall derive-fun x y same-arg)))
1113 (convert-back-numeric-type-list result)
1116 *universal-type*))))
1117 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1118 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1119 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1121 (let ((results nil))
1123 ;; Since the args are the same LVARs, just run down the
1126 (let ((result (deriver x x same-arg)))
1128 (setf results (append results result))
1129 (push result results))))
1130 ;; Try all pairwise combinations.
1133 (let ((result (or (deriver x y same-arg)
1134 (numeric-contagion x y))))
1136 (setf results (append results result))
1137 (push result results))))))
1139 (make-canonical-union-type results)
1140 (first results)))))))
1142 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1144 (defoptimizer (+ derive-type) ((x y))
1145 (derive-integer-type
1152 (values (frob (numeric-type-low x) (numeric-type-low y))
1153 (frob (numeric-type-high x) (numeric-type-high y)))))))
1155 (defoptimizer (- derive-type) ((x y))
1156 (derive-integer-type
1163 (values (frob (numeric-type-low x) (numeric-type-high y))
1164 (frob (numeric-type-high x) (numeric-type-low y)))))))
1166 (defoptimizer (* derive-type) ((x y))
1167 (derive-integer-type
1170 (let ((x-low (numeric-type-low x))
1171 (x-high (numeric-type-high x))
1172 (y-low (numeric-type-low y))
1173 (y-high (numeric-type-high y)))
1174 (cond ((not (and x-low y-low))
1176 ((or (minusp x-low) (minusp y-low))
1177 (if (and x-high y-high)
1178 (let ((max (* (max (abs x-low) (abs x-high))
1179 (max (abs y-low) (abs y-high)))))
1180 (values (- max) max))
1183 (values (* x-low y-low)
1184 (if (and x-high y-high)
1188 (defoptimizer (/ derive-type) ((x y))
1189 (numeric-contagion (lvar-type x) (lvar-type y)))
1193 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1195 (defun +-derive-type-aux (x y same-arg)
1196 (if (and (numeric-type-real-p x)
1197 (numeric-type-real-p y))
1200 (let ((x-int (numeric-type->interval x)))
1201 (interval-add x-int x-int))
1202 (interval-add (numeric-type->interval x)
1203 (numeric-type->interval y))))
1204 (result-type (numeric-contagion x y)))
1205 ;; If the result type is a float, we need to be sure to coerce
1206 ;; the bounds into the correct type.
1207 (when (eq (numeric-type-class result-type) 'float)
1208 (setf result (interval-func
1210 (coerce x (or (numeric-type-format result-type)
1214 :class (if (and (eq (numeric-type-class x) 'integer)
1215 (eq (numeric-type-class y) 'integer))
1216 ;; The sum of integers is always an integer.
1218 (numeric-type-class result-type))
1219 :format (numeric-type-format result-type)
1220 :low (interval-low result)
1221 :high (interval-high result)))
1222 ;; general contagion
1223 (numeric-contagion x y)))
1225 (defoptimizer (+ derive-type) ((x y))
1226 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1228 (defun --derive-type-aux (x y same-arg)
1229 (if (and (numeric-type-real-p x)
1230 (numeric-type-real-p y))
1232 ;; (- X X) is always 0.
1234 (make-interval :low 0 :high 0)
1235 (interval-sub (numeric-type->interval x)
1236 (numeric-type->interval y))))
1237 (result-type (numeric-contagion x y)))
1238 ;; If the result type is a float, we need to be sure to coerce
1239 ;; the bounds into the correct type.
1240 (when (eq (numeric-type-class result-type) 'float)
1241 (setf result (interval-func
1243 (coerce x (or (numeric-type-format result-type)
1247 :class (if (and (eq (numeric-type-class x) 'integer)
1248 (eq (numeric-type-class y) 'integer))
1249 ;; The difference of integers is always an integer.
1251 (numeric-type-class result-type))
1252 :format (numeric-type-format result-type)
1253 :low (interval-low result)
1254 :high (interval-high result)))
1255 ;; general contagion
1256 (numeric-contagion x y)))
1258 (defoptimizer (- derive-type) ((x y))
1259 (two-arg-derive-type x y #'--derive-type-aux #'-))
1261 (defun *-derive-type-aux (x y same-arg)
1262 (if (and (numeric-type-real-p x)
1263 (numeric-type-real-p y))
1265 ;; (* X X) is always positive, so take care to do it right.
1267 (interval-sqr (numeric-type->interval x))
1268 (interval-mul (numeric-type->interval x)
1269 (numeric-type->interval y))))
1270 (result-type (numeric-contagion x y)))
1271 ;; If the result type is a float, we need to be sure to coerce
1272 ;; the bounds into the correct type.
1273 (when (eq (numeric-type-class result-type) 'float)
1274 (setf result (interval-func
1276 (coerce x (or (numeric-type-format result-type)
1280 :class (if (and (eq (numeric-type-class x) 'integer)
1281 (eq (numeric-type-class y) 'integer))
1282 ;; The product of integers is always an integer.
1284 (numeric-type-class result-type))
1285 :format (numeric-type-format result-type)
1286 :low (interval-low result)
1287 :high (interval-high result)))
1288 (numeric-contagion x y)))
1290 (defoptimizer (* derive-type) ((x y))
1291 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1293 (defun /-derive-type-aux (x y same-arg)
1294 (if (and (numeric-type-real-p x)
1295 (numeric-type-real-p y))
1297 ;; (/ X X) is always 1, except if X can contain 0. In
1298 ;; that case, we shouldn't optimize the division away
1299 ;; because we want 0/0 to signal an error.
1301 (not (interval-contains-p
1302 0 (interval-closure (numeric-type->interval y)))))
1303 (make-interval :low 1 :high 1)
1304 (interval-div (numeric-type->interval x)
1305 (numeric-type->interval y))))
1306 (result-type (numeric-contagion x y)))
1307 ;; If the result type is a float, we need to be sure to coerce
1308 ;; the bounds into the correct type.
1309 (when (eq (numeric-type-class result-type) 'float)
1310 (setf result (interval-func
1312 (coerce x (or (numeric-type-format result-type)
1315 (make-numeric-type :class (numeric-type-class result-type)
1316 :format (numeric-type-format result-type)
1317 :low (interval-low result)
1318 :high (interval-high result)))
1319 (numeric-contagion x y)))
1321 (defoptimizer (/ derive-type) ((x y))
1322 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1326 (defun ash-derive-type-aux (n-type shift same-arg)
1327 (declare (ignore same-arg))
1328 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1329 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1330 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1331 ;; two bignums yielding zero) and it's hard to avoid that
1332 ;; calculation in here.
1333 #+(and cmu sb-xc-host)
1334 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1335 (typep (numeric-type-high n-type) 'bignum))
1336 (or (typep (numeric-type-low shift) 'bignum)
1337 (typep (numeric-type-high shift) 'bignum)))
1338 (return-from ash-derive-type-aux *universal-type*))
1339 (flet ((ash-outer (n s)
1340 (when (and (fixnump s)
1342 (> s sb!xc:most-negative-fixnum))
1344 ;; KLUDGE: The bare 64's here should be related to
1345 ;; symbolic machine word size values somehow.
1348 (if (and (fixnump s)
1349 (> s sb!xc:most-negative-fixnum))
1351 (if (minusp n) -1 0))))
1352 (or (and (csubtypep n-type (specifier-type 'integer))
1353 (csubtypep shift (specifier-type 'integer))
1354 (let ((n-low (numeric-type-low n-type))
1355 (n-high (numeric-type-high n-type))
1356 (s-low (numeric-type-low shift))
1357 (s-high (numeric-type-high shift)))
1358 (make-numeric-type :class 'integer :complexp :real
1361 (ash-outer n-low s-high)
1362 (ash-inner n-low s-low)))
1365 (ash-inner n-high s-low)
1366 (ash-outer n-high s-high))))))
1369 (defoptimizer (ash derive-type) ((n shift))
1370 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1372 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1373 (macrolet ((frob (fun)
1374 `#'(lambda (type type2)
1375 (declare (ignore type2))
1376 (let ((lo (numeric-type-low type))
1377 (hi (numeric-type-high type)))
1378 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1380 (defoptimizer (%negate derive-type) ((num))
1381 (derive-integer-type num num (frob -))))
1383 (defun lognot-derive-type-aux (int)
1384 (derive-integer-type-aux int int
1385 (lambda (type type2)
1386 (declare (ignore type2))
1387 (let ((lo (numeric-type-low type))
1388 (hi (numeric-type-high type)))
1389 (values (if hi (lognot hi) nil)
1390 (if lo (lognot lo) nil)
1391 (numeric-type-class type)
1392 (numeric-type-format type))))))
1394 (defoptimizer (lognot derive-type) ((int))
1395 (lognot-derive-type-aux (lvar-type int)))
1397 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1398 (defoptimizer (%negate derive-type) ((num))
1399 (flet ((negate-bound (b)
1401 (set-bound (- (type-bound-number b))
1403 (one-arg-derive-type num
1405 (modified-numeric-type
1407 :low (negate-bound (numeric-type-high type))
1408 :high (negate-bound (numeric-type-low type))))
1411 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1412 (defoptimizer (abs derive-type) ((num))
1413 (let ((type (lvar-type num)))
1414 (if (and (numeric-type-p type)
1415 (eq (numeric-type-class type) 'integer)
1416 (eq (numeric-type-complexp type) :real))
1417 (let ((lo (numeric-type-low type))
1418 (hi (numeric-type-high type)))
1419 (make-numeric-type :class 'integer :complexp :real
1420 :low (cond ((and hi (minusp hi))
1426 :high (if (and hi lo)
1427 (max (abs hi) (abs lo))
1429 (numeric-contagion type type))))
1431 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1432 (defun abs-derive-type-aux (type)
1433 (cond ((eq (numeric-type-complexp type) :complex)
1434 ;; The absolute value of a complex number is always a
1435 ;; non-negative float.
1436 (let* ((format (case (numeric-type-class type)
1437 ((integer rational) 'single-float)
1438 (t (numeric-type-format type))))
1439 (bound-format (or format 'float)))
1440 (make-numeric-type :class 'float
1443 :low (coerce 0 bound-format)
1446 ;; The absolute value of a real number is a non-negative real
1447 ;; of the same type.
1448 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1449 (class (numeric-type-class type))
1450 (format (numeric-type-format type))
1451 (bound-type (or format class 'real)))
1456 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1457 :high (coerce-numeric-bound
1458 (interval-high abs-bnd) bound-type))))))
1460 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1461 (defoptimizer (abs derive-type) ((num))
1462 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1464 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1465 (defoptimizer (truncate derive-type) ((number divisor))
1466 (let ((number-type (lvar-type number))
1467 (divisor-type (lvar-type divisor))
1468 (integer-type (specifier-type 'integer)))
1469 (if (and (numeric-type-p number-type)
1470 (csubtypep number-type integer-type)
1471 (numeric-type-p divisor-type)
1472 (csubtypep divisor-type integer-type))
1473 (let ((number-low (numeric-type-low number-type))
1474 (number-high (numeric-type-high number-type))
1475 (divisor-low (numeric-type-low divisor-type))
1476 (divisor-high (numeric-type-high divisor-type)))
1477 (values-specifier-type
1478 `(values ,(integer-truncate-derive-type number-low number-high
1479 divisor-low divisor-high)
1480 ,(integer-rem-derive-type number-low number-high
1481 divisor-low divisor-high))))
1484 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1487 (defun rem-result-type (number-type divisor-type)
1488 ;; Figure out what the remainder type is. The remainder is an
1489 ;; integer if both args are integers; a rational if both args are
1490 ;; rational; and a float otherwise.
1491 (cond ((and (csubtypep number-type (specifier-type 'integer))
1492 (csubtypep divisor-type (specifier-type 'integer)))
1494 ((and (csubtypep number-type (specifier-type 'rational))
1495 (csubtypep divisor-type (specifier-type 'rational)))
1497 ((and (csubtypep number-type (specifier-type 'float))
1498 (csubtypep divisor-type (specifier-type 'float)))
1499 ;; Both are floats so the result is also a float, of
1500 ;; the largest type.
1501 (or (float-format-max (numeric-type-format number-type)
1502 (numeric-type-format divisor-type))
1504 ((and (csubtypep number-type (specifier-type 'float))
1505 (csubtypep divisor-type (specifier-type 'rational)))
1506 ;; One of the arguments is a float and the other is a
1507 ;; rational. The remainder is a float of the same
1509 (or (numeric-type-format number-type) 'float))
1510 ((and (csubtypep divisor-type (specifier-type 'float))
1511 (csubtypep number-type (specifier-type 'rational)))
1512 ;; One of the arguments is a float and the other is a
1513 ;; rational. The remainder is a float of the same
1515 (or (numeric-type-format divisor-type) 'float))
1517 ;; Some unhandled combination. This usually means both args
1518 ;; are REAL so the result is a REAL.
1521 (defun truncate-derive-type-quot (number-type divisor-type)
1522 (let* ((rem-type (rem-result-type number-type divisor-type))
1523 (number-interval (numeric-type->interval number-type))
1524 (divisor-interval (numeric-type->interval divisor-type)))
1525 ;;(declare (type (member '(integer rational float)) rem-type))
1526 ;; We have real numbers now.
1527 (cond ((eq rem-type 'integer)
1528 ;; Since the remainder type is INTEGER, both args are
1530 (let* ((res (integer-truncate-derive-type
1531 (interval-low number-interval)
1532 (interval-high number-interval)
1533 (interval-low divisor-interval)
1534 (interval-high divisor-interval))))
1535 (specifier-type (if (listp res) res 'integer))))
1537 (let ((quot (truncate-quotient-bound
1538 (interval-div number-interval
1539 divisor-interval))))
1540 (specifier-type `(integer ,(or (interval-low quot) '*)
1541 ,(or (interval-high quot) '*))))))))
1543 (defun truncate-derive-type-rem (number-type divisor-type)
1544 (let* ((rem-type (rem-result-type number-type divisor-type))
1545 (number-interval (numeric-type->interval number-type))
1546 (divisor-interval (numeric-type->interval divisor-type))
1547 (rem (truncate-rem-bound number-interval divisor-interval)))
1548 ;;(declare (type (member '(integer rational float)) rem-type))
1549 ;; We have real numbers now.
1550 (cond ((eq rem-type 'integer)
1551 ;; Since the remainder type is INTEGER, both args are
1553 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1554 ,(or (interval-high rem) '*))))
1556 (multiple-value-bind (class format)
1559 (values 'integer nil))
1561 (values 'rational nil))
1562 ((or single-float double-float #!+long-float long-float)
1563 (values 'float rem-type))
1565 (values 'float nil))
1568 (when (member rem-type '(float single-float double-float
1569 #!+long-float long-float))
1570 (setf rem (interval-func #'(lambda (x)
1571 (coerce x rem-type))
1573 (make-numeric-type :class class
1575 :low (interval-low rem)
1576 :high (interval-high rem)))))))
1578 (defun truncate-derive-type-quot-aux (num div same-arg)
1579 (declare (ignore same-arg))
1580 (if (and (numeric-type-real-p num)
1581 (numeric-type-real-p div))
1582 (truncate-derive-type-quot num div)
1585 (defun truncate-derive-type-rem-aux (num div same-arg)
1586 (declare (ignore same-arg))
1587 (if (and (numeric-type-real-p num)
1588 (numeric-type-real-p div))
1589 (truncate-derive-type-rem num div)
1592 (defoptimizer (truncate derive-type) ((number divisor))
1593 (let ((quot (two-arg-derive-type number divisor
1594 #'truncate-derive-type-quot-aux #'truncate))
1595 (rem (two-arg-derive-type number divisor
1596 #'truncate-derive-type-rem-aux #'rem)))
1597 (when (and quot rem)
1598 (make-values-type :required (list quot rem)))))
1600 (defun ftruncate-derive-type-quot (number-type divisor-type)
1601 ;; The bounds are the same as for truncate. However, the first
1602 ;; result is a float of some type. We need to determine what that
1603 ;; type is. Basically it's the more contagious of the two types.
1604 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1605 (res-type (numeric-contagion number-type divisor-type)))
1606 (make-numeric-type :class 'float
1607 :format (numeric-type-format res-type)
1608 :low (numeric-type-low q-type)
1609 :high (numeric-type-high q-type))))
1611 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1612 (declare (ignore same-arg))
1613 (if (and (numeric-type-real-p n)
1614 (numeric-type-real-p d))
1615 (ftruncate-derive-type-quot n d)
1618 (defoptimizer (ftruncate derive-type) ((number divisor))
1620 (two-arg-derive-type number divisor
1621 #'ftruncate-derive-type-quot-aux #'ftruncate))
1622 (rem (two-arg-derive-type number divisor
1623 #'truncate-derive-type-rem-aux #'rem)))
1624 (when (and quot rem)
1625 (make-values-type :required (list quot rem)))))
1627 (defun %unary-truncate-derive-type-aux (number)
1628 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1630 (defoptimizer (%unary-truncate derive-type) ((number))
1631 (one-arg-derive-type number
1632 #'%unary-truncate-derive-type-aux
1635 (defoptimizer (%unary-ftruncate derive-type) ((number))
1636 (let ((divisor (specifier-type '(integer 1 1))))
1637 (one-arg-derive-type number
1639 (ftruncate-derive-type-quot-aux n divisor nil))
1640 #'%unary-ftruncate)))
1642 ;;; Define optimizers for FLOOR and CEILING.
1644 ((def (name q-name r-name)
1645 (let ((q-aux (symbolicate q-name "-AUX"))
1646 (r-aux (symbolicate r-name "-AUX")))
1648 ;; Compute type of quotient (first) result.
1649 (defun ,q-aux (number-type divisor-type)
1650 (let* ((number-interval
1651 (numeric-type->interval number-type))
1653 (numeric-type->interval divisor-type))
1654 (quot (,q-name (interval-div number-interval
1655 divisor-interval))))
1656 (specifier-type `(integer ,(or (interval-low quot) '*)
1657 ,(or (interval-high quot) '*)))))
1658 ;; Compute type of remainder.
1659 (defun ,r-aux (number-type divisor-type)
1660 (let* ((divisor-interval
1661 (numeric-type->interval divisor-type))
1662 (rem (,r-name divisor-interval))
1663 (result-type (rem-result-type number-type divisor-type)))
1664 (multiple-value-bind (class format)
1667 (values 'integer nil))
1669 (values 'rational nil))
1670 ((or single-float double-float #!+long-float long-float)
1671 (values 'float result-type))
1673 (values 'float nil))
1676 (when (member result-type '(float single-float double-float
1677 #!+long-float long-float))
1678 ;; Make sure that the limits on the interval have
1680 (setf rem (interval-func (lambda (x)
1681 (coerce x result-type))
1683 (make-numeric-type :class class
1685 :low (interval-low rem)
1686 :high (interval-high rem)))))
1687 ;; the optimizer itself
1688 (defoptimizer (,name derive-type) ((number divisor))
1689 (flet ((derive-q (n d same-arg)
1690 (declare (ignore same-arg))
1691 (if (and (numeric-type-real-p n)
1692 (numeric-type-real-p d))
1695 (derive-r (n d same-arg)
1696 (declare (ignore same-arg))
1697 (if (and (numeric-type-real-p n)
1698 (numeric-type-real-p d))
1701 (let ((quot (two-arg-derive-type
1702 number divisor #'derive-q #',name))
1703 (rem (two-arg-derive-type
1704 number divisor #'derive-r #'mod)))
1705 (when (and quot rem)
1706 (make-values-type :required (list quot rem))))))))))
1708 (def floor floor-quotient-bound floor-rem-bound)
1709 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1711 ;;; Define optimizers for FFLOOR and FCEILING
1712 (macrolet ((def (name q-name r-name)
1713 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1714 (r-aux (symbolicate r-name "-AUX")))
1716 ;; Compute type of quotient (first) result.
1717 (defun ,q-aux (number-type divisor-type)
1718 (let* ((number-interval
1719 (numeric-type->interval number-type))
1721 (numeric-type->interval divisor-type))
1722 (quot (,q-name (interval-div number-interval
1724 (res-type (numeric-contagion number-type
1727 :class (numeric-type-class res-type)
1728 :format (numeric-type-format res-type)
1729 :low (interval-low quot)
1730 :high (interval-high quot))))
1732 (defoptimizer (,name derive-type) ((number divisor))
1733 (flet ((derive-q (n d same-arg)
1734 (declare (ignore same-arg))
1735 (if (and (numeric-type-real-p n)
1736 (numeric-type-real-p d))
1739 (derive-r (n d same-arg)
1740 (declare (ignore same-arg))
1741 (if (and (numeric-type-real-p n)
1742 (numeric-type-real-p d))
1745 (let ((quot (two-arg-derive-type
1746 number divisor #'derive-q #',name))
1747 (rem (two-arg-derive-type
1748 number divisor #'derive-r #'mod)))
1749 (when (and quot rem)
1750 (make-values-type :required (list quot rem))))))))))
1752 (def ffloor floor-quotient-bound floor-rem-bound)
1753 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
1755 ;;; functions to compute the bounds on the quotient and remainder for
1756 ;;; the FLOOR function
1757 (defun floor-quotient-bound (quot)
1758 ;; Take the floor of the quotient and then massage it into what we
1760 (let ((lo (interval-low quot))
1761 (hi (interval-high quot)))
1762 ;; Take the floor of the lower bound. The result is always a
1763 ;; closed lower bound.
1765 (floor (type-bound-number lo))
1767 ;; For the upper bound, we need to be careful.
1770 ;; An open bound. We need to be careful here because
1771 ;; the floor of '(10.0) is 9, but the floor of
1773 (multiple-value-bind (q r) (floor (first hi))
1778 ;; A closed bound, so the answer is obvious.
1782 (make-interval :low lo :high hi)))
1783 (defun floor-rem-bound (div)
1784 ;; The remainder depends only on the divisor. Try to get the
1785 ;; correct sign for the remainder if we can.
1786 (case (interval-range-info div)
1788 ;; The divisor is always positive.
1789 (let ((rem (interval-abs div)))
1790 (setf (interval-low rem) 0)
1791 (when (and (numberp (interval-high rem))
1792 (not (zerop (interval-high rem))))
1793 ;; The remainder never contains the upper bound. However,
1794 ;; watch out for the case where the high limit is zero!
1795 (setf (interval-high rem) (list (interval-high rem))))
1798 ;; The divisor is always negative.
1799 (let ((rem (interval-neg (interval-abs div))))
1800 (setf (interval-high rem) 0)
1801 (when (numberp (interval-low rem))
1802 ;; The remainder never contains the lower bound.
1803 (setf (interval-low rem) (list (interval-low rem))))
1806 ;; The divisor can be positive or negative. All bets off. The
1807 ;; magnitude of remainder is the maximum value of the divisor.
1808 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1809 ;; The bound never reaches the limit, so make the interval open.
1810 (make-interval :low (if limit
1813 :high (list limit))))))
1815 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1816 => #S(INTERVAL :LOW 0 :HIGH 10)
1817 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1818 => #S(INTERVAL :LOW 0 :HIGH 10)
1819 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1820 => #S(INTERVAL :LOW 0 :HIGH 10)
1821 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1822 => #S(INTERVAL :LOW 0 :HIGH 9)
1823 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1824 => #S(INTERVAL :LOW 0 :HIGH 10)
1825 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1826 => #S(INTERVAL :LOW 0 :HIGH 10)
1827 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1828 => #S(INTERVAL :LOW -2 :HIGH 10)
1829 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1830 => #S(INTERVAL :LOW -1 :HIGH 10)
1831 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1832 => #S(INTERVAL :LOW -1 :HIGH 10)
1834 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1835 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1836 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1837 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1838 (floor-rem-bound (make-interval :low -10 :high -2.3))
1839 #S(INTERVAL :LOW (-10) :HIGH 0)
1840 (floor-rem-bound (make-interval :low 0.3 :high 10))
1841 => #S(INTERVAL :LOW 0 :HIGH '(10))
1842 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1843 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1844 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1845 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1848 ;;; same functions for CEILING
1849 (defun ceiling-quotient-bound (quot)
1850 ;; Take the ceiling of the quotient and then massage it into what we
1852 (let ((lo (interval-low quot))
1853 (hi (interval-high quot)))
1854 ;; Take the ceiling of the upper bound. The result is always a
1855 ;; closed upper bound.
1857 (ceiling (type-bound-number hi))
1859 ;; For the lower bound, we need to be careful.
1862 ;; An open bound. We need to be careful here because
1863 ;; the ceiling of '(10.0) is 11, but the ceiling of
1865 (multiple-value-bind (q r) (ceiling (first lo))
1870 ;; A closed bound, so the answer is obvious.
1874 (make-interval :low lo :high hi)))
1875 (defun ceiling-rem-bound (div)
1876 ;; The remainder depends only on the divisor. Try to get the
1877 ;; correct sign for the remainder if we can.
1878 (case (interval-range-info div)
1880 ;; Divisor is always positive. The remainder is negative.
1881 (let ((rem (interval-neg (interval-abs div))))
1882 (setf (interval-high rem) 0)
1883 (when (and (numberp (interval-low rem))
1884 (not (zerop (interval-low rem))))
1885 ;; The remainder never contains the upper bound. However,
1886 ;; watch out for the case when the upper bound is zero!
1887 (setf (interval-low rem) (list (interval-low rem))))
1890 ;; Divisor is always negative. The remainder is positive
1891 (let ((rem (interval-abs div)))
1892 (setf (interval-low rem) 0)
1893 (when (numberp (interval-high rem))
1894 ;; The remainder never contains the lower bound.
1895 (setf (interval-high rem) (list (interval-high rem))))
1898 ;; The divisor can be positive or negative. All bets off. The
1899 ;; magnitude of remainder is the maximum value of the divisor.
1900 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1901 ;; The bound never reaches the limit, so make the interval open.
1902 (make-interval :low (if limit
1905 :high (list limit))))))
1908 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
1909 => #S(INTERVAL :LOW 1 :HIGH 11)
1910 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1911 => #S(INTERVAL :LOW 1 :HIGH 11)
1912 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
1913 => #S(INTERVAL :LOW 1 :HIGH 10)
1914 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
1915 => #S(INTERVAL :LOW 1 :HIGH 10)
1916 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
1917 => #S(INTERVAL :LOW 1 :HIGH 11)
1918 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
1919 => #S(INTERVAL :LOW 1 :HIGH 11)
1920 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1921 => #S(INTERVAL :LOW -1 :HIGH 11)
1922 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1923 => #S(INTERVAL :LOW 0 :HIGH 11)
1924 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
1925 => #S(INTERVAL :LOW -1 :HIGH 11)
1927 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
1928 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
1929 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
1930 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1931 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
1932 => #S(INTERVAL :LOW 0 :HIGH (10))
1933 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
1934 => #S(INTERVAL :LOW (-10) :HIGH 0)
1935 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
1936 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
1937 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
1938 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1941 (defun truncate-quotient-bound (quot)
1942 ;; For positive quotients, truncate is exactly like floor. For
1943 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
1944 ;; it's the union of the two pieces.
1945 (case (interval-range-info quot)
1948 (floor-quotient-bound quot))
1950 ;; just like CEILING
1951 (ceiling-quotient-bound quot))
1953 ;; Split the interval into positive and negative pieces, compute
1954 ;; the result for each piece and put them back together.
1955 (destructuring-bind (neg pos) (interval-split 0 quot t t)
1956 (interval-merge-pair (ceiling-quotient-bound neg)
1957 (floor-quotient-bound pos))))))
1959 (defun truncate-rem-bound (num div)
1960 ;; This is significantly more complicated than FLOOR or CEILING. We
1961 ;; need both the number and the divisor to determine the range. The
1962 ;; basic idea is to split the ranges of NUM and DEN into positive
1963 ;; and negative pieces and deal with each of the four possibilities
1965 (case (interval-range-info num)
1967 (case (interval-range-info div)
1969 (floor-rem-bound div))
1971 (ceiling-rem-bound div))
1973 (destructuring-bind (neg pos) (interval-split 0 div t t)
1974 (interval-merge-pair (truncate-rem-bound num neg)
1975 (truncate-rem-bound num pos))))))
1977 (case (interval-range-info div)
1979 (ceiling-rem-bound div))
1981 (floor-rem-bound div))
1983 (destructuring-bind (neg pos) (interval-split 0 div t t)
1984 (interval-merge-pair (truncate-rem-bound num neg)
1985 (truncate-rem-bound num pos))))))
1987 (destructuring-bind (neg pos) (interval-split 0 num t t)
1988 (interval-merge-pair (truncate-rem-bound neg div)
1989 (truncate-rem-bound pos div))))))
1992 ;;; Derive useful information about the range. Returns three values:
1993 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
1994 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
1995 ;;; - The abs of the maximal value if there is one, or nil if it is
1997 (defun numeric-range-info (low high)
1998 (cond ((and low (not (minusp low)))
1999 (values '+ low high))
2000 ((and high (not (plusp high)))
2001 (values '- (- high) (if low (- low) nil)))
2003 (values nil 0 (and low high (max (- low) high))))))
2005 (defun integer-truncate-derive-type
2006 (number-low number-high divisor-low divisor-high)
2007 ;; The result cannot be larger in magnitude than the number, but the
2008 ;; sign might change. If we can determine the sign of either the
2009 ;; number or the divisor, we can eliminate some of the cases.
2010 (multiple-value-bind (number-sign number-min number-max)
2011 (numeric-range-info number-low number-high)
2012 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2013 (numeric-range-info divisor-low divisor-high)
2014 (when (and divisor-max (zerop divisor-max))
2015 ;; We've got a problem: guaranteed division by zero.
2016 (return-from integer-truncate-derive-type t))
2017 (when (zerop divisor-min)
2018 ;; We'll assume that they aren't going to divide by zero.
2020 (cond ((and number-sign divisor-sign)
2021 ;; We know the sign of both.
2022 (if (eq number-sign divisor-sign)
2023 ;; Same sign, so the result will be positive.
2024 `(integer ,(if divisor-max
2025 (truncate number-min divisor-max)
2028 (truncate number-max divisor-min)
2030 ;; Different signs, the result will be negative.
2031 `(integer ,(if number-max
2032 (- (truncate number-max divisor-min))
2035 (- (truncate number-min divisor-max))
2037 ((eq divisor-sign '+)
2038 ;; The divisor is positive. Therefore, the number will just
2039 ;; become closer to zero.
2040 `(integer ,(if number-low
2041 (truncate number-low divisor-min)
2044 (truncate number-high divisor-min)
2046 ((eq divisor-sign '-)
2047 ;; The divisor is negative. Therefore, the absolute value of
2048 ;; the number will become closer to zero, but the sign will also
2050 `(integer ,(if number-high
2051 (- (truncate number-high divisor-min))
2054 (- (truncate number-low divisor-min))
2056 ;; The divisor could be either positive or negative.
2058 ;; The number we are dividing has a bound. Divide that by the
2059 ;; smallest posible divisor.
2060 (let ((bound (truncate number-max divisor-min)))
2061 `(integer ,(- bound) ,bound)))
2063 ;; The number we are dividing is unbounded, so we can't tell
2064 ;; anything about the result.
2067 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2068 (defun integer-rem-derive-type
2069 (number-low number-high divisor-low divisor-high)
2070 (if (and divisor-low divisor-high)
2071 ;; We know the range of the divisor, and the remainder must be
2072 ;; smaller than the divisor. We can tell the sign of the
2073 ;; remainer if we know the sign of the number.
2074 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2075 `(integer ,(if (or (null number-low)
2076 (minusp number-low))
2079 ,(if (or (null number-high)
2080 (plusp number-high))
2083 ;; The divisor is potentially either very positive or very
2084 ;; negative. Therefore, the remainer is unbounded, but we might
2085 ;; be able to tell something about the sign from the number.
2086 `(integer ,(if (and number-low (not (minusp number-low)))
2087 ;; The number we are dividing is positive.
2088 ;; Therefore, the remainder must be positive.
2091 ,(if (and number-high (not (plusp number-high)))
2092 ;; The number we are dividing is negative.
2093 ;; Therefore, the remainder must be negative.
2097 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2098 (defoptimizer (random derive-type) ((bound &optional state))
2099 (let ((type (lvar-type bound)))
2100 (when (numeric-type-p type)
2101 (let ((class (numeric-type-class type))
2102 (high (numeric-type-high type))
2103 (format (numeric-type-format type)))
2107 :low (coerce 0 (or format class 'real))
2108 :high (cond ((not high) nil)
2109 ((eq class 'integer) (max (1- high) 0))
2110 ((or (consp high) (zerop high)) high)
2113 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2114 (defun random-derive-type-aux (type)
2115 (let ((class (numeric-type-class type))
2116 (high (numeric-type-high type))
2117 (format (numeric-type-format type)))
2121 :low (coerce 0 (or format class 'real))
2122 :high (cond ((not high) nil)
2123 ((eq class 'integer) (max (1- high) 0))
2124 ((or (consp high) (zerop high)) high)
2127 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2128 (defoptimizer (random derive-type) ((bound &optional state))
2129 (one-arg-derive-type bound #'random-derive-type-aux nil))
2131 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2133 ;;; Return the maximum number of bits an integer of the supplied type
2134 ;;; can take up, or NIL if it is unbounded. The second (third) value
2135 ;;; is T if the integer can be positive (negative) and NIL if not.
2136 ;;; Zero counts as positive.
2137 (defun integer-type-length (type)
2138 (if (numeric-type-p type)
2139 (let ((min (numeric-type-low type))
2140 (max (numeric-type-high type)))
2141 (values (and min max (max (integer-length min) (integer-length max)))
2142 (or (null max) (not (minusp max)))
2143 (or (null min) (minusp min))))
2146 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2147 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2148 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2149 ;;; versions in CMUCL, from which these functions copy liberally.
2151 (defun logand-derive-unsigned-low-bound (x y)
2152 (let ((a (numeric-type-low x))
2153 (b (numeric-type-high x))
2154 (c (numeric-type-low y))
2155 (d (numeric-type-high y)))
2156 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2158 (unless (zerop (logand m (lognot a) (lognot c)))
2159 (let ((temp (logandc2 (logior a m) (1- m))))
2163 (setf temp (logandc2 (logior c m) (1- m)))
2167 finally (return (logand a c)))))
2169 (defun logand-derive-unsigned-high-bound (x y)
2170 (let ((a (numeric-type-low x))
2171 (b (numeric-type-high x))
2172 (c (numeric-type-low y))
2173 (d (numeric-type-high y)))
2174 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2177 ((not (zerop (logand b (lognot d) m)))
2178 (let ((temp (logior (logandc2 b m) (1- m))))
2182 ((not (zerop (logand (lognot b) d m)))
2183 (let ((temp (logior (logandc2 d m) (1- m))))
2187 finally (return (logand b d)))))
2189 (defun logand-derive-type-aux (x y &optional same-leaf)
2191 (return-from logand-derive-type-aux x))
2192 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2193 (declare (ignore x-pos))
2194 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2195 (declare (ignore y-pos))
2197 ;; X must be positive.
2199 ;; They must both be positive.
2200 (cond ((and (null x-len) (null y-len))
2201 (specifier-type 'unsigned-byte))
2203 (specifier-type `(unsigned-byte* ,y-len)))
2205 (specifier-type `(unsigned-byte* ,x-len)))
2207 (let ((low (logand-derive-unsigned-low-bound x y))
2208 (high (logand-derive-unsigned-high-bound x y)))
2209 (specifier-type `(integer ,low ,high)))))
2210 ;; X is positive, but Y might be negative.
2212 (specifier-type 'unsigned-byte))
2214 (specifier-type `(unsigned-byte* ,x-len)))))
2215 ;; X might be negative.
2217 ;; Y must be positive.
2219 (specifier-type 'unsigned-byte))
2220 (t (specifier-type `(unsigned-byte* ,y-len))))
2221 ;; Either might be negative.
2222 (if (and x-len y-len)
2223 ;; The result is bounded.
2224 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2225 ;; We can't tell squat about the result.
2226 (specifier-type 'integer)))))))
2228 (defun logior-derive-unsigned-low-bound (x y)
2229 (let ((a (numeric-type-low x))
2230 (b (numeric-type-high x))
2231 (c (numeric-type-low y))
2232 (d (numeric-type-high y)))
2233 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2236 ((not (zerop (logandc2 (logand c m) a)))
2237 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2241 ((not (zerop (logandc2 (logand a m) c)))
2242 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2246 finally (return (logior a c)))))
2248 (defun logior-derive-unsigned-high-bound (x y)
2249 (let ((a (numeric-type-low x))
2250 (b (numeric-type-high x))
2251 (c (numeric-type-low y))
2252 (d (numeric-type-high y)))
2253 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2255 (unless (zerop (logand b d m))
2256 (let ((temp (logior (- b m) (1- m))))
2260 (setf temp (logior (- d m) (1- m)))
2264 finally (return (logior b d)))))
2266 (defun logior-derive-type-aux (x y &optional same-leaf)
2268 (return-from logior-derive-type-aux x))
2269 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2270 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2272 ((and (not x-neg) (not y-neg))
2273 ;; Both are positive.
2274 (if (and x-len y-len)
2275 (let ((low (logior-derive-unsigned-low-bound x y))
2276 (high (logior-derive-unsigned-high-bound x y)))
2277 (specifier-type `(integer ,low ,high)))
2278 (specifier-type `(unsigned-byte* *))))
2280 ;; X must be negative.
2282 ;; Both are negative. The result is going to be negative
2283 ;; and be the same length or shorter than the smaller.
2284 (if (and x-len y-len)
2286 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2288 (specifier-type '(integer * -1)))
2289 ;; X is negative, but we don't know about Y. The result
2290 ;; will be negative, but no more negative than X.
2292 `(integer ,(or (numeric-type-low x) '*)
2295 ;; X might be either positive or negative.
2297 ;; But Y is negative. The result will be negative.
2299 `(integer ,(or (numeric-type-low y) '*)
2301 ;; We don't know squat about either. It won't get any bigger.
2302 (if (and x-len y-len)
2304 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2306 (specifier-type 'integer))))))))
2308 (defun logxor-derive-unsigned-low-bound (x y)
2309 (let ((a (numeric-type-low x))
2310 (b (numeric-type-high x))
2311 (c (numeric-type-low y))
2312 (d (numeric-type-high y)))
2313 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2316 ((not (zerop (logandc2 (logand c m) a)))
2317 (let ((temp (logand (logior a m)
2321 ((not (zerop (logandc2 (logand a m) c)))
2322 (let ((temp (logand (logior c m)
2326 finally (return (logxor a c)))))
2328 (defun logxor-derive-unsigned-high-bound (x y)
2329 (let ((a (numeric-type-low x))
2330 (b (numeric-type-high x))
2331 (c (numeric-type-low y))
2332 (d (numeric-type-high y)))
2333 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2335 (unless (zerop (logand b d m))
2336 (let ((temp (logior (- b m) (1- m))))
2338 ((>= temp a) (setf b temp))
2339 (t (let ((temp (logior (- d m) (1- m))))
2342 finally (return (logxor b d)))))
2344 (defun logxor-derive-type-aux (x y &optional same-leaf)
2346 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2347 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2348 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2350 ((and (not x-neg) (not y-neg))
2351 ;; Both are positive
2352 (if (and x-len y-len)
2353 (let ((low (logxor-derive-unsigned-low-bound x y))
2354 (high (logxor-derive-unsigned-high-bound x y)))
2355 (specifier-type `(integer ,low ,high)))
2356 (specifier-type '(unsigned-byte* *))))
2357 ((and (not x-pos) (not y-pos))
2358 ;; Both are negative. The result will be positive, and as long
2360 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2363 ((or (and (not x-pos) (not y-neg))
2364 (and (not y-pos) (not x-neg)))
2365 ;; Either X is negative and Y is positive or vice-versa. The
2366 ;; result will be negative.
2367 (specifier-type `(integer ,(if (and x-len y-len)
2368 (ash -1 (max x-len y-len))
2371 ;; We can't tell what the sign of the result is going to be.
2372 ;; All we know is that we don't create new bits.
2374 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2376 (specifier-type 'integer))))))
2378 (macrolet ((deffrob (logfun)
2379 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2380 `(defoptimizer (,logfun derive-type) ((x y))
2381 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2386 (defoptimizer (logeqv derive-type) ((x y))
2387 (two-arg-derive-type x y (lambda (x y same-leaf)
2388 (lognot-derive-type-aux
2389 (logxor-derive-type-aux x y same-leaf)))
2391 (defoptimizer (lognand derive-type) ((x y))
2392 (two-arg-derive-type x y (lambda (x y same-leaf)
2393 (lognot-derive-type-aux
2394 (logand-derive-type-aux x y same-leaf)))
2396 (defoptimizer (lognor derive-type) ((x y))
2397 (two-arg-derive-type x y (lambda (x y same-leaf)
2398 (lognot-derive-type-aux
2399 (logior-derive-type-aux x y same-leaf)))
2401 (defoptimizer (logandc1 derive-type) ((x y))
2402 (two-arg-derive-type x y (lambda (x y same-leaf)
2404 (specifier-type '(eql 0))
2405 (logand-derive-type-aux
2406 (lognot-derive-type-aux x) y nil)))
2408 (defoptimizer (logandc2 derive-type) ((x y))
2409 (two-arg-derive-type x y (lambda (x y same-leaf)
2411 (specifier-type '(eql 0))
2412 (logand-derive-type-aux
2413 x (lognot-derive-type-aux y) nil)))
2415 (defoptimizer (logorc1 derive-type) ((x y))
2416 (two-arg-derive-type x y (lambda (x y same-leaf)
2418 (specifier-type '(eql -1))
2419 (logior-derive-type-aux
2420 (lognot-derive-type-aux x) y nil)))
2422 (defoptimizer (logorc2 derive-type) ((x y))
2423 (two-arg-derive-type x y (lambda (x y same-leaf)
2425 (specifier-type '(eql -1))
2426 (logior-derive-type-aux
2427 x (lognot-derive-type-aux y) nil)))
2430 ;;;; miscellaneous derive-type methods
2432 (defoptimizer (integer-length derive-type) ((x))
2433 (let ((x-type (lvar-type x)))
2434 (when (numeric-type-p x-type)
2435 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2436 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2437 ;; careful about LO or HI being NIL, though. Also, if 0 is
2438 ;; contained in X, the lower bound is obviously 0.
2439 (flet ((null-or-min (a b)
2440 (and a b (min (integer-length a)
2441 (integer-length b))))
2443 (and a b (max (integer-length a)
2444 (integer-length b)))))
2445 (let* ((min (numeric-type-low x-type))
2446 (max (numeric-type-high x-type))
2447 (min-len (null-or-min min max))
2448 (max-len (null-or-max min max)))
2449 (when (ctypep 0 x-type)
2451 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2453 (defoptimizer (isqrt derive-type) ((x))
2454 (let ((x-type (lvar-type x)))
2455 (when (numeric-type-p x-type)
2456 (let* ((lo (numeric-type-low x-type))
2457 (hi (numeric-type-high x-type))
2458 (lo-res (if lo (isqrt lo) '*))
2459 (hi-res (if hi (isqrt hi) '*)))
2460 (specifier-type `(integer ,lo-res ,hi-res))))))
2462 (defoptimizer (code-char derive-type) ((code))
2463 (let ((type (lvar-type code)))
2464 ;; FIXME: unions of integral ranges? It ought to be easier to do
2465 ;; this, given that CHARACTER-SET is basically an integral range
2466 ;; type. -- CSR, 2004-10-04
2467 (when (numeric-type-p type)
2468 (let* ((lo (numeric-type-low type))
2469 (hi (numeric-type-high type))
2470 (type (specifier-type `(character-set ((,lo . ,hi))))))
2472 ;; KLUDGE: when running on the host, we lose a slight amount
2473 ;; of precision so that we don't have to "unparse" types
2474 ;; that formally we can't, such as (CHARACTER-SET ((0
2475 ;; . 0))). -- CSR, 2004-10-06
2477 ((csubtypep type (specifier-type 'standard-char)) type)
2479 ((csubtypep type (specifier-type 'base-char))
2480 (specifier-type 'base-char))
2482 ((csubtypep type (specifier-type 'extended-char))
2483 (specifier-type 'extended-char))
2484 (t #+sb-xc-host (specifier-type 'character)
2485 #-sb-xc-host type))))))
2487 (defoptimizer (values derive-type) ((&rest values))
2488 (make-values-type :required (mapcar #'lvar-type values)))
2490 (defun signum-derive-type-aux (type)
2491 (if (eq (numeric-type-complexp type) :complex)
2492 (let* ((format (case (numeric-type-class type)
2493 ((integer rational) 'single-float)
2494 (t (numeric-type-format type))))
2495 (bound-format (or format 'float)))
2496 (make-numeric-type :class 'float
2499 :low (coerce -1 bound-format)
2500 :high (coerce 1 bound-format)))
2501 (let* ((interval (numeric-type->interval type))
2502 (range-info (interval-range-info interval))
2503 (contains-0-p (interval-contains-p 0 interval))
2504 (class (numeric-type-class type))
2505 (format (numeric-type-format type))
2506 (one (coerce 1 (or format class 'real)))
2507 (zero (coerce 0 (or format class 'real)))
2508 (minus-one (coerce -1 (or format class 'real)))
2509 (plus (make-numeric-type :class class :format format
2510 :low one :high one))
2511 (minus (make-numeric-type :class class :format format
2512 :low minus-one :high minus-one))
2513 ;; KLUDGE: here we have a fairly horrible hack to deal
2514 ;; with the schizophrenia in the type derivation engine.
2515 ;; The problem is that the type derivers reinterpret
2516 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2517 ;; 0d0) within the derivation mechanism doesn't include
2518 ;; -0d0. Ugh. So force it in here, instead.
2519 (zero (make-numeric-type :class class :format format
2520 :low (- zero) :high zero)))
2522 (+ (if contains-0-p (type-union plus zero) plus))
2523 (- (if contains-0-p (type-union minus zero) minus))
2524 (t (type-union minus zero plus))))))
2526 (defoptimizer (signum derive-type) ((num))
2527 (one-arg-derive-type num #'signum-derive-type-aux nil))
2529 ;;;; byte operations
2531 ;;;; We try to turn byte operations into simple logical operations.
2532 ;;;; First, we convert byte specifiers into separate size and position
2533 ;;;; arguments passed to internal %FOO functions. We then attempt to
2534 ;;;; transform the %FOO functions into boolean operations when the
2535 ;;;; size and position are constant and the operands are fixnums.
2537 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2538 ;; expressions that evaluate to the SIZE and POSITION of
2539 ;; the byte-specifier form SPEC. We may wrap a let around
2540 ;; the result of the body to bind some variables.
2542 ;; If the spec is a BYTE form, then bind the vars to the
2543 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2544 ;; and BYTE-POSITION. The goal of this transformation is to
2545 ;; avoid consing up byte specifiers and then immediately
2546 ;; throwing them away.
2547 (with-byte-specifier ((size-var pos-var spec) &body body)
2548 (once-only ((spec `(macroexpand ,spec))
2550 `(if (and (consp ,spec)
2551 (eq (car ,spec) 'byte)
2552 (= (length ,spec) 3))
2553 (let ((,size-var (second ,spec))
2554 (,pos-var (third ,spec)))
2556 (let ((,size-var `(byte-size ,,temp))
2557 (,pos-var `(byte-position ,,temp)))
2558 `(let ((,,temp ,,spec))
2561 (define-source-transform ldb (spec int)
2562 (with-byte-specifier (size pos spec)
2563 `(%ldb ,size ,pos ,int)))
2565 (define-source-transform dpb (newbyte spec int)
2566 (with-byte-specifier (size pos spec)
2567 `(%dpb ,newbyte ,size ,pos ,int)))
2569 (define-source-transform mask-field (spec int)
2570 (with-byte-specifier (size pos spec)
2571 `(%mask-field ,size ,pos ,int)))
2573 (define-source-transform deposit-field (newbyte spec int)
2574 (with-byte-specifier (size pos spec)
2575 `(%deposit-field ,newbyte ,size ,pos ,int))))
2577 (defoptimizer (%ldb derive-type) ((size posn num))
2578 (let ((size (lvar-type size)))
2579 (if (and (numeric-type-p size)
2580 (csubtypep size (specifier-type 'integer)))
2581 (let ((size-high (numeric-type-high size)))
2582 (if (and size-high (<= size-high sb!vm:n-word-bits))
2583 (specifier-type `(unsigned-byte* ,size-high))
2584 (specifier-type 'unsigned-byte)))
2587 (defoptimizer (%mask-field derive-type) ((size posn num))
2588 (let ((size (lvar-type size))
2589 (posn (lvar-type posn)))
2590 (if (and (numeric-type-p size)
2591 (csubtypep size (specifier-type 'integer))
2592 (numeric-type-p posn)
2593 (csubtypep posn (specifier-type 'integer)))
2594 (let ((size-high (numeric-type-high size))
2595 (posn-high (numeric-type-high posn)))
2596 (if (and size-high posn-high
2597 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2598 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2599 (specifier-type 'unsigned-byte)))
2602 (defun %deposit-field-derive-type-aux (size posn int)
2603 (let ((size (lvar-type size))
2604 (posn (lvar-type posn))
2605 (int (lvar-type int)))
2606 (when (and (numeric-type-p size)
2607 (numeric-type-p posn)
2608 (numeric-type-p int))
2609 (let ((size-high (numeric-type-high size))
2610 (posn-high (numeric-type-high posn))
2611 (high (numeric-type-high int))
2612 (low (numeric-type-low int)))
2613 (when (and size-high posn-high high low
2614 ;; KLUDGE: we need this cutoff here, otherwise we
2615 ;; will merrily derive the type of %DPB as
2616 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2617 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2618 ;; 1073741822))), with hilarious consequences. We
2619 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2620 ;; over a reasonable amount of shifting, even on
2621 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2622 ;; machine integers are 64-bits. -- CSR,
2624 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2625 (let ((raw-bit-count (max (integer-length high)
2626 (integer-length low)
2627 (+ size-high posn-high))))
2630 `(signed-byte ,(1+ raw-bit-count))
2631 `(unsigned-byte* ,raw-bit-count)))))))))
2633 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2634 (%deposit-field-derive-type-aux size posn int))
2636 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2637 (%deposit-field-derive-type-aux size posn int))
2639 (deftransform %ldb ((size posn int)
2640 (fixnum fixnum integer)
2641 (unsigned-byte #.sb!vm:n-word-bits))
2642 "convert to inline logical operations"
2643 `(logand (ash int (- posn))
2644 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2645 (- size ,sb!vm:n-word-bits))))
2647 (deftransform %mask-field ((size posn int)
2648 (fixnum fixnum integer)
2649 (unsigned-byte #.sb!vm:n-word-bits))
2650 "convert to inline logical operations"
2652 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2653 (- size ,sb!vm:n-word-bits))
2656 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2657 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2658 ;;; as the result type, as that would allow result types that cover
2659 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2660 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2662 (deftransform %dpb ((new size posn int)
2664 (unsigned-byte #.sb!vm:n-word-bits))
2665 "convert to inline logical operations"
2666 `(let ((mask (ldb (byte size 0) -1)))
2667 (logior (ash (logand new mask) posn)
2668 (logand int (lognot (ash mask posn))))))
2670 (deftransform %dpb ((new size posn int)
2672 (signed-byte #.sb!vm:n-word-bits))
2673 "convert to inline logical operations"
2674 `(let ((mask (ldb (byte size 0) -1)))
2675 (logior (ash (logand new mask) posn)
2676 (logand int (lognot (ash mask posn))))))
2678 (deftransform %deposit-field ((new size posn int)
2680 (unsigned-byte #.sb!vm:n-word-bits))
2681 "convert to inline logical operations"
2682 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2683 (logior (logand new mask)
2684 (logand int (lognot mask)))))
2686 (deftransform %deposit-field ((new size posn int)
2688 (signed-byte #.sb!vm:n-word-bits))
2689 "convert to inline logical operations"
2690 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2691 (logior (logand new mask)
2692 (logand int (lognot mask)))))
2694 (defoptimizer (mask-signed-field derive-type) ((size x))
2695 (let ((size (lvar-type size)))
2696 (if (numeric-type-p size)
2697 (let ((size-high (numeric-type-high size)))
2698 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2699 (specifier-type `(signed-byte ,size-high))
2704 ;;; Modular functions
2706 ;;; (ldb (byte s 0) (foo x y ...)) =
2707 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2709 ;;; and similar for other arguments.
2711 (defun make-modular-fun-type-deriver (prototype class width)
2713 (binding* ((info (info :function :info prototype) :exit-if-null)
2714 (fun (fun-info-derive-type info) :exit-if-null)
2715 (mask-type (specifier-type
2717 (:unsigned (let ((mask (1- (ash 1 width))))
2718 `(integer ,mask ,mask)))
2719 (:signed `(signed-byte ,width))))))
2721 (let ((res (funcall fun call)))
2723 (if (eq class :unsigned)
2724 (logand-derive-type-aux res mask-type))))))
2727 (binding* ((info (info :function :info prototype) :exit-if-null)
2728 (fun (fun-info-derive-type info) :exit-if-null)
2729 (res (funcall fun call) :exit-if-null)
2730 (mask-type (specifier-type
2732 (:unsigned (let ((mask (1- (ash 1 width))))
2733 `(integer ,mask ,mask)))
2734 (:signed `(signed-byte ,width))))))
2735 (if (eq class :unsigned)
2736 (logand-derive-type-aux res mask-type)))))
2738 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2740 ;;; For good functions, we just recursively cut arguments; their
2741 ;;; "goodness" means that the result will not increase (in the
2742 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2743 ;;; replaced with the version, cutting its result to WIDTH or more
2744 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2745 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2746 ;;; arguments (maybe to a different width) and returning the name of a
2747 ;;; modular version, if it exists, or NIL. If we have changed
2748 ;;; anything, we need to flush old derived types, because they have
2749 ;;; nothing in common with the new code.
2750 (defun cut-to-width (lvar class width)
2751 (declare (type lvar lvar) (type (integer 0) width))
2752 (let ((type (specifier-type (if (zerop width)
2754 `(,(ecase class (:unsigned 'unsigned-byte)
2755 (:signed 'signed-byte))
2757 (labels ((reoptimize-node (node name)
2758 (setf (node-derived-type node)
2760 (info :function :type name)))
2761 (setf (lvar-%derived-type (node-lvar node)) nil)
2762 (setf (node-reoptimize node) t)
2763 (setf (block-reoptimize (node-block node)) t)
2764 (reoptimize-component (node-component node) :maybe))
2765 (cut-node (node &aux did-something)
2766 (when (and (not (block-delete-p (node-block node)))
2767 (combination-p node)
2768 (eq (basic-combination-kind node) :known))
2769 (let* ((fun-ref (lvar-use (combination-fun node)))
2770 (fun-name (leaf-source-name (ref-leaf fun-ref)))
2771 (modular-fun (find-modular-version fun-name class width)))
2772 (when (and modular-fun
2773 (not (and (eq fun-name 'logand)
2775 (single-value-type (node-derived-type node))
2777 (binding* ((name (etypecase modular-fun
2778 ((eql :good) fun-name)
2780 (modular-fun-info-name modular-fun))
2782 (funcall modular-fun node width)))
2784 (unless (eql modular-fun :good)
2785 (setq did-something t)
2788 (find-free-fun name "in a strange place"))
2789 (setf (combination-kind node) :full))
2790 (unless (functionp modular-fun)
2791 (dolist (arg (basic-combination-args node))
2792 (when (cut-lvar arg)
2793 (setq did-something t))))
2795 (reoptimize-node node name))
2797 (cut-lvar (lvar &aux did-something)
2798 (do-uses (node lvar)
2799 (when (cut-node node)
2800 (setq did-something t)))
2804 (defoptimizer (logand optimizer) ((x y) node)
2805 (let ((result-type (single-value-type (node-derived-type node))))
2806 (when (numeric-type-p result-type)
2807 (let ((low (numeric-type-low result-type))
2808 (high (numeric-type-high result-type)))
2809 (when (and (numberp low)
2812 (let ((width (integer-length high)))
2813 (when (some (lambda (x) (<= width x))
2814 (modular-class-widths *unsigned-modular-class*))
2815 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2816 (cut-to-width x :unsigned width)
2817 (cut-to-width y :unsigned width)
2818 nil ; After fixing above, replace with T.
2821 (defoptimizer (mask-signed-field optimizer) ((width x) node)
2822 (let ((result-type (single-value-type (node-derived-type node))))
2823 (when (numeric-type-p result-type)
2824 (let ((low (numeric-type-low result-type))
2825 (high (numeric-type-high result-type)))
2826 (when (and (numberp low) (numberp high))
2827 (let ((width (max (integer-length high) (integer-length low))))
2828 (when (some (lambda (x) (<= width x))
2829 (modular-class-widths *signed-modular-class*))
2830 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2831 (cut-to-width x :signed width)
2832 nil ; After fixing above, replace with T.
2835 ;;; miscellanous numeric transforms
2837 ;;; If a constant appears as the first arg, swap the args.
2838 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2839 (if (and (constant-lvar-p x)
2840 (not (constant-lvar-p y)))
2841 `(,(lvar-fun-name (basic-combination-fun node))
2844 (give-up-ir1-transform)))
2846 (dolist (x '(= char= + * logior logand logxor))
2847 (%deftransform x '(function * *) #'commutative-arg-swap
2848 "place constant arg last"))
2850 ;;; Handle the case of a constant BOOLE-CODE.
2851 (deftransform boole ((op x y) * *)
2852 "convert to inline logical operations"
2853 (unless (constant-lvar-p op)
2854 (give-up-ir1-transform "BOOLE code is not a constant."))
2855 (let ((control (lvar-value op)))
2857 (#.sb!xc:boole-clr 0)
2858 (#.sb!xc:boole-set -1)
2859 (#.sb!xc:boole-1 'x)
2860 (#.sb!xc:boole-2 'y)
2861 (#.sb!xc:boole-c1 '(lognot x))
2862 (#.sb!xc:boole-c2 '(lognot y))
2863 (#.sb!xc:boole-and '(logand x y))
2864 (#.sb!xc:boole-ior '(logior x y))
2865 (#.sb!xc:boole-xor '(logxor x y))
2866 (#.sb!xc:boole-eqv '(logeqv x y))
2867 (#.sb!xc:boole-nand '(lognand x y))
2868 (#.sb!xc:boole-nor '(lognor x y))
2869 (#.sb!xc:boole-andc1 '(logandc1 x y))
2870 (#.sb!xc:boole-andc2 '(logandc2 x y))
2871 (#.sb!xc:boole-orc1 '(logorc1 x y))
2872 (#.sb!xc:boole-orc2 '(logorc2 x y))
2874 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2877 ;;;; converting special case multiply/divide to shifts
2879 ;;; If arg is a constant power of two, turn * into a shift.
2880 (deftransform * ((x y) (integer integer) *)
2881 "convert x*2^k to shift"
2882 (unless (constant-lvar-p y)
2883 (give-up-ir1-transform))
2884 (let* ((y (lvar-value y))
2886 (len (1- (integer-length y-abs))))
2887 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2888 (give-up-ir1-transform))
2893 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2894 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
2896 (flet ((frob (y ceil-p)
2897 (unless (constant-lvar-p y)
2898 (give-up-ir1-transform))
2899 (let* ((y (lvar-value y))
2901 (len (1- (integer-length y-abs))))
2902 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2903 (give-up-ir1-transform))
2904 (let ((shift (- len))
2906 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
2907 `(let ((x (+ x ,delta)))
2909 `(values (ash (- x) ,shift)
2910 (- (- (logand (- x) ,mask)) ,delta))
2911 `(values (ash x ,shift)
2912 (- (logand x ,mask) ,delta))))))))
2913 (deftransform floor ((x y) (integer integer) *)
2914 "convert division by 2^k to shift"
2916 (deftransform ceiling ((x y) (integer integer) *)
2917 "convert division by 2^k to shift"
2920 ;;; Do the same for MOD.
2921 (deftransform mod ((x y) (integer integer) *)
2922 "convert remainder mod 2^k to LOGAND"
2923 (unless (constant-lvar-p y)
2924 (give-up-ir1-transform))
2925 (let* ((y (lvar-value y))
2927 (len (1- (integer-length y-abs))))
2928 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2929 (give-up-ir1-transform))
2930 (let ((mask (1- y-abs)))
2932 `(- (logand (- x) ,mask))
2933 `(logand x ,mask)))))
2935 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2936 (deftransform truncate ((x y) (integer integer))
2937 "convert division by 2^k to shift"
2938 (unless (constant-lvar-p y)
2939 (give-up-ir1-transform))
2940 (let* ((y (lvar-value y))
2942 (len (1- (integer-length y-abs))))
2943 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2944 (give-up-ir1-transform))
2945 (let* ((shift (- len))
2948 (values ,(if (minusp y)
2950 `(- (ash (- x) ,shift)))
2951 (- (logand (- x) ,mask)))
2952 (values ,(if (minusp y)
2953 `(ash (- ,mask x) ,shift)
2955 (logand x ,mask))))))
2957 ;;; And the same for REM.
2958 (deftransform rem ((x y) (integer integer) *)
2959 "convert remainder mod 2^k to LOGAND"
2960 (unless (constant-lvar-p y)
2961 (give-up-ir1-transform))
2962 (let* ((y (lvar-value y))
2964 (len (1- (integer-length y-abs))))
2965 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2966 (give-up-ir1-transform))
2967 (let ((mask (1- y-abs)))
2969 (- (logand (- x) ,mask))
2970 (logand x ,mask)))))
2972 ;;;; arithmetic and logical identity operation elimination
2974 ;;; Flush calls to various arith functions that convert to the
2975 ;;; identity function or a constant.
2976 (macrolet ((def (name identity result)
2977 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
2978 "fold identity operations"
2985 (def logxor -1 (lognot x))
2988 (deftransform logand ((x y) (* (constant-arg t)) *)
2989 "fold identity operation"
2990 (let ((y (lvar-value y)))
2991 (unless (and (plusp y)
2992 (= y (1- (ash 1 (integer-length y)))))
2993 (give-up-ir1-transform))
2994 (unless (csubtypep (lvar-type x)
2995 (specifier-type `(integer 0 ,y)))
2996 (give-up-ir1-transform))
2999 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3000 "fold identity operation"
3001 (let ((size (lvar-value size)))
3002 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3003 (give-up-ir1-transform))
3006 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3007 ;;; (* 0 -4.0) is -0.0.
3008 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3009 "convert (- 0 x) to negate"
3011 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3012 "convert (* x 0) to 0"
3015 ;;; Return T if in an arithmetic op including lvars X and Y, the
3016 ;;; result type is not affected by the type of X. That is, Y is at
3017 ;;; least as contagious as X.
3019 (defun not-more-contagious (x y)
3020 (declare (type continuation x y))
3021 (let ((x (lvar-type x))
3023 (values (type= (numeric-contagion x y)
3024 (numeric-contagion y y)))))
3025 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3026 ;;; XXX needs more work as valid transforms are missed; some cases are
3027 ;;; specific to particular transform functions so the use of this
3028 ;;; function may need a re-think.
3029 (defun not-more-contagious (x y)
3030 (declare (type lvar x y))
3031 (flet ((simple-numeric-type (num)
3032 (and (numeric-type-p num)
3033 ;; Return non-NIL if NUM is integer, rational, or a float
3034 ;; of some type (but not FLOAT)
3035 (case (numeric-type-class num)
3039 (numeric-type-format num))
3042 (let ((x (lvar-type x))
3044 (if (and (simple-numeric-type x)
3045 (simple-numeric-type y))
3046 (values (type= (numeric-contagion x y)
3047 (numeric-contagion y y)))))))
3051 ;;; If y is not constant, not zerop, or is contagious, or a positive
3052 ;;; float +0.0 then give up.
3053 (deftransform + ((x y) (t (constant-arg t)) *)
3055 (let ((val (lvar-value y)))
3056 (unless (and (zerop val)
3057 (not (and (floatp val) (plusp (float-sign val))))
3058 (not-more-contagious y x))
3059 (give-up-ir1-transform)))
3064 ;;; If y is not constant, not zerop, or is contagious, or a negative
3065 ;;; float -0.0 then give up.
3066 (deftransform - ((x y) (t (constant-arg t)) *)
3068 (let ((val (lvar-value y)))
3069 (unless (and (zerop val)
3070 (not (and (floatp val) (minusp (float-sign val))))
3071 (not-more-contagious y x))
3072 (give-up-ir1-transform)))
3075 ;;; Fold (OP x +/-1)
3076 (macrolet ((def (name result minus-result)
3077 `(deftransform ,name ((x y) (t (constant-arg real)) *)
3078 "fold identity operations"
3079 (let ((val (lvar-value y)))
3080 (unless (and (= (abs val) 1)
3081 (not-more-contagious y x))
3082 (give-up-ir1-transform))
3083 (if (minusp val) ',minus-result ',result)))))
3084 (def * x (%negate x))
3085 (def / x (%negate x))
3086 (def expt x (/ 1 x)))
3088 ;;; Fold (expt x n) into multiplications for small integral values of
3089 ;;; N; convert (expt x 1/2) to sqrt.
3090 (deftransform expt ((x y) (t (constant-arg real)) *)
3091 "recode as multiplication or sqrt"
3092 (let ((val (lvar-value y)))
3093 ;; If Y would cause the result to be promoted to the same type as
3094 ;; Y, we give up. If not, then the result will be the same type
3095 ;; as X, so we can replace the exponentiation with simple
3096 ;; multiplication and division for small integral powers.
3097 (unless (not-more-contagious y x)
3098 (give-up-ir1-transform))
3100 (let ((x-type (lvar-type x)))
3101 (cond ((csubtypep x-type (specifier-type '(or rational
3102 (complex rational))))
3104 ((csubtypep x-type (specifier-type 'real))
3108 ((csubtypep x-type (specifier-type 'complex))
3109 ;; both parts are float
3111 (t (give-up-ir1-transform)))))
3112 ((= val 2) '(* x x))
3113 ((= val -2) '(/ (* x x)))
3114 ((= val 3) '(* x x x))
3115 ((= val -3) '(/ (* x x x)))
3116 ((= val 1/2) '(sqrt x))
3117 ((= val -1/2) '(/ (sqrt x)))
3118 (t (give-up-ir1-transform)))))
3120 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3121 ;;; transformations?
3122 ;;; Perhaps we should have to prove that the denominator is nonzero before
3123 ;;; doing them? -- WHN 19990917
3124 (macrolet ((def (name)
3125 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3132 (macrolet ((def (name)
3133 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3142 ;;;; character operations
3144 (deftransform char-equal ((a b) (base-char base-char))
3146 '(let* ((ac (char-code a))
3148 (sum (logxor ac bc)))
3150 (when (eql sum #x20)
3151 (let ((sum (+ ac bc)))
3152 (or (and (> sum 161) (< sum 213))
3153 (and (> sum 415) (< sum 461))
3154 (and (> sum 463) (< sum 477))))))))
3156 (deftransform char-upcase ((x) (base-char))
3158 '(let ((n-code (char-code x)))
3159 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3160 (< n-code #o173)) ; Octal 172 is #\z.
3161 (and (> n-code #o337)
3163 (and (> n-code #o367)
3165 (code-char (logxor #x20 n-code))
3168 (deftransform char-downcase ((x) (base-char))
3170 '(let ((n-code (char-code x)))
3171 (if (or (and (> n-code 64) ; 65 is #\A.
3172 (< n-code 91)) ; 90 is #\Z.
3177 (code-char (logxor #x20 n-code))
3180 ;;;; equality predicate transforms
3182 ;;; Return true if X and Y are lvars whose only use is a
3183 ;;; reference to the same leaf, and the value of the leaf cannot
3185 (defun same-leaf-ref-p (x y)
3186 (declare (type lvar x y))
3187 (let ((x-use (principal-lvar-use x))
3188 (y-use (principal-lvar-use y)))
3191 (eq (ref-leaf x-use) (ref-leaf y-use))
3192 (constant-reference-p x-use))))
3194 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3195 ;;; if there is no intersection between the types of the arguments,
3196 ;;; then the result is definitely false.
3197 (deftransform simple-equality-transform ((x y) * *
3200 ((same-leaf-ref-p x y) t)
3201 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3203 (t (give-up-ir1-transform))))
3206 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3210 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3211 ;;; try to convert to a type-specific predicate or EQ:
3212 ;;; -- If both args are characters, convert to CHAR=. This is better than
3213 ;;; just converting to EQ, since CHAR= may have special compilation
3214 ;;; strategies for non-standard representations, etc.
3215 ;;; -- If either arg is definitely a fixnum we punt and let the backend
3217 ;;; -- If either arg is definitely not a number or a fixnum, then we
3218 ;;; can compare with EQ.
3219 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3220 ;;; is constant then we put it second. If X is a subtype of Y, we put
3221 ;;; it second. These rules make it easier for the back end to match
3222 ;;; these interesting cases.
3223 (deftransform eql ((x y) * *)
3224 "convert to simpler equality predicate"
3225 (let ((x-type (lvar-type x))
3226 (y-type (lvar-type y))
3227 (char-type (specifier-type 'character)))
3228 (flet ((simple-type-p (type)
3229 (csubtypep type (specifier-type '(or fixnum (not number)))))
3230 (fixnum-type-p (type)
3231 (csubtypep type (specifier-type 'fixnum))))
3233 ((same-leaf-ref-p x y) t)
3234 ((not (types-equal-or-intersect x-type y-type))
3236 ((and (csubtypep x-type char-type)
3237 (csubtypep y-type char-type))
3239 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3240 (give-up-ir1-transform))
3241 ((or (simple-type-p x-type) (simple-type-p y-type))
3243 ((and (not (constant-lvar-p y))
3244 (or (constant-lvar-p x)
3245 (and (csubtypep x-type y-type)
3246 (not (csubtypep y-type x-type)))))
3249 (give-up-ir1-transform))))))
3251 ;;; similarly to the EQL transform above, we attempt to constant-fold
3252 ;;; or convert to a simpler predicate: mostly we have to be careful
3253 ;;; with strings and bit-vectors.
3254 (deftransform equal ((x y) * *)
3255 "convert to simpler equality predicate"
3256 (let ((x-type (lvar-type x))
3257 (y-type (lvar-type y))
3258 (string-type (specifier-type 'string))
3259 (bit-vector-type (specifier-type 'bit-vector)))
3261 ((same-leaf-ref-p x y) t)
3262 ((and (csubtypep x-type string-type)
3263 (csubtypep y-type string-type))
3265 ((and (csubtypep x-type bit-vector-type)
3266 (csubtypep y-type bit-vector-type))
3267 '(bit-vector-= x y))
3268 ;; if at least one is not a string, and at least one is not a
3269 ;; bit-vector, then we can reason from types.
3270 ((and (not (and (types-equal-or-intersect x-type string-type)
3271 (types-equal-or-intersect y-type string-type)))
3272 (not (and (types-equal-or-intersect x-type bit-vector-type)
3273 (types-equal-or-intersect y-type bit-vector-type)))
3274 (not (types-equal-or-intersect x-type y-type)))
3276 (t (give-up-ir1-transform)))))
3278 ;;; Convert to EQL if both args are rational and complexp is specified
3279 ;;; and the same for both.
3280 (deftransform = ((x y) * *)
3282 (let ((x-type (lvar-type x))
3283 (y-type (lvar-type y)))
3284 (if (and (csubtypep x-type (specifier-type 'number))
3285 (csubtypep y-type (specifier-type 'number)))
3286 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3287 (csubtypep y-type (specifier-type 'float)))
3288 (and (csubtypep x-type (specifier-type '(complex float)))
3289 (csubtypep y-type (specifier-type '(complex float)))))
3290 ;; They are both floats. Leave as = so that -0.0 is
3291 ;; handled correctly.
3292 (give-up-ir1-transform))
3293 ((or (and (csubtypep x-type (specifier-type 'rational))
3294 (csubtypep y-type (specifier-type 'rational)))
3295 (and (csubtypep x-type
3296 (specifier-type '(complex rational)))
3298 (specifier-type '(complex rational)))))
3299 ;; They are both rationals and complexp is the same.
3303 (give-up-ir1-transform
3304 "The operands might not be the same type.")))
3305 (give-up-ir1-transform
3306 "The operands might not be the same type."))))
3308 ;;; If LVAR's type is a numeric type, then return the type, otherwise
3309 ;;; GIVE-UP-IR1-TRANSFORM.
3310 (defun numeric-type-or-lose (lvar)
3311 (declare (type lvar lvar))
3312 (let ((res (lvar-type lvar)))
3313 (unless (numeric-type-p res) (give-up-ir1-transform))
3316 ;;; See whether we can statically determine (< X Y) using type
3317 ;;; information. If X's high bound is < Y's low, then X < Y.
3318 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3319 ;;; NIL). If not, at least make sure any constant arg is second.
3320 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3321 `(deftransform ,name ((x y))
3322 (if (same-leaf-ref-p x y)
3324 (let ((ix (or (type-approximate-interval (lvar-type x))
3325 (give-up-ir1-transform)))
3326 (iy (or (type-approximate-interval (lvar-type y))
3327 (give-up-ir1-transform))))
3332 ((and (constant-lvar-p x)
3333 (not (constant-lvar-p y)))
3336 (give-up-ir1-transform))))))))
3337 (def < > nil (interval-< ix iy) (interval->= ix iy))
3338 (def > < nil (interval-< iy ix) (interval->= iy ix))
3339 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3340 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3342 (defun ir1-transform-char< (x y first second inverse)
3344 ((same-leaf-ref-p x y) nil)
3345 ;; If we had interval representation of character types, as we
3346 ;; might eventually have to to support 2^21 characters, then here
3347 ;; we could do some compile-time computation as in transforms for
3348 ;; < above. -- CSR, 2003-07-01
3349 ((and (constant-lvar-p first)
3350 (not (constant-lvar-p second)))
3352 (t (give-up-ir1-transform))))
3354 (deftransform char< ((x y) (character character) *)
3355 (ir1-transform-char< x y x y 'char>))
3357 (deftransform char> ((x y) (character character) *)
3358 (ir1-transform-char< y x x y 'char<))
3360 ;;;; converting N-arg comparisons
3362 ;;;; We convert calls to N-arg comparison functions such as < into
3363 ;;;; two-arg calls. This transformation is enabled for all such
3364 ;;;; comparisons in this file. If any of these predicates are not
3365 ;;;; open-coded, then the transformation should be removed at some
3366 ;;;; point to avoid pessimization.
3368 ;;; This function is used for source transformation of N-arg
3369 ;;; comparison functions other than inequality. We deal both with
3370 ;;; converting to two-arg calls and inverting the sense of the test,
3371 ;;; if necessary. If the call has two args, then we pass or return a
3372 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3373 ;;; then we transform to code that returns true. Otherwise, we bind
3374 ;;; all the arguments and expand into a bunch of IFs.
3375 (declaim (ftype (function (symbol list boolean t) *) multi-compare))
3376 (defun multi-compare (predicate args not-p type)
3377 (let ((nargs (length args)))
3378 (cond ((< nargs 1) (values nil t))
3379 ((= nargs 1) `(progn (the ,type ,@args) t))
3382 `(if (,predicate ,(first args) ,(second args)) nil t)
3385 (do* ((i (1- nargs) (1- i))
3387 (current (gensym) (gensym))
3388 (vars (list current) (cons current vars))
3390 `(if (,predicate ,current ,last)
3392 `(if (,predicate ,current ,last)
3395 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3398 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3399 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3400 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3401 (define-source-transform <= (&rest args) (multi-compare '> args t 'real))
3402 (define-source-transform >= (&rest args) (multi-compare '< args t 'real))
3404 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3406 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3408 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3410 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3412 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3415 (define-source-transform char-equal (&rest args)
3416 (multi-compare 'char-equal args nil 'character))
3417 (define-source-transform char-lessp (&rest args)
3418 (multi-compare 'char-lessp args nil 'character))
3419 (define-source-transform char-greaterp (&rest args)
3420 (multi-compare 'char-greaterp args nil 'character))
3421 (define-source-transform char-not-greaterp (&rest args)
3422 (multi-compare 'char-greaterp args t 'character))
3423 (define-source-transform char-not-lessp (&rest args)
3424 (multi-compare 'char-lessp args t 'character))
3426 ;;; This function does source transformation of N-arg inequality
3427 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3428 ;;; arg cases. If there are more than two args, then we expand into
3429 ;;; the appropriate n^2 comparisons only when speed is important.
3430 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3431 (defun multi-not-equal (predicate args type)
3432 (let ((nargs (length args)))
3433 (cond ((< nargs 1) (values nil t))
3434 ((= nargs 1) `(progn (the ,type ,@args) t))
3436 `(if (,predicate ,(first args) ,(second args)) nil t))
3437 ((not (policy *lexenv*
3438 (and (>= speed space)
3439 (>= speed compilation-speed))))
3442 (let ((vars (make-gensym-list nargs)))
3443 (do ((var vars next)
3444 (next (cdr vars) (cdr next))
3447 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3449 (let ((v1 (first var)))
3451 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3453 (define-source-transform /= (&rest args)
3454 (multi-not-equal '= args 'number))
3455 (define-source-transform char/= (&rest args)
3456 (multi-not-equal 'char= args 'character))
3457 (define-source-transform char-not-equal (&rest args)
3458 (multi-not-equal 'char-equal args 'character))
3460 ;;; Expand MAX and MIN into the obvious comparisons.
3461 (define-source-transform max (arg0 &rest rest)
3462 (once-only ((arg0 arg0))
3464 `(values (the real ,arg0))
3465 `(let ((maxrest (max ,@rest)))
3466 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3467 (define-source-transform min (arg0 &rest rest)
3468 (once-only ((arg0 arg0))
3470 `(values (the real ,arg0))
3471 `(let ((minrest (min ,@rest)))
3472 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3474 ;;;; converting N-arg arithmetic functions
3476 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3477 ;;;; versions, and degenerate cases are flushed.
3479 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3480 (declaim (ftype (function (symbol t list) list) associate-args))
3481 (defun associate-args (function first-arg more-args)
3482 (let ((next (rest more-args))
3483 (arg (first more-args)))
3485 `(,function ,first-arg ,arg)
3486 (associate-args function `(,function ,first-arg ,arg) next))))
3488 ;;; Do source transformations for transitive functions such as +.
3489 ;;; One-arg cases are replaced with the arg and zero arg cases with
3490 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3491 ;;; ensure (with THE) that the argument in one-argument calls is.
3492 (defun source-transform-transitive (fun args identity
3493 &optional one-arg-result-type)
3494 (declare (symbol fun) (list args))
3497 (1 (if one-arg-result-type
3498 `(values (the ,one-arg-result-type ,(first args)))
3499 `(values ,(first args))))
3502 (associate-args fun (first args) (rest args)))))
3504 (define-source-transform + (&rest args)
3505 (source-transform-transitive '+ args 0 'number))
3506 (define-source-transform * (&rest args)
3507 (source-transform-transitive '* args 1 'number))
3508 (define-source-transform logior (&rest args)
3509 (source-transform-transitive 'logior args 0 'integer))
3510 (define-source-transform logxor (&rest args)
3511 (source-transform-transitive 'logxor args 0 'integer))
3512 (define-source-transform logand (&rest args)
3513 (source-transform-transitive 'logand args -1 'integer))
3514 (define-source-transform logeqv (&rest args)
3515 (source-transform-transitive 'logeqv args -1 'integer))
3517 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3518 ;;; because when they are given one argument, they return its absolute
3521 (define-source-transform gcd (&rest args)
3524 (1 `(abs (the integer ,(first args))))
3526 (t (associate-args 'gcd (first args) (rest args)))))
3528 (define-source-transform lcm (&rest args)
3531 (1 `(abs (the integer ,(first args))))
3533 (t (associate-args 'lcm (first args) (rest args)))))
3535 ;;; Do source transformations for intransitive n-arg functions such as
3536 ;;; /. With one arg, we form the inverse. With two args we pass.
3537 ;;; Otherwise we associate into two-arg calls.
3538 (declaim (ftype (function (symbol list t)
3539 (values list &optional (member nil t)))
3540 source-transform-intransitive))
3541 (defun source-transform-intransitive (function args inverse)
3543 ((0 2) (values nil t))
3544 (1 `(,@inverse ,(first args)))
3545 (t (associate-args function (first args) (rest args)))))
3547 (define-source-transform - (&rest args)
3548 (source-transform-intransitive '- args '(%negate)))
3549 (define-source-transform / (&rest args)
3550 (source-transform-intransitive '/ args '(/ 1)))
3552 ;;;; transforming APPLY
3554 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3555 ;;; only needs to understand one kind of variable-argument call. It is
3556 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3557 (define-source-transform apply (fun arg &rest more-args)
3558 (let ((args (cons arg more-args)))
3559 `(multiple-value-call ,fun
3560 ,@(mapcar (lambda (x)
3563 (values-list ,(car (last args))))))
3565 ;;;; transforming FORMAT
3567 ;;;; If the control string is a compile-time constant, then replace it
3568 ;;;; with a use of the FORMATTER macro so that the control string is
3569 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3570 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3571 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3573 ;;; for compile-time argument count checking.
3575 ;;; FIXME II: In some cases, type information could be correlated; for
3576 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3577 ;;; of a corresponding argument is known and does not intersect the
3578 ;;; list type, a warning could be signalled.
3579 (defun check-format-args (string args fun)
3580 (declare (type string string))
3581 (unless (typep string 'simple-string)
3582 (setq string (coerce string 'simple-string)))
3583 (multiple-value-bind (min max)
3584 (handler-case (sb!format:%compiler-walk-format-string string args)
3585 (sb!format:format-error (c)
3586 (compiler-warn "~A" c)))
3588 (let ((nargs (length args)))
3591 (warn 'format-too-few-args-warning
3593 "Too few arguments (~D) to ~S ~S: requires at least ~D."
3594 :format-arguments (list nargs fun string min)))
3596 (warn 'format-too-many-args-warning
3598 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3599 :format-arguments (list nargs fun string max))))))))
3601 (defoptimizer (format optimizer) ((dest control &rest args))
3602 (when (constant-lvar-p control)
3603 (let ((x (lvar-value control)))
3605 (check-format-args x args 'format)))))
3607 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3608 :policy (> speed space))
3609 (unless (constant-lvar-p control)
3610 (give-up-ir1-transform "The control string is not a constant."))
3611 (let ((arg-names (make-gensym-list (length args))))
3612 `(lambda (dest control ,@arg-names)
3613 (declare (ignore control))
3614 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
3616 (deftransform format ((stream control &rest args) (stream function &rest t) *
3617 :policy (> speed space))
3618 (let ((arg-names (make-gensym-list (length args))))
3619 `(lambda (stream control ,@arg-names)
3620 (funcall control stream ,@arg-names)
3623 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3624 :policy (> speed space))
3625 (let ((arg-names (make-gensym-list (length args))))
3626 `(lambda (tee control ,@arg-names)
3627 (declare (ignore tee))
3628 (funcall control *standard-output* ,@arg-names)
3633 `(defoptimizer (,name optimizer) ((control &rest args))
3634 (when (constant-lvar-p control)
3635 (let ((x (lvar-value control)))
3637 (check-format-args x args ',name)))))))
3640 #+sb-xc-host ; Only we should be using these
3643 (def compiler-abort)
3644 (def compiler-error)
3646 (def compiler-style-warn)
3647 (def compiler-notify)
3648 (def maybe-compiler-notify)
3651 (defoptimizer (cerror optimizer) ((report control &rest args))
3652 (when (and (constant-lvar-p control)
3653 (constant-lvar-p report))
3654 (let ((x (lvar-value control))
3655 (y (lvar-value report)))
3656 (when (and (stringp x) (stringp y))
3657 (multiple-value-bind (min1 max1)
3659 (sb!format:%compiler-walk-format-string x args)
3660 (sb!format:format-error (c)
3661 (compiler-warn "~A" c)))
3663 (multiple-value-bind (min2 max2)
3665 (sb!format:%compiler-walk-format-string y args)
3666 (sb!format:format-error (c)
3667 (compiler-warn "~A" c)))
3669 (let ((nargs (length args)))
3671 ((< nargs (min min1 min2))
3672 (warn 'format-too-few-args-warning
3674 "Too few arguments (~D) to ~S ~S ~S: ~
3675 requires at least ~D."
3677 (list nargs 'cerror y x (min min1 min2))))
3678 ((> nargs (max max1 max2))
3679 (warn 'format-too-many-args-warning
3681 "Too many arguments (~D) to ~S ~S ~S: ~
3684 (list nargs 'cerror y x (max max1 max2))))))))))))))
3686 (defoptimizer (coerce derive-type) ((value type))
3688 ((constant-lvar-p type)
3689 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3690 ;; but dealing with the niggle that complex canonicalization gets
3691 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3693 (let* ((specifier (lvar-value type))
3694 (result-typeoid (careful-specifier-type specifier)))
3696 ((null result-typeoid) nil)
3697 ((csubtypep result-typeoid (specifier-type 'number))
3698 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3699 ;; Rule of Canonical Representation for Complex Rationals,
3700 ;; which is a truly nasty delivery to field.
3702 ((csubtypep result-typeoid (specifier-type 'real))
3703 ;; cleverness required here: it would be nice to deduce
3704 ;; that something of type (INTEGER 2 3) coerced to type
3705 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3706 ;; FLOAT gets its own clause because it's implemented as
3707 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3710 ((and (numeric-type-p result-typeoid)
3711 (eq (numeric-type-complexp result-typeoid) :real))
3712 ;; FIXME: is this clause (a) necessary or (b) useful?
3714 ((or (csubtypep result-typeoid
3715 (specifier-type '(complex single-float)))
3716 (csubtypep result-typeoid
3717 (specifier-type '(complex double-float)))
3719 (csubtypep result-typeoid
3720 (specifier-type '(complex long-float))))
3721 ;; float complex types are never canonicalized.
3724 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3725 ;; probably just a COMPLEX or equivalent. So, in that
3726 ;; case, we will return a complex or an object of the
3727 ;; provided type if it's rational:
3728 (type-union result-typeoid
3729 (type-intersection (lvar-type value)
3730 (specifier-type 'rational))))))
3731 (t result-typeoid))))
3733 ;; OK, the result-type argument isn't constant. However, there
3734 ;; are common uses where we can still do better than just
3735 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3736 ;; where Y is of a known type. See messages on cmucl-imp
3737 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3738 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3739 ;; the basis that it's unlikely that other uses are both
3740 ;; time-critical and get to this branch of the COND (non-constant
3741 ;; second argument to COERCE). -- CSR, 2002-12-16
3742 (let ((value-type (lvar-type value))
3743 (type-type (lvar-type type)))
3745 ((good-cons-type-p (cons-type)
3746 ;; Make sure the cons-type we're looking at is something
3747 ;; we're prepared to handle which is basically something
3748 ;; that array-element-type can return.
3749 (or (and (member-type-p cons-type)
3750 (null (rest (member-type-members cons-type)))
3751 (null (first (member-type-members cons-type))))
3752 (let ((car-type (cons-type-car-type cons-type)))
3753 (and (member-type-p car-type)
3754 (null (rest (member-type-members car-type)))
3755 (or (symbolp (first (member-type-members car-type)))
3756 (numberp (first (member-type-members car-type)))
3757 (and (listp (first (member-type-members
3759 (numberp (first (first (member-type-members
3761 (good-cons-type-p (cons-type-cdr-type cons-type))))))
3762 (unconsify-type (good-cons-type)
3763 ;; Convert the "printed" respresentation of a cons
3764 ;; specifier into a type specifier. That is, the
3765 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3766 ;; NULL)) is converted to (SIGNED-BYTE 16).
3767 (cond ((or (null good-cons-type)
3768 (eq good-cons-type 'null))
3770 ((and (eq (first good-cons-type) 'cons)
3771 (eq (first (second good-cons-type)) 'member))
3772 `(,(second (second good-cons-type))
3773 ,@(unconsify-type (caddr good-cons-type))))))
3774 (coerceable-p (c-type)
3775 ;; Can the value be coerced to the given type? Coerce is
3776 ;; complicated, so we don't handle every possible case
3777 ;; here---just the most common and easiest cases:
3779 ;; * Any REAL can be coerced to a FLOAT type.
3780 ;; * Any NUMBER can be coerced to a (COMPLEX
3781 ;; SINGLE/DOUBLE-FLOAT).
3783 ;; FIXME I: we should also be able to deal with characters
3786 ;; FIXME II: I'm not sure that anything is necessary
3787 ;; here, at least while COMPLEX is not a specialized
3788 ;; array element type in the system. Reasoning: if
3789 ;; something cannot be coerced to the requested type, an
3790 ;; error will be raised (and so any downstream compiled
3791 ;; code on the assumption of the returned type is
3792 ;; unreachable). If something can, then it will be of
3793 ;; the requested type, because (by assumption) COMPLEX
3794 ;; (and other difficult types like (COMPLEX INTEGER)
3795 ;; aren't specialized types.
3796 (let ((coerced-type c-type))
3797 (or (and (subtypep coerced-type 'float)
3798 (csubtypep value-type (specifier-type 'real)))
3799 (and (subtypep coerced-type
3800 '(or (complex single-float)
3801 (complex double-float)))
3802 (csubtypep value-type (specifier-type 'number))))))
3803 (process-types (type)
3804 ;; FIXME: This needs some work because we should be able
3805 ;; to derive the resulting type better than just the
3806 ;; type arg of coerce. That is, if X is (INTEGER 10
3807 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3808 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3810 (cond ((member-type-p type)
3811 (let ((members (member-type-members type)))
3812 (if (every #'coerceable-p members)
3813 (specifier-type `(or ,@members))
3815 ((and (cons-type-p type)
3816 (good-cons-type-p type))
3817 (let ((c-type (unconsify-type (type-specifier type))))
3818 (if (coerceable-p c-type)
3819 (specifier-type c-type)
3822 *universal-type*))))
3823 (cond ((union-type-p type-type)
3824 (apply #'type-union (mapcar #'process-types
3825 (union-type-types type-type))))
3826 ((or (member-type-p type-type)
3827 (cons-type-p type-type))
3828 (process-types type-type))
3830 *universal-type*)))))))
3832 (defoptimizer (compile derive-type) ((nameoid function))
3833 (when (csubtypep (lvar-type nameoid)
3834 (specifier-type 'null))
3835 (values-specifier-type '(values function boolean boolean))))
3837 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3838 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3839 ;;; optimizer, above).
3840 (defoptimizer (array-element-type derive-type) ((array))
3841 (let ((array-type (lvar-type array)))
3842 (labels ((consify (list)
3845 `(cons (eql ,(car list)) ,(consify (rest list)))))
3846 (get-element-type (a)
3848 (type-specifier (array-type-specialized-element-type a))))
3849 (cond ((eq element-type '*)
3850 (specifier-type 'type-specifier))
3851 ((symbolp element-type)
3852 (make-member-type :members (list element-type)))
3853 ((consp element-type)
3854 (specifier-type (consify element-type)))
3856 (error "can't understand type ~S~%" element-type))))))
3857 (cond ((array-type-p array-type)
3858 (get-element-type array-type))
3859 ((union-type-p array-type)
3861 (mapcar #'get-element-type (union-type-types array-type))))
3863 *universal-type*)))))
3865 ;;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3866 ;;; isn't really related to the CMU CL code, since instead of trying
3867 ;;; to generalize the CMU CL code to allow START and END values, this
3868 ;;; code has been written from scratch following Chapter 7 of
3869 ;;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3870 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
3871 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3872 ;; isn't really related to the CMU CL code, since instead of trying
3873 ;; to generalize the CMU CL code to allow START and END values, this
3874 ;; code has been written from scratch following Chapter 7 of
3875 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3876 `(macrolet ((%index (x) `(truly-the index ,x))
3877 (%parent (i) `(ash ,i -1))
3878 (%left (i) `(%index (ash ,i 1)))
3879 (%right (i) `(%index (1+ (ash ,i 1))))
3882 (left (%left i) (%left i)))
3883 ((> left current-heap-size))
3884 (declare (type index i left))
3885 (let* ((i-elt (%elt i))
3886 (i-key (funcall keyfun i-elt))
3887 (left-elt (%elt left))
3888 (left-key (funcall keyfun left-elt)))
3889 (multiple-value-bind (large large-elt large-key)
3890 (if (funcall ,',predicate i-key left-key)
3891 (values left left-elt left-key)
3892 (values i i-elt i-key))
3893 (let ((right (%right i)))
3894 (multiple-value-bind (largest largest-elt)
3895 (if (> right current-heap-size)
3896 (values large large-elt)
3897 (let* ((right-elt (%elt right))
3898 (right-key (funcall keyfun right-elt)))
3899 (if (funcall ,',predicate large-key right-key)
3900 (values right right-elt)
3901 (values large large-elt))))
3902 (cond ((= largest i)
3905 (setf (%elt i) largest-elt
3906 (%elt largest) i-elt
3908 (%sort-vector (keyfun &optional (vtype 'vector))
3909 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
3910 ;; trouble getting type inference to
3911 ;; propagate all the way through this
3912 ;; tangled mess of inlining. The TRULY-THE
3913 ;; here works around that. -- WHN
3915 `(aref (truly-the ,',vtype ,',',vector)
3916 (%index (+ (%index ,i) start-1)))))
3917 (let (;; Heaps prefer 1-based addressing.
3918 (start-1 (1- ,',start))
3919 (current-heap-size (- ,',end ,',start))
3921 (declare (type (integer -1 #.(1- most-positive-fixnum))
3923 (declare (type index current-heap-size))
3924 (declare (type function keyfun))
3925 (loop for i of-type index
3926 from (ash current-heap-size -1) downto 1 do
3929 (when (< current-heap-size 2)
3931 (rotatef (%elt 1) (%elt current-heap-size))
3932 (decf current-heap-size)
3934 (if (typep ,vector 'simple-vector)
3935 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
3936 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
3938 ;; Special-casing the KEY=NIL case lets us avoid some
3940 (%sort-vector #'identity simple-vector)
3941 (%sort-vector ,key simple-vector))
3942 ;; It's hard to anticipate many speed-critical applications for
3943 ;; sorting vector types other than (VECTOR T), so we just lump
3944 ;; them all together in one slow dynamically typed mess.
3946 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
3947 (%sort-vector (or ,key #'identity))))))
3949 ;;;; debuggers' little helpers
3951 ;;; for debugging when transforms are behaving mysteriously,
3952 ;;; e.g. when debugging a problem with an ASH transform
3953 ;;; (defun foo (&optional s)
3954 ;;; (sb-c::/report-lvar s "S outside WHEN")
3955 ;;; (when (and (integerp s) (> s 3))
3956 ;;; (sb-c::/report-lvar s "S inside WHEN")
3957 ;;; (let ((bound (ash 1 (1- s))))
3958 ;;; (sb-c::/report-lvar bound "BOUND")
3959 ;;; (let ((x (- bound))
3961 ;;; (sb-c::/report-lvar x "X")
3962 ;;; (sb-c::/report-lvar x "Y"))
3963 ;;; `(integer ,(- bound) ,(1- bound)))))
3964 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
3965 ;;; and the function doesn't do anything at all.)
3968 (defknown /report-lvar (t t) null)
3969 (deftransform /report-lvar ((x message) (t t))
3970 (format t "~%/in /REPORT-LVAR~%")
3971 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
3972 (when (constant-lvar-p x)
3973 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
3974 (format t "/MESSAGE=~S~%" (lvar-value message))
3975 (give-up-ir1-transform "not a real transform"))
3976 (defun /report-lvar (x message)
3977 (declare (ignore x message))))