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
312 ;;; ANSI contaigon specifies coercion to floating point if one of the
313 ;;; arguments is floating point. Here we should check to be sure that
314 ;;; the other argument is within the bounds of that floating point
317 (defmacro safely-binop (op x y)
319 ((typep ,x 'single-float)
320 (if (or (typep ,y 'single-float)
321 (<= most-negative-single-float ,y most-positive-single-float))
323 ((typep ,x 'double-float)
324 (if (or (typep ,y 'double-float)
325 (<= most-negative-double-float ,y most-positive-double-float))
327 ((typep ,y 'single-float)
328 (if (<= most-negative-single-float ,x most-positive-single-float)
330 ((typep ,y 'double-float)
331 (if (<= most-negative-double-float ,x most-positive-double-float)
335 (defmacro bound-binop (op x y)
337 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
338 (set-bound (safely-binop ,op (type-bound-number ,x)
339 (type-bound-number ,y))
340 (or (consp ,x) (consp ,y))))))
342 (defun coerce-for-bound (val type)
344 (list (coerce-for-bound (car val) type))
346 ((subtypep type 'double-float)
347 (if (<= most-negative-double-float val most-positive-double-float)
349 ((or (subtypep type 'single-float) (subtypep type 'float))
350 ;; coerce to float returns a single-float
351 (if (<= most-negative-single-float val most-positive-single-float)
353 (t (coerce val type)))))
355 (defun coerce-and-truncate-floats (val type)
358 (list (coerce-and-truncate-floats (car val) type))
360 ((subtypep type 'double-float)
361 (if (<= most-negative-double-float val most-positive-double-float)
363 (if (< val most-negative-double-float)
364 most-negative-double-float most-positive-double-float)))
365 ((or (subtypep type 'single-float) (subtypep type 'float))
366 ;; coerce to float returns a single-float
367 (if (<= most-negative-single-float val most-positive-single-float)
369 (if (< val most-negative-single-float)
370 most-negative-single-float most-positive-single-float)))
371 (t (coerce val type))))))
373 ;;; Convert a numeric-type object to an interval object.
374 (defun numeric-type->interval (x)
375 (declare (type numeric-type x))
376 (make-interval :low (numeric-type-low x)
377 :high (numeric-type-high x)))
379 (defun type-approximate-interval (type)
380 (declare (type ctype type))
381 (let ((types (prepare-arg-for-derive-type type))
384 (let ((type (if (member-type-p type)
385 (convert-member-type type)
387 (unless (numeric-type-p type)
388 (return-from type-approximate-interval nil))
389 (let ((interval (numeric-type->interval type)))
392 (interval-approximate-union result interval)
396 (defun copy-interval-limit (limit)
401 (defun copy-interval (x)
402 (declare (type interval x))
403 (make-interval :low (copy-interval-limit (interval-low x))
404 :high (copy-interval-limit (interval-high x))))
406 ;;; Given a point P contained in the interval X, split X into two
407 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
408 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
409 ;;; contains P. You can specify both to be T or NIL.
410 (defun interval-split (p x &optional close-lower close-upper)
411 (declare (type number p)
413 (list (make-interval :low (copy-interval-limit (interval-low x))
414 :high (if close-lower p (list p)))
415 (make-interval :low (if close-upper (list p) p)
416 :high (copy-interval-limit (interval-high x)))))
418 ;;; Return the closure of the interval. That is, convert open bounds
419 ;;; to closed bounds.
420 (defun interval-closure (x)
421 (declare (type interval x))
422 (make-interval :low (type-bound-number (interval-low x))
423 :high (type-bound-number (interval-high x))))
425 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
426 ;;; '-. Otherwise return NIL.
427 (defun interval-range-info (x &optional (point 0))
428 (declare (type interval x))
429 (let ((lo (interval-low x))
430 (hi (interval-high x)))
431 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
433 ((and hi (signed-zero->= point (type-bound-number hi)))
438 ;;; Test to see whether the interval X is bounded. HOW determines the
439 ;;; test, and should be either ABOVE, BELOW, or BOTH.
440 (defun interval-bounded-p (x how)
441 (declare (type interval x))
448 (and (interval-low x) (interval-high x)))))
450 ;;; See whether the interval X contains the number P, taking into
451 ;;; account that the interval might not be closed.
452 (defun interval-contains-p (p x)
453 (declare (type number p)
455 ;; Does the interval X contain the number P? This would be a lot
456 ;; easier if all intervals were closed!
457 (let ((lo (interval-low x))
458 (hi (interval-high x)))
460 ;; The interval is bounded
461 (if (and (signed-zero-<= (type-bound-number lo) p)
462 (signed-zero-<= p (type-bound-number hi)))
463 ;; P is definitely in the closure of the interval.
464 ;; We just need to check the end points now.
465 (cond ((signed-zero-= p (type-bound-number lo))
467 ((signed-zero-= p (type-bound-number hi))
472 ;; Interval with upper bound
473 (if (signed-zero-< p (type-bound-number hi))
475 (and (numberp hi) (signed-zero-= p hi))))
477 ;; Interval with lower bound
478 (if (signed-zero-> p (type-bound-number lo))
480 (and (numberp lo) (signed-zero-= p lo))))
482 ;; Interval with no bounds
485 ;;; Determine whether two intervals X and Y intersect. Return T if so.
486 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
487 ;;; were closed. Otherwise the intervals are treated as they are.
489 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
490 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
491 ;;; is T, then they do intersect because we use the closure of X = [0,
492 ;;; 1] and Y = [1, 2] to determine intersection.
493 (defun interval-intersect-p (x y &optional closed-intervals-p)
494 (declare (type interval x y))
495 (multiple-value-bind (intersect diff)
496 (interval-intersection/difference (if closed-intervals-p
499 (if closed-intervals-p
502 (declare (ignore diff))
505 ;;; Are the two intervals adjacent? That is, is there a number
506 ;;; between the two intervals that is not an element of either
507 ;;; interval? If so, they are not adjacent. For example [0, 1) and
508 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
509 ;;; between both intervals.
510 (defun interval-adjacent-p (x y)
511 (declare (type interval x y))
512 (flet ((adjacent (lo hi)
513 ;; Check to see whether lo and hi are adjacent. If either is
514 ;; nil, they can't be adjacent.
515 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
516 ;; The bounds are equal. They are adjacent if one of
517 ;; them is closed (a number). If both are open (consp),
518 ;; then there is a number that lies between them.
519 (or (numberp lo) (numberp hi)))))
520 (or (adjacent (interval-low y) (interval-high x))
521 (adjacent (interval-low x) (interval-high y)))))
523 ;;; Compute the intersection and difference between two intervals.
524 ;;; Two values are returned: the intersection and the difference.
526 ;;; Let the two intervals be X and Y, and let I and D be the two
527 ;;; values returned by this function. Then I = X intersect Y. If I
528 ;;; is NIL (the empty set), then D is X union Y, represented as the
529 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
530 ;;; - I, which is a list of two intervals.
532 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
533 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
534 (defun interval-intersection/difference (x y)
535 (declare (type interval x y))
536 (let ((x-lo (interval-low x))
537 (x-hi (interval-high x))
538 (y-lo (interval-low y))
539 (y-hi (interval-high y)))
542 ;; If p is an open bound, make it closed. If p is a closed
543 ;; bound, make it open.
548 ;; Test whether P is in the interval.
549 (when (interval-contains-p (type-bound-number p)
550 (interval-closure int))
551 (let ((lo (interval-low int))
552 (hi (interval-high int)))
553 ;; Check for endpoints.
554 (cond ((and lo (= (type-bound-number p) (type-bound-number lo)))
555 (not (and (consp p) (numberp lo))))
556 ((and hi (= (type-bound-number p) (type-bound-number hi)))
557 (not (and (numberp p) (consp hi))))
559 (test-lower-bound (p int)
560 ;; P is a lower bound of an interval.
563 (not (interval-bounded-p int 'below))))
564 (test-upper-bound (p int)
565 ;; P is an upper bound of an interval.
568 (not (interval-bounded-p int 'above)))))
569 (let ((x-lo-in-y (test-lower-bound x-lo y))
570 (x-hi-in-y (test-upper-bound x-hi y))
571 (y-lo-in-x (test-lower-bound y-lo x))
572 (y-hi-in-x (test-upper-bound y-hi x)))
573 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
574 ;; Intervals intersect. Let's compute the intersection
575 ;; and the difference.
576 (multiple-value-bind (lo left-lo left-hi)
577 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
578 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
579 (multiple-value-bind (hi right-lo right-hi)
581 (values x-hi (opposite-bound x-hi) y-hi))
583 (values y-hi (opposite-bound y-hi) x-hi)))
584 (values (make-interval :low lo :high hi)
585 (list (make-interval :low left-lo
587 (make-interval :low right-lo
590 (values nil (list x y))))))))
592 ;;; If intervals X and Y intersect, return a new interval that is the
593 ;;; union of the two. If they do not intersect, return NIL.
594 (defun interval-merge-pair (x y)
595 (declare (type interval x y))
596 ;; If x and y intersect or are adjacent, create the union.
597 ;; Otherwise return nil
598 (when (or (interval-intersect-p x y)
599 (interval-adjacent-p x y))
600 (flet ((select-bound (x1 x2 min-op max-op)
601 (let ((x1-val (type-bound-number x1))
602 (x2-val (type-bound-number x2)))
604 ;; Both bounds are finite. Select the right one.
605 (cond ((funcall min-op x1-val x2-val)
606 ;; x1 is definitely better.
608 ((funcall max-op x1-val x2-val)
609 ;; x2 is definitely better.
612 ;; Bounds are equal. Select either
613 ;; value and make it open only if
615 (set-bound x1-val (and (consp x1) (consp x2))))))
617 ;; At least one bound is not finite. The
618 ;; non-finite bound always wins.
620 (let* ((x-lo (copy-interval-limit (interval-low x)))
621 (x-hi (copy-interval-limit (interval-high x)))
622 (y-lo (copy-interval-limit (interval-low y)))
623 (y-hi (copy-interval-limit (interval-high y))))
624 (make-interval :low (select-bound x-lo y-lo #'< #'>)
625 :high (select-bound x-hi y-hi #'> #'<))))))
627 ;;; return the minimal interval, containing X and Y
628 (defun interval-approximate-union (x y)
629 (cond ((interval-merge-pair x y))
631 (make-interval :low (copy-interval-limit (interval-low x))
632 :high (copy-interval-limit (interval-high y))))
634 (make-interval :low (copy-interval-limit (interval-low y))
635 :high (copy-interval-limit (interval-high x))))))
637 ;;; basic arithmetic operations on intervals. We probably should do
638 ;;; true interval arithmetic here, but it's complicated because we
639 ;;; have float and integer types and bounds can be open or closed.
641 ;;; the negative of an interval
642 (defun interval-neg (x)
643 (declare (type interval x))
644 (make-interval :low (bound-func #'- (interval-high x))
645 :high (bound-func #'- (interval-low x))))
647 ;;; Add two intervals.
648 (defun interval-add (x y)
649 (declare (type interval x y))
650 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
651 :high (bound-binop + (interval-high x) (interval-high y))))
653 ;;; Subtract two intervals.
654 (defun interval-sub (x y)
655 (declare (type interval x y))
656 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
657 :high (bound-binop - (interval-high x) (interval-low y))))
659 ;;; Multiply two intervals.
660 (defun interval-mul (x y)
661 (declare (type interval x y))
662 (flet ((bound-mul (x y)
663 (cond ((or (null x) (null y))
664 ;; Multiply by infinity is infinity
666 ((or (and (numberp x) (zerop x))
667 (and (numberp y) (zerop y)))
668 ;; Multiply by closed zero is special. The result
669 ;; is always a closed bound. But don't replace this
670 ;; with zero; we want the multiplication to produce
671 ;; the correct signed zero, if needed.
672 (* (type-bound-number x) (type-bound-number y)))
673 ((or (and (floatp x) (float-infinity-p x))
674 (and (floatp y) (float-infinity-p y)))
675 ;; Infinity times anything is infinity
678 ;; General multiply. The result is open if either is open.
679 (bound-binop * x y)))))
680 (let ((x-range (interval-range-info x))
681 (y-range (interval-range-info y)))
682 (cond ((null x-range)
683 ;; Split x into two and multiply each separately
684 (destructuring-bind (x- x+) (interval-split 0 x t t)
685 (interval-merge-pair (interval-mul x- y)
686 (interval-mul x+ y))))
688 ;; Split y into two and multiply each separately
689 (destructuring-bind (y- y+) (interval-split 0 y t t)
690 (interval-merge-pair (interval-mul x y-)
691 (interval-mul x y+))))
693 (interval-neg (interval-mul (interval-neg x) y)))
695 (interval-neg (interval-mul x (interval-neg y))))
696 ((and (eq x-range '+) (eq y-range '+))
697 ;; If we are here, X and Y are both positive.
699 :low (bound-mul (interval-low x) (interval-low y))
700 :high (bound-mul (interval-high x) (interval-high y))))
702 (bug "excluded case in INTERVAL-MUL"))))))
704 ;;; Divide two intervals.
705 (defun interval-div (top bot)
706 (declare (type interval top bot))
707 (flet ((bound-div (x y y-low-p)
710 ;; Divide by infinity means result is 0. However,
711 ;; we need to watch out for the sign of the result,
712 ;; to correctly handle signed zeros. We also need
713 ;; to watch out for positive or negative infinity.
714 (if (floatp (type-bound-number x))
716 (- (float-sign (type-bound-number x) 0.0))
717 (float-sign (type-bound-number x) 0.0))
719 ((zerop (type-bound-number y))
720 ;; Divide by zero means result is infinity
722 ((and (numberp x) (zerop x))
723 ;; Zero divided by anything is zero.
726 (bound-binop / x y)))))
727 (let ((top-range (interval-range-info top))
728 (bot-range (interval-range-info bot)))
729 (cond ((null bot-range)
730 ;; The denominator contains zero, so anything goes!
731 (make-interval :low nil :high nil))
733 ;; Denominator is negative so flip the sign, compute the
734 ;; result, and flip it back.
735 (interval-neg (interval-div top (interval-neg bot))))
737 ;; Split top into two positive and negative parts, and
738 ;; divide each separately
739 (destructuring-bind (top- top+) (interval-split 0 top t t)
740 (interval-merge-pair (interval-div top- bot)
741 (interval-div top+ bot))))
743 ;; Top is negative so flip the sign, divide, and flip the
744 ;; sign of the result.
745 (interval-neg (interval-div (interval-neg top) bot)))
746 ((and (eq top-range '+) (eq bot-range '+))
749 :low (bound-div (interval-low top) (interval-high bot) t)
750 :high (bound-div (interval-high top) (interval-low bot) nil)))
752 (bug "excluded case in INTERVAL-DIV"))))))
754 ;;; Apply the function F to the interval X. If X = [a, b], then the
755 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
756 ;;; result makes sense. It will if F is monotonic increasing (or
758 (defun interval-func (f x)
759 (declare (type function f)
761 (let ((lo (bound-func f (interval-low x)))
762 (hi (bound-func f (interval-high x))))
763 (make-interval :low lo :high hi)))
765 ;;; Return T if X < Y. That is every number in the interval X is
766 ;;; always less than any number in the interval Y.
767 (defun interval-< (x y)
768 (declare (type interval x y))
769 ;; X < Y only if X is bounded above, Y is bounded below, and they
771 (when (and (interval-bounded-p x 'above)
772 (interval-bounded-p y 'below))
773 ;; Intervals are bounded in the appropriate way. Make sure they
775 (let ((left (interval-high x))
776 (right (interval-low y)))
777 (cond ((> (type-bound-number left)
778 (type-bound-number right))
779 ;; The intervals definitely overlap, so result is NIL.
781 ((< (type-bound-number left)
782 (type-bound-number right))
783 ;; The intervals definitely don't touch, so result is T.
786 ;; Limits are equal. Check for open or closed bounds.
787 ;; Don't overlap if one or the other are open.
788 (or (consp left) (consp right)))))))
790 ;;; Return T if X >= Y. That is, every number in the interval X is
791 ;;; always greater than any number in the interval Y.
792 (defun interval->= (x y)
793 (declare (type interval x y))
794 ;; X >= Y if lower bound of X >= upper bound of Y
795 (when (and (interval-bounded-p x 'below)
796 (interval-bounded-p y 'above))
797 (>= (type-bound-number (interval-low x))
798 (type-bound-number (interval-high y)))))
800 ;;; Return an interval that is the absolute value of X. Thus, if
801 ;;; X = [-1 10], the result is [0, 10].
802 (defun interval-abs (x)
803 (declare (type interval x))
804 (case (interval-range-info x)
810 (destructuring-bind (x- x+) (interval-split 0 x t t)
811 (interval-merge-pair (interval-neg x-) x+)))))
813 ;;; Compute the square of an interval.
814 (defun interval-sqr (x)
815 (declare (type interval x))
816 (interval-func (lambda (x) (* x x))
819 ;;;; numeric DERIVE-TYPE methods
821 ;;; a utility for defining derive-type methods of integer operations. If
822 ;;; the types of both X and Y are integer types, then we compute a new
823 ;;; integer type with bounds determined Fun when applied to X and Y.
824 ;;; Otherwise, we use NUMERIC-CONTAGION.
825 (defun derive-integer-type-aux (x y fun)
826 (declare (type function fun))
827 (if (and (numeric-type-p x) (numeric-type-p y)
828 (eq (numeric-type-class x) 'integer)
829 (eq (numeric-type-class y) 'integer)
830 (eq (numeric-type-complexp x) :real)
831 (eq (numeric-type-complexp y) :real))
832 (multiple-value-bind (low high) (funcall fun x y)
833 (make-numeric-type :class 'integer
837 (numeric-contagion x y)))
839 (defun derive-integer-type (x y fun)
840 (declare (type lvar x y) (type function fun))
841 (let ((x (lvar-type x))
843 (derive-integer-type-aux x y fun)))
845 ;;; simple utility to flatten a list
846 (defun flatten-list (x)
847 (labels ((flatten-and-append (tree list)
848 (cond ((null tree) list)
849 ((atom tree) (cons tree list))
850 (t (flatten-and-append
851 (car tree) (flatten-and-append (cdr tree) list))))))
852 (flatten-and-append x nil)))
854 ;;; Take some type of lvar and massage it so that we get a list of the
855 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
857 (defun prepare-arg-for-derive-type (arg)
858 (flet ((listify (arg)
863 (union-type-types arg))
866 (unless (eq arg *empty-type*)
867 ;; Make sure all args are some type of numeric-type. For member
868 ;; types, convert the list of members into a union of equivalent
869 ;; single-element member-type's.
870 (let ((new-args nil))
871 (dolist (arg (listify arg))
872 (if (member-type-p arg)
873 ;; Run down the list of members and convert to a list of
875 (dolist (member (member-type-members arg))
876 (push (if (numberp member)
877 (make-member-type :members (list member))
880 (push arg new-args)))
881 (unless (member *empty-type* new-args)
884 ;;; Convert from the standard type convention for which -0.0 and 0.0
885 ;;; are equal to an intermediate convention for which they are
886 ;;; considered different which is more natural for some of the
888 (defun convert-numeric-type (type)
889 (declare (type numeric-type type))
890 ;;; Only convert real float interval delimiters types.
891 (if (eq (numeric-type-complexp type) :real)
892 (let* ((lo (numeric-type-low type))
893 (lo-val (type-bound-number lo))
894 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
895 (hi (numeric-type-high type))
896 (hi-val (type-bound-number hi))
897 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
898 (if (or lo-float-zero-p hi-float-zero-p)
900 :class (numeric-type-class type)
901 :format (numeric-type-format type)
903 :low (if lo-float-zero-p
905 (list (float 0.0 lo-val))
906 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
908 :high (if hi-float-zero-p
910 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
917 ;;; Convert back from the intermediate convention for which -0.0 and
918 ;;; 0.0 are considered different to the standard type convention for
920 (defun convert-back-numeric-type (type)
921 (declare (type numeric-type type))
922 ;;; Only convert real float interval delimiters types.
923 (if (eq (numeric-type-complexp type) :real)
924 (let* ((lo (numeric-type-low type))
925 (lo-val (type-bound-number lo))
927 (and lo (floatp lo-val) (= lo-val 0.0)
928 (float-sign lo-val)))
929 (hi (numeric-type-high type))
930 (hi-val (type-bound-number hi))
932 (and hi (floatp hi-val) (= hi-val 0.0)
933 (float-sign hi-val))))
935 ;; (float +0.0 +0.0) => (member 0.0)
936 ;; (float -0.0 -0.0) => (member -0.0)
937 ((and lo-float-zero-p hi-float-zero-p)
938 ;; shouldn't have exclusive bounds here..
939 (aver (and (not (consp lo)) (not (consp hi))))
940 (if (= lo-float-zero-p hi-float-zero-p)
941 ;; (float +0.0 +0.0) => (member 0.0)
942 ;; (float -0.0 -0.0) => (member -0.0)
943 (specifier-type `(member ,lo-val))
944 ;; (float -0.0 +0.0) => (float 0.0 0.0)
945 ;; (float +0.0 -0.0) => (float 0.0 0.0)
946 (make-numeric-type :class (numeric-type-class type)
947 :format (numeric-type-format type)
953 ;; (float -0.0 x) => (float 0.0 x)
954 ((and (not (consp lo)) (minusp lo-float-zero-p))
955 (make-numeric-type :class (numeric-type-class type)
956 :format (numeric-type-format type)
958 :low (float 0.0 lo-val)
960 ;; (float (+0.0) x) => (float (0.0) x)
961 ((and (consp lo) (plusp lo-float-zero-p))
962 (make-numeric-type :class (numeric-type-class type)
963 :format (numeric-type-format type)
965 :low (list (float 0.0 lo-val))
968 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
969 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
970 (list (make-member-type :members (list (float 0.0 lo-val)))
971 (make-numeric-type :class (numeric-type-class type)
972 :format (numeric-type-format type)
974 :low (list (float 0.0 lo-val))
978 ;; (float x +0.0) => (float x 0.0)
979 ((and (not (consp hi)) (plusp hi-float-zero-p))
980 (make-numeric-type :class (numeric-type-class type)
981 :format (numeric-type-format type)
984 :high (float 0.0 hi-val)))
985 ;; (float x (-0.0)) => (float x (0.0))
986 ((and (consp hi) (minusp hi-float-zero-p))
987 (make-numeric-type :class (numeric-type-class type)
988 :format (numeric-type-format type)
991 :high (list (float 0.0 hi-val))))
993 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
994 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
995 (list (make-member-type :members (list (float -0.0 hi-val)))
996 (make-numeric-type :class (numeric-type-class type)
997 :format (numeric-type-format type)
1000 :high (list (float 0.0 hi-val)))))))
1006 ;;; Convert back a possible list of numeric types.
1007 (defun convert-back-numeric-type-list (type-list)
1010 (let ((results '()))
1011 (dolist (type type-list)
1012 (if (numeric-type-p type)
1013 (let ((result (convert-back-numeric-type type)))
1015 (setf results (append results result))
1016 (push result results)))
1017 (push type results)))
1020 (convert-back-numeric-type type-list))
1022 (convert-back-numeric-type-list (union-type-types type-list)))
1026 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
1027 ;;; belong in the kernel's type logic, invoked always, instead of in
1028 ;;; the compiler, invoked only during some type optimizations. (In
1029 ;;; fact, as of 0.pre8.100 or so they probably are, under
1030 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
1032 ;;; Take a list of types and return a canonical type specifier,
1033 ;;; combining any MEMBER types together. If both positive and negative
1034 ;;; MEMBER types are present they are converted to a float type.
1035 ;;; XXX This would be far simpler if the type-union methods could handle
1036 ;;; member/number unions.
1037 (defun make-canonical-union-type (type-list)
1040 (dolist (type type-list)
1041 (if (member-type-p type)
1042 (setf members (union members (member-type-members type)))
1043 (push type misc-types)))
1045 (when (null (set-difference `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0) members))
1046 (push (specifier-type '(long-float 0.0l0 0.0l0)) misc-types)
1047 (setf members (set-difference members `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0))))
1048 (when (null (set-difference `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0) members))
1049 (push (specifier-type '(double-float 0.0d0 0.0d0)) misc-types)
1050 (setf members (set-difference members `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0))))
1051 (when (null (set-difference `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0) members))
1052 (push (specifier-type '(single-float 0.0f0 0.0f0)) misc-types)
1053 (setf members (set-difference members `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0))))
1055 (apply #'type-union (make-member-type :members members) misc-types)
1056 (apply #'type-union misc-types))))
1058 ;;; Convert a member type with a single member to a numeric type.
1059 (defun convert-member-type (arg)
1060 (let* ((members (member-type-members arg))
1061 (member (first members))
1062 (member-type (type-of member)))
1063 (aver (not (rest members)))
1064 (specifier-type (cond ((typep member 'integer)
1065 `(integer ,member ,member))
1066 ((memq member-type '(short-float single-float
1067 double-float long-float))
1068 `(,member-type ,member ,member))
1072 ;;; This is used in defoptimizers for computing the resulting type of
1075 ;;; Given the lvar ARG, derive the resulting type using the
1076 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1077 ;;; "atomic" lvar type like numeric-type or member-type (containing
1078 ;;; just one element). It should return the resulting type, which can
1079 ;;; be a list of types.
1081 ;;; For the case of member types, if a MEMBER-FUN is given it is
1082 ;;; called to compute the result otherwise the member type is first
1083 ;;; converted to a numeric type and the DERIVE-FUN is called.
1084 (defun one-arg-derive-type (arg derive-fun member-fun
1085 &optional (convert-type t))
1086 (declare (type function derive-fun)
1087 (type (or null function) member-fun))
1088 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1094 (with-float-traps-masked
1095 (:underflow :overflow :divide-by-zero)
1097 `(eql ,(funcall member-fun
1098 (first (member-type-members x))))))
1099 ;; Otherwise convert to a numeric type.
1100 (let ((result-type-list
1101 (funcall derive-fun (convert-member-type x))))
1103 (convert-back-numeric-type-list result-type-list)
1104 result-type-list))))
1107 (convert-back-numeric-type-list
1108 (funcall derive-fun (convert-numeric-type x)))
1109 (funcall derive-fun x)))
1111 *universal-type*))))
1112 ;; Run down the list of args and derive the type of each one,
1113 ;; saving all of the results in a list.
1114 (let ((results nil))
1115 (dolist (arg arg-list)
1116 (let ((result (deriver arg)))
1118 (setf results (append results result))
1119 (push result results))))
1121 (make-canonical-union-type results)
1122 (first results)))))))
1124 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1125 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1126 ;;; original args and a third which is T to indicate if the two args
1127 ;;; really represent the same lvar. This is useful for deriving the
1128 ;;; type of things like (* x x), which should always be positive. If
1129 ;;; we didn't do this, we wouldn't be able to tell.
1130 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1131 &optional (convert-type t))
1132 (declare (type function derive-fun fun))
1133 (flet ((deriver (x y same-arg)
1134 (cond ((and (member-type-p x) (member-type-p y))
1135 (let* ((x (first (member-type-members x)))
1136 (y (first (member-type-members y)))
1137 (result (ignore-errors
1138 (with-float-traps-masked
1139 (:underflow :overflow :divide-by-zero
1141 (funcall fun x y)))))
1142 (cond ((null result) *empty-type*)
1143 ((and (floatp result) (float-nan-p result))
1144 (make-numeric-type :class 'float
1145 :format (type-of result)
1148 (specifier-type `(eql ,result))))))
1149 ((and (member-type-p x) (numeric-type-p y))
1150 (let* ((x (convert-member-type x))
1151 (y (if convert-type (convert-numeric-type y) y))
1152 (result (funcall derive-fun x y same-arg)))
1154 (convert-back-numeric-type-list result)
1156 ((and (numeric-type-p x) (member-type-p y))
1157 (let* ((x (if convert-type (convert-numeric-type x) x))
1158 (y (convert-member-type y))
1159 (result (funcall derive-fun x y same-arg)))
1161 (convert-back-numeric-type-list result)
1163 ((and (numeric-type-p x) (numeric-type-p y))
1164 (let* ((x (if convert-type (convert-numeric-type x) x))
1165 (y (if convert-type (convert-numeric-type y) y))
1166 (result (funcall derive-fun x y same-arg)))
1168 (convert-back-numeric-type-list result)
1171 *universal-type*))))
1172 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1173 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1174 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1176 (let ((results nil))
1178 ;; Since the args are the same LVARs, just run down the
1181 (let ((result (deriver x x same-arg)))
1183 (setf results (append results result))
1184 (push result results))))
1185 ;; Try all pairwise combinations.
1188 (let ((result (or (deriver x y same-arg)
1189 (numeric-contagion x y))))
1191 (setf results (append results result))
1192 (push result results))))))
1194 (make-canonical-union-type results)
1195 (first results)))))))
1197 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1199 (defoptimizer (+ derive-type) ((x y))
1200 (derive-integer-type
1207 (values (frob (numeric-type-low x) (numeric-type-low y))
1208 (frob (numeric-type-high x) (numeric-type-high y)))))))
1210 (defoptimizer (- derive-type) ((x y))
1211 (derive-integer-type
1218 (values (frob (numeric-type-low x) (numeric-type-high y))
1219 (frob (numeric-type-high x) (numeric-type-low y)))))))
1221 (defoptimizer (* derive-type) ((x y))
1222 (derive-integer-type
1225 (let ((x-low (numeric-type-low x))
1226 (x-high (numeric-type-high x))
1227 (y-low (numeric-type-low y))
1228 (y-high (numeric-type-high y)))
1229 (cond ((not (and x-low y-low))
1231 ((or (minusp x-low) (minusp y-low))
1232 (if (and x-high y-high)
1233 (let ((max (* (max (abs x-low) (abs x-high))
1234 (max (abs y-low) (abs y-high)))))
1235 (values (- max) max))
1238 (values (* x-low y-low)
1239 (if (and x-high y-high)
1243 (defoptimizer (/ derive-type) ((x y))
1244 (numeric-contagion (lvar-type x) (lvar-type y)))
1248 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1250 (defun +-derive-type-aux (x y same-arg)
1251 (if (and (numeric-type-real-p x)
1252 (numeric-type-real-p y))
1255 (let ((x-int (numeric-type->interval x)))
1256 (interval-add x-int x-int))
1257 (interval-add (numeric-type->interval x)
1258 (numeric-type->interval y))))
1259 (result-type (numeric-contagion x y)))
1260 ;; If the result type is a float, we need to be sure to coerce
1261 ;; the bounds into the correct type.
1262 (when (eq (numeric-type-class result-type) 'float)
1263 (setf result (interval-func
1265 (coerce-for-bound x (or (numeric-type-format result-type)
1269 :class (if (and (eq (numeric-type-class x) 'integer)
1270 (eq (numeric-type-class y) 'integer))
1271 ;; The sum of integers is always an integer.
1273 (numeric-type-class result-type))
1274 :format (numeric-type-format result-type)
1275 :low (interval-low result)
1276 :high (interval-high result)))
1277 ;; general contagion
1278 (numeric-contagion x y)))
1280 (defoptimizer (+ derive-type) ((x y))
1281 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1283 (defun --derive-type-aux (x y same-arg)
1284 (if (and (numeric-type-real-p x)
1285 (numeric-type-real-p y))
1287 ;; (- X X) is always 0.
1289 (make-interval :low 0 :high 0)
1290 (interval-sub (numeric-type->interval x)
1291 (numeric-type->interval y))))
1292 (result-type (numeric-contagion x y)))
1293 ;; If the result type is a float, we need to be sure to coerce
1294 ;; the bounds into the correct type.
1295 (when (eq (numeric-type-class result-type) 'float)
1296 (setf result (interval-func
1298 (coerce-for-bound x (or (numeric-type-format result-type)
1302 :class (if (and (eq (numeric-type-class x) 'integer)
1303 (eq (numeric-type-class y) 'integer))
1304 ;; The difference of integers is always an integer.
1306 (numeric-type-class result-type))
1307 :format (numeric-type-format result-type)
1308 :low (interval-low result)
1309 :high (interval-high result)))
1310 ;; general contagion
1311 (numeric-contagion x y)))
1313 (defoptimizer (- derive-type) ((x y))
1314 (two-arg-derive-type x y #'--derive-type-aux #'-))
1316 (defun *-derive-type-aux (x y same-arg)
1317 (if (and (numeric-type-real-p x)
1318 (numeric-type-real-p y))
1320 ;; (* X X) is always positive, so take care to do it right.
1322 (interval-sqr (numeric-type->interval x))
1323 (interval-mul (numeric-type->interval x)
1324 (numeric-type->interval y))))
1325 (result-type (numeric-contagion x y)))
1326 ;; If the result type is a float, we need to be sure to coerce
1327 ;; the bounds into the correct type.
1328 (when (eq (numeric-type-class result-type) 'float)
1329 (setf result (interval-func
1331 (coerce-for-bound x (or (numeric-type-format result-type)
1335 :class (if (and (eq (numeric-type-class x) 'integer)
1336 (eq (numeric-type-class y) 'integer))
1337 ;; The product of integers is always an integer.
1339 (numeric-type-class result-type))
1340 :format (numeric-type-format result-type)
1341 :low (interval-low result)
1342 :high (interval-high result)))
1343 (numeric-contagion x y)))
1345 (defoptimizer (* derive-type) ((x y))
1346 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1348 (defun /-derive-type-aux (x y same-arg)
1349 (if (and (numeric-type-real-p x)
1350 (numeric-type-real-p y))
1352 ;; (/ X X) is always 1, except if X can contain 0. In
1353 ;; that case, we shouldn't optimize the division away
1354 ;; because we want 0/0 to signal an error.
1356 (not (interval-contains-p
1357 0 (interval-closure (numeric-type->interval y)))))
1358 (make-interval :low 1 :high 1)
1359 (interval-div (numeric-type->interval x)
1360 (numeric-type->interval y))))
1361 (result-type (numeric-contagion x y)))
1362 ;; If the result type is a float, we need to be sure to coerce
1363 ;; the bounds into the correct type.
1364 (when (eq (numeric-type-class result-type) 'float)
1365 (setf result (interval-func
1367 (coerce-for-bound x (or (numeric-type-format result-type)
1370 (make-numeric-type :class (numeric-type-class result-type)
1371 :format (numeric-type-format result-type)
1372 :low (interval-low result)
1373 :high (interval-high result)))
1374 (numeric-contagion x y)))
1376 (defoptimizer (/ derive-type) ((x y))
1377 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1381 (defun ash-derive-type-aux (n-type shift same-arg)
1382 (declare (ignore same-arg))
1383 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1384 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1385 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1386 ;; two bignums yielding zero) and it's hard to avoid that
1387 ;; calculation in here.
1388 #+(and cmu sb-xc-host)
1389 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1390 (typep (numeric-type-high n-type) 'bignum))
1391 (or (typep (numeric-type-low shift) 'bignum)
1392 (typep (numeric-type-high shift) 'bignum)))
1393 (return-from ash-derive-type-aux *universal-type*))
1394 (flet ((ash-outer (n s)
1395 (when (and (fixnump s)
1397 (> s sb!xc:most-negative-fixnum))
1399 ;; KLUDGE: The bare 64's here should be related to
1400 ;; symbolic machine word size values somehow.
1403 (if (and (fixnump s)
1404 (> s sb!xc:most-negative-fixnum))
1406 (if (minusp n) -1 0))))
1407 (or (and (csubtypep n-type (specifier-type 'integer))
1408 (csubtypep shift (specifier-type 'integer))
1409 (let ((n-low (numeric-type-low n-type))
1410 (n-high (numeric-type-high n-type))
1411 (s-low (numeric-type-low shift))
1412 (s-high (numeric-type-high shift)))
1413 (make-numeric-type :class 'integer :complexp :real
1416 (ash-outer n-low s-high)
1417 (ash-inner n-low s-low)))
1420 (ash-inner n-high s-low)
1421 (ash-outer n-high s-high))))))
1424 (defoptimizer (ash derive-type) ((n shift))
1425 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1427 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1428 (macrolet ((frob (fun)
1429 `#'(lambda (type type2)
1430 (declare (ignore type2))
1431 (let ((lo (numeric-type-low type))
1432 (hi (numeric-type-high type)))
1433 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1435 (defoptimizer (%negate derive-type) ((num))
1436 (derive-integer-type num num (frob -))))
1438 (defun lognot-derive-type-aux (int)
1439 (derive-integer-type-aux int int
1440 (lambda (type type2)
1441 (declare (ignore type2))
1442 (let ((lo (numeric-type-low type))
1443 (hi (numeric-type-high type)))
1444 (values (if hi (lognot hi) nil)
1445 (if lo (lognot lo) nil)
1446 (numeric-type-class type)
1447 (numeric-type-format type))))))
1449 (defoptimizer (lognot derive-type) ((int))
1450 (lognot-derive-type-aux (lvar-type int)))
1452 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1453 (defoptimizer (%negate derive-type) ((num))
1454 (flet ((negate-bound (b)
1456 (set-bound (- (type-bound-number b))
1458 (one-arg-derive-type num
1460 (modified-numeric-type
1462 :low (negate-bound (numeric-type-high type))
1463 :high (negate-bound (numeric-type-low type))))
1466 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1467 (defoptimizer (abs derive-type) ((num))
1468 (let ((type (lvar-type num)))
1469 (if (and (numeric-type-p type)
1470 (eq (numeric-type-class type) 'integer)
1471 (eq (numeric-type-complexp type) :real))
1472 (let ((lo (numeric-type-low type))
1473 (hi (numeric-type-high type)))
1474 (make-numeric-type :class 'integer :complexp :real
1475 :low (cond ((and hi (minusp hi))
1481 :high (if (and hi lo)
1482 (max (abs hi) (abs lo))
1484 (numeric-contagion type type))))
1486 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1487 (defun abs-derive-type-aux (type)
1488 (cond ((eq (numeric-type-complexp type) :complex)
1489 ;; The absolute value of a complex number is always a
1490 ;; non-negative float.
1491 (let* ((format (case (numeric-type-class type)
1492 ((integer rational) 'single-float)
1493 (t (numeric-type-format type))))
1494 (bound-format (or format 'float)))
1495 (make-numeric-type :class 'float
1498 :low (coerce 0 bound-format)
1501 ;; The absolute value of a real number is a non-negative real
1502 ;; of the same type.
1503 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1504 (class (numeric-type-class type))
1505 (format (numeric-type-format type))
1506 (bound-type (or format class 'real)))
1511 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1512 :high (coerce-and-truncate-floats
1513 (interval-high abs-bnd) bound-type))))))
1515 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1516 (defoptimizer (abs derive-type) ((num))
1517 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1519 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1520 (defoptimizer (truncate derive-type) ((number divisor))
1521 (let ((number-type (lvar-type number))
1522 (divisor-type (lvar-type divisor))
1523 (integer-type (specifier-type 'integer)))
1524 (if (and (numeric-type-p number-type)
1525 (csubtypep number-type integer-type)
1526 (numeric-type-p divisor-type)
1527 (csubtypep divisor-type integer-type))
1528 (let ((number-low (numeric-type-low number-type))
1529 (number-high (numeric-type-high number-type))
1530 (divisor-low (numeric-type-low divisor-type))
1531 (divisor-high (numeric-type-high divisor-type)))
1532 (values-specifier-type
1533 `(values ,(integer-truncate-derive-type number-low number-high
1534 divisor-low divisor-high)
1535 ,(integer-rem-derive-type number-low number-high
1536 divisor-low divisor-high))))
1539 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1542 (defun rem-result-type (number-type divisor-type)
1543 ;; Figure out what the remainder type is. The remainder is an
1544 ;; integer if both args are integers; a rational if both args are
1545 ;; rational; and a float otherwise.
1546 (cond ((and (csubtypep number-type (specifier-type 'integer))
1547 (csubtypep divisor-type (specifier-type 'integer)))
1549 ((and (csubtypep number-type (specifier-type 'rational))
1550 (csubtypep divisor-type (specifier-type 'rational)))
1552 ((and (csubtypep number-type (specifier-type 'float))
1553 (csubtypep divisor-type (specifier-type 'float)))
1554 ;; Both are floats so the result is also a float, of
1555 ;; the largest type.
1556 (or (float-format-max (numeric-type-format number-type)
1557 (numeric-type-format divisor-type))
1559 ((and (csubtypep number-type (specifier-type 'float))
1560 (csubtypep divisor-type (specifier-type 'rational)))
1561 ;; One of the arguments is a float and the other is a
1562 ;; rational. The remainder is a float of the same
1564 (or (numeric-type-format number-type) 'float))
1565 ((and (csubtypep divisor-type (specifier-type 'float))
1566 (csubtypep number-type (specifier-type 'rational)))
1567 ;; One of the arguments is a float and the other is a
1568 ;; rational. The remainder is a float of the same
1570 (or (numeric-type-format divisor-type) 'float))
1572 ;; Some unhandled combination. This usually means both args
1573 ;; are REAL so the result is a REAL.
1576 (defun truncate-derive-type-quot (number-type divisor-type)
1577 (let* ((rem-type (rem-result-type number-type divisor-type))
1578 (number-interval (numeric-type->interval number-type))
1579 (divisor-interval (numeric-type->interval divisor-type)))
1580 ;;(declare (type (member '(integer rational float)) rem-type))
1581 ;; We have real numbers now.
1582 (cond ((eq rem-type 'integer)
1583 ;; Since the remainder type is INTEGER, both args are
1585 (let* ((res (integer-truncate-derive-type
1586 (interval-low number-interval)
1587 (interval-high number-interval)
1588 (interval-low divisor-interval)
1589 (interval-high divisor-interval))))
1590 (specifier-type (if (listp res) res 'integer))))
1592 (let ((quot (truncate-quotient-bound
1593 (interval-div number-interval
1594 divisor-interval))))
1595 (specifier-type `(integer ,(or (interval-low quot) '*)
1596 ,(or (interval-high quot) '*))))))))
1598 (defun truncate-derive-type-rem (number-type divisor-type)
1599 (let* ((rem-type (rem-result-type number-type divisor-type))
1600 (number-interval (numeric-type->interval number-type))
1601 (divisor-interval (numeric-type->interval divisor-type))
1602 (rem (truncate-rem-bound number-interval divisor-interval)))
1603 ;;(declare (type (member '(integer rational float)) rem-type))
1604 ;; We have real numbers now.
1605 (cond ((eq rem-type 'integer)
1606 ;; Since the remainder type is INTEGER, both args are
1608 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1609 ,(or (interval-high rem) '*))))
1611 (multiple-value-bind (class format)
1614 (values 'integer nil))
1616 (values 'rational nil))
1617 ((or single-float double-float #!+long-float long-float)
1618 (values 'float rem-type))
1620 (values 'float nil))
1623 (when (member rem-type '(float single-float double-float
1624 #!+long-float long-float))
1625 (setf rem (interval-func #'(lambda (x)
1626 (coerce-for-bound x rem-type))
1628 (make-numeric-type :class class
1630 :low (interval-low rem)
1631 :high (interval-high rem)))))))
1633 (defun truncate-derive-type-quot-aux (num div same-arg)
1634 (declare (ignore same-arg))
1635 (if (and (numeric-type-real-p num)
1636 (numeric-type-real-p div))
1637 (truncate-derive-type-quot num div)
1640 (defun truncate-derive-type-rem-aux (num div same-arg)
1641 (declare (ignore same-arg))
1642 (if (and (numeric-type-real-p num)
1643 (numeric-type-real-p div))
1644 (truncate-derive-type-rem num div)
1647 (defoptimizer (truncate derive-type) ((number divisor))
1648 (let ((quot (two-arg-derive-type number divisor
1649 #'truncate-derive-type-quot-aux #'truncate))
1650 (rem (two-arg-derive-type number divisor
1651 #'truncate-derive-type-rem-aux #'rem)))
1652 (when (and quot rem)
1653 (make-values-type :required (list quot rem)))))
1655 (defun ftruncate-derive-type-quot (number-type divisor-type)
1656 ;; The bounds are the same as for truncate. However, the first
1657 ;; result is a float of some type. We need to determine what that
1658 ;; type is. Basically it's the more contagious of the two types.
1659 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1660 (res-type (numeric-contagion number-type divisor-type)))
1661 (make-numeric-type :class 'float
1662 :format (numeric-type-format res-type)
1663 :low (numeric-type-low q-type)
1664 :high (numeric-type-high q-type))))
1666 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1667 (declare (ignore same-arg))
1668 (if (and (numeric-type-real-p n)
1669 (numeric-type-real-p d))
1670 (ftruncate-derive-type-quot n d)
1673 (defoptimizer (ftruncate derive-type) ((number divisor))
1675 (two-arg-derive-type number divisor
1676 #'ftruncate-derive-type-quot-aux #'ftruncate))
1677 (rem (two-arg-derive-type number divisor
1678 #'truncate-derive-type-rem-aux #'rem)))
1679 (when (and quot rem)
1680 (make-values-type :required (list quot rem)))))
1682 (defun %unary-truncate-derive-type-aux (number)
1683 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1685 (defoptimizer (%unary-truncate derive-type) ((number))
1686 (one-arg-derive-type number
1687 #'%unary-truncate-derive-type-aux
1690 (defoptimizer (%unary-ftruncate derive-type) ((number))
1691 (let ((divisor (specifier-type '(integer 1 1))))
1692 (one-arg-derive-type number
1694 (ftruncate-derive-type-quot-aux n divisor nil))
1695 #'%unary-ftruncate)))
1697 ;;; Define optimizers for FLOOR and CEILING.
1699 ((def (name q-name r-name)
1700 (let ((q-aux (symbolicate q-name "-AUX"))
1701 (r-aux (symbolicate r-name "-AUX")))
1703 ;; Compute type of quotient (first) result.
1704 (defun ,q-aux (number-type divisor-type)
1705 (let* ((number-interval
1706 (numeric-type->interval number-type))
1708 (numeric-type->interval divisor-type))
1709 (quot (,q-name (interval-div number-interval
1710 divisor-interval))))
1711 (specifier-type `(integer ,(or (interval-low quot) '*)
1712 ,(or (interval-high quot) '*)))))
1713 ;; Compute type of remainder.
1714 (defun ,r-aux (number-type divisor-type)
1715 (let* ((divisor-interval
1716 (numeric-type->interval divisor-type))
1717 (rem (,r-name divisor-interval))
1718 (result-type (rem-result-type number-type divisor-type)))
1719 (multiple-value-bind (class format)
1722 (values 'integer nil))
1724 (values 'rational nil))
1725 ((or single-float double-float #!+long-float long-float)
1726 (values 'float result-type))
1728 (values 'float nil))
1731 (when (member result-type '(float single-float double-float
1732 #!+long-float long-float))
1733 ;; Make sure that the limits on the interval have
1735 (setf rem (interval-func (lambda (x)
1736 (coerce-for-bound x result-type))
1738 (make-numeric-type :class class
1740 :low (interval-low rem)
1741 :high (interval-high rem)))))
1742 ;; the optimizer itself
1743 (defoptimizer (,name derive-type) ((number divisor))
1744 (flet ((derive-q (n d same-arg)
1745 (declare (ignore same-arg))
1746 (if (and (numeric-type-real-p n)
1747 (numeric-type-real-p d))
1750 (derive-r (n d same-arg)
1751 (declare (ignore same-arg))
1752 (if (and (numeric-type-real-p n)
1753 (numeric-type-real-p d))
1756 (let ((quot (two-arg-derive-type
1757 number divisor #'derive-q #',name))
1758 (rem (two-arg-derive-type
1759 number divisor #'derive-r #'mod)))
1760 (when (and quot rem)
1761 (make-values-type :required (list quot rem))))))))))
1763 (def floor floor-quotient-bound floor-rem-bound)
1764 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1766 ;;; Define optimizers for FFLOOR and FCEILING
1767 (macrolet ((def (name q-name r-name)
1768 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1769 (r-aux (symbolicate r-name "-AUX")))
1771 ;; Compute type of quotient (first) result.
1772 (defun ,q-aux (number-type divisor-type)
1773 (let* ((number-interval
1774 (numeric-type->interval number-type))
1776 (numeric-type->interval divisor-type))
1777 (quot (,q-name (interval-div number-interval
1779 (res-type (numeric-contagion number-type
1782 :class (numeric-type-class res-type)
1783 :format (numeric-type-format res-type)
1784 :low (interval-low quot)
1785 :high (interval-high quot))))
1787 (defoptimizer (,name derive-type) ((number divisor))
1788 (flet ((derive-q (n d same-arg)
1789 (declare (ignore same-arg))
1790 (if (and (numeric-type-real-p n)
1791 (numeric-type-real-p d))
1794 (derive-r (n d same-arg)
1795 (declare (ignore same-arg))
1796 (if (and (numeric-type-real-p n)
1797 (numeric-type-real-p d))
1800 (let ((quot (two-arg-derive-type
1801 number divisor #'derive-q #',name))
1802 (rem (two-arg-derive-type
1803 number divisor #'derive-r #'mod)))
1804 (when (and quot rem)
1805 (make-values-type :required (list quot rem))))))))))
1807 (def ffloor floor-quotient-bound floor-rem-bound)
1808 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
1810 ;;; functions to compute the bounds on the quotient and remainder for
1811 ;;; the FLOOR function
1812 (defun floor-quotient-bound (quot)
1813 ;; Take the floor of the quotient and then massage it into what we
1815 (let ((lo (interval-low quot))
1816 (hi (interval-high quot)))
1817 ;; Take the floor of the lower bound. The result is always a
1818 ;; closed lower bound.
1820 (floor (type-bound-number lo))
1822 ;; For the upper bound, we need to be careful.
1825 ;; An open bound. We need to be careful here because
1826 ;; the floor of '(10.0) is 9, but the floor of
1828 (multiple-value-bind (q r) (floor (first hi))
1833 ;; A closed bound, so the answer is obvious.
1837 (make-interval :low lo :high hi)))
1838 (defun floor-rem-bound (div)
1839 ;; The remainder depends only on the divisor. Try to get the
1840 ;; correct sign for the remainder if we can.
1841 (case (interval-range-info div)
1843 ;; The divisor is always positive.
1844 (let ((rem (interval-abs div)))
1845 (setf (interval-low rem) 0)
1846 (when (and (numberp (interval-high rem))
1847 (not (zerop (interval-high rem))))
1848 ;; The remainder never contains the upper bound. However,
1849 ;; watch out for the case where the high limit is zero!
1850 (setf (interval-high rem) (list (interval-high rem))))
1853 ;; The divisor is always negative.
1854 (let ((rem (interval-neg (interval-abs div))))
1855 (setf (interval-high rem) 0)
1856 (when (numberp (interval-low rem))
1857 ;; The remainder never contains the lower bound.
1858 (setf (interval-low rem) (list (interval-low rem))))
1861 ;; The divisor can be positive or negative. All bets off. The
1862 ;; magnitude of remainder is the maximum value of the divisor.
1863 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1864 ;; The bound never reaches the limit, so make the interval open.
1865 (make-interval :low (if limit
1868 :high (list limit))))))
1870 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1871 => #S(INTERVAL :LOW 0 :HIGH 10)
1872 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1873 => #S(INTERVAL :LOW 0 :HIGH 10)
1874 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1875 => #S(INTERVAL :LOW 0 :HIGH 10)
1876 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1877 => #S(INTERVAL :LOW 0 :HIGH 9)
1878 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1879 => #S(INTERVAL :LOW 0 :HIGH 10)
1880 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1881 => #S(INTERVAL :LOW 0 :HIGH 10)
1882 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1883 => #S(INTERVAL :LOW -2 :HIGH 10)
1884 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1885 => #S(INTERVAL :LOW -1 :HIGH 10)
1886 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1887 => #S(INTERVAL :LOW -1 :HIGH 10)
1889 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1890 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1891 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1892 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1893 (floor-rem-bound (make-interval :low -10 :high -2.3))
1894 #S(INTERVAL :LOW (-10) :HIGH 0)
1895 (floor-rem-bound (make-interval :low 0.3 :high 10))
1896 => #S(INTERVAL :LOW 0 :HIGH '(10))
1897 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1898 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1899 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1900 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1903 ;;; same functions for CEILING
1904 (defun ceiling-quotient-bound (quot)
1905 ;; Take the ceiling of the quotient and then massage it into what we
1907 (let ((lo (interval-low quot))
1908 (hi (interval-high quot)))
1909 ;; Take the ceiling of the upper bound. The result is always a
1910 ;; closed upper bound.
1912 (ceiling (type-bound-number hi))
1914 ;; For the lower bound, we need to be careful.
1917 ;; An open bound. We need to be careful here because
1918 ;; the ceiling of '(10.0) is 11, but the ceiling of
1920 (multiple-value-bind (q r) (ceiling (first lo))
1925 ;; A closed bound, so the answer is obvious.
1929 (make-interval :low lo :high hi)))
1930 (defun ceiling-rem-bound (div)
1931 ;; The remainder depends only on the divisor. Try to get the
1932 ;; correct sign for the remainder if we can.
1933 (case (interval-range-info div)
1935 ;; Divisor is always positive. The remainder is negative.
1936 (let ((rem (interval-neg (interval-abs div))))
1937 (setf (interval-high rem) 0)
1938 (when (and (numberp (interval-low rem))
1939 (not (zerop (interval-low rem))))
1940 ;; The remainder never contains the upper bound. However,
1941 ;; watch out for the case when the upper bound is zero!
1942 (setf (interval-low rem) (list (interval-low rem))))
1945 ;; Divisor is always negative. The remainder is positive
1946 (let ((rem (interval-abs div)))
1947 (setf (interval-low rem) 0)
1948 (when (numberp (interval-high rem))
1949 ;; The remainder never contains the lower bound.
1950 (setf (interval-high rem) (list (interval-high rem))))
1953 ;; The divisor can be positive or negative. All bets off. The
1954 ;; magnitude of remainder is the maximum value of the divisor.
1955 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1956 ;; The bound never reaches the limit, so make the interval open.
1957 (make-interval :low (if limit
1960 :high (list limit))))))
1963 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
1964 => #S(INTERVAL :LOW 1 :HIGH 11)
1965 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1966 => #S(INTERVAL :LOW 1 :HIGH 11)
1967 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
1968 => #S(INTERVAL :LOW 1 :HIGH 10)
1969 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
1970 => #S(INTERVAL :LOW 1 :HIGH 10)
1971 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
1972 => #S(INTERVAL :LOW 1 :HIGH 11)
1973 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
1974 => #S(INTERVAL :LOW 1 :HIGH 11)
1975 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1976 => #S(INTERVAL :LOW -1 :HIGH 11)
1977 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1978 => #S(INTERVAL :LOW 0 :HIGH 11)
1979 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
1980 => #S(INTERVAL :LOW -1 :HIGH 11)
1982 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
1983 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
1984 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
1985 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1986 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
1987 => #S(INTERVAL :LOW 0 :HIGH (10))
1988 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
1989 => #S(INTERVAL :LOW (-10) :HIGH 0)
1990 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
1991 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
1992 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
1993 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1996 (defun truncate-quotient-bound (quot)
1997 ;; For positive quotients, truncate is exactly like floor. For
1998 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
1999 ;; it's the union of the two pieces.
2000 (case (interval-range-info quot)
2003 (floor-quotient-bound quot))
2005 ;; just like CEILING
2006 (ceiling-quotient-bound quot))
2008 ;; Split the interval into positive and negative pieces, compute
2009 ;; the result for each piece and put them back together.
2010 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2011 (interval-merge-pair (ceiling-quotient-bound neg)
2012 (floor-quotient-bound pos))))))
2014 (defun truncate-rem-bound (num div)
2015 ;; This is significantly more complicated than FLOOR or CEILING. We
2016 ;; need both the number and the divisor to determine the range. The
2017 ;; basic idea is to split the ranges of NUM and DEN into positive
2018 ;; and negative pieces and deal with each of the four possibilities
2020 (case (interval-range-info num)
2022 (case (interval-range-info div)
2024 (floor-rem-bound div))
2026 (ceiling-rem-bound div))
2028 (destructuring-bind (neg pos) (interval-split 0 div t t)
2029 (interval-merge-pair (truncate-rem-bound num neg)
2030 (truncate-rem-bound num pos))))))
2032 (case (interval-range-info div)
2034 (ceiling-rem-bound div))
2036 (floor-rem-bound div))
2038 (destructuring-bind (neg pos) (interval-split 0 div t t)
2039 (interval-merge-pair (truncate-rem-bound num neg)
2040 (truncate-rem-bound num pos))))))
2042 (destructuring-bind (neg pos) (interval-split 0 num t t)
2043 (interval-merge-pair (truncate-rem-bound neg div)
2044 (truncate-rem-bound pos div))))))
2047 ;;; Derive useful information about the range. Returns three values:
2048 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2049 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2050 ;;; - The abs of the maximal value if there is one, or nil if it is
2052 (defun numeric-range-info (low high)
2053 (cond ((and low (not (minusp low)))
2054 (values '+ low high))
2055 ((and high (not (plusp high)))
2056 (values '- (- high) (if low (- low) nil)))
2058 (values nil 0 (and low high (max (- low) high))))))
2060 (defun integer-truncate-derive-type
2061 (number-low number-high divisor-low divisor-high)
2062 ;; The result cannot be larger in magnitude than the number, but the
2063 ;; sign might change. If we can determine the sign of either the
2064 ;; number or the divisor, we can eliminate some of the cases.
2065 (multiple-value-bind (number-sign number-min number-max)
2066 (numeric-range-info number-low number-high)
2067 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2068 (numeric-range-info divisor-low divisor-high)
2069 (when (and divisor-max (zerop divisor-max))
2070 ;; We've got a problem: guaranteed division by zero.
2071 (return-from integer-truncate-derive-type t))
2072 (when (zerop divisor-min)
2073 ;; We'll assume that they aren't going to divide by zero.
2075 (cond ((and number-sign divisor-sign)
2076 ;; We know the sign of both.
2077 (if (eq number-sign divisor-sign)
2078 ;; Same sign, so the result will be positive.
2079 `(integer ,(if divisor-max
2080 (truncate number-min divisor-max)
2083 (truncate number-max divisor-min)
2085 ;; Different signs, the result will be negative.
2086 `(integer ,(if number-max
2087 (- (truncate number-max divisor-min))
2090 (- (truncate number-min divisor-max))
2092 ((eq divisor-sign '+)
2093 ;; The divisor is positive. Therefore, the number will just
2094 ;; become closer to zero.
2095 `(integer ,(if number-low
2096 (truncate number-low divisor-min)
2099 (truncate number-high divisor-min)
2101 ((eq divisor-sign '-)
2102 ;; The divisor is negative. Therefore, the absolute value of
2103 ;; the number will become closer to zero, but the sign will also
2105 `(integer ,(if number-high
2106 (- (truncate number-high divisor-min))
2109 (- (truncate number-low divisor-min))
2111 ;; The divisor could be either positive or negative.
2113 ;; The number we are dividing has a bound. Divide that by the
2114 ;; smallest posible divisor.
2115 (let ((bound (truncate number-max divisor-min)))
2116 `(integer ,(- bound) ,bound)))
2118 ;; The number we are dividing is unbounded, so we can't tell
2119 ;; anything about the result.
2122 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2123 (defun integer-rem-derive-type
2124 (number-low number-high divisor-low divisor-high)
2125 (if (and divisor-low divisor-high)
2126 ;; We know the range of the divisor, and the remainder must be
2127 ;; smaller than the divisor. We can tell the sign of the
2128 ;; remainer if we know the sign of the number.
2129 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2130 `(integer ,(if (or (null number-low)
2131 (minusp number-low))
2134 ,(if (or (null number-high)
2135 (plusp number-high))
2138 ;; The divisor is potentially either very positive or very
2139 ;; negative. Therefore, the remainer is unbounded, but we might
2140 ;; be able to tell something about the sign from the number.
2141 `(integer ,(if (and number-low (not (minusp number-low)))
2142 ;; The number we are dividing is positive.
2143 ;; Therefore, the remainder must be positive.
2146 ,(if (and number-high (not (plusp number-high)))
2147 ;; The number we are dividing is negative.
2148 ;; Therefore, the remainder must be negative.
2152 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2153 (defoptimizer (random derive-type) ((bound &optional state))
2154 (let ((type (lvar-type bound)))
2155 (when (numeric-type-p type)
2156 (let ((class (numeric-type-class type))
2157 (high (numeric-type-high type))
2158 (format (numeric-type-format type)))
2162 :low (coerce 0 (or format class 'real))
2163 :high (cond ((not high) nil)
2164 ((eq class 'integer) (max (1- high) 0))
2165 ((or (consp high) (zerop high)) high)
2168 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2169 (defun random-derive-type-aux (type)
2170 (let ((class (numeric-type-class type))
2171 (high (numeric-type-high type))
2172 (format (numeric-type-format type)))
2176 :low (coerce 0 (or format class 'real))
2177 :high (cond ((not high) nil)
2178 ((eq class 'integer) (max (1- high) 0))
2179 ((or (consp high) (zerop high)) high)
2182 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2183 (defoptimizer (random derive-type) ((bound &optional state))
2184 (one-arg-derive-type bound #'random-derive-type-aux nil))
2186 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2188 ;;; Return the maximum number of bits an integer of the supplied type
2189 ;;; can take up, or NIL if it is unbounded. The second (third) value
2190 ;;; is T if the integer can be positive (negative) and NIL if not.
2191 ;;; Zero counts as positive.
2192 (defun integer-type-length (type)
2193 (if (numeric-type-p type)
2194 (let ((min (numeric-type-low type))
2195 (max (numeric-type-high type)))
2196 (values (and min max (max (integer-length min) (integer-length max)))
2197 (or (null max) (not (minusp max)))
2198 (or (null min) (minusp min))))
2201 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2202 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2203 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2204 ;;; versions in CMUCL, from which these functions copy liberally.
2206 (defun logand-derive-unsigned-low-bound (x y)
2207 (let ((a (numeric-type-low x))
2208 (b (numeric-type-high x))
2209 (c (numeric-type-low y))
2210 (d (numeric-type-high y)))
2211 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2213 (unless (zerop (logand m (lognot a) (lognot c)))
2214 (let ((temp (logandc2 (logior a m) (1- m))))
2218 (setf temp (logandc2 (logior c m) (1- m)))
2222 finally (return (logand a c)))))
2224 (defun logand-derive-unsigned-high-bound (x y)
2225 (let ((a (numeric-type-low x))
2226 (b (numeric-type-high x))
2227 (c (numeric-type-low y))
2228 (d (numeric-type-high y)))
2229 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2232 ((not (zerop (logand b (lognot d) m)))
2233 (let ((temp (logior (logandc2 b m) (1- m))))
2237 ((not (zerop (logand (lognot b) d m)))
2238 (let ((temp (logior (logandc2 d m) (1- m))))
2242 finally (return (logand b d)))))
2244 (defun logand-derive-type-aux (x y &optional same-leaf)
2246 (return-from logand-derive-type-aux x))
2247 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2248 (declare (ignore x-pos))
2249 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2250 (declare (ignore y-pos))
2252 ;; X must be positive.
2254 ;; They must both be positive.
2255 (cond ((and (null x-len) (null y-len))
2256 (specifier-type 'unsigned-byte))
2258 (specifier-type `(unsigned-byte* ,y-len)))
2260 (specifier-type `(unsigned-byte* ,x-len)))
2262 (let ((low (logand-derive-unsigned-low-bound x y))
2263 (high (logand-derive-unsigned-high-bound x y)))
2264 (specifier-type `(integer ,low ,high)))))
2265 ;; X is positive, but Y might be negative.
2267 (specifier-type 'unsigned-byte))
2269 (specifier-type `(unsigned-byte* ,x-len)))))
2270 ;; X might be negative.
2272 ;; Y must be positive.
2274 (specifier-type 'unsigned-byte))
2275 (t (specifier-type `(unsigned-byte* ,y-len))))
2276 ;; Either might be negative.
2277 (if (and x-len y-len)
2278 ;; The result is bounded.
2279 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2280 ;; We can't tell squat about the result.
2281 (specifier-type 'integer)))))))
2283 (defun logior-derive-unsigned-low-bound (x y)
2284 (let ((a (numeric-type-low x))
2285 (b (numeric-type-high x))
2286 (c (numeric-type-low y))
2287 (d (numeric-type-high y)))
2288 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2291 ((not (zerop (logandc2 (logand c m) a)))
2292 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2296 ((not (zerop (logandc2 (logand a m) c)))
2297 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2301 finally (return (logior a c)))))
2303 (defun logior-derive-unsigned-high-bound (x y)
2304 (let ((a (numeric-type-low x))
2305 (b (numeric-type-high x))
2306 (c (numeric-type-low y))
2307 (d (numeric-type-high y)))
2308 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2310 (unless (zerop (logand b d m))
2311 (let ((temp (logior (- b m) (1- m))))
2315 (setf temp (logior (- d m) (1- m)))
2319 finally (return (logior b d)))))
2321 (defun logior-derive-type-aux (x y &optional same-leaf)
2323 (return-from logior-derive-type-aux x))
2324 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2325 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2327 ((and (not x-neg) (not y-neg))
2328 ;; Both are positive.
2329 (if (and x-len y-len)
2330 (let ((low (logior-derive-unsigned-low-bound x y))
2331 (high (logior-derive-unsigned-high-bound x y)))
2332 (specifier-type `(integer ,low ,high)))
2333 (specifier-type `(unsigned-byte* *))))
2335 ;; X must be negative.
2337 ;; Both are negative. The result is going to be negative
2338 ;; and be the same length or shorter than the smaller.
2339 (if (and x-len y-len)
2341 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2343 (specifier-type '(integer * -1)))
2344 ;; X is negative, but we don't know about Y. The result
2345 ;; will be negative, but no more negative than X.
2347 `(integer ,(or (numeric-type-low x) '*)
2350 ;; X might be either positive or negative.
2352 ;; But Y is negative. The result will be negative.
2354 `(integer ,(or (numeric-type-low y) '*)
2356 ;; We don't know squat about either. It won't get any bigger.
2357 (if (and x-len y-len)
2359 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2361 (specifier-type 'integer))))))))
2363 (defun logxor-derive-unsigned-low-bound (x y)
2364 (let ((a (numeric-type-low x))
2365 (b (numeric-type-high x))
2366 (c (numeric-type-low y))
2367 (d (numeric-type-high y)))
2368 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2371 ((not (zerop (logandc2 (logand c m) a)))
2372 (let ((temp (logand (logior a m)
2376 ((not (zerop (logandc2 (logand a m) c)))
2377 (let ((temp (logand (logior c m)
2381 finally (return (logxor a c)))))
2383 (defun logxor-derive-unsigned-high-bound (x y)
2384 (let ((a (numeric-type-low x))
2385 (b (numeric-type-high x))
2386 (c (numeric-type-low y))
2387 (d (numeric-type-high y)))
2388 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2390 (unless (zerop (logand b d m))
2391 (let ((temp (logior (- b m) (1- m))))
2393 ((>= temp a) (setf b temp))
2394 (t (let ((temp (logior (- d m) (1- m))))
2397 finally (return (logxor b d)))))
2399 (defun logxor-derive-type-aux (x y &optional same-leaf)
2401 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2402 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2403 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2405 ((and (not x-neg) (not y-neg))
2406 ;; Both are positive
2407 (if (and x-len y-len)
2408 (let ((low (logxor-derive-unsigned-low-bound x y))
2409 (high (logxor-derive-unsigned-high-bound x y)))
2410 (specifier-type `(integer ,low ,high)))
2411 (specifier-type '(unsigned-byte* *))))
2412 ((and (not x-pos) (not y-pos))
2413 ;; Both are negative. The result will be positive, and as long
2415 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2418 ((or (and (not x-pos) (not y-neg))
2419 (and (not y-pos) (not x-neg)))
2420 ;; Either X is negative and Y is positive or vice-versa. The
2421 ;; result will be negative.
2422 (specifier-type `(integer ,(if (and x-len y-len)
2423 (ash -1 (max x-len y-len))
2426 ;; We can't tell what the sign of the result is going to be.
2427 ;; All we know is that we don't create new bits.
2429 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2431 (specifier-type 'integer))))))
2433 (macrolet ((deffrob (logfun)
2434 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2435 `(defoptimizer (,logfun derive-type) ((x y))
2436 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2441 (defoptimizer (logeqv derive-type) ((x y))
2442 (two-arg-derive-type x y (lambda (x y same-leaf)
2443 (lognot-derive-type-aux
2444 (logxor-derive-type-aux x y same-leaf)))
2446 (defoptimizer (lognand derive-type) ((x y))
2447 (two-arg-derive-type x y (lambda (x y same-leaf)
2448 (lognot-derive-type-aux
2449 (logand-derive-type-aux x y same-leaf)))
2451 (defoptimizer (lognor derive-type) ((x y))
2452 (two-arg-derive-type x y (lambda (x y same-leaf)
2453 (lognot-derive-type-aux
2454 (logior-derive-type-aux x y same-leaf)))
2456 (defoptimizer (logandc1 derive-type) ((x y))
2457 (two-arg-derive-type x y (lambda (x y same-leaf)
2459 (specifier-type '(eql 0))
2460 (logand-derive-type-aux
2461 (lognot-derive-type-aux x) y nil)))
2463 (defoptimizer (logandc2 derive-type) ((x y))
2464 (two-arg-derive-type x y (lambda (x y same-leaf)
2466 (specifier-type '(eql 0))
2467 (logand-derive-type-aux
2468 x (lognot-derive-type-aux y) nil)))
2470 (defoptimizer (logorc1 derive-type) ((x y))
2471 (two-arg-derive-type x y (lambda (x y same-leaf)
2473 (specifier-type '(eql -1))
2474 (logior-derive-type-aux
2475 (lognot-derive-type-aux x) y nil)))
2477 (defoptimizer (logorc2 derive-type) ((x y))
2478 (two-arg-derive-type x y (lambda (x y same-leaf)
2480 (specifier-type '(eql -1))
2481 (logior-derive-type-aux
2482 x (lognot-derive-type-aux y) nil)))
2485 ;;;; miscellaneous derive-type methods
2487 (defoptimizer (integer-length derive-type) ((x))
2488 (let ((x-type (lvar-type x)))
2489 (when (numeric-type-p x-type)
2490 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2491 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2492 ;; careful about LO or HI being NIL, though. Also, if 0 is
2493 ;; contained in X, the lower bound is obviously 0.
2494 (flet ((null-or-min (a b)
2495 (and a b (min (integer-length a)
2496 (integer-length b))))
2498 (and a b (max (integer-length a)
2499 (integer-length b)))))
2500 (let* ((min (numeric-type-low x-type))
2501 (max (numeric-type-high x-type))
2502 (min-len (null-or-min min max))
2503 (max-len (null-or-max min max)))
2504 (when (ctypep 0 x-type)
2506 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2508 (defoptimizer (isqrt derive-type) ((x))
2509 (let ((x-type (lvar-type x)))
2510 (when (numeric-type-p x-type)
2511 (let* ((lo (numeric-type-low x-type))
2512 (hi (numeric-type-high x-type))
2513 (lo-res (if lo (isqrt lo) '*))
2514 (hi-res (if hi (isqrt hi) '*)))
2515 (specifier-type `(integer ,lo-res ,hi-res))))))
2517 (defoptimizer (code-char derive-type) ((code))
2518 (let ((type (lvar-type code)))
2519 ;; FIXME: unions of integral ranges? It ought to be easier to do
2520 ;; this, given that CHARACTER-SET is basically an integral range
2521 ;; type. -- CSR, 2004-10-04
2522 (when (numeric-type-p type)
2523 (let* ((lo (numeric-type-low type))
2524 (hi (numeric-type-high type))
2525 (type (specifier-type `(character-set ((,lo . ,hi))))))
2527 ;; KLUDGE: when running on the host, we lose a slight amount
2528 ;; of precision so that we don't have to "unparse" types
2529 ;; that formally we can't, such as (CHARACTER-SET ((0
2530 ;; . 0))). -- CSR, 2004-10-06
2532 ((csubtypep type (specifier-type 'standard-char)) type)
2534 ((csubtypep type (specifier-type 'base-char))
2535 (specifier-type 'base-char))
2537 ((csubtypep type (specifier-type 'extended-char))
2538 (specifier-type 'extended-char))
2539 (t #+sb-xc-host (specifier-type 'character)
2540 #-sb-xc-host type))))))
2542 (defoptimizer (values derive-type) ((&rest values))
2543 (make-values-type :required (mapcar #'lvar-type values)))
2545 (defun signum-derive-type-aux (type)
2546 (if (eq (numeric-type-complexp type) :complex)
2547 (let* ((format (case (numeric-type-class type)
2548 ((integer rational) 'single-float)
2549 (t (numeric-type-format type))))
2550 (bound-format (or format 'float)))
2551 (make-numeric-type :class 'float
2554 :low (coerce -1 bound-format)
2555 :high (coerce 1 bound-format)))
2556 (let* ((interval (numeric-type->interval type))
2557 (range-info (interval-range-info interval))
2558 (contains-0-p (interval-contains-p 0 interval))
2559 (class (numeric-type-class type))
2560 (format (numeric-type-format type))
2561 (one (coerce 1 (or format class 'real)))
2562 (zero (coerce 0 (or format class 'real)))
2563 (minus-one (coerce -1 (or format class 'real)))
2564 (plus (make-numeric-type :class class :format format
2565 :low one :high one))
2566 (minus (make-numeric-type :class class :format format
2567 :low minus-one :high minus-one))
2568 ;; KLUDGE: here we have a fairly horrible hack to deal
2569 ;; with the schizophrenia in the type derivation engine.
2570 ;; The problem is that the type derivers reinterpret
2571 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2572 ;; 0d0) within the derivation mechanism doesn't include
2573 ;; -0d0. Ugh. So force it in here, instead.
2574 (zero (make-numeric-type :class class :format format
2575 :low (- zero) :high zero)))
2577 (+ (if contains-0-p (type-union plus zero) plus))
2578 (- (if contains-0-p (type-union minus zero) minus))
2579 (t (type-union minus zero plus))))))
2581 (defoptimizer (signum derive-type) ((num))
2582 (one-arg-derive-type num #'signum-derive-type-aux nil))
2584 ;;;; byte operations
2586 ;;;; We try to turn byte operations into simple logical operations.
2587 ;;;; First, we convert byte specifiers into separate size and position
2588 ;;;; arguments passed to internal %FOO functions. We then attempt to
2589 ;;;; transform the %FOO functions into boolean operations when the
2590 ;;;; size and position are constant and the operands are fixnums.
2592 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2593 ;; expressions that evaluate to the SIZE and POSITION of
2594 ;; the byte-specifier form SPEC. We may wrap a let around
2595 ;; the result of the body to bind some variables.
2597 ;; If the spec is a BYTE form, then bind the vars to the
2598 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2599 ;; and BYTE-POSITION. The goal of this transformation is to
2600 ;; avoid consing up byte specifiers and then immediately
2601 ;; throwing them away.
2602 (with-byte-specifier ((size-var pos-var spec) &body body)
2603 (once-only ((spec `(macroexpand ,spec))
2605 `(if (and (consp ,spec)
2606 (eq (car ,spec) 'byte)
2607 (= (length ,spec) 3))
2608 (let ((,size-var (second ,spec))
2609 (,pos-var (third ,spec)))
2611 (let ((,size-var `(byte-size ,,temp))
2612 (,pos-var `(byte-position ,,temp)))
2613 `(let ((,,temp ,,spec))
2616 (define-source-transform ldb (spec int)
2617 (with-byte-specifier (size pos spec)
2618 `(%ldb ,size ,pos ,int)))
2620 (define-source-transform dpb (newbyte spec int)
2621 (with-byte-specifier (size pos spec)
2622 `(%dpb ,newbyte ,size ,pos ,int)))
2624 (define-source-transform mask-field (spec int)
2625 (with-byte-specifier (size pos spec)
2626 `(%mask-field ,size ,pos ,int)))
2628 (define-source-transform deposit-field (newbyte spec int)
2629 (with-byte-specifier (size pos spec)
2630 `(%deposit-field ,newbyte ,size ,pos ,int))))
2632 (defoptimizer (%ldb derive-type) ((size posn num))
2633 (let ((size (lvar-type size)))
2634 (if (and (numeric-type-p size)
2635 (csubtypep size (specifier-type 'integer)))
2636 (let ((size-high (numeric-type-high size)))
2637 (if (and size-high (<= size-high sb!vm:n-word-bits))
2638 (specifier-type `(unsigned-byte* ,size-high))
2639 (specifier-type 'unsigned-byte)))
2642 (defoptimizer (%mask-field derive-type) ((size posn num))
2643 (let ((size (lvar-type size))
2644 (posn (lvar-type posn)))
2645 (if (and (numeric-type-p size)
2646 (csubtypep size (specifier-type 'integer))
2647 (numeric-type-p posn)
2648 (csubtypep posn (specifier-type 'integer)))
2649 (let ((size-high (numeric-type-high size))
2650 (posn-high (numeric-type-high posn)))
2651 (if (and size-high posn-high
2652 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2653 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2654 (specifier-type 'unsigned-byte)))
2657 (defun %deposit-field-derive-type-aux (size posn int)
2658 (let ((size (lvar-type size))
2659 (posn (lvar-type posn))
2660 (int (lvar-type int)))
2661 (when (and (numeric-type-p size)
2662 (numeric-type-p posn)
2663 (numeric-type-p int))
2664 (let ((size-high (numeric-type-high size))
2665 (posn-high (numeric-type-high posn))
2666 (high (numeric-type-high int))
2667 (low (numeric-type-low int)))
2668 (when (and size-high posn-high high low
2669 ;; KLUDGE: we need this cutoff here, otherwise we
2670 ;; will merrily derive the type of %DPB as
2671 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2672 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2673 ;; 1073741822))), with hilarious consequences. We
2674 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2675 ;; over a reasonable amount of shifting, even on
2676 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2677 ;; machine integers are 64-bits. -- CSR,
2679 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2680 (let ((raw-bit-count (max (integer-length high)
2681 (integer-length low)
2682 (+ size-high posn-high))))
2685 `(signed-byte ,(1+ raw-bit-count))
2686 `(unsigned-byte* ,raw-bit-count)))))))))
2688 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2689 (%deposit-field-derive-type-aux size posn int))
2691 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2692 (%deposit-field-derive-type-aux size posn int))
2694 (deftransform %ldb ((size posn int)
2695 (fixnum fixnum integer)
2696 (unsigned-byte #.sb!vm:n-word-bits))
2697 "convert to inline logical operations"
2698 `(logand (ash int (- posn))
2699 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2700 (- size ,sb!vm:n-word-bits))))
2702 (deftransform %mask-field ((size posn int)
2703 (fixnum fixnum integer)
2704 (unsigned-byte #.sb!vm:n-word-bits))
2705 "convert to inline logical operations"
2707 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2708 (- size ,sb!vm:n-word-bits))
2711 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2712 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2713 ;;; as the result type, as that would allow result types that cover
2714 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2715 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2717 (deftransform %dpb ((new size posn int)
2719 (unsigned-byte #.sb!vm:n-word-bits))
2720 "convert to inline logical operations"
2721 `(let ((mask (ldb (byte size 0) -1)))
2722 (logior (ash (logand new mask) posn)
2723 (logand int (lognot (ash mask posn))))))
2725 (deftransform %dpb ((new size posn int)
2727 (signed-byte #.sb!vm:n-word-bits))
2728 "convert to inline logical operations"
2729 `(let ((mask (ldb (byte size 0) -1)))
2730 (logior (ash (logand new mask) posn)
2731 (logand int (lognot (ash mask posn))))))
2733 (deftransform %deposit-field ((new size posn int)
2735 (unsigned-byte #.sb!vm:n-word-bits))
2736 "convert to inline logical operations"
2737 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2738 (logior (logand new mask)
2739 (logand int (lognot mask)))))
2741 (deftransform %deposit-field ((new size posn int)
2743 (signed-byte #.sb!vm:n-word-bits))
2744 "convert to inline logical operations"
2745 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2746 (logior (logand new mask)
2747 (logand int (lognot mask)))))
2749 (defoptimizer (mask-signed-field derive-type) ((size x))
2750 (let ((size (lvar-type size)))
2751 (if (numeric-type-p size)
2752 (let ((size-high (numeric-type-high size)))
2753 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2754 (specifier-type `(signed-byte ,size-high))
2759 ;;; Modular functions
2761 ;;; (ldb (byte s 0) (foo x y ...)) =
2762 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2764 ;;; and similar for other arguments.
2766 (defun make-modular-fun-type-deriver (prototype class width)
2768 (binding* ((info (info :function :info prototype) :exit-if-null)
2769 (fun (fun-info-derive-type info) :exit-if-null)
2770 (mask-type (specifier-type
2772 (:unsigned (let ((mask (1- (ash 1 width))))
2773 `(integer ,mask ,mask)))
2774 (:signed `(signed-byte ,width))))))
2776 (let ((res (funcall fun call)))
2778 (if (eq class :unsigned)
2779 (logand-derive-type-aux res mask-type))))))
2782 (binding* ((info (info :function :info prototype) :exit-if-null)
2783 (fun (fun-info-derive-type info) :exit-if-null)
2784 (res (funcall fun call) :exit-if-null)
2785 (mask-type (specifier-type
2787 (:unsigned (let ((mask (1- (ash 1 width))))
2788 `(integer ,mask ,mask)))
2789 (:signed `(signed-byte ,width))))))
2790 (if (eq class :unsigned)
2791 (logand-derive-type-aux res mask-type)))))
2793 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2795 ;;; For good functions, we just recursively cut arguments; their
2796 ;;; "goodness" means that the result will not increase (in the
2797 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2798 ;;; replaced with the version, cutting its result to WIDTH or more
2799 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2800 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2801 ;;; arguments (maybe to a different width) and returning the name of a
2802 ;;; modular version, if it exists, or NIL. If we have changed
2803 ;;; anything, we need to flush old derived types, because they have
2804 ;;; nothing in common with the new code.
2805 (defun cut-to-width (lvar class width)
2806 (declare (type lvar lvar) (type (integer 0) width))
2807 (let ((type (specifier-type (if (zerop width)
2809 `(,(ecase class (:unsigned 'unsigned-byte)
2810 (:signed 'signed-byte))
2812 (labels ((reoptimize-node (node name)
2813 (setf (node-derived-type node)
2815 (info :function :type name)))
2816 (setf (lvar-%derived-type (node-lvar node)) nil)
2817 (setf (node-reoptimize node) t)
2818 (setf (block-reoptimize (node-block node)) t)
2819 (reoptimize-component (node-component node) :maybe))
2820 (cut-node (node &aux did-something)
2821 (when (and (not (block-delete-p (node-block node)))
2822 (combination-p node)
2823 (eq (basic-combination-kind node) :known))
2824 (let* ((fun-ref (lvar-use (combination-fun node)))
2825 (fun-name (leaf-source-name (ref-leaf fun-ref)))
2826 (modular-fun (find-modular-version fun-name class width)))
2827 (when (and modular-fun
2828 (not (and (eq fun-name 'logand)
2830 (single-value-type (node-derived-type node))
2832 (binding* ((name (etypecase modular-fun
2833 ((eql :good) fun-name)
2835 (modular-fun-info-name modular-fun))
2837 (funcall modular-fun node width)))
2839 (unless (eql modular-fun :good)
2840 (setq did-something t)
2843 (find-free-fun name "in a strange place"))
2844 (setf (combination-kind node) :full))
2845 (unless (functionp modular-fun)
2846 (dolist (arg (basic-combination-args node))
2847 (when (cut-lvar arg)
2848 (setq did-something t))))
2850 (reoptimize-node node name))
2852 (cut-lvar (lvar &aux did-something)
2853 (do-uses (node lvar)
2854 (when (cut-node node)
2855 (setq did-something t)))
2859 (defoptimizer (logand optimizer) ((x y) node)
2860 (let ((result-type (single-value-type (node-derived-type node))))
2861 (when (numeric-type-p result-type)
2862 (let ((low (numeric-type-low result-type))
2863 (high (numeric-type-high result-type)))
2864 (when (and (numberp low)
2867 (let ((width (integer-length high)))
2868 (when (some (lambda (x) (<= width x))
2869 (modular-class-widths *unsigned-modular-class*))
2870 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2871 (cut-to-width x :unsigned width)
2872 (cut-to-width y :unsigned width)
2873 nil ; After fixing above, replace with T.
2876 (defoptimizer (mask-signed-field optimizer) ((width x) node)
2877 (let ((result-type (single-value-type (node-derived-type node))))
2878 (when (numeric-type-p result-type)
2879 (let ((low (numeric-type-low result-type))
2880 (high (numeric-type-high result-type)))
2881 (when (and (numberp low) (numberp high))
2882 (let ((width (max (integer-length high) (integer-length low))))
2883 (when (some (lambda (x) (<= width x))
2884 (modular-class-widths *signed-modular-class*))
2885 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2886 (cut-to-width x :signed width)
2887 nil ; After fixing above, replace with T.
2890 ;;; miscellanous numeric transforms
2892 ;;; If a constant appears as the first arg, swap the args.
2893 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2894 (if (and (constant-lvar-p x)
2895 (not (constant-lvar-p y)))
2896 `(,(lvar-fun-name (basic-combination-fun node))
2899 (give-up-ir1-transform)))
2901 (dolist (x '(= char= + * logior logand logxor))
2902 (%deftransform x '(function * *) #'commutative-arg-swap
2903 "place constant arg last"))
2905 ;;; Handle the case of a constant BOOLE-CODE.
2906 (deftransform boole ((op x y) * *)
2907 "convert to inline logical operations"
2908 (unless (constant-lvar-p op)
2909 (give-up-ir1-transform "BOOLE code is not a constant."))
2910 (let ((control (lvar-value op)))
2912 (#.sb!xc:boole-clr 0)
2913 (#.sb!xc:boole-set -1)
2914 (#.sb!xc:boole-1 'x)
2915 (#.sb!xc:boole-2 'y)
2916 (#.sb!xc:boole-c1 '(lognot x))
2917 (#.sb!xc:boole-c2 '(lognot y))
2918 (#.sb!xc:boole-and '(logand x y))
2919 (#.sb!xc:boole-ior '(logior x y))
2920 (#.sb!xc:boole-xor '(logxor x y))
2921 (#.sb!xc:boole-eqv '(logeqv x y))
2922 (#.sb!xc:boole-nand '(lognand x y))
2923 (#.sb!xc:boole-nor '(lognor x y))
2924 (#.sb!xc:boole-andc1 '(logandc1 x y))
2925 (#.sb!xc:boole-andc2 '(logandc2 x y))
2926 (#.sb!xc:boole-orc1 '(logorc1 x y))
2927 (#.sb!xc:boole-orc2 '(logorc2 x y))
2929 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2932 ;;;; converting special case multiply/divide to shifts
2934 ;;; If arg is a constant power of two, turn * into a shift.
2935 (deftransform * ((x y) (integer integer) *)
2936 "convert x*2^k to shift"
2937 (unless (constant-lvar-p y)
2938 (give-up-ir1-transform))
2939 (let* ((y (lvar-value y))
2941 (len (1- (integer-length y-abs))))
2942 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2943 (give-up-ir1-transform))
2948 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2949 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
2951 (flet ((frob (y ceil-p)
2952 (unless (constant-lvar-p y)
2953 (give-up-ir1-transform))
2954 (let* ((y (lvar-value y))
2956 (len (1- (integer-length y-abs))))
2957 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2958 (give-up-ir1-transform))
2959 (let ((shift (- len))
2961 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
2962 `(let ((x (+ x ,delta)))
2964 `(values (ash (- x) ,shift)
2965 (- (- (logand (- x) ,mask)) ,delta))
2966 `(values (ash x ,shift)
2967 (- (logand x ,mask) ,delta))))))))
2968 (deftransform floor ((x y) (integer integer) *)
2969 "convert division by 2^k to shift"
2971 (deftransform ceiling ((x y) (integer integer) *)
2972 "convert division by 2^k to shift"
2975 ;;; Do the same for MOD.
2976 (deftransform mod ((x y) (integer integer) *)
2977 "convert remainder mod 2^k to LOGAND"
2978 (unless (constant-lvar-p y)
2979 (give-up-ir1-transform))
2980 (let* ((y (lvar-value y))
2982 (len (1- (integer-length y-abs))))
2983 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2984 (give-up-ir1-transform))
2985 (let ((mask (1- y-abs)))
2987 `(- (logand (- x) ,mask))
2988 `(logand x ,mask)))))
2990 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2991 (deftransform truncate ((x y) (integer integer))
2992 "convert division by 2^k to shift"
2993 (unless (constant-lvar-p y)
2994 (give-up-ir1-transform))
2995 (let* ((y (lvar-value y))
2997 (len (1- (integer-length y-abs))))
2998 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2999 (give-up-ir1-transform))
3000 (let* ((shift (- len))
3003 (values ,(if (minusp y)
3005 `(- (ash (- x) ,shift)))
3006 (- (logand (- x) ,mask)))
3007 (values ,(if (minusp y)
3008 `(ash (- ,mask x) ,shift)
3010 (logand x ,mask))))))
3012 ;;; And the same for REM.
3013 (deftransform rem ((x y) (integer integer) *)
3014 "convert remainder mod 2^k to LOGAND"
3015 (unless (constant-lvar-p y)
3016 (give-up-ir1-transform))
3017 (let* ((y (lvar-value y))
3019 (len (1- (integer-length y-abs))))
3020 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3021 (give-up-ir1-transform))
3022 (let ((mask (1- y-abs)))
3024 (- (logand (- x) ,mask))
3025 (logand x ,mask)))))
3027 ;;;; arithmetic and logical identity operation elimination
3029 ;;; Flush calls to various arith functions that convert to the
3030 ;;; identity function or a constant.
3031 (macrolet ((def (name identity result)
3032 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3033 "fold identity operations"
3040 (def logxor -1 (lognot x))
3043 (deftransform logand ((x y) (* (constant-arg t)) *)
3044 "fold identity operation"
3045 (let ((y (lvar-value y)))
3046 (unless (and (plusp y)
3047 (= y (1- (ash 1 (integer-length y)))))
3048 (give-up-ir1-transform))
3049 (unless (csubtypep (lvar-type x)
3050 (specifier-type `(integer 0 ,y)))
3051 (give-up-ir1-transform))
3054 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3055 "fold identity operation"
3056 (let ((size (lvar-value size)))
3057 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3058 (give-up-ir1-transform))
3061 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3062 ;;; (* 0 -4.0) is -0.0.
3063 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3064 "convert (- 0 x) to negate"
3066 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3067 "convert (* x 0) to 0"
3070 ;;; Return T if in an arithmetic op including lvars X and Y, the
3071 ;;; result type is not affected by the type of X. That is, Y is at
3072 ;;; least as contagious as X.
3074 (defun not-more-contagious (x y)
3075 (declare (type continuation x y))
3076 (let ((x (lvar-type x))
3078 (values (type= (numeric-contagion x y)
3079 (numeric-contagion y y)))))
3080 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3081 ;;; XXX needs more work as valid transforms are missed; some cases are
3082 ;;; specific to particular transform functions so the use of this
3083 ;;; function may need a re-think.
3084 (defun not-more-contagious (x y)
3085 (declare (type lvar x y))
3086 (flet ((simple-numeric-type (num)
3087 (and (numeric-type-p num)
3088 ;; Return non-NIL if NUM is integer, rational, or a float
3089 ;; of some type (but not FLOAT)
3090 (case (numeric-type-class num)
3094 (numeric-type-format num))
3097 (let ((x (lvar-type x))
3099 (if (and (simple-numeric-type x)
3100 (simple-numeric-type y))
3101 (values (type= (numeric-contagion x y)
3102 (numeric-contagion y y)))))))
3106 ;;; If y is not constant, not zerop, or is contagious, or a positive
3107 ;;; float +0.0 then give up.
3108 (deftransform + ((x y) (t (constant-arg t)) *)
3110 (let ((val (lvar-value y)))
3111 (unless (and (zerop val)
3112 (not (and (floatp val) (plusp (float-sign val))))
3113 (not-more-contagious y x))
3114 (give-up-ir1-transform)))
3119 ;;; If y is not constant, not zerop, or is contagious, or a negative
3120 ;;; float -0.0 then give up.
3121 (deftransform - ((x y) (t (constant-arg t)) *)
3123 (let ((val (lvar-value y)))
3124 (unless (and (zerop val)
3125 (not (and (floatp val) (minusp (float-sign val))))
3126 (not-more-contagious y x))
3127 (give-up-ir1-transform)))
3130 ;;; Fold (OP x +/-1)
3131 (macrolet ((def (name result minus-result)
3132 `(deftransform ,name ((x y) (t (constant-arg real)) *)
3133 "fold identity operations"
3134 (let ((val (lvar-value y)))
3135 (unless (and (= (abs val) 1)
3136 (not-more-contagious y x))
3137 (give-up-ir1-transform))
3138 (if (minusp val) ',minus-result ',result)))))
3139 (def * x (%negate x))
3140 (def / x (%negate x))
3141 (def expt x (/ 1 x)))
3143 ;;; Fold (expt x n) into multiplications for small integral values of
3144 ;;; N; convert (expt x 1/2) to sqrt.
3145 (deftransform expt ((x y) (t (constant-arg real)) *)
3146 "recode as multiplication or sqrt"
3147 (let ((val (lvar-value y)))
3148 ;; If Y would cause the result to be promoted to the same type as
3149 ;; Y, we give up. If not, then the result will be the same type
3150 ;; as X, so we can replace the exponentiation with simple
3151 ;; multiplication and division for small integral powers.
3152 (unless (not-more-contagious y x)
3153 (give-up-ir1-transform))
3155 (let ((x-type (lvar-type x)))
3156 (cond ((csubtypep x-type (specifier-type '(or rational
3157 (complex rational))))
3159 ((csubtypep x-type (specifier-type 'real))
3163 ((csubtypep x-type (specifier-type 'complex))
3164 ;; both parts are float
3166 (t (give-up-ir1-transform)))))
3167 ((= val 2) '(* x x))
3168 ((= val -2) '(/ (* x x)))
3169 ((= val 3) '(* x x x))
3170 ((= val -3) '(/ (* x x x)))
3171 ((= val 1/2) '(sqrt x))
3172 ((= val -1/2) '(/ (sqrt x)))
3173 (t (give-up-ir1-transform)))))
3175 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3176 ;;; transformations?
3177 ;;; Perhaps we should have to prove that the denominator is nonzero before
3178 ;;; doing them? -- WHN 19990917
3179 (macrolet ((def (name)
3180 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3187 (macrolet ((def (name)
3188 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3197 ;;;; character operations
3199 (deftransform char-equal ((a b) (base-char base-char))
3201 '(let* ((ac (char-code a))
3203 (sum (logxor ac bc)))
3205 (when (eql sum #x20)
3206 (let ((sum (+ ac bc)))
3207 (or (and (> sum 161) (< sum 213))
3208 (and (> sum 415) (< sum 461))
3209 (and (> sum 463) (< sum 477))))))))
3211 (deftransform char-upcase ((x) (base-char))
3213 '(let ((n-code (char-code x)))
3214 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3215 (< n-code #o173)) ; Octal 172 is #\z.
3216 (and (> n-code #o337)
3218 (and (> n-code #o367)
3220 (code-char (logxor #x20 n-code))
3223 (deftransform char-downcase ((x) (base-char))
3225 '(let ((n-code (char-code x)))
3226 (if (or (and (> n-code 64) ; 65 is #\A.
3227 (< n-code 91)) ; 90 is #\Z.
3232 (code-char (logxor #x20 n-code))
3235 ;;;; equality predicate transforms
3237 ;;; Return true if X and Y are lvars whose only use is a
3238 ;;; reference to the same leaf, and the value of the leaf cannot
3240 (defun same-leaf-ref-p (x y)
3241 (declare (type lvar x y))
3242 (let ((x-use (principal-lvar-use x))
3243 (y-use (principal-lvar-use y)))
3246 (eq (ref-leaf x-use) (ref-leaf y-use))
3247 (constant-reference-p x-use))))
3249 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3250 ;;; if there is no intersection between the types of the arguments,
3251 ;;; then the result is definitely false.
3252 (deftransform simple-equality-transform ((x y) * *
3255 ((same-leaf-ref-p x y) t)
3256 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3258 (t (give-up-ir1-transform))))
3261 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3265 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3266 ;;; try to convert to a type-specific predicate or EQ:
3267 ;;; -- If both args are characters, convert to CHAR=. This is better than
3268 ;;; just converting to EQ, since CHAR= may have special compilation
3269 ;;; strategies for non-standard representations, etc.
3270 ;;; -- If either arg is definitely a fixnum we punt and let the backend
3272 ;;; -- If either arg is definitely not a number or a fixnum, then we
3273 ;;; can compare with EQ.
3274 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3275 ;;; is constant then we put it second. If X is a subtype of Y, we put
3276 ;;; it second. These rules make it easier for the back end to match
3277 ;;; these interesting cases.
3278 (deftransform eql ((x y) * *)
3279 "convert to simpler equality predicate"
3280 (let ((x-type (lvar-type x))
3281 (y-type (lvar-type y))
3282 (char-type (specifier-type 'character)))
3283 (flet ((simple-type-p (type)
3284 (csubtypep type (specifier-type '(or fixnum (not number)))))
3285 (fixnum-type-p (type)
3286 (csubtypep type (specifier-type 'fixnum))))
3288 ((same-leaf-ref-p x y) t)
3289 ((not (types-equal-or-intersect x-type y-type))
3291 ((and (csubtypep x-type char-type)
3292 (csubtypep y-type char-type))
3294 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3295 (give-up-ir1-transform))
3296 ((or (simple-type-p x-type) (simple-type-p y-type))
3298 ((and (not (constant-lvar-p y))
3299 (or (constant-lvar-p x)
3300 (and (csubtypep x-type y-type)
3301 (not (csubtypep y-type x-type)))))
3304 (give-up-ir1-transform))))))
3306 ;;; similarly to the EQL transform above, we attempt to constant-fold
3307 ;;; or convert to a simpler predicate: mostly we have to be careful
3308 ;;; with strings and bit-vectors.
3309 (deftransform equal ((x y) * *)
3310 "convert to simpler equality predicate"
3311 (let ((x-type (lvar-type x))
3312 (y-type (lvar-type y))
3313 (string-type (specifier-type 'string))
3314 (bit-vector-type (specifier-type 'bit-vector)))
3316 ((same-leaf-ref-p x y) t)
3317 ((and (csubtypep x-type string-type)
3318 (csubtypep y-type string-type))
3320 ((and (csubtypep x-type bit-vector-type)
3321 (csubtypep y-type bit-vector-type))
3322 '(bit-vector-= x y))
3323 ;; if at least one is not a string, and at least one is not a
3324 ;; bit-vector, then we can reason from types.
3325 ((and (not (and (types-equal-or-intersect x-type string-type)
3326 (types-equal-or-intersect y-type string-type)))
3327 (not (and (types-equal-or-intersect x-type bit-vector-type)
3328 (types-equal-or-intersect y-type bit-vector-type)))
3329 (not (types-equal-or-intersect x-type y-type)))
3331 (t (give-up-ir1-transform)))))
3333 ;;; Convert to EQL if both args are rational and complexp is specified
3334 ;;; and the same for both.
3335 (deftransform = ((x y) * *)
3337 (let ((x-type (lvar-type x))
3338 (y-type (lvar-type y)))
3339 (if (and (csubtypep x-type (specifier-type 'number))
3340 (csubtypep y-type (specifier-type 'number)))
3341 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3342 (csubtypep y-type (specifier-type 'float)))
3343 (and (csubtypep x-type (specifier-type '(complex float)))
3344 (csubtypep y-type (specifier-type '(complex float)))))
3345 ;; They are both floats. Leave as = so that -0.0 is
3346 ;; handled correctly.
3347 (give-up-ir1-transform))
3348 ((or (and (csubtypep x-type (specifier-type 'rational))
3349 (csubtypep y-type (specifier-type 'rational)))
3350 (and (csubtypep x-type
3351 (specifier-type '(complex rational)))
3353 (specifier-type '(complex rational)))))
3354 ;; They are both rationals and complexp is the same.
3358 (give-up-ir1-transform
3359 "The operands might not be the same type.")))
3360 (give-up-ir1-transform
3361 "The operands might not be the same type."))))
3363 ;;; If LVAR's type is a numeric type, then return the type, otherwise
3364 ;;; GIVE-UP-IR1-TRANSFORM.
3365 (defun numeric-type-or-lose (lvar)
3366 (declare (type lvar lvar))
3367 (let ((res (lvar-type lvar)))
3368 (unless (numeric-type-p res) (give-up-ir1-transform))
3371 ;;; See whether we can statically determine (< X Y) using type
3372 ;;; information. If X's high bound is < Y's low, then X < Y.
3373 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3374 ;;; NIL). If not, at least make sure any constant arg is second.
3375 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3376 `(deftransform ,name ((x y))
3377 (if (same-leaf-ref-p x y)
3379 (let ((ix (or (type-approximate-interval (lvar-type x))
3380 (give-up-ir1-transform)))
3381 (iy (or (type-approximate-interval (lvar-type y))
3382 (give-up-ir1-transform))))
3387 ((and (constant-lvar-p x)
3388 (not (constant-lvar-p y)))
3391 (give-up-ir1-transform))))))))
3392 (def < > nil (interval-< ix iy) (interval->= ix iy))
3393 (def > < nil (interval-< iy ix) (interval->= iy ix))
3394 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3395 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3397 (defun ir1-transform-char< (x y first second inverse)
3399 ((same-leaf-ref-p x y) nil)
3400 ;; If we had interval representation of character types, as we
3401 ;; might eventually have to to support 2^21 characters, then here
3402 ;; we could do some compile-time computation as in transforms for
3403 ;; < above. -- CSR, 2003-07-01
3404 ((and (constant-lvar-p first)
3405 (not (constant-lvar-p second)))
3407 (t (give-up-ir1-transform))))
3409 (deftransform char< ((x y) (character character) *)
3410 (ir1-transform-char< x y x y 'char>))
3412 (deftransform char> ((x y) (character character) *)
3413 (ir1-transform-char< y x x y 'char<))
3415 ;;;; converting N-arg comparisons
3417 ;;;; We convert calls to N-arg comparison functions such as < into
3418 ;;;; two-arg calls. This transformation is enabled for all such
3419 ;;;; comparisons in this file. If any of these predicates are not
3420 ;;;; open-coded, then the transformation should be removed at some
3421 ;;;; point to avoid pessimization.
3423 ;;; This function is used for source transformation of N-arg
3424 ;;; comparison functions other than inequality. We deal both with
3425 ;;; converting to two-arg calls and inverting the sense of the test,
3426 ;;; if necessary. If the call has two args, then we pass or return a
3427 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3428 ;;; then we transform to code that returns true. Otherwise, we bind
3429 ;;; all the arguments and expand into a bunch of IFs.
3430 (declaim (ftype (function (symbol list boolean t) *) multi-compare))
3431 (defun multi-compare (predicate args not-p type)
3432 (let ((nargs (length args)))
3433 (cond ((< nargs 1) (values nil t))
3434 ((= nargs 1) `(progn (the ,type ,@args) t))
3437 `(if (,predicate ,(first args) ,(second args)) nil t)
3440 (do* ((i (1- nargs) (1- i))
3442 (current (gensym) (gensym))
3443 (vars (list current) (cons current vars))
3445 `(if (,predicate ,current ,last)
3447 `(if (,predicate ,current ,last)
3450 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3453 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3454 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3455 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3456 (define-source-transform <= (&rest args) (multi-compare '> args t 'real))
3457 (define-source-transform >= (&rest args) (multi-compare '< args t 'real))
3459 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3461 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3463 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3465 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3467 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3470 (define-source-transform char-equal (&rest args)
3471 (multi-compare 'char-equal args nil 'character))
3472 (define-source-transform char-lessp (&rest args)
3473 (multi-compare 'char-lessp args nil 'character))
3474 (define-source-transform char-greaterp (&rest args)
3475 (multi-compare 'char-greaterp args nil 'character))
3476 (define-source-transform char-not-greaterp (&rest args)
3477 (multi-compare 'char-greaterp args t 'character))
3478 (define-source-transform char-not-lessp (&rest args)
3479 (multi-compare 'char-lessp args t 'character))
3481 ;;; This function does source transformation of N-arg inequality
3482 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3483 ;;; arg cases. If there are more than two args, then we expand into
3484 ;;; the appropriate n^2 comparisons only when speed is important.
3485 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3486 (defun multi-not-equal (predicate args type)
3487 (let ((nargs (length args)))
3488 (cond ((< nargs 1) (values nil t))
3489 ((= nargs 1) `(progn (the ,type ,@args) t))
3491 `(if (,predicate ,(first args) ,(second args)) nil t))
3492 ((not (policy *lexenv*
3493 (and (>= speed space)
3494 (>= speed compilation-speed))))
3497 (let ((vars (make-gensym-list nargs)))
3498 (do ((var vars next)
3499 (next (cdr vars) (cdr next))
3502 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3504 (let ((v1 (first var)))
3506 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3508 (define-source-transform /= (&rest args)
3509 (multi-not-equal '= args 'number))
3510 (define-source-transform char/= (&rest args)
3511 (multi-not-equal 'char= args 'character))
3512 (define-source-transform char-not-equal (&rest args)
3513 (multi-not-equal 'char-equal args 'character))
3515 ;;; Expand MAX and MIN into the obvious comparisons.
3516 (define-source-transform max (arg0 &rest rest)
3517 (once-only ((arg0 arg0))
3519 `(values (the real ,arg0))
3520 `(let ((maxrest (max ,@rest)))
3521 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3522 (define-source-transform min (arg0 &rest rest)
3523 (once-only ((arg0 arg0))
3525 `(values (the real ,arg0))
3526 `(let ((minrest (min ,@rest)))
3527 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3529 ;;;; converting N-arg arithmetic functions
3531 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3532 ;;;; versions, and degenerate cases are flushed.
3534 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3535 (declaim (ftype (function (symbol t list) list) associate-args))
3536 (defun associate-args (function first-arg more-args)
3537 (let ((next (rest more-args))
3538 (arg (first more-args)))
3540 `(,function ,first-arg ,arg)
3541 (associate-args function `(,function ,first-arg ,arg) next))))
3543 ;;; Do source transformations for transitive functions such as +.
3544 ;;; One-arg cases are replaced with the arg and zero arg cases with
3545 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3546 ;;; ensure (with THE) that the argument in one-argument calls is.
3547 (defun source-transform-transitive (fun args identity
3548 &optional one-arg-result-type)
3549 (declare (symbol fun) (list args))
3552 (1 (if one-arg-result-type
3553 `(values (the ,one-arg-result-type ,(first args)))
3554 `(values ,(first args))))
3557 (associate-args fun (first args) (rest args)))))
3559 (define-source-transform + (&rest args)
3560 (source-transform-transitive '+ args 0 'number))
3561 (define-source-transform * (&rest args)
3562 (source-transform-transitive '* args 1 'number))
3563 (define-source-transform logior (&rest args)
3564 (source-transform-transitive 'logior args 0 'integer))
3565 (define-source-transform logxor (&rest args)
3566 (source-transform-transitive 'logxor args 0 'integer))
3567 (define-source-transform logand (&rest args)
3568 (source-transform-transitive 'logand args -1 'integer))
3569 (define-source-transform logeqv (&rest args)
3570 (source-transform-transitive 'logeqv args -1 'integer))
3572 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3573 ;;; because when they are given one argument, they return its absolute
3576 (define-source-transform gcd (&rest args)
3579 (1 `(abs (the integer ,(first args))))
3581 (t (associate-args 'gcd (first args) (rest args)))))
3583 (define-source-transform lcm (&rest args)
3586 (1 `(abs (the integer ,(first args))))
3588 (t (associate-args 'lcm (first args) (rest args)))))
3590 ;;; Do source transformations for intransitive n-arg functions such as
3591 ;;; /. With one arg, we form the inverse. With two args we pass.
3592 ;;; Otherwise we associate into two-arg calls.
3593 (declaim (ftype (function (symbol list t)
3594 (values list &optional (member nil t)))
3595 source-transform-intransitive))
3596 (defun source-transform-intransitive (function args inverse)
3598 ((0 2) (values nil t))
3599 (1 `(,@inverse ,(first args)))
3600 (t (associate-args function (first args) (rest args)))))
3602 (define-source-transform - (&rest args)
3603 (source-transform-intransitive '- args '(%negate)))
3604 (define-source-transform / (&rest args)
3605 (source-transform-intransitive '/ args '(/ 1)))
3607 ;;;; transforming APPLY
3609 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3610 ;;; only needs to understand one kind of variable-argument call. It is
3611 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3612 (define-source-transform apply (fun arg &rest more-args)
3613 (let ((args (cons arg more-args)))
3614 `(multiple-value-call ,fun
3615 ,@(mapcar (lambda (x)
3618 (values-list ,(car (last args))))))
3620 ;;;; transforming FORMAT
3622 ;;;; If the control string is a compile-time constant, then replace it
3623 ;;;; with a use of the FORMATTER macro so that the control string is
3624 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3625 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3626 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3628 ;;; for compile-time argument count checking.
3630 ;;; FIXME II: In some cases, type information could be correlated; for
3631 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3632 ;;; of a corresponding argument is known and does not intersect the
3633 ;;; list type, a warning could be signalled.
3634 (defun check-format-args (string args fun)
3635 (declare (type string string))
3636 (unless (typep string 'simple-string)
3637 (setq string (coerce string 'simple-string)))
3638 (multiple-value-bind (min max)
3639 (handler-case (sb!format:%compiler-walk-format-string string args)
3640 (sb!format:format-error (c)
3641 (compiler-warn "~A" c)))
3643 (let ((nargs (length args)))
3646 (warn 'format-too-few-args-warning
3648 "Too few arguments (~D) to ~S ~S: requires at least ~D."
3649 :format-arguments (list nargs fun string min)))
3651 (warn 'format-too-many-args-warning
3653 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3654 :format-arguments (list nargs fun string max))))))))
3656 (defoptimizer (format optimizer) ((dest control &rest args))
3657 (when (constant-lvar-p control)
3658 (let ((x (lvar-value control)))
3660 (check-format-args x args 'format)))))
3662 ;;; We disable this transform in the cross-compiler to save memory in
3663 ;;; the target image; most of the uses of FORMAT in the compiler are for
3664 ;;; error messages, and those don't need to be particularly fast.
3666 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3667 :policy (> speed space))
3668 (unless (constant-lvar-p control)
3669 (give-up-ir1-transform "The control string is not a constant."))
3670 (let ((arg-names (make-gensym-list (length args))))
3671 `(lambda (dest control ,@arg-names)
3672 (declare (ignore control))
3673 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
3675 (deftransform format ((stream control &rest args) (stream function &rest t) *
3676 :policy (> speed space))
3677 (let ((arg-names (make-gensym-list (length args))))
3678 `(lambda (stream control ,@arg-names)
3679 (funcall control stream ,@arg-names)
3682 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3683 :policy (> speed space))
3684 (let ((arg-names (make-gensym-list (length args))))
3685 `(lambda (tee control ,@arg-names)
3686 (declare (ignore tee))
3687 (funcall control *standard-output* ,@arg-names)
3692 `(defoptimizer (,name optimizer) ((control &rest args))
3693 (when (constant-lvar-p control)
3694 (let ((x (lvar-value control)))
3696 (check-format-args x args ',name)))))))
3699 #+sb-xc-host ; Only we should be using these
3702 (def compiler-abort)
3703 (def compiler-error)
3705 (def compiler-style-warn)
3706 (def compiler-notify)
3707 (def maybe-compiler-notify)
3710 (defoptimizer (cerror optimizer) ((report control &rest args))
3711 (when (and (constant-lvar-p control)
3712 (constant-lvar-p report))
3713 (let ((x (lvar-value control))
3714 (y (lvar-value report)))
3715 (when (and (stringp x) (stringp y))
3716 (multiple-value-bind (min1 max1)
3718 (sb!format:%compiler-walk-format-string x args)
3719 (sb!format:format-error (c)
3720 (compiler-warn "~A" c)))
3722 (multiple-value-bind (min2 max2)
3724 (sb!format:%compiler-walk-format-string y args)
3725 (sb!format:format-error (c)
3726 (compiler-warn "~A" c)))
3728 (let ((nargs (length args)))
3730 ((< nargs (min min1 min2))
3731 (warn 'format-too-few-args-warning
3733 "Too few arguments (~D) to ~S ~S ~S: ~
3734 requires at least ~D."
3736 (list nargs 'cerror y x (min min1 min2))))
3737 ((> nargs (max max1 max2))
3738 (warn 'format-too-many-args-warning
3740 "Too many arguments (~D) to ~S ~S ~S: ~
3743 (list nargs 'cerror y x (max max1 max2))))))))))))))
3745 (defoptimizer (coerce derive-type) ((value type))
3747 ((constant-lvar-p type)
3748 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3749 ;; but dealing with the niggle that complex canonicalization gets
3750 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3752 (let* ((specifier (lvar-value type))
3753 (result-typeoid (careful-specifier-type specifier)))
3755 ((null result-typeoid) nil)
3756 ((csubtypep result-typeoid (specifier-type 'number))
3757 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3758 ;; Rule of Canonical Representation for Complex Rationals,
3759 ;; which is a truly nasty delivery to field.
3761 ((csubtypep result-typeoid (specifier-type 'real))
3762 ;; cleverness required here: it would be nice to deduce
3763 ;; that something of type (INTEGER 2 3) coerced to type
3764 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3765 ;; FLOAT gets its own clause because it's implemented as
3766 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3769 ((and (numeric-type-p result-typeoid)
3770 (eq (numeric-type-complexp result-typeoid) :real))
3771 ;; FIXME: is this clause (a) necessary or (b) useful?
3773 ((or (csubtypep result-typeoid
3774 (specifier-type '(complex single-float)))
3775 (csubtypep result-typeoid
3776 (specifier-type '(complex double-float)))
3778 (csubtypep result-typeoid
3779 (specifier-type '(complex long-float))))
3780 ;; float complex types are never canonicalized.
3783 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3784 ;; probably just a COMPLEX or equivalent. So, in that
3785 ;; case, we will return a complex or an object of the
3786 ;; provided type if it's rational:
3787 (type-union result-typeoid
3788 (type-intersection (lvar-type value)
3789 (specifier-type 'rational))))))
3790 (t result-typeoid))))
3792 ;; OK, the result-type argument isn't constant. However, there
3793 ;; are common uses where we can still do better than just
3794 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3795 ;; where Y is of a known type. See messages on cmucl-imp
3796 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3797 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3798 ;; the basis that it's unlikely that other uses are both
3799 ;; time-critical and get to this branch of the COND (non-constant
3800 ;; second argument to COERCE). -- CSR, 2002-12-16
3801 (let ((value-type (lvar-type value))
3802 (type-type (lvar-type type)))
3804 ((good-cons-type-p (cons-type)
3805 ;; Make sure the cons-type we're looking at is something
3806 ;; we're prepared to handle which is basically something
3807 ;; that array-element-type can return.
3808 (or (and (member-type-p cons-type)
3809 (null (rest (member-type-members cons-type)))
3810 (null (first (member-type-members cons-type))))
3811 (let ((car-type (cons-type-car-type cons-type)))
3812 (and (member-type-p car-type)
3813 (null (rest (member-type-members car-type)))
3814 (or (symbolp (first (member-type-members car-type)))
3815 (numberp (first (member-type-members car-type)))
3816 (and (listp (first (member-type-members
3818 (numberp (first (first (member-type-members
3820 (good-cons-type-p (cons-type-cdr-type cons-type))))))
3821 (unconsify-type (good-cons-type)
3822 ;; Convert the "printed" respresentation of a cons
3823 ;; specifier into a type specifier. That is, the
3824 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3825 ;; NULL)) is converted to (SIGNED-BYTE 16).
3826 (cond ((or (null good-cons-type)
3827 (eq good-cons-type 'null))
3829 ((and (eq (first good-cons-type) 'cons)
3830 (eq (first (second good-cons-type)) 'member))
3831 `(,(second (second good-cons-type))
3832 ,@(unconsify-type (caddr good-cons-type))))))
3833 (coerceable-p (c-type)
3834 ;; Can the value be coerced to the given type? Coerce is
3835 ;; complicated, so we don't handle every possible case
3836 ;; here---just the most common and easiest cases:
3838 ;; * Any REAL can be coerced to a FLOAT type.
3839 ;; * Any NUMBER can be coerced to a (COMPLEX
3840 ;; SINGLE/DOUBLE-FLOAT).
3842 ;; FIXME I: we should also be able to deal with characters
3845 ;; FIXME II: I'm not sure that anything is necessary
3846 ;; here, at least while COMPLEX is not a specialized
3847 ;; array element type in the system. Reasoning: if
3848 ;; something cannot be coerced to the requested type, an
3849 ;; error will be raised (and so any downstream compiled
3850 ;; code on the assumption of the returned type is
3851 ;; unreachable). If something can, then it will be of
3852 ;; the requested type, because (by assumption) COMPLEX
3853 ;; (and other difficult types like (COMPLEX INTEGER)
3854 ;; aren't specialized types.
3855 (let ((coerced-type c-type))
3856 (or (and (subtypep coerced-type 'float)
3857 (csubtypep value-type (specifier-type 'real)))
3858 (and (subtypep coerced-type
3859 '(or (complex single-float)
3860 (complex double-float)))
3861 (csubtypep value-type (specifier-type 'number))))))
3862 (process-types (type)
3863 ;; FIXME: This needs some work because we should be able
3864 ;; to derive the resulting type better than just the
3865 ;; type arg of coerce. That is, if X is (INTEGER 10
3866 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3867 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3869 (cond ((member-type-p type)
3870 (let ((members (member-type-members type)))
3871 (if (every #'coerceable-p members)
3872 (specifier-type `(or ,@members))
3874 ((and (cons-type-p type)
3875 (good-cons-type-p type))
3876 (let ((c-type (unconsify-type (type-specifier type))))
3877 (if (coerceable-p c-type)
3878 (specifier-type c-type)
3881 *universal-type*))))
3882 (cond ((union-type-p type-type)
3883 (apply #'type-union (mapcar #'process-types
3884 (union-type-types type-type))))
3885 ((or (member-type-p type-type)
3886 (cons-type-p type-type))
3887 (process-types type-type))
3889 *universal-type*)))))))
3891 (defoptimizer (compile derive-type) ((nameoid function))
3892 (when (csubtypep (lvar-type nameoid)
3893 (specifier-type 'null))
3894 (values-specifier-type '(values function boolean boolean))))
3896 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3897 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3898 ;;; optimizer, above).
3899 (defoptimizer (array-element-type derive-type) ((array))
3900 (let ((array-type (lvar-type array)))
3901 (labels ((consify (list)
3904 `(cons (eql ,(car list)) ,(consify (rest list)))))
3905 (get-element-type (a)
3907 (type-specifier (array-type-specialized-element-type a))))
3908 (cond ((eq element-type '*)
3909 (specifier-type 'type-specifier))
3910 ((symbolp element-type)
3911 (make-member-type :members (list element-type)))
3912 ((consp element-type)
3913 (specifier-type (consify element-type)))
3915 (error "can't understand type ~S~%" element-type))))))
3916 (cond ((array-type-p array-type)
3917 (get-element-type array-type))
3918 ((union-type-p array-type)
3920 (mapcar #'get-element-type (union-type-types array-type))))
3922 *universal-type*)))))
3924 ;;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3925 ;;; isn't really related to the CMU CL code, since instead of trying
3926 ;;; to generalize the CMU CL code to allow START and END values, this
3927 ;;; code has been written from scratch following Chapter 7 of
3928 ;;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3929 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
3930 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3931 ;; isn't really related to the CMU CL code, since instead of trying
3932 ;; to generalize the CMU CL code to allow START and END values, this
3933 ;; code has been written from scratch following Chapter 7 of
3934 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3935 `(macrolet ((%index (x) `(truly-the index ,x))
3936 (%parent (i) `(ash ,i -1))
3937 (%left (i) `(%index (ash ,i 1)))
3938 (%right (i) `(%index (1+ (ash ,i 1))))
3941 (left (%left i) (%left i)))
3942 ((> left current-heap-size))
3943 (declare (type index i left))
3944 (let* ((i-elt (%elt i))
3945 (i-key (funcall keyfun i-elt))
3946 (left-elt (%elt left))
3947 (left-key (funcall keyfun left-elt)))
3948 (multiple-value-bind (large large-elt large-key)
3949 (if (funcall ,',predicate i-key left-key)
3950 (values left left-elt left-key)
3951 (values i i-elt i-key))
3952 (let ((right (%right i)))
3953 (multiple-value-bind (largest largest-elt)
3954 (if (> right current-heap-size)
3955 (values large large-elt)
3956 (let* ((right-elt (%elt right))
3957 (right-key (funcall keyfun right-elt)))
3958 (if (funcall ,',predicate large-key right-key)
3959 (values right right-elt)
3960 (values large large-elt))))
3961 (cond ((= largest i)
3964 (setf (%elt i) largest-elt
3965 (%elt largest) i-elt
3967 (%sort-vector (keyfun &optional (vtype 'vector))
3968 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
3969 ;; trouble getting type inference to
3970 ;; propagate all the way through this
3971 ;; tangled mess of inlining. The TRULY-THE
3972 ;; here works around that. -- WHN
3974 `(aref (truly-the ,',vtype ,',',vector)
3975 (%index (+ (%index ,i) start-1)))))
3976 (let (;; Heaps prefer 1-based addressing.
3977 (start-1 (1- ,',start))
3978 (current-heap-size (- ,',end ,',start))
3980 (declare (type (integer -1 #.(1- most-positive-fixnum))
3982 (declare (type index current-heap-size))
3983 (declare (type function keyfun))
3984 (loop for i of-type index
3985 from (ash current-heap-size -1) downto 1 do
3988 (when (< current-heap-size 2)
3990 (rotatef (%elt 1) (%elt current-heap-size))
3991 (decf current-heap-size)
3993 (if (typep ,vector 'simple-vector)
3994 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
3995 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
3997 ;; Special-casing the KEY=NIL case lets us avoid some
3999 (%sort-vector #'identity simple-vector)
4000 (%sort-vector ,key simple-vector))
4001 ;; It's hard to anticipate many speed-critical applications for
4002 ;; sorting vector types other than (VECTOR T), so we just lump
4003 ;; them all together in one slow dynamically typed mess.
4005 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4006 (%sort-vector (or ,key #'identity))))))
4008 ;;;; debuggers' little helpers
4010 ;;; for debugging when transforms are behaving mysteriously,
4011 ;;; e.g. when debugging a problem with an ASH transform
4012 ;;; (defun foo (&optional s)
4013 ;;; (sb-c::/report-lvar s "S outside WHEN")
4014 ;;; (when (and (integerp s) (> s 3))
4015 ;;; (sb-c::/report-lvar s "S inside WHEN")
4016 ;;; (let ((bound (ash 1 (1- s))))
4017 ;;; (sb-c::/report-lvar bound "BOUND")
4018 ;;; (let ((x (- bound))
4020 ;;; (sb-c::/report-lvar x "X")
4021 ;;; (sb-c::/report-lvar x "Y"))
4022 ;;; `(integer ,(- bound) ,(1- bound)))))
4023 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4024 ;;; and the function doesn't do anything at all.)
4027 (defknown /report-lvar (t t) null)
4028 (deftransform /report-lvar ((x message) (t t))
4029 (format t "~%/in /REPORT-LVAR~%")
4030 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4031 (when (constant-lvar-p x)
4032 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4033 (format t "/MESSAGE=~S~%" (lvar-value message))
4034 (give-up-ir1-transform "not a real transform"))
4035 (defun /report-lvar (x message)
4036 (declare (ignore x message))))