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 (<= most-negative-single-float ,y most-positive-single-float)
322 ((typep ,x 'double-float)
323 (if (<= most-negative-double-float ,y most-positive-double-float)
325 ((typep ,y 'single-float)
326 (if (<= most-negative-single-float ,x most-positive-single-float)
328 ((typep ,y 'double-float)
329 (if (<= most-negative-double-float ,x most-positive-double-float)
333 (defmacro bound-binop (op x y)
335 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
336 (set-bound (safely-binop ,op (type-bound-number ,x)
337 (type-bound-number ,y))
338 (or (consp ,x) (consp ,y))))))
340 (defun coerce-for-bound (val type)
342 (list (coerce-for-bound (car val) type))
344 ((subtypep type 'double-float)
345 (if (<= most-negative-double-float val most-positive-double-float)
347 ((or (subtypep type 'single-float) (subtypep type 'float))
348 ;; coerce to float returns a single-float
349 (if (<= most-negative-single-float val most-positive-single-float)
351 (t (coerce val type)))))
353 (defun coerce-and-truncate-floats (val type)
356 (list (coerce-and-truncate-floats (car val) type))
358 ((subtypep type 'double-float)
359 (if (<= most-negative-double-float val most-positive-double-float)
361 (if (< val most-negative-double-float)
362 most-negative-double-float most-positive-double-float)))
363 ((or (subtypep type 'single-float) (subtypep type 'float))
364 ;; coerce to float returns a single-float
365 (if (<= most-negative-single-float val most-positive-single-float)
367 (if (< val most-negative-single-float)
368 most-negative-single-float most-positive-single-float)))
369 (t (coerce val type))))))
371 ;;; Convert a numeric-type object to an interval object.
372 (defun numeric-type->interval (x)
373 (declare (type numeric-type x))
374 (make-interval :low (numeric-type-low x)
375 :high (numeric-type-high x)))
377 (defun type-approximate-interval (type)
378 (declare (type ctype type))
379 (let ((types (prepare-arg-for-derive-type type))
382 (let ((type (if (member-type-p type)
383 (convert-member-type type)
385 (unless (numeric-type-p type)
386 (return-from type-approximate-interval nil))
387 (let ((interval (numeric-type->interval type)))
390 (interval-approximate-union result interval)
394 (defun copy-interval-limit (limit)
399 (defun copy-interval (x)
400 (declare (type interval x))
401 (make-interval :low (copy-interval-limit (interval-low x))
402 :high (copy-interval-limit (interval-high x))))
404 ;;; Given a point P contained in the interval X, split X into two
405 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
406 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
407 ;;; contains P. You can specify both to be T or NIL.
408 (defun interval-split (p x &optional close-lower close-upper)
409 (declare (type number p)
411 (list (make-interval :low (copy-interval-limit (interval-low x))
412 :high (if close-lower p (list p)))
413 (make-interval :low (if close-upper (list p) p)
414 :high (copy-interval-limit (interval-high x)))))
416 ;;; Return the closure of the interval. That is, convert open bounds
417 ;;; to closed bounds.
418 (defun interval-closure (x)
419 (declare (type interval x))
420 (make-interval :low (type-bound-number (interval-low x))
421 :high (type-bound-number (interval-high x))))
423 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
424 ;;; '-. Otherwise return NIL.
425 (defun interval-range-info (x &optional (point 0))
426 (declare (type interval x))
427 (let ((lo (interval-low x))
428 (hi (interval-high x)))
429 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
431 ((and hi (signed-zero->= point (type-bound-number hi)))
436 ;;; Test to see whether the interval X is bounded. HOW determines the
437 ;;; test, and should be either ABOVE, BELOW, or BOTH.
438 (defun interval-bounded-p (x how)
439 (declare (type interval x))
446 (and (interval-low x) (interval-high x)))))
448 ;;; See whether the interval X contains the number P, taking into
449 ;;; account that the interval might not be closed.
450 (defun interval-contains-p (p x)
451 (declare (type number p)
453 ;; Does the interval X contain the number P? This would be a lot
454 ;; easier if all intervals were closed!
455 (let ((lo (interval-low x))
456 (hi (interval-high x)))
458 ;; The interval is bounded
459 (if (and (signed-zero-<= (type-bound-number lo) p)
460 (signed-zero-<= p (type-bound-number hi)))
461 ;; P is definitely in the closure of the interval.
462 ;; We just need to check the end points now.
463 (cond ((signed-zero-= p (type-bound-number lo))
465 ((signed-zero-= p (type-bound-number hi))
470 ;; Interval with upper bound
471 (if (signed-zero-< p (type-bound-number hi))
473 (and (numberp hi) (signed-zero-= p hi))))
475 ;; Interval with lower bound
476 (if (signed-zero-> p (type-bound-number lo))
478 (and (numberp lo) (signed-zero-= p lo))))
480 ;; Interval with no bounds
483 ;;; Determine whether two intervals X and Y intersect. Return T if so.
484 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
485 ;;; were closed. Otherwise the intervals are treated as they are.
487 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
488 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
489 ;;; is T, then they do intersect because we use the closure of X = [0,
490 ;;; 1] and Y = [1, 2] to determine intersection.
491 (defun interval-intersect-p (x y &optional closed-intervals-p)
492 (declare (type interval x y))
493 (multiple-value-bind (intersect diff)
494 (interval-intersection/difference (if closed-intervals-p
497 (if closed-intervals-p
500 (declare (ignore diff))
503 ;;; Are the two intervals adjacent? That is, is there a number
504 ;;; between the two intervals that is not an element of either
505 ;;; interval? If so, they are not adjacent. For example [0, 1) and
506 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
507 ;;; between both intervals.
508 (defun interval-adjacent-p (x y)
509 (declare (type interval x y))
510 (flet ((adjacent (lo hi)
511 ;; Check to see whether lo and hi are adjacent. If either is
512 ;; nil, they can't be adjacent.
513 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
514 ;; The bounds are equal. They are adjacent if one of
515 ;; them is closed (a number). If both are open (consp),
516 ;; then there is a number that lies between them.
517 (or (numberp lo) (numberp hi)))))
518 (or (adjacent (interval-low y) (interval-high x))
519 (adjacent (interval-low x) (interval-high y)))))
521 ;;; Compute the intersection and difference between two intervals.
522 ;;; Two values are returned: the intersection and the difference.
524 ;;; Let the two intervals be X and Y, and let I and D be the two
525 ;;; values returned by this function. Then I = X intersect Y. If I
526 ;;; is NIL (the empty set), then D is X union Y, represented as the
527 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
528 ;;; - I, which is a list of two intervals.
530 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
531 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
532 (defun interval-intersection/difference (x y)
533 (declare (type interval x y))
534 (let ((x-lo (interval-low x))
535 (x-hi (interval-high x))
536 (y-lo (interval-low y))
537 (y-hi (interval-high y)))
540 ;; If p is an open bound, make it closed. If p is a closed
541 ;; bound, make it open.
546 ;; Test whether P is in the interval.
547 (when (interval-contains-p (type-bound-number p)
548 (interval-closure int))
549 (let ((lo (interval-low int))
550 (hi (interval-high int)))
551 ;; Check for endpoints.
552 (cond ((and lo (= (type-bound-number p) (type-bound-number lo)))
553 (not (and (consp p) (numberp lo))))
554 ((and hi (= (type-bound-number p) (type-bound-number hi)))
555 (not (and (numberp p) (consp hi))))
557 (test-lower-bound (p int)
558 ;; P is a lower bound of an interval.
561 (not (interval-bounded-p int 'below))))
562 (test-upper-bound (p int)
563 ;; P is an upper bound of an interval.
566 (not (interval-bounded-p int 'above)))))
567 (let ((x-lo-in-y (test-lower-bound x-lo y))
568 (x-hi-in-y (test-upper-bound x-hi y))
569 (y-lo-in-x (test-lower-bound y-lo x))
570 (y-hi-in-x (test-upper-bound y-hi x)))
571 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
572 ;; Intervals intersect. Let's compute the intersection
573 ;; and the difference.
574 (multiple-value-bind (lo left-lo left-hi)
575 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
576 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
577 (multiple-value-bind (hi right-lo right-hi)
579 (values x-hi (opposite-bound x-hi) y-hi))
581 (values y-hi (opposite-bound y-hi) x-hi)))
582 (values (make-interval :low lo :high hi)
583 (list (make-interval :low left-lo
585 (make-interval :low right-lo
588 (values nil (list x y))))))))
590 ;;; If intervals X and Y intersect, return a new interval that is the
591 ;;; union of the two. If they do not intersect, return NIL.
592 (defun interval-merge-pair (x y)
593 (declare (type interval x y))
594 ;; If x and y intersect or are adjacent, create the union.
595 ;; Otherwise return nil
596 (when (or (interval-intersect-p x y)
597 (interval-adjacent-p x y))
598 (flet ((select-bound (x1 x2 min-op max-op)
599 (let ((x1-val (type-bound-number x1))
600 (x2-val (type-bound-number x2)))
602 ;; Both bounds are finite. Select the right one.
603 (cond ((funcall min-op x1-val x2-val)
604 ;; x1 is definitely better.
606 ((funcall max-op x1-val x2-val)
607 ;; x2 is definitely better.
610 ;; Bounds are equal. Select either
611 ;; value and make it open only if
613 (set-bound x1-val (and (consp x1) (consp x2))))))
615 ;; At least one bound is not finite. The
616 ;; non-finite bound always wins.
618 (let* ((x-lo (copy-interval-limit (interval-low x)))
619 (x-hi (copy-interval-limit (interval-high x)))
620 (y-lo (copy-interval-limit (interval-low y)))
621 (y-hi (copy-interval-limit (interval-high y))))
622 (make-interval :low (select-bound x-lo y-lo #'< #'>)
623 :high (select-bound x-hi y-hi #'> #'<))))))
625 ;;; return the minimal interval, containing X and Y
626 (defun interval-approximate-union (x y)
627 (cond ((interval-merge-pair x y))
629 (make-interval :low (copy-interval-limit (interval-low x))
630 :high (copy-interval-limit (interval-high y))))
632 (make-interval :low (copy-interval-limit (interval-low y))
633 :high (copy-interval-limit (interval-high x))))))
635 ;;; basic arithmetic operations on intervals. We probably should do
636 ;;; true interval arithmetic here, but it's complicated because we
637 ;;; have float and integer types and bounds can be open or closed.
639 ;;; the negative of an interval
640 (defun interval-neg (x)
641 (declare (type interval x))
642 (make-interval :low (bound-func #'- (interval-high x))
643 :high (bound-func #'- (interval-low x))))
645 ;;; Add two intervals.
646 (defun interval-add (x y)
647 (declare (type interval x y))
648 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
649 :high (bound-binop + (interval-high x) (interval-high y))))
651 ;;; Subtract two intervals.
652 (defun interval-sub (x y)
653 (declare (type interval x y))
654 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
655 :high (bound-binop - (interval-high x) (interval-low y))))
657 ;;; Multiply two intervals.
658 (defun interval-mul (x y)
659 (declare (type interval x y))
660 (flet ((bound-mul (x y)
661 (cond ((or (null x) (null y))
662 ;; Multiply by infinity is infinity
664 ((or (and (numberp x) (zerop x))
665 (and (numberp y) (zerop y)))
666 ;; Multiply by closed zero is special. The result
667 ;; is always a closed bound. But don't replace this
668 ;; with zero; we want the multiplication to produce
669 ;; the correct signed zero, if needed.
670 (* (type-bound-number x) (type-bound-number y)))
671 ((or (and (floatp x) (float-infinity-p x))
672 (and (floatp y) (float-infinity-p y)))
673 ;; Infinity times anything is infinity
676 ;; General multiply. The result is open if either is open.
677 (bound-binop * x y)))))
678 (let ((x-range (interval-range-info x))
679 (y-range (interval-range-info y)))
680 (cond ((null x-range)
681 ;; Split x into two and multiply each separately
682 (destructuring-bind (x- x+) (interval-split 0 x t t)
683 (interval-merge-pair (interval-mul x- y)
684 (interval-mul x+ y))))
686 ;; Split y into two and multiply each separately
687 (destructuring-bind (y- y+) (interval-split 0 y t t)
688 (interval-merge-pair (interval-mul x y-)
689 (interval-mul x y+))))
691 (interval-neg (interval-mul (interval-neg x) y)))
693 (interval-neg (interval-mul x (interval-neg y))))
694 ((and (eq x-range '+) (eq y-range '+))
695 ;; If we are here, X and Y are both positive.
697 :low (bound-mul (interval-low x) (interval-low y))
698 :high (bound-mul (interval-high x) (interval-high y))))
700 (bug "excluded case in INTERVAL-MUL"))))))
702 ;;; Divide two intervals.
703 (defun interval-div (top bot)
704 (declare (type interval top bot))
705 (flet ((bound-div (x y y-low-p)
708 ;; Divide by infinity means result is 0. However,
709 ;; we need to watch out for the sign of the result,
710 ;; to correctly handle signed zeros. We also need
711 ;; to watch out for positive or negative infinity.
712 (if (floatp (type-bound-number x))
714 (- (float-sign (type-bound-number x) 0.0))
715 (float-sign (type-bound-number x) 0.0))
717 ((zerop (type-bound-number y))
718 ;; Divide by zero means result is infinity
720 ((and (numberp x) (zerop x))
721 ;; Zero divided by anything is zero.
724 (bound-binop / x y)))))
725 (let ((top-range (interval-range-info top))
726 (bot-range (interval-range-info bot)))
727 (cond ((null bot-range)
728 ;; The denominator contains zero, so anything goes!
729 (make-interval :low nil :high nil))
731 ;; Denominator is negative so flip the sign, compute the
732 ;; result, and flip it back.
733 (interval-neg (interval-div top (interval-neg bot))))
735 ;; Split top into two positive and negative parts, and
736 ;; divide each separately
737 (destructuring-bind (top- top+) (interval-split 0 top t t)
738 (interval-merge-pair (interval-div top- bot)
739 (interval-div top+ bot))))
741 ;; Top is negative so flip the sign, divide, and flip the
742 ;; sign of the result.
743 (interval-neg (interval-div (interval-neg top) bot)))
744 ((and (eq top-range '+) (eq bot-range '+))
747 :low (bound-div (interval-low top) (interval-high bot) t)
748 :high (bound-div (interval-high top) (interval-low bot) nil)))
750 (bug "excluded case in INTERVAL-DIV"))))))
752 ;;; Apply the function F to the interval X. If X = [a, b], then the
753 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
754 ;;; result makes sense. It will if F is monotonic increasing (or
756 (defun interval-func (f x)
757 (declare (type function f)
759 (let ((lo (bound-func f (interval-low x)))
760 (hi (bound-func f (interval-high x))))
761 (make-interval :low lo :high hi)))
763 ;;; Return T if X < Y. That is every number in the interval X is
764 ;;; always less than any number in the interval Y.
765 (defun interval-< (x y)
766 (declare (type interval x y))
767 ;; X < Y only if X is bounded above, Y is bounded below, and they
769 (when (and (interval-bounded-p x 'above)
770 (interval-bounded-p y 'below))
771 ;; Intervals are bounded in the appropriate way. Make sure they
773 (let ((left (interval-high x))
774 (right (interval-low y)))
775 (cond ((> (type-bound-number left)
776 (type-bound-number right))
777 ;; The intervals definitely overlap, so result is NIL.
779 ((< (type-bound-number left)
780 (type-bound-number right))
781 ;; The intervals definitely don't touch, so result is T.
784 ;; Limits are equal. Check for open or closed bounds.
785 ;; Don't overlap if one or the other are open.
786 (or (consp left) (consp right)))))))
788 ;;; Return T if X >= Y. That is, every number in the interval X is
789 ;;; always greater than any number in the interval Y.
790 (defun interval->= (x y)
791 (declare (type interval x y))
792 ;; X >= Y if lower bound of X >= upper bound of Y
793 (when (and (interval-bounded-p x 'below)
794 (interval-bounded-p y 'above))
795 (>= (type-bound-number (interval-low x))
796 (type-bound-number (interval-high y)))))
798 ;;; Return an interval that is the absolute value of X. Thus, if
799 ;;; X = [-1 10], the result is [0, 10].
800 (defun interval-abs (x)
801 (declare (type interval x))
802 (case (interval-range-info x)
808 (destructuring-bind (x- x+) (interval-split 0 x t t)
809 (interval-merge-pair (interval-neg x-) x+)))))
811 ;;; Compute the square of an interval.
812 (defun interval-sqr (x)
813 (declare (type interval x))
814 (interval-func (lambda (x) (* x x))
817 ;;;; numeric DERIVE-TYPE methods
819 ;;; a utility for defining derive-type methods of integer operations. If
820 ;;; the types of both X and Y are integer types, then we compute a new
821 ;;; integer type with bounds determined Fun when applied to X and Y.
822 ;;; Otherwise, we use NUMERIC-CONTAGION.
823 (defun derive-integer-type-aux (x y fun)
824 (declare (type function fun))
825 (if (and (numeric-type-p x) (numeric-type-p y)
826 (eq (numeric-type-class x) 'integer)
827 (eq (numeric-type-class y) 'integer)
828 (eq (numeric-type-complexp x) :real)
829 (eq (numeric-type-complexp y) :real))
830 (multiple-value-bind (low high) (funcall fun x y)
831 (make-numeric-type :class 'integer
835 (numeric-contagion x y)))
837 (defun derive-integer-type (x y fun)
838 (declare (type lvar x y) (type function fun))
839 (let ((x (lvar-type x))
841 (derive-integer-type-aux x y fun)))
843 ;;; simple utility to flatten a list
844 (defun flatten-list (x)
845 (labels ((flatten-and-append (tree list)
846 (cond ((null tree) list)
847 ((atom tree) (cons tree list))
848 (t (flatten-and-append
849 (car tree) (flatten-and-append (cdr tree) list))))))
850 (flatten-and-append x nil)))
852 ;;; Take some type of lvar and massage it so that we get a list of the
853 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
855 (defun prepare-arg-for-derive-type (arg)
856 (flet ((listify (arg)
861 (union-type-types arg))
864 (unless (eq arg *empty-type*)
865 ;; Make sure all args are some type of numeric-type. For member
866 ;; types, convert the list of members into a union of equivalent
867 ;; single-element member-type's.
868 (let ((new-args nil))
869 (dolist (arg (listify arg))
870 (if (member-type-p arg)
871 ;; Run down the list of members and convert to a list of
873 (dolist (member (member-type-members arg))
874 (push (if (numberp member)
875 (make-member-type :members (list member))
878 (push arg new-args)))
879 (unless (member *empty-type* new-args)
882 ;;; Convert from the standard type convention for which -0.0 and 0.0
883 ;;; are equal to an intermediate convention for which they are
884 ;;; considered different which is more natural for some of the
886 (defun convert-numeric-type (type)
887 (declare (type numeric-type type))
888 ;;; Only convert real float interval delimiters types.
889 (if (eq (numeric-type-complexp type) :real)
890 (let* ((lo (numeric-type-low type))
891 (lo-val (type-bound-number lo))
892 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
893 (hi (numeric-type-high type))
894 (hi-val (type-bound-number hi))
895 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
896 (if (or lo-float-zero-p hi-float-zero-p)
898 :class (numeric-type-class type)
899 :format (numeric-type-format type)
901 :low (if lo-float-zero-p
903 (list (float 0.0 lo-val))
904 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
906 :high (if hi-float-zero-p
908 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
915 ;;; Convert back from the intermediate convention for which -0.0 and
916 ;;; 0.0 are considered different to the standard type convention for
918 (defun convert-back-numeric-type (type)
919 (declare (type numeric-type type))
920 ;;; Only convert real float interval delimiters types.
921 (if (eq (numeric-type-complexp type) :real)
922 (let* ((lo (numeric-type-low type))
923 (lo-val (type-bound-number lo))
925 (and lo (floatp lo-val) (= lo-val 0.0)
926 (float-sign lo-val)))
927 (hi (numeric-type-high type))
928 (hi-val (type-bound-number hi))
930 (and hi (floatp hi-val) (= hi-val 0.0)
931 (float-sign hi-val))))
933 ;; (float +0.0 +0.0) => (member 0.0)
934 ;; (float -0.0 -0.0) => (member -0.0)
935 ((and lo-float-zero-p hi-float-zero-p)
936 ;; shouldn't have exclusive bounds here..
937 (aver (and (not (consp lo)) (not (consp hi))))
938 (if (= lo-float-zero-p hi-float-zero-p)
939 ;; (float +0.0 +0.0) => (member 0.0)
940 ;; (float -0.0 -0.0) => (member -0.0)
941 (specifier-type `(member ,lo-val))
942 ;; (float -0.0 +0.0) => (float 0.0 0.0)
943 ;; (float +0.0 -0.0) => (float 0.0 0.0)
944 (make-numeric-type :class (numeric-type-class type)
945 :format (numeric-type-format type)
951 ;; (float -0.0 x) => (float 0.0 x)
952 ((and (not (consp lo)) (minusp lo-float-zero-p))
953 (make-numeric-type :class (numeric-type-class type)
954 :format (numeric-type-format type)
956 :low (float 0.0 lo-val)
958 ;; (float (+0.0) x) => (float (0.0) x)
959 ((and (consp lo) (plusp lo-float-zero-p))
960 (make-numeric-type :class (numeric-type-class type)
961 :format (numeric-type-format type)
963 :low (list (float 0.0 lo-val))
966 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
967 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
968 (list (make-member-type :members (list (float 0.0 lo-val)))
969 (make-numeric-type :class (numeric-type-class type)
970 :format (numeric-type-format type)
972 :low (list (float 0.0 lo-val))
976 ;; (float x +0.0) => (float x 0.0)
977 ((and (not (consp hi)) (plusp hi-float-zero-p))
978 (make-numeric-type :class (numeric-type-class type)
979 :format (numeric-type-format type)
982 :high (float 0.0 hi-val)))
983 ;; (float x (-0.0)) => (float x (0.0))
984 ((and (consp hi) (minusp hi-float-zero-p))
985 (make-numeric-type :class (numeric-type-class type)
986 :format (numeric-type-format type)
989 :high (list (float 0.0 hi-val))))
991 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
992 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
993 (list (make-member-type :members (list (float -0.0 hi-val)))
994 (make-numeric-type :class (numeric-type-class type)
995 :format (numeric-type-format type)
998 :high (list (float 0.0 hi-val)))))))
1004 ;;; Convert back a possible list of numeric types.
1005 (defun convert-back-numeric-type-list (type-list)
1008 (let ((results '()))
1009 (dolist (type type-list)
1010 (if (numeric-type-p type)
1011 (let ((result (convert-back-numeric-type type)))
1013 (setf results (append results result))
1014 (push result results)))
1015 (push type results)))
1018 (convert-back-numeric-type type-list))
1020 (convert-back-numeric-type-list (union-type-types type-list)))
1024 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
1025 ;;; belong in the kernel's type logic, invoked always, instead of in
1026 ;;; the compiler, invoked only during some type optimizations. (In
1027 ;;; fact, as of 0.pre8.100 or so they probably are, under
1028 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
1030 ;;; Take a list of types and return a canonical type specifier,
1031 ;;; combining any MEMBER types together. If both positive and negative
1032 ;;; MEMBER types are present they are converted to a float type.
1033 ;;; XXX This would be far simpler if the type-union methods could handle
1034 ;;; member/number unions.
1035 (defun make-canonical-union-type (type-list)
1038 (dolist (type type-list)
1039 (if (member-type-p type)
1040 (setf members (union members (member-type-members type)))
1041 (push type misc-types)))
1043 (when (null (set-difference `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0) members))
1044 (push (specifier-type '(long-float 0.0l0 0.0l0)) misc-types)
1045 (setf members (set-difference members `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0))))
1046 (when (null (set-difference `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0) members))
1047 (push (specifier-type '(double-float 0.0d0 0.0d0)) misc-types)
1048 (setf members (set-difference members `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0))))
1049 (when (null (set-difference `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0) members))
1050 (push (specifier-type '(single-float 0.0f0 0.0f0)) misc-types)
1051 (setf members (set-difference members `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0))))
1053 (apply #'type-union (make-member-type :members members) misc-types)
1054 (apply #'type-union misc-types))))
1056 ;;; Convert a member type with a single member to a numeric type.
1057 (defun convert-member-type (arg)
1058 (let* ((members (member-type-members arg))
1059 (member (first members))
1060 (member-type (type-of member)))
1061 (aver (not (rest members)))
1062 (specifier-type (cond ((typep member 'integer)
1063 `(integer ,member ,member))
1064 ((memq member-type '(short-float single-float
1065 double-float long-float))
1066 `(,member-type ,member ,member))
1070 ;;; This is used in defoptimizers for computing the resulting type of
1073 ;;; Given the lvar ARG, derive the resulting type using the
1074 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1075 ;;; "atomic" lvar type like numeric-type or member-type (containing
1076 ;;; just one element). It should return the resulting type, which can
1077 ;;; be a list of types.
1079 ;;; For the case of member types, if a MEMBER-FUN is given it is
1080 ;;; called to compute the result otherwise the member type is first
1081 ;;; converted to a numeric type and the DERIVE-FUN is called.
1082 (defun one-arg-derive-type (arg derive-fun member-fun
1083 &optional (convert-type t))
1084 (declare (type function derive-fun)
1085 (type (or null function) member-fun))
1086 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1092 (with-float-traps-masked
1093 (:underflow :overflow :divide-by-zero)
1095 `(eql ,(funcall member-fun
1096 (first (member-type-members x))))))
1097 ;; Otherwise convert to a numeric type.
1098 (let ((result-type-list
1099 (funcall derive-fun (convert-member-type x))))
1101 (convert-back-numeric-type-list result-type-list)
1102 result-type-list))))
1105 (convert-back-numeric-type-list
1106 (funcall derive-fun (convert-numeric-type x)))
1107 (funcall derive-fun x)))
1109 *universal-type*))))
1110 ;; Run down the list of args and derive the type of each one,
1111 ;; saving all of the results in a list.
1112 (let ((results nil))
1113 (dolist (arg arg-list)
1114 (let ((result (deriver arg)))
1116 (setf results (append results result))
1117 (push result results))))
1119 (make-canonical-union-type results)
1120 (first results)))))))
1122 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1123 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1124 ;;; original args and a third which is T to indicate if the two args
1125 ;;; really represent the same lvar. This is useful for deriving the
1126 ;;; type of things like (* x x), which should always be positive. If
1127 ;;; we didn't do this, we wouldn't be able to tell.
1128 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1129 &optional (convert-type t))
1130 (declare (type function derive-fun fun))
1131 (flet ((deriver (x y same-arg)
1132 (cond ((and (member-type-p x) (member-type-p y))
1133 (let* ((x (first (member-type-members x)))
1134 (y (first (member-type-members y)))
1135 (result (ignore-errors
1136 (with-float-traps-masked
1137 (:underflow :overflow :divide-by-zero
1139 (funcall fun x y)))))
1140 (cond ((null result) *empty-type*)
1141 ((and (floatp result) (float-nan-p result))
1142 (make-numeric-type :class 'float
1143 :format (type-of result)
1146 (specifier-type `(eql ,result))))))
1147 ((and (member-type-p x) (numeric-type-p y))
1148 (let* ((x (convert-member-type x))
1149 (y (if convert-type (convert-numeric-type y) y))
1150 (result (funcall derive-fun x y same-arg)))
1152 (convert-back-numeric-type-list result)
1154 ((and (numeric-type-p x) (member-type-p y))
1155 (let* ((x (if convert-type (convert-numeric-type x) x))
1156 (y (convert-member-type y))
1157 (result (funcall derive-fun x y same-arg)))
1159 (convert-back-numeric-type-list result)
1161 ((and (numeric-type-p x) (numeric-type-p y))
1162 (let* ((x (if convert-type (convert-numeric-type x) x))
1163 (y (if convert-type (convert-numeric-type y) y))
1164 (result (funcall derive-fun x y same-arg)))
1166 (convert-back-numeric-type-list result)
1169 *universal-type*))))
1170 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1171 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1172 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1174 (let ((results nil))
1176 ;; Since the args are the same LVARs, just run down the
1179 (let ((result (deriver x x same-arg)))
1181 (setf results (append results result))
1182 (push result results))))
1183 ;; Try all pairwise combinations.
1186 (let ((result (or (deriver x y same-arg)
1187 (numeric-contagion x y))))
1189 (setf results (append results result))
1190 (push result results))))))
1192 (make-canonical-union-type results)
1193 (first results)))))))
1195 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1197 (defoptimizer (+ derive-type) ((x y))
1198 (derive-integer-type
1205 (values (frob (numeric-type-low x) (numeric-type-low y))
1206 (frob (numeric-type-high x) (numeric-type-high y)))))))
1208 (defoptimizer (- derive-type) ((x y))
1209 (derive-integer-type
1216 (values (frob (numeric-type-low x) (numeric-type-high y))
1217 (frob (numeric-type-high x) (numeric-type-low y)))))))
1219 (defoptimizer (* derive-type) ((x y))
1220 (derive-integer-type
1223 (let ((x-low (numeric-type-low x))
1224 (x-high (numeric-type-high x))
1225 (y-low (numeric-type-low y))
1226 (y-high (numeric-type-high y)))
1227 (cond ((not (and x-low y-low))
1229 ((or (minusp x-low) (minusp y-low))
1230 (if (and x-high y-high)
1231 (let ((max (* (max (abs x-low) (abs x-high))
1232 (max (abs y-low) (abs y-high)))))
1233 (values (- max) max))
1236 (values (* x-low y-low)
1237 (if (and x-high y-high)
1241 (defoptimizer (/ derive-type) ((x y))
1242 (numeric-contagion (lvar-type x) (lvar-type y)))
1246 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1248 (defun +-derive-type-aux (x y same-arg)
1249 (if (and (numeric-type-real-p x)
1250 (numeric-type-real-p y))
1253 (let ((x-int (numeric-type->interval x)))
1254 (interval-add x-int x-int))
1255 (interval-add (numeric-type->interval x)
1256 (numeric-type->interval y))))
1257 (result-type (numeric-contagion x y)))
1258 ;; If the result type is a float, we need to be sure to coerce
1259 ;; the bounds into the correct type.
1260 (when (eq (numeric-type-class result-type) 'float)
1261 (setf result (interval-func
1263 (coerce-for-bound x (or (numeric-type-format result-type)
1267 :class (if (and (eq (numeric-type-class x) 'integer)
1268 (eq (numeric-type-class y) 'integer))
1269 ;; The sum of integers is always an integer.
1271 (numeric-type-class result-type))
1272 :format (numeric-type-format result-type)
1273 :low (interval-low result)
1274 :high (interval-high result)))
1275 ;; general contagion
1276 (numeric-contagion x y)))
1278 (defoptimizer (+ derive-type) ((x y))
1279 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1281 (defun --derive-type-aux (x y same-arg)
1282 (if (and (numeric-type-real-p x)
1283 (numeric-type-real-p y))
1285 ;; (- X X) is always 0.
1287 (make-interval :low 0 :high 0)
1288 (interval-sub (numeric-type->interval x)
1289 (numeric-type->interval y))))
1290 (result-type (numeric-contagion x y)))
1291 ;; If the result type is a float, we need to be sure to coerce
1292 ;; the bounds into the correct type.
1293 (when (eq (numeric-type-class result-type) 'float)
1294 (setf result (interval-func
1296 (coerce-for-bound x (or (numeric-type-format result-type)
1300 :class (if (and (eq (numeric-type-class x) 'integer)
1301 (eq (numeric-type-class y) 'integer))
1302 ;; The difference of integers is always an integer.
1304 (numeric-type-class result-type))
1305 :format (numeric-type-format result-type)
1306 :low (interval-low result)
1307 :high (interval-high result)))
1308 ;; general contagion
1309 (numeric-contagion x y)))
1311 (defoptimizer (- derive-type) ((x y))
1312 (two-arg-derive-type x y #'--derive-type-aux #'-))
1314 (defun *-derive-type-aux (x y same-arg)
1315 (if (and (numeric-type-real-p x)
1316 (numeric-type-real-p y))
1318 ;; (* X X) is always positive, so take care to do it right.
1320 (interval-sqr (numeric-type->interval x))
1321 (interval-mul (numeric-type->interval x)
1322 (numeric-type->interval y))))
1323 (result-type (numeric-contagion x y)))
1324 ;; If the result type is a float, we need to be sure to coerce
1325 ;; the bounds into the correct type.
1326 (when (eq (numeric-type-class result-type) 'float)
1327 (setf result (interval-func
1329 (coerce-for-bound x (or (numeric-type-format result-type)
1333 :class (if (and (eq (numeric-type-class x) 'integer)
1334 (eq (numeric-type-class y) 'integer))
1335 ;; The product of integers is always an integer.
1337 (numeric-type-class result-type))
1338 :format (numeric-type-format result-type)
1339 :low (interval-low result)
1340 :high (interval-high result)))
1341 (numeric-contagion x y)))
1343 (defoptimizer (* derive-type) ((x y))
1344 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1346 (defun /-derive-type-aux (x y same-arg)
1347 (if (and (numeric-type-real-p x)
1348 (numeric-type-real-p y))
1350 ;; (/ X X) is always 1, except if X can contain 0. In
1351 ;; that case, we shouldn't optimize the division away
1352 ;; because we want 0/0 to signal an error.
1354 (not (interval-contains-p
1355 0 (interval-closure (numeric-type->interval y)))))
1356 (make-interval :low 1 :high 1)
1357 (interval-div (numeric-type->interval x)
1358 (numeric-type->interval y))))
1359 (result-type (numeric-contagion x y)))
1360 ;; If the result type is a float, we need to be sure to coerce
1361 ;; the bounds into the correct type.
1362 (when (eq (numeric-type-class result-type) 'float)
1363 (setf result (interval-func
1365 (coerce-for-bound x (or (numeric-type-format result-type)
1368 (make-numeric-type :class (numeric-type-class result-type)
1369 :format (numeric-type-format result-type)
1370 :low (interval-low result)
1371 :high (interval-high result)))
1372 (numeric-contagion x y)))
1374 (defoptimizer (/ derive-type) ((x y))
1375 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1379 (defun ash-derive-type-aux (n-type shift same-arg)
1380 (declare (ignore same-arg))
1381 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1382 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1383 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1384 ;; two bignums yielding zero) and it's hard to avoid that
1385 ;; calculation in here.
1386 #+(and cmu sb-xc-host)
1387 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1388 (typep (numeric-type-high n-type) 'bignum))
1389 (or (typep (numeric-type-low shift) 'bignum)
1390 (typep (numeric-type-high shift) 'bignum)))
1391 (return-from ash-derive-type-aux *universal-type*))
1392 (flet ((ash-outer (n s)
1393 (when (and (fixnump s)
1395 (> s sb!xc:most-negative-fixnum))
1397 ;; KLUDGE: The bare 64's here should be related to
1398 ;; symbolic machine word size values somehow.
1401 (if (and (fixnump s)
1402 (> s sb!xc:most-negative-fixnum))
1404 (if (minusp n) -1 0))))
1405 (or (and (csubtypep n-type (specifier-type 'integer))
1406 (csubtypep shift (specifier-type 'integer))
1407 (let ((n-low (numeric-type-low n-type))
1408 (n-high (numeric-type-high n-type))
1409 (s-low (numeric-type-low shift))
1410 (s-high (numeric-type-high shift)))
1411 (make-numeric-type :class 'integer :complexp :real
1414 (ash-outer n-low s-high)
1415 (ash-inner n-low s-low)))
1418 (ash-inner n-high s-low)
1419 (ash-outer n-high s-high))))))
1422 (defoptimizer (ash derive-type) ((n shift))
1423 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1425 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1426 (macrolet ((frob (fun)
1427 `#'(lambda (type type2)
1428 (declare (ignore type2))
1429 (let ((lo (numeric-type-low type))
1430 (hi (numeric-type-high type)))
1431 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1433 (defoptimizer (%negate derive-type) ((num))
1434 (derive-integer-type num num (frob -))))
1436 (defun lognot-derive-type-aux (int)
1437 (derive-integer-type-aux int int
1438 (lambda (type type2)
1439 (declare (ignore type2))
1440 (let ((lo (numeric-type-low type))
1441 (hi (numeric-type-high type)))
1442 (values (if hi (lognot hi) nil)
1443 (if lo (lognot lo) nil)
1444 (numeric-type-class type)
1445 (numeric-type-format type))))))
1447 (defoptimizer (lognot derive-type) ((int))
1448 (lognot-derive-type-aux (lvar-type int)))
1450 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1451 (defoptimizer (%negate derive-type) ((num))
1452 (flet ((negate-bound (b)
1454 (set-bound (- (type-bound-number b))
1456 (one-arg-derive-type num
1458 (modified-numeric-type
1460 :low (negate-bound (numeric-type-high type))
1461 :high (negate-bound (numeric-type-low type))))
1464 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1465 (defoptimizer (abs derive-type) ((num))
1466 (let ((type (lvar-type num)))
1467 (if (and (numeric-type-p type)
1468 (eq (numeric-type-class type) 'integer)
1469 (eq (numeric-type-complexp type) :real))
1470 (let ((lo (numeric-type-low type))
1471 (hi (numeric-type-high type)))
1472 (make-numeric-type :class 'integer :complexp :real
1473 :low (cond ((and hi (minusp hi))
1479 :high (if (and hi lo)
1480 (max (abs hi) (abs lo))
1482 (numeric-contagion type type))))
1484 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1485 (defun abs-derive-type-aux (type)
1486 (cond ((eq (numeric-type-complexp type) :complex)
1487 ;; The absolute value of a complex number is always a
1488 ;; non-negative float.
1489 (let* ((format (case (numeric-type-class type)
1490 ((integer rational) 'single-float)
1491 (t (numeric-type-format type))))
1492 (bound-format (or format 'float)))
1493 (make-numeric-type :class 'float
1496 :low (coerce 0 bound-format)
1499 ;; The absolute value of a real number is a non-negative real
1500 ;; of the same type.
1501 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1502 (class (numeric-type-class type))
1503 (format (numeric-type-format type))
1504 (bound-type (or format class 'real)))
1509 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1510 :high (coerce-and-truncate-floats
1511 (interval-high abs-bnd) bound-type))))))
1513 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1514 (defoptimizer (abs derive-type) ((num))
1515 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1517 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1518 (defoptimizer (truncate derive-type) ((number divisor))
1519 (let ((number-type (lvar-type number))
1520 (divisor-type (lvar-type divisor))
1521 (integer-type (specifier-type 'integer)))
1522 (if (and (numeric-type-p number-type)
1523 (csubtypep number-type integer-type)
1524 (numeric-type-p divisor-type)
1525 (csubtypep divisor-type integer-type))
1526 (let ((number-low (numeric-type-low number-type))
1527 (number-high (numeric-type-high number-type))
1528 (divisor-low (numeric-type-low divisor-type))
1529 (divisor-high (numeric-type-high divisor-type)))
1530 (values-specifier-type
1531 `(values ,(integer-truncate-derive-type number-low number-high
1532 divisor-low divisor-high)
1533 ,(integer-rem-derive-type number-low number-high
1534 divisor-low divisor-high))))
1537 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1540 (defun rem-result-type (number-type divisor-type)
1541 ;; Figure out what the remainder type is. The remainder is an
1542 ;; integer if both args are integers; a rational if both args are
1543 ;; rational; and a float otherwise.
1544 (cond ((and (csubtypep number-type (specifier-type 'integer))
1545 (csubtypep divisor-type (specifier-type 'integer)))
1547 ((and (csubtypep number-type (specifier-type 'rational))
1548 (csubtypep divisor-type (specifier-type 'rational)))
1550 ((and (csubtypep number-type (specifier-type 'float))
1551 (csubtypep divisor-type (specifier-type 'float)))
1552 ;; Both are floats so the result is also a float, of
1553 ;; the largest type.
1554 (or (float-format-max (numeric-type-format number-type)
1555 (numeric-type-format divisor-type))
1557 ((and (csubtypep number-type (specifier-type 'float))
1558 (csubtypep divisor-type (specifier-type 'rational)))
1559 ;; One of the arguments is a float and the other is a
1560 ;; rational. The remainder is a float of the same
1562 (or (numeric-type-format number-type) 'float))
1563 ((and (csubtypep divisor-type (specifier-type 'float))
1564 (csubtypep number-type (specifier-type 'rational)))
1565 ;; One of the arguments is a float and the other is a
1566 ;; rational. The remainder is a float of the same
1568 (or (numeric-type-format divisor-type) 'float))
1570 ;; Some unhandled combination. This usually means both args
1571 ;; are REAL so the result is a REAL.
1574 (defun truncate-derive-type-quot (number-type divisor-type)
1575 (let* ((rem-type (rem-result-type number-type divisor-type))
1576 (number-interval (numeric-type->interval number-type))
1577 (divisor-interval (numeric-type->interval divisor-type)))
1578 ;;(declare (type (member '(integer rational float)) rem-type))
1579 ;; We have real numbers now.
1580 (cond ((eq rem-type 'integer)
1581 ;; Since the remainder type is INTEGER, both args are
1583 (let* ((res (integer-truncate-derive-type
1584 (interval-low number-interval)
1585 (interval-high number-interval)
1586 (interval-low divisor-interval)
1587 (interval-high divisor-interval))))
1588 (specifier-type (if (listp res) res 'integer))))
1590 (let ((quot (truncate-quotient-bound
1591 (interval-div number-interval
1592 divisor-interval))))
1593 (specifier-type `(integer ,(or (interval-low quot) '*)
1594 ,(or (interval-high quot) '*))))))))
1596 (defun truncate-derive-type-rem (number-type divisor-type)
1597 (let* ((rem-type (rem-result-type number-type divisor-type))
1598 (number-interval (numeric-type->interval number-type))
1599 (divisor-interval (numeric-type->interval divisor-type))
1600 (rem (truncate-rem-bound number-interval divisor-interval)))
1601 ;;(declare (type (member '(integer rational float)) rem-type))
1602 ;; We have real numbers now.
1603 (cond ((eq rem-type 'integer)
1604 ;; Since the remainder type is INTEGER, both args are
1606 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1607 ,(or (interval-high rem) '*))))
1609 (multiple-value-bind (class format)
1612 (values 'integer nil))
1614 (values 'rational nil))
1615 ((or single-float double-float #!+long-float long-float)
1616 (values 'float rem-type))
1618 (values 'float nil))
1621 (when (member rem-type '(float single-float double-float
1622 #!+long-float long-float))
1623 (setf rem (interval-func #'(lambda (x)
1624 (coerce-for-bound x rem-type))
1626 (make-numeric-type :class class
1628 :low (interval-low rem)
1629 :high (interval-high rem)))))))
1631 (defun truncate-derive-type-quot-aux (num div same-arg)
1632 (declare (ignore same-arg))
1633 (if (and (numeric-type-real-p num)
1634 (numeric-type-real-p div))
1635 (truncate-derive-type-quot num div)
1638 (defun truncate-derive-type-rem-aux (num div same-arg)
1639 (declare (ignore same-arg))
1640 (if (and (numeric-type-real-p num)
1641 (numeric-type-real-p div))
1642 (truncate-derive-type-rem num div)
1645 (defoptimizer (truncate derive-type) ((number divisor))
1646 (let ((quot (two-arg-derive-type number divisor
1647 #'truncate-derive-type-quot-aux #'truncate))
1648 (rem (two-arg-derive-type number divisor
1649 #'truncate-derive-type-rem-aux #'rem)))
1650 (when (and quot rem)
1651 (make-values-type :required (list quot rem)))))
1653 (defun ftruncate-derive-type-quot (number-type divisor-type)
1654 ;; The bounds are the same as for truncate. However, the first
1655 ;; result is a float of some type. We need to determine what that
1656 ;; type is. Basically it's the more contagious of the two types.
1657 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1658 (res-type (numeric-contagion number-type divisor-type)))
1659 (make-numeric-type :class 'float
1660 :format (numeric-type-format res-type)
1661 :low (numeric-type-low q-type)
1662 :high (numeric-type-high q-type))))
1664 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1665 (declare (ignore same-arg))
1666 (if (and (numeric-type-real-p n)
1667 (numeric-type-real-p d))
1668 (ftruncate-derive-type-quot n d)
1671 (defoptimizer (ftruncate derive-type) ((number divisor))
1673 (two-arg-derive-type number divisor
1674 #'ftruncate-derive-type-quot-aux #'ftruncate))
1675 (rem (two-arg-derive-type number divisor
1676 #'truncate-derive-type-rem-aux #'rem)))
1677 (when (and quot rem)
1678 (make-values-type :required (list quot rem)))))
1680 (defun %unary-truncate-derive-type-aux (number)
1681 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1683 (defoptimizer (%unary-truncate derive-type) ((number))
1684 (one-arg-derive-type number
1685 #'%unary-truncate-derive-type-aux
1688 (defoptimizer (%unary-ftruncate derive-type) ((number))
1689 (let ((divisor (specifier-type '(integer 1 1))))
1690 (one-arg-derive-type number
1692 (ftruncate-derive-type-quot-aux n divisor nil))
1693 #'%unary-ftruncate)))
1695 ;;; Define optimizers for FLOOR and CEILING.
1697 ((def (name q-name r-name)
1698 (let ((q-aux (symbolicate q-name "-AUX"))
1699 (r-aux (symbolicate r-name "-AUX")))
1701 ;; Compute type of quotient (first) result.
1702 (defun ,q-aux (number-type divisor-type)
1703 (let* ((number-interval
1704 (numeric-type->interval number-type))
1706 (numeric-type->interval divisor-type))
1707 (quot (,q-name (interval-div number-interval
1708 divisor-interval))))
1709 (specifier-type `(integer ,(or (interval-low quot) '*)
1710 ,(or (interval-high quot) '*)))))
1711 ;; Compute type of remainder.
1712 (defun ,r-aux (number-type divisor-type)
1713 (let* ((divisor-interval
1714 (numeric-type->interval divisor-type))
1715 (rem (,r-name divisor-interval))
1716 (result-type (rem-result-type number-type divisor-type)))
1717 (multiple-value-bind (class format)
1720 (values 'integer nil))
1722 (values 'rational nil))
1723 ((or single-float double-float #!+long-float long-float)
1724 (values 'float result-type))
1726 (values 'float nil))
1729 (when (member result-type '(float single-float double-float
1730 #!+long-float long-float))
1731 ;; Make sure that the limits on the interval have
1733 (setf rem (interval-func (lambda (x)
1734 (coerce-for-bound x result-type))
1736 (make-numeric-type :class class
1738 :low (interval-low rem)
1739 :high (interval-high rem)))))
1740 ;; the optimizer itself
1741 (defoptimizer (,name derive-type) ((number divisor))
1742 (flet ((derive-q (n d same-arg)
1743 (declare (ignore same-arg))
1744 (if (and (numeric-type-real-p n)
1745 (numeric-type-real-p d))
1748 (derive-r (n d same-arg)
1749 (declare (ignore same-arg))
1750 (if (and (numeric-type-real-p n)
1751 (numeric-type-real-p d))
1754 (let ((quot (two-arg-derive-type
1755 number divisor #'derive-q #',name))
1756 (rem (two-arg-derive-type
1757 number divisor #'derive-r #'mod)))
1758 (when (and quot rem)
1759 (make-values-type :required (list quot rem))))))))))
1761 (def floor floor-quotient-bound floor-rem-bound)
1762 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1764 ;;; Define optimizers for FFLOOR and FCEILING
1765 (macrolet ((def (name q-name r-name)
1766 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1767 (r-aux (symbolicate r-name "-AUX")))
1769 ;; Compute type of quotient (first) result.
1770 (defun ,q-aux (number-type divisor-type)
1771 (let* ((number-interval
1772 (numeric-type->interval number-type))
1774 (numeric-type->interval divisor-type))
1775 (quot (,q-name (interval-div number-interval
1777 (res-type (numeric-contagion number-type
1780 :class (numeric-type-class res-type)
1781 :format (numeric-type-format res-type)
1782 :low (interval-low quot)
1783 :high (interval-high quot))))
1785 (defoptimizer (,name derive-type) ((number divisor))
1786 (flet ((derive-q (n d same-arg)
1787 (declare (ignore same-arg))
1788 (if (and (numeric-type-real-p n)
1789 (numeric-type-real-p d))
1792 (derive-r (n d same-arg)
1793 (declare (ignore same-arg))
1794 (if (and (numeric-type-real-p n)
1795 (numeric-type-real-p d))
1798 (let ((quot (two-arg-derive-type
1799 number divisor #'derive-q #',name))
1800 (rem (two-arg-derive-type
1801 number divisor #'derive-r #'mod)))
1802 (when (and quot rem)
1803 (make-values-type :required (list quot rem))))))))))
1805 (def ffloor floor-quotient-bound floor-rem-bound)
1806 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
1808 ;;; functions to compute the bounds on the quotient and remainder for
1809 ;;; the FLOOR function
1810 (defun floor-quotient-bound (quot)
1811 ;; Take the floor of the quotient and then massage it into what we
1813 (let ((lo (interval-low quot))
1814 (hi (interval-high quot)))
1815 ;; Take the floor of the lower bound. The result is always a
1816 ;; closed lower bound.
1818 (floor (type-bound-number lo))
1820 ;; For the upper bound, we need to be careful.
1823 ;; An open bound. We need to be careful here because
1824 ;; the floor of '(10.0) is 9, but the floor of
1826 (multiple-value-bind (q r) (floor (first hi))
1831 ;; A closed bound, so the answer is obvious.
1835 (make-interval :low lo :high hi)))
1836 (defun floor-rem-bound (div)
1837 ;; The remainder depends only on the divisor. Try to get the
1838 ;; correct sign for the remainder if we can.
1839 (case (interval-range-info div)
1841 ;; The divisor is always positive.
1842 (let ((rem (interval-abs div)))
1843 (setf (interval-low rem) 0)
1844 (when (and (numberp (interval-high rem))
1845 (not (zerop (interval-high rem))))
1846 ;; The remainder never contains the upper bound. However,
1847 ;; watch out for the case where the high limit is zero!
1848 (setf (interval-high rem) (list (interval-high rem))))
1851 ;; The divisor is always negative.
1852 (let ((rem (interval-neg (interval-abs div))))
1853 (setf (interval-high rem) 0)
1854 (when (numberp (interval-low rem))
1855 ;; The remainder never contains the lower bound.
1856 (setf (interval-low rem) (list (interval-low rem))))
1859 ;; The divisor can be positive or negative. All bets off. The
1860 ;; magnitude of remainder is the maximum value of the divisor.
1861 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1862 ;; The bound never reaches the limit, so make the interval open.
1863 (make-interval :low (if limit
1866 :high (list limit))))))
1868 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1869 => #S(INTERVAL :LOW 0 :HIGH 10)
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))
1873 => #S(INTERVAL :LOW 0 :HIGH 10)
1874 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1875 => #S(INTERVAL :LOW 0 :HIGH 9)
1876 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1877 => #S(INTERVAL :LOW 0 :HIGH 10)
1878 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1879 => #S(INTERVAL :LOW 0 :HIGH 10)
1880 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1881 => #S(INTERVAL :LOW -2 :HIGH 10)
1882 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1883 => #S(INTERVAL :LOW -1 :HIGH 10)
1884 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1885 => #S(INTERVAL :LOW -1 :HIGH 10)
1887 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1888 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
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 -10 :high -2.3))
1892 #S(INTERVAL :LOW (-10) :HIGH 0)
1893 (floor-rem-bound (make-interval :low 0.3 :high 10))
1894 => #S(INTERVAL :LOW 0 :HIGH '(10))
1895 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1896 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1897 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1898 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1901 ;;; same functions for CEILING
1902 (defun ceiling-quotient-bound (quot)
1903 ;; Take the ceiling of the quotient and then massage it into what we
1905 (let ((lo (interval-low quot))
1906 (hi (interval-high quot)))
1907 ;; Take the ceiling of the upper bound. The result is always a
1908 ;; closed upper bound.
1910 (ceiling (type-bound-number hi))
1912 ;; For the lower bound, we need to be careful.
1915 ;; An open bound. We need to be careful here because
1916 ;; the ceiling of '(10.0) is 11, but the ceiling of
1918 (multiple-value-bind (q r) (ceiling (first lo))
1923 ;; A closed bound, so the answer is obvious.
1927 (make-interval :low lo :high hi)))
1928 (defun ceiling-rem-bound (div)
1929 ;; The remainder depends only on the divisor. Try to get the
1930 ;; correct sign for the remainder if we can.
1931 (case (interval-range-info div)
1933 ;; Divisor is always positive. The remainder is negative.
1934 (let ((rem (interval-neg (interval-abs div))))
1935 (setf (interval-high rem) 0)
1936 (when (and (numberp (interval-low rem))
1937 (not (zerop (interval-low rem))))
1938 ;; The remainder never contains the upper bound. However,
1939 ;; watch out for the case when the upper bound is zero!
1940 (setf (interval-low rem) (list (interval-low rem))))
1943 ;; Divisor is always negative. The remainder is positive
1944 (let ((rem (interval-abs div)))
1945 (setf (interval-low rem) 0)
1946 (when (numberp (interval-high rem))
1947 ;; The remainder never contains the lower bound.
1948 (setf (interval-high rem) (list (interval-high rem))))
1951 ;; The divisor can be positive or negative. All bets off. The
1952 ;; magnitude of remainder is the maximum value of the divisor.
1953 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1954 ;; The bound never reaches the limit, so make the interval open.
1955 (make-interval :low (if limit
1958 :high (list limit))))))
1961 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
1962 => #S(INTERVAL :LOW 1 :HIGH 11)
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))
1966 => #S(INTERVAL :LOW 1 :HIGH 10)
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 10.3))
1970 => #S(INTERVAL :LOW 1 :HIGH 11)
1971 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
1972 => #S(INTERVAL :LOW 1 :HIGH 11)
1973 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1974 => #S(INTERVAL :LOW -1 :HIGH 11)
1975 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1976 => #S(INTERVAL :LOW 0 :HIGH 11)
1977 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
1978 => #S(INTERVAL :LOW -1 :HIGH 11)
1980 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
1981 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
1982 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
1983 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1984 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
1985 => #S(INTERVAL :LOW 0 :HIGH (10))
1986 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
1987 => #S(INTERVAL :LOW (-10) :HIGH 0)
1988 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
1989 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
1990 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
1991 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1994 (defun truncate-quotient-bound (quot)
1995 ;; For positive quotients, truncate is exactly like floor. For
1996 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
1997 ;; it's the union of the two pieces.
1998 (case (interval-range-info quot)
2001 (floor-quotient-bound quot))
2003 ;; just like CEILING
2004 (ceiling-quotient-bound quot))
2006 ;; Split the interval into positive and negative pieces, compute
2007 ;; the result for each piece and put them back together.
2008 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2009 (interval-merge-pair (ceiling-quotient-bound neg)
2010 (floor-quotient-bound pos))))))
2012 (defun truncate-rem-bound (num div)
2013 ;; This is significantly more complicated than FLOOR or CEILING. We
2014 ;; need both the number and the divisor to determine the range. The
2015 ;; basic idea is to split the ranges of NUM and DEN into positive
2016 ;; and negative pieces and deal with each of the four possibilities
2018 (case (interval-range-info num)
2020 (case (interval-range-info div)
2022 (floor-rem-bound div))
2024 (ceiling-rem-bound div))
2026 (destructuring-bind (neg pos) (interval-split 0 div t t)
2027 (interval-merge-pair (truncate-rem-bound num neg)
2028 (truncate-rem-bound num pos))))))
2030 (case (interval-range-info div)
2032 (ceiling-rem-bound div))
2034 (floor-rem-bound div))
2036 (destructuring-bind (neg pos) (interval-split 0 div t t)
2037 (interval-merge-pair (truncate-rem-bound num neg)
2038 (truncate-rem-bound num pos))))))
2040 (destructuring-bind (neg pos) (interval-split 0 num t t)
2041 (interval-merge-pair (truncate-rem-bound neg div)
2042 (truncate-rem-bound pos div))))))
2045 ;;; Derive useful information about the range. Returns three values:
2046 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2047 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2048 ;;; - The abs of the maximal value if there is one, or nil if it is
2050 (defun numeric-range-info (low high)
2051 (cond ((and low (not (minusp low)))
2052 (values '+ low high))
2053 ((and high (not (plusp high)))
2054 (values '- (- high) (if low (- low) nil)))
2056 (values nil 0 (and low high (max (- low) high))))))
2058 (defun integer-truncate-derive-type
2059 (number-low number-high divisor-low divisor-high)
2060 ;; The result cannot be larger in magnitude than the number, but the
2061 ;; sign might change. If we can determine the sign of either the
2062 ;; number or the divisor, we can eliminate some of the cases.
2063 (multiple-value-bind (number-sign number-min number-max)
2064 (numeric-range-info number-low number-high)
2065 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2066 (numeric-range-info divisor-low divisor-high)
2067 (when (and divisor-max (zerop divisor-max))
2068 ;; We've got a problem: guaranteed division by zero.
2069 (return-from integer-truncate-derive-type t))
2070 (when (zerop divisor-min)
2071 ;; We'll assume that they aren't going to divide by zero.
2073 (cond ((and number-sign divisor-sign)
2074 ;; We know the sign of both.
2075 (if (eq number-sign divisor-sign)
2076 ;; Same sign, so the result will be positive.
2077 `(integer ,(if divisor-max
2078 (truncate number-min divisor-max)
2081 (truncate number-max divisor-min)
2083 ;; Different signs, the result will be negative.
2084 `(integer ,(if number-max
2085 (- (truncate number-max divisor-min))
2088 (- (truncate number-min divisor-max))
2090 ((eq divisor-sign '+)
2091 ;; The divisor is positive. Therefore, the number will just
2092 ;; become closer to zero.
2093 `(integer ,(if number-low
2094 (truncate number-low divisor-min)
2097 (truncate number-high divisor-min)
2099 ((eq divisor-sign '-)
2100 ;; The divisor is negative. Therefore, the absolute value of
2101 ;; the number will become closer to zero, but the sign will also
2103 `(integer ,(if number-high
2104 (- (truncate number-high divisor-min))
2107 (- (truncate number-low divisor-min))
2109 ;; The divisor could be either positive or negative.
2111 ;; The number we are dividing has a bound. Divide that by the
2112 ;; smallest posible divisor.
2113 (let ((bound (truncate number-max divisor-min)))
2114 `(integer ,(- bound) ,bound)))
2116 ;; The number we are dividing is unbounded, so we can't tell
2117 ;; anything about the result.
2120 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2121 (defun integer-rem-derive-type
2122 (number-low number-high divisor-low divisor-high)
2123 (if (and divisor-low divisor-high)
2124 ;; We know the range of the divisor, and the remainder must be
2125 ;; smaller than the divisor. We can tell the sign of the
2126 ;; remainer if we know the sign of the number.
2127 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2128 `(integer ,(if (or (null number-low)
2129 (minusp number-low))
2132 ,(if (or (null number-high)
2133 (plusp number-high))
2136 ;; The divisor is potentially either very positive or very
2137 ;; negative. Therefore, the remainer is unbounded, but we might
2138 ;; be able to tell something about the sign from the number.
2139 `(integer ,(if (and number-low (not (minusp number-low)))
2140 ;; The number we are dividing is positive.
2141 ;; Therefore, the remainder must be positive.
2144 ,(if (and number-high (not (plusp number-high)))
2145 ;; The number we are dividing is negative.
2146 ;; Therefore, the remainder must be negative.
2150 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2151 (defoptimizer (random derive-type) ((bound &optional state))
2152 (let ((type (lvar-type bound)))
2153 (when (numeric-type-p type)
2154 (let ((class (numeric-type-class type))
2155 (high (numeric-type-high type))
2156 (format (numeric-type-format type)))
2160 :low (coerce 0 (or format class 'real))
2161 :high (cond ((not high) nil)
2162 ((eq class 'integer) (max (1- high) 0))
2163 ((or (consp high) (zerop high)) high)
2166 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2167 (defun random-derive-type-aux (type)
2168 (let ((class (numeric-type-class type))
2169 (high (numeric-type-high type))
2170 (format (numeric-type-format type)))
2174 :low (coerce 0 (or format class 'real))
2175 :high (cond ((not high) nil)
2176 ((eq class 'integer) (max (1- high) 0))
2177 ((or (consp high) (zerop high)) high)
2180 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2181 (defoptimizer (random derive-type) ((bound &optional state))
2182 (one-arg-derive-type bound #'random-derive-type-aux nil))
2184 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2186 ;;; Return the maximum number of bits an integer of the supplied type
2187 ;;; can take up, or NIL if it is unbounded. The second (third) value
2188 ;;; is T if the integer can be positive (negative) and NIL if not.
2189 ;;; Zero counts as positive.
2190 (defun integer-type-length (type)
2191 (if (numeric-type-p type)
2192 (let ((min (numeric-type-low type))
2193 (max (numeric-type-high type)))
2194 (values (and min max (max (integer-length min) (integer-length max)))
2195 (or (null max) (not (minusp max)))
2196 (or (null min) (minusp min))))
2199 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2200 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2201 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2202 ;;; versions in CMUCL, from which these functions copy liberally.
2204 (defun logand-derive-unsigned-low-bound (x y)
2205 (let ((a (numeric-type-low x))
2206 (b (numeric-type-high x))
2207 (c (numeric-type-low y))
2208 (d (numeric-type-high y)))
2209 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2211 (unless (zerop (logand m (lognot a) (lognot c)))
2212 (let ((temp (logandc2 (logior a m) (1- m))))
2216 (setf temp (logandc2 (logior c m) (1- m)))
2220 finally (return (logand a c)))))
2222 (defun logand-derive-unsigned-high-bound (x y)
2223 (let ((a (numeric-type-low x))
2224 (b (numeric-type-high x))
2225 (c (numeric-type-low y))
2226 (d (numeric-type-high y)))
2227 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2230 ((not (zerop (logand b (lognot d) m)))
2231 (let ((temp (logior (logandc2 b m) (1- m))))
2235 ((not (zerop (logand (lognot b) d m)))
2236 (let ((temp (logior (logandc2 d m) (1- m))))
2240 finally (return (logand b d)))))
2242 (defun logand-derive-type-aux (x y &optional same-leaf)
2244 (return-from logand-derive-type-aux x))
2245 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2246 (declare (ignore x-pos))
2247 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2248 (declare (ignore y-pos))
2250 ;; X must be positive.
2252 ;; They must both be positive.
2253 (cond ((and (null x-len) (null y-len))
2254 (specifier-type 'unsigned-byte))
2256 (specifier-type `(unsigned-byte* ,y-len)))
2258 (specifier-type `(unsigned-byte* ,x-len)))
2260 (let ((low (logand-derive-unsigned-low-bound x y))
2261 (high (logand-derive-unsigned-high-bound x y)))
2262 (specifier-type `(integer ,low ,high)))))
2263 ;; X is positive, but Y might be negative.
2265 (specifier-type 'unsigned-byte))
2267 (specifier-type `(unsigned-byte* ,x-len)))))
2268 ;; X might be negative.
2270 ;; Y must be positive.
2272 (specifier-type 'unsigned-byte))
2273 (t (specifier-type `(unsigned-byte* ,y-len))))
2274 ;; Either might be negative.
2275 (if (and x-len y-len)
2276 ;; The result is bounded.
2277 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2278 ;; We can't tell squat about the result.
2279 (specifier-type 'integer)))))))
2281 (defun logior-derive-unsigned-low-bound (x y)
2282 (let ((a (numeric-type-low x))
2283 (b (numeric-type-high x))
2284 (c (numeric-type-low y))
2285 (d (numeric-type-high y)))
2286 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2289 ((not (zerop (logandc2 (logand c m) a)))
2290 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2294 ((not (zerop (logandc2 (logand a m) c)))
2295 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2299 finally (return (logior a c)))))
2301 (defun logior-derive-unsigned-high-bound (x y)
2302 (let ((a (numeric-type-low x))
2303 (b (numeric-type-high x))
2304 (c (numeric-type-low y))
2305 (d (numeric-type-high y)))
2306 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2308 (unless (zerop (logand b d m))
2309 (let ((temp (logior (- b m) (1- m))))
2313 (setf temp (logior (- d m) (1- m)))
2317 finally (return (logior b d)))))
2319 (defun logior-derive-type-aux (x y &optional same-leaf)
2321 (return-from logior-derive-type-aux x))
2322 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2323 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2325 ((and (not x-neg) (not y-neg))
2326 ;; Both are positive.
2327 (if (and x-len y-len)
2328 (let ((low (logior-derive-unsigned-low-bound x y))
2329 (high (logior-derive-unsigned-high-bound x y)))
2330 (specifier-type `(integer ,low ,high)))
2331 (specifier-type `(unsigned-byte* *))))
2333 ;; X must be negative.
2335 ;; Both are negative. The result is going to be negative
2336 ;; and be the same length or shorter than the smaller.
2337 (if (and x-len y-len)
2339 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2341 (specifier-type '(integer * -1)))
2342 ;; X is negative, but we don't know about Y. The result
2343 ;; will be negative, but no more negative than X.
2345 `(integer ,(or (numeric-type-low x) '*)
2348 ;; X might be either positive or negative.
2350 ;; But Y is negative. The result will be negative.
2352 `(integer ,(or (numeric-type-low y) '*)
2354 ;; We don't know squat about either. It won't get any bigger.
2355 (if (and x-len y-len)
2357 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2359 (specifier-type 'integer))))))))
2361 (defun logxor-derive-unsigned-low-bound (x y)
2362 (let ((a (numeric-type-low x))
2363 (b (numeric-type-high x))
2364 (c (numeric-type-low y))
2365 (d (numeric-type-high y)))
2366 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2369 ((not (zerop (logandc2 (logand c m) a)))
2370 (let ((temp (logand (logior a m)
2374 ((not (zerop (logandc2 (logand a m) c)))
2375 (let ((temp (logand (logior c m)
2379 finally (return (logxor a c)))))
2381 (defun logxor-derive-unsigned-high-bound (x y)
2382 (let ((a (numeric-type-low x))
2383 (b (numeric-type-high x))
2384 (c (numeric-type-low y))
2385 (d (numeric-type-high y)))
2386 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2388 (unless (zerop (logand b d m))
2389 (let ((temp (logior (- b m) (1- m))))
2391 ((>= temp a) (setf b temp))
2392 (t (let ((temp (logior (- d m) (1- m))))
2395 finally (return (logxor b d)))))
2397 (defun logxor-derive-type-aux (x y &optional same-leaf)
2399 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2400 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2401 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2403 ((and (not x-neg) (not y-neg))
2404 ;; Both are positive
2405 (if (and x-len y-len)
2406 (let ((low (logxor-derive-unsigned-low-bound x y))
2407 (high (logxor-derive-unsigned-high-bound x y)))
2408 (specifier-type `(integer ,low ,high)))
2409 (specifier-type '(unsigned-byte* *))))
2410 ((and (not x-pos) (not y-pos))
2411 ;; Both are negative. The result will be positive, and as long
2413 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2416 ((or (and (not x-pos) (not y-neg))
2417 (and (not y-pos) (not x-neg)))
2418 ;; Either X is negative and Y is positive or vice-versa. The
2419 ;; result will be negative.
2420 (specifier-type `(integer ,(if (and x-len y-len)
2421 (ash -1 (max x-len y-len))
2424 ;; We can't tell what the sign of the result is going to be.
2425 ;; All we know is that we don't create new bits.
2427 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2429 (specifier-type 'integer))))))
2431 (macrolet ((deffrob (logfun)
2432 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2433 `(defoptimizer (,logfun derive-type) ((x y))
2434 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2439 (defoptimizer (logeqv derive-type) ((x y))
2440 (two-arg-derive-type x y (lambda (x y same-leaf)
2441 (lognot-derive-type-aux
2442 (logxor-derive-type-aux x y same-leaf)))
2444 (defoptimizer (lognand derive-type) ((x y))
2445 (two-arg-derive-type x y (lambda (x y same-leaf)
2446 (lognot-derive-type-aux
2447 (logand-derive-type-aux x y same-leaf)))
2449 (defoptimizer (lognor derive-type) ((x y))
2450 (two-arg-derive-type x y (lambda (x y same-leaf)
2451 (lognot-derive-type-aux
2452 (logior-derive-type-aux x y same-leaf)))
2454 (defoptimizer (logandc1 derive-type) ((x y))
2455 (two-arg-derive-type x y (lambda (x y same-leaf)
2457 (specifier-type '(eql 0))
2458 (logand-derive-type-aux
2459 (lognot-derive-type-aux x) y nil)))
2461 (defoptimizer (logandc2 derive-type) ((x y))
2462 (two-arg-derive-type x y (lambda (x y same-leaf)
2464 (specifier-type '(eql 0))
2465 (logand-derive-type-aux
2466 x (lognot-derive-type-aux y) nil)))
2468 (defoptimizer (logorc1 derive-type) ((x y))
2469 (two-arg-derive-type x y (lambda (x y same-leaf)
2471 (specifier-type '(eql -1))
2472 (logior-derive-type-aux
2473 (lognot-derive-type-aux x) y nil)))
2475 (defoptimizer (logorc2 derive-type) ((x y))
2476 (two-arg-derive-type x y (lambda (x y same-leaf)
2478 (specifier-type '(eql -1))
2479 (logior-derive-type-aux
2480 x (lognot-derive-type-aux y) nil)))
2483 ;;;; miscellaneous derive-type methods
2485 (defoptimizer (integer-length derive-type) ((x))
2486 (let ((x-type (lvar-type x)))
2487 (when (numeric-type-p x-type)
2488 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2489 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2490 ;; careful about LO or HI being NIL, though. Also, if 0 is
2491 ;; contained in X, the lower bound is obviously 0.
2492 (flet ((null-or-min (a b)
2493 (and a b (min (integer-length a)
2494 (integer-length b))))
2496 (and a b (max (integer-length a)
2497 (integer-length b)))))
2498 (let* ((min (numeric-type-low x-type))
2499 (max (numeric-type-high x-type))
2500 (min-len (null-or-min min max))
2501 (max-len (null-or-max min max)))
2502 (when (ctypep 0 x-type)
2504 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2506 (defoptimizer (isqrt derive-type) ((x))
2507 (let ((x-type (lvar-type x)))
2508 (when (numeric-type-p x-type)
2509 (let* ((lo (numeric-type-low x-type))
2510 (hi (numeric-type-high x-type))
2511 (lo-res (if lo (isqrt lo) '*))
2512 (hi-res (if hi (isqrt hi) '*)))
2513 (specifier-type `(integer ,lo-res ,hi-res))))))
2515 (defoptimizer (code-char derive-type) ((code))
2516 (let ((type (lvar-type code)))
2517 ;; FIXME: unions of integral ranges? It ought to be easier to do
2518 ;; this, given that CHARACTER-SET is basically an integral range
2519 ;; type. -- CSR, 2004-10-04
2520 (when (numeric-type-p type)
2521 (let* ((lo (numeric-type-low type))
2522 (hi (numeric-type-high type))
2523 (type (specifier-type `(character-set ((,lo . ,hi))))))
2525 ;; KLUDGE: when running on the host, we lose a slight amount
2526 ;; of precision so that we don't have to "unparse" types
2527 ;; that formally we can't, such as (CHARACTER-SET ((0
2528 ;; . 0))). -- CSR, 2004-10-06
2530 ((csubtypep type (specifier-type 'standard-char)) type)
2532 ((csubtypep type (specifier-type 'base-char))
2533 (specifier-type 'base-char))
2535 ((csubtypep type (specifier-type 'extended-char))
2536 (specifier-type 'extended-char))
2537 (t #+sb-xc-host (specifier-type 'character)
2538 #-sb-xc-host type))))))
2540 (defoptimizer (values derive-type) ((&rest values))
2541 (make-values-type :required (mapcar #'lvar-type values)))
2543 (defun signum-derive-type-aux (type)
2544 (if (eq (numeric-type-complexp type) :complex)
2545 (let* ((format (case (numeric-type-class type)
2546 ((integer rational) 'single-float)
2547 (t (numeric-type-format type))))
2548 (bound-format (or format 'float)))
2549 (make-numeric-type :class 'float
2552 :low (coerce -1 bound-format)
2553 :high (coerce 1 bound-format)))
2554 (let* ((interval (numeric-type->interval type))
2555 (range-info (interval-range-info interval))
2556 (contains-0-p (interval-contains-p 0 interval))
2557 (class (numeric-type-class type))
2558 (format (numeric-type-format type))
2559 (one (coerce 1 (or format class 'real)))
2560 (zero (coerce 0 (or format class 'real)))
2561 (minus-one (coerce -1 (or format class 'real)))
2562 (plus (make-numeric-type :class class :format format
2563 :low one :high one))
2564 (minus (make-numeric-type :class class :format format
2565 :low minus-one :high minus-one))
2566 ;; KLUDGE: here we have a fairly horrible hack to deal
2567 ;; with the schizophrenia in the type derivation engine.
2568 ;; The problem is that the type derivers reinterpret
2569 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2570 ;; 0d0) within the derivation mechanism doesn't include
2571 ;; -0d0. Ugh. So force it in here, instead.
2572 (zero (make-numeric-type :class class :format format
2573 :low (- zero) :high zero)))
2575 (+ (if contains-0-p (type-union plus zero) plus))
2576 (- (if contains-0-p (type-union minus zero) minus))
2577 (t (type-union minus zero plus))))))
2579 (defoptimizer (signum derive-type) ((num))
2580 (one-arg-derive-type num #'signum-derive-type-aux nil))
2582 ;;;; byte operations
2584 ;;;; We try to turn byte operations into simple logical operations.
2585 ;;;; First, we convert byte specifiers into separate size and position
2586 ;;;; arguments passed to internal %FOO functions. We then attempt to
2587 ;;;; transform the %FOO functions into boolean operations when the
2588 ;;;; size and position are constant and the operands are fixnums.
2590 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2591 ;; expressions that evaluate to the SIZE and POSITION of
2592 ;; the byte-specifier form SPEC. We may wrap a let around
2593 ;; the result of the body to bind some variables.
2595 ;; If the spec is a BYTE form, then bind the vars to the
2596 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2597 ;; and BYTE-POSITION. The goal of this transformation is to
2598 ;; avoid consing up byte specifiers and then immediately
2599 ;; throwing them away.
2600 (with-byte-specifier ((size-var pos-var spec) &body body)
2601 (once-only ((spec `(macroexpand ,spec))
2603 `(if (and (consp ,spec)
2604 (eq (car ,spec) 'byte)
2605 (= (length ,spec) 3))
2606 (let ((,size-var (second ,spec))
2607 (,pos-var (third ,spec)))
2609 (let ((,size-var `(byte-size ,,temp))
2610 (,pos-var `(byte-position ,,temp)))
2611 `(let ((,,temp ,,spec))
2614 (define-source-transform ldb (spec int)
2615 (with-byte-specifier (size pos spec)
2616 `(%ldb ,size ,pos ,int)))
2618 (define-source-transform dpb (newbyte spec int)
2619 (with-byte-specifier (size pos spec)
2620 `(%dpb ,newbyte ,size ,pos ,int)))
2622 (define-source-transform mask-field (spec int)
2623 (with-byte-specifier (size pos spec)
2624 `(%mask-field ,size ,pos ,int)))
2626 (define-source-transform deposit-field (newbyte spec int)
2627 (with-byte-specifier (size pos spec)
2628 `(%deposit-field ,newbyte ,size ,pos ,int))))
2630 (defoptimizer (%ldb derive-type) ((size posn num))
2631 (let ((size (lvar-type size)))
2632 (if (and (numeric-type-p size)
2633 (csubtypep size (specifier-type 'integer)))
2634 (let ((size-high (numeric-type-high size)))
2635 (if (and size-high (<= size-high sb!vm:n-word-bits))
2636 (specifier-type `(unsigned-byte* ,size-high))
2637 (specifier-type 'unsigned-byte)))
2640 (defoptimizer (%mask-field derive-type) ((size posn num))
2641 (let ((size (lvar-type size))
2642 (posn (lvar-type posn)))
2643 (if (and (numeric-type-p size)
2644 (csubtypep size (specifier-type 'integer))
2645 (numeric-type-p posn)
2646 (csubtypep posn (specifier-type 'integer)))
2647 (let ((size-high (numeric-type-high size))
2648 (posn-high (numeric-type-high posn)))
2649 (if (and size-high posn-high
2650 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2651 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2652 (specifier-type 'unsigned-byte)))
2655 (defun %deposit-field-derive-type-aux (size posn int)
2656 (let ((size (lvar-type size))
2657 (posn (lvar-type posn))
2658 (int (lvar-type int)))
2659 (when (and (numeric-type-p size)
2660 (numeric-type-p posn)
2661 (numeric-type-p int))
2662 (let ((size-high (numeric-type-high size))
2663 (posn-high (numeric-type-high posn))
2664 (high (numeric-type-high int))
2665 (low (numeric-type-low int)))
2666 (when (and size-high posn-high high low
2667 ;; KLUDGE: we need this cutoff here, otherwise we
2668 ;; will merrily derive the type of %DPB as
2669 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2670 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2671 ;; 1073741822))), with hilarious consequences. We
2672 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2673 ;; over a reasonable amount of shifting, even on
2674 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2675 ;; machine integers are 64-bits. -- CSR,
2677 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2678 (let ((raw-bit-count (max (integer-length high)
2679 (integer-length low)
2680 (+ size-high posn-high))))
2683 `(signed-byte ,(1+ raw-bit-count))
2684 `(unsigned-byte* ,raw-bit-count)))))))))
2686 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2687 (%deposit-field-derive-type-aux size posn int))
2689 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2690 (%deposit-field-derive-type-aux size posn int))
2692 (deftransform %ldb ((size posn int)
2693 (fixnum fixnum integer)
2694 (unsigned-byte #.sb!vm:n-word-bits))
2695 "convert to inline logical operations"
2696 `(logand (ash int (- posn))
2697 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2698 (- size ,sb!vm:n-word-bits))))
2700 (deftransform %mask-field ((size posn int)
2701 (fixnum fixnum integer)
2702 (unsigned-byte #.sb!vm:n-word-bits))
2703 "convert to inline logical operations"
2705 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2706 (- size ,sb!vm:n-word-bits))
2709 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2710 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2711 ;;; as the result type, as that would allow result types that cover
2712 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2713 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2715 (deftransform %dpb ((new size posn int)
2717 (unsigned-byte #.sb!vm:n-word-bits))
2718 "convert to inline logical operations"
2719 `(let ((mask (ldb (byte size 0) -1)))
2720 (logior (ash (logand new mask) posn)
2721 (logand int (lognot (ash mask posn))))))
2723 (deftransform %dpb ((new size posn int)
2725 (signed-byte #.sb!vm:n-word-bits))
2726 "convert to inline logical operations"
2727 `(let ((mask (ldb (byte size 0) -1)))
2728 (logior (ash (logand new mask) posn)
2729 (logand int (lognot (ash mask posn))))))
2731 (deftransform %deposit-field ((new size posn int)
2733 (unsigned-byte #.sb!vm:n-word-bits))
2734 "convert to inline logical operations"
2735 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2736 (logior (logand new mask)
2737 (logand int (lognot mask)))))
2739 (deftransform %deposit-field ((new size posn int)
2741 (signed-byte #.sb!vm:n-word-bits))
2742 "convert to inline logical operations"
2743 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2744 (logior (logand new mask)
2745 (logand int (lognot mask)))))
2747 (defoptimizer (mask-signed-field derive-type) ((size x))
2748 (let ((size (lvar-type size)))
2749 (if (numeric-type-p size)
2750 (let ((size-high (numeric-type-high size)))
2751 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2752 (specifier-type `(signed-byte ,size-high))
2757 ;;; Modular functions
2759 ;;; (ldb (byte s 0) (foo x y ...)) =
2760 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2762 ;;; and similar for other arguments.
2764 (defun make-modular-fun-type-deriver (prototype class width)
2766 (binding* ((info (info :function :info prototype) :exit-if-null)
2767 (fun (fun-info-derive-type info) :exit-if-null)
2768 (mask-type (specifier-type
2770 (:unsigned (let ((mask (1- (ash 1 width))))
2771 `(integer ,mask ,mask)))
2772 (:signed `(signed-byte ,width))))))
2774 (let ((res (funcall fun call)))
2776 (if (eq class :unsigned)
2777 (logand-derive-type-aux res mask-type))))))
2780 (binding* ((info (info :function :info prototype) :exit-if-null)
2781 (fun (fun-info-derive-type info) :exit-if-null)
2782 (res (funcall fun call) :exit-if-null)
2783 (mask-type (specifier-type
2785 (:unsigned (let ((mask (1- (ash 1 width))))
2786 `(integer ,mask ,mask)))
2787 (:signed `(signed-byte ,width))))))
2788 (if (eq class :unsigned)
2789 (logand-derive-type-aux res mask-type)))))
2791 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2793 ;;; For good functions, we just recursively cut arguments; their
2794 ;;; "goodness" means that the result will not increase (in the
2795 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2796 ;;; replaced with the version, cutting its result to WIDTH or more
2797 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2798 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2799 ;;; arguments (maybe to a different width) and returning the name of a
2800 ;;; modular version, if it exists, or NIL. If we have changed
2801 ;;; anything, we need to flush old derived types, because they have
2802 ;;; nothing in common with the new code.
2803 (defun cut-to-width (lvar class width)
2804 (declare (type lvar lvar) (type (integer 0) width))
2805 (let ((type (specifier-type (if (zerop width)
2807 `(,(ecase class (:unsigned 'unsigned-byte)
2808 (:signed 'signed-byte))
2810 (labels ((reoptimize-node (node name)
2811 (setf (node-derived-type node)
2813 (info :function :type name)))
2814 (setf (lvar-%derived-type (node-lvar node)) nil)
2815 (setf (node-reoptimize node) t)
2816 (setf (block-reoptimize (node-block node)) t)
2817 (reoptimize-component (node-component node) :maybe))
2818 (cut-node (node &aux did-something)
2819 (when (and (not (block-delete-p (node-block node)))
2820 (combination-p node)
2821 (eq (basic-combination-kind node) :known))
2822 (let* ((fun-ref (lvar-use (combination-fun node)))
2823 (fun-name (leaf-source-name (ref-leaf fun-ref)))
2824 (modular-fun (find-modular-version fun-name class width)))
2825 (when (and modular-fun
2826 (not (and (eq fun-name 'logand)
2828 (single-value-type (node-derived-type node))
2830 (binding* ((name (etypecase modular-fun
2831 ((eql :good) fun-name)
2833 (modular-fun-info-name modular-fun))
2835 (funcall modular-fun node width)))
2837 (unless (eql modular-fun :good)
2838 (setq did-something t)
2841 (find-free-fun name "in a strange place"))
2842 (setf (combination-kind node) :full))
2843 (unless (functionp modular-fun)
2844 (dolist (arg (basic-combination-args node))
2845 (when (cut-lvar arg)
2846 (setq did-something t))))
2848 (reoptimize-node node name))
2850 (cut-lvar (lvar &aux did-something)
2851 (do-uses (node lvar)
2852 (when (cut-node node)
2853 (setq did-something t)))
2857 (defoptimizer (logand optimizer) ((x y) node)
2858 (let ((result-type (single-value-type (node-derived-type node))))
2859 (when (numeric-type-p result-type)
2860 (let ((low (numeric-type-low result-type))
2861 (high (numeric-type-high result-type)))
2862 (when (and (numberp low)
2865 (let ((width (integer-length high)))
2866 (when (some (lambda (x) (<= width x))
2867 (modular-class-widths *unsigned-modular-class*))
2868 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2869 (cut-to-width x :unsigned width)
2870 (cut-to-width y :unsigned width)
2871 nil ; After fixing above, replace with T.
2874 (defoptimizer (mask-signed-field optimizer) ((width x) node)
2875 (let ((result-type (single-value-type (node-derived-type node))))
2876 (when (numeric-type-p result-type)
2877 (let ((low (numeric-type-low result-type))
2878 (high (numeric-type-high result-type)))
2879 (when (and (numberp low) (numberp high))
2880 (let ((width (max (integer-length high) (integer-length low))))
2881 (when (some (lambda (x) (<= width x))
2882 (modular-class-widths *signed-modular-class*))
2883 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2884 (cut-to-width x :signed width)
2885 nil ; After fixing above, replace with T.
2888 ;;; miscellanous numeric transforms
2890 ;;; If a constant appears as the first arg, swap the args.
2891 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2892 (if (and (constant-lvar-p x)
2893 (not (constant-lvar-p y)))
2894 `(,(lvar-fun-name (basic-combination-fun node))
2897 (give-up-ir1-transform)))
2899 (dolist (x '(= char= + * logior logand logxor))
2900 (%deftransform x '(function * *) #'commutative-arg-swap
2901 "place constant arg last"))
2903 ;;; Handle the case of a constant BOOLE-CODE.
2904 (deftransform boole ((op x y) * *)
2905 "convert to inline logical operations"
2906 (unless (constant-lvar-p op)
2907 (give-up-ir1-transform "BOOLE code is not a constant."))
2908 (let ((control (lvar-value op)))
2910 (#.sb!xc:boole-clr 0)
2911 (#.sb!xc:boole-set -1)
2912 (#.sb!xc:boole-1 'x)
2913 (#.sb!xc:boole-2 'y)
2914 (#.sb!xc:boole-c1 '(lognot x))
2915 (#.sb!xc:boole-c2 '(lognot y))
2916 (#.sb!xc:boole-and '(logand x y))
2917 (#.sb!xc:boole-ior '(logior x y))
2918 (#.sb!xc:boole-xor '(logxor x y))
2919 (#.sb!xc:boole-eqv '(logeqv x y))
2920 (#.sb!xc:boole-nand '(lognand x y))
2921 (#.sb!xc:boole-nor '(lognor x y))
2922 (#.sb!xc:boole-andc1 '(logandc1 x y))
2923 (#.sb!xc:boole-andc2 '(logandc2 x y))
2924 (#.sb!xc:boole-orc1 '(logorc1 x y))
2925 (#.sb!xc:boole-orc2 '(logorc2 x y))
2927 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2930 ;;;; converting special case multiply/divide to shifts
2932 ;;; If arg is a constant power of two, turn * into a shift.
2933 (deftransform * ((x y) (integer integer) *)
2934 "convert x*2^k to shift"
2935 (unless (constant-lvar-p y)
2936 (give-up-ir1-transform))
2937 (let* ((y (lvar-value y))
2939 (len (1- (integer-length y-abs))))
2940 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2941 (give-up-ir1-transform))
2946 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2947 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
2949 (flet ((frob (y ceil-p)
2950 (unless (constant-lvar-p y)
2951 (give-up-ir1-transform))
2952 (let* ((y (lvar-value y))
2954 (len (1- (integer-length y-abs))))
2955 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2956 (give-up-ir1-transform))
2957 (let ((shift (- len))
2959 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
2960 `(let ((x (+ x ,delta)))
2962 `(values (ash (- x) ,shift)
2963 (- (- (logand (- x) ,mask)) ,delta))
2964 `(values (ash x ,shift)
2965 (- (logand x ,mask) ,delta))))))))
2966 (deftransform floor ((x y) (integer integer) *)
2967 "convert division by 2^k to shift"
2969 (deftransform ceiling ((x y) (integer integer) *)
2970 "convert division by 2^k to shift"
2973 ;;; Do the same for MOD.
2974 (deftransform mod ((x y) (integer integer) *)
2975 "convert remainder mod 2^k to LOGAND"
2976 (unless (constant-lvar-p y)
2977 (give-up-ir1-transform))
2978 (let* ((y (lvar-value y))
2980 (len (1- (integer-length y-abs))))
2981 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2982 (give-up-ir1-transform))
2983 (let ((mask (1- y-abs)))
2985 `(- (logand (- x) ,mask))
2986 `(logand x ,mask)))))
2988 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2989 (deftransform truncate ((x y) (integer integer))
2990 "convert division by 2^k to shift"
2991 (unless (constant-lvar-p y)
2992 (give-up-ir1-transform))
2993 (let* ((y (lvar-value y))
2995 (len (1- (integer-length y-abs))))
2996 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2997 (give-up-ir1-transform))
2998 (let* ((shift (- len))
3001 (values ,(if (minusp y)
3003 `(- (ash (- x) ,shift)))
3004 (- (logand (- x) ,mask)))
3005 (values ,(if (minusp y)
3006 `(ash (- ,mask x) ,shift)
3008 (logand x ,mask))))))
3010 ;;; And the same for REM.
3011 (deftransform rem ((x y) (integer integer) *)
3012 "convert remainder mod 2^k to LOGAND"
3013 (unless (constant-lvar-p y)
3014 (give-up-ir1-transform))
3015 (let* ((y (lvar-value y))
3017 (len (1- (integer-length y-abs))))
3018 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3019 (give-up-ir1-transform))
3020 (let ((mask (1- y-abs)))
3022 (- (logand (- x) ,mask))
3023 (logand x ,mask)))))
3025 ;;;; arithmetic and logical identity operation elimination
3027 ;;; Flush calls to various arith functions that convert to the
3028 ;;; identity function or a constant.
3029 (macrolet ((def (name identity result)
3030 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3031 "fold identity operations"
3038 (def logxor -1 (lognot x))
3041 (deftransform logand ((x y) (* (constant-arg t)) *)
3042 "fold identity operation"
3043 (let ((y (lvar-value y)))
3044 (unless (and (plusp y)
3045 (= y (1- (ash 1 (integer-length y)))))
3046 (give-up-ir1-transform))
3047 (unless (csubtypep (lvar-type x)
3048 (specifier-type `(integer 0 ,y)))
3049 (give-up-ir1-transform))
3052 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3053 "fold identity operation"
3054 (let ((size (lvar-value size)))
3055 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3056 (give-up-ir1-transform))
3059 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3060 ;;; (* 0 -4.0) is -0.0.
3061 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3062 "convert (- 0 x) to negate"
3064 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3065 "convert (* x 0) to 0"
3068 ;;; Return T if in an arithmetic op including lvars X and Y, the
3069 ;;; result type is not affected by the type of X. That is, Y is at
3070 ;;; least as contagious as X.
3072 (defun not-more-contagious (x y)
3073 (declare (type continuation x y))
3074 (let ((x (lvar-type x))
3076 (values (type= (numeric-contagion x y)
3077 (numeric-contagion y y)))))
3078 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3079 ;;; XXX needs more work as valid transforms are missed; some cases are
3080 ;;; specific to particular transform functions so the use of this
3081 ;;; function may need a re-think.
3082 (defun not-more-contagious (x y)
3083 (declare (type lvar x y))
3084 (flet ((simple-numeric-type (num)
3085 (and (numeric-type-p num)
3086 ;; Return non-NIL if NUM is integer, rational, or a float
3087 ;; of some type (but not FLOAT)
3088 (case (numeric-type-class num)
3092 (numeric-type-format num))
3095 (let ((x (lvar-type x))
3097 (if (and (simple-numeric-type x)
3098 (simple-numeric-type y))
3099 (values (type= (numeric-contagion x y)
3100 (numeric-contagion y y)))))))
3104 ;;; If y is not constant, not zerop, or is contagious, or a positive
3105 ;;; float +0.0 then give up.
3106 (deftransform + ((x y) (t (constant-arg t)) *)
3108 (let ((val (lvar-value y)))
3109 (unless (and (zerop val)
3110 (not (and (floatp val) (plusp (float-sign val))))
3111 (not-more-contagious y x))
3112 (give-up-ir1-transform)))
3117 ;;; If y is not constant, not zerop, or is contagious, or a negative
3118 ;;; float -0.0 then give up.
3119 (deftransform - ((x y) (t (constant-arg t)) *)
3121 (let ((val (lvar-value y)))
3122 (unless (and (zerop val)
3123 (not (and (floatp val) (minusp (float-sign val))))
3124 (not-more-contagious y x))
3125 (give-up-ir1-transform)))
3128 ;;; Fold (OP x +/-1)
3129 (macrolet ((def (name result minus-result)
3130 `(deftransform ,name ((x y) (t (constant-arg real)) *)
3131 "fold identity operations"
3132 (let ((val (lvar-value y)))
3133 (unless (and (= (abs val) 1)
3134 (not-more-contagious y x))
3135 (give-up-ir1-transform))
3136 (if (minusp val) ',minus-result ',result)))))
3137 (def * x (%negate x))
3138 (def / x (%negate x))
3139 (def expt x (/ 1 x)))
3141 ;;; Fold (expt x n) into multiplications for small integral values of
3142 ;;; N; convert (expt x 1/2) to sqrt.
3143 (deftransform expt ((x y) (t (constant-arg real)) *)
3144 "recode as multiplication or sqrt"
3145 (let ((val (lvar-value y)))
3146 ;; If Y would cause the result to be promoted to the same type as
3147 ;; Y, we give up. If not, then the result will be the same type
3148 ;; as X, so we can replace the exponentiation with simple
3149 ;; multiplication and division for small integral powers.
3150 (unless (not-more-contagious y x)
3151 (give-up-ir1-transform))
3153 (let ((x-type (lvar-type x)))
3154 (cond ((csubtypep x-type (specifier-type '(or rational
3155 (complex rational))))
3157 ((csubtypep x-type (specifier-type 'real))
3161 ((csubtypep x-type (specifier-type 'complex))
3162 ;; both parts are float
3164 (t (give-up-ir1-transform)))))
3165 ((= val 2) '(* x x))
3166 ((= val -2) '(/ (* x x)))
3167 ((= val 3) '(* x x x))
3168 ((= val -3) '(/ (* x x x)))
3169 ((= val 1/2) '(sqrt x))
3170 ((= val -1/2) '(/ (sqrt x)))
3171 (t (give-up-ir1-transform)))))
3173 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3174 ;;; transformations?
3175 ;;; Perhaps we should have to prove that the denominator is nonzero before
3176 ;;; doing them? -- WHN 19990917
3177 (macrolet ((def (name)
3178 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3185 (macrolet ((def (name)
3186 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3195 ;;;; character operations
3197 (deftransform char-equal ((a b) (base-char base-char))
3199 '(let* ((ac (char-code a))
3201 (sum (logxor ac bc)))
3203 (when (eql sum #x20)
3204 (let ((sum (+ ac bc)))
3205 (or (and (> sum 161) (< sum 213))
3206 (and (> sum 415) (< sum 461))
3207 (and (> sum 463) (< sum 477))))))))
3209 (deftransform char-upcase ((x) (base-char))
3211 '(let ((n-code (char-code x)))
3212 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3213 (< n-code #o173)) ; Octal 172 is #\z.
3214 (and (> n-code #o337)
3216 (and (> n-code #o367)
3218 (code-char (logxor #x20 n-code))
3221 (deftransform char-downcase ((x) (base-char))
3223 '(let ((n-code (char-code x)))
3224 (if (or (and (> n-code 64) ; 65 is #\A.
3225 (< n-code 91)) ; 90 is #\Z.
3230 (code-char (logxor #x20 n-code))
3233 ;;;; equality predicate transforms
3235 ;;; Return true if X and Y are lvars whose only use is a
3236 ;;; reference to the same leaf, and the value of the leaf cannot
3238 (defun same-leaf-ref-p (x y)
3239 (declare (type lvar x y))
3240 (let ((x-use (principal-lvar-use x))
3241 (y-use (principal-lvar-use y)))
3244 (eq (ref-leaf x-use) (ref-leaf y-use))
3245 (constant-reference-p x-use))))
3247 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3248 ;;; if there is no intersection between the types of the arguments,
3249 ;;; then the result is definitely false.
3250 (deftransform simple-equality-transform ((x y) * *
3253 ((same-leaf-ref-p x y) t)
3254 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3256 (t (give-up-ir1-transform))))
3259 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3263 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3264 ;;; try to convert to a type-specific predicate or EQ:
3265 ;;; -- If both args are characters, convert to CHAR=. This is better than
3266 ;;; just converting to EQ, since CHAR= may have special compilation
3267 ;;; strategies for non-standard representations, etc.
3268 ;;; -- If either arg is definitely a fixnum we punt and let the backend
3270 ;;; -- If either arg is definitely not a number or a fixnum, then we
3271 ;;; can compare with EQ.
3272 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3273 ;;; is constant then we put it second. If X is a subtype of Y, we put
3274 ;;; it second. These rules make it easier for the back end to match
3275 ;;; these interesting cases.
3276 (deftransform eql ((x y) * *)
3277 "convert to simpler equality predicate"
3278 (let ((x-type (lvar-type x))
3279 (y-type (lvar-type y))
3280 (char-type (specifier-type 'character)))
3281 (flet ((simple-type-p (type)
3282 (csubtypep type (specifier-type '(or fixnum (not number)))))
3283 (fixnum-type-p (type)
3284 (csubtypep type (specifier-type 'fixnum))))
3286 ((same-leaf-ref-p x y) t)
3287 ((not (types-equal-or-intersect x-type y-type))
3289 ((and (csubtypep x-type char-type)
3290 (csubtypep y-type char-type))
3292 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3293 (give-up-ir1-transform))
3294 ((or (simple-type-p x-type) (simple-type-p y-type))
3296 ((and (not (constant-lvar-p y))
3297 (or (constant-lvar-p x)
3298 (and (csubtypep x-type y-type)
3299 (not (csubtypep y-type x-type)))))
3302 (give-up-ir1-transform))))))
3304 ;;; similarly to the EQL transform above, we attempt to constant-fold
3305 ;;; or convert to a simpler predicate: mostly we have to be careful
3306 ;;; with strings and bit-vectors.
3307 (deftransform equal ((x y) * *)
3308 "convert to simpler equality predicate"
3309 (let ((x-type (lvar-type x))
3310 (y-type (lvar-type y))
3311 (string-type (specifier-type 'string))
3312 (bit-vector-type (specifier-type 'bit-vector)))
3314 ((same-leaf-ref-p x y) t)
3315 ((and (csubtypep x-type string-type)
3316 (csubtypep y-type string-type))
3318 ((and (csubtypep x-type bit-vector-type)
3319 (csubtypep y-type bit-vector-type))
3320 '(bit-vector-= x y))
3321 ;; if at least one is not a string, and at least one is not a
3322 ;; bit-vector, then we can reason from types.
3323 ((and (not (and (types-equal-or-intersect x-type string-type)
3324 (types-equal-or-intersect y-type string-type)))
3325 (not (and (types-equal-or-intersect x-type bit-vector-type)
3326 (types-equal-or-intersect y-type bit-vector-type)))
3327 (not (types-equal-or-intersect x-type y-type)))
3329 (t (give-up-ir1-transform)))))
3331 ;;; Convert to EQL if both args are rational and complexp is specified
3332 ;;; and the same for both.
3333 (deftransform = ((x y) * *)
3335 (let ((x-type (lvar-type x))
3336 (y-type (lvar-type y)))
3337 (if (and (csubtypep x-type (specifier-type 'number))
3338 (csubtypep y-type (specifier-type 'number)))
3339 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3340 (csubtypep y-type (specifier-type 'float)))
3341 (and (csubtypep x-type (specifier-type '(complex float)))
3342 (csubtypep y-type (specifier-type '(complex float)))))
3343 ;; They are both floats. Leave as = so that -0.0 is
3344 ;; handled correctly.
3345 (give-up-ir1-transform))
3346 ((or (and (csubtypep x-type (specifier-type 'rational))
3347 (csubtypep y-type (specifier-type 'rational)))
3348 (and (csubtypep x-type
3349 (specifier-type '(complex rational)))
3351 (specifier-type '(complex rational)))))
3352 ;; They are both rationals and complexp is the same.
3356 (give-up-ir1-transform
3357 "The operands might not be the same type.")))
3358 (give-up-ir1-transform
3359 "The operands might not be the same type."))))
3361 ;;; If LVAR's type is a numeric type, then return the type, otherwise
3362 ;;; GIVE-UP-IR1-TRANSFORM.
3363 (defun numeric-type-or-lose (lvar)
3364 (declare (type lvar lvar))
3365 (let ((res (lvar-type lvar)))
3366 (unless (numeric-type-p res) (give-up-ir1-transform))
3369 ;;; See whether we can statically determine (< X Y) using type
3370 ;;; information. If X's high bound is < Y's low, then X < Y.
3371 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3372 ;;; NIL). If not, at least make sure any constant arg is second.
3373 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3374 `(deftransform ,name ((x y))
3375 (if (same-leaf-ref-p x y)
3377 (let ((ix (or (type-approximate-interval (lvar-type x))
3378 (give-up-ir1-transform)))
3379 (iy (or (type-approximate-interval (lvar-type y))
3380 (give-up-ir1-transform))))
3385 ((and (constant-lvar-p x)
3386 (not (constant-lvar-p y)))
3389 (give-up-ir1-transform))))))))
3390 (def < > nil (interval-< ix iy) (interval->= ix iy))
3391 (def > < nil (interval-< iy ix) (interval->= iy ix))
3392 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3393 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3395 (defun ir1-transform-char< (x y first second inverse)
3397 ((same-leaf-ref-p x y) nil)
3398 ;; If we had interval representation of character types, as we
3399 ;; might eventually have to to support 2^21 characters, then here
3400 ;; we could do some compile-time computation as in transforms for
3401 ;; < above. -- CSR, 2003-07-01
3402 ((and (constant-lvar-p first)
3403 (not (constant-lvar-p second)))
3405 (t (give-up-ir1-transform))))
3407 (deftransform char< ((x y) (character character) *)
3408 (ir1-transform-char< x y x y 'char>))
3410 (deftransform char> ((x y) (character character) *)
3411 (ir1-transform-char< y x x y 'char<))
3413 ;;;; converting N-arg comparisons
3415 ;;;; We convert calls to N-arg comparison functions such as < into
3416 ;;;; two-arg calls. This transformation is enabled for all such
3417 ;;;; comparisons in this file. If any of these predicates are not
3418 ;;;; open-coded, then the transformation should be removed at some
3419 ;;;; point to avoid pessimization.
3421 ;;; This function is used for source transformation of N-arg
3422 ;;; comparison functions other than inequality. We deal both with
3423 ;;; converting to two-arg calls and inverting the sense of the test,
3424 ;;; if necessary. If the call has two args, then we pass or return a
3425 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3426 ;;; then we transform to code that returns true. Otherwise, we bind
3427 ;;; all the arguments and expand into a bunch of IFs.
3428 (declaim (ftype (function (symbol list boolean t) *) multi-compare))
3429 (defun multi-compare (predicate args not-p type)
3430 (let ((nargs (length args)))
3431 (cond ((< nargs 1) (values nil t))
3432 ((= nargs 1) `(progn (the ,type ,@args) t))
3435 `(if (,predicate ,(first args) ,(second args)) nil t)
3438 (do* ((i (1- nargs) (1- i))
3440 (current (gensym) (gensym))
3441 (vars (list current) (cons current vars))
3443 `(if (,predicate ,current ,last)
3445 `(if (,predicate ,current ,last)
3448 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3451 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3452 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3453 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3454 (define-source-transform <= (&rest args) (multi-compare '> args t 'real))
3455 (define-source-transform >= (&rest args) (multi-compare '< args t 'real))
3457 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
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 t
3465 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3468 (define-source-transform char-equal (&rest args)
3469 (multi-compare 'char-equal args nil 'character))
3470 (define-source-transform char-lessp (&rest args)
3471 (multi-compare 'char-lessp args nil 'character))
3472 (define-source-transform char-greaterp (&rest args)
3473 (multi-compare 'char-greaterp args nil 'character))
3474 (define-source-transform char-not-greaterp (&rest args)
3475 (multi-compare 'char-greaterp args t 'character))
3476 (define-source-transform char-not-lessp (&rest args)
3477 (multi-compare 'char-lessp args t 'character))
3479 ;;; This function does source transformation of N-arg inequality
3480 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3481 ;;; arg cases. If there are more than two args, then we expand into
3482 ;;; the appropriate n^2 comparisons only when speed is important.
3483 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3484 (defun multi-not-equal (predicate args type)
3485 (let ((nargs (length args)))
3486 (cond ((< nargs 1) (values nil t))
3487 ((= nargs 1) `(progn (the ,type ,@args) t))
3489 `(if (,predicate ,(first args) ,(second args)) nil t))
3490 ((not (policy *lexenv*
3491 (and (>= speed space)
3492 (>= speed compilation-speed))))
3495 (let ((vars (make-gensym-list nargs)))
3496 (do ((var vars next)
3497 (next (cdr vars) (cdr next))
3500 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3502 (let ((v1 (first var)))
3504 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3506 (define-source-transform /= (&rest args)
3507 (multi-not-equal '= args 'number))
3508 (define-source-transform char/= (&rest args)
3509 (multi-not-equal 'char= args 'character))
3510 (define-source-transform char-not-equal (&rest args)
3511 (multi-not-equal 'char-equal args 'character))
3513 ;;; Expand MAX and MIN into the obvious comparisons.
3514 (define-source-transform max (arg0 &rest rest)
3515 (once-only ((arg0 arg0))
3517 `(values (the real ,arg0))
3518 `(let ((maxrest (max ,@rest)))
3519 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3520 (define-source-transform min (arg0 &rest rest)
3521 (once-only ((arg0 arg0))
3523 `(values (the real ,arg0))
3524 `(let ((minrest (min ,@rest)))
3525 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3527 ;;;; converting N-arg arithmetic functions
3529 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3530 ;;;; versions, and degenerate cases are flushed.
3532 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3533 (declaim (ftype (function (symbol t list) list) associate-args))
3534 (defun associate-args (function first-arg more-args)
3535 (let ((next (rest more-args))
3536 (arg (first more-args)))
3538 `(,function ,first-arg ,arg)
3539 (associate-args function `(,function ,first-arg ,arg) next))))
3541 ;;; Do source transformations for transitive functions such as +.
3542 ;;; One-arg cases are replaced with the arg and zero arg cases with
3543 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3544 ;;; ensure (with THE) that the argument in one-argument calls is.
3545 (defun source-transform-transitive (fun args identity
3546 &optional one-arg-result-type)
3547 (declare (symbol fun) (list args))
3550 (1 (if one-arg-result-type
3551 `(values (the ,one-arg-result-type ,(first args)))
3552 `(values ,(first args))))
3555 (associate-args fun (first args) (rest args)))))
3557 (define-source-transform + (&rest args)
3558 (source-transform-transitive '+ args 0 'number))
3559 (define-source-transform * (&rest args)
3560 (source-transform-transitive '* args 1 'number))
3561 (define-source-transform logior (&rest args)
3562 (source-transform-transitive 'logior args 0 'integer))
3563 (define-source-transform logxor (&rest args)
3564 (source-transform-transitive 'logxor args 0 'integer))
3565 (define-source-transform logand (&rest args)
3566 (source-transform-transitive 'logand args -1 'integer))
3567 (define-source-transform logeqv (&rest args)
3568 (source-transform-transitive 'logeqv args -1 'integer))
3570 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3571 ;;; because when they are given one argument, they return its absolute
3574 (define-source-transform gcd (&rest args)
3577 (1 `(abs (the integer ,(first args))))
3579 (t (associate-args 'gcd (first args) (rest args)))))
3581 (define-source-transform lcm (&rest args)
3584 (1 `(abs (the integer ,(first args))))
3586 (t (associate-args 'lcm (first args) (rest args)))))
3588 ;;; Do source transformations for intransitive n-arg functions such as
3589 ;;; /. With one arg, we form the inverse. With two args we pass.
3590 ;;; Otherwise we associate into two-arg calls.
3591 (declaim (ftype (function (symbol list t)
3592 (values list &optional (member nil t)))
3593 source-transform-intransitive))
3594 (defun source-transform-intransitive (function args inverse)
3596 ((0 2) (values nil t))
3597 (1 `(,@inverse ,(first args)))
3598 (t (associate-args function (first args) (rest args)))))
3600 (define-source-transform - (&rest args)
3601 (source-transform-intransitive '- args '(%negate)))
3602 (define-source-transform / (&rest args)
3603 (source-transform-intransitive '/ args '(/ 1)))
3605 ;;;; transforming APPLY
3607 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3608 ;;; only needs to understand one kind of variable-argument call. It is
3609 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3610 (define-source-transform apply (fun arg &rest more-args)
3611 (let ((args (cons arg more-args)))
3612 `(multiple-value-call ,fun
3613 ,@(mapcar (lambda (x)
3616 (values-list ,(car (last args))))))
3618 ;;;; transforming FORMAT
3620 ;;;; If the control string is a compile-time constant, then replace it
3621 ;;;; with a use of the FORMATTER macro so that the control string is
3622 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3623 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3624 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3626 ;;; for compile-time argument count checking.
3628 ;;; FIXME II: In some cases, type information could be correlated; for
3629 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3630 ;;; of a corresponding argument is known and does not intersect the
3631 ;;; list type, a warning could be signalled.
3632 (defun check-format-args (string args fun)
3633 (declare (type string string))
3634 (unless (typep string 'simple-string)
3635 (setq string (coerce string 'simple-string)))
3636 (multiple-value-bind (min max)
3637 (handler-case (sb!format:%compiler-walk-format-string string args)
3638 (sb!format:format-error (c)
3639 (compiler-warn "~A" c)))
3641 (let ((nargs (length args)))
3644 (warn 'format-too-few-args-warning
3646 "Too few arguments (~D) to ~S ~S: requires at least ~D."
3647 :format-arguments (list nargs fun string min)))
3649 (warn 'format-too-many-args-warning
3651 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3652 :format-arguments (list nargs fun string max))))))))
3654 (defoptimizer (format optimizer) ((dest control &rest args))
3655 (when (constant-lvar-p control)
3656 (let ((x (lvar-value control)))
3658 (check-format-args x args 'format)))))
3660 ;;; We disable this transform in the cross-compiler to save memory in
3661 ;;; the target image; most of the uses of FORMAT in the compiler are for
3662 ;;; error messages, and those don't need to be particularly fast.
3664 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3665 :policy (> speed space))
3666 (unless (constant-lvar-p control)
3667 (give-up-ir1-transform "The control string is not a constant."))
3668 (let ((arg-names (make-gensym-list (length args))))
3669 `(lambda (dest control ,@arg-names)
3670 (declare (ignore control))
3671 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
3673 (deftransform format ((stream control &rest args) (stream function &rest t) *
3674 :policy (> speed space))
3675 (let ((arg-names (make-gensym-list (length args))))
3676 `(lambda (stream control ,@arg-names)
3677 (funcall control stream ,@arg-names)
3680 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3681 :policy (> speed space))
3682 (let ((arg-names (make-gensym-list (length args))))
3683 `(lambda (tee control ,@arg-names)
3684 (declare (ignore tee))
3685 (funcall control *standard-output* ,@arg-names)
3690 `(defoptimizer (,name optimizer) ((control &rest args))
3691 (when (constant-lvar-p control)
3692 (let ((x (lvar-value control)))
3694 (check-format-args x args ',name)))))))
3697 #+sb-xc-host ; Only we should be using these
3700 (def compiler-abort)
3701 (def compiler-error)
3703 (def compiler-style-warn)
3704 (def compiler-notify)
3705 (def maybe-compiler-notify)
3708 (defoptimizer (cerror optimizer) ((report control &rest args))
3709 (when (and (constant-lvar-p control)
3710 (constant-lvar-p report))
3711 (let ((x (lvar-value control))
3712 (y (lvar-value report)))
3713 (when (and (stringp x) (stringp y))
3714 (multiple-value-bind (min1 max1)
3716 (sb!format:%compiler-walk-format-string x args)
3717 (sb!format:format-error (c)
3718 (compiler-warn "~A" c)))
3720 (multiple-value-bind (min2 max2)
3722 (sb!format:%compiler-walk-format-string y args)
3723 (sb!format:format-error (c)
3724 (compiler-warn "~A" c)))
3726 (let ((nargs (length args)))
3728 ((< nargs (min min1 min2))
3729 (warn 'format-too-few-args-warning
3731 "Too few arguments (~D) to ~S ~S ~S: ~
3732 requires at least ~D."
3734 (list nargs 'cerror y x (min min1 min2))))
3735 ((> nargs (max max1 max2))
3736 (warn 'format-too-many-args-warning
3738 "Too many arguments (~D) to ~S ~S ~S: ~
3741 (list nargs 'cerror y x (max max1 max2))))))))))))))
3743 (defoptimizer (coerce derive-type) ((value type))
3745 ((constant-lvar-p type)
3746 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3747 ;; but dealing with the niggle that complex canonicalization gets
3748 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3750 (let* ((specifier (lvar-value type))
3751 (result-typeoid (careful-specifier-type specifier)))
3753 ((null result-typeoid) nil)
3754 ((csubtypep result-typeoid (specifier-type 'number))
3755 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3756 ;; Rule of Canonical Representation for Complex Rationals,
3757 ;; which is a truly nasty delivery to field.
3759 ((csubtypep result-typeoid (specifier-type 'real))
3760 ;; cleverness required here: it would be nice to deduce
3761 ;; that something of type (INTEGER 2 3) coerced to type
3762 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3763 ;; FLOAT gets its own clause because it's implemented as
3764 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3767 ((and (numeric-type-p result-typeoid)
3768 (eq (numeric-type-complexp result-typeoid) :real))
3769 ;; FIXME: is this clause (a) necessary or (b) useful?
3771 ((or (csubtypep result-typeoid
3772 (specifier-type '(complex single-float)))
3773 (csubtypep result-typeoid
3774 (specifier-type '(complex double-float)))
3776 (csubtypep result-typeoid
3777 (specifier-type '(complex long-float))))
3778 ;; float complex types are never canonicalized.
3781 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3782 ;; probably just a COMPLEX or equivalent. So, in that
3783 ;; case, we will return a complex or an object of the
3784 ;; provided type if it's rational:
3785 (type-union result-typeoid
3786 (type-intersection (lvar-type value)
3787 (specifier-type 'rational))))))
3788 (t result-typeoid))))
3790 ;; OK, the result-type argument isn't constant. However, there
3791 ;; are common uses where we can still do better than just
3792 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3793 ;; where Y is of a known type. See messages on cmucl-imp
3794 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3795 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3796 ;; the basis that it's unlikely that other uses are both
3797 ;; time-critical and get to this branch of the COND (non-constant
3798 ;; second argument to COERCE). -- CSR, 2002-12-16
3799 (let ((value-type (lvar-type value))
3800 (type-type (lvar-type type)))
3802 ((good-cons-type-p (cons-type)
3803 ;; Make sure the cons-type we're looking at is something
3804 ;; we're prepared to handle which is basically something
3805 ;; that array-element-type can return.
3806 (or (and (member-type-p cons-type)
3807 (null (rest (member-type-members cons-type)))
3808 (null (first (member-type-members cons-type))))
3809 (let ((car-type (cons-type-car-type cons-type)))
3810 (and (member-type-p car-type)
3811 (null (rest (member-type-members car-type)))
3812 (or (symbolp (first (member-type-members car-type)))
3813 (numberp (first (member-type-members car-type)))
3814 (and (listp (first (member-type-members
3816 (numberp (first (first (member-type-members
3818 (good-cons-type-p (cons-type-cdr-type cons-type))))))
3819 (unconsify-type (good-cons-type)
3820 ;; Convert the "printed" respresentation of a cons
3821 ;; specifier into a type specifier. That is, the
3822 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3823 ;; NULL)) is converted to (SIGNED-BYTE 16).
3824 (cond ((or (null good-cons-type)
3825 (eq good-cons-type 'null))
3827 ((and (eq (first good-cons-type) 'cons)
3828 (eq (first (second good-cons-type)) 'member))
3829 `(,(second (second good-cons-type))
3830 ,@(unconsify-type (caddr good-cons-type))))))
3831 (coerceable-p (c-type)
3832 ;; Can the value be coerced to the given type? Coerce is
3833 ;; complicated, so we don't handle every possible case
3834 ;; here---just the most common and easiest cases:
3836 ;; * Any REAL can be coerced to a FLOAT type.
3837 ;; * Any NUMBER can be coerced to a (COMPLEX
3838 ;; SINGLE/DOUBLE-FLOAT).
3840 ;; FIXME I: we should also be able to deal with characters
3843 ;; FIXME II: I'm not sure that anything is necessary
3844 ;; here, at least while COMPLEX is not a specialized
3845 ;; array element type in the system. Reasoning: if
3846 ;; something cannot be coerced to the requested type, an
3847 ;; error will be raised (and so any downstream compiled
3848 ;; code on the assumption of the returned type is
3849 ;; unreachable). If something can, then it will be of
3850 ;; the requested type, because (by assumption) COMPLEX
3851 ;; (and other difficult types like (COMPLEX INTEGER)
3852 ;; aren't specialized types.
3853 (let ((coerced-type c-type))
3854 (or (and (subtypep coerced-type 'float)
3855 (csubtypep value-type (specifier-type 'real)))
3856 (and (subtypep coerced-type
3857 '(or (complex single-float)
3858 (complex double-float)))
3859 (csubtypep value-type (specifier-type 'number))))))
3860 (process-types (type)
3861 ;; FIXME: This needs some work because we should be able
3862 ;; to derive the resulting type better than just the
3863 ;; type arg of coerce. That is, if X is (INTEGER 10
3864 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3865 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3867 (cond ((member-type-p type)
3868 (let ((members (member-type-members type)))
3869 (if (every #'coerceable-p members)
3870 (specifier-type `(or ,@members))
3872 ((and (cons-type-p type)
3873 (good-cons-type-p type))
3874 (let ((c-type (unconsify-type (type-specifier type))))
3875 (if (coerceable-p c-type)
3876 (specifier-type c-type)
3879 *universal-type*))))
3880 (cond ((union-type-p type-type)
3881 (apply #'type-union (mapcar #'process-types
3882 (union-type-types type-type))))
3883 ((or (member-type-p type-type)
3884 (cons-type-p type-type))
3885 (process-types type-type))
3887 *universal-type*)))))))
3889 (defoptimizer (compile derive-type) ((nameoid function))
3890 (when (csubtypep (lvar-type nameoid)
3891 (specifier-type 'null))
3892 (values-specifier-type '(values function boolean boolean))))
3894 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3895 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3896 ;;; optimizer, above).
3897 (defoptimizer (array-element-type derive-type) ((array))
3898 (let ((array-type (lvar-type array)))
3899 (labels ((consify (list)
3902 `(cons (eql ,(car list)) ,(consify (rest list)))))
3903 (get-element-type (a)
3905 (type-specifier (array-type-specialized-element-type a))))
3906 (cond ((eq element-type '*)
3907 (specifier-type 'type-specifier))
3908 ((symbolp element-type)
3909 (make-member-type :members (list element-type)))
3910 ((consp element-type)
3911 (specifier-type (consify element-type)))
3913 (error "can't understand type ~S~%" element-type))))))
3914 (cond ((array-type-p array-type)
3915 (get-element-type array-type))
3916 ((union-type-p array-type)
3918 (mapcar #'get-element-type (union-type-types array-type))))
3920 *universal-type*)))))
3922 ;;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3923 ;;; isn't really related to the CMU CL code, since instead of trying
3924 ;;; to generalize the CMU CL code to allow START and END values, this
3925 ;;; code has been written from scratch following Chapter 7 of
3926 ;;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3927 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
3928 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3929 ;; isn't really related to the CMU CL code, since instead of trying
3930 ;; to generalize the CMU CL code to allow START and END values, this
3931 ;; code has been written from scratch following Chapter 7 of
3932 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3933 `(macrolet ((%index (x) `(truly-the index ,x))
3934 (%parent (i) `(ash ,i -1))
3935 (%left (i) `(%index (ash ,i 1)))
3936 (%right (i) `(%index (1+ (ash ,i 1))))
3939 (left (%left i) (%left i)))
3940 ((> left current-heap-size))
3941 (declare (type index i left))
3942 (let* ((i-elt (%elt i))
3943 (i-key (funcall keyfun i-elt))
3944 (left-elt (%elt left))
3945 (left-key (funcall keyfun left-elt)))
3946 (multiple-value-bind (large large-elt large-key)
3947 (if (funcall ,',predicate i-key left-key)
3948 (values left left-elt left-key)
3949 (values i i-elt i-key))
3950 (let ((right (%right i)))
3951 (multiple-value-bind (largest largest-elt)
3952 (if (> right current-heap-size)
3953 (values large large-elt)
3954 (let* ((right-elt (%elt right))
3955 (right-key (funcall keyfun right-elt)))
3956 (if (funcall ,',predicate large-key right-key)
3957 (values right right-elt)
3958 (values large large-elt))))
3959 (cond ((= largest i)
3962 (setf (%elt i) largest-elt
3963 (%elt largest) i-elt
3965 (%sort-vector (keyfun &optional (vtype 'vector))
3966 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
3967 ;; trouble getting type inference to
3968 ;; propagate all the way through this
3969 ;; tangled mess of inlining. The TRULY-THE
3970 ;; here works around that. -- WHN
3972 `(aref (truly-the ,',vtype ,',',vector)
3973 (%index (+ (%index ,i) start-1)))))
3974 (let (;; Heaps prefer 1-based addressing.
3975 (start-1 (1- ,',start))
3976 (current-heap-size (- ,',end ,',start))
3978 (declare (type (integer -1 #.(1- most-positive-fixnum))
3980 (declare (type index current-heap-size))
3981 (declare (type function keyfun))
3982 (loop for i of-type index
3983 from (ash current-heap-size -1) downto 1 do
3986 (when (< current-heap-size 2)
3988 (rotatef (%elt 1) (%elt current-heap-size))
3989 (decf current-heap-size)
3991 (if (typep ,vector 'simple-vector)
3992 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
3993 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
3995 ;; Special-casing the KEY=NIL case lets us avoid some
3997 (%sort-vector #'identity simple-vector)
3998 (%sort-vector ,key simple-vector))
3999 ;; It's hard to anticipate many speed-critical applications for
4000 ;; sorting vector types other than (VECTOR T), so we just lump
4001 ;; them all together in one slow dynamically typed mess.
4003 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4004 (%sort-vector (or ,key #'identity))))))
4006 ;;;; debuggers' little helpers
4008 ;;; for debugging when transforms are behaving mysteriously,
4009 ;;; e.g. when debugging a problem with an ASH transform
4010 ;;; (defun foo (&optional s)
4011 ;;; (sb-c::/report-lvar s "S outside WHEN")
4012 ;;; (when (and (integerp s) (> s 3))
4013 ;;; (sb-c::/report-lvar s "S inside WHEN")
4014 ;;; (let ((bound (ash 1 (1- s))))
4015 ;;; (sb-c::/report-lvar bound "BOUND")
4016 ;;; (let ((x (- bound))
4018 ;;; (sb-c::/report-lvar x "X")
4019 ;;; (sb-c::/report-lvar x "Y"))
4020 ;;; `(integer ,(- bound) ,(1- bound)))))
4021 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4022 ;;; and the function doesn't do anything at all.)
4025 (defknown /report-lvar (t t) null)
4026 (deftransform /report-lvar ((x message) (t t))
4027 (format t "~%/in /REPORT-LVAR~%")
4028 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4029 (when (constant-lvar-p x)
4030 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4031 (format t "/MESSAGE=~S~%" (lvar-value message))
4032 (give-up-ir1-transform "not a real transform"))
4033 (defun /report-lvar (x message)
4034 (declare (ignore x message))))