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 (,op (type-bound-number ,x)
337 (type-bound-number ,y))
338 (or (consp ,x) (consp ,y))))))
340 ;;; Convert a numeric-type object to an interval object.
341 (defun numeric-type->interval (x)
342 (declare (type numeric-type x))
343 (make-interval :low (numeric-type-low x)
344 :high (numeric-type-high x)))
346 (defun type-approximate-interval (type)
347 (declare (type ctype type))
348 (let ((types (prepare-arg-for-derive-type type))
351 (let ((type (if (member-type-p type)
352 (convert-member-type type)
354 (unless (numeric-type-p type)
355 (return-from type-approximate-interval nil))
356 (let ((interval (numeric-type->interval type)))
359 (interval-approximate-union result interval)
363 (defun copy-interval-limit (limit)
368 (defun copy-interval (x)
369 (declare (type interval x))
370 (make-interval :low (copy-interval-limit (interval-low x))
371 :high (copy-interval-limit (interval-high x))))
373 ;;; Given a point P contained in the interval X, split X into two
374 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
375 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
376 ;;; contains P. You can specify both to be T or NIL.
377 (defun interval-split (p x &optional close-lower close-upper)
378 (declare (type number p)
380 (list (make-interval :low (copy-interval-limit (interval-low x))
381 :high (if close-lower p (list p)))
382 (make-interval :low (if close-upper (list p) p)
383 :high (copy-interval-limit (interval-high x)))))
385 ;;; Return the closure of the interval. That is, convert open bounds
386 ;;; to closed bounds.
387 (defun interval-closure (x)
388 (declare (type interval x))
389 (make-interval :low (type-bound-number (interval-low x))
390 :high (type-bound-number (interval-high x))))
392 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
393 ;;; '-. Otherwise return NIL.
394 (defun interval-range-info (x &optional (point 0))
395 (declare (type interval x))
396 (let ((lo (interval-low x))
397 (hi (interval-high x)))
398 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
400 ((and hi (signed-zero->= point (type-bound-number hi)))
405 ;;; Test to see whether the interval X is bounded. HOW determines the
406 ;;; test, and should be either ABOVE, BELOW, or BOTH.
407 (defun interval-bounded-p (x how)
408 (declare (type interval x))
415 (and (interval-low x) (interval-high x)))))
417 ;;; See whether the interval X contains the number P, taking into
418 ;;; account that the interval might not be closed.
419 (defun interval-contains-p (p x)
420 (declare (type number p)
422 ;; Does the interval X contain the number P? This would be a lot
423 ;; easier if all intervals were closed!
424 (let ((lo (interval-low x))
425 (hi (interval-high x)))
427 ;; The interval is bounded
428 (if (and (signed-zero-<= (type-bound-number lo) p)
429 (signed-zero-<= p (type-bound-number hi)))
430 ;; P is definitely in the closure of the interval.
431 ;; We just need to check the end points now.
432 (cond ((signed-zero-= p (type-bound-number lo))
434 ((signed-zero-= p (type-bound-number hi))
439 ;; Interval with upper bound
440 (if (signed-zero-< p (type-bound-number hi))
442 (and (numberp hi) (signed-zero-= p hi))))
444 ;; Interval with lower bound
445 (if (signed-zero-> p (type-bound-number lo))
447 (and (numberp lo) (signed-zero-= p lo))))
449 ;; Interval with no bounds
452 ;;; Determine whether two intervals X and Y intersect. Return T if so.
453 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
454 ;;; were closed. Otherwise the intervals are treated as they are.
456 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
457 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
458 ;;; is T, then they do intersect because we use the closure of X = [0,
459 ;;; 1] and Y = [1, 2] to determine intersection.
460 (defun interval-intersect-p (x y &optional closed-intervals-p)
461 (declare (type interval x y))
462 (multiple-value-bind (intersect diff)
463 (interval-intersection/difference (if closed-intervals-p
466 (if closed-intervals-p
469 (declare (ignore diff))
472 ;;; Are the two intervals adjacent? That is, is there a number
473 ;;; between the two intervals that is not an element of either
474 ;;; interval? If so, they are not adjacent. For example [0, 1) and
475 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
476 ;;; between both intervals.
477 (defun interval-adjacent-p (x y)
478 (declare (type interval x y))
479 (flet ((adjacent (lo hi)
480 ;; Check to see whether lo and hi are adjacent. If either is
481 ;; nil, they can't be adjacent.
482 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
483 ;; The bounds are equal. They are adjacent if one of
484 ;; them is closed (a number). If both are open (consp),
485 ;; then there is a number that lies between them.
486 (or (numberp lo) (numberp hi)))))
487 (or (adjacent (interval-low y) (interval-high x))
488 (adjacent (interval-low x) (interval-high y)))))
490 ;;; Compute the intersection and difference between two intervals.
491 ;;; Two values are returned: the intersection and the difference.
493 ;;; Let the two intervals be X and Y, and let I and D be the two
494 ;;; values returned by this function. Then I = X intersect Y. If I
495 ;;; is NIL (the empty set), then D is X union Y, represented as the
496 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
497 ;;; - I, which is a list of two intervals.
499 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
500 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
501 (defun interval-intersection/difference (x y)
502 (declare (type interval x y))
503 (let ((x-lo (interval-low x))
504 (x-hi (interval-high x))
505 (y-lo (interval-low y))
506 (y-hi (interval-high y)))
509 ;; If p is an open bound, make it closed. If p is a closed
510 ;; bound, make it open.
515 ;; Test whether P is in the interval.
516 (when (interval-contains-p (type-bound-number p)
517 (interval-closure int))
518 (let ((lo (interval-low int))
519 (hi (interval-high int)))
520 ;; Check for endpoints.
521 (cond ((and lo (= (type-bound-number p) (type-bound-number lo)))
522 (not (and (consp p) (numberp lo))))
523 ((and hi (= (type-bound-number p) (type-bound-number hi)))
524 (not (and (numberp p) (consp hi))))
526 (test-lower-bound (p int)
527 ;; P is a lower bound of an interval.
530 (not (interval-bounded-p int 'below))))
531 (test-upper-bound (p int)
532 ;; P is an upper bound of an interval.
535 (not (interval-bounded-p int 'above)))))
536 (let ((x-lo-in-y (test-lower-bound x-lo y))
537 (x-hi-in-y (test-upper-bound x-hi y))
538 (y-lo-in-x (test-lower-bound y-lo x))
539 (y-hi-in-x (test-upper-bound y-hi x)))
540 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
541 ;; Intervals intersect. Let's compute the intersection
542 ;; and the difference.
543 (multiple-value-bind (lo left-lo left-hi)
544 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
545 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
546 (multiple-value-bind (hi right-lo right-hi)
548 (values x-hi (opposite-bound x-hi) y-hi))
550 (values y-hi (opposite-bound y-hi) x-hi)))
551 (values (make-interval :low lo :high hi)
552 (list (make-interval :low left-lo
554 (make-interval :low right-lo
557 (values nil (list x y))))))))
559 ;;; If intervals X and Y intersect, return a new interval that is the
560 ;;; union of the two. If they do not intersect, return NIL.
561 (defun interval-merge-pair (x y)
562 (declare (type interval x y))
563 ;; If x and y intersect or are adjacent, create the union.
564 ;; Otherwise return nil
565 (when (or (interval-intersect-p x y)
566 (interval-adjacent-p x y))
567 (flet ((select-bound (x1 x2 min-op max-op)
568 (let ((x1-val (type-bound-number x1))
569 (x2-val (type-bound-number x2)))
571 ;; Both bounds are finite. Select the right one.
572 (cond ((funcall min-op x1-val x2-val)
573 ;; x1 is definitely better.
575 ((funcall max-op x1-val x2-val)
576 ;; x2 is definitely better.
579 ;; Bounds are equal. Select either
580 ;; value and make it open only if
582 (set-bound x1-val (and (consp x1) (consp x2))))))
584 ;; At least one bound is not finite. The
585 ;; non-finite bound always wins.
587 (let* ((x-lo (copy-interval-limit (interval-low x)))
588 (x-hi (copy-interval-limit (interval-high x)))
589 (y-lo (copy-interval-limit (interval-low y)))
590 (y-hi (copy-interval-limit (interval-high y))))
591 (make-interval :low (select-bound x-lo y-lo #'< #'>)
592 :high (select-bound x-hi y-hi #'> #'<))))))
594 ;;; return the minimal interval, containing X and Y
595 (defun interval-approximate-union (x y)
596 (cond ((interval-merge-pair x y))
598 (make-interval :low (copy-interval-limit (interval-low x))
599 :high (copy-interval-limit (interval-high y))))
601 (make-interval :low (copy-interval-limit (interval-low y))
602 :high (copy-interval-limit (interval-high x))))))
604 ;;; basic arithmetic operations on intervals. We probably should do
605 ;;; true interval arithmetic here, but it's complicated because we
606 ;;; have float and integer types and bounds can be open or closed.
608 ;;; the negative of an interval
609 (defun interval-neg (x)
610 (declare (type interval x))
611 (make-interval :low (bound-func #'- (interval-high x))
612 :high (bound-func #'- (interval-low x))))
614 ;;; Add two intervals.
615 (defun interval-add (x y)
616 (declare (type interval x y))
617 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
618 :high (bound-binop + (interval-high x) (interval-high y))))
620 ;;; Subtract two intervals.
621 (defun interval-sub (x y)
622 (declare (type interval x y))
623 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
624 :high (bound-binop - (interval-high x) (interval-low y))))
626 ;;; Multiply two intervals.
627 (defun interval-mul (x y)
628 (declare (type interval x y))
629 (flet ((bound-mul (x y)
630 (cond ((or (null x) (null y))
631 ;; Multiply by infinity is infinity
633 ((or (and (numberp x) (zerop x))
634 (and (numberp y) (zerop y)))
635 ;; Multiply by closed zero is special. The result
636 ;; is always a closed bound. But don't replace this
637 ;; with zero; we want the multiplication to produce
638 ;; the correct signed zero, if needed.
639 (* (type-bound-number x) (type-bound-number y)))
640 ((or (and (floatp x) (float-infinity-p x))
641 (and (floatp y) (float-infinity-p y)))
642 ;; Infinity times anything is infinity
645 ;; General multiply. The result is open if either is open.
646 (bound-binop * x y)))))
647 (let ((x-range (interval-range-info x))
648 (y-range (interval-range-info y)))
649 (cond ((null x-range)
650 ;; Split x into two and multiply each separately
651 (destructuring-bind (x- x+) (interval-split 0 x t t)
652 (interval-merge-pair (interval-mul x- y)
653 (interval-mul x+ y))))
655 ;; Split y into two and multiply each separately
656 (destructuring-bind (y- y+) (interval-split 0 y t t)
657 (interval-merge-pair (interval-mul x y-)
658 (interval-mul x y+))))
660 (interval-neg (interval-mul (interval-neg x) y)))
662 (interval-neg (interval-mul x (interval-neg y))))
663 ((and (eq x-range '+) (eq y-range '+))
664 ;; If we are here, X and Y are both positive.
666 :low (bound-mul (interval-low x) (interval-low y))
667 :high (bound-mul (interval-high x) (interval-high y))))
669 (bug "excluded case in INTERVAL-MUL"))))))
671 ;;; Divide two intervals.
672 (defun interval-div (top bot)
673 (declare (type interval top bot))
674 (flet ((bound-div (x y y-low-p)
677 ;; Divide by infinity means result is 0. However,
678 ;; we need to watch out for the sign of the result,
679 ;; to correctly handle signed zeros. We also need
680 ;; to watch out for positive or negative infinity.
681 (if (floatp (type-bound-number x))
683 (- (float-sign (type-bound-number x) 0.0))
684 (float-sign (type-bound-number x) 0.0))
686 ((zerop (type-bound-number y))
687 ;; Divide by zero means result is infinity
689 ((and (numberp x) (zerop x))
690 ;; Zero divided by anything is zero.
693 (bound-binop / x y)))))
694 (let ((top-range (interval-range-info top))
695 (bot-range (interval-range-info bot)))
696 (cond ((null bot-range)
697 ;; The denominator contains zero, so anything goes!
698 (make-interval :low nil :high nil))
700 ;; Denominator is negative so flip the sign, compute the
701 ;; result, and flip it back.
702 (interval-neg (interval-div top (interval-neg bot))))
704 ;; Split top into two positive and negative parts, and
705 ;; divide each separately
706 (destructuring-bind (top- top+) (interval-split 0 top t t)
707 (interval-merge-pair (interval-div top- bot)
708 (interval-div top+ bot))))
710 ;; Top is negative so flip the sign, divide, and flip the
711 ;; sign of the result.
712 (interval-neg (interval-div (interval-neg top) bot)))
713 ((and (eq top-range '+) (eq bot-range '+))
716 :low (bound-div (interval-low top) (interval-high bot) t)
717 :high (bound-div (interval-high top) (interval-low bot) nil)))
719 (bug "excluded case in INTERVAL-DIV"))))))
721 ;;; Apply the function F to the interval X. If X = [a, b], then the
722 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
723 ;;; result makes sense. It will if F is monotonic increasing (or
725 (defun interval-func (f x)
726 (declare (type function f)
728 (let ((lo (bound-func f (interval-low x)))
729 (hi (bound-func f (interval-high x))))
730 (make-interval :low lo :high hi)))
732 ;;; Return T if X < Y. That is every number in the interval X is
733 ;;; always less than any number in the interval Y.
734 (defun interval-< (x y)
735 (declare (type interval x y))
736 ;; X < Y only if X is bounded above, Y is bounded below, and they
738 (when (and (interval-bounded-p x 'above)
739 (interval-bounded-p y 'below))
740 ;; Intervals are bounded in the appropriate way. Make sure they
742 (let ((left (interval-high x))
743 (right (interval-low y)))
744 (cond ((> (type-bound-number left)
745 (type-bound-number right))
746 ;; The intervals definitely overlap, so result is NIL.
748 ((< (type-bound-number left)
749 (type-bound-number right))
750 ;; The intervals definitely don't touch, so result is T.
753 ;; Limits are equal. Check for open or closed bounds.
754 ;; Don't overlap if one or the other are open.
755 (or (consp left) (consp right)))))))
757 ;;; Return T if X >= Y. That is, every number in the interval X is
758 ;;; always greater than any number in the interval Y.
759 (defun interval->= (x y)
760 (declare (type interval x y))
761 ;; X >= Y if lower bound of X >= upper bound of Y
762 (when (and (interval-bounded-p x 'below)
763 (interval-bounded-p y 'above))
764 (>= (type-bound-number (interval-low x))
765 (type-bound-number (interval-high y)))))
767 ;;; Return an interval that is the absolute value of X. Thus, if
768 ;;; X = [-1 10], the result is [0, 10].
769 (defun interval-abs (x)
770 (declare (type interval x))
771 (case (interval-range-info x)
777 (destructuring-bind (x- x+) (interval-split 0 x t t)
778 (interval-merge-pair (interval-neg x-) x+)))))
780 ;;; Compute the square of an interval.
781 (defun interval-sqr (x)
782 (declare (type interval x))
783 (interval-func (lambda (x) (* x x))
786 ;;;; numeric DERIVE-TYPE methods
788 ;;; a utility for defining derive-type methods of integer operations. If
789 ;;; the types of both X and Y are integer types, then we compute a new
790 ;;; integer type with bounds determined Fun when applied to X and Y.
791 ;;; Otherwise, we use NUMERIC-CONTAGION.
792 (defun derive-integer-type-aux (x y fun)
793 (declare (type function fun))
794 (if (and (numeric-type-p x) (numeric-type-p y)
795 (eq (numeric-type-class x) 'integer)
796 (eq (numeric-type-class y) 'integer)
797 (eq (numeric-type-complexp x) :real)
798 (eq (numeric-type-complexp y) :real))
799 (multiple-value-bind (low high) (funcall fun x y)
800 (make-numeric-type :class 'integer
804 (numeric-contagion x y)))
806 (defun derive-integer-type (x y fun)
807 (declare (type lvar x y) (type function fun))
808 (let ((x (lvar-type x))
810 (derive-integer-type-aux x y fun)))
812 ;;; simple utility to flatten a list
813 (defun flatten-list (x)
814 (labels ((flatten-and-append (tree list)
815 (cond ((null tree) list)
816 ((atom tree) (cons tree list))
817 (t (flatten-and-append
818 (car tree) (flatten-and-append (cdr tree) list))))))
819 (flatten-and-append x nil)))
821 ;;; Take some type of lvar and massage it so that we get a list of the
822 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
824 (defun prepare-arg-for-derive-type (arg)
825 (flet ((listify (arg)
830 (union-type-types arg))
833 (unless (eq arg *empty-type*)
834 ;; Make sure all args are some type of numeric-type. For member
835 ;; types, convert the list of members into a union of equivalent
836 ;; single-element member-type's.
837 (let ((new-args nil))
838 (dolist (arg (listify arg))
839 (if (member-type-p arg)
840 ;; Run down the list of members and convert to a list of
842 (dolist (member (member-type-members arg))
843 (push (if (numberp member)
844 (make-member-type :members (list member))
847 (push arg new-args)))
848 (unless (member *empty-type* new-args)
851 ;;; Convert from the standard type convention for which -0.0 and 0.0
852 ;;; are equal to an intermediate convention for which they are
853 ;;; considered different which is more natural for some of the
855 (defun convert-numeric-type (type)
856 (declare (type numeric-type type))
857 ;;; Only convert real float interval delimiters types.
858 (if (eq (numeric-type-complexp type) :real)
859 (let* ((lo (numeric-type-low type))
860 (lo-val (type-bound-number lo))
861 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
862 (hi (numeric-type-high type))
863 (hi-val (type-bound-number hi))
864 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
865 (if (or lo-float-zero-p hi-float-zero-p)
867 :class (numeric-type-class type)
868 :format (numeric-type-format type)
870 :low (if lo-float-zero-p
872 (list (float 0.0 lo-val))
873 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
875 :high (if hi-float-zero-p
877 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
884 ;;; Convert back from the intermediate convention for which -0.0 and
885 ;;; 0.0 are considered different to the standard type convention for
887 (defun convert-back-numeric-type (type)
888 (declare (type numeric-type type))
889 ;;; Only convert real float interval delimiters types.
890 (if (eq (numeric-type-complexp type) :real)
891 (let* ((lo (numeric-type-low type))
892 (lo-val (type-bound-number lo))
894 (and lo (floatp lo-val) (= lo-val 0.0)
895 (float-sign lo-val)))
896 (hi (numeric-type-high type))
897 (hi-val (type-bound-number hi))
899 (and hi (floatp hi-val) (= hi-val 0.0)
900 (float-sign hi-val))))
902 ;; (float +0.0 +0.0) => (member 0.0)
903 ;; (float -0.0 -0.0) => (member -0.0)
904 ((and lo-float-zero-p hi-float-zero-p)
905 ;; shouldn't have exclusive bounds here..
906 (aver (and (not (consp lo)) (not (consp hi))))
907 (if (= lo-float-zero-p hi-float-zero-p)
908 ;; (float +0.0 +0.0) => (member 0.0)
909 ;; (float -0.0 -0.0) => (member -0.0)
910 (specifier-type `(member ,lo-val))
911 ;; (float -0.0 +0.0) => (float 0.0 0.0)
912 ;; (float +0.0 -0.0) => (float 0.0 0.0)
913 (make-numeric-type :class (numeric-type-class type)
914 :format (numeric-type-format type)
920 ;; (float -0.0 x) => (float 0.0 x)
921 ((and (not (consp lo)) (minusp lo-float-zero-p))
922 (make-numeric-type :class (numeric-type-class type)
923 :format (numeric-type-format type)
925 :low (float 0.0 lo-val)
927 ;; (float (+0.0) x) => (float (0.0) x)
928 ((and (consp lo) (plusp lo-float-zero-p))
929 (make-numeric-type :class (numeric-type-class type)
930 :format (numeric-type-format type)
932 :low (list (float 0.0 lo-val))
935 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
936 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
937 (list (make-member-type :members (list (float 0.0 lo-val)))
938 (make-numeric-type :class (numeric-type-class type)
939 :format (numeric-type-format type)
941 :low (list (float 0.0 lo-val))
945 ;; (float x +0.0) => (float x 0.0)
946 ((and (not (consp hi)) (plusp hi-float-zero-p))
947 (make-numeric-type :class (numeric-type-class type)
948 :format (numeric-type-format type)
951 :high (float 0.0 hi-val)))
952 ;; (float x (-0.0)) => (float x (0.0))
953 ((and (consp hi) (minusp hi-float-zero-p))
954 (make-numeric-type :class (numeric-type-class type)
955 :format (numeric-type-format type)
958 :high (list (float 0.0 hi-val))))
960 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
961 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
962 (list (make-member-type :members (list (float -0.0 hi-val)))
963 (make-numeric-type :class (numeric-type-class type)
964 :format (numeric-type-format type)
967 :high (list (float 0.0 hi-val)))))))
973 ;;; Convert back a possible list of numeric types.
974 (defun convert-back-numeric-type-list (type-list)
978 (dolist (type type-list)
979 (if (numeric-type-p type)
980 (let ((result (convert-back-numeric-type type)))
982 (setf results (append results result))
983 (push result results)))
984 (push type results)))
987 (convert-back-numeric-type type-list))
989 (convert-back-numeric-type-list (union-type-types type-list)))
993 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
994 ;;; belong in the kernel's type logic, invoked always, instead of in
995 ;;; the compiler, invoked only during some type optimizations. (In
996 ;;; fact, as of 0.pre8.100 or so they probably are, under
997 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
999 ;;; Take a list of types and return a canonical type specifier,
1000 ;;; combining any MEMBER types together. If both positive and negative
1001 ;;; MEMBER types are present they are converted to a float type.
1002 ;;; XXX This would be far simpler if the type-union methods could handle
1003 ;;; member/number unions.
1004 (defun make-canonical-union-type (type-list)
1007 (dolist (type type-list)
1008 (if (member-type-p type)
1009 (setf members (union members (member-type-members type)))
1010 (push type misc-types)))
1012 (when (null (set-difference `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0) members))
1013 (push (specifier-type '(long-float 0.0l0 0.0l0)) misc-types)
1014 (setf members (set-difference members `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0))))
1015 (when (null (set-difference `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0) members))
1016 (push (specifier-type '(double-float 0.0d0 0.0d0)) misc-types)
1017 (setf members (set-difference members `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0))))
1018 (when (null (set-difference `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0) members))
1019 (push (specifier-type '(single-float 0.0f0 0.0f0)) misc-types)
1020 (setf members (set-difference members `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0))))
1022 (apply #'type-union (make-member-type :members members) misc-types)
1023 (apply #'type-union misc-types))))
1025 ;;; Convert a member type with a single member to a numeric type.
1026 (defun convert-member-type (arg)
1027 (let* ((members (member-type-members arg))
1028 (member (first members))
1029 (member-type (type-of member)))
1030 (aver (not (rest members)))
1031 (specifier-type (cond ((typep member 'integer)
1032 `(integer ,member ,member))
1033 ((memq member-type '(short-float single-float
1034 double-float long-float))
1035 `(,member-type ,member ,member))
1039 ;;; This is used in defoptimizers for computing the resulting type of
1042 ;;; Given the lvar ARG, derive the resulting type using the
1043 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1044 ;;; "atomic" lvar type like numeric-type or member-type (containing
1045 ;;; just one element). It should return the resulting type, which can
1046 ;;; be a list of types.
1048 ;;; For the case of member types, if a MEMBER-FUN is given it is
1049 ;;; called to compute the result otherwise the member type is first
1050 ;;; converted to a numeric type and the DERIVE-FUN is called.
1051 (defun one-arg-derive-type (arg derive-fun member-fun
1052 &optional (convert-type t))
1053 (declare (type function derive-fun)
1054 (type (or null function) member-fun))
1055 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1061 (with-float-traps-masked
1062 (:underflow :overflow :divide-by-zero)
1064 `(eql ,(funcall member-fun
1065 (first (member-type-members x))))))
1066 ;; Otherwise convert to a numeric type.
1067 (let ((result-type-list
1068 (funcall derive-fun (convert-member-type x))))
1070 (convert-back-numeric-type-list result-type-list)
1071 result-type-list))))
1074 (convert-back-numeric-type-list
1075 (funcall derive-fun (convert-numeric-type x)))
1076 (funcall derive-fun x)))
1078 *universal-type*))))
1079 ;; Run down the list of args and derive the type of each one,
1080 ;; saving all of the results in a list.
1081 (let ((results nil))
1082 (dolist (arg arg-list)
1083 (let ((result (deriver arg)))
1085 (setf results (append results result))
1086 (push result results))))
1088 (make-canonical-union-type results)
1089 (first results)))))))
1091 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1092 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1093 ;;; original args and a third which is T to indicate if the two args
1094 ;;; really represent the same lvar. This is useful for deriving the
1095 ;;; type of things like (* x x), which should always be positive. If
1096 ;;; we didn't do this, we wouldn't be able to tell.
1097 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1098 &optional (convert-type t))
1099 (declare (type function derive-fun fun))
1100 (flet ((deriver (x y same-arg)
1101 (cond ((and (member-type-p x) (member-type-p y))
1102 (let* ((x (first (member-type-members x)))
1103 (y (first (member-type-members y)))
1104 (result (ignore-errors
1105 (with-float-traps-masked
1106 (:underflow :overflow :divide-by-zero
1108 (funcall fun x y)))))
1109 (cond ((null result) *empty-type*)
1110 ((and (floatp result) (float-nan-p result))
1111 (make-numeric-type :class 'float
1112 :format (type-of result)
1115 (specifier-type `(eql ,result))))))
1116 ((and (member-type-p x) (numeric-type-p y))
1117 (let* ((x (convert-member-type x))
1118 (y (if convert-type (convert-numeric-type y) y))
1119 (result (funcall derive-fun x y same-arg)))
1121 (convert-back-numeric-type-list result)
1123 ((and (numeric-type-p x) (member-type-p y))
1124 (let* ((x (if convert-type (convert-numeric-type x) x))
1125 (y (convert-member-type y))
1126 (result (funcall derive-fun x y same-arg)))
1128 (convert-back-numeric-type-list result)
1130 ((and (numeric-type-p x) (numeric-type-p y))
1131 (let* ((x (if convert-type (convert-numeric-type x) x))
1132 (y (if convert-type (convert-numeric-type y) y))
1133 (result (funcall derive-fun x y same-arg)))
1135 (convert-back-numeric-type-list result)
1138 *universal-type*))))
1139 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1140 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1141 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1143 (let ((results nil))
1145 ;; Since the args are the same LVARs, just run down the
1148 (let ((result (deriver x x same-arg)))
1150 (setf results (append results result))
1151 (push result results))))
1152 ;; Try all pairwise combinations.
1155 (let ((result (or (deriver x y same-arg)
1156 (numeric-contagion x y))))
1158 (setf results (append results result))
1159 (push result results))))))
1161 (make-canonical-union-type results)
1162 (first results)))))))
1164 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1166 (defoptimizer (+ derive-type) ((x y))
1167 (derive-integer-type
1174 (values (frob (numeric-type-low x) (numeric-type-low y))
1175 (frob (numeric-type-high x) (numeric-type-high y)))))))
1177 (defoptimizer (- derive-type) ((x y))
1178 (derive-integer-type
1185 (values (frob (numeric-type-low x) (numeric-type-high y))
1186 (frob (numeric-type-high x) (numeric-type-low y)))))))
1188 (defoptimizer (* derive-type) ((x y))
1189 (derive-integer-type
1192 (let ((x-low (numeric-type-low x))
1193 (x-high (numeric-type-high x))
1194 (y-low (numeric-type-low y))
1195 (y-high (numeric-type-high y)))
1196 (cond ((not (and x-low y-low))
1198 ((or (minusp x-low) (minusp y-low))
1199 (if (and x-high y-high)
1200 (let ((max (* (max (abs x-low) (abs x-high))
1201 (max (abs y-low) (abs y-high)))))
1202 (values (- max) max))
1205 (values (* x-low y-low)
1206 (if (and x-high y-high)
1210 (defoptimizer (/ derive-type) ((x y))
1211 (numeric-contagion (lvar-type x) (lvar-type y)))
1215 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1217 (defun +-derive-type-aux (x y same-arg)
1218 (if (and (numeric-type-real-p x)
1219 (numeric-type-real-p y))
1222 (let ((x-int (numeric-type->interval x)))
1223 (interval-add x-int x-int))
1224 (interval-add (numeric-type->interval x)
1225 (numeric-type->interval y))))
1226 (result-type (numeric-contagion x y)))
1227 ;; If the result type is a float, we need to be sure to coerce
1228 ;; the bounds into the correct type.
1229 (when (eq (numeric-type-class result-type) 'float)
1230 (setf result (interval-func
1232 (coerce x (or (numeric-type-format result-type)
1236 :class (if (and (eq (numeric-type-class x) 'integer)
1237 (eq (numeric-type-class y) 'integer))
1238 ;; The sum of integers is always an integer.
1240 (numeric-type-class result-type))
1241 :format (numeric-type-format result-type)
1242 :low (interval-low result)
1243 :high (interval-high result)))
1244 ;; general contagion
1245 (numeric-contagion x y)))
1247 (defoptimizer (+ derive-type) ((x y))
1248 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1250 (defun --derive-type-aux (x y same-arg)
1251 (if (and (numeric-type-real-p x)
1252 (numeric-type-real-p y))
1254 ;; (- X X) is always 0.
1256 (make-interval :low 0 :high 0)
1257 (interval-sub (numeric-type->interval x)
1258 (numeric-type->interval y))))
1259 (result-type (numeric-contagion x y)))
1260 ;; If the result type is a float, we need to be sure to coerce
1261 ;; the bounds into the correct type.
1262 (when (eq (numeric-type-class result-type) 'float)
1263 (setf result (interval-func
1265 (coerce x (or (numeric-type-format result-type)
1269 :class (if (and (eq (numeric-type-class x) 'integer)
1270 (eq (numeric-type-class y) 'integer))
1271 ;; The difference of integers is always an integer.
1273 (numeric-type-class result-type))
1274 :format (numeric-type-format result-type)
1275 :low (interval-low result)
1276 :high (interval-high result)))
1277 ;; general contagion
1278 (numeric-contagion x y)))
1280 (defoptimizer (- derive-type) ((x y))
1281 (two-arg-derive-type x y #'--derive-type-aux #'-))
1283 (defun *-derive-type-aux (x y same-arg)
1284 (if (and (numeric-type-real-p x)
1285 (numeric-type-real-p y))
1287 ;; (* X X) is always positive, so take care to do it right.
1289 (interval-sqr (numeric-type->interval x))
1290 (interval-mul (numeric-type->interval x)
1291 (numeric-type->interval y))))
1292 (result-type (numeric-contagion x y)))
1293 ;; If the result type is a float, we need to be sure to coerce
1294 ;; the bounds into the correct type.
1295 (when (eq (numeric-type-class result-type) 'float)
1296 (setf result (interval-func
1298 (coerce x (or (numeric-type-format result-type)
1302 :class (if (and (eq (numeric-type-class x) 'integer)
1303 (eq (numeric-type-class y) 'integer))
1304 ;; The product of integers is always an integer.
1306 (numeric-type-class result-type))
1307 :format (numeric-type-format result-type)
1308 :low (interval-low result)
1309 :high (interval-high result)))
1310 (numeric-contagion x y)))
1312 (defoptimizer (* derive-type) ((x y))
1313 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1315 (defun /-derive-type-aux (x y same-arg)
1316 (if (and (numeric-type-real-p x)
1317 (numeric-type-real-p y))
1319 ;; (/ X X) is always 1, except if X can contain 0. In
1320 ;; that case, we shouldn't optimize the division away
1321 ;; because we want 0/0 to signal an error.
1323 (not (interval-contains-p
1324 0 (interval-closure (numeric-type->interval y)))))
1325 (make-interval :low 1 :high 1)
1326 (interval-div (numeric-type->interval x)
1327 (numeric-type->interval y))))
1328 (result-type (numeric-contagion x y)))
1329 ;; If the result type is a float, we need to be sure to coerce
1330 ;; the bounds into the correct type.
1331 (when (eq (numeric-type-class result-type) 'float)
1332 (setf result (interval-func
1334 (coerce x (or (numeric-type-format result-type)
1337 (make-numeric-type :class (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 #'/))
1348 (defun ash-derive-type-aux (n-type shift same-arg)
1349 (declare (ignore same-arg))
1350 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1351 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1352 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1353 ;; two bignums yielding zero) and it's hard to avoid that
1354 ;; calculation in here.
1355 #+(and cmu sb-xc-host)
1356 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1357 (typep (numeric-type-high n-type) 'bignum))
1358 (or (typep (numeric-type-low shift) 'bignum)
1359 (typep (numeric-type-high shift) 'bignum)))
1360 (return-from ash-derive-type-aux *universal-type*))
1361 (flet ((ash-outer (n s)
1362 (when (and (fixnump s)
1364 (> s sb!xc:most-negative-fixnum))
1366 ;; KLUDGE: The bare 64's here should be related to
1367 ;; symbolic machine word size values somehow.
1370 (if (and (fixnump s)
1371 (> s sb!xc:most-negative-fixnum))
1373 (if (minusp n) -1 0))))
1374 (or (and (csubtypep n-type (specifier-type 'integer))
1375 (csubtypep shift (specifier-type 'integer))
1376 (let ((n-low (numeric-type-low n-type))
1377 (n-high (numeric-type-high n-type))
1378 (s-low (numeric-type-low shift))
1379 (s-high (numeric-type-high shift)))
1380 (make-numeric-type :class 'integer :complexp :real
1383 (ash-outer n-low s-high)
1384 (ash-inner n-low s-low)))
1387 (ash-inner n-high s-low)
1388 (ash-outer n-high s-high))))))
1391 (defoptimizer (ash derive-type) ((n shift))
1392 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1394 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1395 (macrolet ((frob (fun)
1396 `#'(lambda (type type2)
1397 (declare (ignore type2))
1398 (let ((lo (numeric-type-low type))
1399 (hi (numeric-type-high type)))
1400 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1402 (defoptimizer (%negate derive-type) ((num))
1403 (derive-integer-type num num (frob -))))
1405 (defun lognot-derive-type-aux (int)
1406 (derive-integer-type-aux int int
1407 (lambda (type type2)
1408 (declare (ignore type2))
1409 (let ((lo (numeric-type-low type))
1410 (hi (numeric-type-high type)))
1411 (values (if hi (lognot hi) nil)
1412 (if lo (lognot lo) nil)
1413 (numeric-type-class type)
1414 (numeric-type-format type))))))
1416 (defoptimizer (lognot derive-type) ((int))
1417 (lognot-derive-type-aux (lvar-type int)))
1419 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1420 (defoptimizer (%negate derive-type) ((num))
1421 (flet ((negate-bound (b)
1423 (set-bound (- (type-bound-number b))
1425 (one-arg-derive-type num
1427 (modified-numeric-type
1429 :low (negate-bound (numeric-type-high type))
1430 :high (negate-bound (numeric-type-low type))))
1433 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1434 (defoptimizer (abs derive-type) ((num))
1435 (let ((type (lvar-type num)))
1436 (if (and (numeric-type-p type)
1437 (eq (numeric-type-class type) 'integer)
1438 (eq (numeric-type-complexp type) :real))
1439 (let ((lo (numeric-type-low type))
1440 (hi (numeric-type-high type)))
1441 (make-numeric-type :class 'integer :complexp :real
1442 :low (cond ((and hi (minusp hi))
1448 :high (if (and hi lo)
1449 (max (abs hi) (abs lo))
1451 (numeric-contagion type type))))
1453 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1454 (defun abs-derive-type-aux (type)
1455 (cond ((eq (numeric-type-complexp type) :complex)
1456 ;; The absolute value of a complex number is always a
1457 ;; non-negative float.
1458 (let* ((format (case (numeric-type-class type)
1459 ((integer rational) 'single-float)
1460 (t (numeric-type-format type))))
1461 (bound-format (or format 'float)))
1462 (make-numeric-type :class 'float
1465 :low (coerce 0 bound-format)
1468 ;; The absolute value of a real number is a non-negative real
1469 ;; of the same type.
1470 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1471 (class (numeric-type-class type))
1472 (format (numeric-type-format type))
1473 (bound-type (or format class 'real)))
1478 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1479 :high (coerce-numeric-bound
1480 (interval-high abs-bnd) bound-type))))))
1482 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1483 (defoptimizer (abs derive-type) ((num))
1484 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1486 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1487 (defoptimizer (truncate derive-type) ((number divisor))
1488 (let ((number-type (lvar-type number))
1489 (divisor-type (lvar-type divisor))
1490 (integer-type (specifier-type 'integer)))
1491 (if (and (numeric-type-p number-type)
1492 (csubtypep number-type integer-type)
1493 (numeric-type-p divisor-type)
1494 (csubtypep divisor-type integer-type))
1495 (let ((number-low (numeric-type-low number-type))
1496 (number-high (numeric-type-high number-type))
1497 (divisor-low (numeric-type-low divisor-type))
1498 (divisor-high (numeric-type-high divisor-type)))
1499 (values-specifier-type
1500 `(values ,(integer-truncate-derive-type number-low number-high
1501 divisor-low divisor-high)
1502 ,(integer-rem-derive-type number-low number-high
1503 divisor-low divisor-high))))
1506 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1509 (defun rem-result-type (number-type divisor-type)
1510 ;; Figure out what the remainder type is. The remainder is an
1511 ;; integer if both args are integers; a rational if both args are
1512 ;; rational; and a float otherwise.
1513 (cond ((and (csubtypep number-type (specifier-type 'integer))
1514 (csubtypep divisor-type (specifier-type 'integer)))
1516 ((and (csubtypep number-type (specifier-type 'rational))
1517 (csubtypep divisor-type (specifier-type 'rational)))
1519 ((and (csubtypep number-type (specifier-type 'float))
1520 (csubtypep divisor-type (specifier-type 'float)))
1521 ;; Both are floats so the result is also a float, of
1522 ;; the largest type.
1523 (or (float-format-max (numeric-type-format number-type)
1524 (numeric-type-format divisor-type))
1526 ((and (csubtypep number-type (specifier-type 'float))
1527 (csubtypep divisor-type (specifier-type 'rational)))
1528 ;; One of the arguments is a float and the other is a
1529 ;; rational. The remainder is a float of the same
1531 (or (numeric-type-format number-type) 'float))
1532 ((and (csubtypep divisor-type (specifier-type 'float))
1533 (csubtypep number-type (specifier-type 'rational)))
1534 ;; One of the arguments is a float and the other is a
1535 ;; rational. The remainder is a float of the same
1537 (or (numeric-type-format divisor-type) 'float))
1539 ;; Some unhandled combination. This usually means both args
1540 ;; are REAL so the result is a REAL.
1543 (defun truncate-derive-type-quot (number-type divisor-type)
1544 (let* ((rem-type (rem-result-type number-type divisor-type))
1545 (number-interval (numeric-type->interval number-type))
1546 (divisor-interval (numeric-type->interval divisor-type)))
1547 ;;(declare (type (member '(integer rational float)) rem-type))
1548 ;; We have real numbers now.
1549 (cond ((eq rem-type 'integer)
1550 ;; Since the remainder type is INTEGER, both args are
1552 (let* ((res (integer-truncate-derive-type
1553 (interval-low number-interval)
1554 (interval-high number-interval)
1555 (interval-low divisor-interval)
1556 (interval-high divisor-interval))))
1557 (specifier-type (if (listp res) res 'integer))))
1559 (let ((quot (truncate-quotient-bound
1560 (interval-div number-interval
1561 divisor-interval))))
1562 (specifier-type `(integer ,(or (interval-low quot) '*)
1563 ,(or (interval-high quot) '*))))))))
1565 (defun truncate-derive-type-rem (number-type divisor-type)
1566 (let* ((rem-type (rem-result-type number-type divisor-type))
1567 (number-interval (numeric-type->interval number-type))
1568 (divisor-interval (numeric-type->interval divisor-type))
1569 (rem (truncate-rem-bound number-interval divisor-interval)))
1570 ;;(declare (type (member '(integer rational float)) rem-type))
1571 ;; We have real numbers now.
1572 (cond ((eq rem-type 'integer)
1573 ;; Since the remainder type is INTEGER, both args are
1575 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1576 ,(or (interval-high rem) '*))))
1578 (multiple-value-bind (class format)
1581 (values 'integer nil))
1583 (values 'rational nil))
1584 ((or single-float double-float #!+long-float long-float)
1585 (values 'float rem-type))
1587 (values 'float nil))
1590 (when (member rem-type '(float single-float double-float
1591 #!+long-float long-float))
1592 (setf rem (interval-func #'(lambda (x)
1593 (coerce x rem-type))
1595 (make-numeric-type :class class
1597 :low (interval-low rem)
1598 :high (interval-high rem)))))))
1600 (defun truncate-derive-type-quot-aux (num div same-arg)
1601 (declare (ignore same-arg))
1602 (if (and (numeric-type-real-p num)
1603 (numeric-type-real-p div))
1604 (truncate-derive-type-quot num div)
1607 (defun truncate-derive-type-rem-aux (num div same-arg)
1608 (declare (ignore same-arg))
1609 (if (and (numeric-type-real-p num)
1610 (numeric-type-real-p div))
1611 (truncate-derive-type-rem num div)
1614 (defoptimizer (truncate derive-type) ((number divisor))
1615 (let ((quot (two-arg-derive-type number divisor
1616 #'truncate-derive-type-quot-aux #'truncate))
1617 (rem (two-arg-derive-type number divisor
1618 #'truncate-derive-type-rem-aux #'rem)))
1619 (when (and quot rem)
1620 (make-values-type :required (list quot rem)))))
1622 (defun ftruncate-derive-type-quot (number-type divisor-type)
1623 ;; The bounds are the same as for truncate. However, the first
1624 ;; result is a float of some type. We need to determine what that
1625 ;; type is. Basically it's the more contagious of the two types.
1626 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1627 (res-type (numeric-contagion number-type divisor-type)))
1628 (make-numeric-type :class 'float
1629 :format (numeric-type-format res-type)
1630 :low (numeric-type-low q-type)
1631 :high (numeric-type-high q-type))))
1633 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1634 (declare (ignore same-arg))
1635 (if (and (numeric-type-real-p n)
1636 (numeric-type-real-p d))
1637 (ftruncate-derive-type-quot n d)
1640 (defoptimizer (ftruncate derive-type) ((number divisor))
1642 (two-arg-derive-type number divisor
1643 #'ftruncate-derive-type-quot-aux #'ftruncate))
1644 (rem (two-arg-derive-type number divisor
1645 #'truncate-derive-type-rem-aux #'rem)))
1646 (when (and quot rem)
1647 (make-values-type :required (list quot rem)))))
1649 (defun %unary-truncate-derive-type-aux (number)
1650 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1652 (defoptimizer (%unary-truncate derive-type) ((number))
1653 (one-arg-derive-type number
1654 #'%unary-truncate-derive-type-aux
1657 (defoptimizer (%unary-ftruncate derive-type) ((number))
1658 (let ((divisor (specifier-type '(integer 1 1))))
1659 (one-arg-derive-type number
1661 (ftruncate-derive-type-quot-aux n divisor nil))
1662 #'%unary-ftruncate)))
1664 ;;; Define optimizers for FLOOR and CEILING.
1666 ((def (name q-name r-name)
1667 (let ((q-aux (symbolicate q-name "-AUX"))
1668 (r-aux (symbolicate r-name "-AUX")))
1670 ;; Compute type of quotient (first) result.
1671 (defun ,q-aux (number-type divisor-type)
1672 (let* ((number-interval
1673 (numeric-type->interval number-type))
1675 (numeric-type->interval divisor-type))
1676 (quot (,q-name (interval-div number-interval
1677 divisor-interval))))
1678 (specifier-type `(integer ,(or (interval-low quot) '*)
1679 ,(or (interval-high quot) '*)))))
1680 ;; Compute type of remainder.
1681 (defun ,r-aux (number-type divisor-type)
1682 (let* ((divisor-interval
1683 (numeric-type->interval divisor-type))
1684 (rem (,r-name divisor-interval))
1685 (result-type (rem-result-type number-type divisor-type)))
1686 (multiple-value-bind (class format)
1689 (values 'integer nil))
1691 (values 'rational nil))
1692 ((or single-float double-float #!+long-float long-float)
1693 (values 'float result-type))
1695 (values 'float nil))
1698 (when (member result-type '(float single-float double-float
1699 #!+long-float long-float))
1700 ;; Make sure that the limits on the interval have
1702 (setf rem (interval-func (lambda (x)
1703 (coerce x result-type))
1705 (make-numeric-type :class class
1707 :low (interval-low rem)
1708 :high (interval-high rem)))))
1709 ;; the optimizer itself
1710 (defoptimizer (,name derive-type) ((number divisor))
1711 (flet ((derive-q (n d same-arg)
1712 (declare (ignore same-arg))
1713 (if (and (numeric-type-real-p n)
1714 (numeric-type-real-p d))
1717 (derive-r (n d same-arg)
1718 (declare (ignore same-arg))
1719 (if (and (numeric-type-real-p n)
1720 (numeric-type-real-p d))
1723 (let ((quot (two-arg-derive-type
1724 number divisor #'derive-q #',name))
1725 (rem (two-arg-derive-type
1726 number divisor #'derive-r #'mod)))
1727 (when (and quot rem)
1728 (make-values-type :required (list quot rem))))))))))
1730 (def floor floor-quotient-bound floor-rem-bound)
1731 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1733 ;;; Define optimizers for FFLOOR and FCEILING
1734 (macrolet ((def (name q-name r-name)
1735 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1736 (r-aux (symbolicate r-name "-AUX")))
1738 ;; Compute type of quotient (first) result.
1739 (defun ,q-aux (number-type divisor-type)
1740 (let* ((number-interval
1741 (numeric-type->interval number-type))
1743 (numeric-type->interval divisor-type))
1744 (quot (,q-name (interval-div number-interval
1746 (res-type (numeric-contagion number-type
1749 :class (numeric-type-class res-type)
1750 :format (numeric-type-format res-type)
1751 :low (interval-low quot)
1752 :high (interval-high quot))))
1754 (defoptimizer (,name derive-type) ((number divisor))
1755 (flet ((derive-q (n d same-arg)
1756 (declare (ignore same-arg))
1757 (if (and (numeric-type-real-p n)
1758 (numeric-type-real-p d))
1761 (derive-r (n d same-arg)
1762 (declare (ignore same-arg))
1763 (if (and (numeric-type-real-p n)
1764 (numeric-type-real-p d))
1767 (let ((quot (two-arg-derive-type
1768 number divisor #'derive-q #',name))
1769 (rem (two-arg-derive-type
1770 number divisor #'derive-r #'mod)))
1771 (when (and quot rem)
1772 (make-values-type :required (list quot rem))))))))))
1774 (def ffloor floor-quotient-bound floor-rem-bound)
1775 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
1777 ;;; functions to compute the bounds on the quotient and remainder for
1778 ;;; the FLOOR function
1779 (defun floor-quotient-bound (quot)
1780 ;; Take the floor of the quotient and then massage it into what we
1782 (let ((lo (interval-low quot))
1783 (hi (interval-high quot)))
1784 ;; Take the floor of the lower bound. The result is always a
1785 ;; closed lower bound.
1787 (floor (type-bound-number lo))
1789 ;; For the upper bound, we need to be careful.
1792 ;; An open bound. We need to be careful here because
1793 ;; the floor of '(10.0) is 9, but the floor of
1795 (multiple-value-bind (q r) (floor (first hi))
1800 ;; A closed bound, so the answer is obvious.
1804 (make-interval :low lo :high hi)))
1805 (defun floor-rem-bound (div)
1806 ;; The remainder depends only on the divisor. Try to get the
1807 ;; correct sign for the remainder if we can.
1808 (case (interval-range-info div)
1810 ;; The divisor is always positive.
1811 (let ((rem (interval-abs div)))
1812 (setf (interval-low rem) 0)
1813 (when (and (numberp (interval-high rem))
1814 (not (zerop (interval-high rem))))
1815 ;; The remainder never contains the upper bound. However,
1816 ;; watch out for the case where the high limit is zero!
1817 (setf (interval-high rem) (list (interval-high rem))))
1820 ;; The divisor is always negative.
1821 (let ((rem (interval-neg (interval-abs div))))
1822 (setf (interval-high rem) 0)
1823 (when (numberp (interval-low rem))
1824 ;; The remainder never contains the lower bound.
1825 (setf (interval-low rem) (list (interval-low rem))))
1828 ;; The divisor can be positive or negative. All bets off. The
1829 ;; magnitude of remainder is the maximum value of the divisor.
1830 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1831 ;; The bound never reaches the limit, so make the interval open.
1832 (make-interval :low (if limit
1835 :high (list limit))))))
1837 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1838 => #S(INTERVAL :LOW 0 :HIGH 10)
1839 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1840 => #S(INTERVAL :LOW 0 :HIGH 10)
1841 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1842 => #S(INTERVAL :LOW 0 :HIGH 10)
1843 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1844 => #S(INTERVAL :LOW 0 :HIGH 9)
1845 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1846 => #S(INTERVAL :LOW 0 :HIGH 10)
1847 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1848 => #S(INTERVAL :LOW 0 :HIGH 10)
1849 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1850 => #S(INTERVAL :LOW -2 :HIGH 10)
1851 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1852 => #S(INTERVAL :LOW -1 :HIGH 10)
1853 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1854 => #S(INTERVAL :LOW -1 :HIGH 10)
1856 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1857 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1858 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1859 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1860 (floor-rem-bound (make-interval :low -10 :high -2.3))
1861 #S(INTERVAL :LOW (-10) :HIGH 0)
1862 (floor-rem-bound (make-interval :low 0.3 :high 10))
1863 => #S(INTERVAL :LOW 0 :HIGH '(10))
1864 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1865 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1866 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1867 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1870 ;;; same functions for CEILING
1871 (defun ceiling-quotient-bound (quot)
1872 ;; Take the ceiling of the quotient and then massage it into what we
1874 (let ((lo (interval-low quot))
1875 (hi (interval-high quot)))
1876 ;; Take the ceiling of the upper bound. The result is always a
1877 ;; closed upper bound.
1879 (ceiling (type-bound-number hi))
1881 ;; For the lower bound, we need to be careful.
1884 ;; An open bound. We need to be careful here because
1885 ;; the ceiling of '(10.0) is 11, but the ceiling of
1887 (multiple-value-bind (q r) (ceiling (first lo))
1892 ;; A closed bound, so the answer is obvious.
1896 (make-interval :low lo :high hi)))
1897 (defun ceiling-rem-bound (div)
1898 ;; The remainder depends only on the divisor. Try to get the
1899 ;; correct sign for the remainder if we can.
1900 (case (interval-range-info div)
1902 ;; Divisor is always positive. The remainder is negative.
1903 (let ((rem (interval-neg (interval-abs div))))
1904 (setf (interval-high rem) 0)
1905 (when (and (numberp (interval-low rem))
1906 (not (zerop (interval-low rem))))
1907 ;; The remainder never contains the upper bound. However,
1908 ;; watch out for the case when the upper bound is zero!
1909 (setf (interval-low rem) (list (interval-low rem))))
1912 ;; Divisor is always negative. The remainder is positive
1913 (let ((rem (interval-abs div)))
1914 (setf (interval-low rem) 0)
1915 (when (numberp (interval-high rem))
1916 ;; The remainder never contains the lower bound.
1917 (setf (interval-high rem) (list (interval-high rem))))
1920 ;; The divisor can be positive or negative. All bets off. The
1921 ;; magnitude of remainder is the maximum value of the divisor.
1922 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1923 ;; The bound never reaches the limit, so make the interval open.
1924 (make-interval :low (if limit
1927 :high (list limit))))))
1930 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
1931 => #S(INTERVAL :LOW 1 :HIGH 11)
1932 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1933 => #S(INTERVAL :LOW 1 :HIGH 11)
1934 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
1935 => #S(INTERVAL :LOW 1 :HIGH 10)
1936 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
1937 => #S(INTERVAL :LOW 1 :HIGH 10)
1938 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
1939 => #S(INTERVAL :LOW 1 :HIGH 11)
1940 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
1941 => #S(INTERVAL :LOW 1 :HIGH 11)
1942 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1943 => #S(INTERVAL :LOW -1 :HIGH 11)
1944 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1945 => #S(INTERVAL :LOW 0 :HIGH 11)
1946 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
1947 => #S(INTERVAL :LOW -1 :HIGH 11)
1949 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
1950 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
1951 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
1952 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1953 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
1954 => #S(INTERVAL :LOW 0 :HIGH (10))
1955 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
1956 => #S(INTERVAL :LOW (-10) :HIGH 0)
1957 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
1958 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
1959 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
1960 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1963 (defun truncate-quotient-bound (quot)
1964 ;; For positive quotients, truncate is exactly like floor. For
1965 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
1966 ;; it's the union of the two pieces.
1967 (case (interval-range-info quot)
1970 (floor-quotient-bound quot))
1972 ;; just like CEILING
1973 (ceiling-quotient-bound quot))
1975 ;; Split the interval into positive and negative pieces, compute
1976 ;; the result for each piece and put them back together.
1977 (destructuring-bind (neg pos) (interval-split 0 quot t t)
1978 (interval-merge-pair (ceiling-quotient-bound neg)
1979 (floor-quotient-bound pos))))))
1981 (defun truncate-rem-bound (num div)
1982 ;; This is significantly more complicated than FLOOR or CEILING. We
1983 ;; need both the number and the divisor to determine the range. The
1984 ;; basic idea is to split the ranges of NUM and DEN into positive
1985 ;; and negative pieces and deal with each of the four possibilities
1987 (case (interval-range-info num)
1989 (case (interval-range-info div)
1991 (floor-rem-bound div))
1993 (ceiling-rem-bound div))
1995 (destructuring-bind (neg pos) (interval-split 0 div t t)
1996 (interval-merge-pair (truncate-rem-bound num neg)
1997 (truncate-rem-bound num pos))))))
1999 (case (interval-range-info div)
2001 (ceiling-rem-bound div))
2003 (floor-rem-bound div))
2005 (destructuring-bind (neg pos) (interval-split 0 div t t)
2006 (interval-merge-pair (truncate-rem-bound num neg)
2007 (truncate-rem-bound num pos))))))
2009 (destructuring-bind (neg pos) (interval-split 0 num t t)
2010 (interval-merge-pair (truncate-rem-bound neg div)
2011 (truncate-rem-bound pos div))))))
2014 ;;; Derive useful information about the range. Returns three values:
2015 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2016 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2017 ;;; - The abs of the maximal value if there is one, or nil if it is
2019 (defun numeric-range-info (low high)
2020 (cond ((and low (not (minusp low)))
2021 (values '+ low high))
2022 ((and high (not (plusp high)))
2023 (values '- (- high) (if low (- low) nil)))
2025 (values nil 0 (and low high (max (- low) high))))))
2027 (defun integer-truncate-derive-type
2028 (number-low number-high divisor-low divisor-high)
2029 ;; The result cannot be larger in magnitude than the number, but the
2030 ;; sign might change. If we can determine the sign of either the
2031 ;; number or the divisor, we can eliminate some of the cases.
2032 (multiple-value-bind (number-sign number-min number-max)
2033 (numeric-range-info number-low number-high)
2034 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2035 (numeric-range-info divisor-low divisor-high)
2036 (when (and divisor-max (zerop divisor-max))
2037 ;; We've got a problem: guaranteed division by zero.
2038 (return-from integer-truncate-derive-type t))
2039 (when (zerop divisor-min)
2040 ;; We'll assume that they aren't going to divide by zero.
2042 (cond ((and number-sign divisor-sign)
2043 ;; We know the sign of both.
2044 (if (eq number-sign divisor-sign)
2045 ;; Same sign, so the result will be positive.
2046 `(integer ,(if divisor-max
2047 (truncate number-min divisor-max)
2050 (truncate number-max divisor-min)
2052 ;; Different signs, the result will be negative.
2053 `(integer ,(if number-max
2054 (- (truncate number-max divisor-min))
2057 (- (truncate number-min divisor-max))
2059 ((eq divisor-sign '+)
2060 ;; The divisor is positive. Therefore, the number will just
2061 ;; become closer to zero.
2062 `(integer ,(if number-low
2063 (truncate number-low divisor-min)
2066 (truncate number-high divisor-min)
2068 ((eq divisor-sign '-)
2069 ;; The divisor is negative. Therefore, the absolute value of
2070 ;; the number will become closer to zero, but the sign will also
2072 `(integer ,(if number-high
2073 (- (truncate number-high divisor-min))
2076 (- (truncate number-low divisor-min))
2078 ;; The divisor could be either positive or negative.
2080 ;; The number we are dividing has a bound. Divide that by the
2081 ;; smallest posible divisor.
2082 (let ((bound (truncate number-max divisor-min)))
2083 `(integer ,(- bound) ,bound)))
2085 ;; The number we are dividing is unbounded, so we can't tell
2086 ;; anything about the result.
2089 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2090 (defun integer-rem-derive-type
2091 (number-low number-high divisor-low divisor-high)
2092 (if (and divisor-low divisor-high)
2093 ;; We know the range of the divisor, and the remainder must be
2094 ;; smaller than the divisor. We can tell the sign of the
2095 ;; remainer if we know the sign of the number.
2096 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2097 `(integer ,(if (or (null number-low)
2098 (minusp number-low))
2101 ,(if (or (null number-high)
2102 (plusp number-high))
2105 ;; The divisor is potentially either very positive or very
2106 ;; negative. Therefore, the remainer is unbounded, but we might
2107 ;; be able to tell something about the sign from the number.
2108 `(integer ,(if (and number-low (not (minusp number-low)))
2109 ;; The number we are dividing is positive.
2110 ;; Therefore, the remainder must be positive.
2113 ,(if (and number-high (not (plusp number-high)))
2114 ;; The number we are dividing is negative.
2115 ;; Therefore, the remainder must be negative.
2119 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2120 (defoptimizer (random derive-type) ((bound &optional state))
2121 (let ((type (lvar-type bound)))
2122 (when (numeric-type-p type)
2123 (let ((class (numeric-type-class type))
2124 (high (numeric-type-high type))
2125 (format (numeric-type-format type)))
2129 :low (coerce 0 (or format class 'real))
2130 :high (cond ((not high) nil)
2131 ((eq class 'integer) (max (1- high) 0))
2132 ((or (consp high) (zerop high)) high)
2135 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2136 (defun random-derive-type-aux (type)
2137 (let ((class (numeric-type-class type))
2138 (high (numeric-type-high type))
2139 (format (numeric-type-format type)))
2143 :low (coerce 0 (or format class 'real))
2144 :high (cond ((not high) nil)
2145 ((eq class 'integer) (max (1- high) 0))
2146 ((or (consp high) (zerop high)) high)
2149 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2150 (defoptimizer (random derive-type) ((bound &optional state))
2151 (one-arg-derive-type bound #'random-derive-type-aux nil))
2153 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2155 ;;; Return the maximum number of bits an integer of the supplied type
2156 ;;; can take up, or NIL if it is unbounded. The second (third) value
2157 ;;; is T if the integer can be positive (negative) and NIL if not.
2158 ;;; Zero counts as positive.
2159 (defun integer-type-length (type)
2160 (if (numeric-type-p type)
2161 (let ((min (numeric-type-low type))
2162 (max (numeric-type-high type)))
2163 (values (and min max (max (integer-length min) (integer-length max)))
2164 (or (null max) (not (minusp max)))
2165 (or (null min) (minusp min))))
2168 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2169 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2170 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2171 ;;; versions in CMUCL, from which these functions copy liberally.
2173 (defun logand-derive-unsigned-low-bound (x y)
2174 (let ((a (numeric-type-low x))
2175 (b (numeric-type-high x))
2176 (c (numeric-type-low y))
2177 (d (numeric-type-high y)))
2178 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2180 (unless (zerop (logand m (lognot a) (lognot c)))
2181 (let ((temp (logandc2 (logior a m) (1- m))))
2185 (setf temp (logandc2 (logior c m) (1- m)))
2189 finally (return (logand a c)))))
2191 (defun logand-derive-unsigned-high-bound (x y)
2192 (let ((a (numeric-type-low x))
2193 (b (numeric-type-high x))
2194 (c (numeric-type-low y))
2195 (d (numeric-type-high y)))
2196 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2199 ((not (zerop (logand b (lognot d) m)))
2200 (let ((temp (logior (logandc2 b m) (1- m))))
2204 ((not (zerop (logand (lognot b) d m)))
2205 (let ((temp (logior (logandc2 d m) (1- m))))
2209 finally (return (logand b d)))))
2211 (defun logand-derive-type-aux (x y &optional same-leaf)
2213 (return-from logand-derive-type-aux x))
2214 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2215 (declare (ignore x-pos))
2216 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2217 (declare (ignore y-pos))
2219 ;; X must be positive.
2221 ;; They must both be positive.
2222 (cond ((and (null x-len) (null y-len))
2223 (specifier-type 'unsigned-byte))
2225 (specifier-type `(unsigned-byte* ,y-len)))
2227 (specifier-type `(unsigned-byte* ,x-len)))
2229 (let ((low (logand-derive-unsigned-low-bound x y))
2230 (high (logand-derive-unsigned-high-bound x y)))
2231 (specifier-type `(integer ,low ,high)))))
2232 ;; X is positive, but Y might be negative.
2234 (specifier-type 'unsigned-byte))
2236 (specifier-type `(unsigned-byte* ,x-len)))))
2237 ;; X might be negative.
2239 ;; Y must be positive.
2241 (specifier-type 'unsigned-byte))
2242 (t (specifier-type `(unsigned-byte* ,y-len))))
2243 ;; Either might be negative.
2244 (if (and x-len y-len)
2245 ;; The result is bounded.
2246 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2247 ;; We can't tell squat about the result.
2248 (specifier-type 'integer)))))))
2250 (defun logior-derive-unsigned-low-bound (x y)
2251 (let ((a (numeric-type-low x))
2252 (b (numeric-type-high x))
2253 (c (numeric-type-low y))
2254 (d (numeric-type-high y)))
2255 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2258 ((not (zerop (logandc2 (logand c m) a)))
2259 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2263 ((not (zerop (logandc2 (logand a m) c)))
2264 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2268 finally (return (logior a c)))))
2270 (defun logior-derive-unsigned-high-bound (x y)
2271 (let ((a (numeric-type-low x))
2272 (b (numeric-type-high x))
2273 (c (numeric-type-low y))
2274 (d (numeric-type-high y)))
2275 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2277 (unless (zerop (logand b d m))
2278 (let ((temp (logior (- b m) (1- m))))
2282 (setf temp (logior (- d m) (1- m)))
2286 finally (return (logior b d)))))
2288 (defun logior-derive-type-aux (x y &optional same-leaf)
2290 (return-from logior-derive-type-aux x))
2291 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2292 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2294 ((and (not x-neg) (not y-neg))
2295 ;; Both are positive.
2296 (if (and x-len y-len)
2297 (let ((low (logior-derive-unsigned-low-bound x y))
2298 (high (logior-derive-unsigned-high-bound x y)))
2299 (specifier-type `(integer ,low ,high)))
2300 (specifier-type `(unsigned-byte* *))))
2302 ;; X must be negative.
2304 ;; Both are negative. The result is going to be negative
2305 ;; and be the same length or shorter than the smaller.
2306 (if (and x-len y-len)
2308 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2310 (specifier-type '(integer * -1)))
2311 ;; X is negative, but we don't know about Y. The result
2312 ;; will be negative, but no more negative than X.
2314 `(integer ,(or (numeric-type-low x) '*)
2317 ;; X might be either positive or negative.
2319 ;; But Y is negative. The result will be negative.
2321 `(integer ,(or (numeric-type-low y) '*)
2323 ;; We don't know squat about either. It won't get any bigger.
2324 (if (and x-len y-len)
2326 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2328 (specifier-type 'integer))))))))
2330 (defun logxor-derive-unsigned-low-bound (x y)
2331 (let ((a (numeric-type-low x))
2332 (b (numeric-type-high x))
2333 (c (numeric-type-low y))
2334 (d (numeric-type-high y)))
2335 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2338 ((not (zerop (logandc2 (logand c m) a)))
2339 (let ((temp (logand (logior a m)
2343 ((not (zerop (logandc2 (logand a m) c)))
2344 (let ((temp (logand (logior c m)
2348 finally (return (logxor a c)))))
2350 (defun logxor-derive-unsigned-high-bound (x y)
2351 (let ((a (numeric-type-low x))
2352 (b (numeric-type-high x))
2353 (c (numeric-type-low y))
2354 (d (numeric-type-high y)))
2355 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2357 (unless (zerop (logand b d m))
2358 (let ((temp (logior (- b m) (1- m))))
2360 ((>= temp a) (setf b temp))
2361 (t (let ((temp (logior (- d m) (1- m))))
2364 finally (return (logxor b d)))))
2366 (defun logxor-derive-type-aux (x y &optional same-leaf)
2368 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2369 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2370 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2372 ((and (not x-neg) (not y-neg))
2373 ;; Both are positive
2374 (if (and x-len y-len)
2375 (let ((low (logxor-derive-unsigned-low-bound x y))
2376 (high (logxor-derive-unsigned-high-bound x y)))
2377 (specifier-type `(integer ,low ,high)))
2378 (specifier-type '(unsigned-byte* *))))
2379 ((and (not x-pos) (not y-pos))
2380 ;; Both are negative. The result will be positive, and as long
2382 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2385 ((or (and (not x-pos) (not y-neg))
2386 (and (not y-pos) (not x-neg)))
2387 ;; Either X is negative and Y is positive or vice-versa. The
2388 ;; result will be negative.
2389 (specifier-type `(integer ,(if (and x-len y-len)
2390 (ash -1 (max x-len y-len))
2393 ;; We can't tell what the sign of the result is going to be.
2394 ;; All we know is that we don't create new bits.
2396 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2398 (specifier-type 'integer))))))
2400 (macrolet ((deffrob (logfun)
2401 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2402 `(defoptimizer (,logfun derive-type) ((x y))
2403 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2408 (defoptimizer (logeqv derive-type) ((x y))
2409 (two-arg-derive-type x y (lambda (x y same-leaf)
2410 (lognot-derive-type-aux
2411 (logxor-derive-type-aux x y same-leaf)))
2413 (defoptimizer (lognand derive-type) ((x y))
2414 (two-arg-derive-type x y (lambda (x y same-leaf)
2415 (lognot-derive-type-aux
2416 (logand-derive-type-aux x y same-leaf)))
2418 (defoptimizer (lognor derive-type) ((x y))
2419 (two-arg-derive-type x y (lambda (x y same-leaf)
2420 (lognot-derive-type-aux
2421 (logior-derive-type-aux x y same-leaf)))
2423 (defoptimizer (logandc1 derive-type) ((x y))
2424 (two-arg-derive-type x y (lambda (x y same-leaf)
2426 (specifier-type '(eql 0))
2427 (logand-derive-type-aux
2428 (lognot-derive-type-aux x) y nil)))
2430 (defoptimizer (logandc2 derive-type) ((x y))
2431 (two-arg-derive-type x y (lambda (x y same-leaf)
2433 (specifier-type '(eql 0))
2434 (logand-derive-type-aux
2435 x (lognot-derive-type-aux y) nil)))
2437 (defoptimizer (logorc1 derive-type) ((x y))
2438 (two-arg-derive-type x y (lambda (x y same-leaf)
2440 (specifier-type '(eql -1))
2441 (logior-derive-type-aux
2442 (lognot-derive-type-aux x) y nil)))
2444 (defoptimizer (logorc2 derive-type) ((x y))
2445 (two-arg-derive-type x y (lambda (x y same-leaf)
2447 (specifier-type '(eql -1))
2448 (logior-derive-type-aux
2449 x (lognot-derive-type-aux y) nil)))
2452 ;;;; miscellaneous derive-type methods
2454 (defoptimizer (integer-length derive-type) ((x))
2455 (let ((x-type (lvar-type x)))
2456 (when (numeric-type-p x-type)
2457 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2458 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2459 ;; careful about LO or HI being NIL, though. Also, if 0 is
2460 ;; contained in X, the lower bound is obviously 0.
2461 (flet ((null-or-min (a b)
2462 (and a b (min (integer-length a)
2463 (integer-length b))))
2465 (and a b (max (integer-length a)
2466 (integer-length b)))))
2467 (let* ((min (numeric-type-low x-type))
2468 (max (numeric-type-high x-type))
2469 (min-len (null-or-min min max))
2470 (max-len (null-or-max min max)))
2471 (when (ctypep 0 x-type)
2473 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2475 (defoptimizer (isqrt derive-type) ((x))
2476 (let ((x-type (lvar-type x)))
2477 (when (numeric-type-p x-type)
2478 (let* ((lo (numeric-type-low x-type))
2479 (hi (numeric-type-high x-type))
2480 (lo-res (if lo (isqrt lo) '*))
2481 (hi-res (if hi (isqrt hi) '*)))
2482 (specifier-type `(integer ,lo-res ,hi-res))))))
2484 (defoptimizer (code-char derive-type) ((code))
2485 (let ((type (lvar-type code)))
2486 ;; FIXME: unions of integral ranges? It ought to be easier to do
2487 ;; this, given that CHARACTER-SET is basically an integral range
2488 ;; type. -- CSR, 2004-10-04
2489 (when (numeric-type-p type)
2490 (let* ((lo (numeric-type-low type))
2491 (hi (numeric-type-high type))
2492 (type (specifier-type `(character-set ((,lo . ,hi))))))
2494 ;; KLUDGE: when running on the host, we lose a slight amount
2495 ;; of precision so that we don't have to "unparse" types
2496 ;; that formally we can't, such as (CHARACTER-SET ((0
2497 ;; . 0))). -- CSR, 2004-10-06
2499 ((csubtypep type (specifier-type 'standard-char)) type)
2501 ((csubtypep type (specifier-type 'base-char))
2502 (specifier-type 'base-char))
2504 ((csubtypep type (specifier-type 'extended-char))
2505 (specifier-type 'extended-char))
2506 (t #+sb-xc-host (specifier-type 'character)
2507 #-sb-xc-host type))))))
2509 (defoptimizer (values derive-type) ((&rest values))
2510 (make-values-type :required (mapcar #'lvar-type values)))
2512 (defun signum-derive-type-aux (type)
2513 (if (eq (numeric-type-complexp type) :complex)
2514 (let* ((format (case (numeric-type-class type)
2515 ((integer rational) 'single-float)
2516 (t (numeric-type-format type))))
2517 (bound-format (or format 'float)))
2518 (make-numeric-type :class 'float
2521 :low (coerce -1 bound-format)
2522 :high (coerce 1 bound-format)))
2523 (let* ((interval (numeric-type->interval type))
2524 (range-info (interval-range-info interval))
2525 (contains-0-p (interval-contains-p 0 interval))
2526 (class (numeric-type-class type))
2527 (format (numeric-type-format type))
2528 (one (coerce 1 (or format class 'real)))
2529 (zero (coerce 0 (or format class 'real)))
2530 (minus-one (coerce -1 (or format class 'real)))
2531 (plus (make-numeric-type :class class :format format
2532 :low one :high one))
2533 (minus (make-numeric-type :class class :format format
2534 :low minus-one :high minus-one))
2535 ;; KLUDGE: here we have a fairly horrible hack to deal
2536 ;; with the schizophrenia in the type derivation engine.
2537 ;; The problem is that the type derivers reinterpret
2538 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2539 ;; 0d0) within the derivation mechanism doesn't include
2540 ;; -0d0. Ugh. So force it in here, instead.
2541 (zero (make-numeric-type :class class :format format
2542 :low (- zero) :high zero)))
2544 (+ (if contains-0-p (type-union plus zero) plus))
2545 (- (if contains-0-p (type-union minus zero) minus))
2546 (t (type-union minus zero plus))))))
2548 (defoptimizer (signum derive-type) ((num))
2549 (one-arg-derive-type num #'signum-derive-type-aux nil))
2551 ;;;; byte operations
2553 ;;;; We try to turn byte operations into simple logical operations.
2554 ;;;; First, we convert byte specifiers into separate size and position
2555 ;;;; arguments passed to internal %FOO functions. We then attempt to
2556 ;;;; transform the %FOO functions into boolean operations when the
2557 ;;;; size and position are constant and the operands are fixnums.
2559 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2560 ;; expressions that evaluate to the SIZE and POSITION of
2561 ;; the byte-specifier form SPEC. We may wrap a let around
2562 ;; the result of the body to bind some variables.
2564 ;; If the spec is a BYTE form, then bind the vars to the
2565 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2566 ;; and BYTE-POSITION. The goal of this transformation is to
2567 ;; avoid consing up byte specifiers and then immediately
2568 ;; throwing them away.
2569 (with-byte-specifier ((size-var pos-var spec) &body body)
2570 (once-only ((spec `(macroexpand ,spec))
2572 `(if (and (consp ,spec)
2573 (eq (car ,spec) 'byte)
2574 (= (length ,spec) 3))
2575 (let ((,size-var (second ,spec))
2576 (,pos-var (third ,spec)))
2578 (let ((,size-var `(byte-size ,,temp))
2579 (,pos-var `(byte-position ,,temp)))
2580 `(let ((,,temp ,,spec))
2583 (define-source-transform ldb (spec int)
2584 (with-byte-specifier (size pos spec)
2585 `(%ldb ,size ,pos ,int)))
2587 (define-source-transform dpb (newbyte spec int)
2588 (with-byte-specifier (size pos spec)
2589 `(%dpb ,newbyte ,size ,pos ,int)))
2591 (define-source-transform mask-field (spec int)
2592 (with-byte-specifier (size pos spec)
2593 `(%mask-field ,size ,pos ,int)))
2595 (define-source-transform deposit-field (newbyte spec int)
2596 (with-byte-specifier (size pos spec)
2597 `(%deposit-field ,newbyte ,size ,pos ,int))))
2599 (defoptimizer (%ldb derive-type) ((size posn num))
2600 (let ((size (lvar-type size)))
2601 (if (and (numeric-type-p size)
2602 (csubtypep size (specifier-type 'integer)))
2603 (let ((size-high (numeric-type-high size)))
2604 (if (and size-high (<= size-high sb!vm:n-word-bits))
2605 (specifier-type `(unsigned-byte* ,size-high))
2606 (specifier-type 'unsigned-byte)))
2609 (defoptimizer (%mask-field derive-type) ((size posn num))
2610 (let ((size (lvar-type size))
2611 (posn (lvar-type posn)))
2612 (if (and (numeric-type-p size)
2613 (csubtypep size (specifier-type 'integer))
2614 (numeric-type-p posn)
2615 (csubtypep posn (specifier-type 'integer)))
2616 (let ((size-high (numeric-type-high size))
2617 (posn-high (numeric-type-high posn)))
2618 (if (and size-high posn-high
2619 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2620 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2621 (specifier-type 'unsigned-byte)))
2624 (defun %deposit-field-derive-type-aux (size posn int)
2625 (let ((size (lvar-type size))
2626 (posn (lvar-type posn))
2627 (int (lvar-type int)))
2628 (when (and (numeric-type-p size)
2629 (numeric-type-p posn)
2630 (numeric-type-p int))
2631 (let ((size-high (numeric-type-high size))
2632 (posn-high (numeric-type-high posn))
2633 (high (numeric-type-high int))
2634 (low (numeric-type-low int)))
2635 (when (and size-high posn-high high low
2636 ;; KLUDGE: we need this cutoff here, otherwise we
2637 ;; will merrily derive the type of %DPB as
2638 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2639 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2640 ;; 1073741822))), with hilarious consequences. We
2641 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2642 ;; over a reasonable amount of shifting, even on
2643 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2644 ;; machine integers are 64-bits. -- CSR,
2646 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2647 (let ((raw-bit-count (max (integer-length high)
2648 (integer-length low)
2649 (+ size-high posn-high))))
2652 `(signed-byte ,(1+ raw-bit-count))
2653 `(unsigned-byte* ,raw-bit-count)))))))))
2655 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2656 (%deposit-field-derive-type-aux size posn int))
2658 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2659 (%deposit-field-derive-type-aux size posn int))
2661 (deftransform %ldb ((size posn int)
2662 (fixnum fixnum integer)
2663 (unsigned-byte #.sb!vm:n-word-bits))
2664 "convert to inline logical operations"
2665 `(logand (ash int (- posn))
2666 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2667 (- size ,sb!vm:n-word-bits))))
2669 (deftransform %mask-field ((size posn int)
2670 (fixnum fixnum integer)
2671 (unsigned-byte #.sb!vm:n-word-bits))
2672 "convert to inline logical operations"
2674 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2675 (- size ,sb!vm:n-word-bits))
2678 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2679 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2680 ;;; as the result type, as that would allow result types that cover
2681 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2682 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2684 (deftransform %dpb ((new size posn int)
2686 (unsigned-byte #.sb!vm:n-word-bits))
2687 "convert to inline logical operations"
2688 `(let ((mask (ldb (byte size 0) -1)))
2689 (logior (ash (logand new mask) posn)
2690 (logand int (lognot (ash mask posn))))))
2692 (deftransform %dpb ((new size posn int)
2694 (signed-byte #.sb!vm:n-word-bits))
2695 "convert to inline logical operations"
2696 `(let ((mask (ldb (byte size 0) -1)))
2697 (logior (ash (logand new mask) posn)
2698 (logand int (lognot (ash mask posn))))))
2700 (deftransform %deposit-field ((new size posn int)
2702 (unsigned-byte #.sb!vm:n-word-bits))
2703 "convert to inline logical operations"
2704 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2705 (logior (logand new mask)
2706 (logand int (lognot mask)))))
2708 (deftransform %deposit-field ((new size posn int)
2710 (signed-byte #.sb!vm:n-word-bits))
2711 "convert to inline logical operations"
2712 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2713 (logior (logand new mask)
2714 (logand int (lognot mask)))))
2716 (defoptimizer (mask-signed-field derive-type) ((size x))
2717 (let ((size (lvar-type size)))
2718 (if (numeric-type-p size)
2719 (let ((size-high (numeric-type-high size)))
2720 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2721 (specifier-type `(signed-byte ,size-high))
2726 ;;; Modular functions
2728 ;;; (ldb (byte s 0) (foo x y ...)) =
2729 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2731 ;;; and similar for other arguments.
2733 (defun make-modular-fun-type-deriver (prototype class width)
2735 (binding* ((info (info :function :info prototype) :exit-if-null)
2736 (fun (fun-info-derive-type info) :exit-if-null)
2737 (mask-type (specifier-type
2739 (:unsigned (let ((mask (1- (ash 1 width))))
2740 `(integer ,mask ,mask)))
2741 (:signed `(signed-byte ,width))))))
2743 (let ((res (funcall fun call)))
2745 (if (eq class :unsigned)
2746 (logand-derive-type-aux res mask-type))))))
2749 (binding* ((info (info :function :info prototype) :exit-if-null)
2750 (fun (fun-info-derive-type info) :exit-if-null)
2751 (res (funcall fun call) :exit-if-null)
2752 (mask-type (specifier-type
2754 (:unsigned (let ((mask (1- (ash 1 width))))
2755 `(integer ,mask ,mask)))
2756 (:signed `(signed-byte ,width))))))
2757 (if (eq class :unsigned)
2758 (logand-derive-type-aux res mask-type)))))
2760 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2762 ;;; For good functions, we just recursively cut arguments; their
2763 ;;; "goodness" means that the result will not increase (in the
2764 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2765 ;;; replaced with the version, cutting its result to WIDTH or more
2766 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2767 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2768 ;;; arguments (maybe to a different width) and returning the name of a
2769 ;;; modular version, if it exists, or NIL. If we have changed
2770 ;;; anything, we need to flush old derived types, because they have
2771 ;;; nothing in common with the new code.
2772 (defun cut-to-width (lvar class width)
2773 (declare (type lvar lvar) (type (integer 0) width))
2774 (let ((type (specifier-type (if (zerop width)
2776 `(,(ecase class (:unsigned 'unsigned-byte)
2777 (:signed 'signed-byte))
2779 (labels ((reoptimize-node (node name)
2780 (setf (node-derived-type node)
2782 (info :function :type name)))
2783 (setf (lvar-%derived-type (node-lvar node)) nil)
2784 (setf (node-reoptimize node) t)
2785 (setf (block-reoptimize (node-block node)) t)
2786 (reoptimize-component (node-component node) :maybe))
2787 (cut-node (node &aux did-something)
2788 (when (and (not (block-delete-p (node-block node)))
2789 (combination-p node)
2790 (eq (basic-combination-kind node) :known))
2791 (let* ((fun-ref (lvar-use (combination-fun node)))
2792 (fun-name (leaf-source-name (ref-leaf fun-ref)))
2793 (modular-fun (find-modular-version fun-name class width)))
2794 (when (and modular-fun
2795 (not (and (eq fun-name 'logand)
2797 (single-value-type (node-derived-type node))
2799 (binding* ((name (etypecase modular-fun
2800 ((eql :good) fun-name)
2802 (modular-fun-info-name modular-fun))
2804 (funcall modular-fun node width)))
2806 (unless (eql modular-fun :good)
2807 (setq did-something t)
2810 (find-free-fun name "in a strange place"))
2811 (setf (combination-kind node) :full))
2812 (unless (functionp modular-fun)
2813 (dolist (arg (basic-combination-args node))
2814 (when (cut-lvar arg)
2815 (setq did-something t))))
2817 (reoptimize-node node name))
2819 (cut-lvar (lvar &aux did-something)
2820 (do-uses (node lvar)
2821 (when (cut-node node)
2822 (setq did-something t)))
2826 (defoptimizer (logand optimizer) ((x y) node)
2827 (let ((result-type (single-value-type (node-derived-type node))))
2828 (when (numeric-type-p result-type)
2829 (let ((low (numeric-type-low result-type))
2830 (high (numeric-type-high result-type)))
2831 (when (and (numberp low)
2834 (let ((width (integer-length high)))
2835 (when (some (lambda (x) (<= width x))
2836 (modular-class-widths *unsigned-modular-class*))
2837 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2838 (cut-to-width x :unsigned width)
2839 (cut-to-width y :unsigned width)
2840 nil ; After fixing above, replace with T.
2843 (defoptimizer (mask-signed-field optimizer) ((width x) node)
2844 (let ((result-type (single-value-type (node-derived-type node))))
2845 (when (numeric-type-p result-type)
2846 (let ((low (numeric-type-low result-type))
2847 (high (numeric-type-high result-type)))
2848 (when (and (numberp low) (numberp high))
2849 (let ((width (max (integer-length high) (integer-length low))))
2850 (when (some (lambda (x) (<= width x))
2851 (modular-class-widths *signed-modular-class*))
2852 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2853 (cut-to-width x :signed width)
2854 nil ; After fixing above, replace with T.
2857 ;;; miscellanous numeric transforms
2859 ;;; If a constant appears as the first arg, swap the args.
2860 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2861 (if (and (constant-lvar-p x)
2862 (not (constant-lvar-p y)))
2863 `(,(lvar-fun-name (basic-combination-fun node))
2866 (give-up-ir1-transform)))
2868 (dolist (x '(= char= + * logior logand logxor))
2869 (%deftransform x '(function * *) #'commutative-arg-swap
2870 "place constant arg last"))
2872 ;;; Handle the case of a constant BOOLE-CODE.
2873 (deftransform boole ((op x y) * *)
2874 "convert to inline logical operations"
2875 (unless (constant-lvar-p op)
2876 (give-up-ir1-transform "BOOLE code is not a constant."))
2877 (let ((control (lvar-value op)))
2879 (#.sb!xc:boole-clr 0)
2880 (#.sb!xc:boole-set -1)
2881 (#.sb!xc:boole-1 'x)
2882 (#.sb!xc:boole-2 'y)
2883 (#.sb!xc:boole-c1 '(lognot x))
2884 (#.sb!xc:boole-c2 '(lognot y))
2885 (#.sb!xc:boole-and '(logand x y))
2886 (#.sb!xc:boole-ior '(logior x y))
2887 (#.sb!xc:boole-xor '(logxor x y))
2888 (#.sb!xc:boole-eqv '(logeqv x y))
2889 (#.sb!xc:boole-nand '(lognand x y))
2890 (#.sb!xc:boole-nor '(lognor x y))
2891 (#.sb!xc:boole-andc1 '(logandc1 x y))
2892 (#.sb!xc:boole-andc2 '(logandc2 x y))
2893 (#.sb!xc:boole-orc1 '(logorc1 x y))
2894 (#.sb!xc:boole-orc2 '(logorc2 x y))
2896 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2899 ;;;; converting special case multiply/divide to shifts
2901 ;;; If arg is a constant power of two, turn * into a shift.
2902 (deftransform * ((x y) (integer integer) *)
2903 "convert x*2^k to shift"
2904 (unless (constant-lvar-p y)
2905 (give-up-ir1-transform))
2906 (let* ((y (lvar-value y))
2908 (len (1- (integer-length y-abs))))
2909 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2910 (give-up-ir1-transform))
2915 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2916 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
2918 (flet ((frob (y ceil-p)
2919 (unless (constant-lvar-p y)
2920 (give-up-ir1-transform))
2921 (let* ((y (lvar-value y))
2923 (len (1- (integer-length y-abs))))
2924 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2925 (give-up-ir1-transform))
2926 (let ((shift (- len))
2928 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
2929 `(let ((x (+ x ,delta)))
2931 `(values (ash (- x) ,shift)
2932 (- (- (logand (- x) ,mask)) ,delta))
2933 `(values (ash x ,shift)
2934 (- (logand x ,mask) ,delta))))))))
2935 (deftransform floor ((x y) (integer integer) *)
2936 "convert division by 2^k to shift"
2938 (deftransform ceiling ((x y) (integer integer) *)
2939 "convert division by 2^k to shift"
2942 ;;; Do the same for MOD.
2943 (deftransform mod ((x y) (integer integer) *)
2944 "convert remainder mod 2^k to LOGAND"
2945 (unless (constant-lvar-p y)
2946 (give-up-ir1-transform))
2947 (let* ((y (lvar-value y))
2949 (len (1- (integer-length y-abs))))
2950 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2951 (give-up-ir1-transform))
2952 (let ((mask (1- y-abs)))
2954 `(- (logand (- x) ,mask))
2955 `(logand x ,mask)))))
2957 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2958 (deftransform truncate ((x y) (integer integer))
2959 "convert division by 2^k to shift"
2960 (unless (constant-lvar-p y)
2961 (give-up-ir1-transform))
2962 (let* ((y (lvar-value y))
2964 (len (1- (integer-length y-abs))))
2965 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2966 (give-up-ir1-transform))
2967 (let* ((shift (- len))
2970 (values ,(if (minusp y)
2972 `(- (ash (- x) ,shift)))
2973 (- (logand (- x) ,mask)))
2974 (values ,(if (minusp y)
2975 `(ash (- ,mask x) ,shift)
2977 (logand x ,mask))))))
2979 ;;; And the same for REM.
2980 (deftransform rem ((x y) (integer integer) *)
2981 "convert remainder mod 2^k to LOGAND"
2982 (unless (constant-lvar-p y)
2983 (give-up-ir1-transform))
2984 (let* ((y (lvar-value y))
2986 (len (1- (integer-length y-abs))))
2987 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
2988 (give-up-ir1-transform))
2989 (let ((mask (1- y-abs)))
2991 (- (logand (- x) ,mask))
2992 (logand x ,mask)))))
2994 ;;;; arithmetic and logical identity operation elimination
2996 ;;; Flush calls to various arith functions that convert to the
2997 ;;; identity function or a constant.
2998 (macrolet ((def (name identity result)
2999 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3000 "fold identity operations"
3007 (def logxor -1 (lognot x))
3010 (deftransform logand ((x y) (* (constant-arg t)) *)
3011 "fold identity operation"
3012 (let ((y (lvar-value y)))
3013 (unless (and (plusp y)
3014 (= y (1- (ash 1 (integer-length y)))))
3015 (give-up-ir1-transform))
3016 (unless (csubtypep (lvar-type x)
3017 (specifier-type `(integer 0 ,y)))
3018 (give-up-ir1-transform))
3021 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3022 "fold identity operation"
3023 (let ((size (lvar-value size)))
3024 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3025 (give-up-ir1-transform))
3028 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3029 ;;; (* 0 -4.0) is -0.0.
3030 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3031 "convert (- 0 x) to negate"
3033 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3034 "convert (* x 0) to 0"
3037 ;;; Return T if in an arithmetic op including lvars X and Y, the
3038 ;;; result type is not affected by the type of X. That is, Y is at
3039 ;;; least as contagious as X.
3041 (defun not-more-contagious (x y)
3042 (declare (type continuation x y))
3043 (let ((x (lvar-type x))
3045 (values (type= (numeric-contagion x y)
3046 (numeric-contagion y y)))))
3047 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3048 ;;; XXX needs more work as valid transforms are missed; some cases are
3049 ;;; specific to particular transform functions so the use of this
3050 ;;; function may need a re-think.
3051 (defun not-more-contagious (x y)
3052 (declare (type lvar x y))
3053 (flet ((simple-numeric-type (num)
3054 (and (numeric-type-p num)
3055 ;; Return non-NIL if NUM is integer, rational, or a float
3056 ;; of some type (but not FLOAT)
3057 (case (numeric-type-class num)
3061 (numeric-type-format num))
3064 (let ((x (lvar-type x))
3066 (if (and (simple-numeric-type x)
3067 (simple-numeric-type y))
3068 (values (type= (numeric-contagion x y)
3069 (numeric-contagion y y)))))))
3073 ;;; If y is not constant, not zerop, or is contagious, or a positive
3074 ;;; float +0.0 then give up.
3075 (deftransform + ((x y) (t (constant-arg t)) *)
3077 (let ((val (lvar-value y)))
3078 (unless (and (zerop val)
3079 (not (and (floatp val) (plusp (float-sign val))))
3080 (not-more-contagious y x))
3081 (give-up-ir1-transform)))
3086 ;;; If y is not constant, not zerop, or is contagious, or a negative
3087 ;;; float -0.0 then give up.
3088 (deftransform - ((x y) (t (constant-arg t)) *)
3090 (let ((val (lvar-value y)))
3091 (unless (and (zerop val)
3092 (not (and (floatp val) (minusp (float-sign val))))
3093 (not-more-contagious y x))
3094 (give-up-ir1-transform)))
3097 ;;; Fold (OP x +/-1)
3098 (macrolet ((def (name result minus-result)
3099 `(deftransform ,name ((x y) (t (constant-arg real)) *)
3100 "fold identity operations"
3101 (let ((val (lvar-value y)))
3102 (unless (and (= (abs val) 1)
3103 (not-more-contagious y x))
3104 (give-up-ir1-transform))
3105 (if (minusp val) ',minus-result ',result)))))
3106 (def * x (%negate x))
3107 (def / x (%negate x))
3108 (def expt x (/ 1 x)))
3110 ;;; Fold (expt x n) into multiplications for small integral values of
3111 ;;; N; convert (expt x 1/2) to sqrt.
3112 (deftransform expt ((x y) (t (constant-arg real)) *)
3113 "recode as multiplication or sqrt"
3114 (let ((val (lvar-value y)))
3115 ;; If Y would cause the result to be promoted to the same type as
3116 ;; Y, we give up. If not, then the result will be the same type
3117 ;; as X, so we can replace the exponentiation with simple
3118 ;; multiplication and division for small integral powers.
3119 (unless (not-more-contagious y x)
3120 (give-up-ir1-transform))
3122 (let ((x-type (lvar-type x)))
3123 (cond ((csubtypep x-type (specifier-type '(or rational
3124 (complex rational))))
3126 ((csubtypep x-type (specifier-type 'real))
3130 ((csubtypep x-type (specifier-type 'complex))
3131 ;; both parts are float
3133 (t (give-up-ir1-transform)))))
3134 ((= val 2) '(* x x))
3135 ((= val -2) '(/ (* x x)))
3136 ((= val 3) '(* x x x))
3137 ((= val -3) '(/ (* x x x)))
3138 ((= val 1/2) '(sqrt x))
3139 ((= val -1/2) '(/ (sqrt x)))
3140 (t (give-up-ir1-transform)))))
3142 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3143 ;;; transformations?
3144 ;;; Perhaps we should have to prove that the denominator is nonzero before
3145 ;;; doing them? -- WHN 19990917
3146 (macrolet ((def (name)
3147 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3154 (macrolet ((def (name)
3155 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3164 ;;;; character operations
3166 (deftransform char-equal ((a b) (base-char base-char))
3168 '(let* ((ac (char-code a))
3170 (sum (logxor ac bc)))
3172 (when (eql sum #x20)
3173 (let ((sum (+ ac bc)))
3174 (or (and (> sum 161) (< sum 213))
3175 (and (> sum 415) (< sum 461))
3176 (and (> sum 463) (< sum 477))))))))
3178 (deftransform char-upcase ((x) (base-char))
3180 '(let ((n-code (char-code x)))
3181 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3182 (< n-code #o173)) ; Octal 172 is #\z.
3183 (and (> n-code #o337)
3185 (and (> n-code #o367)
3187 (code-char (logxor #x20 n-code))
3190 (deftransform char-downcase ((x) (base-char))
3192 '(let ((n-code (char-code x)))
3193 (if (or (and (> n-code 64) ; 65 is #\A.
3194 (< n-code 91)) ; 90 is #\Z.
3199 (code-char (logxor #x20 n-code))
3202 ;;;; equality predicate transforms
3204 ;;; Return true if X and Y are lvars whose only use is a
3205 ;;; reference to the same leaf, and the value of the leaf cannot
3207 (defun same-leaf-ref-p (x y)
3208 (declare (type lvar x y))
3209 (let ((x-use (principal-lvar-use x))
3210 (y-use (principal-lvar-use y)))
3213 (eq (ref-leaf x-use) (ref-leaf y-use))
3214 (constant-reference-p x-use))))
3216 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3217 ;;; if there is no intersection between the types of the arguments,
3218 ;;; then the result is definitely false.
3219 (deftransform simple-equality-transform ((x y) * *
3222 ((same-leaf-ref-p x y) t)
3223 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3225 (t (give-up-ir1-transform))))
3228 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3232 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3233 ;;; try to convert to a type-specific predicate or EQ:
3234 ;;; -- If both args are characters, convert to CHAR=. This is better than
3235 ;;; just converting to EQ, since CHAR= may have special compilation
3236 ;;; strategies for non-standard representations, etc.
3237 ;;; -- If either arg is definitely a fixnum we punt and let the backend
3239 ;;; -- If either arg is definitely not a number or a fixnum, then we
3240 ;;; can compare with EQ.
3241 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3242 ;;; is constant then we put it second. If X is a subtype of Y, we put
3243 ;;; it second. These rules make it easier for the back end to match
3244 ;;; these interesting cases.
3245 (deftransform eql ((x y) * *)
3246 "convert to simpler equality predicate"
3247 (let ((x-type (lvar-type x))
3248 (y-type (lvar-type y))
3249 (char-type (specifier-type 'character)))
3250 (flet ((simple-type-p (type)
3251 (csubtypep type (specifier-type '(or fixnum (not number)))))
3252 (fixnum-type-p (type)
3253 (csubtypep type (specifier-type 'fixnum))))
3255 ((same-leaf-ref-p x y) t)
3256 ((not (types-equal-or-intersect x-type y-type))
3258 ((and (csubtypep x-type char-type)
3259 (csubtypep y-type char-type))
3261 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3262 (give-up-ir1-transform))
3263 ((or (simple-type-p x-type) (simple-type-p y-type))
3265 ((and (not (constant-lvar-p y))
3266 (or (constant-lvar-p x)
3267 (and (csubtypep x-type y-type)
3268 (not (csubtypep y-type x-type)))))
3271 (give-up-ir1-transform))))))
3273 ;;; similarly to the EQL transform above, we attempt to constant-fold
3274 ;;; or convert to a simpler predicate: mostly we have to be careful
3275 ;;; with strings and bit-vectors.
3276 (deftransform equal ((x y) * *)
3277 "convert to simpler equality predicate"
3278 (let ((x-type (lvar-type x))
3279 (y-type (lvar-type y))
3280 (string-type (specifier-type 'string))
3281 (bit-vector-type (specifier-type 'bit-vector)))
3283 ((same-leaf-ref-p x y) t)
3284 ((and (csubtypep x-type string-type)
3285 (csubtypep y-type string-type))
3287 ((and (csubtypep x-type bit-vector-type)
3288 (csubtypep y-type bit-vector-type))
3289 '(bit-vector-= x y))
3290 ;; if at least one is not a string, and at least one is not a
3291 ;; bit-vector, then we can reason from types.
3292 ((and (not (and (types-equal-or-intersect x-type string-type)
3293 (types-equal-or-intersect y-type string-type)))
3294 (not (and (types-equal-or-intersect x-type bit-vector-type)
3295 (types-equal-or-intersect y-type bit-vector-type)))
3296 (not (types-equal-or-intersect x-type y-type)))
3298 (t (give-up-ir1-transform)))))
3300 ;;; Convert to EQL if both args are rational and complexp is specified
3301 ;;; and the same for both.
3302 (deftransform = ((x y) * *)
3304 (let ((x-type (lvar-type x))
3305 (y-type (lvar-type y)))
3306 (if (and (csubtypep x-type (specifier-type 'number))
3307 (csubtypep y-type (specifier-type 'number)))
3308 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3309 (csubtypep y-type (specifier-type 'float)))
3310 (and (csubtypep x-type (specifier-type '(complex float)))
3311 (csubtypep y-type (specifier-type '(complex float)))))
3312 ;; They are both floats. Leave as = so that -0.0 is
3313 ;; handled correctly.
3314 (give-up-ir1-transform))
3315 ((or (and (csubtypep x-type (specifier-type 'rational))
3316 (csubtypep y-type (specifier-type 'rational)))
3317 (and (csubtypep x-type
3318 (specifier-type '(complex rational)))
3320 (specifier-type '(complex rational)))))
3321 ;; They are both rationals and complexp is the same.
3325 (give-up-ir1-transform
3326 "The operands might not be the same type.")))
3327 (give-up-ir1-transform
3328 "The operands might not be the same type."))))
3330 ;;; If LVAR's type is a numeric type, then return the type, otherwise
3331 ;;; GIVE-UP-IR1-TRANSFORM.
3332 (defun numeric-type-or-lose (lvar)
3333 (declare (type lvar lvar))
3334 (let ((res (lvar-type lvar)))
3335 (unless (numeric-type-p res) (give-up-ir1-transform))
3338 ;;; See whether we can statically determine (< X Y) using type
3339 ;;; information. If X's high bound is < Y's low, then X < Y.
3340 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3341 ;;; NIL). If not, at least make sure any constant arg is second.
3342 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3343 `(deftransform ,name ((x y))
3344 (if (same-leaf-ref-p x y)
3346 (let ((ix (or (type-approximate-interval (lvar-type x))
3347 (give-up-ir1-transform)))
3348 (iy (or (type-approximate-interval (lvar-type y))
3349 (give-up-ir1-transform))))
3354 ((and (constant-lvar-p x)
3355 (not (constant-lvar-p y)))
3358 (give-up-ir1-transform))))))))
3359 (def < > nil (interval-< ix iy) (interval->= ix iy))
3360 (def > < nil (interval-< iy ix) (interval->= iy ix))
3361 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3362 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3364 (defun ir1-transform-char< (x y first second inverse)
3366 ((same-leaf-ref-p x y) nil)
3367 ;; If we had interval representation of character types, as we
3368 ;; might eventually have to to support 2^21 characters, then here
3369 ;; we could do some compile-time computation as in transforms for
3370 ;; < above. -- CSR, 2003-07-01
3371 ((and (constant-lvar-p first)
3372 (not (constant-lvar-p second)))
3374 (t (give-up-ir1-transform))))
3376 (deftransform char< ((x y) (character character) *)
3377 (ir1-transform-char< x y x y 'char>))
3379 (deftransform char> ((x y) (character character) *)
3380 (ir1-transform-char< y x x y 'char<))
3382 ;;;; converting N-arg comparisons
3384 ;;;; We convert calls to N-arg comparison functions such as < into
3385 ;;;; two-arg calls. This transformation is enabled for all such
3386 ;;;; comparisons in this file. If any of these predicates are not
3387 ;;;; open-coded, then the transformation should be removed at some
3388 ;;;; point to avoid pessimization.
3390 ;;; This function is used for source transformation of N-arg
3391 ;;; comparison functions other than inequality. We deal both with
3392 ;;; converting to two-arg calls and inverting the sense of the test,
3393 ;;; if necessary. If the call has two args, then we pass or return a
3394 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3395 ;;; then we transform to code that returns true. Otherwise, we bind
3396 ;;; all the arguments and expand into a bunch of IFs.
3397 (declaim (ftype (function (symbol list boolean t) *) multi-compare))
3398 (defun multi-compare (predicate args not-p type)
3399 (let ((nargs (length args)))
3400 (cond ((< nargs 1) (values nil t))
3401 ((= nargs 1) `(progn (the ,type ,@args) t))
3404 `(if (,predicate ,(first args) ,(second args)) nil t)
3407 (do* ((i (1- nargs) (1- i))
3409 (current (gensym) (gensym))
3410 (vars (list current) (cons current vars))
3412 `(if (,predicate ,current ,last)
3414 `(if (,predicate ,current ,last)
3417 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3420 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3421 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3422 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3423 (define-source-transform <= (&rest args) (multi-compare '> args t 'real))
3424 (define-source-transform >= (&rest args) (multi-compare '< args t 'real))
3426 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3428 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3430 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3432 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3434 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3437 (define-source-transform char-equal (&rest args)
3438 (multi-compare 'char-equal args nil 'character))
3439 (define-source-transform char-lessp (&rest args)
3440 (multi-compare 'char-lessp args nil 'character))
3441 (define-source-transform char-greaterp (&rest args)
3442 (multi-compare 'char-greaterp args nil 'character))
3443 (define-source-transform char-not-greaterp (&rest args)
3444 (multi-compare 'char-greaterp args t 'character))
3445 (define-source-transform char-not-lessp (&rest args)
3446 (multi-compare 'char-lessp args t 'character))
3448 ;;; This function does source transformation of N-arg inequality
3449 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3450 ;;; arg cases. If there are more than two args, then we expand into
3451 ;;; the appropriate n^2 comparisons only when speed is important.
3452 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3453 (defun multi-not-equal (predicate args type)
3454 (let ((nargs (length args)))
3455 (cond ((< nargs 1) (values nil t))
3456 ((= nargs 1) `(progn (the ,type ,@args) t))
3458 `(if (,predicate ,(first args) ,(second args)) nil t))
3459 ((not (policy *lexenv*
3460 (and (>= speed space)
3461 (>= speed compilation-speed))))
3464 (let ((vars (make-gensym-list nargs)))
3465 (do ((var vars next)
3466 (next (cdr vars) (cdr next))
3469 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3471 (let ((v1 (first var)))
3473 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3475 (define-source-transform /= (&rest args)
3476 (multi-not-equal '= args 'number))
3477 (define-source-transform char/= (&rest args)
3478 (multi-not-equal 'char= args 'character))
3479 (define-source-transform char-not-equal (&rest args)
3480 (multi-not-equal 'char-equal args 'character))
3482 ;;; Expand MAX and MIN into the obvious comparisons.
3483 (define-source-transform max (arg0 &rest rest)
3484 (once-only ((arg0 arg0))
3486 `(values (the real ,arg0))
3487 `(let ((maxrest (max ,@rest)))
3488 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3489 (define-source-transform min (arg0 &rest rest)
3490 (once-only ((arg0 arg0))
3492 `(values (the real ,arg0))
3493 `(let ((minrest (min ,@rest)))
3494 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3496 ;;;; converting N-arg arithmetic functions
3498 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3499 ;;;; versions, and degenerate cases are flushed.
3501 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3502 (declaim (ftype (function (symbol t list) list) associate-args))
3503 (defun associate-args (function first-arg more-args)
3504 (let ((next (rest more-args))
3505 (arg (first more-args)))
3507 `(,function ,first-arg ,arg)
3508 (associate-args function `(,function ,first-arg ,arg) next))))
3510 ;;; Do source transformations for transitive functions such as +.
3511 ;;; One-arg cases are replaced with the arg and zero arg cases with
3512 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3513 ;;; ensure (with THE) that the argument in one-argument calls is.
3514 (defun source-transform-transitive (fun args identity
3515 &optional one-arg-result-type)
3516 (declare (symbol fun) (list args))
3519 (1 (if one-arg-result-type
3520 `(values (the ,one-arg-result-type ,(first args)))
3521 `(values ,(first args))))
3524 (associate-args fun (first args) (rest args)))))
3526 (define-source-transform + (&rest args)
3527 (source-transform-transitive '+ args 0 'number))
3528 (define-source-transform * (&rest args)
3529 (source-transform-transitive '* args 1 'number))
3530 (define-source-transform logior (&rest args)
3531 (source-transform-transitive 'logior args 0 'integer))
3532 (define-source-transform logxor (&rest args)
3533 (source-transform-transitive 'logxor args 0 'integer))
3534 (define-source-transform logand (&rest args)
3535 (source-transform-transitive 'logand args -1 'integer))
3536 (define-source-transform logeqv (&rest args)
3537 (source-transform-transitive 'logeqv args -1 'integer))
3539 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3540 ;;; because when they are given one argument, they return its absolute
3543 (define-source-transform gcd (&rest args)
3546 (1 `(abs (the integer ,(first args))))
3548 (t (associate-args 'gcd (first args) (rest args)))))
3550 (define-source-transform lcm (&rest args)
3553 (1 `(abs (the integer ,(first args))))
3555 (t (associate-args 'lcm (first args) (rest args)))))
3557 ;;; Do source transformations for intransitive n-arg functions such as
3558 ;;; /. With one arg, we form the inverse. With two args we pass.
3559 ;;; Otherwise we associate into two-arg calls.
3560 (declaim (ftype (function (symbol list t)
3561 (values list &optional (member nil t)))
3562 source-transform-intransitive))
3563 (defun source-transform-intransitive (function args inverse)
3565 ((0 2) (values nil t))
3566 (1 `(,@inverse ,(first args)))
3567 (t (associate-args function (first args) (rest args)))))
3569 (define-source-transform - (&rest args)
3570 (source-transform-intransitive '- args '(%negate)))
3571 (define-source-transform / (&rest args)
3572 (source-transform-intransitive '/ args '(/ 1)))
3574 ;;;; transforming APPLY
3576 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3577 ;;; only needs to understand one kind of variable-argument call. It is
3578 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3579 (define-source-transform apply (fun arg &rest more-args)
3580 (let ((args (cons arg more-args)))
3581 `(multiple-value-call ,fun
3582 ,@(mapcar (lambda (x)
3585 (values-list ,(car (last args))))))
3587 ;;;; transforming FORMAT
3589 ;;;; If the control string is a compile-time constant, then replace it
3590 ;;;; with a use of the FORMATTER macro so that the control string is
3591 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3592 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3593 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3595 ;;; for compile-time argument count checking.
3597 ;;; FIXME II: In some cases, type information could be correlated; for
3598 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3599 ;;; of a corresponding argument is known and does not intersect the
3600 ;;; list type, a warning could be signalled.
3601 (defun check-format-args (string args fun)
3602 (declare (type string string))
3603 (unless (typep string 'simple-string)
3604 (setq string (coerce string 'simple-string)))
3605 (multiple-value-bind (min max)
3606 (handler-case (sb!format:%compiler-walk-format-string string args)
3607 (sb!format:format-error (c)
3608 (compiler-warn "~A" c)))
3610 (let ((nargs (length args)))
3613 (warn 'format-too-few-args-warning
3615 "Too few arguments (~D) to ~S ~S: requires at least ~D."
3616 :format-arguments (list nargs fun string min)))
3618 (warn 'format-too-many-args-warning
3620 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3621 :format-arguments (list nargs fun string max))))))))
3623 (defoptimizer (format optimizer) ((dest control &rest args))
3624 (when (constant-lvar-p control)
3625 (let ((x (lvar-value control)))
3627 (check-format-args x args 'format)))))
3629 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3630 :policy (> speed space))
3631 (unless (constant-lvar-p control)
3632 (give-up-ir1-transform "The control string is not a constant."))
3633 (let ((arg-names (make-gensym-list (length args))))
3634 `(lambda (dest control ,@arg-names)
3635 (declare (ignore control))
3636 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
3638 (deftransform format ((stream control &rest args) (stream function &rest t) *
3639 :policy (> speed space))
3640 (let ((arg-names (make-gensym-list (length args))))
3641 `(lambda (stream control ,@arg-names)
3642 (funcall control stream ,@arg-names)
3645 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3646 :policy (> speed space))
3647 (let ((arg-names (make-gensym-list (length args))))
3648 `(lambda (tee control ,@arg-names)
3649 (declare (ignore tee))
3650 (funcall control *standard-output* ,@arg-names)
3655 `(defoptimizer (,name optimizer) ((control &rest args))
3656 (when (constant-lvar-p control)
3657 (let ((x (lvar-value control)))
3659 (check-format-args x args ',name)))))))
3662 #+sb-xc-host ; Only we should be using these
3665 (def compiler-abort)
3666 (def compiler-error)
3668 (def compiler-style-warn)
3669 (def compiler-notify)
3670 (def maybe-compiler-notify)
3673 (defoptimizer (cerror optimizer) ((report control &rest args))
3674 (when (and (constant-lvar-p control)
3675 (constant-lvar-p report))
3676 (let ((x (lvar-value control))
3677 (y (lvar-value report)))
3678 (when (and (stringp x) (stringp y))
3679 (multiple-value-bind (min1 max1)
3681 (sb!format:%compiler-walk-format-string x args)
3682 (sb!format:format-error (c)
3683 (compiler-warn "~A" c)))
3685 (multiple-value-bind (min2 max2)
3687 (sb!format:%compiler-walk-format-string y args)
3688 (sb!format:format-error (c)
3689 (compiler-warn "~A" c)))
3691 (let ((nargs (length args)))
3693 ((< nargs (min min1 min2))
3694 (warn 'format-too-few-args-warning
3696 "Too few arguments (~D) to ~S ~S ~S: ~
3697 requires at least ~D."
3699 (list nargs 'cerror y x (min min1 min2))))
3700 ((> nargs (max max1 max2))
3701 (warn 'format-too-many-args-warning
3703 "Too many arguments (~D) to ~S ~S ~S: ~
3706 (list nargs 'cerror y x (max max1 max2))))))))))))))
3708 (defoptimizer (coerce derive-type) ((value type))
3710 ((constant-lvar-p type)
3711 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3712 ;; but dealing with the niggle that complex canonicalization gets
3713 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3715 (let* ((specifier (lvar-value type))
3716 (result-typeoid (careful-specifier-type specifier)))
3718 ((null result-typeoid) nil)
3719 ((csubtypep result-typeoid (specifier-type 'number))
3720 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3721 ;; Rule of Canonical Representation for Complex Rationals,
3722 ;; which is a truly nasty delivery to field.
3724 ((csubtypep result-typeoid (specifier-type 'real))
3725 ;; cleverness required here: it would be nice to deduce
3726 ;; that something of type (INTEGER 2 3) coerced to type
3727 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3728 ;; FLOAT gets its own clause because it's implemented as
3729 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3732 ((and (numeric-type-p result-typeoid)
3733 (eq (numeric-type-complexp result-typeoid) :real))
3734 ;; FIXME: is this clause (a) necessary or (b) useful?
3736 ((or (csubtypep result-typeoid
3737 (specifier-type '(complex single-float)))
3738 (csubtypep result-typeoid
3739 (specifier-type '(complex double-float)))
3741 (csubtypep result-typeoid
3742 (specifier-type '(complex long-float))))
3743 ;; float complex types are never canonicalized.
3746 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3747 ;; probably just a COMPLEX or equivalent. So, in that
3748 ;; case, we will return a complex or an object of the
3749 ;; provided type if it's rational:
3750 (type-union result-typeoid
3751 (type-intersection (lvar-type value)
3752 (specifier-type 'rational))))))
3753 (t result-typeoid))))
3755 ;; OK, the result-type argument isn't constant. However, there
3756 ;; are common uses where we can still do better than just
3757 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3758 ;; where Y is of a known type. See messages on cmucl-imp
3759 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3760 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3761 ;; the basis that it's unlikely that other uses are both
3762 ;; time-critical and get to this branch of the COND (non-constant
3763 ;; second argument to COERCE). -- CSR, 2002-12-16
3764 (let ((value-type (lvar-type value))
3765 (type-type (lvar-type type)))
3767 ((good-cons-type-p (cons-type)
3768 ;; Make sure the cons-type we're looking at is something
3769 ;; we're prepared to handle which is basically something
3770 ;; that array-element-type can return.
3771 (or (and (member-type-p cons-type)
3772 (null (rest (member-type-members cons-type)))
3773 (null (first (member-type-members cons-type))))
3774 (let ((car-type (cons-type-car-type cons-type)))
3775 (and (member-type-p car-type)
3776 (null (rest (member-type-members car-type)))
3777 (or (symbolp (first (member-type-members car-type)))
3778 (numberp (first (member-type-members car-type)))
3779 (and (listp (first (member-type-members
3781 (numberp (first (first (member-type-members
3783 (good-cons-type-p (cons-type-cdr-type cons-type))))))
3784 (unconsify-type (good-cons-type)
3785 ;; Convert the "printed" respresentation of a cons
3786 ;; specifier into a type specifier. That is, the
3787 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3788 ;; NULL)) is converted to (SIGNED-BYTE 16).
3789 (cond ((or (null good-cons-type)
3790 (eq good-cons-type 'null))
3792 ((and (eq (first good-cons-type) 'cons)
3793 (eq (first (second good-cons-type)) 'member))
3794 `(,(second (second good-cons-type))
3795 ,@(unconsify-type (caddr good-cons-type))))))
3796 (coerceable-p (c-type)
3797 ;; Can the value be coerced to the given type? Coerce is
3798 ;; complicated, so we don't handle every possible case
3799 ;; here---just the most common and easiest cases:
3801 ;; * Any REAL can be coerced to a FLOAT type.
3802 ;; * Any NUMBER can be coerced to a (COMPLEX
3803 ;; SINGLE/DOUBLE-FLOAT).
3805 ;; FIXME I: we should also be able to deal with characters
3808 ;; FIXME II: I'm not sure that anything is necessary
3809 ;; here, at least while COMPLEX is not a specialized
3810 ;; array element type in the system. Reasoning: if
3811 ;; something cannot be coerced to the requested type, an
3812 ;; error will be raised (and so any downstream compiled
3813 ;; code on the assumption of the returned type is
3814 ;; unreachable). If something can, then it will be of
3815 ;; the requested type, because (by assumption) COMPLEX
3816 ;; (and other difficult types like (COMPLEX INTEGER)
3817 ;; aren't specialized types.
3818 (let ((coerced-type c-type))
3819 (or (and (subtypep coerced-type 'float)
3820 (csubtypep value-type (specifier-type 'real)))
3821 (and (subtypep coerced-type
3822 '(or (complex single-float)
3823 (complex double-float)))
3824 (csubtypep value-type (specifier-type 'number))))))
3825 (process-types (type)
3826 ;; FIXME: This needs some work because we should be able
3827 ;; to derive the resulting type better than just the
3828 ;; type arg of coerce. That is, if X is (INTEGER 10
3829 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3830 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3832 (cond ((member-type-p type)
3833 (let ((members (member-type-members type)))
3834 (if (every #'coerceable-p members)
3835 (specifier-type `(or ,@members))
3837 ((and (cons-type-p type)
3838 (good-cons-type-p type))
3839 (let ((c-type (unconsify-type (type-specifier type))))
3840 (if (coerceable-p c-type)
3841 (specifier-type c-type)
3844 *universal-type*))))
3845 (cond ((union-type-p type-type)
3846 (apply #'type-union (mapcar #'process-types
3847 (union-type-types type-type))))
3848 ((or (member-type-p type-type)
3849 (cons-type-p type-type))
3850 (process-types type-type))
3852 *universal-type*)))))))
3854 (defoptimizer (compile derive-type) ((nameoid function))
3855 (when (csubtypep (lvar-type nameoid)
3856 (specifier-type 'null))
3857 (values-specifier-type '(values function boolean boolean))))
3859 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3860 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3861 ;;; optimizer, above).
3862 (defoptimizer (array-element-type derive-type) ((array))
3863 (let ((array-type (lvar-type array)))
3864 (labels ((consify (list)
3867 `(cons (eql ,(car list)) ,(consify (rest list)))))
3868 (get-element-type (a)
3870 (type-specifier (array-type-specialized-element-type a))))
3871 (cond ((eq element-type '*)
3872 (specifier-type 'type-specifier))
3873 ((symbolp element-type)
3874 (make-member-type :members (list element-type)))
3875 ((consp element-type)
3876 (specifier-type (consify element-type)))
3878 (error "can't understand type ~S~%" element-type))))))
3879 (cond ((array-type-p array-type)
3880 (get-element-type array-type))
3881 ((union-type-p array-type)
3883 (mapcar #'get-element-type (union-type-types array-type))))
3885 *universal-type*)))))
3887 ;;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3888 ;;; isn't really related to the CMU CL code, since instead of trying
3889 ;;; to generalize the CMU CL code to allow START and END values, this
3890 ;;; code has been written from scratch following Chapter 7 of
3891 ;;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3892 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
3893 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3894 ;; isn't really related to the CMU CL code, since instead of trying
3895 ;; to generalize the CMU CL code to allow START and END values, this
3896 ;; code has been written from scratch following Chapter 7 of
3897 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3898 `(macrolet ((%index (x) `(truly-the index ,x))
3899 (%parent (i) `(ash ,i -1))
3900 (%left (i) `(%index (ash ,i 1)))
3901 (%right (i) `(%index (1+ (ash ,i 1))))
3904 (left (%left i) (%left i)))
3905 ((> left current-heap-size))
3906 (declare (type index i left))
3907 (let* ((i-elt (%elt i))
3908 (i-key (funcall keyfun i-elt))
3909 (left-elt (%elt left))
3910 (left-key (funcall keyfun left-elt)))
3911 (multiple-value-bind (large large-elt large-key)
3912 (if (funcall ,',predicate i-key left-key)
3913 (values left left-elt left-key)
3914 (values i i-elt i-key))
3915 (let ((right (%right i)))
3916 (multiple-value-bind (largest largest-elt)
3917 (if (> right current-heap-size)
3918 (values large large-elt)
3919 (let* ((right-elt (%elt right))
3920 (right-key (funcall keyfun right-elt)))
3921 (if (funcall ,',predicate large-key right-key)
3922 (values right right-elt)
3923 (values large large-elt))))
3924 (cond ((= largest i)
3927 (setf (%elt i) largest-elt
3928 (%elt largest) i-elt
3930 (%sort-vector (keyfun &optional (vtype 'vector))
3931 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
3932 ;; trouble getting type inference to
3933 ;; propagate all the way through this
3934 ;; tangled mess of inlining. The TRULY-THE
3935 ;; here works around that. -- WHN
3937 `(aref (truly-the ,',vtype ,',',vector)
3938 (%index (+ (%index ,i) start-1)))))
3939 (let (;; Heaps prefer 1-based addressing.
3940 (start-1 (1- ,',start))
3941 (current-heap-size (- ,',end ,',start))
3943 (declare (type (integer -1 #.(1- most-positive-fixnum))
3945 (declare (type index current-heap-size))
3946 (declare (type function keyfun))
3947 (loop for i of-type index
3948 from (ash current-heap-size -1) downto 1 do
3951 (when (< current-heap-size 2)
3953 (rotatef (%elt 1) (%elt current-heap-size))
3954 (decf current-heap-size)
3956 (if (typep ,vector 'simple-vector)
3957 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
3958 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
3960 ;; Special-casing the KEY=NIL case lets us avoid some
3962 (%sort-vector #'identity simple-vector)
3963 (%sort-vector ,key simple-vector))
3964 ;; It's hard to anticipate many speed-critical applications for
3965 ;; sorting vector types other than (VECTOR T), so we just lump
3966 ;; them all together in one slow dynamically typed mess.
3968 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
3969 (%sort-vector (or ,key #'identity))))))
3971 ;;;; debuggers' little helpers
3973 ;;; for debugging when transforms are behaving mysteriously,
3974 ;;; e.g. when debugging a problem with an ASH transform
3975 ;;; (defun foo (&optional s)
3976 ;;; (sb-c::/report-lvar s "S outside WHEN")
3977 ;;; (when (and (integerp s) (> s 3))
3978 ;;; (sb-c::/report-lvar s "S inside WHEN")
3979 ;;; (let ((bound (ash 1 (1- s))))
3980 ;;; (sb-c::/report-lvar bound "BOUND")
3981 ;;; (let ((x (- bound))
3983 ;;; (sb-c::/report-lvar x "X")
3984 ;;; (sb-c::/report-lvar x "Y"))
3985 ;;; `(integer ,(- bound) ,(1- bound)))))
3986 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
3987 ;;; and the function doesn't do anything at all.)
3990 (defknown /report-lvar (t t) null)
3991 (deftransform /report-lvar ((x message) (t t))
3992 (format t "~%/in /REPORT-LVAR~%")
3993 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
3994 (when (constant-lvar-p x)
3995 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
3996 (format t "/MESSAGE=~S~%" (lvar-value message))
3997 (give-up-ir1-transform "not a real transform"))
3998 (defun /report-lvar (x message)
3999 (declare (ignore x message))))