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 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
17 ;;; returns the first value of its argument. Ditto for VALUES with one
19 (define-source-transform identity (x) `(prog1 ,x))
20 (define-source-transform values (x) `(prog1 ,x))
22 ;;; CONSTANTLY is pretty much never worth transforming, but it's good to get the type.
23 (defoptimizer (constantly derive-type) ((value))
25 `(function (&rest t) (values ,(type-specifier (lvar-type value)) &optional))))
27 ;;; If the function has a known number of arguments, then return a
28 ;;; lambda with the appropriate fixed number of args. If the
29 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
30 ;;; MV optimization figure things out.
31 (deftransform complement ((fun) * * :node node)
33 (multiple-value-bind (min max)
34 (fun-type-nargs (lvar-type fun))
36 ((and min (eql min max))
37 (let ((dums (make-gensym-list min)))
38 `#'(lambda ,dums (not (funcall fun ,@dums)))))
39 ((awhen (node-lvar node)
40 (let ((dest (lvar-dest it)))
41 (and (combination-p dest)
42 (eq (combination-fun dest) it))))
43 '#'(lambda (&rest args)
44 (not (apply fun args))))
46 (give-up-ir1-transform
47 "The function doesn't have a fixed argument count.")))))
50 (defun derive-symbol-value-type (lvar node)
51 (if (constant-lvar-p lvar)
52 (let* ((sym (lvar-value lvar))
53 (var (maybe-find-free-var sym))
55 (let ((*lexenv* (node-lexenv node)))
56 (lexenv-find var type-restrictions))))
57 (global-type (info :variable :type sym)))
59 (type-intersection local-type global-type)
63 (defoptimizer (symbol-value derive-type) ((symbol) node)
64 (derive-symbol-value-type symbol node))
66 (defoptimizer (symbol-global-value derive-type) ((symbol) node)
67 (derive-symbol-value-type symbol node))
71 ;;; Translate CxR into CAR/CDR combos.
72 (defun source-transform-cxr (form)
73 (if (/= (length form) 2)
75 (let* ((name (car form))
79 (leaf (leaf-source-name name))))))
80 (do ((i (- (length string) 2) (1- i))
82 `(,(ecase (char string i)
88 ;;; Make source transforms to turn CxR forms into combinations of CAR
89 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
91 (/show0 "about to set CxR source transforms")
92 (loop for i of-type index from 2 upto 4 do
93 ;; Iterate over BUF = all names CxR where x = an I-element
94 ;; string of #\A or #\D characters.
95 (let ((buf (make-string (+ 2 i))))
96 (setf (aref buf 0) #\C
97 (aref buf (1+ i)) #\R)
98 (dotimes (j (ash 2 i))
99 (declare (type index j))
101 (declare (type index k))
102 (setf (aref buf (1+ k))
103 (if (logbitp k j) #\A #\D)))
104 (setf (info :function :source-transform (intern buf))
105 #'source-transform-cxr))))
106 (/show0 "done setting CxR source transforms")
108 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
109 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
110 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
112 (define-source-transform rest (x) `(cdr ,x))
113 (define-source-transform second (x) `(cadr ,x))
114 (define-source-transform third (x) `(caddr ,x))
115 (define-source-transform fourth (x) `(cadddr ,x))
116 (define-source-transform fifth (x) `(nth 4 ,x))
117 (define-source-transform sixth (x) `(nth 5 ,x))
118 (define-source-transform seventh (x) `(nth 6 ,x))
119 (define-source-transform eighth (x) `(nth 7 ,x))
120 (define-source-transform ninth (x) `(nth 8 ,x))
121 (define-source-transform tenth (x) `(nth 9 ,x))
123 ;;; LIST with one arg is an extremely common operation (at least inside
124 ;;; SBCL itself); translate it to CONS to take advantage of common
125 ;;; allocation routines.
126 (define-source-transform list (&rest args)
128 (1 `(cons ,(first args) nil))
131 ;;; And similarly for LIST*.
132 (define-source-transform list* (arg &rest others)
133 (cond ((not others) arg)
134 ((not (cdr others)) `(cons ,arg ,(car others)))
137 (defoptimizer (list* derive-type) ((arg &rest args))
139 (specifier-type 'cons)
142 ;;; Translate RPLACx to LET and SETF.
143 (define-source-transform rplaca (x y)
148 (define-source-transform rplacd (x y)
154 (deftransform last ((list &optional n) (t &optional t))
155 (let ((c (constant-lvar-p n)))
157 (and c (eql 1 (lvar-value n))))
159 ((and c (eql 0 (lvar-value n)))
162 (let ((type (lvar-type n)))
163 (cond ((csubtypep type (specifier-type 'fixnum))
164 '(%lastn/fixnum list n))
165 ((csubtypep type (specifier-type 'bignum))
166 '(%lastn/bignum list n))
168 (give-up-ir1-transform "second argument type too vague"))))))))
170 (define-source-transform gethash (&rest args)
172 (2 `(sb!impl::gethash3 ,@args nil))
173 (3 `(sb!impl::gethash3 ,@args))
175 (define-source-transform get (&rest args)
177 (2 `(sb!impl::get2 ,@args))
178 (3 `(sb!impl::get3 ,@args))
181 (defvar *default-nthcdr-open-code-limit* 6)
182 (defvar *extreme-nthcdr-open-code-limit* 20)
184 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
185 "convert NTHCDR to CAxxR"
186 (unless (constant-lvar-p n)
187 (give-up-ir1-transform))
188 (let ((n (lvar-value n)))
190 (if (policy node (and (= speed 3) (= space 0)))
191 *extreme-nthcdr-open-code-limit*
192 *default-nthcdr-open-code-limit*))
193 (give-up-ir1-transform))
198 `(cdr ,(frob (1- n))))))
201 ;;;; arithmetic and numerology
203 (define-source-transform plusp (x) `(> ,x 0))
204 (define-source-transform minusp (x) `(< ,x 0))
205 (define-source-transform zerop (x) `(= ,x 0))
207 (define-source-transform 1+ (x) `(+ ,x 1))
208 (define-source-transform 1- (x) `(- ,x 1))
210 (define-source-transform oddp (x) `(logtest ,x 1))
211 (define-source-transform evenp (x) `(not (logtest ,x 1)))
213 ;;; Note that all the integer division functions are available for
214 ;;; inline expansion.
216 (macrolet ((deffrob (fun)
217 `(define-source-transform ,fun (x &optional (y nil y-p))
224 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
226 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
229 ;;; This used to be a source transform (hence the lack of restrictions
230 ;;; on the argument types), but we make it a regular transform so that
231 ;;; the VM has a chance to see the bare LOGTEST and potentiall choose
232 ;;; to implement it differently. --njf, 06-02-2006
233 (deftransform logtest ((x y) * *)
234 `(not (zerop (logand x y))))
236 (deftransform logbitp
237 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
238 (unsigned-byte #.sb!vm:n-word-bits))))
239 `(if (>= index #.sb!vm:n-word-bits)
241 (not (zerop (logand integer (ash 1 index))))))
243 (define-source-transform byte (size position)
244 `(cons ,size ,position))
245 (define-source-transform byte-size (spec) `(car ,spec))
246 (define-source-transform byte-position (spec) `(cdr ,spec))
247 (define-source-transform ldb-test (bytespec integer)
248 `(not (zerop (mask-field ,bytespec ,integer))))
250 ;;; With the ratio and complex accessors, we pick off the "identity"
251 ;;; case, and use a primitive to handle the cell access case.
252 (define-source-transform numerator (num)
253 (once-only ((n-num `(the rational ,num)))
257 (define-source-transform denominator (num)
258 (once-only ((n-num `(the rational ,num)))
260 (%denominator ,n-num)
263 ;;;; interval arithmetic for computing bounds
265 ;;;; This is a set of routines for operating on intervals. It
266 ;;;; implements a simple interval arithmetic package. Although SBCL
267 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
268 ;;;; for two reasons:
270 ;;;; 1. This package is simpler than NUMERIC-TYPE.
272 ;;;; 2. It makes debugging much easier because you can just strip
273 ;;;; out these routines and test them independently of SBCL. (This is a
276 ;;;; One disadvantage is a probable increase in consing because we
277 ;;;; have to create these new interval structures even though
278 ;;;; numeric-type has everything we want to know. Reason 2 wins for
281 ;;; Support operations that mimic real arithmetic comparison
282 ;;; operators, but imposing a total order on the floating points such
283 ;;; that negative zeros are strictly less than positive zeros.
284 (macrolet ((def (name op)
287 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
288 (,op (float-sign x) (float-sign y))
290 (def signed-zero->= >=)
291 (def signed-zero-> >)
292 (def signed-zero-= =)
293 (def signed-zero-< <)
294 (def signed-zero-<= <=))
296 ;;; The basic interval type. It can handle open and closed intervals.
297 ;;; A bound is open if it is a list containing a number, just like
298 ;;; Lisp says. NIL means unbounded.
299 (defstruct (interval (:constructor %make-interval)
303 (defun make-interval (&key low high)
304 (labels ((normalize-bound (val)
307 (float-infinity-p val))
308 ;; Handle infinities.
312 ;; Handle any closed bounds.
315 ;; We have an open bound. Normalize the numeric
316 ;; bound. If the normalized bound is still a number
317 ;; (not nil), keep the bound open. Otherwise, the
318 ;; bound is really unbounded, so drop the openness.
319 (let ((new-val (normalize-bound (first val))))
321 ;; The bound exists, so keep it open still.
324 (error "unknown bound type in MAKE-INTERVAL")))))
325 (%make-interval :low (normalize-bound low)
326 :high (normalize-bound high))))
328 ;;; Given a number X, create a form suitable as a bound for an
329 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
330 #!-sb-fluid (declaim (inline set-bound))
331 (defun set-bound (x open-p)
332 (if (and x open-p) (list x) x))
334 ;;; Apply the function F to a bound X. If X is an open bound and the
335 ;;; function is declared strictly monotonic, then the result will be
336 ;;; open. IF X is NIL, the result is NIL.
337 (defun bound-func (f x strict)
338 (declare (type function f))
341 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
342 ;; With these traps masked, we might get things like infinity
343 ;; or negative infinity returned. Check for this and return
344 ;; NIL to indicate unbounded.
345 (let ((y (funcall f (type-bound-number x))))
347 (float-infinity-p y))
349 (set-bound y (and strict (consp x))))))
350 ;; Some numerical operations will signal SIMPLE-TYPE-ERROR, e.g.
351 ;; in the course of converting a bignum to a float. Default to
353 (simple-type-error ()))))
355 (defun safe-double-coercion-p (x)
356 (or (typep x 'double-float)
357 (<= most-negative-double-float x most-positive-double-float)))
359 (defun safe-single-coercion-p (x)
360 (or (typep x 'single-float)
362 ;; Fix for bug 420, and related issues: during type derivation we often
363 ;; end up deriving types for both
365 ;; (some-op <int> <single>)
367 ;; (some-op (coerce <int> 'single-float) <single>)
369 ;; or other equivalent transformed forms. The problem with this
370 ;; is that on x86 (+ <int> <single>) is on the machine level
373 ;; (coerce (+ (coerce <int> 'double-float)
374 ;; (coerce <single> 'double-float))
377 ;; so if the result of (coerce <int> 'single-float) is not exact, the
378 ;; derived types for the transformed forms will have an empty
379 ;; intersection -- which in turn means that the compiler will conclude
380 ;; that the call never returns, and all hell breaks lose when it *does*
381 ;; return at runtime. (This affects not just +, but other operators are
384 ;; See also: SAFE-CTYPE-FOR-SINGLE-COERCION-P
386 ;; FIXME: If we ever add SSE-support for x86, this conditional needs to
389 (not (typep x `(or (integer * (,most-negative-exactly-single-float-fixnum))
390 (integer (,most-positive-exactly-single-float-fixnum) *))))
391 (<= most-negative-single-float x most-positive-single-float))))
393 ;;; Apply a binary operator OP to two bounds X and Y. The result is
394 ;;; NIL if either is NIL. Otherwise bound is computed and the result
395 ;;; is open if either X or Y is open.
397 ;;; FIXME: only used in this file, not needed in target runtime
399 ;;; ANSI contaigon specifies coercion to floating point if one of the
400 ;;; arguments is floating point. Here we should check to be sure that
401 ;;; the other argument is within the bounds of that floating point
404 (defmacro safely-binop (op x y)
406 ((typep ,x 'double-float)
407 (when (safe-double-coercion-p ,y)
409 ((typep ,y 'double-float)
410 (when (safe-double-coercion-p ,x)
412 ((typep ,x 'single-float)
413 (when (safe-single-coercion-p ,y)
415 ((typep ,y 'single-float)
416 (when (safe-single-coercion-p ,x)
420 (defmacro bound-binop (op x y)
421 (with-unique-names (xb yb res)
423 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
424 (let* ((,xb (type-bound-number ,x))
425 (,yb (type-bound-number ,y))
426 (,res (safely-binop ,op ,xb ,yb)))
428 (and (or (consp ,x) (consp ,y))
429 ;; Open bounds can very easily be messed up
430 ;; by FP rounding, so take care here.
433 ;; Multiplying a greater-than-zero with
434 ;; less than one can round to zero.
435 `(or (not (fp-zero-p ,res))
436 (cond ((and (consp ,x) (fp-zero-p ,xb))
438 ((and (consp ,y) (fp-zero-p ,yb))
441 ;; Dividing a greater-than-zero with
442 ;; greater than one can round to zero.
443 `(or (not (fp-zero-p ,res))
444 (cond ((and (consp ,x) (fp-zero-p ,xb))
446 ((and (consp ,y) (fp-zero-p ,yb))
449 ;; Adding or subtracting greater-than-zero
450 ;; can end up with identity.
451 `(and (not (fp-zero-p ,xb))
452 (not (fp-zero-p ,yb))))))))))))
454 (defun coercion-loses-precision-p (val type)
457 (double-float (subtypep type 'single-float))
458 (rational (subtypep type 'float))
459 (t (bug "Unexpected arguments to bounds coercion: ~S ~S" val type))))
461 (defun coerce-for-bound (val type)
463 (let ((xbound (coerce-for-bound (car val) type)))
464 (if (coercion-loses-precision-p (car val) type)
468 ((subtypep type 'double-float)
469 (if (<= most-negative-double-float val most-positive-double-float)
471 ((or (subtypep type 'single-float) (subtypep type 'float))
472 ;; coerce to float returns a single-float
473 (if (<= most-negative-single-float val most-positive-single-float)
475 (t (coerce val type)))))
477 (defun coerce-and-truncate-floats (val type)
480 (let ((xbound (coerce-for-bound (car val) type)))
481 (if (coercion-loses-precision-p (car val) type)
485 ((subtypep type 'double-float)
486 (if (<= most-negative-double-float val most-positive-double-float)
488 (if (< val most-negative-double-float)
489 most-negative-double-float most-positive-double-float)))
490 ((or (subtypep type 'single-float) (subtypep type 'float))
491 ;; coerce to float returns a single-float
492 (if (<= most-negative-single-float val most-positive-single-float)
494 (if (< val most-negative-single-float)
495 most-negative-single-float most-positive-single-float)))
496 (t (coerce val type))))))
498 ;;; Convert a numeric-type object to an interval object.
499 (defun numeric-type->interval (x)
500 (declare (type numeric-type x))
501 (make-interval :low (numeric-type-low x)
502 :high (numeric-type-high x)))
504 (defun type-approximate-interval (type)
505 (declare (type ctype type))
506 (let ((types (prepare-arg-for-derive-type type))
509 (let ((type (if (member-type-p type)
510 (convert-member-type type)
512 (unless (numeric-type-p type)
513 (return-from type-approximate-interval nil))
514 (let ((interval (numeric-type->interval type)))
517 (interval-approximate-union result interval)
521 (defun copy-interval-limit (limit)
526 (defun copy-interval (x)
527 (declare (type interval x))
528 (make-interval :low (copy-interval-limit (interval-low x))
529 :high (copy-interval-limit (interval-high x))))
531 ;;; Given a point P contained in the interval X, split X into two
532 ;;; intervals at the point P. If CLOSE-LOWER is T, then the left
533 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
534 ;;; contains P. You can specify both to be T or NIL.
535 (defun interval-split (p x &optional close-lower close-upper)
536 (declare (type number p)
538 (list (make-interval :low (copy-interval-limit (interval-low x))
539 :high (if close-lower p (list p)))
540 (make-interval :low (if close-upper (list p) p)
541 :high (copy-interval-limit (interval-high x)))))
543 ;;; Return the closure of the interval. That is, convert open bounds
544 ;;; to closed bounds.
545 (defun interval-closure (x)
546 (declare (type interval x))
547 (make-interval :low (type-bound-number (interval-low x))
548 :high (type-bound-number (interval-high x))))
550 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
551 ;;; '-. Otherwise return NIL.
552 (defun interval-range-info (x &optional (point 0))
553 (declare (type interval x))
554 (let ((lo (interval-low x))
555 (hi (interval-high x)))
556 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
558 ((and hi (signed-zero->= point (type-bound-number hi)))
563 ;;; Test to see whether the interval X is bounded. HOW determines the
564 ;;; test, and should be either ABOVE, BELOW, or BOTH.
565 (defun interval-bounded-p (x how)
566 (declare (type interval x))
573 (and (interval-low x) (interval-high x)))))
575 ;;; See whether the interval X contains the number P, taking into
576 ;;; account that the interval might not be closed.
577 (defun interval-contains-p (p x)
578 (declare (type number p)
580 ;; Does the interval X contain the number P? This would be a lot
581 ;; easier if all intervals were closed!
582 (let ((lo (interval-low x))
583 (hi (interval-high x)))
585 ;; The interval is bounded
586 (if (and (signed-zero-<= (type-bound-number lo) p)
587 (signed-zero-<= p (type-bound-number hi)))
588 ;; P is definitely in the closure of the interval.
589 ;; We just need to check the end points now.
590 (cond ((signed-zero-= p (type-bound-number lo))
592 ((signed-zero-= p (type-bound-number hi))
597 ;; Interval with upper bound
598 (if (signed-zero-< p (type-bound-number hi))
600 (and (numberp hi) (signed-zero-= p hi))))
602 ;; Interval with lower bound
603 (if (signed-zero-> p (type-bound-number lo))
605 (and (numberp lo) (signed-zero-= p lo))))
607 ;; Interval with no bounds
610 ;;; Determine whether two intervals X and Y intersect. Return T if so.
611 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
612 ;;; were closed. Otherwise the intervals are treated as they are.
614 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
615 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
616 ;;; is T, then they do intersect because we use the closure of X = [0,
617 ;;; 1] and Y = [1, 2] to determine intersection.
618 (defun interval-intersect-p (x y &optional closed-intervals-p)
619 (declare (type interval x y))
620 (and (interval-intersection/difference (if closed-intervals-p
623 (if closed-intervals-p
628 ;;; Are the two intervals adjacent? That is, is there a number
629 ;;; between the two intervals that is not an element of either
630 ;;; interval? If so, they are not adjacent. For example [0, 1) and
631 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
632 ;;; between both intervals.
633 (defun interval-adjacent-p (x y)
634 (declare (type interval x y))
635 (flet ((adjacent (lo hi)
636 ;; Check to see whether lo and hi are adjacent. If either is
637 ;; nil, they can't be adjacent.
638 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
639 ;; The bounds are equal. They are adjacent if one of
640 ;; them is closed (a number). If both are open (consp),
641 ;; then there is a number that lies between them.
642 (or (numberp lo) (numberp hi)))))
643 (or (adjacent (interval-low y) (interval-high x))
644 (adjacent (interval-low x) (interval-high y)))))
646 ;;; Compute the intersection and difference between two intervals.
647 ;;; Two values are returned: the intersection and the difference.
649 ;;; Let the two intervals be X and Y, and let I and D be the two
650 ;;; values returned by this function. Then I = X intersect Y. If I
651 ;;; is NIL (the empty set), then D is X union Y, represented as the
652 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
653 ;;; - I, which is a list of two intervals.
655 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
656 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
657 (defun interval-intersection/difference (x y)
658 (declare (type interval x y))
659 (let ((x-lo (interval-low x))
660 (x-hi (interval-high x))
661 (y-lo (interval-low y))
662 (y-hi (interval-high y)))
665 ;; If p is an open bound, make it closed. If p is a closed
666 ;; bound, make it open.
670 (test-number (p int bound)
671 ;; Test whether P is in the interval.
672 (let ((pn (type-bound-number p)))
673 (when (interval-contains-p pn (interval-closure int))
674 ;; Check for endpoints.
675 (let* ((lo (interval-low int))
676 (hi (interval-high int))
677 (lon (type-bound-number lo))
678 (hin (type-bound-number hi)))
680 ;; Interval may be a point.
681 ((and lon hin (= lon hin pn))
682 (and (numberp p) (numberp lo) (numberp hi)))
683 ;; Point matches the low end.
684 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
685 ;; (P [P,?} => TRUE P) [P,?} => FALSE
686 ;; (P (P,?} => TRUE P) (P,?} => FALSE
687 ((and lon (= pn lon))
688 (or (and (numberp p) (numberp lo))
689 (and (consp p) (eq :low bound))))
690 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
691 ;; P) {?,P] => TRUE (P {?,P] => FALSE
692 ;; P) {?,P) => TRUE (P {?,P) => FALSE
693 ((and hin (= pn hin))
694 (or (and (numberp p) (numberp hi))
695 (and (consp p) (eq :high bound))))
696 ;; Not an endpoint, all is well.
699 (test-lower-bound (p int)
700 ;; P is a lower bound of an interval.
702 (test-number p int :low)
703 (not (interval-bounded-p int 'below))))
704 (test-upper-bound (p int)
705 ;; P is an upper bound of an interval.
707 (test-number p int :high)
708 (not (interval-bounded-p int 'above)))))
709 (let ((x-lo-in-y (test-lower-bound x-lo y))
710 (x-hi-in-y (test-upper-bound x-hi y))
711 (y-lo-in-x (test-lower-bound y-lo x))
712 (y-hi-in-x (test-upper-bound y-hi x)))
713 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
714 ;; Intervals intersect. Let's compute the intersection
715 ;; and the difference.
716 (multiple-value-bind (lo left-lo left-hi)
717 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
718 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
719 (multiple-value-bind (hi right-lo right-hi)
721 (values x-hi (opposite-bound x-hi) y-hi))
723 (values y-hi (opposite-bound y-hi) x-hi)))
724 (values (make-interval :low lo :high hi)
725 (list (make-interval :low left-lo
727 (make-interval :low right-lo
730 (values nil (list x y))))))))
732 ;;; If intervals X and Y intersect, return a new interval that is the
733 ;;; union of the two. If they do not intersect, return NIL.
734 (defun interval-merge-pair (x y)
735 (declare (type interval x y))
736 ;; If x and y intersect or are adjacent, create the union.
737 ;; Otherwise return nil
738 (when (or (interval-intersect-p x y)
739 (interval-adjacent-p x y))
740 (flet ((select-bound (x1 x2 min-op max-op)
741 (let ((x1-val (type-bound-number x1))
742 (x2-val (type-bound-number x2)))
744 ;; Both bounds are finite. Select the right one.
745 (cond ((funcall min-op x1-val x2-val)
746 ;; x1 is definitely better.
748 ((funcall max-op x1-val x2-val)
749 ;; x2 is definitely better.
752 ;; Bounds are equal. Select either
753 ;; value and make it open only if
755 (set-bound x1-val (and (consp x1) (consp x2))))))
757 ;; At least one bound is not finite. The
758 ;; non-finite bound always wins.
760 (let* ((x-lo (copy-interval-limit (interval-low x)))
761 (x-hi (copy-interval-limit (interval-high x)))
762 (y-lo (copy-interval-limit (interval-low y)))
763 (y-hi (copy-interval-limit (interval-high y))))
764 (make-interval :low (select-bound x-lo y-lo #'< #'>)
765 :high (select-bound x-hi y-hi #'> #'<))))))
767 ;;; return the minimal interval, containing X and Y
768 (defun interval-approximate-union (x y)
769 (cond ((interval-merge-pair x y))
771 (make-interval :low (copy-interval-limit (interval-low x))
772 :high (copy-interval-limit (interval-high y))))
774 (make-interval :low (copy-interval-limit (interval-low y))
775 :high (copy-interval-limit (interval-high x))))))
777 ;;; basic arithmetic operations on intervals. We probably should do
778 ;;; true interval arithmetic here, but it's complicated because we
779 ;;; have float and integer types and bounds can be open or closed.
781 ;;; the negative of an interval
782 (defun interval-neg (x)
783 (declare (type interval x))
784 (make-interval :low (bound-func #'- (interval-high x) t)
785 :high (bound-func #'- (interval-low x) t)))
787 ;;; Add two intervals.
788 (defun interval-add (x y)
789 (declare (type interval x y))
790 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
791 :high (bound-binop + (interval-high x) (interval-high y))))
793 ;;; Subtract two intervals.
794 (defun interval-sub (x y)
795 (declare (type interval x y))
796 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
797 :high (bound-binop - (interval-high x) (interval-low y))))
799 ;;; Multiply two intervals.
800 (defun interval-mul (x y)
801 (declare (type interval x y))
802 (flet ((bound-mul (x y)
803 (cond ((or (null x) (null y))
804 ;; Multiply by infinity is infinity
806 ((or (and (numberp x) (zerop x))
807 (and (numberp y) (zerop y)))
808 ;; Multiply by closed zero is special. The result
809 ;; is always a closed bound. But don't replace this
810 ;; with zero; we want the multiplication to produce
811 ;; the correct signed zero, if needed. Use SIGNUM
812 ;; to avoid trying to multiply huge bignums with 0.0.
813 (* (signum (type-bound-number x)) (signum (type-bound-number y))))
814 ((or (and (floatp x) (float-infinity-p x))
815 (and (floatp y) (float-infinity-p y)))
816 ;; Infinity times anything is infinity
819 ;; General multiply. The result is open if either is open.
820 (bound-binop * x y)))))
821 (let ((x-range (interval-range-info x))
822 (y-range (interval-range-info y)))
823 (cond ((null x-range)
824 ;; Split x into two and multiply each separately
825 (destructuring-bind (x- x+) (interval-split 0 x t t)
826 (interval-merge-pair (interval-mul x- y)
827 (interval-mul x+ y))))
829 ;; Split y into two and multiply each separately
830 (destructuring-bind (y- y+) (interval-split 0 y t t)
831 (interval-merge-pair (interval-mul x y-)
832 (interval-mul x y+))))
834 (interval-neg (interval-mul (interval-neg x) y)))
836 (interval-neg (interval-mul x (interval-neg y))))
837 ((and (eq x-range '+) (eq y-range '+))
838 ;; If we are here, X and Y are both positive.
840 :low (bound-mul (interval-low x) (interval-low y))
841 :high (bound-mul (interval-high x) (interval-high y))))
843 (bug "excluded case in INTERVAL-MUL"))))))
845 ;;; Divide two intervals.
846 (defun interval-div (top bot)
847 (declare (type interval top bot))
848 (flet ((bound-div (x y y-low-p)
851 ;; Divide by infinity means result is 0. However,
852 ;; we need to watch out for the sign of the result,
853 ;; to correctly handle signed zeros. We also need
854 ;; to watch out for positive or negative infinity.
855 (if (floatp (type-bound-number x))
857 (- (float-sign (type-bound-number x) 0.0))
858 (float-sign (type-bound-number x) 0.0))
860 ((zerop (type-bound-number y))
861 ;; Divide by zero means result is infinity
864 (bound-binop / x y)))))
865 (let ((top-range (interval-range-info top))
866 (bot-range (interval-range-info bot)))
867 (cond ((null bot-range)
868 ;; The denominator contains zero, so anything goes!
869 (make-interval :low nil :high nil))
871 ;; Denominator is negative so flip the sign, compute the
872 ;; result, and flip it back.
873 (interval-neg (interval-div top (interval-neg bot))))
875 ;; Split top into two positive and negative parts, and
876 ;; divide each separately
877 (destructuring-bind (top- top+) (interval-split 0 top t t)
878 (interval-merge-pair (interval-div top- bot)
879 (interval-div top+ bot))))
881 ;; Top is negative so flip the sign, divide, and flip the
882 ;; sign of the result.
883 (interval-neg (interval-div (interval-neg top) bot)))
884 ((and (eq top-range '+) (eq bot-range '+))
887 :low (bound-div (interval-low top) (interval-high bot) t)
888 :high (bound-div (interval-high top) (interval-low bot) nil)))
890 (bug "excluded case in INTERVAL-DIV"))))))
892 ;;; Apply the function F to the interval X. If X = [a, b], then the
893 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
894 ;;; result makes sense. It will if F is monotonic increasing (or, if
895 ;;; the interval is closed, non-decreasing).
897 ;;; (Actually most uses of INTERVAL-FUNC are coercions to float types,
898 ;;; which are not monotonic increasing, so default to calling
899 ;;; BOUND-FUNC with a non-strict argument).
900 (defun interval-func (f x &optional increasing)
901 (declare (type function f)
903 (let ((lo (bound-func f (interval-low x) increasing))
904 (hi (bound-func f (interval-high x) increasing)))
905 (make-interval :low lo :high hi)))
907 ;;; Return T if X < Y. That is every number in the interval X is
908 ;;; always less than any number in the interval Y.
909 (defun interval-< (x y)
910 (declare (type interval x y))
911 ;; X < Y only if X is bounded above, Y is bounded below, and they
913 (when (and (interval-bounded-p x 'above)
914 (interval-bounded-p y 'below))
915 ;; Intervals are bounded in the appropriate way. Make sure they
917 (let ((left (interval-high x))
918 (right (interval-low y)))
919 (cond ((> (type-bound-number left)
920 (type-bound-number right))
921 ;; The intervals definitely overlap, so result is NIL.
923 ((< (type-bound-number left)
924 (type-bound-number right))
925 ;; The intervals definitely don't touch, so result is T.
928 ;; Limits are equal. Check for open or closed bounds.
929 ;; Don't overlap if one or the other are open.
930 (or (consp left) (consp right)))))))
932 ;;; Return T if X >= Y. That is, every number in the interval X is
933 ;;; always greater than any number in the interval Y.
934 (defun interval->= (x y)
935 (declare (type interval x y))
936 ;; X >= Y if lower bound of X >= upper bound of Y
937 (when (and (interval-bounded-p x 'below)
938 (interval-bounded-p y 'above))
939 (>= (type-bound-number (interval-low x))
940 (type-bound-number (interval-high y)))))
942 ;;; Return T if X = Y.
943 (defun interval-= (x y)
944 (declare (type interval x y))
945 (and (interval-bounded-p x 'both)
946 (interval-bounded-p y 'both)
950 ;; Open intervals cannot be =
951 (return-from interval-= nil))))
952 ;; Both intervals refer to the same point
953 (= (bound (interval-high x)) (bound (interval-low x))
954 (bound (interval-high y)) (bound (interval-low y))))))
956 ;;; Return T if X /= Y
957 (defun interval-/= (x y)
958 (not (interval-intersect-p x y)))
960 ;;; Return an interval that is the absolute value of X. Thus, if
961 ;;; X = [-1 10], the result is [0, 10].
962 (defun interval-abs (x)
963 (declare (type interval x))
964 (case (interval-range-info x)
970 (destructuring-bind (x- x+) (interval-split 0 x t t)
971 (interval-merge-pair (interval-neg x-) x+)))))
973 ;;; Compute the square of an interval.
974 (defun interval-sqr (x)
975 (declare (type interval x))
976 (interval-func (lambda (x) (* x x)) (interval-abs x)))
978 ;;;; numeric DERIVE-TYPE methods
980 ;;; a utility for defining derive-type methods of integer operations. If
981 ;;; the types of both X and Y are integer types, then we compute a new
982 ;;; integer type with bounds determined by FUN when applied to X and Y.
983 ;;; Otherwise, we use NUMERIC-CONTAGION.
984 (defun derive-integer-type-aux (x y fun)
985 (declare (type function fun))
986 (if (and (numeric-type-p x) (numeric-type-p y)
987 (eq (numeric-type-class x) 'integer)
988 (eq (numeric-type-class y) 'integer)
989 (eq (numeric-type-complexp x) :real)
990 (eq (numeric-type-complexp y) :real))
991 (multiple-value-bind (low high) (funcall fun x y)
992 (make-numeric-type :class 'integer
996 (numeric-contagion x y)))
998 (defun derive-integer-type (x y fun)
999 (declare (type lvar x y) (type function fun))
1000 (let ((x (lvar-type x))
1002 (derive-integer-type-aux x y fun)))
1004 ;;; simple utility to flatten a list
1005 (defun flatten-list (x)
1006 (labels ((flatten-and-append (tree list)
1007 (cond ((null tree) list)
1008 ((atom tree) (cons tree list))
1009 (t (flatten-and-append
1010 (car tree) (flatten-and-append (cdr tree) list))))))
1011 (flatten-and-append x nil)))
1013 ;;; Take some type of lvar and massage it so that we get a list of the
1014 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
1016 (defun prepare-arg-for-derive-type (arg)
1017 (flet ((listify (arg)
1022 (union-type-types arg))
1025 (unless (eq arg *empty-type*)
1026 ;; Make sure all args are some type of numeric-type. For member
1027 ;; types, convert the list of members into a union of equivalent
1028 ;; single-element member-type's.
1029 (let ((new-args nil))
1030 (dolist (arg (listify arg))
1031 (if (member-type-p arg)
1032 ;; Run down the list of members and convert to a list of
1034 (mapc-member-type-members
1036 (push (if (numberp member)
1037 (make-member-type :members (list member))
1041 (push arg new-args)))
1042 (unless (member *empty-type* new-args)
1045 ;;; Convert from the standard type convention for which -0.0 and 0.0
1046 ;;; are equal to an intermediate convention for which they are
1047 ;;; considered different which is more natural for some of the
1049 (defun convert-numeric-type (type)
1050 (declare (type numeric-type type))
1051 ;;; Only convert real float interval delimiters types.
1052 (if (eq (numeric-type-complexp type) :real)
1053 (let* ((lo (numeric-type-low type))
1054 (lo-val (type-bound-number lo))
1055 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
1056 (hi (numeric-type-high type))
1057 (hi-val (type-bound-number hi))
1058 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
1059 (if (or lo-float-zero-p hi-float-zero-p)
1061 :class (numeric-type-class type)
1062 :format (numeric-type-format type)
1064 :low (if lo-float-zero-p
1066 (list (float 0.0 lo-val))
1067 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
1069 :high (if hi-float-zero-p
1071 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
1078 ;;; Convert back from the intermediate convention for which -0.0 and
1079 ;;; 0.0 are considered different to the standard type convention for
1080 ;;; which and equal.
1081 (defun convert-back-numeric-type (type)
1082 (declare (type numeric-type type))
1083 ;;; Only convert real float interval delimiters types.
1084 (if (eq (numeric-type-complexp type) :real)
1085 (let* ((lo (numeric-type-low type))
1086 (lo-val (type-bound-number lo))
1088 (and lo (floatp lo-val) (= lo-val 0.0)
1089 (float-sign lo-val)))
1090 (hi (numeric-type-high type))
1091 (hi-val (type-bound-number hi))
1093 (and hi (floatp hi-val) (= hi-val 0.0)
1094 (float-sign hi-val))))
1096 ;; (float +0.0 +0.0) => (member 0.0)
1097 ;; (float -0.0 -0.0) => (member -0.0)
1098 ((and lo-float-zero-p hi-float-zero-p)
1099 ;; shouldn't have exclusive bounds here..
1100 (aver (and (not (consp lo)) (not (consp hi))))
1101 (if (= lo-float-zero-p hi-float-zero-p)
1102 ;; (float +0.0 +0.0) => (member 0.0)
1103 ;; (float -0.0 -0.0) => (member -0.0)
1104 (specifier-type `(member ,lo-val))
1105 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1106 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1107 (make-numeric-type :class (numeric-type-class type)
1108 :format (numeric-type-format type)
1114 ;; (float -0.0 x) => (float 0.0 x)
1115 ((and (not (consp lo)) (minusp lo-float-zero-p))
1116 (make-numeric-type :class (numeric-type-class type)
1117 :format (numeric-type-format type)
1119 :low (float 0.0 lo-val)
1121 ;; (float (+0.0) x) => (float (0.0) x)
1122 ((and (consp lo) (plusp lo-float-zero-p))
1123 (make-numeric-type :class (numeric-type-class type)
1124 :format (numeric-type-format type)
1126 :low (list (float 0.0 lo-val))
1129 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1130 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1131 (list (make-member-type :members (list (float 0.0 lo-val)))
1132 (make-numeric-type :class (numeric-type-class type)
1133 :format (numeric-type-format type)
1135 :low (list (float 0.0 lo-val))
1139 ;; (float x +0.0) => (float x 0.0)
1140 ((and (not (consp hi)) (plusp hi-float-zero-p))
1141 (make-numeric-type :class (numeric-type-class type)
1142 :format (numeric-type-format type)
1145 :high (float 0.0 hi-val)))
1146 ;; (float x (-0.0)) => (float x (0.0))
1147 ((and (consp hi) (minusp hi-float-zero-p))
1148 (make-numeric-type :class (numeric-type-class type)
1149 :format (numeric-type-format type)
1152 :high (list (float 0.0 hi-val))))
1154 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1155 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1156 (list (make-member-type :members (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val)))
1157 (make-numeric-type :class (numeric-type-class type)
1158 :format (numeric-type-format type)
1161 :high (list (float 0.0 hi-val)))))))
1167 ;;; Convert back a possible list of numeric types.
1168 (defun convert-back-numeric-type-list (type-list)
1171 (let ((results '()))
1172 (dolist (type type-list)
1173 (if (numeric-type-p type)
1174 (let ((result (convert-back-numeric-type type)))
1176 (setf results (append results result))
1177 (push result results)))
1178 (push type results)))
1181 (convert-back-numeric-type type-list))
1183 (convert-back-numeric-type-list (union-type-types type-list)))
1187 ;;; Take a list of types and return a canonical type specifier,
1188 ;;; combining any MEMBER types together. If both positive and negative
1189 ;;; MEMBER types are present they are converted to a float type.
1190 ;;; XXX This would be far simpler if the type-union methods could handle
1191 ;;; member/number unions.
1193 ;;; If we're about to generate an overly complex union of numeric types, start
1194 ;;; collapse the ranges together.
1196 ;;; FIXME: The MEMBER canonicalization parts of MAKE-DERIVED-UNION-TYPE and
1197 ;;; entire CONVERT-MEMBER-TYPE probably belong in the kernel's type logic,
1198 ;;; invoked always, instead of in the compiler, invoked only during some type
1200 (defvar *derived-numeric-union-complexity-limit* 6)
1202 (defun make-derived-union-type (type-list)
1203 (let ((xset (alloc-xset))
1206 (numeric-type *empty-type*))
1207 (dolist (type type-list)
1208 (cond ((member-type-p type)
1209 (mapc-member-type-members
1211 (if (fp-zero-p member)
1212 (unless (member member fp-zeroes)
1213 (pushnew member fp-zeroes))
1214 (add-to-xset member xset)))
1216 ((numeric-type-p type)
1217 (let ((*approximate-numeric-unions*
1218 (when (and (union-type-p numeric-type)
1219 (nthcdr *derived-numeric-union-complexity-limit*
1220 (union-type-types numeric-type)))
1222 (setf numeric-type (type-union type numeric-type))))
1224 (push type misc-types))))
1225 (if (and (xset-empty-p xset) (not fp-zeroes))
1226 (apply #'type-union numeric-type misc-types)
1227 (apply #'type-union (make-member-type :xset xset :fp-zeroes fp-zeroes)
1228 numeric-type misc-types))))
1230 ;;; Convert a member type with a single member to a numeric type.
1231 (defun convert-member-type (arg)
1232 (let* ((members (member-type-members arg))
1233 (member (first members))
1234 (member-type (type-of member)))
1235 (aver (not (rest members)))
1236 (specifier-type (cond ((typep member 'integer)
1237 `(integer ,member ,member))
1238 ((memq member-type '(short-float single-float
1239 double-float long-float))
1240 `(,member-type ,member ,member))
1244 ;;; This is used in defoptimizers for computing the resulting type of
1247 ;;; Given the lvar ARG, derive the resulting type using the
1248 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1249 ;;; "atomic" lvar type like numeric-type or member-type (containing
1250 ;;; just one element). It should return the resulting type, which can
1251 ;;; be a list of types.
1253 ;;; For the case of member types, if a MEMBER-FUN is given it is
1254 ;;; called to compute the result otherwise the member type is first
1255 ;;; converted to a numeric type and the DERIVE-FUN is called.
1256 (defun one-arg-derive-type (arg derive-fun member-fun
1257 &optional (convert-type t))
1258 (declare (type function derive-fun)
1259 (type (or null function) member-fun))
1260 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1266 (with-float-traps-masked
1267 (:underflow :overflow :divide-by-zero)
1269 `(eql ,(funcall member-fun
1270 (first (member-type-members x))))))
1271 ;; Otherwise convert to a numeric type.
1272 (let ((result-type-list
1273 (funcall derive-fun (convert-member-type x))))
1275 (convert-back-numeric-type-list result-type-list)
1276 result-type-list))))
1279 (convert-back-numeric-type-list
1280 (funcall derive-fun (convert-numeric-type x)))
1281 (funcall derive-fun x)))
1283 *universal-type*))))
1284 ;; Run down the list of args and derive the type of each one,
1285 ;; saving all of the results in a list.
1286 (let ((results nil))
1287 (dolist (arg arg-list)
1288 (let ((result (deriver arg)))
1290 (setf results (append results result))
1291 (push result results))))
1293 (make-derived-union-type results)
1294 (first results)))))))
1296 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1297 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1298 ;;; original args and a third which is T to indicate if the two args
1299 ;;; really represent the same lvar. This is useful for deriving the
1300 ;;; type of things like (* x x), which should always be positive. If
1301 ;;; we didn't do this, we wouldn't be able to tell.
1302 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1303 &optional (convert-type t))
1304 (declare (type function derive-fun fun))
1305 (flet ((deriver (x y same-arg)
1306 (cond ((and (member-type-p x) (member-type-p y))
1307 (let* ((x (first (member-type-members x)))
1308 (y (first (member-type-members y)))
1309 (result (ignore-errors
1310 (with-float-traps-masked
1311 (:underflow :overflow :divide-by-zero
1313 (funcall fun x y)))))
1314 (cond ((null result) *empty-type*)
1315 ((and (floatp result) (float-nan-p result))
1316 (make-numeric-type :class 'float
1317 :format (type-of result)
1320 (specifier-type `(eql ,result))))))
1321 ((and (member-type-p x) (numeric-type-p y))
1322 (let* ((x (convert-member-type x))
1323 (y (if convert-type (convert-numeric-type y) y))
1324 (result (funcall derive-fun x y same-arg)))
1326 (convert-back-numeric-type-list result)
1328 ((and (numeric-type-p x) (member-type-p y))
1329 (let* ((x (if convert-type (convert-numeric-type x) x))
1330 (y (convert-member-type y))
1331 (result (funcall derive-fun x y same-arg)))
1333 (convert-back-numeric-type-list result)
1335 ((and (numeric-type-p x) (numeric-type-p y))
1336 (let* ((x (if convert-type (convert-numeric-type x) x))
1337 (y (if convert-type (convert-numeric-type y) y))
1338 (result (funcall derive-fun x y same-arg)))
1340 (convert-back-numeric-type-list result)
1343 *universal-type*))))
1344 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1345 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1346 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1348 (let ((results nil))
1350 ;; Since the args are the same LVARs, just run down the
1353 (let ((result (deriver x x same-arg)))
1355 (setf results (append results result))
1356 (push result results))))
1357 ;; Try all pairwise combinations.
1360 (let ((result (or (deriver x y same-arg)
1361 (numeric-contagion x y))))
1363 (setf results (append results result))
1364 (push result results))))))
1366 (make-derived-union-type results)
1367 (first results)))))))
1369 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1371 (defoptimizer (+ derive-type) ((x y))
1372 (derive-integer-type
1379 (values (frob (numeric-type-low x) (numeric-type-low y))
1380 (frob (numeric-type-high x) (numeric-type-high y)))))))
1382 (defoptimizer (- derive-type) ((x y))
1383 (derive-integer-type
1390 (values (frob (numeric-type-low x) (numeric-type-high y))
1391 (frob (numeric-type-high x) (numeric-type-low y)))))))
1393 (defoptimizer (* derive-type) ((x y))
1394 (derive-integer-type
1397 (let ((x-low (numeric-type-low x))
1398 (x-high (numeric-type-high x))
1399 (y-low (numeric-type-low y))
1400 (y-high (numeric-type-high y)))
1401 (cond ((not (and x-low y-low))
1403 ((or (minusp x-low) (minusp y-low))
1404 (if (and x-high y-high)
1405 (let ((max (* (max (abs x-low) (abs x-high))
1406 (max (abs y-low) (abs y-high)))))
1407 (values (- max) max))
1410 (values (* x-low y-low)
1411 (if (and x-high y-high)
1415 (defoptimizer (/ derive-type) ((x y))
1416 (numeric-contagion (lvar-type x) (lvar-type y)))
1420 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1422 (defun +-derive-type-aux (x y same-arg)
1423 (if (and (numeric-type-real-p x)
1424 (numeric-type-real-p y))
1427 (let ((x-int (numeric-type->interval x)))
1428 (interval-add x-int x-int))
1429 (interval-add (numeric-type->interval x)
1430 (numeric-type->interval y))))
1431 (result-type (numeric-contagion x y)))
1432 ;; If the result type is a float, we need to be sure to coerce
1433 ;; the bounds into the correct type.
1434 (when (eq (numeric-type-class result-type) 'float)
1435 (setf result (interval-func
1437 (coerce-for-bound x (or (numeric-type-format result-type)
1441 :class (if (and (eq (numeric-type-class x) 'integer)
1442 (eq (numeric-type-class y) 'integer))
1443 ;; The sum of integers is always an integer.
1445 (numeric-type-class result-type))
1446 :format (numeric-type-format result-type)
1447 :low (interval-low result)
1448 :high (interval-high result)))
1449 ;; general contagion
1450 (numeric-contagion x y)))
1452 (defoptimizer (+ derive-type) ((x y))
1453 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1455 (defun --derive-type-aux (x y same-arg)
1456 (if (and (numeric-type-real-p x)
1457 (numeric-type-real-p y))
1459 ;; (- X X) is always 0.
1461 (make-interval :low 0 :high 0)
1462 (interval-sub (numeric-type->interval x)
1463 (numeric-type->interval y))))
1464 (result-type (numeric-contagion x y)))
1465 ;; If the result type is a float, we need to be sure to coerce
1466 ;; the bounds into the correct type.
1467 (when (eq (numeric-type-class result-type) 'float)
1468 (setf result (interval-func
1470 (coerce-for-bound x (or (numeric-type-format result-type)
1474 :class (if (and (eq (numeric-type-class x) 'integer)
1475 (eq (numeric-type-class y) 'integer))
1476 ;; The difference of integers is always an integer.
1478 (numeric-type-class result-type))
1479 :format (numeric-type-format result-type)
1480 :low (interval-low result)
1481 :high (interval-high result)))
1482 ;; general contagion
1483 (numeric-contagion x y)))
1485 (defoptimizer (- derive-type) ((x y))
1486 (two-arg-derive-type x y #'--derive-type-aux #'-))
1488 (defun *-derive-type-aux (x y same-arg)
1489 (if (and (numeric-type-real-p x)
1490 (numeric-type-real-p y))
1492 ;; (* X X) is always positive, so take care to do it right.
1494 (interval-sqr (numeric-type->interval x))
1495 (interval-mul (numeric-type->interval x)
1496 (numeric-type->interval y))))
1497 (result-type (numeric-contagion x y)))
1498 ;; If the result type is a float, we need to be sure to coerce
1499 ;; the bounds into the correct type.
1500 (when (eq (numeric-type-class result-type) 'float)
1501 (setf result (interval-func
1503 (coerce-for-bound x (or (numeric-type-format result-type)
1507 :class (if (and (eq (numeric-type-class x) 'integer)
1508 (eq (numeric-type-class y) 'integer))
1509 ;; The product of integers is always an integer.
1511 (numeric-type-class result-type))
1512 :format (numeric-type-format result-type)
1513 :low (interval-low result)
1514 :high (interval-high result)))
1515 (numeric-contagion x y)))
1517 (defoptimizer (* derive-type) ((x y))
1518 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1520 (defun /-derive-type-aux (x y same-arg)
1521 (if (and (numeric-type-real-p x)
1522 (numeric-type-real-p y))
1524 ;; (/ X X) is always 1, except if X can contain 0. In
1525 ;; that case, we shouldn't optimize the division away
1526 ;; because we want 0/0 to signal an error.
1528 (not (interval-contains-p
1529 0 (interval-closure (numeric-type->interval y)))))
1530 (make-interval :low 1 :high 1)
1531 (interval-div (numeric-type->interval x)
1532 (numeric-type->interval y))))
1533 (result-type (numeric-contagion x y)))
1534 ;; If the result type is a float, we need to be sure to coerce
1535 ;; the bounds into the correct type.
1536 (when (eq (numeric-type-class result-type) 'float)
1537 (setf result (interval-func
1539 (coerce-for-bound x (or (numeric-type-format result-type)
1542 (make-numeric-type :class (numeric-type-class result-type)
1543 :format (numeric-type-format result-type)
1544 :low (interval-low result)
1545 :high (interval-high result)))
1546 (numeric-contagion x y)))
1548 (defoptimizer (/ derive-type) ((x y))
1549 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1553 (defun ash-derive-type-aux (n-type shift same-arg)
1554 (declare (ignore same-arg))
1555 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1556 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1557 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1558 ;; two bignums yielding zero) and it's hard to avoid that
1559 ;; calculation in here.
1560 #+(and cmu sb-xc-host)
1561 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1562 (typep (numeric-type-high n-type) 'bignum))
1563 (or (typep (numeric-type-low shift) 'bignum)
1564 (typep (numeric-type-high shift) 'bignum)))
1565 (return-from ash-derive-type-aux *universal-type*))
1566 (flet ((ash-outer (n s)
1567 (when (and (fixnump s)
1569 (> s sb!xc:most-negative-fixnum))
1571 ;; KLUDGE: The bare 64's here should be related to
1572 ;; symbolic machine word size values somehow.
1575 (if (and (fixnump s)
1576 (> s sb!xc:most-negative-fixnum))
1578 (if (minusp n) -1 0))))
1579 (or (and (csubtypep n-type (specifier-type 'integer))
1580 (csubtypep shift (specifier-type 'integer))
1581 (let ((n-low (numeric-type-low n-type))
1582 (n-high (numeric-type-high n-type))
1583 (s-low (numeric-type-low shift))
1584 (s-high (numeric-type-high shift)))
1585 (make-numeric-type :class 'integer :complexp :real
1588 (ash-outer n-low s-high)
1589 (ash-inner n-low s-low)))
1592 (ash-inner n-high s-low)
1593 (ash-outer n-high s-high))))))
1596 (defoptimizer (ash derive-type) ((n shift))
1597 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1599 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1600 (macrolet ((frob (fun)
1601 `#'(lambda (type type2)
1602 (declare (ignore type2))
1603 (let ((lo (numeric-type-low type))
1604 (hi (numeric-type-high type)))
1605 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1607 (defoptimizer (%negate derive-type) ((num))
1608 (derive-integer-type num num (frob -))))
1610 (defun lognot-derive-type-aux (int)
1611 (derive-integer-type-aux int int
1612 (lambda (type type2)
1613 (declare (ignore type2))
1614 (let ((lo (numeric-type-low type))
1615 (hi (numeric-type-high type)))
1616 (values (if hi (lognot hi) nil)
1617 (if lo (lognot lo) nil)
1618 (numeric-type-class type)
1619 (numeric-type-format type))))))
1621 (defoptimizer (lognot derive-type) ((int))
1622 (lognot-derive-type-aux (lvar-type int)))
1624 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1625 (defoptimizer (%negate derive-type) ((num))
1626 (flet ((negate-bound (b)
1628 (set-bound (- (type-bound-number b))
1630 (one-arg-derive-type num
1632 (modified-numeric-type
1634 :low (negate-bound (numeric-type-high type))
1635 :high (negate-bound (numeric-type-low type))))
1638 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1639 (defoptimizer (abs derive-type) ((num))
1640 (let ((type (lvar-type num)))
1641 (if (and (numeric-type-p type)
1642 (eq (numeric-type-class type) 'integer)
1643 (eq (numeric-type-complexp type) :real))
1644 (let ((lo (numeric-type-low type))
1645 (hi (numeric-type-high type)))
1646 (make-numeric-type :class 'integer :complexp :real
1647 :low (cond ((and hi (minusp hi))
1653 :high (if (and hi lo)
1654 (max (abs hi) (abs lo))
1656 (numeric-contagion type type))))
1658 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1659 (defun abs-derive-type-aux (type)
1660 (cond ((eq (numeric-type-complexp type) :complex)
1661 ;; The absolute value of a complex number is always a
1662 ;; non-negative float.
1663 (let* ((format (case (numeric-type-class type)
1664 ((integer rational) 'single-float)
1665 (t (numeric-type-format type))))
1666 (bound-format (or format 'float)))
1667 (make-numeric-type :class 'float
1670 :low (coerce 0 bound-format)
1673 ;; The absolute value of a real number is a non-negative real
1674 ;; of the same type.
1675 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1676 (class (numeric-type-class type))
1677 (format (numeric-type-format type))
1678 (bound-type (or format class 'real)))
1683 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1684 :high (coerce-and-truncate-floats
1685 (interval-high abs-bnd) bound-type))))))
1687 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1688 (defoptimizer (abs derive-type) ((num))
1689 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1691 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1692 (defoptimizer (truncate derive-type) ((number divisor))
1693 (let ((number-type (lvar-type number))
1694 (divisor-type (lvar-type divisor))
1695 (integer-type (specifier-type 'integer)))
1696 (if (and (numeric-type-p number-type)
1697 (csubtypep number-type integer-type)
1698 (numeric-type-p divisor-type)
1699 (csubtypep divisor-type integer-type))
1700 (let ((number-low (numeric-type-low number-type))
1701 (number-high (numeric-type-high number-type))
1702 (divisor-low (numeric-type-low divisor-type))
1703 (divisor-high (numeric-type-high divisor-type)))
1704 (values-specifier-type
1705 `(values ,(integer-truncate-derive-type number-low number-high
1706 divisor-low divisor-high)
1707 ,(integer-rem-derive-type number-low number-high
1708 divisor-low divisor-high))))
1711 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1714 (defun rem-result-type (number-type divisor-type)
1715 ;; Figure out what the remainder type is. The remainder is an
1716 ;; integer if both args are integers; a rational if both args are
1717 ;; rational; and a float otherwise.
1718 (cond ((and (csubtypep number-type (specifier-type 'integer))
1719 (csubtypep divisor-type (specifier-type 'integer)))
1721 ((and (csubtypep number-type (specifier-type 'rational))
1722 (csubtypep divisor-type (specifier-type 'rational)))
1724 ((and (csubtypep number-type (specifier-type 'float))
1725 (csubtypep divisor-type (specifier-type 'float)))
1726 ;; Both are floats so the result is also a float, of
1727 ;; the largest type.
1728 (or (float-format-max (numeric-type-format number-type)
1729 (numeric-type-format divisor-type))
1731 ((and (csubtypep number-type (specifier-type 'float))
1732 (csubtypep divisor-type (specifier-type 'rational)))
1733 ;; One of the arguments is a float and the other is a
1734 ;; rational. The remainder is a float of the same
1736 (or (numeric-type-format number-type) 'float))
1737 ((and (csubtypep divisor-type (specifier-type 'float))
1738 (csubtypep number-type (specifier-type 'rational)))
1739 ;; One of the arguments is a float and the other is a
1740 ;; rational. The remainder is a float of the same
1742 (or (numeric-type-format divisor-type) 'float))
1744 ;; Some unhandled combination. This usually means both args
1745 ;; are REAL so the result is a REAL.
1748 (defun truncate-derive-type-quot (number-type divisor-type)
1749 (let* ((rem-type (rem-result-type number-type divisor-type))
1750 (number-interval (numeric-type->interval number-type))
1751 (divisor-interval (numeric-type->interval divisor-type)))
1752 ;;(declare (type (member '(integer rational float)) rem-type))
1753 ;; We have real numbers now.
1754 (cond ((eq rem-type 'integer)
1755 ;; Since the remainder type is INTEGER, both args are
1757 (let* ((res (integer-truncate-derive-type
1758 (interval-low number-interval)
1759 (interval-high number-interval)
1760 (interval-low divisor-interval)
1761 (interval-high divisor-interval))))
1762 (specifier-type (if (listp res) res 'integer))))
1764 (let ((quot (truncate-quotient-bound
1765 (interval-div number-interval
1766 divisor-interval))))
1767 (specifier-type `(integer ,(or (interval-low quot) '*)
1768 ,(or (interval-high quot) '*))))))))
1770 (defun truncate-derive-type-rem (number-type divisor-type)
1771 (let* ((rem-type (rem-result-type number-type divisor-type))
1772 (number-interval (numeric-type->interval number-type))
1773 (divisor-interval (numeric-type->interval divisor-type))
1774 (rem (truncate-rem-bound number-interval divisor-interval)))
1775 ;;(declare (type (member '(integer rational float)) rem-type))
1776 ;; We have real numbers now.
1777 (cond ((eq rem-type 'integer)
1778 ;; Since the remainder type is INTEGER, both args are
1780 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1781 ,(or (interval-high rem) '*))))
1783 (multiple-value-bind (class format)
1786 (values 'integer nil))
1788 (values 'rational nil))
1789 ((or single-float double-float #!+long-float long-float)
1790 (values 'float rem-type))
1792 (values 'float nil))
1795 (when (member rem-type '(float single-float double-float
1796 #!+long-float long-float))
1797 (setf rem (interval-func #'(lambda (x)
1798 (coerce-for-bound x rem-type))
1800 (make-numeric-type :class class
1802 :low (interval-low rem)
1803 :high (interval-high rem)))))))
1805 (defun truncate-derive-type-quot-aux (num div same-arg)
1806 (declare (ignore same-arg))
1807 (if (and (numeric-type-real-p num)
1808 (numeric-type-real-p div))
1809 (truncate-derive-type-quot num div)
1812 (defun truncate-derive-type-rem-aux (num div same-arg)
1813 (declare (ignore same-arg))
1814 (if (and (numeric-type-real-p num)
1815 (numeric-type-real-p div))
1816 (truncate-derive-type-rem num div)
1819 (defoptimizer (truncate derive-type) ((number divisor))
1820 (let ((quot (two-arg-derive-type number divisor
1821 #'truncate-derive-type-quot-aux #'truncate))
1822 (rem (two-arg-derive-type number divisor
1823 #'truncate-derive-type-rem-aux #'rem)))
1824 (when (and quot rem)
1825 (make-values-type :required (list quot rem)))))
1827 (defun ftruncate-derive-type-quot (number-type divisor-type)
1828 ;; The bounds are the same as for truncate. However, the first
1829 ;; result is a float of some type. We need to determine what that
1830 ;; type is. Basically it's the more contagious of the two types.
1831 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1832 (res-type (numeric-contagion number-type divisor-type)))
1833 (make-numeric-type :class 'float
1834 :format (numeric-type-format res-type)
1835 :low (numeric-type-low q-type)
1836 :high (numeric-type-high q-type))))
1838 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1839 (declare (ignore same-arg))
1840 (if (and (numeric-type-real-p n)
1841 (numeric-type-real-p d))
1842 (ftruncate-derive-type-quot n d)
1845 (defoptimizer (ftruncate derive-type) ((number divisor))
1847 (two-arg-derive-type number divisor
1848 #'ftruncate-derive-type-quot-aux #'ftruncate))
1849 (rem (two-arg-derive-type number divisor
1850 #'truncate-derive-type-rem-aux #'rem)))
1851 (when (and quot rem)
1852 (make-values-type :required (list quot rem)))))
1854 (defun %unary-truncate-derive-type-aux (number)
1855 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1857 (defoptimizer (%unary-truncate derive-type) ((number))
1858 (one-arg-derive-type number
1859 #'%unary-truncate-derive-type-aux
1862 (defoptimizer (%unary-truncate/single-float derive-type) ((number))
1863 (one-arg-derive-type number
1864 #'%unary-truncate-derive-type-aux
1867 (defoptimizer (%unary-truncate/double-float derive-type) ((number))
1868 (one-arg-derive-type number
1869 #'%unary-truncate-derive-type-aux
1872 (defoptimizer (%unary-ftruncate derive-type) ((number))
1873 (let ((divisor (specifier-type '(integer 1 1))))
1874 (one-arg-derive-type number
1876 (ftruncate-derive-type-quot-aux n divisor nil))
1877 #'%unary-ftruncate)))
1879 (defoptimizer (%unary-round derive-type) ((number))
1880 (one-arg-derive-type number
1883 (unless (numeric-type-real-p n)
1884 (return *empty-type*))
1885 (let* ((interval (numeric-type->interval n))
1886 (low (interval-low interval))
1887 (high (interval-high interval)))
1889 (setf low (car low)))
1891 (setf high (car high)))
1901 ;;; Define optimizers for FLOOR and CEILING.
1903 ((def (name q-name r-name)
1904 (let ((q-aux (symbolicate q-name "-AUX"))
1905 (r-aux (symbolicate r-name "-AUX")))
1907 ;; Compute type of quotient (first) result.
1908 (defun ,q-aux (number-type divisor-type)
1909 (let* ((number-interval
1910 (numeric-type->interval number-type))
1912 (numeric-type->interval divisor-type))
1913 (quot (,q-name (interval-div number-interval
1914 divisor-interval))))
1915 (specifier-type `(integer ,(or (interval-low quot) '*)
1916 ,(or (interval-high quot) '*)))))
1917 ;; Compute type of remainder.
1918 (defun ,r-aux (number-type divisor-type)
1919 (let* ((divisor-interval
1920 (numeric-type->interval divisor-type))
1921 (rem (,r-name divisor-interval))
1922 (result-type (rem-result-type number-type divisor-type)))
1923 (multiple-value-bind (class format)
1926 (values 'integer nil))
1928 (values 'rational nil))
1929 ((or single-float double-float #!+long-float long-float)
1930 (values 'float result-type))
1932 (values 'float nil))
1935 (when (member result-type '(float single-float double-float
1936 #!+long-float long-float))
1937 ;; Make sure that the limits on the interval have
1939 (setf rem (interval-func (lambda (x)
1940 (coerce-for-bound x result-type))
1942 (make-numeric-type :class class
1944 :low (interval-low rem)
1945 :high (interval-high rem)))))
1946 ;; the optimizer itself
1947 (defoptimizer (,name derive-type) ((number divisor))
1948 (flet ((derive-q (n d same-arg)
1949 (declare (ignore same-arg))
1950 (if (and (numeric-type-real-p n)
1951 (numeric-type-real-p d))
1954 (derive-r (n d same-arg)
1955 (declare (ignore same-arg))
1956 (if (and (numeric-type-real-p n)
1957 (numeric-type-real-p d))
1960 (let ((quot (two-arg-derive-type
1961 number divisor #'derive-q #',name))
1962 (rem (two-arg-derive-type
1963 number divisor #'derive-r #'mod)))
1964 (when (and quot rem)
1965 (make-values-type :required (list quot rem))))))))))
1967 (def floor floor-quotient-bound floor-rem-bound)
1968 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1970 ;;; Define optimizers for FFLOOR and FCEILING
1971 (macrolet ((def (name q-name r-name)
1972 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1973 (r-aux (symbolicate r-name "-AUX")))
1975 ;; Compute type of quotient (first) result.
1976 (defun ,q-aux (number-type divisor-type)
1977 (let* ((number-interval
1978 (numeric-type->interval number-type))
1980 (numeric-type->interval divisor-type))
1981 (quot (,q-name (interval-div number-interval
1983 (res-type (numeric-contagion number-type
1986 :class (numeric-type-class res-type)
1987 :format (numeric-type-format res-type)
1988 :low (interval-low quot)
1989 :high (interval-high quot))))
1991 (defoptimizer (,name derive-type) ((number divisor))
1992 (flet ((derive-q (n d same-arg)
1993 (declare (ignore same-arg))
1994 (if (and (numeric-type-real-p n)
1995 (numeric-type-real-p d))
1998 (derive-r (n d same-arg)
1999 (declare (ignore same-arg))
2000 (if (and (numeric-type-real-p n)
2001 (numeric-type-real-p d))
2004 (let ((quot (two-arg-derive-type
2005 number divisor #'derive-q #',name))
2006 (rem (two-arg-derive-type
2007 number divisor #'derive-r #'mod)))
2008 (when (and quot rem)
2009 (make-values-type :required (list quot rem))))))))))
2011 (def ffloor floor-quotient-bound floor-rem-bound)
2012 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
2014 ;;; functions to compute the bounds on the quotient and remainder for
2015 ;;; the FLOOR function
2016 (defun floor-quotient-bound (quot)
2017 ;; Take the floor of the quotient and then massage it into what we
2019 (let ((lo (interval-low quot))
2020 (hi (interval-high quot)))
2021 ;; Take the floor of the lower bound. The result is always a
2022 ;; closed lower bound.
2024 (floor (type-bound-number lo))
2026 ;; For the upper bound, we need to be careful.
2029 ;; An open bound. We need to be careful here because
2030 ;; the floor of '(10.0) is 9, but the floor of
2032 (multiple-value-bind (q r) (floor (first hi))
2037 ;; A closed bound, so the answer is obvious.
2041 (make-interval :low lo :high hi)))
2042 (defun floor-rem-bound (div)
2043 ;; The remainder depends only on the divisor. Try to get the
2044 ;; correct sign for the remainder if we can.
2045 (case (interval-range-info div)
2047 ;; The divisor is always positive.
2048 (let ((rem (interval-abs div)))
2049 (setf (interval-low rem) 0)
2050 (when (and (numberp (interval-high rem))
2051 (not (zerop (interval-high rem))))
2052 ;; The remainder never contains the upper bound. However,
2053 ;; watch out for the case where the high limit is zero!
2054 (setf (interval-high rem) (list (interval-high rem))))
2057 ;; The divisor is always negative.
2058 (let ((rem (interval-neg (interval-abs div))))
2059 (setf (interval-high rem) 0)
2060 (when (numberp (interval-low rem))
2061 ;; The remainder never contains the lower bound.
2062 (setf (interval-low rem) (list (interval-low rem))))
2065 ;; The divisor can be positive or negative. All bets off. The
2066 ;; magnitude of remainder is the maximum value of the divisor.
2067 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2068 ;; The bound never reaches the limit, so make the interval open.
2069 (make-interval :low (if limit
2072 :high (list limit))))))
2074 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
2075 => #S(INTERVAL :LOW 0 :HIGH 10)
2076 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2077 => #S(INTERVAL :LOW 0 :HIGH 10)
2078 (floor-quotient-bound (make-interval :low 0.3 :high 10))
2079 => #S(INTERVAL :LOW 0 :HIGH 10)
2080 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
2081 => #S(INTERVAL :LOW 0 :HIGH 9)
2082 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
2083 => #S(INTERVAL :LOW 0 :HIGH 10)
2084 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
2085 => #S(INTERVAL :LOW 0 :HIGH 10)
2086 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2087 => #S(INTERVAL :LOW -2 :HIGH 10)
2088 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2089 => #S(INTERVAL :LOW -1 :HIGH 10)
2090 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
2091 => #S(INTERVAL :LOW -1 :HIGH 10)
2093 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
2094 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2095 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
2096 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2097 (floor-rem-bound (make-interval :low -10 :high -2.3))
2098 #S(INTERVAL :LOW (-10) :HIGH 0)
2099 (floor-rem-bound (make-interval :low 0.3 :high 10))
2100 => #S(INTERVAL :LOW 0 :HIGH '(10))
2101 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
2102 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
2103 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
2104 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2107 ;;; same functions for CEILING
2108 (defun ceiling-quotient-bound (quot)
2109 ;; Take the ceiling of the quotient and then massage it into what we
2111 (let ((lo (interval-low quot))
2112 (hi (interval-high quot)))
2113 ;; Take the ceiling of the upper bound. The result is always a
2114 ;; closed upper bound.
2116 (ceiling (type-bound-number hi))
2118 ;; For the lower bound, we need to be careful.
2121 ;; An open bound. We need to be careful here because
2122 ;; the ceiling of '(10.0) is 11, but the ceiling of
2124 (multiple-value-bind (q r) (ceiling (first lo))
2129 ;; A closed bound, so the answer is obvious.
2133 (make-interval :low lo :high hi)))
2134 (defun ceiling-rem-bound (div)
2135 ;; The remainder depends only on the divisor. Try to get the
2136 ;; correct sign for the remainder if we can.
2137 (case (interval-range-info div)
2139 ;; Divisor is always positive. The remainder is negative.
2140 (let ((rem (interval-neg (interval-abs div))))
2141 (setf (interval-high rem) 0)
2142 (when (and (numberp (interval-low rem))
2143 (not (zerop (interval-low rem))))
2144 ;; The remainder never contains the upper bound. However,
2145 ;; watch out for the case when the upper bound is zero!
2146 (setf (interval-low rem) (list (interval-low rem))))
2149 ;; Divisor is always negative. The remainder is positive
2150 (let ((rem (interval-abs div)))
2151 (setf (interval-low rem) 0)
2152 (when (numberp (interval-high rem))
2153 ;; The remainder never contains the lower bound.
2154 (setf (interval-high rem) (list (interval-high rem))))
2157 ;; The divisor can be positive or negative. All bets off. The
2158 ;; magnitude of remainder is the maximum value of the divisor.
2159 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2160 ;; The bound never reaches the limit, so make the interval open.
2161 (make-interval :low (if limit
2164 :high (list limit))))))
2167 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2168 => #S(INTERVAL :LOW 1 :HIGH 11)
2169 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2170 => #S(INTERVAL :LOW 1 :HIGH 11)
2171 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2172 => #S(INTERVAL :LOW 1 :HIGH 10)
2173 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2174 => #S(INTERVAL :LOW 1 :HIGH 10)
2175 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2176 => #S(INTERVAL :LOW 1 :HIGH 11)
2177 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2178 => #S(INTERVAL :LOW 1 :HIGH 11)
2179 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2180 => #S(INTERVAL :LOW -1 :HIGH 11)
2181 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2182 => #S(INTERVAL :LOW 0 :HIGH 11)
2183 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2184 => #S(INTERVAL :LOW -1 :HIGH 11)
2186 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2187 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2188 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2189 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2190 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2191 => #S(INTERVAL :LOW 0 :HIGH (10))
2192 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2193 => #S(INTERVAL :LOW (-10) :HIGH 0)
2194 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2195 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2196 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2197 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2200 (defun truncate-quotient-bound (quot)
2201 ;; For positive quotients, truncate is exactly like floor. For
2202 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2203 ;; it's the union of the two pieces.
2204 (case (interval-range-info quot)
2207 (floor-quotient-bound quot))
2209 ;; just like CEILING
2210 (ceiling-quotient-bound quot))
2212 ;; Split the interval into positive and negative pieces, compute
2213 ;; the result for each piece and put them back together.
2214 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2215 (interval-merge-pair (ceiling-quotient-bound neg)
2216 (floor-quotient-bound pos))))))
2218 (defun truncate-rem-bound (num div)
2219 ;; This is significantly more complicated than FLOOR or CEILING. We
2220 ;; need both the number and the divisor to determine the range. The
2221 ;; basic idea is to split the ranges of NUM and DEN into positive
2222 ;; and negative pieces and deal with each of the four possibilities
2224 (case (interval-range-info num)
2226 (case (interval-range-info div)
2228 (floor-rem-bound div))
2230 (ceiling-rem-bound div))
2232 (destructuring-bind (neg pos) (interval-split 0 div t t)
2233 (interval-merge-pair (truncate-rem-bound num neg)
2234 (truncate-rem-bound num pos))))))
2236 (case (interval-range-info div)
2238 (ceiling-rem-bound div))
2240 (floor-rem-bound div))
2242 (destructuring-bind (neg pos) (interval-split 0 div t t)
2243 (interval-merge-pair (truncate-rem-bound num neg)
2244 (truncate-rem-bound num pos))))))
2246 (destructuring-bind (neg pos) (interval-split 0 num t t)
2247 (interval-merge-pair (truncate-rem-bound neg div)
2248 (truncate-rem-bound pos div))))))
2251 ;;; Derive useful information about the range. Returns three values:
2252 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2253 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2254 ;;; - The abs of the maximal value if there is one, or nil if it is
2256 (defun numeric-range-info (low high)
2257 (cond ((and low (not (minusp low)))
2258 (values '+ low high))
2259 ((and high (not (plusp high)))
2260 (values '- (- high) (if low (- low) nil)))
2262 (values nil 0 (and low high (max (- low) high))))))
2264 (defun integer-truncate-derive-type
2265 (number-low number-high divisor-low divisor-high)
2266 ;; The result cannot be larger in magnitude than the number, but the
2267 ;; sign might change. If we can determine the sign of either the
2268 ;; number or the divisor, we can eliminate some of the cases.
2269 (multiple-value-bind (number-sign number-min number-max)
2270 (numeric-range-info number-low number-high)
2271 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2272 (numeric-range-info divisor-low divisor-high)
2273 (when (and divisor-max (zerop divisor-max))
2274 ;; We've got a problem: guaranteed division by zero.
2275 (return-from integer-truncate-derive-type t))
2276 (when (zerop divisor-min)
2277 ;; We'll assume that they aren't going to divide by zero.
2279 (cond ((and number-sign divisor-sign)
2280 ;; We know the sign of both.
2281 (if (eq number-sign divisor-sign)
2282 ;; Same sign, so the result will be positive.
2283 `(integer ,(if divisor-max
2284 (truncate number-min divisor-max)
2287 (truncate number-max divisor-min)
2289 ;; Different signs, the result will be negative.
2290 `(integer ,(if number-max
2291 (- (truncate number-max divisor-min))
2294 (- (truncate number-min divisor-max))
2296 ((eq divisor-sign '+)
2297 ;; The divisor is positive. Therefore, the number will just
2298 ;; become closer to zero.
2299 `(integer ,(if number-low
2300 (truncate number-low divisor-min)
2303 (truncate number-high divisor-min)
2305 ((eq divisor-sign '-)
2306 ;; The divisor is negative. Therefore, the absolute value of
2307 ;; the number will become closer to zero, but the sign will also
2309 `(integer ,(if number-high
2310 (- (truncate number-high divisor-min))
2313 (- (truncate number-low divisor-min))
2315 ;; The divisor could be either positive or negative.
2317 ;; The number we are dividing has a bound. Divide that by the
2318 ;; smallest posible divisor.
2319 (let ((bound (truncate number-max divisor-min)))
2320 `(integer ,(- bound) ,bound)))
2322 ;; The number we are dividing is unbounded, so we can't tell
2323 ;; anything about the result.
2326 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2327 (defun integer-rem-derive-type
2328 (number-low number-high divisor-low divisor-high)
2329 (if (and divisor-low divisor-high)
2330 ;; We know the range of the divisor, and the remainder must be
2331 ;; smaller than the divisor. We can tell the sign of the
2332 ;; remainder if we know the sign of the number.
2333 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2334 `(integer ,(if (or (null number-low)
2335 (minusp number-low))
2338 ,(if (or (null number-high)
2339 (plusp number-high))
2342 ;; The divisor is potentially either very positive or very
2343 ;; negative. Therefore, the remainder is unbounded, but we might
2344 ;; be able to tell something about the sign from the number.
2345 `(integer ,(if (and number-low (not (minusp number-low)))
2346 ;; The number we are dividing is positive.
2347 ;; Therefore, the remainder must be positive.
2350 ,(if (and number-high (not (plusp number-high)))
2351 ;; The number we are dividing is negative.
2352 ;; Therefore, the remainder must be negative.
2356 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2357 (defoptimizer (random derive-type) ((bound &optional state))
2358 (let ((type (lvar-type bound)))
2359 (when (numeric-type-p type)
2360 (let ((class (numeric-type-class type))
2361 (high (numeric-type-high type))
2362 (format (numeric-type-format type)))
2366 :low (coerce 0 (or format class 'real))
2367 :high (cond ((not high) nil)
2368 ((eq class 'integer) (max (1- high) 0))
2369 ((or (consp high) (zerop high)) high)
2372 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2373 (defun random-derive-type-aux (type)
2374 (let ((class (numeric-type-class type))
2375 (high (numeric-type-high type))
2376 (format (numeric-type-format type)))
2380 :low (coerce 0 (or format class 'real))
2381 :high (cond ((not high) nil)
2382 ((eq class 'integer) (max (1- high) 0))
2383 ((or (consp high) (zerop high)) high)
2386 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2387 (defoptimizer (random derive-type) ((bound &optional state))
2388 (one-arg-derive-type bound #'random-derive-type-aux nil))
2390 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2392 ;;; Return the maximum number of bits an integer of the supplied type
2393 ;;; can take up, or NIL if it is unbounded. The second (third) value
2394 ;;; is T if the integer can be positive (negative) and NIL if not.
2395 ;;; Zero counts as positive.
2396 (defun integer-type-length (type)
2397 (if (numeric-type-p type)
2398 (let ((min (numeric-type-low type))
2399 (max (numeric-type-high type)))
2400 (values (and min max (max (integer-length min) (integer-length max)))
2401 (or (null max) (not (minusp max)))
2402 (or (null min) (minusp min))))
2405 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2406 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2407 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2408 ;;; versions in CMUCL, from which these functions copy liberally.
2410 (defun logand-derive-unsigned-low-bound (x y)
2411 (let ((a (numeric-type-low x))
2412 (b (numeric-type-high x))
2413 (c (numeric-type-low y))
2414 (d (numeric-type-high y)))
2415 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2417 (unless (zerop (logand m (lognot a) (lognot c)))
2418 (let ((temp (logandc2 (logior a m) (1- m))))
2422 (setf temp (logandc2 (logior c m) (1- m)))
2426 finally (return (logand a c)))))
2428 (defun logand-derive-unsigned-high-bound (x y)
2429 (let ((a (numeric-type-low x))
2430 (b (numeric-type-high x))
2431 (c (numeric-type-low y))
2432 (d (numeric-type-high y)))
2433 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2436 ((not (zerop (logand b (lognot d) m)))
2437 (let ((temp (logior (logandc2 b m) (1- m))))
2441 ((not (zerop (logand (lognot b) d m)))
2442 (let ((temp (logior (logandc2 d m) (1- m))))
2446 finally (return (logand b d)))))
2448 (defun logand-derive-type-aux (x y &optional same-leaf)
2450 (return-from logand-derive-type-aux x))
2451 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2452 (declare (ignore x-pos))
2453 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2454 (declare (ignore y-pos))
2456 ;; X must be positive.
2458 ;; They must both be positive.
2459 (cond ((and (null x-len) (null y-len))
2460 (specifier-type 'unsigned-byte))
2462 (specifier-type `(unsigned-byte* ,y-len)))
2464 (specifier-type `(unsigned-byte* ,x-len)))
2466 (let ((low (logand-derive-unsigned-low-bound x y))
2467 (high (logand-derive-unsigned-high-bound x y)))
2468 (specifier-type `(integer ,low ,high)))))
2469 ;; X is positive, but Y might be negative.
2471 (specifier-type 'unsigned-byte))
2473 (specifier-type `(unsigned-byte* ,x-len)))))
2474 ;; X might be negative.
2476 ;; Y must be positive.
2478 (specifier-type 'unsigned-byte))
2479 (t (specifier-type `(unsigned-byte* ,y-len))))
2480 ;; Either might be negative.
2481 (if (and x-len y-len)
2482 ;; The result is bounded.
2483 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2484 ;; We can't tell squat about the result.
2485 (specifier-type 'integer)))))))
2487 (defun logior-derive-unsigned-low-bound (x y)
2488 (let ((a (numeric-type-low x))
2489 (b (numeric-type-high x))
2490 (c (numeric-type-low y))
2491 (d (numeric-type-high y)))
2492 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2495 ((not (zerop (logandc2 (logand c m) a)))
2496 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2500 ((not (zerop (logandc2 (logand a m) c)))
2501 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2505 finally (return (logior a c)))))
2507 (defun logior-derive-unsigned-high-bound (x y)
2508 (let ((a (numeric-type-low x))
2509 (b (numeric-type-high x))
2510 (c (numeric-type-low y))
2511 (d (numeric-type-high y)))
2512 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2514 (unless (zerop (logand b d m))
2515 (let ((temp (logior (- b m) (1- m))))
2519 (setf temp (logior (- d m) (1- m)))
2523 finally (return (logior b d)))))
2525 (defun logior-derive-type-aux (x y &optional same-leaf)
2527 (return-from logior-derive-type-aux x))
2528 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2529 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2531 ((and (not x-neg) (not y-neg))
2532 ;; Both are positive.
2533 (if (and x-len y-len)
2534 (let ((low (logior-derive-unsigned-low-bound x y))
2535 (high (logior-derive-unsigned-high-bound x y)))
2536 (specifier-type `(integer ,low ,high)))
2537 (specifier-type `(unsigned-byte* *))))
2539 ;; X must be negative.
2541 ;; Both are negative. The result is going to be negative
2542 ;; and be the same length or shorter than the smaller.
2543 (if (and x-len y-len)
2545 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2547 (specifier-type '(integer * -1)))
2548 ;; X is negative, but we don't know about Y. The result
2549 ;; will be negative, but no more negative than X.
2551 `(integer ,(or (numeric-type-low x) '*)
2554 ;; X might be either positive or negative.
2556 ;; But Y is negative. The result will be negative.
2558 `(integer ,(or (numeric-type-low y) '*)
2560 ;; We don't know squat about either. It won't get any bigger.
2561 (if (and x-len y-len)
2563 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2565 (specifier-type 'integer))))))))
2567 (defun logxor-derive-unsigned-low-bound (x y)
2568 (let ((a (numeric-type-low x))
2569 (b (numeric-type-high x))
2570 (c (numeric-type-low y))
2571 (d (numeric-type-high y)))
2572 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2575 ((not (zerop (logandc2 (logand c m) a)))
2576 (let ((temp (logand (logior a m)
2580 ((not (zerop (logandc2 (logand a m) c)))
2581 (let ((temp (logand (logior c m)
2585 finally (return (logxor a c)))))
2587 (defun logxor-derive-unsigned-high-bound (x y)
2588 (let ((a (numeric-type-low x))
2589 (b (numeric-type-high x))
2590 (c (numeric-type-low y))
2591 (d (numeric-type-high y)))
2592 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2594 (unless (zerop (logand b d m))
2595 (let ((temp (logior (- b m) (1- m))))
2597 ((>= temp a) (setf b temp))
2598 (t (let ((temp (logior (- d m) (1- m))))
2601 finally (return (logxor b d)))))
2603 (defun logxor-derive-type-aux (x y &optional same-leaf)
2605 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2606 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2607 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2609 ((and (not x-neg) (not y-neg))
2610 ;; Both are positive
2611 (if (and x-len y-len)
2612 (let ((low (logxor-derive-unsigned-low-bound x y))
2613 (high (logxor-derive-unsigned-high-bound x y)))
2614 (specifier-type `(integer ,low ,high)))
2615 (specifier-type '(unsigned-byte* *))))
2616 ((and (not x-pos) (not y-pos))
2617 ;; Both are negative. The result will be positive, and as long
2619 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2622 ((or (and (not x-pos) (not y-neg))
2623 (and (not y-pos) (not x-neg)))
2624 ;; Either X is negative and Y is positive or vice-versa. The
2625 ;; result will be negative.
2626 (specifier-type `(integer ,(if (and x-len y-len)
2627 (ash -1 (max x-len y-len))
2630 ;; We can't tell what the sign of the result is going to be.
2631 ;; All we know is that we don't create new bits.
2633 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2635 (specifier-type 'integer))))))
2637 (macrolet ((deffrob (logfun)
2638 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2639 `(defoptimizer (,logfun derive-type) ((x y))
2640 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2645 (defoptimizer (logeqv derive-type) ((x y))
2646 (two-arg-derive-type x y (lambda (x y same-leaf)
2647 (lognot-derive-type-aux
2648 (logxor-derive-type-aux x y same-leaf)))
2650 (defoptimizer (lognand derive-type) ((x y))
2651 (two-arg-derive-type x y (lambda (x y same-leaf)
2652 (lognot-derive-type-aux
2653 (logand-derive-type-aux x y same-leaf)))
2655 (defoptimizer (lognor derive-type) ((x y))
2656 (two-arg-derive-type x y (lambda (x y same-leaf)
2657 (lognot-derive-type-aux
2658 (logior-derive-type-aux x y same-leaf)))
2660 (defoptimizer (logandc1 derive-type) ((x y))
2661 (two-arg-derive-type x y (lambda (x y same-leaf)
2663 (specifier-type '(eql 0))
2664 (logand-derive-type-aux
2665 (lognot-derive-type-aux x) y nil)))
2667 (defoptimizer (logandc2 derive-type) ((x y))
2668 (two-arg-derive-type x y (lambda (x y same-leaf)
2670 (specifier-type '(eql 0))
2671 (logand-derive-type-aux
2672 x (lognot-derive-type-aux y) nil)))
2674 (defoptimizer (logorc1 derive-type) ((x y))
2675 (two-arg-derive-type x y (lambda (x y same-leaf)
2677 (specifier-type '(eql -1))
2678 (logior-derive-type-aux
2679 (lognot-derive-type-aux x) y nil)))
2681 (defoptimizer (logorc2 derive-type) ((x y))
2682 (two-arg-derive-type x y (lambda (x y same-leaf)
2684 (specifier-type '(eql -1))
2685 (logior-derive-type-aux
2686 x (lognot-derive-type-aux y) nil)))
2689 ;;;; miscellaneous derive-type methods
2691 (defoptimizer (integer-length derive-type) ((x))
2692 (let ((x-type (lvar-type x)))
2693 (when (numeric-type-p x-type)
2694 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2695 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2696 ;; careful about LO or HI being NIL, though. Also, if 0 is
2697 ;; contained in X, the lower bound is obviously 0.
2698 (flet ((null-or-min (a b)
2699 (and a b (min (integer-length a)
2700 (integer-length b))))
2702 (and a b (max (integer-length a)
2703 (integer-length b)))))
2704 (let* ((min (numeric-type-low x-type))
2705 (max (numeric-type-high x-type))
2706 (min-len (null-or-min min max))
2707 (max-len (null-or-max min max)))
2708 (when (ctypep 0 x-type)
2710 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2712 (defoptimizer (isqrt derive-type) ((x))
2713 (let ((x-type (lvar-type x)))
2714 (when (numeric-type-p x-type)
2715 (let* ((lo (numeric-type-low x-type))
2716 (hi (numeric-type-high x-type))
2717 (lo-res (if lo (isqrt lo) '*))
2718 (hi-res (if hi (isqrt hi) '*)))
2719 (specifier-type `(integer ,lo-res ,hi-res))))))
2721 (defoptimizer (char-code derive-type) ((char))
2722 (let ((type (type-intersection (lvar-type char) (specifier-type 'character))))
2723 (cond ((member-type-p type)
2726 ,@(loop for member in (member-type-members type)
2727 when (characterp member)
2728 collect (char-code member)))))
2729 ((sb!kernel::character-set-type-p type)
2732 ,@(loop for (low . high)
2733 in (character-set-type-pairs type)
2734 collect `(integer ,low ,high)))))
2735 ((csubtypep type (specifier-type 'base-char))
2737 `(mod ,base-char-code-limit)))
2740 `(mod ,char-code-limit))))))
2742 (defoptimizer (code-char derive-type) ((code))
2743 (let ((type (lvar-type code)))
2744 ;; FIXME: unions of integral ranges? It ought to be easier to do
2745 ;; this, given that CHARACTER-SET is basically an integral range
2746 ;; type. -- CSR, 2004-10-04
2747 (when (numeric-type-p type)
2748 (let* ((lo (numeric-type-low type))
2749 (hi (numeric-type-high type))
2750 (type (specifier-type `(character-set ((,lo . ,hi))))))
2752 ;; KLUDGE: when running on the host, we lose a slight amount
2753 ;; of precision so that we don't have to "unparse" types
2754 ;; that formally we can't, such as (CHARACTER-SET ((0
2755 ;; . 0))). -- CSR, 2004-10-06
2757 ((csubtypep type (specifier-type 'standard-char)) type)
2759 ((csubtypep type (specifier-type 'base-char))
2760 (specifier-type 'base-char))
2762 ((csubtypep type (specifier-type 'extended-char))
2763 (specifier-type 'extended-char))
2764 (t #+sb-xc-host (specifier-type 'character)
2765 #-sb-xc-host type))))))
2767 (defoptimizer (values derive-type) ((&rest values))
2768 (make-values-type :required (mapcar #'lvar-type values)))
2770 (defun signum-derive-type-aux (type)
2771 (if (eq (numeric-type-complexp type) :complex)
2772 (let* ((format (case (numeric-type-class type)
2773 ((integer rational) 'single-float)
2774 (t (numeric-type-format type))))
2775 (bound-format (or format 'float)))
2776 (make-numeric-type :class 'float
2779 :low (coerce -1 bound-format)
2780 :high (coerce 1 bound-format)))
2781 (let* ((interval (numeric-type->interval type))
2782 (range-info (interval-range-info interval))
2783 (contains-0-p (interval-contains-p 0 interval))
2784 (class (numeric-type-class type))
2785 (format (numeric-type-format type))
2786 (one (coerce 1 (or format class 'real)))
2787 (zero (coerce 0 (or format class 'real)))
2788 (minus-one (coerce -1 (or format class 'real)))
2789 (plus (make-numeric-type :class class :format format
2790 :low one :high one))
2791 (minus (make-numeric-type :class class :format format
2792 :low minus-one :high minus-one))
2793 ;; KLUDGE: here we have a fairly horrible hack to deal
2794 ;; with the schizophrenia in the type derivation engine.
2795 ;; The problem is that the type derivers reinterpret
2796 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2797 ;; 0d0) within the derivation mechanism doesn't include
2798 ;; -0d0. Ugh. So force it in here, instead.
2799 (zero (make-numeric-type :class class :format format
2800 :low (- zero) :high zero)))
2802 (+ (if contains-0-p (type-union plus zero) plus))
2803 (- (if contains-0-p (type-union minus zero) minus))
2804 (t (type-union minus zero plus))))))
2806 (defoptimizer (signum derive-type) ((num))
2807 (one-arg-derive-type num #'signum-derive-type-aux nil))
2809 ;;;; byte operations
2811 ;;;; We try to turn byte operations into simple logical operations.
2812 ;;;; First, we convert byte specifiers into separate size and position
2813 ;;;; arguments passed to internal %FOO functions. We then attempt to
2814 ;;;; transform the %FOO functions into boolean operations when the
2815 ;;;; size and position are constant and the operands are fixnums.
2817 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2818 ;; expressions that evaluate to the SIZE and POSITION of
2819 ;; the byte-specifier form SPEC. We may wrap a let around
2820 ;; the result of the body to bind some variables.
2822 ;; If the spec is a BYTE form, then bind the vars to the
2823 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2824 ;; and BYTE-POSITION. The goal of this transformation is to
2825 ;; avoid consing up byte specifiers and then immediately
2826 ;; throwing them away.
2827 (with-byte-specifier ((size-var pos-var spec) &body body)
2828 (once-only ((spec `(macroexpand ,spec))
2830 `(if (and (consp ,spec)
2831 (eq (car ,spec) 'byte)
2832 (= (length ,spec) 3))
2833 (let ((,size-var (second ,spec))
2834 (,pos-var (third ,spec)))
2836 (let ((,size-var `(byte-size ,,temp))
2837 (,pos-var `(byte-position ,,temp)))
2838 `(let ((,,temp ,,spec))
2841 (define-source-transform ldb (spec int)
2842 (with-byte-specifier (size pos spec)
2843 `(%ldb ,size ,pos ,int)))
2845 (define-source-transform dpb (newbyte spec int)
2846 (with-byte-specifier (size pos spec)
2847 `(%dpb ,newbyte ,size ,pos ,int)))
2849 (define-source-transform mask-field (spec int)
2850 (with-byte-specifier (size pos spec)
2851 `(%mask-field ,size ,pos ,int)))
2853 (define-source-transform deposit-field (newbyte spec int)
2854 (with-byte-specifier (size pos spec)
2855 `(%deposit-field ,newbyte ,size ,pos ,int))))
2857 (defoptimizer (%ldb derive-type) ((size posn num))
2858 (let ((size (lvar-type size)))
2859 (if (and (numeric-type-p size)
2860 (csubtypep size (specifier-type 'integer)))
2861 (let ((size-high (numeric-type-high size)))
2862 (if (and size-high (<= size-high sb!vm:n-word-bits))
2863 (specifier-type `(unsigned-byte* ,size-high))
2864 (specifier-type 'unsigned-byte)))
2867 (defoptimizer (%mask-field derive-type) ((size posn num))
2868 (let ((size (lvar-type size))
2869 (posn (lvar-type posn)))
2870 (if (and (numeric-type-p size)
2871 (csubtypep size (specifier-type 'integer))
2872 (numeric-type-p posn)
2873 (csubtypep posn (specifier-type 'integer)))
2874 (let ((size-high (numeric-type-high size))
2875 (posn-high (numeric-type-high posn)))
2876 (if (and size-high posn-high
2877 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2878 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2879 (specifier-type 'unsigned-byte)))
2882 (defun %deposit-field-derive-type-aux (size posn int)
2883 (let ((size (lvar-type size))
2884 (posn (lvar-type posn))
2885 (int (lvar-type int)))
2886 (when (and (numeric-type-p size)
2887 (numeric-type-p posn)
2888 (numeric-type-p int))
2889 (let ((size-high (numeric-type-high size))
2890 (posn-high (numeric-type-high posn))
2891 (high (numeric-type-high int))
2892 (low (numeric-type-low int)))
2893 (when (and size-high posn-high high low
2894 ;; KLUDGE: we need this cutoff here, otherwise we
2895 ;; will merrily derive the type of %DPB as
2896 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2897 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2898 ;; 1073741822))), with hilarious consequences. We
2899 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2900 ;; over a reasonable amount of shifting, even on
2901 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2902 ;; machine integers are 64-bits. -- CSR,
2904 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2905 (let ((raw-bit-count (max (integer-length high)
2906 (integer-length low)
2907 (+ size-high posn-high))))
2910 `(signed-byte ,(1+ raw-bit-count))
2911 `(unsigned-byte* ,raw-bit-count)))))))))
2913 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2914 (%deposit-field-derive-type-aux size posn int))
2916 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2917 (%deposit-field-derive-type-aux size posn int))
2919 (deftransform %ldb ((size posn int)
2920 (fixnum fixnum integer)
2921 (unsigned-byte #.sb!vm:n-word-bits))
2922 "convert to inline logical operations"
2923 `(logand (ash int (- posn))
2924 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2925 (- size ,sb!vm:n-word-bits))))
2927 (deftransform %mask-field ((size posn int)
2928 (fixnum fixnum integer)
2929 (unsigned-byte #.sb!vm:n-word-bits))
2930 "convert to inline logical operations"
2932 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2933 (- size ,sb!vm:n-word-bits))
2936 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2937 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2938 ;;; as the result type, as that would allow result types that cover
2939 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2940 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2942 (deftransform %dpb ((new size posn int)
2944 (unsigned-byte #.sb!vm:n-word-bits))
2945 "convert to inline logical operations"
2946 `(let ((mask (ldb (byte size 0) -1)))
2947 (logior (ash (logand new mask) posn)
2948 (logand int (lognot (ash mask posn))))))
2950 (deftransform %dpb ((new size posn int)
2952 (signed-byte #.sb!vm:n-word-bits))
2953 "convert to inline logical operations"
2954 `(let ((mask (ldb (byte size 0) -1)))
2955 (logior (ash (logand new mask) posn)
2956 (logand int (lognot (ash mask posn))))))
2958 (deftransform %deposit-field ((new size posn int)
2960 (unsigned-byte #.sb!vm:n-word-bits))
2961 "convert to inline logical operations"
2962 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2963 (logior (logand new mask)
2964 (logand int (lognot mask)))))
2966 (deftransform %deposit-field ((new size posn int)
2968 (signed-byte #.sb!vm:n-word-bits))
2969 "convert to inline logical operations"
2970 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2971 (logior (logand new mask)
2972 (logand int (lognot mask)))))
2974 (defoptimizer (mask-signed-field derive-type) ((size x))
2975 (let ((size (lvar-type size)))
2976 (if (numeric-type-p size)
2977 (let ((size-high (numeric-type-high size)))
2978 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2979 (specifier-type `(signed-byte ,size-high))
2984 ;;; Modular functions
2986 ;;; (ldb (byte s 0) (foo x y ...)) =
2987 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2989 ;;; and similar for other arguments.
2991 (defun make-modular-fun-type-deriver (prototype kind width signedp)
2992 (declare (ignore kind))
2994 (binding* ((info (info :function :info prototype) :exit-if-null)
2995 (fun (fun-info-derive-type info) :exit-if-null)
2996 (mask-type (specifier-type
2998 ((nil) (let ((mask (1- (ash 1 width))))
2999 `(integer ,mask ,mask)))
3000 ((t) `(signed-byte ,width))))))
3002 (let ((res (funcall fun call)))
3004 (if (eq signedp nil)
3005 (logand-derive-type-aux res mask-type))))))
3008 (binding* ((info (info :function :info prototype) :exit-if-null)
3009 (fun (fun-info-derive-type info) :exit-if-null)
3010 (res (funcall fun call) :exit-if-null)
3011 (mask-type (specifier-type
3013 ((nil) (let ((mask (1- (ash 1 width))))
3014 `(integer ,mask ,mask)))
3015 ((t) `(signed-byte ,width))))))
3016 (if (eq signedp nil)
3017 (logand-derive-type-aux res mask-type)))))
3019 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
3021 ;;; For good functions, we just recursively cut arguments; their
3022 ;;; "goodness" means that the result will not increase (in the
3023 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
3024 ;;; replaced with the version, cutting its result to WIDTH or more
3025 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
3026 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
3027 ;;; arguments (maybe to a different width) and returning the name of a
3028 ;;; modular version, if it exists, or NIL. If we have changed
3029 ;;; anything, we need to flush old derived types, because they have
3030 ;;; nothing in common with the new code.
3031 (defun cut-to-width (lvar kind width signedp)
3032 (declare (type lvar lvar) (type (integer 0) width))
3033 (let ((type (specifier-type (if (zerop width)
3036 ((nil) 'unsigned-byte)
3039 (labels ((reoptimize-node (node name)
3040 (setf (node-derived-type node)
3042 (info :function :type name)))
3043 (setf (lvar-%derived-type (node-lvar node)) nil)
3044 (setf (node-reoptimize node) t)
3045 (setf (block-reoptimize (node-block node)) t)
3046 (reoptimize-component (node-component node) :maybe))
3047 (cut-node (node &aux did-something)
3048 (when (and (not (block-delete-p (node-block node)))
3050 (constant-p (ref-leaf node)))
3051 (let* ((constant-value (constant-value (ref-leaf node)))
3052 (new-value (if signedp
3053 (mask-signed-field width constant-value)
3054 (ldb (byte width 0) constant-value))))
3055 (unless (= constant-value new-value)
3056 (change-ref-leaf node (make-constant new-value))
3057 (setf (lvar-%derived-type (node-lvar node)) (make-values-type :required (list (ctype-of new-value))))
3058 (setf (block-reoptimize (node-block node)) t)
3059 (reoptimize-component (node-component node) :maybe)
3060 (return-from cut-node t))))
3061 (when (and (not (block-delete-p (node-block node)))
3062 (combination-p node)
3063 (eq (basic-combination-kind node) :known))
3064 (let* ((fun-ref (lvar-use (combination-fun node)))
3065 (fun-name (leaf-source-name (ref-leaf fun-ref)))
3066 (modular-fun (find-modular-version fun-name kind signedp width)))
3067 (when (and modular-fun
3068 (not (and (eq fun-name 'logand)
3070 (single-value-type (node-derived-type node))
3072 (binding* ((name (etypecase modular-fun
3073 ((eql :good) fun-name)
3075 (modular-fun-info-name modular-fun))
3077 (funcall modular-fun node width)))
3079 (unless (eql modular-fun :good)
3080 (setq did-something t)
3083 (find-free-fun name "in a strange place"))
3084 (setf (combination-kind node) :full))
3085 (unless (functionp modular-fun)
3086 (dolist (arg (basic-combination-args node))
3087 (when (cut-lvar arg)
3088 (setq did-something t))))
3090 (reoptimize-node node name))
3092 (cut-lvar (lvar &aux did-something)
3093 (do-uses (node lvar)
3094 (when (cut-node node)
3095 (setq did-something t)))
3099 (defun best-modular-version (width signedp)
3100 ;; 1. exact width-matched :untagged
3101 ;; 2. >/>= width-matched :tagged
3102 ;; 3. >/>= width-matched :untagged
3103 (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class*))
3104 (uswidths (modular-class-widths *untagged-signed-modular-class*))
3105 (uwidths (merge 'list uuwidths uswidths #'< :key #'car))
3106 (twidths (modular-class-widths *tagged-modular-class*)))
3107 (let ((exact (find (cons width signedp) uwidths :test #'equal)))
3109 (return-from best-modular-version (values width :untagged signedp))))
3110 (flet ((inexact-match (w)
3112 ((eq signedp (cdr w)) (<= width (car w)))
3113 ((eq signedp nil) (< width (car w))))))
3114 (let ((tgt (find-if #'inexact-match twidths)))
3116 (return-from best-modular-version
3117 (values (car tgt) :tagged (cdr tgt)))))
3118 (let ((ugt (find-if #'inexact-match uwidths)))
3120 (return-from best-modular-version
3121 (values (car ugt) :untagged (cdr ugt))))))))
3123 (defoptimizer (logand optimizer) ((x y) node)
3124 (let ((result-type (single-value-type (node-derived-type node))))
3125 (when (numeric-type-p result-type)
3126 (let ((low (numeric-type-low result-type))
3127 (high (numeric-type-high result-type)))
3128 (when (and (numberp low)
3131 (let ((width (integer-length high)))
3132 (multiple-value-bind (w kind signedp)
3133 (best-modular-version width nil)
3135 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP).
3137 ;; FIXME: I think the FIXME (which is from APD) above
3138 ;; implies that CUT-TO-WIDTH should do /everything/
3139 ;; that's required, including reoptimizing things
3140 ;; itself that it knows are necessary. At the moment,
3141 ;; CUT-TO-WIDTH sets up some new calls with
3142 ;; combination-type :FULL, which later get noticed as
3143 ;; known functions and properly converted.
3145 ;; We cut to W not WIDTH if SIGNEDP is true, because
3146 ;; signed constant replacement needs to know which bit
3147 ;; in the field is the signed bit.
3148 (let ((xact (cut-to-width x kind (if signedp w width) signedp))
3149 (yact (cut-to-width y kind (if signedp w width) signedp)))
3150 (declare (ignore xact yact))
3151 nil) ; After fixing above, replace with T, meaning
3152 ; "don't reoptimize this (LOGAND) node any more".
3155 (defoptimizer (mask-signed-field optimizer) ((width x) node)
3156 (let ((result-type (single-value-type (node-derived-type node))))
3157 (when (numeric-type-p result-type)
3158 (let ((low (numeric-type-low result-type))
3159 (high (numeric-type-high result-type)))
3160 (when (and (numberp low) (numberp high))
3161 (let ((width (max (integer-length high) (integer-length low))))
3162 (multiple-value-bind (w kind)
3163 (best-modular-version width t)
3165 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND W T).
3166 ;; [ see comment above in LOGAND optimizer ]
3167 (cut-to-width x kind w t)
3168 nil ; After fixing above, replace with T.
3171 ;;; miscellanous numeric transforms
3173 ;;; If a constant appears as the first arg, swap the args.
3174 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
3175 (if (and (constant-lvar-p x)
3176 (not (constant-lvar-p y)))
3177 `(,(lvar-fun-name (basic-combination-fun node))
3180 (give-up-ir1-transform)))
3182 (dolist (x '(= char= + * logior logand logxor))
3183 (%deftransform x '(function * *) #'commutative-arg-swap
3184 "place constant arg last"))
3186 ;;; Handle the case of a constant BOOLE-CODE.
3187 (deftransform boole ((op x y) * *)
3188 "convert to inline logical operations"
3189 (unless (constant-lvar-p op)
3190 (give-up-ir1-transform "BOOLE code is not a constant."))
3191 (let ((control (lvar-value op)))
3193 (#.sb!xc:boole-clr 0)
3194 (#.sb!xc:boole-set -1)
3195 (#.sb!xc:boole-1 'x)
3196 (#.sb!xc:boole-2 'y)
3197 (#.sb!xc:boole-c1 '(lognot x))
3198 (#.sb!xc:boole-c2 '(lognot y))
3199 (#.sb!xc:boole-and '(logand x y))
3200 (#.sb!xc:boole-ior '(logior x y))
3201 (#.sb!xc:boole-xor '(logxor x y))
3202 (#.sb!xc:boole-eqv '(logeqv x y))
3203 (#.sb!xc:boole-nand '(lognand x y))
3204 (#.sb!xc:boole-nor '(lognor x y))
3205 (#.sb!xc:boole-andc1 '(logandc1 x y))
3206 (#.sb!xc:boole-andc2 '(logandc2 x y))
3207 (#.sb!xc:boole-orc1 '(logorc1 x y))
3208 (#.sb!xc:boole-orc2 '(logorc2 x y))
3210 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
3213 ;;;; converting special case multiply/divide to shifts
3215 ;;; If arg is a constant power of two, turn * into a shift.
3216 (deftransform * ((x y) (integer integer) *)
3217 "convert x*2^k to shift"
3218 (unless (constant-lvar-p y)
3219 (give-up-ir1-transform))
3220 (let* ((y (lvar-value y))
3222 (len (1- (integer-length y-abs))))
3223 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3224 (give-up-ir1-transform))
3229 ;;; These must come before the ones below, so that they are tried
3230 ;;; first. Since %FLOOR and %CEILING are inlined, this allows
3231 ;;; the general case to be handled by TRUNCATE transforms.
3232 (deftransform floor ((x y))
3235 (deftransform ceiling ((x y))
3238 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3239 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3241 (flet ((frob (y ceil-p)
3242 (unless (constant-lvar-p y)
3243 (give-up-ir1-transform))
3244 (let* ((y (lvar-value y))
3246 (len (1- (integer-length y-abs))))
3247 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3248 (give-up-ir1-transform))
3249 (let ((shift (- len))
3251 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
3252 `(let ((x (+ x ,delta)))
3254 `(values (ash (- x) ,shift)
3255 (- (- (logand (- x) ,mask)) ,delta))
3256 `(values (ash x ,shift)
3257 (- (logand x ,mask) ,delta))))))))
3258 (deftransform floor ((x y) (integer integer) *)
3259 "convert division by 2^k to shift"
3261 (deftransform ceiling ((x y) (integer integer) *)
3262 "convert division by 2^k to shift"
3265 ;;; Do the same for MOD.
3266 (deftransform mod ((x y) (integer integer) *)
3267 "convert remainder mod 2^k to LOGAND"
3268 (unless (constant-lvar-p y)
3269 (give-up-ir1-transform))
3270 (let* ((y (lvar-value y))
3272 (len (1- (integer-length y-abs))))
3273 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3274 (give-up-ir1-transform))
3275 (let ((mask (1- y-abs)))
3277 `(- (logand (- x) ,mask))
3278 `(logand x ,mask)))))
3280 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3281 (deftransform truncate ((x y) (integer integer))
3282 "convert division by 2^k to shift"
3283 (unless (constant-lvar-p y)
3284 (give-up-ir1-transform))
3285 (let* ((y (lvar-value y))
3287 (len (1- (integer-length y-abs))))
3288 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3289 (give-up-ir1-transform))
3290 (let* ((shift (- len))
3293 (values ,(if (minusp y)
3295 `(- (ash (- x) ,shift)))
3296 (- (logand (- x) ,mask)))
3297 (values ,(if (minusp y)
3298 `(ash (- ,mask x) ,shift)
3300 (logand x ,mask))))))
3302 ;;; And the same for REM.
3303 (deftransform rem ((x y) (integer integer) *)
3304 "convert remainder mod 2^k to LOGAND"
3305 (unless (constant-lvar-p y)
3306 (give-up-ir1-transform))
3307 (let* ((y (lvar-value y))
3309 (len (1- (integer-length y-abs))))
3310 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3311 (give-up-ir1-transform))
3312 (let ((mask (1- y-abs)))
3314 (- (logand (- x) ,mask))
3315 (logand x ,mask)))))
3317 ;;; Return an expression to calculate the integer quotient of X and
3318 ;;; constant Y, using multiplication, shift and add/sub instead of
3319 ;;; division. Both arguments must be unsigned, fit in a machine word and
3320 ;;; Y must neither be zero nor a power of two. The quotient is rounded
3322 ;;; The algorithm is taken from the paper "Division by Invariant
3323 ;;; Integers using Multiplication", 1994 by Torbj\"{o}rn Granlund and
3324 ;;; Peter L. Montgomery, Figures 4.2 and 6.2, modified to exclude the
3325 ;;; case of division by powers of two.
3326 ;;; The algorithm includes an adaptive precision argument. Use it, since
3327 ;;; we often have sub-word value ranges. Careful, in this case, we need
3328 ;;; p s.t 2^p > n, not the ceiling of the binary log.
3329 ;;; Also, for some reason, the paper prefers shifting to masking. Mask
3330 ;;; instead. Masking is equivalent to shifting right, then left again;
3331 ;;; all the intermediate values are still words, so we just have to shift
3332 ;;; right a bit more to compensate, at the end.
3334 ;;; The following two examples show an average case and the worst case
3335 ;;; with respect to the complexity of the generated expression, under
3336 ;;; a word size of 64 bits:
3338 ;;; (UNSIGNED-DIV-TRANSFORMER 10 MOST-POSITIVE-WORD) ->
3339 ;;; (ASH (%MULTIPLY (LOGANDC2 X 0) 14757395258967641293) -3)
3341 ;;; (UNSIGNED-DIV-TRANSFORMER 7 MOST-POSITIVE-WORD) ->
3343 ;;; (T1 (%MULTIPLY NUM 2635249153387078803)))
3344 ;;; (ASH (LDB (BYTE 64 0)
3345 ;;; (+ T1 (ASH (LDB (BYTE 64 0)
3350 (defun gen-unsigned-div-by-constant-expr (y max-x)
3351 (declare (type (integer 3 #.most-positive-word) y)
3353 (aver (not (zerop (logand y (1- y)))))
3355 ;; the floor of the binary logarithm of (positive) X
3356 (integer-length (1- x)))
3357 (choose-multiplier (y precision)
3359 (shift l (1- shift))
3360 (expt-2-n+l (expt 2 (+ sb!vm:n-word-bits l)))
3361 (m-low (truncate expt-2-n+l y) (ash m-low -1))
3362 (m-high (truncate (+ expt-2-n+l
3363 (ash expt-2-n+l (- precision)))
3366 ((not (and (< (ash m-low -1) (ash m-high -1))
3368 (values m-high shift)))))
3369 (let ((n (expt 2 sb!vm:n-word-bits))
3370 (precision (integer-length max-x))
3372 (multiple-value-bind (m shift2)
3373 (choose-multiplier y precision)
3374 (when (and (>= m n) (evenp y))
3375 (setq shift1 (ld (logand y (- y))))
3376 (multiple-value-setq (m shift2)
3377 (choose-multiplier (/ y (ash 1 shift1))
3378 (- precision shift1))))
3381 `(truly-the word ,x)))
3383 (t1 (%multiply-high num ,(- m n))))
3384 (ash ,(word `(+ t1 (ash ,(word `(- num t1))
3387 ((and (zerop shift1) (zerop shift2))
3388 (let ((max (truncate max-x y)))
3389 ;; Explicit TRULY-THE needed to get the FIXNUM=>FIXNUM
3391 `(truly-the (integer 0 ,max)
3392 (%multiply-high x ,m))))
3394 `(ash (%multiply-high (logandc2 x ,(1- (ash 1 shift1))) ,m)
3395 ,(- (+ shift1 shift2)))))))))
3397 ;;; If the divisor is constant and both args are positive and fit in a
3398 ;;; machine word, replace the division by a multiplication and possibly
3399 ;;; some shifts and an addition. Calculate the remainder by a second
3400 ;;; multiplication and a subtraction. Dead code elimination will
3401 ;;; suppress the latter part if only the quotient is needed. If the type
3402 ;;; of the dividend allows to derive that the quotient will always have
3403 ;;; the same value, emit much simpler code to handle that. (This case
3404 ;;; may be rare but it's easy to detect and the compiler doesn't find
3405 ;;; this optimization on its own.)
3406 (deftransform truncate ((x y) (word (constant-arg word))
3408 :policy (and (> speed compilation-speed)
3410 "convert integer division to multiplication"
3411 (let* ((y (lvar-value y))
3412 (x-type (lvar-type x))
3413 (max-x (or (and (numeric-type-p x-type)
3414 (numeric-type-high x-type))
3415 most-positive-word)))
3416 ;; Division by zero, one or powers of two is handled elsewhere.
3417 (when (zerop (logand y (1- y)))
3418 (give-up-ir1-transform))
3419 `(let* ((quot ,(gen-unsigned-div-by-constant-expr y max-x))
3420 (rem (ldb (byte #.sb!vm:n-word-bits 0)
3421 (- x (* quot ,y)))))
3422 (values quot rem))))
3424 ;;;; arithmetic and logical identity operation elimination
3426 ;;; Flush calls to various arith functions that convert to the
3427 ;;; identity function or a constant.
3428 (macrolet ((def (name identity result)
3429 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3430 "fold identity operations"
3437 (def logxor -1 (lognot x))
3440 (deftransform logand ((x y) (* (constant-arg t)) *)
3441 "fold identity operation"
3442 (let ((y (lvar-value y)))
3443 (unless (and (plusp y)
3444 (= y (1- (ash 1 (integer-length y)))))
3445 (give-up-ir1-transform))
3446 (unless (csubtypep (lvar-type x)
3447 (specifier-type `(integer 0 ,y)))
3448 (give-up-ir1-transform))
3451 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3452 "fold identity operation"
3453 (let ((size (lvar-value size)))
3454 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3455 (give-up-ir1-transform))
3458 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3459 ;;; (* 0 -4.0) is -0.0.
3460 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3461 "convert (- 0 x) to negate"
3463 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3464 "convert (* x 0) to 0"
3467 ;;; Return T if in an arithmetic op including lvars X and Y, the
3468 ;;; result type is not affected by the type of X. That is, Y is at
3469 ;;; least as contagious as X.
3471 (defun not-more-contagious (x y)
3472 (declare (type continuation x y))
3473 (let ((x (lvar-type x))
3475 (values (type= (numeric-contagion x y)
3476 (numeric-contagion y y)))))
3477 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3478 ;;; XXX needs more work as valid transforms are missed; some cases are
3479 ;;; specific to particular transform functions so the use of this
3480 ;;; function may need a re-think.
3481 (defun not-more-contagious (x y)
3482 (declare (type lvar x y))
3483 (flet ((simple-numeric-type (num)
3484 (and (numeric-type-p num)
3485 ;; Return non-NIL if NUM is integer, rational, or a float
3486 ;; of some type (but not FLOAT)
3487 (case (numeric-type-class num)
3491 (numeric-type-format num))
3494 (let ((x (lvar-type x))
3496 (if (and (simple-numeric-type x)
3497 (simple-numeric-type y))
3498 (values (type= (numeric-contagion x y)
3499 (numeric-contagion y y)))))))
3501 (def!type exact-number ()
3502 '(or rational (complex rational)))
3506 ;;; Only safely applicable for exact numbers. For floating-point
3507 ;;; x, one would have to first show that neither x or y are signed
3508 ;;; 0s, and that x isn't an SNaN.
3509 (deftransform + ((x y) (exact-number (constant-arg (eql 0))) *)
3514 (deftransform - ((x y) (exact-number (constant-arg (eql 0))) *)
3518 ;;; Fold (OP x +/-1)
3520 ;;; %NEGATE might not always signal correctly.
3522 ((def (name result minus-result)
3523 `(deftransform ,name ((x y)
3524 (exact-number (constant-arg (member 1 -1))))
3525 "fold identity operations"
3526 (if (minusp (lvar-value y)) ',minus-result ',result))))
3527 (def * x (%negate x))
3528 (def / x (%negate x))
3529 (def expt x (/ 1 x)))
3531 ;;; Fold (expt x n) into multiplications for small integral values of
3532 ;;; N; convert (expt x 1/2) to sqrt.
3533 (deftransform expt ((x y) (t (constant-arg real)) *)
3534 "recode as multiplication or sqrt"
3535 (let ((val (lvar-value y)))
3536 ;; If Y would cause the result to be promoted to the same type as
3537 ;; Y, we give up. If not, then the result will be the same type
3538 ;; as X, so we can replace the exponentiation with simple
3539 ;; multiplication and division for small integral powers.
3540 (unless (not-more-contagious y x)
3541 (give-up-ir1-transform))
3543 (let ((x-type (lvar-type x)))
3544 (cond ((csubtypep x-type (specifier-type '(or rational
3545 (complex rational))))
3547 ((csubtypep x-type (specifier-type 'real))
3551 ((csubtypep x-type (specifier-type 'complex))
3552 ;; both parts are float
3554 (t (give-up-ir1-transform)))))
3555 ((= val 2) '(* x x))
3556 ((= val -2) '(/ (* x x)))
3557 ((= val 3) '(* x x x))
3558 ((= val -3) '(/ (* x x x)))
3559 ((= val 1/2) '(sqrt x))
3560 ((= val -1/2) '(/ (sqrt x)))
3561 (t (give-up-ir1-transform)))))
3563 (deftransform expt ((x y) ((constant-arg (member -1 -1.0 -1.0d0)) integer) *)
3564 "recode as an ODDP check"
3565 (let ((val (lvar-value x)))
3567 '(- 1 (* 2 (logand 1 y)))
3572 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3573 ;;; transformations?
3574 ;;; Perhaps we should have to prove that the denominator is nonzero before
3575 ;;; doing them? -- WHN 19990917
3576 (macrolet ((def (name)
3577 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3584 (macrolet ((def (name)
3585 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3594 (macrolet ((def (name &optional float)
3595 (let ((x (if float '(float x) 'x)))
3596 `(deftransform ,name ((x y) (integer (constant-arg (member 1 -1)))
3598 "fold division by 1"
3599 `(values ,(if (minusp (lvar-value y))
3612 ;;;; character operations
3614 (deftransform char-equal ((a b) (base-char base-char))
3616 '(let* ((ac (char-code a))
3618 (sum (logxor ac bc)))
3620 (when (eql sum #x20)
3621 (let ((sum (+ ac bc)))
3622 (or (and (> sum 161) (< sum 213))
3623 (and (> sum 415) (< sum 461))
3624 (and (> sum 463) (< sum 477))))))))
3626 (deftransform char-upcase ((x) (base-char))
3628 '(let ((n-code (char-code x)))
3629 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3630 (< n-code #o173)) ; Octal 172 is #\z.
3631 (and (> n-code #o337)
3633 (and (> n-code #o367)
3635 (code-char (logxor #x20 n-code))
3638 (deftransform char-downcase ((x) (base-char))
3640 '(let ((n-code (char-code x)))
3641 (if (or (and (> n-code 64) ; 65 is #\A.
3642 (< n-code 91)) ; 90 is #\Z.
3647 (code-char (logxor #x20 n-code))
3650 ;;;; equality predicate transforms
3652 ;;; Return true if X and Y are lvars whose only use is a
3653 ;;; reference to the same leaf, and the value of the leaf cannot
3655 (defun same-leaf-ref-p (x y)
3656 (declare (type lvar x y))
3657 (let ((x-use (principal-lvar-use x))
3658 (y-use (principal-lvar-use y)))
3661 (eq (ref-leaf x-use) (ref-leaf y-use))
3662 (constant-reference-p x-use))))
3664 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3665 ;;; if there is no intersection between the types of the arguments,
3666 ;;; then the result is definitely false.
3667 (deftransform simple-equality-transform ((x y) * *
3670 ((same-leaf-ref-p x y) t)
3671 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3673 (t (give-up-ir1-transform))))
3676 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3680 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3681 ;;; try to convert to a type-specific predicate or EQ:
3682 ;;; -- If both args are characters, convert to CHAR=. This is better than
3683 ;;; just converting to EQ, since CHAR= may have special compilation
3684 ;;; strategies for non-standard representations, etc.
3685 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3686 ;;; constant and if so, put X second. Doing this results in better
3687 ;;; code from the backend, since the backend assumes that any constant
3688 ;;; argument comes second.
3689 ;;; -- If either arg is definitely not a number or a fixnum, then we
3690 ;;; can compare with EQ.
3691 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3692 ;;; is constant then we put it second. If X is a subtype of Y, we put
3693 ;;; it second. These rules make it easier for the back end to match
3694 ;;; these interesting cases.
3695 (deftransform eql ((x y) * * :node node)
3696 "convert to simpler equality predicate"
3697 (let ((x-type (lvar-type x))
3698 (y-type (lvar-type y))
3699 (char-type (specifier-type 'character)))
3700 (flet ((fixnum-type-p (type)
3701 (csubtypep type (specifier-type 'fixnum))))
3703 ((same-leaf-ref-p x y) t)
3704 ((not (types-equal-or-intersect x-type y-type))
3706 ((and (csubtypep x-type char-type)
3707 (csubtypep y-type char-type))
3709 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3710 (commutative-arg-swap node))
3711 ((or (eq-comparable-type-p x-type) (eq-comparable-type-p y-type))
3713 ((and (not (constant-lvar-p y))
3714 (or (constant-lvar-p x)
3715 (and (csubtypep x-type y-type)
3716 (not (csubtypep y-type x-type)))))
3719 (give-up-ir1-transform))))))
3721 ;;; similarly to the EQL transform above, we attempt to constant-fold
3722 ;;; or convert to a simpler predicate: mostly we have to be careful
3723 ;;; with strings and bit-vectors.
3724 (deftransform equal ((x y) * *)
3725 "convert to simpler equality predicate"
3726 (let ((x-type (lvar-type x))
3727 (y-type (lvar-type y))
3728 (string-type (specifier-type 'string))
3729 (bit-vector-type (specifier-type 'bit-vector)))
3731 ((same-leaf-ref-p x y) t)
3732 ((and (csubtypep x-type string-type)
3733 (csubtypep y-type string-type))
3735 ((and (csubtypep x-type bit-vector-type)
3736 (csubtypep y-type bit-vector-type))
3737 '(bit-vector-= x y))
3738 ;; if at least one is not a string, and at least one is not a
3739 ;; bit-vector, then we can reason from types.
3740 ((and (not (and (types-equal-or-intersect x-type string-type)
3741 (types-equal-or-intersect y-type string-type)))
3742 (not (and (types-equal-or-intersect x-type bit-vector-type)
3743 (types-equal-or-intersect y-type bit-vector-type)))
3744 (not (types-equal-or-intersect x-type y-type)))
3746 (t (give-up-ir1-transform)))))
3748 ;;; Convert to EQL if both args are rational and complexp is specified
3749 ;;; and the same for both.
3750 (deftransform = ((x y) (number number) *)
3752 (let ((x-type (lvar-type x))
3753 (y-type (lvar-type y)))
3754 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3755 (csubtypep y-type (specifier-type 'float)))
3756 (and (csubtypep x-type (specifier-type '(complex float)))
3757 (csubtypep y-type (specifier-type '(complex float))))
3758 #!+complex-float-vops
3759 (and (csubtypep x-type (specifier-type '(or single-float (complex single-float))))
3760 (csubtypep y-type (specifier-type '(or single-float (complex single-float)))))
3761 #!+complex-float-vops
3762 (and (csubtypep x-type (specifier-type '(or double-float (complex double-float))))
3763 (csubtypep y-type (specifier-type '(or double-float (complex double-float))))))
3764 ;; They are both floats. Leave as = so that -0.0 is
3765 ;; handled correctly.
3766 (give-up-ir1-transform))
3767 ((or (and (csubtypep x-type (specifier-type 'rational))
3768 (csubtypep y-type (specifier-type 'rational)))
3769 (and (csubtypep x-type
3770 (specifier-type '(complex rational)))
3772 (specifier-type '(complex rational)))))
3773 ;; They are both rationals and complexp is the same.
3777 (give-up-ir1-transform
3778 "The operands might not be the same type.")))))
3780 (defun maybe-float-lvar-p (lvar)
3781 (neq *empty-type* (type-intersection (specifier-type 'float)
3784 (flet ((maybe-invert (node op inverted x y)
3785 ;; Don't invert if either argument can be a float (NaNs)
3787 ((or (maybe-float-lvar-p x) (maybe-float-lvar-p y))
3788 (delay-ir1-transform node :constraint)
3789 `(or (,op x y) (= x y)))
3791 `(if (,inverted x y) nil t)))))
3792 (deftransform >= ((x y) (number number) * :node node)
3793 "invert or open code"
3794 (maybe-invert node '> '< x y))
3795 (deftransform <= ((x y) (number number) * :node node)
3796 "invert or open code"
3797 (maybe-invert node '< '> x y)))
3799 ;;; See whether we can statically determine (< X Y) using type
3800 ;;; information. If X's high bound is < Y's low, then X < Y.
3801 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3802 ;;; NIL). If not, at least make sure any constant arg is second.
3803 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3804 `(deftransform ,name ((x y))
3805 "optimize using intervals"
3806 (if (and (same-leaf-ref-p x y)
3807 ;; For non-reflexive functions we don't need
3808 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3809 ;; but with reflexive ones we don't know...
3811 '((and (not (maybe-float-lvar-p x))
3812 (not (maybe-float-lvar-p y))))))
3814 (let ((ix (or (type-approximate-interval (lvar-type x))
3815 (give-up-ir1-transform)))
3816 (iy (or (type-approximate-interval (lvar-type y))
3817 (give-up-ir1-transform))))
3822 ((and (constant-lvar-p x)
3823 (not (constant-lvar-p y)))
3826 (give-up-ir1-transform))))))))
3827 (def = = t (interval-= ix iy) (interval-/= ix iy))
3828 (def /= /= nil (interval-/= ix iy) (interval-= ix iy))
3829 (def < > nil (interval-< ix iy) (interval->= ix iy))
3830 (def > < nil (interval-< iy ix) (interval->= iy ix))
3831 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3832 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3834 (defun ir1-transform-char< (x y first second inverse)
3836 ((same-leaf-ref-p x y) nil)
3837 ;; If we had interval representation of character types, as we
3838 ;; might eventually have to to support 2^21 characters, then here
3839 ;; we could do some compile-time computation as in transforms for
3840 ;; < above. -- CSR, 2003-07-01
3841 ((and (constant-lvar-p first)
3842 (not (constant-lvar-p second)))
3844 (t (give-up-ir1-transform))))
3846 (deftransform char< ((x y) (character character) *)
3847 (ir1-transform-char< x y x y 'char>))
3849 (deftransform char> ((x y) (character character) *)
3850 (ir1-transform-char< y x x y 'char<))
3852 ;;;; converting N-arg comparisons
3854 ;;;; We convert calls to N-arg comparison functions such as < into
3855 ;;;; two-arg calls. This transformation is enabled for all such
3856 ;;;; comparisons in this file. If any of these predicates are not
3857 ;;;; open-coded, then the transformation should be removed at some
3858 ;;;; point to avoid pessimization.
3860 ;;; This function is used for source transformation of N-arg
3861 ;;; comparison functions other than inequality. We deal both with
3862 ;;; converting to two-arg calls and inverting the sense of the test,
3863 ;;; if necessary. If the call has two args, then we pass or return a
3864 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3865 ;;; then we transform to code that returns true. Otherwise, we bind
3866 ;;; all the arguments and expand into a bunch of IFs.
3867 (defun multi-compare (predicate args not-p type &optional force-two-arg-p)
3868 (let ((nargs (length args)))
3869 (cond ((< nargs 1) (values nil t))
3870 ((= nargs 1) `(progn (the ,type ,@args) t))
3873 `(if (,predicate ,(first args) ,(second args)) nil t)
3875 `(,predicate ,(first args) ,(second args))
3878 (do* ((i (1- nargs) (1- i))
3880 (current (gensym) (gensym))
3881 (vars (list current) (cons current vars))
3883 `(if (,predicate ,current ,last)
3885 `(if (,predicate ,current ,last)
3888 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3891 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3892 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3893 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3894 ;;; We cannot do the inversion for >= and <= here, since both
3895 ;;; (< NaN X) and (> NaN X)
3896 ;;; are false, and we don't have type-information available yet. The
3897 ;;; deftransforms for two-argument versions of >= and <= takes care of
3898 ;;; the inversion to > and < when possible.
3899 (define-source-transform <= (&rest args) (multi-compare '<= args nil 'real))
3900 (define-source-transform >= (&rest args) (multi-compare '>= args nil 'real))
3902 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3904 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3906 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3908 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3910 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3913 (define-source-transform char-equal (&rest args)
3914 (multi-compare 'sb!impl::two-arg-char-equal args nil 'character t))
3915 (define-source-transform char-lessp (&rest args)
3916 (multi-compare 'sb!impl::two-arg-char-lessp args nil 'character t))
3917 (define-source-transform char-greaterp (&rest args)
3918 (multi-compare 'sb!impl::two-arg-char-greaterp args nil 'character t))
3919 (define-source-transform char-not-greaterp (&rest args)
3920 (multi-compare 'sb!impl::two-arg-char-greaterp args t 'character t))
3921 (define-source-transform char-not-lessp (&rest args)
3922 (multi-compare 'sb!impl::two-arg-char-lessp args t 'character t))
3924 ;;; This function does source transformation of N-arg inequality
3925 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3926 ;;; arg cases. If there are more than two args, then we expand into
3927 ;;; the appropriate n^2 comparisons only when speed is important.
3928 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3929 (defun multi-not-equal (predicate args type)
3930 (let ((nargs (length args)))
3931 (cond ((< nargs 1) (values nil t))
3932 ((= nargs 1) `(progn (the ,type ,@args) t))
3934 `(if (,predicate ,(first args) ,(second args)) nil t))
3935 ((not (policy *lexenv*
3936 (and (>= speed space)
3937 (>= speed compilation-speed))))
3940 (let ((vars (make-gensym-list nargs)))
3941 (do ((var vars next)
3942 (next (cdr vars) (cdr next))
3945 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3947 (let ((v1 (first var)))
3949 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3951 (define-source-transform /= (&rest args)
3952 (multi-not-equal '= args 'number))
3953 (define-source-transform char/= (&rest args)
3954 (multi-not-equal 'char= args 'character))
3955 (define-source-transform char-not-equal (&rest args)
3956 (multi-not-equal 'char-equal args 'character))
3958 ;;; Expand MAX and MIN into the obvious comparisons.
3959 (define-source-transform max (arg0 &rest rest)
3960 (once-only ((arg0 arg0))
3962 `(values (the real ,arg0))
3963 `(let ((maxrest (max ,@rest)))
3964 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3965 (define-source-transform min (arg0 &rest rest)
3966 (once-only ((arg0 arg0))
3968 `(values (the real ,arg0))
3969 `(let ((minrest (min ,@rest)))
3970 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3972 ;;;; converting N-arg arithmetic functions
3974 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3975 ;;;; versions, and degenerate cases are flushed.
3977 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3978 (declaim (ftype (sfunction (symbol t list t) list) associate-args))
3979 (defun associate-args (fun first-arg more-args identity)
3980 (let ((next (rest more-args))
3981 (arg (first more-args)))
3983 `(,fun ,first-arg ,(if arg arg identity))
3984 (associate-args fun `(,fun ,first-arg ,arg) next identity))))
3986 ;;; Reduce constants in ARGS list.
3987 (declaim (ftype (sfunction (symbol list t symbol) list) reduce-constants))
3988 (defun reduce-constants (fun args identity one-arg-result-type)
3989 (let ((one-arg-constant-p (ecase one-arg-result-type
3991 (integer #'integerp)))
3992 (reduced-value identity)
3994 (collect ((not-constants))
3996 (if (funcall one-arg-constant-p arg)
3997 (setf reduced-value (funcall fun reduced-value arg)
3999 (not-constants arg)))
4000 ;; It is tempting to drop constants reduced to identity here,
4001 ;; but if X is SNaN in (* X 1), we cannot drop the 1.
4004 `(,reduced-value ,@(not-constants))
4006 `(,reduced-value)))))
4008 ;;; Do source transformations for transitive functions such as +.
4009 ;;; One-arg cases are replaced with the arg and zero arg cases with
4010 ;;; the identity. ONE-ARG-RESULT-TYPE is the type to ensure (with THE)
4011 ;;; that the argument in one-argument calls is.
4012 (declaim (ftype (function (symbol list t &optional symbol list)
4013 (values t &optional (member nil t)))
4014 source-transform-transitive))
4015 (defun source-transform-transitive (fun args identity
4016 &optional (one-arg-result-type 'number)
4017 (one-arg-prefixes '(values)))
4020 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
4022 (t (let ((reduced-args (reduce-constants fun args identity one-arg-result-type)))
4023 (associate-args fun (first reduced-args) (rest reduced-args) identity)))))
4025 (define-source-transform + (&rest args)
4026 (source-transform-transitive '+ args 0))
4027 (define-source-transform * (&rest args)
4028 (source-transform-transitive '* args 1))
4029 (define-source-transform logior (&rest args)
4030 (source-transform-transitive 'logior args 0 'integer))
4031 (define-source-transform logxor (&rest args)
4032 (source-transform-transitive 'logxor args 0 'integer))
4033 (define-source-transform logand (&rest args)
4034 (source-transform-transitive 'logand args -1 'integer))
4035 (define-source-transform logeqv (&rest args)
4036 (source-transform-transitive 'logeqv args -1 'integer))
4037 (define-source-transform gcd (&rest args)
4038 (source-transform-transitive 'gcd args 0 'integer '(abs)))
4039 (define-source-transform lcm (&rest args)
4040 (source-transform-transitive 'lcm args 1 'integer '(abs)))
4042 ;;; Do source transformations for intransitive n-arg functions such as
4043 ;;; /. With one arg, we form the inverse. With two args we pass.
4044 ;;; Otherwise we associate into two-arg calls.
4045 (declaim (ftype (function (symbol symbol list t list &optional symbol)
4046 (values list &optional (member nil t)))
4047 source-transform-intransitive))
4048 (defun source-transform-intransitive (fun fun* args identity one-arg-prefixes
4049 &optional (one-arg-result-type 'number))
4051 ((0 2) (values nil t))
4052 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
4053 (t (let ((reduced-args
4054 (reduce-constants fun* (rest args) identity one-arg-result-type)))
4055 (associate-args fun (first args) reduced-args identity)))))
4057 (define-source-transform - (&rest args)
4058 (source-transform-intransitive '- '+ args 0 '(%negate)))
4059 (define-source-transform / (&rest args)
4060 (source-transform-intransitive '/ '* args 1 '(/ 1)))
4062 ;;;; transforming APPLY
4064 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
4065 ;;; only needs to understand one kind of variable-argument call. It is
4066 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
4067 (define-source-transform apply (fun arg &rest more-args)
4068 (let ((args (cons arg more-args)))
4069 `(multiple-value-call ,fun
4070 ,@(mapcar (lambda (x) `(values ,x)) (butlast args))
4071 (values-list ,(car (last args))))))
4073 ;;;; transforming references to &REST argument
4075 ;;; We add magical &MORE arguments to all functions with &REST. If ARG names
4076 ;;; the &REST argument, this returns the lambda-vars for the context and
4078 (defun possible-rest-arg-context (arg)
4080 (let* ((var (lexenv-find arg vars))
4081 (info (when (lambda-var-p var)
4082 (lambda-var-arg-info var))))
4084 (eq :rest (arg-info-kind info))
4085 (consp (arg-info-default info)))
4086 (values-list (arg-info-default info))))))
4088 (defun mark-more-context-used (rest-var)
4089 (let ((info (lambda-var-arg-info rest-var)))
4090 (aver (eq :rest (arg-info-kind info)))
4091 (destructuring-bind (context count &optional used) (arg-info-default info)
4093 (setf (arg-info-default info) (list context count t))))))
4095 (defun mark-more-context-invalid (rest-var)
4096 (let ((info (lambda-var-arg-info rest-var)))
4097 (aver (eq :rest (arg-info-kind info)))
4098 (setf (arg-info-default info) t)))
4100 ;;; This determines of we the REF to a &REST variable is headed towards
4101 ;;; parts unknown, or if we can really use the context.
4102 (defun rest-var-more-context-ok (lvar)
4103 (let* ((use (lvar-use lvar))
4104 (var (when (ref-p use) (ref-leaf use)))
4105 (home (when (lambda-var-p var) (lambda-var-home var)))
4106 (info (when (lambda-var-p var) (lambda-var-arg-info var)))
4107 (restp (when info (eq :rest (arg-info-kind info)))))
4108 (flet ((ref-good-for-more-context-p (ref)
4109 (let ((dest (principal-lvar-end (node-lvar ref))))
4110 (and (combination-p dest)
4111 ;; If the destination is to anything but these, we're going to
4112 ;; actually need the rest list -- and since other operations
4113 ;; might modify the list destructively, the using the context
4114 ;; isn't good anywhere else either.
4115 (lvar-fun-is (combination-fun dest)
4116 '(%rest-values %rest-ref %rest-length
4117 %rest-null %rest-true))
4118 ;; If the home lambda is different and isn't DX, it might
4119 ;; escape -- in which case using the more context isn't safe.
4120 (let ((clambda (node-home-lambda dest)))
4121 (or (eq home clambda)
4122 (leaf-dynamic-extent clambda)))))))
4123 (let ((ok (and restp
4124 (consp (arg-info-default info))
4125 (not (lambda-var-specvar var))
4126 (not (lambda-var-sets var))
4127 (every #'ref-good-for-more-context-p (lambda-var-refs var)))))
4129 (mark-more-context-used var)
4131 (mark-more-context-invalid var)))
4134 ;;; VALUES-LIST -> %REST-VALUES
4135 (define-source-transform values-list (list)
4136 (multiple-value-bind (context count) (possible-rest-arg-context list)
4138 `(%rest-values ,list ,context ,count)
4141 ;;; NTH -> %REST-REF
4142 (define-source-transform nth (n list)
4143 (multiple-value-bind (context count) (possible-rest-arg-context list)
4145 `(%rest-ref ,n ,list ,context ,count)
4146 `(car (nthcdr ,n ,list)))))
4148 (define-source-transform elt (seq n)
4149 (multiple-value-bind (context count) (possible-rest-arg-context seq)
4151 `(%rest-ref ,n ,seq ,context ,count)
4154 ;;; CAR -> %REST-REF
4155 (defun source-transform-car (list)
4156 (multiple-value-bind (context count) (possible-rest-arg-context list)
4158 `(%rest-ref 0 ,list ,context ,count)
4160 (define-source-transform car (list) (source-transform-car list))
4161 (define-source-transform first (list) (source-transform-car list))
4163 ;;; LENGTH -> %REST-LENGTH
4164 (defun source-transform-length (list)
4165 (multiple-value-bind (context count) (possible-rest-arg-context list)
4167 `(%rest-length ,list ,context ,count)
4169 (define-source-transform length (list) (source-transform-length list))
4170 (define-source-transform list-length (list) (source-transform-length list))
4172 ;;; ENDP, NULL and NOT -> %REST-NULL
4174 ;;; Outside &REST convert into an IF so that IF optimizations will eliminate
4175 ;;; redundant negations.
4176 (defun source-transform-null (x op)
4177 (multiple-value-bind (context count) (possible-rest-arg-context x)
4179 `(%rest-null ',op ,x ,context ,count))
4181 `(if (the list ,x) nil t))
4184 (define-source-transform not (x) (source-transform-null x 'not))
4185 (define-source-transform null (x) (source-transform-null x 'null))
4186 (define-source-transform endp (x) (source-transform-null x 'endp))
4188 (deftransform %rest-values ((list context count))
4189 (if (rest-var-more-context-ok list)
4190 `(%more-arg-values context 0 count)
4191 `(values-list list)))
4193 (deftransform %rest-ref ((n list context count))
4194 (cond ((rest-var-more-context-ok list)
4195 `(%more-arg context n))
4196 ((and (constant-lvar-p n) (zerop (lvar-value n)))
4201 (deftransform %rest-length ((list context count))
4202 (if (rest-var-more-context-ok list)
4206 (deftransform %rest-null ((op list context count))
4207 (aver (constant-lvar-p op))
4208 (if (rest-var-more-context-ok list)
4210 `(,(lvar-value op) list)))
4212 (deftransform %rest-true ((list context count))
4213 (if (rest-var-more-context-ok list)
4214 `(not (eql 0 count))
4217 ;;;; transforming FORMAT
4219 ;;;; If the control string is a compile-time constant, then replace it
4220 ;;;; with a use of the FORMATTER macro so that the control string is
4221 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
4222 ;;;; or T and the control string is a function (i.e. FORMATTER), then
4223 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
4225 ;;; for compile-time argument count checking.
4227 ;;; FIXME II: In some cases, type information could be correlated; for
4228 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
4229 ;;; of a corresponding argument is known and does not intersect the
4230 ;;; list type, a warning could be signalled.
4231 (defun check-format-args (string args fun)
4232 (declare (type string string))
4233 (unless (typep string 'simple-string)
4234 (setq string (coerce string 'simple-string)))
4235 (multiple-value-bind (min max)
4236 (handler-case (sb!format:%compiler-walk-format-string string args)
4237 (sb!format:format-error (c)
4238 (compiler-warn "~A" c)))
4240 (let ((nargs (length args)))
4243 (warn 'format-too-few-args-warning
4245 "Too few arguments (~D) to ~S ~S: requires at least ~D."
4246 :format-arguments (list nargs fun string min)))
4248 (warn 'format-too-many-args-warning
4250 "Too many arguments (~D) to ~S ~S: uses at most ~D."
4251 :format-arguments (list nargs fun string max))))))))
4253 (defoptimizer (format optimizer) ((dest control &rest args))
4254 (when (constant-lvar-p control)
4255 (let ((x (lvar-value control)))
4257 (check-format-args x args 'format)))))
4259 ;;; We disable this transform in the cross-compiler to save memory in
4260 ;;; the target image; most of the uses of FORMAT in the compiler are for
4261 ;;; error messages, and those don't need to be particularly fast.
4263 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
4264 :policy (>= speed space))
4265 (unless (constant-lvar-p control)
4266 (give-up-ir1-transform "The control string is not a constant."))
4267 (let ((arg-names (make-gensym-list (length args))))
4268 `(lambda (dest control ,@arg-names)
4269 (declare (ignore control))
4270 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
4272 (deftransform format ((stream control &rest args) (stream function &rest t))
4273 (let ((arg-names (make-gensym-list (length args))))
4274 `(lambda (stream control ,@arg-names)
4275 (funcall control stream ,@arg-names)
4278 (deftransform format ((tee control &rest args) ((member t) function &rest t))
4279 (let ((arg-names (make-gensym-list (length args))))
4280 `(lambda (tee control ,@arg-names)
4281 (declare (ignore tee))
4282 (funcall control *standard-output* ,@arg-names)
4285 (deftransform pathname ((pathspec) (pathname) *)
4288 (deftransform pathname ((pathspec) (string) *)
4289 '(values (parse-namestring pathspec)))
4293 `(defoptimizer (,name optimizer) ((control &rest args))
4294 (when (constant-lvar-p control)
4295 (let ((x (lvar-value control)))
4297 (check-format-args x args ',name)))))))
4300 #+sb-xc-host ; Only we should be using these
4303 (def compiler-error)
4305 (def compiler-style-warn)
4306 (def compiler-notify)
4307 (def maybe-compiler-notify)
4310 (defoptimizer (cerror optimizer) ((report control &rest args))
4311 (when (and (constant-lvar-p control)
4312 (constant-lvar-p report))
4313 (let ((x (lvar-value control))
4314 (y (lvar-value report)))
4315 (when (and (stringp x) (stringp y))
4316 (multiple-value-bind (min1 max1)
4318 (sb!format:%compiler-walk-format-string x args)
4319 (sb!format:format-error (c)
4320 (compiler-warn "~A" c)))
4322 (multiple-value-bind (min2 max2)
4324 (sb!format:%compiler-walk-format-string y args)
4325 (sb!format:format-error (c)
4326 (compiler-warn "~A" c)))
4328 (let ((nargs (length args)))
4330 ((< nargs (min min1 min2))
4331 (warn 'format-too-few-args-warning
4333 "Too few arguments (~D) to ~S ~S ~S: ~
4334 requires at least ~D."
4336 (list nargs 'cerror y x (min min1 min2))))
4337 ((> nargs (max max1 max2))
4338 (warn 'format-too-many-args-warning
4340 "Too many arguments (~D) to ~S ~S ~S: ~
4343 (list nargs 'cerror y x (max max1 max2))))))))))))))
4345 (defoptimizer (coerce derive-type) ((value type) node)
4347 ((constant-lvar-p type)
4348 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
4349 ;; but dealing with the niggle that complex canonicalization gets
4350 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
4352 (let* ((specifier (lvar-value type))
4353 (result-typeoid (careful-specifier-type specifier)))
4355 ((null result-typeoid) nil)
4356 ((csubtypep result-typeoid (specifier-type 'number))
4357 ;; the difficult case: we have to cope with ANSI 12.1.5.3
4358 ;; Rule of Canonical Representation for Complex Rationals,
4359 ;; which is a truly nasty delivery to field.
4361 ((csubtypep result-typeoid (specifier-type 'real))
4362 ;; cleverness required here: it would be nice to deduce
4363 ;; that something of type (INTEGER 2 3) coerced to type
4364 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
4365 ;; FLOAT gets its own clause because it's implemented as
4366 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
4369 ((and (numeric-type-p result-typeoid)
4370 (eq (numeric-type-complexp result-typeoid) :real))
4371 ;; FIXME: is this clause (a) necessary or (b) useful?
4373 ((or (csubtypep result-typeoid
4374 (specifier-type '(complex single-float)))
4375 (csubtypep result-typeoid
4376 (specifier-type '(complex double-float)))
4378 (csubtypep result-typeoid
4379 (specifier-type '(complex long-float))))
4380 ;; float complex types are never canonicalized.
4383 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
4384 ;; probably just a COMPLEX or equivalent. So, in that
4385 ;; case, we will return a complex or an object of the
4386 ;; provided type if it's rational:
4387 (type-union result-typeoid
4388 (type-intersection (lvar-type value)
4389 (specifier-type 'rational))))))
4390 ((and (policy node (zerop safety))
4391 (csubtypep result-typeoid (specifier-type '(array * (*)))))
4392 ;; At zero safety the deftransform for COERCE can elide dimension
4393 ;; checks for the things like (COERCE X '(SIMPLE-VECTOR 5)) -- so we
4394 ;; need to simplify the type to drop the dimension information.
4395 (let ((vtype (simplify-vector-type result-typeoid)))
4397 (specifier-type vtype)
4402 ;; OK, the result-type argument isn't constant. However, there
4403 ;; are common uses where we can still do better than just
4404 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
4405 ;; where Y is of a known type. See messages on cmucl-imp
4406 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
4407 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
4408 ;; the basis that it's unlikely that other uses are both
4409 ;; time-critical and get to this branch of the COND (non-constant
4410 ;; second argument to COERCE). -- CSR, 2002-12-16
4411 (let ((value-type (lvar-type value))
4412 (type-type (lvar-type type)))
4414 ((good-cons-type-p (cons-type)
4415 ;; Make sure the cons-type we're looking at is something
4416 ;; we're prepared to handle which is basically something
4417 ;; that array-element-type can return.
4418 (or (and (member-type-p cons-type)
4419 (eql 1 (member-type-size cons-type))
4420 (null (first (member-type-members cons-type))))
4421 (let ((car-type (cons-type-car-type cons-type)))
4422 (and (member-type-p car-type)
4423 (eql 1 (member-type-members car-type))
4424 (let ((elt (first (member-type-members car-type))))
4428 (numberp (first elt)))))
4429 (good-cons-type-p (cons-type-cdr-type cons-type))))))
4430 (unconsify-type (good-cons-type)
4431 ;; Convert the "printed" respresentation of a cons
4432 ;; specifier into a type specifier. That is, the
4433 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
4434 ;; NULL)) is converted to (SIGNED-BYTE 16).
4435 (cond ((or (null good-cons-type)
4436 (eq good-cons-type 'null))
4438 ((and (eq (first good-cons-type) 'cons)
4439 (eq (first (second good-cons-type)) 'member))
4440 `(,(second (second good-cons-type))
4441 ,@(unconsify-type (caddr good-cons-type))))))
4442 (coerceable-p (part)
4443 ;; Can the value be coerced to the given type? Coerce is
4444 ;; complicated, so we don't handle every possible case
4445 ;; here---just the most common and easiest cases:
4447 ;; * Any REAL can be coerced to a FLOAT type.
4448 ;; * Any NUMBER can be coerced to a (COMPLEX
4449 ;; SINGLE/DOUBLE-FLOAT).
4451 ;; FIXME I: we should also be able to deal with characters
4454 ;; FIXME II: I'm not sure that anything is necessary
4455 ;; here, at least while COMPLEX is not a specialized
4456 ;; array element type in the system. Reasoning: if
4457 ;; something cannot be coerced to the requested type, an
4458 ;; error will be raised (and so any downstream compiled
4459 ;; code on the assumption of the returned type is
4460 ;; unreachable). If something can, then it will be of
4461 ;; the requested type, because (by assumption) COMPLEX
4462 ;; (and other difficult types like (COMPLEX INTEGER)
4463 ;; aren't specialized types.
4464 (let ((coerced-type (careful-specifier-type part)))
4466 (or (and (csubtypep coerced-type (specifier-type 'float))
4467 (csubtypep value-type (specifier-type 'real)))
4468 (and (csubtypep coerced-type
4469 (specifier-type `(or (complex single-float)
4470 (complex double-float))))
4471 (csubtypep value-type (specifier-type 'number)))))))
4472 (process-types (type)
4473 ;; FIXME: This needs some work because we should be able
4474 ;; to derive the resulting type better than just the
4475 ;; type arg of coerce. That is, if X is (INTEGER 10
4476 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
4477 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
4479 (cond ((member-type-p type)
4482 (mapc-member-type-members
4484 (if (coerceable-p member)
4485 (push member members)
4486 (return-from punt *universal-type*)))
4488 (specifier-type `(or ,@members)))))
4489 ((and (cons-type-p type)
4490 (good-cons-type-p type))
4491 (let ((c-type (unconsify-type (type-specifier type))))
4492 (if (coerceable-p c-type)
4493 (specifier-type c-type)
4496 *universal-type*))))
4497 (cond ((union-type-p type-type)
4498 (apply #'type-union (mapcar #'process-types
4499 (union-type-types type-type))))
4500 ((or (member-type-p type-type)
4501 (cons-type-p type-type))
4502 (process-types type-type))
4504 *universal-type*)))))))
4506 (defoptimizer (compile derive-type) ((nameoid function))
4507 (when (csubtypep (lvar-type nameoid)
4508 (specifier-type 'null))
4509 (values-specifier-type '(values function boolean boolean))))
4511 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
4512 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
4513 ;;; optimizer, above).
4514 (defoptimizer (array-element-type derive-type) ((array))
4515 (let ((array-type (lvar-type array)))
4516 (labels ((consify (list)
4519 `(cons (eql ,(car list)) ,(consify (rest list)))))
4520 (get-element-type (a)
4522 (type-specifier (array-type-specialized-element-type a))))
4523 (cond ((eq element-type '*)
4524 (specifier-type 'type-specifier))
4525 ((symbolp element-type)
4526 (make-member-type :members (list element-type)))
4527 ((consp element-type)
4528 (specifier-type (consify element-type)))
4530 (error "can't understand type ~S~%" element-type))))))
4531 (labels ((recurse (type)
4532 (cond ((array-type-p type)
4533 (get-element-type type))
4534 ((union-type-p type)
4536 (mapcar #'recurse (union-type-types type))))
4538 *universal-type*))))
4539 (recurse array-type)))))
4541 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
4542 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4543 ;; isn't really related to the CMU CL code, since instead of trying
4544 ;; to generalize the CMU CL code to allow START and END values, this
4545 ;; code has been written from scratch following Chapter 7 of
4546 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4547 `(macrolet ((%index (x) `(truly-the index ,x))
4548 (%parent (i) `(ash ,i -1))
4549 (%left (i) `(%index (ash ,i 1)))
4550 (%right (i) `(%index (1+ (ash ,i 1))))
4553 (left (%left i) (%left i)))
4554 ((> left current-heap-size))
4555 (declare (type index i left))
4556 (let* ((i-elt (%elt i))
4557 (i-key (funcall keyfun i-elt))
4558 (left-elt (%elt left))
4559 (left-key (funcall keyfun left-elt)))
4560 (multiple-value-bind (large large-elt large-key)
4561 (if (funcall ,',predicate i-key left-key)
4562 (values left left-elt left-key)
4563 (values i i-elt i-key))
4564 (let ((right (%right i)))
4565 (multiple-value-bind (largest largest-elt)
4566 (if (> right current-heap-size)
4567 (values large large-elt)
4568 (let* ((right-elt (%elt right))
4569 (right-key (funcall keyfun right-elt)))
4570 (if (funcall ,',predicate large-key right-key)
4571 (values right right-elt)
4572 (values large large-elt))))
4573 (cond ((= largest i)
4576 (setf (%elt i) largest-elt
4577 (%elt largest) i-elt
4579 (%sort-vector (keyfun &optional (vtype 'vector))
4580 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4581 ;; trouble getting type inference to
4582 ;; propagate all the way through this
4583 ;; tangled mess of inlining. The TRULY-THE
4584 ;; here works around that. -- WHN
4586 `(aref (truly-the ,',vtype ,',',vector)
4587 (%index (+ (%index ,i) start-1)))))
4588 (let (;; Heaps prefer 1-based addressing.
4589 (start-1 (1- ,',start))
4590 (current-heap-size (- ,',end ,',start))
4592 (declare (type (integer -1 #.(1- sb!xc:most-positive-fixnum))
4594 (declare (type index current-heap-size))
4595 (declare (type function keyfun))
4596 (loop for i of-type index
4597 from (ash current-heap-size -1) downto 1 do
4600 (when (< current-heap-size 2)
4602 (rotatef (%elt 1) (%elt current-heap-size))
4603 (decf current-heap-size)
4605 (if (typep ,vector 'simple-vector)
4606 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4607 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4609 ;; Special-casing the KEY=NIL case lets us avoid some
4611 (%sort-vector #'identity simple-vector)
4612 (%sort-vector ,key simple-vector))
4613 ;; It's hard to anticipate many speed-critical applications for
4614 ;; sorting vector types other than (VECTOR T), so we just lump
4615 ;; them all together in one slow dynamically typed mess.
4617 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4618 (%sort-vector (or ,key #'identity))))))
4620 ;;;; debuggers' little helpers
4622 ;;; for debugging when transforms are behaving mysteriously,
4623 ;;; e.g. when debugging a problem with an ASH transform
4624 ;;; (defun foo (&optional s)
4625 ;;; (sb-c::/report-lvar s "S outside WHEN")
4626 ;;; (when (and (integerp s) (> s 3))
4627 ;;; (sb-c::/report-lvar s "S inside WHEN")
4628 ;;; (let ((bound (ash 1 (1- s))))
4629 ;;; (sb-c::/report-lvar bound "BOUND")
4630 ;;; (let ((x (- bound))
4632 ;;; (sb-c::/report-lvar x "X")
4633 ;;; (sb-c::/report-lvar x "Y"))
4634 ;;; `(integer ,(- bound) ,(1- bound)))))
4635 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4636 ;;; and the function doesn't do anything at all.)
4639 (defknown /report-lvar (t t) null)
4640 (deftransform /report-lvar ((x message) (t t))
4641 (format t "~%/in /REPORT-LVAR~%")
4642 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4643 (when (constant-lvar-p x)
4644 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4645 (format t "/MESSAGE=~S~%" (lvar-value message))
4646 (give-up-ir1-transform "not a real transform"))
4647 (defun /report-lvar (x message)
4648 (declare (ignore x message))))
4651 ;;;; Transforms for internal compiler utilities
4653 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4654 ;;; checking that it's still valid at run-time.
4655 (deftransform policy-quality ((policy quality-name)
4657 (unless (and (constant-lvar-p quality-name)
4658 (policy-quality-name-p (lvar-value quality-name)))
4659 (give-up-ir1-transform))
4660 '(%policy-quality policy quality-name))