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 ;;; Don't transform CAD*R, they are treated specially for &more args
94 (/show0 "about to set CxR source transforms")
95 (loop for i of-type index from 2 upto 4 do
96 ;; Iterate over BUF = all names CxR where x = an I-element
97 ;; string of #\A or #\D characters.
98 (let ((buf (make-string (+ 2 i))))
99 (setf (aref buf 0) #\C
100 (aref buf (1+ i)) #\R)
101 (dotimes (j (ash 2 i))
102 (declare (type index j))
104 (declare (type index k))
105 (setf (aref buf (1+ k))
106 (if (logbitp k j) #\A #\D)))
107 (unless (member buf '("CADR" "CADDR" "CADDDR")
109 (setf (info :function :source-transform (intern buf))
110 #'source-transform-cxr)))))
111 (/show0 "done setting CxR source transforms")
113 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
114 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
115 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
117 (define-source-transform rest (x) `(cdr ,x))
118 (define-source-transform first (x) `(car ,x))
119 (define-source-transform second (x) `(cadr ,x))
120 (define-source-transform third (x) `(caddr ,x))
121 (define-source-transform fourth (x) `(cadddr ,x))
122 (define-source-transform fifth (x) `(nth 4 ,x))
123 (define-source-transform sixth (x) `(nth 5 ,x))
124 (define-source-transform seventh (x) `(nth 6 ,x))
125 (define-source-transform eighth (x) `(nth 7 ,x))
126 (define-source-transform ninth (x) `(nth 8 ,x))
127 (define-source-transform tenth (x) `(nth 9 ,x))
129 ;;; LIST with one arg is an extremely common operation (at least inside
130 ;;; SBCL itself); translate it to CONS to take advantage of common
131 ;;; allocation routines.
132 (define-source-transform list (&rest args)
134 (1 `(cons ,(first args) nil))
137 (defoptimizer (list derive-type) ((&rest args) node)
139 (specifier-type 'cons)
140 (specifier-type 'null)))
142 ;;; And similarly for LIST*.
143 (define-source-transform list* (arg &rest others)
144 (cond ((not others) arg)
145 ((not (cdr others)) `(cons ,arg ,(car others)))
148 (defoptimizer (list* derive-type) ((arg &rest args))
150 (specifier-type 'cons)
155 (define-source-transform nconc (&rest args)
161 ;;; (append nil nil nil fixnum) => fixnum
162 ;;; (append x x cons x x) => cons
163 ;;; (append x x x x list) => list
164 ;;; (append x x x x sequence) => sequence
165 ;;; (append fixnum x ...) => nil
166 (defun derive-append-type (args)
168 (specifier-type 'null))
170 (let ((cons-type (specifier-type 'cons))
171 (null-type (specifier-type 'null))
172 (list-type (specifier-type 'list))
173 (last (lvar-type (car (last args)))))
175 ;; Check that all but the last arguments are lists first
176 (loop for (arg next) on args
179 (let ((lvar-type (lvar-type arg)))
180 (unless (or (csubtypep list-type lvar-type)
181 (csubtypep lvar-type list-type))
182 (assert-lvar-type arg list-type
183 (lexenv-policy *lexenv*))
184 (return *empty-type*))))
185 (loop with all-nil = t
186 for (arg next) on args
187 for lvar-type = (lvar-type arg)
191 ;; Cons in the middle guarantees the result will be a cons
192 ((csubtypep lvar-type cons-type)
194 ;; If all but the last are NIL the type of the last arg
196 ((csubtypep lvar-type null-type))
203 ((csubtypep last cons-type)
205 ((csubtypep last list-type)
207 ;; If the last is SEQUENCE (or similar) it'll
208 ;; be either that sequence or a cons, which is a
210 ((csubtypep list-type last)
213 (defoptimizer (append derive-type) ((&rest args))
214 (derive-append-type args))
216 (defoptimizer (sb!impl::append2 derive-type) ((&rest args))
217 (derive-append-type args))
219 (defoptimizer (nconc derive-type) ((&rest args))
220 (derive-append-type args))
222 ;;; Translate RPLACx to LET and SETF.
223 (define-source-transform rplaca (x y)
228 (define-source-transform rplacd (x y)
234 (deftransform last ((list &optional n) (t &optional t))
235 (let ((c (constant-lvar-p n)))
237 (and c (eql 1 (lvar-value n))))
239 ((and c (eql 0 (lvar-value n)))
242 (let ((type (lvar-type n)))
243 (cond ((csubtypep type (specifier-type 'fixnum))
244 '(%lastn/fixnum list n))
245 ((csubtypep type (specifier-type 'bignum))
246 '(%lastn/bignum list n))
248 (give-up-ir1-transform "second argument type too vague"))))))))
250 (define-source-transform gethash (&rest args)
252 (2 `(sb!impl::gethash3 ,@args nil))
253 (3 `(sb!impl::gethash3 ,@args))
255 (define-source-transform get (&rest args)
257 (2 `(sb!impl::get2 ,@args))
258 (3 `(sb!impl::get3 ,@args))
261 (defvar *default-nthcdr-open-code-limit* 6)
262 (defvar *extreme-nthcdr-open-code-limit* 20)
264 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
265 "convert NTHCDR to CAxxR"
266 (unless (constant-lvar-p n)
267 (give-up-ir1-transform))
268 (let ((n (lvar-value n)))
270 (if (policy node (and (= speed 3) (= space 0)))
271 *extreme-nthcdr-open-code-limit*
272 *default-nthcdr-open-code-limit*))
273 (give-up-ir1-transform))
278 `(cdr ,(frob (1- n))))))
281 ;;;; arithmetic and numerology
283 (define-source-transform plusp (x) `(> ,x 0))
284 (define-source-transform minusp (x) `(< ,x 0))
285 (define-source-transform zerop (x) `(= ,x 0))
287 (define-source-transform 1+ (x) `(+ ,x 1))
288 (define-source-transform 1- (x) `(- ,x 1))
290 (define-source-transform oddp (x) `(logtest ,x 1))
291 (define-source-transform evenp (x) `(not (logtest ,x 1)))
293 ;;; Note that all the integer division functions are available for
294 ;;; inline expansion.
296 (macrolet ((deffrob (fun)
297 `(define-source-transform ,fun (x &optional (y nil y-p))
304 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
306 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
309 ;;; This used to be a source transform (hence the lack of restrictions
310 ;;; on the argument types), but we make it a regular transform so that
311 ;;; the VM has a chance to see the bare LOGTEST and potentiall choose
312 ;;; to implement it differently. --njf, 06-02-2006
314 ;;; Other transforms may be useful even with direct LOGTEST VOPs; let
315 ;;; them fire (including the type-directed constant folding below), but
316 ;;; disable the inlining rewrite in such cases. -- PK, 2013-05-20
317 (deftransform logtest ((x y) * * :node node)
318 (let ((type (two-arg-derive-type x y
319 #'logand-derive-type-aux
321 (multiple-value-bind (typep definitely)
323 (cond ((and (not typep) definitely)
325 ((type= type (specifier-type '(eql 0)))
327 ((neq :default (combination-implementation-style node))
328 (give-up-ir1-transform))
330 `(not (zerop (logand x y))))))))
332 (deftransform logbitp
333 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
334 (unsigned-byte #.sb!vm:n-word-bits))))
335 `(if (>= index #.sb!vm:n-word-bits)
337 (not (zerop (logand integer (ash 1 index))))))
339 (define-source-transform byte (size position)
340 `(cons ,size ,position))
341 (define-source-transform byte-size (spec) `(car ,spec))
342 (define-source-transform byte-position (spec) `(cdr ,spec))
343 (define-source-transform ldb-test (bytespec integer)
344 `(not (zerop (mask-field ,bytespec ,integer))))
346 ;;; With the ratio and complex accessors, we pick off the "identity"
347 ;;; case, and use a primitive to handle the cell access case.
348 (define-source-transform numerator (num)
349 (once-only ((n-num `(the rational ,num)))
353 (define-source-transform denominator (num)
354 (once-only ((n-num `(the rational ,num)))
356 (%denominator ,n-num)
359 ;;;; interval arithmetic for computing bounds
361 ;;;; This is a set of routines for operating on intervals. It
362 ;;;; implements a simple interval arithmetic package. Although SBCL
363 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
364 ;;;; for two reasons:
366 ;;;; 1. This package is simpler than NUMERIC-TYPE.
368 ;;;; 2. It makes debugging much easier because you can just strip
369 ;;;; out these routines and test them independently of SBCL. (This is a
372 ;;;; One disadvantage is a probable increase in consing because we
373 ;;;; have to create these new interval structures even though
374 ;;;; numeric-type has everything we want to know. Reason 2 wins for
377 ;;; Support operations that mimic real arithmetic comparison
378 ;;; operators, but imposing a total order on the floating points such
379 ;;; that negative zeros are strictly less than positive zeros.
380 (macrolet ((def (name op)
383 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
384 (,op (float-sign x) (float-sign y))
386 (def signed-zero->= >=)
387 (def signed-zero-> >)
388 (def signed-zero-= =)
389 (def signed-zero-< <)
390 (def signed-zero-<= <=))
392 ;;; The basic interval type. It can handle open and closed intervals.
393 ;;; A bound is open if it is a list containing a number, just like
394 ;;; Lisp says. NIL means unbounded.
395 (defstruct (interval (:constructor %make-interval)
399 (defun make-interval (&key low high)
400 (labels ((normalize-bound (val)
403 (float-infinity-p val))
404 ;; Handle infinities.
408 ;; Handle any closed bounds.
411 ;; We have an open bound. Normalize the numeric
412 ;; bound. If the normalized bound is still a number
413 ;; (not nil), keep the bound open. Otherwise, the
414 ;; bound is really unbounded, so drop the openness.
415 (let ((new-val (normalize-bound (first val))))
417 ;; The bound exists, so keep it open still.
420 (error "unknown bound type in MAKE-INTERVAL")))))
421 (%make-interval :low (normalize-bound low)
422 :high (normalize-bound high))))
424 ;;; Given a number X, create a form suitable as a bound for an
425 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
426 #!-sb-fluid (declaim (inline set-bound))
427 (defun set-bound (x open-p)
428 (if (and x open-p) (list x) x))
430 ;;; Apply the function F to a bound X. If X is an open bound and the
431 ;;; function is declared strictly monotonic, then the result will be
432 ;;; open. IF X is NIL, the result is NIL.
433 (defun bound-func (f x strict)
434 (declare (type function f))
437 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
438 ;; With these traps masked, we might get things like infinity
439 ;; or negative infinity returned. Check for this and return
440 ;; NIL to indicate unbounded.
441 (let ((y (funcall f (type-bound-number x))))
443 (float-infinity-p y))
445 (set-bound y (and strict (consp x))))))
446 ;; Some numerical operations will signal SIMPLE-TYPE-ERROR, e.g.
447 ;; in the course of converting a bignum to a float. Default to
449 (simple-type-error ()))))
451 (defun safe-double-coercion-p (x)
452 (or (typep x 'double-float)
453 (<= most-negative-double-float x most-positive-double-float)))
455 (defun safe-single-coercion-p (x)
456 (or (typep x 'single-float)
458 ;; Fix for bug 420, and related issues: during type derivation we often
459 ;; end up deriving types for both
461 ;; (some-op <int> <single>)
463 ;; (some-op (coerce <int> 'single-float) <single>)
465 ;; or other equivalent transformed forms. The problem with this
466 ;; is that on x86 (+ <int> <single>) is on the machine level
469 ;; (coerce (+ (coerce <int> 'double-float)
470 ;; (coerce <single> 'double-float))
473 ;; so if the result of (coerce <int> 'single-float) is not exact, the
474 ;; derived types for the transformed forms will have an empty
475 ;; intersection -- which in turn means that the compiler will conclude
476 ;; that the call never returns, and all hell breaks lose when it *does*
477 ;; return at runtime. (This affects not just +, but other operators are
480 ;; See also: SAFE-CTYPE-FOR-SINGLE-COERCION-P
482 ;; FIXME: If we ever add SSE-support for x86, this conditional needs to
485 (not (typep x `(or (integer * (,most-negative-exactly-single-float-fixnum))
486 (integer (,most-positive-exactly-single-float-fixnum) *))))
487 (<= most-negative-single-float x most-positive-single-float))))
489 ;;; Apply a binary operator OP to two bounds X and Y. The result is
490 ;;; NIL if either is NIL. Otherwise bound is computed and the result
491 ;;; is open if either X or Y is open.
493 ;;; FIXME: only used in this file, not needed in target runtime
495 ;;; ANSI contaigon specifies coercion to floating point if one of the
496 ;;; arguments is floating point. Here we should check to be sure that
497 ;;; the other argument is within the bounds of that floating point
500 (defmacro safely-binop (op x y)
502 ((typep ,x 'double-float)
503 (when (safe-double-coercion-p ,y)
505 ((typep ,y 'double-float)
506 (when (safe-double-coercion-p ,x)
508 ((typep ,x 'single-float)
509 (when (safe-single-coercion-p ,y)
511 ((typep ,y 'single-float)
512 (when (safe-single-coercion-p ,x)
516 (defmacro bound-binop (op x y)
517 (with-unique-names (xb yb res)
519 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
520 (let* ((,xb (type-bound-number ,x))
521 (,yb (type-bound-number ,y))
522 (,res (safely-binop ,op ,xb ,yb)))
524 (and (or (consp ,x) (consp ,y))
525 ;; Open bounds can very easily be messed up
526 ;; by FP rounding, so take care here.
529 ;; Multiplying a greater-than-zero with
530 ;; less than one can round to zero.
531 `(or (not (fp-zero-p ,res))
532 (cond ((and (consp ,x) (fp-zero-p ,xb))
534 ((and (consp ,y) (fp-zero-p ,yb))
537 ;; Dividing a greater-than-zero with
538 ;; greater than one can round to zero.
539 `(or (not (fp-zero-p ,res))
540 (cond ((and (consp ,x) (fp-zero-p ,xb))
542 ((and (consp ,y) (fp-zero-p ,yb))
545 ;; Adding or subtracting greater-than-zero
546 ;; can end up with identity.
547 `(and (not (fp-zero-p ,xb))
548 (not (fp-zero-p ,yb))))))))))))
550 (defun coercion-loses-precision-p (val type)
553 (double-float (subtypep type 'single-float))
554 (rational (subtypep type 'float))
555 (t (bug "Unexpected arguments to bounds coercion: ~S ~S" val type))))
557 (defun coerce-for-bound (val type)
559 (let ((xbound (coerce-for-bound (car val) type)))
560 (if (coercion-loses-precision-p (car val) type)
564 ((subtypep type 'double-float)
565 (if (<= most-negative-double-float val most-positive-double-float)
567 ((or (subtypep type 'single-float) (subtypep type 'float))
568 ;; coerce to float returns a single-float
569 (if (<= most-negative-single-float val most-positive-single-float)
571 (t (coerce val type)))))
573 (defun coerce-and-truncate-floats (val type)
576 (let ((xbound (coerce-for-bound (car val) type)))
577 (if (coercion-loses-precision-p (car val) type)
581 ((subtypep type 'double-float)
582 (if (<= most-negative-double-float val most-positive-double-float)
584 (if (< val most-negative-double-float)
585 most-negative-double-float most-positive-double-float)))
586 ((or (subtypep type 'single-float) (subtypep type 'float))
587 ;; coerce to float returns a single-float
588 (if (<= most-negative-single-float val most-positive-single-float)
590 (if (< val most-negative-single-float)
591 most-negative-single-float most-positive-single-float)))
592 (t (coerce val type))))))
594 ;;; Convert a numeric-type object to an interval object.
595 (defun numeric-type->interval (x)
596 (declare (type numeric-type x))
597 (make-interval :low (numeric-type-low x)
598 :high (numeric-type-high x)))
600 (defun type-approximate-interval (type)
601 (declare (type ctype type))
602 (let ((types (prepare-arg-for-derive-type type))
605 (let ((type (if (member-type-p type)
606 (convert-member-type type)
608 (unless (numeric-type-p type)
609 (return-from type-approximate-interval nil))
610 (let ((interval (numeric-type->interval type)))
613 (interval-approximate-union result interval)
617 (defun copy-interval-limit (limit)
622 (defun copy-interval (x)
623 (declare (type interval x))
624 (make-interval :low (copy-interval-limit (interval-low x))
625 :high (copy-interval-limit (interval-high x))))
627 ;;; Given a point P contained in the interval X, split X into two
628 ;;; intervals at the point P. If CLOSE-LOWER is T, then the left
629 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
630 ;;; contains P. You can specify both to be T or NIL.
631 (defun interval-split (p x &optional close-lower close-upper)
632 (declare (type number p)
634 (list (make-interval :low (copy-interval-limit (interval-low x))
635 :high (if close-lower p (list p)))
636 (make-interval :low (if close-upper (list p) p)
637 :high (copy-interval-limit (interval-high x)))))
639 ;;; Return the closure of the interval. That is, convert open bounds
640 ;;; to closed bounds.
641 (defun interval-closure (x)
642 (declare (type interval x))
643 (make-interval :low (type-bound-number (interval-low x))
644 :high (type-bound-number (interval-high x))))
646 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
647 ;;; '-. Otherwise return NIL.
648 (defun interval-range-info (x &optional (point 0))
649 (declare (type interval x))
650 (let ((lo (interval-low x))
651 (hi (interval-high x)))
652 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
654 ((and hi (signed-zero->= point (type-bound-number hi)))
659 ;;; Test to see whether the interval X is bounded. HOW determines the
660 ;;; test, and should be either ABOVE, BELOW, or BOTH.
661 (defun interval-bounded-p (x how)
662 (declare (type interval x))
669 (and (interval-low x) (interval-high x)))))
671 ;;; See whether the interval X contains the number P, taking into
672 ;;; account that the interval might not be closed.
673 (defun interval-contains-p (p x)
674 (declare (type number p)
676 ;; Does the interval X contain the number P? This would be a lot
677 ;; easier if all intervals were closed!
678 (let ((lo (interval-low x))
679 (hi (interval-high x)))
681 ;; The interval is bounded
682 (if (and (signed-zero-<= (type-bound-number lo) p)
683 (signed-zero-<= p (type-bound-number hi)))
684 ;; P is definitely in the closure of the interval.
685 ;; We just need to check the end points now.
686 (cond ((signed-zero-= p (type-bound-number lo))
688 ((signed-zero-= p (type-bound-number hi))
693 ;; Interval with upper bound
694 (if (signed-zero-< p (type-bound-number hi))
696 (and (numberp hi) (signed-zero-= p hi))))
698 ;; Interval with lower bound
699 (if (signed-zero-> p (type-bound-number lo))
701 (and (numberp lo) (signed-zero-= p lo))))
703 ;; Interval with no bounds
706 ;;; Determine whether two intervals X and Y intersect. Return T if so.
707 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
708 ;;; were closed. Otherwise the intervals are treated as they are.
710 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
711 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
712 ;;; is T, then they do intersect because we use the closure of X = [0,
713 ;;; 1] and Y = [1, 2] to determine intersection.
714 (defun interval-intersect-p (x y &optional closed-intervals-p)
715 (declare (type interval x y))
716 (and (interval-intersection/difference (if closed-intervals-p
719 (if closed-intervals-p
724 ;;; Are the two intervals adjacent? That is, is there a number
725 ;;; between the two intervals that is not an element of either
726 ;;; interval? If so, they are not adjacent. For example [0, 1) and
727 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
728 ;;; between both intervals.
729 (defun interval-adjacent-p (x y)
730 (declare (type interval x y))
731 (flet ((adjacent (lo hi)
732 ;; Check to see whether lo and hi are adjacent. If either is
733 ;; nil, they can't be adjacent.
734 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
735 ;; The bounds are equal. They are adjacent if one of
736 ;; them is closed (a number). If both are open (consp),
737 ;; then there is a number that lies between them.
738 (or (numberp lo) (numberp hi)))))
739 (or (adjacent (interval-low y) (interval-high x))
740 (adjacent (interval-low x) (interval-high y)))))
742 ;;; Compute the intersection and difference between two intervals.
743 ;;; Two values are returned: the intersection and the difference.
745 ;;; Let the two intervals be X and Y, and let I and D be the two
746 ;;; values returned by this function. Then I = X intersect Y. If I
747 ;;; is NIL (the empty set), then D is X union Y, represented as the
748 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
749 ;;; - I, which is a list of two intervals.
751 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
752 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
753 (defun interval-intersection/difference (x y)
754 (declare (type interval x y))
755 (let ((x-lo (interval-low x))
756 (x-hi (interval-high x))
757 (y-lo (interval-low y))
758 (y-hi (interval-high y)))
761 ;; If p is an open bound, make it closed. If p is a closed
762 ;; bound, make it open.
766 (test-number (p int bound)
767 ;; Test whether P is in the interval.
768 (let ((pn (type-bound-number p)))
769 (when (interval-contains-p pn (interval-closure int))
770 ;; Check for endpoints.
771 (let* ((lo (interval-low int))
772 (hi (interval-high int))
773 (lon (type-bound-number lo))
774 (hin (type-bound-number hi)))
776 ;; Interval may be a point.
777 ((and lon hin (= lon hin pn))
778 (and (numberp p) (numberp lo) (numberp hi)))
779 ;; Point matches the low end.
780 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
781 ;; (P [P,?} => TRUE P) [P,?} => FALSE
782 ;; (P (P,?} => TRUE P) (P,?} => FALSE
783 ((and lon (= pn lon))
784 (or (and (numberp p) (numberp lo))
785 (and (consp p) (eq :low bound))))
786 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
787 ;; P) {?,P] => TRUE (P {?,P] => FALSE
788 ;; P) {?,P) => TRUE (P {?,P) => FALSE
789 ((and hin (= pn hin))
790 (or (and (numberp p) (numberp hi))
791 (and (consp p) (eq :high bound))))
792 ;; Not an endpoint, all is well.
795 (test-lower-bound (p int)
796 ;; P is a lower bound of an interval.
798 (test-number p int :low)
799 (not (interval-bounded-p int 'below))))
800 (test-upper-bound (p int)
801 ;; P is an upper bound of an interval.
803 (test-number p int :high)
804 (not (interval-bounded-p int 'above)))))
805 (let ((x-lo-in-y (test-lower-bound x-lo y))
806 (x-hi-in-y (test-upper-bound x-hi y))
807 (y-lo-in-x (test-lower-bound y-lo x))
808 (y-hi-in-x (test-upper-bound y-hi x)))
809 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
810 ;; Intervals intersect. Let's compute the intersection
811 ;; and the difference.
812 (multiple-value-bind (lo left-lo left-hi)
813 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
814 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
815 (multiple-value-bind (hi right-lo right-hi)
817 (values x-hi (opposite-bound x-hi) y-hi))
819 (values y-hi (opposite-bound y-hi) x-hi)))
820 (values (make-interval :low lo :high hi)
821 (list (make-interval :low left-lo
823 (make-interval :low right-lo
826 (values nil (list x y))))))))
828 ;;; If intervals X and Y intersect, return a new interval that is the
829 ;;; union of the two. If they do not intersect, return NIL.
830 (defun interval-merge-pair (x y)
831 (declare (type interval x y))
832 ;; If x and y intersect or are adjacent, create the union.
833 ;; Otherwise return nil
834 (when (or (interval-intersect-p x y)
835 (interval-adjacent-p x y))
836 (flet ((select-bound (x1 x2 min-op max-op)
837 (let ((x1-val (type-bound-number x1))
838 (x2-val (type-bound-number x2)))
840 ;; Both bounds are finite. Select the right one.
841 (cond ((funcall min-op x1-val x2-val)
842 ;; x1 is definitely better.
844 ((funcall max-op x1-val x2-val)
845 ;; x2 is definitely better.
848 ;; Bounds are equal. Select either
849 ;; value and make it open only if
851 (set-bound x1-val (and (consp x1) (consp x2))))))
853 ;; At least one bound is not finite. The
854 ;; non-finite bound always wins.
856 (let* ((x-lo (copy-interval-limit (interval-low x)))
857 (x-hi (copy-interval-limit (interval-high x)))
858 (y-lo (copy-interval-limit (interval-low y)))
859 (y-hi (copy-interval-limit (interval-high y))))
860 (make-interval :low (select-bound x-lo y-lo #'< #'>)
861 :high (select-bound x-hi y-hi #'> #'<))))))
863 ;;; return the minimal interval, containing X and Y
864 (defun interval-approximate-union (x y)
865 (cond ((interval-merge-pair x y))
867 (make-interval :low (copy-interval-limit (interval-low x))
868 :high (copy-interval-limit (interval-high y))))
870 (make-interval :low (copy-interval-limit (interval-low y))
871 :high (copy-interval-limit (interval-high x))))))
873 ;;; basic arithmetic operations on intervals. We probably should do
874 ;;; true interval arithmetic here, but it's complicated because we
875 ;;; have float and integer types and bounds can be open or closed.
877 ;;; the negative of an interval
878 (defun interval-neg (x)
879 (declare (type interval x))
880 (make-interval :low (bound-func #'- (interval-high x) t)
881 :high (bound-func #'- (interval-low x) t)))
883 ;;; Add two intervals.
884 (defun interval-add (x y)
885 (declare (type interval x y))
886 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
887 :high (bound-binop + (interval-high x) (interval-high y))))
889 ;;; Subtract two intervals.
890 (defun interval-sub (x y)
891 (declare (type interval x y))
892 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
893 :high (bound-binop - (interval-high x) (interval-low y))))
895 ;;; Multiply two intervals.
896 (defun interval-mul (x y)
897 (declare (type interval x y))
898 (flet ((bound-mul (x y)
899 (cond ((or (null x) (null y))
900 ;; Multiply by infinity is infinity
902 ((or (and (numberp x) (zerop x))
903 (and (numberp y) (zerop y)))
904 ;; Multiply by closed zero is special. The result
905 ;; is always a closed bound. But don't replace this
906 ;; with zero; we want the multiplication to produce
907 ;; the correct signed zero, if needed. Use SIGNUM
908 ;; to avoid trying to multiply huge bignums with 0.0.
909 (* (signum (type-bound-number x)) (signum (type-bound-number y))))
910 ((or (and (floatp x) (float-infinity-p x))
911 (and (floatp y) (float-infinity-p y)))
912 ;; Infinity times anything is infinity
915 ;; General multiply. The result is open if either is open.
916 (bound-binop * x y)))))
917 (let ((x-range (interval-range-info x))
918 (y-range (interval-range-info y)))
919 (cond ((null x-range)
920 ;; Split x into two and multiply each separately
921 (destructuring-bind (x- x+) (interval-split 0 x t t)
922 (interval-merge-pair (interval-mul x- y)
923 (interval-mul x+ y))))
925 ;; Split y into two and multiply each separately
926 (destructuring-bind (y- y+) (interval-split 0 y t t)
927 (interval-merge-pair (interval-mul x y-)
928 (interval-mul x y+))))
930 (interval-neg (interval-mul (interval-neg x) y)))
932 (interval-neg (interval-mul x (interval-neg y))))
933 ((and (eq x-range '+) (eq y-range '+))
934 ;; If we are here, X and Y are both positive.
936 :low (bound-mul (interval-low x) (interval-low y))
937 :high (bound-mul (interval-high x) (interval-high y))))
939 (bug "excluded case in INTERVAL-MUL"))))))
941 ;;; Divide two intervals.
942 (defun interval-div (top bot)
943 (declare (type interval top bot))
944 (flet ((bound-div (x y y-low-p)
947 ;; Divide by infinity means result is 0. However,
948 ;; we need to watch out for the sign of the result,
949 ;; to correctly handle signed zeros. We also need
950 ;; to watch out for positive or negative infinity.
951 (if (floatp (type-bound-number x))
953 (- (float-sign (type-bound-number x) 0.0))
954 (float-sign (type-bound-number x) 0.0))
956 ((zerop (type-bound-number y))
957 ;; Divide by zero means result is infinity
960 (bound-binop / x y)))))
961 (let ((top-range (interval-range-info top))
962 (bot-range (interval-range-info bot)))
963 (cond ((null bot-range)
964 ;; The denominator contains zero, so anything goes!
965 (make-interval :low nil :high nil))
967 ;; Denominator is negative so flip the sign, compute the
968 ;; result, and flip it back.
969 (interval-neg (interval-div top (interval-neg bot))))
971 ;; Split top into two positive and negative parts, and
972 ;; divide each separately
973 (destructuring-bind (top- top+) (interval-split 0 top t t)
974 (interval-merge-pair (interval-div top- bot)
975 (interval-div top+ bot))))
977 ;; Top is negative so flip the sign, divide, and flip the
978 ;; sign of the result.
979 (interval-neg (interval-div (interval-neg top) bot)))
980 ((and (eq top-range '+) (eq bot-range '+))
983 :low (bound-div (interval-low top) (interval-high bot) t)
984 :high (bound-div (interval-high top) (interval-low bot) nil)))
986 (bug "excluded case in INTERVAL-DIV"))))))
988 ;;; Apply the function F to the interval X. If X = [a, b], then the
989 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
990 ;;; result makes sense. It will if F is monotonic increasing (or, if
991 ;;; the interval is closed, non-decreasing).
993 ;;; (Actually most uses of INTERVAL-FUNC are coercions to float types,
994 ;;; which are not monotonic increasing, so default to calling
995 ;;; BOUND-FUNC with a non-strict argument).
996 (defun interval-func (f x &optional increasing)
997 (declare (type function f)
999 (let ((lo (bound-func f (interval-low x) increasing))
1000 (hi (bound-func f (interval-high x) increasing)))
1001 (make-interval :low lo :high hi)))
1003 ;;; Return T if X < Y. That is every number in the interval X is
1004 ;;; always less than any number in the interval Y.
1005 (defun interval-< (x y)
1006 (declare (type interval x y))
1007 ;; X < Y only if X is bounded above, Y is bounded below, and they
1009 (when (and (interval-bounded-p x 'above)
1010 (interval-bounded-p y 'below))
1011 ;; Intervals are bounded in the appropriate way. Make sure they
1013 (let ((left (interval-high x))
1014 (right (interval-low y)))
1015 (cond ((> (type-bound-number left)
1016 (type-bound-number right))
1017 ;; The intervals definitely overlap, so result is NIL.
1019 ((< (type-bound-number left)
1020 (type-bound-number right))
1021 ;; The intervals definitely don't touch, so result is T.
1024 ;; Limits are equal. Check for open or closed bounds.
1025 ;; Don't overlap if one or the other are open.
1026 (or (consp left) (consp right)))))))
1028 ;;; Return T if X >= Y. That is, every number in the interval X is
1029 ;;; always greater than any number in the interval Y.
1030 (defun interval->= (x y)
1031 (declare (type interval x y))
1032 ;; X >= Y if lower bound of X >= upper bound of Y
1033 (when (and (interval-bounded-p x 'below)
1034 (interval-bounded-p y 'above))
1035 (>= (type-bound-number (interval-low x))
1036 (type-bound-number (interval-high y)))))
1038 ;;; Return T if X = Y.
1039 (defun interval-= (x y)
1040 (declare (type interval x y))
1041 (and (interval-bounded-p x 'both)
1042 (interval-bounded-p y 'both)
1046 ;; Open intervals cannot be =
1047 (return-from interval-= nil))))
1048 ;; Both intervals refer to the same point
1049 (= (bound (interval-high x)) (bound (interval-low x))
1050 (bound (interval-high y)) (bound (interval-low y))))))
1052 ;;; Return T if X /= Y
1053 (defun interval-/= (x y)
1054 (not (interval-intersect-p x y)))
1056 ;;; Return an interval that is the absolute value of X. Thus, if
1057 ;;; X = [-1 10], the result is [0, 10].
1058 (defun interval-abs (x)
1059 (declare (type interval x))
1060 (case (interval-range-info x)
1066 (destructuring-bind (x- x+) (interval-split 0 x t t)
1067 (interval-merge-pair (interval-neg x-) x+)))))
1069 ;;; Compute the square of an interval.
1070 (defun interval-sqr (x)
1071 (declare (type interval x))
1072 (interval-func (lambda (x) (* x x)) (interval-abs x)))
1074 ;;;; numeric DERIVE-TYPE methods
1076 ;;; a utility for defining derive-type methods of integer operations. If
1077 ;;; the types of both X and Y are integer types, then we compute a new
1078 ;;; integer type with bounds determined by FUN when applied to X and Y.
1079 ;;; Otherwise, we use NUMERIC-CONTAGION.
1080 (defun derive-integer-type-aux (x y fun)
1081 (declare (type function fun))
1082 (if (and (numeric-type-p x) (numeric-type-p y)
1083 (eq (numeric-type-class x) 'integer)
1084 (eq (numeric-type-class y) 'integer)
1085 (eq (numeric-type-complexp x) :real)
1086 (eq (numeric-type-complexp y) :real))
1087 (multiple-value-bind (low high) (funcall fun x y)
1088 (make-numeric-type :class 'integer
1092 (numeric-contagion x y)))
1094 (defun derive-integer-type (x y fun)
1095 (declare (type lvar x y) (type function fun))
1096 (let ((x (lvar-type x))
1098 (derive-integer-type-aux x y fun)))
1100 ;;; simple utility to flatten a list
1101 (defun flatten-list (x)
1102 (labels ((flatten-and-append (tree list)
1103 (cond ((null tree) list)
1104 ((atom tree) (cons tree list))
1105 (t (flatten-and-append
1106 (car tree) (flatten-and-append (cdr tree) list))))))
1107 (flatten-and-append x nil)))
1109 ;;; Take some type of lvar and massage it so that we get a list of the
1110 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
1112 (defun prepare-arg-for-derive-type (arg)
1113 (flet ((listify (arg)
1118 (union-type-types arg))
1121 (unless (eq arg *empty-type*)
1122 ;; Make sure all args are some type of numeric-type. For member
1123 ;; types, convert the list of members into a union of equivalent
1124 ;; single-element member-type's.
1125 (let ((new-args nil))
1126 (dolist (arg (listify arg))
1127 (if (member-type-p arg)
1128 ;; Run down the list of members and convert to a list of
1130 (mapc-member-type-members
1132 (push (if (numberp member)
1133 (make-member-type :members (list member))
1137 (push arg new-args)))
1138 (unless (member *empty-type* new-args)
1141 ;;; Convert from the standard type convention for which -0.0 and 0.0
1142 ;;; are equal to an intermediate convention for which they are
1143 ;;; considered different which is more natural for some of the
1145 (defun convert-numeric-type (type)
1146 (declare (type numeric-type type))
1147 ;;; Only convert real float interval delimiters types.
1148 (if (eq (numeric-type-complexp type) :real)
1149 (let* ((lo (numeric-type-low type))
1150 (lo-val (type-bound-number lo))
1151 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
1152 (hi (numeric-type-high type))
1153 (hi-val (type-bound-number hi))
1154 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
1155 (if (or lo-float-zero-p hi-float-zero-p)
1157 :class (numeric-type-class type)
1158 :format (numeric-type-format type)
1160 :low (if lo-float-zero-p
1162 (list (float 0.0 lo-val))
1163 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
1165 :high (if hi-float-zero-p
1167 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
1174 ;;; Convert back from the intermediate convention for which -0.0 and
1175 ;;; 0.0 are considered different to the standard type convention for
1176 ;;; which and equal.
1177 (defun convert-back-numeric-type (type)
1178 (declare (type numeric-type type))
1179 ;;; Only convert real float interval delimiters types.
1180 (if (eq (numeric-type-complexp type) :real)
1181 (let* ((lo (numeric-type-low type))
1182 (lo-val (type-bound-number lo))
1184 (and lo (floatp lo-val) (= lo-val 0.0)
1185 (float-sign lo-val)))
1186 (hi (numeric-type-high type))
1187 (hi-val (type-bound-number hi))
1189 (and hi (floatp hi-val) (= hi-val 0.0)
1190 (float-sign hi-val))))
1192 ;; (float +0.0 +0.0) => (member 0.0)
1193 ;; (float -0.0 -0.0) => (member -0.0)
1194 ((and lo-float-zero-p hi-float-zero-p)
1195 ;; shouldn't have exclusive bounds here..
1196 (aver (and (not (consp lo)) (not (consp hi))))
1197 (if (= lo-float-zero-p hi-float-zero-p)
1198 ;; (float +0.0 +0.0) => (member 0.0)
1199 ;; (float -0.0 -0.0) => (member -0.0)
1200 (specifier-type `(member ,lo-val))
1201 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1202 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1203 (make-numeric-type :class (numeric-type-class type)
1204 :format (numeric-type-format type)
1210 ;; (float -0.0 x) => (float 0.0 x)
1211 ((and (not (consp lo)) (minusp lo-float-zero-p))
1212 (make-numeric-type :class (numeric-type-class type)
1213 :format (numeric-type-format type)
1215 :low (float 0.0 lo-val)
1217 ;; (float (+0.0) x) => (float (0.0) x)
1218 ((and (consp lo) (plusp lo-float-zero-p))
1219 (make-numeric-type :class (numeric-type-class type)
1220 :format (numeric-type-format type)
1222 :low (list (float 0.0 lo-val))
1225 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1226 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1227 (list (make-member-type :members (list (float 0.0 lo-val)))
1228 (make-numeric-type :class (numeric-type-class type)
1229 :format (numeric-type-format type)
1231 :low (list (float 0.0 lo-val))
1235 ;; (float x +0.0) => (float x 0.0)
1236 ((and (not (consp hi)) (plusp hi-float-zero-p))
1237 (make-numeric-type :class (numeric-type-class type)
1238 :format (numeric-type-format type)
1241 :high (float 0.0 hi-val)))
1242 ;; (float x (-0.0)) => (float x (0.0))
1243 ((and (consp hi) (minusp hi-float-zero-p))
1244 (make-numeric-type :class (numeric-type-class type)
1245 :format (numeric-type-format type)
1248 :high (list (float 0.0 hi-val))))
1250 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1251 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1252 (list (make-member-type :members (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val)))
1253 (make-numeric-type :class (numeric-type-class type)
1254 :format (numeric-type-format type)
1257 :high (list (float 0.0 hi-val)))))))
1263 ;;; Convert back a possible list of numeric types.
1264 (defun convert-back-numeric-type-list (type-list)
1267 (let ((results '()))
1268 (dolist (type type-list)
1269 (if (numeric-type-p type)
1270 (let ((result (convert-back-numeric-type type)))
1272 (setf results (append results result))
1273 (push result results)))
1274 (push type results)))
1277 (convert-back-numeric-type type-list))
1279 (convert-back-numeric-type-list (union-type-types type-list)))
1283 ;;; Take a list of types and return a canonical type specifier,
1284 ;;; combining any MEMBER types together. If both positive and negative
1285 ;;; MEMBER types are present they are converted to a float type.
1286 ;;; XXX This would be far simpler if the type-union methods could handle
1287 ;;; member/number unions.
1289 ;;; If we're about to generate an overly complex union of numeric types, start
1290 ;;; collapse the ranges together.
1292 ;;; FIXME: The MEMBER canonicalization parts of MAKE-DERIVED-UNION-TYPE and
1293 ;;; entire CONVERT-MEMBER-TYPE probably belong in the kernel's type logic,
1294 ;;; invoked always, instead of in the compiler, invoked only during some type
1296 (defvar *derived-numeric-union-complexity-limit* 6)
1298 (defun make-derived-union-type (type-list)
1299 (let ((xset (alloc-xset))
1302 (numeric-type *empty-type*))
1303 (dolist (type type-list)
1304 (cond ((member-type-p type)
1305 (mapc-member-type-members
1307 (if (fp-zero-p member)
1308 (unless (member member fp-zeroes)
1309 (pushnew member fp-zeroes))
1310 (add-to-xset member xset)))
1312 ((numeric-type-p type)
1313 (let ((*approximate-numeric-unions*
1314 (when (and (union-type-p numeric-type)
1315 (nthcdr *derived-numeric-union-complexity-limit*
1316 (union-type-types numeric-type)))
1318 (setf numeric-type (type-union type numeric-type))))
1320 (push type misc-types))))
1321 (if (and (xset-empty-p xset) (not fp-zeroes))
1322 (apply #'type-union numeric-type misc-types)
1323 (apply #'type-union (make-member-type :xset xset :fp-zeroes fp-zeroes)
1324 numeric-type misc-types))))
1326 ;;; Convert a member type with a single member to a numeric type.
1327 (defun convert-member-type (arg)
1328 (let* ((members (member-type-members arg))
1329 (member (first members))
1330 (member-type (type-of member)))
1331 (aver (not (rest members)))
1332 (specifier-type (cond ((typep member 'integer)
1333 `(integer ,member ,member))
1334 ((memq member-type '(short-float single-float
1335 double-float long-float))
1336 `(,member-type ,member ,member))
1340 ;;; This is used in defoptimizers for computing the resulting type of
1343 ;;; Given the lvar ARG, derive the resulting type using the
1344 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1345 ;;; "atomic" lvar type like numeric-type or member-type (containing
1346 ;;; just one element). It should return the resulting type, which can
1347 ;;; be a list of types.
1349 ;;; For the case of member types, if a MEMBER-FUN is given it is
1350 ;;; called to compute the result otherwise the member type is first
1351 ;;; converted to a numeric type and the DERIVE-FUN is called.
1352 (defun one-arg-derive-type (arg derive-fun member-fun
1353 &optional (convert-type t))
1354 (declare (type function derive-fun)
1355 (type (or null function) member-fun))
1356 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1362 (with-float-traps-masked
1363 (:underflow :overflow :divide-by-zero)
1365 `(eql ,(funcall member-fun
1366 (first (member-type-members x))))))
1367 ;; Otherwise convert to a numeric type.
1368 (let ((result-type-list
1369 (funcall derive-fun (convert-member-type x))))
1371 (convert-back-numeric-type-list result-type-list)
1372 result-type-list))))
1375 (convert-back-numeric-type-list
1376 (funcall derive-fun (convert-numeric-type x)))
1377 (funcall derive-fun x)))
1379 *universal-type*))))
1380 ;; Run down the list of args and derive the type of each one,
1381 ;; saving all of the results in a list.
1382 (let ((results nil))
1383 (dolist (arg arg-list)
1384 (let ((result (deriver arg)))
1386 (setf results (append results result))
1387 (push result results))))
1389 (make-derived-union-type results)
1390 (first results)))))))
1392 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1393 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1394 ;;; original args and a third which is T to indicate if the two args
1395 ;;; really represent the same lvar. This is useful for deriving the
1396 ;;; type of things like (* x x), which should always be positive. If
1397 ;;; we didn't do this, we wouldn't be able to tell.
1398 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1399 &optional (convert-type t))
1400 (declare (type function derive-fun fun))
1401 (flet ((deriver (x y same-arg)
1402 (cond ((and (member-type-p x) (member-type-p y))
1403 (let* ((x (first (member-type-members x)))
1404 (y (first (member-type-members y)))
1405 (result (ignore-errors
1406 (with-float-traps-masked
1407 (:underflow :overflow :divide-by-zero
1409 (funcall fun x y)))))
1410 (cond ((null result) *empty-type*)
1411 ((and (floatp result) (float-nan-p result))
1412 (make-numeric-type :class 'float
1413 :format (type-of result)
1416 (specifier-type `(eql ,result))))))
1417 ((and (member-type-p x) (numeric-type-p y))
1418 (let* ((x (convert-member-type x))
1419 (y (if convert-type (convert-numeric-type y) y))
1420 (result (funcall derive-fun x y same-arg)))
1422 (convert-back-numeric-type-list result)
1424 ((and (numeric-type-p x) (member-type-p y))
1425 (let* ((x (if convert-type (convert-numeric-type x) x))
1426 (y (convert-member-type y))
1427 (result (funcall derive-fun x y same-arg)))
1429 (convert-back-numeric-type-list result)
1431 ((and (numeric-type-p x) (numeric-type-p y))
1432 (let* ((x (if convert-type (convert-numeric-type x) x))
1433 (y (if convert-type (convert-numeric-type y) y))
1434 (result (funcall derive-fun x y same-arg)))
1436 (convert-back-numeric-type-list result)
1439 *universal-type*))))
1440 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1441 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1442 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1444 (let ((results nil))
1446 ;; Since the args are the same LVARs, just run down the
1449 (let ((result (deriver x x same-arg)))
1451 (setf results (append results result))
1452 (push result results))))
1453 ;; Try all pairwise combinations.
1456 (let ((result (or (deriver x y same-arg)
1457 (numeric-contagion x y))))
1459 (setf results (append results result))
1460 (push result results))))))
1462 (make-derived-union-type results)
1463 (first results)))))))
1465 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1467 (defoptimizer (+ derive-type) ((x y))
1468 (derive-integer-type
1475 (values (frob (numeric-type-low x) (numeric-type-low y))
1476 (frob (numeric-type-high x) (numeric-type-high y)))))))
1478 (defoptimizer (- derive-type) ((x y))
1479 (derive-integer-type
1486 (values (frob (numeric-type-low x) (numeric-type-high y))
1487 (frob (numeric-type-high x) (numeric-type-low y)))))))
1489 (defoptimizer (* derive-type) ((x y))
1490 (derive-integer-type
1493 (let ((x-low (numeric-type-low x))
1494 (x-high (numeric-type-high x))
1495 (y-low (numeric-type-low y))
1496 (y-high (numeric-type-high y)))
1497 (cond ((not (and x-low y-low))
1499 ((or (minusp x-low) (minusp y-low))
1500 (if (and x-high y-high)
1501 (let ((max (* (max (abs x-low) (abs x-high))
1502 (max (abs y-low) (abs y-high)))))
1503 (values (- max) max))
1506 (values (* x-low y-low)
1507 (if (and x-high y-high)
1511 (defoptimizer (/ derive-type) ((x y))
1512 (numeric-contagion (lvar-type x) (lvar-type y)))
1516 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1518 (defun +-derive-type-aux (x y same-arg)
1519 (if (and (numeric-type-real-p x)
1520 (numeric-type-real-p y))
1523 (let ((x-int (numeric-type->interval x)))
1524 (interval-add x-int x-int))
1525 (interval-add (numeric-type->interval x)
1526 (numeric-type->interval y))))
1527 (result-type (numeric-contagion x y)))
1528 ;; If the result type is a float, we need to be sure to coerce
1529 ;; the bounds into the correct type.
1530 (when (eq (numeric-type-class result-type) 'float)
1531 (setf result (interval-func
1533 (coerce-for-bound x (or (numeric-type-format result-type)
1537 :class (if (and (eq (numeric-type-class x) 'integer)
1538 (eq (numeric-type-class y) 'integer))
1539 ;; The sum of integers is always an integer.
1541 (numeric-type-class result-type))
1542 :format (numeric-type-format result-type)
1543 :low (interval-low result)
1544 :high (interval-high result)))
1545 ;; general contagion
1546 (numeric-contagion x y)))
1548 (defoptimizer (+ derive-type) ((x y))
1549 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1551 (defun --derive-type-aux (x y same-arg)
1552 (if (and (numeric-type-real-p x)
1553 (numeric-type-real-p y))
1555 ;; (- X X) is always 0.
1557 (make-interval :low 0 :high 0)
1558 (interval-sub (numeric-type->interval x)
1559 (numeric-type->interval y))))
1560 (result-type (numeric-contagion x y)))
1561 ;; If the result type is a float, we need to be sure to coerce
1562 ;; the bounds into the correct type.
1563 (when (eq (numeric-type-class result-type) 'float)
1564 (setf result (interval-func
1566 (coerce-for-bound x (or (numeric-type-format result-type)
1570 :class (if (and (eq (numeric-type-class x) 'integer)
1571 (eq (numeric-type-class y) 'integer))
1572 ;; The difference of integers is always an integer.
1574 (numeric-type-class result-type))
1575 :format (numeric-type-format result-type)
1576 :low (interval-low result)
1577 :high (interval-high result)))
1578 ;; general contagion
1579 (numeric-contagion x y)))
1581 (defoptimizer (- derive-type) ((x y))
1582 (two-arg-derive-type x y #'--derive-type-aux #'-))
1584 (defun *-derive-type-aux (x y same-arg)
1585 (if (and (numeric-type-real-p x)
1586 (numeric-type-real-p y))
1588 ;; (* X X) is always positive, so take care to do it right.
1590 (interval-sqr (numeric-type->interval x))
1591 (interval-mul (numeric-type->interval x)
1592 (numeric-type->interval y))))
1593 (result-type (numeric-contagion x y)))
1594 ;; If the result type is a float, we need to be sure to coerce
1595 ;; the bounds into the correct type.
1596 (when (eq (numeric-type-class result-type) 'float)
1597 (setf result (interval-func
1599 (coerce-for-bound x (or (numeric-type-format result-type)
1603 :class (if (and (eq (numeric-type-class x) 'integer)
1604 (eq (numeric-type-class y) 'integer))
1605 ;; The product of integers is always an integer.
1607 (numeric-type-class result-type))
1608 :format (numeric-type-format result-type)
1609 :low (interval-low result)
1610 :high (interval-high result)))
1611 (numeric-contagion x y)))
1613 (defoptimizer (* derive-type) ((x y))
1614 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1616 (defun /-derive-type-aux (x y same-arg)
1617 (if (and (numeric-type-real-p x)
1618 (numeric-type-real-p y))
1620 ;; (/ X X) is always 1, except if X can contain 0. In
1621 ;; that case, we shouldn't optimize the division away
1622 ;; because we want 0/0 to signal an error.
1624 (not (interval-contains-p
1625 0 (interval-closure (numeric-type->interval y)))))
1626 (make-interval :low 1 :high 1)
1627 (interval-div (numeric-type->interval x)
1628 (numeric-type->interval y))))
1629 (result-type (numeric-contagion x y)))
1630 ;; If the result type is a float, we need to be sure to coerce
1631 ;; the bounds into the correct type.
1632 (when (eq (numeric-type-class result-type) 'float)
1633 (setf result (interval-func
1635 (coerce-for-bound x (or (numeric-type-format result-type)
1638 (make-numeric-type :class (numeric-type-class result-type)
1639 :format (numeric-type-format result-type)
1640 :low (interval-low result)
1641 :high (interval-high result)))
1642 (numeric-contagion x y)))
1644 (defoptimizer (/ derive-type) ((x y))
1645 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1649 (defun ash-derive-type-aux (n-type shift same-arg)
1650 (declare (ignore same-arg))
1651 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1652 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1653 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1654 ;; two bignums yielding zero) and it's hard to avoid that
1655 ;; calculation in here.
1656 #+(and cmu sb-xc-host)
1657 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1658 (typep (numeric-type-high n-type) 'bignum))
1659 (or (typep (numeric-type-low shift) 'bignum)
1660 (typep (numeric-type-high shift) 'bignum)))
1661 (return-from ash-derive-type-aux *universal-type*))
1662 (flet ((ash-outer (n s)
1663 (when (and (fixnump s)
1665 (> s sb!xc:most-negative-fixnum))
1667 ;; KLUDGE: The bare 64's here should be related to
1668 ;; symbolic machine word size values somehow.
1671 (if (and (fixnump s)
1672 (> s sb!xc:most-negative-fixnum))
1674 (if (minusp n) -1 0))))
1675 (or (and (csubtypep n-type (specifier-type 'integer))
1676 (csubtypep shift (specifier-type 'integer))
1677 (let ((n-low (numeric-type-low n-type))
1678 (n-high (numeric-type-high n-type))
1679 (s-low (numeric-type-low shift))
1680 (s-high (numeric-type-high shift)))
1681 (make-numeric-type :class 'integer :complexp :real
1684 (ash-outer n-low s-high)
1685 (ash-inner n-low s-low)))
1688 (ash-inner n-high s-low)
1689 (ash-outer n-high s-high))))))
1692 (defoptimizer (ash derive-type) ((n shift))
1693 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1695 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1696 (macrolet ((frob (fun)
1697 `#'(lambda (type type2)
1698 (declare (ignore type2))
1699 (let ((lo (numeric-type-low type))
1700 (hi (numeric-type-high type)))
1701 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1703 (defoptimizer (%negate derive-type) ((num))
1704 (derive-integer-type num num (frob -))))
1706 (defun lognot-derive-type-aux (int)
1707 (derive-integer-type-aux int int
1708 (lambda (type type2)
1709 (declare (ignore type2))
1710 (let ((lo (numeric-type-low type))
1711 (hi (numeric-type-high type)))
1712 (values (if hi (lognot hi) nil)
1713 (if lo (lognot lo) nil)
1714 (numeric-type-class type)
1715 (numeric-type-format type))))))
1717 (defoptimizer (lognot derive-type) ((int))
1718 (lognot-derive-type-aux (lvar-type int)))
1720 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1721 (defoptimizer (%negate derive-type) ((num))
1722 (flet ((negate-bound (b)
1724 (set-bound (- (type-bound-number b))
1726 (one-arg-derive-type num
1728 (modified-numeric-type
1730 :low (negate-bound (numeric-type-high type))
1731 :high (negate-bound (numeric-type-low type))))
1734 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1735 (defoptimizer (abs derive-type) ((num))
1736 (let ((type (lvar-type num)))
1737 (if (and (numeric-type-p type)
1738 (eq (numeric-type-class type) 'integer)
1739 (eq (numeric-type-complexp type) :real))
1740 (let ((lo (numeric-type-low type))
1741 (hi (numeric-type-high type)))
1742 (make-numeric-type :class 'integer :complexp :real
1743 :low (cond ((and hi (minusp hi))
1749 :high (if (and hi lo)
1750 (max (abs hi) (abs lo))
1752 (numeric-contagion type type))))
1754 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1755 (defun abs-derive-type-aux (type)
1756 (cond ((eq (numeric-type-complexp type) :complex)
1757 ;; The absolute value of a complex number is always a
1758 ;; non-negative float.
1759 (let* ((format (case (numeric-type-class type)
1760 ((integer rational) 'single-float)
1761 (t (numeric-type-format type))))
1762 (bound-format (or format 'float)))
1763 (make-numeric-type :class 'float
1766 :low (coerce 0 bound-format)
1769 ;; The absolute value of a real number is a non-negative real
1770 ;; of the same type.
1771 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1772 (class (numeric-type-class type))
1773 (format (numeric-type-format type))
1774 (bound-type (or format class 'real)))
1779 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1780 :high (coerce-and-truncate-floats
1781 (interval-high abs-bnd) bound-type))))))
1783 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1784 (defoptimizer (abs derive-type) ((num))
1785 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1787 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1788 (defoptimizer (truncate derive-type) ((number divisor))
1789 (let ((number-type (lvar-type number))
1790 (divisor-type (lvar-type divisor))
1791 (integer-type (specifier-type 'integer)))
1792 (if (and (numeric-type-p number-type)
1793 (csubtypep number-type integer-type)
1794 (numeric-type-p divisor-type)
1795 (csubtypep divisor-type integer-type))
1796 (let ((number-low (numeric-type-low number-type))
1797 (number-high (numeric-type-high number-type))
1798 (divisor-low (numeric-type-low divisor-type))
1799 (divisor-high (numeric-type-high divisor-type)))
1800 (values-specifier-type
1801 `(values ,(integer-truncate-derive-type number-low number-high
1802 divisor-low divisor-high)
1803 ,(integer-rem-derive-type number-low number-high
1804 divisor-low divisor-high))))
1807 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1810 (defun rem-result-type (number-type divisor-type)
1811 ;; Figure out what the remainder type is. The remainder is an
1812 ;; integer if both args are integers; a rational if both args are
1813 ;; rational; and a float otherwise.
1814 (cond ((and (csubtypep number-type (specifier-type 'integer))
1815 (csubtypep divisor-type (specifier-type 'integer)))
1817 ((and (csubtypep number-type (specifier-type 'rational))
1818 (csubtypep divisor-type (specifier-type 'rational)))
1820 ((and (csubtypep number-type (specifier-type 'float))
1821 (csubtypep divisor-type (specifier-type 'float)))
1822 ;; Both are floats so the result is also a float, of
1823 ;; the largest type.
1824 (or (float-format-max (numeric-type-format number-type)
1825 (numeric-type-format divisor-type))
1827 ((and (csubtypep number-type (specifier-type 'float))
1828 (csubtypep divisor-type (specifier-type 'rational)))
1829 ;; One of the arguments is a float and the other is a
1830 ;; rational. The remainder is a float of the same
1832 (or (numeric-type-format number-type) 'float))
1833 ((and (csubtypep divisor-type (specifier-type 'float))
1834 (csubtypep number-type (specifier-type 'rational)))
1835 ;; One of the arguments is a float and the other is a
1836 ;; rational. The remainder is a float of the same
1838 (or (numeric-type-format divisor-type) 'float))
1840 ;; Some unhandled combination. This usually means both args
1841 ;; are REAL so the result is a REAL.
1844 (defun truncate-derive-type-quot (number-type divisor-type)
1845 (let* ((rem-type (rem-result-type number-type divisor-type))
1846 (number-interval (numeric-type->interval number-type))
1847 (divisor-interval (numeric-type->interval divisor-type)))
1848 ;;(declare (type (member '(integer rational float)) rem-type))
1849 ;; We have real numbers now.
1850 (cond ((eq rem-type 'integer)
1851 ;; Since the remainder type is INTEGER, both args are
1853 (let* ((res (integer-truncate-derive-type
1854 (interval-low number-interval)
1855 (interval-high number-interval)
1856 (interval-low divisor-interval)
1857 (interval-high divisor-interval))))
1858 (specifier-type (if (listp res) res 'integer))))
1860 (let ((quot (truncate-quotient-bound
1861 (interval-div number-interval
1862 divisor-interval))))
1863 (specifier-type `(integer ,(or (interval-low quot) '*)
1864 ,(or (interval-high quot) '*))))))))
1866 (defun truncate-derive-type-rem (number-type divisor-type)
1867 (let* ((rem-type (rem-result-type number-type divisor-type))
1868 (number-interval (numeric-type->interval number-type))
1869 (divisor-interval (numeric-type->interval divisor-type))
1870 (rem (truncate-rem-bound number-interval divisor-interval)))
1871 ;;(declare (type (member '(integer rational float)) rem-type))
1872 ;; We have real numbers now.
1873 (cond ((eq rem-type 'integer)
1874 ;; Since the remainder type is INTEGER, both args are
1876 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1877 ,(or (interval-high rem) '*))))
1879 (multiple-value-bind (class format)
1882 (values 'integer nil))
1884 (values 'rational nil))
1885 ((or single-float double-float #!+long-float long-float)
1886 (values 'float rem-type))
1888 (values 'float nil))
1891 (when (member rem-type '(float single-float double-float
1892 #!+long-float long-float))
1893 (setf rem (interval-func #'(lambda (x)
1894 (coerce-for-bound x rem-type))
1896 (make-numeric-type :class class
1898 :low (interval-low rem)
1899 :high (interval-high rem)))))))
1901 (defun truncate-derive-type-quot-aux (num div same-arg)
1902 (declare (ignore same-arg))
1903 (if (and (numeric-type-real-p num)
1904 (numeric-type-real-p div))
1905 (truncate-derive-type-quot num div)
1908 (defun truncate-derive-type-rem-aux (num div same-arg)
1909 (declare (ignore same-arg))
1910 (if (and (numeric-type-real-p num)
1911 (numeric-type-real-p div))
1912 (truncate-derive-type-rem num div)
1915 (defoptimizer (truncate derive-type) ((number divisor))
1916 (let ((quot (two-arg-derive-type number divisor
1917 #'truncate-derive-type-quot-aux #'truncate))
1918 (rem (two-arg-derive-type number divisor
1919 #'truncate-derive-type-rem-aux #'rem)))
1920 (when (and quot rem)
1921 (make-values-type :required (list quot rem)))))
1923 (defun ftruncate-derive-type-quot (number-type divisor-type)
1924 ;; The bounds are the same as for truncate. However, the first
1925 ;; result is a float of some type. We need to determine what that
1926 ;; type is. Basically it's the more contagious of the two types.
1927 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1928 (res-type (numeric-contagion number-type divisor-type)))
1929 (make-numeric-type :class 'float
1930 :format (numeric-type-format res-type)
1931 :low (numeric-type-low q-type)
1932 :high (numeric-type-high q-type))))
1934 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1935 (declare (ignore same-arg))
1936 (if (and (numeric-type-real-p n)
1937 (numeric-type-real-p d))
1938 (ftruncate-derive-type-quot n d)
1941 (defoptimizer (ftruncate derive-type) ((number divisor))
1943 (two-arg-derive-type number divisor
1944 #'ftruncate-derive-type-quot-aux #'ftruncate))
1945 (rem (two-arg-derive-type number divisor
1946 #'truncate-derive-type-rem-aux #'rem)))
1947 (when (and quot rem)
1948 (make-values-type :required (list quot rem)))))
1950 (defun %unary-truncate-derive-type-aux (number)
1951 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1953 (defoptimizer (%unary-truncate derive-type) ((number))
1954 (one-arg-derive-type number
1955 #'%unary-truncate-derive-type-aux
1958 (defoptimizer (%unary-truncate/single-float derive-type) ((number))
1959 (one-arg-derive-type number
1960 #'%unary-truncate-derive-type-aux
1963 (defoptimizer (%unary-truncate/double-float derive-type) ((number))
1964 (one-arg-derive-type number
1965 #'%unary-truncate-derive-type-aux
1968 (defoptimizer (%unary-ftruncate derive-type) ((number))
1969 (let ((divisor (specifier-type '(integer 1 1))))
1970 (one-arg-derive-type number
1972 (ftruncate-derive-type-quot-aux n divisor nil))
1973 #'%unary-ftruncate)))
1975 (defoptimizer (%unary-round derive-type) ((number))
1976 (one-arg-derive-type number
1979 (unless (numeric-type-real-p n)
1980 (return *empty-type*))
1981 (let* ((interval (numeric-type->interval n))
1982 (low (interval-low interval))
1983 (high (interval-high interval)))
1985 (setf low (car low)))
1987 (setf high (car high)))
1997 ;;; Define optimizers for FLOOR and CEILING.
1999 ((def (name q-name r-name)
2000 (let ((q-aux (symbolicate q-name "-AUX"))
2001 (r-aux (symbolicate r-name "-AUX")))
2003 ;; Compute type of quotient (first) result.
2004 (defun ,q-aux (number-type divisor-type)
2005 (let* ((number-interval
2006 (numeric-type->interval number-type))
2008 (numeric-type->interval divisor-type))
2009 (quot (,q-name (interval-div number-interval
2010 divisor-interval))))
2011 (specifier-type `(integer ,(or (interval-low quot) '*)
2012 ,(or (interval-high quot) '*)))))
2013 ;; Compute type of remainder.
2014 (defun ,r-aux (number-type divisor-type)
2015 (let* ((divisor-interval
2016 (numeric-type->interval divisor-type))
2017 (rem (,r-name divisor-interval))
2018 (result-type (rem-result-type number-type divisor-type)))
2019 (multiple-value-bind (class format)
2022 (values 'integer nil))
2024 (values 'rational nil))
2025 ((or single-float double-float #!+long-float long-float)
2026 (values 'float result-type))
2028 (values 'float nil))
2031 (when (member result-type '(float single-float double-float
2032 #!+long-float long-float))
2033 ;; Make sure that the limits on the interval have
2035 (setf rem (interval-func (lambda (x)
2036 (coerce-for-bound x result-type))
2038 (make-numeric-type :class class
2040 :low (interval-low rem)
2041 :high (interval-high rem)))))
2042 ;; the optimizer itself
2043 (defoptimizer (,name derive-type) ((number divisor))
2044 (flet ((derive-q (n d same-arg)
2045 (declare (ignore same-arg))
2046 (if (and (numeric-type-real-p n)
2047 (numeric-type-real-p d))
2050 (derive-r (n d same-arg)
2051 (declare (ignore same-arg))
2052 (if (and (numeric-type-real-p n)
2053 (numeric-type-real-p d))
2056 (let ((quot (two-arg-derive-type
2057 number divisor #'derive-q #',name))
2058 (rem (two-arg-derive-type
2059 number divisor #'derive-r #'mod)))
2060 (when (and quot rem)
2061 (make-values-type :required (list quot rem))))))))))
2063 (def floor floor-quotient-bound floor-rem-bound)
2064 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
2066 ;;; Define optimizers for FFLOOR and FCEILING
2067 (macrolet ((def (name q-name r-name)
2068 (let ((q-aux (symbolicate "F" q-name "-AUX"))
2069 (r-aux (symbolicate r-name "-AUX")))
2071 ;; Compute type of quotient (first) result.
2072 (defun ,q-aux (number-type divisor-type)
2073 (let* ((number-interval
2074 (numeric-type->interval number-type))
2076 (numeric-type->interval divisor-type))
2077 (quot (,q-name (interval-div number-interval
2079 (res-type (numeric-contagion number-type
2082 :class (numeric-type-class res-type)
2083 :format (numeric-type-format res-type)
2084 :low (interval-low quot)
2085 :high (interval-high quot))))
2087 (defoptimizer (,name derive-type) ((number divisor))
2088 (flet ((derive-q (n d same-arg)
2089 (declare (ignore same-arg))
2090 (if (and (numeric-type-real-p n)
2091 (numeric-type-real-p d))
2094 (derive-r (n d same-arg)
2095 (declare (ignore same-arg))
2096 (if (and (numeric-type-real-p n)
2097 (numeric-type-real-p d))
2100 (let ((quot (two-arg-derive-type
2101 number divisor #'derive-q #',name))
2102 (rem (two-arg-derive-type
2103 number divisor #'derive-r #'mod)))
2104 (when (and quot rem)
2105 (make-values-type :required (list quot rem))))))))))
2107 (def ffloor floor-quotient-bound floor-rem-bound)
2108 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
2110 ;;; functions to compute the bounds on the quotient and remainder for
2111 ;;; the FLOOR function
2112 (defun floor-quotient-bound (quot)
2113 ;; Take the floor of the quotient and then massage it into what we
2115 (let ((lo (interval-low quot))
2116 (hi (interval-high quot)))
2117 ;; Take the floor of the lower bound. The result is always a
2118 ;; closed lower bound.
2120 (floor (type-bound-number lo))
2122 ;; For the upper bound, we need to be careful.
2125 ;; An open bound. We need to be careful here because
2126 ;; the floor of '(10.0) is 9, but the floor of
2128 (multiple-value-bind (q r) (floor (first hi))
2133 ;; A closed bound, so the answer is obvious.
2137 (make-interval :low lo :high hi)))
2138 (defun floor-rem-bound (div)
2139 ;; The remainder depends only on the divisor. Try to get the
2140 ;; correct sign for the remainder if we can.
2141 (case (interval-range-info div)
2143 ;; The divisor is always positive.
2144 (let ((rem (interval-abs div)))
2145 (setf (interval-low rem) 0)
2146 (when (and (numberp (interval-high rem))
2147 (not (zerop (interval-high rem))))
2148 ;; The remainder never contains the upper bound. However,
2149 ;; watch out for the case where the high limit is zero!
2150 (setf (interval-high rem) (list (interval-high rem))))
2153 ;; The divisor is always negative.
2154 (let ((rem (interval-neg (interval-abs div))))
2155 (setf (interval-high rem) 0)
2156 (when (numberp (interval-low rem))
2157 ;; The remainder never contains the lower bound.
2158 (setf (interval-low rem) (list (interval-low rem))))
2161 ;; The divisor can be positive or negative. All bets off. The
2162 ;; magnitude of remainder is the maximum value of the divisor.
2163 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2164 ;; The bound never reaches the limit, so make the interval open.
2165 (make-interval :low (if limit
2168 :high (list limit))))))
2170 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
2171 => #S(INTERVAL :LOW 0 :HIGH 10)
2172 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2173 => #S(INTERVAL :LOW 0 :HIGH 10)
2174 (floor-quotient-bound (make-interval :low 0.3 :high 10))
2175 => #S(INTERVAL :LOW 0 :HIGH 10)
2176 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
2177 => #S(INTERVAL :LOW 0 :HIGH 9)
2178 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
2179 => #S(INTERVAL :LOW 0 :HIGH 10)
2180 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
2181 => #S(INTERVAL :LOW 0 :HIGH 10)
2182 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2183 => #S(INTERVAL :LOW -2 :HIGH 10)
2184 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2185 => #S(INTERVAL :LOW -1 :HIGH 10)
2186 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
2187 => #S(INTERVAL :LOW -1 :HIGH 10)
2189 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
2190 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2191 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
2192 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2193 (floor-rem-bound (make-interval :low -10 :high -2.3))
2194 #S(INTERVAL :LOW (-10) :HIGH 0)
2195 (floor-rem-bound (make-interval :low 0.3 :high 10))
2196 => #S(INTERVAL :LOW 0 :HIGH '(10))
2197 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
2198 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
2199 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
2200 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2203 ;;; same functions for CEILING
2204 (defun ceiling-quotient-bound (quot)
2205 ;; Take the ceiling of the quotient and then massage it into what we
2207 (let ((lo (interval-low quot))
2208 (hi (interval-high quot)))
2209 ;; Take the ceiling of the upper bound. The result is always a
2210 ;; closed upper bound.
2212 (ceiling (type-bound-number hi))
2214 ;; For the lower bound, we need to be careful.
2217 ;; An open bound. We need to be careful here because
2218 ;; the ceiling of '(10.0) is 11, but the ceiling of
2220 (multiple-value-bind (q r) (ceiling (first lo))
2225 ;; A closed bound, so the answer is obvious.
2229 (make-interval :low lo :high hi)))
2230 (defun ceiling-rem-bound (div)
2231 ;; The remainder depends only on the divisor. Try to get the
2232 ;; correct sign for the remainder if we can.
2233 (case (interval-range-info div)
2235 ;; Divisor is always positive. The remainder is negative.
2236 (let ((rem (interval-neg (interval-abs div))))
2237 (setf (interval-high rem) 0)
2238 (when (and (numberp (interval-low rem))
2239 (not (zerop (interval-low rem))))
2240 ;; The remainder never contains the upper bound. However,
2241 ;; watch out for the case when the upper bound is zero!
2242 (setf (interval-low rem) (list (interval-low rem))))
2245 ;; Divisor is always negative. The remainder is positive
2246 (let ((rem (interval-abs div)))
2247 (setf (interval-low rem) 0)
2248 (when (numberp (interval-high rem))
2249 ;; The remainder never contains the lower bound.
2250 (setf (interval-high rem) (list (interval-high rem))))
2253 ;; The divisor can be positive or negative. All bets off. The
2254 ;; magnitude of remainder is the maximum value of the divisor.
2255 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2256 ;; The bound never reaches the limit, so make the interval open.
2257 (make-interval :low (if limit
2260 :high (list limit))))))
2263 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2264 => #S(INTERVAL :LOW 1 :HIGH 11)
2265 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2266 => #S(INTERVAL :LOW 1 :HIGH 11)
2267 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2268 => #S(INTERVAL :LOW 1 :HIGH 10)
2269 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2270 => #S(INTERVAL :LOW 1 :HIGH 10)
2271 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2272 => #S(INTERVAL :LOW 1 :HIGH 11)
2273 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2274 => #S(INTERVAL :LOW 1 :HIGH 11)
2275 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2276 => #S(INTERVAL :LOW -1 :HIGH 11)
2277 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2278 => #S(INTERVAL :LOW 0 :HIGH 11)
2279 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2280 => #S(INTERVAL :LOW -1 :HIGH 11)
2282 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2283 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2284 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2285 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2286 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2287 => #S(INTERVAL :LOW 0 :HIGH (10))
2288 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2289 => #S(INTERVAL :LOW (-10) :HIGH 0)
2290 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2291 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2292 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2293 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2296 (defun truncate-quotient-bound (quot)
2297 ;; For positive quotients, truncate is exactly like floor. For
2298 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2299 ;; it's the union of the two pieces.
2300 (case (interval-range-info quot)
2303 (floor-quotient-bound quot))
2305 ;; just like CEILING
2306 (ceiling-quotient-bound quot))
2308 ;; Split the interval into positive and negative pieces, compute
2309 ;; the result for each piece and put them back together.
2310 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2311 (interval-merge-pair (ceiling-quotient-bound neg)
2312 (floor-quotient-bound pos))))))
2314 (defun truncate-rem-bound (num div)
2315 ;; This is significantly more complicated than FLOOR or CEILING. We
2316 ;; need both the number and the divisor to determine the range. The
2317 ;; basic idea is to split the ranges of NUM and DEN into positive
2318 ;; and negative pieces and deal with each of the four possibilities
2320 (case (interval-range-info num)
2322 (case (interval-range-info div)
2324 (floor-rem-bound div))
2326 (ceiling-rem-bound div))
2328 (destructuring-bind (neg pos) (interval-split 0 div t t)
2329 (interval-merge-pair (truncate-rem-bound num neg)
2330 (truncate-rem-bound num pos))))))
2332 (case (interval-range-info div)
2334 (ceiling-rem-bound div))
2336 (floor-rem-bound div))
2338 (destructuring-bind (neg pos) (interval-split 0 div t t)
2339 (interval-merge-pair (truncate-rem-bound num neg)
2340 (truncate-rem-bound num pos))))))
2342 (destructuring-bind (neg pos) (interval-split 0 num t t)
2343 (interval-merge-pair (truncate-rem-bound neg div)
2344 (truncate-rem-bound pos div))))))
2347 ;;; Derive useful information about the range. Returns three values:
2348 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2349 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2350 ;;; - The abs of the maximal value if there is one, or nil if it is
2352 (defun numeric-range-info (low high)
2353 (cond ((and low (not (minusp low)))
2354 (values '+ low high))
2355 ((and high (not (plusp high)))
2356 (values '- (- high) (if low (- low) nil)))
2358 (values nil 0 (and low high (max (- low) high))))))
2360 (defun integer-truncate-derive-type
2361 (number-low number-high divisor-low divisor-high)
2362 ;; The result cannot be larger in magnitude than the number, but the
2363 ;; sign might change. If we can determine the sign of either the
2364 ;; number or the divisor, we can eliminate some of the cases.
2365 (multiple-value-bind (number-sign number-min number-max)
2366 (numeric-range-info number-low number-high)
2367 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2368 (numeric-range-info divisor-low divisor-high)
2369 (when (and divisor-max (zerop divisor-max))
2370 ;; We've got a problem: guaranteed division by zero.
2371 (return-from integer-truncate-derive-type t))
2372 (when (zerop divisor-min)
2373 ;; We'll assume that they aren't going to divide by zero.
2375 (cond ((and number-sign divisor-sign)
2376 ;; We know the sign of both.
2377 (if (eq number-sign divisor-sign)
2378 ;; Same sign, so the result will be positive.
2379 `(integer ,(if divisor-max
2380 (truncate number-min divisor-max)
2383 (truncate number-max divisor-min)
2385 ;; Different signs, the result will be negative.
2386 `(integer ,(if number-max
2387 (- (truncate number-max divisor-min))
2390 (- (truncate number-min divisor-max))
2392 ((eq divisor-sign '+)
2393 ;; The divisor is positive. Therefore, the number will just
2394 ;; become closer to zero.
2395 `(integer ,(if number-low
2396 (truncate number-low divisor-min)
2399 (truncate number-high divisor-min)
2401 ((eq divisor-sign '-)
2402 ;; The divisor is negative. Therefore, the absolute value of
2403 ;; the number will become closer to zero, but the sign will also
2405 `(integer ,(if number-high
2406 (- (truncate number-high divisor-min))
2409 (- (truncate number-low divisor-min))
2411 ;; The divisor could be either positive or negative.
2413 ;; The number we are dividing has a bound. Divide that by the
2414 ;; smallest posible divisor.
2415 (let ((bound (truncate number-max divisor-min)))
2416 `(integer ,(- bound) ,bound)))
2418 ;; The number we are dividing is unbounded, so we can't tell
2419 ;; anything about the result.
2422 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2423 (defun integer-rem-derive-type
2424 (number-low number-high divisor-low divisor-high)
2425 (if (and divisor-low divisor-high)
2426 ;; We know the range of the divisor, and the remainder must be
2427 ;; smaller than the divisor. We can tell the sign of the
2428 ;; remainder if we know the sign of the number.
2429 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2430 `(integer ,(if (or (null number-low)
2431 (minusp number-low))
2434 ,(if (or (null number-high)
2435 (plusp number-high))
2438 ;; The divisor is potentially either very positive or very
2439 ;; negative. Therefore, the remainder is unbounded, but we might
2440 ;; be able to tell something about the sign from the number.
2441 `(integer ,(if (and number-low (not (minusp number-low)))
2442 ;; The number we are dividing is positive.
2443 ;; Therefore, the remainder must be positive.
2446 ,(if (and number-high (not (plusp number-high)))
2447 ;; The number we are dividing is negative.
2448 ;; Therefore, the remainder must be negative.
2452 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2453 (defoptimizer (random derive-type) ((bound &optional state))
2454 (let ((type (lvar-type bound)))
2455 (when (numeric-type-p type)
2456 (let ((class (numeric-type-class type))
2457 (high (numeric-type-high type))
2458 (format (numeric-type-format type)))
2462 :low (coerce 0 (or format class 'real))
2463 :high (cond ((not high) nil)
2464 ((eq class 'integer) (max (1- high) 0))
2465 ((or (consp high) (zerop high)) high)
2468 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2469 (defun random-derive-type-aux (type)
2470 (let ((class (numeric-type-class type))
2471 (high (numeric-type-high type))
2472 (format (numeric-type-format type)))
2476 :low (coerce 0 (or format class 'real))
2477 :high (cond ((not high) nil)
2478 ((eq class 'integer) (max (1- high) 0))
2479 ((or (consp high) (zerop high)) high)
2482 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2483 (defoptimizer (random derive-type) ((bound &optional state))
2484 (one-arg-derive-type bound #'random-derive-type-aux nil))
2486 ;;;; miscellaneous derive-type methods
2488 (defoptimizer (integer-length derive-type) ((x))
2489 (let ((x-type (lvar-type x)))
2490 (when (numeric-type-p x-type)
2491 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2492 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2493 ;; careful about LO or HI being NIL, though. Also, if 0 is
2494 ;; contained in X, the lower bound is obviously 0.
2495 (flet ((null-or-min (a b)
2496 (and a b (min (integer-length a)
2497 (integer-length b))))
2499 (and a b (max (integer-length a)
2500 (integer-length b)))))
2501 (let* ((min (numeric-type-low x-type))
2502 (max (numeric-type-high x-type))
2503 (min-len (null-or-min min max))
2504 (max-len (null-or-max min max)))
2505 (when (ctypep 0 x-type)
2507 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2509 (defoptimizer (isqrt derive-type) ((x))
2510 (let ((x-type (lvar-type x)))
2511 (when (numeric-type-p x-type)
2512 (let* ((lo (numeric-type-low x-type))
2513 (hi (numeric-type-high x-type))
2514 (lo-res (if lo (isqrt lo) '*))
2515 (hi-res (if hi (isqrt hi) '*)))
2516 (specifier-type `(integer ,lo-res ,hi-res))))))
2518 (defoptimizer (char-code derive-type) ((char))
2519 (let ((type (type-intersection (lvar-type char) (specifier-type 'character))))
2520 (cond ((member-type-p type)
2523 ,@(loop for member in (member-type-members type)
2524 when (characterp member)
2525 collect (char-code member)))))
2526 ((sb!kernel::character-set-type-p type)
2529 ,@(loop for (low . high)
2530 in (character-set-type-pairs type)
2531 collect `(integer ,low ,high)))))
2532 ((csubtypep type (specifier-type 'base-char))
2534 `(mod ,base-char-code-limit)))
2537 `(mod ,char-code-limit))))))
2539 (defoptimizer (code-char derive-type) ((code))
2540 (let ((type (lvar-type code)))
2541 ;; FIXME: unions of integral ranges? It ought to be easier to do
2542 ;; this, given that CHARACTER-SET is basically an integral range
2543 ;; type. -- CSR, 2004-10-04
2544 (when (numeric-type-p type)
2545 (let* ((lo (numeric-type-low type))
2546 (hi (numeric-type-high type))
2547 (type (specifier-type `(character-set ((,lo . ,hi))))))
2549 ;; KLUDGE: when running on the host, we lose a slight amount
2550 ;; of precision so that we don't have to "unparse" types
2551 ;; that formally we can't, such as (CHARACTER-SET ((0
2552 ;; . 0))). -- CSR, 2004-10-06
2554 ((csubtypep type (specifier-type 'standard-char)) type)
2556 ((csubtypep type (specifier-type 'base-char))
2557 (specifier-type 'base-char))
2559 ((csubtypep type (specifier-type 'extended-char))
2560 (specifier-type 'extended-char))
2561 (t #+sb-xc-host (specifier-type 'character)
2562 #-sb-xc-host type))))))
2564 (defoptimizer (values derive-type) ((&rest values))
2565 (make-values-type :required (mapcar #'lvar-type values)))
2567 (defun signum-derive-type-aux (type)
2568 (if (eq (numeric-type-complexp type) :complex)
2569 (let* ((format (case (numeric-type-class type)
2570 ((integer rational) 'single-float)
2571 (t (numeric-type-format type))))
2572 (bound-format (or format 'float)))
2573 (make-numeric-type :class 'float
2576 :low (coerce -1 bound-format)
2577 :high (coerce 1 bound-format)))
2578 (let* ((interval (numeric-type->interval type))
2579 (range-info (interval-range-info interval))
2580 (contains-0-p (interval-contains-p 0 interval))
2581 (class (numeric-type-class type))
2582 (format (numeric-type-format type))
2583 (one (coerce 1 (or format class 'real)))
2584 (zero (coerce 0 (or format class 'real)))
2585 (minus-one (coerce -1 (or format class 'real)))
2586 (plus (make-numeric-type :class class :format format
2587 :low one :high one))
2588 (minus (make-numeric-type :class class :format format
2589 :low minus-one :high minus-one))
2590 ;; KLUDGE: here we have a fairly horrible hack to deal
2591 ;; with the schizophrenia in the type derivation engine.
2592 ;; The problem is that the type derivers reinterpret
2593 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2594 ;; 0d0) within the derivation mechanism doesn't include
2595 ;; -0d0. Ugh. So force it in here, instead.
2596 (zero (make-numeric-type :class class :format format
2597 :low (- zero) :high zero)))
2599 (+ (if contains-0-p (type-union plus zero) plus))
2600 (- (if contains-0-p (type-union minus zero) minus))
2601 (t (type-union minus zero plus))))))
2603 (defoptimizer (signum derive-type) ((num))
2604 (one-arg-derive-type num #'signum-derive-type-aux nil))
2606 ;;;; byte operations
2608 ;;;; We try to turn byte operations into simple logical operations.
2609 ;;;; First, we convert byte specifiers into separate size and position
2610 ;;;; arguments passed to internal %FOO functions. We then attempt to
2611 ;;;; transform the %FOO functions into boolean operations when the
2612 ;;;; size and position are constant and the operands are fixnums.
2614 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2615 ;; expressions that evaluate to the SIZE and POSITION of
2616 ;; the byte-specifier form SPEC. We may wrap a let around
2617 ;; the result of the body to bind some variables.
2619 ;; If the spec is a BYTE form, then bind the vars to the
2620 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2621 ;; and BYTE-POSITION. The goal of this transformation is to
2622 ;; avoid consing up byte specifiers and then immediately
2623 ;; throwing them away.
2624 (with-byte-specifier ((size-var pos-var spec) &body body)
2625 (once-only ((spec `(macroexpand ,spec))
2627 `(if (and (consp ,spec)
2628 (eq (car ,spec) 'byte)
2629 (= (length ,spec) 3))
2630 (let ((,size-var (second ,spec))
2631 (,pos-var (third ,spec)))
2633 (let ((,size-var `(byte-size ,,temp))
2634 (,pos-var `(byte-position ,,temp)))
2635 `(let ((,,temp ,,spec))
2638 (define-source-transform ldb (spec int)
2639 (with-byte-specifier (size pos spec)
2640 `(%ldb ,size ,pos ,int)))
2642 (define-source-transform dpb (newbyte spec int)
2643 (with-byte-specifier (size pos spec)
2644 `(%dpb ,newbyte ,size ,pos ,int)))
2646 (define-source-transform mask-field (spec int)
2647 (with-byte-specifier (size pos spec)
2648 `(%mask-field ,size ,pos ,int)))
2650 (define-source-transform deposit-field (newbyte spec int)
2651 (with-byte-specifier (size pos spec)
2652 `(%deposit-field ,newbyte ,size ,pos ,int))))
2654 (defoptimizer (%ldb derive-type) ((size posn num))
2655 (let ((size (lvar-type size)))
2656 (if (and (numeric-type-p size)
2657 (csubtypep size (specifier-type 'integer)))
2658 (let ((size-high (numeric-type-high size)))
2659 (if (and size-high (<= size-high sb!vm:n-word-bits))
2660 (specifier-type `(unsigned-byte* ,size-high))
2661 (specifier-type 'unsigned-byte)))
2664 (defoptimizer (%mask-field derive-type) ((size posn num))
2665 (let ((size (lvar-type size))
2666 (posn (lvar-type posn)))
2667 (if (and (numeric-type-p size)
2668 (csubtypep size (specifier-type 'integer))
2669 (numeric-type-p posn)
2670 (csubtypep posn (specifier-type 'integer)))
2671 (let ((size-high (numeric-type-high size))
2672 (posn-high (numeric-type-high posn)))
2673 (if (and size-high posn-high
2674 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2675 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2676 (specifier-type 'unsigned-byte)))
2679 (defun %deposit-field-derive-type-aux (size posn int)
2680 (let ((size (lvar-type size))
2681 (posn (lvar-type posn))
2682 (int (lvar-type int)))
2683 (when (and (numeric-type-p size)
2684 (numeric-type-p posn)
2685 (numeric-type-p int))
2686 (let ((size-high (numeric-type-high size))
2687 (posn-high (numeric-type-high posn))
2688 (high (numeric-type-high int))
2689 (low (numeric-type-low int)))
2690 (when (and size-high posn-high high low
2691 ;; KLUDGE: we need this cutoff here, otherwise we
2692 ;; will merrily derive the type of %DPB as
2693 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2694 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2695 ;; 1073741822))), with hilarious consequences. We
2696 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2697 ;; over a reasonable amount of shifting, even on
2698 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2699 ;; machine integers are 64-bits. -- CSR,
2701 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2702 (let ((raw-bit-count (max (integer-length high)
2703 (integer-length low)
2704 (+ size-high posn-high))))
2707 `(signed-byte ,(1+ raw-bit-count))
2708 `(unsigned-byte* ,raw-bit-count)))))))))
2710 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2711 (%deposit-field-derive-type-aux size posn int))
2713 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2714 (%deposit-field-derive-type-aux size posn int))
2716 (deftransform %ldb ((size posn int)
2717 (fixnum fixnum integer)
2718 (unsigned-byte #.sb!vm:n-word-bits))
2719 "convert to inline logical operations"
2720 `(logand (ash int (- posn))
2721 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2722 (- size ,sb!vm:n-word-bits))))
2724 (deftransform %mask-field ((size posn int)
2725 (fixnum fixnum integer)
2726 (unsigned-byte #.sb!vm:n-word-bits))
2727 "convert to inline logical operations"
2729 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2730 (- size ,sb!vm:n-word-bits))
2733 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2734 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2735 ;;; as the result type, as that would allow result types that cover
2736 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2737 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2739 (deftransform %dpb ((new size posn int)
2741 (unsigned-byte #.sb!vm:n-word-bits))
2742 "convert to inline logical operations"
2743 `(let ((mask (ldb (byte size 0) -1)))
2744 (logior (ash (logand new mask) posn)
2745 (logand int (lognot (ash mask posn))))))
2747 (deftransform %dpb ((new size posn int)
2749 (signed-byte #.sb!vm:n-word-bits))
2750 "convert to inline logical operations"
2751 `(let ((mask (ldb (byte size 0) -1)))
2752 (logior (ash (logand new mask) posn)
2753 (logand int (lognot (ash mask posn))))))
2755 (deftransform %deposit-field ((new size posn int)
2757 (unsigned-byte #.sb!vm:n-word-bits))
2758 "convert to inline logical operations"
2759 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2760 (logior (logand new mask)
2761 (logand int (lognot mask)))))
2763 (deftransform %deposit-field ((new size posn int)
2765 (signed-byte #.sb!vm:n-word-bits))
2766 "convert to inline logical operations"
2767 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2768 (logior (logand new mask)
2769 (logand int (lognot mask)))))
2771 (defoptimizer (mask-signed-field derive-type) ((size x))
2772 (let ((size (lvar-type size)))
2773 (if (numeric-type-p size)
2774 (let ((size-high (numeric-type-high size)))
2775 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2776 (specifier-type `(signed-byte ,size-high))
2783 (defun %ash/right (integer amount)
2784 (ash integer (- amount)))
2786 (deftransform ash ((integer amount) (sb!vm:signed-word (integer * 0)))
2787 "Convert ASH of signed word to %ASH/RIGHT"
2788 (when (constant-lvar-p amount)
2789 (give-up-ir1-transform))
2790 (let ((use (lvar-uses amount)))
2791 (cond ((and (combination-p use)
2792 (eql '%negate (lvar-fun-name (combination-fun use))))
2793 (splice-fun-args amount '%negate 1)
2794 `(lambda (integer amount)
2795 (declare (type unsigned-byte amount))
2796 (%ash/right integer (if (>= amount ,sb!vm:n-word-bits)
2797 ,(1- sb!vm:n-word-bits)
2800 `(%ash/right integer (if (<= amount ,(- sb!vm:n-word-bits))
2801 ,(1- sb!vm:n-word-bits)
2804 (deftransform ash ((integer amount) (word (integer * 0)))
2805 "Convert ASH of word to %ASH/RIGHT"
2806 (when (constant-lvar-p amount)
2807 (give-up-ir1-transform))
2808 (let ((use (lvar-uses amount)))
2809 (cond ((and (combination-p use)
2810 (eql '%negate (lvar-fun-name (combination-fun use))))
2811 (splice-fun-args amount '%negate 1)
2812 `(lambda (integer amount)
2813 (declare (type unsigned-byte amount))
2814 (if (>= amount ,sb!vm:n-word-bits)
2816 (%ash/right integer amount))))
2818 `(if (<= amount ,(- sb!vm:n-word-bits))
2820 (%ash/right integer (- amount)))))))
2822 (deftransform %ash/right ((integer amount) (integer (constant-arg unsigned-byte)))
2823 "Convert %ASH/RIGHT by constant back to ASH"
2824 `(ash integer ,(- (lvar-value amount))))
2826 (deftransform %ash/right ((integer amount) * (member -1 0) :node node)
2827 ;; constant-fold large shifts
2828 (let ((return-type (single-value-type (node-derived-type node))))
2829 (cond ((type= return-type (specifier-type '(eql 0)))
2831 ((type= return-type (specifier-type '(eql -1)))
2834 (aver (csubtypep (lvar-type integer) (specifier-type 'sb!vm:signed-word)))
2835 `(ash integer ,(- 1 sb!vm:n-word-bits))))))
2837 (defun %ash/right-derive-type-aux (n-type shift same-arg)
2838 (declare (ignore same-arg))
2839 (or (and (or (csubtypep n-type (specifier-type 'sb!vm:signed-word))
2840 (csubtypep n-type (specifier-type 'word)))
2841 (csubtypep shift (specifier-type `(mod ,sb!vm:n-word-bits)))
2842 (let ((n-low (numeric-type-low n-type))
2843 (n-high (numeric-type-high n-type))
2844 (s-low (numeric-type-low shift))
2845 (s-high (numeric-type-high shift)))
2846 (make-numeric-type :class 'integer :complexp :real
2849 (ash n-low (- s-low))
2850 (ash n-low (- s-high))))
2853 (ash n-high (- s-high))
2854 (ash n-high (- s-low)))))))
2857 (defoptimizer (%ash/right derive-type) ((n shift))
2858 (two-arg-derive-type n shift #'%ash/right-derive-type-aux #'%ash/right))
2861 ;;; Modular functions
2863 ;;; (ldb (byte s 0) (foo x y ...)) =
2864 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2866 ;;; and similar for other arguments.
2868 (defun make-modular-fun-type-deriver (prototype kind width signedp)
2869 (declare (ignore kind))
2871 (binding* ((info (info :function :info prototype) :exit-if-null)
2872 (fun (fun-info-derive-type info) :exit-if-null)
2873 (mask-type (specifier-type
2875 ((nil) (let ((mask (1- (ash 1 width))))
2876 `(integer ,mask ,mask)))
2877 ((t) `(signed-byte ,width))))))
2879 (let ((res (funcall fun call)))
2881 (if (eq signedp nil)
2882 (logand-derive-type-aux res mask-type))))))
2885 (binding* ((info (info :function :info prototype) :exit-if-null)
2886 (fun (fun-info-derive-type info) :exit-if-null)
2887 (res (funcall fun call) :exit-if-null)
2888 (mask-type (specifier-type
2890 ((nil) (let ((mask (1- (ash 1 width))))
2891 `(integer ,mask ,mask)))
2892 ((t) `(signed-byte ,width))))))
2893 (if (eq signedp nil)
2894 (logand-derive-type-aux res mask-type)))))
2896 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2898 ;;; For good functions, we just recursively cut arguments; their
2899 ;;; "goodness" means that the result will not increase (in the
2900 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2901 ;;; replaced with the version, cutting its result to WIDTH or more
2902 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2903 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2904 ;;; arguments (maybe to a different width) and returning the name of a
2905 ;;; modular version, if it exists, or NIL. If we have changed
2906 ;;; anything, we need to flush old derived types, because they have
2907 ;;; nothing in common with the new code.
2908 (defun cut-to-width (lvar kind width signedp)
2909 (declare (type lvar lvar) (type (integer 0) width))
2910 (let ((type (specifier-type (if (zerop width)
2913 ((nil) 'unsigned-byte)
2916 (labels ((reoptimize-node (node name)
2917 (setf (node-derived-type node)
2919 (info :function :type name)))
2920 (setf (lvar-%derived-type (node-lvar node)) nil)
2921 (setf (node-reoptimize node) t)
2922 (setf (block-reoptimize (node-block node)) t)
2923 (reoptimize-component (node-component node) :maybe))
2924 (cut-node (node &aux did-something)
2925 (when (block-delete-p (node-block node))
2926 (return-from cut-node))
2929 (typecase (ref-leaf node)
2931 (let* ((constant-value (constant-value (ref-leaf node)))
2932 (new-value (if signedp
2933 (mask-signed-field width constant-value)
2934 (ldb (byte width 0) constant-value))))
2935 (unless (= constant-value new-value)
2936 (change-ref-leaf node (make-constant new-value)
2938 (let ((lvar (node-lvar node)))
2939 (setf (lvar-%derived-type lvar)
2940 (and (lvar-has-single-use-p lvar)
2941 (make-values-type :required (list (ctype-of new-value))))))
2942 (setf (block-reoptimize (node-block node)) t)
2943 (reoptimize-component (node-component node) :maybe)
2946 (binding* ((dest (lvar-dest lvar) :exit-if-null)
2947 (nil (combination-p dest) :exit-if-null)
2948 (name (lvar-fun-name (combination-fun dest))))
2949 ;; we're about to insert an m-s-f/logand between a ref to
2950 ;; a variable and another m-s-f/logand. No point in doing
2951 ;; that; the parent m-s-f/logand was already cut to width
2953 (unless (or (cond (signedp
2954 (and (eql name 'mask-signed-field)
2959 (eql name 'logand)))
2960 (csubtypep (lvar-type lvar) type))
2963 `(mask-signed-field ,width 'dummy)
2964 `(logand 'dummy ,(ldb (byte width 0) -1))))
2965 (setf (block-reoptimize (node-block node)) t)
2966 (reoptimize-component (node-component node) :maybe)
2969 (when (eq (basic-combination-kind node) :known)
2970 (let* ((fun-ref (lvar-use (combination-fun node)))
2971 (fun-name (lvar-fun-name (combination-fun node)))
2972 (modular-fun (find-modular-version fun-name kind
2974 (when (and modular-fun
2975 (not (and (eq fun-name 'logand)
2977 (single-value-type (node-derived-type node))
2979 (binding* ((name (etypecase modular-fun
2980 ((eql :good) fun-name)
2982 (modular-fun-info-name modular-fun))
2984 (funcall modular-fun node width)))
2986 (unless (eql modular-fun :good)
2987 (setq did-something t)
2990 (find-free-fun name "in a strange place"))
2991 (setf (combination-kind node) :full))
2992 (unless (functionp modular-fun)
2993 (dolist (arg (basic-combination-args node))
2994 (when (cut-lvar arg)
2995 (setq did-something t))))
2997 (reoptimize-node node name))
2998 did-something)))))))
2999 (cut-lvar (lvar &aux did-something)
3000 (do-uses (node lvar)
3001 (when (cut-node node)
3002 (setq did-something t)))
3006 (defun best-modular-version (width signedp)
3007 ;; 1. exact width-matched :untagged
3008 ;; 2. >/>= width-matched :tagged
3009 ;; 3. >/>= width-matched :untagged
3010 (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class*))
3011 (uswidths (modular-class-widths *untagged-signed-modular-class*))
3012 (uwidths (merge 'list uuwidths uswidths #'< :key #'car))
3013 (twidths (modular-class-widths *tagged-modular-class*)))
3014 (let ((exact (find (cons width signedp) uwidths :test #'equal)))
3016 (return-from best-modular-version (values width :untagged signedp))))
3017 (flet ((inexact-match (w)
3019 ((eq signedp (cdr w)) (<= width (car w)))
3020 ((eq signedp nil) (< width (car w))))))
3021 (let ((tgt (find-if #'inexact-match twidths)))
3023 (return-from best-modular-version
3024 (values (car tgt) :tagged (cdr tgt)))))
3025 (let ((ugt (find-if #'inexact-match uwidths)))
3027 (return-from best-modular-version
3028 (values (car ugt) :untagged (cdr ugt))))))))
3030 (defoptimizer (logand optimizer) ((x y) node)
3031 (let ((result-type (single-value-type (node-derived-type node))))
3032 (when (numeric-type-p result-type)
3033 (let ((low (numeric-type-low result-type))
3034 (high (numeric-type-high result-type)))
3035 (when (and (numberp low)
3038 (let ((width (integer-length high)))
3039 (multiple-value-bind (w kind signedp)
3040 (best-modular-version width nil)
3042 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP).
3044 ;; FIXME: I think the FIXME (which is from APD) above
3045 ;; implies that CUT-TO-WIDTH should do /everything/
3046 ;; that's required, including reoptimizing things
3047 ;; itself that it knows are necessary. At the moment,
3048 ;; CUT-TO-WIDTH sets up some new calls with
3049 ;; combination-type :FULL, which later get noticed as
3050 ;; known functions and properly converted.
3052 ;; We cut to W not WIDTH if SIGNEDP is true, because
3053 ;; signed constant replacement needs to know which bit
3054 ;; in the field is the signed bit.
3055 (let ((xact (cut-to-width x kind (if signedp w width) signedp))
3056 (yact (cut-to-width y kind (if signedp w width) signedp)))
3057 (declare (ignore xact yact))
3058 nil) ; After fixing above, replace with T, meaning
3059 ; "don't reoptimize this (LOGAND) node any more".
3062 (defoptimizer (mask-signed-field optimizer) ((width x) node)
3063 (let ((result-type (single-value-type (node-derived-type node))))
3064 (when (numeric-type-p result-type)
3065 (let ((low (numeric-type-low result-type))
3066 (high (numeric-type-high result-type)))
3067 (when (and (numberp low) (numberp high))
3068 (let ((width (max (integer-length high) (integer-length low))))
3069 (multiple-value-bind (w kind)
3070 (best-modular-version (1+ width) t)
3072 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND W T).
3073 ;; [ see comment above in LOGAND optimizer ]
3074 (cut-to-width x kind w t)
3075 nil ; After fixing above, replace with T.
3078 ;;; miscellanous numeric transforms
3080 ;;; If a constant appears as the first arg, swap the args.
3081 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
3082 (if (and (constant-lvar-p x)
3083 (not (constant-lvar-p y)))
3084 `(,(lvar-fun-name (basic-combination-fun node))
3085 (truly-the ,(lvar-type y) y)
3087 (give-up-ir1-transform)))
3089 (dolist (x '(= char= + * logior logand logxor logtest))
3090 (%deftransform x '(function * *) #'commutative-arg-swap
3091 "place constant arg last"))
3093 ;;; Handle the case of a constant BOOLE-CODE.
3094 (deftransform boole ((op x y) * *)
3095 "convert to inline logical operations"
3096 (unless (constant-lvar-p op)
3097 (give-up-ir1-transform "BOOLE code is not a constant."))
3098 (let ((control (lvar-value op)))
3100 (#.sb!xc:boole-clr 0)
3101 (#.sb!xc:boole-set -1)
3102 (#.sb!xc:boole-1 'x)
3103 (#.sb!xc:boole-2 'y)
3104 (#.sb!xc:boole-c1 '(lognot x))
3105 (#.sb!xc:boole-c2 '(lognot y))
3106 (#.sb!xc:boole-and '(logand x y))
3107 (#.sb!xc:boole-ior '(logior x y))
3108 (#.sb!xc:boole-xor '(logxor x y))
3109 (#.sb!xc:boole-eqv '(logeqv x y))
3110 (#.sb!xc:boole-nand '(lognand x y))
3111 (#.sb!xc:boole-nor '(lognor x y))
3112 (#.sb!xc:boole-andc1 '(logandc1 x y))
3113 (#.sb!xc:boole-andc2 '(logandc2 x y))
3114 (#.sb!xc:boole-orc1 '(logorc1 x y))
3115 (#.sb!xc:boole-orc2 '(logorc2 x y))
3117 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
3120 ;;;; converting special case multiply/divide to shifts
3122 ;;; If arg is a constant power of two, turn * into a shift.
3123 (deftransform * ((x y) (integer integer) *)
3124 "convert x*2^k to shift"
3125 (unless (constant-lvar-p y)
3126 (give-up-ir1-transform))
3127 (let* ((y (lvar-value y))
3129 (len (1- (integer-length y-abs))))
3130 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3131 (give-up-ir1-transform))
3136 ;;; These must come before the ones below, so that they are tried
3137 ;;; first. Since %FLOOR and %CEILING are inlined, this allows
3138 ;;; the general case to be handled by TRUNCATE transforms.
3139 (deftransform floor ((x y))
3142 (deftransform ceiling ((x y))
3145 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3146 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3148 (flet ((frob (y ceil-p)
3149 (unless (constant-lvar-p y)
3150 (give-up-ir1-transform))
3151 (let* ((y (lvar-value y))
3153 (len (1- (integer-length y-abs))))
3154 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3155 (give-up-ir1-transform))
3156 (let ((shift (- len))
3158 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
3159 `(let ((x (+ x ,delta)))
3161 `(values (ash (- x) ,shift)
3162 (- (- (logand (- x) ,mask)) ,delta))
3163 `(values (ash x ,shift)
3164 (- (logand x ,mask) ,delta))))))))
3165 (deftransform floor ((x y) (integer integer) *)
3166 "convert division by 2^k to shift"
3168 (deftransform ceiling ((x y) (integer integer) *)
3169 "convert division by 2^k to shift"
3172 ;;; Do the same for MOD.
3173 (deftransform mod ((x y) (integer integer) *)
3174 "convert remainder mod 2^k to LOGAND"
3175 (unless (constant-lvar-p y)
3176 (give-up-ir1-transform))
3177 (let* ((y (lvar-value y))
3179 (len (1- (integer-length y-abs))))
3180 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3181 (give-up-ir1-transform))
3182 (let ((mask (1- y-abs)))
3184 `(- (logand (- x) ,mask))
3185 `(logand x ,mask)))))
3187 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3188 (deftransform truncate ((x y) (integer integer))
3189 "convert division by 2^k to shift"
3190 (unless (constant-lvar-p y)
3191 (give-up-ir1-transform))
3192 (let* ((y (lvar-value y))
3194 (len (1- (integer-length y-abs))))
3195 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3196 (give-up-ir1-transform))
3197 (let* ((shift (- len))
3200 (values ,(if (minusp y)
3202 `(- (ash (- x) ,shift)))
3203 (- (logand (- x) ,mask)))
3204 (values ,(if (minusp y)
3205 `(ash (- ,mask x) ,shift)
3207 (logand x ,mask))))))
3209 ;;; And the same for REM.
3210 (deftransform rem ((x y) (integer integer) *)
3211 "convert remainder mod 2^k to LOGAND"
3212 (unless (constant-lvar-p y)
3213 (give-up-ir1-transform))
3214 (let* ((y (lvar-value y))
3216 (len (1- (integer-length y-abs))))
3217 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3218 (give-up-ir1-transform))
3219 (let ((mask (1- y-abs)))
3221 (- (logand (- x) ,mask))
3222 (logand x ,mask)))))
3224 ;;; Return an expression to calculate the integer quotient of X and
3225 ;;; constant Y, using multiplication, shift and add/sub instead of
3226 ;;; division. Both arguments must be unsigned, fit in a machine word and
3227 ;;; Y must neither be zero nor a power of two. The quotient is rounded
3229 ;;; The algorithm is taken from the paper "Division by Invariant
3230 ;;; Integers using Multiplication", 1994 by Torbj\"{o}rn Granlund and
3231 ;;; Peter L. Montgomery, Figures 4.2 and 6.2, modified to exclude the
3232 ;;; case of division by powers of two.
3233 ;;; The algorithm includes an adaptive precision argument. Use it, since
3234 ;;; we often have sub-word value ranges. Careful, in this case, we need
3235 ;;; p s.t 2^p > n, not the ceiling of the binary log.
3236 ;;; Also, for some reason, the paper prefers shifting to masking. Mask
3237 ;;; instead. Masking is equivalent to shifting right, then left again;
3238 ;;; all the intermediate values are still words, so we just have to shift
3239 ;;; right a bit more to compensate, at the end.
3241 ;;; The following two examples show an average case and the worst case
3242 ;;; with respect to the complexity of the generated expression, under
3243 ;;; a word size of 64 bits:
3245 ;;; (UNSIGNED-DIV-TRANSFORMER 10 MOST-POSITIVE-WORD) ->
3246 ;;; (ASH (%MULTIPLY (LOGANDC2 X 0) 14757395258967641293) -3)
3248 ;;; (UNSIGNED-DIV-TRANSFORMER 7 MOST-POSITIVE-WORD) ->
3250 ;;; (T1 (%MULTIPLY NUM 2635249153387078803)))
3251 ;;; (ASH (LDB (BYTE 64 0)
3252 ;;; (+ T1 (ASH (LDB (BYTE 64 0)
3257 (defun gen-unsigned-div-by-constant-expr (y max-x)
3258 (declare (type (integer 3 #.most-positive-word) y)
3260 (aver (not (zerop (logand y (1- y)))))
3262 ;; the floor of the binary logarithm of (positive) X
3263 (integer-length (1- x)))
3264 (choose-multiplier (y precision)
3266 (shift l (1- shift))
3267 (expt-2-n+l (expt 2 (+ sb!vm:n-word-bits l)))
3268 (m-low (truncate expt-2-n+l y) (ash m-low -1))
3269 (m-high (truncate (+ expt-2-n+l
3270 (ash expt-2-n+l (- precision)))
3273 ((not (and (< (ash m-low -1) (ash m-high -1))
3275 (values m-high shift)))))
3276 (let ((n (expt 2 sb!vm:n-word-bits))
3277 (precision (integer-length max-x))
3279 (multiple-value-bind (m shift2)
3280 (choose-multiplier y precision)
3281 (when (and (>= m n) (evenp y))
3282 (setq shift1 (ld (logand y (- y))))
3283 (multiple-value-setq (m shift2)
3284 (choose-multiplier (/ y (ash 1 shift1))
3285 (- precision shift1))))
3288 `(truly-the word ,x)))
3290 (t1 (%multiply-high num ,(- m n))))
3291 (ash ,(word `(+ t1 (ash ,(word `(- num t1))
3294 ((and (zerop shift1) (zerop shift2))
3295 (let ((max (truncate max-x y)))
3296 ;; Explicit TRULY-THE needed to get the FIXNUM=>FIXNUM
3298 `(truly-the (integer 0 ,max)
3299 (%multiply-high x ,m))))
3301 `(ash (%multiply-high (logandc2 x ,(1- (ash 1 shift1))) ,m)
3302 ,(- (+ shift1 shift2)))))))))
3304 ;;; If the divisor is constant and both args are positive and fit in a
3305 ;;; machine word, replace the division by a multiplication and possibly
3306 ;;; some shifts and an addition. Calculate the remainder by a second
3307 ;;; multiplication and a subtraction. Dead code elimination will
3308 ;;; suppress the latter part if only the quotient is needed. If the type
3309 ;;; of the dividend allows to derive that the quotient will always have
3310 ;;; the same value, emit much simpler code to handle that. (This case
3311 ;;; may be rare but it's easy to detect and the compiler doesn't find
3312 ;;; this optimization on its own.)
3313 (deftransform truncate ((x y) (word (constant-arg word))
3315 :policy (and (> speed compilation-speed)
3317 "convert integer division to multiplication"
3318 (let* ((y (lvar-value y))
3319 (x-type (lvar-type x))
3320 (max-x (or (and (numeric-type-p x-type)
3321 (numeric-type-high x-type))
3322 most-positive-word)))
3323 ;; Division by zero, one or powers of two is handled elsewhere.
3324 (when (zerop (logand y (1- y)))
3325 (give-up-ir1-transform))
3326 `(let* ((quot ,(gen-unsigned-div-by-constant-expr y max-x))
3327 (rem (ldb (byte #.sb!vm:n-word-bits 0)
3328 (- x (* quot ,y)))))
3329 (values quot rem))))
3331 ;;;; arithmetic and logical identity operation elimination
3333 ;;; Flush calls to various arith functions that convert to the
3334 ;;; identity function or a constant.
3335 (macrolet ((def (name identity result)
3336 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3337 "fold identity operations"
3344 (def logxor -1 (lognot x))
3347 (deftransform logand ((x y) (* (constant-arg t)) *)
3348 "fold identity operation"
3349 (let ((y (lvar-value y)))
3350 (unless (and (plusp y)
3351 (= y (1- (ash 1 (integer-length y)))))
3352 (give-up-ir1-transform))
3353 (unless (csubtypep (lvar-type x)
3354 (specifier-type `(integer 0 ,y)))
3355 (give-up-ir1-transform))
3358 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3359 "fold identity operation"
3360 (let ((size (lvar-value size)))
3361 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3362 (give-up-ir1-transform))
3365 ;;; Pick off easy association opportunities for constant folding.
3366 ;;; More complicated stuff that also depends on commutativity
3367 ;;; (e.g. (f (f x k1) (f y k2)) => (f (f x y) (f k1 k2))) should
3368 ;;; probably be handled with a more general tree-rewriting pass.
3369 (macrolet ((def (operator &key (type 'integer) (folded operator))
3370 `(deftransform ,operator ((x z) (,type (constant-arg ,type)))
3371 ,(format nil "associate ~A/~A of constants"
3373 (binding* ((node (if (lvar-has-single-use-p x)
3375 (give-up-ir1-transform)))
3376 (nil (or (and (combination-p node)
3378 (combination-fun node))
3380 (give-up-ir1-transform)))
3381 (y (second (combination-args node)))
3382 (nil (or (constant-lvar-p y)
3383 (give-up-ir1-transform)))
3385 (unless (typep y ',type)
3386 (give-up-ir1-transform))
3387 (splice-fun-args x ',folded 2)
3389 (declare (ignore y z))
3390 (,',operator x ',(,folded y (lvar-value z))))))))
3394 (def logtest :folded logand)
3395 (def + :type rational)
3396 (def * :type rational))
3398 (deftransform mask-signed-field ((width x) ((constant-arg unsigned-byte) *))
3399 "Fold mask-signed-field/mask-signed-field of constant width"
3400 (binding* ((node (if (lvar-has-single-use-p x)
3402 (give-up-ir1-transform)))
3403 (nil (or (combination-p node)
3404 (give-up-ir1-transform)))
3405 (nil (or (eq (lvar-fun-name (combination-fun node))
3407 (give-up-ir1-transform)))
3408 (x-width (first (combination-args node)))
3409 (nil (or (constant-lvar-p x-width)
3410 (give-up-ir1-transform)))
3411 (x-width (lvar-value x-width)))
3412 (unless (typep x-width 'unsigned-byte)
3413 (give-up-ir1-transform))
3414 (splice-fun-args x 'mask-signed-field 2)
3415 `(lambda (width x-width x)
3416 (declare (ignore width x-width))
3417 (mask-signed-field ,(min (lvar-value width) x-width) x))))
3419 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3420 ;;; (* 0 -4.0) is -0.0.
3421 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3422 "convert (- 0 x) to negate"
3424 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3425 "convert (* x 0) to 0"
3428 (deftransform %negate ((x) (rational))
3429 "Eliminate %negate/%negate of rationals"
3430 (splice-fun-args x '%negate 1)
3433 (deftransform %negate ((x) (number))
3435 (let ((use (lvar-uses x))
3437 (unless (and (combination-p use)
3438 (eql '* (lvar-fun-name (combination-fun use)))
3439 (constant-lvar-p (setf arg (second (combination-args use))))
3440 (numberp (setf arg (lvar-value arg))))
3441 (give-up-ir1-transform))
3442 (splice-fun-args x '* 2)
3444 (declare (ignore y))
3447 ;;; Return T if in an arithmetic op including lvars X and Y, the
3448 ;;; result type is not affected by the type of X. That is, Y is at
3449 ;;; least as contagious as X.
3451 (defun not-more-contagious (x y)
3452 (declare (type continuation x y))
3453 (let ((x (lvar-type x))
3455 (values (type= (numeric-contagion x y)
3456 (numeric-contagion y y)))))
3457 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3458 ;;; XXX needs more work as valid transforms are missed; some cases are
3459 ;;; specific to particular transform functions so the use of this
3460 ;;; function may need a re-think.
3461 (defun not-more-contagious (x y)
3462 (declare (type lvar x y))
3463 (flet ((simple-numeric-type (num)
3464 (and (numeric-type-p num)
3465 ;; Return non-NIL if NUM is integer, rational, or a float
3466 ;; of some type (but not FLOAT)
3467 (case (numeric-type-class num)
3471 (numeric-type-format num))
3474 (let ((x (lvar-type x))
3476 (if (and (simple-numeric-type x)
3477 (simple-numeric-type y))
3478 (values (type= (numeric-contagion x y)
3479 (numeric-contagion y y)))))))
3481 (def!type exact-number ()
3482 '(or rational (complex rational)))
3486 ;;; Only safely applicable for exact numbers. For floating-point
3487 ;;; x, one would have to first show that neither x or y are signed
3488 ;;; 0s, and that x isn't an SNaN.
3489 (deftransform + ((x y) (exact-number (constant-arg (eql 0))) *)
3494 (deftransform - ((x y) (exact-number (constant-arg (eql 0))) *)
3498 ;;; Fold (OP x +/-1)
3500 ;;; %NEGATE might not always signal correctly.
3502 ((def (name result minus-result)
3503 `(deftransform ,name ((x y)
3504 (exact-number (constant-arg (member 1 -1))))
3505 "fold identity operations"
3506 (if (minusp (lvar-value y)) ',minus-result ',result))))
3507 (def * x (%negate x))
3508 (def / x (%negate x))
3509 (def expt x (/ 1 x)))
3511 ;;; Fold (expt x n) into multiplications for small integral values of
3512 ;;; N; convert (expt x 1/2) to sqrt.
3513 (deftransform expt ((x y) (t (constant-arg real)) *)
3514 "recode as multiplication or sqrt"
3515 (let ((val (lvar-value y)))
3516 ;; If Y would cause the result to be promoted to the same type as
3517 ;; Y, we give up. If not, then the result will be the same type
3518 ;; as X, so we can replace the exponentiation with simple
3519 ;; multiplication and division for small integral powers.
3520 (unless (not-more-contagious y x)
3521 (give-up-ir1-transform))
3523 (let ((x-type (lvar-type x)))
3524 (cond ((csubtypep x-type (specifier-type '(or rational
3525 (complex rational))))
3527 ((csubtypep x-type (specifier-type 'real))
3531 ((csubtypep x-type (specifier-type 'complex))
3532 ;; both parts are float
3534 (t (give-up-ir1-transform)))))
3535 ((= val 2) '(* x x))
3536 ((= val -2) '(/ (* x x)))
3537 ((= val 3) '(* x x x))
3538 ((= val -3) '(/ (* x x x)))
3539 ((= val 1/2) '(sqrt x))
3540 ((= val -1/2) '(/ (sqrt x)))
3541 (t (give-up-ir1-transform)))))
3543 (deftransform expt ((x y) ((constant-arg (member -1 -1.0 -1.0d0)) integer) *)
3544 "recode as an ODDP check"
3545 (let ((val (lvar-value x)))
3547 '(- 1 (* 2 (logand 1 y)))
3552 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3553 ;;; transformations?
3554 ;;; Perhaps we should have to prove that the denominator is nonzero before
3555 ;;; doing them? -- WHN 19990917
3556 (macrolet ((def (name)
3557 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3564 (macrolet ((def (name)
3565 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3574 (macrolet ((def (name &optional float)
3575 (let ((x (if float '(float x) 'x)))
3576 `(deftransform ,name ((x y) (integer (constant-arg (member 1 -1)))
3578 "fold division by 1"
3579 `(values ,(if (minusp (lvar-value y))
3592 ;;;; character operations
3594 (deftransform char-equal ((a b) (base-char base-char))
3596 '(let* ((ac (char-code a))
3598 (sum (logxor ac bc)))
3600 (when (eql sum #x20)
3601 (let ((sum (+ ac bc)))
3602 (or (and (> sum 161) (< sum 213))
3603 (and (> sum 415) (< sum 461))
3604 (and (> sum 463) (< sum 477))))))))
3606 (deftransform char-upcase ((x) (base-char))
3608 '(let ((n-code (char-code x)))
3609 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3610 (< n-code #o173)) ; Octal 172 is #\z.
3611 (and (> n-code #o337)
3613 (and (> n-code #o367)
3615 (code-char (logxor #x20 n-code))
3618 (deftransform char-downcase ((x) (base-char))
3620 '(let ((n-code (char-code x)))
3621 (if (or (and (> n-code 64) ; 65 is #\A.
3622 (< n-code 91)) ; 90 is #\Z.
3627 (code-char (logxor #x20 n-code))
3630 ;;;; equality predicate transforms
3632 ;;; Return true if X and Y are lvars whose only use is a
3633 ;;; reference to the same leaf, and the value of the leaf cannot
3635 (defun same-leaf-ref-p (x y)
3636 (declare (type lvar x y))
3637 (let ((x-use (principal-lvar-use x))
3638 (y-use (principal-lvar-use y)))
3641 (eq (ref-leaf x-use) (ref-leaf y-use))
3642 (constant-reference-p x-use))))
3644 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3645 ;;; if there is no intersection between the types of the arguments,
3646 ;;; then the result is definitely false.
3647 (deftransform simple-equality-transform ((x y) * *
3650 ((same-leaf-ref-p x y) t)
3651 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3653 (t (give-up-ir1-transform))))
3656 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3660 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3661 ;;; try to convert to a type-specific predicate or EQ:
3662 ;;; -- If both args are characters, convert to CHAR=. This is better than
3663 ;;; just converting to EQ, since CHAR= may have special compilation
3664 ;;; strategies for non-standard representations, etc.
3665 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3666 ;;; constant and if so, put X second. Doing this results in better
3667 ;;; code from the backend, since the backend assumes that any constant
3668 ;;; argument comes second.
3669 ;;; -- If either arg is definitely not a number or a fixnum, then we
3670 ;;; can compare with EQ.
3671 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3672 ;;; is constant then we put it second. If X is a subtype of Y, we put
3673 ;;; it second. These rules make it easier for the back end to match
3674 ;;; these interesting cases.
3675 (deftransform eql ((x y) * * :node node)
3676 "convert to simpler equality predicate"
3677 (let ((x-type (lvar-type x))
3678 (y-type (lvar-type y))
3679 (char-type (specifier-type 'character)))
3680 (flet ((fixnum-type-p (type)
3681 (csubtypep type (specifier-type 'fixnum))))
3683 ((same-leaf-ref-p x y) t)
3684 ((not (types-equal-or-intersect x-type y-type))
3686 ((and (csubtypep x-type char-type)
3687 (csubtypep y-type char-type))
3689 ((or (eq-comparable-type-p x-type) (eq-comparable-type-p y-type))
3690 (if (and (constant-lvar-p x) (not (constant-lvar-p y)))
3693 ((and (not (constant-lvar-p y))
3694 (or (constant-lvar-p x)
3695 (and (csubtypep x-type y-type)
3696 (not (csubtypep y-type x-type)))))
3699 (give-up-ir1-transform))))))
3701 ;;; similarly to the EQL transform above, we attempt to constant-fold
3702 ;;; or convert to a simpler predicate: mostly we have to be careful
3703 ;;; with strings and bit-vectors.
3704 (deftransform equal ((x y) * *)
3705 "convert to simpler equality predicate"
3706 (let ((x-type (lvar-type x))
3707 (y-type (lvar-type y))
3708 (string-type (specifier-type 'string))
3709 (bit-vector-type (specifier-type 'bit-vector)))
3711 ((same-leaf-ref-p x y) t)
3712 ((and (csubtypep x-type string-type)
3713 (csubtypep y-type string-type))
3715 ((and (csubtypep x-type bit-vector-type)
3716 (csubtypep y-type bit-vector-type))
3717 '(bit-vector-= x y))
3718 ;; if at least one is not a string, and at least one is not a
3719 ;; bit-vector, then we can reason from types.
3720 ((and (not (and (types-equal-or-intersect x-type string-type)
3721 (types-equal-or-intersect y-type string-type)))
3722 (not (and (types-equal-or-intersect x-type bit-vector-type)
3723 (types-equal-or-intersect y-type bit-vector-type)))
3724 (not (types-equal-or-intersect x-type y-type)))
3726 (t (give-up-ir1-transform)))))
3728 ;;; Convert to EQL if both args are rational and complexp is specified
3729 ;;; and the same for both.
3730 (deftransform = ((x y) (number number) *)
3732 (let ((x-type (lvar-type x))
3733 (y-type (lvar-type y)))
3734 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3735 (csubtypep y-type (specifier-type 'float)))
3736 (and (csubtypep x-type (specifier-type '(complex float)))
3737 (csubtypep y-type (specifier-type '(complex float))))
3738 #!+complex-float-vops
3739 (and (csubtypep x-type (specifier-type '(or single-float (complex single-float))))
3740 (csubtypep y-type (specifier-type '(or single-float (complex single-float)))))
3741 #!+complex-float-vops
3742 (and (csubtypep x-type (specifier-type '(or double-float (complex double-float))))
3743 (csubtypep y-type (specifier-type '(or double-float (complex double-float))))))
3744 ;; They are both floats. Leave as = so that -0.0 is
3745 ;; handled correctly.
3746 (give-up-ir1-transform))
3747 ((or (and (csubtypep x-type (specifier-type 'rational))
3748 (csubtypep y-type (specifier-type 'rational)))
3749 (and (csubtypep x-type
3750 (specifier-type '(complex rational)))
3752 (specifier-type '(complex rational)))))
3753 ;; They are both rationals and complexp is the same.
3757 (give-up-ir1-transform
3758 "The operands might not be the same type.")))))
3760 (defun maybe-float-lvar-p (lvar)
3761 (neq *empty-type* (type-intersection (specifier-type 'float)
3764 (flet ((maybe-invert (node op inverted x y)
3765 ;; Don't invert if either argument can be a float (NaNs)
3767 ((or (maybe-float-lvar-p x) (maybe-float-lvar-p y))
3768 (delay-ir1-transform node :constraint)
3769 `(or (,op x y) (= x y)))
3771 `(if (,inverted x y) nil t)))))
3772 (deftransform >= ((x y) (number number) * :node node)
3773 "invert or open code"
3774 (maybe-invert node '> '< x y))
3775 (deftransform <= ((x y) (number number) * :node node)
3776 "invert or open code"
3777 (maybe-invert node '< '> x y)))
3779 ;;; See whether we can statically determine (< X Y) using type
3780 ;;; information. If X's high bound is < Y's low, then X < Y.
3781 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3782 ;;; NIL). If not, at least make sure any constant arg is second.
3783 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3784 `(deftransform ,name ((x y))
3785 "optimize using intervals"
3786 (if (and (same-leaf-ref-p x y)
3787 ;; For non-reflexive functions we don't need
3788 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3789 ;; but with reflexive ones we don't know...
3791 '((and (not (maybe-float-lvar-p x))
3792 (not (maybe-float-lvar-p y))))))
3794 (let ((ix (or (type-approximate-interval (lvar-type x))
3795 (give-up-ir1-transform)))
3796 (iy (or (type-approximate-interval (lvar-type y))
3797 (give-up-ir1-transform))))
3802 ((and (constant-lvar-p x)
3803 (not (constant-lvar-p y)))
3806 (give-up-ir1-transform))))))))
3807 (def = = t (interval-= ix iy) (interval-/= ix iy))
3808 (def /= /= nil (interval-/= ix iy) (interval-= ix iy))
3809 (def < > nil (interval-< ix iy) (interval->= ix iy))
3810 (def > < nil (interval-< iy ix) (interval->= iy ix))
3811 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3812 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3814 (defun ir1-transform-char< (x y first second inverse)
3816 ((same-leaf-ref-p x y) nil)
3817 ;; If we had interval representation of character types, as we
3818 ;; might eventually have to to support 2^21 characters, then here
3819 ;; we could do some compile-time computation as in transforms for
3820 ;; < above. -- CSR, 2003-07-01
3821 ((and (constant-lvar-p first)
3822 (not (constant-lvar-p second)))
3824 (t (give-up-ir1-transform))))
3826 (deftransform char< ((x y) (character character) *)
3827 (ir1-transform-char< x y x y 'char>))
3829 (deftransform char> ((x y) (character character) *)
3830 (ir1-transform-char< y x x y 'char<))
3832 ;;;; converting N-arg comparisons
3834 ;;;; We convert calls to N-arg comparison functions such as < into
3835 ;;;; two-arg calls. This transformation is enabled for all such
3836 ;;;; comparisons in this file. If any of these predicates are not
3837 ;;;; open-coded, then the transformation should be removed at some
3838 ;;;; point to avoid pessimization.
3840 ;;; This function is used for source transformation of N-arg
3841 ;;; comparison functions other than inequality. We deal both with
3842 ;;; converting to two-arg calls and inverting the sense of the test,
3843 ;;; if necessary. If the call has two args, then we pass or return a
3844 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3845 ;;; then we transform to code that returns true. Otherwise, we bind
3846 ;;; all the arguments and expand into a bunch of IFs.
3847 (defun multi-compare (predicate args not-p type &optional force-two-arg-p)
3848 (let ((nargs (length args)))
3849 (cond ((< nargs 1) (values nil t))
3850 ((= nargs 1) `(progn (the ,type ,@args) t))
3853 `(if (,predicate ,(first args) ,(second args)) nil t)
3855 `(,predicate ,(first args) ,(second args))
3858 (do* ((i (1- nargs) (1- i))
3860 (current (gensym) (gensym))
3861 (vars (list current) (cons current vars))
3863 `(if (,predicate ,current ,last)
3865 `(if (,predicate ,current ,last)
3868 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3871 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3872 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3873 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3874 ;;; We cannot do the inversion for >= and <= here, since both
3875 ;;; (< NaN X) and (> NaN X)
3876 ;;; are false, and we don't have type-information available yet. The
3877 ;;; deftransforms for two-argument versions of >= and <= takes care of
3878 ;;; the inversion to > and < when possible.
3879 (define-source-transform <= (&rest args) (multi-compare '<= args nil 'real))
3880 (define-source-transform >= (&rest args) (multi-compare '>= args nil 'real))
3882 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3884 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3886 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3888 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3890 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3893 (define-source-transform char-equal (&rest args)
3894 (multi-compare 'sb!impl::two-arg-char-equal args nil 'character t))
3895 (define-source-transform char-lessp (&rest args)
3896 (multi-compare 'sb!impl::two-arg-char-lessp args nil 'character t))
3897 (define-source-transform char-greaterp (&rest args)
3898 (multi-compare 'sb!impl::two-arg-char-greaterp args nil 'character t))
3899 (define-source-transform char-not-greaterp (&rest args)
3900 (multi-compare 'sb!impl::two-arg-char-greaterp args t 'character t))
3901 (define-source-transform char-not-lessp (&rest args)
3902 (multi-compare 'sb!impl::two-arg-char-lessp args t 'character t))
3904 ;;; This function does source transformation of N-arg inequality
3905 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3906 ;;; arg cases. If there are more than two args, then we expand into
3907 ;;; the appropriate n^2 comparisons only when speed is important.
3908 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3909 (defun multi-not-equal (predicate args type)
3910 (let ((nargs (length args)))
3911 (cond ((< nargs 1) (values nil t))
3912 ((= nargs 1) `(progn (the ,type ,@args) t))
3914 `(if (,predicate ,(first args) ,(second args)) nil t))
3915 ((not (policy *lexenv*
3916 (and (>= speed space)
3917 (>= speed compilation-speed))))
3920 (let ((vars (make-gensym-list nargs)))
3921 (do ((var vars next)
3922 (next (cdr vars) (cdr next))
3925 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3927 (let ((v1 (first var)))
3929 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3931 (define-source-transform /= (&rest args)
3932 (multi-not-equal '= args 'number))
3933 (define-source-transform char/= (&rest args)
3934 (multi-not-equal 'char= args 'character))
3935 (define-source-transform char-not-equal (&rest args)
3936 (multi-not-equal 'char-equal args 'character))
3938 ;;; Expand MAX and MIN into the obvious comparisons.
3939 (define-source-transform max (arg0 &rest rest)
3940 (once-only ((arg0 arg0))
3942 `(values (the real ,arg0))
3943 `(let ((maxrest (max ,@rest)))
3944 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3945 (define-source-transform min (arg0 &rest rest)
3946 (once-only ((arg0 arg0))
3948 `(values (the real ,arg0))
3949 `(let ((minrest (min ,@rest)))
3950 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3952 ;;;; converting N-arg arithmetic functions
3954 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3955 ;;;; versions, and degenerate cases are flushed.
3957 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3958 (declaim (ftype (sfunction (symbol t list t) list) associate-args))
3959 (defun associate-args (fun first-arg more-args identity)
3960 (let ((next (rest more-args))
3961 (arg (first more-args)))
3963 `(,fun ,first-arg ,(if arg arg identity))
3964 (associate-args fun `(,fun ,first-arg ,arg) next identity))))
3966 ;;; Reduce constants in ARGS list.
3967 (declaim (ftype (sfunction (symbol list t symbol) list) reduce-constants))
3968 (defun reduce-constants (fun args identity one-arg-result-type)
3969 (let ((one-arg-constant-p (ecase one-arg-result-type
3971 (integer #'integerp)))
3972 (reduced-value identity)
3974 (collect ((not-constants))
3976 (if (funcall one-arg-constant-p arg)
3977 (setf reduced-value (funcall fun reduced-value arg)
3979 (not-constants arg)))
3980 ;; It is tempting to drop constants reduced to identity here,
3981 ;; but if X is SNaN in (* X 1), we cannot drop the 1.
3984 `(,reduced-value ,@(not-constants))
3986 `(,reduced-value)))))
3988 ;;; Do source transformations for transitive functions such as +.
3989 ;;; One-arg cases are replaced with the arg and zero arg cases with
3990 ;;; the identity. ONE-ARG-RESULT-TYPE is the type to ensure (with THE)
3991 ;;; that the argument in one-argument calls is.
3992 (declaim (ftype (function (symbol list t &optional symbol list)
3993 (values t &optional (member nil t)))
3994 source-transform-transitive))
3995 (defun source-transform-transitive (fun args identity
3996 &optional (one-arg-result-type 'number)
3997 (one-arg-prefixes '(values)))
4000 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
4002 (t (let ((reduced-args (reduce-constants fun args identity one-arg-result-type)))
4003 (associate-args fun (first reduced-args) (rest reduced-args) identity)))))
4005 (define-source-transform + (&rest args)
4006 (source-transform-transitive '+ args 0))
4007 (define-source-transform * (&rest args)
4008 (source-transform-transitive '* args 1))
4009 (define-source-transform logior (&rest args)
4010 (source-transform-transitive 'logior args 0 'integer))
4011 (define-source-transform logxor (&rest args)
4012 (source-transform-transitive 'logxor args 0 'integer))
4013 (define-source-transform logand (&rest args)
4014 (source-transform-transitive 'logand args -1 'integer))
4015 (define-source-transform logeqv (&rest args)
4016 (source-transform-transitive 'logeqv args -1 'integer))
4017 (define-source-transform gcd (&rest args)
4018 (source-transform-transitive 'gcd args 0 'integer '(abs)))
4019 (define-source-transform lcm (&rest args)
4020 (source-transform-transitive 'lcm args 1 'integer '(abs)))
4022 ;;; Do source transformations for intransitive n-arg functions such as
4023 ;;; /. With one arg, we form the inverse. With two args we pass.
4024 ;;; Otherwise we associate into two-arg calls.
4025 (declaim (ftype (function (symbol symbol list t list &optional symbol)
4026 (values list &optional (member nil t)))
4027 source-transform-intransitive))
4028 (defun source-transform-intransitive (fun fun* args identity one-arg-prefixes
4029 &optional (one-arg-result-type 'number))
4031 ((0 2) (values nil t))
4032 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
4033 (t (let ((reduced-args
4034 (reduce-constants fun* (rest args) identity one-arg-result-type)))
4035 (associate-args fun (first args) reduced-args identity)))))
4037 (define-source-transform - (&rest args)
4038 (source-transform-intransitive '- '+ args 0 '(%negate)))
4039 (define-source-transform / (&rest args)
4040 (source-transform-intransitive '/ '* args 1 '(/ 1)))
4042 ;;;; transforming APPLY
4044 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
4045 ;;; only needs to understand one kind of variable-argument call. It is
4046 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
4047 (define-source-transform apply (fun arg &rest more-args)
4048 (let ((args (cons arg more-args)))
4049 `(multiple-value-call ,fun
4050 ,@(mapcar (lambda (x) `(values ,x)) (butlast args))
4051 (values-list ,(car (last args))))))
4053 ;;;; transforming references to &REST argument
4055 ;;; We add magical &MORE arguments to all functions with &REST. If ARG names
4056 ;;; the &REST argument, this returns the lambda-vars for the context and
4058 (defun possible-rest-arg-context (arg)
4060 (let* ((var (lexenv-find arg vars))
4061 (info (when (lambda-var-p var)
4062 (lambda-var-arg-info var))))
4064 (eq :rest (arg-info-kind info))
4065 (consp (arg-info-default info)))
4066 (values-list (arg-info-default info))))))
4068 (defun mark-more-context-used (rest-var)
4069 (let ((info (lambda-var-arg-info rest-var)))
4070 (aver (eq :rest (arg-info-kind info)))
4071 (destructuring-bind (context count &optional used) (arg-info-default info)
4073 (setf (arg-info-default info) (list context count t))))))
4075 (defun mark-more-context-invalid (rest-var)
4076 (let ((info (lambda-var-arg-info rest-var)))
4077 (aver (eq :rest (arg-info-kind info)))
4078 (setf (arg-info-default info) t)))
4080 ;;; This determines of we the REF to a &REST variable is headed towards
4081 ;;; parts unknown, or if we can really use the context.
4082 (defun rest-var-more-context-ok (lvar)
4083 (let* ((use (lvar-use lvar))
4084 (var (when (ref-p use) (ref-leaf use)))
4085 (home (when (lambda-var-p var) (lambda-var-home var)))
4086 (info (when (lambda-var-p var) (lambda-var-arg-info var)))
4087 (restp (when info (eq :rest (arg-info-kind info)))))
4088 (flet ((ref-good-for-more-context-p (ref)
4089 (let ((dest (principal-lvar-end (node-lvar ref))))
4090 (and (combination-p dest)
4091 ;; If the destination is to anything but these, we're going to
4092 ;; actually need the rest list -- and since other operations
4093 ;; might modify the list destructively, the using the context
4094 ;; isn't good anywhere else either.
4095 (lvar-fun-is (combination-fun dest)
4096 '(%rest-values %rest-ref %rest-length
4097 %rest-null %rest-true))
4098 ;; If the home lambda is different and isn't DX, it might
4099 ;; escape -- in which case using the more context isn't safe.
4100 (let ((clambda (node-home-lambda dest)))
4101 (or (eq home clambda)
4102 (leaf-dynamic-extent clambda)))))))
4103 (let ((ok (and restp
4104 (consp (arg-info-default info))
4105 (not (lambda-var-specvar var))
4106 (not (lambda-var-sets var))
4107 (every #'ref-good-for-more-context-p (lambda-var-refs var)))))
4109 (mark-more-context-used var)
4111 (mark-more-context-invalid var)))
4114 ;;; VALUES-LIST -> %REST-VALUES
4115 (define-source-transform values-list (list)
4116 (multiple-value-bind (context count) (possible-rest-arg-context list)
4118 `(%rest-values ,list ,context ,count)
4121 ;;; NTH -> %REST-REF
4122 (define-source-transform nth (n list)
4123 (multiple-value-bind (context count) (possible-rest-arg-context list)
4125 `(%rest-ref ,n ,list ,context ,count)
4126 `(car (nthcdr ,n ,list)))))
4128 (define-source-transform elt (seq n)
4129 (if (policy *lexenv* (= safety 3))
4131 (multiple-value-bind (context count) (possible-rest-arg-context seq)
4133 `(%rest-ref ,n ,seq ,context ,count)
4136 ;;; CAxR -> %REST-REF
4137 (defun source-transform-car (list nth)
4138 (multiple-value-bind (context count) (possible-rest-arg-context list)
4140 `(%rest-ref ,nth ,list ,context ,count)
4143 (define-source-transform car (list)
4144 (source-transform-car list 0))
4146 (define-source-transform cadr (list)
4147 (or (source-transform-car list 1)
4148 `(car (cdr ,list))))
4150 (define-source-transform caddr (list)
4151 (or (source-transform-car list 2)
4152 `(car (cdr (cdr ,list)))))
4154 (define-source-transform cadddr (list)
4155 (or (source-transform-car list 3)
4156 `(car (cdr (cdr (cdr ,list))))))
4158 ;;; LENGTH -> %REST-LENGTH
4159 (defun source-transform-length (list)
4160 (multiple-value-bind (context count) (possible-rest-arg-context list)
4162 `(%rest-length ,list ,context ,count)
4164 (define-source-transform length (list) (source-transform-length list))
4165 (define-source-transform list-length (list) (source-transform-length list))
4167 ;;; ENDP, NULL and NOT -> %REST-NULL
4169 ;;; Outside &REST convert into an IF so that IF optimizations will eliminate
4170 ;;; redundant negations.
4171 (defun source-transform-null (x op)
4172 (multiple-value-bind (context count) (possible-rest-arg-context x)
4174 `(%rest-null ',op ,x ,context ,count))
4176 `(if (the list ,x) nil t))
4179 (define-source-transform not (x) (source-transform-null x 'not))
4180 (define-source-transform null (x) (source-transform-null x 'null))
4181 (define-source-transform endp (x) (source-transform-null x 'endp))
4183 (deftransform %rest-values ((list context count))
4184 (if (rest-var-more-context-ok list)
4185 `(%more-arg-values context 0 count)
4186 `(values-list list)))
4188 (deftransform %rest-ref ((n list context count))
4189 (cond ((rest-var-more-context-ok list)
4190 `(and (< (the index n) count)
4191 (%more-arg context n)))
4192 ((and (constant-lvar-p n) (zerop (lvar-value n)))
4197 (deftransform %rest-length ((list context count))
4198 (if (rest-var-more-context-ok list)
4202 (deftransform %rest-null ((op list context count))
4203 (aver (constant-lvar-p op))
4204 (if (rest-var-more-context-ok list)
4206 `(,(lvar-value op) list)))
4208 (deftransform %rest-true ((list context count))
4209 (if (rest-var-more-context-ok list)
4210 `(not (eql 0 count))
4213 ;;;; transforming FORMAT
4215 ;;;; If the control string is a compile-time constant, then replace it
4216 ;;;; with a use of the FORMATTER macro so that the control string is
4217 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
4218 ;;;; or T and the control string is a function (i.e. FORMATTER), then
4219 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
4221 ;;; for compile-time argument count checking.
4223 ;;; FIXME II: In some cases, type information could be correlated; for
4224 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
4225 ;;; of a corresponding argument is known and does not intersect the
4226 ;;; list type, a warning could be signalled.
4227 (defun check-format-args (string args fun)
4228 (declare (type string string))
4229 (unless (typep string 'simple-string)
4230 (setq string (coerce string 'simple-string)))
4231 (multiple-value-bind (min max)
4232 (handler-case (sb!format:%compiler-walk-format-string string args)
4233 (sb!format:format-error (c)
4234 (compiler-warn "~A" c)))
4236 (let ((nargs (length args)))
4239 (warn 'format-too-few-args-warning
4241 "Too few arguments (~D) to ~S ~S: requires at least ~D."
4242 :format-arguments (list nargs fun string min)))
4244 (warn 'format-too-many-args-warning
4246 "Too many arguments (~D) to ~S ~S: uses at most ~D."
4247 :format-arguments (list nargs fun string max))))))))
4249 (defoptimizer (format optimizer) ((dest control &rest args))
4250 (when (constant-lvar-p control)
4251 (let ((x (lvar-value control)))
4253 (check-format-args x args 'format)))))
4255 ;;; We disable this transform in the cross-compiler to save memory in
4256 ;;; the target image; most of the uses of FORMAT in the compiler are for
4257 ;;; error messages, and those don't need to be particularly fast.
4259 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
4260 :policy (>= speed space))
4261 (unless (constant-lvar-p control)
4262 (give-up-ir1-transform "The control string is not a constant."))
4263 (let ((arg-names (make-gensym-list (length args))))
4264 `(lambda (dest control ,@arg-names)
4265 (declare (ignore control))
4266 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
4268 (deftransform format ((stream control &rest args) (stream function &rest t))
4269 (let ((arg-names (make-gensym-list (length args))))
4270 `(lambda (stream control ,@arg-names)
4271 (funcall control stream ,@arg-names)
4274 (deftransform format ((tee control &rest args) ((member t) function &rest t))
4275 (let ((arg-names (make-gensym-list (length args))))
4276 `(lambda (tee control ,@arg-names)
4277 (declare (ignore tee))
4278 (funcall control *standard-output* ,@arg-names)
4281 (deftransform pathname ((pathspec) (pathname) *)
4284 (deftransform pathname ((pathspec) (string) *)
4285 '(values (parse-namestring pathspec)))
4289 `(defoptimizer (,name optimizer) ((control &rest args))
4290 (when (constant-lvar-p control)
4291 (let ((x (lvar-value control)))
4293 (check-format-args x args ',name)))))))
4296 #+sb-xc-host ; Only we should be using these
4299 (def compiler-error)
4301 (def compiler-style-warn)
4302 (def compiler-notify)
4303 (def maybe-compiler-notify)
4306 (defoptimizer (cerror optimizer) ((report control &rest args))
4307 (when (and (constant-lvar-p control)
4308 (constant-lvar-p report))
4309 (let ((x (lvar-value control))
4310 (y (lvar-value report)))
4311 (when (and (stringp x) (stringp y))
4312 (multiple-value-bind (min1 max1)
4314 (sb!format:%compiler-walk-format-string x args)
4315 (sb!format:format-error (c)
4316 (compiler-warn "~A" c)))
4318 (multiple-value-bind (min2 max2)
4320 (sb!format:%compiler-walk-format-string y args)
4321 (sb!format:format-error (c)
4322 (compiler-warn "~A" c)))
4324 (let ((nargs (length args)))
4326 ((< nargs (min min1 min2))
4327 (warn 'format-too-few-args-warning
4329 "Too few arguments (~D) to ~S ~S ~S: ~
4330 requires at least ~D."
4332 (list nargs 'cerror y x (min min1 min2))))
4333 ((> nargs (max max1 max2))
4334 (warn 'format-too-many-args-warning
4336 "Too many arguments (~D) to ~S ~S ~S: ~
4339 (list nargs 'cerror y x (max max1 max2))))))))))))))
4341 (defoptimizer (coerce derive-type) ((value type) node)
4343 ((constant-lvar-p type)
4344 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
4345 ;; but dealing with the niggle that complex canonicalization gets
4346 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
4348 (let* ((specifier (lvar-value type))
4349 (result-typeoid (careful-specifier-type specifier)))
4351 ((null result-typeoid) nil)
4352 ((csubtypep result-typeoid (specifier-type 'number))
4353 ;; the difficult case: we have to cope with ANSI 12.1.5.3
4354 ;; Rule of Canonical Representation for Complex Rationals,
4355 ;; which is a truly nasty delivery to field.
4357 ((csubtypep result-typeoid (specifier-type 'real))
4358 ;; cleverness required here: it would be nice to deduce
4359 ;; that something of type (INTEGER 2 3) coerced to type
4360 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
4361 ;; FLOAT gets its own clause because it's implemented as
4362 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
4365 ((and (numeric-type-p result-typeoid)
4366 (eq (numeric-type-complexp result-typeoid) :real))
4367 ;; FIXME: is this clause (a) necessary or (b) useful?
4369 ((or (csubtypep result-typeoid
4370 (specifier-type '(complex single-float)))
4371 (csubtypep result-typeoid
4372 (specifier-type '(complex double-float)))
4374 (csubtypep result-typeoid
4375 (specifier-type '(complex long-float))))
4376 ;; float complex types are never canonicalized.
4379 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
4380 ;; probably just a COMPLEX or equivalent. So, in that
4381 ;; case, we will return a complex or an object of the
4382 ;; provided type if it's rational:
4383 (type-union result-typeoid
4384 (type-intersection (lvar-type value)
4385 (specifier-type 'rational))))))
4386 ((and (policy node (zerop safety))
4387 (csubtypep result-typeoid (specifier-type '(array * (*)))))
4388 ;; At zero safety the deftransform for COERCE can elide dimension
4389 ;; checks for the things like (COERCE X '(SIMPLE-VECTOR 5)) -- so we
4390 ;; need to simplify the type to drop the dimension information.
4391 (let ((vtype (simplify-vector-type result-typeoid)))
4393 (specifier-type vtype)
4398 ;; OK, the result-type argument isn't constant. However, there
4399 ;; are common uses where we can still do better than just
4400 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
4401 ;; where Y is of a known type. See messages on cmucl-imp
4402 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
4403 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
4404 ;; the basis that it's unlikely that other uses are both
4405 ;; time-critical and get to this branch of the COND (non-constant
4406 ;; second argument to COERCE). -- CSR, 2002-12-16
4407 (let ((value-type (lvar-type value))
4408 (type-type (lvar-type type)))
4410 ((good-cons-type-p (cons-type)
4411 ;; Make sure the cons-type we're looking at is something
4412 ;; we're prepared to handle which is basically something
4413 ;; that array-element-type can return.
4414 (or (and (member-type-p cons-type)
4415 (eql 1 (member-type-size cons-type))
4416 (null (first (member-type-members cons-type))))
4417 (let ((car-type (cons-type-car-type cons-type)))
4418 (and (member-type-p car-type)
4419 (eql 1 (member-type-members car-type))
4420 (let ((elt (first (member-type-members car-type))))
4424 (numberp (first elt)))))
4425 (good-cons-type-p (cons-type-cdr-type cons-type))))))
4426 (unconsify-type (good-cons-type)
4427 ;; Convert the "printed" respresentation of a cons
4428 ;; specifier into a type specifier. That is, the
4429 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
4430 ;; NULL)) is converted to (SIGNED-BYTE 16).
4431 (cond ((or (null good-cons-type)
4432 (eq good-cons-type 'null))
4434 ((and (eq (first good-cons-type) 'cons)
4435 (eq (first (second good-cons-type)) 'member))
4436 `(,(second (second good-cons-type))
4437 ,@(unconsify-type (caddr good-cons-type))))))
4438 (coerceable-p (part)
4439 ;; Can the value be coerced to the given type? Coerce is
4440 ;; complicated, so we don't handle every possible case
4441 ;; here---just the most common and easiest cases:
4443 ;; * Any REAL can be coerced to a FLOAT type.
4444 ;; * Any NUMBER can be coerced to a (COMPLEX
4445 ;; SINGLE/DOUBLE-FLOAT).
4447 ;; FIXME I: we should also be able to deal with characters
4450 ;; FIXME II: I'm not sure that anything is necessary
4451 ;; here, at least while COMPLEX is not a specialized
4452 ;; array element type in the system. Reasoning: if
4453 ;; something cannot be coerced to the requested type, an
4454 ;; error will be raised (and so any downstream compiled
4455 ;; code on the assumption of the returned type is
4456 ;; unreachable). If something can, then it will be of
4457 ;; the requested type, because (by assumption) COMPLEX
4458 ;; (and other difficult types like (COMPLEX INTEGER)
4459 ;; aren't specialized types.
4460 (let ((coerced-type (careful-specifier-type part)))
4462 (or (and (csubtypep coerced-type (specifier-type 'float))
4463 (csubtypep value-type (specifier-type 'real)))
4464 (and (csubtypep coerced-type
4465 (specifier-type `(or (complex single-float)
4466 (complex double-float))))
4467 (csubtypep value-type (specifier-type 'number)))))))
4468 (process-types (type)
4469 ;; FIXME: This needs some work because we should be able
4470 ;; to derive the resulting type better than just the
4471 ;; type arg of coerce. That is, if X is (INTEGER 10
4472 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
4473 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
4475 (cond ((member-type-p type)
4478 (mapc-member-type-members
4480 (if (coerceable-p member)
4481 (push member members)
4482 (return-from punt *universal-type*)))
4484 (specifier-type `(or ,@members)))))
4485 ((and (cons-type-p type)
4486 (good-cons-type-p type))
4487 (let ((c-type (unconsify-type (type-specifier type))))
4488 (if (coerceable-p c-type)
4489 (specifier-type c-type)
4492 *universal-type*))))
4493 (cond ((union-type-p type-type)
4494 (apply #'type-union (mapcar #'process-types
4495 (union-type-types type-type))))
4496 ((or (member-type-p type-type)
4497 (cons-type-p type-type))
4498 (process-types type-type))
4500 *universal-type*)))))))
4502 (defoptimizer (compile derive-type) ((nameoid function))
4503 (when (csubtypep (lvar-type nameoid)
4504 (specifier-type 'null))
4505 (values-specifier-type '(values function boolean boolean))))
4507 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
4508 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
4509 ;;; optimizer, above).
4510 (defoptimizer (array-element-type derive-type) ((array))
4511 (let ((array-type (lvar-type array)))
4512 (labels ((consify (list)
4515 `(cons (eql ,(car list)) ,(consify (rest list)))))
4516 (get-element-type (a)
4518 (type-specifier (array-type-specialized-element-type a))))
4519 (cond ((eq element-type '*)
4520 (specifier-type 'type-specifier))
4521 ((symbolp element-type)
4522 (make-member-type :members (list element-type)))
4523 ((consp element-type)
4524 (specifier-type (consify element-type)))
4526 (error "can't understand type ~S~%" element-type))))))
4527 (labels ((recurse (type)
4528 (cond ((array-type-p type)
4529 (get-element-type type))
4530 ((union-type-p type)
4532 (mapcar #'recurse (union-type-types type))))
4534 *universal-type*))))
4535 (recurse array-type)))))
4537 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
4538 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4539 ;; isn't really related to the CMU CL code, since instead of trying
4540 ;; to generalize the CMU CL code to allow START and END values, this
4541 ;; code has been written from scratch following Chapter 7 of
4542 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4543 `(macrolet ((%index (x) `(truly-the index ,x))
4544 (%parent (i) `(ash ,i -1))
4545 (%left (i) `(%index (ash ,i 1)))
4546 (%right (i) `(%index (1+ (ash ,i 1))))
4549 (left (%left i) (%left i)))
4550 ((> left current-heap-size))
4551 (declare (type index i left))
4552 (let* ((i-elt (%elt i))
4553 (i-key (funcall keyfun i-elt))
4554 (left-elt (%elt left))
4555 (left-key (funcall keyfun left-elt)))
4556 (multiple-value-bind (large large-elt large-key)
4557 (if (funcall ,',predicate i-key left-key)
4558 (values left left-elt left-key)
4559 (values i i-elt i-key))
4560 (let ((right (%right i)))
4561 (multiple-value-bind (largest largest-elt)
4562 (if (> right current-heap-size)
4563 (values large large-elt)
4564 (let* ((right-elt (%elt right))
4565 (right-key (funcall keyfun right-elt)))
4566 (if (funcall ,',predicate large-key right-key)
4567 (values right right-elt)
4568 (values large large-elt))))
4569 (cond ((= largest i)
4572 (setf (%elt i) largest-elt
4573 (%elt largest) i-elt
4575 (%sort-vector (keyfun &optional (vtype 'vector))
4576 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4577 ;; trouble getting type inference to
4578 ;; propagate all the way through this
4579 ;; tangled mess of inlining. The TRULY-THE
4580 ;; here works around that. -- WHN
4582 `(aref (truly-the ,',vtype ,',',vector)
4583 (%index (+ (%index ,i) start-1)))))
4584 (let (;; Heaps prefer 1-based addressing.
4585 (start-1 (1- ,',start))
4586 (current-heap-size (- ,',end ,',start))
4588 (declare (type (integer -1 #.(1- sb!xc:most-positive-fixnum))
4590 (declare (type index current-heap-size))
4591 (declare (type function keyfun))
4592 (loop for i of-type index
4593 from (ash current-heap-size -1) downto 1 do
4596 (when (< current-heap-size 2)
4598 (rotatef (%elt 1) (%elt current-heap-size))
4599 (decf current-heap-size)
4601 (if (typep ,vector 'simple-vector)
4602 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4603 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4605 ;; Special-casing the KEY=NIL case lets us avoid some
4607 (%sort-vector #'identity simple-vector)
4608 (%sort-vector ,key simple-vector))
4609 ;; It's hard to anticipate many speed-critical applications for
4610 ;; sorting vector types other than (VECTOR T), so we just lump
4611 ;; them all together in one slow dynamically typed mess.
4613 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4614 (%sort-vector (or ,key #'identity))))))
4616 ;;;; debuggers' little helpers
4618 ;;; for debugging when transforms are behaving mysteriously,
4619 ;;; e.g. when debugging a problem with an ASH transform
4620 ;;; (defun foo (&optional s)
4621 ;;; (sb-c::/report-lvar s "S outside WHEN")
4622 ;;; (when (and (integerp s) (> s 3))
4623 ;;; (sb-c::/report-lvar s "S inside WHEN")
4624 ;;; (let ((bound (ash 1 (1- s))))
4625 ;;; (sb-c::/report-lvar bound "BOUND")
4626 ;;; (let ((x (- bound))
4628 ;;; (sb-c::/report-lvar x "X")
4629 ;;; (sb-c::/report-lvar x "Y"))
4630 ;;; `(integer ,(- bound) ,(1- bound)))))
4631 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4632 ;;; and the function doesn't do anything at all.)
4635 (defknown /report-lvar (t t) null)
4636 (deftransform /report-lvar ((x message) (t t))
4637 (format t "~%/in /REPORT-LVAR~%")
4638 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4639 (when (constant-lvar-p x)
4640 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4641 (format t "/MESSAGE=~S~%" (lvar-value message))
4642 (give-up-ir1-transform "not a real transform"))
4643 (defun /report-lvar (x message)
4644 (declare (ignore x message))))
4647 ;;;; Transforms for internal compiler utilities
4649 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4650 ;;; checking that it's still valid at run-time.
4651 (deftransform policy-quality ((policy quality-name)
4653 (unless (and (constant-lvar-p quality-name)
4654 (policy-quality-name-p (lvar-value quality-name)))
4655 (give-up-ir1-transform))
4656 '(%policy-quality policy quality-name))