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
313 (deftransform logtest ((x y) * *)
314 `(not (zerop (logand x y))))
316 (deftransform logbitp
317 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
318 (unsigned-byte #.sb!vm:n-word-bits))))
319 `(if (>= index #.sb!vm:n-word-bits)
321 (not (zerop (logand integer (ash 1 index))))))
323 (define-source-transform byte (size position)
324 `(cons ,size ,position))
325 (define-source-transform byte-size (spec) `(car ,spec))
326 (define-source-transform byte-position (spec) `(cdr ,spec))
327 (define-source-transform ldb-test (bytespec integer)
328 `(not (zerop (mask-field ,bytespec ,integer))))
330 ;;; With the ratio and complex accessors, we pick off the "identity"
331 ;;; case, and use a primitive to handle the cell access case.
332 (define-source-transform numerator (num)
333 (once-only ((n-num `(the rational ,num)))
337 (define-source-transform denominator (num)
338 (once-only ((n-num `(the rational ,num)))
340 (%denominator ,n-num)
343 ;;;; interval arithmetic for computing bounds
345 ;;;; This is a set of routines for operating on intervals. It
346 ;;;; implements a simple interval arithmetic package. Although SBCL
347 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
348 ;;;; for two reasons:
350 ;;;; 1. This package is simpler than NUMERIC-TYPE.
352 ;;;; 2. It makes debugging much easier because you can just strip
353 ;;;; out these routines and test them independently of SBCL. (This is a
356 ;;;; One disadvantage is a probable increase in consing because we
357 ;;;; have to create these new interval structures even though
358 ;;;; numeric-type has everything we want to know. Reason 2 wins for
361 ;;; Support operations that mimic real arithmetic comparison
362 ;;; operators, but imposing a total order on the floating points such
363 ;;; that negative zeros are strictly less than positive zeros.
364 (macrolet ((def (name op)
367 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
368 (,op (float-sign x) (float-sign y))
370 (def signed-zero->= >=)
371 (def signed-zero-> >)
372 (def signed-zero-= =)
373 (def signed-zero-< <)
374 (def signed-zero-<= <=))
376 ;;; The basic interval type. It can handle open and closed intervals.
377 ;;; A bound is open if it is a list containing a number, just like
378 ;;; Lisp says. NIL means unbounded.
379 (defstruct (interval (:constructor %make-interval)
383 (defun make-interval (&key low high)
384 (labels ((normalize-bound (val)
387 (float-infinity-p val))
388 ;; Handle infinities.
392 ;; Handle any closed bounds.
395 ;; We have an open bound. Normalize the numeric
396 ;; bound. If the normalized bound is still a number
397 ;; (not nil), keep the bound open. Otherwise, the
398 ;; bound is really unbounded, so drop the openness.
399 (let ((new-val (normalize-bound (first val))))
401 ;; The bound exists, so keep it open still.
404 (error "unknown bound type in MAKE-INTERVAL")))))
405 (%make-interval :low (normalize-bound low)
406 :high (normalize-bound high))))
408 ;;; Given a number X, create a form suitable as a bound for an
409 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
410 #!-sb-fluid (declaim (inline set-bound))
411 (defun set-bound (x open-p)
412 (if (and x open-p) (list x) x))
414 ;;; Apply the function F to a bound X. If X is an open bound and the
415 ;;; function is declared strictly monotonic, then the result will be
416 ;;; open. IF X is NIL, the result is NIL.
417 (defun bound-func (f x strict)
418 (declare (type function f))
421 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
422 ;; With these traps masked, we might get things like infinity
423 ;; or negative infinity returned. Check for this and return
424 ;; NIL to indicate unbounded.
425 (let ((y (funcall f (type-bound-number x))))
427 (float-infinity-p y))
429 (set-bound y (and strict (consp x))))))
430 ;; Some numerical operations will signal SIMPLE-TYPE-ERROR, e.g.
431 ;; in the course of converting a bignum to a float. Default to
433 (simple-type-error ()))))
435 (defun safe-double-coercion-p (x)
436 (or (typep x 'double-float)
437 (<= most-negative-double-float x most-positive-double-float)))
439 (defun safe-single-coercion-p (x)
440 (or (typep x 'single-float)
442 ;; Fix for bug 420, and related issues: during type derivation we often
443 ;; end up deriving types for both
445 ;; (some-op <int> <single>)
447 ;; (some-op (coerce <int> 'single-float) <single>)
449 ;; or other equivalent transformed forms. The problem with this
450 ;; is that on x86 (+ <int> <single>) is on the machine level
453 ;; (coerce (+ (coerce <int> 'double-float)
454 ;; (coerce <single> 'double-float))
457 ;; so if the result of (coerce <int> 'single-float) is not exact, the
458 ;; derived types for the transformed forms will have an empty
459 ;; intersection -- which in turn means that the compiler will conclude
460 ;; that the call never returns, and all hell breaks lose when it *does*
461 ;; return at runtime. (This affects not just +, but other operators are
464 ;; See also: SAFE-CTYPE-FOR-SINGLE-COERCION-P
466 ;; FIXME: If we ever add SSE-support for x86, this conditional needs to
469 (not (typep x `(or (integer * (,most-negative-exactly-single-float-fixnum))
470 (integer (,most-positive-exactly-single-float-fixnum) *))))
471 (<= most-negative-single-float x most-positive-single-float))))
473 ;;; Apply a binary operator OP to two bounds X and Y. The result is
474 ;;; NIL if either is NIL. Otherwise bound is computed and the result
475 ;;; is open if either X or Y is open.
477 ;;; FIXME: only used in this file, not needed in target runtime
479 ;;; ANSI contaigon specifies coercion to floating point if one of the
480 ;;; arguments is floating point. Here we should check to be sure that
481 ;;; the other argument is within the bounds of that floating point
484 (defmacro safely-binop (op x y)
486 ((typep ,x 'double-float)
487 (when (safe-double-coercion-p ,y)
489 ((typep ,y 'double-float)
490 (when (safe-double-coercion-p ,x)
492 ((typep ,x 'single-float)
493 (when (safe-single-coercion-p ,y)
495 ((typep ,y 'single-float)
496 (when (safe-single-coercion-p ,x)
500 (defmacro bound-binop (op x y)
501 (with-unique-names (xb yb res)
503 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
504 (let* ((,xb (type-bound-number ,x))
505 (,yb (type-bound-number ,y))
506 (,res (safely-binop ,op ,xb ,yb)))
508 (and (or (consp ,x) (consp ,y))
509 ;; Open bounds can very easily be messed up
510 ;; by FP rounding, so take care here.
513 ;; Multiplying a greater-than-zero with
514 ;; less than one can round to zero.
515 `(or (not (fp-zero-p ,res))
516 (cond ((and (consp ,x) (fp-zero-p ,xb))
518 ((and (consp ,y) (fp-zero-p ,yb))
521 ;; Dividing a greater-than-zero with
522 ;; greater than one can round to zero.
523 `(or (not (fp-zero-p ,res))
524 (cond ((and (consp ,x) (fp-zero-p ,xb))
526 ((and (consp ,y) (fp-zero-p ,yb))
529 ;; Adding or subtracting greater-than-zero
530 ;; can end up with identity.
531 `(and (not (fp-zero-p ,xb))
532 (not (fp-zero-p ,yb))))))))))))
534 (defun coercion-loses-precision-p (val type)
537 (double-float (subtypep type 'single-float))
538 (rational (subtypep type 'float))
539 (t (bug "Unexpected arguments to bounds coercion: ~S ~S" val type))))
541 (defun coerce-for-bound (val type)
543 (let ((xbound (coerce-for-bound (car val) type)))
544 (if (coercion-loses-precision-p (car val) type)
548 ((subtypep type 'double-float)
549 (if (<= most-negative-double-float val most-positive-double-float)
551 ((or (subtypep type 'single-float) (subtypep type 'float))
552 ;; coerce to float returns a single-float
553 (if (<= most-negative-single-float val most-positive-single-float)
555 (t (coerce val type)))))
557 (defun coerce-and-truncate-floats (val type)
560 (let ((xbound (coerce-for-bound (car val) type)))
561 (if (coercion-loses-precision-p (car val) type)
565 ((subtypep type 'double-float)
566 (if (<= most-negative-double-float val most-positive-double-float)
568 (if (< val most-negative-double-float)
569 most-negative-double-float most-positive-double-float)))
570 ((or (subtypep type 'single-float) (subtypep type 'float))
571 ;; coerce to float returns a single-float
572 (if (<= most-negative-single-float val most-positive-single-float)
574 (if (< val most-negative-single-float)
575 most-negative-single-float most-positive-single-float)))
576 (t (coerce val type))))))
578 ;;; Convert a numeric-type object to an interval object.
579 (defun numeric-type->interval (x)
580 (declare (type numeric-type x))
581 (make-interval :low (numeric-type-low x)
582 :high (numeric-type-high x)))
584 (defun type-approximate-interval (type)
585 (declare (type ctype type))
586 (let ((types (prepare-arg-for-derive-type type))
589 (let ((type (if (member-type-p type)
590 (convert-member-type type)
592 (unless (numeric-type-p type)
593 (return-from type-approximate-interval nil))
594 (let ((interval (numeric-type->interval type)))
597 (interval-approximate-union result interval)
601 (defun copy-interval-limit (limit)
606 (defun copy-interval (x)
607 (declare (type interval x))
608 (make-interval :low (copy-interval-limit (interval-low x))
609 :high (copy-interval-limit (interval-high x))))
611 ;;; Given a point P contained in the interval X, split X into two
612 ;;; intervals at the point P. If CLOSE-LOWER is T, then the left
613 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
614 ;;; contains P. You can specify both to be T or NIL.
615 (defun interval-split (p x &optional close-lower close-upper)
616 (declare (type number p)
618 (list (make-interval :low (copy-interval-limit (interval-low x))
619 :high (if close-lower p (list p)))
620 (make-interval :low (if close-upper (list p) p)
621 :high (copy-interval-limit (interval-high x)))))
623 ;;; Return the closure of the interval. That is, convert open bounds
624 ;;; to closed bounds.
625 (defun interval-closure (x)
626 (declare (type interval x))
627 (make-interval :low (type-bound-number (interval-low x))
628 :high (type-bound-number (interval-high x))))
630 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
631 ;;; '-. Otherwise return NIL.
632 (defun interval-range-info (x &optional (point 0))
633 (declare (type interval x))
634 (let ((lo (interval-low x))
635 (hi (interval-high x)))
636 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
638 ((and hi (signed-zero->= point (type-bound-number hi)))
643 ;;; Test to see whether the interval X is bounded. HOW determines the
644 ;;; test, and should be either ABOVE, BELOW, or BOTH.
645 (defun interval-bounded-p (x how)
646 (declare (type interval x))
653 (and (interval-low x) (interval-high x)))))
655 ;;; See whether the interval X contains the number P, taking into
656 ;;; account that the interval might not be closed.
657 (defun interval-contains-p (p x)
658 (declare (type number p)
660 ;; Does the interval X contain the number P? This would be a lot
661 ;; easier if all intervals were closed!
662 (let ((lo (interval-low x))
663 (hi (interval-high x)))
665 ;; The interval is bounded
666 (if (and (signed-zero-<= (type-bound-number lo) p)
667 (signed-zero-<= p (type-bound-number hi)))
668 ;; P is definitely in the closure of the interval.
669 ;; We just need to check the end points now.
670 (cond ((signed-zero-= p (type-bound-number lo))
672 ((signed-zero-= p (type-bound-number hi))
677 ;; Interval with upper bound
678 (if (signed-zero-< p (type-bound-number hi))
680 (and (numberp hi) (signed-zero-= p hi))))
682 ;; Interval with lower bound
683 (if (signed-zero-> p (type-bound-number lo))
685 (and (numberp lo) (signed-zero-= p lo))))
687 ;; Interval with no bounds
690 ;;; Determine whether two intervals X and Y intersect. Return T if so.
691 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
692 ;;; were closed. Otherwise the intervals are treated as they are.
694 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
695 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
696 ;;; is T, then they do intersect because we use the closure of X = [0,
697 ;;; 1] and Y = [1, 2] to determine intersection.
698 (defun interval-intersect-p (x y &optional closed-intervals-p)
699 (declare (type interval x y))
700 (and (interval-intersection/difference (if closed-intervals-p
703 (if closed-intervals-p
708 ;;; Are the two intervals adjacent? That is, is there a number
709 ;;; between the two intervals that is not an element of either
710 ;;; interval? If so, they are not adjacent. For example [0, 1) and
711 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
712 ;;; between both intervals.
713 (defun interval-adjacent-p (x y)
714 (declare (type interval x y))
715 (flet ((adjacent (lo hi)
716 ;; Check to see whether lo and hi are adjacent. If either is
717 ;; nil, they can't be adjacent.
718 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
719 ;; The bounds are equal. They are adjacent if one of
720 ;; them is closed (a number). If both are open (consp),
721 ;; then there is a number that lies between them.
722 (or (numberp lo) (numberp hi)))))
723 (or (adjacent (interval-low y) (interval-high x))
724 (adjacent (interval-low x) (interval-high y)))))
726 ;;; Compute the intersection and difference between two intervals.
727 ;;; Two values are returned: the intersection and the difference.
729 ;;; Let the two intervals be X and Y, and let I and D be the two
730 ;;; values returned by this function. Then I = X intersect Y. If I
731 ;;; is NIL (the empty set), then D is X union Y, represented as the
732 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
733 ;;; - I, which is a list of two intervals.
735 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
736 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
737 (defun interval-intersection/difference (x y)
738 (declare (type interval x y))
739 (let ((x-lo (interval-low x))
740 (x-hi (interval-high x))
741 (y-lo (interval-low y))
742 (y-hi (interval-high y)))
745 ;; If p is an open bound, make it closed. If p is a closed
746 ;; bound, make it open.
750 (test-number (p int bound)
751 ;; Test whether P is in the interval.
752 (let ((pn (type-bound-number p)))
753 (when (interval-contains-p pn (interval-closure int))
754 ;; Check for endpoints.
755 (let* ((lo (interval-low int))
756 (hi (interval-high int))
757 (lon (type-bound-number lo))
758 (hin (type-bound-number hi)))
760 ;; Interval may be a point.
761 ((and lon hin (= lon hin pn))
762 (and (numberp p) (numberp lo) (numberp hi)))
763 ;; Point matches the low end.
764 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
765 ;; (P [P,?} => TRUE P) [P,?} => FALSE
766 ;; (P (P,?} => TRUE P) (P,?} => FALSE
767 ((and lon (= pn lon))
768 (or (and (numberp p) (numberp lo))
769 (and (consp p) (eq :low bound))))
770 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
771 ;; P) {?,P] => TRUE (P {?,P] => FALSE
772 ;; P) {?,P) => TRUE (P {?,P) => FALSE
773 ((and hin (= pn hin))
774 (or (and (numberp p) (numberp hi))
775 (and (consp p) (eq :high bound))))
776 ;; Not an endpoint, all is well.
779 (test-lower-bound (p int)
780 ;; P is a lower bound of an interval.
782 (test-number p int :low)
783 (not (interval-bounded-p int 'below))))
784 (test-upper-bound (p int)
785 ;; P is an upper bound of an interval.
787 (test-number p int :high)
788 (not (interval-bounded-p int 'above)))))
789 (let ((x-lo-in-y (test-lower-bound x-lo y))
790 (x-hi-in-y (test-upper-bound x-hi y))
791 (y-lo-in-x (test-lower-bound y-lo x))
792 (y-hi-in-x (test-upper-bound y-hi x)))
793 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
794 ;; Intervals intersect. Let's compute the intersection
795 ;; and the difference.
796 (multiple-value-bind (lo left-lo left-hi)
797 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
798 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
799 (multiple-value-bind (hi right-lo right-hi)
801 (values x-hi (opposite-bound x-hi) y-hi))
803 (values y-hi (opposite-bound y-hi) x-hi)))
804 (values (make-interval :low lo :high hi)
805 (list (make-interval :low left-lo
807 (make-interval :low right-lo
810 (values nil (list x y))))))))
812 ;;; If intervals X and Y intersect, return a new interval that is the
813 ;;; union of the two. If they do not intersect, return NIL.
814 (defun interval-merge-pair (x y)
815 (declare (type interval x y))
816 ;; If x and y intersect or are adjacent, create the union.
817 ;; Otherwise return nil
818 (when (or (interval-intersect-p x y)
819 (interval-adjacent-p x y))
820 (flet ((select-bound (x1 x2 min-op max-op)
821 (let ((x1-val (type-bound-number x1))
822 (x2-val (type-bound-number x2)))
824 ;; Both bounds are finite. Select the right one.
825 (cond ((funcall min-op x1-val x2-val)
826 ;; x1 is definitely better.
828 ((funcall max-op x1-val x2-val)
829 ;; x2 is definitely better.
832 ;; Bounds are equal. Select either
833 ;; value and make it open only if
835 (set-bound x1-val (and (consp x1) (consp x2))))))
837 ;; At least one bound is not finite. The
838 ;; non-finite bound always wins.
840 (let* ((x-lo (copy-interval-limit (interval-low x)))
841 (x-hi (copy-interval-limit (interval-high x)))
842 (y-lo (copy-interval-limit (interval-low y)))
843 (y-hi (copy-interval-limit (interval-high y))))
844 (make-interval :low (select-bound x-lo y-lo #'< #'>)
845 :high (select-bound x-hi y-hi #'> #'<))))))
847 ;;; return the minimal interval, containing X and Y
848 (defun interval-approximate-union (x y)
849 (cond ((interval-merge-pair x y))
851 (make-interval :low (copy-interval-limit (interval-low x))
852 :high (copy-interval-limit (interval-high y))))
854 (make-interval :low (copy-interval-limit (interval-low y))
855 :high (copy-interval-limit (interval-high x))))))
857 ;;; basic arithmetic operations on intervals. We probably should do
858 ;;; true interval arithmetic here, but it's complicated because we
859 ;;; have float and integer types and bounds can be open or closed.
861 ;;; the negative of an interval
862 (defun interval-neg (x)
863 (declare (type interval x))
864 (make-interval :low (bound-func #'- (interval-high x) t)
865 :high (bound-func #'- (interval-low x) t)))
867 ;;; Add two intervals.
868 (defun interval-add (x y)
869 (declare (type interval x y))
870 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
871 :high (bound-binop + (interval-high x) (interval-high y))))
873 ;;; Subtract two intervals.
874 (defun interval-sub (x y)
875 (declare (type interval x y))
876 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
877 :high (bound-binop - (interval-high x) (interval-low y))))
879 ;;; Multiply two intervals.
880 (defun interval-mul (x y)
881 (declare (type interval x y))
882 (flet ((bound-mul (x y)
883 (cond ((or (null x) (null y))
884 ;; Multiply by infinity is infinity
886 ((or (and (numberp x) (zerop x))
887 (and (numberp y) (zerop y)))
888 ;; Multiply by closed zero is special. The result
889 ;; is always a closed bound. But don't replace this
890 ;; with zero; we want the multiplication to produce
891 ;; the correct signed zero, if needed. Use SIGNUM
892 ;; to avoid trying to multiply huge bignums with 0.0.
893 (* (signum (type-bound-number x)) (signum (type-bound-number y))))
894 ((or (and (floatp x) (float-infinity-p x))
895 (and (floatp y) (float-infinity-p y)))
896 ;; Infinity times anything is infinity
899 ;; General multiply. The result is open if either is open.
900 (bound-binop * x y)))))
901 (let ((x-range (interval-range-info x))
902 (y-range (interval-range-info y)))
903 (cond ((null x-range)
904 ;; Split x into two and multiply each separately
905 (destructuring-bind (x- x+) (interval-split 0 x t t)
906 (interval-merge-pair (interval-mul x- y)
907 (interval-mul x+ y))))
909 ;; Split y into two and multiply each separately
910 (destructuring-bind (y- y+) (interval-split 0 y t t)
911 (interval-merge-pair (interval-mul x y-)
912 (interval-mul x y+))))
914 (interval-neg (interval-mul (interval-neg x) y)))
916 (interval-neg (interval-mul x (interval-neg y))))
917 ((and (eq x-range '+) (eq y-range '+))
918 ;; If we are here, X and Y are both positive.
920 :low (bound-mul (interval-low x) (interval-low y))
921 :high (bound-mul (interval-high x) (interval-high y))))
923 (bug "excluded case in INTERVAL-MUL"))))))
925 ;;; Divide two intervals.
926 (defun interval-div (top bot)
927 (declare (type interval top bot))
928 (flet ((bound-div (x y y-low-p)
931 ;; Divide by infinity means result is 0. However,
932 ;; we need to watch out for the sign of the result,
933 ;; to correctly handle signed zeros. We also need
934 ;; to watch out for positive or negative infinity.
935 (if (floatp (type-bound-number x))
937 (- (float-sign (type-bound-number x) 0.0))
938 (float-sign (type-bound-number x) 0.0))
940 ((zerop (type-bound-number y))
941 ;; Divide by zero means result is infinity
944 (bound-binop / x y)))))
945 (let ((top-range (interval-range-info top))
946 (bot-range (interval-range-info bot)))
947 (cond ((null bot-range)
948 ;; The denominator contains zero, so anything goes!
949 (make-interval :low nil :high nil))
951 ;; Denominator is negative so flip the sign, compute the
952 ;; result, and flip it back.
953 (interval-neg (interval-div top (interval-neg bot))))
955 ;; Split top into two positive and negative parts, and
956 ;; divide each separately
957 (destructuring-bind (top- top+) (interval-split 0 top t t)
958 (interval-merge-pair (interval-div top- bot)
959 (interval-div top+ bot))))
961 ;; Top is negative so flip the sign, divide, and flip the
962 ;; sign of the result.
963 (interval-neg (interval-div (interval-neg top) bot)))
964 ((and (eq top-range '+) (eq bot-range '+))
967 :low (bound-div (interval-low top) (interval-high bot) t)
968 :high (bound-div (interval-high top) (interval-low bot) nil)))
970 (bug "excluded case in INTERVAL-DIV"))))))
972 ;;; Apply the function F to the interval X. If X = [a, b], then the
973 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
974 ;;; result makes sense. It will if F is monotonic increasing (or, if
975 ;;; the interval is closed, non-decreasing).
977 ;;; (Actually most uses of INTERVAL-FUNC are coercions to float types,
978 ;;; which are not monotonic increasing, so default to calling
979 ;;; BOUND-FUNC with a non-strict argument).
980 (defun interval-func (f x &optional increasing)
981 (declare (type function f)
983 (let ((lo (bound-func f (interval-low x) increasing))
984 (hi (bound-func f (interval-high x) increasing)))
985 (make-interval :low lo :high hi)))
987 ;;; Return T if X < Y. That is every number in the interval X is
988 ;;; always less than any number in the interval Y.
989 (defun interval-< (x y)
990 (declare (type interval x y))
991 ;; X < Y only if X is bounded above, Y is bounded below, and they
993 (when (and (interval-bounded-p x 'above)
994 (interval-bounded-p y 'below))
995 ;; Intervals are bounded in the appropriate way. Make sure they
997 (let ((left (interval-high x))
998 (right (interval-low y)))
999 (cond ((> (type-bound-number left)
1000 (type-bound-number right))
1001 ;; The intervals definitely overlap, so result is NIL.
1003 ((< (type-bound-number left)
1004 (type-bound-number right))
1005 ;; The intervals definitely don't touch, so result is T.
1008 ;; Limits are equal. Check for open or closed bounds.
1009 ;; Don't overlap if one or the other are open.
1010 (or (consp left) (consp right)))))))
1012 ;;; Return T if X >= Y. That is, every number in the interval X is
1013 ;;; always greater than any number in the interval Y.
1014 (defun interval->= (x y)
1015 (declare (type interval x y))
1016 ;; X >= Y if lower bound of X >= upper bound of Y
1017 (when (and (interval-bounded-p x 'below)
1018 (interval-bounded-p y 'above))
1019 (>= (type-bound-number (interval-low x))
1020 (type-bound-number (interval-high y)))))
1022 ;;; Return T if X = Y.
1023 (defun interval-= (x y)
1024 (declare (type interval x y))
1025 (and (interval-bounded-p x 'both)
1026 (interval-bounded-p y 'both)
1030 ;; Open intervals cannot be =
1031 (return-from interval-= nil))))
1032 ;; Both intervals refer to the same point
1033 (= (bound (interval-high x)) (bound (interval-low x))
1034 (bound (interval-high y)) (bound (interval-low y))))))
1036 ;;; Return T if X /= Y
1037 (defun interval-/= (x y)
1038 (not (interval-intersect-p x y)))
1040 ;;; Return an interval that is the absolute value of X. Thus, if
1041 ;;; X = [-1 10], the result is [0, 10].
1042 (defun interval-abs (x)
1043 (declare (type interval x))
1044 (case (interval-range-info x)
1050 (destructuring-bind (x- x+) (interval-split 0 x t t)
1051 (interval-merge-pair (interval-neg x-) x+)))))
1053 ;;; Compute the square of an interval.
1054 (defun interval-sqr (x)
1055 (declare (type interval x))
1056 (interval-func (lambda (x) (* x x)) (interval-abs x)))
1058 ;;;; numeric DERIVE-TYPE methods
1060 ;;; a utility for defining derive-type methods of integer operations. If
1061 ;;; the types of both X and Y are integer types, then we compute a new
1062 ;;; integer type with bounds determined by FUN when applied to X and Y.
1063 ;;; Otherwise, we use NUMERIC-CONTAGION.
1064 (defun derive-integer-type-aux (x y fun)
1065 (declare (type function fun))
1066 (if (and (numeric-type-p x) (numeric-type-p y)
1067 (eq (numeric-type-class x) 'integer)
1068 (eq (numeric-type-class y) 'integer)
1069 (eq (numeric-type-complexp x) :real)
1070 (eq (numeric-type-complexp y) :real))
1071 (multiple-value-bind (low high) (funcall fun x y)
1072 (make-numeric-type :class 'integer
1076 (numeric-contagion x y)))
1078 (defun derive-integer-type (x y fun)
1079 (declare (type lvar x y) (type function fun))
1080 (let ((x (lvar-type x))
1082 (derive-integer-type-aux x y fun)))
1084 ;;; simple utility to flatten a list
1085 (defun flatten-list (x)
1086 (labels ((flatten-and-append (tree list)
1087 (cond ((null tree) list)
1088 ((atom tree) (cons tree list))
1089 (t (flatten-and-append
1090 (car tree) (flatten-and-append (cdr tree) list))))))
1091 (flatten-and-append x nil)))
1093 ;;; Take some type of lvar and massage it so that we get a list of the
1094 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
1096 (defun prepare-arg-for-derive-type (arg)
1097 (flet ((listify (arg)
1102 (union-type-types arg))
1105 (unless (eq arg *empty-type*)
1106 ;; Make sure all args are some type of numeric-type. For member
1107 ;; types, convert the list of members into a union of equivalent
1108 ;; single-element member-type's.
1109 (let ((new-args nil))
1110 (dolist (arg (listify arg))
1111 (if (member-type-p arg)
1112 ;; Run down the list of members and convert to a list of
1114 (mapc-member-type-members
1116 (push (if (numberp member)
1117 (make-member-type :members (list member))
1121 (push arg new-args)))
1122 (unless (member *empty-type* new-args)
1125 ;;; Convert from the standard type convention for which -0.0 and 0.0
1126 ;;; are equal to an intermediate convention for which they are
1127 ;;; considered different which is more natural for some of the
1129 (defun convert-numeric-type (type)
1130 (declare (type numeric-type type))
1131 ;;; Only convert real float interval delimiters types.
1132 (if (eq (numeric-type-complexp type) :real)
1133 (let* ((lo (numeric-type-low type))
1134 (lo-val (type-bound-number lo))
1135 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
1136 (hi (numeric-type-high type))
1137 (hi-val (type-bound-number hi))
1138 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
1139 (if (or lo-float-zero-p hi-float-zero-p)
1141 :class (numeric-type-class type)
1142 :format (numeric-type-format type)
1144 :low (if lo-float-zero-p
1146 (list (float 0.0 lo-val))
1147 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
1149 :high (if hi-float-zero-p
1151 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
1158 ;;; Convert back from the intermediate convention for which -0.0 and
1159 ;;; 0.0 are considered different to the standard type convention for
1160 ;;; which and equal.
1161 (defun convert-back-numeric-type (type)
1162 (declare (type numeric-type type))
1163 ;;; Only convert real float interval delimiters types.
1164 (if (eq (numeric-type-complexp type) :real)
1165 (let* ((lo (numeric-type-low type))
1166 (lo-val (type-bound-number lo))
1168 (and lo (floatp lo-val) (= lo-val 0.0)
1169 (float-sign lo-val)))
1170 (hi (numeric-type-high type))
1171 (hi-val (type-bound-number hi))
1173 (and hi (floatp hi-val) (= hi-val 0.0)
1174 (float-sign hi-val))))
1176 ;; (float +0.0 +0.0) => (member 0.0)
1177 ;; (float -0.0 -0.0) => (member -0.0)
1178 ((and lo-float-zero-p hi-float-zero-p)
1179 ;; shouldn't have exclusive bounds here..
1180 (aver (and (not (consp lo)) (not (consp hi))))
1181 (if (= lo-float-zero-p hi-float-zero-p)
1182 ;; (float +0.0 +0.0) => (member 0.0)
1183 ;; (float -0.0 -0.0) => (member -0.0)
1184 (specifier-type `(member ,lo-val))
1185 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1186 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1187 (make-numeric-type :class (numeric-type-class type)
1188 :format (numeric-type-format type)
1194 ;; (float -0.0 x) => (float 0.0 x)
1195 ((and (not (consp lo)) (minusp lo-float-zero-p))
1196 (make-numeric-type :class (numeric-type-class type)
1197 :format (numeric-type-format type)
1199 :low (float 0.0 lo-val)
1201 ;; (float (+0.0) x) => (float (0.0) x)
1202 ((and (consp lo) (plusp lo-float-zero-p))
1203 (make-numeric-type :class (numeric-type-class type)
1204 :format (numeric-type-format type)
1206 :low (list (float 0.0 lo-val))
1209 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1210 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1211 (list (make-member-type :members (list (float 0.0 lo-val)))
1212 (make-numeric-type :class (numeric-type-class type)
1213 :format (numeric-type-format type)
1215 :low (list (float 0.0 lo-val))
1219 ;; (float x +0.0) => (float x 0.0)
1220 ((and (not (consp hi)) (plusp hi-float-zero-p))
1221 (make-numeric-type :class (numeric-type-class type)
1222 :format (numeric-type-format type)
1225 :high (float 0.0 hi-val)))
1226 ;; (float x (-0.0)) => (float x (0.0))
1227 ((and (consp hi) (minusp hi-float-zero-p))
1228 (make-numeric-type :class (numeric-type-class type)
1229 :format (numeric-type-format type)
1232 :high (list (float 0.0 hi-val))))
1234 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1235 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1236 (list (make-member-type :members (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val)))
1237 (make-numeric-type :class (numeric-type-class type)
1238 :format (numeric-type-format type)
1241 :high (list (float 0.0 hi-val)))))))
1247 ;;; Convert back a possible list of numeric types.
1248 (defun convert-back-numeric-type-list (type-list)
1251 (let ((results '()))
1252 (dolist (type type-list)
1253 (if (numeric-type-p type)
1254 (let ((result (convert-back-numeric-type type)))
1256 (setf results (append results result))
1257 (push result results)))
1258 (push type results)))
1261 (convert-back-numeric-type type-list))
1263 (convert-back-numeric-type-list (union-type-types type-list)))
1267 ;;; Take a list of types and return a canonical type specifier,
1268 ;;; combining any MEMBER types together. If both positive and negative
1269 ;;; MEMBER types are present they are converted to a float type.
1270 ;;; XXX This would be far simpler if the type-union methods could handle
1271 ;;; member/number unions.
1273 ;;; If we're about to generate an overly complex union of numeric types, start
1274 ;;; collapse the ranges together.
1276 ;;; FIXME: The MEMBER canonicalization parts of MAKE-DERIVED-UNION-TYPE and
1277 ;;; entire CONVERT-MEMBER-TYPE probably belong in the kernel's type logic,
1278 ;;; invoked always, instead of in the compiler, invoked only during some type
1280 (defvar *derived-numeric-union-complexity-limit* 6)
1282 (defun make-derived-union-type (type-list)
1283 (let ((xset (alloc-xset))
1286 (numeric-type *empty-type*))
1287 (dolist (type type-list)
1288 (cond ((member-type-p type)
1289 (mapc-member-type-members
1291 (if (fp-zero-p member)
1292 (unless (member member fp-zeroes)
1293 (pushnew member fp-zeroes))
1294 (add-to-xset member xset)))
1296 ((numeric-type-p type)
1297 (let ((*approximate-numeric-unions*
1298 (when (and (union-type-p numeric-type)
1299 (nthcdr *derived-numeric-union-complexity-limit*
1300 (union-type-types numeric-type)))
1302 (setf numeric-type (type-union type numeric-type))))
1304 (push type misc-types))))
1305 (if (and (xset-empty-p xset) (not fp-zeroes))
1306 (apply #'type-union numeric-type misc-types)
1307 (apply #'type-union (make-member-type :xset xset :fp-zeroes fp-zeroes)
1308 numeric-type misc-types))))
1310 ;;; Convert a member type with a single member to a numeric type.
1311 (defun convert-member-type (arg)
1312 (let* ((members (member-type-members arg))
1313 (member (first members))
1314 (member-type (type-of member)))
1315 (aver (not (rest members)))
1316 (specifier-type (cond ((typep member 'integer)
1317 `(integer ,member ,member))
1318 ((memq member-type '(short-float single-float
1319 double-float long-float))
1320 `(,member-type ,member ,member))
1324 ;;; This is used in defoptimizers for computing the resulting type of
1327 ;;; Given the lvar ARG, derive the resulting type using the
1328 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1329 ;;; "atomic" lvar type like numeric-type or member-type (containing
1330 ;;; just one element). It should return the resulting type, which can
1331 ;;; be a list of types.
1333 ;;; For the case of member types, if a MEMBER-FUN is given it is
1334 ;;; called to compute the result otherwise the member type is first
1335 ;;; converted to a numeric type and the DERIVE-FUN is called.
1336 (defun one-arg-derive-type (arg derive-fun member-fun
1337 &optional (convert-type t))
1338 (declare (type function derive-fun)
1339 (type (or null function) member-fun))
1340 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1346 (with-float-traps-masked
1347 (:underflow :overflow :divide-by-zero)
1349 `(eql ,(funcall member-fun
1350 (first (member-type-members x))))))
1351 ;; Otherwise convert to a numeric type.
1352 (let ((result-type-list
1353 (funcall derive-fun (convert-member-type x))))
1355 (convert-back-numeric-type-list result-type-list)
1356 result-type-list))))
1359 (convert-back-numeric-type-list
1360 (funcall derive-fun (convert-numeric-type x)))
1361 (funcall derive-fun x)))
1363 *universal-type*))))
1364 ;; Run down the list of args and derive the type of each one,
1365 ;; saving all of the results in a list.
1366 (let ((results nil))
1367 (dolist (arg arg-list)
1368 (let ((result (deriver arg)))
1370 (setf results (append results result))
1371 (push result results))))
1373 (make-derived-union-type results)
1374 (first results)))))))
1376 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1377 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1378 ;;; original args and a third which is T to indicate if the two args
1379 ;;; really represent the same lvar. This is useful for deriving the
1380 ;;; type of things like (* x x), which should always be positive. If
1381 ;;; we didn't do this, we wouldn't be able to tell.
1382 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1383 &optional (convert-type t))
1384 (declare (type function derive-fun fun))
1385 (flet ((deriver (x y same-arg)
1386 (cond ((and (member-type-p x) (member-type-p y))
1387 (let* ((x (first (member-type-members x)))
1388 (y (first (member-type-members y)))
1389 (result (ignore-errors
1390 (with-float-traps-masked
1391 (:underflow :overflow :divide-by-zero
1393 (funcall fun x y)))))
1394 (cond ((null result) *empty-type*)
1395 ((and (floatp result) (float-nan-p result))
1396 (make-numeric-type :class 'float
1397 :format (type-of result)
1400 (specifier-type `(eql ,result))))))
1401 ((and (member-type-p x) (numeric-type-p y))
1402 (let* ((x (convert-member-type x))
1403 (y (if convert-type (convert-numeric-type y) y))
1404 (result (funcall derive-fun x y same-arg)))
1406 (convert-back-numeric-type-list result)
1408 ((and (numeric-type-p x) (member-type-p y))
1409 (let* ((x (if convert-type (convert-numeric-type x) x))
1410 (y (convert-member-type y))
1411 (result (funcall derive-fun x y same-arg)))
1413 (convert-back-numeric-type-list result)
1415 ((and (numeric-type-p x) (numeric-type-p y))
1416 (let* ((x (if convert-type (convert-numeric-type x) x))
1417 (y (if convert-type (convert-numeric-type y) y))
1418 (result (funcall derive-fun x y same-arg)))
1420 (convert-back-numeric-type-list result)
1423 *universal-type*))))
1424 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1425 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1426 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1428 (let ((results nil))
1430 ;; Since the args are the same LVARs, just run down the
1433 (let ((result (deriver x x same-arg)))
1435 (setf results (append results result))
1436 (push result results))))
1437 ;; Try all pairwise combinations.
1440 (let ((result (or (deriver x y same-arg)
1441 (numeric-contagion x y))))
1443 (setf results (append results result))
1444 (push result results))))))
1446 (make-derived-union-type results)
1447 (first results)))))))
1449 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1451 (defoptimizer (+ derive-type) ((x y))
1452 (derive-integer-type
1459 (values (frob (numeric-type-low x) (numeric-type-low y))
1460 (frob (numeric-type-high x) (numeric-type-high y)))))))
1462 (defoptimizer (- derive-type) ((x y))
1463 (derive-integer-type
1470 (values (frob (numeric-type-low x) (numeric-type-high y))
1471 (frob (numeric-type-high x) (numeric-type-low y)))))))
1473 (defoptimizer (* derive-type) ((x y))
1474 (derive-integer-type
1477 (let ((x-low (numeric-type-low x))
1478 (x-high (numeric-type-high x))
1479 (y-low (numeric-type-low y))
1480 (y-high (numeric-type-high y)))
1481 (cond ((not (and x-low y-low))
1483 ((or (minusp x-low) (minusp y-low))
1484 (if (and x-high y-high)
1485 (let ((max (* (max (abs x-low) (abs x-high))
1486 (max (abs y-low) (abs y-high)))))
1487 (values (- max) max))
1490 (values (* x-low y-low)
1491 (if (and x-high y-high)
1495 (defoptimizer (/ derive-type) ((x y))
1496 (numeric-contagion (lvar-type x) (lvar-type y)))
1500 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1502 (defun +-derive-type-aux (x y same-arg)
1503 (if (and (numeric-type-real-p x)
1504 (numeric-type-real-p y))
1507 (let ((x-int (numeric-type->interval x)))
1508 (interval-add x-int x-int))
1509 (interval-add (numeric-type->interval x)
1510 (numeric-type->interval y))))
1511 (result-type (numeric-contagion x y)))
1512 ;; If the result type is a float, we need to be sure to coerce
1513 ;; the bounds into the correct type.
1514 (when (eq (numeric-type-class result-type) 'float)
1515 (setf result (interval-func
1517 (coerce-for-bound x (or (numeric-type-format result-type)
1521 :class (if (and (eq (numeric-type-class x) 'integer)
1522 (eq (numeric-type-class y) 'integer))
1523 ;; The sum of integers is always an integer.
1525 (numeric-type-class result-type))
1526 :format (numeric-type-format result-type)
1527 :low (interval-low result)
1528 :high (interval-high result)))
1529 ;; general contagion
1530 (numeric-contagion x y)))
1532 (defoptimizer (+ derive-type) ((x y))
1533 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1535 (defun --derive-type-aux (x y same-arg)
1536 (if (and (numeric-type-real-p x)
1537 (numeric-type-real-p y))
1539 ;; (- X X) is always 0.
1541 (make-interval :low 0 :high 0)
1542 (interval-sub (numeric-type->interval x)
1543 (numeric-type->interval y))))
1544 (result-type (numeric-contagion x y)))
1545 ;; If the result type is a float, we need to be sure to coerce
1546 ;; the bounds into the correct type.
1547 (when (eq (numeric-type-class result-type) 'float)
1548 (setf result (interval-func
1550 (coerce-for-bound x (or (numeric-type-format result-type)
1554 :class (if (and (eq (numeric-type-class x) 'integer)
1555 (eq (numeric-type-class y) 'integer))
1556 ;; The difference of integers is always an integer.
1558 (numeric-type-class result-type))
1559 :format (numeric-type-format result-type)
1560 :low (interval-low result)
1561 :high (interval-high result)))
1562 ;; general contagion
1563 (numeric-contagion x y)))
1565 (defoptimizer (- derive-type) ((x y))
1566 (two-arg-derive-type x y #'--derive-type-aux #'-))
1568 (defun *-derive-type-aux (x y same-arg)
1569 (if (and (numeric-type-real-p x)
1570 (numeric-type-real-p y))
1572 ;; (* X X) is always positive, so take care to do it right.
1574 (interval-sqr (numeric-type->interval x))
1575 (interval-mul (numeric-type->interval x)
1576 (numeric-type->interval y))))
1577 (result-type (numeric-contagion x y)))
1578 ;; If the result type is a float, we need to be sure to coerce
1579 ;; the bounds into the correct type.
1580 (when (eq (numeric-type-class result-type) 'float)
1581 (setf result (interval-func
1583 (coerce-for-bound x (or (numeric-type-format result-type)
1587 :class (if (and (eq (numeric-type-class x) 'integer)
1588 (eq (numeric-type-class y) 'integer))
1589 ;; The product of integers is always an integer.
1591 (numeric-type-class result-type))
1592 :format (numeric-type-format result-type)
1593 :low (interval-low result)
1594 :high (interval-high result)))
1595 (numeric-contagion x y)))
1597 (defoptimizer (* derive-type) ((x y))
1598 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1600 (defun /-derive-type-aux (x y same-arg)
1601 (if (and (numeric-type-real-p x)
1602 (numeric-type-real-p y))
1604 ;; (/ X X) is always 1, except if X can contain 0. In
1605 ;; that case, we shouldn't optimize the division away
1606 ;; because we want 0/0 to signal an error.
1608 (not (interval-contains-p
1609 0 (interval-closure (numeric-type->interval y)))))
1610 (make-interval :low 1 :high 1)
1611 (interval-div (numeric-type->interval x)
1612 (numeric-type->interval y))))
1613 (result-type (numeric-contagion x y)))
1614 ;; If the result type is a float, we need to be sure to coerce
1615 ;; the bounds into the correct type.
1616 (when (eq (numeric-type-class result-type) 'float)
1617 (setf result (interval-func
1619 (coerce-for-bound x (or (numeric-type-format result-type)
1622 (make-numeric-type :class (numeric-type-class result-type)
1623 :format (numeric-type-format result-type)
1624 :low (interval-low result)
1625 :high (interval-high result)))
1626 (numeric-contagion x y)))
1628 (defoptimizer (/ derive-type) ((x y))
1629 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1633 (defun ash-derive-type-aux (n-type shift same-arg)
1634 (declare (ignore same-arg))
1635 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1636 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1637 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1638 ;; two bignums yielding zero) and it's hard to avoid that
1639 ;; calculation in here.
1640 #+(and cmu sb-xc-host)
1641 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1642 (typep (numeric-type-high n-type) 'bignum))
1643 (or (typep (numeric-type-low shift) 'bignum)
1644 (typep (numeric-type-high shift) 'bignum)))
1645 (return-from ash-derive-type-aux *universal-type*))
1646 (flet ((ash-outer (n s)
1647 (when (and (fixnump s)
1649 (> s sb!xc:most-negative-fixnum))
1651 ;; KLUDGE: The bare 64's here should be related to
1652 ;; symbolic machine word size values somehow.
1655 (if (and (fixnump s)
1656 (> s sb!xc:most-negative-fixnum))
1658 (if (minusp n) -1 0))))
1659 (or (and (csubtypep n-type (specifier-type 'integer))
1660 (csubtypep shift (specifier-type 'integer))
1661 (let ((n-low (numeric-type-low n-type))
1662 (n-high (numeric-type-high n-type))
1663 (s-low (numeric-type-low shift))
1664 (s-high (numeric-type-high shift)))
1665 (make-numeric-type :class 'integer :complexp :real
1668 (ash-outer n-low s-high)
1669 (ash-inner n-low s-low)))
1672 (ash-inner n-high s-low)
1673 (ash-outer n-high s-high))))))
1676 (defoptimizer (ash derive-type) ((n shift))
1677 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1679 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1680 (macrolet ((frob (fun)
1681 `#'(lambda (type type2)
1682 (declare (ignore type2))
1683 (let ((lo (numeric-type-low type))
1684 (hi (numeric-type-high type)))
1685 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1687 (defoptimizer (%negate derive-type) ((num))
1688 (derive-integer-type num num (frob -))))
1690 (defun lognot-derive-type-aux (int)
1691 (derive-integer-type-aux int int
1692 (lambda (type type2)
1693 (declare (ignore type2))
1694 (let ((lo (numeric-type-low type))
1695 (hi (numeric-type-high type)))
1696 (values (if hi (lognot hi) nil)
1697 (if lo (lognot lo) nil)
1698 (numeric-type-class type)
1699 (numeric-type-format type))))))
1701 (defoptimizer (lognot derive-type) ((int))
1702 (lognot-derive-type-aux (lvar-type int)))
1704 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1705 (defoptimizer (%negate derive-type) ((num))
1706 (flet ((negate-bound (b)
1708 (set-bound (- (type-bound-number b))
1710 (one-arg-derive-type num
1712 (modified-numeric-type
1714 :low (negate-bound (numeric-type-high type))
1715 :high (negate-bound (numeric-type-low type))))
1718 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1719 (defoptimizer (abs derive-type) ((num))
1720 (let ((type (lvar-type num)))
1721 (if (and (numeric-type-p type)
1722 (eq (numeric-type-class type) 'integer)
1723 (eq (numeric-type-complexp type) :real))
1724 (let ((lo (numeric-type-low type))
1725 (hi (numeric-type-high type)))
1726 (make-numeric-type :class 'integer :complexp :real
1727 :low (cond ((and hi (minusp hi))
1733 :high (if (and hi lo)
1734 (max (abs hi) (abs lo))
1736 (numeric-contagion type type))))
1738 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1739 (defun abs-derive-type-aux (type)
1740 (cond ((eq (numeric-type-complexp type) :complex)
1741 ;; The absolute value of a complex number is always a
1742 ;; non-negative float.
1743 (let* ((format (case (numeric-type-class type)
1744 ((integer rational) 'single-float)
1745 (t (numeric-type-format type))))
1746 (bound-format (or format 'float)))
1747 (make-numeric-type :class 'float
1750 :low (coerce 0 bound-format)
1753 ;; The absolute value of a real number is a non-negative real
1754 ;; of the same type.
1755 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1756 (class (numeric-type-class type))
1757 (format (numeric-type-format type))
1758 (bound-type (or format class 'real)))
1763 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1764 :high (coerce-and-truncate-floats
1765 (interval-high abs-bnd) bound-type))))))
1767 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1768 (defoptimizer (abs derive-type) ((num))
1769 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1771 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1772 (defoptimizer (truncate derive-type) ((number divisor))
1773 (let ((number-type (lvar-type number))
1774 (divisor-type (lvar-type divisor))
1775 (integer-type (specifier-type 'integer)))
1776 (if (and (numeric-type-p number-type)
1777 (csubtypep number-type integer-type)
1778 (numeric-type-p divisor-type)
1779 (csubtypep divisor-type integer-type))
1780 (let ((number-low (numeric-type-low number-type))
1781 (number-high (numeric-type-high number-type))
1782 (divisor-low (numeric-type-low divisor-type))
1783 (divisor-high (numeric-type-high divisor-type)))
1784 (values-specifier-type
1785 `(values ,(integer-truncate-derive-type number-low number-high
1786 divisor-low divisor-high)
1787 ,(integer-rem-derive-type number-low number-high
1788 divisor-low divisor-high))))
1791 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1794 (defun rem-result-type (number-type divisor-type)
1795 ;; Figure out what the remainder type is. The remainder is an
1796 ;; integer if both args are integers; a rational if both args are
1797 ;; rational; and a float otherwise.
1798 (cond ((and (csubtypep number-type (specifier-type 'integer))
1799 (csubtypep divisor-type (specifier-type 'integer)))
1801 ((and (csubtypep number-type (specifier-type 'rational))
1802 (csubtypep divisor-type (specifier-type 'rational)))
1804 ((and (csubtypep number-type (specifier-type 'float))
1805 (csubtypep divisor-type (specifier-type 'float)))
1806 ;; Both are floats so the result is also a float, of
1807 ;; the largest type.
1808 (or (float-format-max (numeric-type-format number-type)
1809 (numeric-type-format divisor-type))
1811 ((and (csubtypep number-type (specifier-type 'float))
1812 (csubtypep divisor-type (specifier-type 'rational)))
1813 ;; One of the arguments is a float and the other is a
1814 ;; rational. The remainder is a float of the same
1816 (or (numeric-type-format number-type) 'float))
1817 ((and (csubtypep divisor-type (specifier-type 'float))
1818 (csubtypep number-type (specifier-type 'rational)))
1819 ;; One of the arguments is a float and the other is a
1820 ;; rational. The remainder is a float of the same
1822 (or (numeric-type-format divisor-type) 'float))
1824 ;; Some unhandled combination. This usually means both args
1825 ;; are REAL so the result is a REAL.
1828 (defun truncate-derive-type-quot (number-type divisor-type)
1829 (let* ((rem-type (rem-result-type number-type divisor-type))
1830 (number-interval (numeric-type->interval number-type))
1831 (divisor-interval (numeric-type->interval divisor-type)))
1832 ;;(declare (type (member '(integer rational float)) rem-type))
1833 ;; We have real numbers now.
1834 (cond ((eq rem-type 'integer)
1835 ;; Since the remainder type is INTEGER, both args are
1837 (let* ((res (integer-truncate-derive-type
1838 (interval-low number-interval)
1839 (interval-high number-interval)
1840 (interval-low divisor-interval)
1841 (interval-high divisor-interval))))
1842 (specifier-type (if (listp res) res 'integer))))
1844 (let ((quot (truncate-quotient-bound
1845 (interval-div number-interval
1846 divisor-interval))))
1847 (specifier-type `(integer ,(or (interval-low quot) '*)
1848 ,(or (interval-high quot) '*))))))))
1850 (defun truncate-derive-type-rem (number-type divisor-type)
1851 (let* ((rem-type (rem-result-type number-type divisor-type))
1852 (number-interval (numeric-type->interval number-type))
1853 (divisor-interval (numeric-type->interval divisor-type))
1854 (rem (truncate-rem-bound number-interval divisor-interval)))
1855 ;;(declare (type (member '(integer rational float)) rem-type))
1856 ;; We have real numbers now.
1857 (cond ((eq rem-type 'integer)
1858 ;; Since the remainder type is INTEGER, both args are
1860 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1861 ,(or (interval-high rem) '*))))
1863 (multiple-value-bind (class format)
1866 (values 'integer nil))
1868 (values 'rational nil))
1869 ((or single-float double-float #!+long-float long-float)
1870 (values 'float rem-type))
1872 (values 'float nil))
1875 (when (member rem-type '(float single-float double-float
1876 #!+long-float long-float))
1877 (setf rem (interval-func #'(lambda (x)
1878 (coerce-for-bound x rem-type))
1880 (make-numeric-type :class class
1882 :low (interval-low rem)
1883 :high (interval-high rem)))))))
1885 (defun truncate-derive-type-quot-aux (num div same-arg)
1886 (declare (ignore same-arg))
1887 (if (and (numeric-type-real-p num)
1888 (numeric-type-real-p div))
1889 (truncate-derive-type-quot num div)
1892 (defun truncate-derive-type-rem-aux (num div same-arg)
1893 (declare (ignore same-arg))
1894 (if (and (numeric-type-real-p num)
1895 (numeric-type-real-p div))
1896 (truncate-derive-type-rem num div)
1899 (defoptimizer (truncate derive-type) ((number divisor))
1900 (let ((quot (two-arg-derive-type number divisor
1901 #'truncate-derive-type-quot-aux #'truncate))
1902 (rem (two-arg-derive-type number divisor
1903 #'truncate-derive-type-rem-aux #'rem)))
1904 (when (and quot rem)
1905 (make-values-type :required (list quot rem)))))
1907 (defun ftruncate-derive-type-quot (number-type divisor-type)
1908 ;; The bounds are the same as for truncate. However, the first
1909 ;; result is a float of some type. We need to determine what that
1910 ;; type is. Basically it's the more contagious of the two types.
1911 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1912 (res-type (numeric-contagion number-type divisor-type)))
1913 (make-numeric-type :class 'float
1914 :format (numeric-type-format res-type)
1915 :low (numeric-type-low q-type)
1916 :high (numeric-type-high q-type))))
1918 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1919 (declare (ignore same-arg))
1920 (if (and (numeric-type-real-p n)
1921 (numeric-type-real-p d))
1922 (ftruncate-derive-type-quot n d)
1925 (defoptimizer (ftruncate derive-type) ((number divisor))
1927 (two-arg-derive-type number divisor
1928 #'ftruncate-derive-type-quot-aux #'ftruncate))
1929 (rem (two-arg-derive-type number divisor
1930 #'truncate-derive-type-rem-aux #'rem)))
1931 (when (and quot rem)
1932 (make-values-type :required (list quot rem)))))
1934 (defun %unary-truncate-derive-type-aux (number)
1935 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1937 (defoptimizer (%unary-truncate derive-type) ((number))
1938 (one-arg-derive-type number
1939 #'%unary-truncate-derive-type-aux
1942 (defoptimizer (%unary-truncate/single-float derive-type) ((number))
1943 (one-arg-derive-type number
1944 #'%unary-truncate-derive-type-aux
1947 (defoptimizer (%unary-truncate/double-float derive-type) ((number))
1948 (one-arg-derive-type number
1949 #'%unary-truncate-derive-type-aux
1952 (defoptimizer (%unary-ftruncate derive-type) ((number))
1953 (let ((divisor (specifier-type '(integer 1 1))))
1954 (one-arg-derive-type number
1956 (ftruncate-derive-type-quot-aux n divisor nil))
1957 #'%unary-ftruncate)))
1959 (defoptimizer (%unary-round derive-type) ((number))
1960 (one-arg-derive-type number
1963 (unless (numeric-type-real-p n)
1964 (return *empty-type*))
1965 (let* ((interval (numeric-type->interval n))
1966 (low (interval-low interval))
1967 (high (interval-high interval)))
1969 (setf low (car low)))
1971 (setf high (car high)))
1981 ;;; Define optimizers for FLOOR and CEILING.
1983 ((def (name q-name r-name)
1984 (let ((q-aux (symbolicate q-name "-AUX"))
1985 (r-aux (symbolicate r-name "-AUX")))
1987 ;; Compute type of quotient (first) result.
1988 (defun ,q-aux (number-type divisor-type)
1989 (let* ((number-interval
1990 (numeric-type->interval number-type))
1992 (numeric-type->interval divisor-type))
1993 (quot (,q-name (interval-div number-interval
1994 divisor-interval))))
1995 (specifier-type `(integer ,(or (interval-low quot) '*)
1996 ,(or (interval-high quot) '*)))))
1997 ;; Compute type of remainder.
1998 (defun ,r-aux (number-type divisor-type)
1999 (let* ((divisor-interval
2000 (numeric-type->interval divisor-type))
2001 (rem (,r-name divisor-interval))
2002 (result-type (rem-result-type number-type divisor-type)))
2003 (multiple-value-bind (class format)
2006 (values 'integer nil))
2008 (values 'rational nil))
2009 ((or single-float double-float #!+long-float long-float)
2010 (values 'float result-type))
2012 (values 'float nil))
2015 (when (member result-type '(float single-float double-float
2016 #!+long-float long-float))
2017 ;; Make sure that the limits on the interval have
2019 (setf rem (interval-func (lambda (x)
2020 (coerce-for-bound x result-type))
2022 (make-numeric-type :class class
2024 :low (interval-low rem)
2025 :high (interval-high rem)))))
2026 ;; the optimizer itself
2027 (defoptimizer (,name derive-type) ((number divisor))
2028 (flet ((derive-q (n d same-arg)
2029 (declare (ignore same-arg))
2030 (if (and (numeric-type-real-p n)
2031 (numeric-type-real-p d))
2034 (derive-r (n d same-arg)
2035 (declare (ignore same-arg))
2036 (if (and (numeric-type-real-p n)
2037 (numeric-type-real-p d))
2040 (let ((quot (two-arg-derive-type
2041 number divisor #'derive-q #',name))
2042 (rem (two-arg-derive-type
2043 number divisor #'derive-r #'mod)))
2044 (when (and quot rem)
2045 (make-values-type :required (list quot rem))))))))))
2047 (def floor floor-quotient-bound floor-rem-bound)
2048 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
2050 ;;; Define optimizers for FFLOOR and FCEILING
2051 (macrolet ((def (name q-name r-name)
2052 (let ((q-aux (symbolicate "F" q-name "-AUX"))
2053 (r-aux (symbolicate r-name "-AUX")))
2055 ;; Compute type of quotient (first) result.
2056 (defun ,q-aux (number-type divisor-type)
2057 (let* ((number-interval
2058 (numeric-type->interval number-type))
2060 (numeric-type->interval divisor-type))
2061 (quot (,q-name (interval-div number-interval
2063 (res-type (numeric-contagion number-type
2066 :class (numeric-type-class res-type)
2067 :format (numeric-type-format res-type)
2068 :low (interval-low quot)
2069 :high (interval-high quot))))
2071 (defoptimizer (,name derive-type) ((number divisor))
2072 (flet ((derive-q (n d same-arg)
2073 (declare (ignore same-arg))
2074 (if (and (numeric-type-real-p n)
2075 (numeric-type-real-p d))
2078 (derive-r (n d same-arg)
2079 (declare (ignore same-arg))
2080 (if (and (numeric-type-real-p n)
2081 (numeric-type-real-p d))
2084 (let ((quot (two-arg-derive-type
2085 number divisor #'derive-q #',name))
2086 (rem (two-arg-derive-type
2087 number divisor #'derive-r #'mod)))
2088 (when (and quot rem)
2089 (make-values-type :required (list quot rem))))))))))
2091 (def ffloor floor-quotient-bound floor-rem-bound)
2092 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
2094 ;;; functions to compute the bounds on the quotient and remainder for
2095 ;;; the FLOOR function
2096 (defun floor-quotient-bound (quot)
2097 ;; Take the floor of the quotient and then massage it into what we
2099 (let ((lo (interval-low quot))
2100 (hi (interval-high quot)))
2101 ;; Take the floor of the lower bound. The result is always a
2102 ;; closed lower bound.
2104 (floor (type-bound-number lo))
2106 ;; For the upper bound, we need to be careful.
2109 ;; An open bound. We need to be careful here because
2110 ;; the floor of '(10.0) is 9, but the floor of
2112 (multiple-value-bind (q r) (floor (first hi))
2117 ;; A closed bound, so the answer is obvious.
2121 (make-interval :low lo :high hi)))
2122 (defun floor-rem-bound (div)
2123 ;; The remainder depends only on the divisor. Try to get the
2124 ;; correct sign for the remainder if we can.
2125 (case (interval-range-info div)
2127 ;; The divisor is always positive.
2128 (let ((rem (interval-abs div)))
2129 (setf (interval-low rem) 0)
2130 (when (and (numberp (interval-high rem))
2131 (not (zerop (interval-high rem))))
2132 ;; The remainder never contains the upper bound. However,
2133 ;; watch out for the case where the high limit is zero!
2134 (setf (interval-high rem) (list (interval-high rem))))
2137 ;; The divisor is always negative.
2138 (let ((rem (interval-neg (interval-abs div))))
2139 (setf (interval-high rem) 0)
2140 (when (numberp (interval-low rem))
2141 ;; The remainder never contains the lower bound.
2142 (setf (interval-low rem) (list (interval-low rem))))
2145 ;; The divisor can be positive or negative. All bets off. The
2146 ;; magnitude of remainder is the maximum value of the divisor.
2147 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2148 ;; The bound never reaches the limit, so make the interval open.
2149 (make-interval :low (if limit
2152 :high (list limit))))))
2154 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
2155 => #S(INTERVAL :LOW 0 :HIGH 10)
2156 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2157 => #S(INTERVAL :LOW 0 :HIGH 10)
2158 (floor-quotient-bound (make-interval :low 0.3 :high 10))
2159 => #S(INTERVAL :LOW 0 :HIGH 10)
2160 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
2161 => #S(INTERVAL :LOW 0 :HIGH 9)
2162 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
2163 => #S(INTERVAL :LOW 0 :HIGH 10)
2164 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
2165 => #S(INTERVAL :LOW 0 :HIGH 10)
2166 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2167 => #S(INTERVAL :LOW -2 :HIGH 10)
2168 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2169 => #S(INTERVAL :LOW -1 :HIGH 10)
2170 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
2171 => #S(INTERVAL :LOW -1 :HIGH 10)
2173 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
2174 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2175 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
2176 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2177 (floor-rem-bound (make-interval :low -10 :high -2.3))
2178 #S(INTERVAL :LOW (-10) :HIGH 0)
2179 (floor-rem-bound (make-interval :low 0.3 :high 10))
2180 => #S(INTERVAL :LOW 0 :HIGH '(10))
2181 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
2182 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
2183 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
2184 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2187 ;;; same functions for CEILING
2188 (defun ceiling-quotient-bound (quot)
2189 ;; Take the ceiling of the quotient and then massage it into what we
2191 (let ((lo (interval-low quot))
2192 (hi (interval-high quot)))
2193 ;; Take the ceiling of the upper bound. The result is always a
2194 ;; closed upper bound.
2196 (ceiling (type-bound-number hi))
2198 ;; For the lower bound, we need to be careful.
2201 ;; An open bound. We need to be careful here because
2202 ;; the ceiling of '(10.0) is 11, but the ceiling of
2204 (multiple-value-bind (q r) (ceiling (first lo))
2209 ;; A closed bound, so the answer is obvious.
2213 (make-interval :low lo :high hi)))
2214 (defun ceiling-rem-bound (div)
2215 ;; The remainder depends only on the divisor. Try to get the
2216 ;; correct sign for the remainder if we can.
2217 (case (interval-range-info div)
2219 ;; Divisor is always positive. The remainder is negative.
2220 (let ((rem (interval-neg (interval-abs div))))
2221 (setf (interval-high rem) 0)
2222 (when (and (numberp (interval-low rem))
2223 (not (zerop (interval-low rem))))
2224 ;; The remainder never contains the upper bound. However,
2225 ;; watch out for the case when the upper bound is zero!
2226 (setf (interval-low rem) (list (interval-low rem))))
2229 ;; Divisor is always negative. The remainder is positive
2230 (let ((rem (interval-abs div)))
2231 (setf (interval-low rem) 0)
2232 (when (numberp (interval-high rem))
2233 ;; The remainder never contains the lower bound.
2234 (setf (interval-high rem) (list (interval-high rem))))
2237 ;; The divisor can be positive or negative. All bets off. The
2238 ;; magnitude of remainder is the maximum value of the divisor.
2239 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2240 ;; The bound never reaches the limit, so make the interval open.
2241 (make-interval :low (if limit
2244 :high (list limit))))))
2247 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2248 => #S(INTERVAL :LOW 1 :HIGH 11)
2249 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2250 => #S(INTERVAL :LOW 1 :HIGH 11)
2251 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2252 => #S(INTERVAL :LOW 1 :HIGH 10)
2253 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2254 => #S(INTERVAL :LOW 1 :HIGH 10)
2255 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2256 => #S(INTERVAL :LOW 1 :HIGH 11)
2257 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2258 => #S(INTERVAL :LOW 1 :HIGH 11)
2259 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2260 => #S(INTERVAL :LOW -1 :HIGH 11)
2261 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2262 => #S(INTERVAL :LOW 0 :HIGH 11)
2263 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2264 => #S(INTERVAL :LOW -1 :HIGH 11)
2266 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2267 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2268 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2269 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2270 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2271 => #S(INTERVAL :LOW 0 :HIGH (10))
2272 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2273 => #S(INTERVAL :LOW (-10) :HIGH 0)
2274 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2275 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2276 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2277 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2280 (defun truncate-quotient-bound (quot)
2281 ;; For positive quotients, truncate is exactly like floor. For
2282 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2283 ;; it's the union of the two pieces.
2284 (case (interval-range-info quot)
2287 (floor-quotient-bound quot))
2289 ;; just like CEILING
2290 (ceiling-quotient-bound quot))
2292 ;; Split the interval into positive and negative pieces, compute
2293 ;; the result for each piece and put them back together.
2294 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2295 (interval-merge-pair (ceiling-quotient-bound neg)
2296 (floor-quotient-bound pos))))))
2298 (defun truncate-rem-bound (num div)
2299 ;; This is significantly more complicated than FLOOR or CEILING. We
2300 ;; need both the number and the divisor to determine the range. The
2301 ;; basic idea is to split the ranges of NUM and DEN into positive
2302 ;; and negative pieces and deal with each of the four possibilities
2304 (case (interval-range-info num)
2306 (case (interval-range-info div)
2308 (floor-rem-bound div))
2310 (ceiling-rem-bound div))
2312 (destructuring-bind (neg pos) (interval-split 0 div t t)
2313 (interval-merge-pair (truncate-rem-bound num neg)
2314 (truncate-rem-bound num pos))))))
2316 (case (interval-range-info div)
2318 (ceiling-rem-bound div))
2320 (floor-rem-bound div))
2322 (destructuring-bind (neg pos) (interval-split 0 div t t)
2323 (interval-merge-pair (truncate-rem-bound num neg)
2324 (truncate-rem-bound num pos))))))
2326 (destructuring-bind (neg pos) (interval-split 0 num t t)
2327 (interval-merge-pair (truncate-rem-bound neg div)
2328 (truncate-rem-bound pos div))))))
2331 ;;; Derive useful information about the range. Returns three values:
2332 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2333 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2334 ;;; - The abs of the maximal value if there is one, or nil if it is
2336 (defun numeric-range-info (low high)
2337 (cond ((and low (not (minusp low)))
2338 (values '+ low high))
2339 ((and high (not (plusp high)))
2340 (values '- (- high) (if low (- low) nil)))
2342 (values nil 0 (and low high (max (- low) high))))))
2344 (defun integer-truncate-derive-type
2345 (number-low number-high divisor-low divisor-high)
2346 ;; The result cannot be larger in magnitude than the number, but the
2347 ;; sign might change. If we can determine the sign of either the
2348 ;; number or the divisor, we can eliminate some of the cases.
2349 (multiple-value-bind (number-sign number-min number-max)
2350 (numeric-range-info number-low number-high)
2351 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2352 (numeric-range-info divisor-low divisor-high)
2353 (when (and divisor-max (zerop divisor-max))
2354 ;; We've got a problem: guaranteed division by zero.
2355 (return-from integer-truncate-derive-type t))
2356 (when (zerop divisor-min)
2357 ;; We'll assume that they aren't going to divide by zero.
2359 (cond ((and number-sign divisor-sign)
2360 ;; We know the sign of both.
2361 (if (eq number-sign divisor-sign)
2362 ;; Same sign, so the result will be positive.
2363 `(integer ,(if divisor-max
2364 (truncate number-min divisor-max)
2367 (truncate number-max divisor-min)
2369 ;; Different signs, the result will be negative.
2370 `(integer ,(if number-max
2371 (- (truncate number-max divisor-min))
2374 (- (truncate number-min divisor-max))
2376 ((eq divisor-sign '+)
2377 ;; The divisor is positive. Therefore, the number will just
2378 ;; become closer to zero.
2379 `(integer ,(if number-low
2380 (truncate number-low divisor-min)
2383 (truncate number-high divisor-min)
2385 ((eq divisor-sign '-)
2386 ;; The divisor is negative. Therefore, the absolute value of
2387 ;; the number will become closer to zero, but the sign will also
2389 `(integer ,(if number-high
2390 (- (truncate number-high divisor-min))
2393 (- (truncate number-low divisor-min))
2395 ;; The divisor could be either positive or negative.
2397 ;; The number we are dividing has a bound. Divide that by the
2398 ;; smallest posible divisor.
2399 (let ((bound (truncate number-max divisor-min)))
2400 `(integer ,(- bound) ,bound)))
2402 ;; The number we are dividing is unbounded, so we can't tell
2403 ;; anything about the result.
2406 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2407 (defun integer-rem-derive-type
2408 (number-low number-high divisor-low divisor-high)
2409 (if (and divisor-low divisor-high)
2410 ;; We know the range of the divisor, and the remainder must be
2411 ;; smaller than the divisor. We can tell the sign of the
2412 ;; remainder if we know the sign of the number.
2413 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2414 `(integer ,(if (or (null number-low)
2415 (minusp number-low))
2418 ,(if (or (null number-high)
2419 (plusp number-high))
2422 ;; The divisor is potentially either very positive or very
2423 ;; negative. Therefore, the remainder is unbounded, but we might
2424 ;; be able to tell something about the sign from the number.
2425 `(integer ,(if (and number-low (not (minusp number-low)))
2426 ;; The number we are dividing is positive.
2427 ;; Therefore, the remainder must be positive.
2430 ,(if (and number-high (not (plusp number-high)))
2431 ;; The number we are dividing is negative.
2432 ;; Therefore, the remainder must be negative.
2436 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2437 (defoptimizer (random derive-type) ((bound &optional state))
2438 (let ((type (lvar-type bound)))
2439 (when (numeric-type-p type)
2440 (let ((class (numeric-type-class type))
2441 (high (numeric-type-high type))
2442 (format (numeric-type-format type)))
2446 :low (coerce 0 (or format class 'real))
2447 :high (cond ((not high) nil)
2448 ((eq class 'integer) (max (1- high) 0))
2449 ((or (consp high) (zerop high)) high)
2452 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2453 (defun random-derive-type-aux (type)
2454 (let ((class (numeric-type-class type))
2455 (high (numeric-type-high type))
2456 (format (numeric-type-format type)))
2460 :low (coerce 0 (or format class 'real))
2461 :high (cond ((not high) nil)
2462 ((eq class 'integer) (max (1- high) 0))
2463 ((or (consp high) (zerop high)) high)
2466 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2467 (defoptimizer (random derive-type) ((bound &optional state))
2468 (one-arg-derive-type bound #'random-derive-type-aux nil))
2470 ;;;; miscellaneous derive-type methods
2472 (defoptimizer (integer-length derive-type) ((x))
2473 (let ((x-type (lvar-type x)))
2474 (when (numeric-type-p x-type)
2475 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2476 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2477 ;; careful about LO or HI being NIL, though. Also, if 0 is
2478 ;; contained in X, the lower bound is obviously 0.
2479 (flet ((null-or-min (a b)
2480 (and a b (min (integer-length a)
2481 (integer-length b))))
2483 (and a b (max (integer-length a)
2484 (integer-length b)))))
2485 (let* ((min (numeric-type-low x-type))
2486 (max (numeric-type-high x-type))
2487 (min-len (null-or-min min max))
2488 (max-len (null-or-max min max)))
2489 (when (ctypep 0 x-type)
2491 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2493 (defoptimizer (isqrt derive-type) ((x))
2494 (let ((x-type (lvar-type x)))
2495 (when (numeric-type-p x-type)
2496 (let* ((lo (numeric-type-low x-type))
2497 (hi (numeric-type-high x-type))
2498 (lo-res (if lo (isqrt lo) '*))
2499 (hi-res (if hi (isqrt hi) '*)))
2500 (specifier-type `(integer ,lo-res ,hi-res))))))
2502 (defoptimizer (char-code derive-type) ((char))
2503 (let ((type (type-intersection (lvar-type char) (specifier-type 'character))))
2504 (cond ((member-type-p type)
2507 ,@(loop for member in (member-type-members type)
2508 when (characterp member)
2509 collect (char-code member)))))
2510 ((sb!kernel::character-set-type-p type)
2513 ,@(loop for (low . high)
2514 in (character-set-type-pairs type)
2515 collect `(integer ,low ,high)))))
2516 ((csubtypep type (specifier-type 'base-char))
2518 `(mod ,base-char-code-limit)))
2521 `(mod ,char-code-limit))))))
2523 (defoptimizer (code-char derive-type) ((code))
2524 (let ((type (lvar-type code)))
2525 ;; FIXME: unions of integral ranges? It ought to be easier to do
2526 ;; this, given that CHARACTER-SET is basically an integral range
2527 ;; type. -- CSR, 2004-10-04
2528 (when (numeric-type-p type)
2529 (let* ((lo (numeric-type-low type))
2530 (hi (numeric-type-high type))
2531 (type (specifier-type `(character-set ((,lo . ,hi))))))
2533 ;; KLUDGE: when running on the host, we lose a slight amount
2534 ;; of precision so that we don't have to "unparse" types
2535 ;; that formally we can't, such as (CHARACTER-SET ((0
2536 ;; . 0))). -- CSR, 2004-10-06
2538 ((csubtypep type (specifier-type 'standard-char)) type)
2540 ((csubtypep type (specifier-type 'base-char))
2541 (specifier-type 'base-char))
2543 ((csubtypep type (specifier-type 'extended-char))
2544 (specifier-type 'extended-char))
2545 (t #+sb-xc-host (specifier-type 'character)
2546 #-sb-xc-host type))))))
2548 (defoptimizer (values derive-type) ((&rest values))
2549 (make-values-type :required (mapcar #'lvar-type values)))
2551 (defun signum-derive-type-aux (type)
2552 (if (eq (numeric-type-complexp type) :complex)
2553 (let* ((format (case (numeric-type-class type)
2554 ((integer rational) 'single-float)
2555 (t (numeric-type-format type))))
2556 (bound-format (or format 'float)))
2557 (make-numeric-type :class 'float
2560 :low (coerce -1 bound-format)
2561 :high (coerce 1 bound-format)))
2562 (let* ((interval (numeric-type->interval type))
2563 (range-info (interval-range-info interval))
2564 (contains-0-p (interval-contains-p 0 interval))
2565 (class (numeric-type-class type))
2566 (format (numeric-type-format type))
2567 (one (coerce 1 (or format class 'real)))
2568 (zero (coerce 0 (or format class 'real)))
2569 (minus-one (coerce -1 (or format class 'real)))
2570 (plus (make-numeric-type :class class :format format
2571 :low one :high one))
2572 (minus (make-numeric-type :class class :format format
2573 :low minus-one :high minus-one))
2574 ;; KLUDGE: here we have a fairly horrible hack to deal
2575 ;; with the schizophrenia in the type derivation engine.
2576 ;; The problem is that the type derivers reinterpret
2577 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2578 ;; 0d0) within the derivation mechanism doesn't include
2579 ;; -0d0. Ugh. So force it in here, instead.
2580 (zero (make-numeric-type :class class :format format
2581 :low (- zero) :high zero)))
2583 (+ (if contains-0-p (type-union plus zero) plus))
2584 (- (if contains-0-p (type-union minus zero) minus))
2585 (t (type-union minus zero plus))))))
2587 (defoptimizer (signum derive-type) ((num))
2588 (one-arg-derive-type num #'signum-derive-type-aux nil))
2590 ;;;; byte operations
2592 ;;;; We try to turn byte operations into simple logical operations.
2593 ;;;; First, we convert byte specifiers into separate size and position
2594 ;;;; arguments passed to internal %FOO functions. We then attempt to
2595 ;;;; transform the %FOO functions into boolean operations when the
2596 ;;;; size and position are constant and the operands are fixnums.
2598 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2599 ;; expressions that evaluate to the SIZE and POSITION of
2600 ;; the byte-specifier form SPEC. We may wrap a let around
2601 ;; the result of the body to bind some variables.
2603 ;; If the spec is a BYTE form, then bind the vars to the
2604 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2605 ;; and BYTE-POSITION. The goal of this transformation is to
2606 ;; avoid consing up byte specifiers and then immediately
2607 ;; throwing them away.
2608 (with-byte-specifier ((size-var pos-var spec) &body body)
2609 (once-only ((spec `(macroexpand ,spec))
2611 `(if (and (consp ,spec)
2612 (eq (car ,spec) 'byte)
2613 (= (length ,spec) 3))
2614 (let ((,size-var (second ,spec))
2615 (,pos-var (third ,spec)))
2617 (let ((,size-var `(byte-size ,,temp))
2618 (,pos-var `(byte-position ,,temp)))
2619 `(let ((,,temp ,,spec))
2622 (define-source-transform ldb (spec int)
2623 (with-byte-specifier (size pos spec)
2624 `(%ldb ,size ,pos ,int)))
2626 (define-source-transform dpb (newbyte spec int)
2627 (with-byte-specifier (size pos spec)
2628 `(%dpb ,newbyte ,size ,pos ,int)))
2630 (define-source-transform mask-field (spec int)
2631 (with-byte-specifier (size pos spec)
2632 `(%mask-field ,size ,pos ,int)))
2634 (define-source-transform deposit-field (newbyte spec int)
2635 (with-byte-specifier (size pos spec)
2636 `(%deposit-field ,newbyte ,size ,pos ,int))))
2638 (defoptimizer (%ldb derive-type) ((size posn num))
2639 (let ((size (lvar-type size)))
2640 (if (and (numeric-type-p size)
2641 (csubtypep size (specifier-type 'integer)))
2642 (let ((size-high (numeric-type-high size)))
2643 (if (and size-high (<= size-high sb!vm:n-word-bits))
2644 (specifier-type `(unsigned-byte* ,size-high))
2645 (specifier-type 'unsigned-byte)))
2648 (defoptimizer (%mask-field derive-type) ((size posn num))
2649 (let ((size (lvar-type size))
2650 (posn (lvar-type posn)))
2651 (if (and (numeric-type-p size)
2652 (csubtypep size (specifier-type 'integer))
2653 (numeric-type-p posn)
2654 (csubtypep posn (specifier-type 'integer)))
2655 (let ((size-high (numeric-type-high size))
2656 (posn-high (numeric-type-high posn)))
2657 (if (and size-high posn-high
2658 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2659 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2660 (specifier-type 'unsigned-byte)))
2663 (defun %deposit-field-derive-type-aux (size posn int)
2664 (let ((size (lvar-type size))
2665 (posn (lvar-type posn))
2666 (int (lvar-type int)))
2667 (when (and (numeric-type-p size)
2668 (numeric-type-p posn)
2669 (numeric-type-p int))
2670 (let ((size-high (numeric-type-high size))
2671 (posn-high (numeric-type-high posn))
2672 (high (numeric-type-high int))
2673 (low (numeric-type-low int)))
2674 (when (and size-high posn-high high low
2675 ;; KLUDGE: we need this cutoff here, otherwise we
2676 ;; will merrily derive the type of %DPB as
2677 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2678 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2679 ;; 1073741822))), with hilarious consequences. We
2680 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2681 ;; over a reasonable amount of shifting, even on
2682 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2683 ;; machine integers are 64-bits. -- CSR,
2685 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2686 (let ((raw-bit-count (max (integer-length high)
2687 (integer-length low)
2688 (+ size-high posn-high))))
2691 `(signed-byte ,(1+ raw-bit-count))
2692 `(unsigned-byte* ,raw-bit-count)))))))))
2694 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2695 (%deposit-field-derive-type-aux size posn int))
2697 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2698 (%deposit-field-derive-type-aux size posn int))
2700 (deftransform %ldb ((size posn int)
2701 (fixnum fixnum integer)
2702 (unsigned-byte #.sb!vm:n-word-bits))
2703 "convert to inline logical operations"
2704 `(logand (ash int (- posn))
2705 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2706 (- size ,sb!vm:n-word-bits))))
2708 (deftransform %mask-field ((size posn int)
2709 (fixnum fixnum integer)
2710 (unsigned-byte #.sb!vm:n-word-bits))
2711 "convert to inline logical operations"
2713 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2714 (- size ,sb!vm:n-word-bits))
2717 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2718 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2719 ;;; as the result type, as that would allow result types that cover
2720 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2721 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2723 (deftransform %dpb ((new size posn int)
2725 (unsigned-byte #.sb!vm:n-word-bits))
2726 "convert to inline logical operations"
2727 `(let ((mask (ldb (byte size 0) -1)))
2728 (logior (ash (logand new mask) posn)
2729 (logand int (lognot (ash mask posn))))))
2731 (deftransform %dpb ((new size posn int)
2733 (signed-byte #.sb!vm:n-word-bits))
2734 "convert to inline logical operations"
2735 `(let ((mask (ldb (byte size 0) -1)))
2736 (logior (ash (logand new mask) posn)
2737 (logand int (lognot (ash mask posn))))))
2739 (deftransform %deposit-field ((new size posn int)
2741 (unsigned-byte #.sb!vm:n-word-bits))
2742 "convert to inline logical operations"
2743 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2744 (logior (logand new mask)
2745 (logand int (lognot mask)))))
2747 (deftransform %deposit-field ((new size posn int)
2749 (signed-byte #.sb!vm:n-word-bits))
2750 "convert to inline logical operations"
2751 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2752 (logior (logand new mask)
2753 (logand int (lognot mask)))))
2755 (defoptimizer (mask-signed-field derive-type) ((size x))
2756 (let ((size (lvar-type size)))
2757 (if (numeric-type-p size)
2758 (let ((size-high (numeric-type-high size)))
2759 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2760 (specifier-type `(signed-byte ,size-high))
2765 ;;; Modular functions
2767 ;;; (ldb (byte s 0) (foo x y ...)) =
2768 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2770 ;;; and similar for other arguments.
2772 (defun make-modular-fun-type-deriver (prototype kind width signedp)
2773 (declare (ignore kind))
2775 (binding* ((info (info :function :info prototype) :exit-if-null)
2776 (fun (fun-info-derive-type info) :exit-if-null)
2777 (mask-type (specifier-type
2779 ((nil) (let ((mask (1- (ash 1 width))))
2780 `(integer ,mask ,mask)))
2781 ((t) `(signed-byte ,width))))))
2783 (let ((res (funcall fun call)))
2785 (if (eq signedp nil)
2786 (logand-derive-type-aux res mask-type))))))
2789 (binding* ((info (info :function :info prototype) :exit-if-null)
2790 (fun (fun-info-derive-type info) :exit-if-null)
2791 (res (funcall fun call) :exit-if-null)
2792 (mask-type (specifier-type
2794 ((nil) (let ((mask (1- (ash 1 width))))
2795 `(integer ,mask ,mask)))
2796 ((t) `(signed-byte ,width))))))
2797 (if (eq signedp nil)
2798 (logand-derive-type-aux res mask-type)))))
2800 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2802 ;;; For good functions, we just recursively cut arguments; their
2803 ;;; "goodness" means that the result will not increase (in the
2804 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2805 ;;; replaced with the version, cutting its result to WIDTH or more
2806 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2807 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2808 ;;; arguments (maybe to a different width) and returning the name of a
2809 ;;; modular version, if it exists, or NIL. If we have changed
2810 ;;; anything, we need to flush old derived types, because they have
2811 ;;; nothing in common with the new code.
2812 (defun cut-to-width (lvar kind width signedp)
2813 (declare (type lvar lvar) (type (integer 0) width))
2814 (let ((type (specifier-type (if (zerop width)
2817 ((nil) 'unsigned-byte)
2820 (labels ((reoptimize-node (node name)
2821 (setf (node-derived-type node)
2823 (info :function :type name)))
2824 (setf (lvar-%derived-type (node-lvar node)) nil)
2825 (setf (node-reoptimize node) t)
2826 (setf (block-reoptimize (node-block node)) t)
2827 (reoptimize-component (node-component node) :maybe))
2828 (cut-node (node &aux did-something)
2829 (when (block-delete-p (node-block node))
2830 (return-from cut-node))
2833 (typecase (ref-leaf node)
2835 (let* ((constant-value (constant-value (ref-leaf node)))
2836 (new-value (if signedp
2837 (mask-signed-field width constant-value)
2838 (ldb (byte width 0) constant-value))))
2839 (unless (= constant-value new-value)
2840 (change-ref-leaf node (make-constant new-value))
2841 (let ((lvar (node-lvar node)))
2842 (setf (lvar-%derived-type lvar)
2843 (and (lvar-has-single-use-p lvar)
2844 (make-values-type :required (list (ctype-of new-value))))))
2845 (setf (block-reoptimize (node-block node)) t)
2846 (reoptimize-component (node-component node) :maybe)
2849 (binding* ((dest (lvar-dest lvar) :exit-if-null)
2850 (nil (combination-p dest) :exit-if-null)
2851 (fun-ref (lvar-use (combination-fun dest)))
2852 (leaf (ref-leaf fun-ref))
2853 (name (and (leaf-has-source-name-p leaf)
2854 (leaf-source-name leaf))))
2855 ;; we're about to insert an m-s-f/logand between a ref to
2856 ;; a variable and another m-s-f/logand. No point in doing
2857 ;; that; the parent m-s-f/logand was already cut to width
2859 (unless (or (cond (signedp
2860 (and (eql name 'mask-signed-field)
2865 (eql name 'logand)))
2866 (csubtypep (lvar-type lvar) type))
2870 (mask-signed-field ,width x))
2872 `(logand 'dummy ,(ldb (byte width 0) -1))))
2873 (setf (block-reoptimize (node-block node)) t)
2874 (reoptimize-component (node-component node) :maybe)
2877 (when (eq (basic-combination-kind node) :known)
2878 (let* ((fun-ref (lvar-use (combination-fun node)))
2879 (fun-name (leaf-source-name (ref-leaf fun-ref)))
2880 (modular-fun (find-modular-version fun-name kind
2882 (when (and modular-fun
2883 (not (and (eq fun-name 'logand)
2885 (single-value-type (node-derived-type node))
2887 (binding* ((name (etypecase modular-fun
2888 ((eql :good) fun-name)
2890 (modular-fun-info-name modular-fun))
2892 (funcall modular-fun node width)))
2894 (unless (eql modular-fun :good)
2895 (setq did-something t)
2898 (find-free-fun name "in a strange place"))
2899 (setf (combination-kind node) :full))
2900 (unless (functionp modular-fun)
2901 (dolist (arg (basic-combination-args node))
2902 (when (cut-lvar arg)
2903 (setq did-something t))))
2905 (reoptimize-node node name))
2906 did-something)))))))
2907 (cut-lvar (lvar &aux did-something)
2908 (do-uses (node lvar)
2909 (when (cut-node node)
2910 (setq did-something t)))
2914 (defun best-modular-version (width signedp)
2915 ;; 1. exact width-matched :untagged
2916 ;; 2. >/>= width-matched :tagged
2917 ;; 3. >/>= width-matched :untagged
2918 (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class*))
2919 (uswidths (modular-class-widths *untagged-signed-modular-class*))
2920 (uwidths (merge 'list uuwidths uswidths #'< :key #'car))
2921 (twidths (modular-class-widths *tagged-modular-class*)))
2922 (let ((exact (find (cons width signedp) uwidths :test #'equal)))
2924 (return-from best-modular-version (values width :untagged signedp))))
2925 (flet ((inexact-match (w)
2927 ((eq signedp (cdr w)) (<= width (car w)))
2928 ((eq signedp nil) (< width (car w))))))
2929 (let ((tgt (find-if #'inexact-match twidths)))
2931 (return-from best-modular-version
2932 (values (car tgt) :tagged (cdr tgt)))))
2933 (let ((ugt (find-if #'inexact-match uwidths)))
2935 (return-from best-modular-version
2936 (values (car ugt) :untagged (cdr ugt))))))))
2938 (defoptimizer (logand optimizer) ((x y) node)
2939 (let ((result-type (single-value-type (node-derived-type node))))
2940 (when (numeric-type-p result-type)
2941 (let ((low (numeric-type-low result-type))
2942 (high (numeric-type-high result-type)))
2943 (when (and (numberp low)
2946 (let ((width (integer-length high)))
2947 (multiple-value-bind (w kind signedp)
2948 (best-modular-version width nil)
2950 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP).
2952 ;; FIXME: I think the FIXME (which is from APD) above
2953 ;; implies that CUT-TO-WIDTH should do /everything/
2954 ;; that's required, including reoptimizing things
2955 ;; itself that it knows are necessary. At the moment,
2956 ;; CUT-TO-WIDTH sets up some new calls with
2957 ;; combination-type :FULL, which later get noticed as
2958 ;; known functions and properly converted.
2960 ;; We cut to W not WIDTH if SIGNEDP is true, because
2961 ;; signed constant replacement needs to know which bit
2962 ;; in the field is the signed bit.
2963 (let ((xact (cut-to-width x kind (if signedp w width) signedp))
2964 (yact (cut-to-width y kind (if signedp w width) signedp)))
2965 (declare (ignore xact yact))
2966 nil) ; After fixing above, replace with T, meaning
2967 ; "don't reoptimize this (LOGAND) node any more".
2970 (defoptimizer (mask-signed-field optimizer) ((width x) node)
2971 (let ((result-type (single-value-type (node-derived-type node))))
2972 (when (numeric-type-p result-type)
2973 (let ((low (numeric-type-low result-type))
2974 (high (numeric-type-high result-type)))
2975 (when (and (numberp low) (numberp high))
2976 (let ((width (max (integer-length high) (integer-length low))))
2977 (multiple-value-bind (w kind)
2978 (best-modular-version (1+ width) t)
2980 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND W T).
2981 ;; [ see comment above in LOGAND optimizer ]
2982 (cut-to-width x kind w t)
2983 nil ; After fixing above, replace with T.
2986 ;;; miscellanous numeric transforms
2988 ;;; If a constant appears as the first arg, swap the args.
2989 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2990 (if (and (constant-lvar-p x)
2991 (not (constant-lvar-p y)))
2992 `(,(lvar-fun-name (basic-combination-fun node))
2995 (give-up-ir1-transform)))
2997 (dolist (x '(= char= + * logior logand logxor))
2998 (%deftransform x '(function * *) #'commutative-arg-swap
2999 "place constant arg last"))
3001 ;;; Handle the case of a constant BOOLE-CODE.
3002 (deftransform boole ((op x y) * *)
3003 "convert to inline logical operations"
3004 (unless (constant-lvar-p op)
3005 (give-up-ir1-transform "BOOLE code is not a constant."))
3006 (let ((control (lvar-value op)))
3008 (#.sb!xc:boole-clr 0)
3009 (#.sb!xc:boole-set -1)
3010 (#.sb!xc:boole-1 'x)
3011 (#.sb!xc:boole-2 'y)
3012 (#.sb!xc:boole-c1 '(lognot x))
3013 (#.sb!xc:boole-c2 '(lognot y))
3014 (#.sb!xc:boole-and '(logand x y))
3015 (#.sb!xc:boole-ior '(logior x y))
3016 (#.sb!xc:boole-xor '(logxor x y))
3017 (#.sb!xc:boole-eqv '(logeqv x y))
3018 (#.sb!xc:boole-nand '(lognand x y))
3019 (#.sb!xc:boole-nor '(lognor x y))
3020 (#.sb!xc:boole-andc1 '(logandc1 x y))
3021 (#.sb!xc:boole-andc2 '(logandc2 x y))
3022 (#.sb!xc:boole-orc1 '(logorc1 x y))
3023 (#.sb!xc:boole-orc2 '(logorc2 x y))
3025 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
3028 ;;;; converting special case multiply/divide to shifts
3030 ;;; If arg is a constant power of two, turn * into a shift.
3031 (deftransform * ((x y) (integer integer) *)
3032 "convert x*2^k to shift"
3033 (unless (constant-lvar-p y)
3034 (give-up-ir1-transform))
3035 (let* ((y (lvar-value y))
3037 (len (1- (integer-length y-abs))))
3038 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3039 (give-up-ir1-transform))
3044 ;;; These must come before the ones below, so that they are tried
3045 ;;; first. Since %FLOOR and %CEILING are inlined, this allows
3046 ;;; the general case to be handled by TRUNCATE transforms.
3047 (deftransform floor ((x y))
3050 (deftransform ceiling ((x y))
3053 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3054 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3056 (flet ((frob (y ceil-p)
3057 (unless (constant-lvar-p y)
3058 (give-up-ir1-transform))
3059 (let* ((y (lvar-value y))
3061 (len (1- (integer-length y-abs))))
3062 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3063 (give-up-ir1-transform))
3064 (let ((shift (- len))
3066 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
3067 `(let ((x (+ x ,delta)))
3069 `(values (ash (- x) ,shift)
3070 (- (- (logand (- x) ,mask)) ,delta))
3071 `(values (ash x ,shift)
3072 (- (logand x ,mask) ,delta))))))))
3073 (deftransform floor ((x y) (integer integer) *)
3074 "convert division by 2^k to shift"
3076 (deftransform ceiling ((x y) (integer integer) *)
3077 "convert division by 2^k to shift"
3080 ;;; Do the same for MOD.
3081 (deftransform mod ((x y) (integer integer) *)
3082 "convert remainder mod 2^k to LOGAND"
3083 (unless (constant-lvar-p y)
3084 (give-up-ir1-transform))
3085 (let* ((y (lvar-value y))
3087 (len (1- (integer-length y-abs))))
3088 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3089 (give-up-ir1-transform))
3090 (let ((mask (1- y-abs)))
3092 `(- (logand (- x) ,mask))
3093 `(logand x ,mask)))))
3095 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3096 (deftransform truncate ((x y) (integer integer))
3097 "convert division by 2^k to shift"
3098 (unless (constant-lvar-p y)
3099 (give-up-ir1-transform))
3100 (let* ((y (lvar-value y))
3102 (len (1- (integer-length y-abs))))
3103 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3104 (give-up-ir1-transform))
3105 (let* ((shift (- len))
3108 (values ,(if (minusp y)
3110 `(- (ash (- x) ,shift)))
3111 (- (logand (- x) ,mask)))
3112 (values ,(if (minusp y)
3113 `(ash (- ,mask x) ,shift)
3115 (logand x ,mask))))))
3117 ;;; And the same for REM.
3118 (deftransform rem ((x y) (integer integer) *)
3119 "convert remainder mod 2^k to LOGAND"
3120 (unless (constant-lvar-p y)
3121 (give-up-ir1-transform))
3122 (let* ((y (lvar-value y))
3124 (len (1- (integer-length y-abs))))
3125 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3126 (give-up-ir1-transform))
3127 (let ((mask (1- y-abs)))
3129 (- (logand (- x) ,mask))
3130 (logand x ,mask)))))
3132 ;;; Return an expression to calculate the integer quotient of X and
3133 ;;; constant Y, using multiplication, shift and add/sub instead of
3134 ;;; division. Both arguments must be unsigned, fit in a machine word and
3135 ;;; Y must neither be zero nor a power of two. The quotient is rounded
3137 ;;; The algorithm is taken from the paper "Division by Invariant
3138 ;;; Integers using Multiplication", 1994 by Torbj\"{o}rn Granlund and
3139 ;;; Peter L. Montgomery, Figures 4.2 and 6.2, modified to exclude the
3140 ;;; case of division by powers of two.
3141 ;;; The algorithm includes an adaptive precision argument. Use it, since
3142 ;;; we often have sub-word value ranges. Careful, in this case, we need
3143 ;;; p s.t 2^p > n, not the ceiling of the binary log.
3144 ;;; Also, for some reason, the paper prefers shifting to masking. Mask
3145 ;;; instead. Masking is equivalent to shifting right, then left again;
3146 ;;; all the intermediate values are still words, so we just have to shift
3147 ;;; right a bit more to compensate, at the end.
3149 ;;; The following two examples show an average case and the worst case
3150 ;;; with respect to the complexity of the generated expression, under
3151 ;;; a word size of 64 bits:
3153 ;;; (UNSIGNED-DIV-TRANSFORMER 10 MOST-POSITIVE-WORD) ->
3154 ;;; (ASH (%MULTIPLY (LOGANDC2 X 0) 14757395258967641293) -3)
3156 ;;; (UNSIGNED-DIV-TRANSFORMER 7 MOST-POSITIVE-WORD) ->
3158 ;;; (T1 (%MULTIPLY NUM 2635249153387078803)))
3159 ;;; (ASH (LDB (BYTE 64 0)
3160 ;;; (+ T1 (ASH (LDB (BYTE 64 0)
3165 (defun gen-unsigned-div-by-constant-expr (y max-x)
3166 (declare (type (integer 3 #.most-positive-word) y)
3168 (aver (not (zerop (logand y (1- y)))))
3170 ;; the floor of the binary logarithm of (positive) X
3171 (integer-length (1- x)))
3172 (choose-multiplier (y precision)
3174 (shift l (1- shift))
3175 (expt-2-n+l (expt 2 (+ sb!vm:n-word-bits l)))
3176 (m-low (truncate expt-2-n+l y) (ash m-low -1))
3177 (m-high (truncate (+ expt-2-n+l
3178 (ash expt-2-n+l (- precision)))
3181 ((not (and (< (ash m-low -1) (ash m-high -1))
3183 (values m-high shift)))))
3184 (let ((n (expt 2 sb!vm:n-word-bits))
3185 (precision (integer-length max-x))
3187 (multiple-value-bind (m shift2)
3188 (choose-multiplier y precision)
3189 (when (and (>= m n) (evenp y))
3190 (setq shift1 (ld (logand y (- y))))
3191 (multiple-value-setq (m shift2)
3192 (choose-multiplier (/ y (ash 1 shift1))
3193 (- precision shift1))))
3196 `(truly-the word ,x)))
3198 (t1 (%multiply-high num ,(- m n))))
3199 (ash ,(word `(+ t1 (ash ,(word `(- num t1))
3202 ((and (zerop shift1) (zerop shift2))
3203 (let ((max (truncate max-x y)))
3204 ;; Explicit TRULY-THE needed to get the FIXNUM=>FIXNUM
3206 `(truly-the (integer 0 ,max)
3207 (%multiply-high x ,m))))
3209 `(ash (%multiply-high (logandc2 x ,(1- (ash 1 shift1))) ,m)
3210 ,(- (+ shift1 shift2)))))))))
3212 ;;; If the divisor is constant and both args are positive and fit in a
3213 ;;; machine word, replace the division by a multiplication and possibly
3214 ;;; some shifts and an addition. Calculate the remainder by a second
3215 ;;; multiplication and a subtraction. Dead code elimination will
3216 ;;; suppress the latter part if only the quotient is needed. If the type
3217 ;;; of the dividend allows to derive that the quotient will always have
3218 ;;; the same value, emit much simpler code to handle that. (This case
3219 ;;; may be rare but it's easy to detect and the compiler doesn't find
3220 ;;; this optimization on its own.)
3221 (deftransform truncate ((x y) (word (constant-arg word))
3223 :policy (and (> speed compilation-speed)
3225 "convert integer division to multiplication"
3226 (let* ((y (lvar-value y))
3227 (x-type (lvar-type x))
3228 (max-x (or (and (numeric-type-p x-type)
3229 (numeric-type-high x-type))
3230 most-positive-word)))
3231 ;; Division by zero, one or powers of two is handled elsewhere.
3232 (when (zerop (logand y (1- y)))
3233 (give-up-ir1-transform))
3234 `(let* ((quot ,(gen-unsigned-div-by-constant-expr y max-x))
3235 (rem (ldb (byte #.sb!vm:n-word-bits 0)
3236 (- x (* quot ,y)))))
3237 (values quot rem))))
3239 ;;;; arithmetic and logical identity operation elimination
3241 ;;; Flush calls to various arith functions that convert to the
3242 ;;; identity function or a constant.
3243 (macrolet ((def (name identity result)
3244 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3245 "fold identity operations"
3252 (def logxor -1 (lognot x))
3255 (deftransform logand ((x y) (* (constant-arg t)) *)
3256 "fold identity operation"
3257 (let ((y (lvar-value y)))
3258 (unless (and (plusp y)
3259 (= y (1- (ash 1 (integer-length y)))))
3260 (give-up-ir1-transform))
3261 (unless (csubtypep (lvar-type x)
3262 (specifier-type `(integer 0 ,y)))
3263 (give-up-ir1-transform))
3266 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3267 "fold identity operation"
3268 (let ((size (lvar-value size)))
3269 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3270 (give-up-ir1-transform))
3273 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3274 ;;; (* 0 -4.0) is -0.0.
3275 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3276 "convert (- 0 x) to negate"
3278 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3279 "convert (* x 0) to 0"
3282 ;;; Return T if in an arithmetic op including lvars X and Y, the
3283 ;;; result type is not affected by the type of X. That is, Y is at
3284 ;;; least as contagious as X.
3286 (defun not-more-contagious (x y)
3287 (declare (type continuation x y))
3288 (let ((x (lvar-type x))
3290 (values (type= (numeric-contagion x y)
3291 (numeric-contagion y y)))))
3292 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3293 ;;; XXX needs more work as valid transforms are missed; some cases are
3294 ;;; specific to particular transform functions so the use of this
3295 ;;; function may need a re-think.
3296 (defun not-more-contagious (x y)
3297 (declare (type lvar x y))
3298 (flet ((simple-numeric-type (num)
3299 (and (numeric-type-p num)
3300 ;; Return non-NIL if NUM is integer, rational, or a float
3301 ;; of some type (but not FLOAT)
3302 (case (numeric-type-class num)
3306 (numeric-type-format num))
3309 (let ((x (lvar-type x))
3311 (if (and (simple-numeric-type x)
3312 (simple-numeric-type y))
3313 (values (type= (numeric-contagion x y)
3314 (numeric-contagion y y)))))))
3316 (def!type exact-number ()
3317 '(or rational (complex rational)))
3321 ;;; Only safely applicable for exact numbers. For floating-point
3322 ;;; x, one would have to first show that neither x or y are signed
3323 ;;; 0s, and that x isn't an SNaN.
3324 (deftransform + ((x y) (exact-number (constant-arg (eql 0))) *)
3329 (deftransform - ((x y) (exact-number (constant-arg (eql 0))) *)
3333 ;;; Fold (OP x +/-1)
3335 ;;; %NEGATE might not always signal correctly.
3337 ((def (name result minus-result)
3338 `(deftransform ,name ((x y)
3339 (exact-number (constant-arg (member 1 -1))))
3340 "fold identity operations"
3341 (if (minusp (lvar-value y)) ',minus-result ',result))))
3342 (def * x (%negate x))
3343 (def / x (%negate x))
3344 (def expt x (/ 1 x)))
3346 ;;; Fold (expt x n) into multiplications for small integral values of
3347 ;;; N; convert (expt x 1/2) to sqrt.
3348 (deftransform expt ((x y) (t (constant-arg real)) *)
3349 "recode as multiplication or sqrt"
3350 (let ((val (lvar-value y)))
3351 ;; If Y would cause the result to be promoted to the same type as
3352 ;; Y, we give up. If not, then the result will be the same type
3353 ;; as X, so we can replace the exponentiation with simple
3354 ;; multiplication and division for small integral powers.
3355 (unless (not-more-contagious y x)
3356 (give-up-ir1-transform))
3358 (let ((x-type (lvar-type x)))
3359 (cond ((csubtypep x-type (specifier-type '(or rational
3360 (complex rational))))
3362 ((csubtypep x-type (specifier-type 'real))
3366 ((csubtypep x-type (specifier-type 'complex))
3367 ;; both parts are float
3369 (t (give-up-ir1-transform)))))
3370 ((= val 2) '(* x x))
3371 ((= val -2) '(/ (* x x)))
3372 ((= val 3) '(* x x x))
3373 ((= val -3) '(/ (* x x x)))
3374 ((= val 1/2) '(sqrt x))
3375 ((= val -1/2) '(/ (sqrt x)))
3376 (t (give-up-ir1-transform)))))
3378 (deftransform expt ((x y) ((constant-arg (member -1 -1.0 -1.0d0)) integer) *)
3379 "recode as an ODDP check"
3380 (let ((val (lvar-value x)))
3382 '(- 1 (* 2 (logand 1 y)))
3387 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3388 ;;; transformations?
3389 ;;; Perhaps we should have to prove that the denominator is nonzero before
3390 ;;; doing them? -- WHN 19990917
3391 (macrolet ((def (name)
3392 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3399 (macrolet ((def (name)
3400 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3409 (macrolet ((def (name &optional float)
3410 (let ((x (if float '(float x) 'x)))
3411 `(deftransform ,name ((x y) (integer (constant-arg (member 1 -1)))
3413 "fold division by 1"
3414 `(values ,(if (minusp (lvar-value y))
3427 ;;;; character operations
3429 (deftransform char-equal ((a b) (base-char base-char))
3431 '(let* ((ac (char-code a))
3433 (sum (logxor ac bc)))
3435 (when (eql sum #x20)
3436 (let ((sum (+ ac bc)))
3437 (or (and (> sum 161) (< sum 213))
3438 (and (> sum 415) (< sum 461))
3439 (and (> sum 463) (< sum 477))))))))
3441 (deftransform char-upcase ((x) (base-char))
3443 '(let ((n-code (char-code x)))
3444 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3445 (< n-code #o173)) ; Octal 172 is #\z.
3446 (and (> n-code #o337)
3448 (and (> n-code #o367)
3450 (code-char (logxor #x20 n-code))
3453 (deftransform char-downcase ((x) (base-char))
3455 '(let ((n-code (char-code x)))
3456 (if (or (and (> n-code 64) ; 65 is #\A.
3457 (< n-code 91)) ; 90 is #\Z.
3462 (code-char (logxor #x20 n-code))
3465 ;;;; equality predicate transforms
3467 ;;; Return true if X and Y are lvars whose only use is a
3468 ;;; reference to the same leaf, and the value of the leaf cannot
3470 (defun same-leaf-ref-p (x y)
3471 (declare (type lvar x y))
3472 (let ((x-use (principal-lvar-use x))
3473 (y-use (principal-lvar-use y)))
3476 (eq (ref-leaf x-use) (ref-leaf y-use))
3477 (constant-reference-p x-use))))
3479 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3480 ;;; if there is no intersection between the types of the arguments,
3481 ;;; then the result is definitely false.
3482 (deftransform simple-equality-transform ((x y) * *
3485 ((same-leaf-ref-p x y) t)
3486 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3488 (t (give-up-ir1-transform))))
3491 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3495 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3496 ;;; try to convert to a type-specific predicate or EQ:
3497 ;;; -- If both args are characters, convert to CHAR=. This is better than
3498 ;;; just converting to EQ, since CHAR= may have special compilation
3499 ;;; strategies for non-standard representations, etc.
3500 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3501 ;;; constant and if so, put X second. Doing this results in better
3502 ;;; code from the backend, since the backend assumes that any constant
3503 ;;; argument comes second.
3504 ;;; -- If either arg is definitely not a number or a fixnum, then we
3505 ;;; can compare with EQ.
3506 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3507 ;;; is constant then we put it second. If X is a subtype of Y, we put
3508 ;;; it second. These rules make it easier for the back end to match
3509 ;;; these interesting cases.
3510 (deftransform eql ((x y) * * :node node)
3511 "convert to simpler equality predicate"
3512 (let ((x-type (lvar-type x))
3513 (y-type (lvar-type y))
3514 (char-type (specifier-type 'character)))
3515 (flet ((fixnum-type-p (type)
3516 (csubtypep type (specifier-type 'fixnum))))
3518 ((same-leaf-ref-p x y) t)
3519 ((not (types-equal-or-intersect x-type y-type))
3521 ((and (csubtypep x-type char-type)
3522 (csubtypep y-type char-type))
3524 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3525 (commutative-arg-swap node))
3526 ((or (eq-comparable-type-p x-type) (eq-comparable-type-p y-type))
3528 ((and (not (constant-lvar-p y))
3529 (or (constant-lvar-p x)
3530 (and (csubtypep x-type y-type)
3531 (not (csubtypep y-type x-type)))))
3534 (give-up-ir1-transform))))))
3536 ;;; similarly to the EQL transform above, we attempt to constant-fold
3537 ;;; or convert to a simpler predicate: mostly we have to be careful
3538 ;;; with strings and bit-vectors.
3539 (deftransform equal ((x y) * *)
3540 "convert to simpler equality predicate"
3541 (let ((x-type (lvar-type x))
3542 (y-type (lvar-type y))
3543 (string-type (specifier-type 'string))
3544 (bit-vector-type (specifier-type 'bit-vector)))
3546 ((same-leaf-ref-p x y) t)
3547 ((and (csubtypep x-type string-type)
3548 (csubtypep y-type string-type))
3550 ((and (csubtypep x-type bit-vector-type)
3551 (csubtypep y-type bit-vector-type))
3552 '(bit-vector-= x y))
3553 ;; if at least one is not a string, and at least one is not a
3554 ;; bit-vector, then we can reason from types.
3555 ((and (not (and (types-equal-or-intersect x-type string-type)
3556 (types-equal-or-intersect y-type string-type)))
3557 (not (and (types-equal-or-intersect x-type bit-vector-type)
3558 (types-equal-or-intersect y-type bit-vector-type)))
3559 (not (types-equal-or-intersect x-type y-type)))
3561 (t (give-up-ir1-transform)))))
3563 ;;; Convert to EQL if both args are rational and complexp is specified
3564 ;;; and the same for both.
3565 (deftransform = ((x y) (number number) *)
3567 (let ((x-type (lvar-type x))
3568 (y-type (lvar-type y)))
3569 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3570 (csubtypep y-type (specifier-type 'float)))
3571 (and (csubtypep x-type (specifier-type '(complex float)))
3572 (csubtypep y-type (specifier-type '(complex float))))
3573 #!+complex-float-vops
3574 (and (csubtypep x-type (specifier-type '(or single-float (complex single-float))))
3575 (csubtypep y-type (specifier-type '(or single-float (complex single-float)))))
3576 #!+complex-float-vops
3577 (and (csubtypep x-type (specifier-type '(or double-float (complex double-float))))
3578 (csubtypep y-type (specifier-type '(or double-float (complex double-float))))))
3579 ;; They are both floats. Leave as = so that -0.0 is
3580 ;; handled correctly.
3581 (give-up-ir1-transform))
3582 ((or (and (csubtypep x-type (specifier-type 'rational))
3583 (csubtypep y-type (specifier-type 'rational)))
3584 (and (csubtypep x-type
3585 (specifier-type '(complex rational)))
3587 (specifier-type '(complex rational)))))
3588 ;; They are both rationals and complexp is the same.
3592 (give-up-ir1-transform
3593 "The operands might not be the same type.")))))
3595 (defun maybe-float-lvar-p (lvar)
3596 (neq *empty-type* (type-intersection (specifier-type 'float)
3599 (flet ((maybe-invert (node op inverted x y)
3600 ;; Don't invert if either argument can be a float (NaNs)
3602 ((or (maybe-float-lvar-p x) (maybe-float-lvar-p y))
3603 (delay-ir1-transform node :constraint)
3604 `(or (,op x y) (= x y)))
3606 `(if (,inverted x y) nil t)))))
3607 (deftransform >= ((x y) (number number) * :node node)
3608 "invert or open code"
3609 (maybe-invert node '> '< x y))
3610 (deftransform <= ((x y) (number number) * :node node)
3611 "invert or open code"
3612 (maybe-invert node '< '> x y)))
3614 ;;; See whether we can statically determine (< X Y) using type
3615 ;;; information. If X's high bound is < Y's low, then X < Y.
3616 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3617 ;;; NIL). If not, at least make sure any constant arg is second.
3618 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3619 `(deftransform ,name ((x y))
3620 "optimize using intervals"
3621 (if (and (same-leaf-ref-p x y)
3622 ;; For non-reflexive functions we don't need
3623 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3624 ;; but with reflexive ones we don't know...
3626 '((and (not (maybe-float-lvar-p x))
3627 (not (maybe-float-lvar-p y))))))
3629 (let ((ix (or (type-approximate-interval (lvar-type x))
3630 (give-up-ir1-transform)))
3631 (iy (or (type-approximate-interval (lvar-type y))
3632 (give-up-ir1-transform))))
3637 ((and (constant-lvar-p x)
3638 (not (constant-lvar-p y)))
3641 (give-up-ir1-transform))))))))
3642 (def = = t (interval-= ix iy) (interval-/= ix iy))
3643 (def /= /= nil (interval-/= ix iy) (interval-= ix iy))
3644 (def < > nil (interval-< ix iy) (interval->= ix iy))
3645 (def > < nil (interval-< iy ix) (interval->= iy ix))
3646 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3647 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3649 (defun ir1-transform-char< (x y first second inverse)
3651 ((same-leaf-ref-p x y) nil)
3652 ;; If we had interval representation of character types, as we
3653 ;; might eventually have to to support 2^21 characters, then here
3654 ;; we could do some compile-time computation as in transforms for
3655 ;; < above. -- CSR, 2003-07-01
3656 ((and (constant-lvar-p first)
3657 (not (constant-lvar-p second)))
3659 (t (give-up-ir1-transform))))
3661 (deftransform char< ((x y) (character character) *)
3662 (ir1-transform-char< x y x y 'char>))
3664 (deftransform char> ((x y) (character character) *)
3665 (ir1-transform-char< y x x y 'char<))
3667 ;;;; converting N-arg comparisons
3669 ;;;; We convert calls to N-arg comparison functions such as < into
3670 ;;;; two-arg calls. This transformation is enabled for all such
3671 ;;;; comparisons in this file. If any of these predicates are not
3672 ;;;; open-coded, then the transformation should be removed at some
3673 ;;;; point to avoid pessimization.
3675 ;;; This function is used for source transformation of N-arg
3676 ;;; comparison functions other than inequality. We deal both with
3677 ;;; converting to two-arg calls and inverting the sense of the test,
3678 ;;; if necessary. If the call has two args, then we pass or return a
3679 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3680 ;;; then we transform to code that returns true. Otherwise, we bind
3681 ;;; all the arguments and expand into a bunch of IFs.
3682 (defun multi-compare (predicate args not-p type &optional force-two-arg-p)
3683 (let ((nargs (length args)))
3684 (cond ((< nargs 1) (values nil t))
3685 ((= nargs 1) `(progn (the ,type ,@args) t))
3688 `(if (,predicate ,(first args) ,(second args)) nil t)
3690 `(,predicate ,(first args) ,(second args))
3693 (do* ((i (1- nargs) (1- i))
3695 (current (gensym) (gensym))
3696 (vars (list current) (cons current vars))
3698 `(if (,predicate ,current ,last)
3700 `(if (,predicate ,current ,last)
3703 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3706 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3707 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3708 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3709 ;;; We cannot do the inversion for >= and <= here, since both
3710 ;;; (< NaN X) and (> NaN X)
3711 ;;; are false, and we don't have type-information available yet. The
3712 ;;; deftransforms for two-argument versions of >= and <= takes care of
3713 ;;; the inversion to > and < when possible.
3714 (define-source-transform <= (&rest args) (multi-compare '<= args nil 'real))
3715 (define-source-transform >= (&rest args) (multi-compare '>= args nil 'real))
3717 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3719 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3721 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3723 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3725 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3728 (define-source-transform char-equal (&rest args)
3729 (multi-compare 'sb!impl::two-arg-char-equal args nil 'character t))
3730 (define-source-transform char-lessp (&rest args)
3731 (multi-compare 'sb!impl::two-arg-char-lessp args nil 'character t))
3732 (define-source-transform char-greaterp (&rest args)
3733 (multi-compare 'sb!impl::two-arg-char-greaterp args nil 'character t))
3734 (define-source-transform char-not-greaterp (&rest args)
3735 (multi-compare 'sb!impl::two-arg-char-greaterp args t 'character t))
3736 (define-source-transform char-not-lessp (&rest args)
3737 (multi-compare 'sb!impl::two-arg-char-lessp args t 'character t))
3739 ;;; This function does source transformation of N-arg inequality
3740 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3741 ;;; arg cases. If there are more than two args, then we expand into
3742 ;;; the appropriate n^2 comparisons only when speed is important.
3743 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3744 (defun multi-not-equal (predicate args type)
3745 (let ((nargs (length args)))
3746 (cond ((< nargs 1) (values nil t))
3747 ((= nargs 1) `(progn (the ,type ,@args) t))
3749 `(if (,predicate ,(first args) ,(second args)) nil t))
3750 ((not (policy *lexenv*
3751 (and (>= speed space)
3752 (>= speed compilation-speed))))
3755 (let ((vars (make-gensym-list nargs)))
3756 (do ((var vars next)
3757 (next (cdr vars) (cdr next))
3760 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3762 (let ((v1 (first var)))
3764 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3766 (define-source-transform /= (&rest args)
3767 (multi-not-equal '= args 'number))
3768 (define-source-transform char/= (&rest args)
3769 (multi-not-equal 'char= args 'character))
3770 (define-source-transform char-not-equal (&rest args)
3771 (multi-not-equal 'char-equal args 'character))
3773 ;;; Expand MAX and MIN into the obvious comparisons.
3774 (define-source-transform max (arg0 &rest rest)
3775 (once-only ((arg0 arg0))
3777 `(values (the real ,arg0))
3778 `(let ((maxrest (max ,@rest)))
3779 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3780 (define-source-transform min (arg0 &rest rest)
3781 (once-only ((arg0 arg0))
3783 `(values (the real ,arg0))
3784 `(let ((minrest (min ,@rest)))
3785 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3787 ;;;; converting N-arg arithmetic functions
3789 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3790 ;;;; versions, and degenerate cases are flushed.
3792 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3793 (declaim (ftype (sfunction (symbol t list t) list) associate-args))
3794 (defun associate-args (fun first-arg more-args identity)
3795 (let ((next (rest more-args))
3796 (arg (first more-args)))
3798 `(,fun ,first-arg ,(if arg arg identity))
3799 (associate-args fun `(,fun ,first-arg ,arg) next identity))))
3801 ;;; Reduce constants in ARGS list.
3802 (declaim (ftype (sfunction (symbol list t symbol) list) reduce-constants))
3803 (defun reduce-constants (fun args identity one-arg-result-type)
3804 (let ((one-arg-constant-p (ecase one-arg-result-type
3806 (integer #'integerp)))
3807 (reduced-value identity)
3809 (collect ((not-constants))
3811 (if (funcall one-arg-constant-p arg)
3812 (setf reduced-value (funcall fun reduced-value arg)
3814 (not-constants arg)))
3815 ;; It is tempting to drop constants reduced to identity here,
3816 ;; but if X is SNaN in (* X 1), we cannot drop the 1.
3819 `(,reduced-value ,@(not-constants))
3821 `(,reduced-value)))))
3823 ;;; Do source transformations for transitive functions such as +.
3824 ;;; One-arg cases are replaced with the arg and zero arg cases with
3825 ;;; the identity. ONE-ARG-RESULT-TYPE is the type to ensure (with THE)
3826 ;;; that the argument in one-argument calls is.
3827 (declaim (ftype (function (symbol list t &optional symbol list)
3828 (values t &optional (member nil t)))
3829 source-transform-transitive))
3830 (defun source-transform-transitive (fun args identity
3831 &optional (one-arg-result-type 'number)
3832 (one-arg-prefixes '(values)))
3835 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
3837 (t (let ((reduced-args (reduce-constants fun args identity one-arg-result-type)))
3838 (associate-args fun (first reduced-args) (rest reduced-args) identity)))))
3840 (define-source-transform + (&rest args)
3841 (source-transform-transitive '+ args 0))
3842 (define-source-transform * (&rest args)
3843 (source-transform-transitive '* args 1))
3844 (define-source-transform logior (&rest args)
3845 (source-transform-transitive 'logior args 0 'integer))
3846 (define-source-transform logxor (&rest args)
3847 (source-transform-transitive 'logxor args 0 'integer))
3848 (define-source-transform logand (&rest args)
3849 (source-transform-transitive 'logand args -1 'integer))
3850 (define-source-transform logeqv (&rest args)
3851 (source-transform-transitive 'logeqv args -1 'integer))
3852 (define-source-transform gcd (&rest args)
3853 (source-transform-transitive 'gcd args 0 'integer '(abs)))
3854 (define-source-transform lcm (&rest args)
3855 (source-transform-transitive 'lcm args 1 'integer '(abs)))
3857 ;;; Do source transformations for intransitive n-arg functions such as
3858 ;;; /. With one arg, we form the inverse. With two args we pass.
3859 ;;; Otherwise we associate into two-arg calls.
3860 (declaim (ftype (function (symbol symbol list t list &optional symbol)
3861 (values list &optional (member nil t)))
3862 source-transform-intransitive))
3863 (defun source-transform-intransitive (fun fun* args identity one-arg-prefixes
3864 &optional (one-arg-result-type 'number))
3866 ((0 2) (values nil t))
3867 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
3868 (t (let ((reduced-args
3869 (reduce-constants fun* (rest args) identity one-arg-result-type)))
3870 (associate-args fun (first args) reduced-args identity)))))
3872 (define-source-transform - (&rest args)
3873 (source-transform-intransitive '- '+ args 0 '(%negate)))
3874 (define-source-transform / (&rest args)
3875 (source-transform-intransitive '/ '* args 1 '(/ 1)))
3877 ;;;; transforming APPLY
3879 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3880 ;;; only needs to understand one kind of variable-argument call. It is
3881 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3882 (define-source-transform apply (fun arg &rest more-args)
3883 (let ((args (cons arg more-args)))
3884 `(multiple-value-call ,fun
3885 ,@(mapcar (lambda (x) `(values ,x)) (butlast args))
3886 (values-list ,(car (last args))))))
3888 ;;;; transforming references to &REST argument
3890 ;;; We add magical &MORE arguments to all functions with &REST. If ARG names
3891 ;;; the &REST argument, this returns the lambda-vars for the context and
3893 (defun possible-rest-arg-context (arg)
3895 (let* ((var (lexenv-find arg vars))
3896 (info (when (lambda-var-p var)
3897 (lambda-var-arg-info var))))
3899 (eq :rest (arg-info-kind info))
3900 (consp (arg-info-default info)))
3901 (values-list (arg-info-default info))))))
3903 (defun mark-more-context-used (rest-var)
3904 (let ((info (lambda-var-arg-info rest-var)))
3905 (aver (eq :rest (arg-info-kind info)))
3906 (destructuring-bind (context count &optional used) (arg-info-default info)
3908 (setf (arg-info-default info) (list context count t))))))
3910 (defun mark-more-context-invalid (rest-var)
3911 (let ((info (lambda-var-arg-info rest-var)))
3912 (aver (eq :rest (arg-info-kind info)))
3913 (setf (arg-info-default info) t)))
3915 ;;; This determines of we the REF to a &REST variable is headed towards
3916 ;;; parts unknown, or if we can really use the context.
3917 (defun rest-var-more-context-ok (lvar)
3918 (let* ((use (lvar-use lvar))
3919 (var (when (ref-p use) (ref-leaf use)))
3920 (home (when (lambda-var-p var) (lambda-var-home var)))
3921 (info (when (lambda-var-p var) (lambda-var-arg-info var)))
3922 (restp (when info (eq :rest (arg-info-kind info)))))
3923 (flet ((ref-good-for-more-context-p (ref)
3924 (let ((dest (principal-lvar-end (node-lvar ref))))
3925 (and (combination-p dest)
3926 ;; If the destination is to anything but these, we're going to
3927 ;; actually need the rest list -- and since other operations
3928 ;; might modify the list destructively, the using the context
3929 ;; isn't good anywhere else either.
3930 (lvar-fun-is (combination-fun dest)
3931 '(%rest-values %rest-ref %rest-length
3932 %rest-null %rest-true))
3933 ;; If the home lambda is different and isn't DX, it might
3934 ;; escape -- in which case using the more context isn't safe.
3935 (let ((clambda (node-home-lambda dest)))
3936 (or (eq home clambda)
3937 (leaf-dynamic-extent clambda)))))))
3938 (let ((ok (and restp
3939 (consp (arg-info-default info))
3940 (not (lambda-var-specvar var))
3941 (not (lambda-var-sets var))
3942 (every #'ref-good-for-more-context-p (lambda-var-refs var)))))
3944 (mark-more-context-used var)
3946 (mark-more-context-invalid var)))
3949 ;;; VALUES-LIST -> %REST-VALUES
3950 (define-source-transform values-list (list)
3951 (multiple-value-bind (context count) (possible-rest-arg-context list)
3953 `(%rest-values ,list ,context ,count)
3956 ;;; NTH -> %REST-REF
3957 (define-source-transform nth (n list)
3958 (multiple-value-bind (context count) (possible-rest-arg-context list)
3960 `(%rest-ref ,n ,list ,context ,count)
3961 `(car (nthcdr ,n ,list)))))
3963 (define-source-transform elt (seq n)
3964 (if (policy *lexenv* (= safety 3))
3966 (multiple-value-bind (context count) (possible-rest-arg-context seq)
3968 `(%rest-ref ,n ,seq ,context ,count)
3971 ;;; CAxR -> %REST-REF
3972 (defun source-transform-car (list nth)
3973 (multiple-value-bind (context count) (possible-rest-arg-context list)
3975 `(%rest-ref ,nth ,list ,context ,count)
3978 (define-source-transform car (list)
3979 (source-transform-car list 0))
3981 (define-source-transform cadr (list)
3982 (or (source-transform-car list 1)
3983 `(car (cdr ,list))))
3985 (define-source-transform caddr (list)
3986 (or (source-transform-car list 2)
3987 `(car (cdr (cdr ,list)))))
3989 (define-source-transform cadddr (list)
3990 (or (source-transform-car list 3)
3991 `(car (cdr (cdr (cdr ,list))))))
3993 ;;; LENGTH -> %REST-LENGTH
3994 (defun source-transform-length (list)
3995 (multiple-value-bind (context count) (possible-rest-arg-context list)
3997 `(%rest-length ,list ,context ,count)
3999 (define-source-transform length (list) (source-transform-length list))
4000 (define-source-transform list-length (list) (source-transform-length list))
4002 ;;; ENDP, NULL and NOT -> %REST-NULL
4004 ;;; Outside &REST convert into an IF so that IF optimizations will eliminate
4005 ;;; redundant negations.
4006 (defun source-transform-null (x op)
4007 (multiple-value-bind (context count) (possible-rest-arg-context x)
4009 `(%rest-null ',op ,x ,context ,count))
4011 `(if (the list ,x) nil t))
4014 (define-source-transform not (x) (source-transform-null x 'not))
4015 (define-source-transform null (x) (source-transform-null x 'null))
4016 (define-source-transform endp (x) (source-transform-null x 'endp))
4018 (deftransform %rest-values ((list context count))
4019 (if (rest-var-more-context-ok list)
4020 `(%more-arg-values context 0 count)
4021 `(values-list list)))
4023 (deftransform %rest-ref ((n list context count))
4024 (cond ((rest-var-more-context-ok list)
4025 `(and (< (the index n) count)
4026 (%more-arg context n)))
4027 ((and (constant-lvar-p n) (zerop (lvar-value n)))
4032 (deftransform %rest-length ((list context count))
4033 (if (rest-var-more-context-ok list)
4037 (deftransform %rest-null ((op list context count))
4038 (aver (constant-lvar-p op))
4039 (if (rest-var-more-context-ok list)
4041 `(,(lvar-value op) list)))
4043 (deftransform %rest-true ((list context count))
4044 (if (rest-var-more-context-ok list)
4045 `(not (eql 0 count))
4048 ;;;; transforming FORMAT
4050 ;;;; If the control string is a compile-time constant, then replace it
4051 ;;;; with a use of the FORMATTER macro so that the control string is
4052 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
4053 ;;;; or T and the control string is a function (i.e. FORMATTER), then
4054 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
4056 ;;; for compile-time argument count checking.
4058 ;;; FIXME II: In some cases, type information could be correlated; for
4059 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
4060 ;;; of a corresponding argument is known and does not intersect the
4061 ;;; list type, a warning could be signalled.
4062 (defun check-format-args (string args fun)
4063 (declare (type string string))
4064 (unless (typep string 'simple-string)
4065 (setq string (coerce string 'simple-string)))
4066 (multiple-value-bind (min max)
4067 (handler-case (sb!format:%compiler-walk-format-string string args)
4068 (sb!format:format-error (c)
4069 (compiler-warn "~A" c)))
4071 (let ((nargs (length args)))
4074 (warn 'format-too-few-args-warning
4076 "Too few arguments (~D) to ~S ~S: requires at least ~D."
4077 :format-arguments (list nargs fun string min)))
4079 (warn 'format-too-many-args-warning
4081 "Too many arguments (~D) to ~S ~S: uses at most ~D."
4082 :format-arguments (list nargs fun string max))))))))
4084 (defoptimizer (format optimizer) ((dest control &rest args))
4085 (when (constant-lvar-p control)
4086 (let ((x (lvar-value control)))
4088 (check-format-args x args 'format)))))
4090 ;;; We disable this transform in the cross-compiler to save memory in
4091 ;;; the target image; most of the uses of FORMAT in the compiler are for
4092 ;;; error messages, and those don't need to be particularly fast.
4094 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
4095 :policy (>= speed space))
4096 (unless (constant-lvar-p control)
4097 (give-up-ir1-transform "The control string is not a constant."))
4098 (let ((arg-names (make-gensym-list (length args))))
4099 `(lambda (dest control ,@arg-names)
4100 (declare (ignore control))
4101 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
4103 (deftransform format ((stream control &rest args) (stream function &rest t))
4104 (let ((arg-names (make-gensym-list (length args))))
4105 `(lambda (stream control ,@arg-names)
4106 (funcall control stream ,@arg-names)
4109 (deftransform format ((tee control &rest args) ((member t) function &rest t))
4110 (let ((arg-names (make-gensym-list (length args))))
4111 `(lambda (tee control ,@arg-names)
4112 (declare (ignore tee))
4113 (funcall control *standard-output* ,@arg-names)
4116 (deftransform pathname ((pathspec) (pathname) *)
4119 (deftransform pathname ((pathspec) (string) *)
4120 '(values (parse-namestring pathspec)))
4124 `(defoptimizer (,name optimizer) ((control &rest args))
4125 (when (constant-lvar-p control)
4126 (let ((x (lvar-value control)))
4128 (check-format-args x args ',name)))))))
4131 #+sb-xc-host ; Only we should be using these
4134 (def compiler-error)
4136 (def compiler-style-warn)
4137 (def compiler-notify)
4138 (def maybe-compiler-notify)
4141 (defoptimizer (cerror optimizer) ((report control &rest args))
4142 (when (and (constant-lvar-p control)
4143 (constant-lvar-p report))
4144 (let ((x (lvar-value control))
4145 (y (lvar-value report)))
4146 (when (and (stringp x) (stringp y))
4147 (multiple-value-bind (min1 max1)
4149 (sb!format:%compiler-walk-format-string x args)
4150 (sb!format:format-error (c)
4151 (compiler-warn "~A" c)))
4153 (multiple-value-bind (min2 max2)
4155 (sb!format:%compiler-walk-format-string y args)
4156 (sb!format:format-error (c)
4157 (compiler-warn "~A" c)))
4159 (let ((nargs (length args)))
4161 ((< nargs (min min1 min2))
4162 (warn 'format-too-few-args-warning
4164 "Too few arguments (~D) to ~S ~S ~S: ~
4165 requires at least ~D."
4167 (list nargs 'cerror y x (min min1 min2))))
4168 ((> nargs (max max1 max2))
4169 (warn 'format-too-many-args-warning
4171 "Too many arguments (~D) to ~S ~S ~S: ~
4174 (list nargs 'cerror y x (max max1 max2))))))))))))))
4176 (defoptimizer (coerce derive-type) ((value type) node)
4178 ((constant-lvar-p type)
4179 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
4180 ;; but dealing with the niggle that complex canonicalization gets
4181 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
4183 (let* ((specifier (lvar-value type))
4184 (result-typeoid (careful-specifier-type specifier)))
4186 ((null result-typeoid) nil)
4187 ((csubtypep result-typeoid (specifier-type 'number))
4188 ;; the difficult case: we have to cope with ANSI 12.1.5.3
4189 ;; Rule of Canonical Representation for Complex Rationals,
4190 ;; which is a truly nasty delivery to field.
4192 ((csubtypep result-typeoid (specifier-type 'real))
4193 ;; cleverness required here: it would be nice to deduce
4194 ;; that something of type (INTEGER 2 3) coerced to type
4195 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
4196 ;; FLOAT gets its own clause because it's implemented as
4197 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
4200 ((and (numeric-type-p result-typeoid)
4201 (eq (numeric-type-complexp result-typeoid) :real))
4202 ;; FIXME: is this clause (a) necessary or (b) useful?
4204 ((or (csubtypep result-typeoid
4205 (specifier-type '(complex single-float)))
4206 (csubtypep result-typeoid
4207 (specifier-type '(complex double-float)))
4209 (csubtypep result-typeoid
4210 (specifier-type '(complex long-float))))
4211 ;; float complex types are never canonicalized.
4214 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
4215 ;; probably just a COMPLEX or equivalent. So, in that
4216 ;; case, we will return a complex or an object of the
4217 ;; provided type if it's rational:
4218 (type-union result-typeoid
4219 (type-intersection (lvar-type value)
4220 (specifier-type 'rational))))))
4221 ((and (policy node (zerop safety))
4222 (csubtypep result-typeoid (specifier-type '(array * (*)))))
4223 ;; At zero safety the deftransform for COERCE can elide dimension
4224 ;; checks for the things like (COERCE X '(SIMPLE-VECTOR 5)) -- so we
4225 ;; need to simplify the type to drop the dimension information.
4226 (let ((vtype (simplify-vector-type result-typeoid)))
4228 (specifier-type vtype)
4233 ;; OK, the result-type argument isn't constant. However, there
4234 ;; are common uses where we can still do better than just
4235 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
4236 ;; where Y is of a known type. See messages on cmucl-imp
4237 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
4238 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
4239 ;; the basis that it's unlikely that other uses are both
4240 ;; time-critical and get to this branch of the COND (non-constant
4241 ;; second argument to COERCE). -- CSR, 2002-12-16
4242 (let ((value-type (lvar-type value))
4243 (type-type (lvar-type type)))
4245 ((good-cons-type-p (cons-type)
4246 ;; Make sure the cons-type we're looking at is something
4247 ;; we're prepared to handle which is basically something
4248 ;; that array-element-type can return.
4249 (or (and (member-type-p cons-type)
4250 (eql 1 (member-type-size cons-type))
4251 (null (first (member-type-members cons-type))))
4252 (let ((car-type (cons-type-car-type cons-type)))
4253 (and (member-type-p car-type)
4254 (eql 1 (member-type-members car-type))
4255 (let ((elt (first (member-type-members car-type))))
4259 (numberp (first elt)))))
4260 (good-cons-type-p (cons-type-cdr-type cons-type))))))
4261 (unconsify-type (good-cons-type)
4262 ;; Convert the "printed" respresentation of a cons
4263 ;; specifier into a type specifier. That is, the
4264 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
4265 ;; NULL)) is converted to (SIGNED-BYTE 16).
4266 (cond ((or (null good-cons-type)
4267 (eq good-cons-type 'null))
4269 ((and (eq (first good-cons-type) 'cons)
4270 (eq (first (second good-cons-type)) 'member))
4271 `(,(second (second good-cons-type))
4272 ,@(unconsify-type (caddr good-cons-type))))))
4273 (coerceable-p (part)
4274 ;; Can the value be coerced to the given type? Coerce is
4275 ;; complicated, so we don't handle every possible case
4276 ;; here---just the most common and easiest cases:
4278 ;; * Any REAL can be coerced to a FLOAT type.
4279 ;; * Any NUMBER can be coerced to a (COMPLEX
4280 ;; SINGLE/DOUBLE-FLOAT).
4282 ;; FIXME I: we should also be able to deal with characters
4285 ;; FIXME II: I'm not sure that anything is necessary
4286 ;; here, at least while COMPLEX is not a specialized
4287 ;; array element type in the system. Reasoning: if
4288 ;; something cannot be coerced to the requested type, an
4289 ;; error will be raised (and so any downstream compiled
4290 ;; code on the assumption of the returned type is
4291 ;; unreachable). If something can, then it will be of
4292 ;; the requested type, because (by assumption) COMPLEX
4293 ;; (and other difficult types like (COMPLEX INTEGER)
4294 ;; aren't specialized types.
4295 (let ((coerced-type (careful-specifier-type part)))
4297 (or (and (csubtypep coerced-type (specifier-type 'float))
4298 (csubtypep value-type (specifier-type 'real)))
4299 (and (csubtypep coerced-type
4300 (specifier-type `(or (complex single-float)
4301 (complex double-float))))
4302 (csubtypep value-type (specifier-type 'number)))))))
4303 (process-types (type)
4304 ;; FIXME: This needs some work because we should be able
4305 ;; to derive the resulting type better than just the
4306 ;; type arg of coerce. That is, if X is (INTEGER 10
4307 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
4308 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
4310 (cond ((member-type-p type)
4313 (mapc-member-type-members
4315 (if (coerceable-p member)
4316 (push member members)
4317 (return-from punt *universal-type*)))
4319 (specifier-type `(or ,@members)))))
4320 ((and (cons-type-p type)
4321 (good-cons-type-p type))
4322 (let ((c-type (unconsify-type (type-specifier type))))
4323 (if (coerceable-p c-type)
4324 (specifier-type c-type)
4327 *universal-type*))))
4328 (cond ((union-type-p type-type)
4329 (apply #'type-union (mapcar #'process-types
4330 (union-type-types type-type))))
4331 ((or (member-type-p type-type)
4332 (cons-type-p type-type))
4333 (process-types type-type))
4335 *universal-type*)))))))
4337 (defoptimizer (compile derive-type) ((nameoid function))
4338 (when (csubtypep (lvar-type nameoid)
4339 (specifier-type 'null))
4340 (values-specifier-type '(values function boolean boolean))))
4342 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
4343 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
4344 ;;; optimizer, above).
4345 (defoptimizer (array-element-type derive-type) ((array))
4346 (let ((array-type (lvar-type array)))
4347 (labels ((consify (list)
4350 `(cons (eql ,(car list)) ,(consify (rest list)))))
4351 (get-element-type (a)
4353 (type-specifier (array-type-specialized-element-type a))))
4354 (cond ((eq element-type '*)
4355 (specifier-type 'type-specifier))
4356 ((symbolp element-type)
4357 (make-member-type :members (list element-type)))
4358 ((consp element-type)
4359 (specifier-type (consify element-type)))
4361 (error "can't understand type ~S~%" element-type))))))
4362 (labels ((recurse (type)
4363 (cond ((array-type-p type)
4364 (get-element-type type))
4365 ((union-type-p type)
4367 (mapcar #'recurse (union-type-types type))))
4369 *universal-type*))))
4370 (recurse array-type)))))
4372 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
4373 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4374 ;; isn't really related to the CMU CL code, since instead of trying
4375 ;; to generalize the CMU CL code to allow START and END values, this
4376 ;; code has been written from scratch following Chapter 7 of
4377 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4378 `(macrolet ((%index (x) `(truly-the index ,x))
4379 (%parent (i) `(ash ,i -1))
4380 (%left (i) `(%index (ash ,i 1)))
4381 (%right (i) `(%index (1+ (ash ,i 1))))
4384 (left (%left i) (%left i)))
4385 ((> left current-heap-size))
4386 (declare (type index i left))
4387 (let* ((i-elt (%elt i))
4388 (i-key (funcall keyfun i-elt))
4389 (left-elt (%elt left))
4390 (left-key (funcall keyfun left-elt)))
4391 (multiple-value-bind (large large-elt large-key)
4392 (if (funcall ,',predicate i-key left-key)
4393 (values left left-elt left-key)
4394 (values i i-elt i-key))
4395 (let ((right (%right i)))
4396 (multiple-value-bind (largest largest-elt)
4397 (if (> right current-heap-size)
4398 (values large large-elt)
4399 (let* ((right-elt (%elt right))
4400 (right-key (funcall keyfun right-elt)))
4401 (if (funcall ,',predicate large-key right-key)
4402 (values right right-elt)
4403 (values large large-elt))))
4404 (cond ((= largest i)
4407 (setf (%elt i) largest-elt
4408 (%elt largest) i-elt
4410 (%sort-vector (keyfun &optional (vtype 'vector))
4411 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4412 ;; trouble getting type inference to
4413 ;; propagate all the way through this
4414 ;; tangled mess of inlining. The TRULY-THE
4415 ;; here works around that. -- WHN
4417 `(aref (truly-the ,',vtype ,',',vector)
4418 (%index (+ (%index ,i) start-1)))))
4419 (let (;; Heaps prefer 1-based addressing.
4420 (start-1 (1- ,',start))
4421 (current-heap-size (- ,',end ,',start))
4423 (declare (type (integer -1 #.(1- sb!xc:most-positive-fixnum))
4425 (declare (type index current-heap-size))
4426 (declare (type function keyfun))
4427 (loop for i of-type index
4428 from (ash current-heap-size -1) downto 1 do
4431 (when (< current-heap-size 2)
4433 (rotatef (%elt 1) (%elt current-heap-size))
4434 (decf current-heap-size)
4436 (if (typep ,vector 'simple-vector)
4437 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4438 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4440 ;; Special-casing the KEY=NIL case lets us avoid some
4442 (%sort-vector #'identity simple-vector)
4443 (%sort-vector ,key simple-vector))
4444 ;; It's hard to anticipate many speed-critical applications for
4445 ;; sorting vector types other than (VECTOR T), so we just lump
4446 ;; them all together in one slow dynamically typed mess.
4448 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4449 (%sort-vector (or ,key #'identity))))))
4451 ;;;; debuggers' little helpers
4453 ;;; for debugging when transforms are behaving mysteriously,
4454 ;;; e.g. when debugging a problem with an ASH transform
4455 ;;; (defun foo (&optional s)
4456 ;;; (sb-c::/report-lvar s "S outside WHEN")
4457 ;;; (when (and (integerp s) (> s 3))
4458 ;;; (sb-c::/report-lvar s "S inside WHEN")
4459 ;;; (let ((bound (ash 1 (1- s))))
4460 ;;; (sb-c::/report-lvar bound "BOUND")
4461 ;;; (let ((x (- bound))
4463 ;;; (sb-c::/report-lvar x "X")
4464 ;;; (sb-c::/report-lvar x "Y"))
4465 ;;; `(integer ,(- bound) ,(1- bound)))))
4466 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4467 ;;; and the function doesn't do anything at all.)
4470 (defknown /report-lvar (t t) null)
4471 (deftransform /report-lvar ((x message) (t t))
4472 (format t "~%/in /REPORT-LVAR~%")
4473 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4474 (when (constant-lvar-p x)
4475 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4476 (format t "/MESSAGE=~S~%" (lvar-value message))
4477 (give-up-ir1-transform "not a real transform"))
4478 (defun /report-lvar (x message)
4479 (declare (ignore x message))))
4482 ;;;; Transforms for internal compiler utilities
4484 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4485 ;;; checking that it's still valid at run-time.
4486 (deftransform policy-quality ((policy quality-name)
4488 (unless (and (constant-lvar-p quality-name)
4489 (policy-quality-name-p (lvar-value quality-name)))
4490 (give-up-ir1-transform))
4491 '(%policy-quality policy quality-name))