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 (return-from derive-append-type (specifier-type 'null)))
169 (let* ((cons-type (specifier-type 'cons))
170 (null-type (specifier-type 'null))
171 (list-type (specifier-type 'list))
172 (last (lvar-type (car (last args)))))
173 ;; Derive the actual return type, assuming that all but the last
174 ;; arguments are LISTs (otherwise, APPEND/NCONC doesn't return).
175 (loop with all-nil = t ; all but the last args are NIL?
176 with some-cons = nil ; some args are conses?
177 for (arg next) on args
178 for lvar-type = (type-approx-intersection2 (lvar-type arg)
181 do (multiple-value-bind (typep definitely)
182 (ctypep nil lvar-type)
183 (cond ((type= lvar-type *empty-type*)
184 ;; type mismatch! insert an inline check that'll cause
185 ;; compile-time warnings.
186 (assert-lvar-type arg list-type
187 (lexenv-policy *lexenv*)))
188 (some-cons) ; we know result's a cons -- nothing to do
189 ((and (not typep) definitely) ; can't be NIL
190 (setf some-cons t)) ; must be a CONS
192 (setf all-nil (csubtypep lvar-type null-type)))))
194 ;; if some of the previous arguments are CONSes so is the result;
195 ;; if all the previous values are NIL, we're a fancy identity;
196 ;; otherwise, could be either
197 (return (cond (some-cons cons-type)
199 (t (type-union last cons-type)))))))
201 (defoptimizer (append derive-type) ((&rest args))
202 (derive-append-type args))
204 (defoptimizer (sb!impl::append2 derive-type) ((&rest args))
205 (derive-append-type args))
207 (defoptimizer (nconc derive-type) ((&rest args))
208 (derive-append-type args))
210 ;;; Translate RPLACx to LET and SETF.
211 (define-source-transform rplaca (x y)
216 (define-source-transform rplacd (x y)
222 (deftransform last ((list &optional n) (t &optional t))
223 (let ((c (constant-lvar-p n)))
225 (and c (eql 1 (lvar-value n))))
227 ((and c (eql 0 (lvar-value n)))
230 (let ((type (lvar-type n)))
231 (cond ((csubtypep type (specifier-type 'fixnum))
232 '(%lastn/fixnum list n))
233 ((csubtypep type (specifier-type 'bignum))
234 '(%lastn/bignum list n))
236 (give-up-ir1-transform "second argument type too vague"))))))))
238 (define-source-transform gethash (&rest args)
240 (2 `(sb!impl::gethash3 ,@args nil))
241 (3 `(sb!impl::gethash3 ,@args))
243 (define-source-transform get (&rest args)
245 (2 `(sb!impl::get2 ,@args))
246 (3 `(sb!impl::get3 ,@args))
249 (defvar *default-nthcdr-open-code-limit* 6)
250 (defvar *extreme-nthcdr-open-code-limit* 20)
252 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
253 "convert NTHCDR to CAxxR"
254 (unless (constant-lvar-p n)
255 (give-up-ir1-transform))
256 (let ((n (lvar-value n)))
258 (if (policy node (and (= speed 3) (= space 0)))
259 *extreme-nthcdr-open-code-limit*
260 *default-nthcdr-open-code-limit*))
261 (give-up-ir1-transform))
266 `(cdr ,(frob (1- n))))))
269 ;;;; arithmetic and numerology
271 (define-source-transform plusp (x) `(> ,x 0))
272 (define-source-transform minusp (x) `(< ,x 0))
273 (define-source-transform zerop (x) `(= ,x 0))
275 (define-source-transform 1+ (x) `(+ ,x 1))
276 (define-source-transform 1- (x) `(- ,x 1))
278 (define-source-transform oddp (x) `(logtest ,x 1))
279 (define-source-transform evenp (x) `(not (logtest ,x 1)))
281 ;;; Note that all the integer division functions are available for
282 ;;; inline expansion.
284 (macrolet ((deffrob (fun)
285 `(define-source-transform ,fun (x &optional (y nil y-p))
292 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
294 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
297 ;;; This used to be a source transform (hence the lack of restrictions
298 ;;; on the argument types), but we make it a regular transform so that
299 ;;; the VM has a chance to see the bare LOGTEST and potentiall choose
300 ;;; to implement it differently. --njf, 06-02-2006
302 ;;; Other transforms may be useful even with direct LOGTEST VOPs; let
303 ;;; them fire (including the type-directed constant folding below), but
304 ;;; disable the inlining rewrite in such cases. -- PK, 2013-05-20
305 (deftransform logtest ((x y) * * :node node)
306 (let ((type (two-arg-derive-type x y
307 #'logand-derive-type-aux
309 (multiple-value-bind (typep definitely)
311 (cond ((and (not typep) definitely)
313 ((type= type (specifier-type '(eql 0)))
315 ((neq :default (combination-implementation-style node))
316 (give-up-ir1-transform))
318 `(not (zerop (logand x y))))))))
320 (deftransform logbitp
321 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
322 (unsigned-byte #.sb!vm:n-word-bits))))
323 `(if (>= index #.sb!vm:n-word-bits)
325 (not (zerop (logand integer (ash 1 index))))))
327 (define-source-transform byte (size position)
328 `(cons ,size ,position))
329 (define-source-transform byte-size (spec) `(car ,spec))
330 (define-source-transform byte-position (spec) `(cdr ,spec))
331 (define-source-transform ldb-test (bytespec integer)
332 `(not (zerop (mask-field ,bytespec ,integer))))
334 ;;; With the ratio and complex accessors, we pick off the "identity"
335 ;;; case, and use a primitive to handle the cell access case.
336 (define-source-transform numerator (num)
337 (once-only ((n-num `(the rational ,num)))
341 (define-source-transform denominator (num)
342 (once-only ((n-num `(the rational ,num)))
344 (%denominator ,n-num)
347 ;;;; interval arithmetic for computing bounds
349 ;;;; This is a set of routines for operating on intervals. It
350 ;;;; implements a simple interval arithmetic package. Although SBCL
351 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
352 ;;;; for two reasons:
354 ;;;; 1. This package is simpler than NUMERIC-TYPE.
356 ;;;; 2. It makes debugging much easier because you can just strip
357 ;;;; out these routines and test them independently of SBCL. (This is a
360 ;;;; One disadvantage is a probable increase in consing because we
361 ;;;; have to create these new interval structures even though
362 ;;;; numeric-type has everything we want to know. Reason 2 wins for
365 ;;; Support operations that mimic real arithmetic comparison
366 ;;; operators, but imposing a total order on the floating points such
367 ;;; that negative zeros are strictly less than positive zeros.
368 (macrolet ((def (name op)
371 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
372 (,op (float-sign x) (float-sign y))
374 (def signed-zero->= >=)
375 (def signed-zero-> >)
376 (def signed-zero-= =)
377 (def signed-zero-< <)
378 (def signed-zero-<= <=))
380 ;;; The basic interval type. It can handle open and closed intervals.
381 ;;; A bound is open if it is a list containing a number, just like
382 ;;; Lisp says. NIL means unbounded.
383 (defstruct (interval (:constructor %make-interval)
387 (defun make-interval (&key low high)
388 (labels ((normalize-bound (val)
391 (float-infinity-p val))
392 ;; Handle infinities.
396 ;; Handle any closed bounds.
399 ;; We have an open bound. Normalize the numeric
400 ;; bound. If the normalized bound is still a number
401 ;; (not nil), keep the bound open. Otherwise, the
402 ;; bound is really unbounded, so drop the openness.
403 (let ((new-val (normalize-bound (first val))))
405 ;; The bound exists, so keep it open still.
408 (error "unknown bound type in MAKE-INTERVAL")))))
409 (%make-interval :low (normalize-bound low)
410 :high (normalize-bound high))))
412 ;;; Given a number X, create a form suitable as a bound for an
413 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
414 #!-sb-fluid (declaim (inline set-bound))
415 (defun set-bound (x open-p)
416 (if (and x open-p) (list x) x))
418 ;;; Apply the function F to a bound X. If X is an open bound and the
419 ;;; function is declared strictly monotonic, then the result will be
420 ;;; open. IF X is NIL, the result is NIL.
421 (defun bound-func (f x strict)
422 (declare (type function f))
425 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
426 ;; With these traps masked, we might get things like infinity
427 ;; or negative infinity returned. Check for this and return
428 ;; NIL to indicate unbounded.
429 (let ((y (funcall f (type-bound-number x))))
431 (float-infinity-p y))
433 (set-bound y (and strict (consp x))))))
434 ;; Some numerical operations will signal SIMPLE-TYPE-ERROR, e.g.
435 ;; in the course of converting a bignum to a float. Default to
437 (simple-type-error ()))))
439 (defun safe-double-coercion-p (x)
440 (or (typep x 'double-float)
441 (<= most-negative-double-float x most-positive-double-float)))
443 (defun safe-single-coercion-p (x)
444 (or (typep x 'single-float)
446 ;; Fix for bug 420, and related issues: during type derivation we often
447 ;; end up deriving types for both
449 ;; (some-op <int> <single>)
451 ;; (some-op (coerce <int> 'single-float) <single>)
453 ;; or other equivalent transformed forms. The problem with this
454 ;; is that on x86 (+ <int> <single>) is on the machine level
457 ;; (coerce (+ (coerce <int> 'double-float)
458 ;; (coerce <single> 'double-float))
461 ;; so if the result of (coerce <int> 'single-float) is not exact, the
462 ;; derived types for the transformed forms will have an empty
463 ;; intersection -- which in turn means that the compiler will conclude
464 ;; that the call never returns, and all hell breaks lose when it *does*
465 ;; return at runtime. (This affects not just +, but other operators are
468 ;; See also: SAFE-CTYPE-FOR-SINGLE-COERCION-P
470 ;; FIXME: If we ever add SSE-support for x86, this conditional needs to
473 (not (typep x `(or (integer * (,most-negative-exactly-single-float-fixnum))
474 (integer (,most-positive-exactly-single-float-fixnum) *))))
475 (<= most-negative-single-float x most-positive-single-float))))
477 ;;; Apply a binary operator OP to two bounds X and Y. The result is
478 ;;; NIL if either is NIL. Otherwise bound is computed and the result
479 ;;; is open if either X or Y is open.
481 ;;; FIXME: only used in this file, not needed in target runtime
483 ;;; ANSI contaigon specifies coercion to floating point if one of the
484 ;;; arguments is floating point. Here we should check to be sure that
485 ;;; the other argument is within the bounds of that floating point
488 (defmacro safely-binop (op x y)
490 ((typep ,x 'double-float)
491 (when (safe-double-coercion-p ,y)
493 ((typep ,y 'double-float)
494 (when (safe-double-coercion-p ,x)
496 ((typep ,x 'single-float)
497 (when (safe-single-coercion-p ,y)
499 ((typep ,y 'single-float)
500 (when (safe-single-coercion-p ,x)
504 (defmacro bound-binop (op x y)
505 (with-unique-names (xb yb res)
507 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
508 (let* ((,xb (type-bound-number ,x))
509 (,yb (type-bound-number ,y))
510 (,res (safely-binop ,op ,xb ,yb)))
512 (and (or (consp ,x) (consp ,y))
513 ;; Open bounds can very easily be messed up
514 ;; by FP rounding, so take care here.
517 ;; Multiplying a greater-than-zero with
518 ;; less than one can round to zero.
519 `(or (not (fp-zero-p ,res))
520 (cond ((and (consp ,x) (fp-zero-p ,xb))
522 ((and (consp ,y) (fp-zero-p ,yb))
525 ;; Dividing a greater-than-zero with
526 ;; greater than one can round to zero.
527 `(or (not (fp-zero-p ,res))
528 (cond ((and (consp ,x) (fp-zero-p ,xb))
530 ((and (consp ,y) (fp-zero-p ,yb))
533 ;; Adding or subtracting greater-than-zero
534 ;; can end up with identity.
535 `(and (not (fp-zero-p ,xb))
536 (not (fp-zero-p ,yb))))))))))))
538 (defun coercion-loses-precision-p (val type)
541 (double-float (subtypep type 'single-float))
542 (rational (subtypep type 'float))
543 (t (bug "Unexpected arguments to bounds coercion: ~S ~S" val type))))
545 (defun coerce-for-bound (val type)
547 (let ((xbound (coerce-for-bound (car val) type)))
548 (if (coercion-loses-precision-p (car val) type)
552 ((subtypep type 'double-float)
553 (if (<= most-negative-double-float val most-positive-double-float)
555 ((or (subtypep type 'single-float) (subtypep type 'float))
556 ;; coerce to float returns a single-float
557 (if (<= most-negative-single-float val most-positive-single-float)
559 (t (coerce val type)))))
561 (defun coerce-and-truncate-floats (val type)
564 (let ((xbound (coerce-for-bound (car val) type)))
565 (if (coercion-loses-precision-p (car val) type)
569 ((subtypep type 'double-float)
570 (if (<= most-negative-double-float val most-positive-double-float)
572 (if (< val most-negative-double-float)
573 most-negative-double-float most-positive-double-float)))
574 ((or (subtypep type 'single-float) (subtypep type 'float))
575 ;; coerce to float returns a single-float
576 (if (<= most-negative-single-float val most-positive-single-float)
578 (if (< val most-negative-single-float)
579 most-negative-single-float most-positive-single-float)))
580 (t (coerce val type))))))
582 ;;; Convert a numeric-type object to an interval object.
583 (defun numeric-type->interval (x)
584 (declare (type numeric-type x))
585 (make-interval :low (numeric-type-low x)
586 :high (numeric-type-high x)))
588 (defun type-approximate-interval (type)
589 (declare (type ctype type))
590 (let ((types (prepare-arg-for-derive-type type))
593 (let ((type (if (member-type-p type)
594 (convert-member-type type)
596 (unless (numeric-type-p type)
597 (return-from type-approximate-interval nil))
598 (let ((interval (numeric-type->interval type)))
601 (interval-approximate-union result interval)
605 (defun copy-interval-limit (limit)
610 (defun copy-interval (x)
611 (declare (type interval x))
612 (make-interval :low (copy-interval-limit (interval-low x))
613 :high (copy-interval-limit (interval-high x))))
615 ;;; Given a point P contained in the interval X, split X into two
616 ;;; intervals at the point P. If CLOSE-LOWER is T, then the left
617 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
618 ;;; contains P. You can specify both to be T or NIL.
619 (defun interval-split (p x &optional close-lower close-upper)
620 (declare (type number p)
622 (list (make-interval :low (copy-interval-limit (interval-low x))
623 :high (if close-lower p (list p)))
624 (make-interval :low (if close-upper (list p) p)
625 :high (copy-interval-limit (interval-high x)))))
627 ;;; Return the closure of the interval. That is, convert open bounds
628 ;;; to closed bounds.
629 (defun interval-closure (x)
630 (declare (type interval x))
631 (make-interval :low (type-bound-number (interval-low x))
632 :high (type-bound-number (interval-high x))))
634 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
635 ;;; '-. Otherwise return NIL.
636 (defun interval-range-info (x &optional (point 0))
637 (declare (type interval x))
638 (let ((lo (interval-low x))
639 (hi (interval-high x)))
640 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
642 ((and hi (signed-zero->= point (type-bound-number hi)))
647 ;;; Test to see whether the interval X is bounded. HOW determines the
648 ;;; test, and should be either ABOVE, BELOW, or BOTH.
649 (defun interval-bounded-p (x how)
650 (declare (type interval x))
657 (and (interval-low x) (interval-high x)))))
659 ;;; See whether the interval X contains the number P, taking into
660 ;;; account that the interval might not be closed.
661 (defun interval-contains-p (p x)
662 (declare (type number p)
664 ;; Does the interval X contain the number P? This would be a lot
665 ;; easier if all intervals were closed!
666 (let ((lo (interval-low x))
667 (hi (interval-high x)))
669 ;; The interval is bounded
670 (if (and (signed-zero-<= (type-bound-number lo) p)
671 (signed-zero-<= p (type-bound-number hi)))
672 ;; P is definitely in the closure of the interval.
673 ;; We just need to check the end points now.
674 (cond ((signed-zero-= p (type-bound-number lo))
676 ((signed-zero-= p (type-bound-number hi))
681 ;; Interval with upper bound
682 (if (signed-zero-< p (type-bound-number hi))
684 (and (numberp hi) (signed-zero-= p hi))))
686 ;; Interval with lower bound
687 (if (signed-zero-> p (type-bound-number lo))
689 (and (numberp lo) (signed-zero-= p lo))))
691 ;; Interval with no bounds
694 ;;; Determine whether two intervals X and Y intersect. Return T if so.
695 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
696 ;;; were closed. Otherwise the intervals are treated as they are.
698 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
699 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
700 ;;; is T, then they do intersect because we use the closure of X = [0,
701 ;;; 1] and Y = [1, 2] to determine intersection.
702 (defun interval-intersect-p (x y &optional closed-intervals-p)
703 (declare (type interval x y))
704 (and (interval-intersection/difference (if closed-intervals-p
707 (if closed-intervals-p
712 ;;; Are the two intervals adjacent? That is, is there a number
713 ;;; between the two intervals that is not an element of either
714 ;;; interval? If so, they are not adjacent. For example [0, 1) and
715 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
716 ;;; between both intervals.
717 (defun interval-adjacent-p (x y)
718 (declare (type interval x y))
719 (flet ((adjacent (lo hi)
720 ;; Check to see whether lo and hi are adjacent. If either is
721 ;; nil, they can't be adjacent.
722 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
723 ;; The bounds are equal. They are adjacent if one of
724 ;; them is closed (a number). If both are open (consp),
725 ;; then there is a number that lies between them.
726 (or (numberp lo) (numberp hi)))))
727 (or (adjacent (interval-low y) (interval-high x))
728 (adjacent (interval-low x) (interval-high y)))))
730 ;;; Compute the intersection and difference between two intervals.
731 ;;; Two values are returned: the intersection and the difference.
733 ;;; Let the two intervals be X and Y, and let I and D be the two
734 ;;; values returned by this function. Then I = X intersect Y. If I
735 ;;; is NIL (the empty set), then D is X union Y, represented as the
736 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
737 ;;; - I, which is a list of two intervals.
739 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
740 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
741 (defun interval-intersection/difference (x y)
742 (declare (type interval x y))
743 (let ((x-lo (interval-low x))
744 (x-hi (interval-high x))
745 (y-lo (interval-low y))
746 (y-hi (interval-high y)))
749 ;; If p is an open bound, make it closed. If p is a closed
750 ;; bound, make it open.
754 (test-number (p int bound)
755 ;; Test whether P is in the interval.
756 (let ((pn (type-bound-number p)))
757 (when (interval-contains-p pn (interval-closure int))
758 ;; Check for endpoints.
759 (let* ((lo (interval-low int))
760 (hi (interval-high int))
761 (lon (type-bound-number lo))
762 (hin (type-bound-number hi)))
764 ;; Interval may be a point.
765 ((and lon hin (= lon hin pn))
766 (and (numberp p) (numberp lo) (numberp hi)))
767 ;; Point matches the low end.
768 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
769 ;; (P [P,?} => TRUE P) [P,?} => FALSE
770 ;; (P (P,?} => TRUE P) (P,?} => FALSE
771 ((and lon (= pn lon))
772 (or (and (numberp p) (numberp lo))
773 (and (consp p) (eq :low bound))))
774 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
775 ;; P) {?,P] => TRUE (P {?,P] => FALSE
776 ;; P) {?,P) => TRUE (P {?,P) => FALSE
777 ((and hin (= pn hin))
778 (or (and (numberp p) (numberp hi))
779 (and (consp p) (eq :high bound))))
780 ;; Not an endpoint, all is well.
783 (test-lower-bound (p int)
784 ;; P is a lower bound of an interval.
786 (test-number p int :low)
787 (not (interval-bounded-p int 'below))))
788 (test-upper-bound (p int)
789 ;; P is an upper bound of an interval.
791 (test-number p int :high)
792 (not (interval-bounded-p int 'above)))))
793 (let ((x-lo-in-y (test-lower-bound x-lo y))
794 (x-hi-in-y (test-upper-bound x-hi y))
795 (y-lo-in-x (test-lower-bound y-lo x))
796 (y-hi-in-x (test-upper-bound y-hi x)))
797 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
798 ;; Intervals intersect. Let's compute the intersection
799 ;; and the difference.
800 (multiple-value-bind (lo left-lo left-hi)
801 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
802 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
803 (multiple-value-bind (hi right-lo right-hi)
805 (values x-hi (opposite-bound x-hi) y-hi))
807 (values y-hi (opposite-bound y-hi) x-hi)))
808 (values (make-interval :low lo :high hi)
809 (list (make-interval :low left-lo
811 (make-interval :low right-lo
814 (values nil (list x y))))))))
816 ;;; If intervals X and Y intersect, return a new interval that is the
817 ;;; union of the two. If they do not intersect, return NIL.
818 (defun interval-merge-pair (x y)
819 (declare (type interval x y))
820 ;; If x and y intersect or are adjacent, create the union.
821 ;; Otherwise return nil
822 (when (or (interval-intersect-p x y)
823 (interval-adjacent-p x y))
824 (flet ((select-bound (x1 x2 min-op max-op)
825 (let ((x1-val (type-bound-number x1))
826 (x2-val (type-bound-number x2)))
828 ;; Both bounds are finite. Select the right one.
829 (cond ((funcall min-op x1-val x2-val)
830 ;; x1 is definitely better.
832 ((funcall max-op x1-val x2-val)
833 ;; x2 is definitely better.
836 ;; Bounds are equal. Select either
837 ;; value and make it open only if
839 (set-bound x1-val (and (consp x1) (consp x2))))))
841 ;; At least one bound is not finite. The
842 ;; non-finite bound always wins.
844 (let* ((x-lo (copy-interval-limit (interval-low x)))
845 (x-hi (copy-interval-limit (interval-high x)))
846 (y-lo (copy-interval-limit (interval-low y)))
847 (y-hi (copy-interval-limit (interval-high y))))
848 (make-interval :low (select-bound x-lo y-lo #'< #'>)
849 :high (select-bound x-hi y-hi #'> #'<))))))
851 ;;; return the minimal interval, containing X and Y
852 (defun interval-approximate-union (x y)
853 (cond ((interval-merge-pair x y))
855 (make-interval :low (copy-interval-limit (interval-low x))
856 :high (copy-interval-limit (interval-high y))))
858 (make-interval :low (copy-interval-limit (interval-low y))
859 :high (copy-interval-limit (interval-high x))))))
861 ;;; basic arithmetic operations on intervals. We probably should do
862 ;;; true interval arithmetic here, but it's complicated because we
863 ;;; have float and integer types and bounds can be open or closed.
865 ;;; the negative of an interval
866 (defun interval-neg (x)
867 (declare (type interval x))
868 (make-interval :low (bound-func #'- (interval-high x) t)
869 :high (bound-func #'- (interval-low x) t)))
871 ;;; Add two intervals.
872 (defun interval-add (x y)
873 (declare (type interval x y))
874 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
875 :high (bound-binop + (interval-high x) (interval-high y))))
877 ;;; Subtract two intervals.
878 (defun interval-sub (x y)
879 (declare (type interval x y))
880 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
881 :high (bound-binop - (interval-high x) (interval-low y))))
883 ;;; Multiply two intervals.
884 (defun interval-mul (x y)
885 (declare (type interval x y))
886 (flet ((bound-mul (x y)
887 (cond ((or (null x) (null y))
888 ;; Multiply by infinity is infinity
890 ((or (and (numberp x) (zerop x))
891 (and (numberp y) (zerop y)))
892 ;; Multiply by closed zero is special. The result
893 ;; is always a closed bound. But don't replace this
894 ;; with zero; we want the multiplication to produce
895 ;; the correct signed zero, if needed. Use SIGNUM
896 ;; to avoid trying to multiply huge bignums with 0.0.
897 (* (signum (type-bound-number x)) (signum (type-bound-number y))))
898 ((or (and (floatp x) (float-infinity-p x))
899 (and (floatp y) (float-infinity-p y)))
900 ;; Infinity times anything is infinity
903 ;; General multiply. The result is open if either is open.
904 (bound-binop * x y)))))
905 (let ((x-range (interval-range-info x))
906 (y-range (interval-range-info y)))
907 (cond ((null x-range)
908 ;; Split x into two and multiply each separately
909 (destructuring-bind (x- x+) (interval-split 0 x t t)
910 (interval-merge-pair (interval-mul x- y)
911 (interval-mul x+ y))))
913 ;; Split y into two and multiply each separately
914 (destructuring-bind (y- y+) (interval-split 0 y t t)
915 (interval-merge-pair (interval-mul x y-)
916 (interval-mul x y+))))
918 (interval-neg (interval-mul (interval-neg x) y)))
920 (interval-neg (interval-mul x (interval-neg y))))
921 ((and (eq x-range '+) (eq y-range '+))
922 ;; If we are here, X and Y are both positive.
924 :low (bound-mul (interval-low x) (interval-low y))
925 :high (bound-mul (interval-high x) (interval-high y))))
927 (bug "excluded case in INTERVAL-MUL"))))))
929 ;;; Divide two intervals.
930 (defun interval-div (top bot)
931 (declare (type interval top bot))
932 (flet ((bound-div (x y y-low-p)
935 ;; Divide by infinity means result is 0. However,
936 ;; we need to watch out for the sign of the result,
937 ;; to correctly handle signed zeros. We also need
938 ;; to watch out for positive or negative infinity.
939 (if (floatp (type-bound-number x))
941 (- (float-sign (type-bound-number x) 0.0))
942 (float-sign (type-bound-number x) 0.0))
944 ((zerop (type-bound-number y))
945 ;; Divide by zero means result is infinity
948 (bound-binop / x y)))))
949 (let ((top-range (interval-range-info top))
950 (bot-range (interval-range-info bot)))
951 (cond ((null bot-range)
952 ;; The denominator contains zero, so anything goes!
953 (make-interval :low nil :high nil))
955 ;; Denominator is negative so flip the sign, compute the
956 ;; result, and flip it back.
957 (interval-neg (interval-div top (interval-neg bot))))
959 ;; Split top into two positive and negative parts, and
960 ;; divide each separately
961 (destructuring-bind (top- top+) (interval-split 0 top t t)
962 (interval-merge-pair (interval-div top- bot)
963 (interval-div top+ bot))))
965 ;; Top is negative so flip the sign, divide, and flip the
966 ;; sign of the result.
967 (interval-neg (interval-div (interval-neg top) bot)))
968 ((and (eq top-range '+) (eq bot-range '+))
971 :low (bound-div (interval-low top) (interval-high bot) t)
972 :high (bound-div (interval-high top) (interval-low bot) nil)))
974 (bug "excluded case in INTERVAL-DIV"))))))
976 ;;; Apply the function F to the interval X. If X = [a, b], then the
977 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
978 ;;; result makes sense. It will if F is monotonic increasing (or, if
979 ;;; the interval is closed, non-decreasing).
981 ;;; (Actually most uses of INTERVAL-FUNC are coercions to float types,
982 ;;; which are not monotonic increasing, so default to calling
983 ;;; BOUND-FUNC with a non-strict argument).
984 (defun interval-func (f x &optional increasing)
985 (declare (type function f)
987 (let ((lo (bound-func f (interval-low x) increasing))
988 (hi (bound-func f (interval-high x) increasing)))
989 (make-interval :low lo :high hi)))
991 ;;; Return T if X < Y. That is every number in the interval X is
992 ;;; always less than any number in the interval Y.
993 (defun interval-< (x y)
994 (declare (type interval x y))
995 ;; X < Y only if X is bounded above, Y is bounded below, and they
997 (when (and (interval-bounded-p x 'above)
998 (interval-bounded-p y 'below))
999 ;; Intervals are bounded in the appropriate way. Make sure they
1001 (let ((left (interval-high x))
1002 (right (interval-low y)))
1003 (cond ((> (type-bound-number left)
1004 (type-bound-number right))
1005 ;; The intervals definitely overlap, so result is NIL.
1007 ((< (type-bound-number left)
1008 (type-bound-number right))
1009 ;; The intervals definitely don't touch, so result is T.
1012 ;; Limits are equal. Check for open or closed bounds.
1013 ;; Don't overlap if one or the other are open.
1014 (or (consp left) (consp right)))))))
1016 ;;; Return T if X >= Y. That is, every number in the interval X is
1017 ;;; always greater than any number in the interval Y.
1018 (defun interval->= (x y)
1019 (declare (type interval x y))
1020 ;; X >= Y if lower bound of X >= upper bound of Y
1021 (when (and (interval-bounded-p x 'below)
1022 (interval-bounded-p y 'above))
1023 (>= (type-bound-number (interval-low x))
1024 (type-bound-number (interval-high y)))))
1026 ;;; Return T if X = Y.
1027 (defun interval-= (x y)
1028 (declare (type interval x y))
1029 (and (interval-bounded-p x 'both)
1030 (interval-bounded-p y 'both)
1034 ;; Open intervals cannot be =
1035 (return-from interval-= nil))))
1036 ;; Both intervals refer to the same point
1037 (= (bound (interval-high x)) (bound (interval-low x))
1038 (bound (interval-high y)) (bound (interval-low y))))))
1040 ;;; Return T if X /= Y
1041 (defun interval-/= (x y)
1042 (not (interval-intersect-p x y)))
1044 ;;; Return an interval that is the absolute value of X. Thus, if
1045 ;;; X = [-1 10], the result is [0, 10].
1046 (defun interval-abs (x)
1047 (declare (type interval x))
1048 (case (interval-range-info x)
1054 (destructuring-bind (x- x+) (interval-split 0 x t t)
1055 (interval-merge-pair (interval-neg x-) x+)))))
1057 ;;; Compute the square of an interval.
1058 (defun interval-sqr (x)
1059 (declare (type interval x))
1060 (interval-func (lambda (x) (* x x)) (interval-abs x)))
1062 ;;;; numeric DERIVE-TYPE methods
1064 ;;; a utility for defining derive-type methods of integer operations. If
1065 ;;; the types of both X and Y are integer types, then we compute a new
1066 ;;; integer type with bounds determined by FUN when applied to X and Y.
1067 ;;; Otherwise, we use NUMERIC-CONTAGION.
1068 (defun derive-integer-type-aux (x y fun)
1069 (declare (type function fun))
1070 (if (and (numeric-type-p x) (numeric-type-p y)
1071 (eq (numeric-type-class x) 'integer)
1072 (eq (numeric-type-class y) 'integer)
1073 (eq (numeric-type-complexp x) :real)
1074 (eq (numeric-type-complexp y) :real))
1075 (multiple-value-bind (low high) (funcall fun x y)
1076 (make-numeric-type :class 'integer
1080 (numeric-contagion x y)))
1082 (defun derive-integer-type (x y fun)
1083 (declare (type lvar x y) (type function fun))
1084 (let ((x (lvar-type x))
1086 (derive-integer-type-aux x y fun)))
1088 ;;; simple utility to flatten a list
1089 (defun flatten-list (x)
1090 (labels ((flatten-and-append (tree list)
1091 (cond ((null tree) list)
1092 ((atom tree) (cons tree list))
1093 (t (flatten-and-append
1094 (car tree) (flatten-and-append (cdr tree) list))))))
1095 (flatten-and-append x nil)))
1097 ;;; Take some type of lvar and massage it so that we get a list of the
1098 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
1100 (defun prepare-arg-for-derive-type (arg)
1101 (flet ((listify (arg)
1106 (union-type-types arg))
1109 (unless (eq arg *empty-type*)
1110 ;; Make sure all args are some type of numeric-type. For member
1111 ;; types, convert the list of members into a union of equivalent
1112 ;; single-element member-type's.
1113 (let ((new-args nil))
1114 (dolist (arg (listify arg))
1115 (if (member-type-p arg)
1116 ;; Run down the list of members and convert to a list of
1118 (mapc-member-type-members
1120 (push (if (numberp member)
1121 (make-member-type :members (list member))
1125 (push arg new-args)))
1126 (unless (member *empty-type* new-args)
1129 ;;; Convert from the standard type convention for which -0.0 and 0.0
1130 ;;; are equal to an intermediate convention for which they are
1131 ;;; considered different which is more natural for some of the
1133 (defun convert-numeric-type (type)
1134 (declare (type numeric-type type))
1135 ;;; Only convert real float interval delimiters types.
1136 (if (eq (numeric-type-complexp type) :real)
1137 (let* ((lo (numeric-type-low type))
1138 (lo-val (type-bound-number lo))
1139 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
1140 (hi (numeric-type-high type))
1141 (hi-val (type-bound-number hi))
1142 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
1143 (if (or lo-float-zero-p hi-float-zero-p)
1145 :class (numeric-type-class type)
1146 :format (numeric-type-format type)
1148 :low (if lo-float-zero-p
1150 (list (float 0.0 lo-val))
1151 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
1153 :high (if hi-float-zero-p
1155 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
1162 ;;; Convert back from the intermediate convention for which -0.0 and
1163 ;;; 0.0 are considered different to the standard type convention for
1164 ;;; which and equal.
1165 (defun convert-back-numeric-type (type)
1166 (declare (type numeric-type type))
1167 ;;; Only convert real float interval delimiters types.
1168 (if (eq (numeric-type-complexp type) :real)
1169 (let* ((lo (numeric-type-low type))
1170 (lo-val (type-bound-number lo))
1172 (and lo (floatp lo-val) (= lo-val 0.0)
1173 (float-sign lo-val)))
1174 (hi (numeric-type-high type))
1175 (hi-val (type-bound-number hi))
1177 (and hi (floatp hi-val) (= hi-val 0.0)
1178 (float-sign hi-val))))
1180 ;; (float +0.0 +0.0) => (member 0.0)
1181 ;; (float -0.0 -0.0) => (member -0.0)
1182 ((and lo-float-zero-p hi-float-zero-p)
1183 ;; shouldn't have exclusive bounds here..
1184 (aver (and (not (consp lo)) (not (consp hi))))
1185 (if (= lo-float-zero-p hi-float-zero-p)
1186 ;; (float +0.0 +0.0) => (member 0.0)
1187 ;; (float -0.0 -0.0) => (member -0.0)
1188 (specifier-type `(member ,lo-val))
1189 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1190 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1191 (make-numeric-type :class (numeric-type-class type)
1192 :format (numeric-type-format type)
1198 ;; (float -0.0 x) => (float 0.0 x)
1199 ((and (not (consp lo)) (minusp lo-float-zero-p))
1200 (make-numeric-type :class (numeric-type-class type)
1201 :format (numeric-type-format type)
1203 :low (float 0.0 lo-val)
1205 ;; (float (+0.0) x) => (float (0.0) x)
1206 ((and (consp lo) (plusp lo-float-zero-p))
1207 (make-numeric-type :class (numeric-type-class type)
1208 :format (numeric-type-format type)
1210 :low (list (float 0.0 lo-val))
1213 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1214 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1215 (list (make-member-type :members (list (float 0.0 lo-val)))
1216 (make-numeric-type :class (numeric-type-class type)
1217 :format (numeric-type-format type)
1219 :low (list (float 0.0 lo-val))
1223 ;; (float x +0.0) => (float x 0.0)
1224 ((and (not (consp hi)) (plusp hi-float-zero-p))
1225 (make-numeric-type :class (numeric-type-class type)
1226 :format (numeric-type-format type)
1229 :high (float 0.0 hi-val)))
1230 ;; (float x (-0.0)) => (float x (0.0))
1231 ((and (consp hi) (minusp hi-float-zero-p))
1232 (make-numeric-type :class (numeric-type-class type)
1233 :format (numeric-type-format type)
1236 :high (list (float 0.0 hi-val))))
1238 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1239 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1240 (list (make-member-type :members (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val)))
1241 (make-numeric-type :class (numeric-type-class type)
1242 :format (numeric-type-format type)
1245 :high (list (float 0.0 hi-val)))))))
1251 ;;; Convert back a possible list of numeric types.
1252 (defun convert-back-numeric-type-list (type-list)
1255 (let ((results '()))
1256 (dolist (type type-list)
1257 (if (numeric-type-p type)
1258 (let ((result (convert-back-numeric-type type)))
1260 (setf results (append results result))
1261 (push result results)))
1262 (push type results)))
1265 (convert-back-numeric-type type-list))
1267 (convert-back-numeric-type-list (union-type-types type-list)))
1271 ;;; Take a list of types and return a canonical type specifier,
1272 ;;; combining any MEMBER types together. If both positive and negative
1273 ;;; MEMBER types are present they are converted to a float type.
1274 ;;; XXX This would be far simpler if the type-union methods could handle
1275 ;;; member/number unions.
1277 ;;; If we're about to generate an overly complex union of numeric types, start
1278 ;;; collapse the ranges together.
1280 ;;; FIXME: The MEMBER canonicalization parts of MAKE-DERIVED-UNION-TYPE and
1281 ;;; entire CONVERT-MEMBER-TYPE probably belong in the kernel's type logic,
1282 ;;; invoked always, instead of in the compiler, invoked only during some type
1284 (defvar *derived-numeric-union-complexity-limit* 6)
1286 (defun make-derived-union-type (type-list)
1287 (let ((xset (alloc-xset))
1290 (numeric-type *empty-type*))
1291 (dolist (type type-list)
1292 (cond ((member-type-p type)
1293 (mapc-member-type-members
1295 (if (fp-zero-p member)
1296 (unless (member member fp-zeroes)
1297 (pushnew member fp-zeroes))
1298 (add-to-xset member xset)))
1300 ((numeric-type-p type)
1301 (let ((*approximate-numeric-unions*
1302 (when (and (union-type-p numeric-type)
1303 (nthcdr *derived-numeric-union-complexity-limit*
1304 (union-type-types numeric-type)))
1306 (setf numeric-type (type-union type numeric-type))))
1308 (push type misc-types))))
1309 (if (and (xset-empty-p xset) (not fp-zeroes))
1310 (apply #'type-union numeric-type misc-types)
1311 (apply #'type-union (make-member-type :xset xset :fp-zeroes fp-zeroes)
1312 numeric-type misc-types))))
1314 ;;; Convert a member type with a single member to a numeric type.
1315 (defun convert-member-type (arg)
1316 (let* ((members (member-type-members arg))
1317 (member (first members))
1318 (member-type (type-of member)))
1319 (aver (not (rest members)))
1320 (specifier-type (cond ((typep member 'integer)
1321 `(integer ,member ,member))
1322 ((memq member-type '(short-float single-float
1323 double-float long-float))
1324 `(,member-type ,member ,member))
1328 ;;; This is used in defoptimizers for computing the resulting type of
1331 ;;; Given the lvar ARG, derive the resulting type using the
1332 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1333 ;;; "atomic" lvar type like numeric-type or member-type (containing
1334 ;;; just one element). It should return the resulting type, which can
1335 ;;; be a list of types.
1337 ;;; For the case of member types, if a MEMBER-FUN is given it is
1338 ;;; called to compute the result otherwise the member type is first
1339 ;;; converted to a numeric type and the DERIVE-FUN is called.
1340 (defun one-arg-derive-type (arg derive-fun member-fun
1341 &optional (convert-type t))
1342 (declare (type function derive-fun)
1343 (type (or null function) member-fun))
1344 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1350 (with-float-traps-masked
1351 (:underflow :overflow :divide-by-zero)
1353 `(eql ,(funcall member-fun
1354 (first (member-type-members x))))))
1355 ;; Otherwise convert to a numeric type.
1356 (let ((result-type-list
1357 (funcall derive-fun (convert-member-type x))))
1359 (convert-back-numeric-type-list result-type-list)
1360 result-type-list))))
1363 (convert-back-numeric-type-list
1364 (funcall derive-fun (convert-numeric-type x)))
1365 (funcall derive-fun x)))
1367 *universal-type*))))
1368 ;; Run down the list of args and derive the type of each one,
1369 ;; saving all of the results in a list.
1370 (let ((results nil))
1371 (dolist (arg arg-list)
1372 (let ((result (deriver arg)))
1374 (setf results (append results result))
1375 (push result results))))
1377 (make-derived-union-type results)
1378 (first results)))))))
1380 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1381 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1382 ;;; original args and a third which is T to indicate if the two args
1383 ;;; really represent the same lvar. This is useful for deriving the
1384 ;;; type of things like (* x x), which should always be positive. If
1385 ;;; we didn't do this, we wouldn't be able to tell.
1386 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1387 &optional (convert-type t))
1388 (declare (type function derive-fun fun))
1389 (flet ((deriver (x y same-arg)
1390 (cond ((and (member-type-p x) (member-type-p y))
1391 (let* ((x (first (member-type-members x)))
1392 (y (first (member-type-members y)))
1393 (result (ignore-errors
1394 (with-float-traps-masked
1395 (:underflow :overflow :divide-by-zero
1397 (funcall fun x y)))))
1398 (cond ((null result) *empty-type*)
1399 ((and (floatp result) (float-nan-p result))
1400 (make-numeric-type :class 'float
1401 :format (type-of result)
1404 (specifier-type `(eql ,result))))))
1405 ((and (member-type-p x) (numeric-type-p y))
1406 (let* ((x (convert-member-type x))
1407 (y (if convert-type (convert-numeric-type y) y))
1408 (result (funcall derive-fun x y same-arg)))
1410 (convert-back-numeric-type-list result)
1412 ((and (numeric-type-p x) (member-type-p y))
1413 (let* ((x (if convert-type (convert-numeric-type x) x))
1414 (y (convert-member-type y))
1415 (result (funcall derive-fun x y same-arg)))
1417 (convert-back-numeric-type-list result)
1419 ((and (numeric-type-p x) (numeric-type-p y))
1420 (let* ((x (if convert-type (convert-numeric-type x) x))
1421 (y (if convert-type (convert-numeric-type y) y))
1422 (result (funcall derive-fun x y same-arg)))
1424 (convert-back-numeric-type-list result)
1427 *universal-type*))))
1428 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1429 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1430 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1432 (let ((results nil))
1434 ;; Since the args are the same LVARs, just run down the
1437 (let ((result (deriver x x same-arg)))
1439 (setf results (append results result))
1440 (push result results))))
1441 ;; Try all pairwise combinations.
1444 (let ((result (or (deriver x y same-arg)
1445 (numeric-contagion x y))))
1447 (setf results (append results result))
1448 (push result results))))))
1450 (make-derived-union-type results)
1451 (first results)))))))
1453 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1455 (defoptimizer (+ derive-type) ((x y))
1456 (derive-integer-type
1463 (values (frob (numeric-type-low x) (numeric-type-low y))
1464 (frob (numeric-type-high x) (numeric-type-high y)))))))
1466 (defoptimizer (- derive-type) ((x y))
1467 (derive-integer-type
1474 (values (frob (numeric-type-low x) (numeric-type-high y))
1475 (frob (numeric-type-high x) (numeric-type-low y)))))))
1477 (defoptimizer (* derive-type) ((x y))
1478 (derive-integer-type
1481 (let ((x-low (numeric-type-low x))
1482 (x-high (numeric-type-high x))
1483 (y-low (numeric-type-low y))
1484 (y-high (numeric-type-high y)))
1485 (cond ((not (and x-low y-low))
1487 ((or (minusp x-low) (minusp y-low))
1488 (if (and x-high y-high)
1489 (let ((max (* (max (abs x-low) (abs x-high))
1490 (max (abs y-low) (abs y-high)))))
1491 (values (- max) max))
1494 (values (* x-low y-low)
1495 (if (and x-high y-high)
1499 (defoptimizer (/ derive-type) ((x y))
1500 (numeric-contagion (lvar-type x) (lvar-type y)))
1504 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1506 (defun +-derive-type-aux (x y same-arg)
1507 (if (and (numeric-type-real-p x)
1508 (numeric-type-real-p y))
1511 (let ((x-int (numeric-type->interval x)))
1512 (interval-add x-int x-int))
1513 (interval-add (numeric-type->interval x)
1514 (numeric-type->interval y))))
1515 (result-type (numeric-contagion x y)))
1516 ;; If the result type is a float, we need to be sure to coerce
1517 ;; the bounds into the correct type.
1518 (when (eq (numeric-type-class result-type) 'float)
1519 (setf result (interval-func
1521 (coerce-for-bound x (or (numeric-type-format result-type)
1525 :class (if (and (eq (numeric-type-class x) 'integer)
1526 (eq (numeric-type-class y) 'integer))
1527 ;; The sum of integers is always an integer.
1529 (numeric-type-class result-type))
1530 :format (numeric-type-format result-type)
1531 :low (interval-low result)
1532 :high (interval-high result)))
1533 ;; general contagion
1534 (numeric-contagion x y)))
1536 (defoptimizer (+ derive-type) ((x y))
1537 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1539 (defun --derive-type-aux (x y same-arg)
1540 (if (and (numeric-type-real-p x)
1541 (numeric-type-real-p y))
1543 ;; (- X X) is always 0.
1545 (make-interval :low 0 :high 0)
1546 (interval-sub (numeric-type->interval x)
1547 (numeric-type->interval y))))
1548 (result-type (numeric-contagion x y)))
1549 ;; If the result type is a float, we need to be sure to coerce
1550 ;; the bounds into the correct type.
1551 (when (eq (numeric-type-class result-type) 'float)
1552 (setf result (interval-func
1554 (coerce-for-bound x (or (numeric-type-format result-type)
1558 :class (if (and (eq (numeric-type-class x) 'integer)
1559 (eq (numeric-type-class y) 'integer))
1560 ;; The difference of integers is always an integer.
1562 (numeric-type-class result-type))
1563 :format (numeric-type-format result-type)
1564 :low (interval-low result)
1565 :high (interval-high result)))
1566 ;; general contagion
1567 (numeric-contagion x y)))
1569 (defoptimizer (- derive-type) ((x y))
1570 (two-arg-derive-type x y #'--derive-type-aux #'-))
1572 (defun *-derive-type-aux (x y same-arg)
1573 (if (and (numeric-type-real-p x)
1574 (numeric-type-real-p y))
1576 ;; (* X X) is always positive, so take care to do it right.
1578 (interval-sqr (numeric-type->interval x))
1579 (interval-mul (numeric-type->interval x)
1580 (numeric-type->interval y))))
1581 (result-type (numeric-contagion x y)))
1582 ;; If the result type is a float, we need to be sure to coerce
1583 ;; the bounds into the correct type.
1584 (when (eq (numeric-type-class result-type) 'float)
1585 (setf result (interval-func
1587 (coerce-for-bound x (or (numeric-type-format result-type)
1591 :class (if (and (eq (numeric-type-class x) 'integer)
1592 (eq (numeric-type-class y) 'integer))
1593 ;; The product of integers is always an integer.
1595 (numeric-type-class result-type))
1596 :format (numeric-type-format result-type)
1597 :low (interval-low result)
1598 :high (interval-high result)))
1599 (numeric-contagion x y)))
1601 (defoptimizer (* derive-type) ((x y))
1602 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1604 (defun /-derive-type-aux (x y same-arg)
1605 (if (and (numeric-type-real-p x)
1606 (numeric-type-real-p y))
1608 ;; (/ X X) is always 1, except if X can contain 0. In
1609 ;; that case, we shouldn't optimize the division away
1610 ;; because we want 0/0 to signal an error.
1612 (not (interval-contains-p
1613 0 (interval-closure (numeric-type->interval y)))))
1614 (make-interval :low 1 :high 1)
1615 (interval-div (numeric-type->interval x)
1616 (numeric-type->interval y))))
1617 (result-type (numeric-contagion x y)))
1618 ;; If the result type is a float, we need to be sure to coerce
1619 ;; the bounds into the correct type.
1620 (when (eq (numeric-type-class result-type) 'float)
1621 (setf result (interval-func
1623 (coerce-for-bound x (or (numeric-type-format result-type)
1626 (make-numeric-type :class (numeric-type-class result-type)
1627 :format (numeric-type-format result-type)
1628 :low (interval-low result)
1629 :high (interval-high result)))
1630 (numeric-contagion x y)))
1632 (defoptimizer (/ derive-type) ((x y))
1633 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1637 (defun ash-derive-type-aux (n-type shift same-arg)
1638 (declare (ignore same-arg))
1639 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1640 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1641 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1642 ;; two bignums yielding zero) and it's hard to avoid that
1643 ;; calculation in here.
1644 #+(and cmu sb-xc-host)
1645 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1646 (typep (numeric-type-high n-type) 'bignum))
1647 (or (typep (numeric-type-low shift) 'bignum)
1648 (typep (numeric-type-high shift) 'bignum)))
1649 (return-from ash-derive-type-aux *universal-type*))
1650 (flet ((ash-outer (n s)
1651 (when (and (fixnump s)
1653 (> s sb!xc:most-negative-fixnum))
1655 ;; KLUDGE: The bare 64's here should be related to
1656 ;; symbolic machine word size values somehow.
1659 (if (and (fixnump s)
1660 (> s sb!xc:most-negative-fixnum))
1662 (if (minusp n) -1 0))))
1663 (or (and (csubtypep n-type (specifier-type 'integer))
1664 (csubtypep shift (specifier-type 'integer))
1665 (let ((n-low (numeric-type-low n-type))
1666 (n-high (numeric-type-high n-type))
1667 (s-low (numeric-type-low shift))
1668 (s-high (numeric-type-high shift)))
1669 (make-numeric-type :class 'integer :complexp :real
1672 (ash-outer n-low s-high)
1673 (ash-inner n-low s-low)))
1676 (ash-inner n-high s-low)
1677 (ash-outer n-high s-high))))))
1680 (defoptimizer (ash derive-type) ((n shift))
1681 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1683 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1684 (macrolet ((frob (fun)
1685 `#'(lambda (type type2)
1686 (declare (ignore type2))
1687 (let ((lo (numeric-type-low type))
1688 (hi (numeric-type-high type)))
1689 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1691 (defoptimizer (%negate derive-type) ((num))
1692 (derive-integer-type num num (frob -))))
1694 (defun lognot-derive-type-aux (int)
1695 (derive-integer-type-aux int int
1696 (lambda (type type2)
1697 (declare (ignore type2))
1698 (let ((lo (numeric-type-low type))
1699 (hi (numeric-type-high type)))
1700 (values (if hi (lognot hi) nil)
1701 (if lo (lognot lo) nil)
1702 (numeric-type-class type)
1703 (numeric-type-format type))))))
1705 (defoptimizer (lognot derive-type) ((int))
1706 (lognot-derive-type-aux (lvar-type int)))
1708 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1709 (defoptimizer (%negate derive-type) ((num))
1710 (flet ((negate-bound (b)
1712 (set-bound (- (type-bound-number b))
1714 (one-arg-derive-type num
1716 (modified-numeric-type
1718 :low (negate-bound (numeric-type-high type))
1719 :high (negate-bound (numeric-type-low type))))
1722 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1723 (defoptimizer (abs derive-type) ((num))
1724 (let ((type (lvar-type num)))
1725 (if (and (numeric-type-p type)
1726 (eq (numeric-type-class type) 'integer)
1727 (eq (numeric-type-complexp type) :real))
1728 (let ((lo (numeric-type-low type))
1729 (hi (numeric-type-high type)))
1730 (make-numeric-type :class 'integer :complexp :real
1731 :low (cond ((and hi (minusp hi))
1737 :high (if (and hi lo)
1738 (max (abs hi) (abs lo))
1740 (numeric-contagion type type))))
1742 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1743 (defun abs-derive-type-aux (type)
1744 (cond ((eq (numeric-type-complexp type) :complex)
1745 ;; The absolute value of a complex number is always a
1746 ;; non-negative float.
1747 (let* ((format (case (numeric-type-class type)
1748 ((integer rational) 'single-float)
1749 (t (numeric-type-format type))))
1750 (bound-format (or format 'float)))
1751 (make-numeric-type :class 'float
1754 :low (coerce 0 bound-format)
1757 ;; The absolute value of a real number is a non-negative real
1758 ;; of the same type.
1759 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1760 (class (numeric-type-class type))
1761 (format (numeric-type-format type))
1762 (bound-type (or format class 'real)))
1767 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1768 :high (coerce-and-truncate-floats
1769 (interval-high abs-bnd) bound-type))))))
1771 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1772 (defoptimizer (abs derive-type) ((num))
1773 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1775 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1776 (defoptimizer (truncate derive-type) ((number divisor))
1777 (let ((number-type (lvar-type number))
1778 (divisor-type (lvar-type divisor))
1779 (integer-type (specifier-type 'integer)))
1780 (if (and (numeric-type-p number-type)
1781 (csubtypep number-type integer-type)
1782 (numeric-type-p divisor-type)
1783 (csubtypep divisor-type integer-type))
1784 (let ((number-low (numeric-type-low number-type))
1785 (number-high (numeric-type-high number-type))
1786 (divisor-low (numeric-type-low divisor-type))
1787 (divisor-high (numeric-type-high divisor-type)))
1788 (values-specifier-type
1789 `(values ,(integer-truncate-derive-type number-low number-high
1790 divisor-low divisor-high)
1791 ,(integer-rem-derive-type number-low number-high
1792 divisor-low divisor-high))))
1795 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1798 (defun rem-result-type (number-type divisor-type)
1799 ;; Figure out what the remainder type is. The remainder is an
1800 ;; integer if both args are integers; a rational if both args are
1801 ;; rational; and a float otherwise.
1802 (cond ((and (csubtypep number-type (specifier-type 'integer))
1803 (csubtypep divisor-type (specifier-type 'integer)))
1805 ((and (csubtypep number-type (specifier-type 'rational))
1806 (csubtypep divisor-type (specifier-type 'rational)))
1808 ((and (csubtypep number-type (specifier-type 'float))
1809 (csubtypep divisor-type (specifier-type 'float)))
1810 ;; Both are floats so the result is also a float, of
1811 ;; the largest type.
1812 (or (float-format-max (numeric-type-format number-type)
1813 (numeric-type-format divisor-type))
1815 ((and (csubtypep number-type (specifier-type 'float))
1816 (csubtypep divisor-type (specifier-type 'rational)))
1817 ;; One of the arguments is a float and the other is a
1818 ;; rational. The remainder is a float of the same
1820 (or (numeric-type-format number-type) 'float))
1821 ((and (csubtypep divisor-type (specifier-type 'float))
1822 (csubtypep number-type (specifier-type 'rational)))
1823 ;; One of the arguments is a float and the other is a
1824 ;; rational. The remainder is a float of the same
1826 (or (numeric-type-format divisor-type) 'float))
1828 ;; Some unhandled combination. This usually means both args
1829 ;; are REAL so the result is a REAL.
1832 (defun truncate-derive-type-quot (number-type divisor-type)
1833 (let* ((rem-type (rem-result-type number-type divisor-type))
1834 (number-interval (numeric-type->interval number-type))
1835 (divisor-interval (numeric-type->interval divisor-type)))
1836 ;;(declare (type (member '(integer rational float)) rem-type))
1837 ;; We have real numbers now.
1838 (cond ((eq rem-type 'integer)
1839 ;; Since the remainder type is INTEGER, both args are
1841 (let* ((res (integer-truncate-derive-type
1842 (interval-low number-interval)
1843 (interval-high number-interval)
1844 (interval-low divisor-interval)
1845 (interval-high divisor-interval))))
1846 (specifier-type (if (listp res) res 'integer))))
1848 (let ((quot (truncate-quotient-bound
1849 (interval-div number-interval
1850 divisor-interval))))
1851 (specifier-type `(integer ,(or (interval-low quot) '*)
1852 ,(or (interval-high quot) '*))))))))
1854 (defun truncate-derive-type-rem (number-type divisor-type)
1855 (let* ((rem-type (rem-result-type number-type divisor-type))
1856 (number-interval (numeric-type->interval number-type))
1857 (divisor-interval (numeric-type->interval divisor-type))
1858 (rem (truncate-rem-bound number-interval divisor-interval)))
1859 ;;(declare (type (member '(integer rational float)) rem-type))
1860 ;; We have real numbers now.
1861 (cond ((eq rem-type 'integer)
1862 ;; Since the remainder type is INTEGER, both args are
1864 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1865 ,(or (interval-high rem) '*))))
1867 (multiple-value-bind (class format)
1870 (values 'integer nil))
1872 (values 'rational nil))
1873 ((or single-float double-float #!+long-float long-float)
1874 (values 'float rem-type))
1876 (values 'float nil))
1879 (when (member rem-type '(float single-float double-float
1880 #!+long-float long-float))
1881 (setf rem (interval-func #'(lambda (x)
1882 (coerce-for-bound x rem-type))
1884 (make-numeric-type :class class
1886 :low (interval-low rem)
1887 :high (interval-high rem)))))))
1889 (defun truncate-derive-type-quot-aux (num div same-arg)
1890 (declare (ignore same-arg))
1891 (if (and (numeric-type-real-p num)
1892 (numeric-type-real-p div))
1893 (truncate-derive-type-quot num div)
1896 (defun truncate-derive-type-rem-aux (num div same-arg)
1897 (declare (ignore same-arg))
1898 (if (and (numeric-type-real-p num)
1899 (numeric-type-real-p div))
1900 (truncate-derive-type-rem num div)
1903 (defoptimizer (truncate derive-type) ((number divisor))
1904 (let ((quot (two-arg-derive-type number divisor
1905 #'truncate-derive-type-quot-aux #'truncate))
1906 (rem (two-arg-derive-type number divisor
1907 #'truncate-derive-type-rem-aux #'rem)))
1908 (when (and quot rem)
1909 (make-values-type :required (list quot rem)))))
1911 (defun ftruncate-derive-type-quot (number-type divisor-type)
1912 ;; The bounds are the same as for truncate. However, the first
1913 ;; result is a float of some type. We need to determine what that
1914 ;; type is. Basically it's the more contagious of the two types.
1915 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1916 (res-type (numeric-contagion number-type divisor-type)))
1917 (make-numeric-type :class 'float
1918 :format (numeric-type-format res-type)
1919 :low (numeric-type-low q-type)
1920 :high (numeric-type-high q-type))))
1922 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1923 (declare (ignore same-arg))
1924 (if (and (numeric-type-real-p n)
1925 (numeric-type-real-p d))
1926 (ftruncate-derive-type-quot n d)
1929 (defoptimizer (ftruncate derive-type) ((number divisor))
1931 (two-arg-derive-type number divisor
1932 #'ftruncate-derive-type-quot-aux #'ftruncate))
1933 (rem (two-arg-derive-type number divisor
1934 #'truncate-derive-type-rem-aux #'rem)))
1935 (when (and quot rem)
1936 (make-values-type :required (list quot rem)))))
1938 (defun %unary-truncate-derive-type-aux (number)
1939 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1941 (defoptimizer (%unary-truncate derive-type) ((number))
1942 (one-arg-derive-type number
1943 #'%unary-truncate-derive-type-aux
1946 (defoptimizer (%unary-truncate/single-float derive-type) ((number))
1947 (one-arg-derive-type number
1948 #'%unary-truncate-derive-type-aux
1951 (defoptimizer (%unary-truncate/double-float derive-type) ((number))
1952 (one-arg-derive-type number
1953 #'%unary-truncate-derive-type-aux
1956 (defoptimizer (%unary-ftruncate derive-type) ((number))
1957 (let ((divisor (specifier-type '(integer 1 1))))
1958 (one-arg-derive-type number
1960 (ftruncate-derive-type-quot-aux n divisor nil))
1961 #'%unary-ftruncate)))
1963 (defoptimizer (%unary-round derive-type) ((number))
1964 (one-arg-derive-type number
1967 (unless (numeric-type-real-p n)
1968 (return *empty-type*))
1969 (let* ((interval (numeric-type->interval n))
1970 (low (interval-low interval))
1971 (high (interval-high interval)))
1973 (setf low (car low)))
1975 (setf high (car high)))
1985 ;;; Define optimizers for FLOOR and CEILING.
1987 ((def (name q-name r-name)
1988 (let ((q-aux (symbolicate q-name "-AUX"))
1989 (r-aux (symbolicate r-name "-AUX")))
1991 ;; Compute type of quotient (first) result.
1992 (defun ,q-aux (number-type divisor-type)
1993 (let* ((number-interval
1994 (numeric-type->interval number-type))
1996 (numeric-type->interval divisor-type))
1997 (quot (,q-name (interval-div number-interval
1998 divisor-interval))))
1999 (specifier-type `(integer ,(or (interval-low quot) '*)
2000 ,(or (interval-high quot) '*)))))
2001 ;; Compute type of remainder.
2002 (defun ,r-aux (number-type divisor-type)
2003 (let* ((divisor-interval
2004 (numeric-type->interval divisor-type))
2005 (rem (,r-name divisor-interval))
2006 (result-type (rem-result-type number-type divisor-type)))
2007 (multiple-value-bind (class format)
2010 (values 'integer nil))
2012 (values 'rational nil))
2013 ((or single-float double-float #!+long-float long-float)
2014 (values 'float result-type))
2016 (values 'float nil))
2019 (when (member result-type '(float single-float double-float
2020 #!+long-float long-float))
2021 ;; Make sure that the limits on the interval have
2023 (setf rem (interval-func (lambda (x)
2024 (coerce-for-bound x result-type))
2026 (make-numeric-type :class class
2028 :low (interval-low rem)
2029 :high (interval-high rem)))))
2030 ;; the optimizer itself
2031 (defoptimizer (,name derive-type) ((number divisor))
2032 (flet ((derive-q (n d same-arg)
2033 (declare (ignore same-arg))
2034 (if (and (numeric-type-real-p n)
2035 (numeric-type-real-p d))
2038 (derive-r (n d same-arg)
2039 (declare (ignore same-arg))
2040 (if (and (numeric-type-real-p n)
2041 (numeric-type-real-p d))
2044 (let ((quot (two-arg-derive-type
2045 number divisor #'derive-q #',name))
2046 (rem (two-arg-derive-type
2047 number divisor #'derive-r #'mod)))
2048 (when (and quot rem)
2049 (make-values-type :required (list quot rem))))))))))
2051 (def floor floor-quotient-bound floor-rem-bound)
2052 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
2054 ;;; Define optimizers for FFLOOR and FCEILING
2055 (macrolet ((def (name q-name r-name)
2056 (let ((q-aux (symbolicate "F" q-name "-AUX"))
2057 (r-aux (symbolicate r-name "-AUX")))
2059 ;; Compute type of quotient (first) result.
2060 (defun ,q-aux (number-type divisor-type)
2061 (let* ((number-interval
2062 (numeric-type->interval number-type))
2064 (numeric-type->interval divisor-type))
2065 (quot (,q-name (interval-div number-interval
2067 (res-type (numeric-contagion number-type
2070 :class (numeric-type-class res-type)
2071 :format (numeric-type-format res-type)
2072 :low (interval-low quot)
2073 :high (interval-high quot))))
2075 (defoptimizer (,name derive-type) ((number divisor))
2076 (flet ((derive-q (n d same-arg)
2077 (declare (ignore same-arg))
2078 (if (and (numeric-type-real-p n)
2079 (numeric-type-real-p d))
2082 (derive-r (n d same-arg)
2083 (declare (ignore same-arg))
2084 (if (and (numeric-type-real-p n)
2085 (numeric-type-real-p d))
2088 (let ((quot (two-arg-derive-type
2089 number divisor #'derive-q #',name))
2090 (rem (two-arg-derive-type
2091 number divisor #'derive-r #'mod)))
2092 (when (and quot rem)
2093 (make-values-type :required (list quot rem))))))))))
2095 (def ffloor floor-quotient-bound floor-rem-bound)
2096 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
2098 ;;; functions to compute the bounds on the quotient and remainder for
2099 ;;; the FLOOR function
2100 (defun floor-quotient-bound (quot)
2101 ;; Take the floor of the quotient and then massage it into what we
2103 (let ((lo (interval-low quot))
2104 (hi (interval-high quot)))
2105 ;; Take the floor of the lower bound. The result is always a
2106 ;; closed lower bound.
2108 (floor (type-bound-number lo))
2110 ;; For the upper bound, we need to be careful.
2113 ;; An open bound. We need to be careful here because
2114 ;; the floor of '(10.0) is 9, but the floor of
2116 (multiple-value-bind (q r) (floor (first hi))
2121 ;; A closed bound, so the answer is obvious.
2125 (make-interval :low lo :high hi)))
2126 (defun floor-rem-bound (div)
2127 ;; The remainder depends only on the divisor. Try to get the
2128 ;; correct sign for the remainder if we can.
2129 (case (interval-range-info div)
2131 ;; The divisor is always positive.
2132 (let ((rem (interval-abs div)))
2133 (setf (interval-low rem) 0)
2134 (when (and (numberp (interval-high rem))
2135 (not (zerop (interval-high rem))))
2136 ;; The remainder never contains the upper bound. However,
2137 ;; watch out for the case where the high limit is zero!
2138 (setf (interval-high rem) (list (interval-high rem))))
2141 ;; The divisor is always negative.
2142 (let ((rem (interval-neg (interval-abs div))))
2143 (setf (interval-high rem) 0)
2144 (when (numberp (interval-low rem))
2145 ;; The remainder never contains the lower bound.
2146 (setf (interval-low rem) (list (interval-low rem))))
2149 ;; The divisor can be positive or negative. All bets off. The
2150 ;; magnitude of remainder is the maximum value of the divisor.
2151 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2152 ;; The bound never reaches the limit, so make the interval open.
2153 (make-interval :low (if limit
2156 :high (list limit))))))
2158 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
2159 => #S(INTERVAL :LOW 0 :HIGH 10)
2160 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2161 => #S(INTERVAL :LOW 0 :HIGH 10)
2162 (floor-quotient-bound (make-interval :low 0.3 :high 10))
2163 => #S(INTERVAL :LOW 0 :HIGH 10)
2164 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
2165 => #S(INTERVAL :LOW 0 :HIGH 9)
2166 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
2167 => #S(INTERVAL :LOW 0 :HIGH 10)
2168 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
2169 => #S(INTERVAL :LOW 0 :HIGH 10)
2170 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2171 => #S(INTERVAL :LOW -2 :HIGH 10)
2172 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2173 => #S(INTERVAL :LOW -1 :HIGH 10)
2174 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
2175 => #S(INTERVAL :LOW -1 :HIGH 10)
2177 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
2178 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2179 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
2180 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2181 (floor-rem-bound (make-interval :low -10 :high -2.3))
2182 #S(INTERVAL :LOW (-10) :HIGH 0)
2183 (floor-rem-bound (make-interval :low 0.3 :high 10))
2184 => #S(INTERVAL :LOW 0 :HIGH '(10))
2185 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
2186 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
2187 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
2188 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2191 ;;; same functions for CEILING
2192 (defun ceiling-quotient-bound (quot)
2193 ;; Take the ceiling of the quotient and then massage it into what we
2195 (let ((lo (interval-low quot))
2196 (hi (interval-high quot)))
2197 ;; Take the ceiling of the upper bound. The result is always a
2198 ;; closed upper bound.
2200 (ceiling (type-bound-number hi))
2202 ;; For the lower bound, we need to be careful.
2205 ;; An open bound. We need to be careful here because
2206 ;; the ceiling of '(10.0) is 11, but the ceiling of
2208 (multiple-value-bind (q r) (ceiling (first lo))
2213 ;; A closed bound, so the answer is obvious.
2217 (make-interval :low lo :high hi)))
2218 (defun ceiling-rem-bound (div)
2219 ;; The remainder depends only on the divisor. Try to get the
2220 ;; correct sign for the remainder if we can.
2221 (case (interval-range-info div)
2223 ;; Divisor is always positive. The remainder is negative.
2224 (let ((rem (interval-neg (interval-abs div))))
2225 (setf (interval-high rem) 0)
2226 (when (and (numberp (interval-low rem))
2227 (not (zerop (interval-low rem))))
2228 ;; The remainder never contains the upper bound. However,
2229 ;; watch out for the case when the upper bound is zero!
2230 (setf (interval-low rem) (list (interval-low rem))))
2233 ;; Divisor is always negative. The remainder is positive
2234 (let ((rem (interval-abs div)))
2235 (setf (interval-low rem) 0)
2236 (when (numberp (interval-high rem))
2237 ;; The remainder never contains the lower bound.
2238 (setf (interval-high rem) (list (interval-high rem))))
2241 ;; The divisor can be positive or negative. All bets off. The
2242 ;; magnitude of remainder is the maximum value of the divisor.
2243 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2244 ;; The bound never reaches the limit, so make the interval open.
2245 (make-interval :low (if limit
2248 :high (list limit))))))
2251 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2252 => #S(INTERVAL :LOW 1 :HIGH 11)
2253 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2254 => #S(INTERVAL :LOW 1 :HIGH 11)
2255 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2256 => #S(INTERVAL :LOW 1 :HIGH 10)
2257 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2258 => #S(INTERVAL :LOW 1 :HIGH 10)
2259 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2260 => #S(INTERVAL :LOW 1 :HIGH 11)
2261 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2262 => #S(INTERVAL :LOW 1 :HIGH 11)
2263 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2264 => #S(INTERVAL :LOW -1 :HIGH 11)
2265 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2266 => #S(INTERVAL :LOW 0 :HIGH 11)
2267 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2268 => #S(INTERVAL :LOW -1 :HIGH 11)
2270 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2271 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2272 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2273 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2274 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2275 => #S(INTERVAL :LOW 0 :HIGH (10))
2276 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2277 => #S(INTERVAL :LOW (-10) :HIGH 0)
2278 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2279 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2280 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2281 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2284 (defun truncate-quotient-bound (quot)
2285 ;; For positive quotients, truncate is exactly like floor. For
2286 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2287 ;; it's the union of the two pieces.
2288 (case (interval-range-info quot)
2291 (floor-quotient-bound quot))
2293 ;; just like CEILING
2294 (ceiling-quotient-bound quot))
2296 ;; Split the interval into positive and negative pieces, compute
2297 ;; the result for each piece and put them back together.
2298 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2299 (interval-merge-pair (ceiling-quotient-bound neg)
2300 (floor-quotient-bound pos))))))
2302 (defun truncate-rem-bound (num div)
2303 ;; This is significantly more complicated than FLOOR or CEILING. We
2304 ;; need both the number and the divisor to determine the range. The
2305 ;; basic idea is to split the ranges of NUM and DEN into positive
2306 ;; and negative pieces and deal with each of the four possibilities
2308 (case (interval-range-info num)
2310 (case (interval-range-info div)
2312 (floor-rem-bound div))
2314 (ceiling-rem-bound div))
2316 (destructuring-bind (neg pos) (interval-split 0 div t t)
2317 (interval-merge-pair (truncate-rem-bound num neg)
2318 (truncate-rem-bound num pos))))))
2320 (case (interval-range-info div)
2322 (ceiling-rem-bound div))
2324 (floor-rem-bound div))
2326 (destructuring-bind (neg pos) (interval-split 0 div t t)
2327 (interval-merge-pair (truncate-rem-bound num neg)
2328 (truncate-rem-bound num pos))))))
2330 (destructuring-bind (neg pos) (interval-split 0 num t t)
2331 (interval-merge-pair (truncate-rem-bound neg div)
2332 (truncate-rem-bound pos div))))))
2335 ;;; Derive useful information about the range. Returns three values:
2336 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2337 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2338 ;;; - The abs of the maximal value if there is one, or nil if it is
2340 (defun numeric-range-info (low high)
2341 (cond ((and low (not (minusp low)))
2342 (values '+ low high))
2343 ((and high (not (plusp high)))
2344 (values '- (- high) (if low (- low) nil)))
2346 (values nil 0 (and low high (max (- low) high))))))
2348 (defun integer-truncate-derive-type
2349 (number-low number-high divisor-low divisor-high)
2350 ;; The result cannot be larger in magnitude than the number, but the
2351 ;; sign might change. If we can determine the sign of either the
2352 ;; number or the divisor, we can eliminate some of the cases.
2353 (multiple-value-bind (number-sign number-min number-max)
2354 (numeric-range-info number-low number-high)
2355 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2356 (numeric-range-info divisor-low divisor-high)
2357 (when (and divisor-max (zerop divisor-max))
2358 ;; We've got a problem: guaranteed division by zero.
2359 (return-from integer-truncate-derive-type t))
2360 (when (zerop divisor-min)
2361 ;; We'll assume that they aren't going to divide by zero.
2363 (cond ((and number-sign divisor-sign)
2364 ;; We know the sign of both.
2365 (if (eq number-sign divisor-sign)
2366 ;; Same sign, so the result will be positive.
2367 `(integer ,(if divisor-max
2368 (truncate number-min divisor-max)
2371 (truncate number-max divisor-min)
2373 ;; Different signs, the result will be negative.
2374 `(integer ,(if number-max
2375 (- (truncate number-max divisor-min))
2378 (- (truncate number-min divisor-max))
2380 ((eq divisor-sign '+)
2381 ;; The divisor is positive. Therefore, the number will just
2382 ;; become closer to zero.
2383 `(integer ,(if number-low
2384 (truncate number-low divisor-min)
2387 (truncate number-high divisor-min)
2389 ((eq divisor-sign '-)
2390 ;; The divisor is negative. Therefore, the absolute value of
2391 ;; the number will become closer to zero, but the sign will also
2393 `(integer ,(if number-high
2394 (- (truncate number-high divisor-min))
2397 (- (truncate number-low divisor-min))
2399 ;; The divisor could be either positive or negative.
2401 ;; The number we are dividing has a bound. Divide that by the
2402 ;; smallest posible divisor.
2403 (let ((bound (truncate number-max divisor-min)))
2404 `(integer ,(- bound) ,bound)))
2406 ;; The number we are dividing is unbounded, so we can't tell
2407 ;; anything about the result.
2410 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2411 (defun integer-rem-derive-type
2412 (number-low number-high divisor-low divisor-high)
2413 (if (and divisor-low divisor-high)
2414 ;; We know the range of the divisor, and the remainder must be
2415 ;; smaller than the divisor. We can tell the sign of the
2416 ;; remainder if we know the sign of the number.
2417 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2418 `(integer ,(if (or (null number-low)
2419 (minusp number-low))
2422 ,(if (or (null number-high)
2423 (plusp number-high))
2426 ;; The divisor is potentially either very positive or very
2427 ;; negative. Therefore, the remainder is unbounded, but we might
2428 ;; be able to tell something about the sign from the number.
2429 `(integer ,(if (and number-low (not (minusp number-low)))
2430 ;; The number we are dividing is positive.
2431 ;; Therefore, the remainder must be positive.
2434 ,(if (and number-high (not (plusp number-high)))
2435 ;; The number we are dividing is negative.
2436 ;; Therefore, the remainder must be negative.
2440 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2441 (defoptimizer (random derive-type) ((bound &optional state))
2442 (let ((type (lvar-type bound)))
2443 (when (numeric-type-p type)
2444 (let ((class (numeric-type-class type))
2445 (high (numeric-type-high type))
2446 (format (numeric-type-format type)))
2450 :low (coerce 0 (or format class 'real))
2451 :high (cond ((not high) nil)
2452 ((eq class 'integer) (max (1- high) 0))
2453 ((or (consp high) (zerop high)) high)
2456 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2457 (defun random-derive-type-aux (type)
2458 (let ((class (numeric-type-class type))
2459 (high (numeric-type-high type))
2460 (format (numeric-type-format type)))
2464 :low (coerce 0 (or format class 'real))
2465 :high (cond ((not high) nil)
2466 ((eq class 'integer) (max (1- high) 0))
2467 ((or (consp high) (zerop high)) high)
2470 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2471 (defoptimizer (random derive-type) ((bound &optional state))
2472 (one-arg-derive-type bound #'random-derive-type-aux nil))
2474 ;;;; miscellaneous derive-type methods
2476 (defoptimizer (integer-length derive-type) ((x))
2477 (let ((x-type (lvar-type x)))
2478 (when (numeric-type-p x-type)
2479 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2480 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2481 ;; careful about LO or HI being NIL, though. Also, if 0 is
2482 ;; contained in X, the lower bound is obviously 0.
2483 (flet ((null-or-min (a b)
2484 (and a b (min (integer-length a)
2485 (integer-length b))))
2487 (and a b (max (integer-length a)
2488 (integer-length b)))))
2489 (let* ((min (numeric-type-low x-type))
2490 (max (numeric-type-high x-type))
2491 (min-len (null-or-min min max))
2492 (max-len (null-or-max min max)))
2493 (when (ctypep 0 x-type)
2495 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2497 (defoptimizer (isqrt derive-type) ((x))
2498 (let ((x-type (lvar-type x)))
2499 (when (numeric-type-p x-type)
2500 (let* ((lo (numeric-type-low x-type))
2501 (hi (numeric-type-high x-type))
2502 (lo-res (if lo (isqrt lo) '*))
2503 (hi-res (if hi (isqrt hi) '*)))
2504 (specifier-type `(integer ,lo-res ,hi-res))))))
2506 (defoptimizer (char-code derive-type) ((char))
2507 (let ((type (type-intersection (lvar-type char) (specifier-type 'character))))
2508 (cond ((member-type-p type)
2511 ,@(loop for member in (member-type-members type)
2512 when (characterp member)
2513 collect (char-code member)))))
2514 ((sb!kernel::character-set-type-p type)
2517 ,@(loop for (low . high)
2518 in (character-set-type-pairs type)
2519 collect `(integer ,low ,high)))))
2520 ((csubtypep type (specifier-type 'base-char))
2522 `(mod ,base-char-code-limit)))
2525 `(mod ,char-code-limit))))))
2527 (defoptimizer (code-char derive-type) ((code))
2528 (let ((type (lvar-type code)))
2529 ;; FIXME: unions of integral ranges? It ought to be easier to do
2530 ;; this, given that CHARACTER-SET is basically an integral range
2531 ;; type. -- CSR, 2004-10-04
2532 (when (numeric-type-p type)
2533 (let* ((lo (numeric-type-low type))
2534 (hi (numeric-type-high type))
2535 (type (specifier-type `(character-set ((,lo . ,hi))))))
2537 ;; KLUDGE: when running on the host, we lose a slight amount
2538 ;; of precision so that we don't have to "unparse" types
2539 ;; that formally we can't, such as (CHARACTER-SET ((0
2540 ;; . 0))). -- CSR, 2004-10-06
2542 ((csubtypep type (specifier-type 'standard-char)) type)
2544 ((csubtypep type (specifier-type 'base-char))
2545 (specifier-type 'base-char))
2547 ((csubtypep type (specifier-type 'extended-char))
2548 (specifier-type 'extended-char))
2549 (t #+sb-xc-host (specifier-type 'character)
2550 #-sb-xc-host type))))))
2552 (defoptimizer (values derive-type) ((&rest values))
2553 (make-values-type :required (mapcar #'lvar-type values)))
2555 (defun signum-derive-type-aux (type)
2556 (if (eq (numeric-type-complexp type) :complex)
2557 (let* ((format (case (numeric-type-class type)
2558 ((integer rational) 'single-float)
2559 (t (numeric-type-format type))))
2560 (bound-format (or format 'float)))
2561 (make-numeric-type :class 'float
2564 :low (coerce -1 bound-format)
2565 :high (coerce 1 bound-format)))
2566 (let* ((interval (numeric-type->interval type))
2567 (range-info (interval-range-info interval))
2568 (contains-0-p (interval-contains-p 0 interval))
2569 (class (numeric-type-class type))
2570 (format (numeric-type-format type))
2571 (one (coerce 1 (or format class 'real)))
2572 (zero (coerce 0 (or format class 'real)))
2573 (minus-one (coerce -1 (or format class 'real)))
2574 (plus (make-numeric-type :class class :format format
2575 :low one :high one))
2576 (minus (make-numeric-type :class class :format format
2577 :low minus-one :high minus-one))
2578 ;; KLUDGE: here we have a fairly horrible hack to deal
2579 ;; with the schizophrenia in the type derivation engine.
2580 ;; The problem is that the type derivers reinterpret
2581 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2582 ;; 0d0) within the derivation mechanism doesn't include
2583 ;; -0d0. Ugh. So force it in here, instead.
2584 (zero (make-numeric-type :class class :format format
2585 :low (- zero) :high zero)))
2587 (+ (if contains-0-p (type-union plus zero) plus))
2588 (- (if contains-0-p (type-union minus zero) minus))
2589 (t (type-union minus zero plus))))))
2591 (defoptimizer (signum derive-type) ((num))
2592 (one-arg-derive-type num #'signum-derive-type-aux nil))
2594 ;;;; byte operations
2596 ;;;; We try to turn byte operations into simple logical operations.
2597 ;;;; First, we convert byte specifiers into separate size and position
2598 ;;;; arguments passed to internal %FOO functions. We then attempt to
2599 ;;;; transform the %FOO functions into boolean operations when the
2600 ;;;; size and position are constant and the operands are fixnums.
2602 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2603 ;; expressions that evaluate to the SIZE and POSITION of
2604 ;; the byte-specifier form SPEC. We may wrap a let around
2605 ;; the result of the body to bind some variables.
2607 ;; If the spec is a BYTE form, then bind the vars to the
2608 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2609 ;; and BYTE-POSITION. The goal of this transformation is to
2610 ;; avoid consing up byte specifiers and then immediately
2611 ;; throwing them away.
2612 (with-byte-specifier ((size-var pos-var spec) &body body)
2613 (once-only ((spec `(macroexpand ,spec))
2615 `(if (and (consp ,spec)
2616 (eq (car ,spec) 'byte)
2617 (= (length ,spec) 3))
2618 (let ((,size-var (second ,spec))
2619 (,pos-var (third ,spec)))
2621 (let ((,size-var `(byte-size ,,temp))
2622 (,pos-var `(byte-position ,,temp)))
2623 `(let ((,,temp ,,spec))
2626 (define-source-transform ldb (spec int)
2627 (with-byte-specifier (size pos spec)
2628 `(%ldb ,size ,pos ,int)))
2630 (define-source-transform dpb (newbyte spec int)
2631 (with-byte-specifier (size pos spec)
2632 `(%dpb ,newbyte ,size ,pos ,int)))
2634 (define-source-transform mask-field (spec int)
2635 (with-byte-specifier (size pos spec)
2636 `(%mask-field ,size ,pos ,int)))
2638 (define-source-transform deposit-field (newbyte spec int)
2639 (with-byte-specifier (size pos spec)
2640 `(%deposit-field ,newbyte ,size ,pos ,int))))
2642 (defoptimizer (%ldb derive-type) ((size posn num))
2643 (let ((size (lvar-type size)))
2644 (if (and (numeric-type-p size)
2645 (csubtypep size (specifier-type 'integer)))
2646 (let ((size-high (numeric-type-high size)))
2647 (if (and size-high (<= size-high sb!vm:n-word-bits))
2648 (specifier-type `(unsigned-byte* ,size-high))
2649 (specifier-type 'unsigned-byte)))
2652 (defoptimizer (%mask-field derive-type) ((size posn num))
2653 (let ((size (lvar-type size))
2654 (posn (lvar-type posn)))
2655 (if (and (numeric-type-p size)
2656 (csubtypep size (specifier-type 'integer))
2657 (numeric-type-p posn)
2658 (csubtypep posn (specifier-type 'integer)))
2659 (let ((size-high (numeric-type-high size))
2660 (posn-high (numeric-type-high posn)))
2661 (if (and size-high posn-high
2662 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2663 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2664 (specifier-type 'unsigned-byte)))
2667 (defun %deposit-field-derive-type-aux (size posn int)
2668 (let ((size (lvar-type size))
2669 (posn (lvar-type posn))
2670 (int (lvar-type int)))
2671 (when (and (numeric-type-p size)
2672 (numeric-type-p posn)
2673 (numeric-type-p int))
2674 (let ((size-high (numeric-type-high size))
2675 (posn-high (numeric-type-high posn))
2676 (high (numeric-type-high int))
2677 (low (numeric-type-low int)))
2678 (when (and size-high posn-high high low
2679 ;; KLUDGE: we need this cutoff here, otherwise we
2680 ;; will merrily derive the type of %DPB as
2681 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2682 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2683 ;; 1073741822))), with hilarious consequences. We
2684 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2685 ;; over a reasonable amount of shifting, even on
2686 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2687 ;; machine integers are 64-bits. -- CSR,
2689 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2690 (let ((raw-bit-count (max (integer-length high)
2691 (integer-length low)
2692 (+ size-high posn-high))))
2695 `(signed-byte ,(1+ raw-bit-count))
2696 `(unsigned-byte* ,raw-bit-count)))))))))
2698 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2699 (%deposit-field-derive-type-aux size posn int))
2701 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2702 (%deposit-field-derive-type-aux size posn int))
2704 (deftransform %ldb ((size posn int)
2705 (fixnum fixnum integer)
2706 (unsigned-byte #.sb!vm:n-word-bits))
2707 "convert to inline logical operations"
2708 `(logand (ash int (- posn))
2709 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2710 (- size ,sb!vm:n-word-bits))))
2712 (deftransform %mask-field ((size posn int)
2713 (fixnum fixnum integer)
2714 (unsigned-byte #.sb!vm:n-word-bits))
2715 "convert to inline logical operations"
2717 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2718 (- size ,sb!vm:n-word-bits))
2721 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2722 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2723 ;;; as the result type, as that would allow result types that cover
2724 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2725 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2727 (deftransform %dpb ((new size posn int)
2729 (unsigned-byte #.sb!vm:n-word-bits))
2730 "convert to inline logical operations"
2731 `(let ((mask (ldb (byte size 0) -1)))
2732 (logior (ash (logand new mask) posn)
2733 (logand int (lognot (ash mask posn))))))
2735 (deftransform %dpb ((new size posn int)
2737 (signed-byte #.sb!vm:n-word-bits))
2738 "convert to inline logical operations"
2739 `(let ((mask (ldb (byte size 0) -1)))
2740 (logior (ash (logand new mask) posn)
2741 (logand int (lognot (ash mask posn))))))
2743 (deftransform %deposit-field ((new size posn int)
2745 (unsigned-byte #.sb!vm:n-word-bits))
2746 "convert to inline logical operations"
2747 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2748 (logior (logand new mask)
2749 (logand int (lognot mask)))))
2751 (deftransform %deposit-field ((new size posn int)
2753 (signed-byte #.sb!vm:n-word-bits))
2754 "convert to inline logical operations"
2755 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2756 (logior (logand new mask)
2757 (logand int (lognot mask)))))
2759 (defoptimizer (mask-signed-field derive-type) ((size x))
2760 (let ((size (lvar-type size)))
2761 (if (numeric-type-p size)
2762 (let ((size-high (numeric-type-high size)))
2763 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2764 (specifier-type `(signed-byte ,size-high))
2771 (defun %ash/right (integer amount)
2772 (ash integer (- amount)))
2774 (deftransform ash ((integer amount) (sb!vm:signed-word (integer * 0)))
2775 "Convert ASH of signed word to %ASH/RIGHT"
2776 (when (constant-lvar-p amount)
2777 (give-up-ir1-transform))
2778 (let ((use (lvar-uses amount)))
2779 (cond ((and (combination-p use)
2780 (eql '%negate (lvar-fun-name (combination-fun use))))
2781 (splice-fun-args amount '%negate 1)
2782 `(lambda (integer amount)
2783 (declare (type unsigned-byte amount))
2784 (%ash/right integer (if (>= amount ,sb!vm:n-word-bits)
2785 ,(1- sb!vm:n-word-bits)
2788 `(%ash/right integer (if (<= amount ,(- sb!vm:n-word-bits))
2789 ,(1- sb!vm:n-word-bits)
2792 (deftransform ash ((integer amount) (word (integer * 0)))
2793 "Convert ASH of word to %ASH/RIGHT"
2794 (when (constant-lvar-p amount)
2795 (give-up-ir1-transform))
2796 (let ((use (lvar-uses amount)))
2797 (cond ((and (combination-p use)
2798 (eql '%negate (lvar-fun-name (combination-fun use))))
2799 (splice-fun-args amount '%negate 1)
2800 `(lambda (integer amount)
2801 (declare (type unsigned-byte amount))
2802 (if (>= amount ,sb!vm:n-word-bits)
2804 (%ash/right integer amount))))
2806 `(if (<= amount ,(- sb!vm:n-word-bits))
2808 (%ash/right integer (- amount)))))))
2810 (deftransform %ash/right ((integer amount) (integer (constant-arg unsigned-byte)))
2811 "Convert %ASH/RIGHT by constant back to ASH"
2812 `(ash integer ,(- (lvar-value amount))))
2814 (deftransform %ash/right ((integer amount) * * :node node)
2815 "strength reduce large variable right shift"
2816 (let ((return-type (single-value-type (node-derived-type node))))
2817 (cond ((type= return-type (specifier-type '(eql 0)))
2819 ((type= return-type (specifier-type '(eql -1)))
2821 ((csubtypep return-type (specifier-type '(member -1 0)))
2822 `(ash integer ,(- sb!vm:n-word-bits)))
2824 (give-up-ir1-transform)))))
2826 (defun %ash/right-derive-type-aux (n-type shift same-arg)
2827 (declare (ignore same-arg))
2828 (or (and (or (csubtypep n-type (specifier-type 'sb!vm:signed-word))
2829 (csubtypep n-type (specifier-type 'word)))
2830 (csubtypep shift (specifier-type `(mod ,sb!vm:n-word-bits)))
2831 (let ((n-low (numeric-type-low n-type))
2832 (n-high (numeric-type-high n-type))
2833 (s-low (numeric-type-low shift))
2834 (s-high (numeric-type-high shift)))
2835 (make-numeric-type :class 'integer :complexp :real
2838 (ash n-low (- s-low))
2839 (ash n-low (- s-high))))
2842 (ash n-high (- s-high))
2843 (ash n-high (- s-low)))))))
2846 (defoptimizer (%ash/right derive-type) ((n shift))
2847 (two-arg-derive-type n shift #'%ash/right-derive-type-aux #'%ash/right))
2850 ;;; Modular functions
2852 ;;; (ldb (byte s 0) (foo x y ...)) =
2853 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2855 ;;; and similar for other arguments.
2857 (defun make-modular-fun-type-deriver (prototype kind width signedp)
2858 (declare (ignore kind))
2860 (binding* ((info (info :function :info prototype) :exit-if-null)
2861 (fun (fun-info-derive-type info) :exit-if-null)
2862 (mask-type (specifier-type
2864 ((nil) (let ((mask (1- (ash 1 width))))
2865 `(integer ,mask ,mask)))
2866 ((t) `(signed-byte ,width))))))
2868 (let ((res (funcall fun call)))
2870 (if (eq signedp nil)
2871 (logand-derive-type-aux res mask-type))))))
2874 (binding* ((info (info :function :info prototype) :exit-if-null)
2875 (fun (fun-info-derive-type info) :exit-if-null)
2876 (res (funcall fun call) :exit-if-null)
2877 (mask-type (specifier-type
2879 ((nil) (let ((mask (1- (ash 1 width))))
2880 `(integer ,mask ,mask)))
2881 ((t) `(signed-byte ,width))))))
2882 (if (eq signedp nil)
2883 (logand-derive-type-aux res mask-type)))))
2885 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2887 ;;; For good functions, we just recursively cut arguments; their
2888 ;;; "goodness" means that the result will not increase (in the
2889 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2890 ;;; replaced with the version, cutting its result to WIDTH or more
2891 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2892 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2893 ;;; arguments (maybe to a different width) and returning the name of a
2894 ;;; modular version, if it exists, or NIL. If we have changed
2895 ;;; anything, we need to flush old derived types, because they have
2896 ;;; nothing in common with the new code.
2897 (defun cut-to-width (lvar kind width signedp)
2898 (declare (type lvar lvar) (type (integer 0) width))
2899 (let ((type (specifier-type (if (zerop width)
2902 ((nil) 'unsigned-byte)
2905 (labels ((reoptimize-node (node name)
2906 (setf (node-derived-type node)
2908 (info :function :type name)))
2909 (setf (lvar-%derived-type (node-lvar node)) nil)
2910 (setf (node-reoptimize node) t)
2911 (setf (block-reoptimize (node-block node)) t)
2912 (reoptimize-component (node-component node) :maybe))
2913 (cut-node (node &aux did-something)
2914 (when (block-delete-p (node-block node))
2915 (return-from cut-node))
2918 (typecase (ref-leaf node)
2920 (let* ((constant-value (constant-value (ref-leaf node)))
2921 (new-value (if signedp
2922 (mask-signed-field width constant-value)
2923 (ldb (byte width 0) constant-value))))
2924 (unless (= constant-value new-value)
2925 (change-ref-leaf node (make-constant new-value)
2927 (let ((lvar (node-lvar node)))
2928 (setf (lvar-%derived-type lvar)
2929 (and (lvar-has-single-use-p lvar)
2930 (make-values-type :required (list (ctype-of new-value))))))
2931 (setf (block-reoptimize (node-block node)) t)
2932 (reoptimize-component (node-component node) :maybe)
2935 (binding* ((dest (lvar-dest lvar) :exit-if-null)
2936 (nil (combination-p dest) :exit-if-null)
2937 (name (lvar-fun-name (combination-fun dest))))
2938 ;; we're about to insert an m-s-f/logand between a ref to
2939 ;; a variable and another m-s-f/logand. No point in doing
2940 ;; that; the parent m-s-f/logand was already cut to width
2942 (unless (or (cond (signedp
2943 (and (eql name 'mask-signed-field)
2948 (eql name 'logand)))
2949 (csubtypep (lvar-type lvar) type))
2952 `(mask-signed-field ,width 'dummy)
2953 `(logand 'dummy ,(ldb (byte width 0) -1))))
2954 (setf (block-reoptimize (node-block node)) t)
2955 (reoptimize-component (node-component node) :maybe)
2958 (when (eq (basic-combination-kind node) :known)
2959 (let* ((fun-ref (lvar-use (combination-fun node)))
2960 (fun-name (lvar-fun-name (combination-fun node)))
2961 (modular-fun (find-modular-version fun-name kind
2963 (when (and modular-fun
2964 (not (and (eq fun-name 'logand)
2966 (single-value-type (node-derived-type node))
2968 (binding* ((name (etypecase modular-fun
2969 ((eql :good) fun-name)
2971 (modular-fun-info-name modular-fun))
2973 (funcall modular-fun node width)))
2975 (unless (eql modular-fun :good)
2976 (setq did-something t)
2979 (find-free-fun name "in a strange place"))
2980 (setf (combination-kind node) :full))
2981 (unless (functionp modular-fun)
2982 (dolist (arg (basic-combination-args node))
2983 (when (cut-lvar arg)
2984 (setq did-something t))))
2986 (reoptimize-node node name))
2987 did-something)))))))
2988 (cut-lvar (lvar &aux did-something)
2989 (do-uses (node lvar)
2990 (when (cut-node node)
2991 (setq did-something t)))
2995 (defun best-modular-version (width signedp)
2996 ;; 1. exact width-matched :untagged
2997 ;; 2. >/>= width-matched :tagged
2998 ;; 3. >/>= width-matched :untagged
2999 (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class*))
3000 (uswidths (modular-class-widths *untagged-signed-modular-class*))
3001 (uwidths (merge 'list uuwidths uswidths #'< :key #'car))
3002 (twidths (modular-class-widths *tagged-modular-class*)))
3003 (let ((exact (find (cons width signedp) uwidths :test #'equal)))
3005 (return-from best-modular-version (values width :untagged signedp))))
3006 (flet ((inexact-match (w)
3008 ((eq signedp (cdr w)) (<= width (car w)))
3009 ((eq signedp nil) (< width (car w))))))
3010 (let ((tgt (find-if #'inexact-match twidths)))
3012 (return-from best-modular-version
3013 (values (car tgt) :tagged (cdr tgt)))))
3014 (let ((ugt (find-if #'inexact-match uwidths)))
3016 (return-from best-modular-version
3017 (values (car ugt) :untagged (cdr ugt))))))))
3019 (defoptimizer (logand optimizer) ((x y) node)
3020 (let ((result-type (single-value-type (node-derived-type node))))
3021 (when (numeric-type-p result-type)
3022 (let ((low (numeric-type-low result-type))
3023 (high (numeric-type-high result-type)))
3024 (when (and (numberp low)
3027 (let ((width (integer-length high)))
3028 (multiple-value-bind (w kind signedp)
3029 (best-modular-version width nil)
3031 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP).
3033 ;; FIXME: I think the FIXME (which is from APD) above
3034 ;; implies that CUT-TO-WIDTH should do /everything/
3035 ;; that's required, including reoptimizing things
3036 ;; itself that it knows are necessary. At the moment,
3037 ;; CUT-TO-WIDTH sets up some new calls with
3038 ;; combination-type :FULL, which later get noticed as
3039 ;; known functions and properly converted.
3041 ;; We cut to W not WIDTH if SIGNEDP is true, because
3042 ;; signed constant replacement needs to know which bit
3043 ;; in the field is the signed bit.
3044 (let ((xact (cut-to-width x kind (if signedp w width) signedp))
3045 (yact (cut-to-width y kind (if signedp w width) signedp)))
3046 (declare (ignore xact yact))
3047 nil) ; After fixing above, replace with T, meaning
3048 ; "don't reoptimize this (LOGAND) node any more".
3051 (defoptimizer (mask-signed-field optimizer) ((width x) node)
3052 (let ((result-type (single-value-type (node-derived-type node))))
3053 (when (numeric-type-p result-type)
3054 (let ((low (numeric-type-low result-type))
3055 (high (numeric-type-high result-type)))
3056 (when (and (numberp low) (numberp high))
3057 (let ((width (max (integer-length high) (integer-length low))))
3058 (multiple-value-bind (w kind)
3059 (best-modular-version (1+ width) t)
3061 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND W T).
3062 ;; [ see comment above in LOGAND optimizer ]
3063 (cut-to-width x kind w t)
3064 nil ; After fixing above, replace with T.
3067 ;;; miscellanous numeric transforms
3069 ;;; If a constant appears as the first arg, swap the args.
3070 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
3071 (if (and (constant-lvar-p x)
3072 (not (constant-lvar-p y)))
3073 `(,(lvar-fun-name (basic-combination-fun node))
3074 (truly-the ,(lvar-type y) y)
3076 (give-up-ir1-transform)))
3078 (dolist (x '(= char= + * logior logand logxor logtest))
3079 (%deftransform x '(function * *) #'commutative-arg-swap
3080 "place constant arg last"))
3082 ;;; Handle the case of a constant BOOLE-CODE.
3083 (deftransform boole ((op x y) * *)
3084 "convert to inline logical operations"
3085 (unless (constant-lvar-p op)
3086 (give-up-ir1-transform "BOOLE code is not a constant."))
3087 (let ((control (lvar-value op)))
3089 (#.sb!xc:boole-clr 0)
3090 (#.sb!xc:boole-set -1)
3091 (#.sb!xc:boole-1 'x)
3092 (#.sb!xc:boole-2 'y)
3093 (#.sb!xc:boole-c1 '(lognot x))
3094 (#.sb!xc:boole-c2 '(lognot y))
3095 (#.sb!xc:boole-and '(logand x y))
3096 (#.sb!xc:boole-ior '(logior x y))
3097 (#.sb!xc:boole-xor '(logxor x y))
3098 (#.sb!xc:boole-eqv '(logeqv x y))
3099 (#.sb!xc:boole-nand '(lognand x y))
3100 (#.sb!xc:boole-nor '(lognor x y))
3101 (#.sb!xc:boole-andc1 '(logandc1 x y))
3102 (#.sb!xc:boole-andc2 '(logandc2 x y))
3103 (#.sb!xc:boole-orc1 '(logorc1 x y))
3104 (#.sb!xc:boole-orc2 '(logorc2 x y))
3106 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
3109 ;;;; converting special case multiply/divide to shifts
3111 ;;; If arg is a constant power of two, turn * into a shift.
3112 (deftransform * ((x y) (integer integer) *)
3113 "convert x*2^k to shift"
3114 (unless (constant-lvar-p y)
3115 (give-up-ir1-transform))
3116 (let* ((y (lvar-value y))
3118 (len (1- (integer-length y-abs))))
3119 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3120 (give-up-ir1-transform))
3125 ;;; These must come before the ones below, so that they are tried
3126 ;;; first. Since %FLOOR and %CEILING are inlined, this allows
3127 ;;; the general case to be handled by TRUNCATE transforms.
3128 (deftransform floor ((x y))
3131 (deftransform ceiling ((x y))
3134 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3135 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3137 (flet ((frob (y ceil-p)
3138 (unless (constant-lvar-p y)
3139 (give-up-ir1-transform))
3140 (let* ((y (lvar-value y))
3142 (len (1- (integer-length y-abs))))
3143 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3144 (give-up-ir1-transform))
3145 (let ((shift (- len))
3147 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
3148 `(let ((x (+ x ,delta)))
3150 `(values (ash (- x) ,shift)
3151 (- (- (logand (- x) ,mask)) ,delta))
3152 `(values (ash x ,shift)
3153 (- (logand x ,mask) ,delta))))))))
3154 (deftransform floor ((x y) (integer integer) *)
3155 "convert division by 2^k to shift"
3157 (deftransform ceiling ((x y) (integer integer) *)
3158 "convert division by 2^k to shift"
3161 ;;; Do the same for MOD.
3162 (deftransform mod ((x y) (integer integer) *)
3163 "convert remainder mod 2^k to LOGAND"
3164 (unless (constant-lvar-p y)
3165 (give-up-ir1-transform))
3166 (let* ((y (lvar-value y))
3168 (len (1- (integer-length y-abs))))
3169 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3170 (give-up-ir1-transform))
3171 (let ((mask (1- y-abs)))
3173 `(- (logand (- x) ,mask))
3174 `(logand x ,mask)))))
3176 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3177 (deftransform truncate ((x y) (integer integer))
3178 "convert division by 2^k to shift"
3179 (unless (constant-lvar-p y)
3180 (give-up-ir1-transform))
3181 (let* ((y (lvar-value y))
3183 (len (1- (integer-length y-abs))))
3184 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3185 (give-up-ir1-transform))
3186 (let* ((shift (- len))
3189 (values ,(if (minusp y)
3191 `(- (ash (- x) ,shift)))
3192 (- (logand (- x) ,mask)))
3193 (values ,(if (minusp y)
3194 `(ash (- ,mask x) ,shift)
3196 (logand x ,mask))))))
3198 ;;; And the same for REM.
3199 (deftransform rem ((x y) (integer integer) *)
3200 "convert remainder mod 2^k to LOGAND"
3201 (unless (constant-lvar-p y)
3202 (give-up-ir1-transform))
3203 (let* ((y (lvar-value y))
3205 (len (1- (integer-length y-abs))))
3206 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3207 (give-up-ir1-transform))
3208 (let ((mask (1- y-abs)))
3210 (- (logand (- x) ,mask))
3211 (logand x ,mask)))))
3213 ;;; Return an expression to calculate the integer quotient of X and
3214 ;;; constant Y, using multiplication, shift and add/sub instead of
3215 ;;; division. Both arguments must be unsigned, fit in a machine word and
3216 ;;; Y must neither be zero nor a power of two. The quotient is rounded
3218 ;;; The algorithm is taken from the paper "Division by Invariant
3219 ;;; Integers using Multiplication", 1994 by Torbj\"{o}rn Granlund and
3220 ;;; Peter L. Montgomery, Figures 4.2 and 6.2, modified to exclude the
3221 ;;; case of division by powers of two.
3222 ;;; The algorithm includes an adaptive precision argument. Use it, since
3223 ;;; we often have sub-word value ranges. Careful, in this case, we need
3224 ;;; p s.t 2^p > n, not the ceiling of the binary log.
3225 ;;; Also, for some reason, the paper prefers shifting to masking. Mask
3226 ;;; instead. Masking is equivalent to shifting right, then left again;
3227 ;;; all the intermediate values are still words, so we just have to shift
3228 ;;; right a bit more to compensate, at the end.
3230 ;;; The following two examples show an average case and the worst case
3231 ;;; with respect to the complexity of the generated expression, under
3232 ;;; a word size of 64 bits:
3234 ;;; (UNSIGNED-DIV-TRANSFORMER 10 MOST-POSITIVE-WORD) ->
3235 ;;; (ASH (%MULTIPLY (LOGANDC2 X 0) 14757395258967641293) -3)
3237 ;;; (UNSIGNED-DIV-TRANSFORMER 7 MOST-POSITIVE-WORD) ->
3239 ;;; (T1 (%MULTIPLY NUM 2635249153387078803)))
3240 ;;; (ASH (LDB (BYTE 64 0)
3241 ;;; (+ T1 (ASH (LDB (BYTE 64 0)
3246 (defun gen-unsigned-div-by-constant-expr (y max-x)
3247 (declare (type (integer 3 #.most-positive-word) y)
3249 (aver (not (zerop (logand y (1- y)))))
3251 ;; the floor of the binary logarithm of (positive) X
3252 (integer-length (1- x)))
3253 (choose-multiplier (y precision)
3255 (shift l (1- shift))
3256 (expt-2-n+l (expt 2 (+ sb!vm:n-word-bits l)))
3257 (m-low (truncate expt-2-n+l y) (ash m-low -1))
3258 (m-high (truncate (+ expt-2-n+l
3259 (ash expt-2-n+l (- precision)))
3262 ((not (and (< (ash m-low -1) (ash m-high -1))
3264 (values m-high shift)))))
3265 (let ((n (expt 2 sb!vm:n-word-bits))
3266 (precision (integer-length max-x))
3268 (multiple-value-bind (m shift2)
3269 (choose-multiplier y precision)
3270 (when (and (>= m n) (evenp y))
3271 (setq shift1 (ld (logand y (- y))))
3272 (multiple-value-setq (m shift2)
3273 (choose-multiplier (/ y (ash 1 shift1))
3274 (- precision shift1))))
3277 `(truly-the word ,x)))
3279 (t1 (%multiply-high num ,(- m n))))
3280 (ash ,(word `(+ t1 (ash ,(word `(- num t1))
3283 ((and (zerop shift1) (zerop shift2))
3284 (let ((max (truncate max-x y)))
3285 ;; Explicit TRULY-THE needed to get the FIXNUM=>FIXNUM
3287 `(truly-the (integer 0 ,max)
3288 (%multiply-high x ,m))))
3290 `(ash (%multiply-high (logandc2 x ,(1- (ash 1 shift1))) ,m)
3291 ,(- (+ shift1 shift2)))))))))
3293 ;;; If the divisor is constant and both args are positive and fit in a
3294 ;;; machine word, replace the division by a multiplication and possibly
3295 ;;; some shifts and an addition. Calculate the remainder by a second
3296 ;;; multiplication and a subtraction. Dead code elimination will
3297 ;;; suppress the latter part if only the quotient is needed. If the type
3298 ;;; of the dividend allows to derive that the quotient will always have
3299 ;;; the same value, emit much simpler code to handle that. (This case
3300 ;;; may be rare but it's easy to detect and the compiler doesn't find
3301 ;;; this optimization on its own.)
3302 (deftransform truncate ((x y) (word (constant-arg word))
3304 :policy (and (> speed compilation-speed)
3306 "convert integer division to multiplication"
3307 (let* ((y (lvar-value y))
3308 (x-type (lvar-type x))
3309 (max-x (or (and (numeric-type-p x-type)
3310 (numeric-type-high x-type))
3311 most-positive-word)))
3312 ;; Division by zero, one or powers of two is handled elsewhere.
3313 (when (zerop (logand y (1- y)))
3314 (give-up-ir1-transform))
3315 `(let* ((quot ,(gen-unsigned-div-by-constant-expr y max-x))
3316 (rem (ldb (byte #.sb!vm:n-word-bits 0)
3317 (- x (* quot ,y)))))
3318 (values quot rem))))
3320 ;;;; arithmetic and logical identity operation elimination
3322 ;;; Flush calls to various arith functions that convert to the
3323 ;;; identity function or a constant.
3324 (macrolet ((def (name identity result)
3325 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3326 "fold identity operations"
3333 (def logxor -1 (lognot x))
3336 (deftransform logand ((x y) (* (constant-arg t)) *)
3337 "fold identity operation"
3338 (let ((y (lvar-value y)))
3339 (unless (and (plusp y)
3340 (= y (1- (ash 1 (integer-length y)))))
3341 (give-up-ir1-transform))
3342 (unless (csubtypep (lvar-type x)
3343 (specifier-type `(integer 0 ,y)))
3344 (give-up-ir1-transform))
3347 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3348 "fold identity operation"
3349 (let ((size (lvar-value size)))
3350 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3351 (give-up-ir1-transform))
3354 ;;; Pick off easy association opportunities for constant folding.
3355 ;;; More complicated stuff that also depends on commutativity
3356 ;;; (e.g. (f (f x k1) (f y k2)) => (f (f x y) (f k1 k2))) should
3357 ;;; probably be handled with a more general tree-rewriting pass.
3358 (macrolet ((def (operator &key (type 'integer) (folded operator))
3359 `(deftransform ,operator ((x z) (,type (constant-arg ,type)))
3360 ,(format nil "associate ~A/~A of constants"
3362 (binding* ((node (if (lvar-has-single-use-p x)
3364 (give-up-ir1-transform)))
3365 (nil (or (and (combination-p node)
3367 (combination-fun node))
3369 (give-up-ir1-transform)))
3370 (y (second (combination-args node)))
3371 (nil (or (constant-lvar-p y)
3372 (give-up-ir1-transform)))
3374 (unless (typep y ',type)
3375 (give-up-ir1-transform))
3376 (splice-fun-args x ',folded 2)
3378 (declare (ignore y z))
3379 (,',operator x ',(,folded y (lvar-value z))))))))
3383 (def logtest :folded logand)
3384 (def + :type rational)
3385 (def * :type rational))
3387 (deftransform mask-signed-field ((width x) ((constant-arg unsigned-byte) *))
3388 "Fold mask-signed-field/mask-signed-field of constant width"
3389 (binding* ((node (if (lvar-has-single-use-p x)
3391 (give-up-ir1-transform)))
3392 (nil (or (combination-p node)
3393 (give-up-ir1-transform)))
3394 (nil (or (eq (lvar-fun-name (combination-fun node))
3396 (give-up-ir1-transform)))
3397 (x-width (first (combination-args node)))
3398 (nil (or (constant-lvar-p x-width)
3399 (give-up-ir1-transform)))
3400 (x-width (lvar-value x-width)))
3401 (unless (typep x-width 'unsigned-byte)
3402 (give-up-ir1-transform))
3403 (splice-fun-args x 'mask-signed-field 2)
3404 `(lambda (width x-width x)
3405 (declare (ignore width x-width))
3406 (mask-signed-field ,(min (lvar-value width) x-width) x))))
3408 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3409 ;;; (* 0 -4.0) is -0.0.
3410 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3411 "convert (- 0 x) to negate"
3413 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3414 "convert (* x 0) to 0"
3417 (deftransform %negate ((x) (rational))
3418 "Eliminate %negate/%negate of rationals"
3419 (splice-fun-args x '%negate 1)
3422 (deftransform %negate ((x) (number))
3424 (let ((use (lvar-uses x))
3426 (unless (and (combination-p use)
3427 (eql '* (lvar-fun-name (combination-fun use)))
3428 (constant-lvar-p (setf arg (second (combination-args use))))
3429 (numberp (setf arg (lvar-value arg))))
3430 (give-up-ir1-transform))
3431 (splice-fun-args x '* 2)
3433 (declare (ignore y))
3436 ;;; Return T if in an arithmetic op including lvars X and Y, the
3437 ;;; result type is not affected by the type of X. That is, Y is at
3438 ;;; least as contagious as X.
3440 (defun not-more-contagious (x y)
3441 (declare (type continuation x y))
3442 (let ((x (lvar-type x))
3444 (values (type= (numeric-contagion x y)
3445 (numeric-contagion y y)))))
3446 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3447 ;;; XXX needs more work as valid transforms are missed; some cases are
3448 ;;; specific to particular transform functions so the use of this
3449 ;;; function may need a re-think.
3450 (defun not-more-contagious (x y)
3451 (declare (type lvar x y))
3452 (flet ((simple-numeric-type (num)
3453 (and (numeric-type-p num)
3454 ;; Return non-NIL if NUM is integer, rational, or a float
3455 ;; of some type (but not FLOAT)
3456 (case (numeric-type-class num)
3460 (numeric-type-format num))
3463 (let ((x (lvar-type x))
3465 (if (and (simple-numeric-type x)
3466 (simple-numeric-type y))
3467 (values (type= (numeric-contagion x y)
3468 (numeric-contagion y y)))))))
3470 (def!type exact-number ()
3471 '(or rational (complex rational)))
3475 ;;; Only safely applicable for exact numbers. For floating-point
3476 ;;; x, one would have to first show that neither x or y are signed
3477 ;;; 0s, and that x isn't an SNaN.
3478 (deftransform + ((x y) (exact-number (constant-arg (eql 0))) *)
3483 (deftransform - ((x y) (exact-number (constant-arg (eql 0))) *)
3487 ;;; Fold (OP x +/-1)
3489 ;;; %NEGATE might not always signal correctly.
3491 ((def (name result minus-result)
3492 `(deftransform ,name ((x y)
3493 (exact-number (constant-arg (member 1 -1))))
3494 "fold identity operations"
3495 (if (minusp (lvar-value y)) ',minus-result ',result))))
3496 (def * x (%negate x))
3497 (def / x (%negate x))
3498 (def expt x (/ 1 x)))
3500 ;;; Fold (expt x n) into multiplications for small integral values of
3501 ;;; N; convert (expt x 1/2) to sqrt.
3502 (deftransform expt ((x y) (t (constant-arg real)) *)
3503 "recode as multiplication or sqrt"
3504 (let ((val (lvar-value y)))
3505 ;; If Y would cause the result to be promoted to the same type as
3506 ;; Y, we give up. If not, then the result will be the same type
3507 ;; as X, so we can replace the exponentiation with simple
3508 ;; multiplication and division for small integral powers.
3509 (unless (not-more-contagious y x)
3510 (give-up-ir1-transform))
3512 (let ((x-type (lvar-type x)))
3513 (cond ((csubtypep x-type (specifier-type '(or rational
3514 (complex rational))))
3516 ((csubtypep x-type (specifier-type 'real))
3520 ((csubtypep x-type (specifier-type 'complex))
3521 ;; both parts are float
3523 (t (give-up-ir1-transform)))))
3524 ((= val 2) '(* x x))
3525 ((= val -2) '(/ (* x x)))
3526 ((= val 3) '(* x x x))
3527 ((= val -3) '(/ (* x x x)))
3528 ((= val 1/2) '(sqrt x))
3529 ((= val -1/2) '(/ (sqrt x)))
3530 (t (give-up-ir1-transform)))))
3532 (deftransform expt ((x y) ((constant-arg (member -1 -1.0 -1.0d0)) integer) *)
3533 "recode as an ODDP check"
3534 (let ((val (lvar-value x)))
3536 '(- 1 (* 2 (logand 1 y)))
3541 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3542 ;;; transformations?
3543 ;;; Perhaps we should have to prove that the denominator is nonzero before
3544 ;;; doing them? -- WHN 19990917
3545 (macrolet ((def (name)
3546 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3553 (macrolet ((def (name)
3554 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3563 (macrolet ((def (name &optional float)
3564 (let ((x (if float '(float x) 'x)))
3565 `(deftransform ,name ((x y) (integer (constant-arg (member 1 -1)))
3567 "fold division by 1"
3568 `(values ,(if (minusp (lvar-value y))
3581 ;;;; character operations
3583 (deftransform char-equal ((a b) (base-char base-char))
3585 '(let* ((ac (char-code a))
3587 (sum (logxor ac bc)))
3589 (when (eql sum #x20)
3590 (let ((sum (+ ac bc)))
3591 (or (and (> sum 161) (< sum 213))
3592 (and (> sum 415) (< sum 461))
3593 (and (> sum 463) (< sum 477))))))))
3595 (deftransform char-upcase ((x) (base-char))
3597 '(let ((n-code (char-code x)))
3598 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3599 (< n-code #o173)) ; Octal 172 is #\z.
3600 (and (> n-code #o337)
3602 (and (> n-code #o367)
3604 (code-char (logxor #x20 n-code))
3607 (deftransform char-downcase ((x) (base-char))
3609 '(let ((n-code (char-code x)))
3610 (if (or (and (> n-code 64) ; 65 is #\A.
3611 (< n-code 91)) ; 90 is #\Z.
3616 (code-char (logxor #x20 n-code))
3619 ;;;; equality predicate transforms
3621 ;;; Return true if X and Y are lvars whose only use is a
3622 ;;; reference to the same leaf, and the value of the leaf cannot
3624 (defun same-leaf-ref-p (x y)
3625 (declare (type lvar x y))
3626 (let ((x-use (principal-lvar-use x))
3627 (y-use (principal-lvar-use y)))
3630 (eq (ref-leaf x-use) (ref-leaf y-use))
3631 (constant-reference-p x-use))))
3633 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3634 ;;; if there is no intersection between the types of the arguments,
3635 ;;; then the result is definitely false.
3636 (deftransform simple-equality-transform ((x y) * *
3639 ((same-leaf-ref-p x y) t)
3640 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3642 (t (give-up-ir1-transform))))
3645 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3649 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3650 ;;; try to convert to a type-specific predicate or EQ:
3651 ;;; -- If both args are characters, convert to CHAR=. This is better than
3652 ;;; just converting to EQ, since CHAR= may have special compilation
3653 ;;; strategies for non-standard representations, etc.
3654 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3655 ;;; constant and if so, put X second. Doing this results in better
3656 ;;; code from the backend, since the backend assumes that any constant
3657 ;;; argument comes second.
3658 ;;; -- If either arg is definitely not a number or a fixnum, then we
3659 ;;; can compare with EQ.
3660 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3661 ;;; is constant then we put it second. If X is a subtype of Y, we put
3662 ;;; it second. These rules make it easier for the back end to match
3663 ;;; these interesting cases.
3664 (deftransform eql ((x y) * * :node node)
3665 "convert to simpler equality predicate"
3666 (let ((x-type (lvar-type x))
3667 (y-type (lvar-type y))
3668 (char-type (specifier-type 'character)))
3669 (flet ((fixnum-type-p (type)
3670 (csubtypep type (specifier-type 'fixnum))))
3672 ((same-leaf-ref-p x y) t)
3673 ((not (types-equal-or-intersect x-type y-type))
3675 ((and (csubtypep x-type char-type)
3676 (csubtypep y-type char-type))
3678 ((or (eq-comparable-type-p x-type) (eq-comparable-type-p y-type))
3679 (if (and (constant-lvar-p x) (not (constant-lvar-p y)))
3682 ((and (not (constant-lvar-p y))
3683 (or (constant-lvar-p x)
3684 (and (csubtypep x-type y-type)
3685 (not (csubtypep y-type x-type)))))
3688 (give-up-ir1-transform))))))
3690 ;;; similarly to the EQL transform above, we attempt to constant-fold
3691 ;;; or convert to a simpler predicate: mostly we have to be careful
3692 ;;; with strings and bit-vectors.
3693 (deftransform equal ((x y) * *)
3694 "convert to simpler equality predicate"
3695 (let ((x-type (lvar-type x))
3696 (y-type (lvar-type y))
3697 (string-type (specifier-type 'string))
3698 (bit-vector-type (specifier-type 'bit-vector)))
3700 ((same-leaf-ref-p x y) t)
3701 ((and (csubtypep x-type string-type)
3702 (csubtypep y-type string-type))
3704 ((and (csubtypep x-type bit-vector-type)
3705 (csubtypep y-type bit-vector-type))
3706 '(bit-vector-= x y))
3707 ;; if at least one is not a string, and at least one is not a
3708 ;; bit-vector, then we can reason from types.
3709 ((and (not (and (types-equal-or-intersect x-type string-type)
3710 (types-equal-or-intersect y-type string-type)))
3711 (not (and (types-equal-or-intersect x-type bit-vector-type)
3712 (types-equal-or-intersect y-type bit-vector-type)))
3713 (not (types-equal-or-intersect x-type y-type)))
3715 (t (give-up-ir1-transform)))))
3717 ;;; Convert to EQL if both args are rational and complexp is specified
3718 ;;; and the same for both.
3719 (deftransform = ((x y) (number number) *)
3721 (let ((x-type (lvar-type x))
3722 (y-type (lvar-type y)))
3723 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3724 (csubtypep y-type (specifier-type 'float)))
3725 (and (csubtypep x-type (specifier-type '(complex float)))
3726 (csubtypep y-type (specifier-type '(complex float))))
3727 #!+complex-float-vops
3728 (and (csubtypep x-type (specifier-type '(or single-float (complex single-float))))
3729 (csubtypep y-type (specifier-type '(or single-float (complex single-float)))))
3730 #!+complex-float-vops
3731 (and (csubtypep x-type (specifier-type '(or double-float (complex double-float))))
3732 (csubtypep y-type (specifier-type '(or double-float (complex double-float))))))
3733 ;; They are both floats. Leave as = so that -0.0 is
3734 ;; handled correctly.
3735 (give-up-ir1-transform))
3736 ((or (and (csubtypep x-type (specifier-type 'rational))
3737 (csubtypep y-type (specifier-type 'rational)))
3738 (and (csubtypep x-type
3739 (specifier-type '(complex rational)))
3741 (specifier-type '(complex rational)))))
3742 ;; They are both rationals and complexp is the same.
3746 (give-up-ir1-transform
3747 "The operands might not be the same type.")))))
3749 (defun maybe-float-lvar-p (lvar)
3750 (neq *empty-type* (type-intersection (specifier-type 'float)
3753 (flet ((maybe-invert (node op inverted x y)
3754 ;; Don't invert if either argument can be a float (NaNs)
3756 ((or (maybe-float-lvar-p x) (maybe-float-lvar-p y))
3757 (delay-ir1-transform node :constraint)
3758 `(or (,op x y) (= x y)))
3760 `(if (,inverted x y) nil t)))))
3761 (deftransform >= ((x y) (number number) * :node node)
3762 "invert or open code"
3763 (maybe-invert node '> '< x y))
3764 (deftransform <= ((x y) (number number) * :node node)
3765 "invert or open code"
3766 (maybe-invert node '< '> x y)))
3768 ;;; See whether we can statically determine (< X Y) using type
3769 ;;; information. If X's high bound is < Y's low, then X < Y.
3770 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3771 ;;; NIL). If not, at least make sure any constant arg is second.
3772 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3773 `(deftransform ,name ((x y))
3774 "optimize using intervals"
3775 (if (and (same-leaf-ref-p x y)
3776 ;; For non-reflexive functions we don't need
3777 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3778 ;; but with reflexive ones we don't know...
3780 '((and (not (maybe-float-lvar-p x))
3781 (not (maybe-float-lvar-p y))))))
3783 (let ((ix (or (type-approximate-interval (lvar-type x))
3784 (give-up-ir1-transform)))
3785 (iy (or (type-approximate-interval (lvar-type y))
3786 (give-up-ir1-transform))))
3791 ((and (constant-lvar-p x)
3792 (not (constant-lvar-p y)))
3795 (give-up-ir1-transform))))))))
3796 (def = = t (interval-= ix iy) (interval-/= ix iy))
3797 (def /= /= nil (interval-/= ix iy) (interval-= ix iy))
3798 (def < > nil (interval-< ix iy) (interval->= ix iy))
3799 (def > < nil (interval-< iy ix) (interval->= iy ix))
3800 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3801 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3803 (defun ir1-transform-char< (x y first second inverse)
3805 ((same-leaf-ref-p x y) nil)
3806 ;; If we had interval representation of character types, as we
3807 ;; might eventually have to to support 2^21 characters, then here
3808 ;; we could do some compile-time computation as in transforms for
3809 ;; < above. -- CSR, 2003-07-01
3810 ((and (constant-lvar-p first)
3811 (not (constant-lvar-p second)))
3813 (t (give-up-ir1-transform))))
3815 (deftransform char< ((x y) (character character) *)
3816 (ir1-transform-char< x y x y 'char>))
3818 (deftransform char> ((x y) (character character) *)
3819 (ir1-transform-char< y x x y 'char<))
3821 ;;;; converting N-arg comparisons
3823 ;;;; We convert calls to N-arg comparison functions such as < into
3824 ;;;; two-arg calls. This transformation is enabled for all such
3825 ;;;; comparisons in this file. If any of these predicates are not
3826 ;;;; open-coded, then the transformation should be removed at some
3827 ;;;; point to avoid pessimization.
3829 ;;; This function is used for source transformation of N-arg
3830 ;;; comparison functions other than inequality. We deal both with
3831 ;;; converting to two-arg calls and inverting the sense of the test,
3832 ;;; if necessary. If the call has two args, then we pass or return a
3833 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3834 ;;; then we transform to code that returns true. Otherwise, we bind
3835 ;;; all the arguments and expand into a bunch of IFs.
3836 (defun multi-compare (predicate args not-p type &optional force-two-arg-p)
3837 (let ((nargs (length args)))
3838 (cond ((< nargs 1) (values nil t))
3839 ((= nargs 1) `(progn (the ,type ,@args) t))
3842 `(if (,predicate ,(first args) ,(second args)) nil t)
3844 `(,predicate ,(first args) ,(second args))
3847 (do* ((i (1- nargs) (1- i))
3849 (current (gensym) (gensym))
3850 (vars (list current) (cons current vars))
3852 `(if (,predicate ,current ,last)
3854 `(if (,predicate ,current ,last)
3857 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3860 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3861 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3862 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3863 ;;; We cannot do the inversion for >= and <= here, since both
3864 ;;; (< NaN X) and (> NaN X)
3865 ;;; are false, and we don't have type-information available yet. The
3866 ;;; deftransforms for two-argument versions of >= and <= takes care of
3867 ;;; the inversion to > and < when possible.
3868 (define-source-transform <= (&rest args) (multi-compare '<= args nil 'real))
3869 (define-source-transform >= (&rest args) (multi-compare '>= args nil 'real))
3871 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3873 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3875 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3877 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3879 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3882 (define-source-transform char-equal (&rest args)
3883 (multi-compare 'sb!impl::two-arg-char-equal args nil 'character t))
3884 (define-source-transform char-lessp (&rest args)
3885 (multi-compare 'sb!impl::two-arg-char-lessp args nil 'character t))
3886 (define-source-transform char-greaterp (&rest args)
3887 (multi-compare 'sb!impl::two-arg-char-greaterp args nil 'character t))
3888 (define-source-transform char-not-greaterp (&rest args)
3889 (multi-compare 'sb!impl::two-arg-char-greaterp args t 'character t))
3890 (define-source-transform char-not-lessp (&rest args)
3891 (multi-compare 'sb!impl::two-arg-char-lessp args t 'character t))
3893 ;;; This function does source transformation of N-arg inequality
3894 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3895 ;;; arg cases. If there are more than two args, then we expand into
3896 ;;; the appropriate n^2 comparisons only when speed is important.
3897 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3898 (defun multi-not-equal (predicate args type)
3899 (let ((nargs (length args)))
3900 (cond ((< nargs 1) (values nil t))
3901 ((= nargs 1) `(progn (the ,type ,@args) t))
3903 `(if (,predicate ,(first args) ,(second args)) nil t))
3904 ((not (policy *lexenv*
3905 (and (>= speed space)
3906 (>= speed compilation-speed))))
3909 (let ((vars (make-gensym-list nargs)))
3910 (do ((var vars next)
3911 (next (cdr vars) (cdr next))
3914 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3916 (let ((v1 (first var)))
3918 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3920 (define-source-transform /= (&rest args)
3921 (multi-not-equal '= args 'number))
3922 (define-source-transform char/= (&rest args)
3923 (multi-not-equal 'char= args 'character))
3924 (define-source-transform char-not-equal (&rest args)
3925 (multi-not-equal 'char-equal args 'character))
3927 ;;; Expand MAX and MIN into the obvious comparisons.
3928 (define-source-transform max (arg0 &rest rest)
3929 (once-only ((arg0 arg0))
3931 `(values (the real ,arg0))
3932 `(let ((maxrest (max ,@rest)))
3933 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3934 (define-source-transform min (arg0 &rest rest)
3935 (once-only ((arg0 arg0))
3937 `(values (the real ,arg0))
3938 `(let ((minrest (min ,@rest)))
3939 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3941 ;;;; converting N-arg arithmetic functions
3943 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3944 ;;;; versions, and degenerate cases are flushed.
3946 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3947 (declaim (ftype (sfunction (symbol t list t) list) associate-args))
3948 (defun associate-args (fun first-arg more-args identity)
3949 (let ((next (rest more-args))
3950 (arg (first more-args)))
3952 `(,fun ,first-arg ,(if arg arg identity))
3953 (associate-args fun `(,fun ,first-arg ,arg) next identity))))
3955 ;;; Reduce constants in ARGS list.
3956 (declaim (ftype (sfunction (symbol list t symbol) list) reduce-constants))
3957 (defun reduce-constants (fun args identity one-arg-result-type)
3958 (let ((one-arg-constant-p (ecase one-arg-result-type
3960 (integer #'integerp)))
3961 (reduced-value identity)
3963 (collect ((not-constants))
3965 (if (funcall one-arg-constant-p arg)
3966 (setf reduced-value (funcall fun reduced-value arg)
3968 (not-constants arg)))
3969 ;; It is tempting to drop constants reduced to identity here,
3970 ;; but if X is SNaN in (* X 1), we cannot drop the 1.
3973 `(,reduced-value ,@(not-constants))
3975 `(,reduced-value)))))
3977 ;;; Do source transformations for transitive functions such as +.
3978 ;;; One-arg cases are replaced with the arg and zero arg cases with
3979 ;;; the identity. ONE-ARG-RESULT-TYPE is the type to ensure (with THE)
3980 ;;; that the argument in one-argument calls is.
3981 (declaim (ftype (function (symbol list t &optional symbol list)
3982 (values t &optional (member nil t)))
3983 source-transform-transitive))
3984 (defun source-transform-transitive (fun args identity
3985 &optional (one-arg-result-type 'number)
3986 (one-arg-prefixes '(values)))
3989 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
3991 (t (let ((reduced-args (reduce-constants fun args identity one-arg-result-type)))
3992 (associate-args fun (first reduced-args) (rest reduced-args) identity)))))
3994 (define-source-transform + (&rest args)
3995 (source-transform-transitive '+ args 0))
3996 (define-source-transform * (&rest args)
3997 (source-transform-transitive '* args 1))
3998 (define-source-transform logior (&rest args)
3999 (source-transform-transitive 'logior args 0 'integer))
4000 (define-source-transform logxor (&rest args)
4001 (source-transform-transitive 'logxor args 0 'integer))
4002 (define-source-transform logand (&rest args)
4003 (source-transform-transitive 'logand args -1 'integer))
4004 (define-source-transform logeqv (&rest args)
4005 (source-transform-transitive 'logeqv args -1 'integer))
4006 (define-source-transform gcd (&rest args)
4007 (source-transform-transitive 'gcd args 0 'integer '(abs)))
4008 (define-source-transform lcm (&rest args)
4009 (source-transform-transitive 'lcm args 1 'integer '(abs)))
4011 ;;; Do source transformations for intransitive n-arg functions such as
4012 ;;; /. With one arg, we form the inverse. With two args we pass.
4013 ;;; Otherwise we associate into two-arg calls.
4014 (declaim (ftype (function (symbol symbol list t list &optional symbol)
4015 (values list &optional (member nil t)))
4016 source-transform-intransitive))
4017 (defun source-transform-intransitive (fun fun* args identity one-arg-prefixes
4018 &optional (one-arg-result-type 'number))
4020 ((0 2) (values nil t))
4021 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
4022 (t (let ((reduced-args
4023 (reduce-constants fun* (rest args) identity one-arg-result-type)))
4024 (associate-args fun (first args) reduced-args identity)))))
4026 (define-source-transform - (&rest args)
4027 (source-transform-intransitive '- '+ args 0 '(%negate)))
4028 (define-source-transform / (&rest args)
4029 (source-transform-intransitive '/ '* args 1 '(/ 1)))
4031 ;;;; transforming APPLY
4033 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
4034 ;;; only needs to understand one kind of variable-argument call. It is
4035 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
4036 (define-source-transform apply (fun arg &rest more-args)
4037 (let ((args (cons arg more-args)))
4038 `(multiple-value-call ,fun
4039 ,@(mapcar (lambda (x) `(values ,x)) (butlast args))
4040 (values-list ,(car (last args))))))
4042 ;;;; transforming references to &REST argument
4044 ;;; We add magical &MORE arguments to all functions with &REST. If ARG names
4045 ;;; the &REST argument, this returns the lambda-vars for the context and
4047 (defun possible-rest-arg-context (arg)
4049 (let* ((var (lexenv-find arg vars))
4050 (info (when (lambda-var-p var)
4051 (lambda-var-arg-info var))))
4053 (eq :rest (arg-info-kind info))
4054 (consp (arg-info-default info)))
4055 (values-list (arg-info-default info))))))
4057 (defun mark-more-context-used (rest-var)
4058 (let ((info (lambda-var-arg-info rest-var)))
4059 (aver (eq :rest (arg-info-kind info)))
4060 (destructuring-bind (context count &optional used) (arg-info-default info)
4062 (setf (arg-info-default info) (list context count t))))))
4064 (defun mark-more-context-invalid (rest-var)
4065 (let ((info (lambda-var-arg-info rest-var)))
4066 (aver (eq :rest (arg-info-kind info)))
4067 (setf (arg-info-default info) t)))
4069 ;;; This determines of we the REF to a &REST variable is headed towards
4070 ;;; parts unknown, or if we can really use the context.
4071 (defun rest-var-more-context-ok (lvar)
4072 (let* ((use (lvar-use lvar))
4073 (var (when (ref-p use) (ref-leaf use)))
4074 (home (when (lambda-var-p var) (lambda-var-home var)))
4075 (info (when (lambda-var-p var) (lambda-var-arg-info var)))
4076 (restp (when info (eq :rest (arg-info-kind info)))))
4077 (flet ((ref-good-for-more-context-p (ref)
4078 (let ((dest (principal-lvar-end (node-lvar ref))))
4079 (and (combination-p dest)
4080 ;; If the destination is to anything but these, we're going to
4081 ;; actually need the rest list -- and since other operations
4082 ;; might modify the list destructively, the using the context
4083 ;; isn't good anywhere else either.
4084 (lvar-fun-is (combination-fun dest)
4085 '(%rest-values %rest-ref %rest-length
4086 %rest-null %rest-true))
4087 ;; If the home lambda is different and isn't DX, it might
4088 ;; escape -- in which case using the more context isn't safe.
4089 (let ((clambda (node-home-lambda dest)))
4090 (or (eq home clambda)
4091 (leaf-dynamic-extent clambda)))))))
4092 (let ((ok (and restp
4093 (consp (arg-info-default info))
4094 (not (lambda-var-specvar var))
4095 (not (lambda-var-sets var))
4096 (every #'ref-good-for-more-context-p (lambda-var-refs var)))))
4098 (mark-more-context-used var)
4100 (mark-more-context-invalid var)))
4103 ;;; VALUES-LIST -> %REST-VALUES
4104 (define-source-transform values-list (list)
4105 (multiple-value-bind (context count) (possible-rest-arg-context list)
4107 `(%rest-values ,list ,context ,count)
4110 ;;; NTH -> %REST-REF
4111 (define-source-transform nth (n list)
4112 (multiple-value-bind (context count) (possible-rest-arg-context list)
4114 `(%rest-ref ,n ,list ,context ,count)
4115 `(car (nthcdr ,n ,list)))))
4117 (define-source-transform elt (seq n)
4118 (if (policy *lexenv* (= safety 3))
4120 (multiple-value-bind (context count) (possible-rest-arg-context seq)
4122 `(%rest-ref ,n ,seq ,context ,count)
4125 ;;; CAxR -> %REST-REF
4126 (defun source-transform-car (list nth)
4127 (multiple-value-bind (context count) (possible-rest-arg-context list)
4129 `(%rest-ref ,nth ,list ,context ,count)
4132 (define-source-transform car (list)
4133 (source-transform-car list 0))
4135 (define-source-transform cadr (list)
4136 (or (source-transform-car list 1)
4137 `(car (cdr ,list))))
4139 (define-source-transform caddr (list)
4140 (or (source-transform-car list 2)
4141 `(car (cdr (cdr ,list)))))
4143 (define-source-transform cadddr (list)
4144 (or (source-transform-car list 3)
4145 `(car (cdr (cdr (cdr ,list))))))
4147 ;;; LENGTH -> %REST-LENGTH
4148 (defun source-transform-length (list)
4149 (multiple-value-bind (context count) (possible-rest-arg-context list)
4151 `(%rest-length ,list ,context ,count)
4153 (define-source-transform length (list) (source-transform-length list))
4154 (define-source-transform list-length (list) (source-transform-length list))
4156 ;;; ENDP, NULL and NOT -> %REST-NULL
4158 ;;; Outside &REST convert into an IF so that IF optimizations will eliminate
4159 ;;; redundant negations.
4160 (defun source-transform-null (x op)
4161 (multiple-value-bind (context count) (possible-rest-arg-context x)
4163 `(%rest-null ',op ,x ,context ,count))
4165 `(if (the list ,x) nil t))
4168 (define-source-transform not (x) (source-transform-null x 'not))
4169 (define-source-transform null (x) (source-transform-null x 'null))
4170 (define-source-transform endp (x) (source-transform-null x 'endp))
4172 (deftransform %rest-values ((list context count))
4173 (if (rest-var-more-context-ok list)
4174 `(%more-arg-values context 0 count)
4175 `(values-list list)))
4177 (deftransform %rest-ref ((n list context count))
4178 (cond ((rest-var-more-context-ok list)
4179 `(and (< (the index n) count)
4180 (%more-arg context n)))
4181 ((and (constant-lvar-p n) (zerop (lvar-value n)))
4186 (deftransform %rest-length ((list context count))
4187 (if (rest-var-more-context-ok list)
4191 (deftransform %rest-null ((op list context count))
4192 (aver (constant-lvar-p op))
4193 (if (rest-var-more-context-ok list)
4195 `(,(lvar-value op) list)))
4197 (deftransform %rest-true ((list context count))
4198 (if (rest-var-more-context-ok list)
4199 `(not (eql 0 count))
4202 ;;;; transforming FORMAT
4204 ;;;; If the control string is a compile-time constant, then replace it
4205 ;;;; with a use of the FORMATTER macro so that the control string is
4206 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
4207 ;;;; or T and the control string is a function (i.e. FORMATTER), then
4208 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
4210 ;;; for compile-time argument count checking.
4212 ;;; FIXME II: In some cases, type information could be correlated; for
4213 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
4214 ;;; of a corresponding argument is known and does not intersect the
4215 ;;; list type, a warning could be signalled.
4216 (defun check-format-args (string args fun)
4217 (declare (type string string))
4218 (unless (typep string 'simple-string)
4219 (setq string (coerce string 'simple-string)))
4220 (multiple-value-bind (min max)
4221 (handler-case (sb!format:%compiler-walk-format-string string args)
4222 (sb!format:format-error (c)
4223 (compiler-warn "~A" c)))
4225 (let ((nargs (length args)))
4228 (warn 'format-too-few-args-warning
4230 "Too few arguments (~D) to ~S ~S: requires at least ~D."
4231 :format-arguments (list nargs fun string min)))
4233 (warn 'format-too-many-args-warning
4235 "Too many arguments (~D) to ~S ~S: uses at most ~D."
4236 :format-arguments (list nargs fun string max))))))))
4238 (defoptimizer (format optimizer) ((dest control &rest args))
4239 (when (constant-lvar-p control)
4240 (let ((x (lvar-value control)))
4242 (check-format-args x args 'format)))))
4244 ;;; We disable this transform in the cross-compiler to save memory in
4245 ;;; the target image; most of the uses of FORMAT in the compiler are for
4246 ;;; error messages, and those don't need to be particularly fast.
4248 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
4249 :policy (>= speed space))
4250 (unless (constant-lvar-p control)
4251 (give-up-ir1-transform "The control string is not a constant."))
4252 (let ((arg-names (make-gensym-list (length args))))
4253 `(lambda (dest control ,@arg-names)
4254 (declare (ignore control))
4255 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
4257 (deftransform format ((stream control &rest args) (stream function &rest t))
4258 (let ((arg-names (make-gensym-list (length args))))
4259 `(lambda (stream control ,@arg-names)
4260 (funcall control stream ,@arg-names)
4263 (deftransform format ((tee control &rest args) ((member t) function &rest t))
4264 (let ((arg-names (make-gensym-list (length args))))
4265 `(lambda (tee control ,@arg-names)
4266 (declare (ignore tee))
4267 (funcall control *standard-output* ,@arg-names)
4270 (deftransform pathname ((pathspec) (pathname) *)
4273 (deftransform pathname ((pathspec) (string) *)
4274 '(values (parse-namestring pathspec)))
4278 `(defoptimizer (,name optimizer) ((control &rest args))
4279 (when (constant-lvar-p control)
4280 (let ((x (lvar-value control)))
4282 (check-format-args x args ',name)))))))
4285 #+sb-xc-host ; Only we should be using these
4288 (def compiler-error)
4290 (def compiler-style-warn)
4291 (def compiler-notify)
4292 (def maybe-compiler-notify)
4295 (defoptimizer (cerror optimizer) ((report control &rest args))
4296 (when (and (constant-lvar-p control)
4297 (constant-lvar-p report))
4298 (let ((x (lvar-value control))
4299 (y (lvar-value report)))
4300 (when (and (stringp x) (stringp y))
4301 (multiple-value-bind (min1 max1)
4303 (sb!format:%compiler-walk-format-string x args)
4304 (sb!format:format-error (c)
4305 (compiler-warn "~A" c)))
4307 (multiple-value-bind (min2 max2)
4309 (sb!format:%compiler-walk-format-string y args)
4310 (sb!format:format-error (c)
4311 (compiler-warn "~A" c)))
4313 (let ((nargs (length args)))
4315 ((< nargs (min min1 min2))
4316 (warn 'format-too-few-args-warning
4318 "Too few arguments (~D) to ~S ~S ~S: ~
4319 requires at least ~D."
4321 (list nargs 'cerror y x (min min1 min2))))
4322 ((> nargs (max max1 max2))
4323 (warn 'format-too-many-args-warning
4325 "Too many arguments (~D) to ~S ~S ~S: ~
4328 (list nargs 'cerror y x (max max1 max2))))))))))))))
4330 (defoptimizer (coerce derive-type) ((value type) node)
4332 ((constant-lvar-p type)
4333 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
4334 ;; but dealing with the niggle that complex canonicalization gets
4335 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
4337 (let* ((specifier (lvar-value type))
4338 (result-typeoid (careful-specifier-type specifier)))
4340 ((null result-typeoid) nil)
4341 ((csubtypep result-typeoid (specifier-type 'number))
4342 ;; the difficult case: we have to cope with ANSI 12.1.5.3
4343 ;; Rule of Canonical Representation for Complex Rationals,
4344 ;; which is a truly nasty delivery to field.
4346 ((csubtypep result-typeoid (specifier-type 'real))
4347 ;; cleverness required here: it would be nice to deduce
4348 ;; that something of type (INTEGER 2 3) coerced to type
4349 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
4350 ;; FLOAT gets its own clause because it's implemented as
4351 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
4354 ((and (numeric-type-p result-typeoid)
4355 (eq (numeric-type-complexp result-typeoid) :real))
4356 ;; FIXME: is this clause (a) necessary or (b) useful?
4358 ((or (csubtypep result-typeoid
4359 (specifier-type '(complex single-float)))
4360 (csubtypep result-typeoid
4361 (specifier-type '(complex double-float)))
4363 (csubtypep result-typeoid
4364 (specifier-type '(complex long-float))))
4365 ;; float complex types are never canonicalized.
4368 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
4369 ;; probably just a COMPLEX or equivalent. So, in that
4370 ;; case, we will return a complex or an object of the
4371 ;; provided type if it's rational:
4372 (type-union result-typeoid
4373 (type-intersection (lvar-type value)
4374 (specifier-type 'rational))))))
4375 ((and (policy node (zerop safety))
4376 (csubtypep result-typeoid (specifier-type '(array * (*)))))
4377 ;; At zero safety the deftransform for COERCE can elide dimension
4378 ;; checks for the things like (COERCE X '(SIMPLE-VECTOR 5)) -- so we
4379 ;; need to simplify the type to drop the dimension information.
4380 (let ((vtype (simplify-vector-type result-typeoid)))
4382 (specifier-type vtype)
4387 ;; OK, the result-type argument isn't constant. However, there
4388 ;; are common uses where we can still do better than just
4389 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
4390 ;; where Y is of a known type. See messages on cmucl-imp
4391 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
4392 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
4393 ;; the basis that it's unlikely that other uses are both
4394 ;; time-critical and get to this branch of the COND (non-constant
4395 ;; second argument to COERCE). -- CSR, 2002-12-16
4396 (let ((value-type (lvar-type value))
4397 (type-type (lvar-type type)))
4399 ((good-cons-type-p (cons-type)
4400 ;; Make sure the cons-type we're looking at is something
4401 ;; we're prepared to handle which is basically something
4402 ;; that array-element-type can return.
4403 (or (and (member-type-p cons-type)
4404 (eql 1 (member-type-size cons-type))
4405 (null (first (member-type-members cons-type))))
4406 (let ((car-type (cons-type-car-type cons-type)))
4407 (and (member-type-p car-type)
4408 (eql 1 (member-type-members car-type))
4409 (let ((elt (first (member-type-members car-type))))
4413 (numberp (first elt)))))
4414 (good-cons-type-p (cons-type-cdr-type cons-type))))))
4415 (unconsify-type (good-cons-type)
4416 ;; Convert the "printed" respresentation of a cons
4417 ;; specifier into a type specifier. That is, the
4418 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
4419 ;; NULL)) is converted to (SIGNED-BYTE 16).
4420 (cond ((or (null good-cons-type)
4421 (eq good-cons-type 'null))
4423 ((and (eq (first good-cons-type) 'cons)
4424 (eq (first (second good-cons-type)) 'member))
4425 `(,(second (second good-cons-type))
4426 ,@(unconsify-type (caddr good-cons-type))))))
4427 (coerceable-p (part)
4428 ;; Can the value be coerced to the given type? Coerce is
4429 ;; complicated, so we don't handle every possible case
4430 ;; here---just the most common and easiest cases:
4432 ;; * Any REAL can be coerced to a FLOAT type.
4433 ;; * Any NUMBER can be coerced to a (COMPLEX
4434 ;; SINGLE/DOUBLE-FLOAT).
4436 ;; FIXME I: we should also be able to deal with characters
4439 ;; FIXME II: I'm not sure that anything is necessary
4440 ;; here, at least while COMPLEX is not a specialized
4441 ;; array element type in the system. Reasoning: if
4442 ;; something cannot be coerced to the requested type, an
4443 ;; error will be raised (and so any downstream compiled
4444 ;; code on the assumption of the returned type is
4445 ;; unreachable). If something can, then it will be of
4446 ;; the requested type, because (by assumption) COMPLEX
4447 ;; (and other difficult types like (COMPLEX INTEGER)
4448 ;; aren't specialized types.
4449 (let ((coerced-type (careful-specifier-type part)))
4451 (or (and (csubtypep coerced-type (specifier-type 'float))
4452 (csubtypep value-type (specifier-type 'real)))
4453 (and (csubtypep coerced-type
4454 (specifier-type `(or (complex single-float)
4455 (complex double-float))))
4456 (csubtypep value-type (specifier-type 'number)))))))
4457 (process-types (type)
4458 ;; FIXME: This needs some work because we should be able
4459 ;; to derive the resulting type better than just the
4460 ;; type arg of coerce. That is, if X is (INTEGER 10
4461 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
4462 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
4464 (cond ((member-type-p type)
4467 (mapc-member-type-members
4469 (if (coerceable-p member)
4470 (push member members)
4471 (return-from punt *universal-type*)))
4473 (specifier-type `(or ,@members)))))
4474 ((and (cons-type-p type)
4475 (good-cons-type-p type))
4476 (let ((c-type (unconsify-type (type-specifier type))))
4477 (if (coerceable-p c-type)
4478 (specifier-type c-type)
4481 *universal-type*))))
4482 (cond ((union-type-p type-type)
4483 (apply #'type-union (mapcar #'process-types
4484 (union-type-types type-type))))
4485 ((or (member-type-p type-type)
4486 (cons-type-p type-type))
4487 (process-types type-type))
4489 *universal-type*)))))))
4491 (defoptimizer (compile derive-type) ((nameoid function))
4492 (when (csubtypep (lvar-type nameoid)
4493 (specifier-type 'null))
4494 (values-specifier-type '(values function boolean boolean))))
4496 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
4497 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
4498 ;;; optimizer, above).
4499 (defoptimizer (array-element-type derive-type) ((array))
4500 (let ((array-type (lvar-type array)))
4501 (labels ((consify (list)
4504 `(cons (eql ,(car list)) ,(consify (rest list)))))
4505 (get-element-type (a)
4507 (type-specifier (array-type-specialized-element-type a))))
4508 (cond ((eq element-type '*)
4509 (specifier-type 'type-specifier))
4510 ((symbolp element-type)
4511 (make-member-type :members (list element-type)))
4512 ((consp element-type)
4513 (specifier-type (consify element-type)))
4515 (error "can't understand type ~S~%" element-type))))))
4516 (labels ((recurse (type)
4517 (cond ((array-type-p type)
4518 (get-element-type type))
4519 ((union-type-p type)
4521 (mapcar #'recurse (union-type-types type))))
4523 *universal-type*))))
4524 (recurse array-type)))))
4526 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
4527 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4528 ;; isn't really related to the CMU CL code, since instead of trying
4529 ;; to generalize the CMU CL code to allow START and END values, this
4530 ;; code has been written from scratch following Chapter 7 of
4531 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4532 `(macrolet ((%index (x) `(truly-the index ,x))
4533 (%parent (i) `(ash ,i -1))
4534 (%left (i) `(%index (ash ,i 1)))
4535 (%right (i) `(%index (1+ (ash ,i 1))))
4538 (left (%left i) (%left i)))
4539 ((> left current-heap-size))
4540 (declare (type index i left))
4541 (let* ((i-elt (%elt i))
4542 (i-key (funcall keyfun i-elt))
4543 (left-elt (%elt left))
4544 (left-key (funcall keyfun left-elt)))
4545 (multiple-value-bind (large large-elt large-key)
4546 (if (funcall ,',predicate i-key left-key)
4547 (values left left-elt left-key)
4548 (values i i-elt i-key))
4549 (let ((right (%right i)))
4550 (multiple-value-bind (largest largest-elt)
4551 (if (> right current-heap-size)
4552 (values large large-elt)
4553 (let* ((right-elt (%elt right))
4554 (right-key (funcall keyfun right-elt)))
4555 (if (funcall ,',predicate large-key right-key)
4556 (values right right-elt)
4557 (values large large-elt))))
4558 (cond ((= largest i)
4561 (setf (%elt i) largest-elt
4562 (%elt largest) i-elt
4564 (%sort-vector (keyfun &optional (vtype 'vector))
4565 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4566 ;; trouble getting type inference to
4567 ;; propagate all the way through this
4568 ;; tangled mess of inlining. The TRULY-THE
4569 ;; here works around that. -- WHN
4571 `(aref (truly-the ,',vtype ,',',vector)
4572 (%index (+ (%index ,i) start-1)))))
4573 (let (;; Heaps prefer 1-based addressing.
4574 (start-1 (1- ,',start))
4575 (current-heap-size (- ,',end ,',start))
4577 (declare (type (integer -1 #.(1- sb!xc:most-positive-fixnum))
4579 (declare (type index current-heap-size))
4580 (declare (type function keyfun))
4581 (loop for i of-type index
4582 from (ash current-heap-size -1) downto 1 do
4585 (when (< current-heap-size 2)
4587 (rotatef (%elt 1) (%elt current-heap-size))
4588 (decf current-heap-size)
4590 (if (typep ,vector 'simple-vector)
4591 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4592 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4594 ;; Special-casing the KEY=NIL case lets us avoid some
4596 (%sort-vector #'identity simple-vector)
4597 (%sort-vector ,key simple-vector))
4598 ;; It's hard to anticipate many speed-critical applications for
4599 ;; sorting vector types other than (VECTOR T), so we just lump
4600 ;; them all together in one slow dynamically typed mess.
4602 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4603 (%sort-vector (or ,key #'identity))))))
4605 ;;;; debuggers' little helpers
4607 ;;; for debugging when transforms are behaving mysteriously,
4608 ;;; e.g. when debugging a problem with an ASH transform
4609 ;;; (defun foo (&optional s)
4610 ;;; (sb-c::/report-lvar s "S outside WHEN")
4611 ;;; (when (and (integerp s) (> s 3))
4612 ;;; (sb-c::/report-lvar s "S inside WHEN")
4613 ;;; (let ((bound (ash 1 (1- s))))
4614 ;;; (sb-c::/report-lvar bound "BOUND")
4615 ;;; (let ((x (- bound))
4617 ;;; (sb-c::/report-lvar x "X")
4618 ;;; (sb-c::/report-lvar x "Y"))
4619 ;;; `(integer ,(- bound) ,(1- bound)))))
4620 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4621 ;;; and the function doesn't do anything at all.)
4624 (defknown /report-lvar (t t) null)
4625 (deftransform /report-lvar ((x message) (t t))
4626 (format t "~%/in /REPORT-LVAR~%")
4627 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4628 (when (constant-lvar-p x)
4629 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4630 (format t "/MESSAGE=~S~%" (lvar-value message))
4631 (give-up-ir1-transform "not a real transform"))
4632 (defun /report-lvar (x message)
4633 (declare (ignore x message))))
4636 ;;;; Transforms for internal compiler utilities
4638 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4639 ;;; checking that it's still valid at run-time.
4640 (deftransform policy-quality ((policy quality-name)
4642 (unless (and (constant-lvar-p quality-name)
4643 (policy-quality-name-p (lvar-value quality-name)))
4644 (give-up-ir1-transform))
4645 '(%policy-quality policy quality-name))
4647 (deftransform encode-universal-time
4648 ((second minute hour date month year &optional time-zone)
4649 ((constant-arg (mod 60)) (constant-arg (mod 60))
4650 (constant-arg (mod 24))
4651 (constant-arg (integer 1 31))
4652 (constant-arg (integer 1 12))
4653 (constant-arg (integer 1899))
4654 (constant-arg (rational -24 24))))
4655 (let ((second (lvar-value second))
4656 (minute (lvar-value minute))
4657 (hour (lvar-value hour))
4658 (date (lvar-value date))
4659 (month (lvar-value month))
4660 (year (lvar-value year))
4661 (time-zone (lvar-value time-zone)))
4662 (if (zerop (rem time-zone 1/3600))
4663 (encode-universal-time second minute hour date month year time-zone)
4664 (give-up-ir1-transform))))
4666 #!-(and win32 (not sb-thread))
4667 (deftransform sleep ((seconds) ((integer 0 #.(expt 10 8))))
4668 `(sb!unix:nanosleep seconds 0))
4670 #!-(and win32 (not sb-thread))
4671 (deftransform sleep ((seconds) ((constant-arg (real 0))))
4672 (let ((seconds-value (lvar-value seconds)))
4673 (multiple-value-bind (seconds nano)
4674 (sb!impl::split-seconds-for-sleep seconds-value)
4675 (if (> seconds (expt 10 8))
4676 (give-up-ir1-transform)
4677 `(sb!unix:nanosleep ,seconds ,nano)))))