1 ;;;; This file contains macro-like source transformations which
2 ;;;; convert uses of certain functions into the canonical form desired
3 ;;;; within the compiler. FIXME: and other IR1 transforms and stuff.
5 ;;;; This software is part of the SBCL system. See the README file for
8 ;;;; This software is derived from the CMU CL system, which was
9 ;;;; written at Carnegie Mellon University and released into the
10 ;;;; public domain. The software is in the public domain and is
11 ;;;; provided with absolutely no warranty. See the COPYING and CREDITS
12 ;;;; files for more information.
16 ;;; Convert into an IF so that IF optimizations will eliminate redundant
18 (define-source-transform not (x) `(if ,x nil t))
19 (define-source-transform null (x) `(if ,x nil t))
21 ;;; ENDP is just NULL with a LIST assertion. The assertion will be
22 ;;; optimized away when SAFETY optimization is low; hopefully that
23 ;;; is consistent with ANSI's "should return an error".
24 (define-source-transform endp (x) `(null (the list ,x)))
26 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
27 ;;; returns the first value of its argument. Ditto for VALUES with one
29 (define-source-transform identity (x) `(prog1 ,x))
30 (define-source-transform values (x) `(prog1 ,x))
33 ;;; CONSTANTLY is pretty much never worth transforming, but it's good to get the type.
34 (defoptimizer (constantly derive-type) ((value))
36 `(function (&rest t) (values ,(type-specifier (lvar-type value)) &optional))))
38 ;;; If the function has a known number of arguments, then return a
39 ;;; lambda with the appropriate fixed number of args. If the
40 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
41 ;;; MV optimization figure things out.
42 (deftransform complement ((fun) * * :node node)
44 (multiple-value-bind (min max)
45 (fun-type-nargs (lvar-type fun))
47 ((and min (eql min max))
48 (let ((dums (make-gensym-list min)))
49 `#'(lambda ,dums (not (funcall fun ,@dums)))))
50 ((awhen (node-lvar node)
51 (let ((dest (lvar-dest it)))
52 (and (combination-p dest)
53 (eq (combination-fun dest) it))))
54 '#'(lambda (&rest args)
55 (not (apply fun args))))
57 (give-up-ir1-transform
58 "The function doesn't have a fixed argument count.")))))
61 (defun derive-symbol-value-type (lvar node)
62 (if (constant-lvar-p lvar)
63 (let* ((sym (lvar-value lvar))
64 (var (maybe-find-free-var sym))
66 (let ((*lexenv* (node-lexenv node)))
67 (lexenv-find var type-restrictions))))
68 (global-type (info :variable :type sym)))
70 (type-intersection local-type global-type)
74 (defoptimizer (symbol-value derive-type) ((symbol) node)
75 (derive-symbol-value-type symbol node))
77 (defoptimizer (symbol-global-value derive-type) ((symbol) node)
78 (derive-symbol-value-type symbol node))
82 ;;; Translate CxR into CAR/CDR combos.
83 (defun source-transform-cxr (form)
84 (if (/= (length form) 2)
86 (let* ((name (car form))
90 (leaf (leaf-source-name name))))))
91 (do ((i (- (length string) 2) (1- i))
93 `(,(ecase (char string i)
99 ;;; Make source transforms to turn CxR forms into combinations of CAR
100 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
102 (/show0 "about to set CxR source transforms")
103 (loop for i of-type index from 2 upto 4 do
104 ;; Iterate over BUF = all names CxR where x = an I-element
105 ;; string of #\A or #\D characters.
106 (let ((buf (make-string (+ 2 i))))
107 (setf (aref buf 0) #\C
108 (aref buf (1+ i)) #\R)
109 (dotimes (j (ash 2 i))
110 (declare (type index j))
112 (declare (type index k))
113 (setf (aref buf (1+ k))
114 (if (logbitp k j) #\A #\D)))
115 (setf (info :function :source-transform (intern buf))
116 #'source-transform-cxr))))
117 (/show0 "done setting CxR source transforms")
119 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
120 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
121 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
123 (define-source-transform first (x) `(car ,x))
124 (define-source-transform rest (x) `(cdr ,x))
125 (define-source-transform second (x) `(cadr ,x))
126 (define-source-transform third (x) `(caddr ,x))
127 (define-source-transform fourth (x) `(cadddr ,x))
128 (define-source-transform fifth (x) `(nth 4 ,x))
129 (define-source-transform sixth (x) `(nth 5 ,x))
130 (define-source-transform seventh (x) `(nth 6 ,x))
131 (define-source-transform eighth (x) `(nth 7 ,x))
132 (define-source-transform ninth (x) `(nth 8 ,x))
133 (define-source-transform tenth (x) `(nth 9 ,x))
135 ;;; LIST with one arg is an extremely common operation (at least inside
136 ;;; SBCL itself); translate it to CONS to take advantage of common
137 ;;; allocation routines.
138 (define-source-transform list (&rest args)
140 (1 `(cons ,(first args) nil))
143 ;;; And similarly for LIST*.
144 (define-source-transform list* (arg &rest others)
145 (cond ((not others) arg)
146 ((not (cdr others)) `(cons ,arg ,(car others)))
149 (defoptimizer (list* derive-type) ((arg &rest args))
151 (specifier-type 'cons)
154 ;;; Translate RPLACx to LET and SETF.
155 (define-source-transform rplaca (x y)
160 (define-source-transform rplacd (x y)
166 (define-source-transform nth (n l) `(car (nthcdr ,n ,l)))
168 (deftransform last ((list &optional n) (t &optional t))
169 (let ((c (constant-lvar-p n)))
171 (and c (eql 1 (lvar-value n))))
173 ((and c (eql 0 (lvar-value n)))
176 (let ((type (lvar-type n)))
177 (cond ((csubtypep type (specifier-type 'fixnum))
178 '(%lastn/fixnum list n))
179 ((csubtypep type (specifier-type 'bignum))
180 '(%lastn/bignum list n))
182 (give-up-ir1-transform "second argument type too vague"))))))))
184 (define-source-transform gethash (&rest args)
186 (2 `(sb!impl::gethash3 ,@args nil))
187 (3 `(sb!impl::gethash3 ,@args))
189 (define-source-transform get (&rest args)
191 (2 `(sb!impl::get2 ,@args))
192 (3 `(sb!impl::get3 ,@args))
195 (defvar *default-nthcdr-open-code-limit* 6)
196 (defvar *extreme-nthcdr-open-code-limit* 20)
198 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
199 "convert NTHCDR to CAxxR"
200 (unless (constant-lvar-p n)
201 (give-up-ir1-transform))
202 (let ((n (lvar-value n)))
204 (if (policy node (and (= speed 3) (= space 0)))
205 *extreme-nthcdr-open-code-limit*
206 *default-nthcdr-open-code-limit*))
207 (give-up-ir1-transform))
212 `(cdr ,(frob (1- n))))))
215 ;;;; arithmetic and numerology
217 (define-source-transform plusp (x) `(> ,x 0))
218 (define-source-transform minusp (x) `(< ,x 0))
219 (define-source-transform zerop (x) `(= ,x 0))
221 (define-source-transform 1+ (x) `(+ ,x 1))
222 (define-source-transform 1- (x) `(- ,x 1))
224 (define-source-transform oddp (x) `(logtest ,x 1))
225 (define-source-transform evenp (x) `(not (logtest ,x 1)))
227 ;;; Note that all the integer division functions are available for
228 ;;; inline expansion.
230 (macrolet ((deffrob (fun)
231 `(define-source-transform ,fun (x &optional (y nil y-p))
238 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
240 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
243 ;;; This used to be a source transform (hence the lack of restrictions
244 ;;; on the argument types), but we make it a regular transform so that
245 ;;; the VM has a chance to see the bare LOGTEST and potentiall choose
246 ;;; to implement it differently. --njf, 06-02-2006
247 (deftransform logtest ((x y) * *)
248 `(not (zerop (logand x y))))
250 (deftransform logbitp
251 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
252 (unsigned-byte #.sb!vm:n-word-bits))))
253 `(if (>= index #.sb!vm:n-word-bits)
255 (not (zerop (logand integer (ash 1 index))))))
257 (define-source-transform byte (size position)
258 `(cons ,size ,position))
259 (define-source-transform byte-size (spec) `(car ,spec))
260 (define-source-transform byte-position (spec) `(cdr ,spec))
261 (define-source-transform ldb-test (bytespec integer)
262 `(not (zerop (mask-field ,bytespec ,integer))))
264 ;;; With the ratio and complex accessors, we pick off the "identity"
265 ;;; case, and use a primitive to handle the cell access case.
266 (define-source-transform numerator (num)
267 (once-only ((n-num `(the rational ,num)))
271 (define-source-transform denominator (num)
272 (once-only ((n-num `(the rational ,num)))
274 (%denominator ,n-num)
277 ;;;; interval arithmetic for computing bounds
279 ;;;; This is a set of routines for operating on intervals. It
280 ;;;; implements a simple interval arithmetic package. Although SBCL
281 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
282 ;;;; for two reasons:
284 ;;;; 1. This package is simpler than NUMERIC-TYPE.
286 ;;;; 2. It makes debugging much easier because you can just strip
287 ;;;; out these routines and test them independently of SBCL. (This is a
290 ;;;; One disadvantage is a probable increase in consing because we
291 ;;;; have to create these new interval structures even though
292 ;;;; numeric-type has everything we want to know. Reason 2 wins for
295 ;;; Support operations that mimic real arithmetic comparison
296 ;;; operators, but imposing a total order on the floating points such
297 ;;; that negative zeros are strictly less than positive zeros.
298 (macrolet ((def (name op)
301 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
302 (,op (float-sign x) (float-sign y))
304 (def signed-zero->= >=)
305 (def signed-zero-> >)
306 (def signed-zero-= =)
307 (def signed-zero-< <)
308 (def signed-zero-<= <=))
310 ;;; The basic interval type. It can handle open and closed intervals.
311 ;;; A bound is open if it is a list containing a number, just like
312 ;;; Lisp says. NIL means unbounded.
313 (defstruct (interval (:constructor %make-interval)
317 (defun make-interval (&key low high)
318 (labels ((normalize-bound (val)
321 (float-infinity-p val))
322 ;; Handle infinities.
326 ;; Handle any closed bounds.
329 ;; We have an open bound. Normalize the numeric
330 ;; bound. If the normalized bound is still a number
331 ;; (not nil), keep the bound open. Otherwise, the
332 ;; bound is really unbounded, so drop the openness.
333 (let ((new-val (normalize-bound (first val))))
335 ;; The bound exists, so keep it open still.
338 (error "unknown bound type in MAKE-INTERVAL")))))
339 (%make-interval :low (normalize-bound low)
340 :high (normalize-bound high))))
342 ;;; Given a number X, create a form suitable as a bound for an
343 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
344 #!-sb-fluid (declaim (inline set-bound))
345 (defun set-bound (x open-p)
346 (if (and x open-p) (list x) x))
348 ;;; Apply the function F to a bound X. If X is an open bound and the
349 ;;; function is declared strictly monotonic, then the result will be
350 ;;; open. IF X is NIL, the result is NIL.
351 (defun bound-func (f x strict)
352 (declare (type function f))
355 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
356 ;; With these traps masked, we might get things like infinity
357 ;; or negative infinity returned. Check for this and return
358 ;; NIL to indicate unbounded.
359 (let ((y (funcall f (type-bound-number x))))
361 (float-infinity-p y))
363 (set-bound y (and strict (consp x))))))
364 ;; Some numerical operations will signal SIMPLE-TYPE-ERROR, e.g.
365 ;; in the course of converting a bignum to a float. Default to
367 (simple-type-error ()))))
369 (defun safe-double-coercion-p (x)
370 (or (typep x 'double-float)
371 (<= most-negative-double-float x most-positive-double-float)))
373 (defun safe-single-coercion-p (x)
374 (or (typep x 'single-float)
376 ;; Fix for bug 420, and related issues: during type derivation we often
377 ;; end up deriving types for both
379 ;; (some-op <int> <single>)
381 ;; (some-op (coerce <int> 'single-float) <single>)
383 ;; or other equivalent transformed forms. The problem with this
384 ;; is that on x86 (+ <int> <single>) is on the machine level
387 ;; (coerce (+ (coerce <int> 'double-float)
388 ;; (coerce <single> 'double-float))
391 ;; so if the result of (coerce <int> 'single-float) is not exact, the
392 ;; derived types for the transformed forms will have an empty
393 ;; intersection -- which in turn means that the compiler will conclude
394 ;; that the call never returns, and all hell breaks lose when it *does*
395 ;; return at runtime. (This affects not just +, but other operators are
398 ;; See also: SAFE-CTYPE-FOR-SINGLE-COERCION-P
400 ;; FIXME: If we ever add SSE-support for x86, this conditional needs to
403 (not (typep x `(or (integer * (,most-negative-exactly-single-float-fixnum))
404 (integer (,most-positive-exactly-single-float-fixnum) *))))
405 (<= most-negative-single-float x most-positive-single-float))))
407 ;;; Apply a binary operator OP to two bounds X and Y. The result is
408 ;;; NIL if either is NIL. Otherwise bound is computed and the result
409 ;;; is open if either X or Y is open.
411 ;;; FIXME: only used in this file, not needed in target runtime
413 ;;; ANSI contaigon specifies coercion to floating point if one of the
414 ;;; arguments is floating point. Here we should check to be sure that
415 ;;; the other argument is within the bounds of that floating point
418 (defmacro safely-binop (op x y)
420 ((typep ,x 'double-float)
421 (when (safe-double-coercion-p ,y)
423 ((typep ,y 'double-float)
424 (when (safe-double-coercion-p ,x)
426 ((typep ,x 'single-float)
427 (when (safe-single-coercion-p ,y)
429 ((typep ,y 'single-float)
430 (when (safe-single-coercion-p ,x)
434 (defmacro bound-binop (op x y)
435 (with-unique-names (xb yb res)
437 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
438 (let* ((,xb (type-bound-number ,x))
439 (,yb (type-bound-number ,y))
440 (,res (safely-binop ,op ,xb ,yb)))
442 (and (or (consp ,x) (consp ,y))
443 ;; Open bounds can very easily be messed up
444 ;; by FP rounding, so take care here.
447 ;; Multiplying a greater-than-zero with
448 ;; less than one can round to zero.
449 `(or (not (fp-zero-p ,res))
450 (cond ((and (consp ,x) (fp-zero-p ,xb))
452 ((and (consp ,y) (fp-zero-p ,yb))
455 ;; Dividing a greater-than-zero with
456 ;; greater than one can round to zero.
457 `(or (not (fp-zero-p ,res))
458 (cond ((and (consp ,x) (fp-zero-p ,xb))
460 ((and (consp ,y) (fp-zero-p ,yb))
463 ;; Adding or subtracting greater-than-zero
464 ;; can end up with identity.
465 `(and (not (fp-zero-p ,xb))
466 (not (fp-zero-p ,yb))))))))))))
468 (defun coercion-loses-precision-p (val type)
471 (double-float (subtypep type 'single-float))
472 (rational (subtypep type 'float))
473 (t (bug "Unexpected arguments to bounds coercion: ~S ~S" val type))))
475 (defun coerce-for-bound (val type)
477 (let ((xbound (coerce-for-bound (car val) type)))
478 (if (coercion-loses-precision-p (car val) type)
482 ((subtypep type 'double-float)
483 (if (<= most-negative-double-float val most-positive-double-float)
485 ((or (subtypep type 'single-float) (subtypep type 'float))
486 ;; coerce to float returns a single-float
487 (if (<= most-negative-single-float val most-positive-single-float)
489 (t (coerce val type)))))
491 (defun coerce-and-truncate-floats (val type)
494 (let ((xbound (coerce-for-bound (car val) type)))
495 (if (coercion-loses-precision-p (car val) type)
499 ((subtypep type 'double-float)
500 (if (<= most-negative-double-float val most-positive-double-float)
502 (if (< val most-negative-double-float)
503 most-negative-double-float most-positive-double-float)))
504 ((or (subtypep type 'single-float) (subtypep type 'float))
505 ;; coerce to float returns a single-float
506 (if (<= most-negative-single-float val most-positive-single-float)
508 (if (< val most-negative-single-float)
509 most-negative-single-float most-positive-single-float)))
510 (t (coerce val type))))))
512 ;;; Convert a numeric-type object to an interval object.
513 (defun numeric-type->interval (x)
514 (declare (type numeric-type x))
515 (make-interval :low (numeric-type-low x)
516 :high (numeric-type-high x)))
518 (defun type-approximate-interval (type)
519 (declare (type ctype type))
520 (let ((types (prepare-arg-for-derive-type type))
523 (let ((type (if (member-type-p type)
524 (convert-member-type type)
526 (unless (numeric-type-p type)
527 (return-from type-approximate-interval nil))
528 (let ((interval (numeric-type->interval type)))
531 (interval-approximate-union result interval)
535 (defun copy-interval-limit (limit)
540 (defun copy-interval (x)
541 (declare (type interval x))
542 (make-interval :low (copy-interval-limit (interval-low x))
543 :high (copy-interval-limit (interval-high x))))
545 ;;; Given a point P contained in the interval X, split X into two
546 ;;; intervals at the point P. If CLOSE-LOWER is T, then the left
547 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
548 ;;; contains P. You can specify both to be T or NIL.
549 (defun interval-split (p x &optional close-lower close-upper)
550 (declare (type number p)
552 (list (make-interval :low (copy-interval-limit (interval-low x))
553 :high (if close-lower p (list p)))
554 (make-interval :low (if close-upper (list p) p)
555 :high (copy-interval-limit (interval-high x)))))
557 ;;; Return the closure of the interval. That is, convert open bounds
558 ;;; to closed bounds.
559 (defun interval-closure (x)
560 (declare (type interval x))
561 (make-interval :low (type-bound-number (interval-low x))
562 :high (type-bound-number (interval-high x))))
564 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
565 ;;; '-. Otherwise return NIL.
566 (defun interval-range-info (x &optional (point 0))
567 (declare (type interval x))
568 (let ((lo (interval-low x))
569 (hi (interval-high x)))
570 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
572 ((and hi (signed-zero->= point (type-bound-number hi)))
577 ;;; Test to see whether the interval X is bounded. HOW determines the
578 ;;; test, and should be either ABOVE, BELOW, or BOTH.
579 (defun interval-bounded-p (x how)
580 (declare (type interval x))
587 (and (interval-low x) (interval-high x)))))
589 ;;; See whether the interval X contains the number P, taking into
590 ;;; account that the interval might not be closed.
591 (defun interval-contains-p (p x)
592 (declare (type number p)
594 ;; Does the interval X contain the number P? This would be a lot
595 ;; easier if all intervals were closed!
596 (let ((lo (interval-low x))
597 (hi (interval-high x)))
599 ;; The interval is bounded
600 (if (and (signed-zero-<= (type-bound-number lo) p)
601 (signed-zero-<= p (type-bound-number hi)))
602 ;; P is definitely in the closure of the interval.
603 ;; We just need to check the end points now.
604 (cond ((signed-zero-= p (type-bound-number lo))
606 ((signed-zero-= p (type-bound-number hi))
611 ;; Interval with upper bound
612 (if (signed-zero-< p (type-bound-number hi))
614 (and (numberp hi) (signed-zero-= p hi))))
616 ;; Interval with lower bound
617 (if (signed-zero-> p (type-bound-number lo))
619 (and (numberp lo) (signed-zero-= p lo))))
621 ;; Interval with no bounds
624 ;;; Determine whether two intervals X and Y intersect. Return T if so.
625 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
626 ;;; were closed. Otherwise the intervals are treated as they are.
628 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
629 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
630 ;;; is T, then they do intersect because we use the closure of X = [0,
631 ;;; 1] and Y = [1, 2] to determine intersection.
632 (defun interval-intersect-p (x y &optional closed-intervals-p)
633 (declare (type interval x y))
634 (and (interval-intersection/difference (if closed-intervals-p
637 (if closed-intervals-p
642 ;;; Are the two intervals adjacent? That is, is there a number
643 ;;; between the two intervals that is not an element of either
644 ;;; interval? If so, they are not adjacent. For example [0, 1) and
645 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
646 ;;; between both intervals.
647 (defun interval-adjacent-p (x y)
648 (declare (type interval x y))
649 (flet ((adjacent (lo hi)
650 ;; Check to see whether lo and hi are adjacent. If either is
651 ;; nil, they can't be adjacent.
652 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
653 ;; The bounds are equal. They are adjacent if one of
654 ;; them is closed (a number). If both are open (consp),
655 ;; then there is a number that lies between them.
656 (or (numberp lo) (numberp hi)))))
657 (or (adjacent (interval-low y) (interval-high x))
658 (adjacent (interval-low x) (interval-high y)))))
660 ;;; Compute the intersection and difference between two intervals.
661 ;;; Two values are returned: the intersection and the difference.
663 ;;; Let the two intervals be X and Y, and let I and D be the two
664 ;;; values returned by this function. Then I = X intersect Y. If I
665 ;;; is NIL (the empty set), then D is X union Y, represented as the
666 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
667 ;;; - I, which is a list of two intervals.
669 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
670 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
671 (defun interval-intersection/difference (x y)
672 (declare (type interval x y))
673 (let ((x-lo (interval-low x))
674 (x-hi (interval-high x))
675 (y-lo (interval-low y))
676 (y-hi (interval-high y)))
679 ;; If p is an open bound, make it closed. If p is a closed
680 ;; bound, make it open.
684 (test-number (p int bound)
685 ;; Test whether P is in the interval.
686 (let ((pn (type-bound-number p)))
687 (when (interval-contains-p pn (interval-closure int))
688 ;; Check for endpoints.
689 (let* ((lo (interval-low int))
690 (hi (interval-high int))
691 (lon (type-bound-number lo))
692 (hin (type-bound-number hi)))
694 ;; Interval may be a point.
695 ((and lon hin (= lon hin pn))
696 (and (numberp p) (numberp lo) (numberp hi)))
697 ;; Point matches the low end.
698 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
699 ;; (P [P,?} => TRUE P) [P,?} => FALSE
700 ;; (P (P,?} => TRUE P) (P,?} => FALSE
701 ((and lon (= pn lon))
702 (or (and (numberp p) (numberp lo))
703 (and (consp p) (eq :low bound))))
704 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
705 ;; P) {?,P] => TRUE (P {?,P] => FALSE
706 ;; P) {?,P) => TRUE (P {?,P) => FALSE
707 ((and hin (= pn hin))
708 (or (and (numberp p) (numberp hi))
709 (and (consp p) (eq :high bound))))
710 ;; Not an endpoint, all is well.
713 (test-lower-bound (p int)
714 ;; P is a lower bound of an interval.
716 (test-number p int :low)
717 (not (interval-bounded-p int 'below))))
718 (test-upper-bound (p int)
719 ;; P is an upper bound of an interval.
721 (test-number p int :high)
722 (not (interval-bounded-p int 'above)))))
723 (let ((x-lo-in-y (test-lower-bound x-lo y))
724 (x-hi-in-y (test-upper-bound x-hi y))
725 (y-lo-in-x (test-lower-bound y-lo x))
726 (y-hi-in-x (test-upper-bound y-hi x)))
727 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
728 ;; Intervals intersect. Let's compute the intersection
729 ;; and the difference.
730 (multiple-value-bind (lo left-lo left-hi)
731 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
732 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
733 (multiple-value-bind (hi right-lo right-hi)
735 (values x-hi (opposite-bound x-hi) y-hi))
737 (values y-hi (opposite-bound y-hi) x-hi)))
738 (values (make-interval :low lo :high hi)
739 (list (make-interval :low left-lo
741 (make-interval :low right-lo
744 (values nil (list x y))))))))
746 ;;; If intervals X and Y intersect, return a new interval that is the
747 ;;; union of the two. If they do not intersect, return NIL.
748 (defun interval-merge-pair (x y)
749 (declare (type interval x y))
750 ;; If x and y intersect or are adjacent, create the union.
751 ;; Otherwise return nil
752 (when (or (interval-intersect-p x y)
753 (interval-adjacent-p x y))
754 (flet ((select-bound (x1 x2 min-op max-op)
755 (let ((x1-val (type-bound-number x1))
756 (x2-val (type-bound-number x2)))
758 ;; Both bounds are finite. Select the right one.
759 (cond ((funcall min-op x1-val x2-val)
760 ;; x1 is definitely better.
762 ((funcall max-op x1-val x2-val)
763 ;; x2 is definitely better.
766 ;; Bounds are equal. Select either
767 ;; value and make it open only if
769 (set-bound x1-val (and (consp x1) (consp x2))))))
771 ;; At least one bound is not finite. The
772 ;; non-finite bound always wins.
774 (let* ((x-lo (copy-interval-limit (interval-low x)))
775 (x-hi (copy-interval-limit (interval-high x)))
776 (y-lo (copy-interval-limit (interval-low y)))
777 (y-hi (copy-interval-limit (interval-high y))))
778 (make-interval :low (select-bound x-lo y-lo #'< #'>)
779 :high (select-bound x-hi y-hi #'> #'<))))))
781 ;;; return the minimal interval, containing X and Y
782 (defun interval-approximate-union (x y)
783 (cond ((interval-merge-pair x y))
785 (make-interval :low (copy-interval-limit (interval-low x))
786 :high (copy-interval-limit (interval-high y))))
788 (make-interval :low (copy-interval-limit (interval-low y))
789 :high (copy-interval-limit (interval-high x))))))
791 ;;; basic arithmetic operations on intervals. We probably should do
792 ;;; true interval arithmetic here, but it's complicated because we
793 ;;; have float and integer types and bounds can be open or closed.
795 ;;; the negative of an interval
796 (defun interval-neg (x)
797 (declare (type interval x))
798 (make-interval :low (bound-func #'- (interval-high x) t)
799 :high (bound-func #'- (interval-low x) t)))
801 ;;; Add two intervals.
802 (defun interval-add (x y)
803 (declare (type interval x y))
804 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
805 :high (bound-binop + (interval-high x) (interval-high y))))
807 ;;; Subtract two intervals.
808 (defun interval-sub (x y)
809 (declare (type interval x y))
810 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
811 :high (bound-binop - (interval-high x) (interval-low y))))
813 ;;; Multiply two intervals.
814 (defun interval-mul (x y)
815 (declare (type interval x y))
816 (flet ((bound-mul (x y)
817 (cond ((or (null x) (null y))
818 ;; Multiply by infinity is infinity
820 ((or (and (numberp x) (zerop x))
821 (and (numberp y) (zerop y)))
822 ;; Multiply by closed zero is special. The result
823 ;; is always a closed bound. But don't replace this
824 ;; with zero; we want the multiplication to produce
825 ;; the correct signed zero, if needed. Use SIGNUM
826 ;; to avoid trying to multiply huge bignums with 0.0.
827 (* (signum (type-bound-number x)) (signum (type-bound-number y))))
828 ((or (and (floatp x) (float-infinity-p x))
829 (and (floatp y) (float-infinity-p y)))
830 ;; Infinity times anything is infinity
833 ;; General multiply. The result is open if either is open.
834 (bound-binop * x y)))))
835 (let ((x-range (interval-range-info x))
836 (y-range (interval-range-info y)))
837 (cond ((null x-range)
838 ;; Split x into two and multiply each separately
839 (destructuring-bind (x- x+) (interval-split 0 x t t)
840 (interval-merge-pair (interval-mul x- y)
841 (interval-mul x+ y))))
843 ;; Split y into two and multiply each separately
844 (destructuring-bind (y- y+) (interval-split 0 y t t)
845 (interval-merge-pair (interval-mul x y-)
846 (interval-mul x y+))))
848 (interval-neg (interval-mul (interval-neg x) y)))
850 (interval-neg (interval-mul x (interval-neg y))))
851 ((and (eq x-range '+) (eq y-range '+))
852 ;; If we are here, X and Y are both positive.
854 :low (bound-mul (interval-low x) (interval-low y))
855 :high (bound-mul (interval-high x) (interval-high y))))
857 (bug "excluded case in INTERVAL-MUL"))))))
859 ;;; Divide two intervals.
860 (defun interval-div (top bot)
861 (declare (type interval top bot))
862 (flet ((bound-div (x y y-low-p)
865 ;; Divide by infinity means result is 0. However,
866 ;; we need to watch out for the sign of the result,
867 ;; to correctly handle signed zeros. We also need
868 ;; to watch out for positive or negative infinity.
869 (if (floatp (type-bound-number x))
871 (- (float-sign (type-bound-number x) 0.0))
872 (float-sign (type-bound-number x) 0.0))
874 ((zerop (type-bound-number y))
875 ;; Divide by zero means result is infinity
878 (bound-binop / x y)))))
879 (let ((top-range (interval-range-info top))
880 (bot-range (interval-range-info bot)))
881 (cond ((null bot-range)
882 ;; The denominator contains zero, so anything goes!
883 (make-interval :low nil :high nil))
885 ;; Denominator is negative so flip the sign, compute the
886 ;; result, and flip it back.
887 (interval-neg (interval-div top (interval-neg bot))))
889 ;; Split top into two positive and negative parts, and
890 ;; divide each separately
891 (destructuring-bind (top- top+) (interval-split 0 top t t)
892 (interval-merge-pair (interval-div top- bot)
893 (interval-div top+ bot))))
895 ;; Top is negative so flip the sign, divide, and flip the
896 ;; sign of the result.
897 (interval-neg (interval-div (interval-neg top) bot)))
898 ((and (eq top-range '+) (eq bot-range '+))
901 :low (bound-div (interval-low top) (interval-high bot) t)
902 :high (bound-div (interval-high top) (interval-low bot) nil)))
904 (bug "excluded case in INTERVAL-DIV"))))))
906 ;;; Apply the function F to the interval X. If X = [a, b], then the
907 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
908 ;;; result makes sense. It will if F is monotonic increasing (or, if
909 ;;; the interval is closed, non-decreasing).
911 ;;; (Actually most uses of INTERVAL-FUNC are coercions to float types,
912 ;;; which are not monotonic increasing, so default to calling
913 ;;; BOUND-FUNC with a non-strict argument).
914 (defun interval-func (f x &optional increasing)
915 (declare (type function f)
917 (let ((lo (bound-func f (interval-low x) increasing))
918 (hi (bound-func f (interval-high x) increasing)))
919 (make-interval :low lo :high hi)))
921 ;;; Return T if X < Y. That is every number in the interval X is
922 ;;; always less than any number in the interval Y.
923 (defun interval-< (x y)
924 (declare (type interval x y))
925 ;; X < Y only if X is bounded above, Y is bounded below, and they
927 (when (and (interval-bounded-p x 'above)
928 (interval-bounded-p y 'below))
929 ;; Intervals are bounded in the appropriate way. Make sure they
931 (let ((left (interval-high x))
932 (right (interval-low y)))
933 (cond ((> (type-bound-number left)
934 (type-bound-number right))
935 ;; The intervals definitely overlap, so result is NIL.
937 ((< (type-bound-number left)
938 (type-bound-number right))
939 ;; The intervals definitely don't touch, so result is T.
942 ;; Limits are equal. Check for open or closed bounds.
943 ;; Don't overlap if one or the other are open.
944 (or (consp left) (consp right)))))))
946 ;;; Return T if X >= Y. That is, every number in the interval X is
947 ;;; always greater than any number in the interval Y.
948 (defun interval->= (x y)
949 (declare (type interval x y))
950 ;; X >= Y if lower bound of X >= upper bound of Y
951 (when (and (interval-bounded-p x 'below)
952 (interval-bounded-p y 'above))
953 (>= (type-bound-number (interval-low x))
954 (type-bound-number (interval-high y)))))
956 ;;; Return T if X = Y.
957 (defun interval-= (x y)
958 (declare (type interval x y))
959 (and (interval-bounded-p x 'both)
960 (interval-bounded-p y 'both)
964 ;; Open intervals cannot be =
965 (return-from interval-= nil))))
966 ;; Both intervals refer to the same point
967 (= (bound (interval-high x)) (bound (interval-low x))
968 (bound (interval-high y)) (bound (interval-low y))))))
970 ;;; Return T if X /= Y
971 (defun interval-/= (x y)
972 (not (interval-intersect-p x y)))
974 ;;; Return an interval that is the absolute value of X. Thus, if
975 ;;; X = [-1 10], the result is [0, 10].
976 (defun interval-abs (x)
977 (declare (type interval x))
978 (case (interval-range-info x)
984 (destructuring-bind (x- x+) (interval-split 0 x t t)
985 (interval-merge-pair (interval-neg x-) x+)))))
987 ;;; Compute the square of an interval.
988 (defun interval-sqr (x)
989 (declare (type interval x))
990 (interval-func (lambda (x) (* x x)) (interval-abs x)))
992 ;;;; numeric DERIVE-TYPE methods
994 ;;; a utility for defining derive-type methods of integer operations. If
995 ;;; the types of both X and Y are integer types, then we compute a new
996 ;;; integer type with bounds determined by FUN when applied to X and Y.
997 ;;; Otherwise, we use NUMERIC-CONTAGION.
998 (defun derive-integer-type-aux (x y fun)
999 (declare (type function fun))
1000 (if (and (numeric-type-p x) (numeric-type-p y)
1001 (eq (numeric-type-class x) 'integer)
1002 (eq (numeric-type-class y) 'integer)
1003 (eq (numeric-type-complexp x) :real)
1004 (eq (numeric-type-complexp y) :real))
1005 (multiple-value-bind (low high) (funcall fun x y)
1006 (make-numeric-type :class 'integer
1010 (numeric-contagion x y)))
1012 (defun derive-integer-type (x y fun)
1013 (declare (type lvar x y) (type function fun))
1014 (let ((x (lvar-type x))
1016 (derive-integer-type-aux x y fun)))
1018 ;;; simple utility to flatten a list
1019 (defun flatten-list (x)
1020 (labels ((flatten-and-append (tree list)
1021 (cond ((null tree) list)
1022 ((atom tree) (cons tree list))
1023 (t (flatten-and-append
1024 (car tree) (flatten-and-append (cdr tree) list))))))
1025 (flatten-and-append x nil)))
1027 ;;; Take some type of lvar and massage it so that we get a list of the
1028 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
1030 (defun prepare-arg-for-derive-type (arg)
1031 (flet ((listify (arg)
1036 (union-type-types arg))
1039 (unless (eq arg *empty-type*)
1040 ;; Make sure all args are some type of numeric-type. For member
1041 ;; types, convert the list of members into a union of equivalent
1042 ;; single-element member-type's.
1043 (let ((new-args nil))
1044 (dolist (arg (listify arg))
1045 (if (member-type-p arg)
1046 ;; Run down the list of members and convert to a list of
1048 (mapc-member-type-members
1050 (push (if (numberp member)
1051 (make-member-type :members (list member))
1055 (push arg new-args)))
1056 (unless (member *empty-type* new-args)
1059 ;;; Convert from the standard type convention for which -0.0 and 0.0
1060 ;;; are equal to an intermediate convention for which they are
1061 ;;; considered different which is more natural for some of the
1063 (defun convert-numeric-type (type)
1064 (declare (type numeric-type type))
1065 ;;; Only convert real float interval delimiters types.
1066 (if (eq (numeric-type-complexp type) :real)
1067 (let* ((lo (numeric-type-low type))
1068 (lo-val (type-bound-number lo))
1069 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
1070 (hi (numeric-type-high type))
1071 (hi-val (type-bound-number hi))
1072 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
1073 (if (or lo-float-zero-p hi-float-zero-p)
1075 :class (numeric-type-class type)
1076 :format (numeric-type-format type)
1078 :low (if lo-float-zero-p
1080 (list (float 0.0 lo-val))
1081 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
1083 :high (if hi-float-zero-p
1085 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
1092 ;;; Convert back from the intermediate convention for which -0.0 and
1093 ;;; 0.0 are considered different to the standard type convention for
1094 ;;; which and equal.
1095 (defun convert-back-numeric-type (type)
1096 (declare (type numeric-type type))
1097 ;;; Only convert real float interval delimiters types.
1098 (if (eq (numeric-type-complexp type) :real)
1099 (let* ((lo (numeric-type-low type))
1100 (lo-val (type-bound-number lo))
1102 (and lo (floatp lo-val) (= lo-val 0.0)
1103 (float-sign lo-val)))
1104 (hi (numeric-type-high type))
1105 (hi-val (type-bound-number hi))
1107 (and hi (floatp hi-val) (= hi-val 0.0)
1108 (float-sign hi-val))))
1110 ;; (float +0.0 +0.0) => (member 0.0)
1111 ;; (float -0.0 -0.0) => (member -0.0)
1112 ((and lo-float-zero-p hi-float-zero-p)
1113 ;; shouldn't have exclusive bounds here..
1114 (aver (and (not (consp lo)) (not (consp hi))))
1115 (if (= lo-float-zero-p hi-float-zero-p)
1116 ;; (float +0.0 +0.0) => (member 0.0)
1117 ;; (float -0.0 -0.0) => (member -0.0)
1118 (specifier-type `(member ,lo-val))
1119 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1120 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1121 (make-numeric-type :class (numeric-type-class type)
1122 :format (numeric-type-format type)
1128 ;; (float -0.0 x) => (float 0.0 x)
1129 ((and (not (consp lo)) (minusp lo-float-zero-p))
1130 (make-numeric-type :class (numeric-type-class type)
1131 :format (numeric-type-format type)
1133 :low (float 0.0 lo-val)
1135 ;; (float (+0.0) x) => (float (0.0) x)
1136 ((and (consp lo) (plusp lo-float-zero-p))
1137 (make-numeric-type :class (numeric-type-class type)
1138 :format (numeric-type-format type)
1140 :low (list (float 0.0 lo-val))
1143 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1144 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1145 (list (make-member-type :members (list (float 0.0 lo-val)))
1146 (make-numeric-type :class (numeric-type-class type)
1147 :format (numeric-type-format type)
1149 :low (list (float 0.0 lo-val))
1153 ;; (float x +0.0) => (float x 0.0)
1154 ((and (not (consp hi)) (plusp hi-float-zero-p))
1155 (make-numeric-type :class (numeric-type-class type)
1156 :format (numeric-type-format type)
1159 :high (float 0.0 hi-val)))
1160 ;; (float x (-0.0)) => (float x (0.0))
1161 ((and (consp hi) (minusp hi-float-zero-p))
1162 (make-numeric-type :class (numeric-type-class type)
1163 :format (numeric-type-format type)
1166 :high (list (float 0.0 hi-val))))
1168 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1169 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1170 (list (make-member-type :members (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val)))
1171 (make-numeric-type :class (numeric-type-class type)
1172 :format (numeric-type-format type)
1175 :high (list (float 0.0 hi-val)))))))
1181 ;;; Convert back a possible list of numeric types.
1182 (defun convert-back-numeric-type-list (type-list)
1185 (let ((results '()))
1186 (dolist (type type-list)
1187 (if (numeric-type-p type)
1188 (let ((result (convert-back-numeric-type type)))
1190 (setf results (append results result))
1191 (push result results)))
1192 (push type results)))
1195 (convert-back-numeric-type type-list))
1197 (convert-back-numeric-type-list (union-type-types type-list)))
1201 ;;; Take a list of types and return a canonical type specifier,
1202 ;;; combining any MEMBER types together. If both positive and negative
1203 ;;; MEMBER types are present they are converted to a float type.
1204 ;;; XXX This would be far simpler if the type-union methods could handle
1205 ;;; member/number unions.
1207 ;;; If we're about to generate an overly complex union of numeric types, start
1208 ;;; collapse the ranges together.
1210 ;;; FIXME: The MEMBER canonicalization parts of MAKE-DERIVED-UNION-TYPE and
1211 ;;; entire CONVERT-MEMBER-TYPE probably belong in the kernel's type logic,
1212 ;;; invoked always, instead of in the compiler, invoked only during some type
1214 (defvar *derived-numeric-union-complexity-limit* 6)
1216 (defun make-derived-union-type (type-list)
1217 (let ((xset (alloc-xset))
1220 (numeric-type *empty-type*))
1221 (dolist (type type-list)
1222 (cond ((member-type-p type)
1223 (mapc-member-type-members
1225 (if (fp-zero-p member)
1226 (unless (member member fp-zeroes)
1227 (pushnew member fp-zeroes))
1228 (add-to-xset member xset)))
1230 ((numeric-type-p type)
1231 (let ((*approximate-numeric-unions*
1232 (when (and (union-type-p numeric-type)
1233 (nthcdr *derived-numeric-union-complexity-limit*
1234 (union-type-types numeric-type)))
1236 (setf numeric-type (type-union type numeric-type))))
1238 (push type misc-types))))
1239 (if (and (xset-empty-p xset) (not fp-zeroes))
1240 (apply #'type-union numeric-type misc-types)
1241 (apply #'type-union (make-member-type :xset xset :fp-zeroes fp-zeroes)
1242 numeric-type misc-types))))
1244 ;;; Convert a member type with a single member to a numeric type.
1245 (defun convert-member-type (arg)
1246 (let* ((members (member-type-members arg))
1247 (member (first members))
1248 (member-type (type-of member)))
1249 (aver (not (rest members)))
1250 (specifier-type (cond ((typep member 'integer)
1251 `(integer ,member ,member))
1252 ((memq member-type '(short-float single-float
1253 double-float long-float))
1254 `(,member-type ,member ,member))
1258 ;;; This is used in defoptimizers for computing the resulting type of
1261 ;;; Given the lvar ARG, derive the resulting type using the
1262 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1263 ;;; "atomic" lvar type like numeric-type or member-type (containing
1264 ;;; just one element). It should return the resulting type, which can
1265 ;;; be a list of types.
1267 ;;; For the case of member types, if a MEMBER-FUN is given it is
1268 ;;; called to compute the result otherwise the member type is first
1269 ;;; converted to a numeric type and the DERIVE-FUN is called.
1270 (defun one-arg-derive-type (arg derive-fun member-fun
1271 &optional (convert-type t))
1272 (declare (type function derive-fun)
1273 (type (or null function) member-fun))
1274 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1280 (with-float-traps-masked
1281 (:underflow :overflow :divide-by-zero)
1283 `(eql ,(funcall member-fun
1284 (first (member-type-members x))))))
1285 ;; Otherwise convert to a numeric type.
1286 (let ((result-type-list
1287 (funcall derive-fun (convert-member-type x))))
1289 (convert-back-numeric-type-list result-type-list)
1290 result-type-list))))
1293 (convert-back-numeric-type-list
1294 (funcall derive-fun (convert-numeric-type x)))
1295 (funcall derive-fun x)))
1297 *universal-type*))))
1298 ;; Run down the list of args and derive the type of each one,
1299 ;; saving all of the results in a list.
1300 (let ((results nil))
1301 (dolist (arg arg-list)
1302 (let ((result (deriver arg)))
1304 (setf results (append results result))
1305 (push result results))))
1307 (make-derived-union-type results)
1308 (first results)))))))
1310 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1311 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1312 ;;; original args and a third which is T to indicate if the two args
1313 ;;; really represent the same lvar. This is useful for deriving the
1314 ;;; type of things like (* x x), which should always be positive. If
1315 ;;; we didn't do this, we wouldn't be able to tell.
1316 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1317 &optional (convert-type t))
1318 (declare (type function derive-fun fun))
1319 (flet ((deriver (x y same-arg)
1320 (cond ((and (member-type-p x) (member-type-p y))
1321 (let* ((x (first (member-type-members x)))
1322 (y (first (member-type-members y)))
1323 (result (ignore-errors
1324 (with-float-traps-masked
1325 (:underflow :overflow :divide-by-zero
1327 (funcall fun x y)))))
1328 (cond ((null result) *empty-type*)
1329 ((and (floatp result) (float-nan-p result))
1330 (make-numeric-type :class 'float
1331 :format (type-of result)
1334 (specifier-type `(eql ,result))))))
1335 ((and (member-type-p x) (numeric-type-p y))
1336 (let* ((x (convert-member-type x))
1337 (y (if convert-type (convert-numeric-type y) y))
1338 (result (funcall derive-fun x y same-arg)))
1340 (convert-back-numeric-type-list result)
1342 ((and (numeric-type-p x) (member-type-p y))
1343 (let* ((x (if convert-type (convert-numeric-type x) x))
1344 (y (convert-member-type y))
1345 (result (funcall derive-fun x y same-arg)))
1347 (convert-back-numeric-type-list result)
1349 ((and (numeric-type-p x) (numeric-type-p y))
1350 (let* ((x (if convert-type (convert-numeric-type x) x))
1351 (y (if convert-type (convert-numeric-type y) y))
1352 (result (funcall derive-fun x y same-arg)))
1354 (convert-back-numeric-type-list result)
1357 *universal-type*))))
1358 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1359 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1360 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1362 (let ((results nil))
1364 ;; Since the args are the same LVARs, just run down the
1367 (let ((result (deriver x x same-arg)))
1369 (setf results (append results result))
1370 (push result results))))
1371 ;; Try all pairwise combinations.
1374 (let ((result (or (deriver x y same-arg)
1375 (numeric-contagion x y))))
1377 (setf results (append results result))
1378 (push result results))))))
1380 (make-derived-union-type results)
1381 (first results)))))))
1383 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1385 (defoptimizer (+ derive-type) ((x y))
1386 (derive-integer-type
1393 (values (frob (numeric-type-low x) (numeric-type-low y))
1394 (frob (numeric-type-high x) (numeric-type-high y)))))))
1396 (defoptimizer (- derive-type) ((x y))
1397 (derive-integer-type
1404 (values (frob (numeric-type-low x) (numeric-type-high y))
1405 (frob (numeric-type-high x) (numeric-type-low y)))))))
1407 (defoptimizer (* derive-type) ((x y))
1408 (derive-integer-type
1411 (let ((x-low (numeric-type-low x))
1412 (x-high (numeric-type-high x))
1413 (y-low (numeric-type-low y))
1414 (y-high (numeric-type-high y)))
1415 (cond ((not (and x-low y-low))
1417 ((or (minusp x-low) (minusp y-low))
1418 (if (and x-high y-high)
1419 (let ((max (* (max (abs x-low) (abs x-high))
1420 (max (abs y-low) (abs y-high)))))
1421 (values (- max) max))
1424 (values (* x-low y-low)
1425 (if (and x-high y-high)
1429 (defoptimizer (/ derive-type) ((x y))
1430 (numeric-contagion (lvar-type x) (lvar-type y)))
1434 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1436 (defun +-derive-type-aux (x y same-arg)
1437 (if (and (numeric-type-real-p x)
1438 (numeric-type-real-p y))
1441 (let ((x-int (numeric-type->interval x)))
1442 (interval-add x-int x-int))
1443 (interval-add (numeric-type->interval x)
1444 (numeric-type->interval y))))
1445 (result-type (numeric-contagion x y)))
1446 ;; If the result type is a float, we need to be sure to coerce
1447 ;; the bounds into the correct type.
1448 (when (eq (numeric-type-class result-type) 'float)
1449 (setf result (interval-func
1451 (coerce-for-bound x (or (numeric-type-format result-type)
1455 :class (if (and (eq (numeric-type-class x) 'integer)
1456 (eq (numeric-type-class y) 'integer))
1457 ;; The sum of integers is always an integer.
1459 (numeric-type-class result-type))
1460 :format (numeric-type-format result-type)
1461 :low (interval-low result)
1462 :high (interval-high result)))
1463 ;; general contagion
1464 (numeric-contagion x y)))
1466 (defoptimizer (+ derive-type) ((x y))
1467 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1469 (defun --derive-type-aux (x y same-arg)
1470 (if (and (numeric-type-real-p x)
1471 (numeric-type-real-p y))
1473 ;; (- X X) is always 0.
1475 (make-interval :low 0 :high 0)
1476 (interval-sub (numeric-type->interval x)
1477 (numeric-type->interval y))))
1478 (result-type (numeric-contagion x y)))
1479 ;; If the result type is a float, we need to be sure to coerce
1480 ;; the bounds into the correct type.
1481 (when (eq (numeric-type-class result-type) 'float)
1482 (setf result (interval-func
1484 (coerce-for-bound x (or (numeric-type-format result-type)
1488 :class (if (and (eq (numeric-type-class x) 'integer)
1489 (eq (numeric-type-class y) 'integer))
1490 ;; The difference of integers is always an integer.
1492 (numeric-type-class result-type))
1493 :format (numeric-type-format result-type)
1494 :low (interval-low result)
1495 :high (interval-high result)))
1496 ;; general contagion
1497 (numeric-contagion x y)))
1499 (defoptimizer (- derive-type) ((x y))
1500 (two-arg-derive-type x y #'--derive-type-aux #'-))
1502 (defun *-derive-type-aux (x y same-arg)
1503 (if (and (numeric-type-real-p x)
1504 (numeric-type-real-p y))
1506 ;; (* X X) is always positive, so take care to do it right.
1508 (interval-sqr (numeric-type->interval x))
1509 (interval-mul (numeric-type->interval x)
1510 (numeric-type->interval y))))
1511 (result-type (numeric-contagion x y)))
1512 ;; If the result type is a float, we need to be sure to coerce
1513 ;; the bounds into the correct type.
1514 (when (eq (numeric-type-class result-type) 'float)
1515 (setf result (interval-func
1517 (coerce-for-bound x (or (numeric-type-format result-type)
1521 :class (if (and (eq (numeric-type-class x) 'integer)
1522 (eq (numeric-type-class y) 'integer))
1523 ;; The product of integers is always an integer.
1525 (numeric-type-class result-type))
1526 :format (numeric-type-format result-type)
1527 :low (interval-low result)
1528 :high (interval-high result)))
1529 (numeric-contagion x y)))
1531 (defoptimizer (* derive-type) ((x y))
1532 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1534 (defun /-derive-type-aux (x y same-arg)
1535 (if (and (numeric-type-real-p x)
1536 (numeric-type-real-p y))
1538 ;; (/ X X) is always 1, except if X can contain 0. In
1539 ;; that case, we shouldn't optimize the division away
1540 ;; because we want 0/0 to signal an error.
1542 (not (interval-contains-p
1543 0 (interval-closure (numeric-type->interval y)))))
1544 (make-interval :low 1 :high 1)
1545 (interval-div (numeric-type->interval x)
1546 (numeric-type->interval y))))
1547 (result-type (numeric-contagion x y)))
1548 ;; If the result type is a float, we need to be sure to coerce
1549 ;; the bounds into the correct type.
1550 (when (eq (numeric-type-class result-type) 'float)
1551 (setf result (interval-func
1553 (coerce-for-bound x (or (numeric-type-format result-type)
1556 (make-numeric-type :class (numeric-type-class result-type)
1557 :format (numeric-type-format result-type)
1558 :low (interval-low result)
1559 :high (interval-high result)))
1560 (numeric-contagion x y)))
1562 (defoptimizer (/ derive-type) ((x y))
1563 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1567 (defun ash-derive-type-aux (n-type shift same-arg)
1568 (declare (ignore same-arg))
1569 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1570 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1571 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1572 ;; two bignums yielding zero) and it's hard to avoid that
1573 ;; calculation in here.
1574 #+(and cmu sb-xc-host)
1575 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1576 (typep (numeric-type-high n-type) 'bignum))
1577 (or (typep (numeric-type-low shift) 'bignum)
1578 (typep (numeric-type-high shift) 'bignum)))
1579 (return-from ash-derive-type-aux *universal-type*))
1580 (flet ((ash-outer (n s)
1581 (when (and (fixnump s)
1583 (> s sb!xc:most-negative-fixnum))
1585 ;; KLUDGE: The bare 64's here should be related to
1586 ;; symbolic machine word size values somehow.
1589 (if (and (fixnump s)
1590 (> s sb!xc:most-negative-fixnum))
1592 (if (minusp n) -1 0))))
1593 (or (and (csubtypep n-type (specifier-type 'integer))
1594 (csubtypep shift (specifier-type 'integer))
1595 (let ((n-low (numeric-type-low n-type))
1596 (n-high (numeric-type-high n-type))
1597 (s-low (numeric-type-low shift))
1598 (s-high (numeric-type-high shift)))
1599 (make-numeric-type :class 'integer :complexp :real
1602 (ash-outer n-low s-high)
1603 (ash-inner n-low s-low)))
1606 (ash-inner n-high s-low)
1607 (ash-outer n-high s-high))))))
1610 (defoptimizer (ash derive-type) ((n shift))
1611 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1613 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1614 (macrolet ((frob (fun)
1615 `#'(lambda (type type2)
1616 (declare (ignore type2))
1617 (let ((lo (numeric-type-low type))
1618 (hi (numeric-type-high type)))
1619 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1621 (defoptimizer (%negate derive-type) ((num))
1622 (derive-integer-type num num (frob -))))
1624 (defun lognot-derive-type-aux (int)
1625 (derive-integer-type-aux int int
1626 (lambda (type type2)
1627 (declare (ignore type2))
1628 (let ((lo (numeric-type-low type))
1629 (hi (numeric-type-high type)))
1630 (values (if hi (lognot hi) nil)
1631 (if lo (lognot lo) nil)
1632 (numeric-type-class type)
1633 (numeric-type-format type))))))
1635 (defoptimizer (lognot derive-type) ((int))
1636 (lognot-derive-type-aux (lvar-type int)))
1638 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1639 (defoptimizer (%negate derive-type) ((num))
1640 (flet ((negate-bound (b)
1642 (set-bound (- (type-bound-number b))
1644 (one-arg-derive-type num
1646 (modified-numeric-type
1648 :low (negate-bound (numeric-type-high type))
1649 :high (negate-bound (numeric-type-low type))))
1652 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1653 (defoptimizer (abs derive-type) ((num))
1654 (let ((type (lvar-type num)))
1655 (if (and (numeric-type-p type)
1656 (eq (numeric-type-class type) 'integer)
1657 (eq (numeric-type-complexp type) :real))
1658 (let ((lo (numeric-type-low type))
1659 (hi (numeric-type-high type)))
1660 (make-numeric-type :class 'integer :complexp :real
1661 :low (cond ((and hi (minusp hi))
1667 :high (if (and hi lo)
1668 (max (abs hi) (abs lo))
1670 (numeric-contagion type type))))
1672 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1673 (defun abs-derive-type-aux (type)
1674 (cond ((eq (numeric-type-complexp type) :complex)
1675 ;; The absolute value of a complex number is always a
1676 ;; non-negative float.
1677 (let* ((format (case (numeric-type-class type)
1678 ((integer rational) 'single-float)
1679 (t (numeric-type-format type))))
1680 (bound-format (or format 'float)))
1681 (make-numeric-type :class 'float
1684 :low (coerce 0 bound-format)
1687 ;; The absolute value of a real number is a non-negative real
1688 ;; of the same type.
1689 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1690 (class (numeric-type-class type))
1691 (format (numeric-type-format type))
1692 (bound-type (or format class 'real)))
1697 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1698 :high (coerce-and-truncate-floats
1699 (interval-high abs-bnd) bound-type))))))
1701 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1702 (defoptimizer (abs derive-type) ((num))
1703 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1705 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1706 (defoptimizer (truncate derive-type) ((number divisor))
1707 (let ((number-type (lvar-type number))
1708 (divisor-type (lvar-type divisor))
1709 (integer-type (specifier-type 'integer)))
1710 (if (and (numeric-type-p number-type)
1711 (csubtypep number-type integer-type)
1712 (numeric-type-p divisor-type)
1713 (csubtypep divisor-type integer-type))
1714 (let ((number-low (numeric-type-low number-type))
1715 (number-high (numeric-type-high number-type))
1716 (divisor-low (numeric-type-low divisor-type))
1717 (divisor-high (numeric-type-high divisor-type)))
1718 (values-specifier-type
1719 `(values ,(integer-truncate-derive-type number-low number-high
1720 divisor-low divisor-high)
1721 ,(integer-rem-derive-type number-low number-high
1722 divisor-low divisor-high))))
1725 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1728 (defun rem-result-type (number-type divisor-type)
1729 ;; Figure out what the remainder type is. The remainder is an
1730 ;; integer if both args are integers; a rational if both args are
1731 ;; rational; and a float otherwise.
1732 (cond ((and (csubtypep number-type (specifier-type 'integer))
1733 (csubtypep divisor-type (specifier-type 'integer)))
1735 ((and (csubtypep number-type (specifier-type 'rational))
1736 (csubtypep divisor-type (specifier-type 'rational)))
1738 ((and (csubtypep number-type (specifier-type 'float))
1739 (csubtypep divisor-type (specifier-type 'float)))
1740 ;; Both are floats so the result is also a float, of
1741 ;; the largest type.
1742 (or (float-format-max (numeric-type-format number-type)
1743 (numeric-type-format divisor-type))
1745 ((and (csubtypep number-type (specifier-type 'float))
1746 (csubtypep divisor-type (specifier-type 'rational)))
1747 ;; One of the arguments is a float and the other is a
1748 ;; rational. The remainder is a float of the same
1750 (or (numeric-type-format number-type) 'float))
1751 ((and (csubtypep divisor-type (specifier-type 'float))
1752 (csubtypep number-type (specifier-type 'rational)))
1753 ;; One of the arguments is a float and the other is a
1754 ;; rational. The remainder is a float of the same
1756 (or (numeric-type-format divisor-type) 'float))
1758 ;; Some unhandled combination. This usually means both args
1759 ;; are REAL so the result is a REAL.
1762 (defun truncate-derive-type-quot (number-type divisor-type)
1763 (let* ((rem-type (rem-result-type number-type divisor-type))
1764 (number-interval (numeric-type->interval number-type))
1765 (divisor-interval (numeric-type->interval divisor-type)))
1766 ;;(declare (type (member '(integer rational float)) rem-type))
1767 ;; We have real numbers now.
1768 (cond ((eq rem-type 'integer)
1769 ;; Since the remainder type is INTEGER, both args are
1771 (let* ((res (integer-truncate-derive-type
1772 (interval-low number-interval)
1773 (interval-high number-interval)
1774 (interval-low divisor-interval)
1775 (interval-high divisor-interval))))
1776 (specifier-type (if (listp res) res 'integer))))
1778 (let ((quot (truncate-quotient-bound
1779 (interval-div number-interval
1780 divisor-interval))))
1781 (specifier-type `(integer ,(or (interval-low quot) '*)
1782 ,(or (interval-high quot) '*))))))))
1784 (defun truncate-derive-type-rem (number-type divisor-type)
1785 (let* ((rem-type (rem-result-type number-type divisor-type))
1786 (number-interval (numeric-type->interval number-type))
1787 (divisor-interval (numeric-type->interval divisor-type))
1788 (rem (truncate-rem-bound number-interval divisor-interval)))
1789 ;;(declare (type (member '(integer rational float)) rem-type))
1790 ;; We have real numbers now.
1791 (cond ((eq rem-type 'integer)
1792 ;; Since the remainder type is INTEGER, both args are
1794 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1795 ,(or (interval-high rem) '*))))
1797 (multiple-value-bind (class format)
1800 (values 'integer nil))
1802 (values 'rational nil))
1803 ((or single-float double-float #!+long-float long-float)
1804 (values 'float rem-type))
1806 (values 'float nil))
1809 (when (member rem-type '(float single-float double-float
1810 #!+long-float long-float))
1811 (setf rem (interval-func #'(lambda (x)
1812 (coerce-for-bound x rem-type))
1814 (make-numeric-type :class class
1816 :low (interval-low rem)
1817 :high (interval-high rem)))))))
1819 (defun truncate-derive-type-quot-aux (num div same-arg)
1820 (declare (ignore same-arg))
1821 (if (and (numeric-type-real-p num)
1822 (numeric-type-real-p div))
1823 (truncate-derive-type-quot num div)
1826 (defun truncate-derive-type-rem-aux (num div same-arg)
1827 (declare (ignore same-arg))
1828 (if (and (numeric-type-real-p num)
1829 (numeric-type-real-p div))
1830 (truncate-derive-type-rem num div)
1833 (defoptimizer (truncate derive-type) ((number divisor))
1834 (let ((quot (two-arg-derive-type number divisor
1835 #'truncate-derive-type-quot-aux #'truncate))
1836 (rem (two-arg-derive-type number divisor
1837 #'truncate-derive-type-rem-aux #'rem)))
1838 (when (and quot rem)
1839 (make-values-type :required (list quot rem)))))
1841 (defun ftruncate-derive-type-quot (number-type divisor-type)
1842 ;; The bounds are the same as for truncate. However, the first
1843 ;; result is a float of some type. We need to determine what that
1844 ;; type is. Basically it's the more contagious of the two types.
1845 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1846 (res-type (numeric-contagion number-type divisor-type)))
1847 (make-numeric-type :class 'float
1848 :format (numeric-type-format res-type)
1849 :low (numeric-type-low q-type)
1850 :high (numeric-type-high q-type))))
1852 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1853 (declare (ignore same-arg))
1854 (if (and (numeric-type-real-p n)
1855 (numeric-type-real-p d))
1856 (ftruncate-derive-type-quot n d)
1859 (defoptimizer (ftruncate derive-type) ((number divisor))
1861 (two-arg-derive-type number divisor
1862 #'ftruncate-derive-type-quot-aux #'ftruncate))
1863 (rem (two-arg-derive-type number divisor
1864 #'truncate-derive-type-rem-aux #'rem)))
1865 (when (and quot rem)
1866 (make-values-type :required (list quot rem)))))
1868 (defun %unary-truncate-derive-type-aux (number)
1869 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1871 (defoptimizer (%unary-truncate derive-type) ((number))
1872 (one-arg-derive-type number
1873 #'%unary-truncate-derive-type-aux
1876 (defoptimizer (%unary-truncate/single-float derive-type) ((number))
1877 (one-arg-derive-type number
1878 #'%unary-truncate-derive-type-aux
1881 (defoptimizer (%unary-truncate/double-float derive-type) ((number))
1882 (one-arg-derive-type number
1883 #'%unary-truncate-derive-type-aux
1886 (defoptimizer (%unary-ftruncate derive-type) ((number))
1887 (let ((divisor (specifier-type '(integer 1 1))))
1888 (one-arg-derive-type number
1890 (ftruncate-derive-type-quot-aux n divisor nil))
1891 #'%unary-ftruncate)))
1893 (defoptimizer (%unary-round derive-type) ((number))
1894 (one-arg-derive-type number
1897 (unless (numeric-type-real-p n)
1898 (return *empty-type*))
1899 (let* ((interval (numeric-type->interval n))
1900 (low (interval-low interval))
1901 (high (interval-high interval)))
1903 (setf low (car low)))
1905 (setf high (car high)))
1915 ;;; Define optimizers for FLOOR and CEILING.
1917 ((def (name q-name r-name)
1918 (let ((q-aux (symbolicate q-name "-AUX"))
1919 (r-aux (symbolicate r-name "-AUX")))
1921 ;; Compute type of quotient (first) result.
1922 (defun ,q-aux (number-type divisor-type)
1923 (let* ((number-interval
1924 (numeric-type->interval number-type))
1926 (numeric-type->interval divisor-type))
1927 (quot (,q-name (interval-div number-interval
1928 divisor-interval))))
1929 (specifier-type `(integer ,(or (interval-low quot) '*)
1930 ,(or (interval-high quot) '*)))))
1931 ;; Compute type of remainder.
1932 (defun ,r-aux (number-type divisor-type)
1933 (let* ((divisor-interval
1934 (numeric-type->interval divisor-type))
1935 (rem (,r-name divisor-interval))
1936 (result-type (rem-result-type number-type divisor-type)))
1937 (multiple-value-bind (class format)
1940 (values 'integer nil))
1942 (values 'rational nil))
1943 ((or single-float double-float #!+long-float long-float)
1944 (values 'float result-type))
1946 (values 'float nil))
1949 (when (member result-type '(float single-float double-float
1950 #!+long-float long-float))
1951 ;; Make sure that the limits on the interval have
1953 (setf rem (interval-func (lambda (x)
1954 (coerce-for-bound x result-type))
1956 (make-numeric-type :class class
1958 :low (interval-low rem)
1959 :high (interval-high rem)))))
1960 ;; the optimizer itself
1961 (defoptimizer (,name derive-type) ((number divisor))
1962 (flet ((derive-q (n d same-arg)
1963 (declare (ignore same-arg))
1964 (if (and (numeric-type-real-p n)
1965 (numeric-type-real-p d))
1968 (derive-r (n d same-arg)
1969 (declare (ignore same-arg))
1970 (if (and (numeric-type-real-p n)
1971 (numeric-type-real-p d))
1974 (let ((quot (two-arg-derive-type
1975 number divisor #'derive-q #',name))
1976 (rem (two-arg-derive-type
1977 number divisor #'derive-r #'mod)))
1978 (when (and quot rem)
1979 (make-values-type :required (list quot rem))))))))))
1981 (def floor floor-quotient-bound floor-rem-bound)
1982 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1984 ;;; Define optimizers for FFLOOR and FCEILING
1985 (macrolet ((def (name q-name r-name)
1986 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1987 (r-aux (symbolicate r-name "-AUX")))
1989 ;; Compute type of quotient (first) result.
1990 (defun ,q-aux (number-type divisor-type)
1991 (let* ((number-interval
1992 (numeric-type->interval number-type))
1994 (numeric-type->interval divisor-type))
1995 (quot (,q-name (interval-div number-interval
1997 (res-type (numeric-contagion number-type
2000 :class (numeric-type-class res-type)
2001 :format (numeric-type-format res-type)
2002 :low (interval-low quot)
2003 :high (interval-high quot))))
2005 (defoptimizer (,name derive-type) ((number divisor))
2006 (flet ((derive-q (n d same-arg)
2007 (declare (ignore same-arg))
2008 (if (and (numeric-type-real-p n)
2009 (numeric-type-real-p d))
2012 (derive-r (n d same-arg)
2013 (declare (ignore same-arg))
2014 (if (and (numeric-type-real-p n)
2015 (numeric-type-real-p d))
2018 (let ((quot (two-arg-derive-type
2019 number divisor #'derive-q #',name))
2020 (rem (two-arg-derive-type
2021 number divisor #'derive-r #'mod)))
2022 (when (and quot rem)
2023 (make-values-type :required (list quot rem))))))))))
2025 (def ffloor floor-quotient-bound floor-rem-bound)
2026 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
2028 ;;; functions to compute the bounds on the quotient and remainder for
2029 ;;; the FLOOR function
2030 (defun floor-quotient-bound (quot)
2031 ;; Take the floor of the quotient and then massage it into what we
2033 (let ((lo (interval-low quot))
2034 (hi (interval-high quot)))
2035 ;; Take the floor of the lower bound. The result is always a
2036 ;; closed lower bound.
2038 (floor (type-bound-number lo))
2040 ;; For the upper bound, we need to be careful.
2043 ;; An open bound. We need to be careful here because
2044 ;; the floor of '(10.0) is 9, but the floor of
2046 (multiple-value-bind (q r) (floor (first hi))
2051 ;; A closed bound, so the answer is obvious.
2055 (make-interval :low lo :high hi)))
2056 (defun floor-rem-bound (div)
2057 ;; The remainder depends only on the divisor. Try to get the
2058 ;; correct sign for the remainder if we can.
2059 (case (interval-range-info div)
2061 ;; The divisor is always positive.
2062 (let ((rem (interval-abs div)))
2063 (setf (interval-low rem) 0)
2064 (when (and (numberp (interval-high rem))
2065 (not (zerop (interval-high rem))))
2066 ;; The remainder never contains the upper bound. However,
2067 ;; watch out for the case where the high limit is zero!
2068 (setf (interval-high rem) (list (interval-high rem))))
2071 ;; The divisor is always negative.
2072 (let ((rem (interval-neg (interval-abs div))))
2073 (setf (interval-high rem) 0)
2074 (when (numberp (interval-low rem))
2075 ;; The remainder never contains the lower bound.
2076 (setf (interval-low rem) (list (interval-low rem))))
2079 ;; The divisor can be positive or negative. All bets off. The
2080 ;; magnitude of remainder is the maximum value of the divisor.
2081 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2082 ;; The bound never reaches the limit, so make the interval open.
2083 (make-interval :low (if limit
2086 :high (list limit))))))
2088 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
2089 => #S(INTERVAL :LOW 0 :HIGH 10)
2090 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2091 => #S(INTERVAL :LOW 0 :HIGH 10)
2092 (floor-quotient-bound (make-interval :low 0.3 :high 10))
2093 => #S(INTERVAL :LOW 0 :HIGH 10)
2094 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
2095 => #S(INTERVAL :LOW 0 :HIGH 9)
2096 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
2097 => #S(INTERVAL :LOW 0 :HIGH 10)
2098 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
2099 => #S(INTERVAL :LOW 0 :HIGH 10)
2100 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2101 => #S(INTERVAL :LOW -2 :HIGH 10)
2102 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2103 => #S(INTERVAL :LOW -1 :HIGH 10)
2104 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
2105 => #S(INTERVAL :LOW -1 :HIGH 10)
2107 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
2108 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2109 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
2110 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2111 (floor-rem-bound (make-interval :low -10 :high -2.3))
2112 #S(INTERVAL :LOW (-10) :HIGH 0)
2113 (floor-rem-bound (make-interval :low 0.3 :high 10))
2114 => #S(INTERVAL :LOW 0 :HIGH '(10))
2115 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
2116 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
2117 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
2118 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2121 ;;; same functions for CEILING
2122 (defun ceiling-quotient-bound (quot)
2123 ;; Take the ceiling of the quotient and then massage it into what we
2125 (let ((lo (interval-low quot))
2126 (hi (interval-high quot)))
2127 ;; Take the ceiling of the upper bound. The result is always a
2128 ;; closed upper bound.
2130 (ceiling (type-bound-number hi))
2132 ;; For the lower bound, we need to be careful.
2135 ;; An open bound. We need to be careful here because
2136 ;; the ceiling of '(10.0) is 11, but the ceiling of
2138 (multiple-value-bind (q r) (ceiling (first lo))
2143 ;; A closed bound, so the answer is obvious.
2147 (make-interval :low lo :high hi)))
2148 (defun ceiling-rem-bound (div)
2149 ;; The remainder depends only on the divisor. Try to get the
2150 ;; correct sign for the remainder if we can.
2151 (case (interval-range-info div)
2153 ;; Divisor is always positive. The remainder is negative.
2154 (let ((rem (interval-neg (interval-abs div))))
2155 (setf (interval-high rem) 0)
2156 (when (and (numberp (interval-low rem))
2157 (not (zerop (interval-low rem))))
2158 ;; The remainder never contains the upper bound. However,
2159 ;; watch out for the case when the upper bound is zero!
2160 (setf (interval-low rem) (list (interval-low rem))))
2163 ;; Divisor is always negative. The remainder is positive
2164 (let ((rem (interval-abs div)))
2165 (setf (interval-low rem) 0)
2166 (when (numberp (interval-high rem))
2167 ;; The remainder never contains the lower bound.
2168 (setf (interval-high rem) (list (interval-high rem))))
2171 ;; The divisor can be positive or negative. All bets off. The
2172 ;; magnitude of remainder is the maximum value of the divisor.
2173 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2174 ;; The bound never reaches the limit, so make the interval open.
2175 (make-interval :low (if limit
2178 :high (list limit))))))
2181 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2182 => #S(INTERVAL :LOW 1 :HIGH 11)
2183 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2184 => #S(INTERVAL :LOW 1 :HIGH 11)
2185 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2186 => #S(INTERVAL :LOW 1 :HIGH 10)
2187 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2188 => #S(INTERVAL :LOW 1 :HIGH 10)
2189 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2190 => #S(INTERVAL :LOW 1 :HIGH 11)
2191 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2192 => #S(INTERVAL :LOW 1 :HIGH 11)
2193 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2194 => #S(INTERVAL :LOW -1 :HIGH 11)
2195 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2196 => #S(INTERVAL :LOW 0 :HIGH 11)
2197 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2198 => #S(INTERVAL :LOW -1 :HIGH 11)
2200 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2201 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2202 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2203 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2204 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2205 => #S(INTERVAL :LOW 0 :HIGH (10))
2206 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2207 => #S(INTERVAL :LOW (-10) :HIGH 0)
2208 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2209 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2210 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2211 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2214 (defun truncate-quotient-bound (quot)
2215 ;; For positive quotients, truncate is exactly like floor. For
2216 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2217 ;; it's the union of the two pieces.
2218 (case (interval-range-info quot)
2221 (floor-quotient-bound quot))
2223 ;; just like CEILING
2224 (ceiling-quotient-bound quot))
2226 ;; Split the interval into positive and negative pieces, compute
2227 ;; the result for each piece and put them back together.
2228 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2229 (interval-merge-pair (ceiling-quotient-bound neg)
2230 (floor-quotient-bound pos))))))
2232 (defun truncate-rem-bound (num div)
2233 ;; This is significantly more complicated than FLOOR or CEILING. We
2234 ;; need both the number and the divisor to determine the range. The
2235 ;; basic idea is to split the ranges of NUM and DEN into positive
2236 ;; and negative pieces and deal with each of the four possibilities
2238 (case (interval-range-info num)
2240 (case (interval-range-info div)
2242 (floor-rem-bound div))
2244 (ceiling-rem-bound div))
2246 (destructuring-bind (neg pos) (interval-split 0 div t t)
2247 (interval-merge-pair (truncate-rem-bound num neg)
2248 (truncate-rem-bound num pos))))))
2250 (case (interval-range-info div)
2252 (ceiling-rem-bound div))
2254 (floor-rem-bound div))
2256 (destructuring-bind (neg pos) (interval-split 0 div t t)
2257 (interval-merge-pair (truncate-rem-bound num neg)
2258 (truncate-rem-bound num pos))))))
2260 (destructuring-bind (neg pos) (interval-split 0 num t t)
2261 (interval-merge-pair (truncate-rem-bound neg div)
2262 (truncate-rem-bound pos div))))))
2265 ;;; Derive useful information about the range. Returns three values:
2266 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2267 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2268 ;;; - The abs of the maximal value if there is one, or nil if it is
2270 (defun numeric-range-info (low high)
2271 (cond ((and low (not (minusp low)))
2272 (values '+ low high))
2273 ((and high (not (plusp high)))
2274 (values '- (- high) (if low (- low) nil)))
2276 (values nil 0 (and low high (max (- low) high))))))
2278 (defun integer-truncate-derive-type
2279 (number-low number-high divisor-low divisor-high)
2280 ;; The result cannot be larger in magnitude than the number, but the
2281 ;; sign might change. If we can determine the sign of either the
2282 ;; number or the divisor, we can eliminate some of the cases.
2283 (multiple-value-bind (number-sign number-min number-max)
2284 (numeric-range-info number-low number-high)
2285 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2286 (numeric-range-info divisor-low divisor-high)
2287 (when (and divisor-max (zerop divisor-max))
2288 ;; We've got a problem: guaranteed division by zero.
2289 (return-from integer-truncate-derive-type t))
2290 (when (zerop divisor-min)
2291 ;; We'll assume that they aren't going to divide by zero.
2293 (cond ((and number-sign divisor-sign)
2294 ;; We know the sign of both.
2295 (if (eq number-sign divisor-sign)
2296 ;; Same sign, so the result will be positive.
2297 `(integer ,(if divisor-max
2298 (truncate number-min divisor-max)
2301 (truncate number-max divisor-min)
2303 ;; Different signs, the result will be negative.
2304 `(integer ,(if number-max
2305 (- (truncate number-max divisor-min))
2308 (- (truncate number-min divisor-max))
2310 ((eq divisor-sign '+)
2311 ;; The divisor is positive. Therefore, the number will just
2312 ;; become closer to zero.
2313 `(integer ,(if number-low
2314 (truncate number-low divisor-min)
2317 (truncate number-high divisor-min)
2319 ((eq divisor-sign '-)
2320 ;; The divisor is negative. Therefore, the absolute value of
2321 ;; the number will become closer to zero, but the sign will also
2323 `(integer ,(if number-high
2324 (- (truncate number-high divisor-min))
2327 (- (truncate number-low divisor-min))
2329 ;; The divisor could be either positive or negative.
2331 ;; The number we are dividing has a bound. Divide that by the
2332 ;; smallest posible divisor.
2333 (let ((bound (truncate number-max divisor-min)))
2334 `(integer ,(- bound) ,bound)))
2336 ;; The number we are dividing is unbounded, so we can't tell
2337 ;; anything about the result.
2340 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2341 (defun integer-rem-derive-type
2342 (number-low number-high divisor-low divisor-high)
2343 (if (and divisor-low divisor-high)
2344 ;; We know the range of the divisor, and the remainder must be
2345 ;; smaller than the divisor. We can tell the sign of the
2346 ;; remainder if we know the sign of the number.
2347 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2348 `(integer ,(if (or (null number-low)
2349 (minusp number-low))
2352 ,(if (or (null number-high)
2353 (plusp number-high))
2356 ;; The divisor is potentially either very positive or very
2357 ;; negative. Therefore, the remainder is unbounded, but we might
2358 ;; be able to tell something about the sign from the number.
2359 `(integer ,(if (and number-low (not (minusp number-low)))
2360 ;; The number we are dividing is positive.
2361 ;; Therefore, the remainder must be positive.
2364 ,(if (and number-high (not (plusp number-high)))
2365 ;; The number we are dividing is negative.
2366 ;; Therefore, the remainder must be negative.
2370 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2371 (defoptimizer (random derive-type) ((bound &optional state))
2372 (let ((type (lvar-type bound)))
2373 (when (numeric-type-p type)
2374 (let ((class (numeric-type-class type))
2375 (high (numeric-type-high type))
2376 (format (numeric-type-format type)))
2380 :low (coerce 0 (or format class 'real))
2381 :high (cond ((not high) nil)
2382 ((eq class 'integer) (max (1- high) 0))
2383 ((or (consp high) (zerop high)) high)
2386 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2387 (defun random-derive-type-aux (type)
2388 (let ((class (numeric-type-class type))
2389 (high (numeric-type-high type))
2390 (format (numeric-type-format type)))
2394 :low (coerce 0 (or format class 'real))
2395 :high (cond ((not high) nil)
2396 ((eq class 'integer) (max (1- high) 0))
2397 ((or (consp high) (zerop high)) high)
2400 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2401 (defoptimizer (random derive-type) ((bound &optional state))
2402 (one-arg-derive-type bound #'random-derive-type-aux nil))
2404 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2406 ;;; Return the maximum number of bits an integer of the supplied type
2407 ;;; can take up, or NIL if it is unbounded. The second (third) value
2408 ;;; is T if the integer can be positive (negative) and NIL if not.
2409 ;;; Zero counts as positive.
2410 (defun integer-type-length (type)
2411 (if (numeric-type-p type)
2412 (let ((min (numeric-type-low type))
2413 (max (numeric-type-high type)))
2414 (values (and min max (max (integer-length min) (integer-length max)))
2415 (or (null max) (not (minusp max)))
2416 (or (null min) (minusp min))))
2419 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2420 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2421 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2422 ;;; versions in CMUCL, from which these functions copy liberally.
2424 (defun logand-derive-unsigned-low-bound (x y)
2425 (let ((a (numeric-type-low x))
2426 (b (numeric-type-high x))
2427 (c (numeric-type-low y))
2428 (d (numeric-type-high y)))
2429 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2431 (unless (zerop (logand m (lognot a) (lognot c)))
2432 (let ((temp (logandc2 (logior a m) (1- m))))
2436 (setf temp (logandc2 (logior c m) (1- m)))
2440 finally (return (logand a c)))))
2442 (defun logand-derive-unsigned-high-bound (x y)
2443 (let ((a (numeric-type-low x))
2444 (b (numeric-type-high x))
2445 (c (numeric-type-low y))
2446 (d (numeric-type-high y)))
2447 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2450 ((not (zerop (logand b (lognot d) m)))
2451 (let ((temp (logior (logandc2 b m) (1- m))))
2455 ((not (zerop (logand (lognot b) d m)))
2456 (let ((temp (logior (logandc2 d m) (1- m))))
2460 finally (return (logand b d)))))
2462 (defun logand-derive-type-aux (x y &optional same-leaf)
2464 (return-from logand-derive-type-aux x))
2465 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2466 (declare (ignore x-pos))
2467 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2468 (declare (ignore y-pos))
2470 ;; X must be positive.
2472 ;; They must both be positive.
2473 (cond ((and (null x-len) (null y-len))
2474 (specifier-type 'unsigned-byte))
2476 (specifier-type `(unsigned-byte* ,y-len)))
2478 (specifier-type `(unsigned-byte* ,x-len)))
2480 (let ((low (logand-derive-unsigned-low-bound x y))
2481 (high (logand-derive-unsigned-high-bound x y)))
2482 (specifier-type `(integer ,low ,high)))))
2483 ;; X is positive, but Y might be negative.
2485 (specifier-type 'unsigned-byte))
2487 (specifier-type `(unsigned-byte* ,x-len)))))
2488 ;; X might be negative.
2490 ;; Y must be positive.
2492 (specifier-type 'unsigned-byte))
2493 (t (specifier-type `(unsigned-byte* ,y-len))))
2494 ;; Either might be negative.
2495 (if (and x-len y-len)
2496 ;; The result is bounded.
2497 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2498 ;; We can't tell squat about the result.
2499 (specifier-type 'integer)))))))
2501 (defun logior-derive-unsigned-low-bound (x y)
2502 (let ((a (numeric-type-low x))
2503 (b (numeric-type-high x))
2504 (c (numeric-type-low y))
2505 (d (numeric-type-high y)))
2506 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2509 ((not (zerop (logandc2 (logand c m) a)))
2510 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2514 ((not (zerop (logandc2 (logand a m) c)))
2515 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2519 finally (return (logior a c)))))
2521 (defun logior-derive-unsigned-high-bound (x y)
2522 (let ((a (numeric-type-low x))
2523 (b (numeric-type-high x))
2524 (c (numeric-type-low y))
2525 (d (numeric-type-high y)))
2526 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2528 (unless (zerop (logand b d m))
2529 (let ((temp (logior (- b m) (1- m))))
2533 (setf temp (logior (- d m) (1- m)))
2537 finally (return (logior b d)))))
2539 (defun logior-derive-type-aux (x y &optional same-leaf)
2541 (return-from logior-derive-type-aux x))
2542 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2543 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2545 ((and (not x-neg) (not y-neg))
2546 ;; Both are positive.
2547 (if (and x-len y-len)
2548 (let ((low (logior-derive-unsigned-low-bound x y))
2549 (high (logior-derive-unsigned-high-bound x y)))
2550 (specifier-type `(integer ,low ,high)))
2551 (specifier-type `(unsigned-byte* *))))
2553 ;; X must be negative.
2555 ;; Both are negative. The result is going to be negative
2556 ;; and be the same length or shorter than the smaller.
2557 (if (and x-len y-len)
2559 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2561 (specifier-type '(integer * -1)))
2562 ;; X is negative, but we don't know about Y. The result
2563 ;; will be negative, but no more negative than X.
2565 `(integer ,(or (numeric-type-low x) '*)
2568 ;; X might be either positive or negative.
2570 ;; But Y is negative. The result will be negative.
2572 `(integer ,(or (numeric-type-low y) '*)
2574 ;; We don't know squat about either. It won't get any bigger.
2575 (if (and x-len y-len)
2577 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2579 (specifier-type 'integer))))))))
2581 (defun logxor-derive-unsigned-low-bound (x y)
2582 (let ((a (numeric-type-low x))
2583 (b (numeric-type-high x))
2584 (c (numeric-type-low y))
2585 (d (numeric-type-high y)))
2586 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2589 ((not (zerop (logandc2 (logand c m) a)))
2590 (let ((temp (logand (logior a m)
2594 ((not (zerop (logandc2 (logand a m) c)))
2595 (let ((temp (logand (logior c m)
2599 finally (return (logxor a c)))))
2601 (defun logxor-derive-unsigned-high-bound (x y)
2602 (let ((a (numeric-type-low x))
2603 (b (numeric-type-high x))
2604 (c (numeric-type-low y))
2605 (d (numeric-type-high y)))
2606 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2608 (unless (zerop (logand b d m))
2609 (let ((temp (logior (- b m) (1- m))))
2611 ((>= temp a) (setf b temp))
2612 (t (let ((temp (logior (- d m) (1- m))))
2615 finally (return (logxor b d)))))
2617 (defun logxor-derive-type-aux (x y &optional same-leaf)
2619 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2620 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2621 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2623 ((and (not x-neg) (not y-neg))
2624 ;; Both are positive
2625 (if (and x-len y-len)
2626 (let ((low (logxor-derive-unsigned-low-bound x y))
2627 (high (logxor-derive-unsigned-high-bound x y)))
2628 (specifier-type `(integer ,low ,high)))
2629 (specifier-type '(unsigned-byte* *))))
2630 ((and (not x-pos) (not y-pos))
2631 ;; Both are negative. The result will be positive, and as long
2633 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2636 ((or (and (not x-pos) (not y-neg))
2637 (and (not y-pos) (not x-neg)))
2638 ;; Either X is negative and Y is positive or vice-versa. The
2639 ;; result will be negative.
2640 (specifier-type `(integer ,(if (and x-len y-len)
2641 (ash -1 (max x-len y-len))
2644 ;; We can't tell what the sign of the result is going to be.
2645 ;; All we know is that we don't create new bits.
2647 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2649 (specifier-type 'integer))))))
2651 (macrolet ((deffrob (logfun)
2652 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2653 `(defoptimizer (,logfun derive-type) ((x y))
2654 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2659 (defoptimizer (logeqv derive-type) ((x y))
2660 (two-arg-derive-type x y (lambda (x y same-leaf)
2661 (lognot-derive-type-aux
2662 (logxor-derive-type-aux x y same-leaf)))
2664 (defoptimizer (lognand derive-type) ((x y))
2665 (two-arg-derive-type x y (lambda (x y same-leaf)
2666 (lognot-derive-type-aux
2667 (logand-derive-type-aux x y same-leaf)))
2669 (defoptimizer (lognor derive-type) ((x y))
2670 (two-arg-derive-type x y (lambda (x y same-leaf)
2671 (lognot-derive-type-aux
2672 (logior-derive-type-aux x y same-leaf)))
2674 (defoptimizer (logandc1 derive-type) ((x y))
2675 (two-arg-derive-type x y (lambda (x y same-leaf)
2677 (specifier-type '(eql 0))
2678 (logand-derive-type-aux
2679 (lognot-derive-type-aux x) y nil)))
2681 (defoptimizer (logandc2 derive-type) ((x y))
2682 (two-arg-derive-type x y (lambda (x y same-leaf)
2684 (specifier-type '(eql 0))
2685 (logand-derive-type-aux
2686 x (lognot-derive-type-aux y) nil)))
2688 (defoptimizer (logorc1 derive-type) ((x y))
2689 (two-arg-derive-type x y (lambda (x y same-leaf)
2691 (specifier-type '(eql -1))
2692 (logior-derive-type-aux
2693 (lognot-derive-type-aux x) y nil)))
2695 (defoptimizer (logorc2 derive-type) ((x y))
2696 (two-arg-derive-type x y (lambda (x y same-leaf)
2698 (specifier-type '(eql -1))
2699 (logior-derive-type-aux
2700 x (lognot-derive-type-aux y) nil)))
2703 ;;;; miscellaneous derive-type methods
2705 (defoptimizer (integer-length derive-type) ((x))
2706 (let ((x-type (lvar-type x)))
2707 (when (numeric-type-p x-type)
2708 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2709 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2710 ;; careful about LO or HI being NIL, though. Also, if 0 is
2711 ;; contained in X, the lower bound is obviously 0.
2712 (flet ((null-or-min (a b)
2713 (and a b (min (integer-length a)
2714 (integer-length b))))
2716 (and a b (max (integer-length a)
2717 (integer-length b)))))
2718 (let* ((min (numeric-type-low x-type))
2719 (max (numeric-type-high x-type))
2720 (min-len (null-or-min min max))
2721 (max-len (null-or-max min max)))
2722 (when (ctypep 0 x-type)
2724 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2726 (defoptimizer (isqrt derive-type) ((x))
2727 (let ((x-type (lvar-type x)))
2728 (when (numeric-type-p x-type)
2729 (let* ((lo (numeric-type-low x-type))
2730 (hi (numeric-type-high x-type))
2731 (lo-res (if lo (isqrt lo) '*))
2732 (hi-res (if hi (isqrt hi) '*)))
2733 (specifier-type `(integer ,lo-res ,hi-res))))))
2735 (defoptimizer (char-code derive-type) ((char))
2736 (let ((type (type-intersection (lvar-type char) (specifier-type 'character))))
2737 (cond ((member-type-p type)
2740 ,@(loop for member in (member-type-members type)
2741 when (characterp member)
2742 collect (char-code member)))))
2743 ((sb!kernel::character-set-type-p type)
2746 ,@(loop for (low . high)
2747 in (character-set-type-pairs type)
2748 collect `(integer ,low ,high)))))
2749 ((csubtypep type (specifier-type 'base-char))
2751 `(mod ,base-char-code-limit)))
2754 `(mod ,char-code-limit))))))
2756 (defoptimizer (code-char derive-type) ((code))
2757 (let ((type (lvar-type code)))
2758 ;; FIXME: unions of integral ranges? It ought to be easier to do
2759 ;; this, given that CHARACTER-SET is basically an integral range
2760 ;; type. -- CSR, 2004-10-04
2761 (when (numeric-type-p type)
2762 (let* ((lo (numeric-type-low type))
2763 (hi (numeric-type-high type))
2764 (type (specifier-type `(character-set ((,lo . ,hi))))))
2766 ;; KLUDGE: when running on the host, we lose a slight amount
2767 ;; of precision so that we don't have to "unparse" types
2768 ;; that formally we can't, such as (CHARACTER-SET ((0
2769 ;; . 0))). -- CSR, 2004-10-06
2771 ((csubtypep type (specifier-type 'standard-char)) type)
2773 ((csubtypep type (specifier-type 'base-char))
2774 (specifier-type 'base-char))
2776 ((csubtypep type (specifier-type 'extended-char))
2777 (specifier-type 'extended-char))
2778 (t #+sb-xc-host (specifier-type 'character)
2779 #-sb-xc-host type))))))
2781 (defoptimizer (values derive-type) ((&rest values))
2782 (make-values-type :required (mapcar #'lvar-type values)))
2784 (defun signum-derive-type-aux (type)
2785 (if (eq (numeric-type-complexp type) :complex)
2786 (let* ((format (case (numeric-type-class type)
2787 ((integer rational) 'single-float)
2788 (t (numeric-type-format type))))
2789 (bound-format (or format 'float)))
2790 (make-numeric-type :class 'float
2793 :low (coerce -1 bound-format)
2794 :high (coerce 1 bound-format)))
2795 (let* ((interval (numeric-type->interval type))
2796 (range-info (interval-range-info interval))
2797 (contains-0-p (interval-contains-p 0 interval))
2798 (class (numeric-type-class type))
2799 (format (numeric-type-format type))
2800 (one (coerce 1 (or format class 'real)))
2801 (zero (coerce 0 (or format class 'real)))
2802 (minus-one (coerce -1 (or format class 'real)))
2803 (plus (make-numeric-type :class class :format format
2804 :low one :high one))
2805 (minus (make-numeric-type :class class :format format
2806 :low minus-one :high minus-one))
2807 ;; KLUDGE: here we have a fairly horrible hack to deal
2808 ;; with the schizophrenia in the type derivation engine.
2809 ;; The problem is that the type derivers reinterpret
2810 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2811 ;; 0d0) within the derivation mechanism doesn't include
2812 ;; -0d0. Ugh. So force it in here, instead.
2813 (zero (make-numeric-type :class class :format format
2814 :low (- zero) :high zero)))
2816 (+ (if contains-0-p (type-union plus zero) plus))
2817 (- (if contains-0-p (type-union minus zero) minus))
2818 (t (type-union minus zero plus))))))
2820 (defoptimizer (signum derive-type) ((num))
2821 (one-arg-derive-type num #'signum-derive-type-aux nil))
2823 ;;;; byte operations
2825 ;;;; We try to turn byte operations into simple logical operations.
2826 ;;;; First, we convert byte specifiers into separate size and position
2827 ;;;; arguments passed to internal %FOO functions. We then attempt to
2828 ;;;; transform the %FOO functions into boolean operations when the
2829 ;;;; size and position are constant and the operands are fixnums.
2831 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2832 ;; expressions that evaluate to the SIZE and POSITION of
2833 ;; the byte-specifier form SPEC. We may wrap a let around
2834 ;; the result of the body to bind some variables.
2836 ;; If the spec is a BYTE form, then bind the vars to the
2837 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2838 ;; and BYTE-POSITION. The goal of this transformation is to
2839 ;; avoid consing up byte specifiers and then immediately
2840 ;; throwing them away.
2841 (with-byte-specifier ((size-var pos-var spec) &body body)
2842 (once-only ((spec `(macroexpand ,spec))
2844 `(if (and (consp ,spec)
2845 (eq (car ,spec) 'byte)
2846 (= (length ,spec) 3))
2847 (let ((,size-var (second ,spec))
2848 (,pos-var (third ,spec)))
2850 (let ((,size-var `(byte-size ,,temp))
2851 (,pos-var `(byte-position ,,temp)))
2852 `(let ((,,temp ,,spec))
2855 (define-source-transform ldb (spec int)
2856 (with-byte-specifier (size pos spec)
2857 `(%ldb ,size ,pos ,int)))
2859 (define-source-transform dpb (newbyte spec int)
2860 (with-byte-specifier (size pos spec)
2861 `(%dpb ,newbyte ,size ,pos ,int)))
2863 (define-source-transform mask-field (spec int)
2864 (with-byte-specifier (size pos spec)
2865 `(%mask-field ,size ,pos ,int)))
2867 (define-source-transform deposit-field (newbyte spec int)
2868 (with-byte-specifier (size pos spec)
2869 `(%deposit-field ,newbyte ,size ,pos ,int))))
2871 (defoptimizer (%ldb derive-type) ((size posn num))
2872 (let ((size (lvar-type size)))
2873 (if (and (numeric-type-p size)
2874 (csubtypep size (specifier-type 'integer)))
2875 (let ((size-high (numeric-type-high size)))
2876 (if (and size-high (<= size-high sb!vm:n-word-bits))
2877 (specifier-type `(unsigned-byte* ,size-high))
2878 (specifier-type 'unsigned-byte)))
2881 (defoptimizer (%mask-field derive-type) ((size posn num))
2882 (let ((size (lvar-type size))
2883 (posn (lvar-type posn)))
2884 (if (and (numeric-type-p size)
2885 (csubtypep size (specifier-type 'integer))
2886 (numeric-type-p posn)
2887 (csubtypep posn (specifier-type 'integer)))
2888 (let ((size-high (numeric-type-high size))
2889 (posn-high (numeric-type-high posn)))
2890 (if (and size-high posn-high
2891 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2892 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2893 (specifier-type 'unsigned-byte)))
2896 (defun %deposit-field-derive-type-aux (size posn int)
2897 (let ((size (lvar-type size))
2898 (posn (lvar-type posn))
2899 (int (lvar-type int)))
2900 (when (and (numeric-type-p size)
2901 (numeric-type-p posn)
2902 (numeric-type-p int))
2903 (let ((size-high (numeric-type-high size))
2904 (posn-high (numeric-type-high posn))
2905 (high (numeric-type-high int))
2906 (low (numeric-type-low int)))
2907 (when (and size-high posn-high high low
2908 ;; KLUDGE: we need this cutoff here, otherwise we
2909 ;; will merrily derive the type of %DPB as
2910 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2911 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2912 ;; 1073741822))), with hilarious consequences. We
2913 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2914 ;; over a reasonable amount of shifting, even on
2915 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2916 ;; machine integers are 64-bits. -- CSR,
2918 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2919 (let ((raw-bit-count (max (integer-length high)
2920 (integer-length low)
2921 (+ size-high posn-high))))
2924 `(signed-byte ,(1+ raw-bit-count))
2925 `(unsigned-byte* ,raw-bit-count)))))))))
2927 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2928 (%deposit-field-derive-type-aux size posn int))
2930 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2931 (%deposit-field-derive-type-aux size posn int))
2933 (deftransform %ldb ((size posn int)
2934 (fixnum fixnum integer)
2935 (unsigned-byte #.sb!vm:n-word-bits))
2936 "convert to inline logical operations"
2937 `(logand (ash int (- posn))
2938 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2939 (- size ,sb!vm:n-word-bits))))
2941 (deftransform %mask-field ((size posn int)
2942 (fixnum fixnum integer)
2943 (unsigned-byte #.sb!vm:n-word-bits))
2944 "convert to inline logical operations"
2946 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2947 (- size ,sb!vm:n-word-bits))
2950 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2951 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2952 ;;; as the result type, as that would allow result types that cover
2953 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2954 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2956 (deftransform %dpb ((new size posn int)
2958 (unsigned-byte #.sb!vm:n-word-bits))
2959 "convert to inline logical operations"
2960 `(let ((mask (ldb (byte size 0) -1)))
2961 (logior (ash (logand new mask) posn)
2962 (logand int (lognot (ash mask posn))))))
2964 (deftransform %dpb ((new size posn int)
2966 (signed-byte #.sb!vm:n-word-bits))
2967 "convert to inline logical operations"
2968 `(let ((mask (ldb (byte size 0) -1)))
2969 (logior (ash (logand new mask) posn)
2970 (logand int (lognot (ash mask posn))))))
2972 (deftransform %deposit-field ((new size posn int)
2974 (unsigned-byte #.sb!vm:n-word-bits))
2975 "convert to inline logical operations"
2976 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2977 (logior (logand new mask)
2978 (logand int (lognot mask)))))
2980 (deftransform %deposit-field ((new size posn int)
2982 (signed-byte #.sb!vm:n-word-bits))
2983 "convert to inline logical operations"
2984 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2985 (logior (logand new mask)
2986 (logand int (lognot mask)))))
2988 (defoptimizer (mask-signed-field derive-type) ((size x))
2989 (let ((size (lvar-type size)))
2990 (if (numeric-type-p size)
2991 (let ((size-high (numeric-type-high size)))
2992 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2993 (specifier-type `(signed-byte ,size-high))
2998 ;;; Modular functions
3000 ;;; (ldb (byte s 0) (foo x y ...)) =
3001 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
3003 ;;; and similar for other arguments.
3005 (defun make-modular-fun-type-deriver (prototype kind width signedp)
3006 (declare (ignore kind))
3008 (binding* ((info (info :function :info prototype) :exit-if-null)
3009 (fun (fun-info-derive-type info) :exit-if-null)
3010 (mask-type (specifier-type
3012 ((nil) (let ((mask (1- (ash 1 width))))
3013 `(integer ,mask ,mask)))
3014 ((t) `(signed-byte ,width))))))
3016 (let ((res (funcall fun call)))
3018 (if (eq signedp nil)
3019 (logand-derive-type-aux res mask-type))))))
3022 (binding* ((info (info :function :info prototype) :exit-if-null)
3023 (fun (fun-info-derive-type info) :exit-if-null)
3024 (res (funcall fun call) :exit-if-null)
3025 (mask-type (specifier-type
3027 ((nil) (let ((mask (1- (ash 1 width))))
3028 `(integer ,mask ,mask)))
3029 ((t) `(signed-byte ,width))))))
3030 (if (eq signedp nil)
3031 (logand-derive-type-aux res mask-type)))))
3033 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
3035 ;;; For good functions, we just recursively cut arguments; their
3036 ;;; "goodness" means that the result will not increase (in the
3037 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
3038 ;;; replaced with the version, cutting its result to WIDTH or more
3039 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
3040 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
3041 ;;; arguments (maybe to a different width) and returning the name of a
3042 ;;; modular version, if it exists, or NIL. If we have changed
3043 ;;; anything, we need to flush old derived types, because they have
3044 ;;; nothing in common with the new code.
3045 (defun cut-to-width (lvar kind width signedp)
3046 (declare (type lvar lvar) (type (integer 0) width))
3047 (let ((type (specifier-type (if (zerop width)
3050 ((nil) 'unsigned-byte)
3053 (labels ((reoptimize-node (node name)
3054 (setf (node-derived-type node)
3056 (info :function :type name)))
3057 (setf (lvar-%derived-type (node-lvar node)) nil)
3058 (setf (node-reoptimize node) t)
3059 (setf (block-reoptimize (node-block node)) t)
3060 (reoptimize-component (node-component node) :maybe))
3061 (cut-node (node &aux did-something)
3062 (when (and (not (block-delete-p (node-block node)))
3064 (constant-p (ref-leaf node)))
3065 (let* ((constant-value (constant-value (ref-leaf node)))
3066 (new-value (if signedp
3067 (mask-signed-field width constant-value)
3068 (ldb (byte width 0) constant-value))))
3069 (unless (= constant-value new-value)
3070 (change-ref-leaf node (make-constant new-value))
3071 (setf (lvar-%derived-type (node-lvar node)) (make-values-type :required (list (ctype-of new-value))))
3072 (setf (block-reoptimize (node-block node)) t)
3073 (reoptimize-component (node-component node) :maybe)
3074 (return-from cut-node t))))
3075 (when (and (not (block-delete-p (node-block node)))
3076 (combination-p node)
3077 (eq (basic-combination-kind node) :known))
3078 (let* ((fun-ref (lvar-use (combination-fun node)))
3079 (fun-name (leaf-source-name (ref-leaf fun-ref)))
3080 (modular-fun (find-modular-version fun-name kind signedp width)))
3081 (when (and modular-fun
3082 (not (and (eq fun-name 'logand)
3084 (single-value-type (node-derived-type node))
3086 (binding* ((name (etypecase modular-fun
3087 ((eql :good) fun-name)
3089 (modular-fun-info-name modular-fun))
3091 (funcall modular-fun node width)))
3093 (unless (eql modular-fun :good)
3094 (setq did-something t)
3097 (find-free-fun name "in a strange place"))
3098 (setf (combination-kind node) :full))
3099 (unless (functionp modular-fun)
3100 (dolist (arg (basic-combination-args node))
3101 (when (cut-lvar arg)
3102 (setq did-something t))))
3104 (reoptimize-node node name))
3106 (cut-lvar (lvar &aux did-something)
3107 (do-uses (node lvar)
3108 (when (cut-node node)
3109 (setq did-something t)))
3113 (defun best-modular-version (width signedp)
3114 ;; 1. exact width-matched :untagged
3115 ;; 2. >/>= width-matched :tagged
3116 ;; 3. >/>= width-matched :untagged
3117 (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class*))
3118 (uswidths (modular-class-widths *untagged-signed-modular-class*))
3119 (uwidths (merge 'list uuwidths uswidths #'< :key #'car))
3120 (twidths (modular-class-widths *tagged-modular-class*)))
3121 (let ((exact (find (cons width signedp) uwidths :test #'equal)))
3123 (return-from best-modular-version (values width :untagged signedp))))
3124 (flet ((inexact-match (w)
3126 ((eq signedp (cdr w)) (<= width (car w)))
3127 ((eq signedp nil) (< width (car w))))))
3128 (let ((tgt (find-if #'inexact-match twidths)))
3130 (return-from best-modular-version
3131 (values (car tgt) :tagged (cdr tgt)))))
3132 (let ((ugt (find-if #'inexact-match uwidths)))
3134 (return-from best-modular-version
3135 (values (car ugt) :untagged (cdr ugt))))))))
3137 (defoptimizer (logand optimizer) ((x y) node)
3138 (let ((result-type (single-value-type (node-derived-type node))))
3139 (when (numeric-type-p result-type)
3140 (let ((low (numeric-type-low result-type))
3141 (high (numeric-type-high result-type)))
3142 (when (and (numberp low)
3145 (let ((width (integer-length high)))
3146 (multiple-value-bind (w kind signedp)
3147 (best-modular-version width nil)
3149 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP).
3151 ;; FIXME: I think the FIXME (which is from APD) above
3152 ;; implies that CUT-TO-WIDTH should do /everything/
3153 ;; that's required, including reoptimizing things
3154 ;; itself that it knows are necessary. At the moment,
3155 ;; CUT-TO-WIDTH sets up some new calls with
3156 ;; combination-type :FULL, which later get noticed as
3157 ;; known functions and properly converted.
3159 ;; We cut to W not WIDTH if SIGNEDP is true, because
3160 ;; signed constant replacement needs to know which bit
3161 ;; in the field is the signed bit.
3162 (let ((xact (cut-to-width x kind (if signedp w width) signedp))
3163 (yact (cut-to-width y kind (if signedp w width) signedp)))
3164 (declare (ignore xact yact))
3165 nil) ; After fixing above, replace with T, meaning
3166 ; "don't reoptimize this (LOGAND) node any more".
3169 (defoptimizer (mask-signed-field optimizer) ((width x) node)
3170 (let ((result-type (single-value-type (node-derived-type node))))
3171 (when (numeric-type-p result-type)
3172 (let ((low (numeric-type-low result-type))
3173 (high (numeric-type-high result-type)))
3174 (when (and (numberp low) (numberp high))
3175 (let ((width (max (integer-length high) (integer-length low))))
3176 (multiple-value-bind (w kind)
3177 (best-modular-version width t)
3179 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND W T).
3180 ;; [ see comment above in LOGAND optimizer ]
3181 (cut-to-width x kind w t)
3182 nil ; After fixing above, replace with T.
3185 ;;; miscellanous numeric transforms
3187 ;;; If a constant appears as the first arg, swap the args.
3188 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
3189 (if (and (constant-lvar-p x)
3190 (not (constant-lvar-p y)))
3191 `(,(lvar-fun-name (basic-combination-fun node))
3194 (give-up-ir1-transform)))
3196 (dolist (x '(= char= + * logior logand logxor))
3197 (%deftransform x '(function * *) #'commutative-arg-swap
3198 "place constant arg last"))
3200 ;;; Handle the case of a constant BOOLE-CODE.
3201 (deftransform boole ((op x y) * *)
3202 "convert to inline logical operations"
3203 (unless (constant-lvar-p op)
3204 (give-up-ir1-transform "BOOLE code is not a constant."))
3205 (let ((control (lvar-value op)))
3207 (#.sb!xc:boole-clr 0)
3208 (#.sb!xc:boole-set -1)
3209 (#.sb!xc:boole-1 'x)
3210 (#.sb!xc:boole-2 'y)
3211 (#.sb!xc:boole-c1 '(lognot x))
3212 (#.sb!xc:boole-c2 '(lognot y))
3213 (#.sb!xc:boole-and '(logand x y))
3214 (#.sb!xc:boole-ior '(logior x y))
3215 (#.sb!xc:boole-xor '(logxor x y))
3216 (#.sb!xc:boole-eqv '(logeqv x y))
3217 (#.sb!xc:boole-nand '(lognand x y))
3218 (#.sb!xc:boole-nor '(lognor x y))
3219 (#.sb!xc:boole-andc1 '(logandc1 x y))
3220 (#.sb!xc:boole-andc2 '(logandc2 x y))
3221 (#.sb!xc:boole-orc1 '(logorc1 x y))
3222 (#.sb!xc:boole-orc2 '(logorc2 x y))
3224 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
3227 ;;;; converting special case multiply/divide to shifts
3229 ;;; If arg is a constant power of two, turn * into a shift.
3230 (deftransform * ((x y) (integer integer) *)
3231 "convert x*2^k to shift"
3232 (unless (constant-lvar-p y)
3233 (give-up-ir1-transform))
3234 (let* ((y (lvar-value y))
3236 (len (1- (integer-length y-abs))))
3237 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3238 (give-up-ir1-transform))
3243 ;;; These must come before the ones below, so that they are tried
3244 ;;; first. Since %FLOOR and %CEILING are inlined, this allows
3245 ;;; the general case to be handled by TRUNCATE transforms.
3246 (deftransform floor ((x y))
3249 (deftransform ceiling ((x y))
3252 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3253 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3255 (flet ((frob (y ceil-p)
3256 (unless (constant-lvar-p y)
3257 (give-up-ir1-transform))
3258 (let* ((y (lvar-value y))
3260 (len (1- (integer-length y-abs))))
3261 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3262 (give-up-ir1-transform))
3263 (let ((shift (- len))
3265 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
3266 `(let ((x (+ x ,delta)))
3268 `(values (ash (- x) ,shift)
3269 (- (- (logand (- x) ,mask)) ,delta))
3270 `(values (ash x ,shift)
3271 (- (logand x ,mask) ,delta))))))))
3272 (deftransform floor ((x y) (integer integer) *)
3273 "convert division by 2^k to shift"
3275 (deftransform ceiling ((x y) (integer integer) *)
3276 "convert division by 2^k to shift"
3279 ;;; Do the same for MOD.
3280 (deftransform mod ((x y) (integer integer) *)
3281 "convert remainder mod 2^k to LOGAND"
3282 (unless (constant-lvar-p y)
3283 (give-up-ir1-transform))
3284 (let* ((y (lvar-value y))
3286 (len (1- (integer-length y-abs))))
3287 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3288 (give-up-ir1-transform))
3289 (let ((mask (1- y-abs)))
3291 `(- (logand (- x) ,mask))
3292 `(logand x ,mask)))))
3294 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3295 (deftransform truncate ((x y) (integer integer))
3296 "convert division by 2^k to shift"
3297 (unless (constant-lvar-p y)
3298 (give-up-ir1-transform))
3299 (let* ((y (lvar-value y))
3301 (len (1- (integer-length y-abs))))
3302 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3303 (give-up-ir1-transform))
3304 (let* ((shift (- len))
3307 (values ,(if (minusp y)
3309 `(- (ash (- x) ,shift)))
3310 (- (logand (- x) ,mask)))
3311 (values ,(if (minusp y)
3312 `(ash (- ,mask x) ,shift)
3314 (logand x ,mask))))))
3316 ;;; And the same for REM.
3317 (deftransform rem ((x y) (integer integer) *)
3318 "convert remainder mod 2^k to LOGAND"
3319 (unless (constant-lvar-p y)
3320 (give-up-ir1-transform))
3321 (let* ((y (lvar-value y))
3323 (len (1- (integer-length y-abs))))
3324 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3325 (give-up-ir1-transform))
3326 (let ((mask (1- y-abs)))
3328 (- (logand (- x) ,mask))
3329 (logand x ,mask)))))
3331 ;;; Return an expression to calculate the integer quotient of X and
3332 ;;; constant Y, using multiplication, shift and add/sub instead of
3333 ;;; division. Both arguments must be unsigned, fit in a machine word and
3334 ;;; Y must neither be zero nor a power of two. The quotient is rounded
3336 ;;; The algorithm is taken from the paper "Division by Invariant
3337 ;;; Integers using Multiplication", 1994 by Torbj\"{o}rn Granlund and
3338 ;;; Peter L. Montgomery, Figures 4.2 and 6.2, modified to exclude the
3339 ;;; case of division by powers of two.
3340 ;;; The algorithm includes an adaptive precision argument. Use it, since
3341 ;;; we often have sub-word value ranges. Careful, in this case, we need
3342 ;;; p s.t 2^p > n, not the ceiling of the binary log.
3343 ;;; Also, for some reason, the paper prefers shifting to masking. Mask
3344 ;;; instead. Masking is equivalent to shifting right, then left again;
3345 ;;; all the intermediate values are still words, so we just have to shift
3346 ;;; right a bit more to compensate, at the end.
3348 ;;; The following two examples show an average case and the worst case
3349 ;;; with respect to the complexity of the generated expression, under
3350 ;;; a word size of 64 bits:
3352 ;;; (UNSIGNED-DIV-TRANSFORMER 10 MOST-POSITIVE-WORD) ->
3353 ;;; (ASH (%MULTIPLY (LOGANDC2 X 0) 14757395258967641293) -3)
3355 ;;; (UNSIGNED-DIV-TRANSFORMER 7 MOST-POSITIVE-WORD) ->
3357 ;;; (T1 (%MULTIPLY NUM 2635249153387078803)))
3358 ;;; (ASH (LDB (BYTE 64 0)
3359 ;;; (+ T1 (ASH (LDB (BYTE 64 0)
3364 (defun gen-unsigned-div-by-constant-expr (y max-x)
3365 (declare (type (integer 3 #.most-positive-word) y)
3367 (aver (not (zerop (logand y (1- y)))))
3369 ;; the floor of the binary logarithm of (positive) X
3370 (integer-length (1- x)))
3371 (choose-multiplier (y precision)
3373 (shift l (1- shift))
3374 (expt-2-n+l (expt 2 (+ sb!vm:n-word-bits l)))
3375 (m-low (truncate expt-2-n+l y) (ash m-low -1))
3376 (m-high (truncate (+ expt-2-n+l
3377 (ash expt-2-n+l (- precision)))
3380 ((not (and (< (ash m-low -1) (ash m-high -1))
3382 (values m-high shift)))))
3383 (let ((n (expt 2 sb!vm:n-word-bits))
3384 (precision (integer-length max-x))
3386 (multiple-value-bind (m shift2)
3387 (choose-multiplier y precision)
3388 (when (and (>= m n) (evenp y))
3389 (setq shift1 (ld (logand y (- y))))
3390 (multiple-value-setq (m shift2)
3391 (choose-multiplier (/ y (ash 1 shift1))
3392 (- precision shift1))))
3395 `(truly-the word ,x)))
3397 (t1 (%multiply-high num ,(- m n))))
3398 (ash ,(word `(+ t1 (ash ,(word `(- num t1))
3401 ((and (zerop shift1) (zerop shift2))
3402 (let ((max (truncate max-x y)))
3403 ;; Explicit TRULY-THE needed to get the FIXNUM=>FIXNUM
3405 `(truly-the (integer 0 ,max)
3406 (%multiply-high x ,m))))
3408 `(ash (%multiply-high (logandc2 x ,(1- (ash 1 shift1))) ,m)
3409 ,(- (+ shift1 shift2)))))))))
3411 ;;; If the divisor is constant and both args are positive and fit in a
3412 ;;; machine word, replace the division by a multiplication and possibly
3413 ;;; some shifts and an addition. Calculate the remainder by a second
3414 ;;; multiplication and a subtraction. Dead code elimination will
3415 ;;; suppress the latter part if only the quotient is needed. If the type
3416 ;;; of the dividend allows to derive that the quotient will always have
3417 ;;; the same value, emit much simpler code to handle that. (This case
3418 ;;; may be rare but it's easy to detect and the compiler doesn't find
3419 ;;; this optimization on its own.)
3420 (deftransform truncate ((x y) (word (constant-arg word))
3422 :policy (and (> speed compilation-speed)
3424 "convert integer division to multiplication"
3425 (let* ((y (lvar-value y))
3426 (x-type (lvar-type x))
3427 (max-x (or (and (numeric-type-p x-type)
3428 (numeric-type-high x-type))
3429 most-positive-word)))
3430 ;; Division by zero, one or powers of two is handled elsewhere.
3431 (when (zerop (logand y (1- y)))
3432 (give-up-ir1-transform))
3433 `(let* ((quot ,(gen-unsigned-div-by-constant-expr y max-x))
3434 (rem (ldb (byte #.sb!vm:n-word-bits 0)
3435 (- x (* quot ,y)))))
3436 (values quot rem))))
3438 ;;;; arithmetic and logical identity operation elimination
3440 ;;; Flush calls to various arith functions that convert to the
3441 ;;; identity function or a constant.
3442 (macrolet ((def (name identity result)
3443 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3444 "fold identity operations"
3451 (def logxor -1 (lognot x))
3454 (deftransform logand ((x y) (* (constant-arg t)) *)
3455 "fold identity operation"
3456 (let ((y (lvar-value y)))
3457 (unless (and (plusp y)
3458 (= y (1- (ash 1 (integer-length y)))))
3459 (give-up-ir1-transform))
3460 (unless (csubtypep (lvar-type x)
3461 (specifier-type `(integer 0 ,y)))
3462 (give-up-ir1-transform))
3465 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3466 "fold identity operation"
3467 (let ((size (lvar-value size)))
3468 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3469 (give-up-ir1-transform))
3472 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3473 ;;; (* 0 -4.0) is -0.0.
3474 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3475 "convert (- 0 x) to negate"
3477 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3478 "convert (* x 0) to 0"
3481 ;;; Return T if in an arithmetic op including lvars X and Y, the
3482 ;;; result type is not affected by the type of X. That is, Y is at
3483 ;;; least as contagious as X.
3485 (defun not-more-contagious (x y)
3486 (declare (type continuation x y))
3487 (let ((x (lvar-type x))
3489 (values (type= (numeric-contagion x y)
3490 (numeric-contagion y y)))))
3491 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3492 ;;; XXX needs more work as valid transforms are missed; some cases are
3493 ;;; specific to particular transform functions so the use of this
3494 ;;; function may need a re-think.
3495 (defun not-more-contagious (x y)
3496 (declare (type lvar x y))
3497 (flet ((simple-numeric-type (num)
3498 (and (numeric-type-p num)
3499 ;; Return non-NIL if NUM is integer, rational, or a float
3500 ;; of some type (but not FLOAT)
3501 (case (numeric-type-class num)
3505 (numeric-type-format num))
3508 (let ((x (lvar-type x))
3510 (if (and (simple-numeric-type x)
3511 (simple-numeric-type y))
3512 (values (type= (numeric-contagion x y)
3513 (numeric-contagion y y)))))))
3515 (def!type exact-number ()
3516 '(or rational (complex rational)))
3520 ;;; Only safely applicable for exact numbers. For floating-point
3521 ;;; x, one would have to first show that neither x or y are signed
3522 ;;; 0s, and that x isn't an SNaN.
3523 (deftransform + ((x y) (exact-number (constant-arg (eql 0))) *)
3528 (deftransform - ((x y) (exact-number (constant-arg (eql 0))) *)
3532 ;;; Fold (OP x +/-1)
3534 ;;; %NEGATE might not always signal correctly.
3536 ((def (name result minus-result)
3537 `(deftransform ,name ((x y)
3538 (exact-number (constant-arg (member 1 -1))))
3539 "fold identity operations"
3540 (if (minusp (lvar-value y)) ',minus-result ',result))))
3541 (def * x (%negate x))
3542 (def / x (%negate x))
3543 (def expt x (/ 1 x)))
3545 ;;; Fold (expt x n) into multiplications for small integral values of
3546 ;;; N; convert (expt x 1/2) to sqrt.
3547 (deftransform expt ((x y) (t (constant-arg real)) *)
3548 "recode as multiplication or sqrt"
3549 (let ((val (lvar-value y)))
3550 ;; If Y would cause the result to be promoted to the same type as
3551 ;; Y, we give up. If not, then the result will be the same type
3552 ;; as X, so we can replace the exponentiation with simple
3553 ;; multiplication and division for small integral powers.
3554 (unless (not-more-contagious y x)
3555 (give-up-ir1-transform))
3557 (let ((x-type (lvar-type x)))
3558 (cond ((csubtypep x-type (specifier-type '(or rational
3559 (complex rational))))
3561 ((csubtypep x-type (specifier-type 'real))
3565 ((csubtypep x-type (specifier-type 'complex))
3566 ;; both parts are float
3568 (t (give-up-ir1-transform)))))
3569 ((= val 2) '(* x x))
3570 ((= val -2) '(/ (* x x)))
3571 ((= val 3) '(* x x x))
3572 ((= val -3) '(/ (* x x x)))
3573 ((= val 1/2) '(sqrt x))
3574 ((= val -1/2) '(/ (sqrt x)))
3575 (t (give-up-ir1-transform)))))
3577 (deftransform expt ((x y) ((constant-arg (member -1 -1.0 -1.0d0)) integer) *)
3578 "recode as an ODDP check"
3579 (let ((val (lvar-value x)))
3581 '(- 1 (* 2 (logand 1 y)))
3586 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3587 ;;; transformations?
3588 ;;; Perhaps we should have to prove that the denominator is nonzero before
3589 ;;; doing them? -- WHN 19990917
3590 (macrolet ((def (name)
3591 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3598 (macrolet ((def (name)
3599 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3608 (macrolet ((def (name &optional float)
3609 (let ((x (if float '(float x) 'x)))
3610 `(deftransform ,name ((x y) (integer (constant-arg (member 1 -1)))
3612 "fold division by 1"
3613 `(values ,(if (minusp (lvar-value y))
3626 ;;;; character operations
3628 (deftransform char-equal ((a b) (base-char base-char))
3630 '(let* ((ac (char-code a))
3632 (sum (logxor ac bc)))
3634 (when (eql sum #x20)
3635 (let ((sum (+ ac bc)))
3636 (or (and (> sum 161) (< sum 213))
3637 (and (> sum 415) (< sum 461))
3638 (and (> sum 463) (< sum 477))))))))
3640 (deftransform char-upcase ((x) (base-char))
3642 '(let ((n-code (char-code x)))
3643 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3644 (< n-code #o173)) ; Octal 172 is #\z.
3645 (and (> n-code #o337)
3647 (and (> n-code #o367)
3649 (code-char (logxor #x20 n-code))
3652 (deftransform char-downcase ((x) (base-char))
3654 '(let ((n-code (char-code x)))
3655 (if (or (and (> n-code 64) ; 65 is #\A.
3656 (< n-code 91)) ; 90 is #\Z.
3661 (code-char (logxor #x20 n-code))
3664 ;;;; equality predicate transforms
3666 ;;; Return true if X and Y are lvars whose only use is a
3667 ;;; reference to the same leaf, and the value of the leaf cannot
3669 (defun same-leaf-ref-p (x y)
3670 (declare (type lvar x y))
3671 (let ((x-use (principal-lvar-use x))
3672 (y-use (principal-lvar-use y)))
3675 (eq (ref-leaf x-use) (ref-leaf y-use))
3676 (constant-reference-p x-use))))
3678 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3679 ;;; if there is no intersection between the types of the arguments,
3680 ;;; then the result is definitely false.
3681 (deftransform simple-equality-transform ((x y) * *
3684 ((same-leaf-ref-p x y) t)
3685 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3687 (t (give-up-ir1-transform))))
3690 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3694 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3695 ;;; try to convert to a type-specific predicate or EQ:
3696 ;;; -- If both args are characters, convert to CHAR=. This is better than
3697 ;;; just converting to EQ, since CHAR= may have special compilation
3698 ;;; strategies for non-standard representations, etc.
3699 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3700 ;;; constant and if so, put X second. Doing this results in better
3701 ;;; code from the backend, since the backend assumes that any constant
3702 ;;; argument comes second.
3703 ;;; -- If either arg is definitely not a number or a fixnum, then we
3704 ;;; can compare with EQ.
3705 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3706 ;;; is constant then we put it second. If X is a subtype of Y, we put
3707 ;;; it second. These rules make it easier for the back end to match
3708 ;;; these interesting cases.
3709 (deftransform eql ((x y) * * :node node)
3710 "convert to simpler equality predicate"
3711 (let ((x-type (lvar-type x))
3712 (y-type (lvar-type y))
3713 (char-type (specifier-type 'character)))
3714 (flet ((fixnum-type-p (type)
3715 (csubtypep type (specifier-type 'fixnum))))
3717 ((same-leaf-ref-p x y) t)
3718 ((not (types-equal-or-intersect x-type y-type))
3720 ((and (csubtypep x-type char-type)
3721 (csubtypep y-type char-type))
3723 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3724 (commutative-arg-swap node))
3725 ((or (eq-comparable-type-p x-type) (eq-comparable-type-p y-type))
3727 ((and (not (constant-lvar-p y))
3728 (or (constant-lvar-p x)
3729 (and (csubtypep x-type y-type)
3730 (not (csubtypep y-type x-type)))))
3733 (give-up-ir1-transform))))))
3735 ;;; similarly to the EQL transform above, we attempt to constant-fold
3736 ;;; or convert to a simpler predicate: mostly we have to be careful
3737 ;;; with strings and bit-vectors.
3738 (deftransform equal ((x y) * *)
3739 "convert to simpler equality predicate"
3740 (let ((x-type (lvar-type x))
3741 (y-type (lvar-type y))
3742 (string-type (specifier-type 'string))
3743 (bit-vector-type (specifier-type 'bit-vector)))
3745 ((same-leaf-ref-p x y) t)
3746 ((and (csubtypep x-type string-type)
3747 (csubtypep y-type string-type))
3749 ((and (csubtypep x-type bit-vector-type)
3750 (csubtypep y-type bit-vector-type))
3751 '(bit-vector-= x y))
3752 ;; if at least one is not a string, and at least one is not a
3753 ;; bit-vector, then we can reason from types.
3754 ((and (not (and (types-equal-or-intersect x-type string-type)
3755 (types-equal-or-intersect y-type string-type)))
3756 (not (and (types-equal-or-intersect x-type bit-vector-type)
3757 (types-equal-or-intersect y-type bit-vector-type)))
3758 (not (types-equal-or-intersect x-type y-type)))
3760 (t (give-up-ir1-transform)))))
3762 ;;; Convert to EQL if both args are rational and complexp is specified
3763 ;;; and the same for both.
3764 (deftransform = ((x y) (number number) *)
3766 (let ((x-type (lvar-type x))
3767 (y-type (lvar-type y)))
3768 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3769 (csubtypep y-type (specifier-type 'float)))
3770 (and (csubtypep x-type (specifier-type '(complex float)))
3771 (csubtypep y-type (specifier-type '(complex float))))
3772 #!+complex-float-vops
3773 (and (csubtypep x-type (specifier-type '(or single-float (complex single-float))))
3774 (csubtypep y-type (specifier-type '(or single-float (complex single-float)))))
3775 #!+complex-float-vops
3776 (and (csubtypep x-type (specifier-type '(or double-float (complex double-float))))
3777 (csubtypep y-type (specifier-type '(or double-float (complex double-float))))))
3778 ;; They are both floats. Leave as = so that -0.0 is
3779 ;; handled correctly.
3780 (give-up-ir1-transform))
3781 ((or (and (csubtypep x-type (specifier-type 'rational))
3782 (csubtypep y-type (specifier-type 'rational)))
3783 (and (csubtypep x-type
3784 (specifier-type '(complex rational)))
3786 (specifier-type '(complex rational)))))
3787 ;; They are both rationals and complexp is the same.
3791 (give-up-ir1-transform
3792 "The operands might not be the same type.")))))
3794 (defun maybe-float-lvar-p (lvar)
3795 (neq *empty-type* (type-intersection (specifier-type 'float)
3798 (flet ((maybe-invert (node op inverted x y)
3799 ;; Don't invert if either argument can be a float (NaNs)
3801 ((or (maybe-float-lvar-p x) (maybe-float-lvar-p y))
3802 (delay-ir1-transform node :constraint)
3803 `(or (,op x y) (= x y)))
3805 `(if (,inverted x y) nil t)))))
3806 (deftransform >= ((x y) (number number) * :node node)
3807 "invert or open code"
3808 (maybe-invert node '> '< x y))
3809 (deftransform <= ((x y) (number number) * :node node)
3810 "invert or open code"
3811 (maybe-invert node '< '> x y)))
3813 ;;; See whether we can statically determine (< X Y) using type
3814 ;;; information. If X's high bound is < Y's low, then X < Y.
3815 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3816 ;;; NIL). If not, at least make sure any constant arg is second.
3817 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3818 `(deftransform ,name ((x y))
3819 "optimize using intervals"
3820 (if (and (same-leaf-ref-p x y)
3821 ;; For non-reflexive functions we don't need
3822 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3823 ;; but with reflexive ones we don't know...
3825 '((and (not (maybe-float-lvar-p x))
3826 (not (maybe-float-lvar-p y))))))
3828 (let ((ix (or (type-approximate-interval (lvar-type x))
3829 (give-up-ir1-transform)))
3830 (iy (or (type-approximate-interval (lvar-type y))
3831 (give-up-ir1-transform))))
3836 ((and (constant-lvar-p x)
3837 (not (constant-lvar-p y)))
3840 (give-up-ir1-transform))))))))
3841 (def = = t (interval-= ix iy) (interval-/= ix iy))
3842 (def /= /= nil (interval-/= ix iy) (interval-= ix iy))
3843 (def < > nil (interval-< ix iy) (interval->= ix iy))
3844 (def > < nil (interval-< iy ix) (interval->= iy ix))
3845 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3846 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3848 (defun ir1-transform-char< (x y first second inverse)
3850 ((same-leaf-ref-p x y) nil)
3851 ;; If we had interval representation of character types, as we
3852 ;; might eventually have to to support 2^21 characters, then here
3853 ;; we could do some compile-time computation as in transforms for
3854 ;; < above. -- CSR, 2003-07-01
3855 ((and (constant-lvar-p first)
3856 (not (constant-lvar-p second)))
3858 (t (give-up-ir1-transform))))
3860 (deftransform char< ((x y) (character character) *)
3861 (ir1-transform-char< x y x y 'char>))
3863 (deftransform char> ((x y) (character character) *)
3864 (ir1-transform-char< y x x y 'char<))
3866 ;;;; converting N-arg comparisons
3868 ;;;; We convert calls to N-arg comparison functions such as < into
3869 ;;;; two-arg calls. This transformation is enabled for all such
3870 ;;;; comparisons in this file. If any of these predicates are not
3871 ;;;; open-coded, then the transformation should be removed at some
3872 ;;;; point to avoid pessimization.
3874 ;;; This function is used for source transformation of N-arg
3875 ;;; comparison functions other than inequality. We deal both with
3876 ;;; converting to two-arg calls and inverting the sense of the test,
3877 ;;; if necessary. If the call has two args, then we pass or return a
3878 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3879 ;;; then we transform to code that returns true. Otherwise, we bind
3880 ;;; all the arguments and expand into a bunch of IFs.
3881 (defun multi-compare (predicate args not-p type &optional force-two-arg-p)
3882 (let ((nargs (length args)))
3883 (cond ((< nargs 1) (values nil t))
3884 ((= nargs 1) `(progn (the ,type ,@args) t))
3887 `(if (,predicate ,(first args) ,(second args)) nil t)
3889 `(,predicate ,(first args) ,(second args))
3892 (do* ((i (1- nargs) (1- i))
3894 (current (gensym) (gensym))
3895 (vars (list current) (cons current vars))
3897 `(if (,predicate ,current ,last)
3899 `(if (,predicate ,current ,last)
3902 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3905 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3906 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3907 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3908 ;;; We cannot do the inversion for >= and <= here, since both
3909 ;;; (< NaN X) and (> NaN X)
3910 ;;; are false, and we don't have type-information available yet. The
3911 ;;; deftransforms for two-argument versions of >= and <= takes care of
3912 ;;; the inversion to > and < when possible.
3913 (define-source-transform <= (&rest args) (multi-compare '<= args nil 'real))
3914 (define-source-transform >= (&rest args) (multi-compare '>= args nil 'real))
3916 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3918 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3920 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3922 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3924 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3927 (define-source-transform char-equal (&rest args)
3928 (multi-compare 'sb!impl::two-arg-char-equal args nil 'character t))
3929 (define-source-transform char-lessp (&rest args)
3930 (multi-compare 'sb!impl::two-arg-char-lessp args nil 'character t))
3931 (define-source-transform char-greaterp (&rest args)
3932 (multi-compare 'sb!impl::two-arg-char-greaterp args nil 'character t))
3933 (define-source-transform char-not-greaterp (&rest args)
3934 (multi-compare 'sb!impl::two-arg-char-greaterp args t 'character t))
3935 (define-source-transform char-not-lessp (&rest args)
3936 (multi-compare 'sb!impl::two-arg-char-lessp args t 'character t))
3938 ;;; This function does source transformation of N-arg inequality
3939 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3940 ;;; arg cases. If there are more than two args, then we expand into
3941 ;;; the appropriate n^2 comparisons only when speed is important.
3942 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3943 (defun multi-not-equal (predicate args type)
3944 (let ((nargs (length args)))
3945 (cond ((< nargs 1) (values nil t))
3946 ((= nargs 1) `(progn (the ,type ,@args) t))
3948 `(if (,predicate ,(first args) ,(second args)) nil t))
3949 ((not (policy *lexenv*
3950 (and (>= speed space)
3951 (>= speed compilation-speed))))
3954 (let ((vars (make-gensym-list nargs)))
3955 (do ((var vars next)
3956 (next (cdr vars) (cdr next))
3959 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3961 (let ((v1 (first var)))
3963 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3965 (define-source-transform /= (&rest args)
3966 (multi-not-equal '= args 'number))
3967 (define-source-transform char/= (&rest args)
3968 (multi-not-equal 'char= args 'character))
3969 (define-source-transform char-not-equal (&rest args)
3970 (multi-not-equal 'char-equal args 'character))
3972 ;;; Expand MAX and MIN into the obvious comparisons.
3973 (define-source-transform max (arg0 &rest rest)
3974 (once-only ((arg0 arg0))
3976 `(values (the real ,arg0))
3977 `(let ((maxrest (max ,@rest)))
3978 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3979 (define-source-transform min (arg0 &rest rest)
3980 (once-only ((arg0 arg0))
3982 `(values (the real ,arg0))
3983 `(let ((minrest (min ,@rest)))
3984 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3986 ;;;; converting N-arg arithmetic functions
3988 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3989 ;;;; versions, and degenerate cases are flushed.
3991 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3992 (declaim (ftype (sfunction (symbol t list t) list) associate-args))
3993 (defun associate-args (fun first-arg more-args identity)
3994 (let ((next (rest more-args))
3995 (arg (first more-args)))
3997 `(,fun ,first-arg ,(if arg arg identity))
3998 (associate-args fun `(,fun ,first-arg ,arg) next identity))))
4000 ;;; Reduce constants in ARGS list.
4001 (declaim (ftype (sfunction (symbol list t symbol) list) reduce-constants))
4002 (defun reduce-constants (fun args identity one-arg-result-type)
4003 (let ((one-arg-constant-p (ecase one-arg-result-type
4005 (integer #'integerp)))
4006 (reduced-value identity)
4008 (collect ((not-constants))
4010 (if (funcall one-arg-constant-p arg)
4011 (setf reduced-value (funcall fun reduced-value arg)
4013 (not-constants arg)))
4014 ;; It is tempting to drop constants reduced to identity here,
4015 ;; but if X is SNaN in (* X 1), we cannot drop the 1.
4018 `(,reduced-value ,@(not-constants))
4020 `(,reduced-value)))))
4022 ;;; Do source transformations for transitive functions such as +.
4023 ;;; One-arg cases are replaced with the arg and zero arg cases with
4024 ;;; the identity. ONE-ARG-RESULT-TYPE is the type to ensure (with THE)
4025 ;;; that the argument in one-argument calls is.
4026 (declaim (ftype (function (symbol list t &optional symbol list)
4027 (values t &optional (member nil t)))
4028 source-transform-transitive))
4029 (defun source-transform-transitive (fun args identity
4030 &optional (one-arg-result-type 'number)
4031 (one-arg-prefixes '(values)))
4034 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
4036 (t (let ((reduced-args (reduce-constants fun args identity one-arg-result-type)))
4037 (associate-args fun (first reduced-args) (rest reduced-args) identity)))))
4039 (define-source-transform + (&rest args)
4040 (source-transform-transitive '+ args 0))
4041 (define-source-transform * (&rest args)
4042 (source-transform-transitive '* args 1))
4043 (define-source-transform logior (&rest args)
4044 (source-transform-transitive 'logior args 0 'integer))
4045 (define-source-transform logxor (&rest args)
4046 (source-transform-transitive 'logxor args 0 'integer))
4047 (define-source-transform logand (&rest args)
4048 (source-transform-transitive 'logand args -1 'integer))
4049 (define-source-transform logeqv (&rest args)
4050 (source-transform-transitive 'logeqv args -1 'integer))
4051 (define-source-transform gcd (&rest args)
4052 (source-transform-transitive 'gcd args 0 'integer '(abs)))
4053 (define-source-transform lcm (&rest args)
4054 (source-transform-transitive 'lcm args 1 'integer '(abs)))
4056 ;;; Do source transformations for intransitive n-arg functions such as
4057 ;;; /. With one arg, we form the inverse. With two args we pass.
4058 ;;; Otherwise we associate into two-arg calls.
4059 (declaim (ftype (function (symbol symbol list t list &optional symbol)
4060 (values list &optional (member nil t)))
4061 source-transform-intransitive))
4062 (defun source-transform-intransitive (fun fun* args identity one-arg-prefixes
4063 &optional (one-arg-result-type 'number))
4065 ((0 2) (values nil t))
4066 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
4067 (t (let ((reduced-args
4068 (reduce-constants fun* (rest args) identity one-arg-result-type)))
4069 (associate-args fun (first args) reduced-args identity)))))
4071 (define-source-transform - (&rest args)
4072 (source-transform-intransitive '- '+ args 0 '(%negate)))
4073 (define-source-transform / (&rest args)
4074 (source-transform-intransitive '/ '* args 1 '(/ 1)))
4076 ;;;; transforming APPLY
4078 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
4079 ;;; only needs to understand one kind of variable-argument call. It is
4080 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
4081 (define-source-transform apply (fun arg &rest more-args)
4082 (let ((args (cons arg more-args)))
4083 `(multiple-value-call ,fun
4084 ,@(mapcar (lambda (x) `(values ,x)) (butlast args))
4085 (values-list ,(car (last args))))))
4087 ;;; When &REST argument are at play, we also have extra context and count
4088 ;;; arguments -- convert to %VALUES-LIST-OR-CONTEXT when possible, so that the
4089 ;;; deftransform can decide what to do after everything has been converted.
4090 (define-source-transform values-list (list)
4092 (let* ((var (lexenv-find list vars))
4093 (info (when (lambda-var-p var)
4094 (lambda-var-arg-info var))))
4096 (eq :rest (arg-info-kind info))
4097 (consp (arg-info-default info)))
4098 (destructuring-bind (context count &optional used) (arg-info-default info)
4099 (declare (ignore used))
4100 `(%values-list-or-context ,list ,context ,count))
4104 (deftransform %values-list-or-context ((list context count) * * :node node)
4105 (let* ((use (lvar-use list))
4106 (var (when (ref-p use) (ref-leaf use)))
4107 (home (when (lambda-var-p var) (lambda-var-home var)))
4108 (info (when (lambda-var-p var) (lambda-var-arg-info var))))
4109 (flet ((ref-good-for-more-context-p (ref)
4110 (let ((dest (principal-lvar-end (node-lvar ref))))
4111 (and (combination-p dest)
4112 ;; Uses outside VALUES-LIST will require a &REST list anyways,
4113 ;; to it's no use saving effort here -- plus they might modify
4114 ;; the list destructively.
4115 (eq '%values-list-or-context (lvar-fun-name (combination-fun dest)))
4116 ;; If the home lambda is different and isn't DX, it might
4117 ;; escape -- in which case using the more context isn't safe.
4118 (let ((clambda (node-home-lambda dest)))
4119 (or (eq home clambda)
4120 (leaf-dynamic-extent clambda)))))))
4123 (consp (arg-info-default info))
4124 (not (lambda-var-specvar var))
4125 (not (lambda-var-sets var))
4126 (every #'ref-good-for-more-context-p (lambda-var-refs var))
4127 (policy node (= 3 rest-conversion)))))
4129 (destructuring-bind (context count &optional used) (arg-info-default info)
4130 (declare (ignore used))
4131 (setf (arg-info-default info) (list context count t)))
4132 `(%more-arg-values context 0 count))
4135 (setf (arg-info-default info) t))
4136 `(values-list list)))))))
4139 ;;;; transforming FORMAT
4141 ;;;; If the control string is a compile-time constant, then replace it
4142 ;;;; with a use of the FORMATTER macro so that the control string is
4143 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
4144 ;;;; or T and the control string is a function (i.e. FORMATTER), then
4145 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
4147 ;;; for compile-time argument count checking.
4149 ;;; FIXME II: In some cases, type information could be correlated; for
4150 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
4151 ;;; of a corresponding argument is known and does not intersect the
4152 ;;; list type, a warning could be signalled.
4153 (defun check-format-args (string args fun)
4154 (declare (type string string))
4155 (unless (typep string 'simple-string)
4156 (setq string (coerce string 'simple-string)))
4157 (multiple-value-bind (min max)
4158 (handler-case (sb!format:%compiler-walk-format-string string args)
4159 (sb!format:format-error (c)
4160 (compiler-warn "~A" c)))
4162 (let ((nargs (length args)))
4165 (warn 'format-too-few-args-warning
4167 "Too few arguments (~D) to ~S ~S: requires at least ~D."
4168 :format-arguments (list nargs fun string min)))
4170 (warn 'format-too-many-args-warning
4172 "Too many arguments (~D) to ~S ~S: uses at most ~D."
4173 :format-arguments (list nargs fun string max))))))))
4175 (defoptimizer (format optimizer) ((dest control &rest args))
4176 (when (constant-lvar-p control)
4177 (let ((x (lvar-value control)))
4179 (check-format-args x args 'format)))))
4181 ;;; We disable this transform in the cross-compiler to save memory in
4182 ;;; the target image; most of the uses of FORMAT in the compiler are for
4183 ;;; error messages, and those don't need to be particularly fast.
4185 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
4186 :policy (>= speed space))
4187 (unless (constant-lvar-p control)
4188 (give-up-ir1-transform "The control string is not a constant."))
4189 (let ((arg-names (make-gensym-list (length args))))
4190 `(lambda (dest control ,@arg-names)
4191 (declare (ignore control))
4192 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
4194 (deftransform format ((stream control &rest args) (stream function &rest t))
4195 (let ((arg-names (make-gensym-list (length args))))
4196 `(lambda (stream control ,@arg-names)
4197 (funcall control stream ,@arg-names)
4200 (deftransform format ((tee control &rest args) ((member t) function &rest t))
4201 (let ((arg-names (make-gensym-list (length args))))
4202 `(lambda (tee control ,@arg-names)
4203 (declare (ignore tee))
4204 (funcall control *standard-output* ,@arg-names)
4207 (deftransform pathname ((pathspec) (pathname) *)
4210 (deftransform pathname ((pathspec) (string) *)
4211 '(values (parse-namestring pathspec)))
4215 `(defoptimizer (,name optimizer) ((control &rest args))
4216 (when (constant-lvar-p control)
4217 (let ((x (lvar-value control)))
4219 (check-format-args x args ',name)))))))
4222 #+sb-xc-host ; Only we should be using these
4225 (def compiler-error)
4227 (def compiler-style-warn)
4228 (def compiler-notify)
4229 (def maybe-compiler-notify)
4232 (defoptimizer (cerror optimizer) ((report control &rest args))
4233 (when (and (constant-lvar-p control)
4234 (constant-lvar-p report))
4235 (let ((x (lvar-value control))
4236 (y (lvar-value report)))
4237 (when (and (stringp x) (stringp y))
4238 (multiple-value-bind (min1 max1)
4240 (sb!format:%compiler-walk-format-string x args)
4241 (sb!format:format-error (c)
4242 (compiler-warn "~A" c)))
4244 (multiple-value-bind (min2 max2)
4246 (sb!format:%compiler-walk-format-string y args)
4247 (sb!format:format-error (c)
4248 (compiler-warn "~A" c)))
4250 (let ((nargs (length args)))
4252 ((< nargs (min min1 min2))
4253 (warn 'format-too-few-args-warning
4255 "Too few arguments (~D) to ~S ~S ~S: ~
4256 requires at least ~D."
4258 (list nargs 'cerror y x (min min1 min2))))
4259 ((> nargs (max max1 max2))
4260 (warn 'format-too-many-args-warning
4262 "Too many arguments (~D) to ~S ~S ~S: ~
4265 (list nargs 'cerror y x (max max1 max2))))))))))))))
4267 (defoptimizer (coerce derive-type) ((value type) node)
4269 ((constant-lvar-p type)
4270 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
4271 ;; but dealing with the niggle that complex canonicalization gets
4272 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
4274 (let* ((specifier (lvar-value type))
4275 (result-typeoid (careful-specifier-type specifier)))
4277 ((null result-typeoid) nil)
4278 ((csubtypep result-typeoid (specifier-type 'number))
4279 ;; the difficult case: we have to cope with ANSI 12.1.5.3
4280 ;; Rule of Canonical Representation for Complex Rationals,
4281 ;; which is a truly nasty delivery to field.
4283 ((csubtypep result-typeoid (specifier-type 'real))
4284 ;; cleverness required here: it would be nice to deduce
4285 ;; that something of type (INTEGER 2 3) coerced to type
4286 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
4287 ;; FLOAT gets its own clause because it's implemented as
4288 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
4291 ((and (numeric-type-p result-typeoid)
4292 (eq (numeric-type-complexp result-typeoid) :real))
4293 ;; FIXME: is this clause (a) necessary or (b) useful?
4295 ((or (csubtypep result-typeoid
4296 (specifier-type '(complex single-float)))
4297 (csubtypep result-typeoid
4298 (specifier-type '(complex double-float)))
4300 (csubtypep result-typeoid
4301 (specifier-type '(complex long-float))))
4302 ;; float complex types are never canonicalized.
4305 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
4306 ;; probably just a COMPLEX or equivalent. So, in that
4307 ;; case, we will return a complex or an object of the
4308 ;; provided type if it's rational:
4309 (type-union result-typeoid
4310 (type-intersection (lvar-type value)
4311 (specifier-type 'rational))))))
4312 ((and (policy node (zerop safety))
4313 (csubtypep result-typeoid (specifier-type '(array * (*)))))
4314 ;; At zero safety the deftransform for COERCE can elide dimension
4315 ;; checks for the things like (COERCE X '(SIMPLE-VECTOR 5)) -- so we
4316 ;; need to simplify the type to drop the dimension information.
4317 (let ((vtype (simplify-vector-type result-typeoid)))
4319 (specifier-type vtype)
4324 ;; OK, the result-type argument isn't constant. However, there
4325 ;; are common uses where we can still do better than just
4326 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
4327 ;; where Y is of a known type. See messages on cmucl-imp
4328 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
4329 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
4330 ;; the basis that it's unlikely that other uses are both
4331 ;; time-critical and get to this branch of the COND (non-constant
4332 ;; second argument to COERCE). -- CSR, 2002-12-16
4333 (let ((value-type (lvar-type value))
4334 (type-type (lvar-type type)))
4336 ((good-cons-type-p (cons-type)
4337 ;; Make sure the cons-type we're looking at is something
4338 ;; we're prepared to handle which is basically something
4339 ;; that array-element-type can return.
4340 (or (and (member-type-p cons-type)
4341 (eql 1 (member-type-size cons-type))
4342 (null (first (member-type-members cons-type))))
4343 (let ((car-type (cons-type-car-type cons-type)))
4344 (and (member-type-p car-type)
4345 (eql 1 (member-type-members car-type))
4346 (let ((elt (first (member-type-members car-type))))
4350 (numberp (first elt)))))
4351 (good-cons-type-p (cons-type-cdr-type cons-type))))))
4352 (unconsify-type (good-cons-type)
4353 ;; Convert the "printed" respresentation of a cons
4354 ;; specifier into a type specifier. That is, the
4355 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
4356 ;; NULL)) is converted to (SIGNED-BYTE 16).
4357 (cond ((or (null good-cons-type)
4358 (eq good-cons-type 'null))
4360 ((and (eq (first good-cons-type) 'cons)
4361 (eq (first (second good-cons-type)) 'member))
4362 `(,(second (second good-cons-type))
4363 ,@(unconsify-type (caddr good-cons-type))))))
4364 (coerceable-p (part)
4365 ;; Can the value be coerced to the given type? Coerce is
4366 ;; complicated, so we don't handle every possible case
4367 ;; here---just the most common and easiest cases:
4369 ;; * Any REAL can be coerced to a FLOAT type.
4370 ;; * Any NUMBER can be coerced to a (COMPLEX
4371 ;; SINGLE/DOUBLE-FLOAT).
4373 ;; FIXME I: we should also be able to deal with characters
4376 ;; FIXME II: I'm not sure that anything is necessary
4377 ;; here, at least while COMPLEX is not a specialized
4378 ;; array element type in the system. Reasoning: if
4379 ;; something cannot be coerced to the requested type, an
4380 ;; error will be raised (and so any downstream compiled
4381 ;; code on the assumption of the returned type is
4382 ;; unreachable). If something can, then it will be of
4383 ;; the requested type, because (by assumption) COMPLEX
4384 ;; (and other difficult types like (COMPLEX INTEGER)
4385 ;; aren't specialized types.
4386 (let ((coerced-type (careful-specifier-type part)))
4388 (or (and (csubtypep coerced-type (specifier-type 'float))
4389 (csubtypep value-type (specifier-type 'real)))
4390 (and (csubtypep coerced-type
4391 (specifier-type `(or (complex single-float)
4392 (complex double-float))))
4393 (csubtypep value-type (specifier-type 'number)))))))
4394 (process-types (type)
4395 ;; FIXME: This needs some work because we should be able
4396 ;; to derive the resulting type better than just the
4397 ;; type arg of coerce. That is, if X is (INTEGER 10
4398 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
4399 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
4401 (cond ((member-type-p type)
4404 (mapc-member-type-members
4406 (if (coerceable-p member)
4407 (push member members)
4408 (return-from punt *universal-type*)))
4410 (specifier-type `(or ,@members)))))
4411 ((and (cons-type-p type)
4412 (good-cons-type-p type))
4413 (let ((c-type (unconsify-type (type-specifier type))))
4414 (if (coerceable-p c-type)
4415 (specifier-type c-type)
4418 *universal-type*))))
4419 (cond ((union-type-p type-type)
4420 (apply #'type-union (mapcar #'process-types
4421 (union-type-types type-type))))
4422 ((or (member-type-p type-type)
4423 (cons-type-p type-type))
4424 (process-types type-type))
4426 *universal-type*)))))))
4428 (defoptimizer (compile derive-type) ((nameoid function))
4429 (when (csubtypep (lvar-type nameoid)
4430 (specifier-type 'null))
4431 (values-specifier-type '(values function boolean boolean))))
4433 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
4434 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
4435 ;;; optimizer, above).
4436 (defoptimizer (array-element-type derive-type) ((array))
4437 (let ((array-type (lvar-type array)))
4438 (labels ((consify (list)
4441 `(cons (eql ,(car list)) ,(consify (rest list)))))
4442 (get-element-type (a)
4444 (type-specifier (array-type-specialized-element-type a))))
4445 (cond ((eq element-type '*)
4446 (specifier-type 'type-specifier))
4447 ((symbolp element-type)
4448 (make-member-type :members (list element-type)))
4449 ((consp element-type)
4450 (specifier-type (consify element-type)))
4452 (error "can't understand type ~S~%" element-type))))))
4453 (labels ((recurse (type)
4454 (cond ((array-type-p type)
4455 (get-element-type type))
4456 ((union-type-p type)
4458 (mapcar #'recurse (union-type-types type))))
4460 *universal-type*))))
4461 (recurse array-type)))))
4463 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
4464 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4465 ;; isn't really related to the CMU CL code, since instead of trying
4466 ;; to generalize the CMU CL code to allow START and END values, this
4467 ;; code has been written from scratch following Chapter 7 of
4468 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4469 `(macrolet ((%index (x) `(truly-the index ,x))
4470 (%parent (i) `(ash ,i -1))
4471 (%left (i) `(%index (ash ,i 1)))
4472 (%right (i) `(%index (1+ (ash ,i 1))))
4475 (left (%left i) (%left i)))
4476 ((> left current-heap-size))
4477 (declare (type index i left))
4478 (let* ((i-elt (%elt i))
4479 (i-key (funcall keyfun i-elt))
4480 (left-elt (%elt left))
4481 (left-key (funcall keyfun left-elt)))
4482 (multiple-value-bind (large large-elt large-key)
4483 (if (funcall ,',predicate i-key left-key)
4484 (values left left-elt left-key)
4485 (values i i-elt i-key))
4486 (let ((right (%right i)))
4487 (multiple-value-bind (largest largest-elt)
4488 (if (> right current-heap-size)
4489 (values large large-elt)
4490 (let* ((right-elt (%elt right))
4491 (right-key (funcall keyfun right-elt)))
4492 (if (funcall ,',predicate large-key right-key)
4493 (values right right-elt)
4494 (values large large-elt))))
4495 (cond ((= largest i)
4498 (setf (%elt i) largest-elt
4499 (%elt largest) i-elt
4501 (%sort-vector (keyfun &optional (vtype 'vector))
4502 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4503 ;; trouble getting type inference to
4504 ;; propagate all the way through this
4505 ;; tangled mess of inlining. The TRULY-THE
4506 ;; here works around that. -- WHN
4508 `(aref (truly-the ,',vtype ,',',vector)
4509 (%index (+ (%index ,i) start-1)))))
4510 (let (;; Heaps prefer 1-based addressing.
4511 (start-1 (1- ,',start))
4512 (current-heap-size (- ,',end ,',start))
4514 (declare (type (integer -1 #.(1- sb!xc:most-positive-fixnum))
4516 (declare (type index current-heap-size))
4517 (declare (type function keyfun))
4518 (loop for i of-type index
4519 from (ash current-heap-size -1) downto 1 do
4522 (when (< current-heap-size 2)
4524 (rotatef (%elt 1) (%elt current-heap-size))
4525 (decf current-heap-size)
4527 (if (typep ,vector 'simple-vector)
4528 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4529 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4531 ;; Special-casing the KEY=NIL case lets us avoid some
4533 (%sort-vector #'identity simple-vector)
4534 (%sort-vector ,key simple-vector))
4535 ;; It's hard to anticipate many speed-critical applications for
4536 ;; sorting vector types other than (VECTOR T), so we just lump
4537 ;; them all together in one slow dynamically typed mess.
4539 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4540 (%sort-vector (or ,key #'identity))))))
4542 ;;;; debuggers' little helpers
4544 ;;; for debugging when transforms are behaving mysteriously,
4545 ;;; e.g. when debugging a problem with an ASH transform
4546 ;;; (defun foo (&optional s)
4547 ;;; (sb-c::/report-lvar s "S outside WHEN")
4548 ;;; (when (and (integerp s) (> s 3))
4549 ;;; (sb-c::/report-lvar s "S inside WHEN")
4550 ;;; (let ((bound (ash 1 (1- s))))
4551 ;;; (sb-c::/report-lvar bound "BOUND")
4552 ;;; (let ((x (- bound))
4554 ;;; (sb-c::/report-lvar x "X")
4555 ;;; (sb-c::/report-lvar x "Y"))
4556 ;;; `(integer ,(- bound) ,(1- bound)))))
4557 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4558 ;;; and the function doesn't do anything at all.)
4561 (defknown /report-lvar (t t) null)
4562 (deftransform /report-lvar ((x message) (t t))
4563 (format t "~%/in /REPORT-LVAR~%")
4564 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4565 (when (constant-lvar-p x)
4566 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4567 (format t "/MESSAGE=~S~%" (lvar-value message))
4568 (give-up-ir1-transform "not a real transform"))
4569 (defun /report-lvar (x message)
4570 (declare (ignore x message))))
4573 ;;;; Transforms for internal compiler utilities
4575 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4576 ;;; checking that it's still valid at run-time.
4577 (deftransform policy-quality ((policy quality-name)
4579 (unless (and (constant-lvar-p quality-name)
4580 (policy-quality-name-p (lvar-value quality-name)))
4581 (give-up-ir1-transform))
4582 '(%policy-quality policy quality-name))