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))
32 ;;; Bind the value and make a closure that returns it.
33 (define-source-transform constantly (value)
34 (with-unique-names (rest n-value)
35 `(let ((,n-value ,value))
37 (declare (ignore ,rest))
40 ;;; If the function has a known number of arguments, then return a
41 ;;; lambda with the appropriate fixed number of args. If the
42 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
43 ;;; MV optimization figure things out.
44 (deftransform complement ((fun) * * :node node)
46 (multiple-value-bind (min max)
47 (fun-type-nargs (lvar-type fun))
49 ((and min (eql min max))
50 (let ((dums (make-gensym-list min)))
51 `#'(lambda ,dums (not (funcall fun ,@dums)))))
52 ((awhen (node-lvar node)
53 (let ((dest (lvar-dest it)))
54 (and (combination-p dest)
55 (eq (combination-fun dest) it))))
56 '#'(lambda (&rest args)
57 (not (apply fun args))))
59 (give-up-ir1-transform
60 "The function doesn't have a fixed argument count.")))))
64 ;;; Translate CxR into CAR/CDR combos.
65 (defun source-transform-cxr (form)
66 (if (/= (length form) 2)
68 (let ((name (symbol-name (car form))))
69 (do ((i (- (length name) 2) (1- i))
71 `(,(ecase (char name i)
77 ;;; Make source transforms to turn CxR forms into combinations of CAR
78 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
80 (/show0 "about to set CxR source transforms")
81 (loop for i of-type index from 2 upto 4 do
82 ;; Iterate over BUF = all names CxR where x = an I-element
83 ;; string of #\A or #\D characters.
84 (let ((buf (make-string (+ 2 i))))
85 (setf (aref buf 0) #\C
86 (aref buf (1+ i)) #\R)
87 (dotimes (j (ash 2 i))
88 (declare (type index j))
90 (declare (type index k))
91 (setf (aref buf (1+ k))
92 (if (logbitp k j) #\A #\D)))
93 (setf (info :function :source-transform (intern buf))
94 #'source-transform-cxr))))
95 (/show0 "done setting CxR source transforms")
97 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
98 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
99 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
101 (define-source-transform first (x) `(car ,x))
102 (define-source-transform rest (x) `(cdr ,x))
103 (define-source-transform second (x) `(cadr ,x))
104 (define-source-transform third (x) `(caddr ,x))
105 (define-source-transform fourth (x) `(cadddr ,x))
106 (define-source-transform fifth (x) `(nth 4 ,x))
107 (define-source-transform sixth (x) `(nth 5 ,x))
108 (define-source-transform seventh (x) `(nth 6 ,x))
109 (define-source-transform eighth (x) `(nth 7 ,x))
110 (define-source-transform ninth (x) `(nth 8 ,x))
111 (define-source-transform tenth (x) `(nth 9 ,x))
113 ;;; Translate RPLACx to LET and SETF.
114 (define-source-transform rplaca (x y)
119 (define-source-transform rplacd (x y)
125 (define-source-transform nth (n l) `(car (nthcdr ,n ,l)))
127 (defvar *default-nthcdr-open-code-limit* 6)
128 (defvar *extreme-nthcdr-open-code-limit* 20)
130 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
131 "convert NTHCDR to CAxxR"
132 (unless (constant-lvar-p n)
133 (give-up-ir1-transform))
134 (let ((n (lvar-value n)))
136 (if (policy node (and (= speed 3) (= space 0)))
137 *extreme-nthcdr-open-code-limit*
138 *default-nthcdr-open-code-limit*))
139 (give-up-ir1-transform))
144 `(cdr ,(frob (1- n))))))
147 ;;;; arithmetic and numerology
149 (define-source-transform plusp (x) `(> ,x 0))
150 (define-source-transform minusp (x) `(< ,x 0))
151 (define-source-transform zerop (x) `(= ,x 0))
153 (define-source-transform 1+ (x) `(+ ,x 1))
154 (define-source-transform 1- (x) `(- ,x 1))
156 (define-source-transform oddp (x) `(not (zerop (logand ,x 1))))
157 (define-source-transform evenp (x) `(zerop (logand ,x 1)))
159 ;;; Note that all the integer division functions are available for
160 ;;; inline expansion.
162 (macrolet ((deffrob (fun)
163 `(define-source-transform ,fun (x &optional (y nil y-p))
170 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
172 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
175 (define-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
177 (deftransform logbitp
178 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
179 (unsigned-byte #.sb!vm:n-word-bits))))
180 `(if (>= index #.sb!vm:n-word-bits)
182 (not (zerop (logand integer (ash 1 index))))))
184 (define-source-transform byte (size position)
185 `(cons ,size ,position))
186 (define-source-transform byte-size (spec) `(car ,spec))
187 (define-source-transform byte-position (spec) `(cdr ,spec))
188 (define-source-transform ldb-test (bytespec integer)
189 `(not (zerop (mask-field ,bytespec ,integer))))
191 ;;; With the ratio and complex accessors, we pick off the "identity"
192 ;;; case, and use a primitive to handle the cell access case.
193 (define-source-transform numerator (num)
194 (once-only ((n-num `(the rational ,num)))
198 (define-source-transform denominator (num)
199 (once-only ((n-num `(the rational ,num)))
201 (%denominator ,n-num)
204 ;;;; interval arithmetic for computing bounds
206 ;;;; This is a set of routines for operating on intervals. It
207 ;;;; implements a simple interval arithmetic package. Although SBCL
208 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
209 ;;;; for two reasons:
211 ;;;; 1. This package is simpler than NUMERIC-TYPE.
213 ;;;; 2. It makes debugging much easier because you can just strip
214 ;;;; out these routines and test them independently of SBCL. (This is a
217 ;;;; One disadvantage is a probable increase in consing because we
218 ;;;; have to create these new interval structures even though
219 ;;;; numeric-type has everything we want to know. Reason 2 wins for
222 ;;; Support operations that mimic real arithmetic comparison
223 ;;; operators, but imposing a total order on the floating points such
224 ;;; that negative zeros are strictly less than positive zeros.
225 (macrolet ((def (name op)
228 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
229 (,op (float-sign x) (float-sign y))
231 (def signed-zero->= >=)
232 (def signed-zero-> >)
233 (def signed-zero-= =)
234 (def signed-zero-< <)
235 (def signed-zero-<= <=))
237 ;;; The basic interval type. It can handle open and closed intervals.
238 ;;; A bound is open if it is a list containing a number, just like
239 ;;; Lisp says. NIL means unbounded.
240 (defstruct (interval (:constructor %make-interval)
244 (defun make-interval (&key low high)
245 (labels ((normalize-bound (val)
248 (float-infinity-p val))
249 ;; Handle infinities.
253 ;; Handle any closed bounds.
256 ;; We have an open bound. Normalize the numeric
257 ;; bound. If the normalized bound is still a number
258 ;; (not nil), keep the bound open. Otherwise, the
259 ;; bound is really unbounded, so drop the openness.
260 (let ((new-val (normalize-bound (first val))))
262 ;; The bound exists, so keep it open still.
265 (error "unknown bound type in MAKE-INTERVAL")))))
266 (%make-interval :low (normalize-bound low)
267 :high (normalize-bound high))))
269 ;;; Given a number X, create a form suitable as a bound for an
270 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
271 #!-sb-fluid (declaim (inline set-bound))
272 (defun set-bound (x open-p)
273 (if (and x open-p) (list x) x))
275 ;;; Apply the function F to a bound X. If X is an open bound, then
276 ;;; the result will be open. IF X is NIL, the result is NIL.
277 (defun bound-func (f x)
278 (declare (type function f))
280 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
281 ;; With these traps masked, we might get things like infinity
282 ;; or negative infinity returned. Check for this and return
283 ;; NIL to indicate unbounded.
284 (let ((y (funcall f (type-bound-number x))))
286 (float-infinity-p y))
288 (set-bound (funcall f (type-bound-number x)) (consp x)))))))
290 ;;; Apply a binary operator OP to two bounds X and Y. The result is
291 ;;; NIL if either is NIL. Otherwise bound is computed and the result
292 ;;; is open if either X or Y is open.
294 ;;; FIXME: only used in this file, not needed in target runtime
295 (defmacro bound-binop (op x y)
297 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
298 (set-bound (,op (type-bound-number ,x)
299 (type-bound-number ,y))
300 (or (consp ,x) (consp ,y))))))
302 ;;; Convert a numeric-type object to an interval object.
303 (defun numeric-type->interval (x)
304 (declare (type numeric-type x))
305 (make-interval :low (numeric-type-low x)
306 :high (numeric-type-high x)))
308 (defun type-approximate-interval (type)
309 (declare (type ctype type))
310 (let ((types (prepare-arg-for-derive-type type))
313 (let ((type (if (member-type-p type)
314 (convert-member-type type)
316 (unless (numeric-type-p type)
317 (return-from type-approximate-interval nil))
318 (let ((interval (numeric-type->interval type)))
321 (interval-approximate-union result interval)
325 (defun copy-interval-limit (limit)
330 (defun copy-interval (x)
331 (declare (type interval x))
332 (make-interval :low (copy-interval-limit (interval-low x))
333 :high (copy-interval-limit (interval-high x))))
335 ;;; Given a point P contained in the interval X, split X into two
336 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
337 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
338 ;;; contains P. You can specify both to be T or NIL.
339 (defun interval-split (p x &optional close-lower close-upper)
340 (declare (type number p)
342 (list (make-interval :low (copy-interval-limit (interval-low x))
343 :high (if close-lower p (list p)))
344 (make-interval :low (if close-upper (list p) p)
345 :high (copy-interval-limit (interval-high x)))))
347 ;;; Return the closure of the interval. That is, convert open bounds
348 ;;; to closed bounds.
349 (defun interval-closure (x)
350 (declare (type interval x))
351 (make-interval :low (type-bound-number (interval-low x))
352 :high (type-bound-number (interval-high x))))
354 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
355 ;;; '-. Otherwise return NIL.
356 (defun interval-range-info (x &optional (point 0))
357 (declare (type interval x))
358 (let ((lo (interval-low x))
359 (hi (interval-high x)))
360 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
362 ((and hi (signed-zero->= point (type-bound-number hi)))
367 ;;; Test to see whether the interval X is bounded. HOW determines the
368 ;;; test, and should be either ABOVE, BELOW, or BOTH.
369 (defun interval-bounded-p (x how)
370 (declare (type interval x))
377 (and (interval-low x) (interval-high x)))))
379 ;;; See whether the interval X contains the number P, taking into
380 ;;; account that the interval might not be closed.
381 (defun interval-contains-p (p x)
382 (declare (type number p)
384 ;; Does the interval X contain the number P? This would be a lot
385 ;; easier if all intervals were closed!
386 (let ((lo (interval-low x))
387 (hi (interval-high x)))
389 ;; The interval is bounded
390 (if (and (signed-zero-<= (type-bound-number lo) p)
391 (signed-zero-<= p (type-bound-number hi)))
392 ;; P is definitely in the closure of the interval.
393 ;; We just need to check the end points now.
394 (cond ((signed-zero-= p (type-bound-number lo))
396 ((signed-zero-= p (type-bound-number hi))
401 ;; Interval with upper bound
402 (if (signed-zero-< p (type-bound-number hi))
404 (and (numberp hi) (signed-zero-= p hi))))
406 ;; Interval with lower bound
407 (if (signed-zero-> p (type-bound-number lo))
409 (and (numberp lo) (signed-zero-= p lo))))
411 ;; Interval with no bounds
414 ;;; Determine whether two intervals X and Y intersect. Return T if so.
415 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
416 ;;; were closed. Otherwise the intervals are treated as they are.
418 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
419 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
420 ;;; is T, then they do intersect because we use the closure of X = [0,
421 ;;; 1] and Y = [1, 2] to determine intersection.
422 (defun interval-intersect-p (x y &optional closed-intervals-p)
423 (declare (type interval x y))
424 (multiple-value-bind (intersect diff)
425 (interval-intersection/difference (if closed-intervals-p
428 (if closed-intervals-p
431 (declare (ignore diff))
434 ;;; Are the two intervals adjacent? That is, is there a number
435 ;;; between the two intervals that is not an element of either
436 ;;; interval? If so, they are not adjacent. For example [0, 1) and
437 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
438 ;;; between both intervals.
439 (defun interval-adjacent-p (x y)
440 (declare (type interval x y))
441 (flet ((adjacent (lo hi)
442 ;; Check to see whether lo and hi are adjacent. If either is
443 ;; nil, they can't be adjacent.
444 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
445 ;; The bounds are equal. They are adjacent if one of
446 ;; them is closed (a number). If both are open (consp),
447 ;; then there is a number that lies between them.
448 (or (numberp lo) (numberp hi)))))
449 (or (adjacent (interval-low y) (interval-high x))
450 (adjacent (interval-low x) (interval-high y)))))
452 ;;; Compute the intersection and difference between two intervals.
453 ;;; Two values are returned: the intersection and the difference.
455 ;;; Let the two intervals be X and Y, and let I and D be the two
456 ;;; values returned by this function. Then I = X intersect Y. If I
457 ;;; is NIL (the empty set), then D is X union Y, represented as the
458 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
459 ;;; - I, which is a list of two intervals.
461 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
462 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
463 (defun interval-intersection/difference (x y)
464 (declare (type interval x y))
465 (let ((x-lo (interval-low x))
466 (x-hi (interval-high x))
467 (y-lo (interval-low y))
468 (y-hi (interval-high y)))
471 ;; If p is an open bound, make it closed. If p is a closed
472 ;; bound, make it open.
477 ;; Test whether P is in the interval.
478 (when (interval-contains-p (type-bound-number p)
479 (interval-closure int))
480 (let ((lo (interval-low int))
481 (hi (interval-high int)))
482 ;; Check for endpoints.
483 (cond ((and lo (= (type-bound-number p) (type-bound-number lo)))
484 (not (and (consp p) (numberp lo))))
485 ((and hi (= (type-bound-number p) (type-bound-number hi)))
486 (not (and (numberp p) (consp hi))))
488 (test-lower-bound (p int)
489 ;; P is a lower bound of an interval.
492 (not (interval-bounded-p int 'below))))
493 (test-upper-bound (p int)
494 ;; P is an upper bound of an interval.
497 (not (interval-bounded-p int 'above)))))
498 (let ((x-lo-in-y (test-lower-bound x-lo y))
499 (x-hi-in-y (test-upper-bound x-hi y))
500 (y-lo-in-x (test-lower-bound y-lo x))
501 (y-hi-in-x (test-upper-bound y-hi x)))
502 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
503 ;; Intervals intersect. Let's compute the intersection
504 ;; and the difference.
505 (multiple-value-bind (lo left-lo left-hi)
506 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
507 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
508 (multiple-value-bind (hi right-lo right-hi)
510 (values x-hi (opposite-bound x-hi) y-hi))
512 (values y-hi (opposite-bound y-hi) x-hi)))
513 (values (make-interval :low lo :high hi)
514 (list (make-interval :low left-lo
516 (make-interval :low right-lo
519 (values nil (list x y))))))))
521 ;;; If intervals X and Y intersect, return a new interval that is the
522 ;;; union of the two. If they do not intersect, return NIL.
523 (defun interval-merge-pair (x y)
524 (declare (type interval x y))
525 ;; If x and y intersect or are adjacent, create the union.
526 ;; Otherwise return nil
527 (when (or (interval-intersect-p x y)
528 (interval-adjacent-p x y))
529 (flet ((select-bound (x1 x2 min-op max-op)
530 (let ((x1-val (type-bound-number x1))
531 (x2-val (type-bound-number x2)))
533 ;; Both bounds are finite. Select the right one.
534 (cond ((funcall min-op x1-val x2-val)
535 ;; x1 is definitely better.
537 ((funcall max-op x1-val x2-val)
538 ;; x2 is definitely better.
541 ;; Bounds are equal. Select either
542 ;; value and make it open only if
544 (set-bound x1-val (and (consp x1) (consp x2))))))
546 ;; At least one bound is not finite. The
547 ;; non-finite bound always wins.
549 (let* ((x-lo (copy-interval-limit (interval-low x)))
550 (x-hi (copy-interval-limit (interval-high x)))
551 (y-lo (copy-interval-limit (interval-low y)))
552 (y-hi (copy-interval-limit (interval-high y))))
553 (make-interval :low (select-bound x-lo y-lo #'< #'>)
554 :high (select-bound x-hi y-hi #'> #'<))))))
556 ;;; return the minimal interval, containing X and Y
557 (defun interval-approximate-union (x y)
558 (cond ((interval-merge-pair x y))
560 (make-interval :low (copy-interval-limit (interval-low x))
561 :high (copy-interval-limit (interval-high y))))
563 (make-interval :low (copy-interval-limit (interval-low y))
564 :high (copy-interval-limit (interval-high x))))))
566 ;;; basic arithmetic operations on intervals. We probably should do
567 ;;; true interval arithmetic here, but it's complicated because we
568 ;;; have float and integer types and bounds can be open or closed.
570 ;;; the negative of an interval
571 (defun interval-neg (x)
572 (declare (type interval x))
573 (make-interval :low (bound-func #'- (interval-high x))
574 :high (bound-func #'- (interval-low x))))
576 ;;; Add two intervals.
577 (defun interval-add (x y)
578 (declare (type interval x y))
579 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
580 :high (bound-binop + (interval-high x) (interval-high y))))
582 ;;; Subtract two intervals.
583 (defun interval-sub (x y)
584 (declare (type interval x y))
585 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
586 :high (bound-binop - (interval-high x) (interval-low y))))
588 ;;; Multiply two intervals.
589 (defun interval-mul (x y)
590 (declare (type interval x y))
591 (flet ((bound-mul (x y)
592 (cond ((or (null x) (null y))
593 ;; Multiply by infinity is infinity
595 ((or (and (numberp x) (zerop x))
596 (and (numberp y) (zerop y)))
597 ;; Multiply by closed zero is special. The result
598 ;; is always a closed bound. But don't replace this
599 ;; with zero; we want the multiplication to produce
600 ;; the correct signed zero, if needed.
601 (* (type-bound-number x) (type-bound-number y)))
602 ((or (and (floatp x) (float-infinity-p x))
603 (and (floatp y) (float-infinity-p y)))
604 ;; Infinity times anything is infinity
607 ;; General multiply. The result is open if either is open.
608 (bound-binop * x y)))))
609 (let ((x-range (interval-range-info x))
610 (y-range (interval-range-info y)))
611 (cond ((null x-range)
612 ;; Split x into two and multiply each separately
613 (destructuring-bind (x- x+) (interval-split 0 x t t)
614 (interval-merge-pair (interval-mul x- y)
615 (interval-mul x+ y))))
617 ;; Split y into two and multiply each separately
618 (destructuring-bind (y- y+) (interval-split 0 y t t)
619 (interval-merge-pair (interval-mul x y-)
620 (interval-mul x y+))))
622 (interval-neg (interval-mul (interval-neg x) y)))
624 (interval-neg (interval-mul x (interval-neg y))))
625 ((and (eq x-range '+) (eq y-range '+))
626 ;; If we are here, X and Y are both positive.
628 :low (bound-mul (interval-low x) (interval-low y))
629 :high (bound-mul (interval-high x) (interval-high y))))
631 (bug "excluded case in INTERVAL-MUL"))))))
633 ;;; Divide two intervals.
634 (defun interval-div (top bot)
635 (declare (type interval top bot))
636 (flet ((bound-div (x y y-low-p)
639 ;; Divide by infinity means result is 0. However,
640 ;; we need to watch out for the sign of the result,
641 ;; to correctly handle signed zeros. We also need
642 ;; to watch out for positive or negative infinity.
643 (if (floatp (type-bound-number x))
645 (- (float-sign (type-bound-number x) 0.0))
646 (float-sign (type-bound-number x) 0.0))
648 ((zerop (type-bound-number y))
649 ;; Divide by zero means result is infinity
651 ((and (numberp x) (zerop x))
652 ;; Zero divided by anything is zero.
655 (bound-binop / x y)))))
656 (let ((top-range (interval-range-info top))
657 (bot-range (interval-range-info bot)))
658 (cond ((null bot-range)
659 ;; The denominator contains zero, so anything goes!
660 (make-interval :low nil :high nil))
662 ;; Denominator is negative so flip the sign, compute the
663 ;; result, and flip it back.
664 (interval-neg (interval-div top (interval-neg bot))))
666 ;; Split top into two positive and negative parts, and
667 ;; divide each separately
668 (destructuring-bind (top- top+) (interval-split 0 top t t)
669 (interval-merge-pair (interval-div top- bot)
670 (interval-div top+ bot))))
672 ;; Top is negative so flip the sign, divide, and flip the
673 ;; sign of the result.
674 (interval-neg (interval-div (interval-neg top) bot)))
675 ((and (eq top-range '+) (eq bot-range '+))
678 :low (bound-div (interval-low top) (interval-high bot) t)
679 :high (bound-div (interval-high top) (interval-low bot) nil)))
681 (bug "excluded case in INTERVAL-DIV"))))))
683 ;;; Apply the function F to the interval X. If X = [a, b], then the
684 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
685 ;;; result makes sense. It will if F is monotonic increasing (or
687 (defun interval-func (f x)
688 (declare (type function f)
690 (let ((lo (bound-func f (interval-low x)))
691 (hi (bound-func f (interval-high x))))
692 (make-interval :low lo :high hi)))
694 ;;; Return T if X < Y. That is every number in the interval X is
695 ;;; always less than any number in the interval Y.
696 (defun interval-< (x y)
697 (declare (type interval x y))
698 ;; X < Y only if X is bounded above, Y is bounded below, and they
700 (when (and (interval-bounded-p x 'above)
701 (interval-bounded-p y 'below))
702 ;; Intervals are bounded in the appropriate way. Make sure they
704 (let ((left (interval-high x))
705 (right (interval-low y)))
706 (cond ((> (type-bound-number left)
707 (type-bound-number right))
708 ;; The intervals definitely overlap, so result is NIL.
710 ((< (type-bound-number left)
711 (type-bound-number right))
712 ;; The intervals definitely don't touch, so result is T.
715 ;; Limits are equal. Check for open or closed bounds.
716 ;; Don't overlap if one or the other are open.
717 (or (consp left) (consp right)))))))
719 ;;; Return T if X >= Y. That is, every number in the interval X is
720 ;;; always greater than any number in the interval Y.
721 (defun interval->= (x y)
722 (declare (type interval x y))
723 ;; X >= Y if lower bound of X >= upper bound of Y
724 (when (and (interval-bounded-p x 'below)
725 (interval-bounded-p y 'above))
726 (>= (type-bound-number (interval-low x))
727 (type-bound-number (interval-high y)))))
729 ;;; Return an interval that is the absolute value of X. Thus, if
730 ;;; X = [-1 10], the result is [0, 10].
731 (defun interval-abs (x)
732 (declare (type interval x))
733 (case (interval-range-info x)
739 (destructuring-bind (x- x+) (interval-split 0 x t t)
740 (interval-merge-pair (interval-neg x-) x+)))))
742 ;;; Compute the square of an interval.
743 (defun interval-sqr (x)
744 (declare (type interval x))
745 (interval-func (lambda (x) (* x x))
748 ;;;; numeric DERIVE-TYPE methods
750 ;;; a utility for defining derive-type methods of integer operations. If
751 ;;; the types of both X and Y are integer types, then we compute a new
752 ;;; integer type with bounds determined Fun when applied to X and Y.
753 ;;; Otherwise, we use NUMERIC-CONTAGION.
754 (defun derive-integer-type-aux (x y fun)
755 (declare (type function fun))
756 (if (and (numeric-type-p x) (numeric-type-p y)
757 (eq (numeric-type-class x) 'integer)
758 (eq (numeric-type-class y) 'integer)
759 (eq (numeric-type-complexp x) :real)
760 (eq (numeric-type-complexp y) :real))
761 (multiple-value-bind (low high) (funcall fun x y)
762 (make-numeric-type :class 'integer
766 (numeric-contagion x y)))
768 (defun derive-integer-type (x y fun)
769 (declare (type lvar x y) (type function fun))
770 (let ((x (lvar-type x))
772 (derive-integer-type-aux x y fun)))
774 ;;; simple utility to flatten a list
775 (defun flatten-list (x)
776 (labels ((flatten-and-append (tree list)
777 (cond ((null tree) list)
778 ((atom tree) (cons tree list))
779 (t (flatten-and-append
780 (car tree) (flatten-and-append (cdr tree) list))))))
781 (flatten-and-append x nil)))
783 ;;; Take some type of lvar and massage it so that we get a list of the
784 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
786 (defun prepare-arg-for-derive-type (arg)
787 (flet ((listify (arg)
792 (union-type-types arg))
795 (unless (eq arg *empty-type*)
796 ;; Make sure all args are some type of numeric-type. For member
797 ;; types, convert the list of members into a union of equivalent
798 ;; single-element member-type's.
799 (let ((new-args nil))
800 (dolist (arg (listify arg))
801 (if (member-type-p arg)
802 ;; Run down the list of members and convert to a list of
804 (dolist (member (member-type-members arg))
805 (push (if (numberp member)
806 (make-member-type :members (list member))
809 (push arg new-args)))
810 (unless (member *empty-type* new-args)
813 ;;; Convert from the standard type convention for which -0.0 and 0.0
814 ;;; are equal to an intermediate convention for which they are
815 ;;; considered different which is more natural for some of the
817 (defun convert-numeric-type (type)
818 (declare (type numeric-type type))
819 ;;; Only convert real float interval delimiters types.
820 (if (eq (numeric-type-complexp type) :real)
821 (let* ((lo (numeric-type-low type))
822 (lo-val (type-bound-number lo))
823 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
824 (hi (numeric-type-high type))
825 (hi-val (type-bound-number hi))
826 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
827 (if (or lo-float-zero-p hi-float-zero-p)
829 :class (numeric-type-class type)
830 :format (numeric-type-format type)
832 :low (if lo-float-zero-p
834 (list (float 0.0 lo-val))
835 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
837 :high (if hi-float-zero-p
839 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
846 ;;; Convert back from the intermediate convention for which -0.0 and
847 ;;; 0.0 are considered different to the standard type convention for
849 (defun convert-back-numeric-type (type)
850 (declare (type numeric-type type))
851 ;;; Only convert real float interval delimiters types.
852 (if (eq (numeric-type-complexp type) :real)
853 (let* ((lo (numeric-type-low type))
854 (lo-val (type-bound-number lo))
856 (and lo (floatp lo-val) (= lo-val 0.0)
857 (float-sign lo-val)))
858 (hi (numeric-type-high type))
859 (hi-val (type-bound-number hi))
861 (and hi (floatp hi-val) (= hi-val 0.0)
862 (float-sign hi-val))))
864 ;; (float +0.0 +0.0) => (member 0.0)
865 ;; (float -0.0 -0.0) => (member -0.0)
866 ((and lo-float-zero-p hi-float-zero-p)
867 ;; shouldn't have exclusive bounds here..
868 (aver (and (not (consp lo)) (not (consp hi))))
869 (if (= lo-float-zero-p hi-float-zero-p)
870 ;; (float +0.0 +0.0) => (member 0.0)
871 ;; (float -0.0 -0.0) => (member -0.0)
872 (specifier-type `(member ,lo-val))
873 ;; (float -0.0 +0.0) => (float 0.0 0.0)
874 ;; (float +0.0 -0.0) => (float 0.0 0.0)
875 (make-numeric-type :class (numeric-type-class type)
876 :format (numeric-type-format type)
882 ;; (float -0.0 x) => (float 0.0 x)
883 ((and (not (consp lo)) (minusp lo-float-zero-p))
884 (make-numeric-type :class (numeric-type-class type)
885 :format (numeric-type-format type)
887 :low (float 0.0 lo-val)
889 ;; (float (+0.0) x) => (float (0.0) x)
890 ((and (consp lo) (plusp lo-float-zero-p))
891 (make-numeric-type :class (numeric-type-class type)
892 :format (numeric-type-format type)
894 :low (list (float 0.0 lo-val))
897 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
898 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
899 (list (make-member-type :members (list (float 0.0 lo-val)))
900 (make-numeric-type :class (numeric-type-class type)
901 :format (numeric-type-format type)
903 :low (list (float 0.0 lo-val))
907 ;; (float x +0.0) => (float x 0.0)
908 ((and (not (consp hi)) (plusp hi-float-zero-p))
909 (make-numeric-type :class (numeric-type-class type)
910 :format (numeric-type-format type)
913 :high (float 0.0 hi-val)))
914 ;; (float x (-0.0)) => (float x (0.0))
915 ((and (consp hi) (minusp hi-float-zero-p))
916 (make-numeric-type :class (numeric-type-class type)
917 :format (numeric-type-format type)
920 :high (list (float 0.0 hi-val))))
922 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
923 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
924 (list (make-member-type :members (list (float -0.0 hi-val)))
925 (make-numeric-type :class (numeric-type-class type)
926 :format (numeric-type-format type)
929 :high (list (float 0.0 hi-val)))))))
935 ;;; Convert back a possible list of numeric types.
936 (defun convert-back-numeric-type-list (type-list)
940 (dolist (type type-list)
941 (if (numeric-type-p type)
942 (let ((result (convert-back-numeric-type type)))
944 (setf results (append results result))
945 (push result results)))
946 (push type results)))
949 (convert-back-numeric-type type-list))
951 (convert-back-numeric-type-list (union-type-types type-list)))
955 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
956 ;;; belong in the kernel's type logic, invoked always, instead of in
957 ;;; the compiler, invoked only during some type optimizations. (In
958 ;;; fact, as of 0.pre8.100 or so they probably are, under
959 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
961 ;;; Take a list of types and return a canonical type specifier,
962 ;;; combining any MEMBER types together. If both positive and negative
963 ;;; MEMBER types are present they are converted to a float type.
964 ;;; XXX This would be far simpler if the type-union methods could handle
965 ;;; member/number unions.
966 (defun make-canonical-union-type (type-list)
969 (dolist (type type-list)
970 (if (member-type-p type)
971 (setf members (union members (member-type-members type)))
972 (push type misc-types)))
974 (when (null (set-difference `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0) members))
975 (push (specifier-type '(long-float 0.0l0 0.0l0)) misc-types)
976 (setf members (set-difference members `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0))))
977 (when (null (set-difference `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0) members))
978 (push (specifier-type '(double-float 0.0d0 0.0d0)) misc-types)
979 (setf members (set-difference members `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0))))
980 (when (null (set-difference `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0) members))
981 (push (specifier-type '(single-float 0.0f0 0.0f0)) misc-types)
982 (setf members (set-difference members `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0))))
984 (apply #'type-union (make-member-type :members members) misc-types)
985 (apply #'type-union misc-types))))
987 ;;; Convert a member type with a single member to a numeric type.
988 (defun convert-member-type (arg)
989 (let* ((members (member-type-members arg))
990 (member (first members))
991 (member-type (type-of member)))
992 (aver (not (rest members)))
993 (specifier-type (cond ((typep member 'integer)
994 `(integer ,member ,member))
995 ((memq member-type '(short-float single-float
996 double-float long-float))
997 `(,member-type ,member ,member))
1001 ;;; This is used in defoptimizers for computing the resulting type of
1004 ;;; Given the lvar ARG, derive the resulting type using the
1005 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1006 ;;; "atomic" lvar type like numeric-type or member-type (containing
1007 ;;; just one element). It should return the resulting type, which can
1008 ;;; be a list of types.
1010 ;;; For the case of member types, if a MEMBER-FUN is given it is
1011 ;;; called to compute the result otherwise the member type is first
1012 ;;; converted to a numeric type and the DERIVE-FUN is called.
1013 (defun one-arg-derive-type (arg derive-fun member-fun
1014 &optional (convert-type t))
1015 (declare (type function derive-fun)
1016 (type (or null function) member-fun))
1017 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1023 (with-float-traps-masked
1024 (:underflow :overflow :divide-by-zero)
1026 `(eql ,(funcall member-fun
1027 (first (member-type-members x))))))
1028 ;; Otherwise convert to a numeric type.
1029 (let ((result-type-list
1030 (funcall derive-fun (convert-member-type x))))
1032 (convert-back-numeric-type-list result-type-list)
1033 result-type-list))))
1036 (convert-back-numeric-type-list
1037 (funcall derive-fun (convert-numeric-type x)))
1038 (funcall derive-fun x)))
1040 *universal-type*))))
1041 ;; Run down the list of args and derive the type of each one,
1042 ;; saving all of the results in a list.
1043 (let ((results nil))
1044 (dolist (arg arg-list)
1045 (let ((result (deriver arg)))
1047 (setf results (append results result))
1048 (push result results))))
1050 (make-canonical-union-type results)
1051 (first results)))))))
1053 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1054 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1055 ;;; original args and a third which is T to indicate if the two args
1056 ;;; really represent the same lvar. This is useful for deriving the
1057 ;;; type of things like (* x x), which should always be positive. If
1058 ;;; we didn't do this, we wouldn't be able to tell.
1059 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1060 &optional (convert-type t))
1061 (declare (type function derive-fun fun))
1062 (flet ((deriver (x y same-arg)
1063 (cond ((and (member-type-p x) (member-type-p y))
1064 (let* ((x (first (member-type-members x)))
1065 (y (first (member-type-members y)))
1066 (result (ignore-errors
1067 (with-float-traps-masked
1068 (:underflow :overflow :divide-by-zero
1070 (funcall fun x y)))))
1071 (cond ((null result) *empty-type*)
1072 ((and (floatp result) (float-nan-p result))
1073 (make-numeric-type :class 'float
1074 :format (type-of result)
1077 (specifier-type `(eql ,result))))))
1078 ((and (member-type-p x) (numeric-type-p y))
1079 (let* ((x (convert-member-type x))
1080 (y (if convert-type (convert-numeric-type y) y))
1081 (result (funcall derive-fun x y same-arg)))
1083 (convert-back-numeric-type-list result)
1085 ((and (numeric-type-p x) (member-type-p y))
1086 (let* ((x (if convert-type (convert-numeric-type x) x))
1087 (y (convert-member-type y))
1088 (result (funcall derive-fun x y same-arg)))
1090 (convert-back-numeric-type-list result)
1092 ((and (numeric-type-p x) (numeric-type-p y))
1093 (let* ((x (if convert-type (convert-numeric-type x) x))
1094 (y (if convert-type (convert-numeric-type y) y))
1095 (result (funcall derive-fun x y same-arg)))
1097 (convert-back-numeric-type-list result)
1100 *universal-type*))))
1101 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1102 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1103 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1105 (let ((results nil))
1107 ;; Since the args are the same LVARs, just run down the
1110 (let ((result (deriver x x same-arg)))
1112 (setf results (append results result))
1113 (push result results))))
1114 ;; Try all pairwise combinations.
1117 (let ((result (or (deriver x y same-arg)
1118 (numeric-contagion x y))))
1120 (setf results (append results result))
1121 (push result results))))))
1123 (make-canonical-union-type results)
1124 (first results)))))))
1126 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1128 (defoptimizer (+ derive-type) ((x y))
1129 (derive-integer-type
1136 (values (frob (numeric-type-low x) (numeric-type-low y))
1137 (frob (numeric-type-high x) (numeric-type-high y)))))))
1139 (defoptimizer (- derive-type) ((x y))
1140 (derive-integer-type
1147 (values (frob (numeric-type-low x) (numeric-type-high y))
1148 (frob (numeric-type-high x) (numeric-type-low y)))))))
1150 (defoptimizer (* derive-type) ((x y))
1151 (derive-integer-type
1154 (let ((x-low (numeric-type-low x))
1155 (x-high (numeric-type-high x))
1156 (y-low (numeric-type-low y))
1157 (y-high (numeric-type-high y)))
1158 (cond ((not (and x-low y-low))
1160 ((or (minusp x-low) (minusp y-low))
1161 (if (and x-high y-high)
1162 (let ((max (* (max (abs x-low) (abs x-high))
1163 (max (abs y-low) (abs y-high)))))
1164 (values (- max) max))
1167 (values (* x-low y-low)
1168 (if (and x-high y-high)
1172 (defoptimizer (/ derive-type) ((x y))
1173 (numeric-contagion (lvar-type x) (lvar-type y)))
1177 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1179 (defun +-derive-type-aux (x y same-arg)
1180 (if (and (numeric-type-real-p x)
1181 (numeric-type-real-p y))
1184 (let ((x-int (numeric-type->interval x)))
1185 (interval-add x-int x-int))
1186 (interval-add (numeric-type->interval x)
1187 (numeric-type->interval y))))
1188 (result-type (numeric-contagion x y)))
1189 ;; If the result type is a float, we need to be sure to coerce
1190 ;; the bounds into the correct type.
1191 (when (eq (numeric-type-class result-type) 'float)
1192 (setf result (interval-func
1194 (coerce x (or (numeric-type-format result-type)
1198 :class (if (and (eq (numeric-type-class x) 'integer)
1199 (eq (numeric-type-class y) 'integer))
1200 ;; The sum of integers is always an integer.
1202 (numeric-type-class result-type))
1203 :format (numeric-type-format result-type)
1204 :low (interval-low result)
1205 :high (interval-high result)))
1206 ;; general contagion
1207 (numeric-contagion x y)))
1209 (defoptimizer (+ derive-type) ((x y))
1210 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1212 (defun --derive-type-aux (x y same-arg)
1213 (if (and (numeric-type-real-p x)
1214 (numeric-type-real-p y))
1216 ;; (- X X) is always 0.
1218 (make-interval :low 0 :high 0)
1219 (interval-sub (numeric-type->interval x)
1220 (numeric-type->interval y))))
1221 (result-type (numeric-contagion x y)))
1222 ;; If the result type is a float, we need to be sure to coerce
1223 ;; the bounds into the correct type.
1224 (when (eq (numeric-type-class result-type) 'float)
1225 (setf result (interval-func
1227 (coerce x (or (numeric-type-format result-type)
1231 :class (if (and (eq (numeric-type-class x) 'integer)
1232 (eq (numeric-type-class y) 'integer))
1233 ;; The difference of integers is always an integer.
1235 (numeric-type-class result-type))
1236 :format (numeric-type-format result-type)
1237 :low (interval-low result)
1238 :high (interval-high result)))
1239 ;; general contagion
1240 (numeric-contagion x y)))
1242 (defoptimizer (- derive-type) ((x y))
1243 (two-arg-derive-type x y #'--derive-type-aux #'-))
1245 (defun *-derive-type-aux (x y same-arg)
1246 (if (and (numeric-type-real-p x)
1247 (numeric-type-real-p y))
1249 ;; (* X X) is always positive, so take care to do it right.
1251 (interval-sqr (numeric-type->interval x))
1252 (interval-mul (numeric-type->interval x)
1253 (numeric-type->interval y))))
1254 (result-type (numeric-contagion x y)))
1255 ;; If the result type is a float, we need to be sure to coerce
1256 ;; the bounds into the correct type.
1257 (when (eq (numeric-type-class result-type) 'float)
1258 (setf result (interval-func
1260 (coerce x (or (numeric-type-format result-type)
1264 :class (if (and (eq (numeric-type-class x) 'integer)
1265 (eq (numeric-type-class y) 'integer))
1266 ;; The product of integers is always an integer.
1268 (numeric-type-class result-type))
1269 :format (numeric-type-format result-type)
1270 :low (interval-low result)
1271 :high (interval-high result)))
1272 (numeric-contagion x y)))
1274 (defoptimizer (* derive-type) ((x y))
1275 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1277 (defun /-derive-type-aux (x y same-arg)
1278 (if (and (numeric-type-real-p x)
1279 (numeric-type-real-p y))
1281 ;; (/ X X) is always 1, except if X can contain 0. In
1282 ;; that case, we shouldn't optimize the division away
1283 ;; because we want 0/0 to signal an error.
1285 (not (interval-contains-p
1286 0 (interval-closure (numeric-type->interval y)))))
1287 (make-interval :low 1 :high 1)
1288 (interval-div (numeric-type->interval x)
1289 (numeric-type->interval y))))
1290 (result-type (numeric-contagion x y)))
1291 ;; If the result type is a float, we need to be sure to coerce
1292 ;; the bounds into the correct type.
1293 (when (eq (numeric-type-class result-type) 'float)
1294 (setf result (interval-func
1296 (coerce x (or (numeric-type-format result-type)
1299 (make-numeric-type :class (numeric-type-class result-type)
1300 :format (numeric-type-format result-type)
1301 :low (interval-low result)
1302 :high (interval-high result)))
1303 (numeric-contagion x y)))
1305 (defoptimizer (/ derive-type) ((x y))
1306 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1310 (defun ash-derive-type-aux (n-type shift same-arg)
1311 (declare (ignore same-arg))
1312 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1313 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1314 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1315 ;; two bignums yielding zero) and it's hard to avoid that
1316 ;; calculation in here.
1317 #+(and cmu sb-xc-host)
1318 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1319 (typep (numeric-type-high n-type) 'bignum))
1320 (or (typep (numeric-type-low shift) 'bignum)
1321 (typep (numeric-type-high shift) 'bignum)))
1322 (return-from ash-derive-type-aux *universal-type*))
1323 (flet ((ash-outer (n s)
1324 (when (and (fixnump s)
1326 (> s sb!xc:most-negative-fixnum))
1328 ;; KLUDGE: The bare 64's here should be related to
1329 ;; symbolic machine word size values somehow.
1332 (if (and (fixnump s)
1333 (> s sb!xc:most-negative-fixnum))
1335 (if (minusp n) -1 0))))
1336 (or (and (csubtypep n-type (specifier-type 'integer))
1337 (csubtypep shift (specifier-type 'integer))
1338 (let ((n-low (numeric-type-low n-type))
1339 (n-high (numeric-type-high n-type))
1340 (s-low (numeric-type-low shift))
1341 (s-high (numeric-type-high shift)))
1342 (make-numeric-type :class 'integer :complexp :real
1345 (ash-outer n-low s-high)
1346 (ash-inner n-low s-low)))
1349 (ash-inner n-high s-low)
1350 (ash-outer n-high s-high))))))
1353 (defoptimizer (ash derive-type) ((n shift))
1354 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1356 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1357 (macrolet ((frob (fun)
1358 `#'(lambda (type type2)
1359 (declare (ignore type2))
1360 (let ((lo (numeric-type-low type))
1361 (hi (numeric-type-high type)))
1362 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1364 (defoptimizer (%negate derive-type) ((num))
1365 (derive-integer-type num num (frob -))))
1367 (defun lognot-derive-type-aux (int)
1368 (derive-integer-type-aux int int
1369 (lambda (type type2)
1370 (declare (ignore type2))
1371 (let ((lo (numeric-type-low type))
1372 (hi (numeric-type-high type)))
1373 (values (if hi (lognot hi) nil)
1374 (if lo (lognot lo) nil)
1375 (numeric-type-class type)
1376 (numeric-type-format type))))))
1378 (defoptimizer (lognot derive-type) ((int))
1379 (lognot-derive-type-aux (lvar-type int)))
1381 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1382 (defoptimizer (%negate derive-type) ((num))
1383 (flet ((negate-bound (b)
1385 (set-bound (- (type-bound-number b))
1387 (one-arg-derive-type num
1389 (modified-numeric-type
1391 :low (negate-bound (numeric-type-high type))
1392 :high (negate-bound (numeric-type-low type))))
1395 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1396 (defoptimizer (abs derive-type) ((num))
1397 (let ((type (lvar-type num)))
1398 (if (and (numeric-type-p type)
1399 (eq (numeric-type-class type) 'integer)
1400 (eq (numeric-type-complexp type) :real))
1401 (let ((lo (numeric-type-low type))
1402 (hi (numeric-type-high type)))
1403 (make-numeric-type :class 'integer :complexp :real
1404 :low (cond ((and hi (minusp hi))
1410 :high (if (and hi lo)
1411 (max (abs hi) (abs lo))
1413 (numeric-contagion type type))))
1415 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1416 (defun abs-derive-type-aux (type)
1417 (cond ((eq (numeric-type-complexp type) :complex)
1418 ;; The absolute value of a complex number is always a
1419 ;; non-negative float.
1420 (let* ((format (case (numeric-type-class type)
1421 ((integer rational) 'single-float)
1422 (t (numeric-type-format type))))
1423 (bound-format (or format 'float)))
1424 (make-numeric-type :class 'float
1427 :low (coerce 0 bound-format)
1430 ;; The absolute value of a real number is a non-negative real
1431 ;; of the same type.
1432 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1433 (class (numeric-type-class type))
1434 (format (numeric-type-format type))
1435 (bound-type (or format class 'real)))
1440 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1441 :high (coerce-numeric-bound
1442 (interval-high abs-bnd) bound-type))))))
1444 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1445 (defoptimizer (abs derive-type) ((num))
1446 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1448 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1449 (defoptimizer (truncate derive-type) ((number divisor))
1450 (let ((number-type (lvar-type number))
1451 (divisor-type (lvar-type divisor))
1452 (integer-type (specifier-type 'integer)))
1453 (if (and (numeric-type-p number-type)
1454 (csubtypep number-type integer-type)
1455 (numeric-type-p divisor-type)
1456 (csubtypep divisor-type integer-type))
1457 (let ((number-low (numeric-type-low number-type))
1458 (number-high (numeric-type-high number-type))
1459 (divisor-low (numeric-type-low divisor-type))
1460 (divisor-high (numeric-type-high divisor-type)))
1461 (values-specifier-type
1462 `(values ,(integer-truncate-derive-type number-low number-high
1463 divisor-low divisor-high)
1464 ,(integer-rem-derive-type number-low number-high
1465 divisor-low divisor-high))))
1468 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1471 (defun rem-result-type (number-type divisor-type)
1472 ;; Figure out what the remainder type is. The remainder is an
1473 ;; integer if both args are integers; a rational if both args are
1474 ;; rational; and a float otherwise.
1475 (cond ((and (csubtypep number-type (specifier-type 'integer))
1476 (csubtypep divisor-type (specifier-type 'integer)))
1478 ((and (csubtypep number-type (specifier-type 'rational))
1479 (csubtypep divisor-type (specifier-type 'rational)))
1481 ((and (csubtypep number-type (specifier-type 'float))
1482 (csubtypep divisor-type (specifier-type 'float)))
1483 ;; Both are floats so the result is also a float, of
1484 ;; the largest type.
1485 (or (float-format-max (numeric-type-format number-type)
1486 (numeric-type-format divisor-type))
1488 ((and (csubtypep number-type (specifier-type 'float))
1489 (csubtypep divisor-type (specifier-type 'rational)))
1490 ;; One of the arguments is a float and the other is a
1491 ;; rational. The remainder is a float of the same
1493 (or (numeric-type-format number-type) 'float))
1494 ((and (csubtypep divisor-type (specifier-type 'float))
1495 (csubtypep number-type (specifier-type 'rational)))
1496 ;; One of the arguments is a float and the other is a
1497 ;; rational. The remainder is a float of the same
1499 (or (numeric-type-format divisor-type) 'float))
1501 ;; Some unhandled combination. This usually means both args
1502 ;; are REAL so the result is a REAL.
1505 (defun truncate-derive-type-quot (number-type divisor-type)
1506 (let* ((rem-type (rem-result-type number-type divisor-type))
1507 (number-interval (numeric-type->interval number-type))
1508 (divisor-interval (numeric-type->interval divisor-type)))
1509 ;;(declare (type (member '(integer rational float)) rem-type))
1510 ;; We have real numbers now.
1511 (cond ((eq rem-type 'integer)
1512 ;; Since the remainder type is INTEGER, both args are
1514 (let* ((res (integer-truncate-derive-type
1515 (interval-low number-interval)
1516 (interval-high number-interval)
1517 (interval-low divisor-interval)
1518 (interval-high divisor-interval))))
1519 (specifier-type (if (listp res) res 'integer))))
1521 (let ((quot (truncate-quotient-bound
1522 (interval-div number-interval
1523 divisor-interval))))
1524 (specifier-type `(integer ,(or (interval-low quot) '*)
1525 ,(or (interval-high quot) '*))))))))
1527 (defun truncate-derive-type-rem (number-type divisor-type)
1528 (let* ((rem-type (rem-result-type number-type divisor-type))
1529 (number-interval (numeric-type->interval number-type))
1530 (divisor-interval (numeric-type->interval divisor-type))
1531 (rem (truncate-rem-bound number-interval divisor-interval)))
1532 ;;(declare (type (member '(integer rational float)) rem-type))
1533 ;; We have real numbers now.
1534 (cond ((eq rem-type 'integer)
1535 ;; Since the remainder type is INTEGER, both args are
1537 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1538 ,(or (interval-high rem) '*))))
1540 (multiple-value-bind (class format)
1543 (values 'integer nil))
1545 (values 'rational nil))
1546 ((or single-float double-float #!+long-float long-float)
1547 (values 'float rem-type))
1549 (values 'float nil))
1552 (when (member rem-type '(float single-float double-float
1553 #!+long-float long-float))
1554 (setf rem (interval-func #'(lambda (x)
1555 (coerce x rem-type))
1557 (make-numeric-type :class class
1559 :low (interval-low rem)
1560 :high (interval-high rem)))))))
1562 (defun truncate-derive-type-quot-aux (num div same-arg)
1563 (declare (ignore same-arg))
1564 (if (and (numeric-type-real-p num)
1565 (numeric-type-real-p div))
1566 (truncate-derive-type-quot num div)
1569 (defun truncate-derive-type-rem-aux (num div same-arg)
1570 (declare (ignore same-arg))
1571 (if (and (numeric-type-real-p num)
1572 (numeric-type-real-p div))
1573 (truncate-derive-type-rem num div)
1576 (defoptimizer (truncate derive-type) ((number divisor))
1577 (let ((quot (two-arg-derive-type number divisor
1578 #'truncate-derive-type-quot-aux #'truncate))
1579 (rem (two-arg-derive-type number divisor
1580 #'truncate-derive-type-rem-aux #'rem)))
1581 (when (and quot rem)
1582 (make-values-type :required (list quot rem)))))
1584 (defun ftruncate-derive-type-quot (number-type divisor-type)
1585 ;; The bounds are the same as for truncate. However, the first
1586 ;; result is a float of some type. We need to determine what that
1587 ;; type is. Basically it's the more contagious of the two types.
1588 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1589 (res-type (numeric-contagion number-type divisor-type)))
1590 (make-numeric-type :class 'float
1591 :format (numeric-type-format res-type)
1592 :low (numeric-type-low q-type)
1593 :high (numeric-type-high q-type))))
1595 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1596 (declare (ignore same-arg))
1597 (if (and (numeric-type-real-p n)
1598 (numeric-type-real-p d))
1599 (ftruncate-derive-type-quot n d)
1602 (defoptimizer (ftruncate derive-type) ((number divisor))
1604 (two-arg-derive-type number divisor
1605 #'ftruncate-derive-type-quot-aux #'ftruncate))
1606 (rem (two-arg-derive-type number divisor
1607 #'truncate-derive-type-rem-aux #'rem)))
1608 (when (and quot rem)
1609 (make-values-type :required (list quot rem)))))
1611 (defun %unary-truncate-derive-type-aux (number)
1612 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1614 (defoptimizer (%unary-truncate derive-type) ((number))
1615 (one-arg-derive-type number
1616 #'%unary-truncate-derive-type-aux
1619 ;;; Define optimizers for FLOOR and CEILING.
1621 ((def (name q-name r-name)
1622 (let ((q-aux (symbolicate q-name "-AUX"))
1623 (r-aux (symbolicate r-name "-AUX")))
1625 ;; Compute type of quotient (first) result.
1626 (defun ,q-aux (number-type divisor-type)
1627 (let* ((number-interval
1628 (numeric-type->interval number-type))
1630 (numeric-type->interval divisor-type))
1631 (quot (,q-name (interval-div number-interval
1632 divisor-interval))))
1633 (specifier-type `(integer ,(or (interval-low quot) '*)
1634 ,(or (interval-high quot) '*)))))
1635 ;; Compute type of remainder.
1636 (defun ,r-aux (number-type divisor-type)
1637 (let* ((divisor-interval
1638 (numeric-type->interval divisor-type))
1639 (rem (,r-name divisor-interval))
1640 (result-type (rem-result-type number-type divisor-type)))
1641 (multiple-value-bind (class format)
1644 (values 'integer nil))
1646 (values 'rational nil))
1647 ((or single-float double-float #!+long-float long-float)
1648 (values 'float result-type))
1650 (values 'float nil))
1653 (when (member result-type '(float single-float double-float
1654 #!+long-float long-float))
1655 ;; Make sure that the limits on the interval have
1657 (setf rem (interval-func (lambda (x)
1658 (coerce x result-type))
1660 (make-numeric-type :class class
1662 :low (interval-low rem)
1663 :high (interval-high rem)))))
1664 ;; the optimizer itself
1665 (defoptimizer (,name derive-type) ((number divisor))
1666 (flet ((derive-q (n d same-arg)
1667 (declare (ignore same-arg))
1668 (if (and (numeric-type-real-p n)
1669 (numeric-type-real-p d))
1672 (derive-r (n d same-arg)
1673 (declare (ignore same-arg))
1674 (if (and (numeric-type-real-p n)
1675 (numeric-type-real-p d))
1678 (let ((quot (two-arg-derive-type
1679 number divisor #'derive-q #',name))
1680 (rem (two-arg-derive-type
1681 number divisor #'derive-r #'mod)))
1682 (when (and quot rem)
1683 (make-values-type :required (list quot rem))))))))))
1685 (def floor floor-quotient-bound floor-rem-bound)
1686 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1688 ;;; Define optimizers for FFLOOR and FCEILING
1689 (macrolet ((def (name q-name r-name)
1690 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1691 (r-aux (symbolicate r-name "-AUX")))
1693 ;; Compute type of quotient (first) result.
1694 (defun ,q-aux (number-type divisor-type)
1695 (let* ((number-interval
1696 (numeric-type->interval number-type))
1698 (numeric-type->interval divisor-type))
1699 (quot (,q-name (interval-div number-interval
1701 (res-type (numeric-contagion number-type
1704 :class (numeric-type-class res-type)
1705 :format (numeric-type-format res-type)
1706 :low (interval-low quot)
1707 :high (interval-high quot))))
1709 (defoptimizer (,name derive-type) ((number divisor))
1710 (flet ((derive-q (n d same-arg)
1711 (declare (ignore same-arg))
1712 (if (and (numeric-type-real-p n)
1713 (numeric-type-real-p d))
1716 (derive-r (n d same-arg)
1717 (declare (ignore same-arg))
1718 (if (and (numeric-type-real-p n)
1719 (numeric-type-real-p d))
1722 (let ((quot (two-arg-derive-type
1723 number divisor #'derive-q #',name))
1724 (rem (two-arg-derive-type
1725 number divisor #'derive-r #'mod)))
1726 (when (and quot rem)
1727 (make-values-type :required (list quot rem))))))))))
1729 (def ffloor floor-quotient-bound floor-rem-bound)
1730 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
1732 ;;; functions to compute the bounds on the quotient and remainder for
1733 ;;; the FLOOR function
1734 (defun floor-quotient-bound (quot)
1735 ;; Take the floor of the quotient and then massage it into what we
1737 (let ((lo (interval-low quot))
1738 (hi (interval-high quot)))
1739 ;; Take the floor of the lower bound. The result is always a
1740 ;; closed lower bound.
1742 (floor (type-bound-number lo))
1744 ;; For the upper bound, we need to be careful.
1747 ;; An open bound. We need to be careful here because
1748 ;; the floor of '(10.0) is 9, but the floor of
1750 (multiple-value-bind (q r) (floor (first hi))
1755 ;; A closed bound, so the answer is obvious.
1759 (make-interval :low lo :high hi)))
1760 (defun floor-rem-bound (div)
1761 ;; The remainder depends only on the divisor. Try to get the
1762 ;; correct sign for the remainder if we can.
1763 (case (interval-range-info div)
1765 ;; The divisor is always positive.
1766 (let ((rem (interval-abs div)))
1767 (setf (interval-low rem) 0)
1768 (when (and (numberp (interval-high rem))
1769 (not (zerop (interval-high rem))))
1770 ;; The remainder never contains the upper bound. However,
1771 ;; watch out for the case where the high limit is zero!
1772 (setf (interval-high rem) (list (interval-high rem))))
1775 ;; The divisor is always negative.
1776 (let ((rem (interval-neg (interval-abs div))))
1777 (setf (interval-high rem) 0)
1778 (when (numberp (interval-low rem))
1779 ;; The remainder never contains the lower bound.
1780 (setf (interval-low rem) (list (interval-low rem))))
1783 ;; The divisor can be positive or negative. All bets off. The
1784 ;; magnitude of remainder is the maximum value of the divisor.
1785 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1786 ;; The bound never reaches the limit, so make the interval open.
1787 (make-interval :low (if limit
1790 :high (list limit))))))
1792 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1793 => #S(INTERVAL :LOW 0 :HIGH 10)
1794 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1795 => #S(INTERVAL :LOW 0 :HIGH 10)
1796 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1797 => #S(INTERVAL :LOW 0 :HIGH 10)
1798 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1799 => #S(INTERVAL :LOW 0 :HIGH 9)
1800 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1801 => #S(INTERVAL :LOW 0 :HIGH 10)
1802 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1803 => #S(INTERVAL :LOW 0 :HIGH 10)
1804 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1805 => #S(INTERVAL :LOW -2 :HIGH 10)
1806 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1807 => #S(INTERVAL :LOW -1 :HIGH 10)
1808 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1809 => #S(INTERVAL :LOW -1 :HIGH 10)
1811 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1812 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1813 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1814 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1815 (floor-rem-bound (make-interval :low -10 :high -2.3))
1816 #S(INTERVAL :LOW (-10) :HIGH 0)
1817 (floor-rem-bound (make-interval :low 0.3 :high 10))
1818 => #S(INTERVAL :LOW 0 :HIGH '(10))
1819 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1820 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1821 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1822 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1825 ;;; same functions for CEILING
1826 (defun ceiling-quotient-bound (quot)
1827 ;; Take the ceiling of the quotient and then massage it into what we
1829 (let ((lo (interval-low quot))
1830 (hi (interval-high quot)))
1831 ;; Take the ceiling of the upper bound. The result is always a
1832 ;; closed upper bound.
1834 (ceiling (type-bound-number hi))
1836 ;; For the lower bound, we need to be careful.
1839 ;; An open bound. We need to be careful here because
1840 ;; the ceiling of '(10.0) is 11, but the ceiling of
1842 (multiple-value-bind (q r) (ceiling (first lo))
1847 ;; A closed bound, so the answer is obvious.
1851 (make-interval :low lo :high hi)))
1852 (defun ceiling-rem-bound (div)
1853 ;; The remainder depends only on the divisor. Try to get the
1854 ;; correct sign for the remainder if we can.
1855 (case (interval-range-info div)
1857 ;; Divisor is always positive. The remainder is negative.
1858 (let ((rem (interval-neg (interval-abs div))))
1859 (setf (interval-high rem) 0)
1860 (when (and (numberp (interval-low rem))
1861 (not (zerop (interval-low rem))))
1862 ;; The remainder never contains the upper bound. However,
1863 ;; watch out for the case when the upper bound is zero!
1864 (setf (interval-low rem) (list (interval-low rem))))
1867 ;; Divisor is always negative. The remainder is positive
1868 (let ((rem (interval-abs div)))
1869 (setf (interval-low rem) 0)
1870 (when (numberp (interval-high rem))
1871 ;; The remainder never contains the lower bound.
1872 (setf (interval-high rem) (list (interval-high rem))))
1875 ;; The divisor can be positive or negative. All bets off. The
1876 ;; magnitude of remainder is the maximum value of the divisor.
1877 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1878 ;; The bound never reaches the limit, so make the interval open.
1879 (make-interval :low (if limit
1882 :high (list limit))))))
1885 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
1886 => #S(INTERVAL :LOW 1 :HIGH 11)
1887 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1888 => #S(INTERVAL :LOW 1 :HIGH 11)
1889 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
1890 => #S(INTERVAL :LOW 1 :HIGH 10)
1891 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
1892 => #S(INTERVAL :LOW 1 :HIGH 10)
1893 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
1894 => #S(INTERVAL :LOW 1 :HIGH 11)
1895 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
1896 => #S(INTERVAL :LOW 1 :HIGH 11)
1897 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1898 => #S(INTERVAL :LOW -1 :HIGH 11)
1899 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1900 => #S(INTERVAL :LOW 0 :HIGH 11)
1901 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
1902 => #S(INTERVAL :LOW -1 :HIGH 11)
1904 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
1905 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
1906 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
1907 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1908 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
1909 => #S(INTERVAL :LOW 0 :HIGH (10))
1910 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
1911 => #S(INTERVAL :LOW (-10) :HIGH 0)
1912 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
1913 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
1914 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
1915 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1918 (defun truncate-quotient-bound (quot)
1919 ;; For positive quotients, truncate is exactly like floor. For
1920 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
1921 ;; it's the union of the two pieces.
1922 (case (interval-range-info quot)
1925 (floor-quotient-bound quot))
1927 ;; just like CEILING
1928 (ceiling-quotient-bound quot))
1930 ;; Split the interval into positive and negative pieces, compute
1931 ;; the result for each piece and put them back together.
1932 (destructuring-bind (neg pos) (interval-split 0 quot t t)
1933 (interval-merge-pair (ceiling-quotient-bound neg)
1934 (floor-quotient-bound pos))))))
1936 (defun truncate-rem-bound (num div)
1937 ;; This is significantly more complicated than FLOOR or CEILING. We
1938 ;; need both the number and the divisor to determine the range. The
1939 ;; basic idea is to split the ranges of NUM and DEN into positive
1940 ;; and negative pieces and deal with each of the four possibilities
1942 (case (interval-range-info num)
1944 (case (interval-range-info div)
1946 (floor-rem-bound div))
1948 (ceiling-rem-bound div))
1950 (destructuring-bind (neg pos) (interval-split 0 div t t)
1951 (interval-merge-pair (truncate-rem-bound num neg)
1952 (truncate-rem-bound num pos))))))
1954 (case (interval-range-info div)
1956 (ceiling-rem-bound div))
1958 (floor-rem-bound div))
1960 (destructuring-bind (neg pos) (interval-split 0 div t t)
1961 (interval-merge-pair (truncate-rem-bound num neg)
1962 (truncate-rem-bound num pos))))))
1964 (destructuring-bind (neg pos) (interval-split 0 num t t)
1965 (interval-merge-pair (truncate-rem-bound neg div)
1966 (truncate-rem-bound pos div))))))
1969 ;;; Derive useful information about the range. Returns three values:
1970 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
1971 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
1972 ;;; - The abs of the maximal value if there is one, or nil if it is
1974 (defun numeric-range-info (low high)
1975 (cond ((and low (not (minusp low)))
1976 (values '+ low high))
1977 ((and high (not (plusp high)))
1978 (values '- (- high) (if low (- low) nil)))
1980 (values nil 0 (and low high (max (- low) high))))))
1982 (defun integer-truncate-derive-type
1983 (number-low number-high divisor-low divisor-high)
1984 ;; The result cannot be larger in magnitude than the number, but the
1985 ;; sign might change. If we can determine the sign of either the
1986 ;; number or the divisor, we can eliminate some of the cases.
1987 (multiple-value-bind (number-sign number-min number-max)
1988 (numeric-range-info number-low number-high)
1989 (multiple-value-bind (divisor-sign divisor-min divisor-max)
1990 (numeric-range-info divisor-low divisor-high)
1991 (when (and divisor-max (zerop divisor-max))
1992 ;; We've got a problem: guaranteed division by zero.
1993 (return-from integer-truncate-derive-type t))
1994 (when (zerop divisor-min)
1995 ;; We'll assume that they aren't going to divide by zero.
1997 (cond ((and number-sign divisor-sign)
1998 ;; We know the sign of both.
1999 (if (eq number-sign divisor-sign)
2000 ;; Same sign, so the result will be positive.
2001 `(integer ,(if divisor-max
2002 (truncate number-min divisor-max)
2005 (truncate number-max divisor-min)
2007 ;; Different signs, the result will be negative.
2008 `(integer ,(if number-max
2009 (- (truncate number-max divisor-min))
2012 (- (truncate number-min divisor-max))
2014 ((eq divisor-sign '+)
2015 ;; The divisor is positive. Therefore, the number will just
2016 ;; become closer to zero.
2017 `(integer ,(if number-low
2018 (truncate number-low divisor-min)
2021 (truncate number-high divisor-min)
2023 ((eq divisor-sign '-)
2024 ;; The divisor is negative. Therefore, the absolute value of
2025 ;; the number will become closer to zero, but the sign will also
2027 `(integer ,(if number-high
2028 (- (truncate number-high divisor-min))
2031 (- (truncate number-low divisor-min))
2033 ;; The divisor could be either positive or negative.
2035 ;; The number we are dividing has a bound. Divide that by the
2036 ;; smallest posible divisor.
2037 (let ((bound (truncate number-max divisor-min)))
2038 `(integer ,(- bound) ,bound)))
2040 ;; The number we are dividing is unbounded, so we can't tell
2041 ;; anything about the result.
2044 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2045 (defun integer-rem-derive-type
2046 (number-low number-high divisor-low divisor-high)
2047 (if (and divisor-low divisor-high)
2048 ;; We know the range of the divisor, and the remainder must be
2049 ;; smaller than the divisor. We can tell the sign of the
2050 ;; remainer if we know the sign of the number.
2051 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2052 `(integer ,(if (or (null number-low)
2053 (minusp number-low))
2056 ,(if (or (null number-high)
2057 (plusp number-high))
2060 ;; The divisor is potentially either very positive or very
2061 ;; negative. Therefore, the remainer is unbounded, but we might
2062 ;; be able to tell something about the sign from the number.
2063 `(integer ,(if (and number-low (not (minusp number-low)))
2064 ;; The number we are dividing is positive.
2065 ;; Therefore, the remainder must be positive.
2068 ,(if (and number-high (not (plusp number-high)))
2069 ;; The number we are dividing is negative.
2070 ;; Therefore, the remainder must be negative.
2074 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2075 (defoptimizer (random derive-type) ((bound &optional state))
2076 (let ((type (lvar-type bound)))
2077 (when (numeric-type-p type)
2078 (let ((class (numeric-type-class type))
2079 (high (numeric-type-high type))
2080 (format (numeric-type-format type)))
2084 :low (coerce 0 (or format class 'real))
2085 :high (cond ((not high) nil)
2086 ((eq class 'integer) (max (1- high) 0))
2087 ((or (consp high) (zerop high)) high)
2090 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2091 (defun random-derive-type-aux (type)
2092 (let ((class (numeric-type-class type))
2093 (high (numeric-type-high type))
2094 (format (numeric-type-format type)))
2098 :low (coerce 0 (or format class 'real))
2099 :high (cond ((not high) nil)
2100 ((eq class 'integer) (max (1- high) 0))
2101 ((or (consp high) (zerop high)) high)
2104 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2105 (defoptimizer (random derive-type) ((bound &optional state))
2106 (one-arg-derive-type bound #'random-derive-type-aux nil))
2108 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2110 ;;; Return the maximum number of bits an integer of the supplied type
2111 ;;; can take up, or NIL if it is unbounded. The second (third) value
2112 ;;; is T if the integer can be positive (negative) and NIL if not.
2113 ;;; Zero counts as positive.
2114 (defun integer-type-length (type)
2115 (if (numeric-type-p type)
2116 (let ((min (numeric-type-low type))
2117 (max (numeric-type-high type)))
2118 (values (and min max (max (integer-length min) (integer-length max)))
2119 (or (null max) (not (minusp max)))
2120 (or (null min) (minusp min))))
2123 (defun logand-derive-type-aux (x y &optional same-leaf)
2125 (return-from logand-derive-type-aux x))
2126 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2127 (declare (ignore x-pos))
2128 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2129 (declare (ignore y-pos))
2131 ;; X must be positive.
2133 ;; They must both be positive.
2134 (cond ((or (null x-len) (null y-len))
2135 (specifier-type 'unsigned-byte))
2137 (specifier-type `(unsigned-byte* ,(min x-len y-len)))))
2138 ;; X is positive, but Y might be negative.
2140 (specifier-type 'unsigned-byte))
2142 (specifier-type `(unsigned-byte* ,x-len)))))
2143 ;; X might be negative.
2145 ;; Y must be positive.
2147 (specifier-type 'unsigned-byte))
2148 (t (specifier-type `(unsigned-byte* ,y-len))))
2149 ;; Either might be negative.
2150 (if (and x-len y-len)
2151 ;; The result is bounded.
2152 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2153 ;; We can't tell squat about the result.
2154 (specifier-type 'integer)))))))
2156 (defun logior-derive-type-aux (x y &optional same-leaf)
2158 (return-from logior-derive-type-aux x))
2159 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2160 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2162 ((and (not x-neg) (not y-neg))
2163 ;; Both are positive.
2164 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2168 ;; X must be negative.
2170 ;; Both are negative. The result is going to be negative
2171 ;; and be the same length or shorter than the smaller.
2172 (if (and x-len y-len)
2174 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2176 (specifier-type '(integer * -1)))
2177 ;; X is negative, but we don't know about Y. The result
2178 ;; will be negative, but no more negative than X.
2180 `(integer ,(or (numeric-type-low x) '*)
2183 ;; X might be either positive or negative.
2185 ;; But Y is negative. The result will be negative.
2187 `(integer ,(or (numeric-type-low y) '*)
2189 ;; We don't know squat about either. It won't get any bigger.
2190 (if (and x-len y-len)
2192 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2194 (specifier-type 'integer))))))))
2196 (defun logxor-derive-type-aux (x y &optional same-leaf)
2198 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2199 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2200 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2202 ((or (and (not x-neg) (not y-neg))
2203 (and (not x-pos) (not y-pos)))
2204 ;; Either both are negative or both are positive. The result
2205 ;; will be positive, and as long as the longer.
2206 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2209 ((or (and (not x-pos) (not y-neg))
2210 (and (not y-neg) (not y-pos)))
2211 ;; Either X is negative and Y is positive or vice-versa. The
2212 ;; result will be negative.
2213 (specifier-type `(integer ,(if (and x-len y-len)
2214 (ash -1 (max x-len y-len))
2217 ;; We can't tell what the sign of the result is going to be.
2218 ;; All we know is that we don't create new bits.
2220 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2222 (specifier-type 'integer))))))
2224 (macrolet ((deffrob (logfun)
2225 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2226 `(defoptimizer (,logfun derive-type) ((x y))
2227 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2232 ;;; FIXME: could actually do stuff with SAME-LEAF
2233 (defoptimizer (logeqv derive-type) ((x y))
2234 (two-arg-derive-type x y (lambda (x y same-leaf)
2235 (lognot-derive-type-aux
2236 (logxor-derive-type-aux x y same-leaf)))
2238 (defoptimizer (lognand derive-type) ((x y))
2239 (two-arg-derive-type x y (lambda (x y same-leaf)
2240 (lognot-derive-type-aux
2241 (logand-derive-type-aux x y same-leaf)))
2243 (defoptimizer (lognor derive-type) ((x y))
2244 (two-arg-derive-type x y (lambda (x y same-leaf)
2245 (lognot-derive-type-aux
2246 (logior-derive-type-aux x y same-leaf)))
2248 ;;; FIXME: use SAME-LEAF instead of ignoring it.
2249 (defoptimizer (logandc1 derive-type) ((x y))
2250 (two-arg-derive-type x y (lambda (x y same-leaf)
2252 (specifier-type '(eql 0))
2253 (logand-derive-type-aux
2254 (lognot-derive-type-aux x) y nil)))
2256 (defoptimizer (logandc2 derive-type) ((x y))
2257 (two-arg-derive-type x y (lambda (x y same-leaf)
2259 (specifier-type '(eql 0))
2260 (logand-derive-type-aux
2261 x (lognot-derive-type-aux y) nil)))
2263 (defoptimizer (logorc1 derive-type) ((x y))
2264 (two-arg-derive-type x y (lambda (x y same-leaf)
2266 (specifier-type '(eql -1))
2267 (logior-derive-type-aux
2268 (lognot-derive-type-aux x) y nil)))
2270 (defoptimizer (logorc2 derive-type) ((x y))
2271 (two-arg-derive-type x y (lambda (x y same-leaf)
2273 (specifier-type '(eql -1))
2274 (logior-derive-type-aux
2275 x (lognot-derive-type-aux y) nil)))
2278 ;;;; miscellaneous derive-type methods
2280 (defoptimizer (integer-length derive-type) ((x))
2281 (let ((x-type (lvar-type x)))
2282 (when (numeric-type-p x-type)
2283 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2284 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2285 ;; careful about LO or HI being NIL, though. Also, if 0 is
2286 ;; contained in X, the lower bound is obviously 0.
2287 (flet ((null-or-min (a b)
2288 (and a b (min (integer-length a)
2289 (integer-length b))))
2291 (and a b (max (integer-length a)
2292 (integer-length b)))))
2293 (let* ((min (numeric-type-low x-type))
2294 (max (numeric-type-high x-type))
2295 (min-len (null-or-min min max))
2296 (max-len (null-or-max min max)))
2297 (when (ctypep 0 x-type)
2299 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2301 (defoptimizer (isqrt derive-type) ((x))
2302 (let ((x-type (lvar-type x)))
2303 (when (numeric-type-p x-type)
2304 (let* ((lo (numeric-type-low x-type))
2305 (hi (numeric-type-high x-type))
2306 (lo-res (if lo (isqrt lo) '*))
2307 (hi-res (if hi (isqrt hi) '*)))
2308 (specifier-type `(integer ,lo-res ,hi-res))))))
2310 (defoptimizer (code-char derive-type) ((code))
2311 (specifier-type 'base-char))
2313 (defoptimizer (values derive-type) ((&rest values))
2314 (make-values-type :required (mapcar #'lvar-type values)))
2316 (defun signum-derive-type-aux (type)
2317 (if (eq (numeric-type-complexp type) :complex)
2318 (let* ((format (case (numeric-type-class type)
2319 ((integer rational) 'single-float)
2320 (t (numeric-type-format type))))
2321 (bound-format (or format 'float)))
2322 (make-numeric-type :class 'float
2325 :low (coerce -1 bound-format)
2326 :high (coerce 1 bound-format)))
2327 (let* ((interval (numeric-type->interval type))
2328 (range-info (interval-range-info interval))
2329 (contains-0-p (interval-contains-p 0 interval))
2330 (class (numeric-type-class type))
2331 (format (numeric-type-format type))
2332 (one (coerce 1 (or format class 'real)))
2333 (zero (coerce 0 (or format class 'real)))
2334 (minus-one (coerce -1 (or format class 'real)))
2335 (plus (make-numeric-type :class class :format format
2336 :low one :high one))
2337 (minus (make-numeric-type :class class :format format
2338 :low minus-one :high minus-one))
2339 ;; KLUDGE: here we have a fairly horrible hack to deal
2340 ;; with the schizophrenia in the type derivation engine.
2341 ;; The problem is that the type derivers reinterpret
2342 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2343 ;; 0d0) within the derivation mechanism doesn't include
2344 ;; -0d0. Ugh. So force it in here, instead.
2345 (zero (make-numeric-type :class class :format format
2346 :low (- zero) :high zero)))
2348 (+ (if contains-0-p (type-union plus zero) plus))
2349 (- (if contains-0-p (type-union minus zero) minus))
2350 (t (type-union minus zero plus))))))
2352 (defoptimizer (signum derive-type) ((num))
2353 (one-arg-derive-type num #'signum-derive-type-aux nil))
2355 ;;;; byte operations
2357 ;;;; We try to turn byte operations into simple logical operations.
2358 ;;;; First, we convert byte specifiers into separate size and position
2359 ;;;; arguments passed to internal %FOO functions. We then attempt to
2360 ;;;; transform the %FOO functions into boolean operations when the
2361 ;;;; size and position are constant and the operands are fixnums.
2363 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2364 ;; expressions that evaluate to the SIZE and POSITION of
2365 ;; the byte-specifier form SPEC. We may wrap a let around
2366 ;; the result of the body to bind some variables.
2368 ;; If the spec is a BYTE form, then bind the vars to the
2369 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2370 ;; and BYTE-POSITION. The goal of this transformation is to
2371 ;; avoid consing up byte specifiers and then immediately
2372 ;; throwing them away.
2373 (with-byte-specifier ((size-var pos-var spec) &body body)
2374 (once-only ((spec `(macroexpand ,spec))
2376 `(if (and (consp ,spec)
2377 (eq (car ,spec) 'byte)
2378 (= (length ,spec) 3))
2379 (let ((,size-var (second ,spec))
2380 (,pos-var (third ,spec)))
2382 (let ((,size-var `(byte-size ,,temp))
2383 (,pos-var `(byte-position ,,temp)))
2384 `(let ((,,temp ,,spec))
2387 (define-source-transform ldb (spec int)
2388 (with-byte-specifier (size pos spec)
2389 `(%ldb ,size ,pos ,int)))
2391 (define-source-transform dpb (newbyte spec int)
2392 (with-byte-specifier (size pos spec)
2393 `(%dpb ,newbyte ,size ,pos ,int)))
2395 (define-source-transform mask-field (spec int)
2396 (with-byte-specifier (size pos spec)
2397 `(%mask-field ,size ,pos ,int)))
2399 (define-source-transform deposit-field (newbyte spec int)
2400 (with-byte-specifier (size pos spec)
2401 `(%deposit-field ,newbyte ,size ,pos ,int))))
2403 (defoptimizer (%ldb derive-type) ((size posn num))
2404 (let ((size (lvar-type size)))
2405 (if (and (numeric-type-p size)
2406 (csubtypep size (specifier-type 'integer)))
2407 (let ((size-high (numeric-type-high size)))
2408 (if (and size-high (<= size-high sb!vm:n-word-bits))
2409 (specifier-type `(unsigned-byte* ,size-high))
2410 (specifier-type 'unsigned-byte)))
2413 (defoptimizer (%mask-field derive-type) ((size posn num))
2414 (let ((size (lvar-type size))
2415 (posn (lvar-type posn)))
2416 (if (and (numeric-type-p size)
2417 (csubtypep size (specifier-type 'integer))
2418 (numeric-type-p posn)
2419 (csubtypep posn (specifier-type 'integer)))
2420 (let ((size-high (numeric-type-high size))
2421 (posn-high (numeric-type-high posn)))
2422 (if (and size-high posn-high
2423 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2424 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2425 (specifier-type 'unsigned-byte)))
2428 (defun %deposit-field-derive-type-aux (size posn int)
2429 (let ((size (lvar-type size))
2430 (posn (lvar-type posn))
2431 (int (lvar-type int)))
2432 (when (and (numeric-type-p size)
2433 (numeric-type-p posn)
2434 (numeric-type-p int))
2435 (let ((size-high (numeric-type-high size))
2436 (posn-high (numeric-type-high posn))
2437 (high (numeric-type-high int))
2438 (low (numeric-type-low int)))
2439 (when (and size-high posn-high high low
2440 ;; KLUDGE: we need this cutoff here, otherwise we
2441 ;; will merrily derive the type of %DPB as
2442 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2443 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2444 ;; 1073741822))), with hilarious consequences. We
2445 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2446 ;; over a reasonable amount of shifting, even on
2447 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2448 ;; machine integers are 64-bits. -- CSR,
2450 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2451 (let ((raw-bit-count (max (integer-length high)
2452 (integer-length low)
2453 (+ size-high posn-high))))
2456 `(signed-byte ,(1+ raw-bit-count))
2457 `(unsigned-byte* ,raw-bit-count)))))))))
2459 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2460 (%deposit-field-derive-type-aux size posn int))
2462 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2463 (%deposit-field-derive-type-aux size posn int))
2465 (deftransform %ldb ((size posn int)
2466 (fixnum fixnum integer)
2467 (unsigned-byte #.sb!vm:n-word-bits))
2468 "convert to inline logical operations"
2469 `(logand (ash int (- posn))
2470 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2471 (- size ,sb!vm:n-word-bits))))
2473 (deftransform %mask-field ((size posn int)
2474 (fixnum fixnum integer)
2475 (unsigned-byte #.sb!vm:n-word-bits))
2476 "convert to inline logical operations"
2478 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2479 (- size ,sb!vm:n-word-bits))
2482 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2483 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2484 ;;; as the result type, as that would allow result types that cover
2485 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2486 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2488 (deftransform %dpb ((new size posn int)
2490 (unsigned-byte #.sb!vm:n-word-bits))
2491 "convert to inline logical operations"
2492 `(let ((mask (ldb (byte size 0) -1)))
2493 (logior (ash (logand new mask) posn)
2494 (logand int (lognot (ash mask posn))))))
2496 (deftransform %dpb ((new size posn int)
2498 (signed-byte #.sb!vm:n-word-bits))
2499 "convert to inline logical operations"
2500 `(let ((mask (ldb (byte size 0) -1)))
2501 (logior (ash (logand new mask) posn)
2502 (logand int (lognot (ash mask posn))))))
2504 (deftransform %deposit-field ((new size posn int)
2506 (unsigned-byte #.sb!vm:n-word-bits))
2507 "convert to inline logical operations"
2508 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2509 (logior (logand new mask)
2510 (logand int (lognot mask)))))
2512 (deftransform %deposit-field ((new size posn int)
2514 (signed-byte #.sb!vm:n-word-bits))
2515 "convert to inline logical operations"
2516 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2517 (logior (logand new mask)
2518 (logand int (lognot mask)))))
2520 ;;; Modular functions
2522 ;;; (ldb (byte s 0) (foo x y ...)) =
2523 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2525 ;;; and similar for other arguments.
2527 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2529 ;;; For good functions, we just recursively cut arguments; their
2530 ;;; "goodness" means that the result will not increase (in the
2531 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2532 ;;; replaced with the version, cutting its result to WIDTH or more
2533 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2534 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2535 ;;; arguments (maybe to a different width) and returning the name of a
2536 ;;; modular version, if it exists, or NIL. If we have changed
2537 ;;; anything, we need to flush old derived types, because they have
2538 ;;; nothing in common with the new code.
2539 (defun cut-to-width (lvar width)
2540 (declare (type lvar lvar) (type (integer 0) width))
2541 (labels ((reoptimize-node (node name)
2542 (setf (node-derived-type node)
2544 (info :function :type name)))
2545 (setf (lvar-%derived-type (node-lvar node)) nil)
2546 (setf (node-reoptimize node) t)
2547 (setf (block-reoptimize (node-block node)) t)
2548 (setf (component-reoptimize (node-component node)) t))
2549 (cut-node (node &aux did-something)
2550 (when (and (not (block-delete-p (node-block node)))
2551 (combination-p node)
2552 (eq (basic-combination-kind node) :known))
2553 (let* ((fun-ref (lvar-use (combination-fun node)))
2554 (fun-name (leaf-source-name (ref-leaf fun-ref)))
2555 (modular-fun (find-modular-version fun-name width)))
2556 (when (and modular-fun
2557 (not (and (eq fun-name 'logand)
2559 (single-value-type (node-derived-type node))
2560 (specifier-type `(unsigned-byte* ,width))))))
2561 (binding* ((name (etypecase modular-fun
2562 ((eql :good) fun-name)
2564 (modular-fun-info-name modular-fun))
2566 (funcall modular-fun node width)))
2568 (unless (eql modular-fun :good)
2569 (setq did-something t)
2572 (find-free-fun name "in a strange place"))
2573 (setf (combination-kind node) :full))
2574 (unless (functionp modular-fun)
2575 (dolist (arg (basic-combination-args node))
2576 (when (cut-lvar arg)
2577 (setq did-something t))))
2579 (reoptimize-node node name))
2581 (cut-lvar (lvar &aux did-something)
2582 (do-uses (node lvar)
2583 (when (cut-node node)
2584 (setq did-something t)))
2588 (defoptimizer (logand optimizer) ((x y) node)
2589 (let ((result-type (single-value-type (node-derived-type node))))
2590 (when (numeric-type-p result-type)
2591 (let ((low (numeric-type-low result-type))
2592 (high (numeric-type-high result-type)))
2593 (when (and (numberp low)
2596 (let ((width (integer-length high)))
2597 (when (some (lambda (x) (<= width x))
2598 *modular-funs-widths*)
2599 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2600 (cut-to-width x width)
2601 (cut-to-width y width)
2602 nil ; After fixing above, replace with T.
2605 ;;; miscellanous numeric transforms
2607 ;;; If a constant appears as the first arg, swap the args.
2608 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2609 (if (and (constant-lvar-p x)
2610 (not (constant-lvar-p y)))
2611 `(,(lvar-fun-name (basic-combination-fun node))
2614 (give-up-ir1-transform)))
2616 (dolist (x '(= char= + * logior logand logxor))
2617 (%deftransform x '(function * *) #'commutative-arg-swap
2618 "place constant arg last"))
2620 ;;; Handle the case of a constant BOOLE-CODE.
2621 (deftransform boole ((op x y) * *)
2622 "convert to inline logical operations"
2623 (unless (constant-lvar-p op)
2624 (give-up-ir1-transform "BOOLE code is not a constant."))
2625 (let ((control (lvar-value op)))
2627 (#.sb!xc:boole-clr 0)
2628 (#.sb!xc:boole-set -1)
2629 (#.sb!xc:boole-1 'x)
2630 (#.sb!xc:boole-2 'y)
2631 (#.sb!xc:boole-c1 '(lognot x))
2632 (#.sb!xc:boole-c2 '(lognot y))
2633 (#.sb!xc:boole-and '(logand x y))
2634 (#.sb!xc:boole-ior '(logior x y))
2635 (#.sb!xc:boole-xor '(logxor x y))
2636 (#.sb!xc:boole-eqv '(logeqv x y))
2637 (#.sb!xc:boole-nand '(lognand x y))
2638 (#.sb!xc:boole-nor '(lognor x y))
2639 (#.sb!xc:boole-andc1 '(logandc1 x y))
2640 (#.sb!xc:boole-andc2 '(logandc2 x y))
2641 (#.sb!xc:boole-orc1 '(logorc1 x y))
2642 (#.sb!xc:boole-orc2 '(logorc2 x y))
2644 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2647 ;;;; converting special case multiply/divide to shifts
2649 ;;; If arg is a constant power of two, turn * into a shift.
2650 (deftransform * ((x y) (integer integer) *)
2651 "convert x*2^k to shift"
2652 (unless (constant-lvar-p y)
2653 (give-up-ir1-transform))
2654 (let* ((y (lvar-value y))
2656 (len (1- (integer-length y-abs))))
2657 (unless (= y-abs (ash 1 len))
2658 (give-up-ir1-transform))
2663 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2664 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
2666 (flet ((frob (y ceil-p)
2667 (unless (constant-lvar-p y)
2668 (give-up-ir1-transform))
2669 (let* ((y (lvar-value y))
2671 (len (1- (integer-length y-abs))))
2672 (unless (= y-abs (ash 1 len))
2673 (give-up-ir1-transform))
2674 (let ((shift (- len))
2676 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
2677 `(let ((x (+ x ,delta)))
2679 `(values (ash (- x) ,shift)
2680 (- (- (logand (- x) ,mask)) ,delta))
2681 `(values (ash x ,shift)
2682 (- (logand x ,mask) ,delta))))))))
2683 (deftransform floor ((x y) (integer integer) *)
2684 "convert division by 2^k to shift"
2686 (deftransform ceiling ((x y) (integer integer) *)
2687 "convert division by 2^k to shift"
2690 ;;; Do the same for MOD.
2691 (deftransform mod ((x y) (integer integer) *)
2692 "convert remainder mod 2^k to LOGAND"
2693 (unless (constant-lvar-p y)
2694 (give-up-ir1-transform))
2695 (let* ((y (lvar-value y))
2697 (len (1- (integer-length y-abs))))
2698 (unless (= y-abs (ash 1 len))
2699 (give-up-ir1-transform))
2700 (let ((mask (1- y-abs)))
2702 `(- (logand (- x) ,mask))
2703 `(logand x ,mask)))))
2705 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2706 (deftransform truncate ((x y) (integer integer))
2707 "convert division by 2^k to shift"
2708 (unless (constant-lvar-p y)
2709 (give-up-ir1-transform))
2710 (let* ((y (lvar-value y))
2712 (len (1- (integer-length y-abs))))
2713 (unless (= y-abs (ash 1 len))
2714 (give-up-ir1-transform))
2715 (let* ((shift (- len))
2718 (values ,(if (minusp y)
2720 `(- (ash (- x) ,shift)))
2721 (- (logand (- x) ,mask)))
2722 (values ,(if (minusp y)
2723 `(ash (- ,mask x) ,shift)
2725 (logand x ,mask))))))
2727 ;;; And the same for REM.
2728 (deftransform rem ((x y) (integer integer) *)
2729 "convert remainder mod 2^k to LOGAND"
2730 (unless (constant-lvar-p y)
2731 (give-up-ir1-transform))
2732 (let* ((y (lvar-value y))
2734 (len (1- (integer-length y-abs))))
2735 (unless (= y-abs (ash 1 len))
2736 (give-up-ir1-transform))
2737 (let ((mask (1- y-abs)))
2739 (- (logand (- x) ,mask))
2740 (logand x ,mask)))))
2742 ;;;; arithmetic and logical identity operation elimination
2744 ;;; Flush calls to various arith functions that convert to the
2745 ;;; identity function or a constant.
2746 (macrolet ((def (name identity result)
2747 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
2748 "fold identity operations"
2755 (def logxor -1 (lognot x))
2758 (deftransform logand ((x y) (* (constant-arg t)) *)
2759 "fold identity operation"
2760 (let ((y (lvar-value y)))
2761 (unless (and (plusp y)
2762 (= y (1- (ash 1 (integer-length y)))))
2763 (give-up-ir1-transform))
2764 (unless (csubtypep (lvar-type x)
2765 (specifier-type `(integer 0 ,y)))
2766 (give-up-ir1-transform))
2769 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2770 ;;; (* 0 -4.0) is -0.0.
2771 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
2772 "convert (- 0 x) to negate"
2774 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
2775 "convert (* x 0) to 0"
2778 ;;; Return T if in an arithmetic op including lvars X and Y, the
2779 ;;; result type is not affected by the type of X. That is, Y is at
2780 ;;; least as contagious as X.
2782 (defun not-more-contagious (x y)
2783 (declare (type continuation x y))
2784 (let ((x (lvar-type x))
2786 (values (type= (numeric-contagion x y)
2787 (numeric-contagion y y)))))
2788 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2789 ;;; XXX needs more work as valid transforms are missed; some cases are
2790 ;;; specific to particular transform functions so the use of this
2791 ;;; function may need a re-think.
2792 (defun not-more-contagious (x y)
2793 (declare (type lvar x y))
2794 (flet ((simple-numeric-type (num)
2795 (and (numeric-type-p num)
2796 ;; Return non-NIL if NUM is integer, rational, or a float
2797 ;; of some type (but not FLOAT)
2798 (case (numeric-type-class num)
2802 (numeric-type-format num))
2805 (let ((x (lvar-type x))
2807 (if (and (simple-numeric-type x)
2808 (simple-numeric-type y))
2809 (values (type= (numeric-contagion x y)
2810 (numeric-contagion y y)))))))
2814 ;;; If y is not constant, not zerop, or is contagious, or a positive
2815 ;;; float +0.0 then give up.
2816 (deftransform + ((x y) (t (constant-arg t)) *)
2818 (let ((val (lvar-value y)))
2819 (unless (and (zerop val)
2820 (not (and (floatp val) (plusp (float-sign val))))
2821 (not-more-contagious y x))
2822 (give-up-ir1-transform)))
2827 ;;; If y is not constant, not zerop, or is contagious, or a negative
2828 ;;; float -0.0 then give up.
2829 (deftransform - ((x y) (t (constant-arg t)) *)
2831 (let ((val (lvar-value y)))
2832 (unless (and (zerop val)
2833 (not (and (floatp val) (minusp (float-sign val))))
2834 (not-more-contagious y x))
2835 (give-up-ir1-transform)))
2838 ;;; Fold (OP x +/-1)
2839 (macrolet ((def (name result minus-result)
2840 `(deftransform ,name ((x y) (t (constant-arg real)) *)
2841 "fold identity operations"
2842 (let ((val (lvar-value y)))
2843 (unless (and (= (abs val) 1)
2844 (not-more-contagious y x))
2845 (give-up-ir1-transform))
2846 (if (minusp val) ',minus-result ',result)))))
2847 (def * x (%negate x))
2848 (def / x (%negate x))
2849 (def expt x (/ 1 x)))
2851 ;;; Fold (expt x n) into multiplications for small integral values of
2852 ;;; N; convert (expt x 1/2) to sqrt.
2853 (deftransform expt ((x y) (t (constant-arg real)) *)
2854 "recode as multiplication or sqrt"
2855 (let ((val (lvar-value y)))
2856 ;; If Y would cause the result to be promoted to the same type as
2857 ;; Y, we give up. If not, then the result will be the same type
2858 ;; as X, so we can replace the exponentiation with simple
2859 ;; multiplication and division for small integral powers.
2860 (unless (not-more-contagious y x)
2861 (give-up-ir1-transform))
2863 (let ((x-type (lvar-type x)))
2864 (cond ((csubtypep x-type (specifier-type '(or rational
2865 (complex rational))))
2867 ((csubtypep x-type (specifier-type 'real))
2871 ((csubtypep x-type (specifier-type 'complex))
2872 ;; both parts are float
2874 (t (give-up-ir1-transform)))))
2875 ((= val 2) '(* x x))
2876 ((= val -2) '(/ (* x x)))
2877 ((= val 3) '(* x x x))
2878 ((= val -3) '(/ (* x x x)))
2879 ((= val 1/2) '(sqrt x))
2880 ((= val -1/2) '(/ (sqrt x)))
2881 (t (give-up-ir1-transform)))))
2883 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
2884 ;;; transformations?
2885 ;;; Perhaps we should have to prove that the denominator is nonzero before
2886 ;;; doing them? -- WHN 19990917
2887 (macrolet ((def (name)
2888 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
2895 (macrolet ((def (name)
2896 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
2905 ;;;; character operations
2907 (deftransform char-equal ((a b) (base-char base-char))
2909 '(let* ((ac (char-code a))
2911 (sum (logxor ac bc)))
2913 (when (eql sum #x20)
2914 (let ((sum (+ ac bc)))
2915 (and (> sum 161) (< sum 213)))))))
2917 (deftransform char-upcase ((x) (base-char))
2919 '(let ((n-code (char-code x)))
2920 (if (and (> n-code #o140) ; Octal 141 is #\a.
2921 (< n-code #o173)) ; Octal 172 is #\z.
2922 (code-char (logxor #x20 n-code))
2925 (deftransform char-downcase ((x) (base-char))
2927 '(let ((n-code (char-code x)))
2928 (if (and (> n-code 64) ; 65 is #\A.
2929 (< n-code 91)) ; 90 is #\Z.
2930 (code-char (logxor #x20 n-code))
2933 ;;;; equality predicate transforms
2935 ;;; Return true if X and Y are lvars whose only use is a
2936 ;;; reference to the same leaf, and the value of the leaf cannot
2938 (defun same-leaf-ref-p (x y)
2939 (declare (type lvar x y))
2940 (let ((x-use (principal-lvar-use x))
2941 (y-use (principal-lvar-use y)))
2944 (eq (ref-leaf x-use) (ref-leaf y-use))
2945 (constant-reference-p x-use))))
2947 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
2948 ;;; if there is no intersection between the types of the arguments,
2949 ;;; then the result is definitely false.
2950 (deftransform simple-equality-transform ((x y) * *
2952 (cond ((same-leaf-ref-p x y)
2954 ((not (types-equal-or-intersect (lvar-type x)
2958 (give-up-ir1-transform))))
2961 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
2966 ;;; This is similar to SIMPLE-EQUALITY-PREDICATE, except that we also
2967 ;;; try to convert to a type-specific predicate or EQ:
2968 ;;; -- If both args are characters, convert to CHAR=. This is better than
2969 ;;; just converting to EQ, since CHAR= may have special compilation
2970 ;;; strategies for non-standard representations, etc.
2971 ;;; -- If either arg is definitely not a number, then we can compare
2973 ;;; -- Otherwise, we try to put the arg we know more about second. If X
2974 ;;; is constant then we put it second. If X is a subtype of Y, we put
2975 ;;; it second. These rules make it easier for the back end to match
2976 ;;; these interesting cases.
2977 ;;; -- If Y is a fixnum, then we quietly pass because the back end can
2978 ;;; handle that case, otherwise give an efficiency note.
2979 (deftransform eql ((x y) * *)
2980 "convert to simpler equality predicate"
2981 (let ((x-type (lvar-type x))
2982 (y-type (lvar-type y))
2983 (char-type (specifier-type 'character))
2984 (number-type (specifier-type 'number)))
2985 (cond ((same-leaf-ref-p x y)
2987 ((not (types-equal-or-intersect x-type y-type))
2989 ((and (csubtypep x-type char-type)
2990 (csubtypep y-type char-type))
2992 ((or (not (types-equal-or-intersect x-type number-type))
2993 (not (types-equal-or-intersect y-type number-type)))
2995 ((and (not (constant-lvar-p y))
2996 (or (constant-lvar-p x)
2997 (and (csubtypep x-type y-type)
2998 (not (csubtypep y-type x-type)))))
3001 (give-up-ir1-transform)))))
3003 ;;; Convert to EQL if both args are rational and complexp is specified
3004 ;;; and the same for both.
3005 (deftransform = ((x y) * *)
3007 (let ((x-type (lvar-type x))
3008 (y-type (lvar-type y)))
3009 (if (and (csubtypep x-type (specifier-type 'number))
3010 (csubtypep y-type (specifier-type 'number)))
3011 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3012 (csubtypep y-type (specifier-type 'float)))
3013 (and (csubtypep x-type (specifier-type '(complex float)))
3014 (csubtypep y-type (specifier-type '(complex float)))))
3015 ;; They are both floats. Leave as = so that -0.0 is
3016 ;; handled correctly.
3017 (give-up-ir1-transform))
3018 ((or (and (csubtypep x-type (specifier-type 'rational))
3019 (csubtypep y-type (specifier-type 'rational)))
3020 (and (csubtypep x-type
3021 (specifier-type '(complex rational)))
3023 (specifier-type '(complex rational)))))
3024 ;; They are both rationals and complexp is the same.
3028 (give-up-ir1-transform
3029 "The operands might not be the same type.")))
3030 (give-up-ir1-transform
3031 "The operands might not be the same type."))))
3033 ;;; If LVAR's type is a numeric type, then return the type, otherwise
3034 ;;; GIVE-UP-IR1-TRANSFORM.
3035 (defun numeric-type-or-lose (lvar)
3036 (declare (type lvar lvar))
3037 (let ((res (lvar-type lvar)))
3038 (unless (numeric-type-p res) (give-up-ir1-transform))
3041 ;;; See whether we can statically determine (< X Y) using type
3042 ;;; information. If X's high bound is < Y's low, then X < Y.
3043 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3044 ;;; NIL). If not, at least make sure any constant arg is second.
3045 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3046 `(deftransform ,name ((x y))
3047 (if (same-leaf-ref-p x y)
3049 (let ((ix (or (type-approximate-interval (lvar-type x))
3050 (give-up-ir1-transform)))
3051 (iy (or (type-approximate-interval (lvar-type y))
3052 (give-up-ir1-transform))))
3057 ((and (constant-lvar-p x)
3058 (not (constant-lvar-p y)))
3061 (give-up-ir1-transform))))))))
3062 (def < > nil (interval-< ix iy) (interval->= ix iy))
3063 (def > < nil (interval-< iy ix) (interval->= iy ix))
3064 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3065 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3067 (defun ir1-transform-char< (x y first second inverse)
3069 ((same-leaf-ref-p x y) nil)
3070 ;; If we had interval representation of character types, as we
3071 ;; might eventually have to to support 2^21 characters, then here
3072 ;; we could do some compile-time computation as in transforms for
3073 ;; < above. -- CSR, 2003-07-01
3074 ((and (constant-lvar-p first)
3075 (not (constant-lvar-p second)))
3077 (t (give-up-ir1-transform))))
3079 (deftransform char< ((x y) (character character) *)
3080 (ir1-transform-char< x y x y 'char>))
3082 (deftransform char> ((x y) (character character) *)
3083 (ir1-transform-char< y x x y 'char<))
3085 ;;;; converting N-arg comparisons
3087 ;;;; We convert calls to N-arg comparison functions such as < into
3088 ;;;; two-arg calls. This transformation is enabled for all such
3089 ;;;; comparisons in this file. If any of these predicates are not
3090 ;;;; open-coded, then the transformation should be removed at some
3091 ;;;; point to avoid pessimization.
3093 ;;; This function is used for source transformation of N-arg
3094 ;;; comparison functions other than inequality. We deal both with
3095 ;;; converting to two-arg calls and inverting the sense of the test,
3096 ;;; if necessary. If the call has two args, then we pass or return a
3097 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3098 ;;; then we transform to code that returns true. Otherwise, we bind
3099 ;;; all the arguments and expand into a bunch of IFs.
3100 (declaim (ftype (function (symbol list boolean t) *) multi-compare))
3101 (defun multi-compare (predicate args not-p type)
3102 (let ((nargs (length args)))
3103 (cond ((< nargs 1) (values nil t))
3104 ((= nargs 1) `(progn (the ,type ,@args) t))
3107 `(if (,predicate ,(first args) ,(second args)) nil t)
3110 (do* ((i (1- nargs) (1- i))
3112 (current (gensym) (gensym))
3113 (vars (list current) (cons current vars))
3115 `(if (,predicate ,current ,last)
3117 `(if (,predicate ,current ,last)
3120 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3123 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3124 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3125 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3126 (define-source-transform <= (&rest args) (multi-compare '> args t 'real))
3127 (define-source-transform >= (&rest args) (multi-compare '< args t 'real))
3129 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3131 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3133 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3135 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3137 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3140 (define-source-transform char-equal (&rest args)
3141 (multi-compare 'char-equal args nil 'character))
3142 (define-source-transform char-lessp (&rest args)
3143 (multi-compare 'char-lessp args nil 'character))
3144 (define-source-transform char-greaterp (&rest args)
3145 (multi-compare 'char-greaterp args nil 'character))
3146 (define-source-transform char-not-greaterp (&rest args)
3147 (multi-compare 'char-greaterp args t 'character))
3148 (define-source-transform char-not-lessp (&rest args)
3149 (multi-compare 'char-lessp args t 'character))
3151 ;;; This function does source transformation of N-arg inequality
3152 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3153 ;;; arg cases. If there are more than two args, then we expand into
3154 ;;; the appropriate n^2 comparisons only when speed is important.
3155 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3156 (defun multi-not-equal (predicate args type)
3157 (let ((nargs (length args)))
3158 (cond ((< nargs 1) (values nil t))
3159 ((= nargs 1) `(progn (the ,type ,@args) t))
3161 `(if (,predicate ,(first args) ,(second args)) nil t))
3162 ((not (policy *lexenv*
3163 (and (>= speed space)
3164 (>= speed compilation-speed))))
3167 (let ((vars (make-gensym-list nargs)))
3168 (do ((var vars next)
3169 (next (cdr vars) (cdr next))
3172 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3174 (let ((v1 (first var)))
3176 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3178 (define-source-transform /= (&rest args)
3179 (multi-not-equal '= args 'number))
3180 (define-source-transform char/= (&rest args)
3181 (multi-not-equal 'char= args 'character))
3182 (define-source-transform char-not-equal (&rest args)
3183 (multi-not-equal 'char-equal args 'character))
3185 ;;; Expand MAX and MIN into the obvious comparisons.
3186 (define-source-transform max (arg0 &rest rest)
3187 (once-only ((arg0 arg0))
3189 `(values (the real ,arg0))
3190 `(let ((maxrest (max ,@rest)))
3191 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3192 (define-source-transform min (arg0 &rest rest)
3193 (once-only ((arg0 arg0))
3195 `(values (the real ,arg0))
3196 `(let ((minrest (min ,@rest)))
3197 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3199 ;;;; converting N-arg arithmetic functions
3201 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3202 ;;;; versions, and degenerate cases are flushed.
3204 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3205 (declaim (ftype (function (symbol t list) list) associate-args))
3206 (defun associate-args (function first-arg more-args)
3207 (let ((next (rest more-args))
3208 (arg (first more-args)))
3210 `(,function ,first-arg ,arg)
3211 (associate-args function `(,function ,first-arg ,arg) next))))
3213 ;;; Do source transformations for transitive functions such as +.
3214 ;;; One-arg cases are replaced with the arg and zero arg cases with
3215 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3216 ;;; ensure (with THE) that the argument in one-argument calls is.
3217 (defun source-transform-transitive (fun args identity
3218 &optional one-arg-result-type)
3219 (declare (symbol fun) (list args))
3222 (1 (if one-arg-result-type
3223 `(values (the ,one-arg-result-type ,(first args)))
3224 `(values ,(first args))))
3227 (associate-args fun (first args) (rest args)))))
3229 (define-source-transform + (&rest args)
3230 (source-transform-transitive '+ args 0 'number))
3231 (define-source-transform * (&rest args)
3232 (source-transform-transitive '* args 1 'number))
3233 (define-source-transform logior (&rest args)
3234 (source-transform-transitive 'logior args 0 'integer))
3235 (define-source-transform logxor (&rest args)
3236 (source-transform-transitive 'logxor args 0 'integer))
3237 (define-source-transform logand (&rest args)
3238 (source-transform-transitive 'logand args -1 'integer))
3239 (define-source-transform logeqv (&rest args)
3240 (source-transform-transitive 'logeqv args -1 'integer))
3242 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3243 ;;; because when they are given one argument, they return its absolute
3246 (define-source-transform gcd (&rest args)
3249 (1 `(abs (the integer ,(first args))))
3251 (t (associate-args 'gcd (first args) (rest args)))))
3253 (define-source-transform lcm (&rest args)
3256 (1 `(abs (the integer ,(first args))))
3258 (t (associate-args 'lcm (first args) (rest args)))))
3260 ;;; Do source transformations for intransitive n-arg functions such as
3261 ;;; /. With one arg, we form the inverse. With two args we pass.
3262 ;;; Otherwise we associate into two-arg calls.
3263 (declaim (ftype (function (symbol list t)
3264 (values list &optional (member nil t)))
3265 source-transform-intransitive))
3266 (defun source-transform-intransitive (function args inverse)
3268 ((0 2) (values nil t))
3269 (1 `(,@inverse ,(first args)))
3270 (t (associate-args function (first args) (rest args)))))
3272 (define-source-transform - (&rest args)
3273 (source-transform-intransitive '- args '(%negate)))
3274 (define-source-transform / (&rest args)
3275 (source-transform-intransitive '/ args '(/ 1)))
3277 ;;;; transforming APPLY
3279 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3280 ;;; only needs to understand one kind of variable-argument call. It is
3281 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3282 (define-source-transform apply (fun arg &rest more-args)
3283 (let ((args (cons arg more-args)))
3284 `(multiple-value-call ,fun
3285 ,@(mapcar (lambda (x)
3288 (values-list ,(car (last args))))))
3290 ;;;; transforming FORMAT
3292 ;;;; If the control string is a compile-time constant, then replace it
3293 ;;;; with a use of the FORMATTER macro so that the control string is
3294 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3295 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3296 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3298 ;;; for compile-time argument count checking.
3300 ;;; FIXME I: this is currently called from DEFTRANSFORMs, the vast
3301 ;;; majority of which are not going to transform the code, but instead
3302 ;;; are going to GIVE-UP-IR1-TRANSFORM unconditionally. It would be
3303 ;;; nice to make this explicit, maybe by implementing a new
3304 ;;; "optimizer" (say, DEFOPTIMIZER CONSISTENCY-CHECK).
3306 ;;; FIXME II: In some cases, type information could be correlated; for
3307 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3308 ;;; of a corresponding argument is known and does not intersect the
3309 ;;; list type, a warning could be signalled.
3310 (defun check-format-args (string args fun)
3311 (declare (type string string))
3312 (unless (typep string 'simple-string)
3313 (setq string (coerce string 'simple-string)))
3314 (multiple-value-bind (min max)
3315 (handler-case (sb!format:%compiler-walk-format-string string args)
3316 (sb!format:format-error (c)
3317 (compiler-warn "~A" c)))
3319 (let ((nargs (length args)))
3322 (compiler-warn "Too few arguments (~D) to ~S ~S: ~
3323 requires at least ~D."
3324 nargs fun string min))
3326 (;; to get warned about probably bogus code at
3327 ;; cross-compile time.
3328 #+sb-xc-host compiler-warn
3329 ;; ANSI saith that too many arguments doesn't cause a
3331 #-sb-xc-host compiler-style-warn
3332 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3333 nargs fun string max)))))))
3335 (defoptimizer (format optimizer) ((dest control &rest args))
3336 (when (constant-lvar-p control)
3337 (let ((x (lvar-value control)))
3339 (check-format-args x args 'format)))))
3341 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3342 :policy (> speed space))
3343 (unless (constant-lvar-p control)
3344 (give-up-ir1-transform "The control string is not a constant."))
3345 (let ((arg-names (make-gensym-list (length args))))
3346 `(lambda (dest control ,@arg-names)
3347 (declare (ignore control))
3348 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
3350 (deftransform format ((stream control &rest args) (stream function &rest t) *
3351 :policy (> speed space))
3352 (let ((arg-names (make-gensym-list (length args))))
3353 `(lambda (stream control ,@arg-names)
3354 (funcall control stream ,@arg-names)
3357 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3358 :policy (> speed space))
3359 (let ((arg-names (make-gensym-list (length args))))
3360 `(lambda (tee control ,@arg-names)
3361 (declare (ignore tee))
3362 (funcall control *standard-output* ,@arg-names)
3367 `(defoptimizer (,name optimizer) ((control &rest args))
3368 (when (constant-lvar-p control)
3369 (let ((x (lvar-value control)))
3371 (check-format-args x args ',name)))))))
3374 #+sb-xc-host ; Only we should be using these
3377 (def compiler-abort)
3378 (def compiler-error)
3380 (def compiler-style-warn)
3381 (def compiler-notify)
3382 (def maybe-compiler-notify)
3385 (defoptimizer (cerror optimizer) ((report control &rest args))
3386 (when (and (constant-lvar-p control)
3387 (constant-lvar-p report))
3388 (let ((x (lvar-value control))
3389 (y (lvar-value report)))
3390 (when (and (stringp x) (stringp y))
3391 (multiple-value-bind (min1 max1)
3393 (sb!format:%compiler-walk-format-string x args)
3394 (sb!format:format-error (c)
3395 (compiler-warn "~A" c)))
3397 (multiple-value-bind (min2 max2)
3399 (sb!format:%compiler-walk-format-string y args)
3400 (sb!format:format-error (c)
3401 (compiler-warn "~A" c)))
3403 (let ((nargs (length args)))
3405 ((< nargs (min min1 min2))
3406 (compiler-warn "Too few arguments (~D) to ~S ~S ~S: ~
3407 requires at least ~D."
3408 nargs 'cerror y x (min min1 min2)))
3409 ((> nargs (max max1 max2))
3410 (;; to get warned about probably bogus code at
3411 ;; cross-compile time.
3412 #+sb-xc-host compiler-warn
3413 ;; ANSI saith that too many arguments doesn't cause a
3415 #-sb-xc-host compiler-style-warn
3416 "Too many arguments (~D) to ~S ~S ~S: uses at most ~D."
3417 nargs 'cerror y x (max max1 max2)))))))))))))
3419 (defoptimizer (coerce derive-type) ((value type))
3421 ((constant-lvar-p type)
3422 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3423 ;; but dealing with the niggle that complex canonicalization gets
3424 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3426 (let* ((specifier (lvar-value type))
3427 (result-typeoid (careful-specifier-type specifier)))
3429 ((null result-typeoid) nil)
3430 ((csubtypep result-typeoid (specifier-type 'number))
3431 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3432 ;; Rule of Canonical Representation for Complex Rationals,
3433 ;; which is a truly nasty delivery to field.
3435 ((csubtypep result-typeoid (specifier-type 'real))
3436 ;; cleverness required here: it would be nice to deduce
3437 ;; that something of type (INTEGER 2 3) coerced to type
3438 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3439 ;; FLOAT gets its own clause because it's implemented as
3440 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3443 ((and (numeric-type-p result-typeoid)
3444 (eq (numeric-type-complexp result-typeoid) :real))
3445 ;; FIXME: is this clause (a) necessary or (b) useful?
3447 ((or (csubtypep result-typeoid
3448 (specifier-type '(complex single-float)))
3449 (csubtypep result-typeoid
3450 (specifier-type '(complex double-float)))
3452 (csubtypep result-typeoid
3453 (specifier-type '(complex long-float))))
3454 ;; float complex types are never canonicalized.
3457 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3458 ;; probably just a COMPLEX or equivalent. So, in that
3459 ;; case, we will return a complex or an object of the
3460 ;; provided type if it's rational:
3461 (type-union result-typeoid
3462 (type-intersection (lvar-type value)
3463 (specifier-type 'rational))))))
3464 (t result-typeoid))))
3466 ;; OK, the result-type argument isn't constant. However, there
3467 ;; are common uses where we can still do better than just
3468 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3469 ;; where Y is of a known type. See messages on cmucl-imp
3470 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3471 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3472 ;; the basis that it's unlikely that other uses are both
3473 ;; time-critical and get to this branch of the COND (non-constant
3474 ;; second argument to COERCE). -- CSR, 2002-12-16
3475 (let ((value-type (lvar-type value))
3476 (type-type (lvar-type type)))
3478 ((good-cons-type-p (cons-type)
3479 ;; Make sure the cons-type we're looking at is something
3480 ;; we're prepared to handle which is basically something
3481 ;; that array-element-type can return.
3482 (or (and (member-type-p cons-type)
3483 (null (rest (member-type-members cons-type)))
3484 (null (first (member-type-members cons-type))))
3485 (let ((car-type (cons-type-car-type cons-type)))
3486 (and (member-type-p car-type)
3487 (null (rest (member-type-members car-type)))
3488 (or (symbolp (first (member-type-members car-type)))
3489 (numberp (first (member-type-members car-type)))
3490 (and (listp (first (member-type-members
3492 (numberp (first (first (member-type-members
3494 (good-cons-type-p (cons-type-cdr-type cons-type))))))
3495 (unconsify-type (good-cons-type)
3496 ;; Convert the "printed" respresentation of a cons
3497 ;; specifier into a type specifier. That is, the
3498 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3499 ;; NULL)) is converted to (SIGNED-BYTE 16).
3500 (cond ((or (null good-cons-type)
3501 (eq good-cons-type 'null))
3503 ((and (eq (first good-cons-type) 'cons)
3504 (eq (first (second good-cons-type)) 'member))
3505 `(,(second (second good-cons-type))
3506 ,@(unconsify-type (caddr good-cons-type))))))
3507 (coerceable-p (c-type)
3508 ;; Can the value be coerced to the given type? Coerce is
3509 ;; complicated, so we don't handle every possible case
3510 ;; here---just the most common and easiest cases:
3512 ;; * Any REAL can be coerced to a FLOAT type.
3513 ;; * Any NUMBER can be coerced to a (COMPLEX
3514 ;; SINGLE/DOUBLE-FLOAT).
3516 ;; FIXME I: we should also be able to deal with characters
3519 ;; FIXME II: I'm not sure that anything is necessary
3520 ;; here, at least while COMPLEX is not a specialized
3521 ;; array element type in the system. Reasoning: if
3522 ;; something cannot be coerced to the requested type, an
3523 ;; error will be raised (and so any downstream compiled
3524 ;; code on the assumption of the returned type is
3525 ;; unreachable). If something can, then it will be of
3526 ;; the requested type, because (by assumption) COMPLEX
3527 ;; (and other difficult types like (COMPLEX INTEGER)
3528 ;; aren't specialized types.
3529 (let ((coerced-type c-type))
3530 (or (and (subtypep coerced-type 'float)
3531 (csubtypep value-type (specifier-type 'real)))
3532 (and (subtypep coerced-type
3533 '(or (complex single-float)
3534 (complex double-float)))
3535 (csubtypep value-type (specifier-type 'number))))))
3536 (process-types (type)
3537 ;; FIXME: This needs some work because we should be able
3538 ;; to derive the resulting type better than just the
3539 ;; type arg of coerce. That is, if X is (INTEGER 10
3540 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3541 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3543 (cond ((member-type-p type)
3544 (let ((members (member-type-members type)))
3545 (if (every #'coerceable-p members)
3546 (specifier-type `(or ,@members))
3548 ((and (cons-type-p type)
3549 (good-cons-type-p type))
3550 (let ((c-type (unconsify-type (type-specifier type))))
3551 (if (coerceable-p c-type)
3552 (specifier-type c-type)
3555 *universal-type*))))
3556 (cond ((union-type-p type-type)
3557 (apply #'type-union (mapcar #'process-types
3558 (union-type-types type-type))))
3559 ((or (member-type-p type-type)
3560 (cons-type-p type-type))
3561 (process-types type-type))
3563 *universal-type*)))))))
3565 (defoptimizer (compile derive-type) ((nameoid function))
3566 (when (csubtypep (lvar-type nameoid)
3567 (specifier-type 'null))
3568 (values-specifier-type '(values function boolean boolean))))
3570 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3571 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3572 ;;; optimizer, above).
3573 (defoptimizer (array-element-type derive-type) ((array))
3574 (let ((array-type (lvar-type array)))
3575 (labels ((consify (list)
3578 `(cons (eql ,(car list)) ,(consify (rest list)))))
3579 (get-element-type (a)
3581 (type-specifier (array-type-specialized-element-type a))))
3582 (cond ((eq element-type '*)
3583 (specifier-type 'type-specifier))
3584 ((symbolp element-type)
3585 (make-member-type :members (list element-type)))
3586 ((consp element-type)
3587 (specifier-type (consify element-type)))
3589 (error "can't understand type ~S~%" element-type))))))
3590 (cond ((array-type-p array-type)
3591 (get-element-type array-type))
3592 ((union-type-p array-type)
3594 (mapcar #'get-element-type (union-type-types array-type))))
3596 *universal-type*)))))
3598 ;;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3599 ;;; isn't really related to the CMU CL code, since instead of trying
3600 ;;; to generalize the CMU CL code to allow START and END values, this
3601 ;;; code has been written from scratch following Chapter 7 of
3602 ;;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3603 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
3604 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
3605 ;; isn't really related to the CMU CL code, since instead of trying
3606 ;; to generalize the CMU CL code to allow START and END values, this
3607 ;; code has been written from scratch following Chapter 7 of
3608 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
3609 `(macrolet ((%index (x) `(truly-the index ,x))
3610 (%parent (i) `(ash ,i -1))
3611 (%left (i) `(%index (ash ,i 1)))
3612 (%right (i) `(%index (1+ (ash ,i 1))))
3615 (left (%left i) (%left i)))
3616 ((> left current-heap-size))
3617 (declare (type index i left))
3618 (let* ((i-elt (%elt i))
3619 (i-key (funcall keyfun i-elt))
3620 (left-elt (%elt left))
3621 (left-key (funcall keyfun left-elt)))
3622 (multiple-value-bind (large large-elt large-key)
3623 (if (funcall ,',predicate i-key left-key)
3624 (values left left-elt left-key)
3625 (values i i-elt i-key))
3626 (let ((right (%right i)))
3627 (multiple-value-bind (largest largest-elt)
3628 (if (> right current-heap-size)
3629 (values large large-elt)
3630 (let* ((right-elt (%elt right))
3631 (right-key (funcall keyfun right-elt)))
3632 (if (funcall ,',predicate large-key right-key)
3633 (values right right-elt)
3634 (values large large-elt))))
3635 (cond ((= largest i)
3638 (setf (%elt i) largest-elt
3639 (%elt largest) i-elt
3641 (%sort-vector (keyfun &optional (vtype 'vector))
3642 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
3643 ;; trouble getting type inference to
3644 ;; propagate all the way through this
3645 ;; tangled mess of inlining. The TRULY-THE
3646 ;; here works around that. -- WHN
3648 `(aref (truly-the ,',vtype ,',',vector)
3649 (%index (+ (%index ,i) start-1)))))
3650 (let (;; Heaps prefer 1-based addressing.
3651 (start-1 (1- ,',start))
3652 (current-heap-size (- ,',end ,',start))
3654 (declare (type (integer -1 #.(1- most-positive-fixnum))
3656 (declare (type index current-heap-size))
3657 (declare (type function keyfun))
3658 (loop for i of-type index
3659 from (ash current-heap-size -1) downto 1 do
3662 (when (< current-heap-size 2)
3664 (rotatef (%elt 1) (%elt current-heap-size))
3665 (decf current-heap-size)
3667 (if (typep ,vector 'simple-vector)
3668 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
3669 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
3671 ;; Special-casing the KEY=NIL case lets us avoid some
3673 (%sort-vector #'identity simple-vector)
3674 (%sort-vector ,key simple-vector))
3675 ;; It's hard to anticipate many speed-critical applications for
3676 ;; sorting vector types other than (VECTOR T), so we just lump
3677 ;; them all together in one slow dynamically typed mess.
3679 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
3680 (%sort-vector (or ,key #'identity))))))
3682 ;;;; debuggers' little helpers
3684 ;;; for debugging when transforms are behaving mysteriously,
3685 ;;; e.g. when debugging a problem with an ASH transform
3686 ;;; (defun foo (&optional s)
3687 ;;; (sb-c::/report-lvar s "S outside WHEN")
3688 ;;; (when (and (integerp s) (> s 3))
3689 ;;; (sb-c::/report-lvar s "S inside WHEN")
3690 ;;; (let ((bound (ash 1 (1- s))))
3691 ;;; (sb-c::/report-lvar bound "BOUND")
3692 ;;; (let ((x (- bound))
3694 ;;; (sb-c::/report-lvar x "X")
3695 ;;; (sb-c::/report-lvar x "Y"))
3696 ;;; `(integer ,(- bound) ,(1- bound)))))
3697 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
3698 ;;; and the function doesn't do anything at all.)
3701 (defknown /report-lvar (t t) null)
3702 (deftransform /report-lvar ((x message) (t t))
3703 (format t "~%/in /REPORT-LVAR~%")
3704 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
3705 (when (constant-lvar-p x)
3706 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
3707 (format t "/MESSAGE=~S~%" (lvar-value message))
3708 (give-up-ir1-transform "not a real transform"))
3709 (defun /report-lvar (x message)
3710 (declare (ignore x message))))