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-helper (x r);; 'r' is the stuff to the 'right'.
780 (t (flatten-helper (car x)
781 (flatten-helper (cdr x) r))))))
782 (flatten-helper x nil)))
784 ;;; Take some type of lvar and massage it so that we get a list of the
785 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
787 (defun prepare-arg-for-derive-type (arg)
788 (flet ((listify (arg)
793 (union-type-types arg))
796 (unless (eq arg *empty-type*)
797 ;; Make sure all args are some type of numeric-type. For member
798 ;; types, convert the list of members into a union of equivalent
799 ;; single-element member-type's.
800 (let ((new-args nil))
801 (dolist (arg (listify arg))
802 (if (member-type-p arg)
803 ;; Run down the list of members and convert to a list of
805 (dolist (member (member-type-members arg))
806 (push (if (numberp member)
807 (make-member-type :members (list member))
810 (push arg new-args)))
811 (unless (member *empty-type* new-args)
814 ;;; Convert from the standard type convention for which -0.0 and 0.0
815 ;;; are equal to an intermediate convention for which they are
816 ;;; considered different which is more natural for some of the
818 (defun convert-numeric-type (type)
819 (declare (type numeric-type type))
820 ;;; Only convert real float interval delimiters types.
821 (if (eq (numeric-type-complexp type) :real)
822 (let* ((lo (numeric-type-low type))
823 (lo-val (type-bound-number lo))
824 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
825 (hi (numeric-type-high type))
826 (hi-val (type-bound-number hi))
827 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
828 (if (or lo-float-zero-p hi-float-zero-p)
830 :class (numeric-type-class type)
831 :format (numeric-type-format type)
833 :low (if lo-float-zero-p
835 (list (float 0.0 lo-val))
836 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
838 :high (if hi-float-zero-p
840 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
847 ;;; Convert back from the intermediate convention for which -0.0 and
848 ;;; 0.0 are considered different to the standard type convention for
850 (defun convert-back-numeric-type (type)
851 (declare (type numeric-type type))
852 ;;; Only convert real float interval delimiters types.
853 (if (eq (numeric-type-complexp type) :real)
854 (let* ((lo (numeric-type-low type))
855 (lo-val (type-bound-number lo))
857 (and lo (floatp lo-val) (= lo-val 0.0)
858 (float-sign lo-val)))
859 (hi (numeric-type-high type))
860 (hi-val (type-bound-number hi))
862 (and hi (floatp hi-val) (= hi-val 0.0)
863 (float-sign hi-val))))
865 ;; (float +0.0 +0.0) => (member 0.0)
866 ;; (float -0.0 -0.0) => (member -0.0)
867 ((and lo-float-zero-p hi-float-zero-p)
868 ;; shouldn't have exclusive bounds here..
869 (aver (and (not (consp lo)) (not (consp hi))))
870 (if (= lo-float-zero-p hi-float-zero-p)
871 ;; (float +0.0 +0.0) => (member 0.0)
872 ;; (float -0.0 -0.0) => (member -0.0)
873 (specifier-type `(member ,lo-val))
874 ;; (float -0.0 +0.0) => (float 0.0 0.0)
875 ;; (float +0.0 -0.0) => (float 0.0 0.0)
876 (make-numeric-type :class (numeric-type-class type)
877 :format (numeric-type-format type)
883 ;; (float -0.0 x) => (float 0.0 x)
884 ((and (not (consp lo)) (minusp lo-float-zero-p))
885 (make-numeric-type :class (numeric-type-class type)
886 :format (numeric-type-format type)
888 :low (float 0.0 lo-val)
890 ;; (float (+0.0) x) => (float (0.0) x)
891 ((and (consp lo) (plusp lo-float-zero-p))
892 (make-numeric-type :class (numeric-type-class type)
893 :format (numeric-type-format type)
895 :low (list (float 0.0 lo-val))
898 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
899 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
900 (list (make-member-type :members (list (float 0.0 lo-val)))
901 (make-numeric-type :class (numeric-type-class type)
902 :format (numeric-type-format type)
904 :low (list (float 0.0 lo-val))
908 ;; (float x +0.0) => (float x 0.0)
909 ((and (not (consp hi)) (plusp hi-float-zero-p))
910 (make-numeric-type :class (numeric-type-class type)
911 :format (numeric-type-format type)
914 :high (float 0.0 hi-val)))
915 ;; (float x (-0.0)) => (float x (0.0))
916 ((and (consp hi) (minusp hi-float-zero-p))
917 (make-numeric-type :class (numeric-type-class type)
918 :format (numeric-type-format type)
921 :high (list (float 0.0 hi-val))))
923 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
924 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
925 (list (make-member-type :members (list (float -0.0 hi-val)))
926 (make-numeric-type :class (numeric-type-class type)
927 :format (numeric-type-format type)
930 :high (list (float 0.0 hi-val)))))))
936 ;;; Convert back a possible list of numeric types.
937 (defun convert-back-numeric-type-list (type-list)
941 (dolist (type type-list)
942 (if (numeric-type-p type)
943 (let ((result (convert-back-numeric-type type)))
945 (setf results (append results result))
946 (push result results)))
947 (push type results)))
950 (convert-back-numeric-type type-list))
952 (convert-back-numeric-type-list (union-type-types type-list)))
956 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
957 ;;; belong in the kernel's type logic, invoked always, instead of in
958 ;;; the compiler, invoked only during some type optimizations. (In
959 ;;; fact, as of 0.pre8.100 or so they probably are, under
960 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
962 ;;; Take a list of types and return a canonical type specifier,
963 ;;; combining any MEMBER types together. If both positive and negative
964 ;;; MEMBER types are present they are converted to a float type.
965 ;;; XXX This would be far simpler if the type-union methods could handle
966 ;;; member/number unions.
967 (defun make-canonical-union-type (type-list)
970 (dolist (type type-list)
971 (if (member-type-p type)
972 (setf members (union members (member-type-members type)))
973 (push type misc-types)))
975 (when (null (set-difference `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0) members))
976 (push (specifier-type '(long-float 0.0l0 0.0l0)) misc-types)
977 (setf members (set-difference members `(,(load-time-value (make-unportable-float :long-float-negative-zero)) 0.0l0))))
978 (when (null (set-difference `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0) members))
979 (push (specifier-type '(double-float 0.0d0 0.0d0)) misc-types)
980 (setf members (set-difference members `(,(load-time-value (make-unportable-float :double-float-negative-zero)) 0.0d0))))
981 (when (null (set-difference `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0) members))
982 (push (specifier-type '(single-float 0.0f0 0.0f0)) misc-types)
983 (setf members (set-difference members `(,(load-time-value (make-unportable-float :single-float-negative-zero)) 0.0f0))))
985 (apply #'type-union (make-member-type :members members) misc-types)
986 (apply #'type-union misc-types))))
988 ;;; Convert a member type with a single member to a numeric type.
989 (defun convert-member-type (arg)
990 (let* ((members (member-type-members arg))
991 (member (first members))
992 (member-type (type-of member)))
993 (aver (not (rest members)))
994 (specifier-type (cond ((typep member 'integer)
995 `(integer ,member ,member))
996 ((memq member-type '(short-float single-float
997 double-float long-float))
998 `(,member-type ,member ,member))
1002 ;;; This is used in defoptimizers for computing the resulting type of
1005 ;;; Given the lvar ARG, derive the resulting type using the
1006 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1007 ;;; "atomic" lvar type like numeric-type or member-type (containing
1008 ;;; just one element). It should return the resulting type, which can
1009 ;;; be a list of types.
1011 ;;; For the case of member types, if a MEMBER-FUN is given it is
1012 ;;; called to compute the result otherwise the member type is first
1013 ;;; converted to a numeric type and the DERIVE-FUN is called.
1014 (defun one-arg-derive-type (arg derive-fun member-fun
1015 &optional (convert-type t))
1016 (declare (type function derive-fun)
1017 (type (or null function) member-fun))
1018 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1024 (with-float-traps-masked
1025 (:underflow :overflow :divide-by-zero)
1029 (first (member-type-members x))))))
1030 ;; Otherwise convert to a numeric type.
1031 (let ((result-type-list
1032 (funcall derive-fun (convert-member-type x))))
1034 (convert-back-numeric-type-list result-type-list)
1035 result-type-list))))
1038 (convert-back-numeric-type-list
1039 (funcall derive-fun (convert-numeric-type x)))
1040 (funcall derive-fun x)))
1042 *universal-type*))))
1043 ;; Run down the list of args and derive the type of each one,
1044 ;; saving all of the results in a list.
1045 (let ((results nil))
1046 (dolist (arg arg-list)
1047 (let ((result (deriver arg)))
1049 (setf results (append results result))
1050 (push result results))))
1052 (make-canonical-union-type results)
1053 (first results)))))))
1055 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1056 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1057 ;;; original args and a third which is T to indicate if the two args
1058 ;;; really represent the same lvar. This is useful for deriving the
1059 ;;; type of things like (* x x), which should always be positive. If
1060 ;;; we didn't do this, we wouldn't be able to tell.
1061 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1062 &optional (convert-type t))
1063 (declare (type function derive-fun fun))
1064 (flet ((deriver (x y same-arg)
1065 (cond ((and (member-type-p x) (member-type-p y))
1066 (let* ((x (first (member-type-members x)))
1067 (y (first (member-type-members y)))
1068 (result (with-float-traps-masked
1069 (:underflow :overflow :divide-by-zero
1071 (funcall fun x y))))
1072 (cond ((null result))
1073 ((and (floatp result) (float-nan-p result))
1074 (make-numeric-type :class 'float
1075 :format (type-of result)
1078 (make-member-type :members (list result))))))
1079 ((and (member-type-p x) (numeric-type-p y))
1080 (let* ((x (convert-member-type x))
1081 (y (if convert-type (convert-numeric-type y) y))
1082 (result (funcall derive-fun x y same-arg)))
1084 (convert-back-numeric-type-list result)
1086 ((and (numeric-type-p x) (member-type-p y))
1087 (let* ((x (if convert-type (convert-numeric-type x) x))
1088 (y (convert-member-type y))
1089 (result (funcall derive-fun x y same-arg)))
1091 (convert-back-numeric-type-list result)
1093 ((and (numeric-type-p x) (numeric-type-p y))
1094 (let* ((x (if convert-type (convert-numeric-type x) x))
1095 (y (if convert-type (convert-numeric-type y) y))
1096 (result (funcall derive-fun x y same-arg)))
1098 (convert-back-numeric-type-list result)
1101 *universal-type*))))
1102 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1103 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1104 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1106 (let ((results nil))
1108 ;; Since the args are the same LVARs, just run down the
1111 (let ((result (deriver x x same-arg)))
1113 (setf results (append results result))
1114 (push result results))))
1115 ;; Try all pairwise combinations.
1118 (let ((result (or (deriver x y same-arg)
1119 (numeric-contagion x y))))
1121 (setf results (append results result))
1122 (push result results))))))
1124 (make-canonical-union-type results)
1125 (first results)))))))
1127 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1129 (defoptimizer (+ derive-type) ((x y))
1130 (derive-integer-type
1137 (values (frob (numeric-type-low x) (numeric-type-low y))
1138 (frob (numeric-type-high x) (numeric-type-high y)))))))
1140 (defoptimizer (- derive-type) ((x y))
1141 (derive-integer-type
1148 (values (frob (numeric-type-low x) (numeric-type-high y))
1149 (frob (numeric-type-high x) (numeric-type-low y)))))))
1151 (defoptimizer (* derive-type) ((x y))
1152 (derive-integer-type
1155 (let ((x-low (numeric-type-low x))
1156 (x-high (numeric-type-high x))
1157 (y-low (numeric-type-low y))
1158 (y-high (numeric-type-high y)))
1159 (cond ((not (and x-low y-low))
1161 ((or (minusp x-low) (minusp y-low))
1162 (if (and x-high y-high)
1163 (let ((max (* (max (abs x-low) (abs x-high))
1164 (max (abs y-low) (abs y-high)))))
1165 (values (- max) max))
1168 (values (* x-low y-low)
1169 (if (and x-high y-high)
1173 (defoptimizer (/ derive-type) ((x y))
1174 (numeric-contagion (lvar-type x) (lvar-type y)))
1178 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1180 (defun +-derive-type-aux (x y same-arg)
1181 (if (and (numeric-type-real-p x)
1182 (numeric-type-real-p y))
1185 (let ((x-int (numeric-type->interval x)))
1186 (interval-add x-int x-int))
1187 (interval-add (numeric-type->interval x)
1188 (numeric-type->interval y))))
1189 (result-type (numeric-contagion x y)))
1190 ;; If the result type is a float, we need to be sure to coerce
1191 ;; the bounds into the correct type.
1192 (when (eq (numeric-type-class result-type) 'float)
1193 (setf result (interval-func
1195 (coerce x (or (numeric-type-format result-type)
1199 :class (if (and (eq (numeric-type-class x) 'integer)
1200 (eq (numeric-type-class y) 'integer))
1201 ;; The sum of integers is always an integer.
1203 (numeric-type-class result-type))
1204 :format (numeric-type-format result-type)
1205 :low (interval-low result)
1206 :high (interval-high result)))
1207 ;; general contagion
1208 (numeric-contagion x y)))
1210 (defoptimizer (+ derive-type) ((x y))
1211 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1213 (defun --derive-type-aux (x y same-arg)
1214 (if (and (numeric-type-real-p x)
1215 (numeric-type-real-p y))
1217 ;; (- X X) is always 0.
1219 (make-interval :low 0 :high 0)
1220 (interval-sub (numeric-type->interval x)
1221 (numeric-type->interval y))))
1222 (result-type (numeric-contagion x y)))
1223 ;; If the result type is a float, we need to be sure to coerce
1224 ;; the bounds into the correct type.
1225 (when (eq (numeric-type-class result-type) 'float)
1226 (setf result (interval-func
1228 (coerce x (or (numeric-type-format result-type)
1232 :class (if (and (eq (numeric-type-class x) 'integer)
1233 (eq (numeric-type-class y) 'integer))
1234 ;; The difference of integers is always an integer.
1236 (numeric-type-class result-type))
1237 :format (numeric-type-format result-type)
1238 :low (interval-low result)
1239 :high (interval-high result)))
1240 ;; general contagion
1241 (numeric-contagion x y)))
1243 (defoptimizer (- derive-type) ((x y))
1244 (two-arg-derive-type x y #'--derive-type-aux #'-))
1246 (defun *-derive-type-aux (x y same-arg)
1247 (if (and (numeric-type-real-p x)
1248 (numeric-type-real-p y))
1250 ;; (* X X) is always positive, so take care to do it right.
1252 (interval-sqr (numeric-type->interval x))
1253 (interval-mul (numeric-type->interval x)
1254 (numeric-type->interval y))))
1255 (result-type (numeric-contagion x y)))
1256 ;; If the result type is a float, we need to be sure to coerce
1257 ;; the bounds into the correct type.
1258 (when (eq (numeric-type-class result-type) 'float)
1259 (setf result (interval-func
1261 (coerce x (or (numeric-type-format result-type)
1265 :class (if (and (eq (numeric-type-class x) 'integer)
1266 (eq (numeric-type-class y) 'integer))
1267 ;; The product of integers is always an integer.
1269 (numeric-type-class result-type))
1270 :format (numeric-type-format result-type)
1271 :low (interval-low result)
1272 :high (interval-high result)))
1273 (numeric-contagion x y)))
1275 (defoptimizer (* derive-type) ((x y))
1276 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1278 (defun /-derive-type-aux (x y same-arg)
1279 (if (and (numeric-type-real-p x)
1280 (numeric-type-real-p y))
1282 ;; (/ X X) is always 1, except if X can contain 0. In
1283 ;; that case, we shouldn't optimize the division away
1284 ;; because we want 0/0 to signal an error.
1286 (not (interval-contains-p
1287 0 (interval-closure (numeric-type->interval y)))))
1288 (make-interval :low 1 :high 1)
1289 (interval-div (numeric-type->interval x)
1290 (numeric-type->interval y))))
1291 (result-type (numeric-contagion x y)))
1292 ;; If the result type is a float, we need to be sure to coerce
1293 ;; the bounds into the correct type.
1294 (when (eq (numeric-type-class result-type) 'float)
1295 (setf result (interval-func
1297 (coerce x (or (numeric-type-format result-type)
1300 (make-numeric-type :class (numeric-type-class result-type)
1301 :format (numeric-type-format result-type)
1302 :low (interval-low result)
1303 :high (interval-high result)))
1304 (numeric-contagion x y)))
1306 (defoptimizer (/ derive-type) ((x y))
1307 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1311 (defun ash-derive-type-aux (n-type shift same-arg)
1312 (declare (ignore same-arg))
1313 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1314 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1315 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1316 ;; two bignums yielding zero) and it's hard to avoid that
1317 ;; calculation in here.
1318 #+(and cmu sb-xc-host)
1319 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1320 (typep (numeric-type-high n-type) 'bignum))
1321 (or (typep (numeric-type-low shift) 'bignum)
1322 (typep (numeric-type-high shift) 'bignum)))
1323 (return-from ash-derive-type-aux *universal-type*))
1324 (flet ((ash-outer (n s)
1325 (when (and (fixnump s)
1327 (> s sb!xc:most-negative-fixnum))
1329 ;; KLUDGE: The bare 64's here should be related to
1330 ;; symbolic machine word size values somehow.
1333 (if (and (fixnump s)
1334 (> s sb!xc:most-negative-fixnum))
1336 (if (minusp n) -1 0))))
1337 (or (and (csubtypep n-type (specifier-type 'integer))
1338 (csubtypep shift (specifier-type 'integer))
1339 (let ((n-low (numeric-type-low n-type))
1340 (n-high (numeric-type-high n-type))
1341 (s-low (numeric-type-low shift))
1342 (s-high (numeric-type-high shift)))
1343 (make-numeric-type :class 'integer :complexp :real
1346 (ash-outer n-low s-high)
1347 (ash-inner n-low s-low)))
1350 (ash-inner n-high s-low)
1351 (ash-outer n-high s-high))))))
1354 (defoptimizer (ash derive-type) ((n shift))
1355 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1357 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1358 (macrolet ((frob (fun)
1359 `#'(lambda (type type2)
1360 (declare (ignore type2))
1361 (let ((lo (numeric-type-low type))
1362 (hi (numeric-type-high type)))
1363 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1365 (defoptimizer (%negate derive-type) ((num))
1366 (derive-integer-type num num (frob -))))
1368 (defun lognot-derive-type-aux (int)
1369 (derive-integer-type-aux int int
1370 (lambda (type type2)
1371 (declare (ignore type2))
1372 (let ((lo (numeric-type-low type))
1373 (hi (numeric-type-high type)))
1374 (values (if hi (lognot hi) nil)
1375 (if lo (lognot lo) nil)
1376 (numeric-type-class type)
1377 (numeric-type-format type))))))
1379 (defoptimizer (lognot derive-type) ((int))
1380 (lognot-derive-type-aux (lvar-type int)))
1382 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1383 (defoptimizer (%negate derive-type) ((num))
1384 (flet ((negate-bound (b)
1386 (set-bound (- (type-bound-number b))
1388 (one-arg-derive-type num
1390 (modified-numeric-type
1392 :low (negate-bound (numeric-type-high type))
1393 :high (negate-bound (numeric-type-low type))))
1396 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1397 (defoptimizer (abs derive-type) ((num))
1398 (let ((type (lvar-type num)))
1399 (if (and (numeric-type-p type)
1400 (eq (numeric-type-class type) 'integer)
1401 (eq (numeric-type-complexp type) :real))
1402 (let ((lo (numeric-type-low type))
1403 (hi (numeric-type-high type)))
1404 (make-numeric-type :class 'integer :complexp :real
1405 :low (cond ((and hi (minusp hi))
1411 :high (if (and hi lo)
1412 (max (abs hi) (abs lo))
1414 (numeric-contagion type type))))
1416 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1417 (defun abs-derive-type-aux (type)
1418 (cond ((eq (numeric-type-complexp type) :complex)
1419 ;; The absolute value of a complex number is always a
1420 ;; non-negative float.
1421 (let* ((format (case (numeric-type-class type)
1422 ((integer rational) 'single-float)
1423 (t (numeric-type-format type))))
1424 (bound-format (or format 'float)))
1425 (make-numeric-type :class 'float
1428 :low (coerce 0 bound-format)
1431 ;; The absolute value of a real number is a non-negative real
1432 ;; of the same type.
1433 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1434 (class (numeric-type-class type))
1435 (format (numeric-type-format type))
1436 (bound-type (or format class 'real)))
1441 :low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
1442 :high (coerce-numeric-bound
1443 (interval-high abs-bnd) bound-type))))))
1445 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1446 (defoptimizer (abs derive-type) ((num))
1447 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1449 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1450 (defoptimizer (truncate derive-type) ((number divisor))
1451 (let ((number-type (lvar-type number))
1452 (divisor-type (lvar-type divisor))
1453 (integer-type (specifier-type 'integer)))
1454 (if (and (numeric-type-p number-type)
1455 (csubtypep number-type integer-type)
1456 (numeric-type-p divisor-type)
1457 (csubtypep divisor-type integer-type))
1458 (let ((number-low (numeric-type-low number-type))
1459 (number-high (numeric-type-high number-type))
1460 (divisor-low (numeric-type-low divisor-type))
1461 (divisor-high (numeric-type-high divisor-type)))
1462 (values-specifier-type
1463 `(values ,(integer-truncate-derive-type number-low number-high
1464 divisor-low divisor-high)
1465 ,(integer-rem-derive-type number-low number-high
1466 divisor-low divisor-high))))
1469 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1472 (defun rem-result-type (number-type divisor-type)
1473 ;; Figure out what the remainder type is. The remainder is an
1474 ;; integer if both args are integers; a rational if both args are
1475 ;; rational; and a float otherwise.
1476 (cond ((and (csubtypep number-type (specifier-type 'integer))
1477 (csubtypep divisor-type (specifier-type 'integer)))
1479 ((and (csubtypep number-type (specifier-type 'rational))
1480 (csubtypep divisor-type (specifier-type 'rational)))
1482 ((and (csubtypep number-type (specifier-type 'float))
1483 (csubtypep divisor-type (specifier-type 'float)))
1484 ;; Both are floats so the result is also a float, of
1485 ;; the largest type.
1486 (or (float-format-max (numeric-type-format number-type)
1487 (numeric-type-format divisor-type))
1489 ((and (csubtypep number-type (specifier-type 'float))
1490 (csubtypep divisor-type (specifier-type 'rational)))
1491 ;; One of the arguments is a float and the other is a
1492 ;; rational. The remainder is a float of the same
1494 (or (numeric-type-format number-type) 'float))
1495 ((and (csubtypep divisor-type (specifier-type 'float))
1496 (csubtypep number-type (specifier-type 'rational)))
1497 ;; One of the arguments is a float and the other is a
1498 ;; rational. The remainder is a float of the same
1500 (or (numeric-type-format divisor-type) 'float))
1502 ;; Some unhandled combination. This usually means both args
1503 ;; are REAL so the result is a REAL.
1506 (defun truncate-derive-type-quot (number-type divisor-type)
1507 (let* ((rem-type (rem-result-type number-type divisor-type))
1508 (number-interval (numeric-type->interval number-type))
1509 (divisor-interval (numeric-type->interval divisor-type)))
1510 ;;(declare (type (member '(integer rational float)) rem-type))
1511 ;; We have real numbers now.
1512 (cond ((eq rem-type 'integer)
1513 ;; Since the remainder type is INTEGER, both args are
1515 (let* ((res (integer-truncate-derive-type
1516 (interval-low number-interval)
1517 (interval-high number-interval)
1518 (interval-low divisor-interval)
1519 (interval-high divisor-interval))))
1520 (specifier-type (if (listp res) res 'integer))))
1522 (let ((quot (truncate-quotient-bound
1523 (interval-div number-interval
1524 divisor-interval))))
1525 (specifier-type `(integer ,(or (interval-low quot) '*)
1526 ,(or (interval-high quot) '*))))))))
1528 (defun truncate-derive-type-rem (number-type divisor-type)
1529 (let* ((rem-type (rem-result-type number-type divisor-type))
1530 (number-interval (numeric-type->interval number-type))
1531 (divisor-interval (numeric-type->interval divisor-type))
1532 (rem (truncate-rem-bound number-interval divisor-interval)))
1533 ;;(declare (type (member '(integer rational float)) rem-type))
1534 ;; We have real numbers now.
1535 (cond ((eq rem-type 'integer)
1536 ;; Since the remainder type is INTEGER, both args are
1538 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1539 ,(or (interval-high rem) '*))))
1541 (multiple-value-bind (class format)
1544 (values 'integer nil))
1546 (values 'rational nil))
1547 ((or single-float double-float #!+long-float long-float)
1548 (values 'float rem-type))
1550 (values 'float nil))
1553 (when (member rem-type '(float single-float double-float
1554 #!+long-float long-float))
1555 (setf rem (interval-func #'(lambda (x)
1556 (coerce x rem-type))
1558 (make-numeric-type :class class
1560 :low (interval-low rem)
1561 :high (interval-high rem)))))))
1563 (defun truncate-derive-type-quot-aux (num div same-arg)
1564 (declare (ignore same-arg))
1565 (if (and (numeric-type-real-p num)
1566 (numeric-type-real-p div))
1567 (truncate-derive-type-quot num div)
1570 (defun truncate-derive-type-rem-aux (num div same-arg)
1571 (declare (ignore same-arg))
1572 (if (and (numeric-type-real-p num)
1573 (numeric-type-real-p div))
1574 (truncate-derive-type-rem num div)
1577 (defoptimizer (truncate derive-type) ((number divisor))
1578 (let ((quot (two-arg-derive-type number divisor
1579 #'truncate-derive-type-quot-aux #'truncate))
1580 (rem (two-arg-derive-type number divisor
1581 #'truncate-derive-type-rem-aux #'rem)))
1582 (when (and quot rem)
1583 (make-values-type :required (list quot rem)))))
1585 (defun ftruncate-derive-type-quot (number-type divisor-type)
1586 ;; The bounds are the same as for truncate. However, the first
1587 ;; result is a float of some type. We need to determine what that
1588 ;; type is. Basically it's the more contagious of the two types.
1589 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1590 (res-type (numeric-contagion number-type divisor-type)))
1591 (make-numeric-type :class 'float
1592 :format (numeric-type-format res-type)
1593 :low (numeric-type-low q-type)
1594 :high (numeric-type-high q-type))))
1596 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1597 (declare (ignore same-arg))
1598 (if (and (numeric-type-real-p n)
1599 (numeric-type-real-p d))
1600 (ftruncate-derive-type-quot n d)
1603 (defoptimizer (ftruncate derive-type) ((number divisor))
1605 (two-arg-derive-type number divisor
1606 #'ftruncate-derive-type-quot-aux #'ftruncate))
1607 (rem (two-arg-derive-type number divisor
1608 #'truncate-derive-type-rem-aux #'rem)))
1609 (when (and quot rem)
1610 (make-values-type :required (list quot rem)))))
1612 (defun %unary-truncate-derive-type-aux (number)
1613 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1615 (defoptimizer (%unary-truncate derive-type) ((number))
1616 (one-arg-derive-type number
1617 #'%unary-truncate-derive-type-aux
1620 ;;; Define optimizers for FLOOR and CEILING.
1622 ((def (name q-name r-name)
1623 (let ((q-aux (symbolicate q-name "-AUX"))
1624 (r-aux (symbolicate r-name "-AUX")))
1626 ;; Compute type of quotient (first) result.
1627 (defun ,q-aux (number-type divisor-type)
1628 (let* ((number-interval
1629 (numeric-type->interval number-type))
1631 (numeric-type->interval divisor-type))
1632 (quot (,q-name (interval-div number-interval
1633 divisor-interval))))
1634 (specifier-type `(integer ,(or (interval-low quot) '*)
1635 ,(or (interval-high quot) '*)))))
1636 ;; Compute type of remainder.
1637 (defun ,r-aux (number-type divisor-type)
1638 (let* ((divisor-interval
1639 (numeric-type->interval divisor-type))
1640 (rem (,r-name divisor-interval))
1641 (result-type (rem-result-type number-type divisor-type)))
1642 (multiple-value-bind (class format)
1645 (values 'integer nil))
1647 (values 'rational nil))
1648 ((or single-float double-float #!+long-float long-float)
1649 (values 'float result-type))
1651 (values 'float nil))
1654 (when (member result-type '(float single-float double-float
1655 #!+long-float long-float))
1656 ;; Make sure that the limits on the interval have
1658 (setf rem (interval-func (lambda (x)
1659 (coerce x result-type))
1661 (make-numeric-type :class class
1663 :low (interval-low rem)
1664 :high (interval-high rem)))))
1665 ;; the optimizer itself
1666 (defoptimizer (,name derive-type) ((number divisor))
1667 (flet ((derive-q (n d same-arg)
1668 (declare (ignore same-arg))
1669 (if (and (numeric-type-real-p n)
1670 (numeric-type-real-p d))
1673 (derive-r (n d same-arg)
1674 (declare (ignore same-arg))
1675 (if (and (numeric-type-real-p n)
1676 (numeric-type-real-p d))
1679 (let ((quot (two-arg-derive-type
1680 number divisor #'derive-q #',name))
1681 (rem (two-arg-derive-type
1682 number divisor #'derive-r #'mod)))
1683 (when (and quot rem)
1684 (make-values-type :required (list quot rem))))))))))
1686 (def floor floor-quotient-bound floor-rem-bound)
1687 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1689 ;;; Define optimizers for FFLOOR and FCEILING
1690 (macrolet ((def (name q-name r-name)
1691 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1692 (r-aux (symbolicate r-name "-AUX")))
1694 ;; Compute type of quotient (first) result.
1695 (defun ,q-aux (number-type divisor-type)
1696 (let* ((number-interval
1697 (numeric-type->interval number-type))
1699 (numeric-type->interval divisor-type))
1700 (quot (,q-name (interval-div number-interval
1702 (res-type (numeric-contagion number-type
1705 :class (numeric-type-class res-type)
1706 :format (numeric-type-format res-type)
1707 :low (interval-low quot)
1708 :high (interval-high quot))))
1710 (defoptimizer (,name derive-type) ((number divisor))
1711 (flet ((derive-q (n d same-arg)
1712 (declare (ignore same-arg))
1713 (if (and (numeric-type-real-p n)
1714 (numeric-type-real-p d))
1717 (derive-r (n d same-arg)
1718 (declare (ignore same-arg))
1719 (if (and (numeric-type-real-p n)
1720 (numeric-type-real-p d))
1723 (let ((quot (two-arg-derive-type
1724 number divisor #'derive-q #',name))
1725 (rem (two-arg-derive-type
1726 number divisor #'derive-r #'mod)))
1727 (when (and quot rem)
1728 (make-values-type :required (list quot rem))))))))))
1730 (def ffloor floor-quotient-bound floor-rem-bound)
1731 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
1733 ;;; functions to compute the bounds on the quotient and remainder for
1734 ;;; the FLOOR function
1735 (defun floor-quotient-bound (quot)
1736 ;; Take the floor of the quotient and then massage it into what we
1738 (let ((lo (interval-low quot))
1739 (hi (interval-high quot)))
1740 ;; Take the floor of the lower bound. The result is always a
1741 ;; closed lower bound.
1743 (floor (type-bound-number lo))
1745 ;; For the upper bound, we need to be careful.
1748 ;; An open bound. We need to be careful here because
1749 ;; the floor of '(10.0) is 9, but the floor of
1751 (multiple-value-bind (q r) (floor (first hi))
1756 ;; A closed bound, so the answer is obvious.
1760 (make-interval :low lo :high hi)))
1761 (defun floor-rem-bound (div)
1762 ;; The remainder depends only on the divisor. Try to get the
1763 ;; correct sign for the remainder if we can.
1764 (case (interval-range-info div)
1766 ;; The divisor is always positive.
1767 (let ((rem (interval-abs div)))
1768 (setf (interval-low rem) 0)
1769 (when (and (numberp (interval-high rem))
1770 (not (zerop (interval-high rem))))
1771 ;; The remainder never contains the upper bound. However,
1772 ;; watch out for the case where the high limit is zero!
1773 (setf (interval-high rem) (list (interval-high rem))))
1776 ;; The divisor is always negative.
1777 (let ((rem (interval-neg (interval-abs div))))
1778 (setf (interval-high rem) 0)
1779 (when (numberp (interval-low rem))
1780 ;; The remainder never contains the lower bound.
1781 (setf (interval-low rem) (list (interval-low rem))))
1784 ;; The divisor can be positive or negative. All bets off. The
1785 ;; magnitude of remainder is the maximum value of the divisor.
1786 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1787 ;; The bound never reaches the limit, so make the interval open.
1788 (make-interval :low (if limit
1791 :high (list limit))))))
1793 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
1794 => #S(INTERVAL :LOW 0 :HIGH 10)
1795 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1796 => #S(INTERVAL :LOW 0 :HIGH 10)
1797 (floor-quotient-bound (make-interval :low 0.3 :high 10))
1798 => #S(INTERVAL :LOW 0 :HIGH 10)
1799 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
1800 => #S(INTERVAL :LOW 0 :HIGH 9)
1801 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
1802 => #S(INTERVAL :LOW 0 :HIGH 10)
1803 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
1804 => #S(INTERVAL :LOW 0 :HIGH 10)
1805 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1806 => #S(INTERVAL :LOW -2 :HIGH 10)
1807 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1808 => #S(INTERVAL :LOW -1 :HIGH 10)
1809 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
1810 => #S(INTERVAL :LOW -1 :HIGH 10)
1812 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
1813 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1814 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
1815 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1816 (floor-rem-bound (make-interval :low -10 :high -2.3))
1817 #S(INTERVAL :LOW (-10) :HIGH 0)
1818 (floor-rem-bound (make-interval :low 0.3 :high 10))
1819 => #S(INTERVAL :LOW 0 :HIGH '(10))
1820 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
1821 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
1822 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
1823 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1826 ;;; same functions for CEILING
1827 (defun ceiling-quotient-bound (quot)
1828 ;; Take the ceiling of the quotient and then massage it into what we
1830 (let ((lo (interval-low quot))
1831 (hi (interval-high quot)))
1832 ;; Take the ceiling of the upper bound. The result is always a
1833 ;; closed upper bound.
1835 (ceiling (type-bound-number hi))
1837 ;; For the lower bound, we need to be careful.
1840 ;; An open bound. We need to be careful here because
1841 ;; the ceiling of '(10.0) is 11, but the ceiling of
1843 (multiple-value-bind (q r) (ceiling (first lo))
1848 ;; A closed bound, so the answer is obvious.
1852 (make-interval :low lo :high hi)))
1853 (defun ceiling-rem-bound (div)
1854 ;; The remainder depends only on the divisor. Try to get the
1855 ;; correct sign for the remainder if we can.
1856 (case (interval-range-info div)
1858 ;; Divisor is always positive. The remainder is negative.
1859 (let ((rem (interval-neg (interval-abs div))))
1860 (setf (interval-high rem) 0)
1861 (when (and (numberp (interval-low rem))
1862 (not (zerop (interval-low rem))))
1863 ;; The remainder never contains the upper bound. However,
1864 ;; watch out for the case when the upper bound is zero!
1865 (setf (interval-low rem) (list (interval-low rem))))
1868 ;; Divisor is always negative. The remainder is positive
1869 (let ((rem (interval-abs div)))
1870 (setf (interval-low rem) 0)
1871 (when (numberp (interval-high rem))
1872 ;; The remainder never contains the lower bound.
1873 (setf (interval-high rem) (list (interval-high rem))))
1876 ;; The divisor can be positive or negative. All bets off. The
1877 ;; magnitude of remainder is the maximum value of the divisor.
1878 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
1879 ;; The bound never reaches the limit, so make the interval open.
1880 (make-interval :low (if limit
1883 :high (list limit))))))
1886 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
1887 => #S(INTERVAL :LOW 1 :HIGH 11)
1888 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
1889 => #S(INTERVAL :LOW 1 :HIGH 11)
1890 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
1891 => #S(INTERVAL :LOW 1 :HIGH 10)
1892 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
1893 => #S(INTERVAL :LOW 1 :HIGH 10)
1894 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
1895 => #S(INTERVAL :LOW 1 :HIGH 11)
1896 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
1897 => #S(INTERVAL :LOW 1 :HIGH 11)
1898 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
1899 => #S(INTERVAL :LOW -1 :HIGH 11)
1900 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
1901 => #S(INTERVAL :LOW 0 :HIGH 11)
1902 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
1903 => #S(INTERVAL :LOW -1 :HIGH 11)
1905 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
1906 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
1907 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
1908 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
1909 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
1910 => #S(INTERVAL :LOW 0 :HIGH (10))
1911 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
1912 => #S(INTERVAL :LOW (-10) :HIGH 0)
1913 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
1914 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
1915 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
1916 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
1919 (defun truncate-quotient-bound (quot)
1920 ;; For positive quotients, truncate is exactly like floor. For
1921 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
1922 ;; it's the union of the two pieces.
1923 (case (interval-range-info quot)
1926 (floor-quotient-bound quot))
1928 ;; just like CEILING
1929 (ceiling-quotient-bound quot))
1931 ;; Split the interval into positive and negative pieces, compute
1932 ;; the result for each piece and put them back together.
1933 (destructuring-bind (neg pos) (interval-split 0 quot t t)
1934 (interval-merge-pair (ceiling-quotient-bound neg)
1935 (floor-quotient-bound pos))))))
1937 (defun truncate-rem-bound (num div)
1938 ;; This is significantly more complicated than FLOOR or CEILING. We
1939 ;; need both the number and the divisor to determine the range. The
1940 ;; basic idea is to split the ranges of NUM and DEN into positive
1941 ;; and negative pieces and deal with each of the four possibilities
1943 (case (interval-range-info num)
1945 (case (interval-range-info div)
1947 (floor-rem-bound div))
1949 (ceiling-rem-bound div))
1951 (destructuring-bind (neg pos) (interval-split 0 div t t)
1952 (interval-merge-pair (truncate-rem-bound num neg)
1953 (truncate-rem-bound num pos))))))
1955 (case (interval-range-info div)
1957 (ceiling-rem-bound div))
1959 (floor-rem-bound div))
1961 (destructuring-bind (neg pos) (interval-split 0 div t t)
1962 (interval-merge-pair (truncate-rem-bound num neg)
1963 (truncate-rem-bound num pos))))))
1965 (destructuring-bind (neg pos) (interval-split 0 num t t)
1966 (interval-merge-pair (truncate-rem-bound neg div)
1967 (truncate-rem-bound pos div))))))
1970 ;;; Derive useful information about the range. Returns three values:
1971 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
1972 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
1973 ;;; - The abs of the maximal value if there is one, or nil if it is
1975 (defun numeric-range-info (low high)
1976 (cond ((and low (not (minusp low)))
1977 (values '+ low high))
1978 ((and high (not (plusp high)))
1979 (values '- (- high) (if low (- low) nil)))
1981 (values nil 0 (and low high (max (- low) high))))))
1983 (defun integer-truncate-derive-type
1984 (number-low number-high divisor-low divisor-high)
1985 ;; The result cannot be larger in magnitude than the number, but the
1986 ;; sign might change. If we can determine the sign of either the
1987 ;; number or the divisor, we can eliminate some of the cases.
1988 (multiple-value-bind (number-sign number-min number-max)
1989 (numeric-range-info number-low number-high)
1990 (multiple-value-bind (divisor-sign divisor-min divisor-max)
1991 (numeric-range-info divisor-low divisor-high)
1992 (when (and divisor-max (zerop divisor-max))
1993 ;; We've got a problem: guaranteed division by zero.
1994 (return-from integer-truncate-derive-type t))
1995 (when (zerop divisor-min)
1996 ;; We'll assume that they aren't going to divide by zero.
1998 (cond ((and number-sign divisor-sign)
1999 ;; We know the sign of both.
2000 (if (eq number-sign divisor-sign)
2001 ;; Same sign, so the result will be positive.
2002 `(integer ,(if divisor-max
2003 (truncate number-min divisor-max)
2006 (truncate number-max divisor-min)
2008 ;; Different signs, the result will be negative.
2009 `(integer ,(if number-max
2010 (- (truncate number-max divisor-min))
2013 (- (truncate number-min divisor-max))
2015 ((eq divisor-sign '+)
2016 ;; The divisor is positive. Therefore, the number will just
2017 ;; become closer to zero.
2018 `(integer ,(if number-low
2019 (truncate number-low divisor-min)
2022 (truncate number-high divisor-min)
2024 ((eq divisor-sign '-)
2025 ;; The divisor is negative. Therefore, the absolute value of
2026 ;; the number will become closer to zero, but the sign will also
2028 `(integer ,(if number-high
2029 (- (truncate number-high divisor-min))
2032 (- (truncate number-low divisor-min))
2034 ;; The divisor could be either positive or negative.
2036 ;; The number we are dividing has a bound. Divide that by the
2037 ;; smallest posible divisor.
2038 (let ((bound (truncate number-max divisor-min)))
2039 `(integer ,(- bound) ,bound)))
2041 ;; The number we are dividing is unbounded, so we can't tell
2042 ;; anything about the result.
2045 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2046 (defun integer-rem-derive-type
2047 (number-low number-high divisor-low divisor-high)
2048 (if (and divisor-low divisor-high)
2049 ;; We know the range of the divisor, and the remainder must be
2050 ;; smaller than the divisor. We can tell the sign of the
2051 ;; remainer if we know the sign of the number.
2052 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2053 `(integer ,(if (or (null number-low)
2054 (minusp number-low))
2057 ,(if (or (null number-high)
2058 (plusp number-high))
2061 ;; The divisor is potentially either very positive or very
2062 ;; negative. Therefore, the remainer is unbounded, but we might
2063 ;; be able to tell something about the sign from the number.
2064 `(integer ,(if (and number-low (not (minusp number-low)))
2065 ;; The number we are dividing is positive.
2066 ;; Therefore, the remainder must be positive.
2069 ,(if (and number-high (not (plusp number-high)))
2070 ;; The number we are dividing is negative.
2071 ;; Therefore, the remainder must be negative.
2075 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2076 (defoptimizer (random derive-type) ((bound &optional state))
2077 (let ((type (lvar-type bound)))
2078 (when (numeric-type-p type)
2079 (let ((class (numeric-type-class type))
2080 (high (numeric-type-high type))
2081 (format (numeric-type-format type)))
2085 :low (coerce 0 (or format class 'real))
2086 :high (cond ((not high) nil)
2087 ((eq class 'integer) (max (1- high) 0))
2088 ((or (consp high) (zerop high)) high)
2091 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2092 (defun random-derive-type-aux (type)
2093 (let ((class (numeric-type-class type))
2094 (high (numeric-type-high type))
2095 (format (numeric-type-format type)))
2099 :low (coerce 0 (or format class 'real))
2100 :high (cond ((not high) nil)
2101 ((eq class 'integer) (max (1- high) 0))
2102 ((or (consp high) (zerop high)) high)
2105 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2106 (defoptimizer (random derive-type) ((bound &optional state))
2107 (one-arg-derive-type bound #'random-derive-type-aux nil))
2109 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2111 ;;; Return the maximum number of bits an integer of the supplied type
2112 ;;; can take up, or NIL if it is unbounded. The second (third) value
2113 ;;; is T if the integer can be positive (negative) and NIL if not.
2114 ;;; Zero counts as positive.
2115 (defun integer-type-length (type)
2116 (if (numeric-type-p type)
2117 (let ((min (numeric-type-low type))
2118 (max (numeric-type-high type)))
2119 (values (and min max (max (integer-length min) (integer-length max)))
2120 (or (null max) (not (minusp max)))
2121 (or (null min) (minusp min))))
2124 (defun logand-derive-type-aux (x y &optional same-leaf)
2125 (declare (ignore same-leaf))
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)
2157 (declare (ignore same-leaf))
2158 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2159 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2161 ((and (not x-neg) (not y-neg))
2162 ;; Both are positive.
2163 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2167 ;; X must be negative.
2169 ;; Both are negative. The result is going to be negative
2170 ;; and be the same length or shorter than the smaller.
2171 (if (and x-len y-len)
2173 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2175 (specifier-type '(integer * -1)))
2176 ;; X is negative, but we don't know about Y. The result
2177 ;; will be negative, but no more negative than X.
2179 `(integer ,(or (numeric-type-low x) '*)
2182 ;; X might be either positive or negative.
2184 ;; But Y is negative. The result will be negative.
2186 `(integer ,(or (numeric-type-low y) '*)
2188 ;; We don't know squat about either. It won't get any bigger.
2189 (if (and x-len y-len)
2191 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2193 (specifier-type 'integer))))))))
2195 (defun logxor-derive-type-aux (x y &optional same-leaf)
2196 (declare (ignore same-leaf))
2197 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2198 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2200 ((or (and (not x-neg) (not y-neg))
2201 (and (not x-pos) (not y-pos)))
2202 ;; Either both are negative or both are positive. The result
2203 ;; will be positive, and as long as the longer.
2204 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2207 ((or (and (not x-pos) (not y-neg))
2208 (and (not y-neg) (not y-pos)))
2209 ;; Either X is negative and Y is positive or vice-versa. The
2210 ;; result will be negative.
2211 (specifier-type `(integer ,(if (and x-len y-len)
2212 (ash -1 (max x-len y-len))
2215 ;; We can't tell what the sign of the result is going to be.
2216 ;; All we know is that we don't create new bits.
2218 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2220 (specifier-type 'integer))))))
2222 (macrolet ((deffrob (logfun)
2223 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2224 `(defoptimizer (,logfun derive-type) ((x y))
2225 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2230 ;;; FIXME: could actually do stuff with SAME-LEAF
2231 (defoptimizer (logeqv derive-type) ((x y))
2232 (two-arg-derive-type x y (lambda (x y same-leaf)
2233 (lognot-derive-type-aux
2234 (logxor-derive-type-aux x y same-leaf)))
2236 (defoptimizer (lognand derive-type) ((x y))
2237 (two-arg-derive-type x y (lambda (x y same-leaf)
2238 (lognot-derive-type-aux
2239 (logand-derive-type-aux x y same-leaf)))
2241 (defoptimizer (lognor derive-type) ((x y))
2242 (two-arg-derive-type x y (lambda (x y same-leaf)
2243 (lognot-derive-type-aux
2244 (logior-derive-type-aux x y same-leaf)))
2246 (defoptimizer (logandc1 derive-type) ((x y))
2247 (two-arg-derive-type x y (lambda (x y same-leaf)
2248 (logand-derive-type-aux
2249 (lognot-derive-type-aux x) y nil))
2251 (defoptimizer (logandc2 derive-type) ((x y))
2252 (two-arg-derive-type x y (lambda (x y same-leaf)
2253 (logand-derive-type-aux
2254 x (lognot-derive-type-aux y) nil))
2256 (defoptimizer (logorc1 derive-type) ((x y))
2257 (two-arg-derive-type x y (lambda (x y same-leaf)
2258 (logior-derive-type-aux
2259 (lognot-derive-type-aux x) y nil))
2261 (defoptimizer (logorc2 derive-type) ((x y))
2262 (two-arg-derive-type x y (lambda (x y same-leaf)
2263 (logior-derive-type-aux
2264 x (lognot-derive-type-aux y) nil))
2267 ;;;; miscellaneous derive-type methods
2269 (defoptimizer (integer-length derive-type) ((x))
2270 (let ((x-type (lvar-type x)))
2271 (when (numeric-type-p x-type)
2272 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2273 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2274 ;; careful about LO or HI being NIL, though. Also, if 0 is
2275 ;; contained in X, the lower bound is obviously 0.
2276 (flet ((null-or-min (a b)
2277 (and a b (min (integer-length a)
2278 (integer-length b))))
2280 (and a b (max (integer-length a)
2281 (integer-length b)))))
2282 (let* ((min (numeric-type-low x-type))
2283 (max (numeric-type-high x-type))
2284 (min-len (null-or-min min max))
2285 (max-len (null-or-max min max)))
2286 (when (ctypep 0 x-type)
2288 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2290 (defoptimizer (isqrt derive-type) ((x))
2291 (let ((x-type (lvar-type x)))
2292 (when (numeric-type-p x-type)
2293 (let* ((lo (numeric-type-low x-type))
2294 (hi (numeric-type-high x-type))
2295 (lo-res (if lo (isqrt lo) '*))
2296 (hi-res (if hi (isqrt hi) '*)))
2297 (specifier-type `(integer ,lo-res ,hi-res))))))
2299 (defoptimizer (code-char derive-type) ((code))
2300 (specifier-type 'base-char))
2302 (defoptimizer (values derive-type) ((&rest values))
2303 (make-values-type :required (mapcar #'lvar-type values)))
2305 ;;;; byte operations
2307 ;;;; We try to turn byte operations into simple logical operations.
2308 ;;;; First, we convert byte specifiers into separate size and position
2309 ;;;; arguments passed to internal %FOO functions. We then attempt to
2310 ;;;; transform the %FOO functions into boolean operations when the
2311 ;;;; size and position are constant and the operands are fixnums.
2313 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2314 ;; expressions that evaluate to the SIZE and POSITION of
2315 ;; the byte-specifier form SPEC. We may wrap a let around
2316 ;; the result of the body to bind some variables.
2318 ;; If the spec is a BYTE form, then bind the vars to the
2319 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2320 ;; and BYTE-POSITION. The goal of this transformation is to
2321 ;; avoid consing up byte specifiers and then immediately
2322 ;; throwing them away.
2323 (with-byte-specifier ((size-var pos-var spec) &body body)
2324 (once-only ((spec `(macroexpand ,spec))
2326 `(if (and (consp ,spec)
2327 (eq (car ,spec) 'byte)
2328 (= (length ,spec) 3))
2329 (let ((,size-var (second ,spec))
2330 (,pos-var (third ,spec)))
2332 (let ((,size-var `(byte-size ,,temp))
2333 (,pos-var `(byte-position ,,temp)))
2334 `(let ((,,temp ,,spec))
2337 (define-source-transform ldb (spec int)
2338 (with-byte-specifier (size pos spec)
2339 `(%ldb ,size ,pos ,int)))
2341 (define-source-transform dpb (newbyte spec int)
2342 (with-byte-specifier (size pos spec)
2343 `(%dpb ,newbyte ,size ,pos ,int)))
2345 (define-source-transform mask-field (spec int)
2346 (with-byte-specifier (size pos spec)
2347 `(%mask-field ,size ,pos ,int)))
2349 (define-source-transform deposit-field (newbyte spec int)
2350 (with-byte-specifier (size pos spec)
2351 `(%deposit-field ,newbyte ,size ,pos ,int))))
2353 (defoptimizer (%ldb derive-type) ((size posn num))
2354 (let ((size (lvar-type size)))
2355 (if (and (numeric-type-p size)
2356 (csubtypep size (specifier-type 'integer)))
2357 (let ((size-high (numeric-type-high size)))
2358 (if (and size-high (<= size-high sb!vm:n-word-bits))
2359 (specifier-type `(unsigned-byte* ,size-high))
2360 (specifier-type 'unsigned-byte)))
2363 (defoptimizer (%mask-field derive-type) ((size posn num))
2364 (let ((size (lvar-type size))
2365 (posn (lvar-type posn)))
2366 (if (and (numeric-type-p size)
2367 (csubtypep size (specifier-type 'integer))
2368 (numeric-type-p posn)
2369 (csubtypep posn (specifier-type 'integer)))
2370 (let ((size-high (numeric-type-high size))
2371 (posn-high (numeric-type-high posn)))
2372 (if (and size-high posn-high
2373 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2374 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2375 (specifier-type 'unsigned-byte)))
2378 (defun %deposit-field-derive-type-aux (size posn int)
2379 (let ((size (lvar-type size))
2380 (posn (lvar-type posn))
2381 (int (lvar-type int)))
2382 (when (and (numeric-type-p size)
2383 (numeric-type-p posn)
2384 (numeric-type-p int))
2385 (let ((size-high (numeric-type-high size))
2386 (posn-high (numeric-type-high posn))
2387 (high (numeric-type-high int))
2388 (low (numeric-type-low int)))
2389 (when (and size-high posn-high high low
2390 ;; KLUDGE: we need this cutoff here, otherwise we
2391 ;; will merrily derive the type of %DPB as
2392 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2393 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2394 ;; 1073741822))), with hilarious consequences. We
2395 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2396 ;; over a reasonable amount of shifting, even on
2397 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2398 ;; machine integers are 64-bits. -- CSR,
2400 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2401 (let ((raw-bit-count (max (integer-length high)
2402 (integer-length low)
2403 (+ size-high posn-high))))
2406 `(signed-byte ,(1+ raw-bit-count))
2407 `(unsigned-byte* ,raw-bit-count)))))))))
2409 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2410 (%deposit-field-derive-type-aux size posn int))
2412 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2413 (%deposit-field-derive-type-aux size posn int))
2415 (deftransform %ldb ((size posn int)
2416 (fixnum fixnum integer)
2417 (unsigned-byte #.sb!vm:n-word-bits))
2418 "convert to inline logical operations"
2419 `(logand (ash int (- posn))
2420 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2421 (- size ,sb!vm:n-word-bits))))
2423 (deftransform %mask-field ((size posn int)
2424 (fixnum fixnum integer)
2425 (unsigned-byte #.sb!vm:n-word-bits))
2426 "convert to inline logical operations"
2428 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2429 (- size ,sb!vm:n-word-bits))
2432 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2433 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2434 ;;; as the result type, as that would allow result types that cover
2435 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2436 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2438 (deftransform %dpb ((new size posn int)
2440 (unsigned-byte #.sb!vm:n-word-bits))
2441 "convert to inline logical operations"
2442 `(let ((mask (ldb (byte size 0) -1)))
2443 (logior (ash (logand new mask) posn)
2444 (logand int (lognot (ash mask posn))))))
2446 (deftransform %dpb ((new size posn int)
2448 (signed-byte #.sb!vm:n-word-bits))
2449 "convert to inline logical operations"
2450 `(let ((mask (ldb (byte size 0) -1)))
2451 (logior (ash (logand new mask) posn)
2452 (logand int (lognot (ash mask posn))))))
2454 (deftransform %deposit-field ((new size posn int)
2456 (unsigned-byte #.sb!vm:n-word-bits))
2457 "convert to inline logical operations"
2458 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2459 (logior (logand new mask)
2460 (logand int (lognot mask)))))
2462 (deftransform %deposit-field ((new size posn int)
2464 (signed-byte #.sb!vm:n-word-bits))
2465 "convert to inline logical operations"
2466 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2467 (logior (logand new mask)
2468 (logand int (lognot mask)))))
2470 ;;; Modular functions
2472 ;;; (ldb (byte s 0) (foo x y ...)) =
2473 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2475 ;;; and similar for other arguments.
2477 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2479 ;;; For good functions, we just recursively cut arguments; their
2480 ;;; "goodness" means that the result will not increase (in the
2481 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2482 ;;; replaced with the version, cutting its result to WIDTH or more
2483 ;;; bits. If we have changed anything, we need to flush old derived
2484 ;;; types, because they have nothing in common with the new code.
2485 (defun cut-to-width (lvar width)
2486 (declare (type lvar lvar) (type (integer 0) width))
2487 (labels ((reoptimize-node (node name)
2488 (setf (node-derived-type node)
2490 (info :function :type name)))
2491 (setf (lvar-%derived-type (node-lvar node)) nil)
2492 (setf (node-reoptimize node) t)
2493 (setf (block-reoptimize (node-block node)) t)
2494 (setf (component-reoptimize (node-component node)) t))
2495 (cut-node (node &aux did-something)
2496 (when (and (combination-p node)
2497 (fun-info-p (basic-combination-kind node)))
2498 (let* ((fun-ref (lvar-use (combination-fun node)))
2499 (fun-name (leaf-source-name (ref-leaf fun-ref)))
2500 (modular-fun (find-modular-version fun-name width))
2501 (name (and (modular-fun-info-p modular-fun)
2502 (modular-fun-info-name modular-fun))))
2503 (when (and modular-fun
2504 (not (and (eq name 'logand)
2506 (single-value-type (node-derived-type node))
2507 (specifier-type `(unsigned-byte ,width))))))
2508 (unless (eq modular-fun :good)
2509 (setq did-something t)
2512 (find-free-fun name "in a strange place"))
2513 (setf (combination-kind node) :full))
2514 (dolist (arg (basic-combination-args node))
2515 (when (cut-lvar arg)
2516 (setq did-something t)))
2518 (reoptimize-node node fun-name))
2520 (cut-lvar (lvar &aux did-something)
2521 (do-uses (node lvar)
2522 (when (cut-node node)
2523 (setq did-something t)))
2527 (defoptimizer (logand optimizer) ((x y) node)
2528 (let ((result-type (single-value-type (node-derived-type node))))
2529 (when (numeric-type-p result-type)
2530 (let ((low (numeric-type-low result-type))
2531 (high (numeric-type-high result-type)))
2532 (when (and (numberp low)
2535 (let ((width (integer-length high)))
2536 (when (some (lambda (x) (<= width x))
2537 *modular-funs-widths*)
2538 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2539 (cut-to-width x width)
2540 (cut-to-width y width)
2541 nil ; After fixing above, replace with T.
2544 ;;; miscellanous numeric transforms
2546 ;;; If a constant appears as the first arg, swap the args.
2547 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
2548 (if (and (constant-lvar-p x)
2549 (not (constant-lvar-p y)))
2550 `(,(lvar-fun-name (basic-combination-fun node))
2553 (give-up-ir1-transform)))
2555 (dolist (x '(= char= + * logior logand logxor))
2556 (%deftransform x '(function * *) #'commutative-arg-swap
2557 "place constant arg last"))
2559 ;;; Handle the case of a constant BOOLE-CODE.
2560 (deftransform boole ((op x y) * *)
2561 "convert to inline logical operations"
2562 (unless (constant-lvar-p op)
2563 (give-up-ir1-transform "BOOLE code is not a constant."))
2564 (let ((control (lvar-value op)))
2570 (#.boole-c1 '(lognot x))
2571 (#.boole-c2 '(lognot y))
2572 (#.boole-and '(logand x y))
2573 (#.boole-ior '(logior x y))
2574 (#.boole-xor '(logxor x y))
2575 (#.boole-eqv '(logeqv x y))
2576 (#.boole-nand '(lognand x y))
2577 (#.boole-nor '(lognor x y))
2578 (#.boole-andc1 '(logandc1 x y))
2579 (#.boole-andc2 '(logandc2 x y))
2580 (#.boole-orc1 '(logorc1 x y))
2581 (#.boole-orc2 '(logorc2 x y))
2583 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2586 ;;;; converting special case multiply/divide to shifts
2588 ;;; If arg is a constant power of two, turn * into a shift.
2589 (deftransform * ((x y) (integer integer) *)
2590 "convert x*2^k to shift"
2591 (unless (constant-lvar-p y)
2592 (give-up-ir1-transform))
2593 (let* ((y (lvar-value y))
2595 (len (1- (integer-length y-abs))))
2596 (unless (= y-abs (ash 1 len))
2597 (give-up-ir1-transform))
2602 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2603 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
2605 (flet ((frob (y ceil-p)
2606 (unless (constant-lvar-p y)
2607 (give-up-ir1-transform))
2608 (let* ((y (lvar-value y))
2610 (len (1- (integer-length y-abs))))
2611 (unless (= y-abs (ash 1 len))
2612 (give-up-ir1-transform))
2613 (let ((shift (- len))
2615 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
2616 `(let ((x (+ x ,delta)))
2618 `(values (ash (- x) ,shift)
2619 (- (- (logand (- x) ,mask)) ,delta))
2620 `(values (ash x ,shift)
2621 (- (logand x ,mask) ,delta))))))))
2622 (deftransform floor ((x y) (integer integer) *)
2623 "convert division by 2^k to shift"
2625 (deftransform ceiling ((x y) (integer integer) *)
2626 "convert division by 2^k to shift"
2629 ;;; Do the same for MOD.
2630 (deftransform mod ((x y) (integer integer) *)
2631 "convert remainder mod 2^k to LOGAND"
2632 (unless (constant-lvar-p y)
2633 (give-up-ir1-transform))
2634 (let* ((y (lvar-value y))
2636 (len (1- (integer-length y-abs))))
2637 (unless (= y-abs (ash 1 len))
2638 (give-up-ir1-transform))
2639 (let ((mask (1- y-abs)))
2641 `(- (logand (- x) ,mask))
2642 `(logand x ,mask)))))
2644 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2645 (deftransform truncate ((x y) (integer integer))
2646 "convert division by 2^k to shift"
2647 (unless (constant-lvar-p y)
2648 (give-up-ir1-transform))
2649 (let* ((y (lvar-value y))
2651 (len (1- (integer-length y-abs))))
2652 (unless (= y-abs (ash 1 len))
2653 (give-up-ir1-transform))
2654 (let* ((shift (- len))
2657 (values ,(if (minusp y)
2659 `(- (ash (- x) ,shift)))
2660 (- (logand (- x) ,mask)))
2661 (values ,(if (minusp y)
2662 `(- (ash (- x) ,shift))
2664 (logand x ,mask))))))
2666 ;;; And the same for REM.
2667 (deftransform rem ((x y) (integer integer) *)
2668 "convert remainder mod 2^k to LOGAND"
2669 (unless (constant-lvar-p y)
2670 (give-up-ir1-transform))
2671 (let* ((y (lvar-value y))
2673 (len (1- (integer-length y-abs))))
2674 (unless (= y-abs (ash 1 len))
2675 (give-up-ir1-transform))
2676 (let ((mask (1- y-abs)))
2678 (- (logand (- x) ,mask))
2679 (logand x ,mask)))))
2681 ;;;; arithmetic and logical identity operation elimination
2683 ;;; Flush calls to various arith functions that convert to the
2684 ;;; identity function or a constant.
2685 (macrolet ((def (name identity result)
2686 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
2687 "fold identity operations"
2694 (def logxor -1 (lognot x))
2697 (deftransform logand ((x y) (* (constant-arg t)) *)
2698 "fold identity operation"
2699 (let ((y (lvar-value y)))
2700 (unless (and (plusp y)
2701 (= y (1- (ash 1 (integer-length y)))))
2702 (give-up-ir1-transform))
2703 (unless (csubtypep (lvar-type x)
2704 (specifier-type `(integer 0 ,y)))
2705 (give-up-ir1-transform))
2708 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2709 ;;; (* 0 -4.0) is -0.0.
2710 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
2711 "convert (- 0 x) to negate"
2713 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
2714 "convert (* x 0) to 0"
2717 ;;; Return T if in an arithmetic op including lvars X and Y, the
2718 ;;; result type is not affected by the type of X. That is, Y is at
2719 ;;; least as contagious as X.
2721 (defun not-more-contagious (x y)
2722 (declare (type continuation x y))
2723 (let ((x (lvar-type x))
2725 (values (type= (numeric-contagion x y)
2726 (numeric-contagion y y)))))
2727 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2728 ;;; XXX needs more work as valid transforms are missed; some cases are
2729 ;;; specific to particular transform functions so the use of this
2730 ;;; function may need a re-think.
2731 (defun not-more-contagious (x y)
2732 (declare (type lvar x y))
2733 (flet ((simple-numeric-type (num)
2734 (and (numeric-type-p num)
2735 ;; Return non-NIL if NUM is integer, rational, or a float
2736 ;; of some type (but not FLOAT)
2737 (case (numeric-type-class num)
2741 (numeric-type-format num))
2744 (let ((x (lvar-type x))
2746 (if (and (simple-numeric-type x)
2747 (simple-numeric-type y))
2748 (values (type= (numeric-contagion x y)
2749 (numeric-contagion y y)))))))
2753 ;;; If y is not constant, not zerop, or is contagious, or a positive
2754 ;;; float +0.0 then give up.
2755 (deftransform + ((x y) (t (constant-arg t)) *)
2757 (let ((val (lvar-value y)))
2758 (unless (and (zerop val)
2759 (not (and (floatp val) (plusp (float-sign val))))
2760 (not-more-contagious y x))
2761 (give-up-ir1-transform)))
2766 ;;; If y is not constant, not zerop, or is contagious, or a negative
2767 ;;; float -0.0 then give up.
2768 (deftransform - ((x y) (t (constant-arg t)) *)
2770 (let ((val (lvar-value y)))
2771 (unless (and (zerop val)
2772 (not (and (floatp val) (minusp (float-sign val))))
2773 (not-more-contagious y x))
2774 (give-up-ir1-transform)))
2777 ;;; Fold (OP x +/-1)
2778 (macrolet ((def (name result minus-result)
2779 `(deftransform ,name ((x y) (t (constant-arg real)) *)
2780 "fold identity operations"
2781 (let ((val (lvar-value y)))
2782 (unless (and (= (abs val) 1)
2783 (not-more-contagious y x))
2784 (give-up-ir1-transform))
2785 (if (minusp val) ',minus-result ',result)))))
2786 (def * x (%negate x))
2787 (def / x (%negate x))
2788 (def expt x (/ 1 x)))
2790 ;;; Fold (expt x n) into multiplications for small integral values of
2791 ;;; N; convert (expt x 1/2) to sqrt.
2792 (deftransform expt ((x y) (t (constant-arg real)) *)
2793 "recode as multiplication or sqrt"
2794 (let ((val (lvar-value y)))
2795 ;; If Y would cause the result to be promoted to the same type as
2796 ;; Y, we give up. If not, then the result will be the same type
2797 ;; as X, so we can replace the exponentiation with simple
2798 ;; multiplication and division for small integral powers.
2799 (unless (not-more-contagious y x)
2800 (give-up-ir1-transform))
2802 (let ((x-type (lvar-type x)))
2803 (cond ((csubtypep x-type (specifier-type '(or rational
2804 (complex rational))))
2806 ((csubtypep x-type (specifier-type 'real))
2810 ((csubtypep x-type (specifier-type 'complex))
2811 ;; both parts are float
2813 (t (give-up-ir1-transform)))))
2814 ((= val 2) '(* x x))
2815 ((= val -2) '(/ (* x x)))
2816 ((= val 3) '(* x x x))
2817 ((= val -3) '(/ (* x x x)))
2818 ((= val 1/2) '(sqrt x))
2819 ((= val -1/2) '(/ (sqrt x)))
2820 (t (give-up-ir1-transform)))))
2822 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
2823 ;;; transformations?
2824 ;;; Perhaps we should have to prove that the denominator is nonzero before
2825 ;;; doing them? -- WHN 19990917
2826 (macrolet ((def (name)
2827 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
2834 (macrolet ((def (name)
2835 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
2844 ;;;; character operations
2846 (deftransform char-equal ((a b) (base-char base-char))
2848 '(let* ((ac (char-code a))
2850 (sum (logxor ac bc)))
2852 (when (eql sum #x20)
2853 (let ((sum (+ ac bc)))
2854 (and (> sum 161) (< sum 213)))))))
2856 (deftransform char-upcase ((x) (base-char))
2858 '(let ((n-code (char-code x)))
2859 (if (and (> n-code #o140) ; Octal 141 is #\a.
2860 (< n-code #o173)) ; Octal 172 is #\z.
2861 (code-char (logxor #x20 n-code))
2864 (deftransform char-downcase ((x) (base-char))
2866 '(let ((n-code (char-code x)))
2867 (if (and (> n-code 64) ; 65 is #\A.
2868 (< n-code 91)) ; 90 is #\Z.
2869 (code-char (logxor #x20 n-code))
2872 ;;;; equality predicate transforms
2874 ;;; Return true if X and Y are lvars whose only use is a
2875 ;;; reference to the same leaf, and the value of the leaf cannot
2877 (defun same-leaf-ref-p (x y)
2878 (declare (type lvar x y))
2879 (let ((x-use (principal-lvar-use x))
2880 (y-use (principal-lvar-use y)))
2883 (eq (ref-leaf x-use) (ref-leaf y-use))
2884 (constant-reference-p x-use))))
2886 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
2887 ;;; if there is no intersection between the types of the arguments,
2888 ;;; then the result is definitely false.
2889 (deftransform simple-equality-transform ((x y) * *
2891 (cond ((same-leaf-ref-p x y)
2893 ((not (types-equal-or-intersect (lvar-type x)
2897 (give-up-ir1-transform))))
2900 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
2905 ;;; This is similar to SIMPLE-EQUALITY-PREDICATE, except that we also
2906 ;;; try to convert to a type-specific predicate or EQ:
2907 ;;; -- If both args are characters, convert to CHAR=. This is better than
2908 ;;; just converting to EQ, since CHAR= may have special compilation
2909 ;;; strategies for non-standard representations, etc.
2910 ;;; -- If either arg is definitely not a number, then we can compare
2912 ;;; -- Otherwise, we try to put the arg we know more about second. If X
2913 ;;; is constant then we put it second. If X is a subtype of Y, we put
2914 ;;; it second. These rules make it easier for the back end to match
2915 ;;; these interesting cases.
2916 ;;; -- If Y is a fixnum, then we quietly pass because the back end can
2917 ;;; handle that case, otherwise give an efficiency note.
2918 (deftransform eql ((x y) * *)
2919 "convert to simpler equality predicate"
2920 (let ((x-type (lvar-type x))
2921 (y-type (lvar-type y))
2922 (char-type (specifier-type 'character))
2923 (number-type (specifier-type 'number)))
2924 (cond ((same-leaf-ref-p x y)
2926 ((not (types-equal-or-intersect x-type y-type))
2928 ((and (csubtypep x-type char-type)
2929 (csubtypep y-type char-type))
2931 ((or (not (types-equal-or-intersect x-type number-type))
2932 (not (types-equal-or-intersect y-type number-type)))
2934 ((and (not (constant-lvar-p y))
2935 (or (constant-lvar-p x)
2936 (and (csubtypep x-type y-type)
2937 (not (csubtypep y-type x-type)))))
2940 (give-up-ir1-transform)))))
2942 ;;; Convert to EQL if both args are rational and complexp is specified
2943 ;;; and the same for both.
2944 (deftransform = ((x y) * *)
2946 (let ((x-type (lvar-type x))
2947 (y-type (lvar-type y)))
2948 (if (and (csubtypep x-type (specifier-type 'number))
2949 (csubtypep y-type (specifier-type 'number)))
2950 (cond ((or (and (csubtypep x-type (specifier-type 'float))
2951 (csubtypep y-type (specifier-type 'float)))
2952 (and (csubtypep x-type (specifier-type '(complex float)))
2953 (csubtypep y-type (specifier-type '(complex float)))))
2954 ;; They are both floats. Leave as = so that -0.0 is
2955 ;; handled correctly.
2956 (give-up-ir1-transform))
2957 ((or (and (csubtypep x-type (specifier-type 'rational))
2958 (csubtypep y-type (specifier-type 'rational)))
2959 (and (csubtypep x-type
2960 (specifier-type '(complex rational)))
2962 (specifier-type '(complex rational)))))
2963 ;; They are both rationals and complexp is the same.
2967 (give-up-ir1-transform
2968 "The operands might not be the same type.")))
2969 (give-up-ir1-transform
2970 "The operands might not be the same type."))))
2972 ;;; If LVAR's type is a numeric type, then return the type, otherwise
2973 ;;; GIVE-UP-IR1-TRANSFORM.
2974 (defun numeric-type-or-lose (lvar)
2975 (declare (type lvar lvar))
2976 (let ((res (lvar-type lvar)))
2977 (unless (numeric-type-p res) (give-up-ir1-transform))
2980 ;;; See whether we can statically determine (< X Y) using type
2981 ;;; information. If X's high bound is < Y's low, then X < Y.
2982 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
2983 ;;; NIL). If not, at least make sure any constant arg is second.
2984 (macrolet ((def (name reflexive-p surely-true surely-false)
2985 `(deftransform ,name ((x y))
2986 (if (same-leaf-ref-p x y)
2988 (let ((x (or (type-approximate-interval (lvar-type x))
2989 (give-up-ir1-transform)))
2990 (y (or (type-approximate-interval (lvar-type y))
2991 (give-up-ir1-transform))))
2996 ((and (constant-lvar-p x)
2997 (not (constant-lvar-p y)))
3000 (give-up-ir1-transform))))))))
3001 (def < nil (interval-< x y) (interval->= x y))
3002 (def > nil (interval-< y x) (interval->= y x))
3003 (def <= t (interval->= y x) (interval-< y x))
3004 (def >= t (interval->= x y) (interval-< x y)))
3006 (defun ir1-transform-char< (x y first second inverse)
3008 ((same-leaf-ref-p x y) nil)
3009 ;; If we had interval representation of character types, as we
3010 ;; might eventually have to to support 2^21 characters, then here
3011 ;; we could do some compile-time computation as in transforms for
3012 ;; < above. -- CSR, 2003-07-01
3013 ((and (constant-lvar-p first)
3014 (not (constant-lvar-p second)))
3016 (t (give-up-ir1-transform))))
3018 (deftransform char< ((x y) (character character) *)
3019 (ir1-transform-char< x y x y 'char>))
3021 (deftransform char> ((x y) (character character) *)
3022 (ir1-transform-char< y x x y 'char<))
3024 ;;;; converting N-arg comparisons
3026 ;;;; We convert calls to N-arg comparison functions such as < into
3027 ;;;; two-arg calls. This transformation is enabled for all such
3028 ;;;; comparisons in this file. If any of these predicates are not
3029 ;;;; open-coded, then the transformation should be removed at some
3030 ;;;; point to avoid pessimization.
3032 ;;; This function is used for source transformation of N-arg
3033 ;;; comparison functions other than inequality. We deal both with
3034 ;;; converting to two-arg calls and inverting the sense of the test,
3035 ;;; if necessary. If the call has two args, then we pass or return a
3036 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3037 ;;; then we transform to code that returns true. Otherwise, we bind
3038 ;;; all the arguments and expand into a bunch of IFs.
3039 (declaim (ftype (function (symbol list boolean t) *) multi-compare))
3040 (defun multi-compare (predicate args not-p type)
3041 (let ((nargs (length args)))
3042 (cond ((< nargs 1) (values nil t))
3043 ((= nargs 1) `(progn (the ,type ,@args) t))
3046 `(if (,predicate ,(first args) ,(second args)) nil t)
3049 (do* ((i (1- nargs) (1- i))
3051 (current (gensym) (gensym))
3052 (vars (list current) (cons current vars))
3054 `(if (,predicate ,current ,last)
3056 `(if (,predicate ,current ,last)
3059 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3062 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3063 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3064 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3065 (define-source-transform <= (&rest args) (multi-compare '> args t 'real))
3066 (define-source-transform >= (&rest args) (multi-compare '< args t 'real))
3068 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3070 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3072 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3074 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3076 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3079 (define-source-transform char-equal (&rest args)
3080 (multi-compare 'char-equal args nil 'character))
3081 (define-source-transform char-lessp (&rest args)
3082 (multi-compare 'char-lessp args nil 'character))
3083 (define-source-transform char-greaterp (&rest args)
3084 (multi-compare 'char-greaterp args nil 'character))
3085 (define-source-transform char-not-greaterp (&rest args)
3086 (multi-compare 'char-greaterp args t 'character))
3087 (define-source-transform char-not-lessp (&rest args)
3088 (multi-compare 'char-lessp args t 'character))
3090 ;;; This function does source transformation of N-arg inequality
3091 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3092 ;;; arg cases. If there are more than two args, then we expand into
3093 ;;; the appropriate n^2 comparisons only when speed is important.
3094 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3095 (defun multi-not-equal (predicate args type)
3096 (let ((nargs (length args)))
3097 (cond ((< nargs 1) (values nil t))
3098 ((= nargs 1) `(progn (the ,type ,@args) t))
3100 `(if (,predicate ,(first args) ,(second args)) nil t))
3101 ((not (policy *lexenv*
3102 (and (>= speed space)
3103 (>= speed compilation-speed))))
3106 (let ((vars (make-gensym-list nargs)))
3107 (do ((var vars next)
3108 (next (cdr vars) (cdr next))
3111 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3113 (let ((v1 (first var)))
3115 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3117 (define-source-transform /= (&rest args)
3118 (multi-not-equal '= args 'number))
3119 (define-source-transform char/= (&rest args)
3120 (multi-not-equal 'char= args 'character))
3121 (define-source-transform char-not-equal (&rest args)
3122 (multi-not-equal 'char-equal args 'character))
3124 ;;; Expand MAX and MIN into the obvious comparisons.
3125 (define-source-transform max (arg0 &rest rest)
3126 (once-only ((arg0 arg0))
3128 `(values (the real ,arg0))
3129 `(let ((maxrest (max ,@rest)))
3130 (if (> ,arg0 maxrest) ,arg0 maxrest)))))
3131 (define-source-transform min (arg0 &rest rest)
3132 (once-only ((arg0 arg0))
3134 `(values (the real ,arg0))
3135 `(let ((minrest (min ,@rest)))
3136 (if (< ,arg0 minrest) ,arg0 minrest)))))
3138 ;;;; converting N-arg arithmetic functions
3140 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3141 ;;;; versions, and degenerate cases are flushed.
3143 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3144 (declaim (ftype (function (symbol t list) list) associate-args))
3145 (defun associate-args (function first-arg more-args)
3146 (let ((next (rest more-args))
3147 (arg (first more-args)))
3149 `(,function ,first-arg ,arg)
3150 (associate-args function `(,function ,first-arg ,arg) next))))
3152 ;;; Do source transformations for transitive functions such as +.
3153 ;;; One-arg cases are replaced with the arg and zero arg cases with
3154 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3155 ;;; ensure (with THE) that the argument in one-argument calls is.
3156 (defun source-transform-transitive (fun args identity
3157 &optional one-arg-result-type)
3158 (declare (symbol fun) (list args))
3161 (1 (if one-arg-result-type
3162 `(values (the ,one-arg-result-type ,(first args)))
3163 `(values ,(first args))))
3166 (associate-args fun (first args) (rest args)))))
3168 (define-source-transform + (&rest args)
3169 (source-transform-transitive '+ args 0 'number))
3170 (define-source-transform * (&rest args)
3171 (source-transform-transitive '* args 1 'number))
3172 (define-source-transform logior (&rest args)
3173 (source-transform-transitive 'logior args 0 'integer))
3174 (define-source-transform logxor (&rest args)
3175 (source-transform-transitive 'logxor args 0 'integer))
3176 (define-source-transform logand (&rest args)
3177 (source-transform-transitive 'logand args -1 'integer))
3178 (define-source-transform logeqv (&rest args)
3179 (source-transform-transitive 'logeqv args -1 'integer))
3181 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3182 ;;; because when they are given one argument, they return its absolute
3185 (define-source-transform gcd (&rest args)
3188 (1 `(abs (the integer ,(first args))))
3190 (t (associate-args 'gcd (first args) (rest args)))))
3192 (define-source-transform lcm (&rest args)
3195 (1 `(abs (the integer ,(first args))))
3197 (t (associate-args 'lcm (first args) (rest args)))))
3199 ;;; Do source transformations for intransitive n-arg functions such as
3200 ;;; /. With one arg, we form the inverse. With two args we pass.
3201 ;;; Otherwise we associate into two-arg calls.
3202 (declaim (ftype (function (symbol list t)
3203 (values list &optional (member nil t)))
3204 source-transform-intransitive))
3205 (defun source-transform-intransitive (function args inverse)
3207 ((0 2) (values nil t))
3208 (1 `(,@inverse ,(first args)))
3209 (t (associate-args function (first args) (rest args)))))
3211 (define-source-transform - (&rest args)
3212 (source-transform-intransitive '- args '(%negate)))
3213 (define-source-transform / (&rest args)
3214 (source-transform-intransitive '/ args '(/ 1)))
3216 ;;;; transforming APPLY
3218 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3219 ;;; only needs to understand one kind of variable-argument call. It is
3220 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3221 (define-source-transform apply (fun arg &rest more-args)
3222 (let ((args (cons arg more-args)))
3223 `(multiple-value-call ,fun
3224 ,@(mapcar (lambda (x)
3227 (values-list ,(car (last args))))))
3229 ;;;; transforming FORMAT
3231 ;;;; If the control string is a compile-time constant, then replace it
3232 ;;;; with a use of the FORMATTER macro so that the control string is
3233 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3234 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3235 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3237 ;;; for compile-time argument count checking.
3239 ;;; FIXME I: this is currently called from DEFTRANSFORMs, the vast
3240 ;;; majority of which are not going to transform the code, but instead
3241 ;;; are going to GIVE-UP-IR1-TRANSFORM unconditionally. It would be
3242 ;;; nice to make this explicit, maybe by implementing a new
3243 ;;; "optimizer" (say, DEFOPTIMIZER CONSISTENCY-CHECK).
3245 ;;; FIXME II: In some cases, type information could be correlated; for
3246 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3247 ;;; of a corresponding argument is known and does not intersect the
3248 ;;; list type, a warning could be signalled.
3249 (defun check-format-args (string args fun)
3250 (declare (type string string))
3251 (unless (typep string 'simple-string)
3252 (setq string (coerce string 'simple-string)))
3253 (multiple-value-bind (min max)
3254 (handler-case (sb!format:%compiler-walk-format-string string args)
3255 (sb!format:format-error (c)
3256 (compiler-warn "~A" c)))
3258 (let ((nargs (length args)))
3261 (compiler-warn "Too few arguments (~D) to ~S ~S: ~
3262 requires at least ~D."
3263 nargs fun string min))
3265 (;; to get warned about probably bogus code at
3266 ;; cross-compile time.
3267 #+sb-xc-host compiler-warn
3268 ;; ANSI saith that too many arguments doesn't cause a
3270 #-sb-xc-host compiler-style-warn
3271 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3272 nargs fun string max)))))))
3274 (defoptimizer (format optimizer) ((dest control &rest args))
3275 (when (constant-lvar-p control)
3276 (let ((x (lvar-value control)))
3278 (check-format-args x args 'format)))))
3280 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3281 :policy (> speed space))
3282 (unless (constant-lvar-p control)
3283 (give-up-ir1-transform "The control string is not a constant."))
3284 (let ((arg-names (make-gensym-list (length args))))
3285 `(lambda (dest control ,@arg-names)
3286 (declare (ignore control))
3287 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
3289 (deftransform format ((stream control &rest args) (stream function &rest t) *
3290 :policy (> speed space))
3291 (let ((arg-names (make-gensym-list (length args))))
3292 `(lambda (stream control ,@arg-names)
3293 (funcall control stream ,@arg-names)
3296 (deftransform format ((tee control &rest args) ((member t) function &rest t) *
3297 :policy (> speed space))
3298 (let ((arg-names (make-gensym-list (length args))))
3299 `(lambda (tee control ,@arg-names)
3300 (declare (ignore tee))
3301 (funcall control *standard-output* ,@arg-names)
3306 `(defoptimizer (,name optimizer) ((control &rest args))
3307 (when (constant-lvar-p control)
3308 (let ((x (lvar-value control)))
3310 (check-format-args x args ',name)))))))
3313 #+sb-xc-host ; Only we should be using these
3316 (def compiler-abort)
3317 (def compiler-error)
3319 (def compiler-style-warn)
3320 (def compiler-notify)
3321 (def maybe-compiler-notify)
3324 (defoptimizer (cerror optimizer) ((report control &rest args))
3325 (when (and (constant-lvar-p control)
3326 (constant-lvar-p report))
3327 (let ((x (lvar-value control))
3328 (y (lvar-value report)))
3329 (when (and (stringp x) (stringp y))
3330 (multiple-value-bind (min1 max1)
3332 (sb!format:%compiler-walk-format-string x args)
3333 (sb!format:format-error (c)
3334 (compiler-warn "~A" c)))
3336 (multiple-value-bind (min2 max2)
3338 (sb!format:%compiler-walk-format-string y args)
3339 (sb!format:format-error (c)
3340 (compiler-warn "~A" c)))
3342 (let ((nargs (length args)))
3344 ((< nargs (min min1 min2))
3345 (compiler-warn "Too few arguments (~D) to ~S ~S ~S: ~
3346 requires at least ~D."
3347 nargs 'cerror y x (min min1 min2)))
3348 ((> nargs (max max1 max2))
3349 (;; to get warned about probably bogus code at
3350 ;; cross-compile time.
3351 #+sb-xc-host compiler-warn
3352 ;; ANSI saith that too many arguments doesn't cause a
3354 #-sb-xc-host compiler-style-warn
3355 "Too many arguments (~D) to ~S ~S ~S: uses at most ~D."
3356 nargs 'cerror y x (max max1 max2)))))))))))))
3358 (defoptimizer (coerce derive-type) ((value type))
3360 ((constant-lvar-p type)
3361 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3362 ;; but dealing with the niggle that complex canonicalization gets
3363 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3365 (let* ((specifier (lvar-value type))
3366 (result-typeoid (careful-specifier-type specifier)))
3368 ((null result-typeoid) nil)
3369 ((csubtypep result-typeoid (specifier-type 'number))
3370 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3371 ;; Rule of Canonical Representation for Complex Rationals,
3372 ;; which is a truly nasty delivery to field.
3374 ((csubtypep result-typeoid (specifier-type 'real))
3375 ;; cleverness required here: it would be nice to deduce
3376 ;; that something of type (INTEGER 2 3) coerced to type
3377 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3378 ;; FLOAT gets its own clause because it's implemented as
3379 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3382 ((and (numeric-type-p result-typeoid)
3383 (eq (numeric-type-complexp result-typeoid) :real))
3384 ;; FIXME: is this clause (a) necessary or (b) useful?
3386 ((or (csubtypep result-typeoid
3387 (specifier-type '(complex single-float)))
3388 (csubtypep result-typeoid
3389 (specifier-type '(complex double-float)))
3391 (csubtypep result-typeoid
3392 (specifier-type '(complex long-float))))
3393 ;; float complex types are never canonicalized.
3396 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3397 ;; probably just a COMPLEX or equivalent. So, in that
3398 ;; case, we will return a complex or an object of the
3399 ;; provided type if it's rational:
3400 (type-union result-typeoid
3401 (type-intersection (lvar-type value)
3402 (specifier-type 'rational))))))
3403 (t result-typeoid))))
3405 ;; OK, the result-type argument isn't constant. However, there
3406 ;; are common uses where we can still do better than just
3407 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3408 ;; where Y is of a known type. See messages on cmucl-imp
3409 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3410 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3411 ;; the basis that it's unlikely that other uses are both
3412 ;; time-critical and get to this branch of the COND (non-constant
3413 ;; second argument to COERCE). -- CSR, 2002-12-16
3414 (let ((value-type (lvar-type value))
3415 (type-type (lvar-type type)))
3417 ((good-cons-type-p (cons-type)
3418 ;; Make sure the cons-type we're looking at is something
3419 ;; we're prepared to handle which is basically something
3420 ;; that array-element-type can return.
3421 (or (and (member-type-p cons-type)
3422 (null (rest (member-type-members cons-type)))
3423 (null (first (member-type-members cons-type))))
3424 (let ((car-type (cons-type-car-type cons-type)))
3425 (and (member-type-p car-type)
3426 (null (rest (member-type-members car-type)))
3427 (or (symbolp (first (member-type-members car-type)))
3428 (numberp (first (member-type-members car-type)))
3429 (and (listp (first (member-type-members
3431 (numberp (first (first (member-type-members
3433 (good-cons-type-p (cons-type-cdr-type cons-type))))))
3434 (unconsify-type (good-cons-type)
3435 ;; Convert the "printed" respresentation of a cons
3436 ;; specifier into a type specifier. That is, the
3437 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3438 ;; NULL)) is converted to (SIGNED-BYTE 16).
3439 (cond ((or (null good-cons-type)
3440 (eq good-cons-type 'null))
3442 ((and (eq (first good-cons-type) 'cons)
3443 (eq (first (second good-cons-type)) 'member))
3444 `(,(second (second good-cons-type))
3445 ,@(unconsify-type (caddr good-cons-type))))))
3446 (coerceable-p (c-type)
3447 ;; Can the value be coerced to the given type? Coerce is
3448 ;; complicated, so we don't handle every possible case
3449 ;; here---just the most common and easiest cases:
3451 ;; * Any REAL can be coerced to a FLOAT type.
3452 ;; * Any NUMBER can be coerced to a (COMPLEX
3453 ;; SINGLE/DOUBLE-FLOAT).
3455 ;; FIXME I: we should also be able to deal with characters
3458 ;; FIXME II: I'm not sure that anything is necessary
3459 ;; here, at least while COMPLEX is not a specialized
3460 ;; array element type in the system. Reasoning: if
3461 ;; something cannot be coerced to the requested type, an
3462 ;; error will be raised (and so any downstream compiled
3463 ;; code on the assumption of the returned type is
3464 ;; unreachable). If something can, then it will be of
3465 ;; the requested type, because (by assumption) COMPLEX
3466 ;; (and other difficult types like (COMPLEX INTEGER)
3467 ;; aren't specialized types.
3468 (let ((coerced-type c-type))
3469 (or (and (subtypep coerced-type 'float)
3470 (csubtypep value-type (specifier-type 'real)))
3471 (and (subtypep coerced-type
3472 '(or (complex single-float)
3473 (complex double-float)))
3474 (csubtypep value-type (specifier-type 'number))))))
3475 (process-types (type)
3476 ;; FIXME: This needs some work because we should be able
3477 ;; to derive the resulting type better than just the
3478 ;; type arg of coerce. That is, if X is (INTEGER 10
3479 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3480 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3482 (cond ((member-type-p type)
3483 (let ((members (member-type-members type)))
3484 (if (every #'coerceable-p members)
3485 (specifier-type `(or ,@members))
3487 ((and (cons-type-p type)
3488 (good-cons-type-p type))
3489 (let ((c-type (unconsify-type (type-specifier type))))
3490 (if (coerceable-p c-type)
3491 (specifier-type c-type)
3494 *universal-type*))))
3495 (cond ((union-type-p type-type)
3496 (apply #'type-union (mapcar #'process-types
3497 (union-type-types type-type))))
3498 ((or (member-type-p type-type)
3499 (cons-type-p type-type))
3500 (process-types type-type))
3502 *universal-type*)))))))
3504 (defoptimizer (compile derive-type) ((nameoid function))
3505 (when (csubtypep (lvar-type nameoid)
3506 (specifier-type 'null))
3507 (values-specifier-type '(values function boolean boolean))))
3509 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3510 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3511 ;;; optimizer, above).
3512 (defoptimizer (array-element-type derive-type) ((array))
3513 (let ((array-type (lvar-type array)))
3514 (labels ((consify (list)
3517 `(cons (eql ,(car list)) ,(consify (rest list)))))
3518 (get-element-type (a)
3520 (type-specifier (array-type-specialized-element-type a))))
3521 (cond ((eq element-type '*)
3522 (specifier-type 'type-specifier))
3523 ((symbolp element-type)
3524 (make-member-type :members (list element-type)))
3525 ((consp element-type)
3526 (specifier-type (consify element-type)))
3528 (error "can't understand type ~S~%" element-type))))))
3529 (cond ((array-type-p array-type)
3530 (get-element-type array-type))
3531 ((union-type-p array-type)
3533 (mapcar #'get-element-type (union-type-types array-type))))
3535 *universal-type*)))))
3537 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
3538 `(macrolet ((%index (x) `(truly-the index ,x))
3539 (%parent (i) `(ash ,i -1))
3540 (%left (i) `(%index (ash ,i 1)))
3541 (%right (i) `(%index (1+ (ash ,i 1))))
3544 (left (%left i) (%left i)))
3545 ((> left current-heap-size))
3546 (declare (type index i left))
3547 (let* ((i-elt (%elt i))
3548 (i-key (funcall keyfun i-elt))
3549 (left-elt (%elt left))
3550 (left-key (funcall keyfun left-elt)))
3551 (multiple-value-bind (large large-elt large-key)
3552 (if (funcall ,',predicate i-key left-key)
3553 (values left left-elt left-key)
3554 (values i i-elt i-key))
3555 (let ((right (%right i)))
3556 (multiple-value-bind (largest largest-elt)
3557 (if (> right current-heap-size)
3558 (values large large-elt)
3559 (let* ((right-elt (%elt right))
3560 (right-key (funcall keyfun right-elt)))
3561 (if (funcall ,',predicate large-key right-key)
3562 (values right right-elt)
3563 (values large large-elt))))
3564 (cond ((= largest i)
3567 (setf (%elt i) largest-elt
3568 (%elt largest) i-elt
3570 (%sort-vector (keyfun &optional (vtype 'vector))
3571 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had trouble getting
3572 ;; type inference to propagate all the way
3573 ;; through this tangled mess of
3574 ;; inlining. The TRULY-THE here works
3575 ;; around that. -- WHN
3577 `(aref (truly-the ,',vtype ,',',vector)
3578 (%index (+ (%index ,i) start-1)))))
3579 (let ((start-1 (1- ,',start)) ; Heaps prefer 1-based addressing.
3580 (current-heap-size (- ,',end ,',start))
3582 (declare (type (integer -1 #.(1- most-positive-fixnum))
3584 (declare (type index current-heap-size))
3585 (declare (type function keyfun))
3586 (loop for i of-type index
3587 from (ash current-heap-size -1) downto 1 do
3590 (when (< current-heap-size 2)
3592 (rotatef (%elt 1) (%elt current-heap-size))
3593 (decf current-heap-size)
3595 (if (typep ,vector 'simple-vector)
3596 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
3597 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
3599 ;; Special-casing the KEY=NIL case lets us avoid some
3601 (%sort-vector #'identity simple-vector)
3602 (%sort-vector ,key simple-vector))
3603 ;; It's hard to anticipate many speed-critical applications for
3604 ;; sorting vector types other than (VECTOR T), so we just lump
3605 ;; them all together in one slow dynamically typed mess.
3607 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
3608 (%sort-vector (or ,key #'identity))))))
3610 ;;;; debuggers' little helpers
3612 ;;; for debugging when transforms are behaving mysteriously,
3613 ;;; e.g. when debugging a problem with an ASH transform
3614 ;;; (defun foo (&optional s)
3615 ;;; (sb-c::/report-lvar s "S outside WHEN")
3616 ;;; (when (and (integerp s) (> s 3))
3617 ;;; (sb-c::/report-lvar s "S inside WHEN")
3618 ;;; (let ((bound (ash 1 (1- s))))
3619 ;;; (sb-c::/report-lvar bound "BOUND")
3620 ;;; (let ((x (- bound))
3622 ;;; (sb-c::/report-lvar x "X")
3623 ;;; (sb-c::/report-lvar x "Y"))
3624 ;;; `(integer ,(- bound) ,(1- bound)))))
3625 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
3626 ;;; and the function doesn't do anything at all.)
3629 (defknown /report-lvar (t t) null)
3630 (deftransform /report-lvar ((x message) (t t))
3631 (format t "~%/in /REPORT-LVAR~%")
3632 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
3633 (when (constant-lvar-p x)
3634 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
3635 (format t "/MESSAGE=~S~%" (lvar-value message))
3636 (give-up-ir1-transform "not a real transform"))
3637 (defun /report-lvar (x message)
3638 (declare (ignore x message))))