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 values and make a closure that returns them.
33 (define-source-transform constantly
(value)
34 (let ((rest (gensym "CONSTANTLY-REST-")))
35 `(lambda (&rest
,rest
)
36 (declare (ignore ,rest
))
39 ;;; If the function has a known number of arguments, then return a
40 ;;; lambda with the appropriate fixed number of args. If the
41 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
42 ;;; MV optimization figure things out.
43 (deftransform complement
((fun) * * :node node
)
45 (multiple-value-bind (min max
)
46 (fun-type-nargs (continuation-type fun
))
48 ((and min
(eql min max
))
49 (let ((dums (make-gensym-list min
)))
50 `#'(lambda ,dums
(not (funcall fun
,@dums
)))))
51 ((let* ((cont (node-cont node
))
52 (dest (continuation-dest cont
)))
53 (and (combination-p dest
)
54 (eq (combination-fun dest
) cont
)))
55 '#'(lambda (&rest args
)
56 (not (apply fun args
))))
58 (give-up-ir1-transform
59 "The function doesn't have a fixed argument count.")))))
63 ;;; Translate CxR into CAR/CDR combos.
64 (defun source-transform-cxr (form)
65 (if (/= (length form
) 2)
67 (let ((name (symbol-name (car form
))))
68 (do ((i (- (length name
) 2) (1- i
))
70 `(,(ecase (char name i
)
76 ;;; Make source transforms to turn CxR forms into combinations of CAR
77 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
79 (/show0
"about to set CxR source transforms")
80 (loop for i of-type index from
2 upto
4 do
81 ;; Iterate over BUF = all names CxR where x = an I-element
82 ;; string of #\A or #\D characters.
83 (let ((buf (make-string (+ 2 i
))))
84 (setf (aref buf
0) #\C
85 (aref buf
(1+ i
)) #\R
)
86 (dotimes (j (ash 2 i
))
87 (declare (type index j
))
89 (declare (type index k
))
90 (setf (aref buf
(1+ k
))
91 (if (logbitp k j
) #\A
#\D
)))
92 (setf (info :function
:source-transform
(intern buf
))
93 #'source-transform-cxr
))))
94 (/show0
"done setting CxR source transforms")
96 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
97 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
98 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
100 (define-source-transform first
(x) `(car ,x
))
101 (define-source-transform rest
(x) `(cdr ,x
))
102 (define-source-transform second
(x) `(cadr ,x
))
103 (define-source-transform third
(x) `(caddr ,x
))
104 (define-source-transform fourth
(x) `(cadddr ,x
))
105 (define-source-transform fifth
(x) `(nth 4 ,x
))
106 (define-source-transform sixth
(x) `(nth 5 ,x
))
107 (define-source-transform seventh
(x) `(nth 6 ,x
))
108 (define-source-transform eighth
(x) `(nth 7 ,x
))
109 (define-source-transform ninth
(x) `(nth 8 ,x
))
110 (define-source-transform tenth
(x) `(nth 9 ,x
))
112 ;;; Translate RPLACx to LET and SETF.
113 (define-source-transform rplaca
(x y
)
118 (define-source-transform rplacd
(x y
)
124 (define-source-transform nth
(n l
) `(car (nthcdr ,n
,l
)))
126 (defvar *default-nthcdr-open-code-limit
* 6)
127 (defvar *extreme-nthcdr-open-code-limit
* 20)
129 (deftransform nthcdr
((n l
) (unsigned-byte t
) * :node node
)
130 "convert NTHCDR to CAxxR"
131 (unless (constant-continuation-p n
)
132 (give-up-ir1-transform))
133 (let ((n (continuation-value n
)))
135 (if (policy node
(and (= speed
3) (= space
0)))
136 *extreme-nthcdr-open-code-limit
*
137 *default-nthcdr-open-code-limit
*))
138 (give-up-ir1-transform))
143 `(cdr ,(frob (1- n
))))))
146 ;;;; arithmetic and numerology
148 (define-source-transform plusp
(x) `(> ,x
0))
149 (define-source-transform minusp
(x) `(< ,x
0))
150 (define-source-transform zerop
(x) `(= ,x
0))
152 (define-source-transform 1+ (x) `(+ ,x
1))
153 (define-source-transform 1-
(x) `(- ,x
1))
155 (define-source-transform oddp
(x) `(not (zerop (logand ,x
1))))
156 (define-source-transform evenp
(x) `(zerop (logand ,x
1)))
158 ;;; Note that all the integer division functions are available for
159 ;;; inline expansion.
161 (macrolet ((deffrob (fun)
162 `(define-source-transform ,fun
(x &optional
(y nil y-p
))
169 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
171 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
174 (define-source-transform lognand
(x y
) `(lognot (logand ,x
,y
)))
175 (define-source-transform lognor
(x y
) `(lognot (logior ,x
,y
)))
176 (define-source-transform logandc1
(x y
) `(logand (lognot ,x
) ,y
))
177 (define-source-transform logandc2
(x y
) `(logand ,x
(lognot ,y
)))
178 (define-source-transform logorc1
(x y
) `(logior (lognot ,x
) ,y
))
179 (define-source-transform logorc2
(x y
) `(logior ,x
(lognot ,y
)))
180 (define-source-transform logtest
(x y
) `(not (zerop (logand ,x
,y
))))
181 (define-source-transform logbitp
(index integer
)
182 `(not (zerop (logand (ash 1 ,index
) ,integer
))))
183 (define-source-transform byte
(size position
)
184 `(cons ,size
,position
))
185 (define-source-transform byte-size
(spec) `(car ,spec
))
186 (define-source-transform byte-position
(spec) `(cdr ,spec
))
187 (define-source-transform ldb-test
(bytespec integer
)
188 `(not (zerop (mask-field ,bytespec
,integer
))))
190 ;;; With the ratio and complex accessors, we pick off the "identity"
191 ;;; case, and use a primitive to handle the cell access case.
192 (define-source-transform numerator
(num)
193 (once-only ((n-num `(the rational
,num
)))
197 (define-source-transform denominator
(num)
198 (once-only ((n-num `(the rational
,num
)))
200 (%denominator
,n-num
)
203 ;;;; interval arithmetic for computing bounds
205 ;;;; This is a set of routines for operating on intervals. It
206 ;;;; implements a simple interval arithmetic package. Although SBCL
207 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
208 ;;;; for two reasons:
210 ;;;; 1. This package is simpler than NUMERIC-TYPE.
212 ;;;; 2. It makes debugging much easier because you can just strip
213 ;;;; out these routines and test them independently of SBCL. (This is a
216 ;;;; One disadvantage is a probable increase in consing because we
217 ;;;; have to create these new interval structures even though
218 ;;;; numeric-type has everything we want to know. Reason 2 wins for
221 ;;; The basic interval type. It can handle open and closed intervals.
222 ;;; A bound is open if it is a list containing a number, just like
223 ;;; Lisp says. NIL means unbounded.
224 (defstruct (interval (:constructor %make-interval
)
228 (defun make-interval (&key low high
)
229 (labels ((normalize-bound (val)
230 (cond ((and (floatp val
)
231 (float-infinity-p val
))
232 ;; Handle infinities.
236 ;; Handle any closed bounds.
239 ;; We have an open bound. Normalize the numeric
240 ;; bound. If the normalized bound is still a number
241 ;; (not nil), keep the bound open. Otherwise, the
242 ;; bound is really unbounded, so drop the openness.
243 (let ((new-val (normalize-bound (first val
))))
245 ;; The bound exists, so keep it open still.
248 (error "unknown bound type in MAKE-INTERVAL")))))
249 (%make-interval
:low
(normalize-bound low
)
250 :high
(normalize-bound high
))))
252 ;;; Given a number X, create a form suitable as a bound for an
253 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
254 #!-sb-fluid
(declaim (inline set-bound
))
255 (defun set-bound (x open-p
)
256 (if (and x open-p
) (list x
) x
))
258 ;;; Apply the function F to a bound X. If X is an open bound, then
259 ;;; the result will be open. IF X is NIL, the result is NIL.
260 (defun bound-func (f x
)
261 (declare (type function f
))
263 (with-float-traps-masked (:underflow
:overflow
:inexact
:divide-by-zero
)
264 ;; With these traps masked, we might get things like infinity
265 ;; or negative infinity returned. Check for this and return
266 ;; NIL to indicate unbounded.
267 (let ((y (funcall f
(type-bound-number x
))))
269 (float-infinity-p y
))
271 (set-bound (funcall f
(type-bound-number x
)) (consp x
)))))))
273 ;;; Apply a binary operator OP to two bounds X and Y. The result is
274 ;;; NIL if either is NIL. Otherwise bound is computed and the result
275 ;;; is open if either X or Y is open.
277 ;;; FIXME: only used in this file, not needed in target runtime
278 (defmacro bound-binop
(op x y
)
280 (with-float-traps-masked (:underflow
:overflow
:inexact
:divide-by-zero
)
281 (set-bound (,op
(type-bound-number ,x
)
282 (type-bound-number ,y
))
283 (or (consp ,x
) (consp ,y
))))))
285 ;;; Convert a numeric-type object to an interval object.
286 (defun numeric-type->interval
(x)
287 (declare (type numeric-type x
))
288 (make-interval :low
(numeric-type-low x
)
289 :high
(numeric-type-high x
)))
291 (defun copy-interval-limit (limit)
296 (defun copy-interval (x)
297 (declare (type interval x
))
298 (make-interval :low
(copy-interval-limit (interval-low x
))
299 :high
(copy-interval-limit (interval-high x
))))
301 ;;; Given a point P contained in the interval X, split X into two
302 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
303 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
304 ;;; contains P. You can specify both to be T or NIL.
305 (defun interval-split (p x
&optional close-lower close-upper
)
306 (declare (type number p
)
308 (list (make-interval :low
(copy-interval-limit (interval-low x
))
309 :high
(if close-lower p
(list p
)))
310 (make-interval :low
(if close-upper
(list p
) p
)
311 :high
(copy-interval-limit (interval-high x
)))))
313 ;;; Return the closure of the interval. That is, convert open bounds
314 ;;; to closed bounds.
315 (defun interval-closure (x)
316 (declare (type interval x
))
317 (make-interval :low
(type-bound-number (interval-low x
))
318 :high
(type-bound-number (interval-high x
))))
320 (defun signed-zero->= (x y
)
324 (>= (float-sign (float x
))
325 (float-sign (float y
))))))
327 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
328 ;;; '-. Otherwise return NIL.
330 (defun interval-range-info (x &optional
(point 0))
331 (declare (type interval x
))
332 (let ((lo (interval-low x
))
333 (hi (interval-high x
)))
334 (cond ((and lo
(signed-zero->= (type-bound-number lo
) point
))
336 ((and hi
(signed-zero->= point
(type-bound-number hi
)))
340 (defun interval-range-info (x &optional
(point 0))
341 (declare (type interval x
))
342 (labels ((signed->= (x y
)
343 (if (and (zerop x
) (zerop y
) (floatp x
) (floatp y
))
344 (>= (float-sign x
) (float-sign y
))
346 (let ((lo (interval-low x
))
347 (hi (interval-high x
)))
348 (cond ((and lo
(signed->= (type-bound-number lo
) point
))
350 ((and hi
(signed->= point
(type-bound-number hi
)))
355 ;;; Test to see whether the interval X is bounded. HOW determines the
356 ;;; test, and should be either ABOVE, BELOW, or BOTH.
357 (defun interval-bounded-p (x how
)
358 (declare (type interval x
))
365 (and (interval-low x
) (interval-high x
)))))
367 ;;; signed zero comparison functions. Use these functions if we need
368 ;;; to distinguish between signed zeroes.
369 (defun signed-zero-< (x y
)
373 (< (float-sign (float x
))
374 (float-sign (float y
))))))
375 (defun signed-zero-> (x y
)
379 (> (float-sign (float x
))
380 (float-sign (float y
))))))
381 (defun signed-zero-= (x y
)
384 (= (float-sign (float x
))
385 (float-sign (float y
)))))
386 (defun signed-zero-<= (x y
)
390 (<= (float-sign (float x
))
391 (float-sign (float y
))))))
393 ;;; See whether the interval X contains the number P, taking into
394 ;;; account that the interval might not be closed.
395 (defun interval-contains-p (p x
)
396 (declare (type number p
)
398 ;; Does the interval X contain the number P? This would be a lot
399 ;; easier if all intervals were closed!
400 (let ((lo (interval-low x
))
401 (hi (interval-high x
)))
403 ;; The interval is bounded
404 (if (and (signed-zero-<= (type-bound-number lo
) p
)
405 (signed-zero-<= p
(type-bound-number hi
)))
406 ;; P is definitely in the closure of the interval.
407 ;; We just need to check the end points now.
408 (cond ((signed-zero-= p
(type-bound-number lo
))
410 ((signed-zero-= p
(type-bound-number hi
))
415 ;; Interval with upper bound
416 (if (signed-zero-< p
(type-bound-number hi
))
418 (and (numberp hi
) (signed-zero-= p hi
))))
420 ;; Interval with lower bound
421 (if (signed-zero-> p
(type-bound-number lo
))
423 (and (numberp lo
) (signed-zero-= p lo
))))
425 ;; Interval with no bounds
428 ;;; Determine whether two intervals X and Y intersect. Return T if so.
429 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
430 ;;; were closed. Otherwise the intervals are treated as they are.
432 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
433 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
434 ;;; is T, then they do intersect because we use the closure of X = [0,
435 ;;; 1] and Y = [1, 2] to determine intersection.
436 (defun interval-intersect-p (x y
&optional closed-intervals-p
)
437 (declare (type interval x y
))
438 (multiple-value-bind (intersect diff
)
439 (interval-intersection/difference
(if closed-intervals-p
442 (if closed-intervals-p
445 (declare (ignore diff
))
448 ;;; Are the two intervals adjacent? That is, is there a number
449 ;;; between the two intervals that is not an element of either
450 ;;; interval? If so, they are not adjacent. For example [0, 1) and
451 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
452 ;;; between both intervals.
453 (defun interval-adjacent-p (x y
)
454 (declare (type interval x y
))
455 (flet ((adjacent (lo hi
)
456 ;; Check to see whether lo and hi are adjacent. If either is
457 ;; nil, they can't be adjacent.
458 (when (and lo hi
(= (type-bound-number lo
) (type-bound-number hi
)))
459 ;; The bounds are equal. They are adjacent if one of
460 ;; them is closed (a number). If both are open (consp),
461 ;; then there is a number that lies between them.
462 (or (numberp lo
) (numberp hi
)))))
463 (or (adjacent (interval-low y
) (interval-high x
))
464 (adjacent (interval-low x
) (interval-high y
)))))
466 ;;; Compute the intersection and difference between two intervals.
467 ;;; Two values are returned: the intersection and the difference.
469 ;;; Let the two intervals be X and Y, and let I and D be the two
470 ;;; values returned by this function. Then I = X intersect Y. If I
471 ;;; is NIL (the empty set), then D is X union Y, represented as the
472 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
473 ;;; - I, which is a list of two intervals.
475 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
476 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
477 (defun interval-intersection/difference
(x y
)
478 (declare (type interval x y
))
479 (let ((x-lo (interval-low x
))
480 (x-hi (interval-high x
))
481 (y-lo (interval-low y
))
482 (y-hi (interval-high y
)))
485 ;; If p is an open bound, make it closed. If p is a closed
486 ;; bound, make it open.
491 ;; Test whether P is in the interval.
492 (when (interval-contains-p (type-bound-number p
)
493 (interval-closure int
))
494 (let ((lo (interval-low int
))
495 (hi (interval-high int
)))
496 ;; Check for endpoints.
497 (cond ((and lo
(= (type-bound-number p
) (type-bound-number lo
)))
498 (not (and (consp p
) (numberp lo
))))
499 ((and hi
(= (type-bound-number p
) (type-bound-number hi
)))
500 (not (and (numberp p
) (consp hi
))))
502 (test-lower-bound (p int
)
503 ;; P is a lower bound of an interval.
506 (not (interval-bounded-p int
'below
))))
507 (test-upper-bound (p int
)
508 ;; P is an upper bound of an interval.
511 (not (interval-bounded-p int
'above
)))))
512 (let ((x-lo-in-y (test-lower-bound x-lo y
))
513 (x-hi-in-y (test-upper-bound x-hi y
))
514 (y-lo-in-x (test-lower-bound y-lo x
))
515 (y-hi-in-x (test-upper-bound y-hi x
)))
516 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x
)
517 ;; Intervals intersect. Let's compute the intersection
518 ;; and the difference.
519 (multiple-value-bind (lo left-lo left-hi
)
520 (cond (x-lo-in-y (values x-lo y-lo
(opposite-bound x-lo
)))
521 (y-lo-in-x (values y-lo x-lo
(opposite-bound y-lo
))))
522 (multiple-value-bind (hi right-lo right-hi
)
524 (values x-hi
(opposite-bound x-hi
) y-hi
))
526 (values y-hi
(opposite-bound y-hi
) x-hi
)))
527 (values (make-interval :low lo
:high hi
)
528 (list (make-interval :low left-lo
530 (make-interval :low right-lo
533 (values nil
(list x y
))))))))
535 ;;; If intervals X and Y intersect, return a new interval that is the
536 ;;; union of the two. If they do not intersect, return NIL.
537 (defun interval-merge-pair (x y
)
538 (declare (type interval x y
))
539 ;; If x and y intersect or are adjacent, create the union.
540 ;; Otherwise return nil
541 (when (or (interval-intersect-p x y
)
542 (interval-adjacent-p x y
))
543 (flet ((select-bound (x1 x2 min-op max-op
)
544 (let ((x1-val (type-bound-number x1
))
545 (x2-val (type-bound-number x2
)))
547 ;; Both bounds are finite. Select the right one.
548 (cond ((funcall min-op x1-val x2-val
)
549 ;; x1 is definitely better.
551 ((funcall max-op x1-val x2-val
)
552 ;; x2 is definitely better.
555 ;; Bounds are equal. Select either
556 ;; value and make it open only if
558 (set-bound x1-val
(and (consp x1
) (consp x2
))))))
560 ;; At least one bound is not finite. The
561 ;; non-finite bound always wins.
563 (let* ((x-lo (copy-interval-limit (interval-low x
)))
564 (x-hi (copy-interval-limit (interval-high x
)))
565 (y-lo (copy-interval-limit (interval-low y
)))
566 (y-hi (copy-interval-limit (interval-high y
))))
567 (make-interval :low
(select-bound x-lo y-lo
#'< #'>)
568 :high
(select-bound x-hi y-hi
#'> #'<))))))
570 ;;; basic arithmetic operations on intervals. We probably should do
571 ;;; true interval arithmetic here, but it's complicated because we
572 ;;; have float and integer types and bounds can be open or closed.
574 ;;; the negative of an interval
575 (defun interval-neg (x)
576 (declare (type interval x
))
577 (make-interval :low
(bound-func #'-
(interval-high x
))
578 :high
(bound-func #'-
(interval-low x
))))
580 ;;; Add two intervals.
581 (defun interval-add (x y
)
582 (declare (type interval x y
))
583 (make-interval :low
(bound-binop + (interval-low x
) (interval-low y
))
584 :high
(bound-binop + (interval-high x
) (interval-high y
))))
586 ;;; Subtract two intervals.
587 (defun interval-sub (x y
)
588 (declare (type interval x y
))
589 (make-interval :low
(bound-binop -
(interval-low x
) (interval-high y
))
590 :high
(bound-binop -
(interval-high x
) (interval-low y
))))
592 ;;; Multiply two intervals.
593 (defun interval-mul (x y
)
594 (declare (type interval x y
))
595 (flet ((bound-mul (x y
)
596 (cond ((or (null x
) (null y
))
597 ;; Multiply by infinity is infinity
599 ((or (and (numberp x
) (zerop x
))
600 (and (numberp y
) (zerop y
)))
601 ;; Multiply by closed zero is special. The result
602 ;; is always a closed bound. But don't replace this
603 ;; with zero; we want the multiplication to produce
604 ;; the correct signed zero, if needed.
605 (* (type-bound-number x
) (type-bound-number y
)))
606 ((or (and (floatp x
) (float-infinity-p x
))
607 (and (floatp y
) (float-infinity-p y
)))
608 ;; Infinity times anything is infinity
611 ;; General multiply. The result is open if either is open.
612 (bound-binop * x y
)))))
613 (let ((x-range (interval-range-info x
))
614 (y-range (interval-range-info y
)))
615 (cond ((null x-range
)
616 ;; Split x into two and multiply each separately
617 (destructuring-bind (x- x
+) (interval-split 0 x t t
)
618 (interval-merge-pair (interval-mul x- y
)
619 (interval-mul x
+ y
))))
621 ;; Split y into two and multiply each separately
622 (destructuring-bind (y- y
+) (interval-split 0 y t t
)
623 (interval-merge-pair (interval-mul x y-
)
624 (interval-mul x y
+))))
626 (interval-neg (interval-mul (interval-neg x
) y
)))
628 (interval-neg (interval-mul x
(interval-neg y
))))
629 ((and (eq x-range
'+) (eq y-range
'+))
630 ;; If we are here, X and Y are both positive.
632 :low
(bound-mul (interval-low x
) (interval-low y
))
633 :high
(bound-mul (interval-high x
) (interval-high y
))))
635 (bug "excluded case in INTERVAL-MUL"))))))
637 ;;; Divide two intervals.
638 (defun interval-div (top bot
)
639 (declare (type interval top bot
))
640 (flet ((bound-div (x y y-low-p
)
643 ;; Divide by infinity means result is 0. However,
644 ;; we need to watch out for the sign of the result,
645 ;; to correctly handle signed zeros. We also need
646 ;; to watch out for positive or negative infinity.
647 (if (floatp (type-bound-number x
))
649 (- (float-sign (type-bound-number x
) 0.0))
650 (float-sign (type-bound-number x
) 0.0))
652 ((zerop (type-bound-number y
))
653 ;; Divide by zero means result is infinity
655 ((and (numberp x
) (zerop x
))
656 ;; Zero divided by anything is zero.
659 (bound-binop / x y
)))))
660 (let ((top-range (interval-range-info top
))
661 (bot-range (interval-range-info bot
)))
662 (cond ((null bot-range
)
663 ;; The denominator contains zero, so anything goes!
664 (make-interval :low nil
:high nil
))
666 ;; Denominator is negative so flip the sign, compute the
667 ;; result, and flip it back.
668 (interval-neg (interval-div top
(interval-neg bot
))))
670 ;; Split top into two positive and negative parts, and
671 ;; divide each separately
672 (destructuring-bind (top- top
+) (interval-split 0 top t t
)
673 (interval-merge-pair (interval-div top- bot
)
674 (interval-div top
+ bot
))))
676 ;; Top is negative so flip the sign, divide, and flip the
677 ;; sign of the result.
678 (interval-neg (interval-div (interval-neg top
) bot
)))
679 ((and (eq top-range
'+) (eq bot-range
'+))
682 :low
(bound-div (interval-low top
) (interval-high bot
) t
)
683 :high
(bound-div (interval-high top
) (interval-low bot
) nil
)))
685 (bug "excluded case in INTERVAL-DIV"))))))
687 ;;; Apply the function F to the interval X. If X = [a, b], then the
688 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
689 ;;; result makes sense. It will if F is monotonic increasing (or
691 (defun interval-func (f x
)
692 (declare (type function f
)
694 (let ((lo (bound-func f
(interval-low x
)))
695 (hi (bound-func f
(interval-high x
))))
696 (make-interval :low lo
:high hi
)))
698 ;;; Return T if X < Y. That is every number in the interval X is
699 ;;; always less than any number in the interval Y.
700 (defun interval-< (x y
)
701 (declare (type interval x y
))
702 ;; X < Y only if X is bounded above, Y is bounded below, and they
704 (when (and (interval-bounded-p x
'above
)
705 (interval-bounded-p y
'below
))
706 ;; Intervals are bounded in the appropriate way. Make sure they
708 (let ((left (interval-high x
))
709 (right (interval-low y
)))
710 (cond ((> (type-bound-number left
)
711 (type-bound-number right
))
712 ;; The intervals definitely overlap, so result is NIL.
714 ((< (type-bound-number left
)
715 (type-bound-number right
))
716 ;; The intervals definitely don't touch, so result is T.
719 ;; Limits are equal. Check for open or closed bounds.
720 ;; Don't overlap if one or the other are open.
721 (or (consp left
) (consp right
)))))))
723 ;;; Return T if X >= Y. That is, every number in the interval X is
724 ;;; always greater than any number in the interval Y.
725 (defun interval->= (x y
)
726 (declare (type interval x y
))
727 ;; X >= Y if lower bound of X >= upper bound of Y
728 (when (and (interval-bounded-p x
'below
)
729 (interval-bounded-p y
'above
))
730 (>= (type-bound-number (interval-low x
))
731 (type-bound-number (interval-high y
)))))
733 ;;; Return an interval that is the absolute value of X. Thus, if
734 ;;; X = [-1 10], the result is [0, 10].
735 (defun interval-abs (x)
736 (declare (type interval x
))
737 (case (interval-range-info x
)
743 (destructuring-bind (x- x
+) (interval-split 0 x t t
)
744 (interval-merge-pair (interval-neg x-
) x
+)))))
746 ;;; Compute the square of an interval.
747 (defun interval-sqr (x)
748 (declare (type interval x
))
749 (interval-func (lambda (x) (* x x
))
752 ;;;; numeric DERIVE-TYPE methods
754 ;;; a utility for defining derive-type methods of integer operations. If
755 ;;; the types of both X and Y are integer types, then we compute a new
756 ;;; integer type with bounds determined Fun when applied to X and Y.
757 ;;; Otherwise, we use Numeric-Contagion.
758 (defun derive-integer-type (x y fun
)
759 (declare (type continuation x y
) (type function fun
))
760 (let ((x (continuation-type x
))
761 (y (continuation-type y
)))
762 (if (and (numeric-type-p x
) (numeric-type-p y
)
763 (eq (numeric-type-class x
) 'integer
)
764 (eq (numeric-type-class y
) 'integer
)
765 (eq (numeric-type-complexp x
) :real
)
766 (eq (numeric-type-complexp y
) :real
))
767 (multiple-value-bind (low high
) (funcall fun x y
)
768 (make-numeric-type :class
'integer
772 (numeric-contagion x y
))))
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 continuation and massage it so that we get a
785 ;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
786 ;;; to indicate failure.
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 #!-negative-zero-is-not-zero
819 (defun convert-numeric-type (type)
820 (declare (type numeric-type type
))
821 ;;; Only convert real float interval delimiters types.
822 (if (eq (numeric-type-complexp type
) :real
)
823 (let* ((lo (numeric-type-low type
))
824 (lo-val (type-bound-number lo
))
825 (lo-float-zero-p (and lo
(floatp lo-val
) (= lo-val
0.0)))
826 (hi (numeric-type-high type
))
827 (hi-val (type-bound-number hi
))
828 (hi-float-zero-p (and hi
(floatp hi-val
) (= hi-val
0.0))))
829 (if (or lo-float-zero-p hi-float-zero-p
)
831 :class
(numeric-type-class type
)
832 :format
(numeric-type-format type
)
834 :low
(if lo-float-zero-p
836 (list (float 0.0 lo-val
))
839 :high
(if hi-float-zero-p
841 (list (float -
0.0 hi-val
))
848 ;;; Convert back from the intermediate convention for which -0.0 and
849 ;;; 0.0 are considered different to the standard type convention for
851 #!-negative-zero-is-not-zero
852 (defun convert-back-numeric-type (type)
853 (declare (type numeric-type type
))
854 ;;; Only convert real float interval delimiters types.
855 (if (eq (numeric-type-complexp type
) :real
)
856 (let* ((lo (numeric-type-low type
))
857 (lo-val (type-bound-number lo
))
859 (and lo
(floatp lo-val
) (= lo-val
0.0)
860 (float-sign lo-val
)))
861 (hi (numeric-type-high type
))
862 (hi-val (type-bound-number hi
))
864 (and hi
(floatp hi-val
) (= hi-val
0.0)
865 (float-sign hi-val
))))
867 ;; (float +0.0 +0.0) => (member 0.0)
868 ;; (float -0.0 -0.0) => (member -0.0)
869 ((and lo-float-zero-p hi-float-zero-p
)
870 ;; shouldn't have exclusive bounds here..
871 (aver (and (not (consp lo
)) (not (consp hi
))))
872 (if (= lo-float-zero-p hi-float-zero-p
)
873 ;; (float +0.0 +0.0) => (member 0.0)
874 ;; (float -0.0 -0.0) => (member -0.0)
875 (specifier-type `(member ,lo-val
))
876 ;; (float -0.0 +0.0) => (float 0.0 0.0)
877 ;; (float +0.0 -0.0) => (float 0.0 0.0)
878 (make-numeric-type :class
(numeric-type-class type
)
879 :format
(numeric-type-format type
)
885 ;; (float -0.0 x) => (float 0.0 x)
886 ((and (not (consp lo
)) (minusp lo-float-zero-p
))
887 (make-numeric-type :class
(numeric-type-class type
)
888 :format
(numeric-type-format type
)
890 :low
(float 0.0 lo-val
)
892 ;; (float (+0.0) x) => (float (0.0) x)
893 ((and (consp lo
) (plusp lo-float-zero-p
))
894 (make-numeric-type :class
(numeric-type-class type
)
895 :format
(numeric-type-format type
)
897 :low
(list (float 0.0 lo-val
))
900 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
901 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
902 (list (make-member-type :members
(list (float 0.0 lo-val
)))
903 (make-numeric-type :class
(numeric-type-class type
)
904 :format
(numeric-type-format type
)
906 :low
(list (float 0.0 lo-val
))
910 ;; (float x +0.0) => (float x 0.0)
911 ((and (not (consp hi
)) (plusp hi-float-zero-p
))
912 (make-numeric-type :class
(numeric-type-class type
)
913 :format
(numeric-type-format type
)
916 :high
(float 0.0 hi-val
)))
917 ;; (float x (-0.0)) => (float x (0.0))
918 ((and (consp hi
) (minusp hi-float-zero-p
))
919 (make-numeric-type :class
(numeric-type-class type
)
920 :format
(numeric-type-format type
)
923 :high
(list (float 0.0 hi-val
))))
925 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
926 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
927 (list (make-member-type :members
(list (float -
0.0 hi-val
)))
928 (make-numeric-type :class
(numeric-type-class type
)
929 :format
(numeric-type-format type
)
932 :high
(list (float 0.0 hi-val
)))))))
938 ;;; Convert back a possible list of numeric types.
939 #!-negative-zero-is-not-zero
940 (defun convert-back-numeric-type-list (type-list)
944 (dolist (type type-list
)
945 (if (numeric-type-p type
)
946 (let ((result (convert-back-numeric-type type
)))
948 (setf results
(append results result
))
949 (push result results
)))
950 (push type results
)))
953 (convert-back-numeric-type type-list
))
955 (convert-back-numeric-type-list (union-type-types type-list
)))
959 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
960 ;;; belong in the kernel's type logic, invoked always, instead of in
961 ;;; the compiler, invoked only during some type optimizations.
963 ;;; Take a list of types and return a canonical type specifier,
964 ;;; combining any MEMBER types together. If both positive and negative
965 ;;; MEMBER types are present they are converted to a float type.
966 ;;; XXX This would be far simpler if the type-union methods could handle
967 ;;; member/number unions.
968 (defun make-canonical-union-type (type-list)
971 (dolist (type type-list
)
972 (if (member-type-p type
)
973 (setf members
(union members
(member-type-members type
)))
974 (push type misc-types
)))
976 (when (null (set-difference '(-0l0 0l0) members
))
977 #!-negative-zero-is-not-zero
978 (push (specifier-type '(long-float 0l0 0l0)) misc-types
)
979 #!+negative-zero-is-not-zero
980 (push (specifier-type '(long-float -
0l0 0l0)) misc-types
)
981 (setf members
(set-difference members
'(-0l0 0l0))))
982 (when (null (set-difference '(-0d0 0d0
) members
))
983 #!-negative-zero-is-not-zero
984 (push (specifier-type '(double-float 0d0
0d0
)) misc-types
)
985 #!+negative-zero-is-not-zero
986 (push (specifier-type '(double-float -
0d0
0d0
)) misc-types
)
987 (setf members
(set-difference members
'(-0d0 0d0
))))
988 (when (null (set-difference '(-0f0 0f0
) members
))
989 #!-negative-zero-is-not-zero
990 (push (specifier-type '(single-float 0f0
0f0
)) misc-types
)
991 #!+negative-zero-is-not-zero
992 (push (specifier-type '(single-float -
0f0
0f0
)) misc-types
)
993 (setf members
(set-difference members
'(-0f0 0f0
))))
995 (apply #'type-union
(make-member-type :members members
) misc-types
)
996 (apply #'type-union misc-types
))))
998 ;;; Convert a member type with a single member to a numeric type.
999 (defun convert-member-type (arg)
1000 (let* ((members (member-type-members arg
))
1001 (member (first members
))
1002 (member-type (type-of member
)))
1003 (aver (not (rest members
)))
1004 (specifier-type `(,(if (subtypep member-type
'integer
)
1009 ;;; This is used in defoptimizers for computing the resulting type of
1012 ;;; Given the continuation ARG, derive the resulting type using the
1013 ;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
1014 ;;; "atomic" continuation type like numeric-type or member-type
1015 ;;; (containing just one element). It should return the resulting
1016 ;;; type, which can be a list of types.
1018 ;;; For the case of member types, if a member-fcn is given it is
1019 ;;; called to compute the result otherwise the member type is first
1020 ;;; converted to a numeric type and the derive-fcn is call.
1021 (defun one-arg-derive-type (arg derive-fcn member-fcn
1022 &optional
(convert-type t
))
1023 (declare (type function derive-fcn
)
1024 (type (or null function
) member-fcn
)
1025 #!+negative-zero-is-not-zero
(ignore convert-type
))
1026 (let ((arg-list (prepare-arg-for-derive-type (continuation-type arg
))))
1032 (with-float-traps-masked
1033 (:underflow
:overflow
:divide-by-zero
)
1037 (first (member-type-members x
))))))
1038 ;; Otherwise convert to a numeric type.
1039 (let ((result-type-list
1040 (funcall derive-fcn
(convert-member-type x
))))
1041 #!-negative-zero-is-not-zero
1043 (convert-back-numeric-type-list result-type-list
)
1045 #!+negative-zero-is-not-zero
1048 #!-negative-zero-is-not-zero
1050 (convert-back-numeric-type-list
1051 (funcall derive-fcn
(convert-numeric-type x
)))
1052 (funcall derive-fcn x
))
1053 #!+negative-zero-is-not-zero
1054 (funcall derive-fcn x
))
1056 *universal-type
*))))
1057 ;; Run down the list of args and derive the type of each one,
1058 ;; saving all of the results in a list.
1059 (let ((results nil
))
1060 (dolist (arg arg-list
)
1061 (let ((result (deriver arg
)))
1063 (setf results
(append results result
))
1064 (push result results
))))
1066 (make-canonical-union-type results
)
1067 (first results
)))))))
1069 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1070 ;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
1071 ;;; original args and a third which is T to indicate if the two args
1072 ;;; really represent the same continuation. This is useful for
1073 ;;; deriving the type of things like (* x x), which should always be
1074 ;;; positive. If we didn't do this, we wouldn't be able to tell.
1075 (defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
1076 &optional
(convert-type t
))
1077 (declare (type function derive-fcn fcn
))
1078 #!+negative-zero-is-not-zero
1079 (declare (ignore convert-type
))
1080 (flet (#!-negative-zero-is-not-zero
1081 (deriver (x y same-arg
)
1082 (cond ((and (member-type-p x
) (member-type-p y
))
1083 (let* ((x (first (member-type-members x
)))
1084 (y (first (member-type-members y
)))
1085 (result (with-float-traps-masked
1086 (:underflow
:overflow
:divide-by-zero
1088 (funcall fcn x y
))))
1089 (cond ((null result
))
1090 ((and (floatp result
) (float-nan-p result
))
1091 (make-numeric-type :class
'float
1092 :format
(type-of result
)
1095 (make-member-type :members
(list result
))))))
1096 ((and (member-type-p x
) (numeric-type-p y
))
1097 (let* ((x (convert-member-type x
))
1098 (y (if convert-type
(convert-numeric-type y
) y
))
1099 (result (funcall derive-fcn x y same-arg
)))
1101 (convert-back-numeric-type-list result
)
1103 ((and (numeric-type-p x
) (member-type-p y
))
1104 (let* ((x (if convert-type
(convert-numeric-type x
) x
))
1105 (y (convert-member-type y
))
1106 (result (funcall derive-fcn x y same-arg
)))
1108 (convert-back-numeric-type-list result
)
1110 ((and (numeric-type-p x
) (numeric-type-p y
))
1111 (let* ((x (if convert-type
(convert-numeric-type x
) x
))
1112 (y (if convert-type
(convert-numeric-type y
) y
))
1113 (result (funcall derive-fcn x y same-arg
)))
1115 (convert-back-numeric-type-list result
)
1119 #!+negative-zero-is-not-zero
1120 (deriver (x y same-arg
)
1121 (cond ((and (member-type-p x
) (member-type-p y
))
1122 (let* ((x (first (member-type-members x
)))
1123 (y (first (member-type-members y
)))
1124 (result (with-float-traps-masked
1125 (:underflow
:overflow
:divide-by-zero
)
1126 (funcall fcn x y
))))
1128 (make-member-type :members
(list result
)))))
1129 ((and (member-type-p x
) (numeric-type-p y
))
1130 (let ((x (convert-member-type x
)))
1131 (funcall derive-fcn x y same-arg
)))
1132 ((and (numeric-type-p x
) (member-type-p y
))
1133 (let ((y (convert-member-type y
)))
1134 (funcall derive-fcn x y same-arg
)))
1135 ((and (numeric-type-p x
) (numeric-type-p y
))
1136 (funcall derive-fcn x y same-arg
))
1138 *universal-type
*))))
1139 (let ((same-arg (same-leaf-ref-p arg1 arg2
))
1140 (a1 (prepare-arg-for-derive-type (continuation-type arg1
)))
1141 (a2 (prepare-arg-for-derive-type (continuation-type arg2
))))
1143 (let ((results nil
))
1145 ;; Since the args are the same continuation, just run
1148 (let ((result (deriver x x same-arg
)))
1150 (setf results
(append results result
))
1151 (push result results
))))
1152 ;; Try all pairwise combinations.
1155 (let ((result (or (deriver x y same-arg
)
1156 (numeric-contagion x y
))))
1158 (setf results
(append results result
))
1159 (push result results
))))))
1161 (make-canonical-union-type results
)
1162 (first results
)))))))
1164 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1166 (defoptimizer (+ derive-type
) ((x y
))
1167 (derive-integer-type
1174 (values (frob (numeric-type-low x
) (numeric-type-low y
))
1175 (frob (numeric-type-high x
) (numeric-type-high y
)))))))
1177 (defoptimizer (- derive-type
) ((x y
))
1178 (derive-integer-type
1185 (values (frob (numeric-type-low x
) (numeric-type-high y
))
1186 (frob (numeric-type-high x
) (numeric-type-low y
)))))))
1188 (defoptimizer (* derive-type
) ((x y
))
1189 (derive-integer-type
1192 (let ((x-low (numeric-type-low x
))
1193 (x-high (numeric-type-high x
))
1194 (y-low (numeric-type-low y
))
1195 (y-high (numeric-type-high y
)))
1196 (cond ((not (and x-low y-low
))
1198 ((or (minusp x-low
) (minusp y-low
))
1199 (if (and x-high y-high
)
1200 (let ((max (* (max (abs x-low
) (abs x-high
))
1201 (max (abs y-low
) (abs y-high
)))))
1202 (values (- max
) max
))
1205 (values (* x-low y-low
)
1206 (if (and x-high y-high
)
1210 (defoptimizer (/ derive-type
) ((x y
))
1211 (numeric-contagion (continuation-type x
) (continuation-type y
)))
1215 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1217 (defun +-derive-type-aux
(x y same-arg
)
1218 (if (and (numeric-type-real-p x
)
1219 (numeric-type-real-p y
))
1222 (let ((x-int (numeric-type->interval x
)))
1223 (interval-add x-int x-int
))
1224 (interval-add (numeric-type->interval x
)
1225 (numeric-type->interval y
))))
1226 (result-type (numeric-contagion x y
)))
1227 ;; If the result type is a float, we need to be sure to coerce
1228 ;; the bounds into the correct type.
1229 (when (eq (numeric-type-class result-type
) 'float
)
1230 (setf result
(interval-func
1232 (coerce x
(or (numeric-type-format result-type
)
1236 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1237 (eq (numeric-type-class y
) 'integer
))
1238 ;; The sum of integers is always an integer.
1240 (numeric-type-class result-type
))
1241 :format
(numeric-type-format result-type
)
1242 :low
(interval-low result
)
1243 :high
(interval-high result
)))
1244 ;; general contagion
1245 (numeric-contagion x y
)))
1247 (defoptimizer (+ derive-type
) ((x y
))
1248 (two-arg-derive-type x y
#'+-derive-type-aux
#'+))
1250 (defun --derive-type-aux (x y same-arg
)
1251 (if (and (numeric-type-real-p x
)
1252 (numeric-type-real-p y
))
1254 ;; (- X X) is always 0.
1256 (make-interval :low
0 :high
0)
1257 (interval-sub (numeric-type->interval x
)
1258 (numeric-type->interval y
))))
1259 (result-type (numeric-contagion x y
)))
1260 ;; If the result type is a float, we need to be sure to coerce
1261 ;; the bounds into the correct type.
1262 (when (eq (numeric-type-class result-type
) 'float
)
1263 (setf result
(interval-func
1265 (coerce x
(or (numeric-type-format result-type
)
1269 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1270 (eq (numeric-type-class y
) 'integer
))
1271 ;; The difference of integers is always an integer.
1273 (numeric-type-class result-type
))
1274 :format
(numeric-type-format result-type
)
1275 :low
(interval-low result
)
1276 :high
(interval-high result
)))
1277 ;; general contagion
1278 (numeric-contagion x y
)))
1280 (defoptimizer (- derive-type
) ((x y
))
1281 (two-arg-derive-type x y
#'--derive-type-aux
#'-
))
1283 (defun *-derive-type-aux
(x y same-arg
)
1284 (if (and (numeric-type-real-p x
)
1285 (numeric-type-real-p y
))
1287 ;; (* X X) is always positive, so take care to do it right.
1289 (interval-sqr (numeric-type->interval x
))
1290 (interval-mul (numeric-type->interval x
)
1291 (numeric-type->interval y
))))
1292 (result-type (numeric-contagion x y
)))
1293 ;; If the result type is a float, we need to be sure to coerce
1294 ;; the bounds into the correct type.
1295 (when (eq (numeric-type-class result-type
) 'float
)
1296 (setf result
(interval-func
1298 (coerce x
(or (numeric-type-format result-type
)
1302 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1303 (eq (numeric-type-class y
) 'integer
))
1304 ;; The product of integers is always an integer.
1306 (numeric-type-class result-type
))
1307 :format
(numeric-type-format result-type
)
1308 :low
(interval-low result
)
1309 :high
(interval-high result
)))
1310 (numeric-contagion x y
)))
1312 (defoptimizer (* derive-type
) ((x y
))
1313 (two-arg-derive-type x y
#'*-derive-type-aux
#'*))
1315 (defun /-derive-type-aux
(x y same-arg
)
1316 (if (and (numeric-type-real-p x
)
1317 (numeric-type-real-p y
))
1319 ;; (/ X X) is always 1, except if X can contain 0. In
1320 ;; that case, we shouldn't optimize the division away
1321 ;; because we want 0/0 to signal an error.
1323 (not (interval-contains-p
1324 0 (interval-closure (numeric-type->interval y
)))))
1325 (make-interval :low
1 :high
1)
1326 (interval-div (numeric-type->interval x
)
1327 (numeric-type->interval y
))))
1328 (result-type (numeric-contagion x y
)))
1329 ;; If the result type is a float, we need to be sure to coerce
1330 ;; the bounds into the correct type.
1331 (when (eq (numeric-type-class result-type
) 'float
)
1332 (setf result
(interval-func
1334 (coerce x
(or (numeric-type-format result-type
)
1337 (make-numeric-type :class
(numeric-type-class result-type
)
1338 :format
(numeric-type-format result-type
)
1339 :low
(interval-low result
)
1340 :high
(interval-high result
)))
1341 (numeric-contagion x y
)))
1343 (defoptimizer (/ derive-type
) ((x y
))
1344 (two-arg-derive-type x y
#'/-derive-type-aux
#'/))
1349 ;;; KLUDGE: All this ASH optimization is suppressed under CMU CL
1350 ;;; because as of version 2.4.6 for Debian, CMU CL blows up on (ASH
1351 ;;; 1000000000 -100000000000) (i.e. ASH of two bignums yielding zero)
1352 ;;; and it's hard to avoid that calculation in here.
1353 #-
(and cmu sb-xc-host
)
1356 (defun ash-derive-type-aux (n-type shift same-arg
)
1357 (declare (ignore same-arg
))
1358 (flet ((ash-outer (n s
)
1359 (when (and (fixnump s
)
1361 (> s sb
!xc
:most-negative-fixnum
))
1363 ;; KLUDGE: The bare 64's here should be related to
1364 ;; symbolic machine word size values somehow.
1367 (if (and (fixnump s
)
1368 (> s sb
!xc
:most-negative-fixnum
))
1370 (if (minusp n
) -
1 0))))
1371 (or (and (csubtypep n-type
(specifier-type 'integer
))
1372 (csubtypep shift
(specifier-type 'integer
))
1373 (let ((n-low (numeric-type-low n-type
))
1374 (n-high (numeric-type-high n-type
))
1375 (s-low (numeric-type-low shift
))
1376 (s-high (numeric-type-high shift
)))
1377 (make-numeric-type :class
'integer
:complexp
:real
1380 (ash-outer n-low s-high
)
1381 (ash-inner n-low s-low
)))
1384 (ash-inner n-high s-low
)
1385 (ash-outer n-high s-high
))))))
1388 (defoptimizer (ash derive-type
) ((n shift
))
1389 (two-arg-derive-type n shift
#'ash-derive-type-aux
#'ash
))
1392 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1393 (macrolet ((frob (fun)
1394 `#'(lambda (type type2
)
1395 (declare (ignore type2
))
1396 (let ((lo (numeric-type-low type
))
1397 (hi (numeric-type-high type
)))
1398 (values (if hi
(,fun hi
) nil
) (if lo
(,fun lo
) nil
))))))
1400 (defoptimizer (%negate derive-type
) ((num))
1401 (derive-integer-type num num
(frob -
))))
1403 (defoptimizer (lognot derive-type
) ((int))
1404 (derive-integer-type int int
1405 (lambda (type type2
)
1406 (declare (ignore type2
))
1407 (let ((lo (numeric-type-low type
))
1408 (hi (numeric-type-high type
)))
1409 (values (if hi
(lognot hi
) nil
)
1410 (if lo
(lognot lo
) nil
)
1411 (numeric-type-class type
)
1412 (numeric-type-format type
))))))
1414 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1415 (defoptimizer (%negate derive-type
) ((num))
1416 (flet ((negate-bound (b)
1418 (set-bound (- (type-bound-number b
))
1420 (one-arg-derive-type num
1422 (modified-numeric-type
1424 :low
(negate-bound (numeric-type-high type
))
1425 :high
(negate-bound (numeric-type-low type
))))
1428 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1429 (defoptimizer (abs derive-type
) ((num))
1430 (let ((type (continuation-type num
)))
1431 (if (and (numeric-type-p type
)
1432 (eq (numeric-type-class type
) 'integer
)
1433 (eq (numeric-type-complexp type
) :real
))
1434 (let ((lo (numeric-type-low type
))
1435 (hi (numeric-type-high type
)))
1436 (make-numeric-type :class
'integer
:complexp
:real
1437 :low
(cond ((and hi
(minusp hi
))
1443 :high
(if (and hi lo
)
1444 (max (abs hi
) (abs lo
))
1446 (numeric-contagion type type
))))
1448 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1449 (defun abs-derive-type-aux (type)
1450 (cond ((eq (numeric-type-complexp type
) :complex
)
1451 ;; The absolute value of a complex number is always a
1452 ;; non-negative float.
1453 (let* ((format (case (numeric-type-class type
)
1454 ((integer rational
) 'single-float
)
1455 (t (numeric-type-format type
))))
1456 (bound-format (or format
'float
)))
1457 (make-numeric-type :class
'float
1460 :low
(coerce 0 bound-format
)
1463 ;; The absolute value of a real number is a non-negative real
1464 ;; of the same type.
1465 (let* ((abs-bnd (interval-abs (numeric-type->interval type
)))
1466 (class (numeric-type-class type
))
1467 (format (numeric-type-format type
))
1468 (bound-type (or format class
'real
)))
1473 :low
(coerce-numeric-bound (interval-low abs-bnd
) bound-type
)
1474 :high
(coerce-numeric-bound
1475 (interval-high abs-bnd
) bound-type
))))))
1477 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1478 (defoptimizer (abs derive-type
) ((num))
1479 (one-arg-derive-type num
#'abs-derive-type-aux
#'abs
))
1481 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1482 (defoptimizer (truncate derive-type
) ((number divisor
))
1483 (let ((number-type (continuation-type number
))
1484 (divisor-type (continuation-type divisor
))
1485 (integer-type (specifier-type 'integer
)))
1486 (if (and (numeric-type-p number-type
)
1487 (csubtypep number-type integer-type
)
1488 (numeric-type-p divisor-type
)
1489 (csubtypep divisor-type integer-type
))
1490 (let ((number-low (numeric-type-low number-type
))
1491 (number-high (numeric-type-high number-type
))
1492 (divisor-low (numeric-type-low divisor-type
))
1493 (divisor-high (numeric-type-high divisor-type
)))
1494 (values-specifier-type
1495 `(values ,(integer-truncate-derive-type number-low number-high
1496 divisor-low divisor-high
)
1497 ,(integer-rem-derive-type number-low number-high
1498 divisor-low divisor-high
))))
1501 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1504 (defun rem-result-type (number-type divisor-type
)
1505 ;; Figure out what the remainder type is. The remainder is an
1506 ;; integer if both args are integers; a rational if both args are
1507 ;; rational; and a float otherwise.
1508 (cond ((and (csubtypep number-type
(specifier-type 'integer
))
1509 (csubtypep divisor-type
(specifier-type 'integer
)))
1511 ((and (csubtypep number-type
(specifier-type 'rational
))
1512 (csubtypep divisor-type
(specifier-type 'rational
)))
1514 ((and (csubtypep number-type
(specifier-type 'float
))
1515 (csubtypep divisor-type
(specifier-type 'float
)))
1516 ;; Both are floats so the result is also a float, of
1517 ;; the largest type.
1518 (or (float-format-max (numeric-type-format number-type
)
1519 (numeric-type-format divisor-type
))
1521 ((and (csubtypep number-type
(specifier-type 'float
))
1522 (csubtypep divisor-type
(specifier-type 'rational
)))
1523 ;; One of the arguments is a float and the other is a
1524 ;; rational. The remainder is a float of the same
1526 (or (numeric-type-format number-type
) 'float
))
1527 ((and (csubtypep divisor-type
(specifier-type 'float
))
1528 (csubtypep number-type
(specifier-type 'rational
)))
1529 ;; One of the arguments is a float and the other is a
1530 ;; rational. The remainder is a float of the same
1532 (or (numeric-type-format divisor-type
) 'float
))
1534 ;; Some unhandled combination. This usually means both args
1535 ;; are REAL so the result is a REAL.
1538 (defun truncate-derive-type-quot (number-type divisor-type
)
1539 (let* ((rem-type (rem-result-type number-type divisor-type
))
1540 (number-interval (numeric-type->interval number-type
))
1541 (divisor-interval (numeric-type->interval divisor-type
)))
1542 ;;(declare (type (member '(integer rational float)) rem-type))
1543 ;; We have real numbers now.
1544 (cond ((eq rem-type
'integer
)
1545 ;; Since the remainder type is INTEGER, both args are
1547 (let* ((res (integer-truncate-derive-type
1548 (interval-low number-interval
)
1549 (interval-high number-interval
)
1550 (interval-low divisor-interval
)
1551 (interval-high divisor-interval
))))
1552 (specifier-type (if (listp res
) res
'integer
))))
1554 (let ((quot (truncate-quotient-bound
1555 (interval-div number-interval
1556 divisor-interval
))))
1557 (specifier-type `(integer ,(or (interval-low quot
) '*)
1558 ,(or (interval-high quot
) '*))))))))
1560 (defun truncate-derive-type-rem (number-type divisor-type
)
1561 (let* ((rem-type (rem-result-type number-type divisor-type
))
1562 (number-interval (numeric-type->interval number-type
))
1563 (divisor-interval (numeric-type->interval divisor-type
))
1564 (rem (truncate-rem-bound number-interval divisor-interval
)))
1565 ;;(declare (type (member '(integer rational float)) rem-type))
1566 ;; We have real numbers now.
1567 (cond ((eq rem-type
'integer
)
1568 ;; Since the remainder type is INTEGER, both args are
1570 (specifier-type `(,rem-type
,(or (interval-low rem
) '*)
1571 ,(or (interval-high rem
) '*))))
1573 (multiple-value-bind (class format
)
1576 (values 'integer nil
))
1578 (values 'rational nil
))
1579 ((or single-float double-float
#!+long-float long-float
)
1580 (values 'float rem-type
))
1582 (values 'float nil
))
1585 (when (member rem-type
'(float single-float double-float
1586 #!+long-float long-float
))
1587 (setf rem
(interval-func #'(lambda (x)
1588 (coerce x rem-type
))
1590 (make-numeric-type :class class
1592 :low
(interval-low rem
)
1593 :high
(interval-high rem
)))))))
1595 (defun truncate-derive-type-quot-aux (num div same-arg
)
1596 (declare (ignore same-arg
))
1597 (if (and (numeric-type-real-p num
)
1598 (numeric-type-real-p div
))
1599 (truncate-derive-type-quot num div
)
1602 (defun truncate-derive-type-rem-aux (num div same-arg
)
1603 (declare (ignore same-arg
))
1604 (if (and (numeric-type-real-p num
)
1605 (numeric-type-real-p div
))
1606 (truncate-derive-type-rem num div
)
1609 (defoptimizer (truncate derive-type
) ((number divisor
))
1610 (let ((quot (two-arg-derive-type number divisor
1611 #'truncate-derive-type-quot-aux
#'truncate
))
1612 (rem (two-arg-derive-type number divisor
1613 #'truncate-derive-type-rem-aux
#'rem
)))
1614 (when (and quot rem
)
1615 (make-values-type :required
(list quot rem
)))))
1617 (defun ftruncate-derive-type-quot (number-type divisor-type
)
1618 ;; The bounds are the same as for truncate. However, the first
1619 ;; result is a float of some type. We need to determine what that
1620 ;; type is. Basically it's the more contagious of the two types.
1621 (let ((q-type (truncate-derive-type-quot number-type divisor-type
))
1622 (res-type (numeric-contagion number-type divisor-type
)))
1623 (make-numeric-type :class
'float
1624 :format
(numeric-type-format res-type
)
1625 :low
(numeric-type-low q-type
)
1626 :high
(numeric-type-high q-type
))))
1628 (defun ftruncate-derive-type-quot-aux (n d same-arg
)
1629 (declare (ignore same-arg
))
1630 (if (and (numeric-type-real-p n
)
1631 (numeric-type-real-p d
))
1632 (ftruncate-derive-type-quot n d
)
1635 (defoptimizer (ftruncate derive-type
) ((number divisor
))
1637 (two-arg-derive-type number divisor
1638 #'ftruncate-derive-type-quot-aux
#'ftruncate
))
1639 (rem (two-arg-derive-type number divisor
1640 #'truncate-derive-type-rem-aux
#'rem
)))
1641 (when (and quot rem
)
1642 (make-values-type :required
(list quot rem
)))))
1644 (defun %unary-truncate-derive-type-aux
(number)
1645 (truncate-derive-type-quot number
(specifier-type '(integer 1 1))))
1647 (defoptimizer (%unary-truncate derive-type
) ((number))
1648 (one-arg-derive-type number
1649 #'%unary-truncate-derive-type-aux
1652 ;;; Define optimizers for FLOOR and CEILING.
1654 ((def (name q-name r-name
)
1655 (let ((q-aux (symbolicate q-name
"-AUX"))
1656 (r-aux (symbolicate r-name
"-AUX")))
1658 ;; Compute type of quotient (first) result.
1659 (defun ,q-aux
(number-type divisor-type
)
1660 (let* ((number-interval
1661 (numeric-type->interval number-type
))
1663 (numeric-type->interval divisor-type
))
1664 (quot (,q-name
(interval-div number-interval
1665 divisor-interval
))))
1666 (specifier-type `(integer ,(or (interval-low quot
) '*)
1667 ,(or (interval-high quot
) '*)))))
1668 ;; Compute type of remainder.
1669 (defun ,r-aux
(number-type divisor-type
)
1670 (let* ((divisor-interval
1671 (numeric-type->interval divisor-type
))
1672 (rem (,r-name divisor-interval
))
1673 (result-type (rem-result-type number-type divisor-type
)))
1674 (multiple-value-bind (class format
)
1677 (values 'integer nil
))
1679 (values 'rational nil
))
1680 ((or single-float double-float
#!+long-float long-float
)
1681 (values 'float result-type
))
1683 (values 'float nil
))
1686 (when (member result-type
'(float single-float double-float
1687 #!+long-float long-float
))
1688 ;; Make sure that the limits on the interval have
1690 (setf rem
(interval-func (lambda (x)
1691 (coerce x result-type
))
1693 (make-numeric-type :class class
1695 :low
(interval-low rem
)
1696 :high
(interval-high rem
)))))
1697 ;; the optimizer itself
1698 (defoptimizer (,name derive-type
) ((number divisor
))
1699 (flet ((derive-q (n d same-arg
)
1700 (declare (ignore same-arg
))
1701 (if (and (numeric-type-real-p n
)
1702 (numeric-type-real-p d
))
1705 (derive-r (n d same-arg
)
1706 (declare (ignore same-arg
))
1707 (if (and (numeric-type-real-p n
)
1708 (numeric-type-real-p d
))
1711 (let ((quot (two-arg-derive-type
1712 number divisor
#'derive-q
#',name
))
1713 (rem (two-arg-derive-type
1714 number divisor
#'derive-r
#'mod
)))
1715 (when (and quot rem
)
1716 (make-values-type :required
(list quot rem
))))))))))
1718 (def floor floor-quotient-bound floor-rem-bound
)
1719 (def ceiling ceiling-quotient-bound ceiling-rem-bound
))
1721 ;;; Define optimizers for FFLOOR and FCEILING
1722 (macrolet ((def (name q-name r-name
)
1723 (let ((q-aux (symbolicate "F" q-name
"-AUX"))
1724 (r-aux (symbolicate r-name
"-AUX")))
1726 ;; Compute type of quotient (first) result.
1727 (defun ,q-aux
(number-type divisor-type
)
1728 (let* ((number-interval
1729 (numeric-type->interval number-type
))
1731 (numeric-type->interval divisor-type
))
1732 (quot (,q-name
(interval-div number-interval
1734 (res-type (numeric-contagion number-type
1737 :class
(numeric-type-class res-type
)
1738 :format
(numeric-type-format res-type
)
1739 :low
(interval-low quot
)
1740 :high
(interval-high quot
))))
1742 (defoptimizer (,name derive-type
) ((number divisor
))
1743 (flet ((derive-q (n d same-arg
)
1744 (declare (ignore same-arg
))
1745 (if (and (numeric-type-real-p n
)
1746 (numeric-type-real-p d
))
1749 (derive-r (n d same-arg
)
1750 (declare (ignore same-arg
))
1751 (if (and (numeric-type-real-p n
)
1752 (numeric-type-real-p d
))
1755 (let ((quot (two-arg-derive-type
1756 number divisor
#'derive-q
#',name
))
1757 (rem (two-arg-derive-type
1758 number divisor
#'derive-r
#'mod
)))
1759 (when (and quot rem
)
1760 (make-values-type :required
(list quot rem
))))))))))
1762 (def ffloor floor-quotient-bound floor-rem-bound
)
1763 (def fceiling ceiling-quotient-bound ceiling-rem-bound
))
1765 ;;; functions to compute the bounds on the quotient and remainder for
1766 ;;; the FLOOR function
1767 (defun floor-quotient-bound (quot)
1768 ;; Take the floor of the quotient and then massage it into what we
1770 (let ((lo (interval-low quot
))
1771 (hi (interval-high quot
)))
1772 ;; Take the floor of the lower bound. The result is always a
1773 ;; closed lower bound.
1775 (floor (type-bound-number lo
))
1777 ;; For the upper bound, we need to be careful.
1780 ;; An open bound. We need to be careful here because
1781 ;; the floor of '(10.0) is 9, but the floor of
1783 (multiple-value-bind (q r
) (floor (first hi
))
1788 ;; A closed bound, so the answer is obvious.
1792 (make-interval :low lo
:high hi
)))
1793 (defun floor-rem-bound (div)
1794 ;; The remainder depends only on the divisor. Try to get the
1795 ;; correct sign for the remainder if we can.
1796 (case (interval-range-info div
)
1798 ;; The divisor is always positive.
1799 (let ((rem (interval-abs div
)))
1800 (setf (interval-low rem
) 0)
1801 (when (and (numberp (interval-high rem
))
1802 (not (zerop (interval-high rem
))))
1803 ;; The remainder never contains the upper bound. However,
1804 ;; watch out for the case where the high limit is zero!
1805 (setf (interval-high rem
) (list (interval-high rem
))))
1808 ;; The divisor is always negative.
1809 (let ((rem (interval-neg (interval-abs div
))))
1810 (setf (interval-high rem
) 0)
1811 (when (numberp (interval-low rem
))
1812 ;; The remainder never contains the lower bound.
1813 (setf (interval-low rem
) (list (interval-low rem
))))
1816 ;; The divisor can be positive or negative. All bets off. The
1817 ;; magnitude of remainder is the maximum value of the divisor.
1818 (let ((limit (type-bound-number (interval-high (interval-abs div
)))))
1819 ;; The bound never reaches the limit, so make the interval open.
1820 (make-interval :low
(if limit
1823 :high
(list limit
))))))
1825 (floor-quotient-bound (make-interval :low
0.3 :high
10.3))
1826 => #S
(INTERVAL :LOW
0 :HIGH
10)
1827 (floor-quotient-bound (make-interval :low
0.3 :high
'(10.3
)))
1828 => #S
(INTERVAL :LOW
0 :HIGH
10)
1829 (floor-quotient-bound (make-interval :low
0.3 :high
10))
1830 => #S
(INTERVAL :LOW
0 :HIGH
10)
1831 (floor-quotient-bound (make-interval :low
0.3 :high
'(10)))
1832 => #S
(INTERVAL :LOW
0 :HIGH
9)
1833 (floor-quotient-bound (make-interval :low
'(0.3
) :high
10.3))
1834 => #S
(INTERVAL :LOW
0 :HIGH
10)
1835 (floor-quotient-bound (make-interval :low
'(0.0
) :high
10.3))
1836 => #S
(INTERVAL :LOW
0 :HIGH
10)
1837 (floor-quotient-bound (make-interval :low
'(-1.3
) :high
10.3))
1838 => #S
(INTERVAL :LOW -
2 :HIGH
10)
1839 (floor-quotient-bound (make-interval :low
'(-1.0
) :high
10.3))
1840 => #S
(INTERVAL :LOW -
1 :HIGH
10)
1841 (floor-quotient-bound (make-interval :low -
1.0 :high
10.3))
1842 => #S
(INTERVAL :LOW -
1 :HIGH
10)
1844 (floor-rem-bound (make-interval :low
0.3 :high
10.3))
1845 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
1846 (floor-rem-bound (make-interval :low
0.3 :high
'(10.3
)))
1847 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
1848 (floor-rem-bound (make-interval :low -
10 :high -
2.3))
1849 #S
(INTERVAL :LOW
(-10) :HIGH
0)
1850 (floor-rem-bound (make-interval :low
0.3 :high
10))
1851 => #S
(INTERVAL :LOW
0 :HIGH
'(10))
1852 (floor-rem-bound (make-interval :low
'(-1.3
) :high
10.3))
1853 => #S
(INTERVAL :LOW
'(-10.3
) :HIGH
'(10.3
))
1854 (floor-rem-bound (make-interval :low
'(-20.3
) :high
10.3))
1855 => #S
(INTERVAL :LOW
(-20.3
) :HIGH
(20.3
))
1858 ;;; same functions for CEILING
1859 (defun ceiling-quotient-bound (quot)
1860 ;; Take the ceiling of the quotient and then massage it into what we
1862 (let ((lo (interval-low quot
))
1863 (hi (interval-high quot
)))
1864 ;; Take the ceiling of the upper bound. The result is always a
1865 ;; closed upper bound.
1867 (ceiling (type-bound-number hi
))
1869 ;; For the lower bound, we need to be careful.
1872 ;; An open bound. We need to be careful here because
1873 ;; the ceiling of '(10.0) is 11, but the ceiling of
1875 (multiple-value-bind (q r
) (ceiling (first lo
))
1880 ;; A closed bound, so the answer is obvious.
1884 (make-interval :low lo
:high hi
)))
1885 (defun ceiling-rem-bound (div)
1886 ;; The remainder depends only on the divisor. Try to get the
1887 ;; correct sign for the remainder if we can.
1888 (case (interval-range-info div
)
1890 ;; Divisor is always positive. The remainder is negative.
1891 (let ((rem (interval-neg (interval-abs div
))))
1892 (setf (interval-high rem
) 0)
1893 (when (and (numberp (interval-low rem
))
1894 (not (zerop (interval-low rem
))))
1895 ;; The remainder never contains the upper bound. However,
1896 ;; watch out for the case when the upper bound is zero!
1897 (setf (interval-low rem
) (list (interval-low rem
))))
1900 ;; Divisor is always negative. The remainder is positive
1901 (let ((rem (interval-abs div
)))
1902 (setf (interval-low rem
) 0)
1903 (when (numberp (interval-high rem
))
1904 ;; The remainder never contains the lower bound.
1905 (setf (interval-high rem
) (list (interval-high rem
))))
1908 ;; The divisor can be positive or negative. All bets off. The
1909 ;; magnitude of remainder is the maximum value of the divisor.
1910 (let ((limit (type-bound-number (interval-high (interval-abs div
)))))
1911 ;; The bound never reaches the limit, so make the interval open.
1912 (make-interval :low
(if limit
1915 :high
(list limit
))))))
1918 (ceiling-quotient-bound (make-interval :low
0.3 :high
10.3))
1919 => #S
(INTERVAL :LOW
1 :HIGH
11)
1920 (ceiling-quotient-bound (make-interval :low
0.3 :high
'(10.3
)))
1921 => #S
(INTERVAL :LOW
1 :HIGH
11)
1922 (ceiling-quotient-bound (make-interval :low
0.3 :high
10))
1923 => #S
(INTERVAL :LOW
1 :HIGH
10)
1924 (ceiling-quotient-bound (make-interval :low
0.3 :high
'(10)))
1925 => #S
(INTERVAL :LOW
1 :HIGH
10)
1926 (ceiling-quotient-bound (make-interval :low
'(0.3
) :high
10.3))
1927 => #S
(INTERVAL :LOW
1 :HIGH
11)
1928 (ceiling-quotient-bound (make-interval :low
'(0.0
) :high
10.3))
1929 => #S
(INTERVAL :LOW
1 :HIGH
11)
1930 (ceiling-quotient-bound (make-interval :low
'(-1.3
) :high
10.3))
1931 => #S
(INTERVAL :LOW -
1 :HIGH
11)
1932 (ceiling-quotient-bound (make-interval :low
'(-1.0
) :high
10.3))
1933 => #S
(INTERVAL :LOW
0 :HIGH
11)
1934 (ceiling-quotient-bound (make-interval :low -
1.0 :high
10.3))
1935 => #S
(INTERVAL :LOW -
1 :HIGH
11)
1937 (ceiling-rem-bound (make-interval :low
0.3 :high
10.3))
1938 => #S
(INTERVAL :LOW
(-10.3
) :HIGH
0)
1939 (ceiling-rem-bound (make-interval :low
0.3 :high
'(10.3
)))
1940 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
1941 (ceiling-rem-bound (make-interval :low -
10 :high -
2.3))
1942 => #S
(INTERVAL :LOW
0 :HIGH
(10))
1943 (ceiling-rem-bound (make-interval :low
0.3 :high
10))
1944 => #S
(INTERVAL :LOW
(-10) :HIGH
0)
1945 (ceiling-rem-bound (make-interval :low
'(-1.3
) :high
10.3))
1946 => #S
(INTERVAL :LOW
(-10.3
) :HIGH
(10.3
))
1947 (ceiling-rem-bound (make-interval :low
'(-20.3
) :high
10.3))
1948 => #S
(INTERVAL :LOW
(-20.3
) :HIGH
(20.3
))
1951 (defun truncate-quotient-bound (quot)
1952 ;; For positive quotients, truncate is exactly like floor. For
1953 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
1954 ;; it's the union of the two pieces.
1955 (case (interval-range-info quot
)
1958 (floor-quotient-bound quot
))
1960 ;; just like CEILING
1961 (ceiling-quotient-bound quot
))
1963 ;; Split the interval into positive and negative pieces, compute
1964 ;; the result for each piece and put them back together.
1965 (destructuring-bind (neg pos
) (interval-split 0 quot t t
)
1966 (interval-merge-pair (ceiling-quotient-bound neg
)
1967 (floor-quotient-bound pos
))))))
1969 (defun truncate-rem-bound (num div
)
1970 ;; This is significantly more complicated than FLOOR or CEILING. We
1971 ;; need both the number and the divisor to determine the range. The
1972 ;; basic idea is to split the ranges of NUM and DEN into positive
1973 ;; and negative pieces and deal with each of the four possibilities
1975 (case (interval-range-info num
)
1977 (case (interval-range-info div
)
1979 (floor-rem-bound div
))
1981 (ceiling-rem-bound div
))
1983 (destructuring-bind (neg pos
) (interval-split 0 div t t
)
1984 (interval-merge-pair (truncate-rem-bound num neg
)
1985 (truncate-rem-bound num pos
))))))
1987 (case (interval-range-info div
)
1989 (ceiling-rem-bound div
))
1991 (floor-rem-bound div
))
1993 (destructuring-bind (neg pos
) (interval-split 0 div t t
)
1994 (interval-merge-pair (truncate-rem-bound num neg
)
1995 (truncate-rem-bound num pos
))))))
1997 (destructuring-bind (neg pos
) (interval-split 0 num t t
)
1998 (interval-merge-pair (truncate-rem-bound neg div
)
1999 (truncate-rem-bound pos div
))))))
2002 ;;; Derive useful information about the range. Returns three values:
2003 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2004 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2005 ;;; - The abs of the maximal value if there is one, or nil if it is
2007 (defun numeric-range-info (low high
)
2008 (cond ((and low
(not (minusp low
)))
2009 (values '+ low high
))
2010 ((and high
(not (plusp high
)))
2011 (values '-
(- high
) (if low
(- low
) nil
)))
2013 (values nil
0 (and low high
(max (- low
) high
))))))
2015 (defun integer-truncate-derive-type
2016 (number-low number-high divisor-low divisor-high
)
2017 ;; The result cannot be larger in magnitude than the number, but the
2018 ;; sign might change. If we can determine the sign of either the
2019 ;; number or the divisor, we can eliminate some of the cases.
2020 (multiple-value-bind (number-sign number-min number-max
)
2021 (numeric-range-info number-low number-high
)
2022 (multiple-value-bind (divisor-sign divisor-min divisor-max
)
2023 (numeric-range-info divisor-low divisor-high
)
2024 (when (and divisor-max
(zerop divisor-max
))
2025 ;; We've got a problem: guaranteed division by zero.
2026 (return-from integer-truncate-derive-type t
))
2027 (when (zerop divisor-min
)
2028 ;; We'll assume that they aren't going to divide by zero.
2030 (cond ((and number-sign divisor-sign
)
2031 ;; We know the sign of both.
2032 (if (eq number-sign divisor-sign
)
2033 ;; Same sign, so the result will be positive.
2034 `(integer ,(if divisor-max
2035 (truncate number-min divisor-max
)
2038 (truncate number-max divisor-min
)
2040 ;; Different signs, the result will be negative.
2041 `(integer ,(if number-max
2042 (- (truncate number-max divisor-min
))
2045 (- (truncate number-min divisor-max
))
2047 ((eq divisor-sign
'+)
2048 ;; The divisor is positive. Therefore, the number will just
2049 ;; become closer to zero.
2050 `(integer ,(if number-low
2051 (truncate number-low divisor-min
)
2054 (truncate number-high divisor-min
)
2056 ((eq divisor-sign
'-
)
2057 ;; The divisor is negative. Therefore, the absolute value of
2058 ;; the number will become closer to zero, but the sign will also
2060 `(integer ,(if number-high
2061 (- (truncate number-high divisor-min
))
2064 (- (truncate number-low divisor-min
))
2066 ;; The divisor could be either positive or negative.
2068 ;; The number we are dividing has a bound. Divide that by the
2069 ;; smallest posible divisor.
2070 (let ((bound (truncate number-max divisor-min
)))
2071 `(integer ,(- bound
) ,bound
)))
2073 ;; The number we are dividing is unbounded, so we can't tell
2074 ;; anything about the result.
2077 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2078 (defun integer-rem-derive-type
2079 (number-low number-high divisor-low divisor-high
)
2080 (if (and divisor-low divisor-high
)
2081 ;; We know the range of the divisor, and the remainder must be
2082 ;; smaller than the divisor. We can tell the sign of the
2083 ;; remainer if we know the sign of the number.
2084 (let ((divisor-max (1- (max (abs divisor-low
) (abs divisor-high
)))))
2085 `(integer ,(if (or (null number-low
)
2086 (minusp number-low
))
2089 ,(if (or (null number-high
)
2090 (plusp number-high
))
2093 ;; The divisor is potentially either very positive or very
2094 ;; negative. Therefore, the remainer is unbounded, but we might
2095 ;; be able to tell something about the sign from the number.
2096 `(integer ,(if (and number-low
(not (minusp number-low
)))
2097 ;; The number we are dividing is positive.
2098 ;; Therefore, the remainder must be positive.
2101 ,(if (and number-high
(not (plusp number-high
)))
2102 ;; The number we are dividing is negative.
2103 ;; Therefore, the remainder must be negative.
2107 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2108 (defoptimizer (random derive-type
) ((bound &optional state
))
2109 (let ((type (continuation-type bound
)))
2110 (when (numeric-type-p type
)
2111 (let ((class (numeric-type-class type
))
2112 (high (numeric-type-high type
))
2113 (format (numeric-type-format type
)))
2117 :low
(coerce 0 (or format class
'real
))
2118 :high
(cond ((not high
) nil
)
2119 ((eq class
'integer
) (max (1- high
) 0))
2120 ((or (consp high
) (zerop high
)) high
)
2123 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2124 (defun random-derive-type-aux (type)
2125 (let ((class (numeric-type-class type
))
2126 (high (numeric-type-high type
))
2127 (format (numeric-type-format type
)))
2131 :low
(coerce 0 (or format class
'real
))
2132 :high
(cond ((not high
) nil
)
2133 ((eq class
'integer
) (max (1- high
) 0))
2134 ((or (consp high
) (zerop high
)) high
)
2137 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2138 (defoptimizer (random derive-type
) ((bound &optional state
))
2139 (one-arg-derive-type bound
#'random-derive-type-aux nil
))
2141 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2143 ;;; Return the maximum number of bits an integer of the supplied type
2144 ;;; can take up, or NIL if it is unbounded. The second (third) value
2145 ;;; is T if the integer can be positive (negative) and NIL if not.
2146 ;;; Zero counts as positive.
2147 (defun integer-type-length (type)
2148 (if (numeric-type-p type
)
2149 (let ((min (numeric-type-low type
))
2150 (max (numeric-type-high type
)))
2151 (values (and min max
(max (integer-length min
) (integer-length max
)))
2152 (or (null max
) (not (minusp max
)))
2153 (or (null min
) (minusp min
))))
2156 (defun logand-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 (declare (ignore x-pos
))
2160 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2161 (declare (ignore y-pos
))
2163 ;; X must be positive.
2165 ;; They must both be positive.
2166 (cond ((or (null x-len
) (null y-len
))
2167 (specifier-type 'unsigned-byte
))
2168 ((or (zerop x-len
) (zerop y-len
))
2169 (specifier-type '(integer 0 0)))
2171 (specifier-type `(unsigned-byte ,(min x-len y-len
)))))
2172 ;; X is positive, but Y might be negative.
2174 (specifier-type 'unsigned-byte
))
2176 (specifier-type '(integer 0 0)))
2178 (specifier-type `(unsigned-byte ,x-len
)))))
2179 ;; X might be negative.
2181 ;; Y must be positive.
2183 (specifier-type 'unsigned-byte
))
2185 (specifier-type '(integer 0 0)))
2188 `(unsigned-byte ,y-len
))))
2189 ;; Either might be negative.
2190 (if (and x-len y-len
)
2191 ;; The result is bounded.
2192 (specifier-type `(signed-byte ,(1+ (max x-len y-len
))))
2193 ;; We can't tell squat about the result.
2194 (specifier-type 'integer
)))))))
2196 (defun logior-derive-type-aux (x y
&optional same-leaf
)
2197 (declare (ignore same-leaf
))
2198 (multiple-value-bind (x-len x-pos x-neg
) (integer-type-length x
)
2199 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2201 ((and (not x-neg
) (not y-neg
))
2202 ;; Both are positive.
2203 (if (and x-len y-len
(zerop x-len
) (zerop y-len
))
2204 (specifier-type '(integer 0 0))
2205 (specifier-type `(unsigned-byte ,(if (and x-len y-len
)
2209 ;; X must be negative.
2211 ;; Both are negative. The result is going to be negative
2212 ;; and be the same length or shorter than the smaller.
2213 (if (and x-len y-len
)
2215 (specifier-type `(integer ,(ash -
1 (min x-len y-len
)) -
1))
2217 (specifier-type '(integer * -
1)))
2218 ;; X is negative, but we don't know about Y. The result
2219 ;; will be negative, but no more negative than X.
2221 `(integer ,(or (numeric-type-low x
) '*)
2224 ;; X might be either positive or negative.
2226 ;; But Y is negative. The result will be negative.
2228 `(integer ,(or (numeric-type-low y
) '*)
2230 ;; We don't know squat about either. It won't get any bigger.
2231 (if (and x-len y-len
)
2233 (specifier-type `(signed-byte ,(1+ (max x-len y-len
))))
2235 (specifier-type 'integer
))))))))
2237 (defun logxor-derive-type-aux (x y
&optional same-leaf
)
2238 (declare (ignore same-leaf
))
2239 (multiple-value-bind (x-len x-pos x-neg
) (integer-type-length x
)
2240 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2242 ((or (and (not x-neg
) (not y-neg
))
2243 (and (not x-pos
) (not y-pos
)))
2244 ;; Either both are negative or both are positive. The result
2245 ;; will be positive, and as long as the longer.
2246 (if (and x-len y-len
(zerop x-len
) (zerop y-len
))
2247 (specifier-type '(integer 0 0))
2248 (specifier-type `(unsigned-byte ,(if (and x-len y-len
)
2251 ((or (and (not x-pos
) (not y-neg
))
2252 (and (not y-neg
) (not y-pos
)))
2253 ;; Either X is negative and Y is positive of vice-versa. The
2254 ;; result will be negative.
2255 (specifier-type `(integer ,(if (and x-len y-len
)
2256 (ash -
1 (max x-len y-len
))
2259 ;; We can't tell what the sign of the result is going to be.
2260 ;; All we know is that we don't create new bits.
2262 (specifier-type `(signed-byte ,(1+ (max x-len y-len
)))))
2264 (specifier-type 'integer
))))))
2266 (macrolet ((deffrob (logfcn)
2267 (let ((fcn-aux (symbolicate logfcn
"-DERIVE-TYPE-AUX")))
2268 `(defoptimizer (,logfcn derive-type
) ((x y
))
2269 (two-arg-derive-type x y
#',fcn-aux
#',logfcn
)))))
2274 ;;;; miscellaneous derive-type methods
2276 (defoptimizer (integer-length derive-type
) ((x))
2277 (let ((x-type (continuation-type x
)))
2278 (when (and (numeric-type-p x-type
)
2279 (csubtypep x-type
(specifier-type 'integer
)))
2280 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2281 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2282 ;; careful about LO or HI being NIL, though. Also, if 0 is
2283 ;; contained in X, the lower bound is obviously 0.
2284 (flet ((null-or-min (a b
)
2285 (and a b
(min (integer-length a
)
2286 (integer-length b
))))
2288 (and a b
(max (integer-length a
)
2289 (integer-length b
)))))
2290 (let* ((min (numeric-type-low x-type
))
2291 (max (numeric-type-high x-type
))
2292 (min-len (null-or-min min max
))
2293 (max-len (null-or-max min max
)))
2294 (when (ctypep 0 x-type
)
2296 (specifier-type `(integer ,(or min-len
'*) ,(or max-len
'*))))))))
2298 (defoptimizer (code-char derive-type
) ((code))
2299 (specifier-type 'base-char
))
2301 (defoptimizer (values derive-type
) ((&rest values
))
2302 (values-specifier-type
2303 `(values ,@(mapcar (lambda (x)
2304 (type-specifier (continuation-type x
)))
2307 ;;;; byte operations
2309 ;;;; We try to turn byte operations into simple logical operations.
2310 ;;;; First, we convert byte specifiers into separate size and position
2311 ;;;; arguments passed to internal %FOO functions. We then attempt to
2312 ;;;; transform the %FOO functions into boolean operations when the
2313 ;;;; size and position are constant and the operands are fixnums.
2315 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2316 ;; expressions that evaluate to the SIZE and POSITION of
2317 ;; the byte-specifier form SPEC. We may wrap a let around
2318 ;; the result of the body to bind some variables.
2320 ;; If the spec is a BYTE form, then bind the vars to the
2321 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2322 ;; and BYTE-POSITION. The goal of this transformation is to
2323 ;; avoid consing up byte specifiers and then immediately
2324 ;; throwing them away.
2325 (with-byte-specifier ((size-var pos-var spec
) &body body
)
2326 (once-only ((spec `(macroexpand ,spec
))
2328 `(if (and (consp ,spec
)
2329 (eq (car ,spec
) 'byte
)
2330 (= (length ,spec
) 3))
2331 (let ((,size-var
(second ,spec
))
2332 (,pos-var
(third ,spec
)))
2334 (let ((,size-var
`(byte-size ,,temp
))
2335 (,pos-var
`(byte-position ,,temp
)))
2336 `(let ((,,temp
,,spec
))
2339 (define-source-transform ldb
(spec int
)
2340 (with-byte-specifier (size pos spec
)
2341 `(%ldb
,size
,pos
,int
)))
2343 (define-source-transform dpb
(newbyte spec int
)
2344 (with-byte-specifier (size pos spec
)
2345 `(%dpb
,newbyte
,size
,pos
,int
)))
2347 (define-source-transform mask-field
(spec int
)
2348 (with-byte-specifier (size pos spec
)
2349 `(%mask-field
,size
,pos
,int
)))
2351 (define-source-transform deposit-field
(newbyte spec int
)
2352 (with-byte-specifier (size pos spec
)
2353 `(%deposit-field
,newbyte
,size
,pos
,int
))))
2355 (defoptimizer (%ldb derive-type
) ((size posn num
))
2356 (let ((size (continuation-type size
)))
2357 (if (and (numeric-type-p size
)
2358 (csubtypep size
(specifier-type 'integer
)))
2359 (let ((size-high (numeric-type-high size
)))
2360 (if (and size-high
(<= size-high sb
!vm
:n-word-bits
))
2361 (specifier-type `(unsigned-byte ,size-high
))
2362 (specifier-type 'unsigned-byte
)))
2365 (defoptimizer (%mask-field derive-type
) ((size posn num
))
2366 (let ((size (continuation-type size
))
2367 (posn (continuation-type posn
)))
2368 (if (and (numeric-type-p size
)
2369 (csubtypep size
(specifier-type 'integer
))
2370 (numeric-type-p posn
)
2371 (csubtypep posn
(specifier-type 'integer
)))
2372 (let ((size-high (numeric-type-high size
))
2373 (posn-high (numeric-type-high posn
)))
2374 (if (and size-high posn-high
2375 (<= (+ size-high posn-high
) sb
!vm
:n-word-bits
))
2376 (specifier-type `(unsigned-byte ,(+ size-high posn-high
)))
2377 (specifier-type 'unsigned-byte
)))
2380 (defoptimizer (%dpb derive-type
) ((newbyte size posn int
))
2381 (let ((size (continuation-type size
))
2382 (posn (continuation-type posn
))
2383 (int (continuation-type int
)))
2384 (if (and (numeric-type-p size
)
2385 (csubtypep size
(specifier-type 'integer
))
2386 (numeric-type-p posn
)
2387 (csubtypep posn
(specifier-type 'integer
))
2388 (numeric-type-p int
)
2389 (csubtypep int
(specifier-type 'integer
)))
2390 (let ((size-high (numeric-type-high size
))
2391 (posn-high (numeric-type-high posn
))
2392 (high (numeric-type-high int
))
2393 (low (numeric-type-low int
)))
2394 (if (and size-high posn-high high low
2395 (<= (+ size-high posn-high
) sb
!vm
:n-word-bits
))
2397 (list (if (minusp low
) 'signed-byte
'unsigned-byte
)
2398 (max (integer-length high
)
2399 (integer-length low
)
2400 (+ size-high posn-high
))))
2404 (defoptimizer (%deposit-field derive-type
) ((newbyte size posn int
))
2405 (let ((size (continuation-type size
))
2406 (posn (continuation-type posn
))
2407 (int (continuation-type int
)))
2408 (if (and (numeric-type-p size
)
2409 (csubtypep size
(specifier-type 'integer
))
2410 (numeric-type-p posn
)
2411 (csubtypep posn
(specifier-type 'integer
))
2412 (numeric-type-p int
)
2413 (csubtypep int
(specifier-type 'integer
)))
2414 (let ((size-high (numeric-type-high size
))
2415 (posn-high (numeric-type-high posn
))
2416 (high (numeric-type-high int
))
2417 (low (numeric-type-low int
)))
2418 (if (and size-high posn-high high low
2419 (<= (+ size-high posn-high
) sb
!vm
:n-word-bits
))
2421 (list (if (minusp low
) 'signed-byte
'unsigned-byte
)
2422 (max (integer-length high
)
2423 (integer-length low
)
2424 (+ size-high posn-high
))))
2428 (deftransform %ldb
((size posn int
)
2429 (fixnum fixnum integer
)
2430 (unsigned-byte #.sb
!vm
:n-word-bits
))
2431 "convert to inline logical operations"
2432 `(logand (ash int
(- posn
))
2433 (ash ,(1- (ash 1 sb
!vm
:n-word-bits
))
2434 (- size
,sb
!vm
:n-word-bits
))))
2436 (deftransform %mask-field
((size posn int
)
2437 (fixnum fixnum integer
)
2438 (unsigned-byte #.sb
!vm
:n-word-bits
))
2439 "convert to inline logical operations"
2441 (ash (ash ,(1- (ash 1 sb
!vm
:n-word-bits
))
2442 (- size
,sb
!vm
:n-word-bits
))
2445 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2446 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2447 ;;; as the result type, as that would allow result types that cover
2448 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2449 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2451 (deftransform %dpb
((new size posn int
)
2453 (unsigned-byte #.sb
!vm
:n-word-bits
))
2454 "convert to inline logical operations"
2455 `(let ((mask (ldb (byte size
0) -
1)))
2456 (logior (ash (logand new mask
) posn
)
2457 (logand int
(lognot (ash mask posn
))))))
2459 (deftransform %dpb
((new size posn int
)
2461 (signed-byte #.sb
!vm
:n-word-bits
))
2462 "convert to inline logical operations"
2463 `(let ((mask (ldb (byte size
0) -
1)))
2464 (logior (ash (logand new mask
) posn
)
2465 (logand int
(lognot (ash mask posn
))))))
2467 (deftransform %deposit-field
((new size posn int
)
2469 (unsigned-byte #.sb
!vm
:n-word-bits
))
2470 "convert to inline logical operations"
2471 `(let ((mask (ash (ldb (byte size
0) -
1) posn
)))
2472 (logior (logand new mask
)
2473 (logand int
(lognot mask
)))))
2475 (deftransform %deposit-field
((new size posn int
)
2477 (signed-byte #.sb
!vm
:n-word-bits
))
2478 "convert to inline logical operations"
2479 `(let ((mask (ash (ldb (byte size
0) -
1) posn
)))
2480 (logior (logand new mask
)
2481 (logand int
(lognot mask
)))))
2483 ;;; miscellanous numeric transforms
2485 ;;; If a constant appears as the first arg, swap the args.
2486 (deftransform commutative-arg-swap
((x y
) * * :defun-only t
:node node
)
2487 (if (and (constant-continuation-p x
)
2488 (not (constant-continuation-p y
)))
2489 `(,(continuation-fun-name (basic-combination-fun node
))
2491 ,(continuation-value x
))
2492 (give-up-ir1-transform)))
2494 (dolist (x '(= char
= + * logior logand logxor
))
2495 (%deftransform x
'(function * *) #'commutative-arg-swap
2496 "place constant arg last"))
2498 ;;; Handle the case of a constant BOOLE-CODE.
2499 (deftransform boole
((op x y
) * *)
2500 "convert to inline logical operations"
2501 (unless (constant-continuation-p op
)
2502 (give-up-ir1-transform "BOOLE code is not a constant."))
2503 (let ((control (continuation-value op
)))
2509 (#.boole-c1
'(lognot x
))
2510 (#.boole-c2
'(lognot y
))
2511 (#.boole-and
'(logand x y
))
2512 (#.boole-ior
'(logior x y
))
2513 (#.boole-xor
'(logxor x y
))
2514 (#.boole-eqv
'(logeqv x y
))
2515 (#.boole-nand
'(lognand x y
))
2516 (#.boole-nor
'(lognor x y
))
2517 (#.boole-andc1
'(logandc1 x y
))
2518 (#.boole-andc2
'(logandc2 x y
))
2519 (#.boole-orc1
'(logorc1 x y
))
2520 (#.boole-orc2
'(logorc2 x y
))
2522 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2525 ;;;; converting special case multiply/divide to shifts
2527 ;;; If arg is a constant power of two, turn * into a shift.
2528 (deftransform * ((x y
) (integer integer
) *)
2529 "convert x*2^k to shift"
2530 (unless (constant-continuation-p y
)
2531 (give-up-ir1-transform))
2532 (let* ((y (continuation-value y
))
2534 (len (1- (integer-length y-abs
))))
2535 (unless (= y-abs
(ash 1 len
))
2536 (give-up-ir1-transform))
2541 ;;; If both arguments and the result are (UNSIGNED-BYTE 32), try to
2542 ;;; come up with a ``better'' multiplication using multiplier
2543 ;;; recoding. There are two different ways the multiplier can be
2544 ;;; recoded. The more obvious is to shift X by the correct amount for
2545 ;;; each bit set in Y and to sum the results. But if there is a string
2546 ;;; of bits that are all set, you can add X shifted by one more then
2547 ;;; the bit position of the first set bit and subtract X shifted by
2548 ;;; the bit position of the last set bit. We can't use this second
2549 ;;; method when the high order bit is bit 31 because shifting by 32
2550 ;;; doesn't work too well.
2551 (deftransform * ((x y
)
2552 ((unsigned-byte 32) (unsigned-byte 32))
2554 "recode as shift and add"
2555 (unless (constant-continuation-p y
)
2556 (give-up-ir1-transform))
2557 (let ((y (continuation-value y
))
2560 (labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x
))
2565 `(+ ,result
,(tub32 next-factor
))
2567 (declare (inline add
))
2568 (dotimes (bitpos 32)
2570 (when (not (logbitp bitpos y
))
2571 (add (if (= (1+ first-one
) bitpos
)
2572 ;; There is only a single bit in the string.
2574 ;; There are at least two.
2575 `(- ,(tub32 `(ash x
,bitpos
))
2576 ,(tub32 `(ash x
,first-one
)))))
2577 (setf first-one nil
))
2578 (when (logbitp bitpos y
)
2579 (setf first-one bitpos
))))
2581 (cond ((= first-one
31))
2585 (add `(- ,(tub32 '(ash x
31)) ,(tub32 `(ash x
,first-one
))))))
2589 ;;; If arg is a constant power of two, turn FLOOR into a shift and
2590 ;;; mask. If CEILING, add in (1- (ABS Y)) and then do FLOOR.
2591 (flet ((frob (y ceil-p
)
2592 (unless (constant-continuation-p y
)
2593 (give-up-ir1-transform))
2594 (let* ((y (continuation-value y
))
2596 (len (1- (integer-length y-abs
))))
2597 (unless (= y-abs
(ash 1 len
))
2598 (give-up-ir1-transform))
2599 (let ((shift (- len
))
2601 `(let ,(when ceil-p
`((x (+ x
,(1- y-abs
)))))
2603 `(values (ash (- x
) ,shift
)
2604 (- (logand (- x
) ,mask
)))
2605 `(values (ash x
,shift
)
2606 (logand x
,mask
))))))))
2607 (deftransform floor
((x y
) (integer integer
) *)
2608 "convert division by 2^k to shift"
2610 (deftransform ceiling
((x y
) (integer integer
) *)
2611 "convert division by 2^k to shift"
2614 ;;; Do the same for MOD.
2615 (deftransform mod
((x y
) (integer integer
) *)
2616 "convert remainder mod 2^k to LOGAND"
2617 (unless (constant-continuation-p y
)
2618 (give-up-ir1-transform))
2619 (let* ((y (continuation-value y
))
2621 (len (1- (integer-length y-abs
))))
2622 (unless (= y-abs
(ash 1 len
))
2623 (give-up-ir1-transform))
2624 (let ((mask (1- y-abs
)))
2626 `(- (logand (- x
) ,mask
))
2627 `(logand x
,mask
)))))
2629 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
2630 (deftransform truncate
((x y
) (integer integer
))
2631 "convert division by 2^k to shift"
2632 (unless (constant-continuation-p y
)
2633 (give-up-ir1-transform))
2634 (let* ((y (continuation-value y
))
2636 (len (1- (integer-length y-abs
))))
2637 (unless (= y-abs
(ash 1 len
))
2638 (give-up-ir1-transform))
2639 (let* ((shift (- len
))
2642 (values ,(if (minusp y
)
2644 `(- (ash (- x
) ,shift
)))
2645 (- (logand (- x
) ,mask
)))
2646 (values ,(if (minusp y
)
2647 `(- (ash (- x
) ,shift
))
2649 (logand x
,mask
))))))
2651 ;;; And the same for REM.
2652 (deftransform rem
((x y
) (integer integer
) *)
2653 "convert remainder mod 2^k to LOGAND"
2654 (unless (constant-continuation-p y
)
2655 (give-up-ir1-transform))
2656 (let* ((y (continuation-value y
))
2658 (len (1- (integer-length y-abs
))))
2659 (unless (= y-abs
(ash 1 len
))
2660 (give-up-ir1-transform))
2661 (let ((mask (1- y-abs
)))
2663 (- (logand (- x
) ,mask
))
2664 (logand x
,mask
)))))
2666 ;;;; arithmetic and logical identity operation elimination
2668 ;;; Flush calls to various arith functions that convert to the
2669 ;;; identity function or a constant.
2670 (macrolet ((def (name identity result
)
2671 `(deftransform ,name
((x y
) (* (constant-arg (member ,identity
))) *)
2672 "fold identity operations"
2679 (def logxor -
1 (lognot x
))
2682 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
2683 ;;; (* 0 -4.0) is -0.0.
2684 (deftransform -
((x y
) ((constant-arg (member 0)) rational
) *)
2685 "convert (- 0 x) to negate"
2687 (deftransform * ((x y
) (rational (constant-arg (member 0))) *)
2688 "convert (* x 0) to 0"
2691 ;;; Return T if in an arithmetic op including continuations X and Y,
2692 ;;; the result type is not affected by the type of X. That is, Y is at
2693 ;;; least as contagious as X.
2695 (defun not-more-contagious (x y
)
2696 (declare (type continuation x y
))
2697 (let ((x (continuation-type x
))
2698 (y (continuation-type y
)))
2699 (values (type= (numeric-contagion x y
)
2700 (numeric-contagion y y
)))))
2701 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
2702 ;;; XXX needs more work as valid transforms are missed; some cases are
2703 ;;; specific to particular transform functions so the use of this
2704 ;;; function may need a re-think.
2705 (defun not-more-contagious (x y
)
2706 (declare (type continuation x y
))
2707 (flet ((simple-numeric-type (num)
2708 (and (numeric-type-p num
)
2709 ;; Return non-NIL if NUM is integer, rational, or a float
2710 ;; of some type (but not FLOAT)
2711 (case (numeric-type-class num
)
2715 (numeric-type-format num
))
2718 (let ((x (continuation-type x
))
2719 (y (continuation-type y
)))
2720 (if (and (simple-numeric-type x
)
2721 (simple-numeric-type y
))
2722 (values (type= (numeric-contagion x y
)
2723 (numeric-contagion y y
)))))))
2727 ;;; If y is not constant, not zerop, or is contagious, or a positive
2728 ;;; float +0.0 then give up.
2729 (deftransform + ((x y
) (t (constant-arg t
)) *)
2731 (let ((val (continuation-value y
)))
2732 (unless (and (zerop val
)
2733 (not (and (floatp val
) (plusp (float-sign val
))))
2734 (not-more-contagious y x
))
2735 (give-up-ir1-transform)))
2740 ;;; If y is not constant, not zerop, or is contagious, or a negative
2741 ;;; float -0.0 then give up.
2742 (deftransform -
((x y
) (t (constant-arg t
)) *)
2744 (let ((val (continuation-value y
)))
2745 (unless (and (zerop val
)
2746 (not (and (floatp val
) (minusp (float-sign val
))))
2747 (not-more-contagious y x
))
2748 (give-up-ir1-transform)))
2751 ;;; Fold (OP x +/-1)
2752 (macrolet ((def (name result minus-result
)
2753 `(deftransform ,name
((x y
) (t (constant-arg real
)) *)
2754 "fold identity operations"
2755 (let ((val (continuation-value y
)))
2756 (unless (and (= (abs val
) 1)
2757 (not-more-contagious y x
))
2758 (give-up-ir1-transform))
2759 (if (minusp val
) ',minus-result
',result
)))))
2760 (def * x
(%negate x
))
2761 (def / x
(%negate x
))
2762 (def expt x
(/ 1 x
)))
2764 ;;; Fold (expt x n) into multiplications for small integral values of
2765 ;;; N; convert (expt x 1/2) to sqrt.
2766 (deftransform expt
((x y
) (t (constant-arg real
)) *)
2767 "recode as multiplication or sqrt"
2768 (let ((val (continuation-value y
)))
2769 ;; If Y would cause the result to be promoted to the same type as
2770 ;; Y, we give up. If not, then the result will be the same type
2771 ;; as X, so we can replace the exponentiation with simple
2772 ;; multiplication and division for small integral powers.
2773 (unless (not-more-contagious y x
)
2774 (give-up-ir1-transform))
2775 (cond ((zerop val
) '(float 1 x
))
2776 ((= val
2) '(* x x
))
2777 ((= val -
2) '(/ (* x x
)))
2778 ((= val
3) '(* x x x
))
2779 ((= val -
3) '(/ (* x x x
)))
2780 ((= val
1/2) '(sqrt x
))
2781 ((= val -
1/2) '(/ (sqrt x
)))
2782 (t (give-up-ir1-transform)))))
2784 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
2785 ;;; transformations?
2786 ;;; Perhaps we should have to prove that the denominator is nonzero before
2787 ;;; doing them? -- WHN 19990917
2788 (macrolet ((def (name)
2789 `(deftransform ,name
((x y
) ((constant-arg (integer 0 0)) integer
)
2796 (macrolet ((def (name)
2797 `(deftransform ,name
((x y
) ((constant-arg (integer 0 0)) integer
)
2806 ;;;; character operations
2808 (deftransform char-equal
((a b
) (base-char base-char
))
2810 '(let* ((ac (char-code a
))
2812 (sum (logxor ac bc
)))
2814 (when (eql sum
#x20
)
2815 (let ((sum (+ ac bc
)))
2816 (and (> sum
161) (< sum
213)))))))
2818 (deftransform char-upcase
((x) (base-char))
2820 '(let ((n-code (char-code x
)))
2821 (if (and (> n-code
#o140
) ; Octal 141 is #\a.
2822 (< n-code
#o173
)) ; Octal 172 is #\z.
2823 (code-char (logxor #x20 n-code
))
2826 (deftransform char-downcase
((x) (base-char))
2828 '(let ((n-code (char-code x
)))
2829 (if (and (> n-code
64) ; 65 is #\A.
2830 (< n-code
91)) ; 90 is #\Z.
2831 (code-char (logxor #x20 n-code
))
2834 ;;;; equality predicate transforms
2836 ;;; Return true if X and Y are continuations whose only use is a
2837 ;;; reference to the same leaf, and the value of the leaf cannot
2839 (defun same-leaf-ref-p (x y
)
2840 (declare (type continuation x y
))
2841 (let ((x-use (continuation-use x
))
2842 (y-use (continuation-use y
)))
2845 (eq (ref-leaf x-use
) (ref-leaf y-use
))
2846 (constant-reference-p x-use
))))
2848 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
2849 ;;; if there is no intersection between the types of the arguments,
2850 ;;; then the result is definitely false.
2851 (deftransform simple-equality-transform
((x y
) * *
2853 (cond ((same-leaf-ref-p x y
)
2855 ((not (types-equal-or-intersect (continuation-type x
)
2856 (continuation-type y
)))
2859 (give-up-ir1-transform))))
2862 `(%deftransform
',x
'(function * *) #'simple-equality-transform
)))
2867 ;;; This is similar to SIMPLE-EQUALITY-PREDICATE, except that we also
2868 ;;; try to convert to a type-specific predicate or EQ:
2869 ;;; -- If both args are characters, convert to CHAR=. This is better than
2870 ;;; just converting to EQ, since CHAR= may have special compilation
2871 ;;; strategies for non-standard representations, etc.
2872 ;;; -- If either arg is definitely not a number, then we can compare
2874 ;;; -- Otherwise, we try to put the arg we know more about second. If X
2875 ;;; is constant then we put it second. If X is a subtype of Y, we put
2876 ;;; it second. These rules make it easier for the back end to match
2877 ;;; these interesting cases.
2878 ;;; -- If Y is a fixnum, then we quietly pass because the back end can
2879 ;;; handle that case, otherwise give an efficiency note.
2880 (deftransform eql
((x y
) * *)
2881 "convert to simpler equality predicate"
2882 (let ((x-type (continuation-type x
))
2883 (y-type (continuation-type y
))
2884 (char-type (specifier-type 'character
))
2885 (number-type (specifier-type 'number
)))
2886 (cond ((same-leaf-ref-p x y
)
2888 ((not (types-equal-or-intersect x-type y-type
))
2890 ((and (csubtypep x-type char-type
)
2891 (csubtypep y-type char-type
))
2893 ((or (not (types-equal-or-intersect x-type number-type
))
2894 (not (types-equal-or-intersect y-type number-type
)))
2896 ((and (not (constant-continuation-p y
))
2897 (or (constant-continuation-p x
)
2898 (and (csubtypep x-type y-type
)
2899 (not (csubtypep y-type x-type
)))))
2902 (give-up-ir1-transform)))))
2904 ;;; Convert to EQL if both args are rational and complexp is specified
2905 ;;; and the same for both.
2906 (deftransform = ((x y
) * *)
2908 (let ((x-type (continuation-type x
))
2909 (y-type (continuation-type y
)))
2910 (if (and (csubtypep x-type
(specifier-type 'number
))
2911 (csubtypep y-type
(specifier-type 'number
)))
2912 (cond ((or (and (csubtypep x-type
(specifier-type 'float
))
2913 (csubtypep y-type
(specifier-type 'float
)))
2914 (and (csubtypep x-type
(specifier-type '(complex float
)))
2915 (csubtypep y-type
(specifier-type '(complex float
)))))
2916 ;; They are both floats. Leave as = so that -0.0 is
2917 ;; handled correctly.
2918 (give-up-ir1-transform))
2919 ((or (and (csubtypep x-type
(specifier-type 'rational
))
2920 (csubtypep y-type
(specifier-type 'rational
)))
2921 (and (csubtypep x-type
2922 (specifier-type '(complex rational
)))
2924 (specifier-type '(complex rational
)))))
2925 ;; They are both rationals and complexp is the same.
2929 (give-up-ir1-transform
2930 "The operands might not be the same type.")))
2931 (give-up-ir1-transform
2932 "The operands might not be the same type."))))
2934 ;;; If CONT's type is a numeric type, then return the type, otherwise
2935 ;;; GIVE-UP-IR1-TRANSFORM.
2936 (defun numeric-type-or-lose (cont)
2937 (declare (type continuation cont
))
2938 (let ((res (continuation-type cont
)))
2939 (unless (numeric-type-p res
) (give-up-ir1-transform))
2942 ;;; See whether we can statically determine (< X Y) using type
2943 ;;; information. If X's high bound is < Y's low, then X < Y.
2944 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
2945 ;;; NIL). If not, at least make sure any constant arg is second.
2947 ;;; FIXME: Why should constant argument be second? It would be nice to
2948 ;;; find out and explain.
2949 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2950 (defun ir1-transform-< (x y first second inverse
)
2951 (if (same-leaf-ref-p x y
)
2953 (let* ((x-type (numeric-type-or-lose x
))
2954 (x-lo (numeric-type-low x-type
))
2955 (x-hi (numeric-type-high x-type
))
2956 (y-type (numeric-type-or-lose y
))
2957 (y-lo (numeric-type-low y-type
))
2958 (y-hi (numeric-type-high y-type
)))
2959 (cond ((and x-hi y-lo
(< x-hi y-lo
))
2961 ((and y-hi x-lo
(>= x-lo y-hi
))
2963 ((and (constant-continuation-p first
)
2964 (not (constant-continuation-p second
)))
2967 (give-up-ir1-transform))))))
2968 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2969 (defun ir1-transform-< (x y first second inverse
)
2970 (if (same-leaf-ref-p x y
)
2972 (let ((xi (numeric-type->interval
(numeric-type-or-lose x
)))
2973 (yi (numeric-type->interval
(numeric-type-or-lose y
))))
2974 (cond ((interval-< xi yi
)
2976 ((interval->= xi yi
)
2978 ((and (constant-continuation-p first
)
2979 (not (constant-continuation-p second
)))
2982 (give-up-ir1-transform))))))
2984 (deftransform < ((x y
) (integer integer
) *)
2985 (ir1-transform-< x y x y
'>))
2987 (deftransform > ((x y
) (integer integer
) *)
2988 (ir1-transform-< y x x y
'<))
2990 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2991 (deftransform < ((x y
) (float float
) *)
2992 (ir1-transform-< x y x y
'>))
2994 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2995 (deftransform > ((x y
) (float float
) *)
2996 (ir1-transform-< y x x y
'<))
2998 ;;;; converting N-arg comparisons
3000 ;;;; We convert calls to N-arg comparison functions such as < into
3001 ;;;; two-arg calls. This transformation is enabled for all such
3002 ;;;; comparisons in this file. If any of these predicates are not
3003 ;;;; open-coded, then the transformation should be removed at some
3004 ;;;; point to avoid pessimization.
3006 ;;; This function is used for source transformation of N-arg
3007 ;;; comparison functions other than inequality. We deal both with
3008 ;;; converting to two-arg calls and inverting the sense of the test,
3009 ;;; if necessary. If the call has two args, then we pass or return a
3010 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3011 ;;; then we transform to code that returns true. Otherwise, we bind
3012 ;;; all the arguments and expand into a bunch of IFs.
3013 (declaim (ftype (function (symbol list boolean
) *) multi-compare
))
3014 (defun multi-compare (predicate args not-p
)
3015 (let ((nargs (length args
)))
3016 (cond ((< nargs
1) (values nil t
))
3017 ((= nargs
1) `(progn ,@args t
))
3020 `(if (,predicate
,(first args
) ,(second args
)) nil t
)
3023 (do* ((i (1- nargs
) (1- i
))
3025 (current (gensym) (gensym))
3026 (vars (list current
) (cons current vars
))
3028 `(if (,predicate
,current
,last
)
3030 `(if (,predicate
,current
,last
)
3033 `((lambda ,vars
,result
) .
,args
)))))))
3035 (define-source-transform = (&rest args
) (multi-compare '= args nil
))
3036 (define-source-transform < (&rest args
) (multi-compare '< args nil
))
3037 (define-source-transform > (&rest args
) (multi-compare '> args nil
))
3038 (define-source-transform <= (&rest args
) (multi-compare '> args t
))
3039 (define-source-transform >= (&rest args
) (multi-compare '< args t
))
3041 (define-source-transform char
= (&rest args
) (multi-compare 'char
= args nil
))
3042 (define-source-transform char
< (&rest args
) (multi-compare 'char
< args nil
))
3043 (define-source-transform char
> (&rest args
) (multi-compare 'char
> args nil
))
3044 (define-source-transform char
<= (&rest args
) (multi-compare 'char
> args t
))
3045 (define-source-transform char
>= (&rest args
) (multi-compare 'char
< args t
))
3047 (define-source-transform char-equal
(&rest args
)
3048 (multi-compare 'char-equal args nil
))
3049 (define-source-transform char-lessp
(&rest args
)
3050 (multi-compare 'char-lessp args nil
))
3051 (define-source-transform char-greaterp
(&rest args
)
3052 (multi-compare 'char-greaterp args nil
))
3053 (define-source-transform char-not-greaterp
(&rest args
)
3054 (multi-compare 'char-greaterp args t
))
3055 (define-source-transform char-not-lessp
(&rest args
)
3056 (multi-compare 'char-lessp args t
))
3058 ;;; This function does source transformation of N-arg inequality
3059 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3060 ;;; arg cases. If there are more than two args, then we expand into
3061 ;;; the appropriate n^2 comparisons only when speed is important.
3062 (declaim (ftype (function (symbol list
) *) multi-not-equal
))
3063 (defun multi-not-equal (predicate args
)
3064 (let ((nargs (length args
)))
3065 (cond ((< nargs
1) (values nil t
))
3066 ((= nargs
1) `(progn ,@args t
))
3068 `(if (,predicate
,(first args
) ,(second args
)) nil t
))
3069 ((not (policy *lexenv
*
3070 (and (>= speed space
)
3071 (>= speed compilation-speed
))))
3074 (let ((vars (make-gensym-list nargs
)))
3075 (do ((var vars next
)
3076 (next (cdr vars
) (cdr next
))
3079 `((lambda ,vars
,result
) .
,args
))
3080 (let ((v1 (first var
)))
3082 (setq result
`(if (,predicate
,v1
,v2
) nil
,result
))))))))))
3084 (define-source-transform /= (&rest args
) (multi-not-equal '= args
))
3085 (define-source-transform char
/= (&rest args
) (multi-not-equal 'char
= args
))
3086 (define-source-transform char-not-equal
(&rest args
)
3087 (multi-not-equal 'char-equal args
))
3089 ;;; FIXME: can go away once bug 194 is fixed and we can use (THE REAL X)
3091 (defun error-not-a-real (x)
3092 (error 'simple-type-error
3094 :expected-type
'real
3095 :format-control
"not a REAL: ~S"
3096 :format-arguments
(list x
)))
3098 ;;; Expand MAX and MIN into the obvious comparisons.
3099 (define-source-transform max
(arg0 &rest rest
)
3100 (once-only ((arg0 arg0
))
3102 `(values (the real
,arg0
))
3103 `(let ((maxrest (max ,@rest
)))
3104 (if (> ,arg0 maxrest
) ,arg0 maxrest
)))))
3105 (define-source-transform min
(arg0 &rest rest
)
3106 (once-only ((arg0 arg0
))
3108 `(values (the real
,arg0
))
3109 `(let ((minrest (min ,@rest
)))
3110 (if (< ,arg0 minrest
) ,arg0 minrest
)))))
3112 ;;;; converting N-arg arithmetic functions
3114 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3115 ;;;; versions, and degenerate cases are flushed.
3117 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3118 (declaim (ftype (function (symbol t list
) list
) associate-args
))
3119 (defun associate-args (function first-arg more-args
)
3120 (let ((next (rest more-args
))
3121 (arg (first more-args
)))
3123 `(,function
,first-arg
,arg
)
3124 (associate-args function
`(,function
,first-arg
,arg
) next
))))
3126 ;;; Do source transformations for transitive functions such as +.
3127 ;;; One-arg cases are replaced with the arg and zero arg cases with
3128 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3129 ;;; ensure (with THE) that the argument in one-argument calls is.
3130 (defun source-transform-transitive (fun args identity
3131 &optional one-arg-result-type
)
3132 (declare (symbol fun leaf-fun
) (list args
))
3135 (1 (if one-arg-result-type
3136 `(values (the ,one-arg-result-type
,(first args
)))
3137 `(values ,(first args
))))
3140 (associate-args fun
(first args
) (rest args
)))))
3142 (define-source-transform + (&rest args
)
3143 (source-transform-transitive '+ args
0 'number
))
3144 (define-source-transform * (&rest args
)
3145 (source-transform-transitive '* args
1 'number
))
3146 (define-source-transform logior
(&rest args
)
3147 (source-transform-transitive 'logior args
0 'integer
))
3148 (define-source-transform logxor
(&rest args
)
3149 (source-transform-transitive 'logxor args
0 'integer
))
3150 (define-source-transform logand
(&rest args
)
3151 (source-transform-transitive 'logand args -
1 'integer
))
3153 (define-source-transform logeqv
(&rest args
)
3154 (if (evenp (length args
))
3155 `(lognot (logxor ,@args
))
3158 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3159 ;;; because when they are given one argument, they return its absolute
3162 (define-source-transform gcd
(&rest args
)
3165 (1 `(abs (the integer
,(first args
))))
3167 (t (associate-args 'gcd
(first args
) (rest args
)))))
3169 (define-source-transform lcm
(&rest args
)
3172 (1 `(abs (the integer
,(first args
))))
3174 (t (associate-args 'lcm
(first args
) (rest args
)))))
3176 ;;; Do source transformations for intransitive n-arg functions such as
3177 ;;; /. With one arg, we form the inverse. With two args we pass.
3178 ;;; Otherwise we associate into two-arg calls.
3179 (declaim (ftype (function (symbol list t
)
3180 (values list
&optional
(member nil t
)))
3181 source-transform-intransitive
))
3182 (defun source-transform-intransitive (function args inverse
)
3184 ((0 2) (values nil t
))
3185 (1 `(,@inverse
,(first args
)))
3186 (t (associate-args function
(first args
) (rest args
)))))
3188 (define-source-transform -
(&rest args
)
3189 (source-transform-intransitive '- args
'(%negate
)))
3190 (define-source-transform / (&rest args
)
3191 (source-transform-intransitive '/ args
'(/ 1)))
3193 ;;;; transforming APPLY
3195 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3196 ;;; only needs to understand one kind of variable-argument call. It is
3197 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3198 (define-source-transform apply
(fun arg
&rest more-args
)
3199 (let ((args (cons arg more-args
)))
3200 `(multiple-value-call ,fun
3201 ,@(mapcar (lambda (x)
3204 (values-list ,(car (last args
))))))
3206 ;;;; transforming FORMAT
3208 ;;;; If the control string is a compile-time constant, then replace it
3209 ;;;; with a use of the FORMATTER macro so that the control string is
3210 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3211 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3212 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3214 (deftransform format
((dest control
&rest args
) (t simple-string
&rest t
) *
3215 :policy
(> speed space
))
3216 (unless (constant-continuation-p control
)
3217 (give-up-ir1-transform "The control string is not a constant."))
3218 (let ((arg-names (make-gensym-list (length args
))))
3219 `(lambda (dest control
,@arg-names
)
3220 (declare (ignore control
))
3221 (format dest
(formatter ,(continuation-value control
)) ,@arg-names
))))
3223 (deftransform format
((stream control
&rest args
) (stream function
&rest t
) *
3224 :policy
(> speed space
))
3225 (let ((arg-names (make-gensym-list (length args
))))
3226 `(lambda (stream control
,@arg-names
)
3227 (funcall control stream
,@arg-names
)
3230 (deftransform format
((tee control
&rest args
) ((member t
) function
&rest t
) *
3231 :policy
(> speed space
))
3232 (let ((arg-names (make-gensym-list (length args
))))
3233 `(lambda (tee control
,@arg-names
)
3234 (declare (ignore tee
))
3235 (funcall control
*standard-output
* ,@arg-names
)
3238 (defoptimizer (coerce derive-type
) ((value type
))
3240 ((constant-continuation-p type
)
3241 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3242 ;; but dealing with the niggle that complex canonicalization gets
3243 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3245 (let* ((specifier (continuation-value type
))
3246 (result-typeoid (careful-specifier-type specifier
)))
3248 ((csubtypep result-typeoid
(specifier-type 'number
))
3249 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3250 ;; Rule of Canonical Representation for Complex Rationals,
3251 ;; which is a truly nasty delivery to field.
3253 ((csubtypep result-typeoid
(specifier-type 'real
))
3254 ;; cleverness required here: it would be nice to deduce
3255 ;; that something of type (INTEGER 2 3) coerced to type
3256 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3257 ;; FLOAT gets its own clause because it's implemented as
3258 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3261 ((and (numeric-type-p result-typeoid
)
3262 (eq (numeric-type-complexp result-typeoid
) :real
))
3263 ;; FIXME: is this clause (a) necessary or (b) useful?
3265 ((or (csubtypep result-typeoid
3266 (specifier-type '(complex single-float
)))
3267 (csubtypep result-typeoid
3268 (specifier-type '(complex double-float
)))
3270 (csubtypep result-typeoid
3271 (specifier-type '(complex long-float
))))
3272 ;; float complex types are never canonicalized.
3275 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3276 ;; probably just a COMPLEX or equivalent. So, in that
3277 ;; case, we will return a complex or an object of the
3278 ;; provided type if it's rational:
3279 (type-union result-typeoid
3280 (type-intersection (continuation-type value
)
3281 (specifier-type 'rational
))))))
3282 (t result-typeoid
))))
3284 ;; OK, the result-type argument isn't constant. However, there
3285 ;; are common uses where we can still do better than just
3286 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3287 ;; where Y is of a known type. See messages on cmucl-imp
3288 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3289 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3290 ;; the basis that it's unlikely that other uses are both
3291 ;; time-critical and get to this branch of the COND (non-constant
3292 ;; second argument to COERCE). -- CSR, 2002-12-16
3293 (let ((value-type (continuation-type value
))
3294 (type-type (continuation-type type
)))
3296 ((good-cons-type-p (cons-type)
3297 ;; Make sure the cons-type we're looking at is something
3298 ;; we're prepared to handle which is basically something
3299 ;; that array-element-type can return.
3300 (or (and (member-type-p cons-type
)
3301 (null (rest (member-type-members cons-type
)))
3302 (null (first (member-type-members cons-type
))))
3303 (let ((car-type (cons-type-car-type cons-type
)))
3304 (and (member-type-p car-type
)
3305 (null (rest (member-type-members car-type
)))
3306 (or (symbolp (first (member-type-members car-type
)))
3307 (numberp (first (member-type-members car-type
)))
3308 (and (listp (first (member-type-members
3310 (numberp (first (first (member-type-members
3312 (good-cons-type-p (cons-type-cdr-type cons-type
))))))
3313 (unconsify-type (good-cons-type)
3314 ;; Convert the "printed" respresentation of a cons
3315 ;; specifier into a type specifier. That is, the
3316 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3317 ;; NULL)) is converted to (SIGNED-BYTE 16).
3318 (cond ((or (null good-cons-type
)
3319 (eq good-cons-type
'null
))
3321 ((and (eq (first good-cons-type
) 'cons
)
3322 (eq (first (second good-cons-type
)) 'member
))
3323 `(,(second (second good-cons-type
))
3324 ,@(unconsify-type (caddr good-cons-type
))))))
3325 (coerceable-p (c-type)
3326 ;; Can the value be coerced to the given type? Coerce is
3327 ;; complicated, so we don't handle every possible case
3328 ;; here---just the most common and easiest cases:
3330 ;; * Any REAL can be coerced to a FLOAT type.
3331 ;; * Any NUMBER can be coerced to a (COMPLEX
3332 ;; SINGLE/DOUBLE-FLOAT).
3334 ;; FIXME I: we should also be able to deal with characters
3337 ;; FIXME II: I'm not sure that anything is necessary
3338 ;; here, at least while COMPLEX is not a specialized
3339 ;; array element type in the system. Reasoning: if
3340 ;; something cannot be coerced to the requested type, an
3341 ;; error will be raised (and so any downstream compiled
3342 ;; code on the assumption of the returned type is
3343 ;; unreachable). If something can, then it will be of
3344 ;; the requested type, because (by assumption) COMPLEX
3345 ;; (and other difficult types like (COMPLEX INTEGER)
3346 ;; aren't specialized types.
3347 (let ((coerced-type c-type
))
3348 (or (and (subtypep coerced-type
'float
)
3349 (csubtypep value-type
(specifier-type 'real
)))
3350 (and (subtypep coerced-type
3351 '(or (complex single-float
)
3352 (complex double-float
)))
3353 (csubtypep value-type
(specifier-type 'number
))))))
3354 (process-types (type)
3355 ;; FIXME: This needs some work because we should be able
3356 ;; to derive the resulting type better than just the
3357 ;; type arg of coerce. That is, if X is (INTEGER 10
3358 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3359 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3361 (cond ((member-type-p type
)
3362 (let ((members (member-type-members type
)))
3363 (if (every #'coerceable-p members
)
3364 (specifier-type `(or ,@members
))
3366 ((and (cons-type-p type
)
3367 (good-cons-type-p type
))
3368 (let ((c-type (unconsify-type (type-specifier type
))))
3369 (if (coerceable-p c-type
)
3370 (specifier-type c-type
)
3373 *universal-type
*))))
3374 (cond ((union-type-p type-type
)
3375 (apply #'type-union
(mapcar #'process-types
3376 (union-type-types type-type
))))
3377 ((or (member-type-p type-type
)
3378 (cons-type-p type-type
))
3379 (process-types type-type
))
3381 *universal-type
*)))))))
3383 (defoptimizer (compile derive-type
) ((nameoid function
))
3384 (when (csubtypep (continuation-type nameoid
)
3385 (specifier-type 'null
))
3386 (specifier-type 'function
)))
3388 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3389 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3390 ;;; optimizer, above).
3391 (defoptimizer (array-element-type derive-type
) ((array))
3392 (let ((array-type (continuation-type array
)))
3393 (labels ((consify (list)
3396 `(cons (eql ,(car list
)) ,(consify (rest list
)))))
3397 (get-element-type (a)
3399 (type-specifier (array-type-specialized-element-type a
))))
3400 (cond ((eq element-type
'*)
3401 (specifier-type 'type-specifier
))
3402 ((symbolp element-type
)
3403 (make-member-type :members
(list element-type
)))
3404 ((consp element-type
)
3405 (specifier-type (consify element-type
)))
3407 (error "can't understand type ~S~%" element-type
))))))
3408 (cond ((array-type-p array-type
)
3409 (get-element-type array-type
))
3410 ((union-type-p array-type
)
3412 (mapcar #'get-element-type
(union-type-types array-type
))))
3414 *universal-type
*)))))
3416 (define-source-transform sb
!impl
::sort-vector
(vector start end predicate key
)
3417 `(macrolet ((%index
(x) `(truly-the index
,x
))
3418 (%parent
(i) `(ash ,i -
1))
3419 (%left
(i) `(%index
(ash ,i
1)))
3420 (%right
(i) `(%index
(1+ (ash ,i
1))))
3423 (left (%left i
) (%left i
)))
3424 ((> left current-heap-size
))
3425 (declare (type index i left
))
3426 (let* ((i-elt (%elt i
))
3427 (i-key (funcall keyfun i-elt
))
3428 (left-elt (%elt left
))
3429 (left-key (funcall keyfun left-elt
)))
3430 (multiple-value-bind (large large-elt large-key
)
3431 (if (funcall ,',predicate i-key left-key
)
3432 (values left left-elt left-key
)
3433 (values i i-elt i-key
))
3434 (let ((right (%right i
)))
3435 (multiple-value-bind (largest largest-elt
)
3436 (if (> right current-heap-size
)
3437 (values large large-elt
)
3438 (let* ((right-elt (%elt right
))
3439 (right-key (funcall keyfun right-elt
)))
3440 (if (funcall ,',predicate large-key right-key
)
3441 (values right right-elt
)
3442 (values large large-elt
))))
3443 (cond ((= largest i
)
3446 (setf (%elt i
) largest-elt
3447 (%elt largest
) i-elt
3449 (%sort-vector
(keyfun &optional
(vtype 'vector
))
3450 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had trouble getting
3451 ;; type inference to propagate all the way
3452 ;; through this tangled mess of
3453 ;; inlining. The TRULY-THE here works
3454 ;; around that. -- WHN
3456 `(aref (truly-the ,',vtype
,',',vector
)
3457 (%index
(+ (%index
,i
) start-1
)))))
3458 (let ((start-1 (1- ,',start
)) ; Heaps prefer 1-based addressing.
3459 (current-heap-size (- ,',end
,',start
))
3461 (declare (type (integer -
1 #.
(1- most-positive-fixnum
))
3463 (declare (type index current-heap-size
))
3464 (declare (type function keyfun
))
3465 (loop for i of-type index
3466 from
(ash current-heap-size -
1) downto
1 do
3469 (when (< current-heap-size
2)
3471 (rotatef (%elt
1) (%elt current-heap-size
))
3472 (decf current-heap-size
)
3474 (if (typep ,vector
'simple-vector
)
3475 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
3476 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
3478 ;; Special-casing the KEY=NIL case lets us avoid some
3480 (%sort-vector
#'identity simple-vector
)
3481 (%sort-vector
,key simple-vector
))
3482 ;; It's hard to anticipate many speed-critical applications for
3483 ;; sorting vector types other than (VECTOR T), so we just lump
3484 ;; them all together in one slow dynamically typed mess.
3486 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
3487 (%sort-vector
(or ,key
#'identity
))))))
3489 ;;;; debuggers' little helpers
3491 ;;; for debugging when transforms are behaving mysteriously,
3492 ;;; e.g. when debugging a problem with an ASH transform
3493 ;;; (defun foo (&optional s)
3494 ;;; (sb-c::/report-continuation s "S outside WHEN")
3495 ;;; (when (and (integerp s) (> s 3))
3496 ;;; (sb-c::/report-continuation s "S inside WHEN")
3497 ;;; (let ((bound (ash 1 (1- s))))
3498 ;;; (sb-c::/report-continuation bound "BOUND")
3499 ;;; (let ((x (- bound))
3501 ;;; (sb-c::/report-continuation x "X")
3502 ;;; (sb-c::/report-continuation x "Y"))
3503 ;;; `(integer ,(- bound) ,(1- bound)))))
3504 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
3505 ;;; and the function doesn't do anything at all.)
3508 (defknown /report-continuation
(t t
) null
)
3509 (deftransform /report-continuation
((x message
) (t t
))
3510 (format t
"~%/in /REPORT-CONTINUATION~%")
3511 (format t
"/(CONTINUATION-TYPE X)=~S~%" (continuation-type x
))
3512 (when (constant-continuation-p x
)
3513 (format t
"/(CONTINUATION-VALUE X)=~S~%" (continuation-value x
)))
3514 (format t
"/MESSAGE=~S~%" (continuation-value message
))
3515 (give-up-ir1-transform "not a real transform"))
3516 (defun /report-continuation
(&rest rest
)
3517 (declare (ignore rest
))))