1 ;;;; This file contains macro-like source transformations which
2 ;;;; convert uses of certain functions into the canonical form desired
3 ;;;; within the compiler. FIXME: and other IR1 transforms and stuff.
5 ;;;; This software is part of the SBCL system. See the README file for
8 ;;;; This software is derived from the CMU CL system, which was
9 ;;;; written at Carnegie Mellon University and released into the
10 ;;;; public domain. The software is in the public domain and is
11 ;;;; provided with absolutely no warranty. See the COPYING and CREDITS
12 ;;;; files for more information.
16 ;;; Convert into an IF so that IF optimizations will eliminate redundant
18 (define-source-transform not
(x) `(if ,x nil t
))
19 (define-source-transform null
(x) `(if ,x nil t
))
21 ;;; ENDP is just NULL with a LIST assertion. The assertion will be
22 ;;; optimized away when SAFETY optimization is low; hopefully that
23 ;;; is consistent with ANSI's "should return an error".
24 (define-source-transform endp
(x) `(null (the list
,x
)))
26 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
27 ;;; returns the first value of its argument. Ditto for VALUES with one
29 (define-source-transform identity
(x) `(prog1 ,x
))
30 (define-source-transform values
(x) `(prog1 ,x
))
32 ;;; Bind the value and make a closure that returns it.
33 (define-source-transform constantly
(value)
34 (with-unique-names (rest n-value
)
35 `(let ((,n-value
,value
))
37 (declare (ignore ,rest
))
40 ;;; If the function has a known number of arguments, then return a
41 ;;; lambda with the appropriate fixed number of args. If the
42 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
43 ;;; MV optimization figure things out.
44 (deftransform complement
((fun) * * :node node
)
46 (multiple-value-bind (min max
)
47 (fun-type-nargs (lvar-type fun
))
49 ((and min
(eql min max
))
50 (let ((dums (make-gensym-list min
)))
51 `#'(lambda ,dums
(not (funcall fun
,@dums
)))))
52 ((awhen (node-lvar node
)
53 (let ((dest (lvar-dest it
)))
54 (and (combination-p dest
)
55 (eq (combination-fun dest
) it
))))
56 '#'(lambda (&rest args
)
57 (not (apply fun args
))))
59 (give-up-ir1-transform
60 "The function doesn't have a fixed argument count.")))))
64 ;;; Translate CxR into CAR/CDR combos.
65 (defun source-transform-cxr (form)
66 (if (/= (length form
) 2)
68 (let* ((name (car form
))
72 (leaf (leaf-source-name name
))))))
73 (do ((i (- (length string
) 2) (1- i
))
75 `(,(ecase (char string i
)
81 ;;; Make source transforms to turn CxR forms into combinations of CAR
82 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
84 (/show0
"about to set CxR source transforms")
85 (loop for i of-type index from
2 upto
4 do
86 ;; Iterate over BUF = all names CxR where x = an I-element
87 ;; string of #\A or #\D characters.
88 (let ((buf (make-string (+ 2 i
))))
89 (setf (aref buf
0) #\C
90 (aref buf
(1+ i
)) #\R
)
91 (dotimes (j (ash 2 i
))
92 (declare (type index j
))
94 (declare (type index k
))
95 (setf (aref buf
(1+ k
))
96 (if (logbitp k j
) #\A
#\D
)))
97 (setf (info :function
:source-transform
(intern buf
))
98 #'source-transform-cxr
))))
99 (/show0
"done setting CxR source transforms")
101 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
102 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
103 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
105 (define-source-transform first
(x) `(car ,x
))
106 (define-source-transform rest
(x) `(cdr ,x
))
107 (define-source-transform second
(x) `(cadr ,x
))
108 (define-source-transform third
(x) `(caddr ,x
))
109 (define-source-transform fourth
(x) `(cadddr ,x
))
110 (define-source-transform fifth
(x) `(nth 4 ,x
))
111 (define-source-transform sixth
(x) `(nth 5 ,x
))
112 (define-source-transform seventh
(x) `(nth 6 ,x
))
113 (define-source-transform eighth
(x) `(nth 7 ,x
))
114 (define-source-transform ninth
(x) `(nth 8 ,x
))
115 (define-source-transform tenth
(x) `(nth 9 ,x
))
117 ;;; LIST with one arg is an extremely common operation (at least inside
118 ;;; SBCL itself); translate it to CONS to take advantage of common
119 ;;; allocation routines.
120 (define-source-transform list
(&rest args
)
122 (1 `(cons ,(first args
) nil
))
125 ;;; And similarly for LIST*.
126 (define-source-transform list
* (&rest args
)
128 (2 `(cons ,(first args
) ,(second args
)))
131 ;;; Translate RPLACx to LET and SETF.
132 (define-source-transform rplaca
(x y
)
137 (define-source-transform rplacd
(x y
)
143 (define-source-transform nth
(n l
) `(car (nthcdr ,n
,l
)))
145 (define-source-transform last
(x) `(sb!impl
::last1
,x
))
146 (define-source-transform gethash
(&rest args
)
148 (2 `(sb!impl
::gethash3
,@args nil
))
149 (3 `(sb!impl
::gethash3
,@args
))
151 (define-source-transform get
(&rest args
)
153 (2 `(sb!impl
::get2
,@args
))
154 (3 `(sb!impl
::get3
,@args
))
157 (defvar *default-nthcdr-open-code-limit
* 6)
158 (defvar *extreme-nthcdr-open-code-limit
* 20)
160 (deftransform nthcdr
((n l
) (unsigned-byte t
) * :node node
)
161 "convert NTHCDR to CAxxR"
162 (unless (constant-lvar-p n
)
163 (give-up-ir1-transform))
164 (let ((n (lvar-value n
)))
166 (if (policy node
(and (= speed
3) (= space
0)))
167 *extreme-nthcdr-open-code-limit
*
168 *default-nthcdr-open-code-limit
*))
169 (give-up-ir1-transform))
174 `(cdr ,(frob (1- n
))))))
177 ;;;; arithmetic and numerology
179 (define-source-transform plusp
(x) `(> ,x
0))
180 (define-source-transform minusp
(x) `(< ,x
0))
181 (define-source-transform zerop
(x) `(= ,x
0))
183 (define-source-transform 1+ (x) `(+ ,x
1))
184 (define-source-transform 1-
(x) `(- ,x
1))
186 (define-source-transform oddp
(x) `(logtest ,x
1))
187 (define-source-transform evenp
(x) `(not (logtest ,x
1)))
189 ;;; Note that all the integer division functions are available for
190 ;;; inline expansion.
192 (macrolet ((deffrob (fun)
193 `(define-source-transform ,fun
(x &optional
(y nil y-p
))
200 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
202 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
205 ;;; This used to be a source transform (hence the lack of restrictions
206 ;;; on the argument types), but we make it a regular transform so that
207 ;;; the VM has a chance to see the bare LOGTEST and potentiall choose
208 ;;; to implement it differently. --njf, 06-02-2006
209 (deftransform logtest
((x y
) * *)
210 `(not (zerop (logand x y
))))
212 (deftransform logbitp
213 ((index integer
) (unsigned-byte (or (signed-byte #.sb
!vm
:n-word-bits
)
214 (unsigned-byte #.sb
!vm
:n-word-bits
))))
215 `(if (>= index
#.sb
!vm
:n-word-bits
)
217 (not (zerop (logand integer
(ash 1 index
))))))
219 (define-source-transform byte
(size position
)
220 `(cons ,size
,position
))
221 (define-source-transform byte-size
(spec) `(car ,spec
))
222 (define-source-transform byte-position
(spec) `(cdr ,spec
))
223 (define-source-transform ldb-test
(bytespec integer
)
224 `(not (zerop (mask-field ,bytespec
,integer
))))
226 ;;; With the ratio and complex accessors, we pick off the "identity"
227 ;;; case, and use a primitive to handle the cell access case.
228 (define-source-transform numerator
(num)
229 (once-only ((n-num `(the rational
,num
)))
233 (define-source-transform denominator
(num)
234 (once-only ((n-num `(the rational
,num
)))
236 (%denominator
,n-num
)
239 ;;;; interval arithmetic for computing bounds
241 ;;;; This is a set of routines for operating on intervals. It
242 ;;;; implements a simple interval arithmetic package. Although SBCL
243 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
244 ;;;; for two reasons:
246 ;;;; 1. This package is simpler than NUMERIC-TYPE.
248 ;;;; 2. It makes debugging much easier because you can just strip
249 ;;;; out these routines and test them independently of SBCL. (This is a
252 ;;;; One disadvantage is a probable increase in consing because we
253 ;;;; have to create these new interval structures even though
254 ;;;; numeric-type has everything we want to know. Reason 2 wins for
257 ;;; Support operations that mimic real arithmetic comparison
258 ;;; operators, but imposing a total order on the floating points such
259 ;;; that negative zeros are strictly less than positive zeros.
260 (macrolet ((def (name op
)
263 (if (and (floatp x
) (floatp y
) (zerop x
) (zerop y
))
264 (,op
(float-sign x
) (float-sign y
))
266 (def signed-zero-
>= >=)
267 (def signed-zero-
> >)
268 (def signed-zero-
= =)
269 (def signed-zero-
< <)
270 (def signed-zero-
<= <=))
272 ;;; The basic interval type. It can handle open and closed intervals.
273 ;;; A bound is open if it is a list containing a number, just like
274 ;;; Lisp says. NIL means unbounded.
275 (defstruct (interval (:constructor %make-interval
)
279 (defun make-interval (&key low high
)
280 (labels ((normalize-bound (val)
283 (float-infinity-p val
))
284 ;; Handle infinities.
288 ;; Handle any closed bounds.
291 ;; We have an open bound. Normalize the numeric
292 ;; bound. If the normalized bound is still a number
293 ;; (not nil), keep the bound open. Otherwise, the
294 ;; bound is really unbounded, so drop the openness.
295 (let ((new-val (normalize-bound (first val
))))
297 ;; The bound exists, so keep it open still.
300 (error "unknown bound type in MAKE-INTERVAL")))))
301 (%make-interval
:low
(normalize-bound low
)
302 :high
(normalize-bound high
))))
304 ;;; Given a number X, create a form suitable as a bound for an
305 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
306 #!-sb-fluid
(declaim (inline set-bound
))
307 (defun set-bound (x open-p
)
308 (if (and x open-p
) (list x
) x
))
310 ;;; Apply the function F to a bound X. If X is an open bound, then
311 ;;; the result will be open. IF X is NIL, the result is NIL.
312 (defun bound-func (f x
)
313 (declare (type function f
))
315 (with-float-traps-masked (:underflow
:overflow
:inexact
:divide-by-zero
)
316 ;; With these traps masked, we might get things like infinity
317 ;; or negative infinity returned. Check for this and return
318 ;; NIL to indicate unbounded.
319 (let ((y (funcall f
(type-bound-number x
))))
321 (float-infinity-p y
))
323 (set-bound y
(consp x
)))))))
325 ;;; Apply a binary operator OP to two bounds X and Y. The result is
326 ;;; NIL if either is NIL. Otherwise bound is computed and the result
327 ;;; is open if either X or Y is open.
329 ;;; FIXME: only used in this file, not needed in target runtime
331 ;;; ANSI contaigon specifies coercion to floating point if one of the
332 ;;; arguments is floating point. Here we should check to be sure that
333 ;;; the other argument is within the bounds of that floating point
336 (defmacro safely-binop
(op x y
)
338 ((typep ,x
'single-float
)
339 (if (or (typep ,y
'single-float
)
340 (<= most-negative-single-float
,y most-positive-single-float
))
342 ((typep ,x
'double-float
)
343 (if (or (typep ,y
'double-float
)
344 (<= most-negative-double-float
,y most-positive-double-float
))
346 ((typep ,y
'single-float
)
347 (if (<= most-negative-single-float
,x most-positive-single-float
)
349 ((typep ,y
'double-float
)
350 (if (<= most-negative-double-float
,x most-positive-double-float
)
354 (defmacro bound-binop
(op x y
)
356 (with-float-traps-masked (:underflow
:overflow
:inexact
:divide-by-zero
)
357 (set-bound (safely-binop ,op
(type-bound-number ,x
)
358 (type-bound-number ,y
))
359 (or (consp ,x
) (consp ,y
))))))
361 (defun coerce-for-bound (val type
)
363 (list (coerce-for-bound (car val
) type
))
365 ((subtypep type
'double-float
)
366 (if (<= most-negative-double-float val most-positive-double-float
)
368 ((or (subtypep type
'single-float
) (subtypep type
'float
))
369 ;; coerce to float returns a single-float
370 (if (<= most-negative-single-float val most-positive-single-float
)
372 (t (coerce val type
)))))
374 (defun coerce-and-truncate-floats (val type
)
377 (list (coerce-and-truncate-floats (car val
) type
))
379 ((subtypep type
'double-float
)
380 (if (<= most-negative-double-float val most-positive-double-float
)
382 (if (< val most-negative-double-float
)
383 most-negative-double-float most-positive-double-float
)))
384 ((or (subtypep type
'single-float
) (subtypep type
'float
))
385 ;; coerce to float returns a single-float
386 (if (<= most-negative-single-float val most-positive-single-float
)
388 (if (< val most-negative-single-float
)
389 most-negative-single-float most-positive-single-float
)))
390 (t (coerce val type
))))))
392 ;;; Convert a numeric-type object to an interval object.
393 (defun numeric-type->interval
(x)
394 (declare (type numeric-type x
))
395 (make-interval :low
(numeric-type-low x
)
396 :high
(numeric-type-high x
)))
398 (defun type-approximate-interval (type)
399 (declare (type ctype type
))
400 (let ((types (prepare-arg-for-derive-type type
))
403 (let ((type (if (member-type-p type
)
404 (convert-member-type type
)
406 (unless (numeric-type-p type
)
407 (return-from type-approximate-interval nil
))
408 (let ((interval (numeric-type->interval type
)))
411 (interval-approximate-union result interval
)
415 (defun copy-interval-limit (limit)
420 (defun copy-interval (x)
421 (declare (type interval x
))
422 (make-interval :low
(copy-interval-limit (interval-low x
))
423 :high
(copy-interval-limit (interval-high x
))))
425 ;;; Given a point P contained in the interval X, split X into two
426 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
427 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
428 ;;; contains P. You can specify both to be T or NIL.
429 (defun interval-split (p x
&optional close-lower close-upper
)
430 (declare (type number p
)
432 (list (make-interval :low
(copy-interval-limit (interval-low x
))
433 :high
(if close-lower p
(list p
)))
434 (make-interval :low
(if close-upper
(list p
) p
)
435 :high
(copy-interval-limit (interval-high x
)))))
437 ;;; Return the closure of the interval. That is, convert open bounds
438 ;;; to closed bounds.
439 (defun interval-closure (x)
440 (declare (type interval x
))
441 (make-interval :low
(type-bound-number (interval-low x
))
442 :high
(type-bound-number (interval-high x
))))
444 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
445 ;;; '-. Otherwise return NIL.
446 (defun interval-range-info (x &optional
(point 0))
447 (declare (type interval x
))
448 (let ((lo (interval-low x
))
449 (hi (interval-high x
)))
450 (cond ((and lo
(signed-zero->= (type-bound-number lo
) point
))
452 ((and hi
(signed-zero->= point
(type-bound-number hi
)))
457 ;;; Test to see whether the interval X is bounded. HOW determines the
458 ;;; test, and should be either ABOVE, BELOW, or BOTH.
459 (defun interval-bounded-p (x how
)
460 (declare (type interval x
))
467 (and (interval-low x
) (interval-high x
)))))
469 ;;; See whether the interval X contains the number P, taking into
470 ;;; account that the interval might not be closed.
471 (defun interval-contains-p (p x
)
472 (declare (type number p
)
474 ;; Does the interval X contain the number P? This would be a lot
475 ;; easier if all intervals were closed!
476 (let ((lo (interval-low x
))
477 (hi (interval-high x
)))
479 ;; The interval is bounded
480 (if (and (signed-zero-<= (type-bound-number lo
) p
)
481 (signed-zero-<= p
(type-bound-number hi
)))
482 ;; P is definitely in the closure of the interval.
483 ;; We just need to check the end points now.
484 (cond ((signed-zero-= p
(type-bound-number lo
))
486 ((signed-zero-= p
(type-bound-number hi
))
491 ;; Interval with upper bound
492 (if (signed-zero-< p
(type-bound-number hi
))
494 (and (numberp hi
) (signed-zero-= p hi
))))
496 ;; Interval with lower bound
497 (if (signed-zero-> p
(type-bound-number lo
))
499 (and (numberp lo
) (signed-zero-= p lo
))))
501 ;; Interval with no bounds
504 ;;; Determine whether two intervals X and Y intersect. Return T if so.
505 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
506 ;;; were closed. Otherwise the intervals are treated as they are.
508 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
509 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
510 ;;; is T, then they do intersect because we use the closure of X = [0,
511 ;;; 1] and Y = [1, 2] to determine intersection.
512 (defun interval-intersect-p (x y
&optional closed-intervals-p
)
513 (declare (type interval x y
))
514 (and (interval-intersection/difference
(if closed-intervals-p
517 (if closed-intervals-p
522 ;;; Are the two intervals adjacent? That is, is there a number
523 ;;; between the two intervals that is not an element of either
524 ;;; interval? If so, they are not adjacent. For example [0, 1) and
525 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
526 ;;; between both intervals.
527 (defun interval-adjacent-p (x y
)
528 (declare (type interval x y
))
529 (flet ((adjacent (lo hi
)
530 ;; Check to see whether lo and hi are adjacent. If either is
531 ;; nil, they can't be adjacent.
532 (when (and lo hi
(= (type-bound-number lo
) (type-bound-number hi
)))
533 ;; The bounds are equal. They are adjacent if one of
534 ;; them is closed (a number). If both are open (consp),
535 ;; then there is a number that lies between them.
536 (or (numberp lo
) (numberp hi
)))))
537 (or (adjacent (interval-low y
) (interval-high x
))
538 (adjacent (interval-low x
) (interval-high y
)))))
540 ;;; Compute the intersection and difference between two intervals.
541 ;;; Two values are returned: the intersection and the difference.
543 ;;; Let the two intervals be X and Y, and let I and D be the two
544 ;;; values returned by this function. Then I = X intersect Y. If I
545 ;;; is NIL (the empty set), then D is X union Y, represented as the
546 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
547 ;;; - I, which is a list of two intervals.
549 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
550 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
551 (defun interval-intersection/difference
(x y
)
552 (declare (type interval x y
))
553 (let ((x-lo (interval-low x
))
554 (x-hi (interval-high x
))
555 (y-lo (interval-low y
))
556 (y-hi (interval-high y
)))
559 ;; If p is an open bound, make it closed. If p is a closed
560 ;; bound, make it open.
564 (test-number (p int bound
)
565 ;; Test whether P is in the interval.
566 (let ((pn (type-bound-number p
)))
567 (when (interval-contains-p pn
(interval-closure int
))
568 ;; Check for endpoints.
569 (let* ((lo (interval-low int
))
570 (hi (interval-high int
))
571 (lon (type-bound-number lo
))
572 (hin (type-bound-number hi
)))
574 ;; Interval may be a point.
575 ((and lon hin
(= lon hin pn
))
576 (and (numberp p
) (numberp lo
) (numberp hi
)))
577 ;; Point matches the low end.
578 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
579 ;; (P [P,?} => TRUE P) [P,?} => FALSE
580 ;; (P (P,?} => TRUE P) (P,?} => FALSE
581 ((and lon
(= pn lon
))
582 (or (and (numberp p
) (numberp lo
))
583 (and (consp p
) (eq :low bound
))))
584 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
585 ;; P) {?,P] => TRUE (P {?,P] => FALSE
586 ;; P) {?,P) => TRUE (P {?,P) => FALSE
587 ((and hin
(= pn hin
))
588 (or (and (numberp p
) (numberp hi
))
589 (and (consp p
) (eq :high bound
))))
590 ;; Not an endpoint, all is well.
593 (test-lower-bound (p int
)
594 ;; P is a lower bound of an interval.
596 (test-number p int
:low
)
597 (not (interval-bounded-p int
'below
))))
598 (test-upper-bound (p int
)
599 ;; P is an upper bound of an interval.
601 (test-number p int
:high
)
602 (not (interval-bounded-p int
'above
)))))
603 (let ((x-lo-in-y (test-lower-bound x-lo y
))
604 (x-hi-in-y (test-upper-bound x-hi y
))
605 (y-lo-in-x (test-lower-bound y-lo x
))
606 (y-hi-in-x (test-upper-bound y-hi x
)))
607 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x
)
608 ;; Intervals intersect. Let's compute the intersection
609 ;; and the difference.
610 (multiple-value-bind (lo left-lo left-hi
)
611 (cond (x-lo-in-y (values x-lo y-lo
(opposite-bound x-lo
)))
612 (y-lo-in-x (values y-lo x-lo
(opposite-bound y-lo
))))
613 (multiple-value-bind (hi right-lo right-hi
)
615 (values x-hi
(opposite-bound x-hi
) y-hi
))
617 (values y-hi
(opposite-bound y-hi
) x-hi
)))
618 (values (make-interval :low lo
:high hi
)
619 (list (make-interval :low left-lo
621 (make-interval :low right-lo
624 (values nil
(list x y
))))))))
626 ;;; If intervals X and Y intersect, return a new interval that is the
627 ;;; union of the two. If they do not intersect, return NIL.
628 (defun interval-merge-pair (x y
)
629 (declare (type interval x y
))
630 ;; If x and y intersect or are adjacent, create the union.
631 ;; Otherwise return nil
632 (when (or (interval-intersect-p x y
)
633 (interval-adjacent-p x y
))
634 (flet ((select-bound (x1 x2 min-op max-op
)
635 (let ((x1-val (type-bound-number x1
))
636 (x2-val (type-bound-number x2
)))
638 ;; Both bounds are finite. Select the right one.
639 (cond ((funcall min-op x1-val x2-val
)
640 ;; x1 is definitely better.
642 ((funcall max-op x1-val x2-val
)
643 ;; x2 is definitely better.
646 ;; Bounds are equal. Select either
647 ;; value and make it open only if
649 (set-bound x1-val
(and (consp x1
) (consp x2
))))))
651 ;; At least one bound is not finite. The
652 ;; non-finite bound always wins.
654 (let* ((x-lo (copy-interval-limit (interval-low x
)))
655 (x-hi (copy-interval-limit (interval-high x
)))
656 (y-lo (copy-interval-limit (interval-low y
)))
657 (y-hi (copy-interval-limit (interval-high y
))))
658 (make-interval :low
(select-bound x-lo y-lo
#'< #'>)
659 :high
(select-bound x-hi y-hi
#'> #'<))))))
661 ;;; return the minimal interval, containing X and Y
662 (defun interval-approximate-union (x y
)
663 (cond ((interval-merge-pair x y
))
665 (make-interval :low
(copy-interval-limit (interval-low x
))
666 :high
(copy-interval-limit (interval-high y
))))
668 (make-interval :low
(copy-interval-limit (interval-low y
))
669 :high
(copy-interval-limit (interval-high x
))))))
671 ;;; basic arithmetic operations on intervals. We probably should do
672 ;;; true interval arithmetic here, but it's complicated because we
673 ;;; have float and integer types and bounds can be open or closed.
675 ;;; the negative of an interval
676 (defun interval-neg (x)
677 (declare (type interval x
))
678 (make-interval :low
(bound-func #'-
(interval-high x
))
679 :high
(bound-func #'-
(interval-low x
))))
681 ;;; Add two intervals.
682 (defun interval-add (x y
)
683 (declare (type interval x y
))
684 (make-interval :low
(bound-binop + (interval-low x
) (interval-low y
))
685 :high
(bound-binop + (interval-high x
) (interval-high y
))))
687 ;;; Subtract two intervals.
688 (defun interval-sub (x y
)
689 (declare (type interval x y
))
690 (make-interval :low
(bound-binop -
(interval-low x
) (interval-high y
))
691 :high
(bound-binop -
(interval-high x
) (interval-low y
))))
693 ;;; Multiply two intervals.
694 (defun interval-mul (x y
)
695 (declare (type interval x y
))
696 (flet ((bound-mul (x y
)
697 (cond ((or (null x
) (null y
))
698 ;; Multiply by infinity is infinity
700 ((or (and (numberp x
) (zerop x
))
701 (and (numberp y
) (zerop y
)))
702 ;; Multiply by closed zero is special. The result
703 ;; is always a closed bound. But don't replace this
704 ;; with zero; we want the multiplication to produce
705 ;; the correct signed zero, if needed. Use SIGNUM
706 ;; to avoid trying to multiply huge bignums with 0.0.
707 (* (signum (type-bound-number x
)) (signum (type-bound-number y
))))
708 ((or (and (floatp x
) (float-infinity-p x
))
709 (and (floatp y
) (float-infinity-p y
)))
710 ;; Infinity times anything is infinity
713 ;; General multiply. The result is open if either is open.
714 (bound-binop * x y
)))))
715 (let ((x-range (interval-range-info x
))
716 (y-range (interval-range-info y
)))
717 (cond ((null x-range
)
718 ;; Split x into two and multiply each separately
719 (destructuring-bind (x- x
+) (interval-split 0 x t t
)
720 (interval-merge-pair (interval-mul x- y
)
721 (interval-mul x
+ y
))))
723 ;; Split y into two and multiply each separately
724 (destructuring-bind (y- y
+) (interval-split 0 y t t
)
725 (interval-merge-pair (interval-mul x y-
)
726 (interval-mul x y
+))))
728 (interval-neg (interval-mul (interval-neg x
) y
)))
730 (interval-neg (interval-mul x
(interval-neg y
))))
731 ((and (eq x-range
'+) (eq y-range
'+))
732 ;; If we are here, X and Y are both positive.
734 :low
(bound-mul (interval-low x
) (interval-low y
))
735 :high
(bound-mul (interval-high x
) (interval-high y
))))
737 (bug "excluded case in INTERVAL-MUL"))))))
739 ;;; Divide two intervals.
740 (defun interval-div (top bot
)
741 (declare (type interval top bot
))
742 (flet ((bound-div (x y y-low-p
)
745 ;; Divide by infinity means result is 0. However,
746 ;; we need to watch out for the sign of the result,
747 ;; to correctly handle signed zeros. We also need
748 ;; to watch out for positive or negative infinity.
749 (if (floatp (type-bound-number x
))
751 (- (float-sign (type-bound-number x
) 0.0))
752 (float-sign (type-bound-number x
) 0.0))
754 ((zerop (type-bound-number y
))
755 ;; Divide by zero means result is infinity
757 ((and (numberp x
) (zerop x
))
758 ;; Zero divided by anything is zero.
761 (bound-binop / x y
)))))
762 (let ((top-range (interval-range-info top
))
763 (bot-range (interval-range-info bot
)))
764 (cond ((null bot-range
)
765 ;; The denominator contains zero, so anything goes!
766 (make-interval :low nil
:high nil
))
768 ;; Denominator is negative so flip the sign, compute the
769 ;; result, and flip it back.
770 (interval-neg (interval-div top
(interval-neg bot
))))
772 ;; Split top into two positive and negative parts, and
773 ;; divide each separately
774 (destructuring-bind (top- top
+) (interval-split 0 top t t
)
775 (interval-merge-pair (interval-div top- bot
)
776 (interval-div top
+ bot
))))
778 ;; Top is negative so flip the sign, divide, and flip the
779 ;; sign of the result.
780 (interval-neg (interval-div (interval-neg top
) bot
)))
781 ((and (eq top-range
'+) (eq bot-range
'+))
784 :low
(bound-div (interval-low top
) (interval-high bot
) t
)
785 :high
(bound-div (interval-high top
) (interval-low bot
) nil
)))
787 (bug "excluded case in INTERVAL-DIV"))))))
789 ;;; Apply the function F to the interval X. If X = [a, b], then the
790 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
791 ;;; result makes sense. It will if F is monotonic increasing (or
793 (defun interval-func (f x
)
794 (declare (type function f
)
796 (let ((lo (bound-func f
(interval-low x
)))
797 (hi (bound-func f
(interval-high x
))))
798 (make-interval :low lo
:high hi
)))
800 ;;; Return T if X < Y. That is every number in the interval X is
801 ;;; always less than any number in the interval Y.
802 (defun interval-< (x y
)
803 (declare (type interval x y
))
804 ;; X < Y only if X is bounded above, Y is bounded below, and they
806 (when (and (interval-bounded-p x
'above
)
807 (interval-bounded-p y
'below
))
808 ;; Intervals are bounded in the appropriate way. Make sure they
810 (let ((left (interval-high x
))
811 (right (interval-low y
)))
812 (cond ((> (type-bound-number left
)
813 (type-bound-number right
))
814 ;; The intervals definitely overlap, so result is NIL.
816 ((< (type-bound-number left
)
817 (type-bound-number right
))
818 ;; The intervals definitely don't touch, so result is T.
821 ;; Limits are equal. Check for open or closed bounds.
822 ;; Don't overlap if one or the other are open.
823 (or (consp left
) (consp right
)))))))
825 ;;; Return T if X >= Y. That is, every number in the interval X is
826 ;;; always greater than any number in the interval Y.
827 (defun interval->= (x y
)
828 (declare (type interval x y
))
829 ;; X >= Y if lower bound of X >= upper bound of Y
830 (when (and (interval-bounded-p x
'below
)
831 (interval-bounded-p y
'above
))
832 (>= (type-bound-number (interval-low x
))
833 (type-bound-number (interval-high y
)))))
835 ;;; Return T if X = Y.
836 (defun interval-= (x y
)
837 (declare (type interval x y
))
838 (and (interval-bounded-p x
'both
)
839 (interval-bounded-p y
'both
)
843 ;; Open intervals cannot be =
844 (return-from interval-
= nil
))))
845 ;; Both intervals refer to the same point
846 (= (bound (interval-high x
)) (bound (interval-low x
))
847 (bound (interval-high y
)) (bound (interval-low y
))))))
849 ;;; Return T if X /= Y
850 (defun interval-/= (x y
)
851 (not (interval-intersect-p x y
)))
853 ;;; Return an interval that is the absolute value of X. Thus, if
854 ;;; X = [-1 10], the result is [0, 10].
855 (defun interval-abs (x)
856 (declare (type interval x
))
857 (case (interval-range-info x
)
863 (destructuring-bind (x- x
+) (interval-split 0 x t t
)
864 (interval-merge-pair (interval-neg x-
) x
+)))))
866 ;;; Compute the square of an interval.
867 (defun interval-sqr (x)
868 (declare (type interval x
))
869 (interval-func (lambda (x) (* x x
))
872 ;;;; numeric DERIVE-TYPE methods
874 ;;; a utility for defining derive-type methods of integer operations. If
875 ;;; the types of both X and Y are integer types, then we compute a new
876 ;;; integer type with bounds determined Fun when applied to X and Y.
877 ;;; Otherwise, we use NUMERIC-CONTAGION.
878 (defun derive-integer-type-aux (x y fun
)
879 (declare (type function fun
))
880 (if (and (numeric-type-p x
) (numeric-type-p y
)
881 (eq (numeric-type-class x
) 'integer
)
882 (eq (numeric-type-class y
) 'integer
)
883 (eq (numeric-type-complexp x
) :real
)
884 (eq (numeric-type-complexp y
) :real
))
885 (multiple-value-bind (low high
) (funcall fun x y
)
886 (make-numeric-type :class
'integer
890 (numeric-contagion x y
)))
892 (defun derive-integer-type (x y fun
)
893 (declare (type lvar x y
) (type function fun
))
894 (let ((x (lvar-type x
))
896 (derive-integer-type-aux x y fun
)))
898 ;;; simple utility to flatten a list
899 (defun flatten-list (x)
900 (labels ((flatten-and-append (tree list
)
901 (cond ((null tree
) list
)
902 ((atom tree
) (cons tree list
))
903 (t (flatten-and-append
904 (car tree
) (flatten-and-append (cdr tree
) list
))))))
905 (flatten-and-append x nil
)))
907 ;;; Take some type of lvar and massage it so that we get a list of the
908 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
910 (defun prepare-arg-for-derive-type (arg)
911 (flet ((listify (arg)
916 (union-type-types arg
))
919 (unless (eq arg
*empty-type
*)
920 ;; Make sure all args are some type of numeric-type. For member
921 ;; types, convert the list of members into a union of equivalent
922 ;; single-element member-type's.
923 (let ((new-args nil
))
924 (dolist (arg (listify arg
))
925 (if (member-type-p arg
)
926 ;; Run down the list of members and convert to a list of
928 (mapc-member-type-members
930 (push (if (numberp member
)
931 (make-member-type :members
(list member
))
935 (push arg new-args
)))
936 (unless (member *empty-type
* new-args
)
939 ;;; Convert from the standard type convention for which -0.0 and 0.0
940 ;;; are equal to an intermediate convention for which they are
941 ;;; considered different which is more natural for some of the
943 (defun convert-numeric-type (type)
944 (declare (type numeric-type type
))
945 ;;; Only convert real float interval delimiters types.
946 (if (eq (numeric-type-complexp type
) :real
)
947 (let* ((lo (numeric-type-low type
))
948 (lo-val (type-bound-number lo
))
949 (lo-float-zero-p (and lo
(floatp lo-val
) (= lo-val
0.0)))
950 (hi (numeric-type-high type
))
951 (hi-val (type-bound-number hi
))
952 (hi-float-zero-p (and hi
(floatp hi-val
) (= hi-val
0.0))))
953 (if (or lo-float-zero-p hi-float-zero-p
)
955 :class
(numeric-type-class type
)
956 :format
(numeric-type-format type
)
958 :low
(if lo-float-zero-p
960 (list (float 0.0 lo-val
))
961 (float (load-time-value (make-unportable-float :single-float-negative-zero
)) lo-val
))
963 :high
(if hi-float-zero-p
965 (list (float (load-time-value (make-unportable-float :single-float-negative-zero
)) hi-val
))
972 ;;; Convert back from the intermediate convention for which -0.0 and
973 ;;; 0.0 are considered different to the standard type convention for
975 (defun convert-back-numeric-type (type)
976 (declare (type numeric-type type
))
977 ;;; Only convert real float interval delimiters types.
978 (if (eq (numeric-type-complexp type
) :real
)
979 (let* ((lo (numeric-type-low type
))
980 (lo-val (type-bound-number lo
))
982 (and lo
(floatp lo-val
) (= lo-val
0.0)
983 (float-sign lo-val
)))
984 (hi (numeric-type-high type
))
985 (hi-val (type-bound-number hi
))
987 (and hi
(floatp hi-val
) (= hi-val
0.0)
988 (float-sign hi-val
))))
990 ;; (float +0.0 +0.0) => (member 0.0)
991 ;; (float -0.0 -0.0) => (member -0.0)
992 ((and lo-float-zero-p hi-float-zero-p
)
993 ;; shouldn't have exclusive bounds here..
994 (aver (and (not (consp lo
)) (not (consp hi
))))
995 (if (= lo-float-zero-p hi-float-zero-p
)
996 ;; (float +0.0 +0.0) => (member 0.0)
997 ;; (float -0.0 -0.0) => (member -0.0)
998 (specifier-type `(member ,lo-val
))
999 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1000 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1001 (make-numeric-type :class
(numeric-type-class type
)
1002 :format
(numeric-type-format type
)
1008 ;; (float -0.0 x) => (float 0.0 x)
1009 ((and (not (consp lo
)) (minusp lo-float-zero-p
))
1010 (make-numeric-type :class
(numeric-type-class type
)
1011 :format
(numeric-type-format type
)
1013 :low
(float 0.0 lo-val
)
1015 ;; (float (+0.0) x) => (float (0.0) x)
1016 ((and (consp lo
) (plusp lo-float-zero-p
))
1017 (make-numeric-type :class
(numeric-type-class type
)
1018 :format
(numeric-type-format type
)
1020 :low
(list (float 0.0 lo-val
))
1023 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1024 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1025 (list (make-member-type :members
(list (float 0.0 lo-val
)))
1026 (make-numeric-type :class
(numeric-type-class type
)
1027 :format
(numeric-type-format type
)
1029 :low
(list (float 0.0 lo-val
))
1033 ;; (float x +0.0) => (float x 0.0)
1034 ((and (not (consp hi
)) (plusp hi-float-zero-p
))
1035 (make-numeric-type :class
(numeric-type-class type
)
1036 :format
(numeric-type-format type
)
1039 :high
(float 0.0 hi-val
)))
1040 ;; (float x (-0.0)) => (float x (0.0))
1041 ((and (consp hi
) (minusp hi-float-zero-p
))
1042 (make-numeric-type :class
(numeric-type-class type
)
1043 :format
(numeric-type-format type
)
1046 :high
(list (float 0.0 hi-val
))))
1048 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1049 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1050 (list (make-member-type :members
(list (float -
0.0 hi-val
)))
1051 (make-numeric-type :class
(numeric-type-class type
)
1052 :format
(numeric-type-format type
)
1055 :high
(list (float 0.0 hi-val
)))))))
1061 ;;; Convert back a possible list of numeric types.
1062 (defun convert-back-numeric-type-list (type-list)
1065 (let ((results '()))
1066 (dolist (type type-list
)
1067 (if (numeric-type-p type
)
1068 (let ((result (convert-back-numeric-type type
)))
1070 (setf results
(append results result
))
1071 (push result results
)))
1072 (push type results
)))
1075 (convert-back-numeric-type type-list
))
1077 (convert-back-numeric-type-list (union-type-types type-list
)))
1081 ;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
1082 ;;; belong in the kernel's type logic, invoked always, instead of in
1083 ;;; the compiler, invoked only during some type optimizations. (In
1084 ;;; fact, as of 0.pre8.100 or so they probably are, under
1085 ;;; MAKE-MEMBER-TYPE, so probably this code can be deleted)
1087 ;;; Take a list of types and return a canonical type specifier,
1088 ;;; combining any MEMBER types together. If both positive and negative
1089 ;;; MEMBER types are present they are converted to a float type.
1090 ;;; XXX This would be far simpler if the type-union methods could handle
1091 ;;; member/number unions.
1092 (defun make-canonical-union-type (type-list)
1093 (let ((xset (alloc-xset))
1096 (dolist (type type-list
)
1097 (cond ((member-type-p type
)
1098 (mapc-member-type-members
1100 (if (fp-zero-p member
)
1101 (unless (member member fp-zeroes
)
1102 (pushnew member fp-zeroes
))
1103 (add-to-xset member xset
)))
1106 (push type misc-types
))))
1107 (if (and (xset-empty-p xset
) (not fp-zeroes
))
1108 (apply #'type-union misc-types
)
1109 (apply #'type-union
(make-member-type :xset xset
:fp-zeroes fp-zeroes
) misc-types
))))
1111 ;;; Convert a member type with a single member to a numeric type.
1112 (defun convert-member-type (arg)
1113 (let* ((members (member-type-members arg
))
1114 (member (first members
))
1115 (member-type (type-of member
)))
1116 (aver (not (rest members
)))
1117 (specifier-type (cond ((typep member
'integer
)
1118 `(integer ,member
,member
))
1119 ((memq member-type
'(short-float single-float
1120 double-float long-float
))
1121 `(,member-type
,member
,member
))
1125 ;;; This is used in defoptimizers for computing the resulting type of
1128 ;;; Given the lvar ARG, derive the resulting type using the
1129 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1130 ;;; "atomic" lvar type like numeric-type or member-type (containing
1131 ;;; just one element). It should return the resulting type, which can
1132 ;;; be a list of types.
1134 ;;; For the case of member types, if a MEMBER-FUN is given it is
1135 ;;; called to compute the result otherwise the member type is first
1136 ;;; converted to a numeric type and the DERIVE-FUN is called.
1137 (defun one-arg-derive-type (arg derive-fun member-fun
1138 &optional
(convert-type t
))
1139 (declare (type function derive-fun
)
1140 (type (or null function
) member-fun
))
1141 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg
))))
1147 (with-float-traps-masked
1148 (:underflow
:overflow
:divide-by-zero
)
1150 `(eql ,(funcall member-fun
1151 (first (member-type-members x
))))))
1152 ;; Otherwise convert to a numeric type.
1153 (let ((result-type-list
1154 (funcall derive-fun
(convert-member-type x
))))
1156 (convert-back-numeric-type-list result-type-list
)
1157 result-type-list
))))
1160 (convert-back-numeric-type-list
1161 (funcall derive-fun
(convert-numeric-type x
)))
1162 (funcall derive-fun x
)))
1164 *universal-type
*))))
1165 ;; Run down the list of args and derive the type of each one,
1166 ;; saving all of the results in a list.
1167 (let ((results nil
))
1168 (dolist (arg arg-list
)
1169 (let ((result (deriver arg
)))
1171 (setf results
(append results result
))
1172 (push result results
))))
1174 (make-canonical-union-type results
)
1175 (first results
)))))))
1177 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1178 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1179 ;;; original args and a third which is T to indicate if the two args
1180 ;;; really represent the same lvar. This is useful for deriving the
1181 ;;; type of things like (* x x), which should always be positive. If
1182 ;;; we didn't do this, we wouldn't be able to tell.
1183 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1184 &optional
(convert-type t
))
1185 (declare (type function derive-fun fun
))
1186 (flet ((deriver (x y same-arg
)
1187 (cond ((and (member-type-p x
) (member-type-p y
))
1188 (let* ((x (first (member-type-members x
)))
1189 (y (first (member-type-members y
)))
1190 (result (ignore-errors
1191 (with-float-traps-masked
1192 (:underflow
:overflow
:divide-by-zero
1194 (funcall fun x y
)))))
1195 (cond ((null result
) *empty-type
*)
1196 ((and (floatp result
) (float-nan-p result
))
1197 (make-numeric-type :class
'float
1198 :format
(type-of result
)
1201 (specifier-type `(eql ,result
))))))
1202 ((and (member-type-p x
) (numeric-type-p y
))
1203 (let* ((x (convert-member-type x
))
1204 (y (if convert-type
(convert-numeric-type y
) y
))
1205 (result (funcall derive-fun x y same-arg
)))
1207 (convert-back-numeric-type-list result
)
1209 ((and (numeric-type-p x
) (member-type-p y
))
1210 (let* ((x (if convert-type
(convert-numeric-type x
) x
))
1211 (y (convert-member-type y
))
1212 (result (funcall derive-fun x y same-arg
)))
1214 (convert-back-numeric-type-list result
)
1216 ((and (numeric-type-p x
) (numeric-type-p y
))
1217 (let* ((x (if convert-type
(convert-numeric-type x
) x
))
1218 (y (if convert-type
(convert-numeric-type y
) y
))
1219 (result (funcall derive-fun x y same-arg
)))
1221 (convert-back-numeric-type-list result
)
1224 *universal-type
*))))
1225 (let ((same-arg (same-leaf-ref-p arg1 arg2
))
1226 (a1 (prepare-arg-for-derive-type (lvar-type arg1
)))
1227 (a2 (prepare-arg-for-derive-type (lvar-type arg2
))))
1229 (let ((results nil
))
1231 ;; Since the args are the same LVARs, just run down the
1234 (let ((result (deriver x x same-arg
)))
1236 (setf results
(append results result
))
1237 (push result results
))))
1238 ;; Try all pairwise combinations.
1241 (let ((result (or (deriver x y same-arg
)
1242 (numeric-contagion x y
))))
1244 (setf results
(append results result
))
1245 (push result results
))))))
1247 (make-canonical-union-type results
)
1248 (first results
)))))))
1250 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1252 (defoptimizer (+ derive-type
) ((x y
))
1253 (derive-integer-type
1260 (values (frob (numeric-type-low x
) (numeric-type-low y
))
1261 (frob (numeric-type-high x
) (numeric-type-high y
)))))))
1263 (defoptimizer (- derive-type
) ((x y
))
1264 (derive-integer-type
1271 (values (frob (numeric-type-low x
) (numeric-type-high y
))
1272 (frob (numeric-type-high x
) (numeric-type-low y
)))))))
1274 (defoptimizer (* derive-type
) ((x y
))
1275 (derive-integer-type
1278 (let ((x-low (numeric-type-low x
))
1279 (x-high (numeric-type-high x
))
1280 (y-low (numeric-type-low y
))
1281 (y-high (numeric-type-high y
)))
1282 (cond ((not (and x-low y-low
))
1284 ((or (minusp x-low
) (minusp y-low
))
1285 (if (and x-high y-high
)
1286 (let ((max (* (max (abs x-low
) (abs x-high
))
1287 (max (abs y-low
) (abs y-high
)))))
1288 (values (- max
) max
))
1291 (values (* x-low y-low
)
1292 (if (and x-high y-high
)
1296 (defoptimizer (/ derive-type
) ((x y
))
1297 (numeric-contagion (lvar-type x
) (lvar-type y
)))
1301 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1303 (defun +-derive-type-aux
(x y same-arg
)
1304 (if (and (numeric-type-real-p x
)
1305 (numeric-type-real-p y
))
1308 (let ((x-int (numeric-type->interval x
)))
1309 (interval-add x-int x-int
))
1310 (interval-add (numeric-type->interval x
)
1311 (numeric-type->interval y
))))
1312 (result-type (numeric-contagion x y
)))
1313 ;; If the result type is a float, we need to be sure to coerce
1314 ;; the bounds into the correct type.
1315 (when (eq (numeric-type-class result-type
) 'float
)
1316 (setf result
(interval-func
1318 (coerce-for-bound x
(or (numeric-type-format result-type
)
1322 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1323 (eq (numeric-type-class y
) 'integer
))
1324 ;; The sum of integers is always an integer.
1326 (numeric-type-class result-type
))
1327 :format
(numeric-type-format result-type
)
1328 :low
(interval-low result
)
1329 :high
(interval-high result
)))
1330 ;; general contagion
1331 (numeric-contagion x y
)))
1333 (defoptimizer (+ derive-type
) ((x y
))
1334 (two-arg-derive-type x y
#'+-derive-type-aux
#'+))
1336 (defun --derive-type-aux (x y same-arg
)
1337 (if (and (numeric-type-real-p x
)
1338 (numeric-type-real-p y
))
1340 ;; (- X X) is always 0.
1342 (make-interval :low
0 :high
0)
1343 (interval-sub (numeric-type->interval x
)
1344 (numeric-type->interval y
))))
1345 (result-type (numeric-contagion x y
)))
1346 ;; If the result type is a float, we need to be sure to coerce
1347 ;; the bounds into the correct type.
1348 (when (eq (numeric-type-class result-type
) 'float
)
1349 (setf result
(interval-func
1351 (coerce-for-bound x
(or (numeric-type-format result-type
)
1355 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1356 (eq (numeric-type-class y
) 'integer
))
1357 ;; The difference of integers is always an integer.
1359 (numeric-type-class result-type
))
1360 :format
(numeric-type-format result-type
)
1361 :low
(interval-low result
)
1362 :high
(interval-high result
)))
1363 ;; general contagion
1364 (numeric-contagion x y
)))
1366 (defoptimizer (- derive-type
) ((x y
))
1367 (two-arg-derive-type x y
#'--derive-type-aux
#'-
))
1369 (defun *-derive-type-aux
(x y same-arg
)
1370 (if (and (numeric-type-real-p x
)
1371 (numeric-type-real-p y
))
1373 ;; (* X X) is always positive, so take care to do it right.
1375 (interval-sqr (numeric-type->interval x
))
1376 (interval-mul (numeric-type->interval x
)
1377 (numeric-type->interval y
))))
1378 (result-type (numeric-contagion x y
)))
1379 ;; If the result type is a float, we need to be sure to coerce
1380 ;; the bounds into the correct type.
1381 (when (eq (numeric-type-class result-type
) 'float
)
1382 (setf result
(interval-func
1384 (coerce-for-bound x
(or (numeric-type-format result-type
)
1388 :class
(if (and (eq (numeric-type-class x
) 'integer
)
1389 (eq (numeric-type-class y
) 'integer
))
1390 ;; The product of integers is always an integer.
1392 (numeric-type-class result-type
))
1393 :format
(numeric-type-format result-type
)
1394 :low
(interval-low result
)
1395 :high
(interval-high result
)))
1396 (numeric-contagion x y
)))
1398 (defoptimizer (* derive-type
) ((x y
))
1399 (two-arg-derive-type x y
#'*-derive-type-aux
#'*))
1401 (defun /-derive-type-aux
(x y same-arg
)
1402 (if (and (numeric-type-real-p x
)
1403 (numeric-type-real-p y
))
1405 ;; (/ X X) is always 1, except if X can contain 0. In
1406 ;; that case, we shouldn't optimize the division away
1407 ;; because we want 0/0 to signal an error.
1409 (not (interval-contains-p
1410 0 (interval-closure (numeric-type->interval y
)))))
1411 (make-interval :low
1 :high
1)
1412 (interval-div (numeric-type->interval x
)
1413 (numeric-type->interval y
))))
1414 (result-type (numeric-contagion x y
)))
1415 ;; If the result type is a float, we need to be sure to coerce
1416 ;; the bounds into the correct type.
1417 (when (eq (numeric-type-class result-type
) 'float
)
1418 (setf result
(interval-func
1420 (coerce-for-bound x
(or (numeric-type-format result-type
)
1423 (make-numeric-type :class
(numeric-type-class result-type
)
1424 :format
(numeric-type-format result-type
)
1425 :low
(interval-low result
)
1426 :high
(interval-high result
)))
1427 (numeric-contagion x y
)))
1429 (defoptimizer (/ derive-type
) ((x y
))
1430 (two-arg-derive-type x y
#'/-derive-type-aux
#'/))
1434 (defun ash-derive-type-aux (n-type shift same-arg
)
1435 (declare (ignore same-arg
))
1436 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1437 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1438 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1439 ;; two bignums yielding zero) and it's hard to avoid that
1440 ;; calculation in here.
1441 #+(and cmu sb-xc-host
)
1442 (when (and (or (typep (numeric-type-low n-type
) 'bignum
)
1443 (typep (numeric-type-high n-type
) 'bignum
))
1444 (or (typep (numeric-type-low shift
) 'bignum
)
1445 (typep (numeric-type-high shift
) 'bignum
)))
1446 (return-from ash-derive-type-aux
*universal-type
*))
1447 (flet ((ash-outer (n s
)
1448 (when (and (fixnump s
)
1450 (> s sb
!xc
:most-negative-fixnum
))
1452 ;; KLUDGE: The bare 64's here should be related to
1453 ;; symbolic machine word size values somehow.
1456 (if (and (fixnump s
)
1457 (> s sb
!xc
:most-negative-fixnum
))
1459 (if (minusp n
) -
1 0))))
1460 (or (and (csubtypep n-type
(specifier-type 'integer
))
1461 (csubtypep shift
(specifier-type 'integer
))
1462 (let ((n-low (numeric-type-low n-type
))
1463 (n-high (numeric-type-high n-type
))
1464 (s-low (numeric-type-low shift
))
1465 (s-high (numeric-type-high shift
)))
1466 (make-numeric-type :class
'integer
:complexp
:real
1469 (ash-outer n-low s-high
)
1470 (ash-inner n-low s-low
)))
1473 (ash-inner n-high s-low
)
1474 (ash-outer n-high s-high
))))))
1477 (defoptimizer (ash derive-type
) ((n shift
))
1478 (two-arg-derive-type n shift
#'ash-derive-type-aux
#'ash
))
1480 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1481 (macrolet ((frob (fun)
1482 `#'(lambda (type type2
)
1483 (declare (ignore type2
))
1484 (let ((lo (numeric-type-low type
))
1485 (hi (numeric-type-high type
)))
1486 (values (if hi
(,fun hi
) nil
) (if lo
(,fun lo
) nil
))))))
1488 (defoptimizer (%negate derive-type
) ((num))
1489 (derive-integer-type num num
(frob -
))))
1491 (defun lognot-derive-type-aux (int)
1492 (derive-integer-type-aux int int
1493 (lambda (type type2
)
1494 (declare (ignore type2
))
1495 (let ((lo (numeric-type-low type
))
1496 (hi (numeric-type-high type
)))
1497 (values (if hi
(lognot hi
) nil
)
1498 (if lo
(lognot lo
) nil
)
1499 (numeric-type-class type
)
1500 (numeric-type-format type
))))))
1502 (defoptimizer (lognot derive-type
) ((int))
1503 (lognot-derive-type-aux (lvar-type int
)))
1505 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1506 (defoptimizer (%negate derive-type
) ((num))
1507 (flet ((negate-bound (b)
1509 (set-bound (- (type-bound-number b
))
1511 (one-arg-derive-type num
1513 (modified-numeric-type
1515 :low
(negate-bound (numeric-type-high type
))
1516 :high
(negate-bound (numeric-type-low type
))))
1519 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1520 (defoptimizer (abs derive-type
) ((num))
1521 (let ((type (lvar-type num
)))
1522 (if (and (numeric-type-p type
)
1523 (eq (numeric-type-class type
) 'integer
)
1524 (eq (numeric-type-complexp type
) :real
))
1525 (let ((lo (numeric-type-low type
))
1526 (hi (numeric-type-high type
)))
1527 (make-numeric-type :class
'integer
:complexp
:real
1528 :low
(cond ((and hi
(minusp hi
))
1534 :high
(if (and hi lo
)
1535 (max (abs hi
) (abs lo
))
1537 (numeric-contagion type type
))))
1539 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1540 (defun abs-derive-type-aux (type)
1541 (cond ((eq (numeric-type-complexp type
) :complex
)
1542 ;; The absolute value of a complex number is always a
1543 ;; non-negative float.
1544 (let* ((format (case (numeric-type-class type
)
1545 ((integer rational
) 'single-float
)
1546 (t (numeric-type-format type
))))
1547 (bound-format (or format
'float
)))
1548 (make-numeric-type :class
'float
1551 :low
(coerce 0 bound-format
)
1554 ;; The absolute value of a real number is a non-negative real
1555 ;; of the same type.
1556 (let* ((abs-bnd (interval-abs (numeric-type->interval type
)))
1557 (class (numeric-type-class type
))
1558 (format (numeric-type-format type
))
1559 (bound-type (or format class
'real
)))
1564 :low
(coerce-and-truncate-floats (interval-low abs-bnd
) bound-type
)
1565 :high
(coerce-and-truncate-floats
1566 (interval-high abs-bnd
) bound-type
))))))
1568 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1569 (defoptimizer (abs derive-type
) ((num))
1570 (one-arg-derive-type num
#'abs-derive-type-aux
#'abs
))
1572 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1573 (defoptimizer (truncate derive-type
) ((number divisor
))
1574 (let ((number-type (lvar-type number
))
1575 (divisor-type (lvar-type divisor
))
1576 (integer-type (specifier-type 'integer
)))
1577 (if (and (numeric-type-p number-type
)
1578 (csubtypep number-type integer-type
)
1579 (numeric-type-p divisor-type
)
1580 (csubtypep divisor-type integer-type
))
1581 (let ((number-low (numeric-type-low number-type
))
1582 (number-high (numeric-type-high number-type
))
1583 (divisor-low (numeric-type-low divisor-type
))
1584 (divisor-high (numeric-type-high divisor-type
)))
1585 (values-specifier-type
1586 `(values ,(integer-truncate-derive-type number-low number-high
1587 divisor-low divisor-high
)
1588 ,(integer-rem-derive-type number-low number-high
1589 divisor-low divisor-high
))))
1592 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1595 (defun rem-result-type (number-type divisor-type
)
1596 ;; Figure out what the remainder type is. The remainder is an
1597 ;; integer if both args are integers; a rational if both args are
1598 ;; rational; and a float otherwise.
1599 (cond ((and (csubtypep number-type
(specifier-type 'integer
))
1600 (csubtypep divisor-type
(specifier-type 'integer
)))
1602 ((and (csubtypep number-type
(specifier-type 'rational
))
1603 (csubtypep divisor-type
(specifier-type 'rational
)))
1605 ((and (csubtypep number-type
(specifier-type 'float
))
1606 (csubtypep divisor-type
(specifier-type 'float
)))
1607 ;; Both are floats so the result is also a float, of
1608 ;; the largest type.
1609 (or (float-format-max (numeric-type-format number-type
)
1610 (numeric-type-format divisor-type
))
1612 ((and (csubtypep number-type
(specifier-type 'float
))
1613 (csubtypep divisor-type
(specifier-type 'rational
)))
1614 ;; One of the arguments is a float and the other is a
1615 ;; rational. The remainder is a float of the same
1617 (or (numeric-type-format number-type
) 'float
))
1618 ((and (csubtypep divisor-type
(specifier-type 'float
))
1619 (csubtypep number-type
(specifier-type 'rational
)))
1620 ;; One of the arguments is a float and the other is a
1621 ;; rational. The remainder is a float of the same
1623 (or (numeric-type-format divisor-type
) 'float
))
1625 ;; Some unhandled combination. This usually means both args
1626 ;; are REAL so the result is a REAL.
1629 (defun truncate-derive-type-quot (number-type divisor-type
)
1630 (let* ((rem-type (rem-result-type number-type divisor-type
))
1631 (number-interval (numeric-type->interval number-type
))
1632 (divisor-interval (numeric-type->interval divisor-type
)))
1633 ;;(declare (type (member '(integer rational float)) rem-type))
1634 ;; We have real numbers now.
1635 (cond ((eq rem-type
'integer
)
1636 ;; Since the remainder type is INTEGER, both args are
1638 (let* ((res (integer-truncate-derive-type
1639 (interval-low number-interval
)
1640 (interval-high number-interval
)
1641 (interval-low divisor-interval
)
1642 (interval-high divisor-interval
))))
1643 (specifier-type (if (listp res
) res
'integer
))))
1645 (let ((quot (truncate-quotient-bound
1646 (interval-div number-interval
1647 divisor-interval
))))
1648 (specifier-type `(integer ,(or (interval-low quot
) '*)
1649 ,(or (interval-high quot
) '*))))))))
1651 (defun truncate-derive-type-rem (number-type divisor-type
)
1652 (let* ((rem-type (rem-result-type number-type divisor-type
))
1653 (number-interval (numeric-type->interval number-type
))
1654 (divisor-interval (numeric-type->interval divisor-type
))
1655 (rem (truncate-rem-bound number-interval divisor-interval
)))
1656 ;;(declare (type (member '(integer rational float)) rem-type))
1657 ;; We have real numbers now.
1658 (cond ((eq rem-type
'integer
)
1659 ;; Since the remainder type is INTEGER, both args are
1661 (specifier-type `(,rem-type
,(or (interval-low rem
) '*)
1662 ,(or (interval-high rem
) '*))))
1664 (multiple-value-bind (class format
)
1667 (values 'integer nil
))
1669 (values 'rational nil
))
1670 ((or single-float double-float
#!+long-float long-float
)
1671 (values 'float rem-type
))
1673 (values 'float nil
))
1676 (when (member rem-type
'(float single-float double-float
1677 #!+long-float long-float
))
1678 (setf rem
(interval-func #'(lambda (x)
1679 (coerce-for-bound x rem-type
))
1681 (make-numeric-type :class class
1683 :low
(interval-low rem
)
1684 :high
(interval-high rem
)))))))
1686 (defun truncate-derive-type-quot-aux (num div same-arg
)
1687 (declare (ignore same-arg
))
1688 (if (and (numeric-type-real-p num
)
1689 (numeric-type-real-p div
))
1690 (truncate-derive-type-quot num div
)
1693 (defun truncate-derive-type-rem-aux (num div same-arg
)
1694 (declare (ignore same-arg
))
1695 (if (and (numeric-type-real-p num
)
1696 (numeric-type-real-p div
))
1697 (truncate-derive-type-rem num div
)
1700 (defoptimizer (truncate derive-type
) ((number divisor
))
1701 (let ((quot (two-arg-derive-type number divisor
1702 #'truncate-derive-type-quot-aux
#'truncate
))
1703 (rem (two-arg-derive-type number divisor
1704 #'truncate-derive-type-rem-aux
#'rem
)))
1705 (when (and quot rem
)
1706 (make-values-type :required
(list quot rem
)))))
1708 (defun ftruncate-derive-type-quot (number-type divisor-type
)
1709 ;; The bounds are the same as for truncate. However, the first
1710 ;; result is a float of some type. We need to determine what that
1711 ;; type is. Basically it's the more contagious of the two types.
1712 (let ((q-type (truncate-derive-type-quot number-type divisor-type
))
1713 (res-type (numeric-contagion number-type divisor-type
)))
1714 (make-numeric-type :class
'float
1715 :format
(numeric-type-format res-type
)
1716 :low
(numeric-type-low q-type
)
1717 :high
(numeric-type-high q-type
))))
1719 (defun ftruncate-derive-type-quot-aux (n d same-arg
)
1720 (declare (ignore same-arg
))
1721 (if (and (numeric-type-real-p n
)
1722 (numeric-type-real-p d
))
1723 (ftruncate-derive-type-quot n d
)
1726 (defoptimizer (ftruncate derive-type
) ((number divisor
))
1728 (two-arg-derive-type number divisor
1729 #'ftruncate-derive-type-quot-aux
#'ftruncate
))
1730 (rem (two-arg-derive-type number divisor
1731 #'truncate-derive-type-rem-aux
#'rem
)))
1732 (when (and quot rem
)
1733 (make-values-type :required
(list quot rem
)))))
1735 (defun %unary-truncate-derive-type-aux
(number)
1736 (truncate-derive-type-quot number
(specifier-type '(integer 1 1))))
1738 (defoptimizer (%unary-truncate derive-type
) ((number))
1739 (one-arg-derive-type number
1740 #'%unary-truncate-derive-type-aux
1743 (defoptimizer (%unary-ftruncate derive-type
) ((number))
1744 (let ((divisor (specifier-type '(integer 1 1))))
1745 (one-arg-derive-type number
1747 (ftruncate-derive-type-quot-aux n divisor nil
))
1748 #'%unary-ftruncate
)))
1750 ;;; Define optimizers for FLOOR and CEILING.
1752 ((def (name q-name r-name
)
1753 (let ((q-aux (symbolicate q-name
"-AUX"))
1754 (r-aux (symbolicate r-name
"-AUX")))
1756 ;; Compute type of quotient (first) result.
1757 (defun ,q-aux
(number-type divisor-type
)
1758 (let* ((number-interval
1759 (numeric-type->interval number-type
))
1761 (numeric-type->interval divisor-type
))
1762 (quot (,q-name
(interval-div number-interval
1763 divisor-interval
))))
1764 (specifier-type `(integer ,(or (interval-low quot
) '*)
1765 ,(or (interval-high quot
) '*)))))
1766 ;; Compute type of remainder.
1767 (defun ,r-aux
(number-type divisor-type
)
1768 (let* ((divisor-interval
1769 (numeric-type->interval divisor-type
))
1770 (rem (,r-name divisor-interval
))
1771 (result-type (rem-result-type number-type divisor-type
)))
1772 (multiple-value-bind (class format
)
1775 (values 'integer nil
))
1777 (values 'rational nil
))
1778 ((or single-float double-float
#!+long-float long-float
)
1779 (values 'float result-type
))
1781 (values 'float nil
))
1784 (when (member result-type
'(float single-float double-float
1785 #!+long-float long-float
))
1786 ;; Make sure that the limits on the interval have
1788 (setf rem
(interval-func (lambda (x)
1789 (coerce-for-bound x result-type
))
1791 (make-numeric-type :class class
1793 :low
(interval-low rem
)
1794 :high
(interval-high rem
)))))
1795 ;; the optimizer itself
1796 (defoptimizer (,name derive-type
) ((number divisor
))
1797 (flet ((derive-q (n d same-arg
)
1798 (declare (ignore same-arg
))
1799 (if (and (numeric-type-real-p n
)
1800 (numeric-type-real-p d
))
1803 (derive-r (n d same-arg
)
1804 (declare (ignore same-arg
))
1805 (if (and (numeric-type-real-p n
)
1806 (numeric-type-real-p d
))
1809 (let ((quot (two-arg-derive-type
1810 number divisor
#'derive-q
#',name
))
1811 (rem (two-arg-derive-type
1812 number divisor
#'derive-r
#'mod
)))
1813 (when (and quot rem
)
1814 (make-values-type :required
(list quot rem
))))))))))
1816 (def floor floor-quotient-bound floor-rem-bound
)
1817 (def ceiling ceiling-quotient-bound ceiling-rem-bound
))
1819 ;;; Define optimizers for FFLOOR and FCEILING
1820 (macrolet ((def (name q-name r-name
)
1821 (let ((q-aux (symbolicate "F" q-name
"-AUX"))
1822 (r-aux (symbolicate r-name
"-AUX")))
1824 ;; Compute type of quotient (first) result.
1825 (defun ,q-aux
(number-type divisor-type
)
1826 (let* ((number-interval
1827 (numeric-type->interval number-type
))
1829 (numeric-type->interval divisor-type
))
1830 (quot (,q-name
(interval-div number-interval
1832 (res-type (numeric-contagion number-type
1835 :class
(numeric-type-class res-type
)
1836 :format
(numeric-type-format res-type
)
1837 :low
(interval-low quot
)
1838 :high
(interval-high quot
))))
1840 (defoptimizer (,name derive-type
) ((number divisor
))
1841 (flet ((derive-q (n d same-arg
)
1842 (declare (ignore same-arg
))
1843 (if (and (numeric-type-real-p n
)
1844 (numeric-type-real-p d
))
1847 (derive-r (n d same-arg
)
1848 (declare (ignore same-arg
))
1849 (if (and (numeric-type-real-p n
)
1850 (numeric-type-real-p d
))
1853 (let ((quot (two-arg-derive-type
1854 number divisor
#'derive-q
#',name
))
1855 (rem (two-arg-derive-type
1856 number divisor
#'derive-r
#'mod
)))
1857 (when (and quot rem
)
1858 (make-values-type :required
(list quot rem
))))))))))
1860 (def ffloor floor-quotient-bound floor-rem-bound
)
1861 (def fceiling ceiling-quotient-bound ceiling-rem-bound
))
1863 ;;; functions to compute the bounds on the quotient and remainder for
1864 ;;; the FLOOR function
1865 (defun floor-quotient-bound (quot)
1866 ;; Take the floor of the quotient and then massage it into what we
1868 (let ((lo (interval-low quot
))
1869 (hi (interval-high quot
)))
1870 ;; Take the floor of the lower bound. The result is always a
1871 ;; closed lower bound.
1873 (floor (type-bound-number lo
))
1875 ;; For the upper bound, we need to be careful.
1878 ;; An open bound. We need to be careful here because
1879 ;; the floor of '(10.0) is 9, but the floor of
1881 (multiple-value-bind (q r
) (floor (first hi
))
1886 ;; A closed bound, so the answer is obvious.
1890 (make-interval :low lo
:high hi
)))
1891 (defun floor-rem-bound (div)
1892 ;; The remainder depends only on the divisor. Try to get the
1893 ;; correct sign for the remainder if we can.
1894 (case (interval-range-info div
)
1896 ;; The divisor is always positive.
1897 (let ((rem (interval-abs div
)))
1898 (setf (interval-low rem
) 0)
1899 (when (and (numberp (interval-high rem
))
1900 (not (zerop (interval-high rem
))))
1901 ;; The remainder never contains the upper bound. However,
1902 ;; watch out for the case where the high limit is zero!
1903 (setf (interval-high rem
) (list (interval-high rem
))))
1906 ;; The divisor is always negative.
1907 (let ((rem (interval-neg (interval-abs div
))))
1908 (setf (interval-high rem
) 0)
1909 (when (numberp (interval-low rem
))
1910 ;; The remainder never contains the lower bound.
1911 (setf (interval-low rem
) (list (interval-low rem
))))
1914 ;; The divisor can be positive or negative. All bets off. The
1915 ;; magnitude of remainder is the maximum value of the divisor.
1916 (let ((limit (type-bound-number (interval-high (interval-abs div
)))))
1917 ;; The bound never reaches the limit, so make the interval open.
1918 (make-interval :low
(if limit
1921 :high
(list limit
))))))
1923 (floor-quotient-bound (make-interval :low
0.3 :high
10.3))
1924 => #S
(INTERVAL :LOW
0 :HIGH
10)
1925 (floor-quotient-bound (make-interval :low
0.3 :high
'(10.3
)))
1926 => #S
(INTERVAL :LOW
0 :HIGH
10)
1927 (floor-quotient-bound (make-interval :low
0.3 :high
10))
1928 => #S
(INTERVAL :LOW
0 :HIGH
10)
1929 (floor-quotient-bound (make-interval :low
0.3 :high
'(10)))
1930 => #S
(INTERVAL :LOW
0 :HIGH
9)
1931 (floor-quotient-bound (make-interval :low
'(0.3
) :high
10.3))
1932 => #S
(INTERVAL :LOW
0 :HIGH
10)
1933 (floor-quotient-bound (make-interval :low
'(0.0
) :high
10.3))
1934 => #S
(INTERVAL :LOW
0 :HIGH
10)
1935 (floor-quotient-bound (make-interval :low
'(-1.3
) :high
10.3))
1936 => #S
(INTERVAL :LOW -
2 :HIGH
10)
1937 (floor-quotient-bound (make-interval :low
'(-1.0
) :high
10.3))
1938 => #S
(INTERVAL :LOW -
1 :HIGH
10)
1939 (floor-quotient-bound (make-interval :low -
1.0 :high
10.3))
1940 => #S
(INTERVAL :LOW -
1 :HIGH
10)
1942 (floor-rem-bound (make-interval :low
0.3 :high
10.3))
1943 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
1944 (floor-rem-bound (make-interval :low
0.3 :high
'(10.3
)))
1945 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
1946 (floor-rem-bound (make-interval :low -
10 :high -
2.3))
1947 #S
(INTERVAL :LOW
(-10) :HIGH
0)
1948 (floor-rem-bound (make-interval :low
0.3 :high
10))
1949 => #S
(INTERVAL :LOW
0 :HIGH
'(10))
1950 (floor-rem-bound (make-interval :low
'(-1.3
) :high
10.3))
1951 => #S
(INTERVAL :LOW
'(-10.3
) :HIGH
'(10.3
))
1952 (floor-rem-bound (make-interval :low
'(-20.3
) :high
10.3))
1953 => #S
(INTERVAL :LOW
(-20.3
) :HIGH
(20.3
))
1956 ;;; same functions for CEILING
1957 (defun ceiling-quotient-bound (quot)
1958 ;; Take the ceiling of the quotient and then massage it into what we
1960 (let ((lo (interval-low quot
))
1961 (hi (interval-high quot
)))
1962 ;; Take the ceiling of the upper bound. The result is always a
1963 ;; closed upper bound.
1965 (ceiling (type-bound-number hi
))
1967 ;; For the lower bound, we need to be careful.
1970 ;; An open bound. We need to be careful here because
1971 ;; the ceiling of '(10.0) is 11, but the ceiling of
1973 (multiple-value-bind (q r
) (ceiling (first lo
))
1978 ;; A closed bound, so the answer is obvious.
1982 (make-interval :low lo
:high hi
)))
1983 (defun ceiling-rem-bound (div)
1984 ;; The remainder depends only on the divisor. Try to get the
1985 ;; correct sign for the remainder if we can.
1986 (case (interval-range-info div
)
1988 ;; Divisor is always positive. The remainder is negative.
1989 (let ((rem (interval-neg (interval-abs div
))))
1990 (setf (interval-high rem
) 0)
1991 (when (and (numberp (interval-low rem
))
1992 (not (zerop (interval-low rem
))))
1993 ;; The remainder never contains the upper bound. However,
1994 ;; watch out for the case when the upper bound is zero!
1995 (setf (interval-low rem
) (list (interval-low rem
))))
1998 ;; Divisor is always negative. The remainder is positive
1999 (let ((rem (interval-abs div
)))
2000 (setf (interval-low rem
) 0)
2001 (when (numberp (interval-high rem
))
2002 ;; The remainder never contains the lower bound.
2003 (setf (interval-high rem
) (list (interval-high rem
))))
2006 ;; The divisor can be positive or negative. All bets off. The
2007 ;; magnitude of remainder is the maximum value of the divisor.
2008 (let ((limit (type-bound-number (interval-high (interval-abs div
)))))
2009 ;; The bound never reaches the limit, so make the interval open.
2010 (make-interval :low
(if limit
2013 :high
(list limit
))))))
2016 (ceiling-quotient-bound (make-interval :low
0.3 :high
10.3))
2017 => #S
(INTERVAL :LOW
1 :HIGH
11)
2018 (ceiling-quotient-bound (make-interval :low
0.3 :high
'(10.3
)))
2019 => #S
(INTERVAL :LOW
1 :HIGH
11)
2020 (ceiling-quotient-bound (make-interval :low
0.3 :high
10))
2021 => #S
(INTERVAL :LOW
1 :HIGH
10)
2022 (ceiling-quotient-bound (make-interval :low
0.3 :high
'(10)))
2023 => #S
(INTERVAL :LOW
1 :HIGH
10)
2024 (ceiling-quotient-bound (make-interval :low
'(0.3
) :high
10.3))
2025 => #S
(INTERVAL :LOW
1 :HIGH
11)
2026 (ceiling-quotient-bound (make-interval :low
'(0.0
) :high
10.3))
2027 => #S
(INTERVAL :LOW
1 :HIGH
11)
2028 (ceiling-quotient-bound (make-interval :low
'(-1.3
) :high
10.3))
2029 => #S
(INTERVAL :LOW -
1 :HIGH
11)
2030 (ceiling-quotient-bound (make-interval :low
'(-1.0
) :high
10.3))
2031 => #S
(INTERVAL :LOW
0 :HIGH
11)
2032 (ceiling-quotient-bound (make-interval :low -
1.0 :high
10.3))
2033 => #S
(INTERVAL :LOW -
1 :HIGH
11)
2035 (ceiling-rem-bound (make-interval :low
0.3 :high
10.3))
2036 => #S
(INTERVAL :LOW
(-10.3
) :HIGH
0)
2037 (ceiling-rem-bound (make-interval :low
0.3 :high
'(10.3
)))
2038 => #S
(INTERVAL :LOW
0 :HIGH
'(10.3
))
2039 (ceiling-rem-bound (make-interval :low -
10 :high -
2.3))
2040 => #S
(INTERVAL :LOW
0 :HIGH
(10))
2041 (ceiling-rem-bound (make-interval :low
0.3 :high
10))
2042 => #S
(INTERVAL :LOW
(-10) :HIGH
0)
2043 (ceiling-rem-bound (make-interval :low
'(-1.3
) :high
10.3))
2044 => #S
(INTERVAL :LOW
(-10.3
) :HIGH
(10.3
))
2045 (ceiling-rem-bound (make-interval :low
'(-20.3
) :high
10.3))
2046 => #S
(INTERVAL :LOW
(-20.3
) :HIGH
(20.3
))
2049 (defun truncate-quotient-bound (quot)
2050 ;; For positive quotients, truncate is exactly like floor. For
2051 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2052 ;; it's the union of the two pieces.
2053 (case (interval-range-info quot
)
2056 (floor-quotient-bound quot
))
2058 ;; just like CEILING
2059 (ceiling-quotient-bound quot
))
2061 ;; Split the interval into positive and negative pieces, compute
2062 ;; the result for each piece and put them back together.
2063 (destructuring-bind (neg pos
) (interval-split 0 quot t t
)
2064 (interval-merge-pair (ceiling-quotient-bound neg
)
2065 (floor-quotient-bound pos
))))))
2067 (defun truncate-rem-bound (num div
)
2068 ;; This is significantly more complicated than FLOOR or CEILING. We
2069 ;; need both the number and the divisor to determine the range. The
2070 ;; basic idea is to split the ranges of NUM and DEN into positive
2071 ;; and negative pieces and deal with each of the four possibilities
2073 (case (interval-range-info num
)
2075 (case (interval-range-info div
)
2077 (floor-rem-bound div
))
2079 (ceiling-rem-bound div
))
2081 (destructuring-bind (neg pos
) (interval-split 0 div t t
)
2082 (interval-merge-pair (truncate-rem-bound num neg
)
2083 (truncate-rem-bound num pos
))))))
2085 (case (interval-range-info div
)
2087 (ceiling-rem-bound div
))
2089 (floor-rem-bound div
))
2091 (destructuring-bind (neg pos
) (interval-split 0 div t t
)
2092 (interval-merge-pair (truncate-rem-bound num neg
)
2093 (truncate-rem-bound num pos
))))))
2095 (destructuring-bind (neg pos
) (interval-split 0 num t t
)
2096 (interval-merge-pair (truncate-rem-bound neg div
)
2097 (truncate-rem-bound pos div
))))))
2100 ;;; Derive useful information about the range. Returns three values:
2101 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2102 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2103 ;;; - The abs of the maximal value if there is one, or nil if it is
2105 (defun numeric-range-info (low high
)
2106 (cond ((and low
(not (minusp low
)))
2107 (values '+ low high
))
2108 ((and high
(not (plusp high
)))
2109 (values '-
(- high
) (if low
(- low
) nil
)))
2111 (values nil
0 (and low high
(max (- low
) high
))))))
2113 (defun integer-truncate-derive-type
2114 (number-low number-high divisor-low divisor-high
)
2115 ;; The result cannot be larger in magnitude than the number, but the
2116 ;; sign might change. If we can determine the sign of either the
2117 ;; number or the divisor, we can eliminate some of the cases.
2118 (multiple-value-bind (number-sign number-min number-max
)
2119 (numeric-range-info number-low number-high
)
2120 (multiple-value-bind (divisor-sign divisor-min divisor-max
)
2121 (numeric-range-info divisor-low divisor-high
)
2122 (when (and divisor-max
(zerop divisor-max
))
2123 ;; We've got a problem: guaranteed division by zero.
2124 (return-from integer-truncate-derive-type t
))
2125 (when (zerop divisor-min
)
2126 ;; We'll assume that they aren't going to divide by zero.
2128 (cond ((and number-sign divisor-sign
)
2129 ;; We know the sign of both.
2130 (if (eq number-sign divisor-sign
)
2131 ;; Same sign, so the result will be positive.
2132 `(integer ,(if divisor-max
2133 (truncate number-min divisor-max
)
2136 (truncate number-max divisor-min
)
2138 ;; Different signs, the result will be negative.
2139 `(integer ,(if number-max
2140 (- (truncate number-max divisor-min
))
2143 (- (truncate number-min divisor-max
))
2145 ((eq divisor-sign
'+)
2146 ;; The divisor is positive. Therefore, the number will just
2147 ;; become closer to zero.
2148 `(integer ,(if number-low
2149 (truncate number-low divisor-min
)
2152 (truncate number-high divisor-min
)
2154 ((eq divisor-sign
'-
)
2155 ;; The divisor is negative. Therefore, the absolute value of
2156 ;; the number will become closer to zero, but the sign will also
2158 `(integer ,(if number-high
2159 (- (truncate number-high divisor-min
))
2162 (- (truncate number-low divisor-min
))
2164 ;; The divisor could be either positive or negative.
2166 ;; The number we are dividing has a bound. Divide that by the
2167 ;; smallest posible divisor.
2168 (let ((bound (truncate number-max divisor-min
)))
2169 `(integer ,(- bound
) ,bound
)))
2171 ;; The number we are dividing is unbounded, so we can't tell
2172 ;; anything about the result.
2175 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2176 (defun integer-rem-derive-type
2177 (number-low number-high divisor-low divisor-high
)
2178 (if (and divisor-low divisor-high
)
2179 ;; We know the range of the divisor, and the remainder must be
2180 ;; smaller than the divisor. We can tell the sign of the
2181 ;; remainer if we know the sign of the number.
2182 (let ((divisor-max (1- (max (abs divisor-low
) (abs divisor-high
)))))
2183 `(integer ,(if (or (null number-low
)
2184 (minusp number-low
))
2187 ,(if (or (null number-high
)
2188 (plusp number-high
))
2191 ;; The divisor is potentially either very positive or very
2192 ;; negative. Therefore, the remainer is unbounded, but we might
2193 ;; be able to tell something about the sign from the number.
2194 `(integer ,(if (and number-low
(not (minusp number-low
)))
2195 ;; The number we are dividing is positive.
2196 ;; Therefore, the remainder must be positive.
2199 ,(if (and number-high
(not (plusp number-high
)))
2200 ;; The number we are dividing is negative.
2201 ;; Therefore, the remainder must be negative.
2205 #+sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2206 (defoptimizer (random derive-type
) ((bound &optional state
))
2207 (let ((type (lvar-type bound
)))
2208 (when (numeric-type-p type
)
2209 (let ((class (numeric-type-class type
))
2210 (high (numeric-type-high type
))
2211 (format (numeric-type-format type
)))
2215 :low
(coerce 0 (or format class
'real
))
2216 :high
(cond ((not high
) nil
)
2217 ((eq class
'integer
) (max (1- high
) 0))
2218 ((or (consp high
) (zerop high
)) high
)
2221 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2222 (defun random-derive-type-aux (type)
2223 (let ((class (numeric-type-class type
))
2224 (high (numeric-type-high type
))
2225 (format (numeric-type-format type
)))
2229 :low
(coerce 0 (or format class
'real
))
2230 :high
(cond ((not high
) nil
)
2231 ((eq class
'integer
) (max (1- high
) 0))
2232 ((or (consp high
) (zerop high
)) high
)
2235 #-sb-xc-host
; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2236 (defoptimizer (random derive-type
) ((bound &optional state
))
2237 (one-arg-derive-type bound
#'random-derive-type-aux nil
))
2239 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2241 ;;; Return the maximum number of bits an integer of the supplied type
2242 ;;; can take up, or NIL if it is unbounded. The second (third) value
2243 ;;; is T if the integer can be positive (negative) and NIL if not.
2244 ;;; Zero counts as positive.
2245 (defun integer-type-length (type)
2246 (if (numeric-type-p type
)
2247 (let ((min (numeric-type-low type
))
2248 (max (numeric-type-high type
)))
2249 (values (and min max
(max (integer-length min
) (integer-length max
)))
2250 (or (null max
) (not (minusp max
)))
2251 (or (null min
) (minusp min
))))
2254 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2255 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2256 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2257 ;;; versions in CMUCL, from which these functions copy liberally.
2259 (defun logand-derive-unsigned-low-bound (x y
)
2260 (let ((a (numeric-type-low x
))
2261 (b (numeric-type-high x
))
2262 (c (numeric-type-low y
))
2263 (d (numeric-type-high y
)))
2264 (loop for m
= (ash 1 (integer-length (lognor a c
))) then
(ash m -
1)
2266 (unless (zerop (logand m
(lognot a
) (lognot c
)))
2267 (let ((temp (logandc2 (logior a m
) (1- m
))))
2271 (setf temp
(logandc2 (logior c m
) (1- m
)))
2275 finally
(return (logand a c
)))))
2277 (defun logand-derive-unsigned-high-bound (x y
)
2278 (let ((a (numeric-type-low x
))
2279 (b (numeric-type-high x
))
2280 (c (numeric-type-low y
))
2281 (d (numeric-type-high y
)))
2282 (loop for m
= (ash 1 (integer-length (logxor b d
))) then
(ash m -
1)
2285 ((not (zerop (logand b
(lognot d
) m
)))
2286 (let ((temp (logior (logandc2 b m
) (1- m
))))
2290 ((not (zerop (logand (lognot b
) d m
)))
2291 (let ((temp (logior (logandc2 d m
) (1- m
))))
2295 finally
(return (logand b d
)))))
2297 (defun logand-derive-type-aux (x y
&optional same-leaf
)
2299 (return-from logand-derive-type-aux x
))
2300 (multiple-value-bind (x-len x-pos x-neg
) (integer-type-length x
)
2301 (declare (ignore x-pos
))
2302 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2303 (declare (ignore y-pos
))
2305 ;; X must be positive.
2307 ;; They must both be positive.
2308 (cond ((and (null x-len
) (null y-len
))
2309 (specifier-type 'unsigned-byte
))
2311 (specifier-type `(unsigned-byte* ,y-len
)))
2313 (specifier-type `(unsigned-byte* ,x-len
)))
2315 (let ((low (logand-derive-unsigned-low-bound x y
))
2316 (high (logand-derive-unsigned-high-bound x y
)))
2317 (specifier-type `(integer ,low
,high
)))))
2318 ;; X is positive, but Y might be negative.
2320 (specifier-type 'unsigned-byte
))
2322 (specifier-type `(unsigned-byte* ,x-len
)))))
2323 ;; X might be negative.
2325 ;; Y must be positive.
2327 (specifier-type 'unsigned-byte
))
2328 (t (specifier-type `(unsigned-byte* ,y-len
))))
2329 ;; Either might be negative.
2330 (if (and x-len y-len
)
2331 ;; The result is bounded.
2332 (specifier-type `(signed-byte ,(1+ (max x-len y-len
))))
2333 ;; We can't tell squat about the result.
2334 (specifier-type 'integer
)))))))
2336 (defun logior-derive-unsigned-low-bound (x y
)
2337 (let ((a (numeric-type-low x
))
2338 (b (numeric-type-high x
))
2339 (c (numeric-type-low y
))
2340 (d (numeric-type-high y
)))
2341 (loop for m
= (ash 1 (integer-length (logxor a c
))) then
(ash m -
1)
2344 ((not (zerop (logandc2 (logand c m
) a
)))
2345 (let ((temp (logand (logior a m
) (1+ (lognot m
)))))
2349 ((not (zerop (logandc2 (logand a m
) c
)))
2350 (let ((temp (logand (logior c m
) (1+ (lognot m
)))))
2354 finally
(return (logior a c
)))))
2356 (defun logior-derive-unsigned-high-bound (x y
)
2357 (let ((a (numeric-type-low x
))
2358 (b (numeric-type-high x
))
2359 (c (numeric-type-low y
))
2360 (d (numeric-type-high y
)))
2361 (loop for m
= (ash 1 (integer-length (logand b d
))) then
(ash m -
1)
2363 (unless (zerop (logand b d m
))
2364 (let ((temp (logior (- b m
) (1- m
))))
2368 (setf temp
(logior (- d m
) (1- m
)))
2372 finally
(return (logior b d
)))))
2374 (defun logior-derive-type-aux (x y
&optional same-leaf
)
2376 (return-from logior-derive-type-aux x
))
2377 (multiple-value-bind (x-len x-pos x-neg
) (integer-type-length x
)
2378 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2380 ((and (not x-neg
) (not y-neg
))
2381 ;; Both are positive.
2382 (if (and x-len y-len
)
2383 (let ((low (logior-derive-unsigned-low-bound x y
))
2384 (high (logior-derive-unsigned-high-bound x y
)))
2385 (specifier-type `(integer ,low
,high
)))
2386 (specifier-type `(unsigned-byte* *))))
2388 ;; X must be negative.
2390 ;; Both are negative. The result is going to be negative
2391 ;; and be the same length or shorter than the smaller.
2392 (if (and x-len y-len
)
2394 (specifier-type `(integer ,(ash -
1 (min x-len y-len
)) -
1))
2396 (specifier-type '(integer * -
1)))
2397 ;; X is negative, but we don't know about Y. The result
2398 ;; will be negative, but no more negative than X.
2400 `(integer ,(or (numeric-type-low x
) '*)
2403 ;; X might be either positive or negative.
2405 ;; But Y is negative. The result will be negative.
2407 `(integer ,(or (numeric-type-low y
) '*)
2409 ;; We don't know squat about either. It won't get any bigger.
2410 (if (and x-len y-len
)
2412 (specifier-type `(signed-byte ,(1+ (max x-len y-len
))))
2414 (specifier-type 'integer
))))))))
2416 (defun logxor-derive-unsigned-low-bound (x y
)
2417 (let ((a (numeric-type-low x
))
2418 (b (numeric-type-high x
))
2419 (c (numeric-type-low y
))
2420 (d (numeric-type-high y
)))
2421 (loop for m
= (ash 1 (integer-length (logxor a c
))) then
(ash m -
1)
2424 ((not (zerop (logandc2 (logand c m
) a
)))
2425 (let ((temp (logand (logior a m
)
2429 ((not (zerop (logandc2 (logand a m
) c
)))
2430 (let ((temp (logand (logior c m
)
2434 finally
(return (logxor a c
)))))
2436 (defun logxor-derive-unsigned-high-bound (x y
)
2437 (let ((a (numeric-type-low x
))
2438 (b (numeric-type-high x
))
2439 (c (numeric-type-low y
))
2440 (d (numeric-type-high y
)))
2441 (loop for m
= (ash 1 (integer-length (logand b d
))) then
(ash m -
1)
2443 (unless (zerop (logand b d m
))
2444 (let ((temp (logior (- b m
) (1- m
))))
2446 ((>= temp a
) (setf b temp
))
2447 (t (let ((temp (logior (- d m
) (1- m
))))
2450 finally
(return (logxor b d
)))))
2452 (defun logxor-derive-type-aux (x y
&optional same-leaf
)
2454 (return-from logxor-derive-type-aux
(specifier-type '(eql 0))))
2455 (multiple-value-bind (x-len x-pos x-neg
) (integer-type-length x
)
2456 (multiple-value-bind (y-len y-pos y-neg
) (integer-type-length y
)
2458 ((and (not x-neg
) (not y-neg
))
2459 ;; Both are positive
2460 (if (and x-len y-len
)
2461 (let ((low (logxor-derive-unsigned-low-bound x y
))
2462 (high (logxor-derive-unsigned-high-bound x y
)))
2463 (specifier-type `(integer ,low
,high
)))
2464 (specifier-type '(unsigned-byte* *))))
2465 ((and (not x-pos
) (not y-pos
))
2466 ;; Both are negative. The result will be positive, and as long
2468 (specifier-type `(unsigned-byte* ,(if (and x-len y-len
)
2471 ((or (and (not x-pos
) (not y-neg
))
2472 (and (not y-pos
) (not x-neg
)))
2473 ;; Either X is negative and Y is positive or vice-versa. The
2474 ;; result will be negative.
2475 (specifier-type `(integer ,(if (and x-len y-len
)
2476 (ash -
1 (max x-len y-len
))
2479 ;; We can't tell what the sign of the result is going to be.
2480 ;; All we know is that we don't create new bits.
2482 (specifier-type `(signed-byte ,(1+ (max x-len y-len
)))))
2484 (specifier-type 'integer
))))))
2486 (macrolet ((deffrob (logfun)
2487 (let ((fun-aux (symbolicate logfun
"-DERIVE-TYPE-AUX")))
2488 `(defoptimizer (,logfun derive-type
) ((x y
))
2489 (two-arg-derive-type x y
#',fun-aux
#',logfun
)))))
2494 (defoptimizer (logeqv derive-type
) ((x y
))
2495 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2496 (lognot-derive-type-aux
2497 (logxor-derive-type-aux x y same-leaf
)))
2499 (defoptimizer (lognand derive-type
) ((x y
))
2500 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2501 (lognot-derive-type-aux
2502 (logand-derive-type-aux x y same-leaf
)))
2504 (defoptimizer (lognor derive-type
) ((x y
))
2505 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2506 (lognot-derive-type-aux
2507 (logior-derive-type-aux x y same-leaf
)))
2509 (defoptimizer (logandc1 derive-type
) ((x y
))
2510 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2512 (specifier-type '(eql 0))
2513 (logand-derive-type-aux
2514 (lognot-derive-type-aux x
) y nil
)))
2516 (defoptimizer (logandc2 derive-type
) ((x y
))
2517 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2519 (specifier-type '(eql 0))
2520 (logand-derive-type-aux
2521 x
(lognot-derive-type-aux y
) nil
)))
2523 (defoptimizer (logorc1 derive-type
) ((x y
))
2524 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2526 (specifier-type '(eql -
1))
2527 (logior-derive-type-aux
2528 (lognot-derive-type-aux x
) y nil
)))
2530 (defoptimizer (logorc2 derive-type
) ((x y
))
2531 (two-arg-derive-type x y
(lambda (x y same-leaf
)
2533 (specifier-type '(eql -
1))
2534 (logior-derive-type-aux
2535 x
(lognot-derive-type-aux y
) nil
)))
2538 ;;;; miscellaneous derive-type methods
2540 (defoptimizer (integer-length derive-type
) ((x))
2541 (let ((x-type (lvar-type x
)))
2542 (when (numeric-type-p x-type
)
2543 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2544 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2545 ;; careful about LO or HI being NIL, though. Also, if 0 is
2546 ;; contained in X, the lower bound is obviously 0.
2547 (flet ((null-or-min (a b
)
2548 (and a b
(min (integer-length a
)
2549 (integer-length b
))))
2551 (and a b
(max (integer-length a
)
2552 (integer-length b
)))))
2553 (let* ((min (numeric-type-low x-type
))
2554 (max (numeric-type-high x-type
))
2555 (min-len (null-or-min min max
))
2556 (max-len (null-or-max min max
)))
2557 (when (ctypep 0 x-type
)
2559 (specifier-type `(integer ,(or min-len
'*) ,(or max-len
'*))))))))
2561 (defoptimizer (isqrt derive-type
) ((x))
2562 (let ((x-type (lvar-type x
)))
2563 (when (numeric-type-p x-type
)
2564 (let* ((lo (numeric-type-low x-type
))
2565 (hi (numeric-type-high x-type
))
2566 (lo-res (if lo
(isqrt lo
) '*))
2567 (hi-res (if hi
(isqrt hi
) '*)))
2568 (specifier-type `(integer ,lo-res
,hi-res
))))))
2570 (defoptimizer (code-char derive-type
) ((code))
2571 (let ((type (lvar-type code
)))
2572 ;; FIXME: unions of integral ranges? It ought to be easier to do
2573 ;; this, given that CHARACTER-SET is basically an integral range
2574 ;; type. -- CSR, 2004-10-04
2575 (when (numeric-type-p type
)
2576 (let* ((lo (numeric-type-low type
))
2577 (hi (numeric-type-high type
))
2578 (type (specifier-type `(character-set ((,lo .
,hi
))))))
2580 ;; KLUDGE: when running on the host, we lose a slight amount
2581 ;; of precision so that we don't have to "unparse" types
2582 ;; that formally we can't, such as (CHARACTER-SET ((0
2583 ;; . 0))). -- CSR, 2004-10-06
2585 ((csubtypep type
(specifier-type 'standard-char
)) type
)
2587 ((csubtypep type
(specifier-type 'base-char
))
2588 (specifier-type 'base-char
))
2590 ((csubtypep type
(specifier-type 'extended-char
))
2591 (specifier-type 'extended-char
))
2592 (t #+sb-xc-host
(specifier-type 'character
)
2593 #-sb-xc-host type
))))))
2595 (defoptimizer (values derive-type
) ((&rest values
))
2596 (make-values-type :required
(mapcar #'lvar-type values
)))
2598 (defun signum-derive-type-aux (type)
2599 (if (eq (numeric-type-complexp type
) :complex
)
2600 (let* ((format (case (numeric-type-class type
)
2601 ((integer rational
) 'single-float
)
2602 (t (numeric-type-format type
))))
2603 (bound-format (or format
'float
)))
2604 (make-numeric-type :class
'float
2607 :low
(coerce -
1 bound-format
)
2608 :high
(coerce 1 bound-format
)))
2609 (let* ((interval (numeric-type->interval type
))
2610 (range-info (interval-range-info interval
))
2611 (contains-0-p (interval-contains-p 0 interval
))
2612 (class (numeric-type-class type
))
2613 (format (numeric-type-format type
))
2614 (one (coerce 1 (or format class
'real
)))
2615 (zero (coerce 0 (or format class
'real
)))
2616 (minus-one (coerce -
1 (or format class
'real
)))
2617 (plus (make-numeric-type :class class
:format format
2618 :low one
:high one
))
2619 (minus (make-numeric-type :class class
:format format
2620 :low minus-one
:high minus-one
))
2621 ;; KLUDGE: here we have a fairly horrible hack to deal
2622 ;; with the schizophrenia in the type derivation engine.
2623 ;; The problem is that the type derivers reinterpret
2624 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2625 ;; 0d0) within the derivation mechanism doesn't include
2626 ;; -0d0. Ugh. So force it in here, instead.
2627 (zero (make-numeric-type :class class
:format format
2628 :low
(- zero
) :high zero
)))
2630 (+ (if contains-0-p
(type-union plus zero
) plus
))
2631 (- (if contains-0-p
(type-union minus zero
) minus
))
2632 (t (type-union minus zero plus
))))))
2634 (defoptimizer (signum derive-type
) ((num))
2635 (one-arg-derive-type num
#'signum-derive-type-aux nil
))
2637 ;;;; byte operations
2639 ;;;; We try to turn byte operations into simple logical operations.
2640 ;;;; First, we convert byte specifiers into separate size and position
2641 ;;;; arguments passed to internal %FOO functions. We then attempt to
2642 ;;;; transform the %FOO functions into boolean operations when the
2643 ;;;; size and position are constant and the operands are fixnums.
2645 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2646 ;; expressions that evaluate to the SIZE and POSITION of
2647 ;; the byte-specifier form SPEC. We may wrap a let around
2648 ;; the result of the body to bind some variables.
2650 ;; If the spec is a BYTE form, then bind the vars to the
2651 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2652 ;; and BYTE-POSITION. The goal of this transformation is to
2653 ;; avoid consing up byte specifiers and then immediately
2654 ;; throwing them away.
2655 (with-byte-specifier ((size-var pos-var spec
) &body body
)
2656 (once-only ((spec `(macroexpand ,spec
))
2658 `(if (and (consp ,spec
)
2659 (eq (car ,spec
) 'byte
)
2660 (= (length ,spec
) 3))
2661 (let ((,size-var
(second ,spec
))
2662 (,pos-var
(third ,spec
)))
2664 (let ((,size-var
`(byte-size ,,temp
))
2665 (,pos-var
`(byte-position ,,temp
)))
2666 `(let ((,,temp
,,spec
))
2669 (define-source-transform ldb
(spec int
)
2670 (with-byte-specifier (size pos spec
)
2671 `(%ldb
,size
,pos
,int
)))
2673 (define-source-transform dpb
(newbyte spec int
)
2674 (with-byte-specifier (size pos spec
)
2675 `(%dpb
,newbyte
,size
,pos
,int
)))
2677 (define-source-transform mask-field
(spec int
)
2678 (with-byte-specifier (size pos spec
)
2679 `(%mask-field
,size
,pos
,int
)))
2681 (define-source-transform deposit-field
(newbyte spec int
)
2682 (with-byte-specifier (size pos spec
)
2683 `(%deposit-field
,newbyte
,size
,pos
,int
))))
2685 (defoptimizer (%ldb derive-type
) ((size posn num
))
2686 (let ((size (lvar-type size
)))
2687 (if (and (numeric-type-p size
)
2688 (csubtypep size
(specifier-type 'integer
)))
2689 (let ((size-high (numeric-type-high size
)))
2690 (if (and size-high
(<= size-high sb
!vm
:n-word-bits
))
2691 (specifier-type `(unsigned-byte* ,size-high
))
2692 (specifier-type 'unsigned-byte
)))
2695 (defoptimizer (%mask-field derive-type
) ((size posn num
))
2696 (let ((size (lvar-type size
))
2697 (posn (lvar-type posn
)))
2698 (if (and (numeric-type-p size
)
2699 (csubtypep size
(specifier-type 'integer
))
2700 (numeric-type-p posn
)
2701 (csubtypep posn
(specifier-type 'integer
)))
2702 (let ((size-high (numeric-type-high size
))
2703 (posn-high (numeric-type-high posn
)))
2704 (if (and size-high posn-high
2705 (<= (+ size-high posn-high
) sb
!vm
:n-word-bits
))
2706 (specifier-type `(unsigned-byte* ,(+ size-high posn-high
)))
2707 (specifier-type 'unsigned-byte
)))
2710 (defun %deposit-field-derive-type-aux
(size posn int
)
2711 (let ((size (lvar-type size
))
2712 (posn (lvar-type posn
))
2713 (int (lvar-type int
)))
2714 (when (and (numeric-type-p size
)
2715 (numeric-type-p posn
)
2716 (numeric-type-p int
))
2717 (let ((size-high (numeric-type-high size
))
2718 (posn-high (numeric-type-high posn
))
2719 (high (numeric-type-high int
))
2720 (low (numeric-type-low int
)))
2721 (when (and size-high posn-high high low
2722 ;; KLUDGE: we need this cutoff here, otherwise we
2723 ;; will merrily derive the type of %DPB as
2724 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2725 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2726 ;; 1073741822))), with hilarious consequences. We
2727 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2728 ;; over a reasonable amount of shifting, even on
2729 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2730 ;; machine integers are 64-bits. -- CSR,
2732 (<= (+ size-high posn-high
) (* 4 sb
!vm
:n-word-bits
)))
2733 (let ((raw-bit-count (max (integer-length high
)
2734 (integer-length low
)
2735 (+ size-high posn-high
))))
2738 `(signed-byte ,(1+ raw-bit-count
))
2739 `(unsigned-byte* ,raw-bit-count
)))))))))
2741 (defoptimizer (%dpb derive-type
) ((newbyte size posn int
))
2742 (%deposit-field-derive-type-aux size posn int
))
2744 (defoptimizer (%deposit-field derive-type
) ((newbyte size posn int
))
2745 (%deposit-field-derive-type-aux size posn int
))
2747 (deftransform %ldb
((size posn int
)
2748 (fixnum fixnum integer
)
2749 (unsigned-byte #.sb
!vm
:n-word-bits
))
2750 "convert to inline logical operations"
2751 `(logand (ash int
(- posn
))
2752 (ash ,(1- (ash 1 sb
!vm
:n-word-bits
))
2753 (- size
,sb
!vm
:n-word-bits
))))
2755 (deftransform %mask-field
((size posn int
)
2756 (fixnum fixnum integer
)
2757 (unsigned-byte #.sb
!vm
:n-word-bits
))
2758 "convert to inline logical operations"
2760 (ash (ash ,(1- (ash 1 sb
!vm
:n-word-bits
))
2761 (- size
,sb
!vm
:n-word-bits
))
2764 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2765 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2766 ;;; as the result type, as that would allow result types that cover
2767 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2768 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2770 (deftransform %dpb
((new size posn int
)
2772 (unsigned-byte #.sb
!vm
:n-word-bits
))
2773 "convert to inline logical operations"
2774 `(let ((mask (ldb (byte size
0) -
1)))
2775 (logior (ash (logand new mask
) posn
)
2776 (logand int
(lognot (ash mask posn
))))))
2778 (deftransform %dpb
((new size posn int
)
2780 (signed-byte #.sb
!vm
:n-word-bits
))
2781 "convert to inline logical operations"
2782 `(let ((mask (ldb (byte size
0) -
1)))
2783 (logior (ash (logand new mask
) posn
)
2784 (logand int
(lognot (ash mask posn
))))))
2786 (deftransform %deposit-field
((new size posn int
)
2788 (unsigned-byte #.sb
!vm
:n-word-bits
))
2789 "convert to inline logical operations"
2790 `(let ((mask (ash (ldb (byte size
0) -
1) posn
)))
2791 (logior (logand new mask
)
2792 (logand int
(lognot mask
)))))
2794 (deftransform %deposit-field
((new size posn int
)
2796 (signed-byte #.sb
!vm
:n-word-bits
))
2797 "convert to inline logical operations"
2798 `(let ((mask (ash (ldb (byte size
0) -
1) posn
)))
2799 (logior (logand new mask
)
2800 (logand int
(lognot mask
)))))
2802 (defoptimizer (mask-signed-field derive-type
) ((size x
))
2803 (let ((size (lvar-type size
)))
2804 (if (numeric-type-p size
)
2805 (let ((size-high (numeric-type-high size
)))
2806 (if (and size-high
(<= 1 size-high sb
!vm
:n-word-bits
))
2807 (specifier-type `(signed-byte ,size-high
))
2812 ;;; Modular functions
2814 ;;; (ldb (byte s 0) (foo x y ...)) =
2815 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2817 ;;; and similar for other arguments.
2819 (defun make-modular-fun-type-deriver (prototype class width
)
2821 (binding* ((info (info :function
:info prototype
) :exit-if-null
)
2822 (fun (fun-info-derive-type info
) :exit-if-null
)
2823 (mask-type (specifier-type
2825 (:unsigned
(let ((mask (1- (ash 1 width
))))
2826 `(integer ,mask
,mask
)))
2827 (:signed
`(signed-byte ,width
))))))
2829 (let ((res (funcall fun call
)))
2831 (if (eq class
:unsigned
)
2832 (logand-derive-type-aux res mask-type
))))))
2835 (binding* ((info (info :function
:info prototype
) :exit-if-null
)
2836 (fun (fun-info-derive-type info
) :exit-if-null
)
2837 (res (funcall fun call
) :exit-if-null
)
2838 (mask-type (specifier-type
2840 (:unsigned
(let ((mask (1- (ash 1 width
))))
2841 `(integer ,mask
,mask
)))
2842 (:signed
`(signed-byte ,width
))))))
2843 (if (eq class
:unsigned
)
2844 (logand-derive-type-aux res mask-type
)))))
2846 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2848 ;;; For good functions, we just recursively cut arguments; their
2849 ;;; "goodness" means that the result will not increase (in the
2850 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2851 ;;; replaced with the version, cutting its result to WIDTH or more
2852 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2853 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2854 ;;; arguments (maybe to a different width) and returning the name of a
2855 ;;; modular version, if it exists, or NIL. If we have changed
2856 ;;; anything, we need to flush old derived types, because they have
2857 ;;; nothing in common with the new code.
2858 (defun cut-to-width (lvar class width
)
2859 (declare (type lvar lvar
) (type (integer 0) width
))
2860 (let ((type (specifier-type (if (zerop width
)
2862 `(,(ecase class
(:unsigned
'unsigned-byte
)
2863 (:signed
'signed-byte
))
2865 (labels ((reoptimize-node (node name
)
2866 (setf (node-derived-type node
)
2868 (info :function
:type name
)))
2869 (setf (lvar-%derived-type
(node-lvar node
)) nil
)
2870 (setf (node-reoptimize node
) t
)
2871 (setf (block-reoptimize (node-block node
)) t
)
2872 (reoptimize-component (node-component node
) :maybe
))
2873 (cut-node (node &aux did-something
)
2874 (when (and (not (block-delete-p (node-block node
)))
2875 (combination-p node
)
2876 (eq (basic-combination-kind node
) :known
))
2877 (let* ((fun-ref (lvar-use (combination-fun node
)))
2878 (fun-name (leaf-source-name (ref-leaf fun-ref
)))
2879 (modular-fun (find-modular-version fun-name class width
)))
2880 (when (and modular-fun
2881 (not (and (eq fun-name
'logand
)
2883 (single-value-type (node-derived-type node
))
2885 (binding* ((name (etypecase modular-fun
2886 ((eql :good
) fun-name
)
2888 (modular-fun-info-name modular-fun
))
2890 (funcall modular-fun node width
)))
2892 (unless (eql modular-fun
:good
)
2893 (setq did-something t
)
2896 (find-free-fun name
"in a strange place"))
2897 (setf (combination-kind node
) :full
))
2898 (unless (functionp modular-fun
)
2899 (dolist (arg (basic-combination-args node
))
2900 (when (cut-lvar arg
)
2901 (setq did-something t
))))
2903 (reoptimize-node node name
))
2905 (cut-lvar (lvar &aux did-something
)
2906 (do-uses (node lvar
)
2907 (when (cut-node node
)
2908 (setq did-something t
)))
2912 (defoptimizer (logand optimizer
) ((x y
) node
)
2913 (let ((result-type (single-value-type (node-derived-type node
))))
2914 (when (numeric-type-p result-type
)
2915 (let ((low (numeric-type-low result-type
))
2916 (high (numeric-type-high result-type
)))
2917 (when (and (numberp low
)
2920 (let ((width (integer-length high
)))
2921 (when (some (lambda (x) (<= width x
))
2922 (modular-class-widths *unsigned-modular-class
*))
2923 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2924 (cut-to-width x
:unsigned width
)
2925 (cut-to-width y
:unsigned width
)
2926 nil
; After fixing above, replace with T.
2929 (defoptimizer (mask-signed-field optimizer
) ((width x
) node
)
2930 (let ((result-type (single-value-type (node-derived-type node
))))
2931 (when (numeric-type-p result-type
)
2932 (let ((low (numeric-type-low result-type
))
2933 (high (numeric-type-high result-type
)))
2934 (when (and (numberp low
) (numberp high
))
2935 (let ((width (max (integer-length high
) (integer-length low
))))
2936 (when (some (lambda (x) (<= width x
))
2937 (modular-class-widths *signed-modular-class
*))
2938 ;; FIXME: This should be (CUT-TO-WIDTH NODE WIDTH).
2939 (cut-to-width x
:signed width
)
2940 nil
; After fixing above, replace with T.
2943 ;;; miscellanous numeric transforms
2945 ;;; If a constant appears as the first arg, swap the args.
2946 (deftransform commutative-arg-swap
((x y
) * * :defun-only t
:node node
)
2947 (if (and (constant-lvar-p x
)
2948 (not (constant-lvar-p y
)))
2949 `(,(lvar-fun-name (basic-combination-fun node
))
2952 (give-up-ir1-transform)))
2954 (dolist (x '(= char
= + * logior logand logxor
))
2955 (%deftransform x
'(function * *) #'commutative-arg-swap
2956 "place constant arg last"))
2958 ;;; Handle the case of a constant BOOLE-CODE.
2959 (deftransform boole
((op x y
) * *)
2960 "convert to inline logical operations"
2961 (unless (constant-lvar-p op
)
2962 (give-up-ir1-transform "BOOLE code is not a constant."))
2963 (let ((control (lvar-value op
)))
2965 (#.sb
!xc
:boole-clr
0)
2966 (#.sb
!xc
:boole-set -
1)
2967 (#.sb
!xc
:boole-1
'x
)
2968 (#.sb
!xc
:boole-2
'y
)
2969 (#.sb
!xc
:boole-c1
'(lognot x
))
2970 (#.sb
!xc
:boole-c2
'(lognot y
))
2971 (#.sb
!xc
:boole-and
'(logand x y
))
2972 (#.sb
!xc
:boole-ior
'(logior x y
))
2973 (#.sb
!xc
:boole-xor
'(logxor x y
))
2974 (#.sb
!xc
:boole-eqv
'(logeqv x y
))
2975 (#.sb
!xc
:boole-nand
'(lognand x y
))
2976 (#.sb
!xc
:boole-nor
'(lognor x y
))
2977 (#.sb
!xc
:boole-andc1
'(logandc1 x y
))
2978 (#.sb
!xc
:boole-andc2
'(logandc2 x y
))
2979 (#.sb
!xc
:boole-orc1
'(logorc1 x y
))
2980 (#.sb
!xc
:boole-orc2
'(logorc2 x y
))
2982 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
2985 ;;;; converting special case multiply/divide to shifts
2987 ;;; If arg is a constant power of two, turn * into a shift.
2988 (deftransform * ((x y
) (integer integer
) *)
2989 "convert x*2^k to shift"
2990 (unless (constant-lvar-p y
)
2991 (give-up-ir1-transform))
2992 (let* ((y (lvar-value y
))
2994 (len (1- (integer-length y-abs
))))
2995 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
2996 (give-up-ir1-transform))
3001 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3002 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3004 (flet ((frob (y ceil-p
)
3005 (unless (constant-lvar-p y
)
3006 (give-up-ir1-transform))
3007 (let* ((y (lvar-value y
))
3009 (len (1- (integer-length y-abs
))))
3010 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3011 (give-up-ir1-transform))
3012 (let ((shift (- len
))
3014 (delta (if ceil-p
(* (signum y
) (1- y-abs
)) 0)))
3015 `(let ((x (+ x
,delta
)))
3017 `(values (ash (- x
) ,shift
)
3018 (- (- (logand (- x
) ,mask
)) ,delta
))
3019 `(values (ash x
,shift
)
3020 (- (logand x
,mask
) ,delta
))))))))
3021 (deftransform floor
((x y
) (integer integer
) *)
3022 "convert division by 2^k to shift"
3024 (deftransform ceiling
((x y
) (integer integer
) *)
3025 "convert division by 2^k to shift"
3028 ;;; Do the same for MOD.
3029 (deftransform mod
((x y
) (integer integer
) *)
3030 "convert remainder mod 2^k to LOGAND"
3031 (unless (constant-lvar-p y
)
3032 (give-up-ir1-transform))
3033 (let* ((y (lvar-value y
))
3035 (len (1- (integer-length y-abs
))))
3036 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3037 (give-up-ir1-transform))
3038 (let ((mask (1- y-abs
)))
3040 `(- (logand (- x
) ,mask
))
3041 `(logand x
,mask
)))))
3043 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3044 (deftransform truncate
((x y
) (integer integer
))
3045 "convert division by 2^k to shift"
3046 (unless (constant-lvar-p y
)
3047 (give-up-ir1-transform))
3048 (let* ((y (lvar-value y
))
3050 (len (1- (integer-length y-abs
))))
3051 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3052 (give-up-ir1-transform))
3053 (let* ((shift (- len
))
3056 (values ,(if (minusp y
)
3058 `(- (ash (- x
) ,shift
)))
3059 (- (logand (- x
) ,mask
)))
3060 (values ,(if (minusp y
)
3061 `(ash (- ,mask x
) ,shift
)
3063 (logand x
,mask
))))))
3065 ;;; And the same for REM.
3066 (deftransform rem
((x y
) (integer integer
) *)
3067 "convert remainder mod 2^k to LOGAND"
3068 (unless (constant-lvar-p y
)
3069 (give-up-ir1-transform))
3070 (let* ((y (lvar-value y
))
3072 (len (1- (integer-length y-abs
))))
3073 (unless (and (> y-abs
0) (= y-abs
(ash 1 len
)))
3074 (give-up-ir1-transform))
3075 (let ((mask (1- y-abs
)))
3077 (- (logand (- x
) ,mask
))
3078 (logand x
,mask
)))))
3080 ;;;; arithmetic and logical identity operation elimination
3082 ;;; Flush calls to various arith functions that convert to the
3083 ;;; identity function or a constant.
3084 (macrolet ((def (name identity result
)
3085 `(deftransform ,name
((x y
) (* (constant-arg (member ,identity
))) *)
3086 "fold identity operations"
3093 (def logxor -
1 (lognot x
))
3096 (deftransform logand
((x y
) (* (constant-arg t
)) *)
3097 "fold identity operation"
3098 (let ((y (lvar-value y
)))
3099 (unless (and (plusp y
)
3100 (= y
(1- (ash 1 (integer-length y
)))))
3101 (give-up-ir1-transform))
3102 (unless (csubtypep (lvar-type x
)
3103 (specifier-type `(integer 0 ,y
)))
3104 (give-up-ir1-transform))
3107 (deftransform mask-signed-field
((size x
) ((constant-arg t
) *) *)
3108 "fold identity operation"
3109 (let ((size (lvar-value size
)))
3110 (unless (csubtypep (lvar-type x
) (specifier-type `(signed-byte ,size
)))
3111 (give-up-ir1-transform))
3114 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3115 ;;; (* 0 -4.0) is -0.0.
3116 (deftransform -
((x y
) ((constant-arg (member 0)) rational
) *)
3117 "convert (- 0 x) to negate"
3119 (deftransform * ((x y
) (rational (constant-arg (member 0))) *)
3120 "convert (* x 0) to 0"
3123 ;;; Return T if in an arithmetic op including lvars X and Y, the
3124 ;;; result type is not affected by the type of X. That is, Y is at
3125 ;;; least as contagious as X.
3127 (defun not-more-contagious (x y
)
3128 (declare (type continuation x y
))
3129 (let ((x (lvar-type x
))
3131 (values (type= (numeric-contagion x y
)
3132 (numeric-contagion y y
)))))
3133 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3134 ;;; XXX needs more work as valid transforms are missed; some cases are
3135 ;;; specific to particular transform functions so the use of this
3136 ;;; function may need a re-think.
3137 (defun not-more-contagious (x y
)
3138 (declare (type lvar x y
))
3139 (flet ((simple-numeric-type (num)
3140 (and (numeric-type-p num
)
3141 ;; Return non-NIL if NUM is integer, rational, or a float
3142 ;; of some type (but not FLOAT)
3143 (case (numeric-type-class num
)
3147 (numeric-type-format num
))
3150 (let ((x (lvar-type x
))
3152 (if (and (simple-numeric-type x
)
3153 (simple-numeric-type y
))
3154 (values (type= (numeric-contagion x y
)
3155 (numeric-contagion y y
)))))))
3159 ;;; If y is not constant, not zerop, or is contagious, or a positive
3160 ;;; float +0.0 then give up.
3161 (deftransform + ((x y
) (t (constant-arg t
)) *)
3163 (let ((val (lvar-value y
)))
3164 (unless (and (zerop val
)
3165 (not (and (floatp val
) (plusp (float-sign val
))))
3166 (not-more-contagious y x
))
3167 (give-up-ir1-transform)))
3172 ;;; If y is not constant, not zerop, or is contagious, or a negative
3173 ;;; float -0.0 then give up.
3174 (deftransform -
((x y
) (t (constant-arg t
)) *)
3176 (let ((val (lvar-value y
)))
3177 (unless (and (zerop val
)
3178 (not (and (floatp val
) (minusp (float-sign val
))))
3179 (not-more-contagious y x
))
3180 (give-up-ir1-transform)))
3183 ;;; Fold (OP x +/-1)
3184 (macrolet ((def (name result minus-result
)
3185 `(deftransform ,name
((x y
) (t (constant-arg real
)) *)
3186 "fold identity operations"
3187 (let ((val (lvar-value y
)))
3188 (unless (and (= (abs val
) 1)
3189 (not-more-contagious y x
))
3190 (give-up-ir1-transform))
3191 (if (minusp val
) ',minus-result
',result
)))))
3192 (def * x
(%negate x
))
3193 (def / x
(%negate x
))
3194 (def expt x
(/ 1 x
)))
3196 ;;; Fold (expt x n) into multiplications for small integral values of
3197 ;;; N; convert (expt x 1/2) to sqrt.
3198 (deftransform expt
((x y
) (t (constant-arg real
)) *)
3199 "recode as multiplication or sqrt"
3200 (let ((val (lvar-value y
)))
3201 ;; If Y would cause the result to be promoted to the same type as
3202 ;; Y, we give up. If not, then the result will be the same type
3203 ;; as X, so we can replace the exponentiation with simple
3204 ;; multiplication and division for small integral powers.
3205 (unless (not-more-contagious y x
)
3206 (give-up-ir1-transform))
3208 (let ((x-type (lvar-type x
)))
3209 (cond ((csubtypep x-type
(specifier-type '(or rational
3210 (complex rational
))))
3212 ((csubtypep x-type
(specifier-type 'real
))
3216 ((csubtypep x-type
(specifier-type 'complex
))
3217 ;; both parts are float
3219 (t (give-up-ir1-transform)))))
3220 ((= val
2) '(* x x
))
3221 ((= val -
2) '(/ (* x x
)))
3222 ((= val
3) '(* x x x
))
3223 ((= val -
3) '(/ (* x x x
)))
3224 ((= val
1/2) '(sqrt x
))
3225 ((= val -
1/2) '(/ (sqrt x
)))
3226 (t (give-up-ir1-transform)))))
3228 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3229 ;;; transformations?
3230 ;;; Perhaps we should have to prove that the denominator is nonzero before
3231 ;;; doing them? -- WHN 19990917
3232 (macrolet ((def (name)
3233 `(deftransform ,name
((x y
) ((constant-arg (integer 0 0)) integer
)
3240 (macrolet ((def (name)
3241 `(deftransform ,name
((x y
) ((constant-arg (integer 0 0)) integer
)
3250 ;;;; character operations
3252 (deftransform char-equal
((a b
) (base-char base-char
))
3254 '(let* ((ac (char-code a
))
3256 (sum (logxor ac bc
)))
3258 (when (eql sum
#x20
)
3259 (let ((sum (+ ac bc
)))
3260 (or (and (> sum
161) (< sum
213))
3261 (and (> sum
415) (< sum
461))
3262 (and (> sum
463) (< sum
477))))))))
3264 (deftransform char-upcase
((x) (base-char))
3266 '(let ((n-code (char-code x
)))
3267 (if (or (and (> n-code
#o140
) ; Octal 141 is #\a.
3268 (< n-code
#o173
)) ; Octal 172 is #\z.
3269 (and (> n-code
#o337
)
3271 (and (> n-code
#o367
)
3273 (code-char (logxor #x20 n-code
))
3276 (deftransform char-downcase
((x) (base-char))
3278 '(let ((n-code (char-code x
)))
3279 (if (or (and (> n-code
64) ; 65 is #\A.
3280 (< n-code
91)) ; 90 is #\Z.
3285 (code-char (logxor #x20 n-code
))
3288 ;;;; equality predicate transforms
3290 ;;; Return true if X and Y are lvars whose only use is a
3291 ;;; reference to the same leaf, and the value of the leaf cannot
3293 (defun same-leaf-ref-p (x y
)
3294 (declare (type lvar x y
))
3295 (let ((x-use (principal-lvar-use x
))
3296 (y-use (principal-lvar-use y
)))
3299 (eq (ref-leaf x-use
) (ref-leaf y-use
))
3300 (constant-reference-p x-use
))))
3302 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3303 ;;; if there is no intersection between the types of the arguments,
3304 ;;; then the result is definitely false.
3305 (deftransform simple-equality-transform
((x y
) * *
3308 ((same-leaf-ref-p x y
) t
)
3309 ((not (types-equal-or-intersect (lvar-type x
) (lvar-type y
)))
3311 (t (give-up-ir1-transform))))
3314 `(%deftransform
',x
'(function * *) #'simple-equality-transform
)))
3318 ;;; True if EQL comparisons involving type can be simplified to EQ.
3319 (defun eq-comparable-type-p (type)
3320 (csubtypep type
(specifier-type '(or fixnum
(not number
)))))
3322 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3323 ;;; try to convert to a type-specific predicate or EQ:
3324 ;;; -- If both args are characters, convert to CHAR=. This is better than
3325 ;;; just converting to EQ, since CHAR= may have special compilation
3326 ;;; strategies for non-standard representations, etc.
3327 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3328 ;;; constant and if so, put X second. Doing this results in better
3329 ;;; code from the backend, since the backend assumes that any constant
3330 ;;; argument comes second.
3331 ;;; -- If either arg is definitely not a number or a fixnum, then we
3332 ;;; can compare with EQ.
3333 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3334 ;;; is constant then we put it second. If X is a subtype of Y, we put
3335 ;;; it second. These rules make it easier for the back end to match
3336 ;;; these interesting cases.
3337 (deftransform eql
((x y
) * * :node node
)
3338 "convert to simpler equality predicate"
3339 (let ((x-type (lvar-type x
))
3340 (y-type (lvar-type y
))
3341 (char-type (specifier-type 'character
)))
3342 (flet ((fixnum-type-p (type)
3343 (csubtypep type
(specifier-type 'fixnum
))))
3345 ((same-leaf-ref-p x y
) t
)
3346 ((not (types-equal-or-intersect x-type y-type
))
3348 ((and (csubtypep x-type char-type
)
3349 (csubtypep y-type char-type
))
3351 ((or (fixnum-type-p x-type
) (fixnum-type-p y-type
))
3352 (commutative-arg-swap node
))
3353 ((or (eq-comparable-type-p x-type
) (eq-comparable-type-p y-type
))
3355 ((and (not (constant-lvar-p y
))
3356 (or (constant-lvar-p x
)
3357 (and (csubtypep x-type y-type
)
3358 (not (csubtypep y-type x-type
)))))
3361 (give-up-ir1-transform))))))
3363 ;;; similarly to the EQL transform above, we attempt to constant-fold
3364 ;;; or convert to a simpler predicate: mostly we have to be careful
3365 ;;; with strings and bit-vectors.
3366 (deftransform equal
((x y
) * *)
3367 "convert to simpler equality predicate"
3368 (let ((x-type (lvar-type x
))
3369 (y-type (lvar-type y
))
3370 (string-type (specifier-type 'string
))
3371 (bit-vector-type (specifier-type 'bit-vector
)))
3373 ((same-leaf-ref-p x y
) t
)
3374 ((and (csubtypep x-type string-type
)
3375 (csubtypep y-type string-type
))
3377 ((and (csubtypep x-type bit-vector-type
)
3378 (csubtypep y-type bit-vector-type
))
3379 '(bit-vector-= x y
))
3380 ;; if at least one is not a string, and at least one is not a
3381 ;; bit-vector, then we can reason from types.
3382 ((and (not (and (types-equal-or-intersect x-type string-type
)
3383 (types-equal-or-intersect y-type string-type
)))
3384 (not (and (types-equal-or-intersect x-type bit-vector-type
)
3385 (types-equal-or-intersect y-type bit-vector-type
)))
3386 (not (types-equal-or-intersect x-type y-type
)))
3388 (t (give-up-ir1-transform)))))
3390 ;;; Convert to EQL if both args are rational and complexp is specified
3391 ;;; and the same for both.
3392 (deftransform = ((x y
) (number number
) *)
3394 (let ((x-type (lvar-type x
))
3395 (y-type (lvar-type y
)))
3396 (cond ((or (and (csubtypep x-type
(specifier-type 'float
))
3397 (csubtypep y-type
(specifier-type 'float
)))
3398 (and (csubtypep x-type
(specifier-type '(complex float
)))
3399 (csubtypep y-type
(specifier-type '(complex float
)))))
3400 ;; They are both floats. Leave as = so that -0.0 is
3401 ;; handled correctly.
3402 (give-up-ir1-transform))
3403 ((or (and (csubtypep x-type
(specifier-type 'rational
))
3404 (csubtypep y-type
(specifier-type 'rational
)))
3405 (and (csubtypep x-type
3406 (specifier-type '(complex rational
)))
3408 (specifier-type '(complex rational
)))))
3409 ;; They are both rationals and complexp is the same.
3413 (give-up-ir1-transform
3414 "The operands might not be the same type.")))))
3416 (defun maybe-float-lvar-p (lvar)
3417 (neq *empty-type
* (type-intersection (specifier-type 'float
)
3420 (flet ((maybe-invert (node op inverted x y
)
3421 ;; Don't invert if either argument can be a float (NaNs)
3423 ((or (maybe-float-lvar-p x
) (maybe-float-lvar-p y
))
3424 (delay-ir1-transform node
:constraint
)
3425 `(or (,op x y
) (= x y
)))
3427 `(if (,inverted x y
) nil t
)))))
3428 (deftransform >= ((x y
) (number number
) * :node node
)
3429 "invert or open code"
3430 (maybe-invert node
'> '< x y
))
3431 (deftransform <= ((x y
) (number number
) * :node node
)
3432 "invert or open code"
3433 (maybe-invert node
'< '> x y
)))
3435 ;;; See whether we can statically determine (< X Y) using type
3436 ;;; information. If X's high bound is < Y's low, then X < Y.
3437 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3438 ;;; NIL). If not, at least make sure any constant arg is second.
3439 (macrolet ((def (name inverse reflexive-p surely-true surely-false
)
3440 `(deftransform ,name
((x y
))
3441 "optimize using intervals"
3442 (if (and (same-leaf-ref-p x y
)
3443 ;; For non-reflexive functions we don't need
3444 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3445 ;; but with reflexive ones we don't know...
3447 '((and (not (maybe-float-lvar-p x
))
3448 (not (maybe-float-lvar-p y
))))))
3450 (let ((ix (or (type-approximate-interval (lvar-type x
))
3451 (give-up-ir1-transform)))
3452 (iy (or (type-approximate-interval (lvar-type y
))
3453 (give-up-ir1-transform))))
3458 ((and (constant-lvar-p x
)
3459 (not (constant-lvar-p y
)))
3462 (give-up-ir1-transform))))))))
3463 (def = = t
(interval-= ix iy
) (interval-/= ix iy
))
3464 (def /= /= nil
(interval-/= ix iy
) (interval-= ix iy
))
3465 (def < > nil
(interval-< ix iy
) (interval->= ix iy
))
3466 (def > < nil
(interval-< iy ix
) (interval->= iy ix
))
3467 (def <= >= t
(interval->= iy ix
) (interval-< iy ix
))
3468 (def >= <= t
(interval->= ix iy
) (interval-< ix iy
)))
3470 (defun ir1-transform-char< (x y first second inverse
)
3472 ((same-leaf-ref-p x y
) nil
)
3473 ;; If we had interval representation of character types, as we
3474 ;; might eventually have to to support 2^21 characters, then here
3475 ;; we could do some compile-time computation as in transforms for
3476 ;; < above. -- CSR, 2003-07-01
3477 ((and (constant-lvar-p first
)
3478 (not (constant-lvar-p second
)))
3480 (t (give-up-ir1-transform))))
3482 (deftransform char
< ((x y
) (character character
) *)
3483 (ir1-transform-char< x y x y
'char
>))
3485 (deftransform char
> ((x y
) (character character
) *)
3486 (ir1-transform-char< y x x y
'char
<))
3488 ;;;; converting N-arg comparisons
3490 ;;;; We convert calls to N-arg comparison functions such as < into
3491 ;;;; two-arg calls. This transformation is enabled for all such
3492 ;;;; comparisons in this file. If any of these predicates are not
3493 ;;;; open-coded, then the transformation should be removed at some
3494 ;;;; point to avoid pessimization.
3496 ;;; This function is used for source transformation of N-arg
3497 ;;; comparison functions other than inequality. We deal both with
3498 ;;; converting to two-arg calls and inverting the sense of the test,
3499 ;;; if necessary. If the call has two args, then we pass or return a
3500 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3501 ;;; then we transform to code that returns true. Otherwise, we bind
3502 ;;; all the arguments and expand into a bunch of IFs.
3503 (defun multi-compare (predicate args not-p type
&optional force-two-arg-p
)
3504 (let ((nargs (length args
)))
3505 (cond ((< nargs
1) (values nil t
))
3506 ((= nargs
1) `(progn (the ,type
,@args
) t
))
3509 `(if (,predicate
,(first args
) ,(second args
)) nil t
)
3511 `(,predicate
,(first args
) ,(second args
))
3514 (do* ((i (1- nargs
) (1- i
))
3516 (current (gensym) (gensym))
3517 (vars (list current
) (cons current vars
))
3519 `(if (,predicate
,current
,last
)
3521 `(if (,predicate
,current
,last
)
3524 `((lambda ,vars
(declare (type ,type
,@vars
)) ,result
)
3527 (define-source-transform = (&rest args
) (multi-compare '= args nil
'number
))
3528 (define-source-transform < (&rest args
) (multi-compare '< args nil
'real
))
3529 (define-source-transform > (&rest args
) (multi-compare '> args nil
'real
))
3530 ;;; We cannot do the inversion for >= and <= here, since both
3531 ;;; (< NaN X) and (> NaN X)
3532 ;;; are false, and we don't have type-inforation available yet. The
3533 ;;; deftransforms for two-argument versions of >= and <= takes care of
3534 ;;; the inversion to > and < when possible.
3535 (define-source-transform <= (&rest args
) (multi-compare '<= args nil
'real
))
3536 (define-source-transform >= (&rest args
) (multi-compare '>= args nil
'real
))
3538 (define-source-transform char
= (&rest args
) (multi-compare 'char
= args nil
3540 (define-source-transform char
< (&rest args
) (multi-compare 'char
< args nil
3542 (define-source-transform char
> (&rest args
) (multi-compare 'char
> args nil
3544 (define-source-transform char
<= (&rest args
) (multi-compare 'char
> args t
3546 (define-source-transform char
>= (&rest args
) (multi-compare 'char
< args t
3549 (define-source-transform char-equal
(&rest args
)
3550 (multi-compare 'sb
!impl
::two-arg-char-equal args nil
'character t
))
3551 (define-source-transform char-lessp
(&rest args
)
3552 (multi-compare 'sb
!impl
::two-arg-char-lessp args nil
'character t
))
3553 (define-source-transform char-greaterp
(&rest args
)
3554 (multi-compare 'sb
!impl
::two-arg-char-greaterp args nil
'character t
))
3555 (define-source-transform char-not-greaterp
(&rest args
)
3556 (multi-compare 'sb
!impl
::two-arg-char-greaterp args t
'character t
))
3557 (define-source-transform char-not-lessp
(&rest args
)
3558 (multi-compare 'sb
!impl
::two-arg-char-lessp args t
'character t
))
3560 ;;; This function does source transformation of N-arg inequality
3561 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3562 ;;; arg cases. If there are more than two args, then we expand into
3563 ;;; the appropriate n^2 comparisons only when speed is important.
3564 (declaim (ftype (function (symbol list t
) *) multi-not-equal
))
3565 (defun multi-not-equal (predicate args type
)
3566 (let ((nargs (length args
)))
3567 (cond ((< nargs
1) (values nil t
))
3568 ((= nargs
1) `(progn (the ,type
,@args
) t
))
3570 `(if (,predicate
,(first args
) ,(second args
)) nil t
))
3571 ((not (policy *lexenv
*
3572 (and (>= speed space
)
3573 (>= speed compilation-speed
))))
3576 (let ((vars (make-gensym-list nargs
)))
3577 (do ((var vars next
)
3578 (next (cdr vars
) (cdr next
))
3581 `((lambda ,vars
(declare (type ,type
,@vars
)) ,result
)
3583 (let ((v1 (first var
)))
3585 (setq result
`(if (,predicate
,v1
,v2
) nil
,result
))))))))))
3587 (define-source-transform /= (&rest args
)
3588 (multi-not-equal '= args
'number
))
3589 (define-source-transform char
/= (&rest args
)
3590 (multi-not-equal 'char
= args
'character
))
3591 (define-source-transform char-not-equal
(&rest args
)
3592 (multi-not-equal 'char-equal args
'character
))
3594 ;;; Expand MAX and MIN into the obvious comparisons.
3595 (define-source-transform max
(arg0 &rest rest
)
3596 (once-only ((arg0 arg0
))
3598 `(values (the real
,arg0
))
3599 `(let ((maxrest (max ,@rest
)))
3600 (if (>= ,arg0 maxrest
) ,arg0 maxrest
)))))
3601 (define-source-transform min
(arg0 &rest rest
)
3602 (once-only ((arg0 arg0
))
3604 `(values (the real
,arg0
))
3605 `(let ((minrest (min ,@rest
)))
3606 (if (<= ,arg0 minrest
) ,arg0 minrest
)))))
3608 ;;;; converting N-arg arithmetic functions
3610 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3611 ;;;; versions, and degenerate cases are flushed.
3613 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3614 (declaim (ftype (function (symbol t list
) list
) associate-args
))
3615 (defun associate-args (function first-arg more-args
)
3616 (let ((next (rest more-args
))
3617 (arg (first more-args
)))
3619 `(,function
,first-arg
,arg
)
3620 (associate-args function
`(,function
,first-arg
,arg
) next
))))
3622 ;;; Do source transformations for transitive functions such as +.
3623 ;;; One-arg cases are replaced with the arg and zero arg cases with
3624 ;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
3625 ;;; ensure (with THE) that the argument in one-argument calls is.
3626 (defun source-transform-transitive (fun args identity
3627 &optional one-arg-result-type
)
3628 (declare (symbol fun
) (list args
))
3631 (1 (if one-arg-result-type
3632 `(values (the ,one-arg-result-type
,(first args
)))
3633 `(values ,(first args
))))
3636 (associate-args fun
(first args
) (rest args
)))))
3638 (define-source-transform + (&rest args
)
3639 (source-transform-transitive '+ args
0 'number
))
3640 (define-source-transform * (&rest args
)
3641 (source-transform-transitive '* args
1 'number
))
3642 (define-source-transform logior
(&rest args
)
3643 (source-transform-transitive 'logior args
0 'integer
))
3644 (define-source-transform logxor
(&rest args
)
3645 (source-transform-transitive 'logxor args
0 'integer
))
3646 (define-source-transform logand
(&rest args
)
3647 (source-transform-transitive 'logand args -
1 'integer
))
3648 (define-source-transform logeqv
(&rest args
)
3649 (source-transform-transitive 'logeqv args -
1 'integer
))
3651 ;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
3652 ;;; because when they are given one argument, they return its absolute
3655 (define-source-transform gcd
(&rest args
)
3658 (1 `(abs (the integer
,(first args
))))
3660 (t (associate-args 'gcd
(first args
) (rest args
)))))
3662 (define-source-transform lcm
(&rest args
)
3665 (1 `(abs (the integer
,(first args
))))
3667 (t (associate-args 'lcm
(first args
) (rest args
)))))
3669 ;;; Do source transformations for intransitive n-arg functions such as
3670 ;;; /. With one arg, we form the inverse. With two args we pass.
3671 ;;; Otherwise we associate into two-arg calls.
3672 (declaim (ftype (function (symbol list t
)
3673 (values list
&optional
(member nil t
)))
3674 source-transform-intransitive
))
3675 (defun source-transform-intransitive (function args inverse
)
3677 ((0 2) (values nil t
))
3678 (1 `(,@inverse
,(first args
)))
3679 (t (associate-args function
(first args
) (rest args
)))))
3681 (define-source-transform -
(&rest args
)
3682 (source-transform-intransitive '- args
'(%negate
)))
3683 (define-source-transform / (&rest args
)
3684 (source-transform-intransitive '/ args
'(/ 1)))
3686 ;;;; transforming APPLY
3688 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3689 ;;; only needs to understand one kind of variable-argument call. It is
3690 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3691 (define-source-transform apply
(fun arg
&rest more-args
)
3692 (let ((args (cons arg more-args
)))
3693 `(multiple-value-call ,fun
3694 ,@(mapcar (lambda (x)
3697 (values-list ,(car (last args
))))))
3699 ;;;; transforming FORMAT
3701 ;;;; If the control string is a compile-time constant, then replace it
3702 ;;;; with a use of the FORMATTER macro so that the control string is
3703 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3704 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3705 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3707 ;;; for compile-time argument count checking.
3709 ;;; FIXME II: In some cases, type information could be correlated; for
3710 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3711 ;;; of a corresponding argument is known and does not intersect the
3712 ;;; list type, a warning could be signalled.
3713 (defun check-format-args (string args fun
)
3714 (declare (type string string
))
3715 (unless (typep string
'simple-string
)
3716 (setq string
(coerce string
'simple-string
)))
3717 (multiple-value-bind (min max
)
3718 (handler-case (sb!format
:%compiler-walk-format-string string args
)
3719 (sb!format
:format-error
(c)
3720 (compiler-warn "~A" c
)))
3722 (let ((nargs (length args
)))
3725 (warn 'format-too-few-args-warning
3727 "Too few arguments (~D) to ~S ~S: requires at least ~D."
3728 :format-arguments
(list nargs fun string min
)))
3730 (warn 'format-too-many-args-warning
3732 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3733 :format-arguments
(list nargs fun string max
))))))))
3735 (defoptimizer (format optimizer
) ((dest control
&rest args
))
3736 (when (constant-lvar-p control
)
3737 (let ((x (lvar-value control
)))
3739 (check-format-args x args
'format
)))))
3741 ;;; We disable this transform in the cross-compiler to save memory in
3742 ;;; the target image; most of the uses of FORMAT in the compiler are for
3743 ;;; error messages, and those don't need to be particularly fast.
3745 (deftransform format
((dest control
&rest args
) (t simple-string
&rest t
) *
3746 :policy
(> speed space
))
3747 (unless (constant-lvar-p control
)
3748 (give-up-ir1-transform "The control string is not a constant."))
3749 (let ((arg-names (make-gensym-list (length args
))))
3750 `(lambda (dest control
,@arg-names
)
3751 (declare (ignore control
))
3752 (format dest
(formatter ,(lvar-value control
)) ,@arg-names
))))
3754 (deftransform format
((stream control
&rest args
) (stream function
&rest t
) *
3755 :policy
(> speed space
))
3756 (let ((arg-names (make-gensym-list (length args
))))
3757 `(lambda (stream control
,@arg-names
)
3758 (funcall control stream
,@arg-names
)
3761 (deftransform format
((tee control
&rest args
) ((member t
) function
&rest t
) *
3762 :policy
(> speed space
))
3763 (let ((arg-names (make-gensym-list (length args
))))
3764 `(lambda (tee control
,@arg-names
)
3765 (declare (ignore tee
))
3766 (funcall control
*standard-output
* ,@arg-names
)
3769 (deftransform pathname
((pathspec) (pathname) *)
3772 (deftransform pathname
((pathspec) (string) *)
3773 '(values (parse-namestring pathspec
)))
3777 `(defoptimizer (,name optimizer
) ((control &rest args
))
3778 (when (constant-lvar-p control
)
3779 (let ((x (lvar-value control
)))
3781 (check-format-args x args
',name
)))))))
3784 #+sb-xc-host
; Only we should be using these
3787 (def compiler-error
)
3789 (def compiler-style-warn
)
3790 (def compiler-notify
)
3791 (def maybe-compiler-notify
)
3794 (defoptimizer (cerror optimizer
) ((report control
&rest args
))
3795 (when (and (constant-lvar-p control
)
3796 (constant-lvar-p report
))
3797 (let ((x (lvar-value control
))
3798 (y (lvar-value report
)))
3799 (when (and (stringp x
) (stringp y
))
3800 (multiple-value-bind (min1 max1
)
3802 (sb!format
:%compiler-walk-format-string x args
)
3803 (sb!format
:format-error
(c)
3804 (compiler-warn "~A" c
)))
3806 (multiple-value-bind (min2 max2
)
3808 (sb!format
:%compiler-walk-format-string y args
)
3809 (sb!format
:format-error
(c)
3810 (compiler-warn "~A" c
)))
3812 (let ((nargs (length args
)))
3814 ((< nargs
(min min1 min2
))
3815 (warn 'format-too-few-args-warning
3817 "Too few arguments (~D) to ~S ~S ~S: ~
3818 requires at least ~D."
3820 (list nargs
'cerror y x
(min min1 min2
))))
3821 ((> nargs
(max max1 max2
))
3822 (warn 'format-too-many-args-warning
3824 "Too many arguments (~D) to ~S ~S ~S: ~
3827 (list nargs
'cerror y x
(max max1 max2
))))))))))))))
3829 (defoptimizer (coerce derive-type
) ((value type
))
3831 ((constant-lvar-p type
)
3832 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
3833 ;; but dealing with the niggle that complex canonicalization gets
3834 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
3836 (let* ((specifier (lvar-value type
))
3837 (result-typeoid (careful-specifier-type specifier
)))
3839 ((null result-typeoid
) nil
)
3840 ((csubtypep result-typeoid
(specifier-type 'number
))
3841 ;; the difficult case: we have to cope with ANSI 12.1.5.3
3842 ;; Rule of Canonical Representation for Complex Rationals,
3843 ;; which is a truly nasty delivery to field.
3845 ((csubtypep result-typeoid
(specifier-type 'real
))
3846 ;; cleverness required here: it would be nice to deduce
3847 ;; that something of type (INTEGER 2 3) coerced to type
3848 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
3849 ;; FLOAT gets its own clause because it's implemented as
3850 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
3853 ((and (numeric-type-p result-typeoid
)
3854 (eq (numeric-type-complexp result-typeoid
) :real
))
3855 ;; FIXME: is this clause (a) necessary or (b) useful?
3857 ((or (csubtypep result-typeoid
3858 (specifier-type '(complex single-float
)))
3859 (csubtypep result-typeoid
3860 (specifier-type '(complex double-float
)))
3862 (csubtypep result-typeoid
3863 (specifier-type '(complex long-float
))))
3864 ;; float complex types are never canonicalized.
3867 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
3868 ;; probably just a COMPLEX or equivalent. So, in that
3869 ;; case, we will return a complex or an object of the
3870 ;; provided type if it's rational:
3871 (type-union result-typeoid
3872 (type-intersection (lvar-type value
)
3873 (specifier-type 'rational
))))))
3874 (t result-typeoid
))))
3876 ;; OK, the result-type argument isn't constant. However, there
3877 ;; are common uses where we can still do better than just
3878 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
3879 ;; where Y is of a known type. See messages on cmucl-imp
3880 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
3881 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
3882 ;; the basis that it's unlikely that other uses are both
3883 ;; time-critical and get to this branch of the COND (non-constant
3884 ;; second argument to COERCE). -- CSR, 2002-12-16
3885 (let ((value-type (lvar-type value
))
3886 (type-type (lvar-type type
)))
3888 ((good-cons-type-p (cons-type)
3889 ;; Make sure the cons-type we're looking at is something
3890 ;; we're prepared to handle which is basically something
3891 ;; that array-element-type can return.
3892 (or (and (member-type-p cons-type
)
3893 (eql 1 (member-type-size cons-type
))
3894 (null (first (member-type-members cons-type
))))
3895 (let ((car-type (cons-type-car-type cons-type
)))
3896 (and (member-type-p car-type
)
3897 (eql 1 (member-type-members car-type
))
3898 (let ((elt (first (member-type-members car-type
))))
3902 (numberp (first elt
)))))
3903 (good-cons-type-p (cons-type-cdr-type cons-type
))))))
3904 (unconsify-type (good-cons-type)
3905 ;; Convert the "printed" respresentation of a cons
3906 ;; specifier into a type specifier. That is, the
3907 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
3908 ;; NULL)) is converted to (SIGNED-BYTE 16).
3909 (cond ((or (null good-cons-type
)
3910 (eq good-cons-type
'null
))
3912 ((and (eq (first good-cons-type
) 'cons
)
3913 (eq (first (second good-cons-type
)) 'member
))
3914 `(,(second (second good-cons-type
))
3915 ,@(unconsify-type (caddr good-cons-type
))))))
3916 (coerceable-p (c-type)
3917 ;; Can the value be coerced to the given type? Coerce is
3918 ;; complicated, so we don't handle every possible case
3919 ;; here---just the most common and easiest cases:
3921 ;; * Any REAL can be coerced to a FLOAT type.
3922 ;; * Any NUMBER can be coerced to a (COMPLEX
3923 ;; SINGLE/DOUBLE-FLOAT).
3925 ;; FIXME I: we should also be able to deal with characters
3928 ;; FIXME II: I'm not sure that anything is necessary
3929 ;; here, at least while COMPLEX is not a specialized
3930 ;; array element type in the system. Reasoning: if
3931 ;; something cannot be coerced to the requested type, an
3932 ;; error will be raised (and so any downstream compiled
3933 ;; code on the assumption of the returned type is
3934 ;; unreachable). If something can, then it will be of
3935 ;; the requested type, because (by assumption) COMPLEX
3936 ;; (and other difficult types like (COMPLEX INTEGER)
3937 ;; aren't specialized types.
3938 (let ((coerced-type c-type
))
3939 (or (and (subtypep coerced-type
'float
)
3940 (csubtypep value-type
(specifier-type 'real
)))
3941 (and (subtypep coerced-type
3942 '(or (complex single-float
)
3943 (complex double-float
)))
3944 (csubtypep value-type
(specifier-type 'number
))))))
3945 (process-types (type)
3946 ;; FIXME: This needs some work because we should be able
3947 ;; to derive the resulting type better than just the
3948 ;; type arg of coerce. That is, if X is (INTEGER 10
3949 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
3950 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
3952 (cond ((member-type-p type
)
3955 (mapc-member-type-members
3957 (if (coerceable-p member
)
3958 (push member members
)
3959 (return-from punt
*universal-type
*)))
3961 (specifier-type `(or ,@members
)))))
3962 ((and (cons-type-p type
)
3963 (good-cons-type-p type
))
3964 (let ((c-type (unconsify-type (type-specifier type
))))
3965 (if (coerceable-p c-type
)
3966 (specifier-type c-type
)
3969 *universal-type
*))))
3970 (cond ((union-type-p type-type
)
3971 (apply #'type-union
(mapcar #'process-types
3972 (union-type-types type-type
))))
3973 ((or (member-type-p type-type
)
3974 (cons-type-p type-type
))
3975 (process-types type-type
))
3977 *universal-type
*)))))))
3979 (defoptimizer (compile derive-type
) ((nameoid function
))
3980 (when (csubtypep (lvar-type nameoid
)
3981 (specifier-type 'null
))
3982 (values-specifier-type '(values function boolean boolean
))))
3984 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
3985 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
3986 ;;; optimizer, above).
3987 (defoptimizer (array-element-type derive-type
) ((array))
3988 (let ((array-type (lvar-type array
)))
3989 (labels ((consify (list)
3992 `(cons (eql ,(car list
)) ,(consify (rest list
)))))
3993 (get-element-type (a)
3995 (type-specifier (array-type-specialized-element-type a
))))
3996 (cond ((eq element-type
'*)
3997 (specifier-type 'type-specifier
))
3998 ((symbolp element-type
)
3999 (make-member-type :members
(list element-type
)))
4000 ((consp element-type
)
4001 (specifier-type (consify element-type
)))
4003 (error "can't understand type ~S~%" element-type
))))))
4004 (cond ((array-type-p array-type
)
4005 (get-element-type array-type
))
4006 ((union-type-p array-type
)
4008 (mapcar #'get-element-type
(union-type-types array-type
))))
4010 *universal-type
*)))))
4012 ;;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4013 ;;; isn't really related to the CMU CL code, since instead of trying
4014 ;;; to generalize the CMU CL code to allow START and END values, this
4015 ;;; code has been written from scratch following Chapter 7 of
4016 ;;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4017 (define-source-transform sb
!impl
::sort-vector
(vector start end predicate key
)
4018 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4019 ;; isn't really related to the CMU CL code, since instead of trying
4020 ;; to generalize the CMU CL code to allow START and END values, this
4021 ;; code has been written from scratch following Chapter 7 of
4022 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4023 `(macrolet ((%index
(x) `(truly-the index
,x
))
4024 (%parent
(i) `(ash ,i -
1))
4025 (%left
(i) `(%index
(ash ,i
1)))
4026 (%right
(i) `(%index
(1+ (ash ,i
1))))
4029 (left (%left i
) (%left i
)))
4030 ((> left current-heap-size
))
4031 (declare (type index i left
))
4032 (let* ((i-elt (%elt i
))
4033 (i-key (funcall keyfun i-elt
))
4034 (left-elt (%elt left
))
4035 (left-key (funcall keyfun left-elt
)))
4036 (multiple-value-bind (large large-elt large-key
)
4037 (if (funcall ,',predicate i-key left-key
)
4038 (values left left-elt left-key
)
4039 (values i i-elt i-key
))
4040 (let ((right (%right i
)))
4041 (multiple-value-bind (largest largest-elt
)
4042 (if (> right current-heap-size
)
4043 (values large large-elt
)
4044 (let* ((right-elt (%elt right
))
4045 (right-key (funcall keyfun right-elt
)))
4046 (if (funcall ,',predicate large-key right-key
)
4047 (values right right-elt
)
4048 (values large large-elt
))))
4049 (cond ((= largest i
)
4052 (setf (%elt i
) largest-elt
4053 (%elt largest
) i-elt
4055 (%sort-vector
(keyfun &optional
(vtype 'vector
))
4056 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4057 ;; trouble getting type inference to
4058 ;; propagate all the way through this
4059 ;; tangled mess of inlining. The TRULY-THE
4060 ;; here works around that. -- WHN
4062 `(aref (truly-the ,',vtype
,',',vector
)
4063 (%index
(+ (%index
,i
) start-1
)))))
4064 (let (;; Heaps prefer 1-based addressing.
4065 (start-1 (1- ,',start
))
4066 (current-heap-size (- ,',end
,',start
))
4068 (declare (type (integer -
1 #.
(1- most-positive-fixnum
))
4070 (declare (type index current-heap-size
))
4071 (declare (type function keyfun
))
4072 (loop for i of-type index
4073 from
(ash current-heap-size -
1) downto
1 do
4076 (when (< current-heap-size
2)
4078 (rotatef (%elt
1) (%elt current-heap-size
))
4079 (decf current-heap-size
)
4081 (if (typep ,vector
'simple-vector
)
4082 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4083 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4085 ;; Special-casing the KEY=NIL case lets us avoid some
4087 (%sort-vector
#'identity simple-vector
)
4088 (%sort-vector
,key simple-vector
))
4089 ;; It's hard to anticipate many speed-critical applications for
4090 ;; sorting vector types other than (VECTOR T), so we just lump
4091 ;; them all together in one slow dynamically typed mess.
4093 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4094 (%sort-vector
(or ,key
#'identity
))))))
4096 ;;;; debuggers' little helpers
4098 ;;; for debugging when transforms are behaving mysteriously,
4099 ;;; e.g. when debugging a problem with an ASH transform
4100 ;;; (defun foo (&optional s)
4101 ;;; (sb-c::/report-lvar s "S outside WHEN")
4102 ;;; (when (and (integerp s) (> s 3))
4103 ;;; (sb-c::/report-lvar s "S inside WHEN")
4104 ;;; (let ((bound (ash 1 (1- s))))
4105 ;;; (sb-c::/report-lvar bound "BOUND")
4106 ;;; (let ((x (- bound))
4108 ;;; (sb-c::/report-lvar x "X")
4109 ;;; (sb-c::/report-lvar x "Y"))
4110 ;;; `(integer ,(- bound) ,(1- bound)))))
4111 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4112 ;;; and the function doesn't do anything at all.)
4115 (defknown /report-lvar
(t t
) null
)
4116 (deftransform /report-lvar
((x message
) (t t
))
4117 (format t
"~%/in /REPORT-LVAR~%")
4118 (format t
"/(LVAR-TYPE X)=~S~%" (lvar-type x
))
4119 (when (constant-lvar-p x
)
4120 (format t
"/(LVAR-VALUE X)=~S~%" (lvar-value x
)))
4121 (format t
"/MESSAGE=~S~%" (lvar-value message
))
4122 (give-up-ir1-transform "not a real transform"))
4123 (defun /report-lvar
(x message
)
4124 (declare (ignore x message
))))
4127 ;;;; Transforms for internal compiler utilities
4129 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4130 ;;; checking that it's still valid at run-time.
4131 (deftransform policy-quality
((policy quality-name
)
4133 (unless (and (constant-lvar-p quality-name
)
4134 (policy-quality-name-p (lvar-value quality-name
)))
4135 (give-up-ir1-transform))
4136 '(%policy-quality policy quality-name
))