1 ;;;; This file contains macro-like source transformations which
2 ;;;; convert uses of certain functions into the canonical form desired
3 ;;;; within the compiler. FIXME: and other IR1 transforms and stuff.
5 ;;;; This software is part of the SBCL system. See the README file for
8 ;;;; This software is derived from the CMU CL system, which was
9 ;;;; written at Carnegie Mellon University and released into the
10 ;;;; public domain. The software is in the public domain and is
11 ;;;; provided with absolutely no warranty. See the COPYING and CREDITS
12 ;;;; files for more information.
16 ;;; Convert into an IF so that IF optimizations will eliminate redundant
18 (define-source-transform not (x) `(if ,x nil t))
19 (define-source-transform null (x) `(if ,x nil t))
21 ;;; ENDP is just NULL with a LIST assertion. The assertion will be
22 ;;; optimized away when SAFETY optimization is low; hopefully that
23 ;;; is consistent with ANSI's "should return an error".
24 (define-source-transform endp (x) `(null (the list ,x)))
26 ;;; We turn IDENTITY into PROG1 so that it is obvious that it just
27 ;;; returns the first value of its argument. Ditto for VALUES with one
29 (define-source-transform identity (x) `(prog1 ,x))
30 (define-source-transform values (x) `(prog1 ,x))
33 ;;; CONSTANTLY is pretty much never worth transforming, but it's good to get the type.
34 (defoptimizer (constantly derive-type) ((value))
36 `(function (&rest t) (values ,(type-specifier (lvar-type value)) &optional))))
38 ;;; If the function has a known number of arguments, then return a
39 ;;; lambda with the appropriate fixed number of args. If the
40 ;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
41 ;;; MV optimization figure things out.
42 (deftransform complement ((fun) * * :node node)
44 (multiple-value-bind (min max)
45 (fun-type-nargs (lvar-type fun))
47 ((and min (eql min max))
48 (let ((dums (make-gensym-list min)))
49 `#'(lambda ,dums (not (funcall fun ,@dums)))))
50 ((awhen (node-lvar node)
51 (let ((dest (lvar-dest it)))
52 (and (combination-p dest)
53 (eq (combination-fun dest) it))))
54 '#'(lambda (&rest args)
55 (not (apply fun args))))
57 (give-up-ir1-transform
58 "The function doesn't have a fixed argument count.")))))
61 (defun derive-symbol-value-type (lvar node)
62 (if (constant-lvar-p lvar)
63 (let* ((sym (lvar-value lvar))
64 (var (maybe-find-free-var sym))
66 (let ((*lexenv* (node-lexenv node)))
67 (lexenv-find var type-restrictions))))
68 (global-type (info :variable :type sym)))
70 (type-intersection local-type global-type)
74 (defoptimizer (symbol-value derive-type) ((symbol) node)
75 (derive-symbol-value-type symbol node))
77 (defoptimizer (symbol-global-value derive-type) ((symbol) node)
78 (derive-symbol-value-type symbol node))
82 ;;; Translate CxR into CAR/CDR combos.
83 (defun source-transform-cxr (form)
84 (if (/= (length form) 2)
86 (let* ((name (car form))
90 (leaf (leaf-source-name name))))))
91 (do ((i (- (length string) 2) (1- i))
93 `(,(ecase (char string i)
99 ;;; Make source transforms to turn CxR forms into combinations of CAR
100 ;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
102 (/show0 "about to set CxR source transforms")
103 (loop for i of-type index from 2 upto 4 do
104 ;; Iterate over BUF = all names CxR where x = an I-element
105 ;; string of #\A or #\D characters.
106 (let ((buf (make-string (+ 2 i))))
107 (setf (aref buf 0) #\C
108 (aref buf (1+ i)) #\R)
109 (dotimes (j (ash 2 i))
110 (declare (type index j))
112 (declare (type index k))
113 (setf (aref buf (1+ k))
114 (if (logbitp k j) #\A #\D)))
115 (setf (info :function :source-transform (intern buf))
116 #'source-transform-cxr))))
117 (/show0 "done setting CxR source transforms")
119 ;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
120 ;;; whatever is right for them is right for us. FIFTH..TENTH turn into
121 ;;; Nth, which can be expanded into a CAR/CDR later on if policy
123 (define-source-transform first (x) `(car ,x))
124 (define-source-transform rest (x) `(cdr ,x))
125 (define-source-transform second (x) `(cadr ,x))
126 (define-source-transform third (x) `(caddr ,x))
127 (define-source-transform fourth (x) `(cadddr ,x))
128 (define-source-transform fifth (x) `(nth 4 ,x))
129 (define-source-transform sixth (x) `(nth 5 ,x))
130 (define-source-transform seventh (x) `(nth 6 ,x))
131 (define-source-transform eighth (x) `(nth 7 ,x))
132 (define-source-transform ninth (x) `(nth 8 ,x))
133 (define-source-transform tenth (x) `(nth 9 ,x))
135 ;;; LIST with one arg is an extremely common operation (at least inside
136 ;;; SBCL itself); translate it to CONS to take advantage of common
137 ;;; allocation routines.
138 (define-source-transform list (&rest args)
140 (1 `(cons ,(first args) nil))
143 ;;; And similarly for LIST*.
144 (define-source-transform list* (arg &rest others)
145 (cond ((not others) arg)
146 ((not (cdr others)) `(cons ,arg ,(car others)))
149 (defoptimizer (list* derive-type) ((arg &rest args))
151 (specifier-type 'cons)
154 ;;; Translate RPLACx to LET and SETF.
155 (define-source-transform rplaca (x y)
160 (define-source-transform rplacd (x y)
166 (define-source-transform nth (n l) `(car (nthcdr ,n ,l)))
168 (deftransform last ((list &optional n) (t &optional t))
169 (let ((c (constant-lvar-p n)))
171 (and c (eql 1 (lvar-value n))))
173 ((and c (eql 0 (lvar-value n)))
176 (let ((type (lvar-type n)))
177 (cond ((csubtypep type (specifier-type 'fixnum))
178 '(%lastn/fixnum list n))
179 ((csubtypep type (specifier-type 'bignum))
180 '(%lastn/bignum list n))
182 (give-up-ir1-transform "second argument type too vague"))))))))
184 (define-source-transform gethash (&rest args)
186 (2 `(sb!impl::gethash3 ,@args nil))
187 (3 `(sb!impl::gethash3 ,@args))
189 (define-source-transform get (&rest args)
191 (2 `(sb!impl::get2 ,@args))
192 (3 `(sb!impl::get3 ,@args))
195 (defvar *default-nthcdr-open-code-limit* 6)
196 (defvar *extreme-nthcdr-open-code-limit* 20)
198 (deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
199 "convert NTHCDR to CAxxR"
200 (unless (constant-lvar-p n)
201 (give-up-ir1-transform))
202 (let ((n (lvar-value n)))
204 (if (policy node (and (= speed 3) (= space 0)))
205 *extreme-nthcdr-open-code-limit*
206 *default-nthcdr-open-code-limit*))
207 (give-up-ir1-transform))
212 `(cdr ,(frob (1- n))))))
215 ;;;; arithmetic and numerology
217 (define-source-transform plusp (x) `(> ,x 0))
218 (define-source-transform minusp (x) `(< ,x 0))
219 (define-source-transform zerop (x) `(= ,x 0))
221 (define-source-transform 1+ (x) `(+ ,x 1))
222 (define-source-transform 1- (x) `(- ,x 1))
224 (define-source-transform oddp (x) `(logtest ,x 1))
225 (define-source-transform evenp (x) `(not (logtest ,x 1)))
227 ;;; Note that all the integer division functions are available for
228 ;;; inline expansion.
230 (macrolet ((deffrob (fun)
231 `(define-source-transform ,fun (x &optional (y nil y-p))
238 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
240 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
243 ;;; This used to be a source transform (hence the lack of restrictions
244 ;;; on the argument types), but we make it a regular transform so that
245 ;;; the VM has a chance to see the bare LOGTEST and potentiall choose
246 ;;; to implement it differently. --njf, 06-02-2006
247 (deftransform logtest ((x y) * *)
248 `(not (zerop (logand x y))))
250 (deftransform logbitp
251 ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits)
252 (unsigned-byte #.sb!vm:n-word-bits))))
253 `(if (>= index #.sb!vm:n-word-bits)
255 (not (zerop (logand integer (ash 1 index))))))
257 (define-source-transform byte (size position)
258 `(cons ,size ,position))
259 (define-source-transform byte-size (spec) `(car ,spec))
260 (define-source-transform byte-position (spec) `(cdr ,spec))
261 (define-source-transform ldb-test (bytespec integer)
262 `(not (zerop (mask-field ,bytespec ,integer))))
264 ;;; With the ratio and complex accessors, we pick off the "identity"
265 ;;; case, and use a primitive to handle the cell access case.
266 (define-source-transform numerator (num)
267 (once-only ((n-num `(the rational ,num)))
271 (define-source-transform denominator (num)
272 (once-only ((n-num `(the rational ,num)))
274 (%denominator ,n-num)
277 ;;;; interval arithmetic for computing bounds
279 ;;;; This is a set of routines for operating on intervals. It
280 ;;;; implements a simple interval arithmetic package. Although SBCL
281 ;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
282 ;;;; for two reasons:
284 ;;;; 1. This package is simpler than NUMERIC-TYPE.
286 ;;;; 2. It makes debugging much easier because you can just strip
287 ;;;; out these routines and test them independently of SBCL. (This is a
290 ;;;; One disadvantage is a probable increase in consing because we
291 ;;;; have to create these new interval structures even though
292 ;;;; numeric-type has everything we want to know. Reason 2 wins for
295 ;;; Support operations that mimic real arithmetic comparison
296 ;;; operators, but imposing a total order on the floating points such
297 ;;; that negative zeros are strictly less than positive zeros.
298 (macrolet ((def (name op)
301 (if (and (floatp x) (floatp y) (zerop x) (zerop y))
302 (,op (float-sign x) (float-sign y))
304 (def signed-zero->= >=)
305 (def signed-zero-> >)
306 (def signed-zero-= =)
307 (def signed-zero-< <)
308 (def signed-zero-<= <=))
310 ;;; The basic interval type. It can handle open and closed intervals.
311 ;;; A bound is open if it is a list containing a number, just like
312 ;;; Lisp says. NIL means unbounded.
313 (defstruct (interval (:constructor %make-interval)
317 (defun make-interval (&key low high)
318 (labels ((normalize-bound (val)
321 (float-infinity-p val))
322 ;; Handle infinities.
326 ;; Handle any closed bounds.
329 ;; We have an open bound. Normalize the numeric
330 ;; bound. If the normalized bound is still a number
331 ;; (not nil), keep the bound open. Otherwise, the
332 ;; bound is really unbounded, so drop the openness.
333 (let ((new-val (normalize-bound (first val))))
335 ;; The bound exists, so keep it open still.
338 (error "unknown bound type in MAKE-INTERVAL")))))
339 (%make-interval :low (normalize-bound low)
340 :high (normalize-bound high))))
342 ;;; Given a number X, create a form suitable as a bound for an
343 ;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
344 #!-sb-fluid (declaim (inline set-bound))
345 (defun set-bound (x open-p)
346 (if (and x open-p) (list x) x))
348 ;;; Apply the function F to a bound X. If X is an open bound, then
349 ;;; the result will be open. IF X is NIL, the result is NIL.
350 (defun bound-func (f x)
351 (declare (type function f))
353 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
354 ;; With these traps masked, we might get things like infinity
355 ;; or negative infinity returned. Check for this and return
356 ;; NIL to indicate unbounded.
357 (let ((y (funcall f (type-bound-number x))))
359 (float-infinity-p y))
361 (set-bound y (consp x)))))))
363 (defun safe-double-coercion-p (x)
364 (or (typep x 'double-float)
365 (<= most-negative-double-float x most-positive-double-float)))
367 (defun safe-single-coercion-p (x)
368 (or (typep x 'single-float)
369 ;; Fix for bug 420, and related issues: during type derivation we often
370 ;; end up deriving types for both
372 ;; (some-op <int> <single>)
374 ;; (some-op (coerce <int> 'single-float) <single>)
376 ;; or other equivalent transformed forms. The problem with this is that
377 ;; on some platforms like x86 (+ <int> <single>) is on the machine level
380 ;; (coerce (+ (coerce <int> 'double-float)
381 ;; (coerce <single> 'double-float))
384 ;; so if the result of (coerce <int> 'single-float) is not exact, the
385 ;; derived types for the transformed forms will have an empty
386 ;; intersection -- which in turn means that the compiler will conclude
387 ;; that the call never returns, and all hell breaks lose when it *does*
388 ;; return at runtime. (This affects not just +, but other operators are
390 (and (not (typep x `(or (integer * (,most-negative-exactly-single-float-fixnum))
391 (integer (,most-positive-exactly-single-float-fixnum) *))))
392 (<= most-negative-single-float x most-positive-single-float))))
394 ;;; Apply a binary operator OP to two bounds X and Y. The result is
395 ;;; NIL if either is NIL. Otherwise bound is computed and the result
396 ;;; is open if either X or Y is open.
398 ;;; FIXME: only used in this file, not needed in target runtime
400 ;;; ANSI contaigon specifies coercion to floating point if one of the
401 ;;; arguments is floating point. Here we should check to be sure that
402 ;;; the other argument is within the bounds of that floating point
405 (defmacro safely-binop (op x y)
407 ((typep ,x 'double-float)
408 (when (safe-double-coercion-p ,y)
410 ((typep ,y 'double-float)
411 (when (safe-double-coercion-p ,x)
413 ((typep ,x 'single-float)
414 (when (safe-single-coercion-p ,y)
416 ((typep ,y 'single-float)
417 (when (safe-single-coercion-p ,x)
421 (defmacro bound-binop (op x y)
423 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
424 (set-bound (safely-binop ,op (type-bound-number ,x)
425 (type-bound-number ,y))
426 (or (consp ,x) (consp ,y))))))
428 (defun coerce-for-bound (val type)
430 (list (coerce-for-bound (car val) type))
432 ((subtypep type 'double-float)
433 (if (<= most-negative-double-float val most-positive-double-float)
435 ((or (subtypep type 'single-float) (subtypep type 'float))
436 ;; coerce to float returns a single-float
437 (if (<= most-negative-single-float val most-positive-single-float)
439 (t (coerce val type)))))
441 (defun coerce-and-truncate-floats (val type)
444 (list (coerce-and-truncate-floats (car val) type))
446 ((subtypep type 'double-float)
447 (if (<= most-negative-double-float val most-positive-double-float)
449 (if (< val most-negative-double-float)
450 most-negative-double-float most-positive-double-float)))
451 ((or (subtypep type 'single-float) (subtypep type 'float))
452 ;; coerce to float returns a single-float
453 (if (<= most-negative-single-float val most-positive-single-float)
455 (if (< val most-negative-single-float)
456 most-negative-single-float most-positive-single-float)))
457 (t (coerce val type))))))
459 ;;; Convert a numeric-type object to an interval object.
460 (defun numeric-type->interval (x)
461 (declare (type numeric-type x))
462 (make-interval :low (numeric-type-low x)
463 :high (numeric-type-high x)))
465 (defun type-approximate-interval (type)
466 (declare (type ctype type))
467 (let ((types (prepare-arg-for-derive-type type))
470 (let ((type (if (member-type-p type)
471 (convert-member-type type)
473 (unless (numeric-type-p type)
474 (return-from type-approximate-interval nil))
475 (let ((interval (numeric-type->interval type)))
478 (interval-approximate-union result interval)
482 (defun copy-interval-limit (limit)
487 (defun copy-interval (x)
488 (declare (type interval x))
489 (make-interval :low (copy-interval-limit (interval-low x))
490 :high (copy-interval-limit (interval-high x))))
492 ;;; Given a point P contained in the interval X, split X into two
493 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
494 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
495 ;;; contains P. You can specify both to be T or NIL.
496 (defun interval-split (p x &optional close-lower close-upper)
497 (declare (type number p)
499 (list (make-interval :low (copy-interval-limit (interval-low x))
500 :high (if close-lower p (list p)))
501 (make-interval :low (if close-upper (list p) p)
502 :high (copy-interval-limit (interval-high x)))))
504 ;;; Return the closure of the interval. That is, convert open bounds
505 ;;; to closed bounds.
506 (defun interval-closure (x)
507 (declare (type interval x))
508 (make-interval :low (type-bound-number (interval-low x))
509 :high (type-bound-number (interval-high x))))
511 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
512 ;;; '-. Otherwise return NIL.
513 (defun interval-range-info (x &optional (point 0))
514 (declare (type interval x))
515 (let ((lo (interval-low x))
516 (hi (interval-high x)))
517 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
519 ((and hi (signed-zero->= point (type-bound-number hi)))
524 ;;; Test to see whether the interval X is bounded. HOW determines the
525 ;;; test, and should be either ABOVE, BELOW, or BOTH.
526 (defun interval-bounded-p (x how)
527 (declare (type interval x))
534 (and (interval-low x) (interval-high x)))))
536 ;;; See whether the interval X contains the number P, taking into
537 ;;; account that the interval might not be closed.
538 (defun interval-contains-p (p x)
539 (declare (type number p)
541 ;; Does the interval X contain the number P? This would be a lot
542 ;; easier if all intervals were closed!
543 (let ((lo (interval-low x))
544 (hi (interval-high x)))
546 ;; The interval is bounded
547 (if (and (signed-zero-<= (type-bound-number lo) p)
548 (signed-zero-<= p (type-bound-number hi)))
549 ;; P is definitely in the closure of the interval.
550 ;; We just need to check the end points now.
551 (cond ((signed-zero-= p (type-bound-number lo))
553 ((signed-zero-= p (type-bound-number hi))
558 ;; Interval with upper bound
559 (if (signed-zero-< p (type-bound-number hi))
561 (and (numberp hi) (signed-zero-= p hi))))
563 ;; Interval with lower bound
564 (if (signed-zero-> p (type-bound-number lo))
566 (and (numberp lo) (signed-zero-= p lo))))
568 ;; Interval with no bounds
571 ;;; Determine whether two intervals X and Y intersect. Return T if so.
572 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
573 ;;; were closed. Otherwise the intervals are treated as they are.
575 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
576 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
577 ;;; is T, then they do intersect because we use the closure of X = [0,
578 ;;; 1] and Y = [1, 2] to determine intersection.
579 (defun interval-intersect-p (x y &optional closed-intervals-p)
580 (declare (type interval x y))
581 (and (interval-intersection/difference (if closed-intervals-p
584 (if closed-intervals-p
589 ;;; Are the two intervals adjacent? That is, is there a number
590 ;;; between the two intervals that is not an element of either
591 ;;; interval? If so, they are not adjacent. For example [0, 1) and
592 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
593 ;;; between both intervals.
594 (defun interval-adjacent-p (x y)
595 (declare (type interval x y))
596 (flet ((adjacent (lo hi)
597 ;; Check to see whether lo and hi are adjacent. If either is
598 ;; nil, they can't be adjacent.
599 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
600 ;; The bounds are equal. They are adjacent if one of
601 ;; them is closed (a number). If both are open (consp),
602 ;; then there is a number that lies between them.
603 (or (numberp lo) (numberp hi)))))
604 (or (adjacent (interval-low y) (interval-high x))
605 (adjacent (interval-low x) (interval-high y)))))
607 ;;; Compute the intersection and difference between two intervals.
608 ;;; Two values are returned: the intersection and the difference.
610 ;;; Let the two intervals be X and Y, and let I and D be the two
611 ;;; values returned by this function. Then I = X intersect Y. If I
612 ;;; is NIL (the empty set), then D is X union Y, represented as the
613 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
614 ;;; - I, which is a list of two intervals.
616 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
617 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
618 (defun interval-intersection/difference (x y)
619 (declare (type interval x y))
620 (let ((x-lo (interval-low x))
621 (x-hi (interval-high x))
622 (y-lo (interval-low y))
623 (y-hi (interval-high y)))
626 ;; If p is an open bound, make it closed. If p is a closed
627 ;; bound, make it open.
631 (test-number (p int bound)
632 ;; Test whether P is in the interval.
633 (let ((pn (type-bound-number p)))
634 (when (interval-contains-p pn (interval-closure int))
635 ;; Check for endpoints.
636 (let* ((lo (interval-low int))
637 (hi (interval-high int))
638 (lon (type-bound-number lo))
639 (hin (type-bound-number hi)))
641 ;; Interval may be a point.
642 ((and lon hin (= lon hin pn))
643 (and (numberp p) (numberp lo) (numberp hi)))
644 ;; Point matches the low end.
645 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
646 ;; (P [P,?} => TRUE P) [P,?} => FALSE
647 ;; (P (P,?} => TRUE P) (P,?} => FALSE
648 ((and lon (= pn lon))
649 (or (and (numberp p) (numberp lo))
650 (and (consp p) (eq :low bound))))
651 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
652 ;; P) {?,P] => TRUE (P {?,P] => FALSE
653 ;; P) {?,P) => TRUE (P {?,P) => FALSE
654 ((and hin (= pn hin))
655 (or (and (numberp p) (numberp hi))
656 (and (consp p) (eq :high bound))))
657 ;; Not an endpoint, all is well.
660 (test-lower-bound (p int)
661 ;; P is a lower bound of an interval.
663 (test-number p int :low)
664 (not (interval-bounded-p int 'below))))
665 (test-upper-bound (p int)
666 ;; P is an upper bound of an interval.
668 (test-number p int :high)
669 (not (interval-bounded-p int 'above)))))
670 (let ((x-lo-in-y (test-lower-bound x-lo y))
671 (x-hi-in-y (test-upper-bound x-hi y))
672 (y-lo-in-x (test-lower-bound y-lo x))
673 (y-hi-in-x (test-upper-bound y-hi x)))
674 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
675 ;; Intervals intersect. Let's compute the intersection
676 ;; and the difference.
677 (multiple-value-bind (lo left-lo left-hi)
678 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
679 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
680 (multiple-value-bind (hi right-lo right-hi)
682 (values x-hi (opposite-bound x-hi) y-hi))
684 (values y-hi (opposite-bound y-hi) x-hi)))
685 (values (make-interval :low lo :high hi)
686 (list (make-interval :low left-lo
688 (make-interval :low right-lo
691 (values nil (list x y))))))))
693 ;;; If intervals X and Y intersect, return a new interval that is the
694 ;;; union of the two. If they do not intersect, return NIL.
695 (defun interval-merge-pair (x y)
696 (declare (type interval x y))
697 ;; If x and y intersect or are adjacent, create the union.
698 ;; Otherwise return nil
699 (when (or (interval-intersect-p x y)
700 (interval-adjacent-p x y))
701 (flet ((select-bound (x1 x2 min-op max-op)
702 (let ((x1-val (type-bound-number x1))
703 (x2-val (type-bound-number x2)))
705 ;; Both bounds are finite. Select the right one.
706 (cond ((funcall min-op x1-val x2-val)
707 ;; x1 is definitely better.
709 ((funcall max-op x1-val x2-val)
710 ;; x2 is definitely better.
713 ;; Bounds are equal. Select either
714 ;; value and make it open only if
716 (set-bound x1-val (and (consp x1) (consp x2))))))
718 ;; At least one bound is not finite. The
719 ;; non-finite bound always wins.
721 (let* ((x-lo (copy-interval-limit (interval-low x)))
722 (x-hi (copy-interval-limit (interval-high x)))
723 (y-lo (copy-interval-limit (interval-low y)))
724 (y-hi (copy-interval-limit (interval-high y))))
725 (make-interval :low (select-bound x-lo y-lo #'< #'>)
726 :high (select-bound x-hi y-hi #'> #'<))))))
728 ;;; return the minimal interval, containing X and Y
729 (defun interval-approximate-union (x y)
730 (cond ((interval-merge-pair x y))
732 (make-interval :low (copy-interval-limit (interval-low x))
733 :high (copy-interval-limit (interval-high y))))
735 (make-interval :low (copy-interval-limit (interval-low y))
736 :high (copy-interval-limit (interval-high x))))))
738 ;;; basic arithmetic operations on intervals. We probably should do
739 ;;; true interval arithmetic here, but it's complicated because we
740 ;;; have float and integer types and bounds can be open or closed.
742 ;;; the negative of an interval
743 (defun interval-neg (x)
744 (declare (type interval x))
745 (make-interval :low (bound-func #'- (interval-high x))
746 :high (bound-func #'- (interval-low x))))
748 ;;; Add two intervals.
749 (defun interval-add (x y)
750 (declare (type interval x y))
751 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
752 :high (bound-binop + (interval-high x) (interval-high y))))
754 ;;; Subtract two intervals.
755 (defun interval-sub (x y)
756 (declare (type interval x y))
757 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
758 :high (bound-binop - (interval-high x) (interval-low y))))
760 ;;; Multiply two intervals.
761 (defun interval-mul (x y)
762 (declare (type interval x y))
763 (flet ((bound-mul (x y)
764 (cond ((or (null x) (null y))
765 ;; Multiply by infinity is infinity
767 ((or (and (numberp x) (zerop x))
768 (and (numberp y) (zerop y)))
769 ;; Multiply by closed zero is special. The result
770 ;; is always a closed bound. But don't replace this
771 ;; with zero; we want the multiplication to produce
772 ;; the correct signed zero, if needed. Use SIGNUM
773 ;; to avoid trying to multiply huge bignums with 0.0.
774 (* (signum (type-bound-number x)) (signum (type-bound-number y))))
775 ((or (and (floatp x) (float-infinity-p x))
776 (and (floatp y) (float-infinity-p y)))
777 ;; Infinity times anything is infinity
780 ;; General multiply. The result is open if either is open.
781 (bound-binop * x y)))))
782 (let ((x-range (interval-range-info x))
783 (y-range (interval-range-info y)))
784 (cond ((null x-range)
785 ;; Split x into two and multiply each separately
786 (destructuring-bind (x- x+) (interval-split 0 x t t)
787 (interval-merge-pair (interval-mul x- y)
788 (interval-mul x+ y))))
790 ;; Split y into two and multiply each separately
791 (destructuring-bind (y- y+) (interval-split 0 y t t)
792 (interval-merge-pair (interval-mul x y-)
793 (interval-mul x y+))))
795 (interval-neg (interval-mul (interval-neg x) y)))
797 (interval-neg (interval-mul x (interval-neg y))))
798 ((and (eq x-range '+) (eq y-range '+))
799 ;; If we are here, X and Y are both positive.
801 :low (bound-mul (interval-low x) (interval-low y))
802 :high (bound-mul (interval-high x) (interval-high y))))
804 (bug "excluded case in INTERVAL-MUL"))))))
806 ;;; Divide two intervals.
807 (defun interval-div (top bot)
808 (declare (type interval top bot))
809 (flet ((bound-div (x y y-low-p)
812 ;; Divide by infinity means result is 0. However,
813 ;; we need to watch out for the sign of the result,
814 ;; to correctly handle signed zeros. We also need
815 ;; to watch out for positive or negative infinity.
816 (if (floatp (type-bound-number x))
818 (- (float-sign (type-bound-number x) 0.0))
819 (float-sign (type-bound-number x) 0.0))
821 ((zerop (type-bound-number y))
822 ;; Divide by zero means result is infinity
824 ((and (numberp x) (zerop x))
825 ;; Zero divided by anything is zero.
828 (bound-binop / x y)))))
829 (let ((top-range (interval-range-info top))
830 (bot-range (interval-range-info bot)))
831 (cond ((null bot-range)
832 ;; The denominator contains zero, so anything goes!
833 (make-interval :low nil :high nil))
835 ;; Denominator is negative so flip the sign, compute the
836 ;; result, and flip it back.
837 (interval-neg (interval-div top (interval-neg bot))))
839 ;; Split top into two positive and negative parts, and
840 ;; divide each separately
841 (destructuring-bind (top- top+) (interval-split 0 top t t)
842 (interval-merge-pair (interval-div top- bot)
843 (interval-div top+ bot))))
845 ;; Top is negative so flip the sign, divide, and flip the
846 ;; sign of the result.
847 (interval-neg (interval-div (interval-neg top) bot)))
848 ((and (eq top-range '+) (eq bot-range '+))
851 :low (bound-div (interval-low top) (interval-high bot) t)
852 :high (bound-div (interval-high top) (interval-low bot) nil)))
854 (bug "excluded case in INTERVAL-DIV"))))))
856 ;;; Apply the function F to the interval X. If X = [a, b], then the
857 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
858 ;;; result makes sense. It will if F is monotonic increasing (or
860 (defun interval-func (f x)
861 (declare (type function f)
863 (let ((lo (bound-func f (interval-low x)))
864 (hi (bound-func f (interval-high x))))
865 (make-interval :low lo :high hi)))
867 ;;; Return T if X < Y. That is every number in the interval X is
868 ;;; always less than any number in the interval Y.
869 (defun interval-< (x y)
870 (declare (type interval x y))
871 ;; X < Y only if X is bounded above, Y is bounded below, and they
873 (when (and (interval-bounded-p x 'above)
874 (interval-bounded-p y 'below))
875 ;; Intervals are bounded in the appropriate way. Make sure they
877 (let ((left (interval-high x))
878 (right (interval-low y)))
879 (cond ((> (type-bound-number left)
880 (type-bound-number right))
881 ;; The intervals definitely overlap, so result is NIL.
883 ((< (type-bound-number left)
884 (type-bound-number right))
885 ;; The intervals definitely don't touch, so result is T.
888 ;; Limits are equal. Check for open or closed bounds.
889 ;; Don't overlap if one or the other are open.
890 (or (consp left) (consp right)))))))
892 ;;; Return T if X >= Y. That is, every number in the interval X is
893 ;;; always greater than any number in the interval Y.
894 (defun interval->= (x y)
895 (declare (type interval x y))
896 ;; X >= Y if lower bound of X >= upper bound of Y
897 (when (and (interval-bounded-p x 'below)
898 (interval-bounded-p y 'above))
899 (>= (type-bound-number (interval-low x))
900 (type-bound-number (interval-high y)))))
902 ;;; Return T if X = Y.
903 (defun interval-= (x y)
904 (declare (type interval x y))
905 (and (interval-bounded-p x 'both)
906 (interval-bounded-p y 'both)
910 ;; Open intervals cannot be =
911 (return-from interval-= nil))))
912 ;; Both intervals refer to the same point
913 (= (bound (interval-high x)) (bound (interval-low x))
914 (bound (interval-high y)) (bound (interval-low y))))))
916 ;;; Return T if X /= Y
917 (defun interval-/= (x y)
918 (not (interval-intersect-p x y)))
920 ;;; Return an interval that is the absolute value of X. Thus, if
921 ;;; X = [-1 10], the result is [0, 10].
922 (defun interval-abs (x)
923 (declare (type interval x))
924 (case (interval-range-info x)
930 (destructuring-bind (x- x+) (interval-split 0 x t t)
931 (interval-merge-pair (interval-neg x-) x+)))))
933 ;;; Compute the square of an interval.
934 (defun interval-sqr (x)
935 (declare (type interval x))
936 (interval-func (lambda (x) (* x x))
939 ;;;; numeric DERIVE-TYPE methods
941 ;;; a utility for defining derive-type methods of integer operations. If
942 ;;; the types of both X and Y are integer types, then we compute a new
943 ;;; integer type with bounds determined Fun when applied to X and Y.
944 ;;; Otherwise, we use NUMERIC-CONTAGION.
945 (defun derive-integer-type-aux (x y fun)
946 (declare (type function fun))
947 (if (and (numeric-type-p x) (numeric-type-p y)
948 (eq (numeric-type-class x) 'integer)
949 (eq (numeric-type-class y) 'integer)
950 (eq (numeric-type-complexp x) :real)
951 (eq (numeric-type-complexp y) :real))
952 (multiple-value-bind (low high) (funcall fun x y)
953 (make-numeric-type :class 'integer
957 (numeric-contagion x y)))
959 (defun derive-integer-type (x y fun)
960 (declare (type lvar x y) (type function fun))
961 (let ((x (lvar-type x))
963 (derive-integer-type-aux x y fun)))
965 ;;; simple utility to flatten a list
966 (defun flatten-list (x)
967 (labels ((flatten-and-append (tree list)
968 (cond ((null tree) list)
969 ((atom tree) (cons tree list))
970 (t (flatten-and-append
971 (car tree) (flatten-and-append (cdr tree) list))))))
972 (flatten-and-append x nil)))
974 ;;; Take some type of lvar and massage it so that we get a list of the
975 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
977 (defun prepare-arg-for-derive-type (arg)
978 (flet ((listify (arg)
983 (union-type-types arg))
986 (unless (eq arg *empty-type*)
987 ;; Make sure all args are some type of numeric-type. For member
988 ;; types, convert the list of members into a union of equivalent
989 ;; single-element member-type's.
990 (let ((new-args nil))
991 (dolist (arg (listify arg))
992 (if (member-type-p arg)
993 ;; Run down the list of members and convert to a list of
995 (mapc-member-type-members
997 (push (if (numberp member)
998 (make-member-type :members (list member))
1002 (push arg new-args)))
1003 (unless (member *empty-type* new-args)
1006 ;;; Convert from the standard type convention for which -0.0 and 0.0
1007 ;;; are equal to an intermediate convention for which they are
1008 ;;; considered different which is more natural for some of the
1010 (defun convert-numeric-type (type)
1011 (declare (type numeric-type type))
1012 ;;; Only convert real float interval delimiters types.
1013 (if (eq (numeric-type-complexp type) :real)
1014 (let* ((lo (numeric-type-low type))
1015 (lo-val (type-bound-number lo))
1016 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
1017 (hi (numeric-type-high type))
1018 (hi-val (type-bound-number hi))
1019 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
1020 (if (or lo-float-zero-p hi-float-zero-p)
1022 :class (numeric-type-class type)
1023 :format (numeric-type-format type)
1025 :low (if lo-float-zero-p
1027 (list (float 0.0 lo-val))
1028 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
1030 :high (if hi-float-zero-p
1032 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
1039 ;;; Convert back from the intermediate convention for which -0.0 and
1040 ;;; 0.0 are considered different to the standard type convention for
1041 ;;; which and equal.
1042 (defun convert-back-numeric-type (type)
1043 (declare (type numeric-type type))
1044 ;;; Only convert real float interval delimiters types.
1045 (if (eq (numeric-type-complexp type) :real)
1046 (let* ((lo (numeric-type-low type))
1047 (lo-val (type-bound-number lo))
1049 (and lo (floatp lo-val) (= lo-val 0.0)
1050 (float-sign lo-val)))
1051 (hi (numeric-type-high type))
1052 (hi-val (type-bound-number hi))
1054 (and hi (floatp hi-val) (= hi-val 0.0)
1055 (float-sign hi-val))))
1057 ;; (float +0.0 +0.0) => (member 0.0)
1058 ;; (float -0.0 -0.0) => (member -0.0)
1059 ((and lo-float-zero-p hi-float-zero-p)
1060 ;; shouldn't have exclusive bounds here..
1061 (aver (and (not (consp lo)) (not (consp hi))))
1062 (if (= lo-float-zero-p hi-float-zero-p)
1063 ;; (float +0.0 +0.0) => (member 0.0)
1064 ;; (float -0.0 -0.0) => (member -0.0)
1065 (specifier-type `(member ,lo-val))
1066 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1067 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1068 (make-numeric-type :class (numeric-type-class type)
1069 :format (numeric-type-format type)
1075 ;; (float -0.0 x) => (float 0.0 x)
1076 ((and (not (consp lo)) (minusp lo-float-zero-p))
1077 (make-numeric-type :class (numeric-type-class type)
1078 :format (numeric-type-format type)
1080 :low (float 0.0 lo-val)
1082 ;; (float (+0.0) x) => (float (0.0) x)
1083 ((and (consp lo) (plusp lo-float-zero-p))
1084 (make-numeric-type :class (numeric-type-class type)
1085 :format (numeric-type-format type)
1087 :low (list (float 0.0 lo-val))
1090 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1091 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1092 (list (make-member-type :members (list (float 0.0 lo-val)))
1093 (make-numeric-type :class (numeric-type-class type)
1094 :format (numeric-type-format type)
1096 :low (list (float 0.0 lo-val))
1100 ;; (float x +0.0) => (float x 0.0)
1101 ((and (not (consp hi)) (plusp hi-float-zero-p))
1102 (make-numeric-type :class (numeric-type-class type)
1103 :format (numeric-type-format type)
1106 :high (float 0.0 hi-val)))
1107 ;; (float x (-0.0)) => (float x (0.0))
1108 ((and (consp hi) (minusp hi-float-zero-p))
1109 (make-numeric-type :class (numeric-type-class type)
1110 :format (numeric-type-format type)
1113 :high (list (float 0.0 hi-val))))
1115 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1116 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1117 (list (make-member-type :members (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val)))
1118 (make-numeric-type :class (numeric-type-class type)
1119 :format (numeric-type-format type)
1122 :high (list (float 0.0 hi-val)))))))
1128 ;;; Convert back a possible list of numeric types.
1129 (defun convert-back-numeric-type-list (type-list)
1132 (let ((results '()))
1133 (dolist (type type-list)
1134 (if (numeric-type-p type)
1135 (let ((result (convert-back-numeric-type type)))
1137 (setf results (append results result))
1138 (push result results)))
1139 (push type results)))
1142 (convert-back-numeric-type type-list))
1144 (convert-back-numeric-type-list (union-type-types type-list)))
1148 ;;; Take a list of types and return a canonical type specifier,
1149 ;;; combining any MEMBER types together. If both positive and negative
1150 ;;; MEMBER types are present they are converted to a float type.
1151 ;;; XXX This would be far simpler if the type-union methods could handle
1152 ;;; member/number unions.
1154 ;;; If we're about to generate an overly complex union of numeric types, start
1155 ;;; collapse the ranges together.
1157 ;;; FIXME: The MEMBER canonicalization parts of MAKE-DERIVED-UNION-TYPE and
1158 ;;; entire CONVERT-MEMBER-TYPE probably belong in the kernel's type logic,
1159 ;;; invoked always, instead of in the compiler, invoked only during some type
1161 (defvar *derived-numeric-union-complexity-limit* 6)
1163 (defun make-derived-union-type (type-list)
1164 (let ((xset (alloc-xset))
1167 (numeric-type *empty-type*))
1168 (dolist (type type-list)
1169 (cond ((member-type-p type)
1170 (mapc-member-type-members
1172 (if (fp-zero-p member)
1173 (unless (member member fp-zeroes)
1174 (pushnew member fp-zeroes))
1175 (add-to-xset member xset)))
1177 ((numeric-type-p type)
1178 (let ((*approximate-numeric-unions*
1179 (when (and (union-type-p numeric-type)
1180 (nthcdr *derived-numeric-union-complexity-limit*
1181 (union-type-types numeric-type)))
1183 (setf numeric-type (type-union type numeric-type))))
1185 (push type misc-types))))
1186 (if (and (xset-empty-p xset) (not fp-zeroes))
1187 (apply #'type-union numeric-type misc-types)
1188 (apply #'type-union (make-member-type :xset xset :fp-zeroes fp-zeroes)
1189 numeric-type misc-types))))
1191 ;;; Convert a member type with a single member to a numeric type.
1192 (defun convert-member-type (arg)
1193 (let* ((members (member-type-members arg))
1194 (member (first members))
1195 (member-type (type-of member)))
1196 (aver (not (rest members)))
1197 (specifier-type (cond ((typep member 'integer)
1198 `(integer ,member ,member))
1199 ((memq member-type '(short-float single-float
1200 double-float long-float))
1201 `(,member-type ,member ,member))
1205 ;;; This is used in defoptimizers for computing the resulting type of
1208 ;;; Given the lvar ARG, derive the resulting type using the
1209 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1210 ;;; "atomic" lvar type like numeric-type or member-type (containing
1211 ;;; just one element). It should return the resulting type, which can
1212 ;;; be a list of types.
1214 ;;; For the case of member types, if a MEMBER-FUN is given it is
1215 ;;; called to compute the result otherwise the member type is first
1216 ;;; converted to a numeric type and the DERIVE-FUN is called.
1217 (defun one-arg-derive-type (arg derive-fun member-fun
1218 &optional (convert-type t))
1219 (declare (type function derive-fun)
1220 (type (or null function) member-fun))
1221 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1227 (with-float-traps-masked
1228 (:underflow :overflow :divide-by-zero)
1230 `(eql ,(funcall member-fun
1231 (first (member-type-members x))))))
1232 ;; Otherwise convert to a numeric type.
1233 (let ((result-type-list
1234 (funcall derive-fun (convert-member-type x))))
1236 (convert-back-numeric-type-list result-type-list)
1237 result-type-list))))
1240 (convert-back-numeric-type-list
1241 (funcall derive-fun (convert-numeric-type x)))
1242 (funcall derive-fun x)))
1244 *universal-type*))))
1245 ;; Run down the list of args and derive the type of each one,
1246 ;; saving all of the results in a list.
1247 (let ((results nil))
1248 (dolist (arg arg-list)
1249 (let ((result (deriver arg)))
1251 (setf results (append results result))
1252 (push result results))))
1254 (make-derived-union-type results)
1255 (first results)))))))
1257 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1258 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1259 ;;; original args and a third which is T to indicate if the two args
1260 ;;; really represent the same lvar. This is useful for deriving the
1261 ;;; type of things like (* x x), which should always be positive. If
1262 ;;; we didn't do this, we wouldn't be able to tell.
1263 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1264 &optional (convert-type t))
1265 (declare (type function derive-fun fun))
1266 (flet ((deriver (x y same-arg)
1267 (cond ((and (member-type-p x) (member-type-p y))
1268 (let* ((x (first (member-type-members x)))
1269 (y (first (member-type-members y)))
1270 (result (ignore-errors
1271 (with-float-traps-masked
1272 (:underflow :overflow :divide-by-zero
1274 (funcall fun x y)))))
1275 (cond ((null result) *empty-type*)
1276 ((and (floatp result) (float-nan-p result))
1277 (make-numeric-type :class 'float
1278 :format (type-of result)
1281 (specifier-type `(eql ,result))))))
1282 ((and (member-type-p x) (numeric-type-p y))
1283 (let* ((x (convert-member-type x))
1284 (y (if convert-type (convert-numeric-type y) y))
1285 (result (funcall derive-fun x y same-arg)))
1287 (convert-back-numeric-type-list result)
1289 ((and (numeric-type-p x) (member-type-p y))
1290 (let* ((x (if convert-type (convert-numeric-type x) x))
1291 (y (convert-member-type y))
1292 (result (funcall derive-fun x y same-arg)))
1294 (convert-back-numeric-type-list result)
1296 ((and (numeric-type-p x) (numeric-type-p y))
1297 (let* ((x (if convert-type (convert-numeric-type x) x))
1298 (y (if convert-type (convert-numeric-type y) y))
1299 (result (funcall derive-fun x y same-arg)))
1301 (convert-back-numeric-type-list result)
1304 *universal-type*))))
1305 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1306 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1307 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1309 (let ((results nil))
1311 ;; Since the args are the same LVARs, just run down the
1314 (let ((result (deriver x x same-arg)))
1316 (setf results (append results result))
1317 (push result results))))
1318 ;; Try all pairwise combinations.
1321 (let ((result (or (deriver x y same-arg)
1322 (numeric-contagion x y))))
1324 (setf results (append results result))
1325 (push result results))))))
1327 (make-derived-union-type results)
1328 (first results)))))))
1330 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1332 (defoptimizer (+ derive-type) ((x y))
1333 (derive-integer-type
1340 (values (frob (numeric-type-low x) (numeric-type-low y))
1341 (frob (numeric-type-high x) (numeric-type-high y)))))))
1343 (defoptimizer (- derive-type) ((x y))
1344 (derive-integer-type
1351 (values (frob (numeric-type-low x) (numeric-type-high y))
1352 (frob (numeric-type-high x) (numeric-type-low y)))))))
1354 (defoptimizer (* derive-type) ((x y))
1355 (derive-integer-type
1358 (let ((x-low (numeric-type-low x))
1359 (x-high (numeric-type-high x))
1360 (y-low (numeric-type-low y))
1361 (y-high (numeric-type-high y)))
1362 (cond ((not (and x-low y-low))
1364 ((or (minusp x-low) (minusp y-low))
1365 (if (and x-high y-high)
1366 (let ((max (* (max (abs x-low) (abs x-high))
1367 (max (abs y-low) (abs y-high)))))
1368 (values (- max) max))
1371 (values (* x-low y-low)
1372 (if (and x-high y-high)
1376 (defoptimizer (/ derive-type) ((x y))
1377 (numeric-contagion (lvar-type x) (lvar-type y)))
1381 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1383 (defun +-derive-type-aux (x y same-arg)
1384 (if (and (numeric-type-real-p x)
1385 (numeric-type-real-p y))
1388 (let ((x-int (numeric-type->interval x)))
1389 (interval-add x-int x-int))
1390 (interval-add (numeric-type->interval x)
1391 (numeric-type->interval y))))
1392 (result-type (numeric-contagion x y)))
1393 ;; If the result type is a float, we need to be sure to coerce
1394 ;; the bounds into the correct type.
1395 (when (eq (numeric-type-class result-type) 'float)
1396 (setf result (interval-func
1398 (coerce-for-bound x (or (numeric-type-format result-type)
1402 :class (if (and (eq (numeric-type-class x) 'integer)
1403 (eq (numeric-type-class y) 'integer))
1404 ;; The sum of integers is always an integer.
1406 (numeric-type-class result-type))
1407 :format (numeric-type-format result-type)
1408 :low (interval-low result)
1409 :high (interval-high result)))
1410 ;; general contagion
1411 (numeric-contagion x y)))
1413 (defoptimizer (+ derive-type) ((x y))
1414 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1416 (defun --derive-type-aux (x y same-arg)
1417 (if (and (numeric-type-real-p x)
1418 (numeric-type-real-p y))
1420 ;; (- X X) is always 0.
1422 (make-interval :low 0 :high 0)
1423 (interval-sub (numeric-type->interval x)
1424 (numeric-type->interval y))))
1425 (result-type (numeric-contagion x y)))
1426 ;; If the result type is a float, we need to be sure to coerce
1427 ;; the bounds into the correct type.
1428 (when (eq (numeric-type-class result-type) 'float)
1429 (setf result (interval-func
1431 (coerce-for-bound x (or (numeric-type-format result-type)
1435 :class (if (and (eq (numeric-type-class x) 'integer)
1436 (eq (numeric-type-class y) 'integer))
1437 ;; The difference of integers is always an integer.
1439 (numeric-type-class result-type))
1440 :format (numeric-type-format result-type)
1441 :low (interval-low result)
1442 :high (interval-high result)))
1443 ;; general contagion
1444 (numeric-contagion x y)))
1446 (defoptimizer (- derive-type) ((x y))
1447 (two-arg-derive-type x y #'--derive-type-aux #'-))
1449 (defun *-derive-type-aux (x y same-arg)
1450 (if (and (numeric-type-real-p x)
1451 (numeric-type-real-p y))
1453 ;; (* X X) is always positive, so take care to do it right.
1455 (interval-sqr (numeric-type->interval x))
1456 (interval-mul (numeric-type->interval x)
1457 (numeric-type->interval y))))
1458 (result-type (numeric-contagion x y)))
1459 ;; If the result type is a float, we need to be sure to coerce
1460 ;; the bounds into the correct type.
1461 (when (eq (numeric-type-class result-type) 'float)
1462 (setf result (interval-func
1464 (coerce-for-bound x (or (numeric-type-format result-type)
1468 :class (if (and (eq (numeric-type-class x) 'integer)
1469 (eq (numeric-type-class y) 'integer))
1470 ;; The product of integers is always an integer.
1472 (numeric-type-class result-type))
1473 :format (numeric-type-format result-type)
1474 :low (interval-low result)
1475 :high (interval-high result)))
1476 (numeric-contagion x y)))
1478 (defoptimizer (* derive-type) ((x y))
1479 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1481 (defun /-derive-type-aux (x y same-arg)
1482 (if (and (numeric-type-real-p x)
1483 (numeric-type-real-p y))
1485 ;; (/ X X) is always 1, except if X can contain 0. In
1486 ;; that case, we shouldn't optimize the division away
1487 ;; because we want 0/0 to signal an error.
1489 (not (interval-contains-p
1490 0 (interval-closure (numeric-type->interval y)))))
1491 (make-interval :low 1 :high 1)
1492 (interval-div (numeric-type->interval x)
1493 (numeric-type->interval y))))
1494 (result-type (numeric-contagion x y)))
1495 ;; If the result type is a float, we need to be sure to coerce
1496 ;; the bounds into the correct type.
1497 (when (eq (numeric-type-class result-type) 'float)
1498 (setf result (interval-func
1500 (coerce-for-bound x (or (numeric-type-format result-type)
1503 (make-numeric-type :class (numeric-type-class result-type)
1504 :format (numeric-type-format result-type)
1505 :low (interval-low result)
1506 :high (interval-high result)))
1507 (numeric-contagion x y)))
1509 (defoptimizer (/ derive-type) ((x y))
1510 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1514 (defun ash-derive-type-aux (n-type shift same-arg)
1515 (declare (ignore same-arg))
1516 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1517 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1518 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1519 ;; two bignums yielding zero) and it's hard to avoid that
1520 ;; calculation in here.
1521 #+(and cmu sb-xc-host)
1522 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1523 (typep (numeric-type-high n-type) 'bignum))
1524 (or (typep (numeric-type-low shift) 'bignum)
1525 (typep (numeric-type-high shift) 'bignum)))
1526 (return-from ash-derive-type-aux *universal-type*))
1527 (flet ((ash-outer (n s)
1528 (when (and (fixnump s)
1530 (> s sb!xc:most-negative-fixnum))
1532 ;; KLUDGE: The bare 64's here should be related to
1533 ;; symbolic machine word size values somehow.
1536 (if (and (fixnump s)
1537 (> s sb!xc:most-negative-fixnum))
1539 (if (minusp n) -1 0))))
1540 (or (and (csubtypep n-type (specifier-type 'integer))
1541 (csubtypep shift (specifier-type 'integer))
1542 (let ((n-low (numeric-type-low n-type))
1543 (n-high (numeric-type-high n-type))
1544 (s-low (numeric-type-low shift))
1545 (s-high (numeric-type-high shift)))
1546 (make-numeric-type :class 'integer :complexp :real
1549 (ash-outer n-low s-high)
1550 (ash-inner n-low s-low)))
1553 (ash-inner n-high s-low)
1554 (ash-outer n-high s-high))))))
1557 (defoptimizer (ash derive-type) ((n shift))
1558 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1560 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1561 (macrolet ((frob (fun)
1562 `#'(lambda (type type2)
1563 (declare (ignore type2))
1564 (let ((lo (numeric-type-low type))
1565 (hi (numeric-type-high type)))
1566 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1568 (defoptimizer (%negate derive-type) ((num))
1569 (derive-integer-type num num (frob -))))
1571 (defun lognot-derive-type-aux (int)
1572 (derive-integer-type-aux int int
1573 (lambda (type type2)
1574 (declare (ignore type2))
1575 (let ((lo (numeric-type-low type))
1576 (hi (numeric-type-high type)))
1577 (values (if hi (lognot hi) nil)
1578 (if lo (lognot lo) nil)
1579 (numeric-type-class type)
1580 (numeric-type-format type))))))
1582 (defoptimizer (lognot derive-type) ((int))
1583 (lognot-derive-type-aux (lvar-type int)))
1585 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1586 (defoptimizer (%negate derive-type) ((num))
1587 (flet ((negate-bound (b)
1589 (set-bound (- (type-bound-number b))
1591 (one-arg-derive-type num
1593 (modified-numeric-type
1595 :low (negate-bound (numeric-type-high type))
1596 :high (negate-bound (numeric-type-low type))))
1599 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1600 (defoptimizer (abs derive-type) ((num))
1601 (let ((type (lvar-type num)))
1602 (if (and (numeric-type-p type)
1603 (eq (numeric-type-class type) 'integer)
1604 (eq (numeric-type-complexp type) :real))
1605 (let ((lo (numeric-type-low type))
1606 (hi (numeric-type-high type)))
1607 (make-numeric-type :class 'integer :complexp :real
1608 :low (cond ((and hi (minusp hi))
1614 :high (if (and hi lo)
1615 (max (abs hi) (abs lo))
1617 (numeric-contagion type type))))
1619 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1620 (defun abs-derive-type-aux (type)
1621 (cond ((eq (numeric-type-complexp type) :complex)
1622 ;; The absolute value of a complex number is always a
1623 ;; non-negative float.
1624 (let* ((format (case (numeric-type-class type)
1625 ((integer rational) 'single-float)
1626 (t (numeric-type-format type))))
1627 (bound-format (or format 'float)))
1628 (make-numeric-type :class 'float
1631 :low (coerce 0 bound-format)
1634 ;; The absolute value of a real number is a non-negative real
1635 ;; of the same type.
1636 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1637 (class (numeric-type-class type))
1638 (format (numeric-type-format type))
1639 (bound-type (or format class 'real)))
1644 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1645 :high (coerce-and-truncate-floats
1646 (interval-high abs-bnd) bound-type))))))
1648 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1649 (defoptimizer (abs derive-type) ((num))
1650 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1652 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1653 (defoptimizer (truncate derive-type) ((number divisor))
1654 (let ((number-type (lvar-type number))
1655 (divisor-type (lvar-type divisor))
1656 (integer-type (specifier-type 'integer)))
1657 (if (and (numeric-type-p number-type)
1658 (csubtypep number-type integer-type)
1659 (numeric-type-p divisor-type)
1660 (csubtypep divisor-type integer-type))
1661 (let ((number-low (numeric-type-low number-type))
1662 (number-high (numeric-type-high number-type))
1663 (divisor-low (numeric-type-low divisor-type))
1664 (divisor-high (numeric-type-high divisor-type)))
1665 (values-specifier-type
1666 `(values ,(integer-truncate-derive-type number-low number-high
1667 divisor-low divisor-high)
1668 ,(integer-rem-derive-type number-low number-high
1669 divisor-low divisor-high))))
1672 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1675 (defun rem-result-type (number-type divisor-type)
1676 ;; Figure out what the remainder type is. The remainder is an
1677 ;; integer if both args are integers; a rational if both args are
1678 ;; rational; and a float otherwise.
1679 (cond ((and (csubtypep number-type (specifier-type 'integer))
1680 (csubtypep divisor-type (specifier-type 'integer)))
1682 ((and (csubtypep number-type (specifier-type 'rational))
1683 (csubtypep divisor-type (specifier-type 'rational)))
1685 ((and (csubtypep number-type (specifier-type 'float))
1686 (csubtypep divisor-type (specifier-type 'float)))
1687 ;; Both are floats so the result is also a float, of
1688 ;; the largest type.
1689 (or (float-format-max (numeric-type-format number-type)
1690 (numeric-type-format divisor-type))
1692 ((and (csubtypep number-type (specifier-type 'float))
1693 (csubtypep divisor-type (specifier-type 'rational)))
1694 ;; One of the arguments is a float and the other is a
1695 ;; rational. The remainder is a float of the same
1697 (or (numeric-type-format number-type) 'float))
1698 ((and (csubtypep divisor-type (specifier-type 'float))
1699 (csubtypep number-type (specifier-type 'rational)))
1700 ;; One of the arguments is a float and the other is a
1701 ;; rational. The remainder is a float of the same
1703 (or (numeric-type-format divisor-type) 'float))
1705 ;; Some unhandled combination. This usually means both args
1706 ;; are REAL so the result is a REAL.
1709 (defun truncate-derive-type-quot (number-type divisor-type)
1710 (let* ((rem-type (rem-result-type number-type divisor-type))
1711 (number-interval (numeric-type->interval number-type))
1712 (divisor-interval (numeric-type->interval divisor-type)))
1713 ;;(declare (type (member '(integer rational float)) rem-type))
1714 ;; We have real numbers now.
1715 (cond ((eq rem-type 'integer)
1716 ;; Since the remainder type is INTEGER, both args are
1718 (let* ((res (integer-truncate-derive-type
1719 (interval-low number-interval)
1720 (interval-high number-interval)
1721 (interval-low divisor-interval)
1722 (interval-high divisor-interval))))
1723 (specifier-type (if (listp res) res 'integer))))
1725 (let ((quot (truncate-quotient-bound
1726 (interval-div number-interval
1727 divisor-interval))))
1728 (specifier-type `(integer ,(or (interval-low quot) '*)
1729 ,(or (interval-high quot) '*))))))))
1731 (defun truncate-derive-type-rem (number-type divisor-type)
1732 (let* ((rem-type (rem-result-type number-type divisor-type))
1733 (number-interval (numeric-type->interval number-type))
1734 (divisor-interval (numeric-type->interval divisor-type))
1735 (rem (truncate-rem-bound number-interval divisor-interval)))
1736 ;;(declare (type (member '(integer rational float)) rem-type))
1737 ;; We have real numbers now.
1738 (cond ((eq rem-type 'integer)
1739 ;; Since the remainder type is INTEGER, both args are
1741 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1742 ,(or (interval-high rem) '*))))
1744 (multiple-value-bind (class format)
1747 (values 'integer nil))
1749 (values 'rational nil))
1750 ((or single-float double-float #!+long-float long-float)
1751 (values 'float rem-type))
1753 (values 'float nil))
1756 (when (member rem-type '(float single-float double-float
1757 #!+long-float long-float))
1758 (setf rem (interval-func #'(lambda (x)
1759 (coerce-for-bound x rem-type))
1761 (make-numeric-type :class class
1763 :low (interval-low rem)
1764 :high (interval-high rem)))))))
1766 (defun truncate-derive-type-quot-aux (num div same-arg)
1767 (declare (ignore same-arg))
1768 (if (and (numeric-type-real-p num)
1769 (numeric-type-real-p div))
1770 (truncate-derive-type-quot num div)
1773 (defun truncate-derive-type-rem-aux (num div same-arg)
1774 (declare (ignore same-arg))
1775 (if (and (numeric-type-real-p num)
1776 (numeric-type-real-p div))
1777 (truncate-derive-type-rem num div)
1780 (defoptimizer (truncate derive-type) ((number divisor))
1781 (let ((quot (two-arg-derive-type number divisor
1782 #'truncate-derive-type-quot-aux #'truncate))
1783 (rem (two-arg-derive-type number divisor
1784 #'truncate-derive-type-rem-aux #'rem)))
1785 (when (and quot rem)
1786 (make-values-type :required (list quot rem)))))
1788 (defun ftruncate-derive-type-quot (number-type divisor-type)
1789 ;; The bounds are the same as for truncate. However, the first
1790 ;; result is a float of some type. We need to determine what that
1791 ;; type is. Basically it's the more contagious of the two types.
1792 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1793 (res-type (numeric-contagion number-type divisor-type)))
1794 (make-numeric-type :class 'float
1795 :format (numeric-type-format res-type)
1796 :low (numeric-type-low q-type)
1797 :high (numeric-type-high q-type))))
1799 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1800 (declare (ignore same-arg))
1801 (if (and (numeric-type-real-p n)
1802 (numeric-type-real-p d))
1803 (ftruncate-derive-type-quot n d)
1806 (defoptimizer (ftruncate derive-type) ((number divisor))
1808 (two-arg-derive-type number divisor
1809 #'ftruncate-derive-type-quot-aux #'ftruncate))
1810 (rem (two-arg-derive-type number divisor
1811 #'truncate-derive-type-rem-aux #'rem)))
1812 (when (and quot rem)
1813 (make-values-type :required (list quot rem)))))
1815 (defun %unary-truncate-derive-type-aux (number)
1816 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1818 (defoptimizer (%unary-truncate derive-type) ((number))
1819 (one-arg-derive-type number
1820 #'%unary-truncate-derive-type-aux
1823 (defoptimizer (%unary-truncate/single-float derive-type) ((number))
1824 (one-arg-derive-type number
1825 #'%unary-truncate-derive-type-aux
1828 (defoptimizer (%unary-truncate/double-float derive-type) ((number))
1829 (one-arg-derive-type number
1830 #'%unary-truncate-derive-type-aux
1833 (defoptimizer (%unary-ftruncate derive-type) ((number))
1834 (let ((divisor (specifier-type '(integer 1 1))))
1835 (one-arg-derive-type number
1837 (ftruncate-derive-type-quot-aux n divisor nil))
1838 #'%unary-ftruncate)))
1840 (defoptimizer (%unary-round derive-type) ((number))
1841 (one-arg-derive-type number
1844 (unless (numeric-type-real-p n)
1845 (return *empty-type*))
1846 (let* ((interval (numeric-type->interval n))
1847 (low (interval-low interval))
1848 (high (interval-high interval)))
1850 (setf low (car low)))
1852 (setf high (car high)))
1862 ;;; Define optimizers for FLOOR and CEILING.
1864 ((def (name q-name r-name)
1865 (let ((q-aux (symbolicate q-name "-AUX"))
1866 (r-aux (symbolicate r-name "-AUX")))
1868 ;; Compute type of quotient (first) result.
1869 (defun ,q-aux (number-type divisor-type)
1870 (let* ((number-interval
1871 (numeric-type->interval number-type))
1873 (numeric-type->interval divisor-type))
1874 (quot (,q-name (interval-div number-interval
1875 divisor-interval))))
1876 (specifier-type `(integer ,(or (interval-low quot) '*)
1877 ,(or (interval-high quot) '*)))))
1878 ;; Compute type of remainder.
1879 (defun ,r-aux (number-type divisor-type)
1880 (let* ((divisor-interval
1881 (numeric-type->interval divisor-type))
1882 (rem (,r-name divisor-interval))
1883 (result-type (rem-result-type number-type divisor-type)))
1884 (multiple-value-bind (class format)
1887 (values 'integer nil))
1889 (values 'rational nil))
1890 ((or single-float double-float #!+long-float long-float)
1891 (values 'float result-type))
1893 (values 'float nil))
1896 (when (member result-type '(float single-float double-float
1897 #!+long-float long-float))
1898 ;; Make sure that the limits on the interval have
1900 (setf rem (interval-func (lambda (x)
1901 (coerce-for-bound x result-type))
1903 (make-numeric-type :class class
1905 :low (interval-low rem)
1906 :high (interval-high rem)))))
1907 ;; the optimizer itself
1908 (defoptimizer (,name derive-type) ((number divisor))
1909 (flet ((derive-q (n d same-arg)
1910 (declare (ignore same-arg))
1911 (if (and (numeric-type-real-p n)
1912 (numeric-type-real-p d))
1915 (derive-r (n d same-arg)
1916 (declare (ignore same-arg))
1917 (if (and (numeric-type-real-p n)
1918 (numeric-type-real-p d))
1921 (let ((quot (two-arg-derive-type
1922 number divisor #'derive-q #',name))
1923 (rem (two-arg-derive-type
1924 number divisor #'derive-r #'mod)))
1925 (when (and quot rem)
1926 (make-values-type :required (list quot rem))))))))))
1928 (def floor floor-quotient-bound floor-rem-bound)
1929 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1931 ;;; Define optimizers for FFLOOR and FCEILING
1932 (macrolet ((def (name q-name r-name)
1933 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1934 (r-aux (symbolicate r-name "-AUX")))
1936 ;; Compute type of quotient (first) result.
1937 (defun ,q-aux (number-type divisor-type)
1938 (let* ((number-interval
1939 (numeric-type->interval number-type))
1941 (numeric-type->interval divisor-type))
1942 (quot (,q-name (interval-div number-interval
1944 (res-type (numeric-contagion number-type
1947 :class (numeric-type-class res-type)
1948 :format (numeric-type-format res-type)
1949 :low (interval-low quot)
1950 :high (interval-high quot))))
1952 (defoptimizer (,name derive-type) ((number divisor))
1953 (flet ((derive-q (n d same-arg)
1954 (declare (ignore same-arg))
1955 (if (and (numeric-type-real-p n)
1956 (numeric-type-real-p d))
1959 (derive-r (n d same-arg)
1960 (declare (ignore same-arg))
1961 (if (and (numeric-type-real-p n)
1962 (numeric-type-real-p d))
1965 (let ((quot (two-arg-derive-type
1966 number divisor #'derive-q #',name))
1967 (rem (two-arg-derive-type
1968 number divisor #'derive-r #'mod)))
1969 (when (and quot rem)
1970 (make-values-type :required (list quot rem))))))))))
1972 (def ffloor floor-quotient-bound floor-rem-bound)
1973 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
1975 ;;; functions to compute the bounds on the quotient and remainder for
1976 ;;; the FLOOR function
1977 (defun floor-quotient-bound (quot)
1978 ;; Take the floor of the quotient and then massage it into what we
1980 (let ((lo (interval-low quot))
1981 (hi (interval-high quot)))
1982 ;; Take the floor of the lower bound. The result is always a
1983 ;; closed lower bound.
1985 (floor (type-bound-number lo))
1987 ;; For the upper bound, we need to be careful.
1990 ;; An open bound. We need to be careful here because
1991 ;; the floor of '(10.0) is 9, but the floor of
1993 (multiple-value-bind (q r) (floor (first hi))
1998 ;; A closed bound, so the answer is obvious.
2002 (make-interval :low lo :high hi)))
2003 (defun floor-rem-bound (div)
2004 ;; The remainder depends only on the divisor. Try to get the
2005 ;; correct sign for the remainder if we can.
2006 (case (interval-range-info div)
2008 ;; The divisor is always positive.
2009 (let ((rem (interval-abs div)))
2010 (setf (interval-low rem) 0)
2011 (when (and (numberp (interval-high rem))
2012 (not (zerop (interval-high rem))))
2013 ;; The remainder never contains the upper bound. However,
2014 ;; watch out for the case where the high limit is zero!
2015 (setf (interval-high rem) (list (interval-high rem))))
2018 ;; The divisor is always negative.
2019 (let ((rem (interval-neg (interval-abs div))))
2020 (setf (interval-high rem) 0)
2021 (when (numberp (interval-low rem))
2022 ;; The remainder never contains the lower bound.
2023 (setf (interval-low rem) (list (interval-low rem))))
2026 ;; The divisor can be positive or negative. All bets off. The
2027 ;; magnitude of remainder is the maximum value of the divisor.
2028 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2029 ;; The bound never reaches the limit, so make the interval open.
2030 (make-interval :low (if limit
2033 :high (list limit))))))
2035 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
2036 => #S(INTERVAL :LOW 0 :HIGH 10)
2037 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2038 => #S(INTERVAL :LOW 0 :HIGH 10)
2039 (floor-quotient-bound (make-interval :low 0.3 :high 10))
2040 => #S(INTERVAL :LOW 0 :HIGH 10)
2041 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
2042 => #S(INTERVAL :LOW 0 :HIGH 9)
2043 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
2044 => #S(INTERVAL :LOW 0 :HIGH 10)
2045 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
2046 => #S(INTERVAL :LOW 0 :HIGH 10)
2047 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2048 => #S(INTERVAL :LOW -2 :HIGH 10)
2049 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2050 => #S(INTERVAL :LOW -1 :HIGH 10)
2051 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
2052 => #S(INTERVAL :LOW -1 :HIGH 10)
2054 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
2055 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2056 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
2057 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2058 (floor-rem-bound (make-interval :low -10 :high -2.3))
2059 #S(INTERVAL :LOW (-10) :HIGH 0)
2060 (floor-rem-bound (make-interval :low 0.3 :high 10))
2061 => #S(INTERVAL :LOW 0 :HIGH '(10))
2062 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
2063 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
2064 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
2065 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2068 ;;; same functions for CEILING
2069 (defun ceiling-quotient-bound (quot)
2070 ;; Take the ceiling of the quotient and then massage it into what we
2072 (let ((lo (interval-low quot))
2073 (hi (interval-high quot)))
2074 ;; Take the ceiling of the upper bound. The result is always a
2075 ;; closed upper bound.
2077 (ceiling (type-bound-number hi))
2079 ;; For the lower bound, we need to be careful.
2082 ;; An open bound. We need to be careful here because
2083 ;; the ceiling of '(10.0) is 11, but the ceiling of
2085 (multiple-value-bind (q r) (ceiling (first lo))
2090 ;; A closed bound, so the answer is obvious.
2094 (make-interval :low lo :high hi)))
2095 (defun ceiling-rem-bound (div)
2096 ;; The remainder depends only on the divisor. Try to get the
2097 ;; correct sign for the remainder if we can.
2098 (case (interval-range-info div)
2100 ;; Divisor is always positive. The remainder is negative.
2101 (let ((rem (interval-neg (interval-abs div))))
2102 (setf (interval-high rem) 0)
2103 (when (and (numberp (interval-low rem))
2104 (not (zerop (interval-low rem))))
2105 ;; The remainder never contains the upper bound. However,
2106 ;; watch out for the case when the upper bound is zero!
2107 (setf (interval-low rem) (list (interval-low rem))))
2110 ;; Divisor is always negative. The remainder is positive
2111 (let ((rem (interval-abs div)))
2112 (setf (interval-low rem) 0)
2113 (when (numberp (interval-high rem))
2114 ;; The remainder never contains the lower bound.
2115 (setf (interval-high rem) (list (interval-high rem))))
2118 ;; The divisor can be positive or negative. All bets off. The
2119 ;; magnitude of remainder is the maximum value of the divisor.
2120 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2121 ;; The bound never reaches the limit, so make the interval open.
2122 (make-interval :low (if limit
2125 :high (list limit))))))
2128 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2129 => #S(INTERVAL :LOW 1 :HIGH 11)
2130 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2131 => #S(INTERVAL :LOW 1 :HIGH 11)
2132 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2133 => #S(INTERVAL :LOW 1 :HIGH 10)
2134 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2135 => #S(INTERVAL :LOW 1 :HIGH 10)
2136 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2137 => #S(INTERVAL :LOW 1 :HIGH 11)
2138 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2139 => #S(INTERVAL :LOW 1 :HIGH 11)
2140 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2141 => #S(INTERVAL :LOW -1 :HIGH 11)
2142 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2143 => #S(INTERVAL :LOW 0 :HIGH 11)
2144 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2145 => #S(INTERVAL :LOW -1 :HIGH 11)
2147 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2148 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2149 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2150 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2151 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2152 => #S(INTERVAL :LOW 0 :HIGH (10))
2153 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2154 => #S(INTERVAL :LOW (-10) :HIGH 0)
2155 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2156 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2157 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2158 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2161 (defun truncate-quotient-bound (quot)
2162 ;; For positive quotients, truncate is exactly like floor. For
2163 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2164 ;; it's the union of the two pieces.
2165 (case (interval-range-info quot)
2168 (floor-quotient-bound quot))
2170 ;; just like CEILING
2171 (ceiling-quotient-bound quot))
2173 ;; Split the interval into positive and negative pieces, compute
2174 ;; the result for each piece and put them back together.
2175 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2176 (interval-merge-pair (ceiling-quotient-bound neg)
2177 (floor-quotient-bound pos))))))
2179 (defun truncate-rem-bound (num div)
2180 ;; This is significantly more complicated than FLOOR or CEILING. We
2181 ;; need both the number and the divisor to determine the range. The
2182 ;; basic idea is to split the ranges of NUM and DEN into positive
2183 ;; and negative pieces and deal with each of the four possibilities
2185 (case (interval-range-info num)
2187 (case (interval-range-info div)
2189 (floor-rem-bound div))
2191 (ceiling-rem-bound div))
2193 (destructuring-bind (neg pos) (interval-split 0 div t t)
2194 (interval-merge-pair (truncate-rem-bound num neg)
2195 (truncate-rem-bound num pos))))))
2197 (case (interval-range-info div)
2199 (ceiling-rem-bound div))
2201 (floor-rem-bound div))
2203 (destructuring-bind (neg pos) (interval-split 0 div t t)
2204 (interval-merge-pair (truncate-rem-bound num neg)
2205 (truncate-rem-bound num pos))))))
2207 (destructuring-bind (neg pos) (interval-split 0 num t t)
2208 (interval-merge-pair (truncate-rem-bound neg div)
2209 (truncate-rem-bound pos div))))))
2212 ;;; Derive useful information about the range. Returns three values:
2213 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2214 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2215 ;;; - The abs of the maximal value if there is one, or nil if it is
2217 (defun numeric-range-info (low high)
2218 (cond ((and low (not (minusp low)))
2219 (values '+ low high))
2220 ((and high (not (plusp high)))
2221 (values '- (- high) (if low (- low) nil)))
2223 (values nil 0 (and low high (max (- low) high))))))
2225 (defun integer-truncate-derive-type
2226 (number-low number-high divisor-low divisor-high)
2227 ;; The result cannot be larger in magnitude than the number, but the
2228 ;; sign might change. If we can determine the sign of either the
2229 ;; number or the divisor, we can eliminate some of the cases.
2230 (multiple-value-bind (number-sign number-min number-max)
2231 (numeric-range-info number-low number-high)
2232 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2233 (numeric-range-info divisor-low divisor-high)
2234 (when (and divisor-max (zerop divisor-max))
2235 ;; We've got a problem: guaranteed division by zero.
2236 (return-from integer-truncate-derive-type t))
2237 (when (zerop divisor-min)
2238 ;; We'll assume that they aren't going to divide by zero.
2240 (cond ((and number-sign divisor-sign)
2241 ;; We know the sign of both.
2242 (if (eq number-sign divisor-sign)
2243 ;; Same sign, so the result will be positive.
2244 `(integer ,(if divisor-max
2245 (truncate number-min divisor-max)
2248 (truncate number-max divisor-min)
2250 ;; Different signs, the result will be negative.
2251 `(integer ,(if number-max
2252 (- (truncate number-max divisor-min))
2255 (- (truncate number-min divisor-max))
2257 ((eq divisor-sign '+)
2258 ;; The divisor is positive. Therefore, the number will just
2259 ;; become closer to zero.
2260 `(integer ,(if number-low
2261 (truncate number-low divisor-min)
2264 (truncate number-high divisor-min)
2266 ((eq divisor-sign '-)
2267 ;; The divisor is negative. Therefore, the absolute value of
2268 ;; the number will become closer to zero, but the sign will also
2270 `(integer ,(if number-high
2271 (- (truncate number-high divisor-min))
2274 (- (truncate number-low divisor-min))
2276 ;; The divisor could be either positive or negative.
2278 ;; The number we are dividing has a bound. Divide that by the
2279 ;; smallest posible divisor.
2280 (let ((bound (truncate number-max divisor-min)))
2281 `(integer ,(- bound) ,bound)))
2283 ;; The number we are dividing is unbounded, so we can't tell
2284 ;; anything about the result.
2287 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2288 (defun integer-rem-derive-type
2289 (number-low number-high divisor-low divisor-high)
2290 (if (and divisor-low divisor-high)
2291 ;; We know the range of the divisor, and the remainder must be
2292 ;; smaller than the divisor. We can tell the sign of the
2293 ;; remainer if we know the sign of the number.
2294 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2295 `(integer ,(if (or (null number-low)
2296 (minusp number-low))
2299 ,(if (or (null number-high)
2300 (plusp number-high))
2303 ;; The divisor is potentially either very positive or very
2304 ;; negative. Therefore, the remainer is unbounded, but we might
2305 ;; be able to tell something about the sign from the number.
2306 `(integer ,(if (and number-low (not (minusp number-low)))
2307 ;; The number we are dividing is positive.
2308 ;; Therefore, the remainder must be positive.
2311 ,(if (and number-high (not (plusp number-high)))
2312 ;; The number we are dividing is negative.
2313 ;; Therefore, the remainder must be negative.
2317 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2318 (defoptimizer (random derive-type) ((bound &optional state))
2319 (let ((type (lvar-type bound)))
2320 (when (numeric-type-p type)
2321 (let ((class (numeric-type-class type))
2322 (high (numeric-type-high type))
2323 (format (numeric-type-format type)))
2327 :low (coerce 0 (or format class 'real))
2328 :high (cond ((not high) nil)
2329 ((eq class 'integer) (max (1- high) 0))
2330 ((or (consp high) (zerop high)) high)
2333 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2334 (defun random-derive-type-aux (type)
2335 (let ((class (numeric-type-class type))
2336 (high (numeric-type-high type))
2337 (format (numeric-type-format type)))
2341 :low (coerce 0 (or format class 'real))
2342 :high (cond ((not high) nil)
2343 ((eq class 'integer) (max (1- high) 0))
2344 ((or (consp high) (zerop high)) high)
2347 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2348 (defoptimizer (random derive-type) ((bound &optional state))
2349 (one-arg-derive-type bound #'random-derive-type-aux nil))
2351 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2353 ;;; Return the maximum number of bits an integer of the supplied type
2354 ;;; can take up, or NIL if it is unbounded. The second (third) value
2355 ;;; is T if the integer can be positive (negative) and NIL if not.
2356 ;;; Zero counts as positive.
2357 (defun integer-type-length (type)
2358 (if (numeric-type-p type)
2359 (let ((min (numeric-type-low type))
2360 (max (numeric-type-high type)))
2361 (values (and min max (max (integer-length min) (integer-length max)))
2362 (or (null max) (not (minusp max)))
2363 (or (null min) (minusp min))))
2366 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2367 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2368 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2369 ;;; versions in CMUCL, from which these functions copy liberally.
2371 (defun logand-derive-unsigned-low-bound (x y)
2372 (let ((a (numeric-type-low x))
2373 (b (numeric-type-high x))
2374 (c (numeric-type-low y))
2375 (d (numeric-type-high y)))
2376 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2378 (unless (zerop (logand m (lognot a) (lognot c)))
2379 (let ((temp (logandc2 (logior a m) (1- m))))
2383 (setf temp (logandc2 (logior c m) (1- m)))
2387 finally (return (logand a c)))))
2389 (defun logand-derive-unsigned-high-bound (x y)
2390 (let ((a (numeric-type-low x))
2391 (b (numeric-type-high x))
2392 (c (numeric-type-low y))
2393 (d (numeric-type-high y)))
2394 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2397 ((not (zerop (logand b (lognot d) m)))
2398 (let ((temp (logior (logandc2 b m) (1- m))))
2402 ((not (zerop (logand (lognot b) d m)))
2403 (let ((temp (logior (logandc2 d m) (1- m))))
2407 finally (return (logand b d)))))
2409 (defun logand-derive-type-aux (x y &optional same-leaf)
2411 (return-from logand-derive-type-aux x))
2412 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2413 (declare (ignore x-pos))
2414 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2415 (declare (ignore y-pos))
2417 ;; X must be positive.
2419 ;; They must both be positive.
2420 (cond ((and (null x-len) (null y-len))
2421 (specifier-type 'unsigned-byte))
2423 (specifier-type `(unsigned-byte* ,y-len)))
2425 (specifier-type `(unsigned-byte* ,x-len)))
2427 (let ((low (logand-derive-unsigned-low-bound x y))
2428 (high (logand-derive-unsigned-high-bound x y)))
2429 (specifier-type `(integer ,low ,high)))))
2430 ;; X is positive, but Y might be negative.
2432 (specifier-type 'unsigned-byte))
2434 (specifier-type `(unsigned-byte* ,x-len)))))
2435 ;; X might be negative.
2437 ;; Y must be positive.
2439 (specifier-type 'unsigned-byte))
2440 (t (specifier-type `(unsigned-byte* ,y-len))))
2441 ;; Either might be negative.
2442 (if (and x-len y-len)
2443 ;; The result is bounded.
2444 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2445 ;; We can't tell squat about the result.
2446 (specifier-type 'integer)))))))
2448 (defun logior-derive-unsigned-low-bound (x y)
2449 (let ((a (numeric-type-low x))
2450 (b (numeric-type-high x))
2451 (c (numeric-type-low y))
2452 (d (numeric-type-high y)))
2453 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2456 ((not (zerop (logandc2 (logand c m) a)))
2457 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2461 ((not (zerop (logandc2 (logand a m) c)))
2462 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2466 finally (return (logior a c)))))
2468 (defun logior-derive-unsigned-high-bound (x y)
2469 (let ((a (numeric-type-low x))
2470 (b (numeric-type-high x))
2471 (c (numeric-type-low y))
2472 (d (numeric-type-high y)))
2473 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2475 (unless (zerop (logand b d m))
2476 (let ((temp (logior (- b m) (1- m))))
2480 (setf temp (logior (- d m) (1- m)))
2484 finally (return (logior b d)))))
2486 (defun logior-derive-type-aux (x y &optional same-leaf)
2488 (return-from logior-derive-type-aux x))
2489 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2490 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2492 ((and (not x-neg) (not y-neg))
2493 ;; Both are positive.
2494 (if (and x-len y-len)
2495 (let ((low (logior-derive-unsigned-low-bound x y))
2496 (high (logior-derive-unsigned-high-bound x y)))
2497 (specifier-type `(integer ,low ,high)))
2498 (specifier-type `(unsigned-byte* *))))
2500 ;; X must be negative.
2502 ;; Both are negative. The result is going to be negative
2503 ;; and be the same length or shorter than the smaller.
2504 (if (and x-len y-len)
2506 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2508 (specifier-type '(integer * -1)))
2509 ;; X is negative, but we don't know about Y. The result
2510 ;; will be negative, but no more negative than X.
2512 `(integer ,(or (numeric-type-low x) '*)
2515 ;; X might be either positive or negative.
2517 ;; But Y is negative. The result will be negative.
2519 `(integer ,(or (numeric-type-low y) '*)
2521 ;; We don't know squat about either. It won't get any bigger.
2522 (if (and x-len y-len)
2524 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2526 (specifier-type 'integer))))))))
2528 (defun logxor-derive-unsigned-low-bound (x y)
2529 (let ((a (numeric-type-low x))
2530 (b (numeric-type-high x))
2531 (c (numeric-type-low y))
2532 (d (numeric-type-high y)))
2533 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2536 ((not (zerop (logandc2 (logand c m) a)))
2537 (let ((temp (logand (logior a m)
2541 ((not (zerop (logandc2 (logand a m) c)))
2542 (let ((temp (logand (logior c m)
2546 finally (return (logxor a c)))))
2548 (defun logxor-derive-unsigned-high-bound (x y)
2549 (let ((a (numeric-type-low x))
2550 (b (numeric-type-high x))
2551 (c (numeric-type-low y))
2552 (d (numeric-type-high y)))
2553 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2555 (unless (zerop (logand b d m))
2556 (let ((temp (logior (- b m) (1- m))))
2558 ((>= temp a) (setf b temp))
2559 (t (let ((temp (logior (- d m) (1- m))))
2562 finally (return (logxor b d)))))
2564 (defun logxor-derive-type-aux (x y &optional same-leaf)
2566 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2567 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2568 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2570 ((and (not x-neg) (not y-neg))
2571 ;; Both are positive
2572 (if (and x-len y-len)
2573 (let ((low (logxor-derive-unsigned-low-bound x y))
2574 (high (logxor-derive-unsigned-high-bound x y)))
2575 (specifier-type `(integer ,low ,high)))
2576 (specifier-type '(unsigned-byte* *))))
2577 ((and (not x-pos) (not y-pos))
2578 ;; Both are negative. The result will be positive, and as long
2580 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2583 ((or (and (not x-pos) (not y-neg))
2584 (and (not y-pos) (not x-neg)))
2585 ;; Either X is negative and Y is positive or vice-versa. The
2586 ;; result will be negative.
2587 (specifier-type `(integer ,(if (and x-len y-len)
2588 (ash -1 (max x-len y-len))
2591 ;; We can't tell what the sign of the result is going to be.
2592 ;; All we know is that we don't create new bits.
2594 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2596 (specifier-type 'integer))))))
2598 (macrolet ((deffrob (logfun)
2599 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2600 `(defoptimizer (,logfun derive-type) ((x y))
2601 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2606 (defoptimizer (logeqv derive-type) ((x y))
2607 (two-arg-derive-type x y (lambda (x y same-leaf)
2608 (lognot-derive-type-aux
2609 (logxor-derive-type-aux x y same-leaf)))
2611 (defoptimizer (lognand derive-type) ((x y))
2612 (two-arg-derive-type x y (lambda (x y same-leaf)
2613 (lognot-derive-type-aux
2614 (logand-derive-type-aux x y same-leaf)))
2616 (defoptimizer (lognor derive-type) ((x y))
2617 (two-arg-derive-type x y (lambda (x y same-leaf)
2618 (lognot-derive-type-aux
2619 (logior-derive-type-aux x y same-leaf)))
2621 (defoptimizer (logandc1 derive-type) ((x y))
2622 (two-arg-derive-type x y (lambda (x y same-leaf)
2624 (specifier-type '(eql 0))
2625 (logand-derive-type-aux
2626 (lognot-derive-type-aux x) y nil)))
2628 (defoptimizer (logandc2 derive-type) ((x y))
2629 (two-arg-derive-type x y (lambda (x y same-leaf)
2631 (specifier-type '(eql 0))
2632 (logand-derive-type-aux
2633 x (lognot-derive-type-aux y) nil)))
2635 (defoptimizer (logorc1 derive-type) ((x y))
2636 (two-arg-derive-type x y (lambda (x y same-leaf)
2638 (specifier-type '(eql -1))
2639 (logior-derive-type-aux
2640 (lognot-derive-type-aux x) y nil)))
2642 (defoptimizer (logorc2 derive-type) ((x y))
2643 (two-arg-derive-type x y (lambda (x y same-leaf)
2645 (specifier-type '(eql -1))
2646 (logior-derive-type-aux
2647 x (lognot-derive-type-aux y) nil)))
2650 ;;;; miscellaneous derive-type methods
2652 (defoptimizer (integer-length derive-type) ((x))
2653 (let ((x-type (lvar-type x)))
2654 (when (numeric-type-p x-type)
2655 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2656 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2657 ;; careful about LO or HI being NIL, though. Also, if 0 is
2658 ;; contained in X, the lower bound is obviously 0.
2659 (flet ((null-or-min (a b)
2660 (and a b (min (integer-length a)
2661 (integer-length b))))
2663 (and a b (max (integer-length a)
2664 (integer-length b)))))
2665 (let* ((min (numeric-type-low x-type))
2666 (max (numeric-type-high x-type))
2667 (min-len (null-or-min min max))
2668 (max-len (null-or-max min max)))
2669 (when (ctypep 0 x-type)
2671 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2673 (defoptimizer (isqrt derive-type) ((x))
2674 (let ((x-type (lvar-type x)))
2675 (when (numeric-type-p x-type)
2676 (let* ((lo (numeric-type-low x-type))
2677 (hi (numeric-type-high x-type))
2678 (lo-res (if lo (isqrt lo) '*))
2679 (hi-res (if hi (isqrt hi) '*)))
2680 (specifier-type `(integer ,lo-res ,hi-res))))))
2682 (defoptimizer (char-code derive-type) ((char))
2683 (let ((type (type-intersection (lvar-type char) (specifier-type 'character))))
2684 (cond ((member-type-p type)
2687 ,@(loop for member in (member-type-members type)
2688 when (characterp member)
2689 collect (char-code member)))))
2690 ((sb!kernel::character-set-type-p type)
2693 ,@(loop for (low . high)
2694 in (character-set-type-pairs type)
2695 collect `(integer ,low ,high)))))
2696 ((csubtypep type (specifier-type 'base-char))
2698 `(mod ,base-char-code-limit)))
2701 `(mod ,char-code-limit))))))
2703 (defoptimizer (code-char derive-type) ((code))
2704 (let ((type (lvar-type code)))
2705 ;; FIXME: unions of integral ranges? It ought to be easier to do
2706 ;; this, given that CHARACTER-SET is basically an integral range
2707 ;; type. -- CSR, 2004-10-04
2708 (when (numeric-type-p type)
2709 (let* ((lo (numeric-type-low type))
2710 (hi (numeric-type-high type))
2711 (type (specifier-type `(character-set ((,lo . ,hi))))))
2713 ;; KLUDGE: when running on the host, we lose a slight amount
2714 ;; of precision so that we don't have to "unparse" types
2715 ;; that formally we can't, such as (CHARACTER-SET ((0
2716 ;; . 0))). -- CSR, 2004-10-06
2718 ((csubtypep type (specifier-type 'standard-char)) type)
2720 ((csubtypep type (specifier-type 'base-char))
2721 (specifier-type 'base-char))
2723 ((csubtypep type (specifier-type 'extended-char))
2724 (specifier-type 'extended-char))
2725 (t #+sb-xc-host (specifier-type 'character)
2726 #-sb-xc-host type))))))
2728 (defoptimizer (values derive-type) ((&rest values))
2729 (make-values-type :required (mapcar #'lvar-type values)))
2731 (defun signum-derive-type-aux (type)
2732 (if (eq (numeric-type-complexp type) :complex)
2733 (let* ((format (case (numeric-type-class type)
2734 ((integer rational) 'single-float)
2735 (t (numeric-type-format type))))
2736 (bound-format (or format 'float)))
2737 (make-numeric-type :class 'float
2740 :low (coerce -1 bound-format)
2741 :high (coerce 1 bound-format)))
2742 (let* ((interval (numeric-type->interval type))
2743 (range-info (interval-range-info interval))
2744 (contains-0-p (interval-contains-p 0 interval))
2745 (class (numeric-type-class type))
2746 (format (numeric-type-format type))
2747 (one (coerce 1 (or format class 'real)))
2748 (zero (coerce 0 (or format class 'real)))
2749 (minus-one (coerce -1 (or format class 'real)))
2750 (plus (make-numeric-type :class class :format format
2751 :low one :high one))
2752 (minus (make-numeric-type :class class :format format
2753 :low minus-one :high minus-one))
2754 ;; KLUDGE: here we have a fairly horrible hack to deal
2755 ;; with the schizophrenia in the type derivation engine.
2756 ;; The problem is that the type derivers reinterpret
2757 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2758 ;; 0d0) within the derivation mechanism doesn't include
2759 ;; -0d0. Ugh. So force it in here, instead.
2760 (zero (make-numeric-type :class class :format format
2761 :low (- zero) :high zero)))
2763 (+ (if contains-0-p (type-union plus zero) plus))
2764 (- (if contains-0-p (type-union minus zero) minus))
2765 (t (type-union minus zero plus))))))
2767 (defoptimizer (signum derive-type) ((num))
2768 (one-arg-derive-type num #'signum-derive-type-aux nil))
2770 ;;;; byte operations
2772 ;;;; We try to turn byte operations into simple logical operations.
2773 ;;;; First, we convert byte specifiers into separate size and position
2774 ;;;; arguments passed to internal %FOO functions. We then attempt to
2775 ;;;; transform the %FOO functions into boolean operations when the
2776 ;;;; size and position are constant and the operands are fixnums.
2778 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2779 ;; expressions that evaluate to the SIZE and POSITION of
2780 ;; the byte-specifier form SPEC. We may wrap a let around
2781 ;; the result of the body to bind some variables.
2783 ;; If the spec is a BYTE form, then bind the vars to the
2784 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2785 ;; and BYTE-POSITION. The goal of this transformation is to
2786 ;; avoid consing up byte specifiers and then immediately
2787 ;; throwing them away.
2788 (with-byte-specifier ((size-var pos-var spec) &body body)
2789 (once-only ((spec `(macroexpand ,spec))
2791 `(if (and (consp ,spec)
2792 (eq (car ,spec) 'byte)
2793 (= (length ,spec) 3))
2794 (let ((,size-var (second ,spec))
2795 (,pos-var (third ,spec)))
2797 (let ((,size-var `(byte-size ,,temp))
2798 (,pos-var `(byte-position ,,temp)))
2799 `(let ((,,temp ,,spec))
2802 (define-source-transform ldb (spec int)
2803 (with-byte-specifier (size pos spec)
2804 `(%ldb ,size ,pos ,int)))
2806 (define-source-transform dpb (newbyte spec int)
2807 (with-byte-specifier (size pos spec)
2808 `(%dpb ,newbyte ,size ,pos ,int)))
2810 (define-source-transform mask-field (spec int)
2811 (with-byte-specifier (size pos spec)
2812 `(%mask-field ,size ,pos ,int)))
2814 (define-source-transform deposit-field (newbyte spec int)
2815 (with-byte-specifier (size pos spec)
2816 `(%deposit-field ,newbyte ,size ,pos ,int))))
2818 (defoptimizer (%ldb derive-type) ((size posn num))
2819 (let ((size (lvar-type size)))
2820 (if (and (numeric-type-p size)
2821 (csubtypep size (specifier-type 'integer)))
2822 (let ((size-high (numeric-type-high size)))
2823 (if (and size-high (<= size-high sb!vm:n-word-bits))
2824 (specifier-type `(unsigned-byte* ,size-high))
2825 (specifier-type 'unsigned-byte)))
2828 (defoptimizer (%mask-field derive-type) ((size posn num))
2829 (let ((size (lvar-type size))
2830 (posn (lvar-type posn)))
2831 (if (and (numeric-type-p size)
2832 (csubtypep size (specifier-type 'integer))
2833 (numeric-type-p posn)
2834 (csubtypep posn (specifier-type 'integer)))
2835 (let ((size-high (numeric-type-high size))
2836 (posn-high (numeric-type-high posn)))
2837 (if (and size-high posn-high
2838 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2839 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2840 (specifier-type 'unsigned-byte)))
2843 (defun %deposit-field-derive-type-aux (size posn int)
2844 (let ((size (lvar-type size))
2845 (posn (lvar-type posn))
2846 (int (lvar-type int)))
2847 (when (and (numeric-type-p size)
2848 (numeric-type-p posn)
2849 (numeric-type-p int))
2850 (let ((size-high (numeric-type-high size))
2851 (posn-high (numeric-type-high posn))
2852 (high (numeric-type-high int))
2853 (low (numeric-type-low int)))
2854 (when (and size-high posn-high high low
2855 ;; KLUDGE: we need this cutoff here, otherwise we
2856 ;; will merrily derive the type of %DPB as
2857 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2858 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2859 ;; 1073741822))), with hilarious consequences. We
2860 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2861 ;; over a reasonable amount of shifting, even on
2862 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2863 ;; machine integers are 64-bits. -- CSR,
2865 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2866 (let ((raw-bit-count (max (integer-length high)
2867 (integer-length low)
2868 (+ size-high posn-high))))
2871 `(signed-byte ,(1+ raw-bit-count))
2872 `(unsigned-byte* ,raw-bit-count)))))))))
2874 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2875 (%deposit-field-derive-type-aux size posn int))
2877 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2878 (%deposit-field-derive-type-aux size posn int))
2880 (deftransform %ldb ((size posn int)
2881 (fixnum fixnum integer)
2882 (unsigned-byte #.sb!vm:n-word-bits))
2883 "convert to inline logical operations"
2884 `(logand (ash int (- posn))
2885 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2886 (- size ,sb!vm:n-word-bits))))
2888 (deftransform %mask-field ((size posn int)
2889 (fixnum fixnum integer)
2890 (unsigned-byte #.sb!vm:n-word-bits))
2891 "convert to inline logical operations"
2893 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2894 (- size ,sb!vm:n-word-bits))
2897 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2898 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2899 ;;; as the result type, as that would allow result types that cover
2900 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2901 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2903 (deftransform %dpb ((new size posn int)
2905 (unsigned-byte #.sb!vm:n-word-bits))
2906 "convert to inline logical operations"
2907 `(let ((mask (ldb (byte size 0) -1)))
2908 (logior (ash (logand new mask) posn)
2909 (logand int (lognot (ash mask posn))))))
2911 (deftransform %dpb ((new size posn int)
2913 (signed-byte #.sb!vm:n-word-bits))
2914 "convert to inline logical operations"
2915 `(let ((mask (ldb (byte size 0) -1)))
2916 (logior (ash (logand new mask) posn)
2917 (logand int (lognot (ash mask posn))))))
2919 (deftransform %deposit-field ((new size posn int)
2921 (unsigned-byte #.sb!vm:n-word-bits))
2922 "convert to inline logical operations"
2923 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2924 (logior (logand new mask)
2925 (logand int (lognot mask)))))
2927 (deftransform %deposit-field ((new size posn int)
2929 (signed-byte #.sb!vm:n-word-bits))
2930 "convert to inline logical operations"
2931 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2932 (logior (logand new mask)
2933 (logand int (lognot mask)))))
2935 (defoptimizer (mask-signed-field derive-type) ((size x))
2936 (let ((size (lvar-type size)))
2937 (if (numeric-type-p size)
2938 (let ((size-high (numeric-type-high size)))
2939 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2940 (specifier-type `(signed-byte ,size-high))
2945 ;;; Modular functions
2947 ;;; (ldb (byte s 0) (foo x y ...)) =
2948 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2950 ;;; and similar for other arguments.
2952 (defun make-modular-fun-type-deriver (prototype kind width signedp)
2953 (declare (ignore kind))
2955 (binding* ((info (info :function :info prototype) :exit-if-null)
2956 (fun (fun-info-derive-type info) :exit-if-null)
2957 (mask-type (specifier-type
2959 ((nil) (let ((mask (1- (ash 1 width))))
2960 `(integer ,mask ,mask)))
2961 ((t) `(signed-byte ,width))))))
2963 (let ((res (funcall fun call)))
2965 (if (eq signedp nil)
2966 (logand-derive-type-aux res mask-type))))))
2969 (binding* ((info (info :function :info prototype) :exit-if-null)
2970 (fun (fun-info-derive-type info) :exit-if-null)
2971 (res (funcall fun call) :exit-if-null)
2972 (mask-type (specifier-type
2974 ((nil) (let ((mask (1- (ash 1 width))))
2975 `(integer ,mask ,mask)))
2976 ((t) `(signed-byte ,width))))))
2977 (if (eq signedp nil)
2978 (logand-derive-type-aux res mask-type)))))
2980 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
2982 ;;; For good functions, we just recursively cut arguments; their
2983 ;;; "goodness" means that the result will not increase (in the
2984 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
2985 ;;; replaced with the version, cutting its result to WIDTH or more
2986 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
2987 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
2988 ;;; arguments (maybe to a different width) and returning the name of a
2989 ;;; modular version, if it exists, or NIL. If we have changed
2990 ;;; anything, we need to flush old derived types, because they have
2991 ;;; nothing in common with the new code.
2992 (defun cut-to-width (lvar kind width signedp)
2993 (declare (type lvar lvar) (type (integer 0) width))
2994 (let ((type (specifier-type (if (zerop width)
2997 ((nil) 'unsigned-byte)
3000 (labels ((reoptimize-node (node name)
3001 (setf (node-derived-type node)
3003 (info :function :type name)))
3004 (setf (lvar-%derived-type (node-lvar node)) nil)
3005 (setf (node-reoptimize node) t)
3006 (setf (block-reoptimize (node-block node)) t)
3007 (reoptimize-component (node-component node) :maybe))
3008 (cut-node (node &aux did-something)
3009 (when (and (not (block-delete-p (node-block node)))
3010 (combination-p node)
3011 (eq (basic-combination-kind node) :known))
3012 (let* ((fun-ref (lvar-use (combination-fun node)))
3013 (fun-name (leaf-source-name (ref-leaf fun-ref)))
3014 (modular-fun (find-modular-version fun-name kind signedp width)))
3015 (when (and modular-fun
3016 (not (and (eq fun-name 'logand)
3018 (single-value-type (node-derived-type node))
3020 (binding* ((name (etypecase modular-fun
3021 ((eql :good) fun-name)
3023 (modular-fun-info-name modular-fun))
3025 (funcall modular-fun node width)))
3027 (unless (eql modular-fun :good)
3028 (setq did-something t)
3031 (find-free-fun name "in a strange place"))
3032 (setf (combination-kind node) :full))
3033 (unless (functionp modular-fun)
3034 (dolist (arg (basic-combination-args node))
3035 (when (cut-lvar arg)
3036 (setq did-something t))))
3038 (reoptimize-node node name))
3040 (cut-lvar (lvar &aux did-something)
3041 (do-uses (node lvar)
3042 (when (cut-node node)
3043 (setq did-something t)))
3047 (defun best-modular-version (width signedp)
3048 ;; 1. exact width-matched :untagged
3049 ;; 2. >/>= width-matched :tagged
3050 ;; 3. >/>= width-matched :untagged
3051 (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class*))
3052 (uswidths (modular-class-widths *untagged-signed-modular-class*))
3053 (uwidths (merge 'list uuwidths uswidths #'< :key #'car))
3054 (twidths (modular-class-widths *tagged-modular-class*)))
3055 (let ((exact (find (cons width signedp) uwidths :test #'equal)))
3057 (return-from best-modular-version (values width :untagged signedp))))
3058 (flet ((inexact-match (w)
3060 ((eq signedp (cdr w)) (<= width (car w)))
3061 ((eq signedp nil) (< width (car w))))))
3062 (let ((tgt (find-if #'inexact-match twidths)))
3064 (return-from best-modular-version
3065 (values (car tgt) :tagged (cdr tgt)))))
3066 (let ((ugt (find-if #'inexact-match uwidths)))
3068 (return-from best-modular-version
3069 (values (car ugt) :untagged (cdr ugt))))))))
3071 (defoptimizer (logand optimizer) ((x y) node)
3072 (let ((result-type (single-value-type (node-derived-type node))))
3073 (when (numeric-type-p result-type)
3074 (let ((low (numeric-type-low result-type))
3075 (high (numeric-type-high result-type)))
3076 (when (and (numberp low)
3079 (let ((width (integer-length high)))
3080 (multiple-value-bind (w kind signedp)
3081 (best-modular-version width nil)
3083 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP).
3084 (cut-to-width x kind width signedp)
3085 (cut-to-width y kind width signedp)
3086 nil ; After fixing above, replace with T.
3089 (defoptimizer (mask-signed-field optimizer) ((width x) node)
3090 (let ((result-type (single-value-type (node-derived-type node))))
3091 (when (numeric-type-p result-type)
3092 (let ((low (numeric-type-low result-type))
3093 (high (numeric-type-high result-type)))
3094 (when (and (numberp low) (numberp high))
3095 (let ((width (max (integer-length high) (integer-length low))))
3096 (multiple-value-bind (w kind)
3097 (best-modular-version width t)
3099 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH T).
3100 (cut-to-width x kind width t)
3101 nil ; After fixing above, replace with T.
3104 ;;; miscellanous numeric transforms
3106 ;;; If a constant appears as the first arg, swap the args.
3107 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
3108 (if (and (constant-lvar-p x)
3109 (not (constant-lvar-p y)))
3110 `(,(lvar-fun-name (basic-combination-fun node))
3113 (give-up-ir1-transform)))
3115 (dolist (x '(= char= + * logior logand logxor))
3116 (%deftransform x '(function * *) #'commutative-arg-swap
3117 "place constant arg last"))
3119 ;;; Handle the case of a constant BOOLE-CODE.
3120 (deftransform boole ((op x y) * *)
3121 "convert to inline logical operations"
3122 (unless (constant-lvar-p op)
3123 (give-up-ir1-transform "BOOLE code is not a constant."))
3124 (let ((control (lvar-value op)))
3126 (#.sb!xc:boole-clr 0)
3127 (#.sb!xc:boole-set -1)
3128 (#.sb!xc:boole-1 'x)
3129 (#.sb!xc:boole-2 'y)
3130 (#.sb!xc:boole-c1 '(lognot x))
3131 (#.sb!xc:boole-c2 '(lognot y))
3132 (#.sb!xc:boole-and '(logand x y))
3133 (#.sb!xc:boole-ior '(logior x y))
3134 (#.sb!xc:boole-xor '(logxor x y))
3135 (#.sb!xc:boole-eqv '(logeqv x y))
3136 (#.sb!xc:boole-nand '(lognand x y))
3137 (#.sb!xc:boole-nor '(lognor x y))
3138 (#.sb!xc:boole-andc1 '(logandc1 x y))
3139 (#.sb!xc:boole-andc2 '(logandc2 x y))
3140 (#.sb!xc:boole-orc1 '(logorc1 x y))
3141 (#.sb!xc:boole-orc2 '(logorc2 x y))
3143 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
3146 ;;;; converting special case multiply/divide to shifts
3148 ;;; If arg is a constant power of two, turn * into a shift.
3149 (deftransform * ((x y) (integer integer) *)
3150 "convert x*2^k to shift"
3151 (unless (constant-lvar-p y)
3152 (give-up-ir1-transform))
3153 (let* ((y (lvar-value y))
3155 (len (1- (integer-length y-abs))))
3156 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3157 (give-up-ir1-transform))
3162 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3163 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3165 (flet ((frob (y ceil-p)
3166 (unless (constant-lvar-p y)
3167 (give-up-ir1-transform))
3168 (let* ((y (lvar-value y))
3170 (len (1- (integer-length y-abs))))
3171 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3172 (give-up-ir1-transform))
3173 (let ((shift (- len))
3175 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
3176 `(let ((x (+ x ,delta)))
3178 `(values (ash (- x) ,shift)
3179 (- (- (logand (- x) ,mask)) ,delta))
3180 `(values (ash x ,shift)
3181 (- (logand x ,mask) ,delta))))))))
3182 (deftransform floor ((x y) (integer integer) *)
3183 "convert division by 2^k to shift"
3185 (deftransform ceiling ((x y) (integer integer) *)
3186 "convert division by 2^k to shift"
3189 ;;; Do the same for MOD.
3190 (deftransform mod ((x y) (integer integer) *)
3191 "convert remainder mod 2^k to LOGAND"
3192 (unless (constant-lvar-p y)
3193 (give-up-ir1-transform))
3194 (let* ((y (lvar-value y))
3196 (len (1- (integer-length y-abs))))
3197 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3198 (give-up-ir1-transform))
3199 (let ((mask (1- y-abs)))
3201 `(- (logand (- x) ,mask))
3202 `(logand x ,mask)))))
3204 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3205 (deftransform truncate ((x y) (integer integer))
3206 "convert division by 2^k to shift"
3207 (unless (constant-lvar-p y)
3208 (give-up-ir1-transform))
3209 (let* ((y (lvar-value y))
3211 (len (1- (integer-length y-abs))))
3212 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3213 (give-up-ir1-transform))
3214 (let* ((shift (- len))
3217 (values ,(if (minusp y)
3219 `(- (ash (- x) ,shift)))
3220 (- (logand (- x) ,mask)))
3221 (values ,(if (minusp y)
3222 `(ash (- ,mask x) ,shift)
3224 (logand x ,mask))))))
3226 ;;; And the same for REM.
3227 (deftransform rem ((x y) (integer integer) *)
3228 "convert remainder mod 2^k to LOGAND"
3229 (unless (constant-lvar-p y)
3230 (give-up-ir1-transform))
3231 (let* ((y (lvar-value y))
3233 (len (1- (integer-length y-abs))))
3234 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3235 (give-up-ir1-transform))
3236 (let ((mask (1- y-abs)))
3238 (- (logand (- x) ,mask))
3239 (logand x ,mask)))))
3241 ;;;; arithmetic and logical identity operation elimination
3243 ;;; Flush calls to various arith functions that convert to the
3244 ;;; identity function or a constant.
3245 (macrolet ((def (name identity result)
3246 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3247 "fold identity operations"
3254 (def logxor -1 (lognot x))
3257 (deftransform logand ((x y) (* (constant-arg t)) *)
3258 "fold identity operation"
3259 (let ((y (lvar-value y)))
3260 (unless (and (plusp y)
3261 (= y (1- (ash 1 (integer-length y)))))
3262 (give-up-ir1-transform))
3263 (unless (csubtypep (lvar-type x)
3264 (specifier-type `(integer 0 ,y)))
3265 (give-up-ir1-transform))
3268 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3269 "fold identity operation"
3270 (let ((size (lvar-value size)))
3271 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3272 (give-up-ir1-transform))
3275 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3276 ;;; (* 0 -4.0) is -0.0.
3277 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3278 "convert (- 0 x) to negate"
3280 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3281 "convert (* x 0) to 0"
3284 ;;; Return T if in an arithmetic op including lvars X and Y, the
3285 ;;; result type is not affected by the type of X. That is, Y is at
3286 ;;; least as contagious as X.
3288 (defun not-more-contagious (x y)
3289 (declare (type continuation x y))
3290 (let ((x (lvar-type x))
3292 (values (type= (numeric-contagion x y)
3293 (numeric-contagion y y)))))
3294 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3295 ;;; XXX needs more work as valid transforms are missed; some cases are
3296 ;;; specific to particular transform functions so the use of this
3297 ;;; function may need a re-think.
3298 (defun not-more-contagious (x y)
3299 (declare (type lvar x y))
3300 (flet ((simple-numeric-type (num)
3301 (and (numeric-type-p num)
3302 ;; Return non-NIL if NUM is integer, rational, or a float
3303 ;; of some type (but not FLOAT)
3304 (case (numeric-type-class num)
3308 (numeric-type-format num))
3311 (let ((x (lvar-type x))
3313 (if (and (simple-numeric-type x)
3314 (simple-numeric-type y))
3315 (values (type= (numeric-contagion x y)
3316 (numeric-contagion y y)))))))
3318 (def!type exact-number ()
3319 '(or rational (complex rational)))
3323 ;;; Only safely applicable for exact numbers. For floating-point
3324 ;;; x, one would have to first show that neither x or y are signed
3325 ;;; 0s, and that x isn't an SNaN.
3326 (deftransform + ((x y) (exact-number (constant-arg (eql 0))) *)
3331 (deftransform - ((x y) (exact-number (constant-arg (eql 0))) *)
3335 ;;; Fold (OP x +/-1)
3337 ;;; %NEGATE might not always signal correctly.
3339 ((def (name result minus-result)
3340 `(deftransform ,name ((x y)
3341 (exact-number (constant-arg (member 1 -1))))
3342 "fold identity operations"
3343 (if (minusp (lvar-value y)) ',minus-result ',result))))
3344 (def * x (%negate x))
3345 (def / x (%negate x))
3346 (def expt x (/ 1 x)))
3348 ;;; Fold (expt x n) into multiplications for small integral values of
3349 ;;; N; convert (expt x 1/2) to sqrt.
3350 (deftransform expt ((x y) (t (constant-arg real)) *)
3351 "recode as multiplication or sqrt"
3352 (let ((val (lvar-value y)))
3353 ;; If Y would cause the result to be promoted to the same type as
3354 ;; Y, we give up. If not, then the result will be the same type
3355 ;; as X, so we can replace the exponentiation with simple
3356 ;; multiplication and division for small integral powers.
3357 (unless (not-more-contagious y x)
3358 (give-up-ir1-transform))
3360 (let ((x-type (lvar-type x)))
3361 (cond ((csubtypep x-type (specifier-type '(or rational
3362 (complex rational))))
3364 ((csubtypep x-type (specifier-type 'real))
3368 ((csubtypep x-type (specifier-type 'complex))
3369 ;; both parts are float
3371 (t (give-up-ir1-transform)))))
3372 ((= val 2) '(* x x))
3373 ((= val -2) '(/ (* x x)))
3374 ((= val 3) '(* x x x))
3375 ((= val -3) '(/ (* x x x)))
3376 ((= val 1/2) '(sqrt x))
3377 ((= val -1/2) '(/ (sqrt x)))
3378 (t (give-up-ir1-transform)))))
3380 (deftransform expt ((x y) ((constant-arg (member -1 -1.0 -1.0d0)) integer) *)
3381 "recode as an ODDP check"
3382 (let ((val (lvar-value x)))
3384 '(- 1 (* 2 (logand 1 y)))
3389 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3390 ;;; transformations?
3391 ;;; Perhaps we should have to prove that the denominator is nonzero before
3392 ;;; doing them? -- WHN 19990917
3393 (macrolet ((def (name)
3394 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3401 (macrolet ((def (name)
3402 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3411 ;;;; character operations
3413 (deftransform char-equal ((a b) (base-char base-char))
3415 '(let* ((ac (char-code a))
3417 (sum (logxor ac bc)))
3419 (when (eql sum #x20)
3420 (let ((sum (+ ac bc)))
3421 (or (and (> sum 161) (< sum 213))
3422 (and (> sum 415) (< sum 461))
3423 (and (> sum 463) (< sum 477))))))))
3425 (deftransform char-upcase ((x) (base-char))
3427 '(let ((n-code (char-code x)))
3428 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3429 (< n-code #o173)) ; Octal 172 is #\z.
3430 (and (> n-code #o337)
3432 (and (> n-code #o367)
3434 (code-char (logxor #x20 n-code))
3437 (deftransform char-downcase ((x) (base-char))
3439 '(let ((n-code (char-code x)))
3440 (if (or (and (> n-code 64) ; 65 is #\A.
3441 (< n-code 91)) ; 90 is #\Z.
3446 (code-char (logxor #x20 n-code))
3449 ;;;; equality predicate transforms
3451 ;;; Return true if X and Y are lvars whose only use is a
3452 ;;; reference to the same leaf, and the value of the leaf cannot
3454 (defun same-leaf-ref-p (x y)
3455 (declare (type lvar x y))
3456 (let ((x-use (principal-lvar-use x))
3457 (y-use (principal-lvar-use y)))
3460 (eq (ref-leaf x-use) (ref-leaf y-use))
3461 (constant-reference-p x-use))))
3463 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3464 ;;; if there is no intersection between the types of the arguments,
3465 ;;; then the result is definitely false.
3466 (deftransform simple-equality-transform ((x y) * *
3469 ((same-leaf-ref-p x y) t)
3470 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3472 (t (give-up-ir1-transform))))
3475 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3479 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3480 ;;; try to convert to a type-specific predicate or EQ:
3481 ;;; -- If both args are characters, convert to CHAR=. This is better than
3482 ;;; just converting to EQ, since CHAR= may have special compilation
3483 ;;; strategies for non-standard representations, etc.
3484 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3485 ;;; constant and if so, put X second. Doing this results in better
3486 ;;; code from the backend, since the backend assumes that any constant
3487 ;;; argument comes second.
3488 ;;; -- If either arg is definitely not a number or a fixnum, then we
3489 ;;; can compare with EQ.
3490 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3491 ;;; is constant then we put it second. If X is a subtype of Y, we put
3492 ;;; it second. These rules make it easier for the back end to match
3493 ;;; these interesting cases.
3494 (deftransform eql ((x y) * * :node node)
3495 "convert to simpler equality predicate"
3496 (let ((x-type (lvar-type x))
3497 (y-type (lvar-type y))
3498 (char-type (specifier-type 'character)))
3499 (flet ((fixnum-type-p (type)
3500 (csubtypep type (specifier-type 'fixnum))))
3502 ((same-leaf-ref-p x y) t)
3503 ((not (types-equal-or-intersect x-type y-type))
3505 ((and (csubtypep x-type char-type)
3506 (csubtypep y-type char-type))
3508 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3509 (commutative-arg-swap node))
3510 ((or (eq-comparable-type-p x-type) (eq-comparable-type-p y-type))
3512 ((and (not (constant-lvar-p y))
3513 (or (constant-lvar-p x)
3514 (and (csubtypep x-type y-type)
3515 (not (csubtypep y-type x-type)))))
3518 (give-up-ir1-transform))))))
3520 ;;; similarly to the EQL transform above, we attempt to constant-fold
3521 ;;; or convert to a simpler predicate: mostly we have to be careful
3522 ;;; with strings and bit-vectors.
3523 (deftransform equal ((x y) * *)
3524 "convert to simpler equality predicate"
3525 (let ((x-type (lvar-type x))
3526 (y-type (lvar-type y))
3527 (string-type (specifier-type 'string))
3528 (bit-vector-type (specifier-type 'bit-vector)))
3530 ((same-leaf-ref-p x y) t)
3531 ((and (csubtypep x-type string-type)
3532 (csubtypep y-type string-type))
3534 ((and (csubtypep x-type bit-vector-type)
3535 (csubtypep y-type bit-vector-type))
3536 '(bit-vector-= x y))
3537 ;; if at least one is not a string, and at least one is not a
3538 ;; bit-vector, then we can reason from types.
3539 ((and (not (and (types-equal-or-intersect x-type string-type)
3540 (types-equal-or-intersect y-type string-type)))
3541 (not (and (types-equal-or-intersect x-type bit-vector-type)
3542 (types-equal-or-intersect y-type bit-vector-type)))
3543 (not (types-equal-or-intersect x-type y-type)))
3545 (t (give-up-ir1-transform)))))
3547 ;;; Convert to EQL if both args are rational and complexp is specified
3548 ;;; and the same for both.
3549 (deftransform = ((x y) (number number) *)
3551 (let ((x-type (lvar-type x))
3552 (y-type (lvar-type y)))
3553 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3554 (csubtypep y-type (specifier-type 'float)))
3555 (and (csubtypep x-type (specifier-type '(complex float)))
3556 (csubtypep y-type (specifier-type '(complex float))))
3557 #!+complex-float-vops
3558 (and (csubtypep x-type (specifier-type '(or single-float (complex single-float))))
3559 (csubtypep y-type (specifier-type '(or single-float (complex single-float)))))
3560 #!+complex-float-vops
3561 (and (csubtypep x-type (specifier-type '(or double-float (complex double-float))))
3562 (csubtypep y-type (specifier-type '(or double-float (complex double-float))))))
3563 ;; They are both floats. Leave as = so that -0.0 is
3564 ;; handled correctly.
3565 (give-up-ir1-transform))
3566 ((or (and (csubtypep x-type (specifier-type 'rational))
3567 (csubtypep y-type (specifier-type 'rational)))
3568 (and (csubtypep x-type
3569 (specifier-type '(complex rational)))
3571 (specifier-type '(complex rational)))))
3572 ;; They are both rationals and complexp is the same.
3576 (give-up-ir1-transform
3577 "The operands might not be the same type.")))))
3579 (defun maybe-float-lvar-p (lvar)
3580 (neq *empty-type* (type-intersection (specifier-type 'float)
3583 (flet ((maybe-invert (node op inverted x y)
3584 ;; Don't invert if either argument can be a float (NaNs)
3586 ((or (maybe-float-lvar-p x) (maybe-float-lvar-p y))
3587 (delay-ir1-transform node :constraint)
3588 `(or (,op x y) (= x y)))
3590 `(if (,inverted x y) nil t)))))
3591 (deftransform >= ((x y) (number number) * :node node)
3592 "invert or open code"
3593 (maybe-invert node '> '< x y))
3594 (deftransform <= ((x y) (number number) * :node node)
3595 "invert or open code"
3596 (maybe-invert node '< '> x y)))
3598 ;;; See whether we can statically determine (< X Y) using type
3599 ;;; information. If X's high bound is < Y's low, then X < Y.
3600 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3601 ;;; NIL). If not, at least make sure any constant arg is second.
3602 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3603 `(deftransform ,name ((x y))
3604 "optimize using intervals"
3605 (if (and (same-leaf-ref-p x y)
3606 ;; For non-reflexive functions we don't need
3607 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3608 ;; but with reflexive ones we don't know...
3610 '((and (not (maybe-float-lvar-p x))
3611 (not (maybe-float-lvar-p y))))))
3613 (let ((ix (or (type-approximate-interval (lvar-type x))
3614 (give-up-ir1-transform)))
3615 (iy (or (type-approximate-interval (lvar-type y))
3616 (give-up-ir1-transform))))
3621 ((and (constant-lvar-p x)
3622 (not (constant-lvar-p y)))
3625 (give-up-ir1-transform))))))))
3626 (def = = t (interval-= ix iy) (interval-/= ix iy))
3627 (def /= /= nil (interval-/= ix iy) (interval-= ix iy))
3628 (def < > nil (interval-< ix iy) (interval->= ix iy))
3629 (def > < nil (interval-< iy ix) (interval->= iy ix))
3630 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3631 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3633 (defun ir1-transform-char< (x y first second inverse)
3635 ((same-leaf-ref-p x y) nil)
3636 ;; If we had interval representation of character types, as we
3637 ;; might eventually have to to support 2^21 characters, then here
3638 ;; we could do some compile-time computation as in transforms for
3639 ;; < above. -- CSR, 2003-07-01
3640 ((and (constant-lvar-p first)
3641 (not (constant-lvar-p second)))
3643 (t (give-up-ir1-transform))))
3645 (deftransform char< ((x y) (character character) *)
3646 (ir1-transform-char< x y x y 'char>))
3648 (deftransform char> ((x y) (character character) *)
3649 (ir1-transform-char< y x x y 'char<))
3651 ;;;; converting N-arg comparisons
3653 ;;;; We convert calls to N-arg comparison functions such as < into
3654 ;;;; two-arg calls. This transformation is enabled for all such
3655 ;;;; comparisons in this file. If any of these predicates are not
3656 ;;;; open-coded, then the transformation should be removed at some
3657 ;;;; point to avoid pessimization.
3659 ;;; This function is used for source transformation of N-arg
3660 ;;; comparison functions other than inequality. We deal both with
3661 ;;; converting to two-arg calls and inverting the sense of the test,
3662 ;;; if necessary. If the call has two args, then we pass or return a
3663 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3664 ;;; then we transform to code that returns true. Otherwise, we bind
3665 ;;; all the arguments and expand into a bunch of IFs.
3666 (defun multi-compare (predicate args not-p type &optional force-two-arg-p)
3667 (let ((nargs (length args)))
3668 (cond ((< nargs 1) (values nil t))
3669 ((= nargs 1) `(progn (the ,type ,@args) t))
3672 `(if (,predicate ,(first args) ,(second args)) nil t)
3674 `(,predicate ,(first args) ,(second args))
3677 (do* ((i (1- nargs) (1- i))
3679 (current (gensym) (gensym))
3680 (vars (list current) (cons current vars))
3682 `(if (,predicate ,current ,last)
3684 `(if (,predicate ,current ,last)
3687 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3690 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3691 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3692 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3693 ;;; We cannot do the inversion for >= and <= here, since both
3694 ;;; (< NaN X) and (> NaN X)
3695 ;;; are false, and we don't have type-inforation available yet. The
3696 ;;; deftransforms for two-argument versions of >= and <= takes care of
3697 ;;; the inversion to > and < when possible.
3698 (define-source-transform <= (&rest args) (multi-compare '<= args nil 'real))
3699 (define-source-transform >= (&rest args) (multi-compare '>= args nil 'real))
3701 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3703 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3705 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3707 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3709 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3712 (define-source-transform char-equal (&rest args)
3713 (multi-compare 'sb!impl::two-arg-char-equal args nil 'character t))
3714 (define-source-transform char-lessp (&rest args)
3715 (multi-compare 'sb!impl::two-arg-char-lessp args nil 'character t))
3716 (define-source-transform char-greaterp (&rest args)
3717 (multi-compare 'sb!impl::two-arg-char-greaterp args nil 'character t))
3718 (define-source-transform char-not-greaterp (&rest args)
3719 (multi-compare 'sb!impl::two-arg-char-greaterp args t 'character t))
3720 (define-source-transform char-not-lessp (&rest args)
3721 (multi-compare 'sb!impl::two-arg-char-lessp args t 'character t))
3723 ;;; This function does source transformation of N-arg inequality
3724 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3725 ;;; arg cases. If there are more than two args, then we expand into
3726 ;;; the appropriate n^2 comparisons only when speed is important.
3727 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3728 (defun multi-not-equal (predicate args type)
3729 (let ((nargs (length args)))
3730 (cond ((< nargs 1) (values nil t))
3731 ((= nargs 1) `(progn (the ,type ,@args) t))
3733 `(if (,predicate ,(first args) ,(second args)) nil t))
3734 ((not (policy *lexenv*
3735 (and (>= speed space)
3736 (>= speed compilation-speed))))
3739 (let ((vars (make-gensym-list nargs)))
3740 (do ((var vars next)
3741 (next (cdr vars) (cdr next))
3744 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3746 (let ((v1 (first var)))
3748 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3750 (define-source-transform /= (&rest args)
3751 (multi-not-equal '= args 'number))
3752 (define-source-transform char/= (&rest args)
3753 (multi-not-equal 'char= args 'character))
3754 (define-source-transform char-not-equal (&rest args)
3755 (multi-not-equal 'char-equal args 'character))
3757 ;;; Expand MAX and MIN into the obvious comparisons.
3758 (define-source-transform max (arg0 &rest rest)
3759 (once-only ((arg0 arg0))
3761 `(values (the real ,arg0))
3762 `(let ((maxrest (max ,@rest)))
3763 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3764 (define-source-transform min (arg0 &rest rest)
3765 (once-only ((arg0 arg0))
3767 `(values (the real ,arg0))
3768 `(let ((minrest (min ,@rest)))
3769 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3771 ;;;; converting N-arg arithmetic functions
3773 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3774 ;;;; versions, and degenerate cases are flushed.
3776 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3777 (declaim (ftype (sfunction (symbol t list t) list) associate-args))
3778 (defun associate-args (fun first-arg more-args identity)
3779 (let ((next (rest more-args))
3780 (arg (first more-args)))
3782 `(,fun ,first-arg ,(if arg arg identity))
3783 (associate-args fun `(,fun ,first-arg ,arg) next identity))))
3785 ;;; Reduce constants in ARGS list.
3786 (declaim (ftype (sfunction (symbol list t symbol) list) reduce-constants))
3787 (defun reduce-constants (fun args identity one-arg-result-type)
3788 (let ((one-arg-constant-p (ecase one-arg-result-type
3790 (integer #'integerp)))
3791 (reduced-value identity)
3793 (collect ((not-constants))
3795 (if (funcall one-arg-constant-p arg)
3796 (setf reduced-value (funcall fun reduced-value arg)
3798 (not-constants arg)))
3799 ;; It is tempting to drop constants reduced to identity here,
3800 ;; but if X is SNaN in (* X 1), we cannot drop the 1.
3803 `(,reduced-value ,@(not-constants))
3805 `(,reduced-value)))))
3807 ;;; Do source transformations for transitive functions such as +.
3808 ;;; One-arg cases are replaced with the arg and zero arg cases with
3809 ;;; the identity. ONE-ARG-RESULT-TYPE is the type to ensure (with THE)
3810 ;;; that the argument in one-argument calls is.
3811 (declaim (ftype (function (symbol list t &optional symbol list)
3812 (values t &optional (member nil t)))
3813 source-transform-transitive))
3814 (defun source-transform-transitive (fun args identity
3815 &optional (one-arg-result-type 'number)
3816 (one-arg-prefixes '(values)))
3819 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
3821 (t (let ((reduced-args (reduce-constants fun args identity one-arg-result-type)))
3822 (associate-args fun (first reduced-args) (rest reduced-args) identity)))))
3824 (define-source-transform + (&rest args)
3825 (source-transform-transitive '+ args 0))
3826 (define-source-transform * (&rest args)
3827 (source-transform-transitive '* args 1))
3828 (define-source-transform logior (&rest args)
3829 (source-transform-transitive 'logior args 0 'integer))
3830 (define-source-transform logxor (&rest args)
3831 (source-transform-transitive 'logxor args 0 'integer))
3832 (define-source-transform logand (&rest args)
3833 (source-transform-transitive 'logand args -1 'integer))
3834 (define-source-transform logeqv (&rest args)
3835 (source-transform-transitive 'logeqv args -1 'integer))
3836 (define-source-transform gcd (&rest args)
3837 (source-transform-transitive 'gcd args 0 'integer '(abs)))
3838 (define-source-transform lcm (&rest args)
3839 (source-transform-transitive 'lcm args 1 'integer '(abs)))
3841 ;;; Do source transformations for intransitive n-arg functions such as
3842 ;;; /. With one arg, we form the inverse. With two args we pass.
3843 ;;; Otherwise we associate into two-arg calls.
3844 (declaim (ftype (function (symbol symbol list t list &optional symbol)
3845 (values list &optional (member nil t)))
3846 source-transform-intransitive))
3847 (defun source-transform-intransitive (fun fun* args identity one-arg-prefixes
3848 &optional (one-arg-result-type 'number))
3850 ((0 2) (values nil t))
3851 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
3852 (t (let ((reduced-args
3853 (reduce-constants fun* (rest args) identity one-arg-result-type)))
3854 (associate-args fun (first args) reduced-args identity)))))
3856 (define-source-transform - (&rest args)
3857 (source-transform-intransitive '- '+ args 0 '(%negate)))
3858 (define-source-transform / (&rest args)
3859 (source-transform-intransitive '/ '* args 1 '(/ 1)))
3861 ;;;; transforming APPLY
3863 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
3864 ;;; only needs to understand one kind of variable-argument call. It is
3865 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
3866 (define-source-transform apply (fun arg &rest more-args)
3867 (let ((args (cons arg more-args)))
3868 `(multiple-value-call ,fun
3869 ,@(mapcar (lambda (x) `(values ,x)) (butlast args))
3870 (values-list ,(car (last args))))))
3872 ;;; When &REST argument are at play, we also have extra context and count
3873 ;;; arguments -- convert to %VALUES-LIST-OR-CONTEXT when possible, so that the
3874 ;;; deftransform can decide what to do after everything has been converted.
3875 (define-source-transform values-list (list)
3877 (let* ((var (lexenv-find list vars))
3878 (info (when (lambda-var-p var)
3879 (lambda-var-arg-info var))))
3881 (eq :rest (arg-info-kind info))
3882 (consp (arg-info-default info)))
3883 (destructuring-bind (context count &optional used) (arg-info-default info)
3884 (declare (ignore used))
3885 `(%values-list-or-context ,list ,context ,count))
3889 (deftransform %values-list-or-context ((list context count) * * :node node)
3890 (let* ((use (lvar-use list))
3891 (var (when (ref-p use) (ref-leaf use)))
3892 (home (when (lambda-var-p var) (lambda-var-home var)))
3893 (info (when (lambda-var-p var) (lambda-var-arg-info var))))
3894 (flet ((ref-good-for-more-context-p (ref)
3895 (let ((dest (principal-lvar-end (node-lvar ref))))
3896 (and (combination-p dest)
3897 ;; Uses outside VALUES-LIST will require a &REST list anyways,
3898 ;; to it's no use saving effort here -- plus they might modify
3899 ;; the list destructively.
3900 (eq '%values-list-or-context (lvar-fun-name (combination-fun dest)))
3901 ;; If the home lambda is different and isn't DX, it might
3902 ;; escape -- in which case using the more context isn't safe.
3903 (let ((clambda (node-home-lambda dest)))
3904 (or (eq home clambda)
3905 (leaf-dynamic-extent clambda)))))))
3908 (consp (arg-info-default info))
3909 (not (lambda-var-specvar var))
3910 (not (lambda-var-sets var))
3911 (every #'ref-good-for-more-context-p (lambda-var-refs var)))))
3913 (destructuring-bind (context count &optional used) (arg-info-default info)
3914 (declare (ignore used))
3915 (setf (arg-info-default info) (list context count t)))
3916 `(%more-arg-values context 0 count))
3919 (setf (arg-info-default info) t))
3920 `(values-list list)))))))
3923 ;;;; transforming FORMAT
3925 ;;;; If the control string is a compile-time constant, then replace it
3926 ;;;; with a use of the FORMATTER macro so that the control string is
3927 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
3928 ;;;; or T and the control string is a function (i.e. FORMATTER), then
3929 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
3931 ;;; for compile-time argument count checking.
3933 ;;; FIXME II: In some cases, type information could be correlated; for
3934 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
3935 ;;; of a corresponding argument is known and does not intersect the
3936 ;;; list type, a warning could be signalled.
3937 (defun check-format-args (string args fun)
3938 (declare (type string string))
3939 (unless (typep string 'simple-string)
3940 (setq string (coerce string 'simple-string)))
3941 (multiple-value-bind (min max)
3942 (handler-case (sb!format:%compiler-walk-format-string string args)
3943 (sb!format:format-error (c)
3944 (compiler-warn "~A" c)))
3946 (let ((nargs (length args)))
3949 (warn 'format-too-few-args-warning
3951 "Too few arguments (~D) to ~S ~S: requires at least ~D."
3952 :format-arguments (list nargs fun string min)))
3954 (warn 'format-too-many-args-warning
3956 "Too many arguments (~D) to ~S ~S: uses at most ~D."
3957 :format-arguments (list nargs fun string max))))))))
3959 (defoptimizer (format optimizer) ((dest control &rest args))
3960 (when (constant-lvar-p control)
3961 (let ((x (lvar-value control)))
3963 (check-format-args x args 'format)))))
3965 ;;; We disable this transform in the cross-compiler to save memory in
3966 ;;; the target image; most of the uses of FORMAT in the compiler are for
3967 ;;; error messages, and those don't need to be particularly fast.
3969 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
3970 :policy (>= speed space))
3971 (unless (constant-lvar-p control)
3972 (give-up-ir1-transform "The control string is not a constant."))
3973 (let ((arg-names (make-gensym-list (length args))))
3974 `(lambda (dest control ,@arg-names)
3975 (declare (ignore control))
3976 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
3978 (deftransform format ((stream control &rest args) (stream function &rest t))
3979 (let ((arg-names (make-gensym-list (length args))))
3980 `(lambda (stream control ,@arg-names)
3981 (funcall control stream ,@arg-names)
3984 (deftransform format ((tee control &rest args) ((member t) function &rest t))
3985 (let ((arg-names (make-gensym-list (length args))))
3986 `(lambda (tee control ,@arg-names)
3987 (declare (ignore tee))
3988 (funcall control *standard-output* ,@arg-names)
3991 (deftransform pathname ((pathspec) (pathname) *)
3994 (deftransform pathname ((pathspec) (string) *)
3995 '(values (parse-namestring pathspec)))
3999 `(defoptimizer (,name optimizer) ((control &rest args))
4000 (when (constant-lvar-p control)
4001 (let ((x (lvar-value control)))
4003 (check-format-args x args ',name)))))))
4006 #+sb-xc-host ; Only we should be using these
4009 (def compiler-error)
4011 (def compiler-style-warn)
4012 (def compiler-notify)
4013 (def maybe-compiler-notify)
4016 (defoptimizer (cerror optimizer) ((report control &rest args))
4017 (when (and (constant-lvar-p control)
4018 (constant-lvar-p report))
4019 (let ((x (lvar-value control))
4020 (y (lvar-value report)))
4021 (when (and (stringp x) (stringp y))
4022 (multiple-value-bind (min1 max1)
4024 (sb!format:%compiler-walk-format-string x args)
4025 (sb!format:format-error (c)
4026 (compiler-warn "~A" c)))
4028 (multiple-value-bind (min2 max2)
4030 (sb!format:%compiler-walk-format-string y args)
4031 (sb!format:format-error (c)
4032 (compiler-warn "~A" c)))
4034 (let ((nargs (length args)))
4036 ((< nargs (min min1 min2))
4037 (warn 'format-too-few-args-warning
4039 "Too few arguments (~D) to ~S ~S ~S: ~
4040 requires at least ~D."
4042 (list nargs 'cerror y x (min min1 min2))))
4043 ((> nargs (max max1 max2))
4044 (warn 'format-too-many-args-warning
4046 "Too many arguments (~D) to ~S ~S ~S: ~
4049 (list nargs 'cerror y x (max max1 max2))))))))))))))
4051 (defoptimizer (coerce derive-type) ((value type) node)
4053 ((constant-lvar-p type)
4054 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
4055 ;; but dealing with the niggle that complex canonicalization gets
4056 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
4058 (let* ((specifier (lvar-value type))
4059 (result-typeoid (careful-specifier-type specifier)))
4061 ((null result-typeoid) nil)
4062 ((csubtypep result-typeoid (specifier-type 'number))
4063 ;; the difficult case: we have to cope with ANSI 12.1.5.3
4064 ;; Rule of Canonical Representation for Complex Rationals,
4065 ;; which is a truly nasty delivery to field.
4067 ((csubtypep result-typeoid (specifier-type 'real))
4068 ;; cleverness required here: it would be nice to deduce
4069 ;; that something of type (INTEGER 2 3) coerced to type
4070 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
4071 ;; FLOAT gets its own clause because it's implemented as
4072 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
4075 ((and (numeric-type-p result-typeoid)
4076 (eq (numeric-type-complexp result-typeoid) :real))
4077 ;; FIXME: is this clause (a) necessary or (b) useful?
4079 ((or (csubtypep result-typeoid
4080 (specifier-type '(complex single-float)))
4081 (csubtypep result-typeoid
4082 (specifier-type '(complex double-float)))
4084 (csubtypep result-typeoid
4085 (specifier-type '(complex long-float))))
4086 ;; float complex types are never canonicalized.
4089 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
4090 ;; probably just a COMPLEX or equivalent. So, in that
4091 ;; case, we will return a complex or an object of the
4092 ;; provided type if it's rational:
4093 (type-union result-typeoid
4094 (type-intersection (lvar-type value)
4095 (specifier-type 'rational))))))
4096 ((and (policy node (zerop safety))
4097 (csubtypep result-typeoid (specifier-type '(array * (*)))))
4098 ;; At zero safety the deftransform for COERCE can elide dimension
4099 ;; checks for the things like (COERCE X '(SIMPLE-VECTOR 5)) -- so we
4100 ;; need to simplify the type to drop the dimension information.
4101 (let ((vtype (simplify-vector-type result-typeoid)))
4103 (specifier-type vtype)
4108 ;; OK, the result-type argument isn't constant. However, there
4109 ;; are common uses where we can still do better than just
4110 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
4111 ;; where Y is of a known type. See messages on cmucl-imp
4112 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
4113 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
4114 ;; the basis that it's unlikely that other uses are both
4115 ;; time-critical and get to this branch of the COND (non-constant
4116 ;; second argument to COERCE). -- CSR, 2002-12-16
4117 (let ((value-type (lvar-type value))
4118 (type-type (lvar-type type)))
4120 ((good-cons-type-p (cons-type)
4121 ;; Make sure the cons-type we're looking at is something
4122 ;; we're prepared to handle which is basically something
4123 ;; that array-element-type can return.
4124 (or (and (member-type-p cons-type)
4125 (eql 1 (member-type-size cons-type))
4126 (null (first (member-type-members cons-type))))
4127 (let ((car-type (cons-type-car-type cons-type)))
4128 (and (member-type-p car-type)
4129 (eql 1 (member-type-members car-type))
4130 (let ((elt (first (member-type-members car-type))))
4134 (numberp (first elt)))))
4135 (good-cons-type-p (cons-type-cdr-type cons-type))))))
4136 (unconsify-type (good-cons-type)
4137 ;; Convert the "printed" respresentation of a cons
4138 ;; specifier into a type specifier. That is, the
4139 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
4140 ;; NULL)) is converted to (SIGNED-BYTE 16).
4141 (cond ((or (null good-cons-type)
4142 (eq good-cons-type 'null))
4144 ((and (eq (first good-cons-type) 'cons)
4145 (eq (first (second good-cons-type)) 'member))
4146 `(,(second (second good-cons-type))
4147 ,@(unconsify-type (caddr good-cons-type))))))
4148 (coerceable-p (part)
4149 ;; Can the value be coerced to the given type? Coerce is
4150 ;; complicated, so we don't handle every possible case
4151 ;; here---just the most common and easiest cases:
4153 ;; * Any REAL can be coerced to a FLOAT type.
4154 ;; * Any NUMBER can be coerced to a (COMPLEX
4155 ;; SINGLE/DOUBLE-FLOAT).
4157 ;; FIXME I: we should also be able to deal with characters
4160 ;; FIXME II: I'm not sure that anything is necessary
4161 ;; here, at least while COMPLEX is not a specialized
4162 ;; array element type in the system. Reasoning: if
4163 ;; something cannot be coerced to the requested type, an
4164 ;; error will be raised (and so any downstream compiled
4165 ;; code on the assumption of the returned type is
4166 ;; unreachable). If something can, then it will be of
4167 ;; the requested type, because (by assumption) COMPLEX
4168 ;; (and other difficult types like (COMPLEX INTEGER)
4169 ;; aren't specialized types.
4170 (let ((coerced-type (careful-specifier-type part)))
4172 (or (and (csubtypep coerced-type (specifier-type 'float))
4173 (csubtypep value-type (specifier-type 'real)))
4174 (and (csubtypep coerced-type
4175 (specifier-type `(or (complex single-float)
4176 (complex double-float))))
4177 (csubtypep value-type (specifier-type 'number)))))))
4178 (process-types (type)
4179 ;; FIXME: This needs some work because we should be able
4180 ;; to derive the resulting type better than just the
4181 ;; type arg of coerce. That is, if X is (INTEGER 10
4182 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
4183 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
4185 (cond ((member-type-p type)
4188 (mapc-member-type-members
4190 (if (coerceable-p member)
4191 (push member members)
4192 (return-from punt *universal-type*)))
4194 (specifier-type `(or ,@members)))))
4195 ((and (cons-type-p type)
4196 (good-cons-type-p type))
4197 (let ((c-type (unconsify-type (type-specifier type))))
4198 (if (coerceable-p c-type)
4199 (specifier-type c-type)
4202 *universal-type*))))
4203 (cond ((union-type-p type-type)
4204 (apply #'type-union (mapcar #'process-types
4205 (union-type-types type-type))))
4206 ((or (member-type-p type-type)
4207 (cons-type-p type-type))
4208 (process-types type-type))
4210 *universal-type*)))))))
4212 (defoptimizer (compile derive-type) ((nameoid function))
4213 (when (csubtypep (lvar-type nameoid)
4214 (specifier-type 'null))
4215 (values-specifier-type '(values function boolean boolean))))
4217 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
4218 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
4219 ;;; optimizer, above).
4220 (defoptimizer (array-element-type derive-type) ((array))
4221 (let ((array-type (lvar-type array)))
4222 (labels ((consify (list)
4225 `(cons (eql ,(car list)) ,(consify (rest list)))))
4226 (get-element-type (a)
4228 (type-specifier (array-type-specialized-element-type a))))
4229 (cond ((eq element-type '*)
4230 (specifier-type 'type-specifier))
4231 ((symbolp element-type)
4232 (make-member-type :members (list element-type)))
4233 ((consp element-type)
4234 (specifier-type (consify element-type)))
4236 (error "can't understand type ~S~%" element-type))))))
4237 (labels ((recurse (type)
4238 (cond ((array-type-p type)
4239 (get-element-type type))
4240 ((union-type-p type)
4242 (mapcar #'recurse (union-type-types type))))
4244 *universal-type*))))
4245 (recurse array-type)))))
4247 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
4248 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4249 ;; isn't really related to the CMU CL code, since instead of trying
4250 ;; to generalize the CMU CL code to allow START and END values, this
4251 ;; code has been written from scratch following Chapter 7 of
4252 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4253 `(macrolet ((%index (x) `(truly-the index ,x))
4254 (%parent (i) `(ash ,i -1))
4255 (%left (i) `(%index (ash ,i 1)))
4256 (%right (i) `(%index (1+ (ash ,i 1))))
4259 (left (%left i) (%left i)))
4260 ((> left current-heap-size))
4261 (declare (type index i left))
4262 (let* ((i-elt (%elt i))
4263 (i-key (funcall keyfun i-elt))
4264 (left-elt (%elt left))
4265 (left-key (funcall keyfun left-elt)))
4266 (multiple-value-bind (large large-elt large-key)
4267 (if (funcall ,',predicate i-key left-key)
4268 (values left left-elt left-key)
4269 (values i i-elt i-key))
4270 (let ((right (%right i)))
4271 (multiple-value-bind (largest largest-elt)
4272 (if (> right current-heap-size)
4273 (values large large-elt)
4274 (let* ((right-elt (%elt right))
4275 (right-key (funcall keyfun right-elt)))
4276 (if (funcall ,',predicate large-key right-key)
4277 (values right right-elt)
4278 (values large large-elt))))
4279 (cond ((= largest i)
4282 (setf (%elt i) largest-elt
4283 (%elt largest) i-elt
4285 (%sort-vector (keyfun &optional (vtype 'vector))
4286 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4287 ;; trouble getting type inference to
4288 ;; propagate all the way through this
4289 ;; tangled mess of inlining. The TRULY-THE
4290 ;; here works around that. -- WHN
4292 `(aref (truly-the ,',vtype ,',',vector)
4293 (%index (+ (%index ,i) start-1)))))
4294 (let (;; Heaps prefer 1-based addressing.
4295 (start-1 (1- ,',start))
4296 (current-heap-size (- ,',end ,',start))
4298 (declare (type (integer -1 #.(1- sb!xc:most-positive-fixnum))
4300 (declare (type index current-heap-size))
4301 (declare (type function keyfun))
4302 (loop for i of-type index
4303 from (ash current-heap-size -1) downto 1 do
4306 (when (< current-heap-size 2)
4308 (rotatef (%elt 1) (%elt current-heap-size))
4309 (decf current-heap-size)
4311 (if (typep ,vector 'simple-vector)
4312 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4313 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4315 ;; Special-casing the KEY=NIL case lets us avoid some
4317 (%sort-vector #'identity simple-vector)
4318 (%sort-vector ,key simple-vector))
4319 ;; It's hard to anticipate many speed-critical applications for
4320 ;; sorting vector types other than (VECTOR T), so we just lump
4321 ;; them all together in one slow dynamically typed mess.
4323 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4324 (%sort-vector (or ,key #'identity))))))
4326 ;;;; debuggers' little helpers
4328 ;;; for debugging when transforms are behaving mysteriously,
4329 ;;; e.g. when debugging a problem with an ASH transform
4330 ;;; (defun foo (&optional s)
4331 ;;; (sb-c::/report-lvar s "S outside WHEN")
4332 ;;; (when (and (integerp s) (> s 3))
4333 ;;; (sb-c::/report-lvar s "S inside WHEN")
4334 ;;; (let ((bound (ash 1 (1- s))))
4335 ;;; (sb-c::/report-lvar bound "BOUND")
4336 ;;; (let ((x (- bound))
4338 ;;; (sb-c::/report-lvar x "X")
4339 ;;; (sb-c::/report-lvar x "Y"))
4340 ;;; `(integer ,(- bound) ,(1- bound)))))
4341 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4342 ;;; and the function doesn't do anything at all.)
4345 (defknown /report-lvar (t t) null)
4346 (deftransform /report-lvar ((x message) (t t))
4347 (format t "~%/in /REPORT-LVAR~%")
4348 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4349 (when (constant-lvar-p x)
4350 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4351 (format t "/MESSAGE=~S~%" (lvar-value message))
4352 (give-up-ir1-transform "not a real transform"))
4353 (defun /report-lvar (x message)
4354 (declare (ignore x message))))
4357 ;;;; Transforms for internal compiler utilities
4359 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4360 ;;; checking that it's still valid at run-time.
4361 (deftransform policy-quality ((policy quality-name)
4363 (unless (and (constant-lvar-p quality-name)
4364 (policy-quality-name-p (lvar-value quality-name)))
4365 (give-up-ir1-transform))
4366 '(%policy-quality policy quality-name))