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))
354 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
355 ;; With these traps masked, we might get things like infinity
356 ;; or negative infinity returned. Check for this and return
357 ;; NIL to indicate unbounded.
358 (let ((y (funcall f (type-bound-number x))))
360 (float-infinity-p y))
362 (set-bound y (consp x)))))
363 ;; Some numerical operations will signal SIMPLE-TYPE-ERROR, e.g.
364 ;; in the course of converting a bignum to a float. Default to
366 (simple-type-error ()))))
368 (defun safe-double-coercion-p (x)
369 (or (typep x 'double-float)
370 (<= most-negative-double-float x most-positive-double-float)))
372 (defun safe-single-coercion-p (x)
373 (or (typep x 'single-float)
374 ;; Fix for bug 420, and related issues: during type derivation we often
375 ;; end up deriving types for both
377 ;; (some-op <int> <single>)
379 ;; (some-op (coerce <int> 'single-float) <single>)
381 ;; or other equivalent transformed forms. The problem with this is that
382 ;; on some platforms like x86 (+ <int> <single>) is on the machine level
385 ;; (coerce (+ (coerce <int> 'double-float)
386 ;; (coerce <single> 'double-float))
389 ;; so if the result of (coerce <int> 'single-float) is not exact, the
390 ;; derived types for the transformed forms will have an empty
391 ;; intersection -- which in turn means that the compiler will conclude
392 ;; that the call never returns, and all hell breaks lose when it *does*
393 ;; return at runtime. (This affects not just +, but other operators are
395 (and (not (typep x `(or (integer * (,most-negative-exactly-single-float-fixnum))
396 (integer (,most-positive-exactly-single-float-fixnum) *))))
397 (<= most-negative-single-float x most-positive-single-float))))
399 ;;; Apply a binary operator OP to two bounds X and Y. The result is
400 ;;; NIL if either is NIL. Otherwise bound is computed and the result
401 ;;; is open if either X or Y is open.
403 ;;; FIXME: only used in this file, not needed in target runtime
405 ;;; ANSI contaigon specifies coercion to floating point if one of the
406 ;;; arguments is floating point. Here we should check to be sure that
407 ;;; the other argument is within the bounds of that floating point
410 (defmacro safely-binop (op x y)
412 ((typep ,x 'double-float)
413 (when (safe-double-coercion-p ,y)
415 ((typep ,y 'double-float)
416 (when (safe-double-coercion-p ,x)
418 ((typep ,x 'single-float)
419 (when (safe-single-coercion-p ,y)
421 ((typep ,y 'single-float)
422 (when (safe-single-coercion-p ,x)
426 (defmacro bound-binop (op x y)
427 (with-unique-names (xb yb res)
429 (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
430 (let* ((,xb (type-bound-number ,x))
431 (,yb (type-bound-number ,y))
432 (,res (safely-binop ,op ,xb ,yb)))
434 (and (or (consp ,x) (consp ,y))
435 ;; Open bounds can very easily be messed up
436 ;; by FP rounding, so take care here.
439 ;; Multiplying a greater-than-zero with
440 ;; less than one can round to zero.
441 `(or (not (fp-zero-p ,res))
442 (cond ((and (consp ,x) (fp-zero-p ,xb))
444 ((and (consp ,y) (fp-zero-p ,yb))
447 ;; Dividing a greater-than-zero with
448 ;; greater than one can round to zero.
449 `(or (not (fp-zero-p ,res))
450 (cond ((and (consp ,x) (fp-zero-p ,xb))
452 ((and (consp ,y) (fp-zero-p ,yb))
455 ;; Adding or subtracting greater-than-zero
456 ;; can end up with identity.
457 `(and (not (fp-zero-p ,xb))
458 (not (fp-zero-p ,yb))))))))))))
460 (defun coerce-for-bound (val type)
462 (list (coerce-for-bound (car val) type))
464 ((subtypep type 'double-float)
465 (if (<= most-negative-double-float val most-positive-double-float)
467 ((or (subtypep type 'single-float) (subtypep type 'float))
468 ;; coerce to float returns a single-float
469 (if (<= most-negative-single-float val most-positive-single-float)
471 (t (coerce val type)))))
473 (defun coerce-and-truncate-floats (val type)
476 (list (coerce-and-truncate-floats (car val) type))
478 ((subtypep type 'double-float)
479 (if (<= most-negative-double-float val most-positive-double-float)
481 (if (< val most-negative-double-float)
482 most-negative-double-float most-positive-double-float)))
483 ((or (subtypep type 'single-float) (subtypep type 'float))
484 ;; coerce to float returns a single-float
485 (if (<= most-negative-single-float val most-positive-single-float)
487 (if (< val most-negative-single-float)
488 most-negative-single-float most-positive-single-float)))
489 (t (coerce val type))))))
491 ;;; Convert a numeric-type object to an interval object.
492 (defun numeric-type->interval (x)
493 (declare (type numeric-type x))
494 (make-interval :low (numeric-type-low x)
495 :high (numeric-type-high x)))
497 (defun type-approximate-interval (type)
498 (declare (type ctype type))
499 (let ((types (prepare-arg-for-derive-type type))
502 (let ((type (if (member-type-p type)
503 (convert-member-type type)
505 (unless (numeric-type-p type)
506 (return-from type-approximate-interval nil))
507 (let ((interval (numeric-type->interval type)))
510 (interval-approximate-union result interval)
514 (defun copy-interval-limit (limit)
519 (defun copy-interval (x)
520 (declare (type interval x))
521 (make-interval :low (copy-interval-limit (interval-low x))
522 :high (copy-interval-limit (interval-high x))))
524 ;;; Given a point P contained in the interval X, split X into two
525 ;;; interval at the point P. If CLOSE-LOWER is T, then the left
526 ;;; interval contains P. If CLOSE-UPPER is T, the right interval
527 ;;; contains P. You can specify both to be T or NIL.
528 (defun interval-split (p x &optional close-lower close-upper)
529 (declare (type number p)
531 (list (make-interval :low (copy-interval-limit (interval-low x))
532 :high (if close-lower p (list p)))
533 (make-interval :low (if close-upper (list p) p)
534 :high (copy-interval-limit (interval-high x)))))
536 ;;; Return the closure of the interval. That is, convert open bounds
537 ;;; to closed bounds.
538 (defun interval-closure (x)
539 (declare (type interval x))
540 (make-interval :low (type-bound-number (interval-low x))
541 :high (type-bound-number (interval-high x))))
543 ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
544 ;;; '-. Otherwise return NIL.
545 (defun interval-range-info (x &optional (point 0))
546 (declare (type interval x))
547 (let ((lo (interval-low x))
548 (hi (interval-high x)))
549 (cond ((and lo (signed-zero->= (type-bound-number lo) point))
551 ((and hi (signed-zero->= point (type-bound-number hi)))
556 ;;; Test to see whether the interval X is bounded. HOW determines the
557 ;;; test, and should be either ABOVE, BELOW, or BOTH.
558 (defun interval-bounded-p (x how)
559 (declare (type interval x))
566 (and (interval-low x) (interval-high x)))))
568 ;;; See whether the interval X contains the number P, taking into
569 ;;; account that the interval might not be closed.
570 (defun interval-contains-p (p x)
571 (declare (type number p)
573 ;; Does the interval X contain the number P? This would be a lot
574 ;; easier if all intervals were closed!
575 (let ((lo (interval-low x))
576 (hi (interval-high x)))
578 ;; The interval is bounded
579 (if (and (signed-zero-<= (type-bound-number lo) p)
580 (signed-zero-<= p (type-bound-number hi)))
581 ;; P is definitely in the closure of the interval.
582 ;; We just need to check the end points now.
583 (cond ((signed-zero-= p (type-bound-number lo))
585 ((signed-zero-= p (type-bound-number hi))
590 ;; Interval with upper bound
591 (if (signed-zero-< p (type-bound-number hi))
593 (and (numberp hi) (signed-zero-= p hi))))
595 ;; Interval with lower bound
596 (if (signed-zero-> p (type-bound-number lo))
598 (and (numberp lo) (signed-zero-= p lo))))
600 ;; Interval with no bounds
603 ;;; Determine whether two intervals X and Y intersect. Return T if so.
604 ;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
605 ;;; were closed. Otherwise the intervals are treated as they are.
607 ;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
608 ;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
609 ;;; is T, then they do intersect because we use the closure of X = [0,
610 ;;; 1] and Y = [1, 2] to determine intersection.
611 (defun interval-intersect-p (x y &optional closed-intervals-p)
612 (declare (type interval x y))
613 (and (interval-intersection/difference (if closed-intervals-p
616 (if closed-intervals-p
621 ;;; Are the two intervals adjacent? That is, is there a number
622 ;;; between the two intervals that is not an element of either
623 ;;; interval? If so, they are not adjacent. For example [0, 1) and
624 ;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
625 ;;; between both intervals.
626 (defun interval-adjacent-p (x y)
627 (declare (type interval x y))
628 (flet ((adjacent (lo hi)
629 ;; Check to see whether lo and hi are adjacent. If either is
630 ;; nil, they can't be adjacent.
631 (when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
632 ;; The bounds are equal. They are adjacent if one of
633 ;; them is closed (a number). If both are open (consp),
634 ;; then there is a number that lies between them.
635 (or (numberp lo) (numberp hi)))))
636 (or (adjacent (interval-low y) (interval-high x))
637 (adjacent (interval-low x) (interval-high y)))))
639 ;;; Compute the intersection and difference between two intervals.
640 ;;; Two values are returned: the intersection and the difference.
642 ;;; Let the two intervals be X and Y, and let I and D be the two
643 ;;; values returned by this function. Then I = X intersect Y. If I
644 ;;; is NIL (the empty set), then D is X union Y, represented as the
645 ;;; list of X and Y. If I is not the empty set, then D is (X union Y)
646 ;;; - I, which is a list of two intervals.
648 ;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
649 ;;; [-1,1) union [3,5], which is returned as a list of two intervals.
650 (defun interval-intersection/difference (x y)
651 (declare (type interval x y))
652 (let ((x-lo (interval-low x))
653 (x-hi (interval-high x))
654 (y-lo (interval-low y))
655 (y-hi (interval-high y)))
658 ;; If p is an open bound, make it closed. If p is a closed
659 ;; bound, make it open.
663 (test-number (p int bound)
664 ;; Test whether P is in the interval.
665 (let ((pn (type-bound-number p)))
666 (when (interval-contains-p pn (interval-closure int))
667 ;; Check for endpoints.
668 (let* ((lo (interval-low int))
669 (hi (interval-high int))
670 (lon (type-bound-number lo))
671 (hin (type-bound-number hi)))
673 ;; Interval may be a point.
674 ((and lon hin (= lon hin pn))
675 (and (numberp p) (numberp lo) (numberp hi)))
676 ;; Point matches the low end.
677 ;; [P] [P,?} => TRUE [P] (P,?} => FALSE
678 ;; (P [P,?} => TRUE P) [P,?} => FALSE
679 ;; (P (P,?} => TRUE P) (P,?} => FALSE
680 ((and lon (= pn lon))
681 (or (and (numberp p) (numberp lo))
682 (and (consp p) (eq :low bound))))
683 ;; [P] {?,P] => TRUE [P] {?,P) => FALSE
684 ;; P) {?,P] => TRUE (P {?,P] => FALSE
685 ;; P) {?,P) => TRUE (P {?,P) => FALSE
686 ((and hin (= pn hin))
687 (or (and (numberp p) (numberp hi))
688 (and (consp p) (eq :high bound))))
689 ;; Not an endpoint, all is well.
692 (test-lower-bound (p int)
693 ;; P is a lower bound of an interval.
695 (test-number p int :low)
696 (not (interval-bounded-p int 'below))))
697 (test-upper-bound (p int)
698 ;; P is an upper bound of an interval.
700 (test-number p int :high)
701 (not (interval-bounded-p int 'above)))))
702 (let ((x-lo-in-y (test-lower-bound x-lo y))
703 (x-hi-in-y (test-upper-bound x-hi y))
704 (y-lo-in-x (test-lower-bound y-lo x))
705 (y-hi-in-x (test-upper-bound y-hi x)))
706 (cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
707 ;; Intervals intersect. Let's compute the intersection
708 ;; and the difference.
709 (multiple-value-bind (lo left-lo left-hi)
710 (cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
711 (y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
712 (multiple-value-bind (hi right-lo right-hi)
714 (values x-hi (opposite-bound x-hi) y-hi))
716 (values y-hi (opposite-bound y-hi) x-hi)))
717 (values (make-interval :low lo :high hi)
718 (list (make-interval :low left-lo
720 (make-interval :low right-lo
723 (values nil (list x y))))))))
725 ;;; If intervals X and Y intersect, return a new interval that is the
726 ;;; union of the two. If they do not intersect, return NIL.
727 (defun interval-merge-pair (x y)
728 (declare (type interval x y))
729 ;; If x and y intersect or are adjacent, create the union.
730 ;; Otherwise return nil
731 (when (or (interval-intersect-p x y)
732 (interval-adjacent-p x y))
733 (flet ((select-bound (x1 x2 min-op max-op)
734 (let ((x1-val (type-bound-number x1))
735 (x2-val (type-bound-number x2)))
737 ;; Both bounds are finite. Select the right one.
738 (cond ((funcall min-op x1-val x2-val)
739 ;; x1 is definitely better.
741 ((funcall max-op x1-val x2-val)
742 ;; x2 is definitely better.
745 ;; Bounds are equal. Select either
746 ;; value and make it open only if
748 (set-bound x1-val (and (consp x1) (consp x2))))))
750 ;; At least one bound is not finite. The
751 ;; non-finite bound always wins.
753 (let* ((x-lo (copy-interval-limit (interval-low x)))
754 (x-hi (copy-interval-limit (interval-high x)))
755 (y-lo (copy-interval-limit (interval-low y)))
756 (y-hi (copy-interval-limit (interval-high y))))
757 (make-interval :low (select-bound x-lo y-lo #'< #'>)
758 :high (select-bound x-hi y-hi #'> #'<))))))
760 ;;; return the minimal interval, containing X and Y
761 (defun interval-approximate-union (x y)
762 (cond ((interval-merge-pair x y))
764 (make-interval :low (copy-interval-limit (interval-low x))
765 :high (copy-interval-limit (interval-high y))))
767 (make-interval :low (copy-interval-limit (interval-low y))
768 :high (copy-interval-limit (interval-high x))))))
770 ;;; basic arithmetic operations on intervals. We probably should do
771 ;;; true interval arithmetic here, but it's complicated because we
772 ;;; have float and integer types and bounds can be open or closed.
774 ;;; the negative of an interval
775 (defun interval-neg (x)
776 (declare (type interval x))
777 (make-interval :low (bound-func #'- (interval-high x))
778 :high (bound-func #'- (interval-low x))))
780 ;;; Add two intervals.
781 (defun interval-add (x y)
782 (declare (type interval x y))
783 (make-interval :low (bound-binop + (interval-low x) (interval-low y))
784 :high (bound-binop + (interval-high x) (interval-high y))))
786 ;;; Subtract two intervals.
787 (defun interval-sub (x y)
788 (declare (type interval x y))
789 (make-interval :low (bound-binop - (interval-low x) (interval-high y))
790 :high (bound-binop - (interval-high x) (interval-low y))))
792 ;;; Multiply two intervals.
793 (defun interval-mul (x y)
794 (declare (type interval x y))
795 (flet ((bound-mul (x y)
796 (cond ((or (null x) (null y))
797 ;; Multiply by infinity is infinity
799 ((or (and (numberp x) (zerop x))
800 (and (numberp y) (zerop y)))
801 ;; Multiply by closed zero is special. The result
802 ;; is always a closed bound. But don't replace this
803 ;; with zero; we want the multiplication to produce
804 ;; the correct signed zero, if needed. Use SIGNUM
805 ;; to avoid trying to multiply huge bignums with 0.0.
806 (* (signum (type-bound-number x)) (signum (type-bound-number y))))
807 ((or (and (floatp x) (float-infinity-p x))
808 (and (floatp y) (float-infinity-p y)))
809 ;; Infinity times anything is infinity
812 ;; General multiply. The result is open if either is open.
813 (bound-binop * x y)))))
814 (let ((x-range (interval-range-info x))
815 (y-range (interval-range-info y)))
816 (cond ((null x-range)
817 ;; Split x into two and multiply each separately
818 (destructuring-bind (x- x+) (interval-split 0 x t t)
819 (interval-merge-pair (interval-mul x- y)
820 (interval-mul x+ y))))
822 ;; Split y into two and multiply each separately
823 (destructuring-bind (y- y+) (interval-split 0 y t t)
824 (interval-merge-pair (interval-mul x y-)
825 (interval-mul x y+))))
827 (interval-neg (interval-mul (interval-neg x) y)))
829 (interval-neg (interval-mul x (interval-neg y))))
830 ((and (eq x-range '+) (eq y-range '+))
831 ;; If we are here, X and Y are both positive.
833 :low (bound-mul (interval-low x) (interval-low y))
834 :high (bound-mul (interval-high x) (interval-high y))))
836 (bug "excluded case in INTERVAL-MUL"))))))
838 ;;; Divide two intervals.
839 (defun interval-div (top bot)
840 (declare (type interval top bot))
841 (flet ((bound-div (x y y-low-p)
844 ;; Divide by infinity means result is 0. However,
845 ;; we need to watch out for the sign of the result,
846 ;; to correctly handle signed zeros. We also need
847 ;; to watch out for positive or negative infinity.
848 (if (floatp (type-bound-number x))
850 (- (float-sign (type-bound-number x) 0.0))
851 (float-sign (type-bound-number x) 0.0))
853 ((zerop (type-bound-number y))
854 ;; Divide by zero means result is infinity
856 ((and (numberp x) (zerop x))
857 ;; Zero divided by anything is zero.
860 (bound-binop / x y)))))
861 (let ((top-range (interval-range-info top))
862 (bot-range (interval-range-info bot)))
863 (cond ((null bot-range)
864 ;; The denominator contains zero, so anything goes!
865 (make-interval :low nil :high nil))
867 ;; Denominator is negative so flip the sign, compute the
868 ;; result, and flip it back.
869 (interval-neg (interval-div top (interval-neg bot))))
871 ;; Split top into two positive and negative parts, and
872 ;; divide each separately
873 (destructuring-bind (top- top+) (interval-split 0 top t t)
874 (interval-merge-pair (interval-div top- bot)
875 (interval-div top+ bot))))
877 ;; Top is negative so flip the sign, divide, and flip the
878 ;; sign of the result.
879 (interval-neg (interval-div (interval-neg top) bot)))
880 ((and (eq top-range '+) (eq bot-range '+))
883 :low (bound-div (interval-low top) (interval-high bot) t)
884 :high (bound-div (interval-high top) (interval-low bot) nil)))
886 (bug "excluded case in INTERVAL-DIV"))))))
888 ;;; Apply the function F to the interval X. If X = [a, b], then the
889 ;;; result is [f(a), f(b)]. It is up to the user to make sure the
890 ;;; result makes sense. It will if F is monotonic increasing (or
892 (defun interval-func (f x)
893 (declare (type function f)
895 (let ((lo (bound-func f (interval-low x)))
896 (hi (bound-func f (interval-high x))))
897 (make-interval :low lo :high hi)))
899 ;;; Return T if X < Y. That is every number in the interval X is
900 ;;; always less than any number in the interval Y.
901 (defun interval-< (x y)
902 (declare (type interval x y))
903 ;; X < Y only if X is bounded above, Y is bounded below, and they
905 (when (and (interval-bounded-p x 'above)
906 (interval-bounded-p y 'below))
907 ;; Intervals are bounded in the appropriate way. Make sure they
909 (let ((left (interval-high x))
910 (right (interval-low y)))
911 (cond ((> (type-bound-number left)
912 (type-bound-number right))
913 ;; The intervals definitely overlap, so result is NIL.
915 ((< (type-bound-number left)
916 (type-bound-number right))
917 ;; The intervals definitely don't touch, so result is T.
920 ;; Limits are equal. Check for open or closed bounds.
921 ;; Don't overlap if one or the other are open.
922 (or (consp left) (consp right)))))))
924 ;;; Return T if X >= Y. That is, every number in the interval X is
925 ;;; always greater than any number in the interval Y.
926 (defun interval->= (x y)
927 (declare (type interval x y))
928 ;; X >= Y if lower bound of X >= upper bound of Y
929 (when (and (interval-bounded-p x 'below)
930 (interval-bounded-p y 'above))
931 (>= (type-bound-number (interval-low x))
932 (type-bound-number (interval-high y)))))
934 ;;; Return T if X = Y.
935 (defun interval-= (x y)
936 (declare (type interval x y))
937 (and (interval-bounded-p x 'both)
938 (interval-bounded-p y 'both)
942 ;; Open intervals cannot be =
943 (return-from interval-= nil))))
944 ;; Both intervals refer to the same point
945 (= (bound (interval-high x)) (bound (interval-low x))
946 (bound (interval-high y)) (bound (interval-low y))))))
948 ;;; Return T if X /= Y
949 (defun interval-/= (x y)
950 (not (interval-intersect-p x y)))
952 ;;; Return an interval that is the absolute value of X. Thus, if
953 ;;; X = [-1 10], the result is [0, 10].
954 (defun interval-abs (x)
955 (declare (type interval x))
956 (case (interval-range-info x)
962 (destructuring-bind (x- x+) (interval-split 0 x t t)
963 (interval-merge-pair (interval-neg x-) x+)))))
965 ;;; Compute the square of an interval.
966 (defun interval-sqr (x)
967 (declare (type interval x))
968 (interval-func (lambda (x) (* x x))
971 ;;;; numeric DERIVE-TYPE methods
973 ;;; a utility for defining derive-type methods of integer operations. If
974 ;;; the types of both X and Y are integer types, then we compute a new
975 ;;; integer type with bounds determined Fun when applied to X and Y.
976 ;;; Otherwise, we use NUMERIC-CONTAGION.
977 (defun derive-integer-type-aux (x y fun)
978 (declare (type function fun))
979 (if (and (numeric-type-p x) (numeric-type-p y)
980 (eq (numeric-type-class x) 'integer)
981 (eq (numeric-type-class y) 'integer)
982 (eq (numeric-type-complexp x) :real)
983 (eq (numeric-type-complexp y) :real))
984 (multiple-value-bind (low high) (funcall fun x y)
985 (make-numeric-type :class 'integer
989 (numeric-contagion x y)))
991 (defun derive-integer-type (x y fun)
992 (declare (type lvar x y) (type function fun))
993 (let ((x (lvar-type x))
995 (derive-integer-type-aux x y fun)))
997 ;;; simple utility to flatten a list
998 (defun flatten-list (x)
999 (labels ((flatten-and-append (tree list)
1000 (cond ((null tree) list)
1001 ((atom tree) (cons tree list))
1002 (t (flatten-and-append
1003 (car tree) (flatten-and-append (cdr tree) list))))))
1004 (flatten-and-append x nil)))
1006 ;;; Take some type of lvar and massage it so that we get a list of the
1007 ;;; constituent types. If ARG is *EMPTY-TYPE*, return NIL to indicate
1009 (defun prepare-arg-for-derive-type (arg)
1010 (flet ((listify (arg)
1015 (union-type-types arg))
1018 (unless (eq arg *empty-type*)
1019 ;; Make sure all args are some type of numeric-type. For member
1020 ;; types, convert the list of members into a union of equivalent
1021 ;; single-element member-type's.
1022 (let ((new-args nil))
1023 (dolist (arg (listify arg))
1024 (if (member-type-p arg)
1025 ;; Run down the list of members and convert to a list of
1027 (mapc-member-type-members
1029 (push (if (numberp member)
1030 (make-member-type :members (list member))
1034 (push arg new-args)))
1035 (unless (member *empty-type* new-args)
1038 ;;; Convert from the standard type convention for which -0.0 and 0.0
1039 ;;; are equal to an intermediate convention for which they are
1040 ;;; considered different which is more natural for some of the
1042 (defun convert-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))
1048 (lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
1049 (hi (numeric-type-high type))
1050 (hi-val (type-bound-number hi))
1051 (hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
1052 (if (or lo-float-zero-p hi-float-zero-p)
1054 :class (numeric-type-class type)
1055 :format (numeric-type-format type)
1057 :low (if lo-float-zero-p
1059 (list (float 0.0 lo-val))
1060 (float (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val))
1062 :high (if hi-float-zero-p
1064 (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val))
1071 ;;; Convert back from the intermediate convention for which -0.0 and
1072 ;;; 0.0 are considered different to the standard type convention for
1073 ;;; which and equal.
1074 (defun convert-back-numeric-type (type)
1075 (declare (type numeric-type type))
1076 ;;; Only convert real float interval delimiters types.
1077 (if (eq (numeric-type-complexp type) :real)
1078 (let* ((lo (numeric-type-low type))
1079 (lo-val (type-bound-number lo))
1081 (and lo (floatp lo-val) (= lo-val 0.0)
1082 (float-sign lo-val)))
1083 (hi (numeric-type-high type))
1084 (hi-val (type-bound-number hi))
1086 (and hi (floatp hi-val) (= hi-val 0.0)
1087 (float-sign hi-val))))
1089 ;; (float +0.0 +0.0) => (member 0.0)
1090 ;; (float -0.0 -0.0) => (member -0.0)
1091 ((and lo-float-zero-p hi-float-zero-p)
1092 ;; shouldn't have exclusive bounds here..
1093 (aver (and (not (consp lo)) (not (consp hi))))
1094 (if (= lo-float-zero-p hi-float-zero-p)
1095 ;; (float +0.0 +0.0) => (member 0.0)
1096 ;; (float -0.0 -0.0) => (member -0.0)
1097 (specifier-type `(member ,lo-val))
1098 ;; (float -0.0 +0.0) => (float 0.0 0.0)
1099 ;; (float +0.0 -0.0) => (float 0.0 0.0)
1100 (make-numeric-type :class (numeric-type-class type)
1101 :format (numeric-type-format type)
1107 ;; (float -0.0 x) => (float 0.0 x)
1108 ((and (not (consp lo)) (minusp lo-float-zero-p))
1109 (make-numeric-type :class (numeric-type-class type)
1110 :format (numeric-type-format type)
1112 :low (float 0.0 lo-val)
1114 ;; (float (+0.0) x) => (float (0.0) x)
1115 ((and (consp lo) (plusp lo-float-zero-p))
1116 (make-numeric-type :class (numeric-type-class type)
1117 :format (numeric-type-format type)
1119 :low (list (float 0.0 lo-val))
1122 ;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
1123 ;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
1124 (list (make-member-type :members (list (float 0.0 lo-val)))
1125 (make-numeric-type :class (numeric-type-class type)
1126 :format (numeric-type-format type)
1128 :low (list (float 0.0 lo-val))
1132 ;; (float x +0.0) => (float x 0.0)
1133 ((and (not (consp hi)) (plusp hi-float-zero-p))
1134 (make-numeric-type :class (numeric-type-class type)
1135 :format (numeric-type-format type)
1138 :high (float 0.0 hi-val)))
1139 ;; (float x (-0.0)) => (float x (0.0))
1140 ((and (consp hi) (minusp hi-float-zero-p))
1141 (make-numeric-type :class (numeric-type-class type)
1142 :format (numeric-type-format type)
1145 :high (list (float 0.0 hi-val))))
1147 ;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
1148 ;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
1149 (list (make-member-type :members (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) hi-val)))
1150 (make-numeric-type :class (numeric-type-class type)
1151 :format (numeric-type-format type)
1154 :high (list (float 0.0 hi-val)))))))
1160 ;;; Convert back a possible list of numeric types.
1161 (defun convert-back-numeric-type-list (type-list)
1164 (let ((results '()))
1165 (dolist (type type-list)
1166 (if (numeric-type-p type)
1167 (let ((result (convert-back-numeric-type type)))
1169 (setf results (append results result))
1170 (push result results)))
1171 (push type results)))
1174 (convert-back-numeric-type type-list))
1176 (convert-back-numeric-type-list (union-type-types type-list)))
1180 ;;; Take a list of types and return a canonical type specifier,
1181 ;;; combining any MEMBER types together. If both positive and negative
1182 ;;; MEMBER types are present they are converted to a float type.
1183 ;;; XXX This would be far simpler if the type-union methods could handle
1184 ;;; member/number unions.
1186 ;;; If we're about to generate an overly complex union of numeric types, start
1187 ;;; collapse the ranges together.
1189 ;;; FIXME: The MEMBER canonicalization parts of MAKE-DERIVED-UNION-TYPE and
1190 ;;; entire CONVERT-MEMBER-TYPE probably belong in the kernel's type logic,
1191 ;;; invoked always, instead of in the compiler, invoked only during some type
1193 (defvar *derived-numeric-union-complexity-limit* 6)
1195 (defun make-derived-union-type (type-list)
1196 (let ((xset (alloc-xset))
1199 (numeric-type *empty-type*))
1200 (dolist (type type-list)
1201 (cond ((member-type-p type)
1202 (mapc-member-type-members
1204 (if (fp-zero-p member)
1205 (unless (member member fp-zeroes)
1206 (pushnew member fp-zeroes))
1207 (add-to-xset member xset)))
1209 ((numeric-type-p type)
1210 (let ((*approximate-numeric-unions*
1211 (when (and (union-type-p numeric-type)
1212 (nthcdr *derived-numeric-union-complexity-limit*
1213 (union-type-types numeric-type)))
1215 (setf numeric-type (type-union type numeric-type))))
1217 (push type misc-types))))
1218 (if (and (xset-empty-p xset) (not fp-zeroes))
1219 (apply #'type-union numeric-type misc-types)
1220 (apply #'type-union (make-member-type :xset xset :fp-zeroes fp-zeroes)
1221 numeric-type misc-types))))
1223 ;;; Convert a member type with a single member to a numeric type.
1224 (defun convert-member-type (arg)
1225 (let* ((members (member-type-members arg))
1226 (member (first members))
1227 (member-type (type-of member)))
1228 (aver (not (rest members)))
1229 (specifier-type (cond ((typep member 'integer)
1230 `(integer ,member ,member))
1231 ((memq member-type '(short-float single-float
1232 double-float long-float))
1233 `(,member-type ,member ,member))
1237 ;;; This is used in defoptimizers for computing the resulting type of
1240 ;;; Given the lvar ARG, derive the resulting type using the
1241 ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some
1242 ;;; "atomic" lvar type like numeric-type or member-type (containing
1243 ;;; just one element). It should return the resulting type, which can
1244 ;;; be a list of types.
1246 ;;; For the case of member types, if a MEMBER-FUN is given it is
1247 ;;; called to compute the result otherwise the member type is first
1248 ;;; converted to a numeric type and the DERIVE-FUN is called.
1249 (defun one-arg-derive-type (arg derive-fun member-fun
1250 &optional (convert-type t))
1251 (declare (type function derive-fun)
1252 (type (or null function) member-fun))
1253 (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg))))
1259 (with-float-traps-masked
1260 (:underflow :overflow :divide-by-zero)
1262 `(eql ,(funcall member-fun
1263 (first (member-type-members x))))))
1264 ;; Otherwise convert to a numeric type.
1265 (let ((result-type-list
1266 (funcall derive-fun (convert-member-type x))))
1268 (convert-back-numeric-type-list result-type-list)
1269 result-type-list))))
1272 (convert-back-numeric-type-list
1273 (funcall derive-fun (convert-numeric-type x)))
1274 (funcall derive-fun x)))
1276 *universal-type*))))
1277 ;; Run down the list of args and derive the type of each one,
1278 ;; saving all of the results in a list.
1279 (let ((results nil))
1280 (dolist (arg arg-list)
1281 (let ((result (deriver arg)))
1283 (setf results (append results result))
1284 (push result results))))
1286 (make-derived-union-type results)
1287 (first results)))))))
1289 ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
1290 ;;; two arguments. DERIVE-FUN takes 3 args in this case: the two
1291 ;;; original args and a third which is T to indicate if the two args
1292 ;;; really represent the same lvar. This is useful for deriving the
1293 ;;; type of things like (* x x), which should always be positive. If
1294 ;;; we didn't do this, we wouldn't be able to tell.
1295 (defun two-arg-derive-type (arg1 arg2 derive-fun fun
1296 &optional (convert-type t))
1297 (declare (type function derive-fun fun))
1298 (flet ((deriver (x y same-arg)
1299 (cond ((and (member-type-p x) (member-type-p y))
1300 (let* ((x (first (member-type-members x)))
1301 (y (first (member-type-members y)))
1302 (result (ignore-errors
1303 (with-float-traps-masked
1304 (:underflow :overflow :divide-by-zero
1306 (funcall fun x y)))))
1307 (cond ((null result) *empty-type*)
1308 ((and (floatp result) (float-nan-p result))
1309 (make-numeric-type :class 'float
1310 :format (type-of result)
1313 (specifier-type `(eql ,result))))))
1314 ((and (member-type-p x) (numeric-type-p y))
1315 (let* ((x (convert-member-type x))
1316 (y (if convert-type (convert-numeric-type y) y))
1317 (result (funcall derive-fun x y same-arg)))
1319 (convert-back-numeric-type-list result)
1321 ((and (numeric-type-p x) (member-type-p y))
1322 (let* ((x (if convert-type (convert-numeric-type x) x))
1323 (y (convert-member-type y))
1324 (result (funcall derive-fun x y same-arg)))
1326 (convert-back-numeric-type-list result)
1328 ((and (numeric-type-p x) (numeric-type-p y))
1329 (let* ((x (if convert-type (convert-numeric-type x) x))
1330 (y (if convert-type (convert-numeric-type y) y))
1331 (result (funcall derive-fun x y same-arg)))
1333 (convert-back-numeric-type-list result)
1336 *universal-type*))))
1337 (let ((same-arg (same-leaf-ref-p arg1 arg2))
1338 (a1 (prepare-arg-for-derive-type (lvar-type arg1)))
1339 (a2 (prepare-arg-for-derive-type (lvar-type arg2))))
1341 (let ((results nil))
1343 ;; Since the args are the same LVARs, just run down the
1346 (let ((result (deriver x x same-arg)))
1348 (setf results (append results result))
1349 (push result results))))
1350 ;; Try all pairwise combinations.
1353 (let ((result (or (deriver x y same-arg)
1354 (numeric-contagion x y))))
1356 (setf results (append results result))
1357 (push result results))))))
1359 (make-derived-union-type results)
1360 (first results)))))))
1362 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1364 (defoptimizer (+ derive-type) ((x y))
1365 (derive-integer-type
1372 (values (frob (numeric-type-low x) (numeric-type-low y))
1373 (frob (numeric-type-high x) (numeric-type-high y)))))))
1375 (defoptimizer (- derive-type) ((x y))
1376 (derive-integer-type
1383 (values (frob (numeric-type-low x) (numeric-type-high y))
1384 (frob (numeric-type-high x) (numeric-type-low y)))))))
1386 (defoptimizer (* derive-type) ((x y))
1387 (derive-integer-type
1390 (let ((x-low (numeric-type-low x))
1391 (x-high (numeric-type-high x))
1392 (y-low (numeric-type-low y))
1393 (y-high (numeric-type-high y)))
1394 (cond ((not (and x-low y-low))
1396 ((or (minusp x-low) (minusp y-low))
1397 (if (and x-high y-high)
1398 (let ((max (* (max (abs x-low) (abs x-high))
1399 (max (abs y-low) (abs y-high)))))
1400 (values (- max) max))
1403 (values (* x-low y-low)
1404 (if (and x-high y-high)
1408 (defoptimizer (/ derive-type) ((x y))
1409 (numeric-contagion (lvar-type x) (lvar-type y)))
1413 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1415 (defun +-derive-type-aux (x y same-arg)
1416 (if (and (numeric-type-real-p x)
1417 (numeric-type-real-p y))
1420 (let ((x-int (numeric-type->interval x)))
1421 (interval-add x-int x-int))
1422 (interval-add (numeric-type->interval x)
1423 (numeric-type->interval y))))
1424 (result-type (numeric-contagion x y)))
1425 ;; If the result type is a float, we need to be sure to coerce
1426 ;; the bounds into the correct type.
1427 (when (eq (numeric-type-class result-type) 'float)
1428 (setf result (interval-func
1430 (coerce-for-bound x (or (numeric-type-format result-type)
1434 :class (if (and (eq (numeric-type-class x) 'integer)
1435 (eq (numeric-type-class y) 'integer))
1436 ;; The sum of integers is always an integer.
1438 (numeric-type-class result-type))
1439 :format (numeric-type-format result-type)
1440 :low (interval-low result)
1441 :high (interval-high result)))
1442 ;; general contagion
1443 (numeric-contagion x y)))
1445 (defoptimizer (+ derive-type) ((x y))
1446 (two-arg-derive-type x y #'+-derive-type-aux #'+))
1448 (defun --derive-type-aux (x y same-arg)
1449 (if (and (numeric-type-real-p x)
1450 (numeric-type-real-p y))
1452 ;; (- X X) is always 0.
1454 (make-interval :low 0 :high 0)
1455 (interval-sub (numeric-type->interval x)
1456 (numeric-type->interval y))))
1457 (result-type (numeric-contagion x y)))
1458 ;; If the result type is a float, we need to be sure to coerce
1459 ;; the bounds into the correct type.
1460 (when (eq (numeric-type-class result-type) 'float)
1461 (setf result (interval-func
1463 (coerce-for-bound x (or (numeric-type-format result-type)
1467 :class (if (and (eq (numeric-type-class x) 'integer)
1468 (eq (numeric-type-class y) 'integer))
1469 ;; The difference of integers is always an integer.
1471 (numeric-type-class result-type))
1472 :format (numeric-type-format result-type)
1473 :low (interval-low result)
1474 :high (interval-high result)))
1475 ;; general contagion
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 positive, so take care to do it right.
1487 (interval-sqr (numeric-type->interval x))
1488 (interval-mul (numeric-type->interval x)
1489 (numeric-type->interval y))))
1490 (result-type (numeric-contagion x y)))
1491 ;; If the result type is a float, we need to be sure to coerce
1492 ;; the bounds into the correct type.
1493 (when (eq (numeric-type-class result-type) 'float)
1494 (setf result (interval-func
1496 (coerce-for-bound x (or (numeric-type-format result-type)
1500 :class (if (and (eq (numeric-type-class x) 'integer)
1501 (eq (numeric-type-class y) 'integer))
1502 ;; The product of integers is always an integer.
1504 (numeric-type-class result-type))
1505 :format (numeric-type-format result-type)
1506 :low (interval-low result)
1507 :high (interval-high result)))
1508 (numeric-contagion x y)))
1510 (defoptimizer (* derive-type) ((x y))
1511 (two-arg-derive-type x y #'*-derive-type-aux #'*))
1513 (defun /-derive-type-aux (x y same-arg)
1514 (if (and (numeric-type-real-p x)
1515 (numeric-type-real-p y))
1517 ;; (/ X X) is always 1, except if X can contain 0. In
1518 ;; that case, we shouldn't optimize the division away
1519 ;; because we want 0/0 to signal an error.
1521 (not (interval-contains-p
1522 0 (interval-closure (numeric-type->interval y)))))
1523 (make-interval :low 1 :high 1)
1524 (interval-div (numeric-type->interval x)
1525 (numeric-type->interval y))))
1526 (result-type (numeric-contagion x y)))
1527 ;; If the result type is a float, we need to be sure to coerce
1528 ;; the bounds into the correct type.
1529 (when (eq (numeric-type-class result-type) 'float)
1530 (setf result (interval-func
1532 (coerce-for-bound x (or (numeric-type-format result-type)
1535 (make-numeric-type :class (numeric-type-class result-type)
1536 :format (numeric-type-format result-type)
1537 :low (interval-low result)
1538 :high (interval-high result)))
1539 (numeric-contagion x y)))
1541 (defoptimizer (/ derive-type) ((x y))
1542 (two-arg-derive-type x y #'/-derive-type-aux #'/))
1546 (defun ash-derive-type-aux (n-type shift same-arg)
1547 (declare (ignore same-arg))
1548 ;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
1549 ;; some bignum cases because as of version 2.4.6 for Debian and 18d,
1550 ;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
1551 ;; two bignums yielding zero) and it's hard to avoid that
1552 ;; calculation in here.
1553 #+(and cmu sb-xc-host)
1554 (when (and (or (typep (numeric-type-low n-type) 'bignum)
1555 (typep (numeric-type-high n-type) 'bignum))
1556 (or (typep (numeric-type-low shift) 'bignum)
1557 (typep (numeric-type-high shift) 'bignum)))
1558 (return-from ash-derive-type-aux *universal-type*))
1559 (flet ((ash-outer (n s)
1560 (when (and (fixnump s)
1562 (> s sb!xc:most-negative-fixnum))
1564 ;; KLUDGE: The bare 64's here should be related to
1565 ;; symbolic machine word size values somehow.
1568 (if (and (fixnump s)
1569 (> s sb!xc:most-negative-fixnum))
1571 (if (minusp n) -1 0))))
1572 (or (and (csubtypep n-type (specifier-type 'integer))
1573 (csubtypep shift (specifier-type 'integer))
1574 (let ((n-low (numeric-type-low n-type))
1575 (n-high (numeric-type-high n-type))
1576 (s-low (numeric-type-low shift))
1577 (s-high (numeric-type-high shift)))
1578 (make-numeric-type :class 'integer :complexp :real
1581 (ash-outer n-low s-high)
1582 (ash-inner n-low s-low)))
1585 (ash-inner n-high s-low)
1586 (ash-outer n-high s-high))))))
1589 (defoptimizer (ash derive-type) ((n shift))
1590 (two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
1592 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1593 (macrolet ((frob (fun)
1594 `#'(lambda (type type2)
1595 (declare (ignore type2))
1596 (let ((lo (numeric-type-low type))
1597 (hi (numeric-type-high type)))
1598 (values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
1600 (defoptimizer (%negate derive-type) ((num))
1601 (derive-integer-type num num (frob -))))
1603 (defun lognot-derive-type-aux (int)
1604 (derive-integer-type-aux int int
1605 (lambda (type type2)
1606 (declare (ignore type2))
1607 (let ((lo (numeric-type-low type))
1608 (hi (numeric-type-high type)))
1609 (values (if hi (lognot hi) nil)
1610 (if lo (lognot lo) nil)
1611 (numeric-type-class type)
1612 (numeric-type-format type))))))
1614 (defoptimizer (lognot derive-type) ((int))
1615 (lognot-derive-type-aux (lvar-type int)))
1617 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1618 (defoptimizer (%negate derive-type) ((num))
1619 (flet ((negate-bound (b)
1621 (set-bound (- (type-bound-number b))
1623 (one-arg-derive-type num
1625 (modified-numeric-type
1627 :low (negate-bound (numeric-type-high type))
1628 :high (negate-bound (numeric-type-low type))))
1631 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1632 (defoptimizer (abs derive-type) ((num))
1633 (let ((type (lvar-type num)))
1634 (if (and (numeric-type-p type)
1635 (eq (numeric-type-class type) 'integer)
1636 (eq (numeric-type-complexp type) :real))
1637 (let ((lo (numeric-type-low type))
1638 (hi (numeric-type-high type)))
1639 (make-numeric-type :class 'integer :complexp :real
1640 :low (cond ((and hi (minusp hi))
1646 :high (if (and hi lo)
1647 (max (abs hi) (abs lo))
1649 (numeric-contagion type type))))
1651 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1652 (defun abs-derive-type-aux (type)
1653 (cond ((eq (numeric-type-complexp type) :complex)
1654 ;; The absolute value of a complex number is always a
1655 ;; non-negative float.
1656 (let* ((format (case (numeric-type-class type)
1657 ((integer rational) 'single-float)
1658 (t (numeric-type-format type))))
1659 (bound-format (or format 'float)))
1660 (make-numeric-type :class 'float
1663 :low (coerce 0 bound-format)
1666 ;; The absolute value of a real number is a non-negative real
1667 ;; of the same type.
1668 (let* ((abs-bnd (interval-abs (numeric-type->interval type)))
1669 (class (numeric-type-class type))
1670 (format (numeric-type-format type))
1671 (bound-type (or format class 'real)))
1676 :low (coerce-and-truncate-floats (interval-low abs-bnd) bound-type)
1677 :high (coerce-and-truncate-floats
1678 (interval-high abs-bnd) bound-type))))))
1680 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1681 (defoptimizer (abs derive-type) ((num))
1682 (one-arg-derive-type num #'abs-derive-type-aux #'abs))
1684 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1685 (defoptimizer (truncate derive-type) ((number divisor))
1686 (let ((number-type (lvar-type number))
1687 (divisor-type (lvar-type divisor))
1688 (integer-type (specifier-type 'integer)))
1689 (if (and (numeric-type-p number-type)
1690 (csubtypep number-type integer-type)
1691 (numeric-type-p divisor-type)
1692 (csubtypep divisor-type integer-type))
1693 (let ((number-low (numeric-type-low number-type))
1694 (number-high (numeric-type-high number-type))
1695 (divisor-low (numeric-type-low divisor-type))
1696 (divisor-high (numeric-type-high divisor-type)))
1697 (values-specifier-type
1698 `(values ,(integer-truncate-derive-type number-low number-high
1699 divisor-low divisor-high)
1700 ,(integer-rem-derive-type number-low number-high
1701 divisor-low divisor-high))))
1704 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
1707 (defun rem-result-type (number-type divisor-type)
1708 ;; Figure out what the remainder type is. The remainder is an
1709 ;; integer if both args are integers; a rational if both args are
1710 ;; rational; and a float otherwise.
1711 (cond ((and (csubtypep number-type (specifier-type 'integer))
1712 (csubtypep divisor-type (specifier-type 'integer)))
1714 ((and (csubtypep number-type (specifier-type 'rational))
1715 (csubtypep divisor-type (specifier-type 'rational)))
1717 ((and (csubtypep number-type (specifier-type 'float))
1718 (csubtypep divisor-type (specifier-type 'float)))
1719 ;; Both are floats so the result is also a float, of
1720 ;; the largest type.
1721 (or (float-format-max (numeric-type-format number-type)
1722 (numeric-type-format divisor-type))
1724 ((and (csubtypep number-type (specifier-type 'float))
1725 (csubtypep divisor-type (specifier-type 'rational)))
1726 ;; One of the arguments is a float and the other is a
1727 ;; rational. The remainder is a float of the same
1729 (or (numeric-type-format number-type) 'float))
1730 ((and (csubtypep divisor-type (specifier-type 'float))
1731 (csubtypep number-type (specifier-type 'rational)))
1732 ;; One of the arguments is a float and the other is a
1733 ;; rational. The remainder is a float of the same
1735 (or (numeric-type-format divisor-type) 'float))
1737 ;; Some unhandled combination. This usually means both args
1738 ;; are REAL so the result is a REAL.
1741 (defun truncate-derive-type-quot (number-type divisor-type)
1742 (let* ((rem-type (rem-result-type number-type divisor-type))
1743 (number-interval (numeric-type->interval number-type))
1744 (divisor-interval (numeric-type->interval divisor-type)))
1745 ;;(declare (type (member '(integer rational float)) rem-type))
1746 ;; We have real numbers now.
1747 (cond ((eq rem-type 'integer)
1748 ;; Since the remainder type is INTEGER, both args are
1750 (let* ((res (integer-truncate-derive-type
1751 (interval-low number-interval)
1752 (interval-high number-interval)
1753 (interval-low divisor-interval)
1754 (interval-high divisor-interval))))
1755 (specifier-type (if (listp res) res 'integer))))
1757 (let ((quot (truncate-quotient-bound
1758 (interval-div number-interval
1759 divisor-interval))))
1760 (specifier-type `(integer ,(or (interval-low quot) '*)
1761 ,(or (interval-high quot) '*))))))))
1763 (defun truncate-derive-type-rem (number-type divisor-type)
1764 (let* ((rem-type (rem-result-type number-type divisor-type))
1765 (number-interval (numeric-type->interval number-type))
1766 (divisor-interval (numeric-type->interval divisor-type))
1767 (rem (truncate-rem-bound number-interval divisor-interval)))
1768 ;;(declare (type (member '(integer rational float)) rem-type))
1769 ;; We have real numbers now.
1770 (cond ((eq rem-type 'integer)
1771 ;; Since the remainder type is INTEGER, both args are
1773 (specifier-type `(,rem-type ,(or (interval-low rem) '*)
1774 ,(or (interval-high rem) '*))))
1776 (multiple-value-bind (class format)
1779 (values 'integer nil))
1781 (values 'rational nil))
1782 ((or single-float double-float #!+long-float long-float)
1783 (values 'float rem-type))
1785 (values 'float nil))
1788 (when (member rem-type '(float single-float double-float
1789 #!+long-float long-float))
1790 (setf rem (interval-func #'(lambda (x)
1791 (coerce-for-bound x rem-type))
1793 (make-numeric-type :class class
1795 :low (interval-low rem)
1796 :high (interval-high rem)))))))
1798 (defun truncate-derive-type-quot-aux (num div same-arg)
1799 (declare (ignore same-arg))
1800 (if (and (numeric-type-real-p num)
1801 (numeric-type-real-p div))
1802 (truncate-derive-type-quot num div)
1805 (defun truncate-derive-type-rem-aux (num div same-arg)
1806 (declare (ignore same-arg))
1807 (if (and (numeric-type-real-p num)
1808 (numeric-type-real-p div))
1809 (truncate-derive-type-rem num div)
1812 (defoptimizer (truncate derive-type) ((number divisor))
1813 (let ((quot (two-arg-derive-type number divisor
1814 #'truncate-derive-type-quot-aux #'truncate))
1815 (rem (two-arg-derive-type number divisor
1816 #'truncate-derive-type-rem-aux #'rem)))
1817 (when (and quot rem)
1818 (make-values-type :required (list quot rem)))))
1820 (defun ftruncate-derive-type-quot (number-type divisor-type)
1821 ;; The bounds are the same as for truncate. However, the first
1822 ;; result is a float of some type. We need to determine what that
1823 ;; type is. Basically it's the more contagious of the two types.
1824 (let ((q-type (truncate-derive-type-quot number-type divisor-type))
1825 (res-type (numeric-contagion number-type divisor-type)))
1826 (make-numeric-type :class 'float
1827 :format (numeric-type-format res-type)
1828 :low (numeric-type-low q-type)
1829 :high (numeric-type-high q-type))))
1831 (defun ftruncate-derive-type-quot-aux (n d same-arg)
1832 (declare (ignore same-arg))
1833 (if (and (numeric-type-real-p n)
1834 (numeric-type-real-p d))
1835 (ftruncate-derive-type-quot n d)
1838 (defoptimizer (ftruncate derive-type) ((number divisor))
1840 (two-arg-derive-type number divisor
1841 #'ftruncate-derive-type-quot-aux #'ftruncate))
1842 (rem (two-arg-derive-type number divisor
1843 #'truncate-derive-type-rem-aux #'rem)))
1844 (when (and quot rem)
1845 (make-values-type :required (list quot rem)))))
1847 (defun %unary-truncate-derive-type-aux (number)
1848 (truncate-derive-type-quot number (specifier-type '(integer 1 1))))
1850 (defoptimizer (%unary-truncate derive-type) ((number))
1851 (one-arg-derive-type number
1852 #'%unary-truncate-derive-type-aux
1855 (defoptimizer (%unary-truncate/single-float derive-type) ((number))
1856 (one-arg-derive-type number
1857 #'%unary-truncate-derive-type-aux
1860 (defoptimizer (%unary-truncate/double-float derive-type) ((number))
1861 (one-arg-derive-type number
1862 #'%unary-truncate-derive-type-aux
1865 (defoptimizer (%unary-ftruncate derive-type) ((number))
1866 (let ((divisor (specifier-type '(integer 1 1))))
1867 (one-arg-derive-type number
1869 (ftruncate-derive-type-quot-aux n divisor nil))
1870 #'%unary-ftruncate)))
1872 (defoptimizer (%unary-round derive-type) ((number))
1873 (one-arg-derive-type number
1876 (unless (numeric-type-real-p n)
1877 (return *empty-type*))
1878 (let* ((interval (numeric-type->interval n))
1879 (low (interval-low interval))
1880 (high (interval-high interval)))
1882 (setf low (car low)))
1884 (setf high (car high)))
1894 ;;; Define optimizers for FLOOR and CEILING.
1896 ((def (name q-name r-name)
1897 (let ((q-aux (symbolicate q-name "-AUX"))
1898 (r-aux (symbolicate r-name "-AUX")))
1900 ;; Compute type of quotient (first) result.
1901 (defun ,q-aux (number-type divisor-type)
1902 (let* ((number-interval
1903 (numeric-type->interval number-type))
1905 (numeric-type->interval divisor-type))
1906 (quot (,q-name (interval-div number-interval
1907 divisor-interval))))
1908 (specifier-type `(integer ,(or (interval-low quot) '*)
1909 ,(or (interval-high quot) '*)))))
1910 ;; Compute type of remainder.
1911 (defun ,r-aux (number-type divisor-type)
1912 (let* ((divisor-interval
1913 (numeric-type->interval divisor-type))
1914 (rem (,r-name divisor-interval))
1915 (result-type (rem-result-type number-type divisor-type)))
1916 (multiple-value-bind (class format)
1919 (values 'integer nil))
1921 (values 'rational nil))
1922 ((or single-float double-float #!+long-float long-float)
1923 (values 'float result-type))
1925 (values 'float nil))
1928 (when (member result-type '(float single-float double-float
1929 #!+long-float long-float))
1930 ;; Make sure that the limits on the interval have
1932 (setf rem (interval-func (lambda (x)
1933 (coerce-for-bound x result-type))
1935 (make-numeric-type :class class
1937 :low (interval-low rem)
1938 :high (interval-high rem)))))
1939 ;; the optimizer itself
1940 (defoptimizer (,name derive-type) ((number divisor))
1941 (flet ((derive-q (n d same-arg)
1942 (declare (ignore same-arg))
1943 (if (and (numeric-type-real-p n)
1944 (numeric-type-real-p d))
1947 (derive-r (n d same-arg)
1948 (declare (ignore same-arg))
1949 (if (and (numeric-type-real-p n)
1950 (numeric-type-real-p d))
1953 (let ((quot (two-arg-derive-type
1954 number divisor #'derive-q #',name))
1955 (rem (two-arg-derive-type
1956 number divisor #'derive-r #'mod)))
1957 (when (and quot rem)
1958 (make-values-type :required (list quot rem))))))))))
1960 (def floor floor-quotient-bound floor-rem-bound)
1961 (def ceiling ceiling-quotient-bound ceiling-rem-bound))
1963 ;;; Define optimizers for FFLOOR and FCEILING
1964 (macrolet ((def (name q-name r-name)
1965 (let ((q-aux (symbolicate "F" q-name "-AUX"))
1966 (r-aux (symbolicate r-name "-AUX")))
1968 ;; Compute type of quotient (first) result.
1969 (defun ,q-aux (number-type divisor-type)
1970 (let* ((number-interval
1971 (numeric-type->interval number-type))
1973 (numeric-type->interval divisor-type))
1974 (quot (,q-name (interval-div number-interval
1976 (res-type (numeric-contagion number-type
1979 :class (numeric-type-class res-type)
1980 :format (numeric-type-format res-type)
1981 :low (interval-low quot)
1982 :high (interval-high quot))))
1984 (defoptimizer (,name derive-type) ((number divisor))
1985 (flet ((derive-q (n d same-arg)
1986 (declare (ignore same-arg))
1987 (if (and (numeric-type-real-p n)
1988 (numeric-type-real-p d))
1991 (derive-r (n d same-arg)
1992 (declare (ignore same-arg))
1993 (if (and (numeric-type-real-p n)
1994 (numeric-type-real-p d))
1997 (let ((quot (two-arg-derive-type
1998 number divisor #'derive-q #',name))
1999 (rem (two-arg-derive-type
2000 number divisor #'derive-r #'mod)))
2001 (when (and quot rem)
2002 (make-values-type :required (list quot rem))))))))))
2004 (def ffloor floor-quotient-bound floor-rem-bound)
2005 (def fceiling ceiling-quotient-bound ceiling-rem-bound))
2007 ;;; functions to compute the bounds on the quotient and remainder for
2008 ;;; the FLOOR function
2009 (defun floor-quotient-bound (quot)
2010 ;; Take the floor of the quotient and then massage it into what we
2012 (let ((lo (interval-low quot))
2013 (hi (interval-high quot)))
2014 ;; Take the floor of the lower bound. The result is always a
2015 ;; closed lower bound.
2017 (floor (type-bound-number lo))
2019 ;; For the upper bound, we need to be careful.
2022 ;; An open bound. We need to be careful here because
2023 ;; the floor of '(10.0) is 9, but the floor of
2025 (multiple-value-bind (q r) (floor (first hi))
2030 ;; A closed bound, so the answer is obvious.
2034 (make-interval :low lo :high hi)))
2035 (defun floor-rem-bound (div)
2036 ;; The remainder depends only on the divisor. Try to get the
2037 ;; correct sign for the remainder if we can.
2038 (case (interval-range-info div)
2040 ;; The divisor is always positive.
2041 (let ((rem (interval-abs div)))
2042 (setf (interval-low rem) 0)
2043 (when (and (numberp (interval-high rem))
2044 (not (zerop (interval-high rem))))
2045 ;; The remainder never contains the upper bound. However,
2046 ;; watch out for the case where the high limit is zero!
2047 (setf (interval-high rem) (list (interval-high rem))))
2050 ;; The divisor is always negative.
2051 (let ((rem (interval-neg (interval-abs div))))
2052 (setf (interval-high rem) 0)
2053 (when (numberp (interval-low rem))
2054 ;; The remainder never contains the lower bound.
2055 (setf (interval-low rem) (list (interval-low rem))))
2058 ;; The divisor can be positive or negative. All bets off. The
2059 ;; magnitude of remainder is the maximum value of the divisor.
2060 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2061 ;; The bound never reaches the limit, so make the interval open.
2062 (make-interval :low (if limit
2065 :high (list limit))))))
2067 (floor-quotient-bound (make-interval :low 0.3 :high 10.3))
2068 => #S(INTERVAL :LOW 0 :HIGH 10)
2069 (floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2070 => #S(INTERVAL :LOW 0 :HIGH 10)
2071 (floor-quotient-bound (make-interval :low 0.3 :high 10))
2072 => #S(INTERVAL :LOW 0 :HIGH 10)
2073 (floor-quotient-bound (make-interval :low 0.3 :high '(10)))
2074 => #S(INTERVAL :LOW 0 :HIGH 9)
2075 (floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
2076 => #S(INTERVAL :LOW 0 :HIGH 10)
2077 (floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
2078 => #S(INTERVAL :LOW 0 :HIGH 10)
2079 (floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2080 => #S(INTERVAL :LOW -2 :HIGH 10)
2081 (floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2082 => #S(INTERVAL :LOW -1 :HIGH 10)
2083 (floor-quotient-bound (make-interval :low -1.0 :high 10.3))
2084 => #S(INTERVAL :LOW -1 :HIGH 10)
2086 (floor-rem-bound (make-interval :low 0.3 :high 10.3))
2087 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2088 (floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
2089 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2090 (floor-rem-bound (make-interval :low -10 :high -2.3))
2091 #S(INTERVAL :LOW (-10) :HIGH 0)
2092 (floor-rem-bound (make-interval :low 0.3 :high 10))
2093 => #S(INTERVAL :LOW 0 :HIGH '(10))
2094 (floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
2095 => #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
2096 (floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
2097 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2100 ;;; same functions for CEILING
2101 (defun ceiling-quotient-bound (quot)
2102 ;; Take the ceiling of the quotient and then massage it into what we
2104 (let ((lo (interval-low quot))
2105 (hi (interval-high quot)))
2106 ;; Take the ceiling of the upper bound. The result is always a
2107 ;; closed upper bound.
2109 (ceiling (type-bound-number hi))
2111 ;; For the lower bound, we need to be careful.
2114 ;; An open bound. We need to be careful here because
2115 ;; the ceiling of '(10.0) is 11, but the ceiling of
2117 (multiple-value-bind (q r) (ceiling (first lo))
2122 ;; A closed bound, so the answer is obvious.
2126 (make-interval :low lo :high hi)))
2127 (defun ceiling-rem-bound (div)
2128 ;; The remainder depends only on the divisor. Try to get the
2129 ;; correct sign for the remainder if we can.
2130 (case (interval-range-info div)
2132 ;; Divisor is always positive. The remainder is negative.
2133 (let ((rem (interval-neg (interval-abs div))))
2134 (setf (interval-high rem) 0)
2135 (when (and (numberp (interval-low rem))
2136 (not (zerop (interval-low rem))))
2137 ;; The remainder never contains the upper bound. However,
2138 ;; watch out for the case when the upper bound is zero!
2139 (setf (interval-low rem) (list (interval-low rem))))
2142 ;; Divisor is always negative. The remainder is positive
2143 (let ((rem (interval-abs div)))
2144 (setf (interval-low rem) 0)
2145 (when (numberp (interval-high rem))
2146 ;; The remainder never contains the lower bound.
2147 (setf (interval-high rem) (list (interval-high rem))))
2150 ;; The divisor can be positive or negative. All bets off. The
2151 ;; magnitude of remainder is the maximum value of the divisor.
2152 (let ((limit (type-bound-number (interval-high (interval-abs div)))))
2153 ;; The bound never reaches the limit, so make the interval open.
2154 (make-interval :low (if limit
2157 :high (list limit))))))
2160 (ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
2161 => #S(INTERVAL :LOW 1 :HIGH 11)
2162 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
2163 => #S(INTERVAL :LOW 1 :HIGH 11)
2164 (ceiling-quotient-bound (make-interval :low 0.3 :high 10))
2165 => #S(INTERVAL :LOW 1 :HIGH 10)
2166 (ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
2167 => #S(INTERVAL :LOW 1 :HIGH 10)
2168 (ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
2169 => #S(INTERVAL :LOW 1 :HIGH 11)
2170 (ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
2171 => #S(INTERVAL :LOW 1 :HIGH 11)
2172 (ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
2173 => #S(INTERVAL :LOW -1 :HIGH 11)
2174 (ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
2175 => #S(INTERVAL :LOW 0 :HIGH 11)
2176 (ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
2177 => #S(INTERVAL :LOW -1 :HIGH 11)
2179 (ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
2180 => #S(INTERVAL :LOW (-10.3) :HIGH 0)
2181 (ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
2182 => #S(INTERVAL :LOW 0 :HIGH '(10.3))
2183 (ceiling-rem-bound (make-interval :low -10 :high -2.3))
2184 => #S(INTERVAL :LOW 0 :HIGH (10))
2185 (ceiling-rem-bound (make-interval :low 0.3 :high 10))
2186 => #S(INTERVAL :LOW (-10) :HIGH 0)
2187 (ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
2188 => #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
2189 (ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
2190 => #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
2193 (defun truncate-quotient-bound (quot)
2194 ;; For positive quotients, truncate is exactly like floor. For
2195 ;; negative quotients, truncate is exactly like ceiling. Otherwise,
2196 ;; it's the union of the two pieces.
2197 (case (interval-range-info quot)
2200 (floor-quotient-bound quot))
2202 ;; just like CEILING
2203 (ceiling-quotient-bound quot))
2205 ;; Split the interval into positive and negative pieces, compute
2206 ;; the result for each piece and put them back together.
2207 (destructuring-bind (neg pos) (interval-split 0 quot t t)
2208 (interval-merge-pair (ceiling-quotient-bound neg)
2209 (floor-quotient-bound pos))))))
2211 (defun truncate-rem-bound (num div)
2212 ;; This is significantly more complicated than FLOOR or CEILING. We
2213 ;; need both the number and the divisor to determine the range. The
2214 ;; basic idea is to split the ranges of NUM and DEN into positive
2215 ;; and negative pieces and deal with each of the four possibilities
2217 (case (interval-range-info num)
2219 (case (interval-range-info div)
2221 (floor-rem-bound div))
2223 (ceiling-rem-bound div))
2225 (destructuring-bind (neg pos) (interval-split 0 div t t)
2226 (interval-merge-pair (truncate-rem-bound num neg)
2227 (truncate-rem-bound num pos))))))
2229 (case (interval-range-info div)
2231 (ceiling-rem-bound div))
2233 (floor-rem-bound div))
2235 (destructuring-bind (neg pos) (interval-split 0 div t t)
2236 (interval-merge-pair (truncate-rem-bound num neg)
2237 (truncate-rem-bound num pos))))))
2239 (destructuring-bind (neg pos) (interval-split 0 num t t)
2240 (interval-merge-pair (truncate-rem-bound neg div)
2241 (truncate-rem-bound pos div))))))
2244 ;;; Derive useful information about the range. Returns three values:
2245 ;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
2246 ;;; - The abs of the minimal value (i.e. closest to 0) in the range.
2247 ;;; - The abs of the maximal value if there is one, or nil if it is
2249 (defun numeric-range-info (low high)
2250 (cond ((and low (not (minusp low)))
2251 (values '+ low high))
2252 ((and high (not (plusp high)))
2253 (values '- (- high) (if low (- low) nil)))
2255 (values nil 0 (and low high (max (- low) high))))))
2257 (defun integer-truncate-derive-type
2258 (number-low number-high divisor-low divisor-high)
2259 ;; The result cannot be larger in magnitude than the number, but the
2260 ;; sign might change. If we can determine the sign of either the
2261 ;; number or the divisor, we can eliminate some of the cases.
2262 (multiple-value-bind (number-sign number-min number-max)
2263 (numeric-range-info number-low number-high)
2264 (multiple-value-bind (divisor-sign divisor-min divisor-max)
2265 (numeric-range-info divisor-low divisor-high)
2266 (when (and divisor-max (zerop divisor-max))
2267 ;; We've got a problem: guaranteed division by zero.
2268 (return-from integer-truncate-derive-type t))
2269 (when (zerop divisor-min)
2270 ;; We'll assume that they aren't going to divide by zero.
2272 (cond ((and number-sign divisor-sign)
2273 ;; We know the sign of both.
2274 (if (eq number-sign divisor-sign)
2275 ;; Same sign, so the result will be positive.
2276 `(integer ,(if divisor-max
2277 (truncate number-min divisor-max)
2280 (truncate number-max divisor-min)
2282 ;; Different signs, the result will be negative.
2283 `(integer ,(if number-max
2284 (- (truncate number-max divisor-min))
2287 (- (truncate number-min divisor-max))
2289 ((eq divisor-sign '+)
2290 ;; The divisor is positive. Therefore, the number will just
2291 ;; become closer to zero.
2292 `(integer ,(if number-low
2293 (truncate number-low divisor-min)
2296 (truncate number-high divisor-min)
2298 ((eq divisor-sign '-)
2299 ;; The divisor is negative. Therefore, the absolute value of
2300 ;; the number will become closer to zero, but the sign will also
2302 `(integer ,(if number-high
2303 (- (truncate number-high divisor-min))
2306 (- (truncate number-low divisor-min))
2308 ;; The divisor could be either positive or negative.
2310 ;; The number we are dividing has a bound. Divide that by the
2311 ;; smallest posible divisor.
2312 (let ((bound (truncate number-max divisor-min)))
2313 `(integer ,(- bound) ,bound)))
2315 ;; The number we are dividing is unbounded, so we can't tell
2316 ;; anything about the result.
2319 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2320 (defun integer-rem-derive-type
2321 (number-low number-high divisor-low divisor-high)
2322 (if (and divisor-low divisor-high)
2323 ;; We know the range of the divisor, and the remainder must be
2324 ;; smaller than the divisor. We can tell the sign of the
2325 ;; remainer if we know the sign of the number.
2326 (let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
2327 `(integer ,(if (or (null number-low)
2328 (minusp number-low))
2331 ,(if (or (null number-high)
2332 (plusp number-high))
2335 ;; The divisor is potentially either very positive or very
2336 ;; negative. Therefore, the remainer is unbounded, but we might
2337 ;; be able to tell something about the sign from the number.
2338 `(integer ,(if (and number-low (not (minusp number-low)))
2339 ;; The number we are dividing is positive.
2340 ;; Therefore, the remainder must be positive.
2343 ,(if (and number-high (not (plusp number-high)))
2344 ;; The number we are dividing is negative.
2345 ;; Therefore, the remainder must be negative.
2349 #+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2350 (defoptimizer (random derive-type) ((bound &optional state))
2351 (let ((type (lvar-type bound)))
2352 (when (numeric-type-p type)
2353 (let ((class (numeric-type-class type))
2354 (high (numeric-type-high type))
2355 (format (numeric-type-format type)))
2359 :low (coerce 0 (or format class 'real))
2360 :high (cond ((not high) nil)
2361 ((eq class 'integer) (max (1- high) 0))
2362 ((or (consp high) (zerop high)) high)
2365 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2366 (defun random-derive-type-aux (type)
2367 (let ((class (numeric-type-class type))
2368 (high (numeric-type-high type))
2369 (format (numeric-type-format type)))
2373 :low (coerce 0 (or format class 'real))
2374 :high (cond ((not high) nil)
2375 ((eq class 'integer) (max (1- high) 0))
2376 ((or (consp high) (zerop high)) high)
2379 #-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
2380 (defoptimizer (random derive-type) ((bound &optional state))
2381 (one-arg-derive-type bound #'random-derive-type-aux nil))
2383 ;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
2385 ;;; Return the maximum number of bits an integer of the supplied type
2386 ;;; can take up, or NIL if it is unbounded. The second (third) value
2387 ;;; is T if the integer can be positive (negative) and NIL if not.
2388 ;;; Zero counts as positive.
2389 (defun integer-type-length (type)
2390 (if (numeric-type-p type)
2391 (let ((min (numeric-type-low type))
2392 (max (numeric-type-high type)))
2393 (values (and min max (max (integer-length min) (integer-length max)))
2394 (or (null max) (not (minusp max)))
2395 (or (null min) (minusp min))))
2398 ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an
2399 ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND.
2400 ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar
2401 ;;; versions in CMUCL, from which these functions copy liberally.
2403 (defun logand-derive-unsigned-low-bound (x y)
2404 (let ((a (numeric-type-low x))
2405 (b (numeric-type-high x))
2406 (c (numeric-type-low y))
2407 (d (numeric-type-high y)))
2408 (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1)
2410 (unless (zerop (logand m (lognot a) (lognot c)))
2411 (let ((temp (logandc2 (logior a m) (1- m))))
2415 (setf temp (logandc2 (logior c m) (1- m)))
2419 finally (return (logand a c)))))
2421 (defun logand-derive-unsigned-high-bound (x y)
2422 (let ((a (numeric-type-low x))
2423 (b (numeric-type-high x))
2424 (c (numeric-type-low y))
2425 (d (numeric-type-high y)))
2426 (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1)
2429 ((not (zerop (logand b (lognot d) m)))
2430 (let ((temp (logior (logandc2 b m) (1- m))))
2434 ((not (zerop (logand (lognot b) d m)))
2435 (let ((temp (logior (logandc2 d m) (1- m))))
2439 finally (return (logand b d)))))
2441 (defun logand-derive-type-aux (x y &optional same-leaf)
2443 (return-from logand-derive-type-aux x))
2444 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2445 (declare (ignore x-pos))
2446 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2447 (declare (ignore y-pos))
2449 ;; X must be positive.
2451 ;; They must both be positive.
2452 (cond ((and (null x-len) (null y-len))
2453 (specifier-type 'unsigned-byte))
2455 (specifier-type `(unsigned-byte* ,y-len)))
2457 (specifier-type `(unsigned-byte* ,x-len)))
2459 (let ((low (logand-derive-unsigned-low-bound x y))
2460 (high (logand-derive-unsigned-high-bound x y)))
2461 (specifier-type `(integer ,low ,high)))))
2462 ;; X is positive, but Y might be negative.
2464 (specifier-type 'unsigned-byte))
2466 (specifier-type `(unsigned-byte* ,x-len)))))
2467 ;; X might be negative.
2469 ;; Y must be positive.
2471 (specifier-type 'unsigned-byte))
2472 (t (specifier-type `(unsigned-byte* ,y-len))))
2473 ;; Either might be negative.
2474 (if (and x-len y-len)
2475 ;; The result is bounded.
2476 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2477 ;; We can't tell squat about the result.
2478 (specifier-type 'integer)))))))
2480 (defun logior-derive-unsigned-low-bound (x y)
2481 (let ((a (numeric-type-low x))
2482 (b (numeric-type-high x))
2483 (c (numeric-type-low y))
2484 (d (numeric-type-high y)))
2485 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2488 ((not (zerop (logandc2 (logand c m) a)))
2489 (let ((temp (logand (logior a m) (1+ (lognot m)))))
2493 ((not (zerop (logandc2 (logand a m) c)))
2494 (let ((temp (logand (logior c m) (1+ (lognot m)))))
2498 finally (return (logior a c)))))
2500 (defun logior-derive-unsigned-high-bound (x y)
2501 (let ((a (numeric-type-low x))
2502 (b (numeric-type-high x))
2503 (c (numeric-type-low y))
2504 (d (numeric-type-high y)))
2505 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2507 (unless (zerop (logand b d m))
2508 (let ((temp (logior (- b m) (1- m))))
2512 (setf temp (logior (- d m) (1- m)))
2516 finally (return (logior b d)))))
2518 (defun logior-derive-type-aux (x y &optional same-leaf)
2520 (return-from logior-derive-type-aux x))
2521 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2522 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2524 ((and (not x-neg) (not y-neg))
2525 ;; Both are positive.
2526 (if (and x-len y-len)
2527 (let ((low (logior-derive-unsigned-low-bound x y))
2528 (high (logior-derive-unsigned-high-bound x y)))
2529 (specifier-type `(integer ,low ,high)))
2530 (specifier-type `(unsigned-byte* *))))
2532 ;; X must be negative.
2534 ;; Both are negative. The result is going to be negative
2535 ;; and be the same length or shorter than the smaller.
2536 (if (and x-len y-len)
2538 (specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
2540 (specifier-type '(integer * -1)))
2541 ;; X is negative, but we don't know about Y. The result
2542 ;; will be negative, but no more negative than X.
2544 `(integer ,(or (numeric-type-low x) '*)
2547 ;; X might be either positive or negative.
2549 ;; But Y is negative. The result will be negative.
2551 `(integer ,(or (numeric-type-low y) '*)
2553 ;; We don't know squat about either. It won't get any bigger.
2554 (if (and x-len y-len)
2556 (specifier-type `(signed-byte ,(1+ (max x-len y-len))))
2558 (specifier-type 'integer))))))))
2560 (defun logxor-derive-unsigned-low-bound (x y)
2561 (let ((a (numeric-type-low x))
2562 (b (numeric-type-high x))
2563 (c (numeric-type-low y))
2564 (d (numeric-type-high y)))
2565 (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1)
2568 ((not (zerop (logandc2 (logand c m) a)))
2569 (let ((temp (logand (logior a m)
2573 ((not (zerop (logandc2 (logand a m) c)))
2574 (let ((temp (logand (logior c m)
2578 finally (return (logxor a c)))))
2580 (defun logxor-derive-unsigned-high-bound (x y)
2581 (let ((a (numeric-type-low x))
2582 (b (numeric-type-high x))
2583 (c (numeric-type-low y))
2584 (d (numeric-type-high y)))
2585 (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1)
2587 (unless (zerop (logand b d m))
2588 (let ((temp (logior (- b m) (1- m))))
2590 ((>= temp a) (setf b temp))
2591 (t (let ((temp (logior (- d m) (1- m))))
2594 finally (return (logxor b d)))))
2596 (defun logxor-derive-type-aux (x y &optional same-leaf)
2598 (return-from logxor-derive-type-aux (specifier-type '(eql 0))))
2599 (multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
2600 (multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
2602 ((and (not x-neg) (not y-neg))
2603 ;; Both are positive
2604 (if (and x-len y-len)
2605 (let ((low (logxor-derive-unsigned-low-bound x y))
2606 (high (logxor-derive-unsigned-high-bound x y)))
2607 (specifier-type `(integer ,low ,high)))
2608 (specifier-type '(unsigned-byte* *))))
2609 ((and (not x-pos) (not y-pos))
2610 ;; Both are negative. The result will be positive, and as long
2612 (specifier-type `(unsigned-byte* ,(if (and x-len y-len)
2615 ((or (and (not x-pos) (not y-neg))
2616 (and (not y-pos) (not x-neg)))
2617 ;; Either X is negative and Y is positive or vice-versa. The
2618 ;; result will be negative.
2619 (specifier-type `(integer ,(if (and x-len y-len)
2620 (ash -1 (max x-len y-len))
2623 ;; We can't tell what the sign of the result is going to be.
2624 ;; All we know is that we don't create new bits.
2626 (specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
2628 (specifier-type 'integer))))))
2630 (macrolet ((deffrob (logfun)
2631 (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX")))
2632 `(defoptimizer (,logfun derive-type) ((x y))
2633 (two-arg-derive-type x y #',fun-aux #',logfun)))))
2638 (defoptimizer (logeqv derive-type) ((x y))
2639 (two-arg-derive-type x y (lambda (x y same-leaf)
2640 (lognot-derive-type-aux
2641 (logxor-derive-type-aux x y same-leaf)))
2643 (defoptimizer (lognand derive-type) ((x y))
2644 (two-arg-derive-type x y (lambda (x y same-leaf)
2645 (lognot-derive-type-aux
2646 (logand-derive-type-aux x y same-leaf)))
2648 (defoptimizer (lognor derive-type) ((x y))
2649 (two-arg-derive-type x y (lambda (x y same-leaf)
2650 (lognot-derive-type-aux
2651 (logior-derive-type-aux x y same-leaf)))
2653 (defoptimizer (logandc1 derive-type) ((x y))
2654 (two-arg-derive-type x y (lambda (x y same-leaf)
2656 (specifier-type '(eql 0))
2657 (logand-derive-type-aux
2658 (lognot-derive-type-aux x) y nil)))
2660 (defoptimizer (logandc2 derive-type) ((x y))
2661 (two-arg-derive-type x y (lambda (x y same-leaf)
2663 (specifier-type '(eql 0))
2664 (logand-derive-type-aux
2665 x (lognot-derive-type-aux y) nil)))
2667 (defoptimizer (logorc1 derive-type) ((x y))
2668 (two-arg-derive-type x y (lambda (x y same-leaf)
2670 (specifier-type '(eql -1))
2671 (logior-derive-type-aux
2672 (lognot-derive-type-aux x) y nil)))
2674 (defoptimizer (logorc2 derive-type) ((x y))
2675 (two-arg-derive-type x y (lambda (x y same-leaf)
2677 (specifier-type '(eql -1))
2678 (logior-derive-type-aux
2679 x (lognot-derive-type-aux y) nil)))
2682 ;;;; miscellaneous derive-type methods
2684 (defoptimizer (integer-length derive-type) ((x))
2685 (let ((x-type (lvar-type x)))
2686 (when (numeric-type-p x-type)
2687 ;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
2688 ;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
2689 ;; careful about LO or HI being NIL, though. Also, if 0 is
2690 ;; contained in X, the lower bound is obviously 0.
2691 (flet ((null-or-min (a b)
2692 (and a b (min (integer-length a)
2693 (integer-length b))))
2695 (and a b (max (integer-length a)
2696 (integer-length b)))))
2697 (let* ((min (numeric-type-low x-type))
2698 (max (numeric-type-high x-type))
2699 (min-len (null-or-min min max))
2700 (max-len (null-or-max min max)))
2701 (when (ctypep 0 x-type)
2703 (specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
2705 (defoptimizer (isqrt derive-type) ((x))
2706 (let ((x-type (lvar-type x)))
2707 (when (numeric-type-p x-type)
2708 (let* ((lo (numeric-type-low x-type))
2709 (hi (numeric-type-high x-type))
2710 (lo-res (if lo (isqrt lo) '*))
2711 (hi-res (if hi (isqrt hi) '*)))
2712 (specifier-type `(integer ,lo-res ,hi-res))))))
2714 (defoptimizer (char-code derive-type) ((char))
2715 (let ((type (type-intersection (lvar-type char) (specifier-type 'character))))
2716 (cond ((member-type-p type)
2719 ,@(loop for member in (member-type-members type)
2720 when (characterp member)
2721 collect (char-code member)))))
2722 ((sb!kernel::character-set-type-p type)
2725 ,@(loop for (low . high)
2726 in (character-set-type-pairs type)
2727 collect `(integer ,low ,high)))))
2728 ((csubtypep type (specifier-type 'base-char))
2730 `(mod ,base-char-code-limit)))
2733 `(mod ,char-code-limit))))))
2735 (defoptimizer (code-char derive-type) ((code))
2736 (let ((type (lvar-type code)))
2737 ;; FIXME: unions of integral ranges? It ought to be easier to do
2738 ;; this, given that CHARACTER-SET is basically an integral range
2739 ;; type. -- CSR, 2004-10-04
2740 (when (numeric-type-p type)
2741 (let* ((lo (numeric-type-low type))
2742 (hi (numeric-type-high type))
2743 (type (specifier-type `(character-set ((,lo . ,hi))))))
2745 ;; KLUDGE: when running on the host, we lose a slight amount
2746 ;; of precision so that we don't have to "unparse" types
2747 ;; that formally we can't, such as (CHARACTER-SET ((0
2748 ;; . 0))). -- CSR, 2004-10-06
2750 ((csubtypep type (specifier-type 'standard-char)) type)
2752 ((csubtypep type (specifier-type 'base-char))
2753 (specifier-type 'base-char))
2755 ((csubtypep type (specifier-type 'extended-char))
2756 (specifier-type 'extended-char))
2757 (t #+sb-xc-host (specifier-type 'character)
2758 #-sb-xc-host type))))))
2760 (defoptimizer (values derive-type) ((&rest values))
2761 (make-values-type :required (mapcar #'lvar-type values)))
2763 (defun signum-derive-type-aux (type)
2764 (if (eq (numeric-type-complexp type) :complex)
2765 (let* ((format (case (numeric-type-class type)
2766 ((integer rational) 'single-float)
2767 (t (numeric-type-format type))))
2768 (bound-format (or format 'float)))
2769 (make-numeric-type :class 'float
2772 :low (coerce -1 bound-format)
2773 :high (coerce 1 bound-format)))
2774 (let* ((interval (numeric-type->interval type))
2775 (range-info (interval-range-info interval))
2776 (contains-0-p (interval-contains-p 0 interval))
2777 (class (numeric-type-class type))
2778 (format (numeric-type-format type))
2779 (one (coerce 1 (or format class 'real)))
2780 (zero (coerce 0 (or format class 'real)))
2781 (minus-one (coerce -1 (or format class 'real)))
2782 (plus (make-numeric-type :class class :format format
2783 :low one :high one))
2784 (minus (make-numeric-type :class class :format format
2785 :low minus-one :high minus-one))
2786 ;; KLUDGE: here we have a fairly horrible hack to deal
2787 ;; with the schizophrenia in the type derivation engine.
2788 ;; The problem is that the type derivers reinterpret
2789 ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0
2790 ;; 0d0) within the derivation mechanism doesn't include
2791 ;; -0d0. Ugh. So force it in here, instead.
2792 (zero (make-numeric-type :class class :format format
2793 :low (- zero) :high zero)))
2795 (+ (if contains-0-p (type-union plus zero) plus))
2796 (- (if contains-0-p (type-union minus zero) minus))
2797 (t (type-union minus zero plus))))))
2799 (defoptimizer (signum derive-type) ((num))
2800 (one-arg-derive-type num #'signum-derive-type-aux nil))
2802 ;;;; byte operations
2804 ;;;; We try to turn byte operations into simple logical operations.
2805 ;;;; First, we convert byte specifiers into separate size and position
2806 ;;;; arguments passed to internal %FOO functions. We then attempt to
2807 ;;;; transform the %FOO functions into boolean operations when the
2808 ;;;; size and position are constant and the operands are fixnums.
2810 (macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
2811 ;; expressions that evaluate to the SIZE and POSITION of
2812 ;; the byte-specifier form SPEC. We may wrap a let around
2813 ;; the result of the body to bind some variables.
2815 ;; If the spec is a BYTE form, then bind the vars to the
2816 ;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
2817 ;; and BYTE-POSITION. The goal of this transformation is to
2818 ;; avoid consing up byte specifiers and then immediately
2819 ;; throwing them away.
2820 (with-byte-specifier ((size-var pos-var spec) &body body)
2821 (once-only ((spec `(macroexpand ,spec))
2823 `(if (and (consp ,spec)
2824 (eq (car ,spec) 'byte)
2825 (= (length ,spec) 3))
2826 (let ((,size-var (second ,spec))
2827 (,pos-var (third ,spec)))
2829 (let ((,size-var `(byte-size ,,temp))
2830 (,pos-var `(byte-position ,,temp)))
2831 `(let ((,,temp ,,spec))
2834 (define-source-transform ldb (spec int)
2835 (with-byte-specifier (size pos spec)
2836 `(%ldb ,size ,pos ,int)))
2838 (define-source-transform dpb (newbyte spec int)
2839 (with-byte-specifier (size pos spec)
2840 `(%dpb ,newbyte ,size ,pos ,int)))
2842 (define-source-transform mask-field (spec int)
2843 (with-byte-specifier (size pos spec)
2844 `(%mask-field ,size ,pos ,int)))
2846 (define-source-transform deposit-field (newbyte spec int)
2847 (with-byte-specifier (size pos spec)
2848 `(%deposit-field ,newbyte ,size ,pos ,int))))
2850 (defoptimizer (%ldb derive-type) ((size posn num))
2851 (let ((size (lvar-type size)))
2852 (if (and (numeric-type-p size)
2853 (csubtypep size (specifier-type 'integer)))
2854 (let ((size-high (numeric-type-high size)))
2855 (if (and size-high (<= size-high sb!vm:n-word-bits))
2856 (specifier-type `(unsigned-byte* ,size-high))
2857 (specifier-type 'unsigned-byte)))
2860 (defoptimizer (%mask-field derive-type) ((size posn num))
2861 (let ((size (lvar-type size))
2862 (posn (lvar-type posn)))
2863 (if (and (numeric-type-p size)
2864 (csubtypep size (specifier-type 'integer))
2865 (numeric-type-p posn)
2866 (csubtypep posn (specifier-type 'integer)))
2867 (let ((size-high (numeric-type-high size))
2868 (posn-high (numeric-type-high posn)))
2869 (if (and size-high posn-high
2870 (<= (+ size-high posn-high) sb!vm:n-word-bits))
2871 (specifier-type `(unsigned-byte* ,(+ size-high posn-high)))
2872 (specifier-type 'unsigned-byte)))
2875 (defun %deposit-field-derive-type-aux (size posn int)
2876 (let ((size (lvar-type size))
2877 (posn (lvar-type posn))
2878 (int (lvar-type int)))
2879 (when (and (numeric-type-p size)
2880 (numeric-type-p posn)
2881 (numeric-type-p int))
2882 (let ((size-high (numeric-type-high size))
2883 (posn-high (numeric-type-high posn))
2884 (high (numeric-type-high int))
2885 (low (numeric-type-low int)))
2886 (when (and size-high posn-high high low
2887 ;; KLUDGE: we need this cutoff here, otherwise we
2888 ;; will merrily derive the type of %DPB as
2889 ;; (UNSIGNED-BYTE 1073741822), and then attempt to
2890 ;; canonicalize this type to (INTEGER 0 (1- (ASH 1
2891 ;; 1073741822))), with hilarious consequences. We
2892 ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference
2893 ;; over a reasonable amount of shifting, even on
2894 ;; the alpha/32 port, where N-WORD-BITS is 32 but
2895 ;; machine integers are 64-bits. -- CSR,
2897 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits)))
2898 (let ((raw-bit-count (max (integer-length high)
2899 (integer-length low)
2900 (+ size-high posn-high))))
2903 `(signed-byte ,(1+ raw-bit-count))
2904 `(unsigned-byte* ,raw-bit-count)))))))))
2906 (defoptimizer (%dpb derive-type) ((newbyte size posn int))
2907 (%deposit-field-derive-type-aux size posn int))
2909 (defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
2910 (%deposit-field-derive-type-aux size posn int))
2912 (deftransform %ldb ((size posn int)
2913 (fixnum fixnum integer)
2914 (unsigned-byte #.sb!vm:n-word-bits))
2915 "convert to inline logical operations"
2916 `(logand (ash int (- posn))
2917 (ash ,(1- (ash 1 sb!vm:n-word-bits))
2918 (- size ,sb!vm:n-word-bits))))
2920 (deftransform %mask-field ((size posn int)
2921 (fixnum fixnum integer)
2922 (unsigned-byte #.sb!vm:n-word-bits))
2923 "convert to inline logical operations"
2925 (ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
2926 (- size ,sb!vm:n-word-bits))
2929 ;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
2930 ;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
2931 ;;; as the result type, as that would allow result types that cover
2932 ;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
2933 ;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
2935 (deftransform %dpb ((new size posn int)
2937 (unsigned-byte #.sb!vm:n-word-bits))
2938 "convert to inline logical operations"
2939 `(let ((mask (ldb (byte size 0) -1)))
2940 (logior (ash (logand new mask) posn)
2941 (logand int (lognot (ash mask posn))))))
2943 (deftransform %dpb ((new size posn int)
2945 (signed-byte #.sb!vm:n-word-bits))
2946 "convert to inline logical operations"
2947 `(let ((mask (ldb (byte size 0) -1)))
2948 (logior (ash (logand new mask) posn)
2949 (logand int (lognot (ash mask posn))))))
2951 (deftransform %deposit-field ((new size posn int)
2953 (unsigned-byte #.sb!vm:n-word-bits))
2954 "convert to inline logical operations"
2955 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2956 (logior (logand new mask)
2957 (logand int (lognot mask)))))
2959 (deftransform %deposit-field ((new size posn int)
2961 (signed-byte #.sb!vm:n-word-bits))
2962 "convert to inline logical operations"
2963 `(let ((mask (ash (ldb (byte size 0) -1) posn)))
2964 (logior (logand new mask)
2965 (logand int (lognot mask)))))
2967 (defoptimizer (mask-signed-field derive-type) ((size x))
2968 (let ((size (lvar-type size)))
2969 (if (numeric-type-p size)
2970 (let ((size-high (numeric-type-high size)))
2971 (if (and size-high (<= 1 size-high sb!vm:n-word-bits))
2972 (specifier-type `(signed-byte ,size-high))
2977 ;;; Modular functions
2979 ;;; (ldb (byte s 0) (foo x y ...)) =
2980 ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...))
2982 ;;; and similar for other arguments.
2984 (defun make-modular-fun-type-deriver (prototype kind width signedp)
2985 (declare (ignore kind))
2987 (binding* ((info (info :function :info prototype) :exit-if-null)
2988 (fun (fun-info-derive-type info) :exit-if-null)
2989 (mask-type (specifier-type
2991 ((nil) (let ((mask (1- (ash 1 width))))
2992 `(integer ,mask ,mask)))
2993 ((t) `(signed-byte ,width))))))
2995 (let ((res (funcall fun call)))
2997 (if (eq signedp nil)
2998 (logand-derive-type-aux res mask-type))))))
3001 (binding* ((info (info :function :info prototype) :exit-if-null)
3002 (fun (fun-info-derive-type info) :exit-if-null)
3003 (res (funcall fun call) :exit-if-null)
3004 (mask-type (specifier-type
3006 ((nil) (let ((mask (1- (ash 1 width))))
3007 `(integer ,mask ,mask)))
3008 ((t) `(signed-byte ,width))))))
3009 (if (eq signedp nil)
3010 (logand-derive-type-aux res mask-type)))))
3012 ;;; Try to recursively cut all uses of LVAR to WIDTH bits.
3014 ;;; For good functions, we just recursively cut arguments; their
3015 ;;; "goodness" means that the result will not increase (in the
3016 ;;; (unsigned-byte +infinity) sense). An ordinary modular function is
3017 ;;; replaced with the version, cutting its result to WIDTH or more
3018 ;;; bits. For most functions (e.g. for +) we cut all arguments; for
3019 ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary
3020 ;;; arguments (maybe to a different width) and returning the name of a
3021 ;;; modular version, if it exists, or NIL. If we have changed
3022 ;;; anything, we need to flush old derived types, because they have
3023 ;;; nothing in common with the new code.
3024 (defun cut-to-width (lvar kind width signedp)
3025 (declare (type lvar lvar) (type (integer 0) width))
3026 (let ((type (specifier-type (if (zerop width)
3029 ((nil) 'unsigned-byte)
3032 (labels ((reoptimize-node (node name)
3033 (setf (node-derived-type node)
3035 (info :function :type name)))
3036 (setf (lvar-%derived-type (node-lvar node)) nil)
3037 (setf (node-reoptimize node) t)
3038 (setf (block-reoptimize (node-block node)) t)
3039 (reoptimize-component (node-component node) :maybe))
3040 (cut-node (node &aux did-something)
3041 (when (and (not (block-delete-p (node-block node)))
3042 (combination-p node)
3043 (eq (basic-combination-kind node) :known))
3044 (let* ((fun-ref (lvar-use (combination-fun node)))
3045 (fun-name (leaf-source-name (ref-leaf fun-ref)))
3046 (modular-fun (find-modular-version fun-name kind signedp width)))
3047 (when (and modular-fun
3048 (not (and (eq fun-name 'logand)
3050 (single-value-type (node-derived-type node))
3052 (binding* ((name (etypecase modular-fun
3053 ((eql :good) fun-name)
3055 (modular-fun-info-name modular-fun))
3057 (funcall modular-fun node width)))
3059 (unless (eql modular-fun :good)
3060 (setq did-something t)
3063 (find-free-fun name "in a strange place"))
3064 (setf (combination-kind node) :full))
3065 (unless (functionp modular-fun)
3066 (dolist (arg (basic-combination-args node))
3067 (when (cut-lvar arg)
3068 (setq did-something t))))
3070 (reoptimize-node node name))
3072 (cut-lvar (lvar &aux did-something)
3073 (do-uses (node lvar)
3074 (when (cut-node node)
3075 (setq did-something t)))
3079 (defun best-modular-version (width signedp)
3080 ;; 1. exact width-matched :untagged
3081 ;; 2. >/>= width-matched :tagged
3082 ;; 3. >/>= width-matched :untagged
3083 (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class*))
3084 (uswidths (modular-class-widths *untagged-signed-modular-class*))
3085 (uwidths (merge 'list uuwidths uswidths #'< :key #'car))
3086 (twidths (modular-class-widths *tagged-modular-class*)))
3087 (let ((exact (find (cons width signedp) uwidths :test #'equal)))
3089 (return-from best-modular-version (values width :untagged signedp))))
3090 (flet ((inexact-match (w)
3092 ((eq signedp (cdr w)) (<= width (car w)))
3093 ((eq signedp nil) (< width (car w))))))
3094 (let ((tgt (find-if #'inexact-match twidths)))
3096 (return-from best-modular-version
3097 (values (car tgt) :tagged (cdr tgt)))))
3098 (let ((ugt (find-if #'inexact-match uwidths)))
3100 (return-from best-modular-version
3101 (values (car ugt) :untagged (cdr ugt))))))))
3103 (defoptimizer (logand optimizer) ((x y) node)
3104 (let ((result-type (single-value-type (node-derived-type node))))
3105 (when (numeric-type-p result-type)
3106 (let ((low (numeric-type-low result-type))
3107 (high (numeric-type-high result-type)))
3108 (when (and (numberp low)
3111 (let ((width (integer-length high)))
3112 (multiple-value-bind (w kind signedp)
3113 (best-modular-version width nil)
3115 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP).
3116 (cut-to-width x kind width signedp)
3117 (cut-to-width y kind width signedp)
3118 nil ; After fixing above, replace with T.
3121 (defoptimizer (mask-signed-field optimizer) ((width x) node)
3122 (let ((result-type (single-value-type (node-derived-type node))))
3123 (when (numeric-type-p result-type)
3124 (let ((low (numeric-type-low result-type))
3125 (high (numeric-type-high result-type)))
3126 (when (and (numberp low) (numberp high))
3127 (let ((width (max (integer-length high) (integer-length low))))
3128 (multiple-value-bind (w kind)
3129 (best-modular-version width t)
3131 ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH T).
3132 (cut-to-width x kind width t)
3133 nil ; After fixing above, replace with T.
3136 ;;; miscellanous numeric transforms
3138 ;;; If a constant appears as the first arg, swap the args.
3139 (deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
3140 (if (and (constant-lvar-p x)
3141 (not (constant-lvar-p y)))
3142 `(,(lvar-fun-name (basic-combination-fun node))
3145 (give-up-ir1-transform)))
3147 (dolist (x '(= char= + * logior logand logxor))
3148 (%deftransform x '(function * *) #'commutative-arg-swap
3149 "place constant arg last"))
3151 ;;; Handle the case of a constant BOOLE-CODE.
3152 (deftransform boole ((op x y) * *)
3153 "convert to inline logical operations"
3154 (unless (constant-lvar-p op)
3155 (give-up-ir1-transform "BOOLE code is not a constant."))
3156 (let ((control (lvar-value op)))
3158 (#.sb!xc:boole-clr 0)
3159 (#.sb!xc:boole-set -1)
3160 (#.sb!xc:boole-1 'x)
3161 (#.sb!xc:boole-2 'y)
3162 (#.sb!xc:boole-c1 '(lognot x))
3163 (#.sb!xc:boole-c2 '(lognot y))
3164 (#.sb!xc:boole-and '(logand x y))
3165 (#.sb!xc:boole-ior '(logior x y))
3166 (#.sb!xc:boole-xor '(logxor x y))
3167 (#.sb!xc:boole-eqv '(logeqv x y))
3168 (#.sb!xc:boole-nand '(lognand x y))
3169 (#.sb!xc:boole-nor '(lognor x y))
3170 (#.sb!xc:boole-andc1 '(logandc1 x y))
3171 (#.sb!xc:boole-andc2 '(logandc2 x y))
3172 (#.sb!xc:boole-orc1 '(logorc1 x y))
3173 (#.sb!xc:boole-orc2 '(logorc2 x y))
3175 (abort-ir1-transform "~S is an illegal control arg to BOOLE."
3178 ;;;; converting special case multiply/divide to shifts
3180 ;;; If arg is a constant power of two, turn * into a shift.
3181 (deftransform * ((x y) (integer integer) *)
3182 "convert x*2^k to shift"
3183 (unless (constant-lvar-p y)
3184 (give-up-ir1-transform))
3185 (let* ((y (lvar-value y))
3187 (len (1- (integer-length y-abs))))
3188 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3189 (give-up-ir1-transform))
3194 ;;; These must come before the ones below, so that they are tried
3195 ;;; first. Since %FLOOR and %CEILING are inlined, this allows
3196 ;;; the general case to be handled by TRUNCATE transforms.
3197 (deftransform floor ((x y))
3200 (deftransform ceiling ((x y))
3203 ;;; If arg is a constant power of two, turn FLOOR into a shift and
3204 ;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
3206 (flet ((frob (y ceil-p)
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))
3216 (delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
3217 `(let ((x (+ x ,delta)))
3219 `(values (ash (- x) ,shift)
3220 (- (- (logand (- x) ,mask)) ,delta))
3221 `(values (ash x ,shift)
3222 (- (logand x ,mask) ,delta))))))))
3223 (deftransform floor ((x y) (integer integer) *)
3224 "convert division by 2^k to shift"
3226 (deftransform ceiling ((x y) (integer integer) *)
3227 "convert division by 2^k to shift"
3230 ;;; Do the same for MOD.
3231 (deftransform mod ((x y) (integer integer) *)
3232 "convert remainder mod 2^k to LOGAND"
3233 (unless (constant-lvar-p y)
3234 (give-up-ir1-transform))
3235 (let* ((y (lvar-value y))
3237 (len (1- (integer-length y-abs))))
3238 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3239 (give-up-ir1-transform))
3240 (let ((mask (1- y-abs)))
3242 `(- (logand (- x) ,mask))
3243 `(logand x ,mask)))))
3245 ;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
3246 (deftransform truncate ((x y) (integer integer))
3247 "convert division by 2^k to shift"
3248 (unless (constant-lvar-p y)
3249 (give-up-ir1-transform))
3250 (let* ((y (lvar-value y))
3252 (len (1- (integer-length y-abs))))
3253 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3254 (give-up-ir1-transform))
3255 (let* ((shift (- len))
3258 (values ,(if (minusp y)
3260 `(- (ash (- x) ,shift)))
3261 (- (logand (- x) ,mask)))
3262 (values ,(if (minusp y)
3263 `(ash (- ,mask x) ,shift)
3265 (logand x ,mask))))))
3267 ;;; And the same for REM.
3268 (deftransform rem ((x y) (integer integer) *)
3269 "convert remainder mod 2^k to LOGAND"
3270 (unless (constant-lvar-p y)
3271 (give-up-ir1-transform))
3272 (let* ((y (lvar-value y))
3274 (len (1- (integer-length y-abs))))
3275 (unless (and (> y-abs 0) (= y-abs (ash 1 len)))
3276 (give-up-ir1-transform))
3277 (let ((mask (1- y-abs)))
3279 (- (logand (- x) ,mask))
3280 (logand x ,mask)))))
3282 ;;; Return an expression to calculate the integer quotient of X and
3283 ;;; constant Y, using multiplication, shift and add/sub instead of
3284 ;;; division. Both arguments must be unsigned, fit in a machine word and
3285 ;;; Y must neither be zero nor a power of two. The quotient is rounded
3287 ;;; The algorithm is taken from the paper "Division by Invariant
3288 ;;; Integers using Multiplication", 1994 by Torbj\"{o}rn Granlund and
3289 ;;; Peter L. Montgomery, Figures 4.2 and 6.2, modified to exclude the
3290 ;;; case of division by powers of two.
3291 ;;; The algorithm includes an adaptive precision argument. Use it, since
3292 ;;; we often have sub-word value ranges. Careful, in this case, we need
3293 ;;; p s.t 2^p > n, not the ceiling of the binary log.
3294 ;;; Also, for some reason, the paper prefers shifting to masking. Mask
3295 ;;; instead. Masking is equivalent to shifting right, then left again;
3296 ;;; all the intermediate values are still words, so we just have to shift
3297 ;;; right a bit more to compensate, at the end.
3299 ;;; The following two examples show an average case and the worst case
3300 ;;; with respect to the complexity of the generated expression, under
3301 ;;; a word size of 64 bits:
3303 ;;; (UNSIGNED-DIV-TRANSFORMER 10 MOST-POSITIVE-WORD) ->
3304 ;;; (ASH (%MULTIPLY (LOGANDC2 X 0) 14757395258967641293) -3)
3306 ;;; (UNSIGNED-DIV-TRANSFORMER 7 MOST-POSITIVE-WORD) ->
3308 ;;; (T1 (%MULTIPLY NUM 2635249153387078803)))
3309 ;;; (ASH (LDB (BYTE 64 0)
3310 ;;; (+ T1 (ASH (LDB (BYTE 64 0)
3315 (defun gen-unsigned-div-by-constant-expr (y max-x)
3316 (declare (type (integer 3 #.most-positive-word) y)
3318 (aver (not (zerop (logand y (1- y)))))
3320 ;; the floor of the binary logarithm of (positive) X
3321 (integer-length (1- x)))
3322 (choose-multiplier (y precision)
3324 (shift l (1- shift))
3325 (expt-2-n+l (expt 2 (+ sb!vm:n-word-bits l)))
3326 (m-low (truncate expt-2-n+l y) (ash m-low -1))
3327 (m-high (truncate (+ expt-2-n+l
3328 (ash expt-2-n+l (- precision)))
3331 ((not (and (< (ash m-low -1) (ash m-high -1))
3333 (values m-high shift)))))
3334 (let ((n (expt 2 sb!vm:n-word-bits))
3335 (precision (integer-length max-x))
3337 (multiple-value-bind (m shift2)
3338 (choose-multiplier y precision)
3339 (when (and (>= m n) (evenp y))
3340 (setq shift1 (ld (logand y (- y))))
3341 (multiple-value-setq (m shift2)
3342 (choose-multiplier (/ y (ash 1 shift1))
3343 (- precision shift1))))
3346 `(truly-the word ,x)))
3348 (t1 (%multiply-high num ,(- m n))))
3349 (ash ,(word `(+ t1 (ash ,(word `(- num t1))
3352 ((and (zerop shift1) (zerop shift2))
3353 (let ((max (truncate max-x y)))
3354 ;; Explicit TRULY-THE needed to get the FIXNUM=>FIXNUM
3356 `(truly-the (integer 0 ,max)
3357 (%multiply-high x ,m))))
3359 `(ash (%multiply-high (logandc2 x ,(1- (ash 1 shift1))) ,m)
3360 ,(- (+ shift1 shift2)))))))))
3362 ;;; If the divisor is constant and both args are positive and fit in a
3363 ;;; machine word, replace the division by a multiplication and possibly
3364 ;;; some shifts and an addition. Calculate the remainder by a second
3365 ;;; multiplication and a subtraction. Dead code elimination will
3366 ;;; suppress the latter part if only the quotient is needed. If the type
3367 ;;; of the dividend allows to derive that the quotient will always have
3368 ;;; the same value, emit much simpler code to handle that. (This case
3369 ;;; may be rare but it's easy to detect and the compiler doesn't find
3370 ;;; this optimization on its own.)
3371 (deftransform truncate ((x y) (word (constant-arg word))
3373 :policy (and (> speed compilation-speed)
3375 "convert integer division to multiplication"
3376 (let* ((y (lvar-value y))
3377 (x-type (lvar-type x))
3378 (max-x (or (and (numeric-type-p x-type)
3379 (numeric-type-high x-type))
3380 most-positive-word)))
3381 ;; Division by zero, one or powers of two is handled elsewhere.
3382 (when (zerop (logand y (1- y)))
3383 (give-up-ir1-transform))
3384 `(let* ((quot ,(gen-unsigned-div-by-constant-expr y max-x))
3385 (rem (ldb (byte #.sb!vm:n-word-bits 0)
3386 (- x (* quot ,y)))))
3387 (values quot rem))))
3389 ;;;; arithmetic and logical identity operation elimination
3391 ;;; Flush calls to various arith functions that convert to the
3392 ;;; identity function or a constant.
3393 (macrolet ((def (name identity result)
3394 `(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
3395 "fold identity operations"
3402 (def logxor -1 (lognot x))
3405 (deftransform logand ((x y) (* (constant-arg t)) *)
3406 "fold identity operation"
3407 (let ((y (lvar-value y)))
3408 (unless (and (plusp y)
3409 (= y (1- (ash 1 (integer-length y)))))
3410 (give-up-ir1-transform))
3411 (unless (csubtypep (lvar-type x)
3412 (specifier-type `(integer 0 ,y)))
3413 (give-up-ir1-transform))
3416 (deftransform mask-signed-field ((size x) ((constant-arg t) *) *)
3417 "fold identity operation"
3418 (let ((size (lvar-value size)))
3419 (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size)))
3420 (give-up-ir1-transform))
3423 ;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
3424 ;;; (* 0 -4.0) is -0.0.
3425 (deftransform - ((x y) ((constant-arg (member 0)) rational) *)
3426 "convert (- 0 x) to negate"
3428 (deftransform * ((x y) (rational (constant-arg (member 0))) *)
3429 "convert (* x 0) to 0"
3432 ;;; Return T if in an arithmetic op including lvars X and Y, the
3433 ;;; result type is not affected by the type of X. That is, Y is at
3434 ;;; least as contagious as X.
3436 (defun not-more-contagious (x y)
3437 (declare (type continuation x y))
3438 (let ((x (lvar-type x))
3440 (values (type= (numeric-contagion x y)
3441 (numeric-contagion y y)))))
3442 ;;; Patched version by Raymond Toy. dtc: Should be safer although it
3443 ;;; XXX needs more work as valid transforms are missed; some cases are
3444 ;;; specific to particular transform functions so the use of this
3445 ;;; function may need a re-think.
3446 (defun not-more-contagious (x y)
3447 (declare (type lvar x y))
3448 (flet ((simple-numeric-type (num)
3449 (and (numeric-type-p num)
3450 ;; Return non-NIL if NUM is integer, rational, or a float
3451 ;; of some type (but not FLOAT)
3452 (case (numeric-type-class num)
3456 (numeric-type-format num))
3459 (let ((x (lvar-type x))
3461 (if (and (simple-numeric-type x)
3462 (simple-numeric-type y))
3463 (values (type= (numeric-contagion x y)
3464 (numeric-contagion y y)))))))
3466 (def!type exact-number ()
3467 '(or rational (complex rational)))
3471 ;;; Only safely applicable for exact numbers. For floating-point
3472 ;;; x, one would have to first show that neither x or y are signed
3473 ;;; 0s, and that x isn't an SNaN.
3474 (deftransform + ((x y) (exact-number (constant-arg (eql 0))) *)
3479 (deftransform - ((x y) (exact-number (constant-arg (eql 0))) *)
3483 ;;; Fold (OP x +/-1)
3485 ;;; %NEGATE might not always signal correctly.
3487 ((def (name result minus-result)
3488 `(deftransform ,name ((x y)
3489 (exact-number (constant-arg (member 1 -1))))
3490 "fold identity operations"
3491 (if (minusp (lvar-value y)) ',minus-result ',result))))
3492 (def * x (%negate x))
3493 (def / x (%negate x))
3494 (def expt x (/ 1 x)))
3496 ;;; Fold (expt x n) into multiplications for small integral values of
3497 ;;; N; convert (expt x 1/2) to sqrt.
3498 (deftransform expt ((x y) (t (constant-arg real)) *)
3499 "recode as multiplication or sqrt"
3500 (let ((val (lvar-value y)))
3501 ;; If Y would cause the result to be promoted to the same type as
3502 ;; Y, we give up. If not, then the result will be the same type
3503 ;; as X, so we can replace the exponentiation with simple
3504 ;; multiplication and division for small integral powers.
3505 (unless (not-more-contagious y x)
3506 (give-up-ir1-transform))
3508 (let ((x-type (lvar-type x)))
3509 (cond ((csubtypep x-type (specifier-type '(or rational
3510 (complex rational))))
3512 ((csubtypep x-type (specifier-type 'real))
3516 ((csubtypep x-type (specifier-type 'complex))
3517 ;; both parts are float
3519 (t (give-up-ir1-transform)))))
3520 ((= val 2) '(* x x))
3521 ((= val -2) '(/ (* x x)))
3522 ((= val 3) '(* x x x))
3523 ((= val -3) '(/ (* x x x)))
3524 ((= val 1/2) '(sqrt x))
3525 ((= val -1/2) '(/ (sqrt x)))
3526 (t (give-up-ir1-transform)))))
3528 (deftransform expt ((x y) ((constant-arg (member -1 -1.0 -1.0d0)) integer) *)
3529 "recode as an ODDP check"
3530 (let ((val (lvar-value x)))
3532 '(- 1 (* 2 (logand 1 y)))
3537 ;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
3538 ;;; transformations?
3539 ;;; Perhaps we should have to prove that the denominator is nonzero before
3540 ;;; doing them? -- WHN 19990917
3541 (macrolet ((def (name)
3542 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3549 (macrolet ((def (name)
3550 `(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
3559 ;;;; character operations
3561 (deftransform char-equal ((a b) (base-char base-char))
3563 '(let* ((ac (char-code a))
3565 (sum (logxor ac bc)))
3567 (when (eql sum #x20)
3568 (let ((sum (+ ac bc)))
3569 (or (and (> sum 161) (< sum 213))
3570 (and (> sum 415) (< sum 461))
3571 (and (> sum 463) (< sum 477))))))))
3573 (deftransform char-upcase ((x) (base-char))
3575 '(let ((n-code (char-code x)))
3576 (if (or (and (> n-code #o140) ; Octal 141 is #\a.
3577 (< n-code #o173)) ; Octal 172 is #\z.
3578 (and (> n-code #o337)
3580 (and (> n-code #o367)
3582 (code-char (logxor #x20 n-code))
3585 (deftransform char-downcase ((x) (base-char))
3587 '(let ((n-code (char-code x)))
3588 (if (or (and (> n-code 64) ; 65 is #\A.
3589 (< n-code 91)) ; 90 is #\Z.
3594 (code-char (logxor #x20 n-code))
3597 ;;;; equality predicate transforms
3599 ;;; Return true if X and Y are lvars whose only use is a
3600 ;;; reference to the same leaf, and the value of the leaf cannot
3602 (defun same-leaf-ref-p (x y)
3603 (declare (type lvar x y))
3604 (let ((x-use (principal-lvar-use x))
3605 (y-use (principal-lvar-use y)))
3608 (eq (ref-leaf x-use) (ref-leaf y-use))
3609 (constant-reference-p x-use))))
3611 ;;; If X and Y are the same leaf, then the result is true. Otherwise,
3612 ;;; if there is no intersection between the types of the arguments,
3613 ;;; then the result is definitely false.
3614 (deftransform simple-equality-transform ((x y) * *
3617 ((same-leaf-ref-p x y) t)
3618 ((not (types-equal-or-intersect (lvar-type x) (lvar-type y)))
3620 (t (give-up-ir1-transform))))
3623 `(%deftransform ',x '(function * *) #'simple-equality-transform)))
3627 ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, except that we also
3628 ;;; try to convert to a type-specific predicate or EQ:
3629 ;;; -- If both args are characters, convert to CHAR=. This is better than
3630 ;;; just converting to EQ, since CHAR= may have special compilation
3631 ;;; strategies for non-standard representations, etc.
3632 ;;; -- If either arg is definitely a fixnum, we check to see if X is
3633 ;;; constant and if so, put X second. Doing this results in better
3634 ;;; code from the backend, since the backend assumes that any constant
3635 ;;; argument comes second.
3636 ;;; -- If either arg is definitely not a number or a fixnum, then we
3637 ;;; can compare with EQ.
3638 ;;; -- Otherwise, we try to put the arg we know more about second. If X
3639 ;;; is constant then we put it second. If X is a subtype of Y, we put
3640 ;;; it second. These rules make it easier for the back end to match
3641 ;;; these interesting cases.
3642 (deftransform eql ((x y) * * :node node)
3643 "convert to simpler equality predicate"
3644 (let ((x-type (lvar-type x))
3645 (y-type (lvar-type y))
3646 (char-type (specifier-type 'character)))
3647 (flet ((fixnum-type-p (type)
3648 (csubtypep type (specifier-type 'fixnum))))
3650 ((same-leaf-ref-p x y) t)
3651 ((not (types-equal-or-intersect x-type y-type))
3653 ((and (csubtypep x-type char-type)
3654 (csubtypep y-type char-type))
3656 ((or (fixnum-type-p x-type) (fixnum-type-p y-type))
3657 (commutative-arg-swap node))
3658 ((or (eq-comparable-type-p x-type) (eq-comparable-type-p y-type))
3660 ((and (not (constant-lvar-p y))
3661 (or (constant-lvar-p x)
3662 (and (csubtypep x-type y-type)
3663 (not (csubtypep y-type x-type)))))
3666 (give-up-ir1-transform))))))
3668 ;;; similarly to the EQL transform above, we attempt to constant-fold
3669 ;;; or convert to a simpler predicate: mostly we have to be careful
3670 ;;; with strings and bit-vectors.
3671 (deftransform equal ((x y) * *)
3672 "convert to simpler equality predicate"
3673 (let ((x-type (lvar-type x))
3674 (y-type (lvar-type y))
3675 (string-type (specifier-type 'string))
3676 (bit-vector-type (specifier-type 'bit-vector)))
3678 ((same-leaf-ref-p x y) t)
3679 ((and (csubtypep x-type string-type)
3680 (csubtypep y-type string-type))
3682 ((and (csubtypep x-type bit-vector-type)
3683 (csubtypep y-type bit-vector-type))
3684 '(bit-vector-= x y))
3685 ;; if at least one is not a string, and at least one is not a
3686 ;; bit-vector, then we can reason from types.
3687 ((and (not (and (types-equal-or-intersect x-type string-type)
3688 (types-equal-or-intersect y-type string-type)))
3689 (not (and (types-equal-or-intersect x-type bit-vector-type)
3690 (types-equal-or-intersect y-type bit-vector-type)))
3691 (not (types-equal-or-intersect x-type y-type)))
3693 (t (give-up-ir1-transform)))))
3695 ;;; Convert to EQL if both args are rational and complexp is specified
3696 ;;; and the same for both.
3697 (deftransform = ((x y) (number number) *)
3699 (let ((x-type (lvar-type x))
3700 (y-type (lvar-type y)))
3701 (cond ((or (and (csubtypep x-type (specifier-type 'float))
3702 (csubtypep y-type (specifier-type 'float)))
3703 (and (csubtypep x-type (specifier-type '(complex float)))
3704 (csubtypep y-type (specifier-type '(complex float))))
3705 #!+complex-float-vops
3706 (and (csubtypep x-type (specifier-type '(or single-float (complex single-float))))
3707 (csubtypep y-type (specifier-type '(or single-float (complex single-float)))))
3708 #!+complex-float-vops
3709 (and (csubtypep x-type (specifier-type '(or double-float (complex double-float))))
3710 (csubtypep y-type (specifier-type '(or double-float (complex double-float))))))
3711 ;; They are both floats. Leave as = so that -0.0 is
3712 ;; handled correctly.
3713 (give-up-ir1-transform))
3714 ((or (and (csubtypep x-type (specifier-type 'rational))
3715 (csubtypep y-type (specifier-type 'rational)))
3716 (and (csubtypep x-type
3717 (specifier-type '(complex rational)))
3719 (specifier-type '(complex rational)))))
3720 ;; They are both rationals and complexp is the same.
3724 (give-up-ir1-transform
3725 "The operands might not be the same type.")))))
3727 (defun maybe-float-lvar-p (lvar)
3728 (neq *empty-type* (type-intersection (specifier-type 'float)
3731 (flet ((maybe-invert (node op inverted x y)
3732 ;; Don't invert if either argument can be a float (NaNs)
3734 ((or (maybe-float-lvar-p x) (maybe-float-lvar-p y))
3735 (delay-ir1-transform node :constraint)
3736 `(or (,op x y) (= x y)))
3738 `(if (,inverted x y) nil t)))))
3739 (deftransform >= ((x y) (number number) * :node node)
3740 "invert or open code"
3741 (maybe-invert node '> '< x y))
3742 (deftransform <= ((x y) (number number) * :node node)
3743 "invert or open code"
3744 (maybe-invert node '< '> x y)))
3746 ;;; See whether we can statically determine (< X Y) using type
3747 ;;; information. If X's high bound is < Y's low, then X < Y.
3748 ;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
3749 ;;; NIL). If not, at least make sure any constant arg is second.
3750 (macrolet ((def (name inverse reflexive-p surely-true surely-false)
3751 `(deftransform ,name ((x y))
3752 "optimize using intervals"
3753 (if (and (same-leaf-ref-p x y)
3754 ;; For non-reflexive functions we don't need
3755 ;; to worry about NaNs: (non-ref-op NaN NaN) => false,
3756 ;; but with reflexive ones we don't know...
3758 '((and (not (maybe-float-lvar-p x))
3759 (not (maybe-float-lvar-p y))))))
3761 (let ((ix (or (type-approximate-interval (lvar-type x))
3762 (give-up-ir1-transform)))
3763 (iy (or (type-approximate-interval (lvar-type y))
3764 (give-up-ir1-transform))))
3769 ((and (constant-lvar-p x)
3770 (not (constant-lvar-p y)))
3773 (give-up-ir1-transform))))))))
3774 (def = = t (interval-= ix iy) (interval-/= ix iy))
3775 (def /= /= nil (interval-/= ix iy) (interval-= ix iy))
3776 (def < > nil (interval-< ix iy) (interval->= ix iy))
3777 (def > < nil (interval-< iy ix) (interval->= iy ix))
3778 (def <= >= t (interval->= iy ix) (interval-< iy ix))
3779 (def >= <= t (interval->= ix iy) (interval-< ix iy)))
3781 (defun ir1-transform-char< (x y first second inverse)
3783 ((same-leaf-ref-p x y) nil)
3784 ;; If we had interval representation of character types, as we
3785 ;; might eventually have to to support 2^21 characters, then here
3786 ;; we could do some compile-time computation as in transforms for
3787 ;; < above. -- CSR, 2003-07-01
3788 ((and (constant-lvar-p first)
3789 (not (constant-lvar-p second)))
3791 (t (give-up-ir1-transform))))
3793 (deftransform char< ((x y) (character character) *)
3794 (ir1-transform-char< x y x y 'char>))
3796 (deftransform char> ((x y) (character character) *)
3797 (ir1-transform-char< y x x y 'char<))
3799 ;;;; converting N-arg comparisons
3801 ;;;; We convert calls to N-arg comparison functions such as < into
3802 ;;;; two-arg calls. This transformation is enabled for all such
3803 ;;;; comparisons in this file. If any of these predicates are not
3804 ;;;; open-coded, then the transformation should be removed at some
3805 ;;;; point to avoid pessimization.
3807 ;;; This function is used for source transformation of N-arg
3808 ;;; comparison functions other than inequality. We deal both with
3809 ;;; converting to two-arg calls and inverting the sense of the test,
3810 ;;; if necessary. If the call has two args, then we pass or return a
3811 ;;; negated test as appropriate. If it is a degenerate one-arg call,
3812 ;;; then we transform to code that returns true. Otherwise, we bind
3813 ;;; all the arguments and expand into a bunch of IFs.
3814 (defun multi-compare (predicate args not-p type &optional force-two-arg-p)
3815 (let ((nargs (length args)))
3816 (cond ((< nargs 1) (values nil t))
3817 ((= nargs 1) `(progn (the ,type ,@args) t))
3820 `(if (,predicate ,(first args) ,(second args)) nil t)
3822 `(,predicate ,(first args) ,(second args))
3825 (do* ((i (1- nargs) (1- i))
3827 (current (gensym) (gensym))
3828 (vars (list current) (cons current vars))
3830 `(if (,predicate ,current ,last)
3832 `(if (,predicate ,current ,last)
3835 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3838 (define-source-transform = (&rest args) (multi-compare '= args nil 'number))
3839 (define-source-transform < (&rest args) (multi-compare '< args nil 'real))
3840 (define-source-transform > (&rest args) (multi-compare '> args nil 'real))
3841 ;;; We cannot do the inversion for >= and <= here, since both
3842 ;;; (< NaN X) and (> NaN X)
3843 ;;; are false, and we don't have type-inforation available yet. The
3844 ;;; deftransforms for two-argument versions of >= and <= takes care of
3845 ;;; the inversion to > and < when possible.
3846 (define-source-transform <= (&rest args) (multi-compare '<= args nil 'real))
3847 (define-source-transform >= (&rest args) (multi-compare '>= args nil 'real))
3849 (define-source-transform char= (&rest args) (multi-compare 'char= args nil
3851 (define-source-transform char< (&rest args) (multi-compare 'char< args nil
3853 (define-source-transform char> (&rest args) (multi-compare 'char> args nil
3855 (define-source-transform char<= (&rest args) (multi-compare 'char> args t
3857 (define-source-transform char>= (&rest args) (multi-compare 'char< args t
3860 (define-source-transform char-equal (&rest args)
3861 (multi-compare 'sb!impl::two-arg-char-equal args nil 'character t))
3862 (define-source-transform char-lessp (&rest args)
3863 (multi-compare 'sb!impl::two-arg-char-lessp args nil 'character t))
3864 (define-source-transform char-greaterp (&rest args)
3865 (multi-compare 'sb!impl::two-arg-char-greaterp args nil 'character t))
3866 (define-source-transform char-not-greaterp (&rest args)
3867 (multi-compare 'sb!impl::two-arg-char-greaterp args t 'character t))
3868 (define-source-transform char-not-lessp (&rest args)
3869 (multi-compare 'sb!impl::two-arg-char-lessp args t 'character t))
3871 ;;; This function does source transformation of N-arg inequality
3872 ;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
3873 ;;; arg cases. If there are more than two args, then we expand into
3874 ;;; the appropriate n^2 comparisons only when speed is important.
3875 (declaim (ftype (function (symbol list t) *) multi-not-equal))
3876 (defun multi-not-equal (predicate args type)
3877 (let ((nargs (length args)))
3878 (cond ((< nargs 1) (values nil t))
3879 ((= nargs 1) `(progn (the ,type ,@args) t))
3881 `(if (,predicate ,(first args) ,(second args)) nil t))
3882 ((not (policy *lexenv*
3883 (and (>= speed space)
3884 (>= speed compilation-speed))))
3887 (let ((vars (make-gensym-list nargs)))
3888 (do ((var vars next)
3889 (next (cdr vars) (cdr next))
3892 `((lambda ,vars (declare (type ,type ,@vars)) ,result)
3894 (let ((v1 (first var)))
3896 (setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
3898 (define-source-transform /= (&rest args)
3899 (multi-not-equal '= args 'number))
3900 (define-source-transform char/= (&rest args)
3901 (multi-not-equal 'char= args 'character))
3902 (define-source-transform char-not-equal (&rest args)
3903 (multi-not-equal 'char-equal args 'character))
3905 ;;; Expand MAX and MIN into the obvious comparisons.
3906 (define-source-transform max (arg0 &rest rest)
3907 (once-only ((arg0 arg0))
3909 `(values (the real ,arg0))
3910 `(let ((maxrest (max ,@rest)))
3911 (if (>= ,arg0 maxrest) ,arg0 maxrest)))))
3912 (define-source-transform min (arg0 &rest rest)
3913 (once-only ((arg0 arg0))
3915 `(values (the real ,arg0))
3916 `(let ((minrest (min ,@rest)))
3917 (if (<= ,arg0 minrest) ,arg0 minrest)))))
3919 ;;;; converting N-arg arithmetic functions
3921 ;;;; N-arg arithmetic and logic functions are associated into two-arg
3922 ;;;; versions, and degenerate cases are flushed.
3924 ;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
3925 (declaim (ftype (sfunction (symbol t list t) list) associate-args))
3926 (defun associate-args (fun first-arg more-args identity)
3927 (let ((next (rest more-args))
3928 (arg (first more-args)))
3930 `(,fun ,first-arg ,(if arg arg identity))
3931 (associate-args fun `(,fun ,first-arg ,arg) next identity))))
3933 ;;; Reduce constants in ARGS list.
3934 (declaim (ftype (sfunction (symbol list t symbol) list) reduce-constants))
3935 (defun reduce-constants (fun args identity one-arg-result-type)
3936 (let ((one-arg-constant-p (ecase one-arg-result-type
3938 (integer #'integerp)))
3939 (reduced-value identity)
3941 (collect ((not-constants))
3943 (if (funcall one-arg-constant-p arg)
3944 (setf reduced-value (funcall fun reduced-value arg)
3946 (not-constants arg)))
3947 ;; It is tempting to drop constants reduced to identity here,
3948 ;; but if X is SNaN in (* X 1), we cannot drop the 1.
3951 `(,reduced-value ,@(not-constants))
3953 `(,reduced-value)))))
3955 ;;; Do source transformations for transitive functions such as +.
3956 ;;; One-arg cases are replaced with the arg and zero arg cases with
3957 ;;; the identity. ONE-ARG-RESULT-TYPE is the type to ensure (with THE)
3958 ;;; that the argument in one-argument calls is.
3959 (declaim (ftype (function (symbol list t &optional symbol list)
3960 (values t &optional (member nil t)))
3961 source-transform-transitive))
3962 (defun source-transform-transitive (fun args identity
3963 &optional (one-arg-result-type 'number)
3964 (one-arg-prefixes '(values)))
3967 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
3969 (t (let ((reduced-args (reduce-constants fun args identity one-arg-result-type)))
3970 (associate-args fun (first reduced-args) (rest reduced-args) identity)))))
3972 (define-source-transform + (&rest args)
3973 (source-transform-transitive '+ args 0))
3974 (define-source-transform * (&rest args)
3975 (source-transform-transitive '* args 1))
3976 (define-source-transform logior (&rest args)
3977 (source-transform-transitive 'logior args 0 'integer))
3978 (define-source-transform logxor (&rest args)
3979 (source-transform-transitive 'logxor args 0 'integer))
3980 (define-source-transform logand (&rest args)
3981 (source-transform-transitive 'logand args -1 'integer))
3982 (define-source-transform logeqv (&rest args)
3983 (source-transform-transitive 'logeqv args -1 'integer))
3984 (define-source-transform gcd (&rest args)
3985 (source-transform-transitive 'gcd args 0 'integer '(abs)))
3986 (define-source-transform lcm (&rest args)
3987 (source-transform-transitive 'lcm args 1 'integer '(abs)))
3989 ;;; Do source transformations for intransitive n-arg functions such as
3990 ;;; /. With one arg, we form the inverse. With two args we pass.
3991 ;;; Otherwise we associate into two-arg calls.
3992 (declaim (ftype (function (symbol symbol list t list &optional symbol)
3993 (values list &optional (member nil t)))
3994 source-transform-intransitive))
3995 (defun source-transform-intransitive (fun fun* args identity one-arg-prefixes
3996 &optional (one-arg-result-type 'number))
3998 ((0 2) (values nil t))
3999 (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args))))
4000 (t (let ((reduced-args
4001 (reduce-constants fun* (rest args) identity one-arg-result-type)))
4002 (associate-args fun (first args) reduced-args identity)))))
4004 (define-source-transform - (&rest args)
4005 (source-transform-intransitive '- '+ args 0 '(%negate)))
4006 (define-source-transform / (&rest args)
4007 (source-transform-intransitive '/ '* args 1 '(/ 1)))
4009 ;;;; transforming APPLY
4011 ;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
4012 ;;; only needs to understand one kind of variable-argument call. It is
4013 ;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
4014 (define-source-transform apply (fun arg &rest more-args)
4015 (let ((args (cons arg more-args)))
4016 `(multiple-value-call ,fun
4017 ,@(mapcar (lambda (x) `(values ,x)) (butlast args))
4018 (values-list ,(car (last args))))))
4020 ;;; When &REST argument are at play, we also have extra context and count
4021 ;;; arguments -- convert to %VALUES-LIST-OR-CONTEXT when possible, so that the
4022 ;;; deftransform can decide what to do after everything has been converted.
4023 (define-source-transform values-list (list)
4025 (let* ((var (lexenv-find list vars))
4026 (info (when (lambda-var-p var)
4027 (lambda-var-arg-info var))))
4029 (eq :rest (arg-info-kind info))
4030 (consp (arg-info-default info)))
4031 (destructuring-bind (context count &optional used) (arg-info-default info)
4032 (declare (ignore used))
4033 `(%values-list-or-context ,list ,context ,count))
4037 (deftransform %values-list-or-context ((list context count) * * :node node)
4038 (let* ((use (lvar-use list))
4039 (var (when (ref-p use) (ref-leaf use)))
4040 (home (when (lambda-var-p var) (lambda-var-home var)))
4041 (info (when (lambda-var-p var) (lambda-var-arg-info var))))
4042 (flet ((ref-good-for-more-context-p (ref)
4043 (let ((dest (principal-lvar-end (node-lvar ref))))
4044 (and (combination-p dest)
4045 ;; Uses outside VALUES-LIST will require a &REST list anyways,
4046 ;; to it's no use saving effort here -- plus they might modify
4047 ;; the list destructively.
4048 (eq '%values-list-or-context (lvar-fun-name (combination-fun dest)))
4049 ;; If the home lambda is different and isn't DX, it might
4050 ;; escape -- in which case using the more context isn't safe.
4051 (let ((clambda (node-home-lambda dest)))
4052 (or (eq home clambda)
4053 (leaf-dynamic-extent clambda)))))))
4056 (consp (arg-info-default info))
4057 (not (lambda-var-specvar var))
4058 (not (lambda-var-sets var))
4059 (every #'ref-good-for-more-context-p (lambda-var-refs var))
4060 (policy node (= 3 rest-conversion)))))
4062 (destructuring-bind (context count &optional used) (arg-info-default info)
4063 (declare (ignore used))
4064 (setf (arg-info-default info) (list context count t)))
4065 `(%more-arg-values context 0 count))
4068 (setf (arg-info-default info) t))
4069 `(values-list list)))))))
4072 ;;;; transforming FORMAT
4074 ;;;; If the control string is a compile-time constant, then replace it
4075 ;;;; with a use of the FORMATTER macro so that the control string is
4076 ;;;; ``compiled.'' Furthermore, if the destination is either a stream
4077 ;;;; or T and the control string is a function (i.e. FORMATTER), then
4078 ;;;; convert the call to FORMAT to just a FUNCALL of that function.
4080 ;;; for compile-time argument count checking.
4082 ;;; FIXME II: In some cases, type information could be correlated; for
4083 ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type
4084 ;;; of a corresponding argument is known and does not intersect the
4085 ;;; list type, a warning could be signalled.
4086 (defun check-format-args (string args fun)
4087 (declare (type string string))
4088 (unless (typep string 'simple-string)
4089 (setq string (coerce string 'simple-string)))
4090 (multiple-value-bind (min max)
4091 (handler-case (sb!format:%compiler-walk-format-string string args)
4092 (sb!format:format-error (c)
4093 (compiler-warn "~A" c)))
4095 (let ((nargs (length args)))
4098 (warn 'format-too-few-args-warning
4100 "Too few arguments (~D) to ~S ~S: requires at least ~D."
4101 :format-arguments (list nargs fun string min)))
4103 (warn 'format-too-many-args-warning
4105 "Too many arguments (~D) to ~S ~S: uses at most ~D."
4106 :format-arguments (list nargs fun string max))))))))
4108 (defoptimizer (format optimizer) ((dest control &rest args))
4109 (when (constant-lvar-p control)
4110 (let ((x (lvar-value control)))
4112 (check-format-args x args 'format)))))
4114 ;;; We disable this transform in the cross-compiler to save memory in
4115 ;;; the target image; most of the uses of FORMAT in the compiler are for
4116 ;;; error messages, and those don't need to be particularly fast.
4118 (deftransform format ((dest control &rest args) (t simple-string &rest t) *
4119 :policy (>= speed space))
4120 (unless (constant-lvar-p control)
4121 (give-up-ir1-transform "The control string is not a constant."))
4122 (let ((arg-names (make-gensym-list (length args))))
4123 `(lambda (dest control ,@arg-names)
4124 (declare (ignore control))
4125 (format dest (formatter ,(lvar-value control)) ,@arg-names))))
4127 (deftransform format ((stream control &rest args) (stream function &rest t))
4128 (let ((arg-names (make-gensym-list (length args))))
4129 `(lambda (stream control ,@arg-names)
4130 (funcall control stream ,@arg-names)
4133 (deftransform format ((tee control &rest args) ((member t) function &rest t))
4134 (let ((arg-names (make-gensym-list (length args))))
4135 `(lambda (tee control ,@arg-names)
4136 (declare (ignore tee))
4137 (funcall control *standard-output* ,@arg-names)
4140 (deftransform pathname ((pathspec) (pathname) *)
4143 (deftransform pathname ((pathspec) (string) *)
4144 '(values (parse-namestring pathspec)))
4148 `(defoptimizer (,name optimizer) ((control &rest args))
4149 (when (constant-lvar-p control)
4150 (let ((x (lvar-value control)))
4152 (check-format-args x args ',name)))))))
4155 #+sb-xc-host ; Only we should be using these
4158 (def compiler-error)
4160 (def compiler-style-warn)
4161 (def compiler-notify)
4162 (def maybe-compiler-notify)
4165 (defoptimizer (cerror optimizer) ((report control &rest args))
4166 (when (and (constant-lvar-p control)
4167 (constant-lvar-p report))
4168 (let ((x (lvar-value control))
4169 (y (lvar-value report)))
4170 (when (and (stringp x) (stringp y))
4171 (multiple-value-bind (min1 max1)
4173 (sb!format:%compiler-walk-format-string x args)
4174 (sb!format:format-error (c)
4175 (compiler-warn "~A" c)))
4177 (multiple-value-bind (min2 max2)
4179 (sb!format:%compiler-walk-format-string y args)
4180 (sb!format:format-error (c)
4181 (compiler-warn "~A" c)))
4183 (let ((nargs (length args)))
4185 ((< nargs (min min1 min2))
4186 (warn 'format-too-few-args-warning
4188 "Too few arguments (~D) to ~S ~S ~S: ~
4189 requires at least ~D."
4191 (list nargs 'cerror y x (min min1 min2))))
4192 ((> nargs (max max1 max2))
4193 (warn 'format-too-many-args-warning
4195 "Too many arguments (~D) to ~S ~S ~S: ~
4198 (list nargs 'cerror y x (max max1 max2))))))))))))))
4200 (defoptimizer (coerce derive-type) ((value type) node)
4202 ((constant-lvar-p type)
4203 ;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
4204 ;; but dealing with the niggle that complex canonicalization gets
4205 ;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
4207 (let* ((specifier (lvar-value type))
4208 (result-typeoid (careful-specifier-type specifier)))
4210 ((null result-typeoid) nil)
4211 ((csubtypep result-typeoid (specifier-type 'number))
4212 ;; the difficult case: we have to cope with ANSI 12.1.5.3
4213 ;; Rule of Canonical Representation for Complex Rationals,
4214 ;; which is a truly nasty delivery to field.
4216 ((csubtypep result-typeoid (specifier-type 'real))
4217 ;; cleverness required here: it would be nice to deduce
4218 ;; that something of type (INTEGER 2 3) coerced to type
4219 ;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
4220 ;; FLOAT gets its own clause because it's implemented as
4221 ;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
4224 ((and (numeric-type-p result-typeoid)
4225 (eq (numeric-type-complexp result-typeoid) :real))
4226 ;; FIXME: is this clause (a) necessary or (b) useful?
4228 ((or (csubtypep result-typeoid
4229 (specifier-type '(complex single-float)))
4230 (csubtypep result-typeoid
4231 (specifier-type '(complex double-float)))
4233 (csubtypep result-typeoid
4234 (specifier-type '(complex long-float))))
4235 ;; float complex types are never canonicalized.
4238 ;; if it's not a REAL, or a COMPLEX FLOAToid, it's
4239 ;; probably just a COMPLEX or equivalent. So, in that
4240 ;; case, we will return a complex or an object of the
4241 ;; provided type if it's rational:
4242 (type-union result-typeoid
4243 (type-intersection (lvar-type value)
4244 (specifier-type 'rational))))))
4245 ((and (policy node (zerop safety))
4246 (csubtypep result-typeoid (specifier-type '(array * (*)))))
4247 ;; At zero safety the deftransform for COERCE can elide dimension
4248 ;; checks for the things like (COERCE X '(SIMPLE-VECTOR 5)) -- so we
4249 ;; need to simplify the type to drop the dimension information.
4250 (let ((vtype (simplify-vector-type result-typeoid)))
4252 (specifier-type vtype)
4257 ;; OK, the result-type argument isn't constant. However, there
4258 ;; are common uses where we can still do better than just
4259 ;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
4260 ;; where Y is of a known type. See messages on cmucl-imp
4261 ;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
4262 ;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
4263 ;; the basis that it's unlikely that other uses are both
4264 ;; time-critical and get to this branch of the COND (non-constant
4265 ;; second argument to COERCE). -- CSR, 2002-12-16
4266 (let ((value-type (lvar-type value))
4267 (type-type (lvar-type type)))
4269 ((good-cons-type-p (cons-type)
4270 ;; Make sure the cons-type we're looking at is something
4271 ;; we're prepared to handle which is basically something
4272 ;; that array-element-type can return.
4273 (or (and (member-type-p cons-type)
4274 (eql 1 (member-type-size cons-type))
4275 (null (first (member-type-members cons-type))))
4276 (let ((car-type (cons-type-car-type cons-type)))
4277 (and (member-type-p car-type)
4278 (eql 1 (member-type-members car-type))
4279 (let ((elt (first (member-type-members car-type))))
4283 (numberp (first elt)))))
4284 (good-cons-type-p (cons-type-cdr-type cons-type))))))
4285 (unconsify-type (good-cons-type)
4286 ;; Convert the "printed" respresentation of a cons
4287 ;; specifier into a type specifier. That is, the
4288 ;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
4289 ;; NULL)) is converted to (SIGNED-BYTE 16).
4290 (cond ((or (null good-cons-type)
4291 (eq good-cons-type 'null))
4293 ((and (eq (first good-cons-type) 'cons)
4294 (eq (first (second good-cons-type)) 'member))
4295 `(,(second (second good-cons-type))
4296 ,@(unconsify-type (caddr good-cons-type))))))
4297 (coerceable-p (part)
4298 ;; Can the value be coerced to the given type? Coerce is
4299 ;; complicated, so we don't handle every possible case
4300 ;; here---just the most common and easiest cases:
4302 ;; * Any REAL can be coerced to a FLOAT type.
4303 ;; * Any NUMBER can be coerced to a (COMPLEX
4304 ;; SINGLE/DOUBLE-FLOAT).
4306 ;; FIXME I: we should also be able to deal with characters
4309 ;; FIXME II: I'm not sure that anything is necessary
4310 ;; here, at least while COMPLEX is not a specialized
4311 ;; array element type in the system. Reasoning: if
4312 ;; something cannot be coerced to the requested type, an
4313 ;; error will be raised (and so any downstream compiled
4314 ;; code on the assumption of the returned type is
4315 ;; unreachable). If something can, then it will be of
4316 ;; the requested type, because (by assumption) COMPLEX
4317 ;; (and other difficult types like (COMPLEX INTEGER)
4318 ;; aren't specialized types.
4319 (let ((coerced-type (careful-specifier-type part)))
4321 (or (and (csubtypep coerced-type (specifier-type 'float))
4322 (csubtypep value-type (specifier-type 'real)))
4323 (and (csubtypep coerced-type
4324 (specifier-type `(or (complex single-float)
4325 (complex double-float))))
4326 (csubtypep value-type (specifier-type 'number)))))))
4327 (process-types (type)
4328 ;; FIXME: This needs some work because we should be able
4329 ;; to derive the resulting type better than just the
4330 ;; type arg of coerce. That is, if X is (INTEGER 10
4331 ;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
4332 ;; (DOUBLE-FLOAT 10d0 20d0) instead of just
4334 (cond ((member-type-p type)
4337 (mapc-member-type-members
4339 (if (coerceable-p member)
4340 (push member members)
4341 (return-from punt *universal-type*)))
4343 (specifier-type `(or ,@members)))))
4344 ((and (cons-type-p type)
4345 (good-cons-type-p type))
4346 (let ((c-type (unconsify-type (type-specifier type))))
4347 (if (coerceable-p c-type)
4348 (specifier-type c-type)
4351 *universal-type*))))
4352 (cond ((union-type-p type-type)
4353 (apply #'type-union (mapcar #'process-types
4354 (union-type-types type-type))))
4355 ((or (member-type-p type-type)
4356 (cons-type-p type-type))
4357 (process-types type-type))
4359 *universal-type*)))))))
4361 (defoptimizer (compile derive-type) ((nameoid function))
4362 (when (csubtypep (lvar-type nameoid)
4363 (specifier-type 'null))
4364 (values-specifier-type '(values function boolean boolean))))
4366 ;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
4367 ;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
4368 ;;; optimizer, above).
4369 (defoptimizer (array-element-type derive-type) ((array))
4370 (let ((array-type (lvar-type array)))
4371 (labels ((consify (list)
4374 `(cons (eql ,(car list)) ,(consify (rest list)))))
4375 (get-element-type (a)
4377 (type-specifier (array-type-specialized-element-type a))))
4378 (cond ((eq element-type '*)
4379 (specifier-type 'type-specifier))
4380 ((symbolp element-type)
4381 (make-member-type :members (list element-type)))
4382 ((consp element-type)
4383 (specifier-type (consify element-type)))
4385 (error "can't understand type ~S~%" element-type))))))
4386 (labels ((recurse (type)
4387 (cond ((array-type-p type)
4388 (get-element-type type))
4389 ((union-type-p type)
4391 (mapcar #'recurse (union-type-types type))))
4393 *universal-type*))))
4394 (recurse array-type)))))
4396 (define-source-transform sb!impl::sort-vector (vector start end predicate key)
4397 ;; Like CMU CL, we use HEAPSORT. However, other than that, this code
4398 ;; isn't really related to the CMU CL code, since instead of trying
4399 ;; to generalize the CMU CL code to allow START and END values, this
4400 ;; code has been written from scratch following Chapter 7 of
4401 ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir.
4402 `(macrolet ((%index (x) `(truly-the index ,x))
4403 (%parent (i) `(ash ,i -1))
4404 (%left (i) `(%index (ash ,i 1)))
4405 (%right (i) `(%index (1+ (ash ,i 1))))
4408 (left (%left i) (%left i)))
4409 ((> left current-heap-size))
4410 (declare (type index i left))
4411 (let* ((i-elt (%elt i))
4412 (i-key (funcall keyfun i-elt))
4413 (left-elt (%elt left))
4414 (left-key (funcall keyfun left-elt)))
4415 (multiple-value-bind (large large-elt large-key)
4416 (if (funcall ,',predicate i-key left-key)
4417 (values left left-elt left-key)
4418 (values i i-elt i-key))
4419 (let ((right (%right i)))
4420 (multiple-value-bind (largest largest-elt)
4421 (if (> right current-heap-size)
4422 (values large large-elt)
4423 (let* ((right-elt (%elt right))
4424 (right-key (funcall keyfun right-elt)))
4425 (if (funcall ,',predicate large-key right-key)
4426 (values right right-elt)
4427 (values large large-elt))))
4428 (cond ((= largest i)
4431 (setf (%elt i) largest-elt
4432 (%elt largest) i-elt
4434 (%sort-vector (keyfun &optional (vtype 'vector))
4435 `(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had
4436 ;; trouble getting type inference to
4437 ;; propagate all the way through this
4438 ;; tangled mess of inlining. The TRULY-THE
4439 ;; here works around that. -- WHN
4441 `(aref (truly-the ,',vtype ,',',vector)
4442 (%index (+ (%index ,i) start-1)))))
4443 (let (;; Heaps prefer 1-based addressing.
4444 (start-1 (1- ,',start))
4445 (current-heap-size (- ,',end ,',start))
4447 (declare (type (integer -1 #.(1- sb!xc:most-positive-fixnum))
4449 (declare (type index current-heap-size))
4450 (declare (type function keyfun))
4451 (loop for i of-type index
4452 from (ash current-heap-size -1) downto 1 do
4455 (when (< current-heap-size 2)
4457 (rotatef (%elt 1) (%elt current-heap-size))
4458 (decf current-heap-size)
4460 (if (typep ,vector 'simple-vector)
4461 ;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
4462 ;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
4464 ;; Special-casing the KEY=NIL case lets us avoid some
4466 (%sort-vector #'identity simple-vector)
4467 (%sort-vector ,key simple-vector))
4468 ;; It's hard to anticipate many speed-critical applications for
4469 ;; sorting vector types other than (VECTOR T), so we just lump
4470 ;; them all together in one slow dynamically typed mess.
4472 (declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
4473 (%sort-vector (or ,key #'identity))))))
4475 ;;;; debuggers' little helpers
4477 ;;; for debugging when transforms are behaving mysteriously,
4478 ;;; e.g. when debugging a problem with an ASH transform
4479 ;;; (defun foo (&optional s)
4480 ;;; (sb-c::/report-lvar s "S outside WHEN")
4481 ;;; (when (and (integerp s) (> s 3))
4482 ;;; (sb-c::/report-lvar s "S inside WHEN")
4483 ;;; (let ((bound (ash 1 (1- s))))
4484 ;;; (sb-c::/report-lvar bound "BOUND")
4485 ;;; (let ((x (- bound))
4487 ;;; (sb-c::/report-lvar x "X")
4488 ;;; (sb-c::/report-lvar x "Y"))
4489 ;;; `(integer ,(- bound) ,(1- bound)))))
4490 ;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
4491 ;;; and the function doesn't do anything at all.)
4494 (defknown /report-lvar (t t) null)
4495 (deftransform /report-lvar ((x message) (t t))
4496 (format t "~%/in /REPORT-LVAR~%")
4497 (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x))
4498 (when (constant-lvar-p x)
4499 (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x)))
4500 (format t "/MESSAGE=~S~%" (lvar-value message))
4501 (give-up-ir1-transform "not a real transform"))
4502 (defun /report-lvar (x message)
4503 (declare (ignore x message))))
4506 ;;;; Transforms for internal compiler utilities
4508 ;;; If QUALITY-NAME is constant and a valid name, don't bother
4509 ;;; checking that it's still valid at run-time.
4510 (deftransform policy-quality ((policy quality-name)
4512 (unless (and (constant-lvar-p quality-name)
4513 (policy-quality-name-p (lvar-value quality-name)))
4514 (give-up-ir1-transform))
4515 '(%policy-quality policy quality-name))