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[98a76d]: src / compiler / srctran.lisp Maximize Restore History

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srctran.lisp    3483 lines (3265 with data), 128.1 kB

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;;;; This file contains macro-like source transformations which
;;;; convert uses of certain functions into the canonical form desired
;;;; within the compiler. FIXME: and other IR1 transforms and stuff.
;;;; This software is part of the SBCL system. See the README file for
;;;; more information.
;;;;
;;;; This software is derived from the CMU CL system, which was
;;;; written at Carnegie Mellon University and released into the
;;;; public domain. The software is in the public domain and is
;;;; provided with absolutely no warranty. See the COPYING and CREDITS
;;;; files for more information.
(in-package "SB!C")
;;; Convert into an IF so that IF optimizations will eliminate redundant
;;; negations.
(define-source-transform not (x) `(if ,x nil t))
(define-source-transform null (x) `(if ,x nil t))
;;; ENDP is just NULL with a LIST assertion. The assertion will be
;;; optimized away when SAFETY optimization is low; hopefully that
;;; is consistent with ANSI's "should return an error".
(define-source-transform endp (x) `(null (the list ,x)))
;;; We turn IDENTITY into PROG1 so that it is obvious that it just
;;; returns the first value of its argument. Ditto for VALUES with one
;;; arg.
(define-source-transform identity (x) `(prog1 ,x))
(define-source-transform values (x) `(prog1 ,x))
;;; Bind the value and make a closure that returns it.
(define-source-transform constantly (value)
(let ((rest (gensym "CONSTANTLY-REST-"))
(n-value (gensym "CONSTANTLY-VALUE-")))
`(let ((,n-value ,value))
(lambda (&rest ,rest)
(declare (ignore ,rest))
,n-value))))
;;; If the function has a known number of arguments, then return a
;;; lambda with the appropriate fixed number of args. If the
;;; destination is a FUNCALL, then do the &REST APPLY thing, and let
;;; MV optimization figure things out.
(deftransform complement ((fun) * * :node node)
"open code"
(multiple-value-bind (min max)
(fun-type-nargs (continuation-type fun))
(cond
((and min (eql min max))
(let ((dums (make-gensym-list min)))
`#'(lambda ,dums (not (funcall fun ,@dums)))))
((let* ((cont (node-cont node))
(dest (continuation-dest cont)))
(and (combination-p dest)
(eq (combination-fun dest) cont)))
'#'(lambda (&rest args)
(not (apply fun args))))
(t
(give-up-ir1-transform
"The function doesn't have a fixed argument count.")))))
;;;; list hackery
;;; Translate CxR into CAR/CDR combos.
(defun source-transform-cxr (form)
(if (/= (length form) 2)
(values nil t)
(let ((name (symbol-name (car form))))
(do ((i (- (length name) 2) (1- i))
(res (cadr form)
`(,(ecase (char name i)
(#\A 'car)
(#\D 'cdr))
,res)))
((zerop i) res)))))
;;; Make source transforms to turn CxR forms into combinations of CAR
;;; and CDR. ANSI specifies that everything up to 4 A/D operations is
;;; defined.
(/show0 "about to set CxR source transforms")
(loop for i of-type index from 2 upto 4 do
;; Iterate over BUF = all names CxR where x = an I-element
;; string of #\A or #\D characters.
(let ((buf (make-string (+ 2 i))))
(setf (aref buf 0) #\C
(aref buf (1+ i)) #\R)
(dotimes (j (ash 2 i))
(declare (type index j))
(dotimes (k i)
(declare (type index k))
(setf (aref buf (1+ k))
(if (logbitp k j) #\A #\D)))
(setf (info :function :source-transform (intern buf))
#'source-transform-cxr))))
(/show0 "done setting CxR source transforms")
;;; Turn FIRST..FOURTH and REST into the obvious synonym, assuming
;;; whatever is right for them is right for us. FIFTH..TENTH turn into
;;; Nth, which can be expanded into a CAR/CDR later on if policy
;;; favors it.
(define-source-transform first (x) `(car ,x))
(define-source-transform rest (x) `(cdr ,x))
(define-source-transform second (x) `(cadr ,x))
(define-source-transform third (x) `(caddr ,x))
(define-source-transform fourth (x) `(cadddr ,x))
(define-source-transform fifth (x) `(nth 4 ,x))
(define-source-transform sixth (x) `(nth 5 ,x))
(define-source-transform seventh (x) `(nth 6 ,x))
(define-source-transform eighth (x) `(nth 7 ,x))
(define-source-transform ninth (x) `(nth 8 ,x))
(define-source-transform tenth (x) `(nth 9 ,x))
;;; Translate RPLACx to LET and SETF.
(define-source-transform rplaca (x y)
(once-only ((n-x x))
`(progn
(setf (car ,n-x) ,y)
,n-x)))
(define-source-transform rplacd (x y)
(once-only ((n-x x))
`(progn
(setf (cdr ,n-x) ,y)
,n-x)))
(define-source-transform nth (n l) `(car (nthcdr ,n ,l)))
(defvar *default-nthcdr-open-code-limit* 6)
(defvar *extreme-nthcdr-open-code-limit* 20)
(deftransform nthcdr ((n l) (unsigned-byte t) * :node node)
"convert NTHCDR to CAxxR"
(unless (constant-continuation-p n)
(give-up-ir1-transform))
(let ((n (continuation-value n)))
(when (> n
(if (policy node (and (= speed 3) (= space 0)))
*extreme-nthcdr-open-code-limit*
*default-nthcdr-open-code-limit*))
(give-up-ir1-transform))
(labels ((frob (n)
(if (zerop n)
'l
`(cdr ,(frob (1- n))))))
(frob n))))
;;;; arithmetic and numerology
(define-source-transform plusp (x) `(> ,x 0))
(define-source-transform minusp (x) `(< ,x 0))
(define-source-transform zerop (x) `(= ,x 0))
(define-source-transform 1+ (x) `(+ ,x 1))
(define-source-transform 1- (x) `(- ,x 1))
(define-source-transform oddp (x) `(not (zerop (logand ,x 1))))
(define-source-transform evenp (x) `(zerop (logand ,x 1)))
;;; Note that all the integer division functions are available for
;;; inline expansion.
(macrolet ((deffrob (fun)
`(define-source-transform ,fun (x &optional (y nil y-p))
(declare (ignore y))
(if y-p
(values nil t)
`(,',fun ,x 1)))))
(deffrob truncate)
(deffrob round)
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(deffrob floor)
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(deffrob ceiling))
(define-source-transform lognand (x y) `(lognot (logand ,x ,y)))
(define-source-transform lognor (x y) `(lognot (logior ,x ,y)))
(define-source-transform logandc1 (x y) `(logand (lognot ,x) ,y))
(define-source-transform logandc2 (x y) `(logand ,x (lognot ,y)))
(define-source-transform logorc1 (x y) `(logior (lognot ,x) ,y))
(define-source-transform logorc2 (x y) `(logior ,x (lognot ,y)))
(define-source-transform logtest (x y) `(not (zerop (logand ,x ,y))))
(define-source-transform logbitp (index integer)
`(not (zerop (logand (ash 1 ,index) ,integer))))
(define-source-transform byte (size position)
`(cons ,size ,position))
(define-source-transform byte-size (spec) `(car ,spec))
(define-source-transform byte-position (spec) `(cdr ,spec))
(define-source-transform ldb-test (bytespec integer)
`(not (zerop (mask-field ,bytespec ,integer))))
;;; With the ratio and complex accessors, we pick off the "identity"
;;; case, and use a primitive to handle the cell access case.
(define-source-transform numerator (num)
(once-only ((n-num `(the rational ,num)))
`(if (ratiop ,n-num)
(%numerator ,n-num)
,n-num)))
(define-source-transform denominator (num)
(once-only ((n-num `(the rational ,num)))
`(if (ratiop ,n-num)
(%denominator ,n-num)
1)))
;;;; interval arithmetic for computing bounds
;;;;
;;;; This is a set of routines for operating on intervals. It
;;;; implements a simple interval arithmetic package. Although SBCL
;;;; has an interval type in NUMERIC-TYPE, we choose to use our own
;;;; for two reasons:
;;;;
;;;; 1. This package is simpler than NUMERIC-TYPE.
;;;;
;;;; 2. It makes debugging much easier because you can just strip
;;;; out these routines and test them independently of SBCL. (This is a
;;;; big win!)
;;;;
;;;; One disadvantage is a probable increase in consing because we
;;;; have to create these new interval structures even though
;;;; numeric-type has everything we want to know. Reason 2 wins for
;;;; now.
;;; The basic interval type. It can handle open and closed intervals.
;;; A bound is open if it is a list containing a number, just like
;;; Lisp says. NIL means unbounded.
(defstruct (interval (:constructor %make-interval)
(:copier nil))
low high)
(defun make-interval (&key low high)
(labels ((normalize-bound (val)
(cond ((and (floatp val)
(float-infinity-p val))
;; Handle infinities.
nil)
((or (numberp val)
(eq val nil))
;; Handle any closed bounds.
val)
((listp val)
;; We have an open bound. Normalize the numeric
;; bound. If the normalized bound is still a number
;; (not nil), keep the bound open. Otherwise, the
;; bound is really unbounded, so drop the openness.
(let ((new-val (normalize-bound (first val))))
(when new-val
;; The bound exists, so keep it open still.
(list new-val))))
(t
(error "unknown bound type in MAKE-INTERVAL")))))
(%make-interval :low (normalize-bound low)
:high (normalize-bound high))))
;;; Given a number X, create a form suitable as a bound for an
;;; interval. Make the bound open if OPEN-P is T. NIL remains NIL.
#!-sb-fluid (declaim (inline set-bound))
(defun set-bound (x open-p)
(if (and x open-p) (list x) x))
;;; Apply the function F to a bound X. If X is an open bound, then
;;; the result will be open. IF X is NIL, the result is NIL.
(defun bound-func (f x)
(declare (type function f))
(and x
(with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
;; With these traps masked, we might get things like infinity
;; or negative infinity returned. Check for this and return
;; NIL to indicate unbounded.
(let ((y (funcall f (type-bound-number x))))
(if (and (floatp y)
(float-infinity-p y))
nil
(set-bound (funcall f (type-bound-number x)) (consp x)))))))
;;; Apply a binary operator OP to two bounds X and Y. The result is
;;; NIL if either is NIL. Otherwise bound is computed and the result
;;; is open if either X or Y is open.
;;;
;;; FIXME: only used in this file, not needed in target runtime
(defmacro bound-binop (op x y)
`(and ,x ,y
(with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
(set-bound (,op (type-bound-number ,x)
(type-bound-number ,y))
(or (consp ,x) (consp ,y))))))
;;; Convert a numeric-type object to an interval object.
(defun numeric-type->interval (x)
(declare (type numeric-type x))
(make-interval :low (numeric-type-low x)
:high (numeric-type-high x)))
(defun copy-interval-limit (limit)
(if (numberp limit)
limit
(copy-list limit)))
(defun copy-interval (x)
(declare (type interval x))
(make-interval :low (copy-interval-limit (interval-low x))
:high (copy-interval-limit (interval-high x))))
;;; Given a point P contained in the interval X, split X into two
;;; interval at the point P. If CLOSE-LOWER is T, then the left
;;; interval contains P. If CLOSE-UPPER is T, the right interval
;;; contains P. You can specify both to be T or NIL.
(defun interval-split (p x &optional close-lower close-upper)
(declare (type number p)
(type interval x))
(list (make-interval :low (copy-interval-limit (interval-low x))
:high (if close-lower p (list p)))
(make-interval :low (if close-upper (list p) p)
:high (copy-interval-limit (interval-high x)))))
;;; Return the closure of the interval. That is, convert open bounds
;;; to closed bounds.
(defun interval-closure (x)
(declare (type interval x))
(make-interval :low (type-bound-number (interval-low x))
:high (type-bound-number (interval-high x))))
(defun signed-zero->= (x y)
(declare (real x y))
(or (> x y)
(and (= x y)
(>= (float-sign (float x))
(float-sign (float y))))))
;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return
;;; '-. Otherwise return NIL.
#+nil
(defun interval-range-info (x &optional (point 0))
(declare (type interval x))
(let ((lo (interval-low x))
(hi (interval-high x)))
(cond ((and lo (signed-zero->= (type-bound-number lo) point))
'+)
((and hi (signed-zero->= point (type-bound-number hi)))
'-)
(t
nil))))
(defun interval-range-info (x &optional (point 0))
(declare (type interval x))
(labels ((signed->= (x y)
(if (and (zerop x) (zerop y) (floatp x) (floatp y))
(>= (float-sign x) (float-sign y))
(>= x y))))
(let ((lo (interval-low x))
(hi (interval-high x)))
(cond ((and lo (signed->= (type-bound-number lo) point))
'+)
((and hi (signed->= point (type-bound-number hi)))
'-)
(t
nil)))))
;;; Test to see whether the interval X is bounded. HOW determines the
;;; test, and should be either ABOVE, BELOW, or BOTH.
(defun interval-bounded-p (x how)
(declare (type interval x))
(ecase how
(above
(interval-high x))
(below
(interval-low x))
(both
(and (interval-low x) (interval-high x)))))
;;; signed zero comparison functions. Use these functions if we need
;;; to distinguish between signed zeroes.
(defun signed-zero-< (x y)
(declare (real x y))
(or (< x y)
(and (= x y)
(< (float-sign (float x))
(float-sign (float y))))))
(defun signed-zero-> (x y)
(declare (real x y))
(or (> x y)
(and (= x y)
(> (float-sign (float x))
(float-sign (float y))))))
(defun signed-zero-= (x y)
(declare (real x y))
(and (= x y)
(= (float-sign (float x))
(float-sign (float y)))))
(defun signed-zero-<= (x y)
(declare (real x y))
(or (< x y)
(and (= x y)
(<= (float-sign (float x))
(float-sign (float y))))))
;;; See whether the interval X contains the number P, taking into
;;; account that the interval might not be closed.
(defun interval-contains-p (p x)
(declare (type number p)
(type interval x))
;; Does the interval X contain the number P? This would be a lot
;; easier if all intervals were closed!
(let ((lo (interval-low x))
(hi (interval-high x)))
(cond ((and lo hi)
;; The interval is bounded
(if (and (signed-zero-<= (type-bound-number lo) p)
(signed-zero-<= p (type-bound-number hi)))
;; P is definitely in the closure of the interval.
;; We just need to check the end points now.
(cond ((signed-zero-= p (type-bound-number lo))
(numberp lo))
((signed-zero-= p (type-bound-number hi))
(numberp hi))
(t t))
nil))
(hi
;; Interval with upper bound
(if (signed-zero-< p (type-bound-number hi))
t
(and (numberp hi) (signed-zero-= p hi))))
(lo
;; Interval with lower bound
(if (signed-zero-> p (type-bound-number lo))
t
(and (numberp lo) (signed-zero-= p lo))))
(t
;; Interval with no bounds
t))))
;;; Determine whether two intervals X and Y intersect. Return T if so.
;;; If CLOSED-INTERVALS-P is T, the treat the intervals as if they
;;; were closed. Otherwise the intervals are treated as they are.
;;;
;;; Thus if X = [0, 1) and Y = (1, 2), then they do not intersect
;;; because no element in X is in Y. However, if CLOSED-INTERVALS-P
;;; is T, then they do intersect because we use the closure of X = [0,
;;; 1] and Y = [1, 2] to determine intersection.
(defun interval-intersect-p (x y &optional closed-intervals-p)
(declare (type interval x y))
(multiple-value-bind (intersect diff)
(interval-intersection/difference (if closed-intervals-p
(interval-closure x)
x)
(if closed-intervals-p
(interval-closure y)
y))
(declare (ignore diff))
intersect))
;;; Are the two intervals adjacent? That is, is there a number
;;; between the two intervals that is not an element of either
;;; interval? If so, they are not adjacent. For example [0, 1) and
;;; [1, 2] are adjacent but [0, 1) and (1, 2] are not because 1 lies
;;; between both intervals.
(defun interval-adjacent-p (x y)
(declare (type interval x y))
(flet ((adjacent (lo hi)
;; Check to see whether lo and hi are adjacent. If either is
;; nil, they can't be adjacent.
(when (and lo hi (= (type-bound-number lo) (type-bound-number hi)))
;; The bounds are equal. They are adjacent if one of
;; them is closed (a number). If both are open (consp),
;; then there is a number that lies between them.
(or (numberp lo) (numberp hi)))))
(or (adjacent (interval-low y) (interval-high x))
(adjacent (interval-low x) (interval-high y)))))
;;; Compute the intersection and difference between two intervals.
;;; Two values are returned: the intersection and the difference.
;;;
;;; Let the two intervals be X and Y, and let I and D be the two
;;; values returned by this function. Then I = X intersect Y. If I
;;; is NIL (the empty set), then D is X union Y, represented as the
;;; list of X and Y. If I is not the empty set, then D is (X union Y)
;;; - I, which is a list of two intervals.
;;;
;;; For example, let X = [1,5] and Y = [-1,3). Then I = [1,3) and D =
;;; [-1,1) union [3,5], which is returned as a list of two intervals.
(defun interval-intersection/difference (x y)
(declare (type interval x y))
(let ((x-lo (interval-low x))
(x-hi (interval-high x))
(y-lo (interval-low y))
(y-hi (interval-high y)))
(labels
((opposite-bound (p)
;; If p is an open bound, make it closed. If p is a closed
;; bound, make it open.
(if (listp p)
(first p)
(list p)))
(test-number (p int)
;; Test whether P is in the interval.
(when (interval-contains-p (type-bound-number p)
(interval-closure int))
(let ((lo (interval-low int))
(hi (interval-high int)))
;; Check for endpoints.
(cond ((and lo (= (type-bound-number p) (type-bound-number lo)))
(not (and (consp p) (numberp lo))))
((and hi (= (type-bound-number p) (type-bound-number hi)))
(not (and (numberp p) (consp hi))))
(t t)))))
(test-lower-bound (p int)
;; P is a lower bound of an interval.
(if p
(test-number p int)
(not (interval-bounded-p int 'below))))
(test-upper-bound (p int)
;; P is an upper bound of an interval.
(if p
(test-number p int)
(not (interval-bounded-p int 'above)))))
(let ((x-lo-in-y (test-lower-bound x-lo y))
(x-hi-in-y (test-upper-bound x-hi y))
(y-lo-in-x (test-lower-bound y-lo x))
(y-hi-in-x (test-upper-bound y-hi x)))
(cond ((or x-lo-in-y x-hi-in-y y-lo-in-x y-hi-in-x)
;; Intervals intersect. Let's compute the intersection
;; and the difference.
(multiple-value-bind (lo left-lo left-hi)
(cond (x-lo-in-y (values x-lo y-lo (opposite-bound x-lo)))
(y-lo-in-x (values y-lo x-lo (opposite-bound y-lo))))
(multiple-value-bind (hi right-lo right-hi)
(cond (x-hi-in-y
(values x-hi (opposite-bound x-hi) y-hi))
(y-hi-in-x
(values y-hi (opposite-bound y-hi) x-hi)))
(values (make-interval :low lo :high hi)
(list (make-interval :low left-lo
:high left-hi)
(make-interval :low right-lo
:high right-hi))))))
(t
(values nil (list x y))))))))
;;; If intervals X and Y intersect, return a new interval that is the
;;; union of the two. If they do not intersect, return NIL.
(defun interval-merge-pair (x y)
(declare (type interval x y))
;; If x and y intersect or are adjacent, create the union.
;; Otherwise return nil
(when (or (interval-intersect-p x y)
(interval-adjacent-p x y))
(flet ((select-bound (x1 x2 min-op max-op)
(let ((x1-val (type-bound-number x1))
(x2-val (type-bound-number x2)))
(cond ((and x1 x2)
;; Both bounds are finite. Select the right one.
(cond ((funcall min-op x1-val x2-val)
;; x1 is definitely better.
x1)
((funcall max-op x1-val x2-val)
;; x2 is definitely better.
x2)
(t
;; Bounds are equal. Select either
;; value and make it open only if
;; both were open.
(set-bound x1-val (and (consp x1) (consp x2))))))
(t
;; At least one bound is not finite. The
;; non-finite bound always wins.
nil)))))
(let* ((x-lo (copy-interval-limit (interval-low x)))
(x-hi (copy-interval-limit (interval-high x)))
(y-lo (copy-interval-limit (interval-low y)))
(y-hi (copy-interval-limit (interval-high y))))
(make-interval :low (select-bound x-lo y-lo #'< #'>)
:high (select-bound x-hi y-hi #'> #'<))))))
;;; basic arithmetic operations on intervals. We probably should do
;;; true interval arithmetic here, but it's complicated because we
;;; have float and integer types and bounds can be open or closed.
;;; the negative of an interval
(defun interval-neg (x)
(declare (type interval x))
(make-interval :low (bound-func #'- (interval-high x))
:high (bound-func #'- (interval-low x))))
;;; Add two intervals.
(defun interval-add (x y)
(declare (type interval x y))
(make-interval :low (bound-binop + (interval-low x) (interval-low y))
:high (bound-binop + (interval-high x) (interval-high y))))
;;; Subtract two intervals.
(defun interval-sub (x y)
(declare (type interval x y))
(make-interval :low (bound-binop - (interval-low x) (interval-high y))
:high (bound-binop - (interval-high x) (interval-low y))))
;;; Multiply two intervals.
(defun interval-mul (x y)
(declare (type interval x y))
(flet ((bound-mul (x y)
(cond ((or (null x) (null y))
;; Multiply by infinity is infinity
nil)
((or (and (numberp x) (zerop x))
(and (numberp y) (zerop y)))
;; Multiply by closed zero is special. The result
;; is always a closed bound. But don't replace this
;; with zero; we want the multiplication to produce
;; the correct signed zero, if needed.
(* (type-bound-number x) (type-bound-number y)))
((or (and (floatp x) (float-infinity-p x))
(and (floatp y) (float-infinity-p y)))
;; Infinity times anything is infinity
nil)
(t
;; General multiply. The result is open if either is open.
(bound-binop * x y)))))
(let ((x-range (interval-range-info x))
(y-range (interval-range-info y)))
(cond ((null x-range)
;; Split x into two and multiply each separately
(destructuring-bind (x- x+) (interval-split 0 x t t)
(interval-merge-pair (interval-mul x- y)
(interval-mul x+ y))))
((null y-range)
;; Split y into two and multiply each separately
(destructuring-bind (y- y+) (interval-split 0 y t t)
(interval-merge-pair (interval-mul x y-)
(interval-mul x y+))))
((eq x-range '-)
(interval-neg (interval-mul (interval-neg x) y)))
((eq y-range '-)
(interval-neg (interval-mul x (interval-neg y))))
((and (eq x-range '+) (eq y-range '+))
;; If we are here, X and Y are both positive.
(make-interval
:low (bound-mul (interval-low x) (interval-low y))
:high (bound-mul (interval-high x) (interval-high y))))
(t
(bug "excluded case in INTERVAL-MUL"))))))
;;; Divide two intervals.
(defun interval-div (top bot)
(declare (type interval top bot))
(flet ((bound-div (x y y-low-p)
;; Compute x/y
(cond ((null y)
;; Divide by infinity means result is 0. However,
;; we need to watch out for the sign of the result,
;; to correctly handle signed zeros. We also need
;; to watch out for positive or negative infinity.
(if (floatp (type-bound-number x))
(if y-low-p
(- (float-sign (type-bound-number x) 0.0))
(float-sign (type-bound-number x) 0.0))
0))
((zerop (type-bound-number y))
;; Divide by zero means result is infinity
nil)
((and (numberp x) (zerop x))
;; Zero divided by anything is zero.
x)
(t
(bound-binop / x y)))))
(let ((top-range (interval-range-info top))
(bot-range (interval-range-info bot)))
(cond ((null bot-range)
;; The denominator contains zero, so anything goes!
(make-interval :low nil :high nil))
((eq bot-range '-)
;; Denominator is negative so flip the sign, compute the
;; result, and flip it back.
(interval-neg (interval-div top (interval-neg bot))))
((null top-range)
;; Split top into two positive and negative parts, and
;; divide each separately
(destructuring-bind (top- top+) (interval-split 0 top t t)
(interval-merge-pair (interval-div top- bot)
(interval-div top+ bot))))
((eq top-range '-)
;; Top is negative so flip the sign, divide, and flip the
;; sign of the result.
(interval-neg (interval-div (interval-neg top) bot)))
((and (eq top-range '+) (eq bot-range '+))
;; the easy case
(make-interval
:low (bound-div (interval-low top) (interval-high bot) t)
:high (bound-div (interval-high top) (interval-low bot) nil)))
(t
(bug "excluded case in INTERVAL-DIV"))))))
;;; Apply the function F to the interval X. If X = [a, b], then the
;;; result is [f(a), f(b)]. It is up to the user to make sure the
;;; result makes sense. It will if F is monotonic increasing (or
;;; non-decreasing).
(defun interval-func (f x)
(declare (type function f)
(type interval x))
(let ((lo (bound-func f (interval-low x)))
(hi (bound-func f (interval-high x))))
(make-interval :low lo :high hi)))
;;; Return T if X < Y. That is every number in the interval X is
;;; always less than any number in the interval Y.
(defun interval-< (x y)
(declare (type interval x y))
;; X < Y only if X is bounded above, Y is bounded below, and they
;; don't overlap.
(when (and (interval-bounded-p x 'above)
(interval-bounded-p y 'below))
;; Intervals are bounded in the appropriate way. Make sure they
;; don't overlap.
(let ((left (interval-high x))
(right (interval-low y)))
(cond ((> (type-bound-number left)
(type-bound-number right))
;; The intervals definitely overlap, so result is NIL.
nil)
((< (type-bound-number left)
(type-bound-number right))
;; The intervals definitely don't touch, so result is T.
t)
(t
;; Limits are equal. Check for open or closed bounds.
;; Don't overlap if one or the other are open.
(or (consp left) (consp right)))))))
;;; Return T if X >= Y. That is, every number in the interval X is
;;; always greater than any number in the interval Y.
(defun interval->= (x y)
(declare (type interval x y))
;; X >= Y if lower bound of X >= upper bound of Y
(when (and (interval-bounded-p x 'below)
(interval-bounded-p y 'above))
(>= (type-bound-number (interval-low x))
(type-bound-number (interval-high y)))))
;;; Return an interval that is the absolute value of X. Thus, if
;;; X = [-1 10], the result is [0, 10].
(defun interval-abs (x)
(declare (type interval x))
(case (interval-range-info x)
(+
(copy-interval x))
(-
(interval-neg x))
(t
(destructuring-bind (x- x+) (interval-split 0 x t t)
(interval-merge-pair (interval-neg x-) x+)))))
;;; Compute the square of an interval.
(defun interval-sqr (x)
(declare (type interval x))
(interval-func (lambda (x) (* x x))
(interval-abs x)))
;;;; numeric DERIVE-TYPE methods
;;; a utility for defining derive-type methods of integer operations. If
;;; the types of both X and Y are integer types, then we compute a new
;;; integer type with bounds determined Fun when applied to X and Y.
;;; Otherwise, we use Numeric-Contagion.
(defun derive-integer-type (x y fun)
(declare (type continuation x y) (type function fun))
(let ((x (continuation-type x))
(y (continuation-type y)))
(if (and (numeric-type-p x) (numeric-type-p y)
(eq (numeric-type-class x) 'integer)
(eq (numeric-type-class y) 'integer)
(eq (numeric-type-complexp x) :real)
(eq (numeric-type-complexp y) :real))
(multiple-value-bind (low high) (funcall fun x y)
(make-numeric-type :class 'integer
:complexp :real
:low low
:high high))
(numeric-contagion x y))))
;;; simple utility to flatten a list
(defun flatten-list (x)
(labels ((flatten-helper (x r);; 'r' is the stuff to the 'right'.
(cond ((null x) r)
((atom x)
(cons x r))
(t (flatten-helper (car x)
(flatten-helper (cdr x) r))))))
(flatten-helper x nil)))
;;; Take some type of continuation and massage it so that we get a
;;; list of the constituent types. If ARG is *EMPTY-TYPE*, return NIL
;;; to indicate failure.
(defun prepare-arg-for-derive-type (arg)
(flet ((listify (arg)
(typecase arg
(numeric-type
(list arg))
(union-type
(union-type-types arg))
(t
(list arg)))))
(unless (eq arg *empty-type*)
;; Make sure all args are some type of numeric-type. For member
;; types, convert the list of members into a union of equivalent
;; single-element member-type's.
(let ((new-args nil))
(dolist (arg (listify arg))
(if (member-type-p arg)
;; Run down the list of members and convert to a list of
;; member types.
(dolist (member (member-type-members arg))
(push (if (numberp member)
(make-member-type :members (list member))
*empty-type*)
new-args))
(push arg new-args)))
(unless (member *empty-type* new-args)
new-args)))))
;;; Convert from the standard type convention for which -0.0 and 0.0
;;; are equal to an intermediate convention for which they are
;;; considered different which is more natural for some of the
;;; optimisers.
(defun convert-numeric-type (type)
(declare (type numeric-type type))
;;; Only convert real float interval delimiters types.
(if (eq (numeric-type-complexp type) :real)
(let* ((lo (numeric-type-low type))
(lo-val (type-bound-number lo))
(lo-float-zero-p (and lo (floatp lo-val) (= lo-val 0.0)))
(hi (numeric-type-high type))
(hi-val (type-bound-number hi))
(hi-float-zero-p (and hi (floatp hi-val) (= hi-val 0.0))))
(if (or lo-float-zero-p hi-float-zero-p)
(make-numeric-type
:class (numeric-type-class type)
:format (numeric-type-format type)
:complexp :real
:low (if lo-float-zero-p
(if (consp lo)
(list (float 0.0 lo-val))
(float -0.0 lo-val))
lo)
:high (if hi-float-zero-p
(if (consp hi)
(list (float -0.0 hi-val))
(float 0.0 hi-val))
hi))
type))
;; Not real float.
type))
;;; Convert back from the intermediate convention for which -0.0 and
;;; 0.0 are considered different to the standard type convention for
;;; which and equal.
(defun convert-back-numeric-type (type)
(declare (type numeric-type type))
;;; Only convert real float interval delimiters types.
(if (eq (numeric-type-complexp type) :real)
(let* ((lo (numeric-type-low type))
(lo-val (type-bound-number lo))
(lo-float-zero-p
(and lo (floatp lo-val) (= lo-val 0.0)
(float-sign lo-val)))
(hi (numeric-type-high type))
(hi-val (type-bound-number hi))
(hi-float-zero-p
(and hi (floatp hi-val) (= hi-val 0.0)
(float-sign hi-val))))
(cond
;; (float +0.0 +0.0) => (member 0.0)
;; (float -0.0 -0.0) => (member -0.0)
((and lo-float-zero-p hi-float-zero-p)
;; shouldn't have exclusive bounds here..
(aver (and (not (consp lo)) (not (consp hi))))
(if (= lo-float-zero-p hi-float-zero-p)
;; (float +0.0 +0.0) => (member 0.0)
;; (float -0.0 -0.0) => (member -0.0)
(specifier-type `(member ,lo-val))
;; (float -0.0 +0.0) => (float 0.0 0.0)
;; (float +0.0 -0.0) => (float 0.0 0.0)
(make-numeric-type :class (numeric-type-class type)
:format (numeric-type-format type)
:complexp :real
:low hi-val
:high hi-val)))
(lo-float-zero-p
(cond
;; (float -0.0 x) => (float 0.0 x)
((and (not (consp lo)) (minusp lo-float-zero-p))
(make-numeric-type :class (numeric-type-class type)
:format (numeric-type-format type)
:complexp :real
:low (float 0.0 lo-val)
:high hi))
;; (float (+0.0) x) => (float (0.0) x)
((and (consp lo) (plusp lo-float-zero-p))
(make-numeric-type :class (numeric-type-class type)
:format (numeric-type-format type)
:complexp :real
:low (list (float 0.0 lo-val))
:high hi))
(t
;; (float +0.0 x) => (or (member 0.0) (float (0.0) x))
;; (float (-0.0) x) => (or (member 0.0) (float (0.0) x))
(list (make-member-type :members (list (float 0.0 lo-val)))
(make-numeric-type :class (numeric-type-class type)
:format (numeric-type-format type)
:complexp :real
:low (list (float 0.0 lo-val))
:high hi)))))
(hi-float-zero-p
(cond
;; (float x +0.0) => (float x 0.0)
((and (not (consp hi)) (plusp hi-float-zero-p))
(make-numeric-type :class (numeric-type-class type)
:format (numeric-type-format type)
:complexp :real
:low lo
:high (float 0.0 hi-val)))
;; (float x (-0.0)) => (float x (0.0))
((and (consp hi) (minusp hi-float-zero-p))
(make-numeric-type :class (numeric-type-class type)
:format (numeric-type-format type)
:complexp :real
:low lo
:high (list (float 0.0 hi-val))))
(t
;; (float x (+0.0)) => (or (member -0.0) (float x (0.0)))
;; (float x -0.0) => (or (member -0.0) (float x (0.0)))
(list (make-member-type :members (list (float -0.0 hi-val)))
(make-numeric-type :class (numeric-type-class type)
:format (numeric-type-format type)
:complexp :real
:low lo
:high (list (float 0.0 hi-val)))))))
(t
type)))
;; not real float
type))
;;; Convert back a possible list of numeric types.
(defun convert-back-numeric-type-list (type-list)
(typecase type-list
(list
(let ((results '()))
(dolist (type type-list)
(if (numeric-type-p type)
(let ((result (convert-back-numeric-type type)))
(if (listp result)
(setf results (append results result))
(push result results)))
(push type results)))
results))
(numeric-type
(convert-back-numeric-type type-list))
(union-type
(convert-back-numeric-type-list (union-type-types type-list)))
(t
type-list)))
;;; FIXME: MAKE-CANONICAL-UNION-TYPE and CONVERT-MEMBER-TYPE probably
;;; belong in the kernel's type logic, invoked always, instead of in
;;; the compiler, invoked only during some type optimizations.
;;; Take a list of types and return a canonical type specifier,
;;; combining any MEMBER types together. If both positive and negative
;;; MEMBER types are present they are converted to a float type.
;;; XXX This would be far simpler if the type-union methods could handle
;;; member/number unions.
(defun make-canonical-union-type (type-list)
(let ((members '())
(misc-types '()))
(dolist (type type-list)
(if (member-type-p type)
(setf members (union members (member-type-members type)))
(push type misc-types)))
#!+long-float
(when (null (set-difference '(-0l0 0l0) members))
(push (specifier-type '(long-float 0l0 0l0)) misc-types)
(setf members (set-difference members '(-0l0 0l0))))
(when (null (set-difference '(-0d0 0d0) members))
(push (specifier-type '(double-float 0d0 0d0)) misc-types)
(setf members (set-difference members '(-0d0 0d0))))
(when (null (set-difference '(-0f0 0f0) members))
(push (specifier-type '(single-float 0f0 0f0)) misc-types)
(setf members (set-difference members '(-0f0 0f0))))
(if members
(apply #'type-union (make-member-type :members members) misc-types)
(apply #'type-union misc-types))))
;;; Convert a member type with a single member to a numeric type.
(defun convert-member-type (arg)
(let* ((members (member-type-members arg))
(member (first members))
(member-type (type-of member)))
(aver (not (rest members)))
(specifier-type `(,(if (subtypep member-type 'integer)
'integer
member-type)
,member ,member))))
;;; This is used in defoptimizers for computing the resulting type of
;;; a function.
;;;
;;; Given the continuation ARG, derive the resulting type using the
;;; DERIVE-FCN. DERIVE-FCN takes exactly one argument which is some
;;; "atomic" continuation type like numeric-type or member-type
;;; (containing just one element). It should return the resulting
;;; type, which can be a list of types.
;;;
;;; For the case of member types, if a member-fcn is given it is
;;; called to compute the result otherwise the member type is first
;;; converted to a numeric type and the derive-fcn is call.
(defun one-arg-derive-type (arg derive-fcn member-fcn
&optional (convert-type t))
(declare (type function derive-fcn)
(type (or null function) member-fcn))
(let ((arg-list (prepare-arg-for-derive-type (continuation-type arg))))
(when arg-list
(flet ((deriver (x)
(typecase x
(member-type
(if member-fcn
(with-float-traps-masked
(:underflow :overflow :divide-by-zero)
(make-member-type
:members (list
(funcall member-fcn
(first (member-type-members x))))))
;; Otherwise convert to a numeric type.
(let ((result-type-list
(funcall derive-fcn (convert-member-type x))))
(if convert-type
(convert-back-numeric-type-list result-type-list)
result-type-list))))
(numeric-type
(if convert-type
(convert-back-numeric-type-list
(funcall derive-fcn (convert-numeric-type x)))
(funcall derive-fcn x)))
(t
*universal-type*))))
;; Run down the list of args and derive the type of each one,
;; saving all of the results in a list.
(let ((results nil))
(dolist (arg arg-list)
(let ((result (deriver arg)))
(if (listp result)
(setf results (append results result))
(push result results))))
(if (rest results)
(make-canonical-union-type results)
(first results)))))))
;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes
;;; two arguments. DERIVE-FCN takes 3 args in this case: the two
;;; original args and a third which is T to indicate if the two args
;;; really represent the same continuation. This is useful for
;;; deriving the type of things like (* x x), which should always be
;;; positive. If we didn't do this, we wouldn't be able to tell.
(defun two-arg-derive-type (arg1 arg2 derive-fcn fcn
&optional (convert-type t))
(declare (type function derive-fcn fcn))
(flet ((deriver (x y same-arg)
(cond ((and (member-type-p x) (member-type-p y))
(let* ((x (first (member-type-members x)))
(y (first (member-type-members y)))
(result (with-float-traps-masked
(:underflow :overflow :divide-by-zero
:invalid)
(funcall fcn x y))))
(cond ((null result))
((and (floatp result) (float-nan-p result))
(make-numeric-type :class 'float
:format (type-of result)
:complexp :real))
(t
(make-member-type :members (list result))))))
((and (member-type-p x) (numeric-type-p y))
(let* ((x (convert-member-type x))
(y (if convert-type (convert-numeric-type y) y))
(result (funcall derive-fcn x y same-arg)))
(if convert-type
(convert-back-numeric-type-list result)
result)))
((and (numeric-type-p x) (member-type-p y))
(let* ((x (if convert-type (convert-numeric-type x) x))
(y (convert-member-type y))
(result (funcall derive-fcn x y same-arg)))
(if convert-type
(convert-back-numeric-type-list result)
result)))
((and (numeric-type-p x) (numeric-type-p y))
(let* ((x (if convert-type (convert-numeric-type x) x))
(y (if convert-type (convert-numeric-type y) y))
(result (funcall derive-fcn x y same-arg)))
(if convert-type
(convert-back-numeric-type-list result)
result)))
(t
*universal-type*))))
(let ((same-arg (same-leaf-ref-p arg1 arg2))
(a1 (prepare-arg-for-derive-type (continuation-type arg1)))
(a2 (prepare-arg-for-derive-type (continuation-type arg2))))
(when (and a1 a2)
(let ((results nil))
(if same-arg
;; Since the args are the same continuation, just run
;; down the lists.
(dolist (x a1)
(let ((result (deriver x x same-arg)))
(if (listp result)
(setf results (append results result))
(push result results))))
;; Try all pairwise combinations.
(dolist (x a1)
(dolist (y a2)
(let ((result (or (deriver x y same-arg)
(numeric-contagion x y))))
(if (listp result)
(setf results (append results result))
(push result results))))))
(if (rest results)
(make-canonical-union-type results)
(first results)))))))
#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(progn
(defoptimizer (+ derive-type) ((x y))
(derive-integer-type
x y
#'(lambda (x y)
(flet ((frob (x y)
(if (and x y)
(+ x y)
nil)))
(values (frob (numeric-type-low x) (numeric-type-low y))
(frob (numeric-type-high x) (numeric-type-high y)))))))
(defoptimizer (- derive-type) ((x y))
(derive-integer-type
x y
#'(lambda (x y)
(flet ((frob (x y)
(if (and x y)
(- x y)
nil)))
(values (frob (numeric-type-low x) (numeric-type-high y))
(frob (numeric-type-high x) (numeric-type-low y)))))))
(defoptimizer (* derive-type) ((x y))
(derive-integer-type
x y
#'(lambda (x y)
(let ((x-low (numeric-type-low x))
(x-high (numeric-type-high x))
(y-low (numeric-type-low y))
(y-high (numeric-type-high y)))
(cond ((not (and x-low y-low))
(values nil nil))
((or (minusp x-low) (minusp y-low))
(if (and x-high y-high)
(let ((max (* (max (abs x-low) (abs x-high))
(max (abs y-low) (abs y-high)))))
(values (- max) max))
(values nil nil)))
(t
(values (* x-low y-low)
(if (and x-high y-high)
(* x-high y-high)
nil))))))))
(defoptimizer (/ derive-type) ((x y))
(numeric-contagion (continuation-type x) (continuation-type y)))
) ; PROGN
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(progn
(defun +-derive-type-aux (x y same-arg)
(if (and (numeric-type-real-p x)
(numeric-type-real-p y))
(let ((result
(if same-arg
(let ((x-int (numeric-type->interval x)))
(interval-add x-int x-int))
(interval-add (numeric-type->interval x)
(numeric-type->interval y))))
(result-type (numeric-contagion x y)))
;; If the result type is a float, we need to be sure to coerce
;; the bounds into the correct type.
(when (eq (numeric-type-class result-type) 'float)
(setf result (interval-func
#'(lambda (x)
(coerce x (or (numeric-type-format result-type)
'float)))
result)))
(make-numeric-type
:class (if (and (eq (numeric-type-class x) 'integer)
(eq (numeric-type-class y) 'integer))
;; The sum of integers is always an integer.
'integer
(numeric-type-class result-type))
:format (numeric-type-format result-type)
:low (interval-low result)
:high (interval-high result)))
;; general contagion
(numeric-contagion x y)))
(defoptimizer (+ derive-type) ((x y))
(two-arg-derive-type x y #'+-derive-type-aux #'+))
(defun --derive-type-aux (x y same-arg)
(if (and (numeric-type-real-p x)
(numeric-type-real-p y))
(let ((result
;; (- X X) is always 0.
(if same-arg
(make-interval :low 0 :high 0)
(interval-sub (numeric-type->interval x)
(numeric-type->interval y))))
(result-type (numeric-contagion x y)))
;; If the result type is a float, we need to be sure to coerce
;; the bounds into the correct type.
(when (eq (numeric-type-class result-type) 'float)
(setf result (interval-func
#'(lambda (x)
(coerce x (or (numeric-type-format result-type)
'float)))
result)))
(make-numeric-type
:class (if (and (eq (numeric-type-class x) 'integer)
(eq (numeric-type-class y) 'integer))
;; The difference of integers is always an integer.
'integer
(numeric-type-class result-type))
:format (numeric-type-format result-type)
:low (interval-low result)
:high (interval-high result)))
;; general contagion
(numeric-contagion x y)))
(defoptimizer (- derive-type) ((x y))
(two-arg-derive-type x y #'--derive-type-aux #'-))
(defun *-derive-type-aux (x y same-arg)
(if (and (numeric-type-real-p x)
(numeric-type-real-p y))
(let ((result
;; (* X X) is always positive, so take care to do it right.
(if same-arg
(interval-sqr (numeric-type->interval x))
(interval-mul (numeric-type->interval x)
(numeric-type->interval y))))
(result-type (numeric-contagion x y)))
;; If the result type is a float, we need to be sure to coerce
;; the bounds into the correct type.
(when (eq (numeric-type-class result-type) 'float)
(setf result (interval-func
#'(lambda (x)
(coerce x (or (numeric-type-format result-type)
'float)))
result)))
(make-numeric-type
:class (if (and (eq (numeric-type-class x) 'integer)
(eq (numeric-type-class y) 'integer))
;; The product of integers is always an integer.
'integer
(numeric-type-class result-type))
:format (numeric-type-format result-type)
:low (interval-low result)
:high (interval-high result)))
(numeric-contagion x y)))
(defoptimizer (* derive-type) ((x y))
(two-arg-derive-type x y #'*-derive-type-aux #'*))
(defun /-derive-type-aux (x y same-arg)
(if (and (numeric-type-real-p x)
(numeric-type-real-p y))
(let ((result
;; (/ X X) is always 1, except if X can contain 0. In
;; that case, we shouldn't optimize the division away
;; because we want 0/0 to signal an error.
(if (and same-arg
(not (interval-contains-p
0 (interval-closure (numeric-type->interval y)))))
(make-interval :low 1 :high 1)
(interval-div (numeric-type->interval x)
(numeric-type->interval y))))
(result-type (numeric-contagion x y)))
;; If the result type is a float, we need to be sure to coerce
;; the bounds into the correct type.
(when (eq (numeric-type-class result-type) 'float)
(setf result (interval-func
#'(lambda (x)
(coerce x (or (numeric-type-format result-type)
'float)))
result)))
(make-numeric-type :class (numeric-type-class result-type)
:format (numeric-type-format result-type)
:low (interval-low result)
:high (interval-high result)))
(numeric-contagion x y)))
(defoptimizer (/ derive-type) ((x y))
(two-arg-derive-type x y #'/-derive-type-aux #'/))
) ; PROGN
(defun ash-derive-type-aux (n-type shift same-arg)
(declare (ignore same-arg))
;; KLUDGE: All this ASH optimization is suppressed under CMU CL for
;; some bignum cases because as of version 2.4.6 for Debian and 18d,
;; CMU CL blows up on (ASH 1000000000 -100000000000) (i.e. ASH of
;; two bignums yielding zero) and it's hard to avoid that
;; calculation in here.
#+(and cmu sb-xc-host)
(when (and (or (typep (numeric-type-low n-type) 'bignum)
(typep (numeric-type-high n-type) 'bignum))
(or (typep (numeric-type-low shift) 'bignum)
(typep (numeric-type-high shift) 'bignum)))
(return-from ash-derive-type-aux *universal-type*))
(flet ((ash-outer (n s)
(when (and (fixnump s)
(<= s 64)
(> s sb!xc:most-negative-fixnum))
(ash n s)))
;; KLUDGE: The bare 64's here should be related to
;; symbolic machine word size values somehow.
(ash-inner (n s)
(if (and (fixnump s)
(> s sb!xc:most-negative-fixnum))
(ash n (min s 64))
(if (minusp n) -1 0))))
(or (and (csubtypep n-type (specifier-type 'integer))
(csubtypep shift (specifier-type 'integer))
(let ((n-low (numeric-type-low n-type))
(n-high (numeric-type-high n-type))
(s-low (numeric-type-low shift))
(s-high (numeric-type-high shift)))
(make-numeric-type :class 'integer :complexp :real
:low (when n-low
(if (minusp n-low)
(ash-outer n-low s-high)
(ash-inner n-low s-low)))
:high (when n-high
(if (minusp n-high)
(ash-inner n-high s-low)
(ash-outer n-high s-high))))))
*universal-type*)))
(defoptimizer (ash derive-type) ((n shift))
(two-arg-derive-type n shift #'ash-derive-type-aux #'ash))
#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(macrolet ((frob (fun)
`#'(lambda (type type2)
(declare (ignore type2))
(let ((lo (numeric-type-low type))
(hi (numeric-type-high type)))
(values (if hi (,fun hi) nil) (if lo (,fun lo) nil))))))
(defoptimizer (%negate derive-type) ((num))
(derive-integer-type num num (frob -))))
(defoptimizer (lognot derive-type) ((int))
(derive-integer-type int int
(lambda (type type2)
(declare (ignore type2))
(let ((lo (numeric-type-low type))
(hi (numeric-type-high type)))
(values (if hi (lognot hi) nil)
(if lo (lognot lo) nil)
(numeric-type-class type)
(numeric-type-format type))))))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defoptimizer (%negate derive-type) ((num))
(flet ((negate-bound (b)
(and b
(set-bound (- (type-bound-number b))
(consp b)))))
(one-arg-derive-type num
(lambda (type)
(modified-numeric-type
type
:low (negate-bound (numeric-type-high type))
:high (negate-bound (numeric-type-low type))))
#'-)))
#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defoptimizer (abs derive-type) ((num))
(let ((type (continuation-type num)))
(if (and (numeric-type-p type)
(eq (numeric-type-class type) 'integer)
(eq (numeric-type-complexp type) :real))
(let ((lo (numeric-type-low type))
(hi (numeric-type-high type)))
(make-numeric-type :class 'integer :complexp :real
:low (cond ((and hi (minusp hi))
(abs hi))
(lo
(max 0 lo))
(t
0))
:high (if (and hi lo)
(max (abs hi) (abs lo))
nil)))
(numeric-contagion type type))))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defun abs-derive-type-aux (type)
(cond ((eq (numeric-type-complexp type) :complex)
;; The absolute value of a complex number is always a
;; non-negative float.
(let* ((format (case (numeric-type-class type)
((integer rational) 'single-float)
(t (numeric-type-format type))))
(bound-format (or format 'float)))
(make-numeric-type :class 'float
:format format
:complexp :real
:low (coerce 0 bound-format)
:high nil)))
(t
;; The absolute value of a real number is a non-negative real
;; of the same type.
(let* ((abs-bnd (interval-abs (numeric-type->interval type)))
(class (numeric-type-class type))
(format (numeric-type-format type))
(bound-type (or format class 'real)))
(make-numeric-type
:class class
:format format
:complexp :real
:low (coerce-numeric-bound (interval-low abs-bnd) bound-type)
:high (coerce-numeric-bound
(interval-high abs-bnd) bound-type))))))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defoptimizer (abs derive-type) ((num))
(one-arg-derive-type num #'abs-derive-type-aux #'abs))
#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defoptimizer (truncate derive-type) ((number divisor))
(let ((number-type (continuation-type number))
(divisor-type (continuation-type divisor))
(integer-type (specifier-type 'integer)))
(if (and (numeric-type-p number-type)
(csubtypep number-type integer-type)
(numeric-type-p divisor-type)
(csubtypep divisor-type integer-type))
(let ((number-low (numeric-type-low number-type))
(number-high (numeric-type-high number-type))
(divisor-low (numeric-type-low divisor-type))
(divisor-high (numeric-type-high divisor-type)))
(values-specifier-type
`(values ,(integer-truncate-derive-type number-low number-high
divisor-low divisor-high)
,(integer-rem-derive-type number-low number-high
divisor-low divisor-high))))
*universal-type*)))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(progn
(defun rem-result-type (number-type divisor-type)
;; Figure out what the remainder type is. The remainder is an
;; integer if both args are integers; a rational if both args are
;; rational; and a float otherwise.
(cond ((and (csubtypep number-type (specifier-type 'integer))
(csubtypep divisor-type (specifier-type 'integer)))
'integer)
((and (csubtypep number-type (specifier-type 'rational))
(csubtypep divisor-type (specifier-type 'rational)))
'rational)
((and (csubtypep number-type (specifier-type 'float))
(csubtypep divisor-type (specifier-type 'float)))
;; Both are floats so the result is also a float, of
;; the largest type.
(or (float-format-max (numeric-type-format number-type)
(numeric-type-format divisor-type))
'float))
((and (csubtypep number-type (specifier-type 'float))
(csubtypep divisor-type (specifier-type 'rational)))
;; One of the arguments is a float and the other is a
;; rational. The remainder is a float of the same
;; type.
(or (numeric-type-format number-type) 'float))
((and (csubtypep divisor-type (specifier-type 'float))
(csubtypep number-type (specifier-type 'rational)))
;; One of the arguments is a float and the other is a
;; rational. The remainder is a float of the same
;; type.
(or (numeric-type-format divisor-type) 'float))
(t
;; Some unhandled combination. This usually means both args
;; are REAL so the result is a REAL.
'real)))
(defun truncate-derive-type-quot (number-type divisor-type)
(let* ((rem-type (rem-result-type number-type divisor-type))
(number-interval (numeric-type->interval number-type))
(divisor-interval (numeric-type->interval divisor-type)))
;;(declare (type (member '(integer rational float)) rem-type))
;; We have real numbers now.
(cond ((eq rem-type 'integer)
;; Since the remainder type is INTEGER, both args are
;; INTEGERs.
(let* ((res (integer-truncate-derive-type
(interval-low number-interval)
(interval-high number-interval)
(interval-low divisor-interval)
(interval-high divisor-interval))))
(specifier-type (if (listp res) res 'integer))))
(t
(let ((quot (truncate-quotient-bound
(interval-div number-interval
divisor-interval))))
(specifier-type `(integer ,(or (interval-low quot) '*)
,(or (interval-high quot) '*))))))))
(defun truncate-derive-type-rem (number-type divisor-type)
(let* ((rem-type (rem-result-type number-type divisor-type))
(number-interval (numeric-type->interval number-type))
(divisor-interval (numeric-type->interval divisor-type))
(rem (truncate-rem-bound number-interval divisor-interval)))
;;(declare (type (member '(integer rational float)) rem-type))
;; We have real numbers now.
(cond ((eq rem-type 'integer)
;; Since the remainder type is INTEGER, both args are
;; INTEGERs.
(specifier-type `(,rem-type ,(or (interval-low rem) '*)
,(or (interval-high rem) '*))))
(t
(multiple-value-bind (class format)
(ecase rem-type
(integer
(values 'integer nil))
(rational
(values 'rational nil))
((or single-float double-float #!+long-float long-float)
(values 'float rem-type))
(float
(values 'float nil))
(real
(values nil nil)))
(when (member rem-type '(float single-float double-float
#!+long-float long-float))
(setf rem (interval-func #'(lambda (x)
(coerce x rem-type))
rem)))
(make-numeric-type :class class
:format format
:low (interval-low rem)
:high (interval-high rem)))))))
(defun truncate-derive-type-quot-aux (num div same-arg)
(declare (ignore same-arg))
(if (and (numeric-type-real-p num)
(numeric-type-real-p div))
(truncate-derive-type-quot num div)
*empty-type*))
(defun truncate-derive-type-rem-aux (num div same-arg)
(declare (ignore same-arg))
(if (and (numeric-type-real-p num)
(numeric-type-real-p div))
(truncate-derive-type-rem num div)
*empty-type*))
(defoptimizer (truncate derive-type) ((number divisor))
(let ((quot (two-arg-derive-type number divisor
#'truncate-derive-type-quot-aux #'truncate))
(rem (two-arg-derive-type number divisor
#'truncate-derive-type-rem-aux #'rem)))
(when (and quot rem)
(make-values-type :required (list quot rem)))))
(defun ftruncate-derive-type-quot (number-type divisor-type)
;; The bounds are the same as for truncate. However, the first
;; result is a float of some type. We need to determine what that
;; type is. Basically it's the more contagious of the two types.
(let ((q-type (truncate-derive-type-quot number-type divisor-type))
(res-type (numeric-contagion number-type divisor-type)))
(make-numeric-type :class 'float
:format (numeric-type-format res-type)
:low (numeric-type-low q-type)
:high (numeric-type-high q-type))))
(defun ftruncate-derive-type-quot-aux (n d same-arg)
(declare (ignore same-arg))
(if (and (numeric-type-real-p n)
(numeric-type-real-p d))
(ftruncate-derive-type-quot n d)
*empty-type*))
(defoptimizer (ftruncate derive-type) ((number divisor))
(let ((quot
(two-arg-derive-type number divisor
#'ftruncate-derive-type-quot-aux #'ftruncate))
(rem (two-arg-derive-type number divisor
#'truncate-derive-type-rem-aux #'rem)))
(when (and quot rem)
(make-values-type :required (list quot rem)))))
(defun %unary-truncate-derive-type-aux (number)
(truncate-derive-type-quot number (specifier-type '(integer 1 1))))
(defoptimizer (%unary-truncate derive-type) ((number))
(one-arg-derive-type number
#'%unary-truncate-derive-type-aux
#'%unary-truncate))
;;; Define optimizers for FLOOR and CEILING.
(macrolet
((def (name q-name r-name)
(let ((q-aux (symbolicate q-name "-AUX"))
(r-aux (symbolicate r-name "-AUX")))
`(progn
;; Compute type of quotient (first) result.
(defun ,q-aux (number-type divisor-type)
(let* ((number-interval
(numeric-type->interval number-type))
(divisor-interval
(numeric-type->interval divisor-type))
(quot (,q-name (interval-div number-interval
divisor-interval))))
(specifier-type `(integer ,(or (interval-low quot) '*)
,(or (interval-high quot) '*)))))
;; Compute type of remainder.
(defun ,r-aux (number-type divisor-type)
(let* ((divisor-interval
(numeric-type->interval divisor-type))
(rem (,r-name divisor-interval))
(result-type (rem-result-type number-type divisor-type)))
(multiple-value-bind (class format)
(ecase result-type
(integer
(values 'integer nil))
(rational
(values 'rational nil))
((or single-float double-float #!+long-float long-float)
(values 'float result-type))
(float
(values 'float nil))
(real
(values nil nil)))
(when (member result-type '(float single-float double-float
#!+long-float long-float))
;; Make sure that the limits on the interval have
;; the right type.
(setf rem (interval-func (lambda (x)
(coerce x result-type))
rem)))
(make-numeric-type :class class
:format format
:low (interval-low rem)
:high (interval-high rem)))))
;; the optimizer itself
(defoptimizer (,name derive-type) ((number divisor))
(flet ((derive-q (n d same-arg)
(declare (ignore same-arg))
(if (and (numeric-type-real-p n)
(numeric-type-real-p d))
(,q-aux n d)
*empty-type*))
(derive-r (n d same-arg)
(declare (ignore same-arg))
(if (and (numeric-type-real-p n)
(numeric-type-real-p d))
(,r-aux n d)
*empty-type*)))
(let ((quot (two-arg-derive-type
number divisor #'derive-q #',name))
(rem (two-arg-derive-type
number divisor #'derive-r #'mod)))
(when (and quot rem)
(make-values-type :required (list quot rem))))))))))
(def floor floor-quotient-bound floor-rem-bound)
(def ceiling ceiling-quotient-bound ceiling-rem-bound))
;;; Define optimizers for FFLOOR and FCEILING
(macrolet ((def (name q-name r-name)
(let ((q-aux (symbolicate "F" q-name "-AUX"))
(r-aux (symbolicate r-name "-AUX")))
`(progn
;; Compute type of quotient (first) result.
(defun ,q-aux (number-type divisor-type)
(let* ((number-interval
(numeric-type->interval number-type))
(divisor-interval
(numeric-type->interval divisor-type))
(quot (,q-name (interval-div number-interval
divisor-interval)))
(res-type (numeric-contagion number-type
divisor-type)))
(make-numeric-type
:class (numeric-type-class res-type)
:format (numeric-type-format res-type)
:low (interval-low quot)
:high (interval-high quot))))
(defoptimizer (,name derive-type) ((number divisor))
(flet ((derive-q (n d same-arg)
(declare (ignore same-arg))
(if (and (numeric-type-real-p n)
(numeric-type-real-p d))
(,q-aux n d)
*empty-type*))
(derive-r (n d same-arg)
(declare (ignore same-arg))
(if (and (numeric-type-real-p n)
(numeric-type-real-p d))
(,r-aux n d)
*empty-type*)))
(let ((quot (two-arg-derive-type
number divisor #'derive-q #',name))
(rem (two-arg-derive-type
number divisor #'derive-r #'mod)))
(when (and quot rem)
(make-values-type :required (list quot rem))))))))))
(def ffloor floor-quotient-bound floor-rem-bound)
(def fceiling ceiling-quotient-bound ceiling-rem-bound))
;;; functions to compute the bounds on the quotient and remainder for
;;; the FLOOR function
(defun floor-quotient-bound (quot)
;; Take the floor of the quotient and then massage it into what we
;; need.
(let ((lo (interval-low quot))
(hi (interval-high quot)))
;; Take the floor of the lower bound. The result is always a
;; closed lower bound.
(setf lo (if lo
(floor (type-bound-number lo))
nil))
;; For the upper bound, we need to be careful.
(setf hi
(cond ((consp hi)
;; An open bound. We need to be careful here because
;; the floor of '(10.0) is 9, but the floor of
;; 10.0 is 10.
(multiple-value-bind (q r) (floor (first hi))
(if (zerop r)
(1- q)
q)))
(hi
;; A closed bound, so the answer is obvious.
(floor hi))
(t
hi)))
(make-interval :low lo :high hi)))
(defun floor-rem-bound (div)
;; The remainder depends only on the divisor. Try to get the
;; correct sign for the remainder if we can.
(case (interval-range-info div)
(+
;; The divisor is always positive.
(let ((rem (interval-abs div)))
(setf (interval-low rem) 0)
(when (and (numberp (interval-high rem))
(not (zerop (interval-high rem))))
;; The remainder never contains the upper bound. However,
;; watch out for the case where the high limit is zero!
(setf (interval-high rem) (list (interval-high rem))))
rem))
(-
;; The divisor is always negative.
(let ((rem (interval-neg (interval-abs div))))
(setf (interval-high rem) 0)
(when (numberp (interval-low rem))
;; The remainder never contains the lower bound.
(setf (interval-low rem) (list (interval-low rem))))
rem))
(otherwise
;; The divisor can be positive or negative. All bets off. The
;; magnitude of remainder is the maximum value of the divisor.
(let ((limit (type-bound-number (interval-high (interval-abs div)))))
;; The bound never reaches the limit, so make the interval open.
(make-interval :low (if limit
(list (- limit))
limit)
:high (list limit))))))
#| Test cases
(floor-quotient-bound (make-interval :low 0.3 :high 10.3))
=> #S(INTERVAL :LOW 0 :HIGH 10)
(floor-quotient-bound (make-interval :low 0.3 :high '(10.3)))
=> #S(INTERVAL :LOW 0 :HIGH 10)
(floor-quotient-bound (make-interval :low 0.3 :high 10))
=> #S(INTERVAL :LOW 0 :HIGH 10)
(floor-quotient-bound (make-interval :low 0.3 :high '(10)))
=> #S(INTERVAL :LOW 0 :HIGH 9)
(floor-quotient-bound (make-interval :low '(0.3) :high 10.3))
=> #S(INTERVAL :LOW 0 :HIGH 10)
(floor-quotient-bound (make-interval :low '(0.0) :high 10.3))
=> #S(INTERVAL :LOW 0 :HIGH 10)
(floor-quotient-bound (make-interval :low '(-1.3) :high 10.3))
=> #S(INTERVAL :LOW -2 :HIGH 10)
(floor-quotient-bound (make-interval :low '(-1.0) :high 10.3))
=> #S(INTERVAL :LOW -1 :HIGH 10)
(floor-quotient-bound (make-interval :low -1.0 :high 10.3))
=> #S(INTERVAL :LOW -1 :HIGH 10)
(floor-rem-bound (make-interval :low 0.3 :high 10.3))
=> #S(INTERVAL :LOW 0 :HIGH '(10.3))
(floor-rem-bound (make-interval :low 0.3 :high '(10.3)))
=> #S(INTERVAL :LOW 0 :HIGH '(10.3))
(floor-rem-bound (make-interval :low -10 :high -2.3))
#S(INTERVAL :LOW (-10) :HIGH 0)
(floor-rem-bound (make-interval :low 0.3 :high 10))
=> #S(INTERVAL :LOW 0 :HIGH '(10))
(floor-rem-bound (make-interval :low '(-1.3) :high 10.3))
=> #S(INTERVAL :LOW '(-10.3) :HIGH '(10.3))
(floor-rem-bound (make-interval :low '(-20.3) :high 10.3))
=> #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
|#
;;; same functions for CEILING
(defun ceiling-quotient-bound (quot)
;; Take the ceiling of the quotient and then massage it into what we
;; need.
(let ((lo (interval-low quot))
(hi (interval-high quot)))
;; Take the ceiling of the upper bound. The result is always a
;; closed upper bound.
(setf hi (if hi
(ceiling (type-bound-number hi))
nil))
;; For the lower bound, we need to be careful.
(setf lo
(cond ((consp lo)
;; An open bound. We need to be careful here because
;; the ceiling of '(10.0) is 11, but the ceiling of
;; 10.0 is 10.
(multiple-value-bind (q r) (ceiling (first lo))
(if (zerop r)
(1+ q)
q)))
(lo
;; A closed bound, so the answer is obvious.
(ceiling lo))
(t
lo)))
(make-interval :low lo :high hi)))
(defun ceiling-rem-bound (div)
;; The remainder depends only on the divisor. Try to get the
;; correct sign for the remainder if we can.
(case (interval-range-info div)
(+
;; Divisor is always positive. The remainder is negative.
(let ((rem (interval-neg (interval-abs div))))
(setf (interval-high rem) 0)
(when (and (numberp (interval-low rem))
(not (zerop (interval-low rem))))
;; The remainder never contains the upper bound. However,
;; watch out for the case when the upper bound is zero!
(setf (interval-low rem) (list (interval-low rem))))
rem))
(-
;; Divisor is always negative. The remainder is positive
(let ((rem (interval-abs div)))
(setf (interval-low rem) 0)
(when (numberp (interval-high rem))
;; The remainder never contains the lower bound.
(setf (interval-high rem) (list (interval-high rem))))
rem))
(otherwise
;; The divisor can be positive or negative. All bets off. The
;; magnitude of remainder is the maximum value of the divisor.
(let ((limit (type-bound-number (interval-high (interval-abs div)))))
;; The bound never reaches the limit, so make the interval open.
(make-interval :low (if limit
(list (- limit))
limit)
:high (list limit))))))
#| Test cases
(ceiling-quotient-bound (make-interval :low 0.3 :high 10.3))
=> #S(INTERVAL :LOW 1 :HIGH 11)
(ceiling-quotient-bound (make-interval :low 0.3 :high '(10.3)))
=> #S(INTERVAL :LOW 1 :HIGH 11)
(ceiling-quotient-bound (make-interval :low 0.3 :high 10))
=> #S(INTERVAL :LOW 1 :HIGH 10)
(ceiling-quotient-bound (make-interval :low 0.3 :high '(10)))
=> #S(INTERVAL :LOW 1 :HIGH 10)
(ceiling-quotient-bound (make-interval :low '(0.3) :high 10.3))
=> #S(INTERVAL :LOW 1 :HIGH 11)
(ceiling-quotient-bound (make-interval :low '(0.0) :high 10.3))
=> #S(INTERVAL :LOW 1 :HIGH 11)
(ceiling-quotient-bound (make-interval :low '(-1.3) :high 10.3))
=> #S(INTERVAL :LOW -1 :HIGH 11)
(ceiling-quotient-bound (make-interval :low '(-1.0) :high 10.3))
=> #S(INTERVAL :LOW 0 :HIGH 11)
(ceiling-quotient-bound (make-interval :low -1.0 :high 10.3))
=> #S(INTERVAL :LOW -1 :HIGH 11)
(ceiling-rem-bound (make-interval :low 0.3 :high 10.3))
=> #S(INTERVAL :LOW (-10.3) :HIGH 0)
(ceiling-rem-bound (make-interval :low 0.3 :high '(10.3)))
=> #S(INTERVAL :LOW 0 :HIGH '(10.3))
(ceiling-rem-bound (make-interval :low -10 :high -2.3))
=> #S(INTERVAL :LOW 0 :HIGH (10))
(ceiling-rem-bound (make-interval :low 0.3 :high 10))
=> #S(INTERVAL :LOW (-10) :HIGH 0)
(ceiling-rem-bound (make-interval :low '(-1.3) :high 10.3))
=> #S(INTERVAL :LOW (-10.3) :HIGH (10.3))
(ceiling-rem-bound (make-interval :low '(-20.3) :high 10.3))
=> #S(INTERVAL :LOW (-20.3) :HIGH (20.3))
|#
(defun truncate-quotient-bound (quot)
;; For positive quotients, truncate is exactly like floor. For
;; negative quotients, truncate is exactly like ceiling. Otherwise,
;; it's the union of the two pieces.
(case (interval-range-info quot)
(+
;; just like FLOOR
(floor-quotient-bound quot))
(-
;; just like CEILING
(ceiling-quotient-bound quot))
(otherwise
;; Split the interval into positive and negative pieces, compute
;; the result for each piece and put them back together.
(destructuring-bind (neg pos) (interval-split 0 quot t t)
(interval-merge-pair (ceiling-quotient-bound neg)
(floor-quotient-bound pos))))))
(defun truncate-rem-bound (num div)
;; This is significantly more complicated than FLOOR or CEILING. We
;; need both the number and the divisor to determine the range. The
;; basic idea is to split the ranges of NUM and DEN into positive
;; and negative pieces and deal with each of the four possibilities
;; in turn.
(case (interval-range-info num)
(+
(case (interval-range-info div)
(+
(floor-rem-bound div))
(-
(ceiling-rem-bound div))
(otherwise
(destructuring-bind (neg pos) (interval-split 0 div t t)
(interval-merge-pair (truncate-rem-bound num neg)
(truncate-rem-bound num pos))))))
(-
(case (interval-range-info div)
(+
(ceiling-rem-bound div))
(-
(floor-rem-bound div))
(otherwise
(destructuring-bind (neg pos) (interval-split 0 div t t)
(interval-merge-pair (truncate-rem-bound num neg)
(truncate-rem-bound num pos))))))
(otherwise
(destructuring-bind (neg pos) (interval-split 0 num t t)
(interval-merge-pair (truncate-rem-bound neg div)
(truncate-rem-bound pos div))))))
) ; PROGN
;;; Derive useful information about the range. Returns three values:
;;; - '+ if its positive, '- negative, or nil if it overlaps 0.
;;; - The abs of the minimal value (i.e. closest to 0) in the range.
;;; - The abs of the maximal value if there is one, or nil if it is
;;; unbounded.
(defun numeric-range-info (low high)
(cond ((and low (not (minusp low)))
(values '+ low high))
((and high (not (plusp high)))
(values '- (- high) (if low (- low) nil)))
(t
(values nil 0 (and low high (max (- low) high))))))
(defun integer-truncate-derive-type
(number-low number-high divisor-low divisor-high)
;; The result cannot be larger in magnitude than the number, but the
;; sign might change. If we can determine the sign of either the
;; number or the divisor, we can eliminate some of the cases.
(multiple-value-bind (number-sign number-min number-max)
(numeric-range-info number-low number-high)
(multiple-value-bind (divisor-sign divisor-min divisor-max)
(numeric-range-info divisor-low divisor-high)
(when (and divisor-max (zerop divisor-max))
;; We've got a problem: guaranteed division by zero.
(return-from integer-truncate-derive-type t))
(when (zerop divisor-min)
;; We'll assume that they aren't going to divide by zero.
(incf divisor-min))
(cond ((and number-sign divisor-sign)
;; We know the sign of both.
(if (eq number-sign divisor-sign)
;; Same sign, so the result will be positive.
`(integer ,(if divisor-max
(truncate number-min divisor-max)
0)
,(if number-max
(truncate number-max divisor-min)
'*))
;; Different signs, the result will be negative.
`(integer ,(if number-max
(- (truncate number-max divisor-min))
'*)
,(if divisor-max
(- (truncate number-min divisor-max))
0))))
((eq divisor-sign '+)
;; The divisor is positive. Therefore, the number will just
;; become closer to zero.
`(integer ,(if number-low
(truncate number-low divisor-min)
'*)
,(if number-high
(truncate number-high divisor-min)
'*)))
((eq divisor-sign '-)
;; The divisor is negative. Therefore, the absolute value of
;; the number will become closer to zero, but the sign will also
;; change.
`(integer ,(if number-high
(- (truncate number-high divisor-min))
'*)
,(if number-low
(- (truncate number-low divisor-min))
'*)))
;; The divisor could be either positive or negative.
(number-max
;; The number we are dividing has a bound. Divide that by the
;; smallest posible divisor.
(let ((bound (truncate number-max divisor-min)))
`(integer ,(- bound) ,bound)))
(t
;; The number we are dividing is unbounded, so we can't tell
;; anything about the result.
`integer)))))
#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defun integer-rem-derive-type
(number-low number-high divisor-low divisor-high)
(if (and divisor-low divisor-high)
;; We know the range of the divisor, and the remainder must be
;; smaller than the divisor. We can tell the sign of the
;; remainer if we know the sign of the number.
(let ((divisor-max (1- (max (abs divisor-low) (abs divisor-high)))))
`(integer ,(if (or (null number-low)
(minusp number-low))
(- divisor-max)
0)
,(if (or (null number-high)
(plusp number-high))
divisor-max
0)))
;; The divisor is potentially either very positive or very
;; negative. Therefore, the remainer is unbounded, but we might
;; be able to tell something about the sign from the number.
`(integer ,(if (and number-low (not (minusp number-low)))
;; The number we are dividing is positive.
;; Therefore, the remainder must be positive.
0
'*)
,(if (and number-high (not (plusp number-high)))
;; The number we are dividing is negative.
;; Therefore, the remainder must be negative.
0
'*))))
#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defoptimizer (random derive-type) ((bound &optional state))
(let ((type (continuation-type bound)))
(when (numeric-type-p type)
(let ((class (numeric-type-class type))
(high (numeric-type-high type))
(format (numeric-type-format type)))
(make-numeric-type
:class class
:format format
:low (coerce 0 (or format class 'real))
:high (cond ((not high) nil)
((eq class 'integer) (max (1- high) 0))
((or (consp high) (zerop high)) high)
(t `(,high))))))))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defun random-derive-type-aux (type)
(let ((class (numeric-type-class type))
(high (numeric-type-high type))
(format (numeric-type-format type)))
(make-numeric-type
:class class
:format format
:low (coerce 0 (or format class 'real))
:high (cond ((not high) nil)
((eq class 'integer) (max (1- high) 0))
((or (consp high) (zerop high)) high)
(t `(,high))))))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defoptimizer (random derive-type) ((bound &optional state))
(one-arg-derive-type bound #'random-derive-type-aux nil))
;;;; DERIVE-TYPE methods for LOGAND, LOGIOR, and friends
;;; Return the maximum number of bits an integer of the supplied type
;;; can take up, or NIL if it is unbounded. The second (third) value
;;; is T if the integer can be positive (negative) and NIL if not.
;;; Zero counts as positive.
(defun integer-type-length (type)
(if (numeric-type-p type)
(let ((min (numeric-type-low type))
(max (numeric-type-high type)))
(values (and min max (max (integer-length min) (integer-length max)))
(or (null max) (not (minusp max)))
(or (null min) (minusp min))))
(values nil t t)))
(defun logand-derive-type-aux (x y &optional same-leaf)
(declare (ignore same-leaf))
(multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
(declare (ignore x-pos))
(multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
(declare (ignore y-pos))
(if (not x-neg)
;; X must be positive.
(if (not y-neg)
;; They must both be positive.
(cond ((or (null x-len) (null y-len))
(specifier-type 'unsigned-byte))
((or (zerop x-len) (zerop y-len))
(specifier-type '(integer 0 0)))
(t
(specifier-type `(unsigned-byte ,(min x-len y-len)))))
;; X is positive, but Y might be negative.
(cond ((null x-len)
(specifier-type 'unsigned-byte))
((zerop x-len)
(specifier-type '(integer 0 0)))
(t
(specifier-type `(unsigned-byte ,x-len)))))
;; X might be negative.
(if (not y-neg)
;; Y must be positive.
(cond ((null y-len)
(specifier-type 'unsigned-byte))
((zerop y-len)
(specifier-type '(integer 0 0)))
(t
(specifier-type
`(unsigned-byte ,y-len))))
;; Either might be negative.
(if (and x-len y-len)
;; The result is bounded.
(specifier-type `(signed-byte ,(1+ (max x-len y-len))))
;; We can't tell squat about the result.
(specifier-type 'integer)))))))
(defun logior-derive-type-aux (x y &optional same-leaf)
(declare (ignore same-leaf))
(multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
(multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
(cond
((and (not x-neg) (not y-neg))
;; Both are positive.
(if (and x-len y-len (zerop x-len) (zerop y-len))
(specifier-type '(integer 0 0))
(specifier-type `(unsigned-byte ,(if (and x-len y-len)
(max x-len y-len)
'*)))))
((not x-pos)
;; X must be negative.
(if (not y-pos)
;; Both are negative. The result is going to be negative
;; and be the same length or shorter than the smaller.
(if (and x-len y-len)
;; It's bounded.
(specifier-type `(integer ,(ash -1 (min x-len y-len)) -1))
;; It's unbounded.
(specifier-type '(integer * -1)))
;; X is negative, but we don't know about Y. The result
;; will be negative, but no more negative than X.
(specifier-type
`(integer ,(or (numeric-type-low x) '*)
-1))))
(t
;; X might be either positive or negative.
(if (not y-pos)
;; But Y is negative. The result will be negative.
(specifier-type
`(integer ,(or (numeric-type-low y) '*)
-1))
;; We don't know squat about either. It won't get any bigger.
(if (and x-len y-len)
;; Bounded.
(specifier-type `(signed-byte ,(1+ (max x-len y-len))))
;; Unbounded.
(specifier-type 'integer))))))))
(defun logxor-derive-type-aux (x y &optional same-leaf)
(declare (ignore same-leaf))
(multiple-value-bind (x-len x-pos x-neg) (integer-type-length x)
(multiple-value-bind (y-len y-pos y-neg) (integer-type-length y)
(cond
((or (and (not x-neg) (not y-neg))
(and (not x-pos) (not y-pos)))
;; Either both are negative or both are positive. The result
;; will be positive, and as long as the longer.
(if (and x-len y-len (zerop x-len) (zerop y-len))
(specifier-type '(integer 0 0))
(specifier-type `(unsigned-byte ,(if (and x-len y-len)
(max x-len y-len)
'*)))))
((or (and (not x-pos) (not y-neg))
(and (not y-neg) (not y-pos)))
;; Either X is negative and Y is positive of vice-versa. The
;; result will be negative.
(specifier-type `(integer ,(if (and x-len y-len)
(ash -1 (max x-len y-len))
'*)
-1)))
;; We can't tell what the sign of the result is going to be.
;; All we know is that we don't create new bits.
((and x-len y-len)
(specifier-type `(signed-byte ,(1+ (max x-len y-len)))))
(t
(specifier-type 'integer))))))
(macrolet ((deffrob (logfcn)
(let ((fcn-aux (symbolicate logfcn "-DERIVE-TYPE-AUX")))
`(defoptimizer (,logfcn derive-type) ((x y))
(two-arg-derive-type x y #',fcn-aux #',logfcn)))))
(deffrob logand)
(deffrob logior)
(deffrob logxor))
;;;; miscellaneous derive-type methods
(defoptimizer (integer-length derive-type) ((x))
(let ((x-type (continuation-type x)))
(when (and (numeric-type-p x-type)
(csubtypep x-type (specifier-type 'integer)))
;; If the X is of type (INTEGER LO HI), then the INTEGER-LENGTH
;; of X is (INTEGER (MIN lo hi) (MAX lo hi), basically. Be
;; careful about LO or HI being NIL, though. Also, if 0 is
;; contained in X, the lower bound is obviously 0.
(flet ((null-or-min (a b)
(and a b (min (integer-length a)
(integer-length b))))
(null-or-max (a b)
(and a b (max (integer-length a)
(integer-length b)))))
(let* ((min (numeric-type-low x-type))
(max (numeric-type-high x-type))
(min-len (null-or-min min max))
(max-len (null-or-max min max)))
(when (ctypep 0 x-type)
(setf min-len 0))
(specifier-type `(integer ,(or min-len '*) ,(or max-len '*))))))))
(defoptimizer (code-char derive-type) ((code))
(specifier-type 'base-char))
(defoptimizer (values derive-type) ((&rest values))
(values-specifier-type
`(values ,@(mapcar (lambda (x)
(type-specifier (continuation-type x)))
values))))
;;;; byte operations
;;;;
;;;; We try to turn byte operations into simple logical operations.
;;;; First, we convert byte specifiers into separate size and position
;;;; arguments passed to internal %FOO functions. We then attempt to
;;;; transform the %FOO functions into boolean operations when the
;;;; size and position are constant and the operands are fixnums.
(macrolet (;; Evaluate body with SIZE-VAR and POS-VAR bound to
;; expressions that evaluate to the SIZE and POSITION of
;; the byte-specifier form SPEC. We may wrap a let around
;; the result of the body to bind some variables.
;;
;; If the spec is a BYTE form, then bind the vars to the
;; subforms. otherwise, evaluate SPEC and use the BYTE-SIZE
;; and BYTE-POSITION. The goal of this transformation is to
;; avoid consing up byte specifiers and then immediately
;; throwing them away.
(with-byte-specifier ((size-var pos-var spec) &body body)
(once-only ((spec `(macroexpand ,spec))
(temp '(gensym)))
`(if (and (consp ,spec)
(eq (car ,spec) 'byte)
(= (length ,spec) 3))
(let ((,size-var (second ,spec))
(,pos-var (third ,spec)))
,@body)
(let ((,size-var `(byte-size ,,temp))
(,pos-var `(byte-position ,,temp)))
`(let ((,,temp ,,spec))
,,@body))))))
(define-source-transform ldb (spec int)
(with-byte-specifier (size pos spec)
`(%ldb ,size ,pos ,int)))
(define-source-transform dpb (newbyte spec int)
(with-byte-specifier (size pos spec)
`(%dpb ,newbyte ,size ,pos ,int)))
(define-source-transform mask-field (spec int)
(with-byte-specifier (size pos spec)
`(%mask-field ,size ,pos ,int)))
(define-source-transform deposit-field (newbyte spec int)
(with-byte-specifier (size pos spec)
`(%deposit-field ,newbyte ,size ,pos ,int))))
(defoptimizer (%ldb derive-type) ((size posn num))
(let ((size (continuation-type size)))
(if (and (numeric-type-p size)
(csubtypep size (specifier-type 'integer)))
(let ((size-high (numeric-type-high size)))
(if (and size-high (<= size-high sb!vm:n-word-bits))
(specifier-type `(unsigned-byte ,size-high))
(specifier-type 'unsigned-byte)))
*universal-type*)))
(defoptimizer (%mask-field derive-type) ((size posn num))
(let ((size (continuation-type size))
(posn (continuation-type posn)))
(if (and (numeric-type-p size)
(csubtypep size (specifier-type 'integer))
(numeric-type-p posn)
(csubtypep posn (specifier-type 'integer)))
(let ((size-high (numeric-type-high size))
(posn-high (numeric-type-high posn)))
(if (and size-high posn-high
(<= (+ size-high posn-high) sb!vm:n-word-bits))
(specifier-type `(unsigned-byte ,(+ size-high posn-high)))
(specifier-type 'unsigned-byte)))
*universal-type*)))
(defoptimizer (%dpb derive-type) ((newbyte size posn int))
(let ((size (continuation-type size))
(posn (continuation-type posn))
(int (continuation-type int)))
(if (and (numeric-type-p size)
(csubtypep size (specifier-type 'integer))
(numeric-type-p posn)
(csubtypep posn (specifier-type 'integer))
(numeric-type-p int)
(csubtypep int (specifier-type 'integer)))
(let ((size-high (numeric-type-high size))
(posn-high (numeric-type-high posn))
(high (numeric-type-high int))
(low (numeric-type-low int)))
(if (and size-high posn-high high low
(<= (+ size-high posn-high) sb!vm:n-word-bits))
(specifier-type
(list (if (minusp low) 'signed-byte 'unsigned-byte)
(max (integer-length high)
(integer-length low)
(+ size-high posn-high))))
*universal-type*))
*universal-type*)))
(defoptimizer (%deposit-field derive-type) ((newbyte size posn int))
(let ((size (continuation-type size))
(posn (continuation-type posn))
(int (continuation-type int)))
(if (and (numeric-type-p size)
(csubtypep size (specifier-type 'integer))
(numeric-type-p posn)
(csubtypep posn (specifier-type 'integer))
(numeric-type-p int)
(csubtypep int (specifier-type 'integer)))
(let ((size-high (numeric-type-high size))
(posn-high (numeric-type-high posn))
(high (numeric-type-high int))
(low (numeric-type-low int)))
(if (and size-high posn-high high low
(<= (+ size-high posn-high) sb!vm:n-word-bits))
(specifier-type
(list (if (minusp low) 'signed-byte 'unsigned-byte)
(max (integer-length high)
(integer-length low)
(+ size-high posn-high))))
*universal-type*))
*universal-type*)))
(deftransform %ldb ((size posn int)
(fixnum fixnum integer)
(unsigned-byte #.sb!vm:n-word-bits))
"convert to inline logical operations"
`(logand (ash int (- posn))
(ash ,(1- (ash 1 sb!vm:n-word-bits))
(- size ,sb!vm:n-word-bits))))
(deftransform %mask-field ((size posn int)
(fixnum fixnum integer)
(unsigned-byte #.sb!vm:n-word-bits))
"convert to inline logical operations"
`(logand int
(ash (ash ,(1- (ash 1 sb!vm:n-word-bits))
(- size ,sb!vm:n-word-bits))
posn)))
;;; Note: for %DPB and %DEPOSIT-FIELD, we can't use
;;; (OR (SIGNED-BYTE N) (UNSIGNED-BYTE N))
;;; as the result type, as that would allow result types that cover
;;; the range -2^(n-1) .. 1-2^n, instead of allowing result types of
;;; (UNSIGNED-BYTE N) and result types of (SIGNED-BYTE N).
(deftransform %dpb ((new size posn int)
*
(unsigned-byte #.sb!vm:n-word-bits))
"convert to inline logical operations"
`(let ((mask (ldb (byte size 0) -1)))
(logior (ash (logand new mask) posn)
(logand int (lognot (ash mask posn))))))
(deftransform %dpb ((new size posn int)
*
(signed-byte #.sb!vm:n-word-bits))
"convert to inline logical operations"
`(let ((mask (ldb (byte size 0) -1)))
(logior (ash (logand new mask) posn)
(logand int (lognot (ash mask posn))))))
(deftransform %deposit-field ((new size posn int)
*
(unsigned-byte #.sb!vm:n-word-bits))
"convert to inline logical operations"
`(let ((mask (ash (ldb (byte size 0) -1) posn)))
(logior (logand new mask)
(logand int (lognot mask)))))
(deftransform %deposit-field ((new size posn int)
*
(signed-byte #.sb!vm:n-word-bits))
"convert to inline logical operations"
`(let ((mask (ash (ldb (byte size 0) -1) posn)))
(logior (logand new mask)
(logand int (lognot mask)))))
;;; miscellanous numeric transforms
;;; If a constant appears as the first arg, swap the args.
(deftransform commutative-arg-swap ((x y) * * :defun-only t :node node)
(if (and (constant-continuation-p x)
(not (constant-continuation-p y)))
`(,(continuation-fun-name (basic-combination-fun node))
y
,(continuation-value x))
(give-up-ir1-transform)))
(dolist (x '(= char= + * logior logand logxor))
(%deftransform x '(function * *) #'commutative-arg-swap
"place constant arg last"))
;;; Handle the case of a constant BOOLE-CODE.
(deftransform boole ((op x y) * *)
"convert to inline logical operations"
(unless (constant-continuation-p op)
(give-up-ir1-transform "BOOLE code is not a constant."))
(let ((control (continuation-value op)))
(case control
(#.boole-clr 0)
(#.boole-set -1)
(#.boole-1 'x)
(#.boole-2 'y)
(#.boole-c1 '(lognot x))
(#.boole-c2 '(lognot y))
(#.boole-and '(logand x y))
(#.boole-ior '(logior x y))
(#.boole-xor '(logxor x y))
(#.boole-eqv '(logeqv x y))
(#.boole-nand '(lognand x y))
(#.boole-nor '(lognor x y))
(#.boole-andc1 '(logandc1 x y))
(#.boole-andc2 '(logandc2 x y))
(#.boole-orc1 '(logorc1 x y))
(#.boole-orc2 '(logorc2 x y))
(t
(abort-ir1-transform "~S is an illegal control arg to BOOLE."
control)))))
;;;; converting special case multiply/divide to shifts
;;; If arg is a constant power of two, turn * into a shift.
(deftransform * ((x y) (integer integer) *)
"convert x*2^k to shift"
(unless (constant-continuation-p y)
(give-up-ir1-transform))
(let* ((y (continuation-value y))
(y-abs (abs y))
(len (1- (integer-length y-abs))))
(unless (= y-abs (ash 1 len))
(give-up-ir1-transform))
(if (minusp y)
`(- (ash x ,len))
`(ash x ,len))))
;;; If both arguments and the result are (UNSIGNED-BYTE 32), try to
;;; come up with a ``better'' multiplication using multiplier
;;; recoding. There are two different ways the multiplier can be
;;; recoded. The more obvious is to shift X by the correct amount for
;;; each bit set in Y and to sum the results. But if there is a string
;;; of bits that are all set, you can add X shifted by one more then
;;; the bit position of the first set bit and subtract X shifted by
;;; the bit position of the last set bit. We can't use this second
;;; method when the high order bit is bit 31 because shifting by 32
;;; doesn't work too well.
(deftransform * ((x y)
((unsigned-byte 32) (unsigned-byte 32))
(unsigned-byte 32))
"recode as shift and add"
(unless (constant-continuation-p y)
(give-up-ir1-transform))
(let ((y (continuation-value y))
(result nil)
(first-one nil))
(labels ((tub32 (x) `(truly-the (unsigned-byte 32) ,x))
(add (next-factor)
(setf result
(tub32
(if result
`(+ ,result ,(tub32 next-factor))
next-factor)))))
(declare (inline add))
(dotimes (bitpos 32)
(if first-one
(when (not (logbitp bitpos y))
(add (if (= (1+ first-one) bitpos)
;; There is only a single bit in the string.
`(ash x ,first-one)
;; There are at least two.
`(- ,(tub32 `(ash x ,bitpos))
,(tub32 `(ash x ,first-one)))))
(setf first-one nil))
(when (logbitp bitpos y)
(setf first-one bitpos))))
(when first-one
(cond ((= first-one 31))
((= first-one 30)
(add '(ash x 30)))
(t
(add `(- ,(tub32 '(ash x 31)) ,(tub32 `(ash x ,first-one))))))
(add '(ash x 31))))
(or result 0)))
;;; If arg is a constant power of two, turn FLOOR into a shift and
;;; mask. If CEILING, add in (1- (ABS Y)), do FLOOR and correct a
;;; remainder.
(flet ((frob (y ceil-p)
(unless (constant-continuation-p y)
(give-up-ir1-transform))
(let* ((y (continuation-value y))
(y-abs (abs y))
(len (1- (integer-length y-abs))))
(unless (= y-abs (ash 1 len))
(give-up-ir1-transform))
(let ((shift (- len))
(mask (1- y-abs))
(delta (if ceil-p (* (signum y) (1- y-abs)) 0)))
`(let ((x (+ x ,delta)))
,(if (minusp y)
`(values (ash (- x) ,shift)
(- (- (logand (- x) ,mask)) ,delta))
`(values (ash x ,shift)
(- (logand x ,mask) ,delta))))))))
(deftransform floor ((x y) (integer integer) *)
"convert division by 2^k to shift"
(frob y nil))
(deftransform ceiling ((x y) (integer integer) *)
"convert division by 2^k to shift"
(frob y t)))
;;; Do the same for MOD.
(deftransform mod ((x y) (integer integer) *)
"convert remainder mod 2^k to LOGAND"
(unless (constant-continuation-p y)
(give-up-ir1-transform))
(let* ((y (continuation-value y))
(y-abs (abs y))
(len (1- (integer-length y-abs))))
(unless (= y-abs (ash 1 len))
(give-up-ir1-transform))
(let ((mask (1- y-abs)))
(if (minusp y)
`(- (logand (- x) ,mask))
`(logand x ,mask)))))
;;; If arg is a constant power of two, turn TRUNCATE into a shift and mask.
(deftransform truncate ((x y) (integer integer))
"convert division by 2^k to shift"
(unless (constant-continuation-p y)
(give-up-ir1-transform))
(let* ((y (continuation-value y))
(y-abs (abs y))
(len (1- (integer-length y-abs))))
(unless (= y-abs (ash 1 len))
(give-up-ir1-transform))
(let* ((shift (- len))
(mask (1- y-abs)))
`(if (minusp x)
(values ,(if (minusp y)
`(ash (- x) ,shift)
`(- (ash (- x) ,shift)))
(- (logand (- x) ,mask)))
(values ,(if (minusp y)
`(- (ash (- x) ,shift))
`(ash x ,shift))
(logand x ,mask))))))
;;; And the same for REM.
(deftransform rem ((x y) (integer integer) *)
"convert remainder mod 2^k to LOGAND"
(unless (constant-continuation-p y)
(give-up-ir1-transform))
(let* ((y (continuation-value y))
(y-abs (abs y))
(len (1- (integer-length y-abs))))
(unless (= y-abs (ash 1 len))
(give-up-ir1-transform))
(let ((mask (1- y-abs)))
`(if (minusp x)
(- (logand (- x) ,mask))
(logand x ,mask)))))
;;;; arithmetic and logical identity operation elimination
;;; Flush calls to various arith functions that convert to the
;;; identity function or a constant.
(macrolet ((def (name identity result)
`(deftransform ,name ((x y) (* (constant-arg (member ,identity))) *)
"fold identity operations"
',result)))
(def ash 0 x)
(def logand -1 x)
(def logand 0 0)
(def logior 0 x)
(def logior -1 -1)
(def logxor -1 (lognot x))
(def logxor 0 x))
;;; These are restricted to rationals, because (- 0 0.0) is 0.0, not -0.0, and
;;; (* 0 -4.0) is -0.0.
(deftransform - ((x y) ((constant-arg (member 0)) rational) *)
"convert (- 0 x) to negate"
'(%negate y))
(deftransform * ((x y) (rational (constant-arg (member 0))) *)
"convert (* x 0) to 0"
0)
;;; Return T if in an arithmetic op including continuations X and Y,
;;; the result type is not affected by the type of X. That is, Y is at
;;; least as contagious as X.
#+nil
(defun not-more-contagious (x y)
(declare (type continuation x y))
(let ((x (continuation-type x))
(y (continuation-type y)))
(values (type= (numeric-contagion x y)
(numeric-contagion y y)))))
;;; Patched version by Raymond Toy. dtc: Should be safer although it
;;; XXX needs more work as valid transforms are missed; some cases are
;;; specific to particular transform functions so the use of this
;;; function may need a re-think.
(defun not-more-contagious (x y)
(declare (type continuation x y))
(flet ((simple-numeric-type (num)
(and (numeric-type-p num)
;; Return non-NIL if NUM is integer, rational, or a float
;; of some type (but not FLOAT)
(case (numeric-type-class num)
((integer rational)
t)
(float
(numeric-type-format num))
(t
nil)))))
(let ((x (continuation-type x))
(y (continuation-type y)))
(if (and (simple-numeric-type x)
(simple-numeric-type y))
(values (type= (numeric-contagion x y)
(numeric-contagion y y)))))))
;;; Fold (+ x 0).
;;;
;;; If y is not constant, not zerop, or is contagious, or a positive
;;; float +0.0 then give up.
(deftransform + ((x y) (t (constant-arg t)) *)
"fold zero arg"
(let ((val (continuation-value y)))
(unless (and (zerop val)
(not (and (floatp val) (plusp (float-sign val))))
(not-more-contagious y x))
(give-up-ir1-transform)))
'x)
;;; Fold (- x 0).
;;;
;;; If y is not constant, not zerop, or is contagious, or a negative
;;; float -0.0 then give up.
(deftransform - ((x y) (t (constant-arg t)) *)
"fold zero arg"
(let ((val (continuation-value y)))
(unless (and (zerop val)
(not (and (floatp val) (minusp (float-sign val))))
(not-more-contagious y x))
(give-up-ir1-transform)))
'x)
;;; Fold (OP x +/-1)
(macrolet ((def (name result minus-result)
`(deftransform ,name ((x y) (t (constant-arg real)) *)
"fold identity operations"
(let ((val (continuation-value y)))
(unless (and (= (abs val) 1)
(not-more-contagious y x))
(give-up-ir1-transform))
(if (minusp val) ',minus-result ',result)))))
(def * x (%negate x))
(def / x (%negate x))
(def expt x (/ 1 x)))
;;; Fold (expt x n) into multiplications for small integral values of
;;; N; convert (expt x 1/2) to sqrt.
(deftransform expt ((x y) (t (constant-arg real)) *)
"recode as multiplication or sqrt"
(let ((val (continuation-value y)))
;; If Y would cause the result to be promoted to the same type as
;; Y, we give up. If not, then the result will be the same type
;; as X, so we can replace the exponentiation with simple
;; multiplication and division for small integral powers.
(unless (not-more-contagious y x)
(give-up-ir1-transform))
(cond ((zerop val) '(float 1 x))
((= val 2) '(* x x))
((= val -2) '(/ (* x x)))
((= val 3) '(* x x x))
((= val -3) '(/ (* x x x)))
((= val 1/2) '(sqrt x))
((= val -1/2) '(/ (sqrt x)))
(t (give-up-ir1-transform)))))
;;; KLUDGE: Shouldn't (/ 0.0 0.0), etc. cause exceptions in these
;;; transformations?
;;; Perhaps we should have to prove that the denominator is nonzero before
;;; doing them? -- WHN 19990917
(macrolet ((def (name)
`(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
*)
"fold zero arg"
0)))
(def ash)
(def /))
(macrolet ((def (name)
`(deftransform ,name ((x y) ((constant-arg (integer 0 0)) integer)
*)
"fold zero arg"
'(values 0 0))))
(def truncate)
(def round)
(def floor)
(def ceiling))
;;;; character operations
(deftransform char-equal ((a b) (base-char base-char))
"open code"
'(let* ((ac (char-code a))
(bc (char-code b))
(sum (logxor ac bc)))
(or (zerop sum)
(when (eql sum #x20)
(let ((sum (+ ac bc)))
(and (> sum 161) (< sum 213)))))))
(deftransform char-upcase ((x) (base-char))
"open code"
'(let ((n-code (char-code x)))
(if (and (> n-code #o140) ; Octal 141 is #\a.
(< n-code #o173)) ; Octal 172 is #\z.
(code-char (logxor #x20 n-code))
x)))
(deftransform char-downcase ((x) (base-char))
"open code"
'(let ((n-code (char-code x)))
(if (and (> n-code 64) ; 65 is #\A.
(< n-code 91)) ; 90 is #\Z.
(code-char (logxor #x20 n-code))
x)))
;;;; equality predicate transforms
;;; Return true if X and Y are continuations whose only use is a
;;; reference to the same leaf, and the value of the leaf cannot
;;; change.
(defun same-leaf-ref-p (x y)
(declare (type continuation x y))
(let ((x-use (continuation-use x))
(y-use (continuation-use y)))
(and (ref-p x-use)
(ref-p y-use)
(eq (ref-leaf x-use) (ref-leaf y-use))
(constant-reference-p x-use))))
;;; If X and Y are the same leaf, then the result is true. Otherwise,
;;; if there is no intersection between the types of the arguments,
;;; then the result is definitely false.
(deftransform simple-equality-transform ((x y) * *
:defun-only t)
(cond ((same-leaf-ref-p x y)
t)
((not (types-equal-or-intersect (continuation-type x)
(continuation-type y)))
nil)
(t
(give-up-ir1-transform))))
(macrolet ((def (x)
`(%deftransform ',x '(function * *) #'simple-equality-transform)))
(def eq)
(def char=)
(def equal))
;;; This is similar to SIMPLE-EQUALITY-PREDICATE, except that we also
;;; try to convert to a type-specific predicate or EQ:
;;; -- If both args are characters, convert to CHAR=. This is better than
;;; just converting to EQ, since CHAR= may have special compilation
;;; strategies for non-standard representations, etc.
;;; -- If either arg is definitely not a number, then we can compare
;;; with EQ.
;;; -- Otherwise, we try to put the arg we know more about second. If X
;;; is constant then we put it second. If X is a subtype of Y, we put
;;; it second. These rules make it easier for the back end to match
;;; these interesting cases.
;;; -- If Y is a fixnum, then we quietly pass because the back end can
;;; handle that case, otherwise give an efficiency note.
(deftransform eql ((x y) * *)
"convert to simpler equality predicate"
(let ((x-type (continuation-type x))
(y-type (continuation-type y))
(char-type (specifier-type 'character))
(number-type (specifier-type 'number)))
(cond ((same-leaf-ref-p x y)
t)
((not (types-equal-or-intersect x-type y-type))
nil)
((and (csubtypep x-type char-type)
(csubtypep y-type char-type))
'(char= x y))
((or (not (types-equal-or-intersect x-type number-type))
(not (types-equal-or-intersect y-type number-type)))
'(eq x y))
((and (not (constant-continuation-p y))
(or (constant-continuation-p x)
(and (csubtypep x-type y-type)
(not (csubtypep y-type x-type)))))
'(eql y x))
(t
(give-up-ir1-transform)))))
;;; Convert to EQL if both args are rational and complexp is specified
;;; and the same for both.
(deftransform = ((x y) * *)
"open code"
(let ((x-type (continuation-type x))
(y-type (continuation-type y)))
(if (and (csubtypep x-type (specifier-type 'number))
(csubtypep y-type (specifier-type 'number)))
(cond ((or (and (csubtypep x-type (specifier-type 'float))
(csubtypep y-type (specifier-type 'float)))
(and (csubtypep x-type (specifier-type '(complex float)))
(csubtypep y-type (specifier-type '(complex float)))))
;; They are both floats. Leave as = so that -0.0 is
;; handled correctly.
(give-up-ir1-transform))
((or (and (csubtypep x-type (specifier-type 'rational))
(csubtypep y-type (specifier-type 'rational)))
(and (csubtypep x-type
(specifier-type '(complex rational)))
(csubtypep y-type
(specifier-type '(complex rational)))))
;; They are both rationals and complexp is the same.
;; Convert to EQL.
'(eql x y))
(t
(give-up-ir1-transform
"The operands might not be the same type.")))
(give-up-ir1-transform
"The operands might not be the same type."))))
;;; If CONT's type is a numeric type, then return the type, otherwise
;;; GIVE-UP-IR1-TRANSFORM.
(defun numeric-type-or-lose (cont)
(declare (type continuation cont))
(let ((res (continuation-type cont)))
(unless (numeric-type-p res) (give-up-ir1-transform))
res))
;;; See whether we can statically determine (< X Y) using type
;;; information. If X's high bound is < Y's low, then X < Y.
;;; Similarly, if X's low is >= to Y's high, the X >= Y (so return
;;; NIL). If not, at least make sure any constant arg is second.
;;;
;;; FIXME: Why should constant argument be second? It would be nice to
;;; find out and explain.
#+sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defun ir1-transform-< (x y first second inverse)
(if (same-leaf-ref-p x y)
nil
(let* ((x-type (numeric-type-or-lose x))
(x-lo (numeric-type-low x-type))
(x-hi (numeric-type-high x-type))
(y-type (numeric-type-or-lose y))
(y-lo (numeric-type-low y-type))
(y-hi (numeric-type-high y-type)))
(cond ((and x-hi y-lo (< x-hi y-lo))
t)
((and y-hi x-lo (>= x-lo y-hi))
nil)
((and (constant-continuation-p first)
(not (constant-continuation-p second)))
`(,inverse y x))
(t
(give-up-ir1-transform))))))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(defun ir1-transform-< (x y first second inverse)
(if (same-leaf-ref-p x y)
nil
(let ((xi (numeric-type->interval (numeric-type-or-lose x)))
(yi (numeric-type->interval (numeric-type-or-lose y))))
(cond ((interval-< xi yi)
t)
((interval->= xi yi)
nil)
((and (constant-continuation-p first)
(not (constant-continuation-p second)))
`(,inverse y x))
(t
(give-up-ir1-transform))))))
(deftransform < ((x y) (integer integer) *)
(ir1-transform-< x y x y '>))
(deftransform > ((x y) (integer integer) *)
(ir1-transform-< y x x y '<))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(deftransform < ((x y) (float float) *)
(ir1-transform-< x y x y '>))
#-sb-xc-host ; (See CROSS-FLOAT-INFINITY-KLUDGE.)
(deftransform > ((x y) (float float) *)
(ir1-transform-< y x x y '<))
;;;; converting N-arg comparisons
;;;;
;;;; We convert calls to N-arg comparison functions such as < into
;;;; two-arg calls. This transformation is enabled for all such
;;;; comparisons in this file. If any of these predicates are not
;;;; open-coded, then the transformation should be removed at some
;;;; point to avoid pessimization.
;;; This function is used for source transformation of N-arg
;;; comparison functions other than inequality. We deal both with
;;; converting to two-arg calls and inverting the sense of the test,
;;; if necessary. If the call has two args, then we pass or return a
;;; negated test as appropriate. If it is a degenerate one-arg call,
;;; then we transform to code that returns true. Otherwise, we bind
;;; all the arguments and expand into a bunch of IFs.
(declaim (ftype (function (symbol list boolean) *) multi-compare))
(defun multi-compare (predicate args not-p)
(let ((nargs (length args)))
(cond ((< nargs 1) (values nil t))
((= nargs 1) `(progn ,@args t))
((= nargs 2)
(if not-p
`(if (,predicate ,(first args) ,(second args)) nil t)
(values nil t)))
(t
(do* ((i (1- nargs) (1- i))
(last nil current)
(current (gensym) (gensym))
(vars (list current) (cons current vars))
(result t (if not-p
`(if (,predicate ,current ,last)
nil ,result)
`(if (,predicate ,current ,last)
,result nil))))
((zerop i)
`((lambda ,vars ,result) . ,args)))))))
(define-source-transform = (&rest args) (multi-compare '= args nil))
(define-source-transform < (&rest args) (multi-compare '< args nil))
(define-source-transform > (&rest args) (multi-compare '> args nil))
(define-source-transform <= (&rest args) (multi-compare '> args t))
(define-source-transform >= (&rest args) (multi-compare '< args t))
(define-source-transform char= (&rest args) (multi-compare 'char= args nil))
(define-source-transform char< (&rest args) (multi-compare 'char< args nil))
(define-source-transform char> (&rest args) (multi-compare 'char> args nil))
(define-source-transform char<= (&rest args) (multi-compare 'char> args t))
(define-source-transform char>= (&rest args) (multi-compare 'char< args t))
(define-source-transform char-equal (&rest args)
(multi-compare 'char-equal args nil))
(define-source-transform char-lessp (&rest args)
(multi-compare 'char-lessp args nil))
(define-source-transform char-greaterp (&rest args)
(multi-compare 'char-greaterp args nil))
(define-source-transform char-not-greaterp (&rest args)
(multi-compare 'char-greaterp args t))
(define-source-transform char-not-lessp (&rest args)
(multi-compare 'char-lessp args t))
;;; This function does source transformation of N-arg inequality
;;; functions such as /=. This is similar to MULTI-COMPARE in the <3
;;; arg cases. If there are more than two args, then we expand into
;;; the appropriate n^2 comparisons only when speed is important.
(declaim (ftype (function (symbol list) *) multi-not-equal))
(defun multi-not-equal (predicate args)
(let ((nargs (length args)))
(cond ((< nargs 1) (values nil t))
((= nargs 1) `(progn ,@args t))
((= nargs 2)
`(if (,predicate ,(first args) ,(second args)) nil t))
((not (policy *lexenv*
(and (>= speed space)
(>= speed compilation-speed))))
(values nil t))
(t
(let ((vars (make-gensym-list nargs)))
(do ((var vars next)
(next (cdr vars) (cdr next))
(result t))
((null next)
`((lambda ,vars ,result) . ,args))
(let ((v1 (first var)))
(dolist (v2 next)
(setq result `(if (,predicate ,v1 ,v2) nil ,result))))))))))
(define-source-transform /= (&rest args) (multi-not-equal '= args))
(define-source-transform char/= (&rest args) (multi-not-equal 'char= args))
(define-source-transform char-not-equal (&rest args)
(multi-not-equal 'char-equal args))
;;; FIXME: can go away once bug 194 is fixed and we can use (THE REAL X)
;;; as God intended
(defun error-not-a-real (x)
(error 'simple-type-error
:datum x
:expected-type 'real
:format-control "not a REAL: ~S"
:format-arguments (list x)))
;;; Expand MAX and MIN into the obvious comparisons.
(define-source-transform max (arg0 &rest rest)
(once-only ((arg0 arg0))
(if (null rest)
`(values (the real ,arg0))
`(let ((maxrest (max ,@rest)))
(if (> ,arg0 maxrest) ,arg0 maxrest)))))
(define-source-transform min (arg0 &rest rest)
(once-only ((arg0 arg0))
(if (null rest)
`(values (the real ,arg0))
`(let ((minrest (min ,@rest)))
(if (< ,arg0 minrest) ,arg0 minrest)))))
;;;; converting N-arg arithmetic functions
;;;;
;;;; N-arg arithmetic and logic functions are associated into two-arg
;;;; versions, and degenerate cases are flushed.
;;; Left-associate FIRST-ARG and MORE-ARGS using FUNCTION.
(declaim (ftype (function (symbol t list) list) associate-args))
(defun associate-args (function first-arg more-args)
(let ((next (rest more-args))
(arg (first more-args)))
(if (null next)
`(,function ,first-arg ,arg)
(associate-args function `(,function ,first-arg ,arg) next))))
;;; Do source transformations for transitive functions such as +.
;;; One-arg cases are replaced with the arg and zero arg cases with
;;; the identity. ONE-ARG-RESULT-TYPE is, if non-NIL, the type to
;;; ensure (with THE) that the argument in one-argument calls is.
(defun source-transform-transitive (fun args identity
&optional one-arg-result-type)
(declare (symbol fun leaf-fun) (list args))
(case (length args)
(0 identity)
(1 (if one-arg-result-type
`(values (the ,one-arg-result-type ,(first args)))
`(values ,(first args))))
(2 (values nil t))
(t
(associate-args fun (first args) (rest args)))))
(define-source-transform + (&rest args)
(source-transform-transitive '+ args 0 'number))
(define-source-transform * (&rest args)
(source-transform-transitive '* args 1 'number))
(define-source-transform logior (&rest args)
(source-transform-transitive 'logior args 0 'integer))
(define-source-transform logxor (&rest args)
(source-transform-transitive 'logxor args 0 'integer))
(define-source-transform logand (&rest args)
(source-transform-transitive 'logand args -1 'integer))
(define-source-transform logeqv (&rest args)
(if (evenp (length args))
`(lognot (logxor ,@args))
`(logxor ,@args)))
;;; Note: we can't use SOURCE-TRANSFORM-TRANSITIVE for GCD and LCM
;;; because when they are given one argument, they return its absolute
;;; value.
(define-source-transform gcd (&rest args)
(case (length args)
(0 0)
(1 `(abs (the integer ,(first args))))
(2 (values nil t))
(t (associate-args 'gcd (first args) (rest args)))))
(define-source-transform lcm (&rest args)
(case (length args)
(0 1)
(1 `(abs (the integer ,(first args))))
(2 (values nil t))
(t (associate-args 'lcm (first args) (rest args)))))
;;; Do source transformations for intransitive n-arg functions such as
;;; /. With one arg, we form the inverse. With two args we pass.
;;; Otherwise we associate into two-arg calls.
(declaim (ftype (function (symbol list t)
(values list &optional (member nil t)))
source-transform-intransitive))
(defun source-transform-intransitive (function args inverse)
(case (length args)
((0 2) (values nil t))
(1 `(,@inverse ,(first args)))
(t (associate-args function (first args) (rest args)))))
(define-source-transform - (&rest args)
(source-transform-intransitive '- args '(%negate)))
(define-source-transform / (&rest args)
(source-transform-intransitive '/ args '(/ 1)))
;;;; transforming APPLY
;;; We convert APPLY into MULTIPLE-VALUE-CALL so that the compiler
;;; only needs to understand one kind of variable-argument call. It is
;;; more efficient to convert APPLY to MV-CALL than MV-CALL to APPLY.
(define-source-transform apply (fun arg &rest more-args)
(let ((args (cons arg more-args)))
`(multiple-value-call ,fun
,@(mapcar (lambda (x)
`(values ,x))
(butlast args))
(values-list ,(car (last args))))))
;;;; transforming FORMAT
;;;;
;;;; If the control string is a compile-time constant, then replace it
;;;; with a use of the FORMATTER macro so that the control string is
;;;; ``compiled.'' Furthermore, if the destination is either a stream
;;;; or T and the control string is a function (i.e. FORMATTER), then
;;;; convert the call to FORMAT to just a FUNCALL of that function.
(deftransform format ((dest control &rest args) (t simple-string &rest t) *
:policy (> speed space))
(unless (constant-continuation-p control)
(give-up-ir1-transform "The control string is not a constant."))
(let ((arg-names (make-gensym-list (length args))))
`(lambda (dest control ,@arg-names)
(declare (ignore control))
(format dest (formatter ,(continuation-value control)) ,@arg-names))))
(deftransform format ((stream control &rest args) (stream function &rest t) *
:policy (> speed space))
(let ((arg-names (make-gensym-list (length args))))
`(lambda (stream control ,@arg-names)
(funcall control stream ,@arg-names)
nil)))
(deftransform format ((tee control &rest args) ((member t) function &rest t) *
:policy (> speed space))
(let ((arg-names (make-gensym-list (length args))))
`(lambda (tee control ,@arg-names)
(declare (ignore tee))
(funcall control *standard-output* ,@arg-names)
nil)))
(defoptimizer (coerce derive-type) ((value type))
(cond
((constant-continuation-p type)
;; This branch is essentially (RESULT-TYPE-SPECIFIER-NTH-ARG 2),
;; but dealing with the niggle that complex canonicalization gets
;; in the way: (COERCE 1 'COMPLEX) returns 1, which is not of
;; type COMPLEX.
(let* ((specifier (continuation-value type))
(result-typeoid (careful-specifier-type specifier)))
(cond
((null result-typeoid) nil)
((csubtypep result-typeoid (specifier-type 'number))
;; the difficult case: we have to cope with ANSI 12.1.5.3
;; Rule of Canonical Representation for Complex Rationals,
;; which is a truly nasty delivery to field.
(cond
((csubtypep result-typeoid (specifier-type 'real))
;; cleverness required here: it would be nice to deduce
;; that something of type (INTEGER 2 3) coerced to type
;; DOUBLE-FLOAT should return (DOUBLE-FLOAT 2.0d0 3.0d0).
;; FLOAT gets its own clause because it's implemented as
;; a UNION-TYPE, so we don't catch it in the NUMERIC-TYPE
;; logic below.
result-typeoid)
((and (numeric-type-p result-typeoid)
(eq (numeric-type-complexp result-typeoid) :real))
;; FIXME: is this clause (a) necessary or (b) useful?
result-typeoid)
((or (csubtypep result-typeoid
(specifier-type '(complex single-float)))
(csubtypep result-typeoid
(specifier-type '(complex double-float)))
#!+long-float
(csubtypep result-typeoid
(specifier-type '(complex long-float))))
;; float complex types are never canonicalized.
result-typeoid)
(t
;; if it's not a REAL, or a COMPLEX FLOAToid, it's
;; probably just a COMPLEX or equivalent. So, in that
;; case, we will return a complex or an object of the
;; provided type if it's rational:
(type-union result-typeoid
(type-intersection (continuation-type value)
(specifier-type 'rational))))))
(t result-typeoid))))
(t
;; OK, the result-type argument isn't constant. However, there
;; are common uses where we can still do better than just
;; *UNIVERSAL-TYPE*: e.g. (COERCE X (ARRAY-ELEMENT-TYPE Y)),
;; where Y is of a known type. See messages on cmucl-imp
;; 2001-02-14 and sbcl-devel 2002-12-12. We only worry here
;; about types that can be returned by (ARRAY-ELEMENT-TYPE Y), on
;; the basis that it's unlikely that other uses are both
;; time-critical and get to this branch of the COND (non-constant
;; second argument to COERCE). -- CSR, 2002-12-16
(let ((value-type (continuation-type value))
(type-type (continuation-type type)))
(labels
((good-cons-type-p (cons-type)
;; Make sure the cons-type we're looking at is something
;; we're prepared to handle which is basically something
;; that array-element-type can return.
(or (and (member-type-p cons-type)
(null (rest (member-type-members cons-type)))
(null (first (member-type-members cons-type))))
(let ((car-type (cons-type-car-type cons-type)))
(and (member-type-p car-type)
(null (rest (member-type-members car-type)))
(or (symbolp (first (member-type-members car-type)))
(numberp (first (member-type-members car-type)))
(and (listp (first (member-type-members
car-type)))
(numberp (first (first (member-type-members
car-type))))))
(good-cons-type-p (cons-type-cdr-type cons-type))))))
(unconsify-type (good-cons-type)
;; Convert the "printed" respresentation of a cons
;; specifier into a type specifier. That is, the
;; specifier (CONS (EQL SIGNED-BYTE) (CONS (EQL 16)
;; NULL)) is converted to (SIGNED-BYTE 16).
(cond ((or (null good-cons-type)
(eq good-cons-type 'null))
nil)
((and (eq (first good-cons-type) 'cons)
(eq (first (second good-cons-type)) 'member))
`(,(second (second good-cons-type))
,@(unconsify-type (caddr good-cons-type))))))
(coerceable-p (c-type)
;; Can the value be coerced to the given type? Coerce is
;; complicated, so we don't handle every possible case
;; here---just the most common and easiest cases:
;;
;; * Any REAL can be coerced to a FLOAT type.
;; * Any NUMBER can be coerced to a (COMPLEX
;; SINGLE/DOUBLE-FLOAT).
;;
;; FIXME I: we should also be able to deal with characters
;; here.
;;
;; FIXME II: I'm not sure that anything is necessary
;; here, at least while COMPLEX is not a specialized
;; array element type in the system. Reasoning: if
;; something cannot be coerced to the requested type, an
;; error will be raised (and so any downstream compiled
;; code on the assumption of the returned type is
;; unreachable). If something can, then it will be of
;; the requested type, because (by assumption) COMPLEX
;; (and other difficult types like (COMPLEX INTEGER)
;; aren't specialized types.
(let ((coerced-type c-type))
(or (and (subtypep coerced-type 'float)
(csubtypep value-type (specifier-type 'real)))
(and (subtypep coerced-type
'(or (complex single-float)
(complex double-float)))
(csubtypep value-type (specifier-type 'number))))))
(process-types (type)
;; FIXME: This needs some work because we should be able
;; to derive the resulting type better than just the
;; type arg of coerce. That is, if X is (INTEGER 10
;; 20), then (COERCE X 'DOUBLE-FLOAT) should say
;; (DOUBLE-FLOAT 10d0 20d0) instead of just
;; double-float.
(cond ((member-type-p type)
(let ((members (member-type-members type)))
(if (every #'coerceable-p members)
(specifier-type `(or ,@members))
*universal-type*)))
((and (cons-type-p type)
(good-cons-type-p type))
(let ((c-type (unconsify-type (type-specifier type))))
(if (coerceable-p c-type)
(specifier-type c-type)
*universal-type*)))
(t
*universal-type*))))
(cond ((union-type-p type-type)
(apply #'type-union (mapcar #'process-types
(union-type-types type-type))))
((or (member-type-p type-type)
(cons-type-p type-type))
(process-types type-type))
(t
*universal-type*)))))))
(defoptimizer (compile derive-type) ((nameoid function))
(when (csubtypep (continuation-type nameoid)
(specifier-type 'null))
(values-specifier-type '(values function boolean boolean))))
;;; FIXME: Maybe also STREAM-ELEMENT-TYPE should be given some loving
;;; treatment along these lines? (See discussion in COERCE DERIVE-TYPE
;;; optimizer, above).
(defoptimizer (array-element-type derive-type) ((array))
(let ((array-type (continuation-type array)))
(labels ((consify (list)
(if (endp list)
'(eql nil)
`(cons (eql ,(car list)) ,(consify (rest list)))))
(get-element-type (a)
(let ((element-type
(type-specifier (array-type-specialized-element-type a))))
(cond ((eq element-type '*)
(specifier-type 'type-specifier))
((symbolp element-type)
(make-member-type :members (list element-type)))
((consp element-type)
(specifier-type (consify element-type)))
(t
(error "can't understand type ~S~%" element-type))))))
(cond ((array-type-p array-type)
(get-element-type array-type))
((union-type-p array-type)
(apply #'type-union
(mapcar #'get-element-type (union-type-types array-type))))
(t
*universal-type*)))))
(define-source-transform sb!impl::sort-vector (vector start end predicate key)
`(macrolet ((%index (x) `(truly-the index ,x))
(%parent (i) `(ash ,i -1))
(%left (i) `(%index (ash ,i 1)))
(%right (i) `(%index (1+ (ash ,i 1))))
(%heapify (i)
`(do* ((i ,i)
(left (%left i) (%left i)))
((> left current-heap-size))
(declare (type index i left))
(let* ((i-elt (%elt i))
(i-key (funcall keyfun i-elt))
(left-elt (%elt left))
(left-key (funcall keyfun left-elt)))
(multiple-value-bind (large large-elt large-key)
(if (funcall ,',predicate i-key left-key)
(values left left-elt left-key)
(values i i-elt i-key))
(let ((right (%right i)))
(multiple-value-bind (largest largest-elt)
(if (> right current-heap-size)
(values large large-elt)
(let* ((right-elt (%elt right))
(right-key (funcall keyfun right-elt)))
(if (funcall ,',predicate large-key right-key)
(values right right-elt)
(values large large-elt))))
(cond ((= largest i)
(return))
(t
(setf (%elt i) largest-elt
(%elt largest) i-elt
i largest)))))))))
(%sort-vector (keyfun &optional (vtype 'vector))
`(macrolet (;; KLUDGE: In SBCL ca. 0.6.10, I had trouble getting
;; type inference to propagate all the way
;; through this tangled mess of
;; inlining. The TRULY-THE here works
;; around that. -- WHN
(%elt (i)
`(aref (truly-the ,',vtype ,',',vector)
(%index (+ (%index ,i) start-1)))))
(let ((start-1 (1- ,',start)) ; Heaps prefer 1-based addressing.
(current-heap-size (- ,',end ,',start))
(keyfun ,keyfun))
(declare (type (integer -1 #.(1- most-positive-fixnum))
start-1))
(declare (type index current-heap-size))
(declare (type function keyfun))
(loop for i of-type index
from (ash current-heap-size -1) downto 1 do
(%heapify i))
(loop
(when (< current-heap-size 2)
(return))
(rotatef (%elt 1) (%elt current-heap-size))
(decf current-heap-size)
(%heapify 1))))))
(if (typep ,vector 'simple-vector)
;; (VECTOR T) is worth optimizing for, and SIMPLE-VECTOR is
;; what we get from (VECTOR T) inside WITH-ARRAY-DATA.
(if (null ,key)
;; Special-casing the KEY=NIL case lets us avoid some
;; function calls.
(%sort-vector #'identity simple-vector)
(%sort-vector ,key simple-vector))
;; It's hard to anticipate many speed-critical applications for
;; sorting vector types other than (VECTOR T), so we just lump
;; them all together in one slow dynamically typed mess.
(locally
(declare (optimize (speed 2) (space 2) (inhibit-warnings 3)))
(%sort-vector (or ,key #'identity))))))
;;;; debuggers' little helpers
;;; for debugging when transforms are behaving mysteriously,
;;; e.g. when debugging a problem with an ASH transform
;;; (defun foo (&optional s)
;;; (sb-c::/report-continuation s "S outside WHEN")
;;; (when (and (integerp s) (> s 3))
;;; (sb-c::/report-continuation s "S inside WHEN")
;;; (let ((bound (ash 1 (1- s))))
;;; (sb-c::/report-continuation bound "BOUND")
;;; (let ((x (- bound))
;;; (y (1- bound)))
;;; (sb-c::/report-continuation x "X")
;;; (sb-c::/report-continuation x "Y"))
;;; `(integer ,(- bound) ,(1- bound)))))
;;; (The DEFTRANSFORM doesn't do anything but report at compile time,
;;; and the function doesn't do anything at all.)
#!+sb-show
(progn
(defknown /report-continuation (t t) null)
(deftransform /report-continuation ((x message) (t t))
(format t "~%/in /REPORT-CONTINUATION~%")
(format t "/(CONTINUATION-TYPE X)=~S~%" (continuation-type x))
(when (constant-continuation-p x)
(format t "/(CONTINUATION-VALUE X)=~S~%" (continuation-value x)))
(format t "/MESSAGE=~S~%" (continuation-value message))
(give-up-ir1-transform "not a real transform"))
(defun /report-continuation (&rest rest)
(declare (ignore rest))))