;;; -*- Package: C; Log: C.Log -*- ;;; ;;; ********************************************************************** ;;; This code was written as part of the CMU Common Lisp project at ;;; Carnegie Mellon University, and has been placed in the public domain. ;;; (ext:file-comment "$Header: /Volumes/share2/src/cmucl/cvs2git/cvsroot/src/compiler/srctran.lisp,v 1.51 1997/06/05 00:33:16 dtc Exp $") ;;; ;;; ********************************************************************** ;;; ;;; This file contains macro-like source transformations which convert ;;; uses of certain functions into the canonical form desired within the ;;; compiler. ### and other IR1 transforms and stuff. Some code adapted from ;;; CLC, written by Wholey and Fahlman. ;;; ;;; Written by Rob MacLachlan ;;; ;;; Propagate-float-type extension by Raymond Toy. ;;; (in-package "C") ;;; Source transform for Not, Null -- Internal ;;; ;;; Convert into an IF so that IF optimizations will eliminate redundant ;;; negations. ;;; (def-source-transform not (x) `(if ,x nil t)) (def-source-transform null (x) `(if ,x nil t)) ;;; Source transform for Endp -- Internal ;;; ;;; Endp is just NULL with a List assertion. ;;; (def-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. (def-source-transform identity (x) `(prog1 ,x)) (def-source-transform values (x) `(prog1 ,x)) ;;; CONSTANTLY source transform -- Internal ;;; ;;; Bind the values and make a closure that returns them. ;;; (def-source-transform constantly (value &rest values) (let ((temps (loop repeat (1+ (length values)) collect (gensym))) (dum (gensym))) `(let ,(loop for temp in temps and value in (list* value values) collect `(,temp ,value)) #'(lambda (&rest ,dum) (declare (ignore ,dum)) (values ,@temps))))) ;;; COMPLEMENT IR1 transform -- Internal ;;; ;;; 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 :when :both) "open code" (multiple-value-bind (min max) (function-type-nargs (continuation-type fun)) (cond ((and min (eql min max)) (let ((dums (loop repeat min collect (gensym)))) `#'(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 "Function doesn't have fixed argument count."))))) ;;;; List hackery: ;;; ;;; Translate CxxR into car/cdr combos. (defun source-transform-cxr (form) (if (or (byte-compiling) (/= (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))))) (do ((i 2 (1+ i)) (b '(1 0) (cons i b))) ((= i 5)) (dotimes (j (ash 1 i)) (setf (info function source-transform (intern (format nil "C~{~:[A~;D~]~}R" (mapcar #'(lambda (x) (logbitp x j)) b)))) #'source-transform-cxr))) ;;; ;;; 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. (def-source-transform first (x) `(car ,x)) (def-source-transform rest (x) `(cdr ,x)) (def-source-transform second (x) `(cadr ,x)) (def-source-transform third (x) `(caddr ,x)) (def-source-transform fourth (x) `(cadddr ,x)) (def-source-transform fifth (x) `(nth 4 ,x)) (def-source-transform sixth (x) `(nth 5 ,x)) (def-source-transform seventh (x) `(nth 6 ,x)) (def-source-transform eighth (x) `(nth 7 ,x)) (def-source-transform ninth (x) `(nth 8 ,x)) (def-source-transform tenth (x) `(nth 9 ,x)) ;;; ;;; Translate RPLACx to LET and SETF. (def-source-transform rplaca (x y) (once-only ((n-x x)) `(progn (setf (car ,n-x) ,y) ,n-x))) ;;; (def-source-transform rplacd (x y) (once-only ((n-x x)) `(progn (setf (cdr ,n-x) ,y) ,n-x))) (def-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)) (let ((n (continuation-value n))) (when (> n (if (policy node (= speed 3) (= space 0)) *extreme-nthcdr-open-code-limit* *default-nthcdr-open-code-limit*)) (give-up)) (labels ((frob (n) (if (zerop n) 'l `(cdr ,(frob (1- n)))))) (frob n)))) ;;;; ARITHMETIC and NUMEROLOGY. (def-source-transform plusp (x) `(> ,x 0)) (def-source-transform minusp (x) `(< ,x 0)) (def-source-transform zerop (x) `(= ,x 0)) (def-source-transform 1+ (x) `(+ ,x 1)) (def-source-transform 1- (x) `(- ,x 1)) (def-source-transform oddp (x) `(not (zerop (logand ,x 1)))) (def-source-transform evenp (x) `(zerop (logand ,x 1))) ;;; Note that all the integer division functions are available for inline ;;; expansion. (macrolet ((frob (fun) `(def-source-transform ,fun (x &optional (y nil y-p)) (declare (ignore y)) (if y-p (values nil t) `(,',fun ,x 1))))) (frob truncate) (frob round) #+propagate-float-type (frob floor) #+propagate-float-type (frob ceiling)) (def-source-transform lognand (x y) `(lognot (logand ,x ,y))) (def-source-transform lognor (x y) `(lognot (logior ,x ,y))) (def-source-transform logandc1 (x y) `(logand (lognot ,x) ,y)) (def-source-transform logandc2 (x y) `(logand ,x (lognot ,y))) (def-source-transform logorc1 (x y) `(logior (lognot ,x) ,y)) (def-source-transform logorc2 (x y) `(logior ,x (lognot ,y))) (def-source-transform logtest (x y) `(not (zerop (logand ,x ,y)))) (def-source-transform logbitp (index integer) `(not (zerop (logand (ash 1 ,index) ,integer)))) (def-source-transform byte (size position) `(cons ,size ,position)) (def-source-transform byte-size (spec) `(car ,spec)) (def-source-transform byte-position (spec) `(cdr ,spec)) (def-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. ;;; (def-source-transform numerator (num) (once-only ((n-num `(the rational ,num))) `(if (ratiop ,n-num) (%numerator ,n-num) ,n-num))) ;;; (def-source-transform denominator (num) (once-only ((n-num `(the rational ,num))) `(if (ratiop ,n-num) (%denominator ,n-num) 1))) ;;; (def-source-transform realpart (num) (once-only ((n-num num)) `(if (complexp ,n-num) (%realpart ,n-num) ,n-num))) ;;; (def-source-transform imagpart (num) (once-only ((n-num num)) `(cond ((complexp ,n-num) (%imagpart ,n-num)) ((floatp ,n-num) (float 0 ,n-num)) (t 0)))) ;;;; Interval arithmetic for computing bounds ;;;; (toy@rtp.ericsson.se) ;;;; ;;;; This is a set of routines for operating on intervals. It ;;;; implements a simple interval arithmetic package. Although CMUCL ;;;; 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 CMUCL. (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. #+propagate-float-type (progn (defun elfun-float-format (format) (if format (if (eq format 'double-float) 'double-float 'single-float))) ;;; 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)) 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 ;; 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)))) (defmacro without-over/under-flow-traps (&body body) "Executes BODY with traps on overflow, underflow, and divide-by-zero turned off" (let ((modes (gensym))) `(let ((,modes (ext:get-floating-point-modes))) (unwind-protect (progn (ext:set-floating-point-modes :traps '(:invalid)) ,@body) (apply #'ext:set-floating-point-modes ,modes))))) (proclaim '(inline bound-value set-bound bound-func)) ;;; Extract the numeric value of a bound. Return NIL, if X is NIL. (defun bound-value (x) (if (consp x) (car x) x)) ;;; 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. (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) (and x (without-over/under-flow-traps (set-bound (funcall f (bound-value 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. (defmacro bound-binop (op x y) `(and ,x ,y (without-over/under-flow-traps (set-bound (,op (bound-value ,x) (bound-value ,y)) (or (consp ,x) (consp ,y)))))) ;;; NUMERIC-TYPE->INTERVAL ;;; ;;; 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)))) ;;; INTERVAL-SPLIT ;;; ;;; Given a point P contained in the interval X, split X into two ;;; interval at the point P. If JOIN-LOWER it T, then the left ;;; interval contains P. Otherwise, the right interval contains P. ;;; You can specify both to be T. (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))))) (defun interval-closure (x) (declare (type interval x)) (make-interval :low (bound-value (interval-low x)) :high (bound-value (interval-high x)))) ;;; INTERVAL-RANGE-INFO ;;; ;;; For an interval X, if X >= 0, return '+. If X <= 0, return ;;; '-. Otherwise return NIL. (defun interval-range-info (x) (declare (type interval x)) (let ((lo (interval-low x)) (hi (interval-high x))) (cond ((and lo (>= (bound-value lo) 0)) '+) ((and hi (<= (bound-value hi) 0)) '-) (t nil)))) ;;; INTERVAL-BOUNDED-P ;;; ;;; Test to see if 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))))) ;;; INTERVAL-CONTAINS-P ;;; ;;; See if 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 (<= (bound-value lo) p (bound-value hi)) ;; P is definitely in the closure of the interval. ;; We just need to check the end points now. (cond ((= p (bound-value lo)) (numberp lo)) ((= p (bound-value hi)) (numberp hi)) (t t)) nil)) (hi ;; Interval with upper bound (if (< p (bound-value hi)) t (and (numberp hi) (= p hi)))) (lo ;; Interval with lower bound (if (> p (bound-value lo)) t (and (numberp lo) (= p lo)))) (t ;; Interval with no bounds t)))) ;;; INTERVAL-INTERSECT-P ;;; ;;; Determine if 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)) (let ((x-lo (interval-low x)) (x-hi (interval-high x)) (y-lo (interval-low y)) (y-hi (interval-high y))) (labels ((test-number (p int) ;; Test if P is in the interval. (when (interval-contains-p (bound-value p) (interval-closure int)) (let ((lo (interval-low int)) (hi (interval-high int))) ;; Check for endpoints (cond ((or (null lo) (null hi)) t) ((= (bound-value p) (bound-value lo)) (or closed-intervals-p (not (and (consp p) (numberp lo))))) ((= (bound-value p) (bound-value hi)) (or closed-intervals-p (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)))) ) (or (test-lower-bound x-lo y) (test-upper-bound x-hi y) (test-lower-bound y-lo x) (test-upper-bound y-hi x))))) ;;; 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 if lo and hi are adjacent. If either is ;; nil, they can't be adjacent. (when (and lo hi (= (bound-value lo) (bound-value 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))))) ;;; INTERVAL-MERGE-PAIR ;;; ;;; 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 (bound-value x1)) (x2-val (bound-value x2))) (cond ((and x1 x2) ;; Both bounds are finite. Select the right one. (cond ((funcall min-op x1-val x2-val) ;; x1 definitely better x1) ((funcall max-op x1-val x2-val) ;; x2 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 ;;; INTERVAL-NEG ;;; ;;; 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)))) ;;; INTERVAL-ADD ;;; ;;; 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)))) ;;; INTERVAL-SUB ;;; ;;; 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)))) ;;; INTERVAL-MUL ;;; ;;; 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 0) ((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 (error "This shouldn't happen!")))))) ;;; INTERVAL-DIV ;;; ;;; Divide two intervals. (defun interval-div (top bot) (declare (type interval top bot)) (flet ((bound-div (x y) ;; Compute x/y (cond ((null y) ;; Divide by infinity means result is 0 0) ((zerop (bound-value 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)) :high (bound-div (interval-high top) (interval-low bot)))) (t (error "This shouldn't happen!")))))) ;;; INTERVAL-FUNC ;;; ;;; 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 interval x)) (let ((lo (bound-func f (interval-low x))) (hi (bound-func f (interval-high x)))) (make-interval :low lo :high hi))) ;;; INTERVAL-< ;;; ;;; 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 that don't overlap. (let ((left (interval-high x)) (right (interval-low y))) (cond ((> (bound-value left) (bound-value right)) ;; Definitely overlap so result is NIL nil) ((< (bound-value left) (bound-value right)) ;; 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))))))) ;;; INTERVAL-ABS ;;; ;;; 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+))))) ;;; INTERVAL-SQR ;;; ;;; Compute the square of an interval. (defun interval-sqr (x) (declare (type interval x)) (interval-func #'(lambda (x) (* x x)) (interval-abs x))) ) ; end progn ;;;; Numeric Derive-Type methods: ;;; Derive-Integer-Type -- Internal ;;; ;;; 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)))) ;;; Derive-Real-Type -- Internal ;;; ;;; Same as derive-integer-type except it can handle float types. ;;; This also contains derive-integer-type as a special case. ;;; #+propagate-float-type (progn ;;; Some functions only take one argument but derive-real-type assumes ;;; two. For those cases of one argument functions, set IGNORE-Y to T ;;; because we don't want derive-real-type to process the second ;;; argument because it's meaningless. (defun derive-real-type (x y fun) (declare (type continuation x y) (type function fun)) (let ((x (continuation-type x)) (y (continuation-type y))) (derive-real-numeric-or-union-type x y fun))) ;;; Some notes: This routine can handle X and Y if they are ;;; numeric-types or unions of numeric types. If this is not true, ;;; general numeric contagion holds. In particular if X is a member ;;; type, we could conceivably compute the right thing by looking ;;; inside the elements of the member type. We don't do this yet. ;;; Perhaps it would be better to let the user say so. Instead of ;;; saying (member 1 2 4), you should say (or (integer 1 1) (integer 2 ;;; 2) (integer 4 4)). (defun derive-real-numeric-or-union-type (x y fun) (labels ((combine (lx ly) ;; Creates a new list containing all possible pairs from LX and LY. (let ((result '())) (dolist (ix lx) (dolist (iy ly) (push (list ix iy) result))) (nreverse result))) (listify (object) ;; If object is a union type, get the list of the types. ;; Otherwise make a list containing the single object. (typecase object (union-type (union-type-types object)) (t (list object))))) (let ((all (combine (listify x) (listify y))) (result '())) (dolist (item all) (destructuring-bind (ix iy) item (push (derive-simple-real-type ix iy fun) result))) (setf result (derive-merged-union-types result)) (if (cdr result) (make-union-type result) (first result))))) (defun merge-types-aux (tlist) ;; Merge the first interval in the list with the rest of ;; intervals in the list. The list of intervals MUST be ;; sorted in ascending order of lower limits. (let* ((cur (first tlist)) (cur-intvrl (numeric-type->interval cur)) (res (list cur))) (dolist (this-interval (rest tlist) res) (let ((this (numeric-type->interval this-interval))) ;; If interval intersects cur or if they are adjacent, we can ;; merge them together, but only if they are the same type of ;; number. If they are different, we can't merge them. (cond ((and (eq (numeric-type-class cur) (numeric-type-class this-interval)) (or (interval-intersect-p cur-intvrl this) (interval-adjacent-p cur-intvrl this))) (let ((result (interval-merge-pair cur-intvrl this))) (when result (setf (numeric-type-high cur) (interval-high result))))) (t (setf res (cons this-interval res)))))))) (defun merge-types (ilist &optional (result '())) ;; Compare the first element with the rest to merge ;; whatever we can into the first element. The first ;; element is totally merged, so we only need to consider ;; whatever is left. (cond ((null ilist) result) ((cdr ilist) (let ((new-types (merge-types-aux ilist))) (merge-types (rest new-types) (cons (first new-types) result)))) (t (cons (first ilist) result)))) (defun derive-merged-union-types (types) (labels ((num-interval-< (a b) (when (and (numeric-type-p a) (numeric-type-p b)) (let ((a-lo (numeric-type-low a)) (b-lo (numeric-type-low b))) (cond ((null a-lo) ;; A has lower bound of -infinity, so it's ;; lower than B, no matter what B is. t) ((null b-lo) ;; At this point A has a numeric lower bound, ;; but B has -infinity, so A is not lower than ;; B. nil) (t ;; Both A and B have numeric lower bounds. Make the right decision (let ((av (bound-value a-lo)) (bv (bound-value b-lo))) (cond ((< av bv) ;; Obviously t) ((= av bv) ;; Bounds are equal. A is lower unless A is open and B is closed. (or (numberp a-lo) (consp b-lo))) (t nil))))))))) (merge-types (stable-sort types #'num-interval-<)))) (defun derive-simple-real-type (x y fun) (declare (type function fun)) ;; We handle the case of real operands. For the other cases, we use ;; general numeric contagion. (if (and (numeric-type-p x) (numeric-type-p y) (eq (numeric-type-complexp x) :real) (eq (numeric-type-complexp y) :real)) (multiple-value-bind (low high type format) (funcall fun x y) (make-numeric-type :class type :complexp :real :format format :low low :high high)) (numeric-contagion x y))) ) ; end progn #-propagate-float-type (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))) ) ; end progn #+propagate-float-type (progn (defoptimizer (+ derive-type) ((x y)) (derive-real-type x y #'(lambda (x y) (declare (type numeric-type x y)) (let ((result (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))) (values (interval-low result) (interval-high result) (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)) (numeric-type-format result-type)))))) (defoptimizer (- derive-type) ((x y)) (derive-real-type x y #'(lambda (x y) (declare (type numeric-type x y)) (let ((result (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))) (values (interval-low result) (interval-high result) (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)) (numeric-type-format result-type)))))) (defoptimizer (* derive-type) ((x y)) (let ((same-arg (same-leaf-ref-p x y))) (derive-real-type x y #'(lambda (x y) (let ((result (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))) (values (interval-low result) (interval-high result) (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)) (numeric-type-format result-type))))))) (defoptimizer (/ derive-type) ((x y)) (derive-real-type x y #'(lambda (x y) (declare (type numeric-type x y)) (let ((result (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))) (values (interval-low result) (interval-high result) (numeric-type-class result-type) (numeric-type-format result-type)))))) ) ;end progn (defoptimizer (ash derive-type) ((n shift)) (or (let ((n-type (continuation-type n))) (when (numeric-type-p n-type) (let ((n-low (numeric-type-low n-type)) (n-high (numeric-type-high n-type))) (if (constant-continuation-p shift) (let ((shift (continuation-value shift))) (make-numeric-type :class 'integer :complexp :real :low (when n-low #+new-compiler (ash n-low shift) ;; ### fuckin' bignum bug. #-new-compiler (* n-low (ash 1 shift))) :high (when n-high (ash n-high shift)))) (let ((s-type (continuation-type shift))) (when (numeric-type-p s-type) (let ((s-low (numeric-type-low s-type)) (s-high (numeric-type-high s-type))) (if (and s-low s-high (<= s-low 32) (<= s-high 32)) (make-numeric-type :class 'integer :complexp :real :low (when n-low (min (ash n-low s-high) (ash n-low s-low))) :high (when n-high (max (ash n-high s-high) (ash n-high s-low)))) (make-numeric-type :class 'integer :complexp :real))))))))) *universal-type*)) #-propagate-float-type (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 (frob lognot)))) #+propagate-float-type (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) (numeric-type-class type) (numeric-type-format type)))))) (defoptimizer (%negate derive-type) ((num)) (flet ((negate-bound (b) (set-bound (- (bound-value b)) (consp b)))) (derive-real-type num num (frob negate-bound)))) (defoptimizer (lognot derive-type) ((int)) (derive-integer-type int int (frob lognot)))) #-propagate-float-type (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)))) #+propagate-float-type (defoptimizer (abs derive-type) ((num)) (let ((type (continuation-type num))) (when (numeric-type-p type) (cond ((eq (numeric-type-complexp type) :complex) ;; The absolute value of a complex number is always a ;; non-negative float. (make-numeric-type :class 'float :format (elfun-float-format (numeric-type-format type)) :complexp :real :low 0 :high nil)) ((eq (numeric-type-complexp type) :real) ;; 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)))) (make-numeric-type :class (numeric-type-class type) :format (numeric-type-format type) :complexp :real :low (interval-low abs-bnd) :high (interval-high abs-bnd)))))))) #-propagate-float-type (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*))) #+propagate-float-type (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. Can this happen? 'real))) (defoptimizer (truncate derive-type) ((number divisor)) (let* ((number-type (continuation-type number)) (divisor-type (continuation-type divisor)) (real-type (specifier-type 'real))) (if (not (and (numeric-type-p number-type) (numeric-type-p divisor-type) (csubtypep number-type real-type) (csubtypep divisor-type real-type))) ;; There's nothing to do if the args are not real numbers *universal-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. (values-specifier-type `(values ,(integer-truncate-derive-type (interval-low number-interval) (interval-high number-interval) (interval-low divisor-interval) (interval-high divisor-interval)) (,rem-type ,(or (interval-low rem) '*) ,(or (interval-high rem) '*))))) (t (let ((quot (truncate-quotient-bound (interval-div number-interval divisor-interval)))) (when (member rem-type '(float single-float double-float)) (setf rem (interval-func #'(lambda (x) (coerce x rem-type)) rem))) (values-specifier-type `(values (integer ,(or (interval-low quot) '*) ,(or (interval-high quot) '*)) (,rem-type ,(or (interval-low rem) '*) ,(or (interval-high rem) '*))))))))))) (defoptimizer (%unary-truncate derive-type) ((number)) (let ((number-type (continuation-type number))) (if (and (numeric-type-p number-type) (csubtypep number-type (specifier-type 'real))) (let ((quot (truncate-quotient-bound (numeric-type->interval number-type)))) (specifier-type `(integer ,(or (interval-low quot) '*) ,(or (interval-high quot) '*)))) *universal-type*))) (macrolet ((frob-opt (name q-name r-name) `(defoptimizer (,name derive-type) ((number divisor)) (let* ((number-type (continuation-type number)) (divisor-type (continuation-type divisor)) (real-type (specifier-type 'real))) (if (and (numeric-type-p number-type) (csubtypep number-type real-type) (numeric-type-p divisor-type) (csubtypep divisor-type real-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))) (rem (,r-name divisor-interval)) (result-type (rem-result-type number-type divisor-type))) (when (member result-type '(float single-float double-float)) ;; Make sure the limits on the interval have the right type. (setf rem (interval-func #'(lambda (x) (coerce x result-type)) rem))) (values-specifier-type `(values (integer ,(or (interval-low quot) '*) ,(or (interval-high quot) '*)) (,result-type ,(or (interval-low rem) '*) ,(or (interval-high rem) '*))))) *universal-type*))))) (frob-opt floor floor-quotient-bound floor-rem-bound) (frob-opt ceiling 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 (bound-value 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) (+ ;; Divisor is always positive. (let ((rem (interval-abs div))) (setf (interval-low rem) 0) (when (numberp (interval-high rem)) ;; The remainder never contains the upper bound. (setf (interval-high rem) (list (interval-high rem)))) rem)) (- ;; 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 (bound-value (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 (bound-value 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 (numberp (interval-low rem)) ;; The remainder never contains the upper bound. (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 (bound-value (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)))))) ) ;;; NUMERIC-RANGE-INFO -- internal. ;;; ;;; 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)))))) ;;; INTEGER-TRUNCATE-DERIVE-TYPE -- internal ;;; (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: guarenteed division by zero. (return-from integer-truncate-derive-type t)) (when (zerop divisor-min) ;; We'll assume that they arn'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))))) #-propagate-float-type (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 '*)))) (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)))))))) ;;;; Logical derive-type methods: ;;; Integer-Type-Length -- Internal ;;; ;;; 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))) (defoptimizer (logand derive-type) ((x y)) (multiple-value-bind (x-len x-pos x-neg) (integer-type-length (continuation-type x)) (declare (ignore x-pos)) (multiple-value-bind (y-len y-pos y-neg) (integer-type-length (continuation-type y)) (declare (ignore y-pos)) (if (not x-neg) ;; X must be positive. (if (not y-neg) ;; The 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))))))) (defoptimizer (logior derive-type) ((x y)) (multiple-value-bind (x-len x-pos x-neg) (integer-type-length (continuation-type x)) (multiple-value-bind (y-len y-pos y-neg) (integer-type-length (continuation-type y)) (cond ((and (not x-neg) (not y-neg)) ;; Both are positive. (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 (continuation-type 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 (continuation-type 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)))))))) (defoptimizer (logxor derive-type) ((x y)) (multiple-value-bind (x-len x-pos x-neg) (integer-type-length (continuation-type x)) (multiple-value-bind (y-len y-pos y-neg) (integer-type-length (continuation-type 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. (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-verca. 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)))))) ;;;; Miscellaneous derive-type methods: (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. ;;; With-Byte-Specifier -- Internal ;;; ;;; 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. ;;; (defmacro 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))))) (def-source-transform ldb (spec int) (with-byte-specifier (size pos spec) `(%ldb ,size ,pos ,int))) (def-source-transform dpb (newbyte spec int) (with-byte-specifier (size pos spec) `(%dpb ,newbyte ,size ,pos ,int))) (def-source-transform mask-field (spec int) (with-byte-specifier (size pos spec) `(%mask-field ,size ,pos ,int))) (def-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 vm: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) vm: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) vm: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) vm: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 #.vm:word-bits)) "convert to inline logical ops" `(logand (ash int (- posn)) (ash ,(1- (ash 1 vm:word-bits)) (- size ,vm:word-bits)))) (deftransform %mask-field ((size posn int) (fixnum fixnum integer) (unsigned-byte #.vm:word-bits)) "convert to inline logical ops" `(logand int (ash (ash ,(1- (ash 1 vm:word-bits)) (- size ,vm: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 #.vm:word-bits)) "convert to inline logical ops" `(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 #.vm:word-bits)) "convert to inline logical ops" `(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 #.vm:word-bits)) "convert to inline logical ops" `(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 #.vm:word-bits)) "convert to inline logical ops" `(let ((mask (ash (ldb (byte size 0) -1) posn))) (logior (logand new mask) (logand int (lognot mask))))) ;;; Miscellanous numeric transforms: ;;; COMMUTATIVE-ARG-SWAP -- Internal ;;; ;;; 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-function-name (basic-combination-fun node)) y ,(continuation-value x)) (give-up))) (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) * * :when :both) "convert to inline logical ops" (unless (constant-continuation-p op) (give-up "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-transform "~S illegal control arg to BOOLE." control))))) ;;;; Convert multiply/divide to shifts. ;;; If arg is a constant power of two, turn * into a shift. ;;; (deftransform * ((x y) (integer integer) * :when :both) "convert x*2^k to shift" (unless (constant-continuation-p y) (give-up)) (let* ((y (continuation-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (= y-abs (ash 1 len)) (give-up)) (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)) (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)) and then do floor. ;;; (flet ((frob (y ceil-p) (unless (constant-continuation-p y) (give-up)) (let* ((y (continuation-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (= y-abs (ash 1 len)) (give-up)) (let ((shift (- len)) (mask (1- y-abs))) `(let ,(when ceil-p `((x (+ x ,(1- y-abs))))) ,(if (minusp y) `(values (ash (- x) ,shift) (- (logand (- x) ,mask))) `(values (ash x ,shift) (logand x ,mask)))))))) (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) * :when :both) "convert remainder mod 2^k to LOGAND" (unless (constant-continuation-p y) (give-up)) (let* ((y (continuation-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (= y-abs (ash 1 len)) (give-up)) (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)) (let* ((y (continuation-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (= y-abs (ash 1 len)) (give-up)) (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) * :when :both) "convert remainder mod 2^k to LOGAND" (unless (constant-continuation-p y) (give-up)) (let* ((y (continuation-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (= y-abs (ash 1 len)) (give-up)) (let ((mask (1- y-abs))) `(if (minusp x) (- (logand (- x) ,mask)) (logand x ,mask))))) ;;;; Arithmetic and logical identity operation elimination: ;;; ;;; Flush calls to random arith functions that convert to the identity ;;; function or a constant. (dolist (stuff '((ash 0 x) (logand -1 x) (logand 0 0) (logior 0 x) (logior -1 -1) (logxor -1 (lognot x)) (logxor 0 x))) (destructuring-bind (name identity result) stuff (deftransform name ((x y) `(* (constant-argument (member ,identity))) '* :eval-name t :when :both) "fold identity operations" result))) ;;; 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-argument (member 0)) rational) * :when :both) "convert (- 0 x) to negate" '(%negate y)) ;;; (deftransform * ((x y) (rational (constant-argument (member 0))) * :when :both) "convert (* x 0) to 0." 0) ;;; NOT-MORE-CONTAGIOUS -- Interface ;;; ;;; 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. ;;; (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))))) ;;; Fold (OP x 0). ;;; ;;; If y is not constant, not zerop, or is contagious, then give up. ;;; (dolist (stuff '((+ x) (- x) (expt 1))) (destructuring-bind (name result) stuff (deftransform name ((x y) '(t (constant-argument t)) '* :eval-name t :when :both) "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))) result))) ;;; Fold (OP x +/-1) ;;; (dolist (stuff '((* x (%negate x)) (/ x (%negate x)) (expt x (/ 1 x)))) (destructuring-bind (name result minus-result) stuff (deftransform name ((x y) '(t (constant-argument real)) '* :eval-name t :when :both) "fold identity operations" (let ((val (continuation-value y))) (unless (and (= (abs val) 1) (not-more-contagious y x)) (give-up)) (if (minusp val) minus-result result))))) ;;; Fold (expt x n) into multiplications for small integral values of N. (deftransform expt ((x y) (t (constant-argument real)) *) "recode as multiplication" (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)) (cond ((= val 2) '(* x x)) ((= val -2) '(/ (* x x))) ((= val 3) '(* x x x)) ((= val -3) '(/ (* x x x))) (t (give-up))))) (dolist (name '(ash /)) (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '* :eval-name t :when :both) "fold zero arg" 0)) (dolist (name '(truncate round floor ceiling)) (deftransform name ((x y) '((constant-argument (integer 0 0)) integer) '* :eval-name t :when :both) "fold zero arg" '(values 0 0))) ;;;; 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: ;;; SAME-LEAF-REF-P -- Internal ;;; ;;; 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)))) ;;; SIMPLE-EQUALITY-TRANSFORM -- Internal ;;; ;;; 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 :when :both) (cond ((same-leaf-ref-p x y) 't) ((not (types-intersect (continuation-type x) (continuation-type y))) 'nil) (t (give-up)))) (dolist (x '(eq char= equal)) (%deftransform x '(function * *) #'simple-equality-transform)) ;;; EQL IR1 Transform -- Internal ;;; ;;; 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 efficency note. ;;; (deftransform eql ((x y) * * :when :both) "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-intersect x-type y-type)) 'nil) ((and (csubtypep x-type char-type) (csubtypep y-type char-type)) '(char= x y)) ((or (not (types-intersect x-type number-type)) (not (types-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 -- Internal ;;; ;;; Convert to EQL if both args are rational and complexp is specified ;;; and the same for both. ;;; (deftransform = ((x y) * * :when :both) "open code" (let ((x-type (continuation-type x)) (y-type (continuation-type y))) (if (and (numeric-type-p x-type) (numeric-type-p y-type)) (let ((x-class (numeric-type-class x-type)) (y-class (numeric-type-class y-type))) (cond ((and (eq x-class 'float) (eq y-class 'float)) ;; They are both floats. Leave as = so that -0.0 is ;; handled correctly. (give-up)) ((and (member x-class '(rational integer)) (member y-class '(rational integer)) (let ((x-complexp (numeric-type-complexp x-type))) (and x-complexp (eq x-complexp (numeric-type-complexp y-type))))) ;; They are both rationals and complexp is the same. Convert ;; to EQL. '(eql x y)) (t (give-up "Operands might not be the same type.")))) (give-up "Operands might not be the same type.")))) ;;; Numeric-Type-Or-Lose -- Interface ;;; ;;; If Cont's type is a numeric type, then return the type, otherwise ;;; GIVE-UP. ;;; (defun numeric-type-or-lose (cont) (declare (type continuation cont)) (let ((res (continuation-type cont))) (unless (numeric-type-p res) (give-up)) res)) ;;; IR1-TRANSFORM-< -- Internal ;;; ;;; See if 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. ;;; #-propagate-float-type (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)))))) #+propagate-float-type (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-< yi xi) nil) ((and (constant-continuation-p first) (not (constant-continuation-p second))) `(,inverse y x)) (t (give-up)))))) (deftransform < ((x y) (integer integer) * :when :both) (ir1-transform-< x y x y '>)) (deftransform > ((x y) (integer integer) * :when :both) (ir1-transform-< y x x y '<)) #+propagate-float-type (deftransform < ((x y) (float float) * :when :both) (ir1-transform-< x y x y '>)) #+propagate-float-type (deftransform > ((x y) (float float) * :when :both) (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. ;;; Multi-Compare -- Internal ;;; ;;; 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. ;;; (proclaim '(function multi-compare (symbol list boolean))) (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))))))) (def-source-transform = (&rest args) (multi-compare '= args nil)) (def-source-transform < (&rest args) (multi-compare '< args nil)) (def-source-transform > (&rest args) (multi-compare '> args nil)) (def-source-transform <= (&rest args) (multi-compare '> args t)) (def-source-transform >= (&rest args) (multi-compare '< args t)) (def-source-transform char= (&rest args) (multi-compare 'char= args nil)) (def-source-transform char< (&rest args) (multi-compare 'char< args nil)) (def-source-transform char> (&rest args) (multi-compare 'char> args nil)) (def-source-transform char<= (&rest args) (multi-compare 'char> args t)) (def-source-transform char>= (&rest args) (multi-compare 'char< args t)) (def-source-transform char-equal (&rest args) (multi-compare 'char-equal args nil)) (def-source-transform char-lessp (&rest args) (multi-compare 'char-lessp args nil)) (def-source-transform char-greaterp (&rest args) (multi-compare 'char-greaterp args nil)) (def-source-transform char-not-greaterp (&rest args) (multi-compare 'char-greaterp args t)) (def-source-transform char-not-lessp (&rest args) (multi-compare 'char-lessp args t)) ;;; Multi-Not-Equal -- Internal ;;; ;;; 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. ;;; (proclaim '(function multi-not-equal (symbol list))) (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 nil (>= speed space) (>= speed cspeed))) (values nil t)) (t (collect ((vars)) (dotimes (i nargs) (vars (gensym))) (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)))))))))) (def-source-transform /= (&rest args) (multi-not-equal '= args)) (def-source-transform char/= (&rest args) (multi-not-equal 'char= args)) (def-source-transform char-not-equal (&rest args) (multi-not-equal 'char-equal args)) ;;; Expand Max and Min into the obvious comparisons. (def-source-transform max (arg &rest more-args) (if (null more-args) `(values ,arg) (once-only ((arg1 arg) (arg2 `(max ,@more-args))) `(if (> ,arg1 ,arg2) ,arg1 ,arg2)))) ;;; (def-source-transform min (arg &rest more-args) (if (null more-args) `(values ,arg) (once-only ((arg1 arg) (arg2 `(min ,@more-args))) `(if (< ,arg1 ,arg2) ,arg1 ,arg2)))) ;;;; Converting N-arg arithmetic functions: ;;; ;;; N-arg arithmetic and logic functions are associated into two-arg ;;; versions, and degenerate cases are flushed. ;;; Associate-Arguments -- Internal ;;; ;;; Left-associate First-Arg and More-Args using Function. ;;; (proclaim '(function associate-arguments (symbol t list) list)) (defun associate-arguments (function first-arg more-args) (let ((next (rest more-args)) (arg (first more-args))) (if (null next) `(,function ,first-arg ,arg) (associate-arguments function `(,function ,first-arg ,arg) next)))) ;;; Source-Transform-Transitive -- Internal ;;; ;;; Do source transformations for transitive functions such as +. One-arg ;;; cases are replaced with the arg and zero arg cases with the identity. If ;;; Leaf-Fun is true, then replace two-arg calls with a call to that function. ;;; (defun source-transform-transitive (fun args identity &optional leaf-fun) (declare (symbol fun leaf-fun) (list args)) (case (length args) (0 identity) (1 `(values ,(first args))) (2 (if leaf-fun `(,leaf-fun ,(first args) ,(second args)) (values nil t))) (t (associate-arguments fun (first args) (rest args))))) (def-source-transform + (&rest args) (source-transform-transitive '+ args 0)) (def-source-transform * (&rest args) (source-transform-transitive '* args 1)) (def-source-transform logior (&rest args) (source-transform-transitive 'logior args 0)) (def-source-transform logxor (&rest args) (source-transform-transitive 'logxor args 0)) (def-source-transform logand (&rest args) (source-transform-transitive 'logand args -1)) (def-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 it's absolute value. (def-source-transform gcd (&rest args) (case (length args) (0 0) (1 `(abs (the integer ,(first args)))) (2 (values nil t)) (t (associate-arguments 'gcd (first args) (rest args))))) (def-source-transform lcm (&rest args) (case (length args) (0 1) (1 `(abs (the integer ,(first args)))) (2 (values nil t)) (t (associate-arguments 'lcm (first args) (rest args))))) ;;; Source-Transform-Intransitive -- Internal ;;; ;;; 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. ;;; (proclaim '(function source-transform-intransitive (symbol list t) list)) (defun source-transform-intransitive (function args inverse) (case (length args) ((0 2) (values nil t)) (1 `(,@inverse ,(first args))) (t (associate-arguments function (first args) (rest args))))) (def-source-transform - (&rest args) (source-transform-intransitive '- args '(%negate))) (def-source-transform / (&rest args) (source-transform-intransitive '/ args '(/ 1))) ;;;; 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. (def-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)))))) ;;;; FORMAT transform: ;;; ;;; 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 "Control string is not a constant.")) (let ((arg-names (mapcar #'(lambda (x) (declare (ignore x)) (gensym)) 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 (mapcar #'(lambda (x) (declare (ignore x)) (gensym)) 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 (mapcar #'(lambda (x) (declare (ignore x)) (gensym)) args))) `(lambda (tee control ,@arg-names) (declare (ignore tee)) (funcall control *standard-output* ,@arg-names) nil)))