;;;; 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") ;;; 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)) ;;; CONSTANTLY is pretty much never worth transforming, but it's good to get the type. (defoptimizer (constantly derive-type) ((value)) (specifier-type `(function (&rest t) (values ,(type-specifier (lvar-type value)) &optional)))) ;;; 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 (lvar-type fun)) (cond ((and min (eql min max)) (let ((dums (make-gensym-list min))) `#'(lambda ,dums (not (funcall fun ,@dums))))) ((awhen (node-lvar node) (let ((dest (lvar-dest it))) (and (combination-p dest) (eq (combination-fun dest) it)))) '#'(lambda (&rest args) (not (apply fun args)))) (t (give-up-ir1-transform "The function doesn't have a fixed argument count."))))) ;;;; SYMBOL-VALUE &co (defun derive-symbol-value-type (lvar node) (if (constant-lvar-p lvar) (let* ((sym (lvar-value lvar)) (var (maybe-find-free-var sym)) (local-type (when var (let ((*lexenv* (node-lexenv node))) (lexenv-find var type-restrictions)))) (global-type (info :variable :type sym))) (if local-type (type-intersection local-type global-type) global-type)) *universal-type*)) (defoptimizer (symbol-value derive-type) ((symbol) node) (derive-symbol-value-type symbol node)) (defoptimizer (symbol-global-value derive-type) ((symbol) node) (derive-symbol-value-type symbol node)) ;;;; list hackery ;;; Translate CxR into CAR/CDR combos. (defun source-transform-cxr (form) (if (/= (length form) 2) (values nil t) (let* ((name (car form)) (string (symbol-name (etypecase name (symbol name) (leaf (leaf-source-name name)))))) (do ((i (- (length string) 2) (1- i)) (res (cadr form) `(,(ecase (char string 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 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)) ;;; LIST with one arg is an extremely common operation (at least inside ;;; SBCL itself); translate it to CONS to take advantage of common ;;; allocation routines. (define-source-transform list (&rest args) (case (length args) (1 `(cons ,(first args) nil)) (t (values nil t)))) ;;; And similarly for LIST*. (define-source-transform list* (arg &rest others) (cond ((not others) arg) ((not (cdr others)) `(cons ,arg ,(car others))) (t (values nil t)))) (defoptimizer (list* derive-type) ((arg &rest args)) (if args (specifier-type 'cons) (lvar-type arg))) ;;; 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))) (deftransform last ((list &optional n) (t &optional t)) (let ((c (constant-lvar-p n))) (cond ((or (not n) (and c (eql 1 (lvar-value n)))) '(%last1 list)) ((and c (eql 0 (lvar-value n))) '(%last0 list)) (t (let ((type (lvar-type n))) (cond ((csubtypep type (specifier-type 'fixnum)) '(%lastn/fixnum list n)) ((csubtypep type (specifier-type 'bignum)) '(%lastn/bignum list n)) (t (give-up-ir1-transform "second argument type too vague")))))))) (define-source-transform gethash (&rest args) (case (length args) (2 `(sb!impl::gethash3 ,@args nil)) (3 `(sb!impl::gethash3 ,@args)) (t (values nil t)))) (define-source-transform get (&rest args) (case (length args) (2 `(sb!impl::get2 ,@args)) (3 `(sb!impl::get3 ,@args)) (t (values nil t)))) (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-lvar-p n) (give-up-ir1-transform)) (let ((n (lvar-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) `(logtest ,x 1)) (define-source-transform evenp (x) `(not (logtest ,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)) ;;; This used to be a source transform (hence the lack of restrictions ;;; on the argument types), but we make it a regular transform so that ;;; the VM has a chance to see the bare LOGTEST and potentiall choose ;;; to implement it differently. --njf, 06-02-2006 (deftransform logtest ((x y) * *) `(not (zerop (logand x y)))) (deftransform logbitp ((index integer) (unsigned-byte (or (signed-byte #.sb!vm:n-word-bits) (unsigned-byte #.sb!vm:n-word-bits)))) `(if (>= index #.sb!vm:n-word-bits) (minusp integer) (not (zerop (logand integer (ash 1 index)))))) (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. ;;; Support operations that mimic real arithmetic comparison ;;; operators, but imposing a total order on the floating points such ;;; that negative zeros are strictly less than positive zeros. (macrolet ((def (name op) `(defun ,name (x y) (declare (real x y)) (if (and (floatp x) (floatp y) (zerop x) (zerop y)) (,op (float-sign x) (float-sign y)) (,op x y))))) (def signed-zero->= >=) (def signed-zero-> >) (def signed-zero-= =) (def signed-zero-< <) (def signed-zero-<= <=)) ;;; 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 #-sb-xc-host ((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 and the ;;; function is declared strictly monotonic, then the result will be ;;; open. IF X is NIL, the result is NIL. (defun bound-func (f x strict) (declare (type function f)) (and x (handler-case (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 y (and strict (consp x)))))) ;; Some numerical operations will signal SIMPLE-TYPE-ERROR, e.g. ;; in the course of converting a bignum to a float. Default to ;; NIL in that case. (simple-type-error ())))) (defun safe-double-coercion-p (x) (or (typep x 'double-float) (<= most-negative-double-float x most-positive-double-float))) (defun safe-single-coercion-p (x) (or (typep x 'single-float) (and ;; Fix for bug 420, and related issues: during type derivation we often ;; end up deriving types for both ;; ;; (some-op ) ;; and ;; (some-op (coerce 'single-float) ) ;; ;; or other equivalent transformed forms. The problem with this ;; is that on x86 (+ ) is on the machine level ;; equivalent of ;; ;; (coerce (+ (coerce 'double-float) ;; (coerce 'double-float)) ;; 'single-float) ;; ;; so if the result of (coerce 'single-float) is not exact, the ;; derived types for the transformed forms will have an empty ;; intersection -- which in turn means that the compiler will conclude ;; that the call never returns, and all hell breaks lose when it *does* ;; return at runtime. (This affects not just +, but other operators are ;; well.) ;; ;; See also: SAFE-CTYPE-FOR-SINGLE-COERCION-P ;; ;; FIXME: If we ever add SSE-support for x86, this conditional needs to ;; change. #!+x86 (not (typep x `(or (integer * (,most-negative-exactly-single-float-fixnum)) (integer (,most-positive-exactly-single-float-fixnum) *)))) (<= most-negative-single-float x most-positive-single-float)))) ;;; 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 ;;; ANSI contaigon specifies coercion to floating point if one of the ;;; arguments is floating point. Here we should check to be sure that ;;; the other argument is within the bounds of that floating point ;;; type. (defmacro safely-binop (op x y) `(cond ((typep ,x 'double-float) (when (safe-double-coercion-p ,y) (,op ,x ,y))) ((typep ,y 'double-float) (when (safe-double-coercion-p ,x) (,op ,x ,y))) ((typep ,x 'single-float) (when (safe-single-coercion-p ,y) (,op ,x ,y))) ((typep ,y 'single-float) (when (safe-single-coercion-p ,x) (,op ,x ,y))) (t (,op ,x ,y)))) (defmacro bound-binop (op x y) (with-unique-names (xb yb res) `(and ,x ,y (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero) (let* ((,xb (type-bound-number ,x)) (,yb (type-bound-number ,y)) (,res (safely-binop ,op ,xb ,yb))) (set-bound ,res (and (or (consp ,x) (consp ,y)) ;; Open bounds can very easily be messed up ;; by FP rounding, so take care here. ,(case op (* ;; Multiplying a greater-than-zero with ;; less than one can round to zero. `(or (not (fp-zero-p ,res)) (cond ((and (consp ,x) (fp-zero-p ,xb)) (>= (abs ,yb) 1)) ((and (consp ,y) (fp-zero-p ,yb)) (>= (abs ,xb) 1))))) (/ ;; Dividing a greater-than-zero with ;; greater than one can round to zero. `(or (not (fp-zero-p ,res)) (cond ((and (consp ,x) (fp-zero-p ,xb)) (<= (abs ,yb) 1)) ((and (consp ,y) (fp-zero-p ,yb)) (<= (abs ,xb) 1))))) ((+ -) ;; Adding or subtracting greater-than-zero ;; can end up with identity. `(and (not (fp-zero-p ,xb)) (not (fp-zero-p ,yb)))))))))))) (defun coercion-loses-precision-p (val type) (typecase val (single-float) (double-float (subtypep type 'single-float)) (rational (subtypep type 'float)) (t (bug "Unexpected arguments to bounds coercion: ~S ~S" val type)))) (defun coerce-for-bound (val type) (if (consp val) (let ((xbound (coerce-for-bound (car val) type))) (if (coercion-loses-precision-p (car val) type) xbound (list xbound))) (cond ((subtypep type 'double-float) (if (<= most-negative-double-float val most-positive-double-float) (coerce val type))) ((or (subtypep type 'single-float) (subtypep type 'float)) ;; coerce to float returns a single-float (if (<= most-negative-single-float val most-positive-single-float) (coerce val type))) (t (coerce val type))))) (defun coerce-and-truncate-floats (val type) (when val (if (consp val) (let ((xbound (coerce-for-bound (car val) type))) (if (coercion-loses-precision-p (car val) type) xbound (list xbound))) (cond ((subtypep type 'double-float) (if (<= most-negative-double-float val most-positive-double-float) (coerce val type) (if (< val most-negative-double-float) most-negative-double-float most-positive-double-float))) ((or (subtypep type 'single-float) (subtypep type 'float)) ;; coerce to float returns a single-float (if (<= most-negative-single-float val most-positive-single-float) (coerce val type) (if (< val most-negative-single-float) most-negative-single-float most-positive-single-float))) (t (coerce val type)))))) ;;; 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 type-approximate-interval (type) (declare (type ctype type)) (let ((types (prepare-arg-for-derive-type type)) (result nil)) (dolist (type types) (let ((type (if (member-type-p type) (convert-member-type type) type))) (unless (numeric-type-p type) (return-from type-approximate-interval nil)) (let ((interval (numeric-type->interval type))) (setq result (if result (interval-approximate-union result interval) interval))))) result)) (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 ;;; intervals 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)))) ;;; For an interval X, if X >= POINT, return '+. If X <= POINT, return ;;; '-. Otherwise return 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)))) ;;; 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))))) ;;; 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)) (and (interval-intersection/difference (if closed-intervals-p (interval-closure x) x) (if closed-intervals-p (interval-closure y) y)) t)) ;;; 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 bound) ;; Test whether P is in the interval. (let ((pn (type-bound-number p))) (when (interval-contains-p pn (interval-closure int)) ;; Check for endpoints. (let* ((lo (interval-low int)) (hi (interval-high int)) (lon (type-bound-number lo)) (hin (type-bound-number hi))) (cond ;; Interval may be a point. ((and lon hin (= lon hin pn)) (and (numberp p) (numberp lo) (numberp hi))) ;; Point matches the low end. ;; [P] [P,?} => TRUE [P] (P,?} => FALSE ;; (P [P,?} => TRUE P) [P,?} => FALSE ;; (P (P,?} => TRUE P) (P,?} => FALSE ((and lon (= pn lon)) (or (and (numberp p) (numberp lo)) (and (consp p) (eq :low bound)))) ;; [P] {?,P] => TRUE [P] {?,P) => FALSE ;; P) {?,P] => TRUE (P {?,P] => FALSE ;; P) {?,P) => TRUE (P {?,P) => FALSE ((and hin (= pn hin)) (or (and (numberp p) (numberp hi)) (and (consp p) (eq :high bound)))) ;; Not an endpoint, all is well. (t t)))))) (test-lower-bound (p int) ;; P is a lower bound of an interval. (if p (test-number p int :low) (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 :high) (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 #'> #'<)))))) ;;; return the minimal interval, containing X and Y (defun interval-approximate-union (x y) (cond ((interval-merge-pair x y)) ((interval-< x y) (make-interval :low (copy-interval-limit (interval-low x)) :high (copy-interval-limit (interval-high y)))) (t (make-interval :low (copy-interval-limit (interval-low y)) :high (copy-interval-limit (interval-high x)))))) ;;; 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) t) :high (bound-func #'- (interval-low x) t))) ;;; 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. Use SIGNUM ;; to avoid trying to multiply huge bignums with 0.0. (* (signum (type-bound-number x)) (signum (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) (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, if ;;; the interval is closed, non-decreasing). ;;; ;;; (Actually most uses of INTERVAL-FUNC are coercions to float types, ;;; which are not monotonic increasing, so default to calling ;;; BOUND-FUNC with a non-strict argument). (defun interval-func (f x &optional increasing) (declare (type function f) (type interval x)) (let ((lo (bound-func f (interval-low x) increasing)) (hi (bound-func f (interval-high x) increasing))) (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 T if X = Y. (defun interval-= (x y) (declare (type interval x y)) (and (interval-bounded-p x 'both) (interval-bounded-p y 'both) (flet ((bound (v) (if (numberp v) v ;; Open intervals cannot be = (return-from interval-= nil)))) ;; Both intervals refer to the same point (= (bound (interval-high x)) (bound (interval-low x)) (bound (interval-high y)) (bound (interval-low y)))))) ;;; Return T if X /= Y (defun interval-/= (x y) (not (interval-intersect-p x 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 by FUN when applied to X and Y. ;;; Otherwise, we use NUMERIC-CONTAGION. (defun derive-integer-type-aux (x y fun) (declare (type function fun)) (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))) (defun derive-integer-type (x y fun) (declare (type lvar x y) (type function fun)) (let ((x (lvar-type x)) (y (lvar-type y))) (derive-integer-type-aux x y fun))) ;;; simple utility to flatten a list (defun flatten-list (x) (labels ((flatten-and-append (tree list) (cond ((null tree) list) ((atom tree) (cons tree list)) (t (flatten-and-append (car tree) (flatten-and-append (cdr tree) list)))))) (flatten-and-append x nil))) ;;; Take some type of lvar 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. (mapc-member-type-members (lambda (member) (push (if (numberp member) (make-member-type :members (list member)) *empty-type*) new-args)) arg) (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 (load-time-value (make-unportable-float :single-float-negative-zero)) lo-val)) lo) :high (if hi-float-zero-p (if (consp hi) (list (float (load-time-value (make-unportable-float :single-float-negative-zero)) 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 (load-time-value (make-unportable-float :single-float-negative-zero)) 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))) ;;; 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. ;;; ;;; If we're about to generate an overly complex union of numeric types, start ;;; collapse the ranges together. ;;; ;;; FIXME: The MEMBER canonicalization parts of MAKE-DERIVED-UNION-TYPE and ;;; entire CONVERT-MEMBER-TYPE probably belong in the kernel's type logic, ;;; invoked always, instead of in the compiler, invoked only during some type ;;; optimizations. (defvar *derived-numeric-union-complexity-limit* 6) (defun make-derived-union-type (type-list) (let ((xset (alloc-xset)) (fp-zeroes '()) (misc-types '()) (numeric-type *empty-type*)) (dolist (type type-list) (cond ((member-type-p type) (mapc-member-type-members (lambda (member) (if (fp-zero-p member) (unless (member member fp-zeroes) (pushnew member fp-zeroes)) (add-to-xset member xset))) type)) ((numeric-type-p type) (let ((*approximate-numeric-unions* (when (and (union-type-p numeric-type) (nthcdr *derived-numeric-union-complexity-limit* (union-type-types numeric-type))) t))) (setf numeric-type (type-union type numeric-type)))) (t (push type misc-types)))) (if (and (xset-empty-p xset) (not fp-zeroes)) (apply #'type-union numeric-type misc-types) (apply #'type-union (make-member-type :xset xset :fp-zeroes fp-zeroes) numeric-type 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 (cond ((typep member 'integer) `(integer ,member ,member)) ((memq member-type '(short-float single-float double-float long-float)) `(,member-type ,member ,member)) (t member-type))))) ;;; This is used in defoptimizers for computing the resulting type of ;;; a function. ;;; ;;; Given the lvar ARG, derive the resulting type using the ;;; DERIVE-FUN. DERIVE-FUN takes exactly one argument which is some ;;; "atomic" lvar 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-FUN is given it is ;;; called to compute the result otherwise the member type is first ;;; converted to a numeric type and the DERIVE-FUN is called. (defun one-arg-derive-type (arg derive-fun member-fun &optional (convert-type t)) (declare (type function derive-fun) (type (or null function) member-fun)) (let ((arg-list (prepare-arg-for-derive-type (lvar-type arg)))) (when arg-list (flet ((deriver (x) (typecase x (member-type (if member-fun (with-float-traps-masked (:underflow :overflow :divide-by-zero) (specifier-type `(eql ,(funcall member-fun (first (member-type-members x)))))) ;; Otherwise convert to a numeric type. (let ((result-type-list (funcall derive-fun (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-fun (convert-numeric-type x))) (funcall derive-fun 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-derived-union-type results) (first results))))))) ;;; Same as ONE-ARG-DERIVE-TYPE, except we assume the function takes ;;; two arguments. DERIVE-FUN 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 lvar. 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-fun fun &optional (convert-type t)) (declare (type function derive-fun fun)) (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 (ignore-errors (with-float-traps-masked (:underflow :overflow :divide-by-zero :invalid) (funcall fun x y))))) (cond ((null result) *empty-type*) ((and (floatp result) (float-nan-p result)) (make-numeric-type :class 'float :format (type-of result) :complexp :real)) (t (specifier-type `(eql ,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-fun 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-fun 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-fun 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 (lvar-type arg1))) (a2 (prepare-arg-for-derive-type (lvar-type arg2)))) (when (and a1 a2) (let ((results nil)) (if same-arg ;; Since the args are the same LVARs, 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-derived-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 (lvar-type x) (lvar-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-for-bound 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-for-bound 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-for-bound 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-for-bound 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 -)))) (defun lognot-derive-type-aux (int) (derive-integer-type-aux 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)))))) (defoptimizer (lognot derive-type) ((int)) (lognot-derive-type-aux (lvar-type int))) #-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 (lvar-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-and-truncate-floats (interval-low abs-bnd) bound-type) :high (coerce-and-truncate-floats (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 (lvar-type number)) (divisor-type (lvar-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-for-bound 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)) (defoptimizer (%unary-truncate/single-float derive-type) ((number)) (one-arg-derive-type number #'%unary-truncate-derive-type-aux #'%unary-truncate)) (defoptimizer (%unary-truncate/double-float derive-type) ((number)) (one-arg-derive-type number #'%unary-truncate-derive-type-aux #'%unary-truncate)) (defoptimizer (%unary-ftruncate derive-type) ((number)) (let ((divisor (specifier-type '(integer 1 1)))) (one-arg-derive-type number #'(lambda (n) (ftruncate-derive-type-quot-aux n divisor nil)) #'%unary-ftruncate))) (defoptimizer (%unary-round derive-type) ((number)) (one-arg-derive-type number (lambda (n) (block nil (unless (numeric-type-real-p n) (return *empty-type*)) (let* ((interval (numeric-type->interval n)) (low (interval-low interval)) (high (interval-high interval))) (when (consp low) (setf low (car low))) (when (consp high) (setf high (car high))) (specifier-type `(integer ,(if low (round low) '*) ,(if high (round high) '*)))))) #'%unary-round)) ;;; 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-for-bound 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 ;; remainder 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 remainder 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 (lvar-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))) ;;; See _Hacker's Delight_, Henry S. Warren, Jr. pp 58-63 for an ;;; explanation of LOG{AND,IOR,XOR}-DERIVE-UNSIGNED-{LOW,HIGH}-BOUND. ;;; Credit also goes to Raymond Toy for writing (and debugging!) similar ;;; versions in CMUCL, from which these functions copy liberally. (defun logand-derive-unsigned-low-bound (x y) (let ((a (numeric-type-low x)) (b (numeric-type-high x)) (c (numeric-type-low y)) (d (numeric-type-high y))) (loop for m = (ash 1 (integer-length (lognor a c))) then (ash m -1) until (zerop m) do (unless (zerop (logand m (lognot a) (lognot c))) (let ((temp (logandc2 (logior a m) (1- m)))) (when (<= temp b) (setf a temp) (loop-finish)) (setf temp (logandc2 (logior c m) (1- m))) (when (<= temp d) (setf c temp) (loop-finish)))) finally (return (logand a c))))) (defun logand-derive-unsigned-high-bound (x y) (let ((a (numeric-type-low x)) (b (numeric-type-high x)) (c (numeric-type-low y)) (d (numeric-type-high y))) (loop for m = (ash 1 (integer-length (logxor b d))) then (ash m -1) until (zerop m) do (cond ((not (zerop (logand b (lognot d) m))) (let ((temp (logior (logandc2 b m) (1- m)))) (when (>= temp a) (setf b temp) (loop-finish)))) ((not (zerop (logand (lognot b) d m))) (let ((temp (logior (logandc2 d m) (1- m)))) (when (>= temp c) (setf d temp) (loop-finish))))) finally (return (logand b d))))) (defun logand-derive-type-aux (x y &optional same-leaf) (when same-leaf (return-from logand-derive-type-aux x)) (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 ((and (null x-len) (null y-len)) (specifier-type 'unsigned-byte)) ((null x-len) (specifier-type `(unsigned-byte* ,y-len))) ((null y-len) (specifier-type `(unsigned-byte* ,x-len))) (t (let ((low (logand-derive-unsigned-low-bound x y)) (high (logand-derive-unsigned-high-bound x y))) (specifier-type `(integer ,low ,high))))) ;; X is positive, but Y might be negative. (cond ((null x-len) (specifier-type 'unsigned-byte)) (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)) (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-unsigned-low-bound (x y) (let ((a (numeric-type-low x)) (b (numeric-type-high x)) (c (numeric-type-low y)) (d (numeric-type-high y))) (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1) until (zerop m) do (cond ((not (zerop (logandc2 (logand c m) a))) (let ((temp (logand (logior a m) (1+ (lognot m))))) (when (<= temp b) (setf a temp) (loop-finish)))) ((not (zerop (logandc2 (logand a m) c))) (let ((temp (logand (logior c m) (1+ (lognot m))))) (when (<= temp d) (setf c temp) (loop-finish))))) finally (return (logior a c))))) (defun logior-derive-unsigned-high-bound (x y) (let ((a (numeric-type-low x)) (b (numeric-type-high x)) (c (numeric-type-low y)) (d (numeric-type-high y))) (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1) until (zerop m) do (unless (zerop (logand b d m)) (let ((temp (logior (- b m) (1- m)))) (when (>= temp a) (setf b temp) (loop-finish)) (setf temp (logior (- d m) (1- m))) (when (>= temp c) (setf d temp) (loop-finish)))) finally (return (logior b d))))) (defun logior-derive-type-aux (x y &optional same-leaf) (when same-leaf (return-from logior-derive-type-aux x)) (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) (let ((low (logior-derive-unsigned-low-bound x y)) (high (logior-derive-unsigned-high-bound x y))) (specifier-type `(integer ,low ,high))) (specifier-type `(unsigned-byte* *)))) ((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-unsigned-low-bound (x y) (let ((a (numeric-type-low x)) (b (numeric-type-high x)) (c (numeric-type-low y)) (d (numeric-type-high y))) (loop for m = (ash 1 (integer-length (logxor a c))) then (ash m -1) until (zerop m) do (cond ((not (zerop (logandc2 (logand c m) a))) (let ((temp (logand (logior a m) (1+ (lognot m))))) (when (<= temp b) (setf a temp)))) ((not (zerop (logandc2 (logand a m) c))) (let ((temp (logand (logior c m) (1+ (lognot m))))) (when (<= temp d) (setf c temp))))) finally (return (logxor a c))))) (defun logxor-derive-unsigned-high-bound (x y) (let ((a (numeric-type-low x)) (b (numeric-type-high x)) (c (numeric-type-low y)) (d (numeric-type-high y))) (loop for m = (ash 1 (integer-length (logand b d))) then (ash m -1) until (zerop m) do (unless (zerop (logand b d m)) (let ((temp (logior (- b m) (1- m)))) (cond ((>= temp a) (setf b temp)) (t (let ((temp (logior (- d m) (1- m)))) (when (>= temp c) (setf d temp))))))) finally (return (logxor b d))))) (defun logxor-derive-type-aux (x y &optional same-leaf) (when same-leaf (return-from logxor-derive-type-aux (specifier-type '(eql 0)))) (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) (let ((low (logxor-derive-unsigned-low-bound x y)) (high (logxor-derive-unsigned-high-bound x y))) (specifier-type `(integer ,low ,high))) (specifier-type '(unsigned-byte* *)))) ((and (not x-pos) (not y-pos)) ;; Both are negative. 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-pos) (not x-neg))) ;; Either X is negative and Y is positive or 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 (logfun) (let ((fun-aux (symbolicate logfun "-DERIVE-TYPE-AUX"))) `(defoptimizer (,logfun derive-type) ((x y)) (two-arg-derive-type x y #',fun-aux #',logfun))))) (deffrob logand) (deffrob logior) (deffrob logxor)) (defoptimizer (logeqv derive-type) ((x y)) (two-arg-derive-type x y (lambda (x y same-leaf) (lognot-derive-type-aux (logxor-derive-type-aux x y same-leaf))) #'logeqv)) (defoptimizer (lognand derive-type) ((x y)) (two-arg-derive-type x y (lambda (x y same-leaf) (lognot-derive-type-aux (logand-derive-type-aux x y same-leaf))) #'lognand)) (defoptimizer (lognor derive-type) ((x y)) (two-arg-derive-type x y (lambda (x y same-leaf) (lognot-derive-type-aux (logior-derive-type-aux x y same-leaf))) #'lognor)) (defoptimizer (logandc1 derive-type) ((x y)) (two-arg-derive-type x y (lambda (x y same-leaf) (if same-leaf (specifier-type '(eql 0)) (logand-derive-type-aux (lognot-derive-type-aux x) y nil))) #'logandc1)) (defoptimizer (logandc2 derive-type) ((x y)) (two-arg-derive-type x y (lambda (x y same-leaf) (if same-leaf (specifier-type '(eql 0)) (logand-derive-type-aux x (lognot-derive-type-aux y) nil))) #'logandc2)) (defoptimizer (logorc1 derive-type) ((x y)) (two-arg-derive-type x y (lambda (x y same-leaf) (if same-leaf (specifier-type '(eql -1)) (logior-derive-type-aux (lognot-derive-type-aux x) y nil))) #'logorc1)) (defoptimizer (logorc2 derive-type) ((x y)) (two-arg-derive-type x y (lambda (x y same-leaf) (if same-leaf (specifier-type '(eql -1)) (logior-derive-type-aux x (lognot-derive-type-aux y) nil))) #'logorc2)) ;;;; miscellaneous derive-type methods (defoptimizer (integer-length derive-type) ((x)) (let ((x-type (lvar-type x))) (when (numeric-type-p x-type) ;; 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 (isqrt derive-type) ((x)) (let ((x-type (lvar-type x))) (when (numeric-type-p x-type) (let* ((lo (numeric-type-low x-type)) (hi (numeric-type-high x-type)) (lo-res (if lo (isqrt lo) '*)) (hi-res (if hi (isqrt hi) '*))) (specifier-type `(integer ,lo-res ,hi-res)))))) (defoptimizer (char-code derive-type) ((char)) (let ((type (type-intersection (lvar-type char) (specifier-type 'character)))) (cond ((member-type-p type) (specifier-type `(member ,@(loop for member in (member-type-members type) when (characterp member) collect (char-code member))))) ((sb!kernel::character-set-type-p type) (specifier-type `(or ,@(loop for (low . high) in (character-set-type-pairs type) collect `(integer ,low ,high))))) ((csubtypep type (specifier-type 'base-char)) (specifier-type `(mod ,base-char-code-limit))) (t (specifier-type `(mod ,char-code-limit)))))) (defoptimizer (code-char derive-type) ((code)) (let ((type (lvar-type code))) ;; FIXME: unions of integral ranges? It ought to be easier to do ;; this, given that CHARACTER-SET is basically an integral range ;; type. -- CSR, 2004-10-04 (when (numeric-type-p type) (let* ((lo (numeric-type-low type)) (hi (numeric-type-high type)) (type (specifier-type `(character-set ((,lo . ,hi)))))) (cond ;; KLUDGE: when running on the host, we lose a slight amount ;; of precision so that we don't have to "unparse" types ;; that formally we can't, such as (CHARACTER-SET ((0 ;; . 0))). -- CSR, 2004-10-06 #+sb-xc-host ((csubtypep type (specifier-type 'standard-char)) type) #+sb-xc-host ((csubtypep type (specifier-type 'base-char)) (specifier-type 'base-char)) #+sb-xc-host ((csubtypep type (specifier-type 'extended-char)) (specifier-type 'extended-char)) (t #+sb-xc-host (specifier-type 'character) #-sb-xc-host type)))))) (defoptimizer (values derive-type) ((&rest values)) (make-values-type :required (mapcar #'lvar-type values))) (defun signum-derive-type-aux (type) (if (eq (numeric-type-complexp type) :complex) (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 :complex :low (coerce -1 bound-format) :high (coerce 1 bound-format))) (let* ((interval (numeric-type->interval type)) (range-info (interval-range-info interval)) (contains-0-p (interval-contains-p 0 interval)) (class (numeric-type-class type)) (format (numeric-type-format type)) (one (coerce 1 (or format class 'real))) (zero (coerce 0 (or format class 'real))) (minus-one (coerce -1 (or format class 'real))) (plus (make-numeric-type :class class :format format :low one :high one)) (minus (make-numeric-type :class class :format format :low minus-one :high minus-one)) ;; KLUDGE: here we have a fairly horrible hack to deal ;; with the schizophrenia in the type derivation engine. ;; The problem is that the type derivers reinterpret ;; numeric types as being exact; so (DOUBLE-FLOAT 0d0 ;; 0d0) within the derivation mechanism doesn't include ;; -0d0. Ugh. So force it in here, instead. (zero (make-numeric-type :class class :format format :low (- zero) :high zero))) (case range-info (+ (if contains-0-p (type-union plus zero) plus)) (- (if contains-0-p (type-union minus zero) minus)) (t (type-union minus zero plus)))))) (defoptimizer (signum derive-type) ((num)) (one-arg-derive-type num #'signum-derive-type-aux nil)) ;;;; 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 (lvar-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 (lvar-type size)) (posn (lvar-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*))) (defun %deposit-field-derive-type-aux (size posn int) (let ((size (lvar-type size)) (posn (lvar-type posn)) (int (lvar-type int))) (when (and (numeric-type-p size) (numeric-type-p posn) (numeric-type-p int)) (let ((size-high (numeric-type-high size)) (posn-high (numeric-type-high posn)) (high (numeric-type-high int)) (low (numeric-type-low int))) (when (and size-high posn-high high low ;; KLUDGE: we need this cutoff here, otherwise we ;; will merrily derive the type of %DPB as ;; (UNSIGNED-BYTE 1073741822), and then attempt to ;; canonicalize this type to (INTEGER 0 (1- (ASH 1 ;; 1073741822))), with hilarious consequences. We ;; cutoff at 4*SB!VM:N-WORD-BITS to allow inference ;; over a reasonable amount of shifting, even on ;; the alpha/32 port, where N-WORD-BITS is 32 but ;; machine integers are 64-bits. -- CSR, ;; 2003-09-12 (<= (+ size-high posn-high) (* 4 sb!vm:n-word-bits))) (let ((raw-bit-count (max (integer-length high) (integer-length low) (+ size-high posn-high)))) (specifier-type (if (minusp low) `(signed-byte ,(1+ raw-bit-count)) `(unsigned-byte* ,raw-bit-count))))))))) (defoptimizer (%dpb derive-type) ((newbyte size posn int)) (%deposit-field-derive-type-aux size posn int)) (defoptimizer (%deposit-field derive-type) ((newbyte size posn int)) (%deposit-field-derive-type-aux size posn int)) (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))))) (defoptimizer (mask-signed-field derive-type) ((size x)) (let ((size (lvar-type size))) (if (numeric-type-p size) (let ((size-high (numeric-type-high size))) (if (and size-high (<= 1 size-high sb!vm:n-word-bits)) (specifier-type `(signed-byte ,size-high)) *universal-type*)) *universal-type*))) ;;; Modular functions ;;; (ldb (byte s 0) (foo x y ...)) = ;;; (ldb (byte s 0) (foo (ldb (byte s 0) x) y ...)) ;;; ;;; and similar for other arguments. (defun make-modular-fun-type-deriver (prototype kind width signedp) (declare (ignore kind)) #!-sb-fluid (binding* ((info (info :function :info prototype) :exit-if-null) (fun (fun-info-derive-type info) :exit-if-null) (mask-type (specifier-type (ecase signedp ((nil) (let ((mask (1- (ash 1 width)))) `(integer ,mask ,mask))) ((t) `(signed-byte ,width)))))) (lambda (call) (let ((res (funcall fun call))) (when res (if (eq signedp nil) (logand-derive-type-aux res mask-type)))))) #!+sb-fluid (lambda (call) (binding* ((info (info :function :info prototype) :exit-if-null) (fun (fun-info-derive-type info) :exit-if-null) (res (funcall fun call) :exit-if-null) (mask-type (specifier-type (ecase signedp ((nil) (let ((mask (1- (ash 1 width)))) `(integer ,mask ,mask))) ((t) `(signed-byte ,width)))))) (if (eq signedp nil) (logand-derive-type-aux res mask-type))))) ;;; Try to recursively cut all uses of LVAR to WIDTH bits. ;;; ;;; For good functions, we just recursively cut arguments; their ;;; "goodness" means that the result will not increase (in the ;;; (unsigned-byte +infinity) sense). An ordinary modular function is ;;; replaced with the version, cutting its result to WIDTH or more ;;; bits. For most functions (e.g. for +) we cut all arguments; for ;;; others (e.g. for ASH) we have "optimizers", cutting only necessary ;;; arguments (maybe to a different width) and returning the name of a ;;; modular version, if it exists, or NIL. If we have changed ;;; anything, we need to flush old derived types, because they have ;;; nothing in common with the new code. (defun cut-to-width (lvar kind width signedp) (declare (type lvar lvar) (type (integer 0) width)) (let ((type (specifier-type (if (zerop width) '(eql 0) `(,(ecase signedp ((nil) 'unsigned-byte) ((t) 'signed-byte)) ,width))))) (labels ((reoptimize-node (node name) (setf (node-derived-type node) (fun-type-returns (info :function :type name))) (setf (lvar-%derived-type (node-lvar node)) nil) (setf (node-reoptimize node) t) (setf (block-reoptimize (node-block node)) t) (reoptimize-component (node-component node) :maybe)) (cut-node (node &aux did-something) (when (and (not (block-delete-p (node-block node))) (ref-p node) (constant-p (ref-leaf node))) (let* ((constant-value (constant-value (ref-leaf node))) (new-value (if signedp (mask-signed-field width constant-value) (ldb (byte width 0) constant-value)))) (unless (= constant-value new-value) (change-ref-leaf node (make-constant new-value)) (setf (lvar-%derived-type (node-lvar node)) (make-values-type :required (list (ctype-of new-value)))) (setf (block-reoptimize (node-block node)) t) (reoptimize-component (node-component node) :maybe) (return-from cut-node t)))) (when (and (not (block-delete-p (node-block node))) (combination-p node) (eq (basic-combination-kind node) :known)) (let* ((fun-ref (lvar-use (combination-fun node))) (fun-name (leaf-source-name (ref-leaf fun-ref))) (modular-fun (find-modular-version fun-name kind signedp width))) (when (and modular-fun (not (and (eq fun-name 'logand) (csubtypep (single-value-type (node-derived-type node)) type)))) (binding* ((name (etypecase modular-fun ((eql :good) fun-name) (modular-fun-info (modular-fun-info-name modular-fun)) (function (funcall modular-fun node width))) :exit-if-null)) (unless (eql modular-fun :good) (setq did-something t) (change-ref-leaf fun-ref (find-free-fun name "in a strange place")) (setf (combination-kind node) :full)) (unless (functionp modular-fun) (dolist (arg (basic-combination-args node)) (when (cut-lvar arg) (setq did-something t)))) (when did-something (reoptimize-node node name)) did-something))))) (cut-lvar (lvar &aux did-something) (do-uses (node lvar) (when (cut-node node) (setq did-something t))) did-something)) (cut-lvar lvar)))) (defun best-modular-version (width signedp) ;; 1. exact width-matched :untagged ;; 2. >/>= width-matched :tagged ;; 3. >/>= width-matched :untagged (let* ((uuwidths (modular-class-widths *untagged-unsigned-modular-class*)) (uswidths (modular-class-widths *untagged-signed-modular-class*)) (uwidths (merge 'list uuwidths uswidths #'< :key #'car)) (twidths (modular-class-widths *tagged-modular-class*))) (let ((exact (find (cons width signedp) uwidths :test #'equal))) (when exact (return-from best-modular-version (values width :untagged signedp)))) (flet ((inexact-match (w) (cond ((eq signedp (cdr w)) (<= width (car w))) ((eq signedp nil) (< width (car w)))))) (let ((tgt (find-if #'inexact-match twidths))) (when tgt (return-from best-modular-version (values (car tgt) :tagged (cdr tgt))))) (let ((ugt (find-if #'inexact-match uwidths))) (when ugt (return-from best-modular-version (values (car ugt) :untagged (cdr ugt)))))))) (defoptimizer (logand optimizer) ((x y) node) (let ((result-type (single-value-type (node-derived-type node)))) (when (numeric-type-p result-type) (let ((low (numeric-type-low result-type)) (high (numeric-type-high result-type))) (when (and (numberp low) (numberp high) (>= low 0)) (let ((width (integer-length high))) (multiple-value-bind (w kind signedp) (best-modular-version width nil) (when w ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND WIDTH SIGNEDP). ;; ;; FIXME: I think the FIXME (which is from APD) above ;; implies that CUT-TO-WIDTH should do /everything/ ;; that's required, including reoptimizing things ;; itself that it knows are necessary. At the moment, ;; CUT-TO-WIDTH sets up some new calls with ;; combination-type :FULL, which later get noticed as ;; known functions and properly converted. ;; ;; We cut to W not WIDTH if SIGNEDP is true, because ;; signed constant replacement needs to know which bit ;; in the field is the signed bit. (let ((xact (cut-to-width x kind (if signedp w width) signedp)) (yact (cut-to-width y kind (if signedp w width) signedp))) (declare (ignore xact yact)) nil) ; After fixing above, replace with T, meaning ; "don't reoptimize this (LOGAND) node any more". )))))))) (defoptimizer (mask-signed-field optimizer) ((width x) node) (let ((result-type (single-value-type (node-derived-type node)))) (when (numeric-type-p result-type) (let ((low (numeric-type-low result-type)) (high (numeric-type-high result-type))) (when (and (numberp low) (numberp high)) (let ((width (max (integer-length high) (integer-length low)))) (multiple-value-bind (w kind) (best-modular-version (1+ width) t) (when w ;; FIXME: This should be (CUT-TO-WIDTH NODE KIND W T). ;; [ see comment above in LOGAND optimizer ] (cut-to-width x kind w t) nil ; After fixing above, replace with T. )))))))) ;;; 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-lvar-p x) (not (constant-lvar-p y))) `(,(lvar-fun-name (basic-combination-fun node)) y ,(lvar-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-lvar-p op) (give-up-ir1-transform "BOOLE code is not a constant.")) (let ((control (lvar-value op))) (case control (#.sb!xc:boole-clr 0) (#.sb!xc:boole-set -1) (#.sb!xc:boole-1 'x) (#.sb!xc:boole-2 'y) (#.sb!xc:boole-c1 '(lognot x)) (#.sb!xc:boole-c2 '(lognot y)) (#.sb!xc:boole-and '(logand x y)) (#.sb!xc:boole-ior '(logior x y)) (#.sb!xc:boole-xor '(logxor x y)) (#.sb!xc:boole-eqv '(logeqv x y)) (#.sb!xc:boole-nand '(lognand x y)) (#.sb!xc:boole-nor '(lognor x y)) (#.sb!xc:boole-andc1 '(logandc1 x y)) (#.sb!xc:boole-andc2 '(logandc2 x y)) (#.sb!xc:boole-orc1 '(logorc1 x y)) (#.sb!xc: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-lvar-p y) (give-up-ir1-transform)) (let* ((y (lvar-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (and (> y-abs 0) (= y-abs (ash 1 len))) (give-up-ir1-transform)) (if (minusp y) `(- (ash x ,len)) `(ash x ,len)))) ;;; These must come before the ones below, so that they are tried ;;; first. Since %FLOOR and %CEILING are inlined, this allows ;;; the general case to be handled by TRUNCATE transforms. (deftransform floor ((x y)) `(%floor x y)) (deftransform ceiling ((x y)) `(%ceiling x y)) ;;; 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-lvar-p y) (give-up-ir1-transform)) (let* ((y (lvar-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (and (> y-abs 0) (= 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-lvar-p y) (give-up-ir1-transform)) (let* ((y (lvar-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (and (> y-abs 0) (= 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-lvar-p y) (give-up-ir1-transform)) (let* ((y (lvar-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (and (> y-abs 0) (= 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 (- ,mask 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-lvar-p y) (give-up-ir1-transform)) (let* ((y (lvar-value y)) (y-abs (abs y)) (len (1- (integer-length y-abs)))) (unless (and (> y-abs 0) (= y-abs (ash 1 len))) (give-up-ir1-transform)) (let ((mask (1- y-abs))) `(if (minusp x) (- (logand (- x) ,mask)) (logand x ,mask))))) ;;; Return an expression to calculate the integer quotient of X and ;;; constant Y, using multiplication, shift and add/sub instead of ;;; division. Both arguments must be unsigned, fit in a machine word and ;;; Y must neither be zero nor a power of two. The quotient is rounded ;;; towards zero. ;;; The algorithm is taken from the paper "Division by Invariant ;;; Integers using Multiplication", 1994 by Torbj\"{o}rn Granlund and ;;; Peter L. Montgomery, Figures 4.2 and 6.2, modified to exclude the ;;; case of division by powers of two. ;;; The algorithm includes an adaptive precision argument. Use it, since ;;; we often have sub-word value ranges. Careful, in this case, we need ;;; p s.t 2^p > n, not the ceiling of the binary log. ;;; Also, for some reason, the paper prefers shifting to masking. Mask ;;; instead. Masking is equivalent to shifting right, then left again; ;;; all the intermediate values are still words, so we just have to shift ;;; right a bit more to compensate, at the end. ;;; ;;; The following two examples show an average case and the worst case ;;; with respect to the complexity of the generated expression, under ;;; a word size of 64 bits: ;;; ;;; (UNSIGNED-DIV-TRANSFORMER 10 MOST-POSITIVE-WORD) -> ;;; (ASH (%MULTIPLY (LOGANDC2 X 0) 14757395258967641293) -3) ;;; ;;; (UNSIGNED-DIV-TRANSFORMER 7 MOST-POSITIVE-WORD) -> ;;; (LET* ((NUM X) ;;; (T1 (%MULTIPLY NUM 2635249153387078803))) ;;; (ASH (LDB (BYTE 64 0) ;;; (+ T1 (ASH (LDB (BYTE 64 0) ;;; (- NUM T1)) ;;; -1))) ;;; -2)) ;;; (defun gen-unsigned-div-by-constant-expr (y max-x) (declare (type (integer 3 #.most-positive-word) y) (type word max-x)) (aver (not (zerop (logand y (1- y))))) (labels ((ld (x) ;; the floor of the binary logarithm of (positive) X (integer-length (1- x))) (choose-multiplier (y precision) (do* ((l (ld y)) (shift l (1- shift)) (expt-2-n+l (expt 2 (+ sb!vm:n-word-bits l))) (m-low (truncate expt-2-n+l y) (ash m-low -1)) (m-high (truncate (+ expt-2-n+l (ash expt-2-n+l (- precision))) y) (ash m-high -1))) ((not (and (< (ash m-low -1) (ash m-high -1)) (> shift 0))) (values m-high shift))))) (let ((n (expt 2 sb!vm:n-word-bits)) (precision (integer-length max-x)) (shift1 0)) (multiple-value-bind (m shift2) (choose-multiplier y precision) (when (and (>= m n) (evenp y)) (setq shift1 (ld (logand y (- y)))) (multiple-value-setq (m shift2) (choose-multiplier (/ y (ash 1 shift1)) (- precision shift1)))) (cond ((>= m n) (flet ((word (x) `(truly-the word ,x))) `(let* ((num x) (t1 (%multiply-high num ,(- m n)))) (ash ,(word `(+ t1 (ash ,(word `(- num t1)) -1))) ,(- 1 shift2))))) ((and (zerop shift1) (zerop shift2)) (let ((max (truncate max-x y))) ;; Explicit TRULY-THE needed to get the FIXNUM=>FIXNUM ;; VOP. `(truly-the (integer 0 ,max) (%multiply-high x ,m)))) (t `(ash (%multiply-high (logandc2 x ,(1- (ash 1 shift1))) ,m) ,(- (+ shift1 shift2))))))))) ;;; If the divisor is constant and both args are positive and fit in a ;;; machine word, replace the division by a multiplication and possibly ;;; some shifts and an addition. Calculate the remainder by a second ;;; multiplication and a subtraction. Dead code elimination will ;;; suppress the latter part if only the quotient is needed. If the type ;;; of the dividend allows to derive that the quotient will always have ;;; the same value, emit much simpler code to handle that. (This case ;;; may be rare but it's easy to detect and the compiler doesn't find ;;; this optimization on its own.) (deftransform truncate ((x y) (word (constant-arg word)) * :policy (and (> speed compilation-speed) (> speed space))) "convert integer division to multiplication" (let* ((y (lvar-value y)) (x-type (lvar-type x)) (max-x (or (and (numeric-type-p x-type) (numeric-type-high x-type)) most-positive-word))) ;; Division by zero, one or powers of two is handled elsewhere. (when (zerop (logand y (1- y))) (give-up-ir1-transform)) `(let* ((quot ,(gen-unsigned-div-by-constant-expr y max-x)) (rem (ldb (byte #.sb!vm:n-word-bits 0) (- x (* quot ,y))))) (values quot rem)))) ;;;; 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)) (deftransform logand ((x y) (* (constant-arg t)) *) "fold identity operation" (let ((y (lvar-value y))) (unless (and (plusp y) (= y (1- (ash 1 (integer-length y))))) (give-up-ir1-transform)) (unless (csubtypep (lvar-type x) (specifier-type `(integer 0 ,y))) (give-up-ir1-transform)) 'x)) (deftransform mask-signed-field ((size x) ((constant-arg t) *) *) "fold identity operation" (let ((size (lvar-value size))) (unless (csubtypep (lvar-type x) (specifier-type `(signed-byte ,size))) (give-up-ir1-transform)) '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 lvars 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 (lvar-type x)) (y (lvar-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 lvar 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 (lvar-type x)) (y (lvar-type y))) (if (and (simple-numeric-type x) (simple-numeric-type y)) (values (type= (numeric-contagion x y) (numeric-contagion y y))))))) (def!type exact-number () '(or rational (complex rational))) ;;; Fold (+ x 0). ;;; ;;; Only safely applicable for exact numbers. For floating-point ;;; x, one would have to first show that neither x or y are signed ;;; 0s, and that x isn't an SNaN. (deftransform + ((x y) (exact-number (constant-arg (eql 0))) *) "fold zero arg" 'x) ;;; Fold (- x 0). (deftransform - ((x y) (exact-number (constant-arg (eql 0))) *) "fold zero arg" 'x) ;;; Fold (OP x +/-1) ;;; ;;; %NEGATE might not always signal correctly. (macrolet ((def (name result minus-result) `(deftransform ,name ((x y) (exact-number (constant-arg (member 1 -1)))) "fold identity operations" (if (minusp (lvar-value y)) ',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 (lvar-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) (let ((x-type (lvar-type x))) (cond ((csubtypep x-type (specifier-type '(or rational (complex rational)))) '1) ((csubtypep x-type (specifier-type 'real)) `(if (rationalp x) 1 (float 1 x))) ((csubtypep x-type (specifier-type 'complex)) ;; both parts are float `(1+ (* x ,val))) (t (give-up-ir1-transform))))) ((= 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))))) (deftransform expt ((x y) ((constant-arg (member -1 -1.0 -1.0d0)) integer) *) "recode as an ODDP check" (let ((val (lvar-value x))) (if (eql -1 val) '(- 1 (* 2 (logand 1 y))) `(if (oddp y) ,val ,(abs val))))) ;;; 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)) (macrolet ((def (name &optional float) (let ((x (if float '(float x) 'x))) `(deftransform ,name ((x y) (integer (constant-arg (member 1 -1))) *) "fold division by 1" `(values ,(if (minusp (lvar-value y)) '(%negate ,x) ',x) 0))))) (def truncate) (def round) (def floor) (def ceiling) (def ftruncate t) (def fround t) (def ffloor t) (def fceiling t)) ;;;; 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))) (or (and (> sum 161) (< sum 213)) (and (> sum 415) (< sum 461)) (and (> sum 463) (< sum 477)))))))) (deftransform char-upcase ((x) (base-char)) "open code" '(let ((n-code (char-code x))) (if (or (and (> n-code #o140) ; Octal 141 is #\a. (< n-code #o173)) ; Octal 172 is #\z. (and (> n-code #o337) (< n-code #o367)) (and (> n-code #o367) (< n-code #o377))) (code-char (logxor #x20 n-code)) x))) (deftransform char-downcase ((x) (base-char)) "open code" '(let ((n-code (char-code x))) (if (or (and (> n-code 64) ; 65 is #\A. (< n-code 91)) ; 90 is #\Z. (and (> n-code 191) (< n-code 215)) (and (> n-code 215) (< n-code 223))) (code-char (logxor #x20 n-code)) x))) ;;;; equality predicate transforms ;;; Return true if X and Y are lvars 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 lvar x y)) (let ((x-use (principal-lvar-use x)) (y-use (principal-lvar-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 (lvar-type x) (lvar-type y))) nil) (t (give-up-ir1-transform)))) (macrolet ((def (x) `(%deftransform ',x '(function * *) #'simple-equality-transform))) (def eq) (def char=)) ;;; This is similar to SIMPLE-EQUALITY-TRANSFORM, 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 a fixnum, we check to see if X is ;;; constant and if so, put X second. Doing this results in better ;;; code from the backend, since the backend assumes that any constant ;;; argument comes second. ;;; -- If either arg is definitely not a number or a fixnum, 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. (deftransform eql ((x y) * * :node node) "convert to simpler equality predicate" (let ((x-type (lvar-type x)) (y-type (lvar-type y)) (char-type (specifier-type 'character))) (flet ((fixnum-type-p (type) (csubtypep type (specifier-type 'fixnum)))) (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 (fixnum-type-p x-type) (fixnum-type-p y-type)) (commutative-arg-swap node)) ((or (eq-comparable-type-p x-type) (eq-comparable-type-p y-type)) '(eq x y)) ((and (not (constant-lvar-p y)) (or (constant-lvar-p x) (and (csubtypep x-type y-type) (not (csubtypep y-type x-type))))) '(eql y x)) (t (give-up-ir1-transform)))))) ;;; similarly to the EQL transform above, we attempt to constant-fold ;;; or convert to a simpler predicate: mostly we have to be careful ;;; with strings and bit-vectors. (deftransform equal ((x y) * *) "convert to simpler equality predicate" (let ((x-type (lvar-type x)) (y-type (lvar-type y)) (string-type (specifier-type 'string)) (bit-vector-type (specifier-type 'bit-vector))) (cond ((same-leaf-ref-p x y) t) ((and (csubtypep x-type string-type) (csubtypep y-type string-type)) '(string= x y)) ((and (csubtypep x-type bit-vector-type) (csubtypep y-type bit-vector-type)) '(bit-vector-= x y)) ;; if at least one is not a string, and at least one is not a ;; bit-vector, then we can reason from types. ((and (not (and (types-equal-or-intersect x-type string-type) (types-equal-or-intersect y-type string-type))) (not (and (types-equal-or-intersect x-type bit-vector-type) (types-equal-or-intersect y-type bit-vector-type))) (not (types-equal-or-intersect x-type y-type))) nil) (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) (number number) *) "open code" (let ((x-type (lvar-type x)) (y-type (lvar-type y))) (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)))) #!+complex-float-vops (and (csubtypep x-type (specifier-type '(or single-float (complex single-float)))) (csubtypep y-type (specifier-type '(or single-float (complex single-float))))) #!+complex-float-vops (and (csubtypep x-type (specifier-type '(or double-float (complex double-float)))) (csubtypep y-type (specifier-type '(or double-float (complex double-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."))))) (defun maybe-float-lvar-p (lvar) (neq *empty-type* (type-intersection (specifier-type 'float) (lvar-type lvar)))) (flet ((maybe-invert (node op inverted x y) ;; Don't invert if either argument can be a float (NaNs) (cond ((or (maybe-float-lvar-p x) (maybe-float-lvar-p y)) (delay-ir1-transform node :constraint) `(or (,op x y) (= x y))) (t `(if (,inverted x y) nil t))))) (deftransform >= ((x y) (number number) * :node node) "invert or open code" (maybe-invert node '> '< x y)) (deftransform <= ((x y) (number number) * :node node) "invert or open code" (maybe-invert node '< '> x y))) ;;; 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. (macrolet ((def (name inverse reflexive-p surely-true surely-false) `(deftransform ,name ((x y)) "optimize using intervals" (if (and (same-leaf-ref-p x y) ;; For non-reflexive functions we don't need ;; to worry about NaNs: (non-ref-op NaN NaN) => false, ;; but with reflexive ones we don't know... ,@(when reflexive-p '((and (not (maybe-float-lvar-p x)) (not (maybe-float-lvar-p y)))))) ,reflexive-p (let ((ix (or (type-approximate-interval (lvar-type x)) (give-up-ir1-transform))) (iy (or (type-approximate-interval (lvar-type y)) (give-up-ir1-transform)))) (cond (,surely-true t) (,surely-false nil) ((and (constant-lvar-p x) (not (constant-lvar-p y))) `(,',inverse y x)) (t (give-up-ir1-transform)))))))) (def = = t (interval-= ix iy) (interval-/= ix iy)) (def /= /= nil (interval-/= ix iy) (interval-= ix iy)) (def < > nil (interval-< ix iy) (interval->= ix iy)) (def > < nil (interval-< iy ix) (interval->= iy ix)) (def <= >= t (interval->= iy ix) (interval-< iy ix)) (def >= <= t (interval->= ix iy) (interval-< ix iy))) (defun ir1-transform-char< (x y first second inverse) (cond ((same-leaf-ref-p x y) nil) ;; If we had interval representation of character types, as we ;; might eventually have to to support 2^21 characters, then here ;; we could do some compile-time computation as in transforms for ;; < above. -- CSR, 2003-07-01 ((and (constant-lvar-p first) (not (constant-lvar-p second))) `(,inverse y x)) (t (give-up-ir1-transform)))) (deftransform char< ((x y) (character character) *) (ir1-transform-char< x y x y 'char>)) (deftransform char> ((x y) (character character) *) (ir1-transform-char< y x x y 'char<)) ;;;; 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. (defun multi-compare (predicate args not-p type &optional force-two-arg-p) (let ((nargs (length args))) (cond ((< nargs 1) (values nil t)) ((= nargs 1) `(progn (the ,type ,@args) t)) ((= nargs 2) (if not-p `(if (,predicate ,(first args) ,(second args)) nil t) (if force-two-arg-p `(,predicate ,(first args) ,(second args)) (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 (declare (type ,type ,@vars)) ,result) ,@args))))))) (define-source-transform = (&rest args) (multi-compare '= args nil 'number)) (define-source-transform < (&rest args) (multi-compare '< args nil 'real)) (define-source-transform > (&rest args) (multi-compare '> args nil 'real)) ;;; We cannot do the inversion for >= and <= here, since both ;;; (< NaN X) and (> NaN X) ;;; are false, and we don't have type-information available yet. The ;;; deftransforms for two-argument versions of >= and <= takes care of ;;; the inversion to > and < when possible. (define-source-transform <= (&rest args) (multi-compare '<= args nil 'real)) (define-source-transform >= (&rest args) (multi-compare '>= args nil 'real)) (define-source-transform char= (&rest args) (multi-compare 'char= args nil 'character)) (define-source-transform char< (&rest args) (multi-compare 'char< args nil 'character)) (define-source-transform char> (&rest args) (multi-compare 'char> args nil 'character)) (define-source-transform char<= (&rest args) (multi-compare 'char> args t 'character)) (define-source-transform char>= (&rest args) (multi-compare 'char< args t 'character)) (define-source-transform char-equal (&rest args) (multi-compare 'sb!impl::two-arg-char-equal args nil 'character t)) (define-source-transform char-lessp (&rest args) (multi-compare 'sb!impl::two-arg-char-lessp args nil 'character t)) (define-source-transform char-greaterp (&rest args) (multi-compare 'sb!impl::two-arg-char-greaterp args nil 'character t)) (define-source-transform char-not-greaterp (&rest args) (multi-compare 'sb!impl::two-arg-char-greaterp args t 'character t)) (define-source-transform char-not-lessp (&rest args) (multi-compare 'sb!impl::two-arg-char-lessp args t 'character 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 t) *) multi-not-equal)) (defun multi-not-equal (predicate args type) (let ((nargs (length args))) (cond ((< nargs 1) (values nil t)) ((= nargs 1) `(progn (the ,type ,@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 (declare (type ,type ,@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 'number)) (define-source-transform char/= (&rest args) (multi-not-equal 'char= args 'character)) (define-source-transform char-not-equal (&rest args) (multi-not-equal 'char-equal args 'character)) ;;; 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 (sfunction (symbol t list t) list) associate-args)) (defun associate-args (fun first-arg more-args identity) (let ((next (rest more-args)) (arg (first more-args))) (if (null next) `(,fun ,first-arg ,(if arg arg identity)) (associate-args fun `(,fun ,first-arg ,arg) next identity)))) ;;; Reduce constants in ARGS list. (declaim (ftype (sfunction (symbol list t symbol) list) reduce-constants)) (defun reduce-constants (fun args identity one-arg-result-type) (let ((one-arg-constant-p (ecase one-arg-result-type (number #'numberp) (integer #'integerp))) (reduced-value identity) (reduced-p nil)) (collect ((not-constants)) (dolist (arg args) (if (funcall one-arg-constant-p arg) (setf reduced-value (funcall fun reduced-value arg) reduced-p t) (not-constants arg))) ;; It is tempting to drop constants reduced to identity here, ;; but if X is SNaN in (* X 1), we cannot drop the 1. (if (not-constants) (if reduced-p `(,reduced-value ,@(not-constants)) (not-constants)) `(,reduced-value))))) ;;; 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 the type to ensure (with THE) ;;; that the argument in one-argument calls is. (declaim (ftype (function (symbol list t &optional symbol list) (values t &optional (member nil t))) source-transform-transitive)) (defun source-transform-transitive (fun args identity &optional (one-arg-result-type 'number) (one-arg-prefixes '(values))) (case (length args) (0 identity) (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args)))) (2 (values nil t)) (t (let ((reduced-args (reduce-constants fun args identity one-arg-result-type))) (associate-args fun (first reduced-args) (rest reduced-args) identity))))) (define-source-transform + (&rest args) (source-transform-transitive '+ args 0)) (define-source-transform * (&rest args) (source-transform-transitive '* args 1)) (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) (source-transform-transitive 'logeqv args -1 'integer)) (define-source-transform gcd (&rest args) (source-transform-transitive 'gcd args 0 'integer '(abs))) (define-source-transform lcm (&rest args) (source-transform-transitive 'lcm args 1 'integer '(abs))) ;;; 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 symbol list t list &optional symbol) (values list &optional (member nil t))) source-transform-intransitive)) (defun source-transform-intransitive (fun fun* args identity one-arg-prefixes &optional (one-arg-result-type 'number)) (case (length args) ((0 2) (values nil t)) (1 `(,@one-arg-prefixes (the ,one-arg-result-type ,(first args)))) (t (let ((reduced-args (reduce-constants fun* (rest args) identity one-arg-result-type))) (associate-args fun (first args) reduced-args identity))))) (define-source-transform - (&rest args) (source-transform-intransitive '- '+ args 0 '(%negate))) (define-source-transform / (&rest args) (source-transform-intransitive '/ '* args 1 '(/ 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 references to &REST argument ;;; We add magical &MORE arguments to all functions with &REST. If ARG names ;;; the &REST argument, this returns the lambda-vars for the context and ;;; count. (defun possible-rest-arg-context (arg) (when (symbolp arg) (let* ((var (lexenv-find arg vars)) (info (when (lambda-var-p var) (lambda-var-arg-info var)))) (when (and info (eq :rest (arg-info-kind info)) (consp (arg-info-default info))) (values-list (arg-info-default info)))))) (defun mark-more-context-used (rest-var) (let ((info (lambda-var-arg-info rest-var))) (aver (eq :rest (arg-info-kind info))) (destructuring-bind (context count &optional used) (arg-info-default info) (unless used (setf (arg-info-default info) (list context count t)))))) (defun mark-more-context-invalid (rest-var) (let ((info (lambda-var-arg-info rest-var))) (aver (eq :rest (arg-info-kind info))) (setf (arg-info-default info) t))) ;;; This determines of we the REF to a &REST variable is headed towards ;;; parts unknown, or if we can really use the context. (defun rest-var-more-context-ok (lvar) (let* ((use (lvar-use lvar)) (var (when (ref-p use) (ref-leaf use))) (home (when (lambda-var-p var) (lambda-var-home var))) (info (when (lambda-var-p var) (lambda-var-arg-info var))) (restp (when info (eq :rest (arg-info-kind info))))) (flet ((ref-good-for-more-context-p (ref) (let ((dest (principal-lvar-end (node-lvar ref)))) (and (combination-p dest) ;; If the destination is to anything but these, we're going to ;; actually need the rest list -- and since other operations ;; might modify the list destructively, the using the context ;; isn't good anywhere else either. (lvar-fun-is (combination-fun dest) '(%rest-values %rest-ref %rest-length %rest-null %rest-true)) ;; If the home lambda is different and isn't DX, it might ;; escape -- in which case using the more context isn't safe. (let ((clambda (node-home-lambda dest))) (or (eq home clambda) (leaf-dynamic-extent clambda))))))) (let ((ok (and restp (consp (arg-info-default info)) (not (lambda-var-specvar var)) (not (lambda-var-sets var)) (every #'ref-good-for-more-context-p (lambda-var-refs var))))) (if ok (mark-more-context-used var) (when restp (mark-more-context-invalid var))) ok)))) ;;; VALUES-LIST -> %REST-VALUES (define-source-transform values-list (list) (multiple-value-bind (context count) (possible-rest-arg-context list) (if context `(%rest-values ,list ,context ,count) (values nil t)))) ;;; NTH -> %REST-REF (define-source-transform nth (n list) (multiple-value-bind (context count) (possible-rest-arg-context list) (if context `(%rest-ref ,n ,list ,context ,count) `(car (nthcdr ,n ,list))))) (define-source-transform elt (seq n) (multiple-value-bind (context count) (possible-rest-arg-context seq) (if context `(%rest-ref ,n ,seq ,context ,count) (values nil t)))) ;;; CAR/FIRST -> %REST-REF (defun source-transform-car (list) (multiple-value-bind (context count) (possible-rest-arg-context list) (if context `(%rest-ref 0 ,list ,context ,count) (values nil t)))) (define-source-transform car (list) (source-transform-car list)) (define-source-transform first (list) (or (source-transform-car list) `(car ,list))) ;;; LENGTH -> %REST-LENGTH (defun source-transform-length (list) (multiple-value-bind (context count) (possible-rest-arg-context list) (if context `(%rest-length ,list ,context ,count) (values nil t)))) (define-source-transform length (list) (source-transform-length list)) (define-source-transform list-length (list) (source-transform-length list)) ;;; ENDP, NULL and NOT -> %REST-NULL ;;; ;;; Outside &REST convert into an IF so that IF optimizations will eliminate ;;; redundant negations. (defun source-transform-null (x op) (multiple-value-bind (context count) (possible-rest-arg-context x) (cond (context `(%rest-null ',op ,x ,context ,count)) ((eq 'endp op) `(if (the list ,x) nil t)) (t `(if ,x nil t))))) (define-source-transform not (x) (source-transform-null x 'not)) (define-source-transform null (x) (source-transform-null x 'null)) (define-source-transform endp (x) (source-transform-null x 'endp)) (deftransform %rest-values ((list context count)) (if (rest-var-more-context-ok list) `(%more-arg-values context 0 count) `(values-list list))) (deftransform %rest-ref ((n list context count)) (cond ((rest-var-more-context-ok list) `(%more-arg context n)) ((and (constant-lvar-p n) (zerop (lvar-value n))) `(car list)) (t `(nth n list)))) (deftransform %rest-length ((list context count)) (if (rest-var-more-context-ok list) 'count `(length list))) (deftransform %rest-null ((op list context count)) (aver (constant-lvar-p op)) (if (rest-var-more-context-ok list) `(eql 0 count) `(,(lvar-value op) list))) (deftransform %rest-true ((list context count)) (if (rest-var-more-context-ok list) `(not (eql 0 count)) `list)) ;;;; 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. ;;; for compile-time argument count checking. ;;; ;;; FIXME II: In some cases, type information could be correlated; for ;;; instance, ~{ ... ~} requires a list argument, so if the lvar-type ;;; of a corresponding argument is known and does not intersect the ;;; list type, a warning could be signalled. (defun check-format-args (string args fun) (declare (type string string)) (unless (typep string 'simple-string) (setq string (coerce string 'simple-string))) (multiple-value-bind (min max) (handler-case (sb!format:%compiler-walk-format-string string args) (sb!format:format-error (c) (compiler-warn "~A" c))) (when min (let ((nargs (length args))) (cond ((< nargs min) (warn 'format-too-few-args-warning :format-control "Too few arguments (~D) to ~S ~S: requires at least ~D." :format-arguments (list nargs fun string min))) ((> nargs max) (warn 'format-too-many-args-warning :format-control "Too many arguments (~D) to ~S ~S: uses at most ~D." :format-arguments (list nargs fun string max)))))))) (defoptimizer (format optimizer) ((dest control &rest args)) (when (constant-lvar-p control) (let ((x (lvar-value control))) (when (stringp x) (check-format-args x args 'format))))) ;;; We disable this transform in the cross-compiler to save memory in ;;; the target image; most of the uses of FORMAT in the compiler are for ;;; error messages, and those don't need to be particularly fast. #+sb-xc (deftransform format ((dest control &rest args) (t simple-string &rest t) * :policy (>= speed space)) (unless (constant-lvar-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 ,(lvar-value control)) ,@arg-names)))) (deftransform format ((stream control &rest args) (stream function &rest t)) (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)) (let ((arg-names (make-gensym-list (length args)))) `(lambda (tee control ,@arg-names) (declare (ignore tee)) (funcall control *standard-output* ,@arg-names) nil))) (deftransform pathname ((pathspec) (pathname) *) 'pathspec) (deftransform pathname ((pathspec) (string) *) '(values (parse-namestring pathspec))) (macrolet ((def (name) `(defoptimizer (,name optimizer) ((control &rest args)) (when (constant-lvar-p control) (let ((x (lvar-value control))) (when (stringp x) (check-format-args x args ',name))))))) (def error) (def warn) #+sb-xc-host ; Only we should be using these (progn (def style-warn) (def compiler-error) (def compiler-warn) (def compiler-style-warn) (def compiler-notify) (def maybe-compiler-notify) (def bug))) (defoptimizer (cerror optimizer) ((report control &rest args)) (when (and (constant-lvar-p control) (constant-lvar-p report)) (let ((x (lvar-value control)) (y (lvar-value report))) (when (and (stringp x) (stringp y)) (multiple-value-bind (min1 max1) (handler-case (sb!format:%compiler-walk-format-string x args) (sb!format:format-error (c) (compiler-warn "~A" c))) (when min1 (multiple-value-bind (min2 max2) (handler-case (sb!format:%compiler-walk-format-string y args) (sb!format:format-error (c) (compiler-warn "~A" c))) (when min2 (let ((nargs (length args))) (cond ((< nargs (min min1 min2)) (warn 'format-too-few-args-warning :format-control "Too few arguments (~D) to ~S ~S ~S: ~ requires at least ~D." :format-arguments (list nargs 'cerror y x (min min1 min2)))) ((> nargs (max max1 max2)) (warn 'format-too-many-args-warning :format-control "Too many arguments (~D) to ~S ~S ~S: ~ uses at most ~D." :format-arguments (list nargs 'cerror y x (max max1 max2)))))))))))))) (defoptimizer (coerce derive-type) ((value type) node) (cond ((constant-lvar-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 (lvar-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 (lvar-type value) (specifier-type 'rational)))))) ((and (policy node (zerop safety)) (csubtypep result-typeoid (specifier-type '(array * (*))))) ;; At zero safety the deftransform for COERCE can elide dimension ;; checks for the things like (COERCE X '(SIMPLE-VECTOR 5)) -- so we ;; need to simplify the type to drop the dimension information. (let ((vtype (simplify-vector-type result-typeoid))) (if vtype (specifier-type vtype) result-typeoid))) (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 (lvar-type value)) (type-type (lvar-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) (eql 1 (member-type-size cons-type)) (null (first (member-type-members cons-type)))) (let ((car-type (cons-type-car-type cons-type))) (and (member-type-p car-type) (eql 1 (member-type-members car-type)) (let ((elt (first (member-type-members car-type)))) (or (symbolp elt) (numberp elt) (and (listp elt) (numberp (first elt))))) (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 (part) ;; 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 (careful-specifier-type part))) (when coerced-type (or (and (csubtypep coerced-type (specifier-type 'float)) (csubtypep value-type (specifier-type 'real))) (and (csubtypep coerced-type (specifier-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) (block punt (let (members) (mapc-member-type-members (lambda (member) (if (coerceable-p member) (push member members) (return-from punt *universal-type*))) type) (specifier-type `(or ,@members))))) ((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 (lvar-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 (lvar-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)))))) (labels ((recurse (type) (cond ((array-type-p type) (get-element-type type)) ((union-type-p type) (apply #'type-union (mapcar #'recurse (union-type-types type)))) (t *universal-type*)))) (recurse array-type))))) (define-source-transform sb!impl::sort-vector (vector start end predicate key) ;; Like CMU CL, we use HEAPSORT. However, other than that, this code ;; isn't really related to the CMU CL code, since instead of trying ;; to generalize the CMU CL code to allow START and END values, this ;; code has been written from scratch following Chapter 7 of ;; _Introduction to Algorithms_ by Corman, Rivest, and Shamir. `(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 (;; Heaps prefer 1-based addressing. (start-1 (1- ,',start)) (current-heap-size (- ,',end ,',start)) (keyfun ,keyfun)) (declare (type (integer -1 #.(1- sb!xc: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-lvar s "S outside WHEN") ;;; (when (and (integerp s) (> s 3)) ;;; (sb-c::/report-lvar s "S inside WHEN") ;;; (let ((bound (ash 1 (1- s)))) ;;; (sb-c::/report-lvar bound "BOUND") ;;; (let ((x (- bound)) ;;; (y (1- bound))) ;;; (sb-c::/report-lvar x "X") ;;; (sb-c::/report-lvar 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-lvar (t t) null) (deftransform /report-lvar ((x message) (t t)) (format t "~%/in /REPORT-LVAR~%") (format t "/(LVAR-TYPE X)=~S~%" (lvar-type x)) (when (constant-lvar-p x) (format t "/(LVAR-VALUE X)=~S~%" (lvar-value x))) (format t "/MESSAGE=~S~%" (lvar-value message)) (give-up-ir1-transform "not a real transform")) (defun /report-lvar (x message) (declare (ignore x message)))) ;;;; Transforms for internal compiler utilities ;;; If QUALITY-NAME is constant and a valid name, don't bother ;;; checking that it's still valid at run-time. (deftransform policy-quality ((policy quality-name) (t symbol)) (unless (and (constant-lvar-p quality-name) (policy-quality-name-p (lvar-value quality-name))) (give-up-ir1-transform)) '(%policy-quality policy quality-name))