(defun bound-func (f x)
(declare (type function f))
(and x
- (with-float-traps-masked (:underflow :overflow :inexact :divide-by-zero)
- ;; With these traps masked, we might get things like infinity
- ;; or negative infinity returned. Check for this and return
- ;; NIL to indicate unbounded.
- (let ((y (funcall f (type-bound-number x))))
- (if (and (floatp y)
- (float-infinity-p y))
- nil
- (set-bound y (consp 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 (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)
`(- (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.
`(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))))
\f
;;;; arithmetic and logical identity operation elimination
projects / sbcl.git / blobdiff