CMUCL commit: src/compiler (float-tran.lisp)
Raymond Toy
rtoy at common-lisp.net
Tue Aug 17 22:17:45 CEST 2010
Date: Tuesday, August 17, 2010 @ 16:17:45
Author: rtoy
Path: /project/cmucl/cvsroot/src/compiler
Modified: float-tran.lisp
Add some smarts to the EXPT derive-type optimizer so it can handle the
case of a negative real to an integer power. Previously, this case
wasn't handled.
-----------------+
float-tran.lisp | 200 +++++++++++++++++++++++++++++++++++++++++++++++++-----
1 file changed, 183 insertions(+), 17 deletions(-)
Index: src/compiler/float-tran.lisp
diff -u src/compiler/float-tran.lisp:1.139 src/compiler/float-tran.lisp:1.140
--- src/compiler/float-tran.lisp:1.139 Tue Apr 20 13:57:46 2010
+++ src/compiler/float-tran.lisp Tue Aug 17 16:17:45 2010
@@ -5,7 +5,7 @@
;;; Carnegie Mellon University, and has been placed in the public domain.
;;;
(ext:file-comment
- "$Header: /project/cmucl/cvsroot/src/compiler/float-tran.lisp,v 1.139 2010-04-20 17:57:46 rtoy Exp $")
+ "$Header: /project/cmucl/cvsroot/src/compiler/float-tran.lisp,v 1.140 2010-08-17 20:17:45 rtoy Exp $")
;;;
;;; **********************************************************************
;;;
@@ -1033,7 +1033,7 @@
(interval-expt-> x y+))))))
;;; Handle the case when x <= 1
-(defun interval-expt-< (x y)
+(defun interval-expt-< (x y &optional integer-power-p)
(case (c::interval-range-info x 0d0)
('+
;; The case of 0 <= x <= 1 is easy
@@ -1067,34 +1067,200 @@
;; Split the interval in half
(destructuring-bind (y- y+)
(c::interval-split 0 y t)
- (list (interval-expt-< x y-)
- (interval-expt-< x y+))))))
+ (list (interval-expt-< x y- integer-power-p)
+ (interval-expt-< x y+ integer-power-p))))))
('-
- ;; The case where x <= 0. Y MUST be an INTEGER for this to
- ;; work! The calling function must insure this! For now we'll
- ;; just return the appropriate unbounded float type.
- (list (c::make-interval :low nil :high nil)))
+ ;; The case where x <= 0.
+ (cond (integer-power-p
+ ;; Y is an integer, so we can do something useful. But we
+ ;; need to split into x < -1 and -1 <= x <= 0, first
+ #+(or)
+ (progn
+ (format t "integer-power-p = ~A~%" integer-power-p)
+ (format t "x = ~A~%" x)
+ (format t "range-info y (~A) = ~A~%" y (interval-range-info y)))
+ (flet ((handle-positive-power-0 (x y)
+ ;; -1 <= X <= 0 and Y is positive. We need to
+ ;; consider if Y contains an odd integer or not.
+ ;;
+ (let* ((y-lo (bound-value (interval-low y)))
+ (min-odd (if (oddp y-lo)
+ y-lo
+ (let ((y-odd (1+ y-lo)))
+ (if (interval-contains-p y-odd y)
+ y-odd
+ nil))))
+ (min-even (if (evenp y-lo)
+ y-lo
+ (let ((y-even (1+ y-lo)))
+ (if (interval-contains-p y-even y)
+ y-even
+ nil)))))
+ ;; At least one of min-odd and min-even must be non-NIL!
+ (assert (or min-odd min-even))
+ (cond ((and min-odd min-even)
+ ;; The Y interval contains both even and odd
+ ;; integers. Then the lower bound is (least
+ ;; x)^(least positive odd), because this
+ ;; creates the most negative value. The upper
+ ;; is (most x)^(least positive even), because
+ ;; this is the most positive number.
+ ;;
+ (let ((lo (safe-expt (bound-value (interval-low x))
+ min-odd))
+ (hi (safe-expt (bound-value (interval-high x))
+ min-even)))
+ (list (make-interval :low lo :high hi))))
+ (min-odd
+ ;; Y consists of just one odd integer.
+ (assert (oddp min-odd))
+ (let ((lo (safe-expt (bound-value (interval-low x))
+ min-odd))
+ (hi (safe-expt (bound-value (interval-high x))
+ min-odd)))
+ (list (make-interval :low lo :high hi))))
+ (min-even
+ ;; Y consists of just one even integer.
+ (assert (evenp min-even))
+ (let ((lo (safe-expt (bound-value (interval-high x))
+ min-even))
+ (hi (safe-expt (bound-value (interval-low x))
+ min-even)))
+ (list (make-interval :low lo :high hi)))))))
+ (handle-positive-power-1 (x y)
+ ;; X <= -1, Y is a positive integer.
+ (let* ((y-hi (bound-value (interval-high y)))
+ (max-odd (if (oddp y-hi)
+ y-hi
+ (let ((y-odd (1- y-hi)))
+ (if (interval-contains-p y-odd y)
+ y-odd
+ nil))))
+ (max-even (if (evenp y-hi)
+ y-hi
+ (let ((y-even (1- y-hi)))
+ (if (interval-contains-p y-even y)
+ y-even
+ nil)))))
+ ;; At least one of max-odd and max-even must be non-NIL!
+ (assert (or max-odd max-even))
+ (cond ((and max-odd max-even)
+ ;; The Y interval contains both even and odd
+ ;; integers. Then the lower bound is (least
+ ;; x)^(most positive odd), because this
+ ;; creates the most negative value. The upper
+ ;; is (least x)^(most positive even), because
+ ;; this is the most positive number.
+ ;;
+ (let ((lo (safe-expt (bound-value (interval-low x))
+ max-odd))
+ (hi (safe-expt (bound-value (interval-low x))
+ max-even)))
+ (list (make-interval :low lo :high hi))))
+ (max-odd
+ ;; Y consists of just one odd integer.
+ (assert (oddp max-odd))
+ (let ((lo (safe-expt (bound-value (interval-low x))
+ max-odd))
+ (hi (safe-expt (bound-value (interval-high x))
+ max-odd)))
+ (list (make-interval :low lo :high hi))))
+ (max-even
+ ;; Y consists of just one even integer.
+ (assert (evenp max-even))
+ (let ((lo (safe-expt (bound-value (interval-high x))
+ max-even))
+ (hi (safe-expt (bound-value (interval-low x))
+ max-even)))
+ (list (make-interval :low lo :high hi))))))))
+ (case (interval-range-info x -1)
+ ('+
+ ;; -1 <= x <= 0
+ #+(or)
+ (format t "x range +~%")
+ (case (interval-range-info y 0)
+ ('+
+ (handle-positive-power-0 x y))
+ ('-
+ ;; Y is negative. We should do something better
+ ;; than this because there's an extra rounding which
+ ;; we shouldn't do.
+ #+(or)
+ (format t "Handle y neg~%")
+ (let ((unit (make-interval :low 1 :high 1))
+ (result (handle-positive-power-0 x (interval-neg y))))
+ #+(or)
+ (format t "result = ~A~%" result)
+ (mapcar #'(lambda (r)
+ (interval-div unit r))
+ result)))
+ (t
+ ;; Split the interval and try again.
+ (multiple-value-bind (y- y+)
+ (values (make-interval :low (interval-low y)
+ :high -1)
+ (make-interval :low 1
+ :high (interval-high y)))
+ (append (list (make-interval :low 1 :high 1))
+ (interval-expt-< x y- integer-power-p)
+ (interval-expt-< x y+ integer-power-p))))))
+ ('-
+ ;; x < -1
+ (case (c::interval-range-info y)
+ ('+
+ ;; Y is positive. We need to consider if Y contains an
+ ;; odd integer or not.
+ ;;
+ (handle-positive-power-1 x y))
+ ('-
+ ;; Y is negative. Do this in a better way
+ (let ((unit (make-interval :low 1 :high 1))
+ (result (handle-positive-power-1 x (interval-neg y))))
+ (mapcar #'(lambda (r)
+ (interval-div unit r))
+ result)))
+ (t
+ ;; Split the interval and try again.
+ #+(or)
+ (format t "split y ~A~%" y)
+ (multiple-value-bind (y- y+)
+ (values (make-interval :low (interval-low y) :high -1)
+ (make-interval :low 1 :high (interval-high y)))
+ (append (list (make-interval :low 1 :high 1))
+ (interval-expt-< x y- integer-power-p)
+ (interval-expt-< x y+ integer-power-p))))))
+ (t
+ #+(or)
+ (format t "splitting x ~A~%" x)
+ (destructuring-bind (neg pos)
+ (interval-split -1 x t t)
+ (append (interval-expt-< neg y integer-power-p)
+ (interval-expt-< pos y integer-power-p)))))))
+ (t
+ ;; Y is not an integer. Just give up and return an
+ ;; unbounded interval.
+ (list (c::make-interval :low nil :high nil)))))
(t
(destructuring-bind (neg pos)
(interval-split 0 x t t)
- (list (interval-expt-< neg y)
- (interval-expt-< pos y))))))
+ (append (interval-expt-< neg y integer-power-p)
+ (interval-expt-< pos y integer-power-p))))))
;;; Compute bounds for (expt x y)
-(defun interval-expt (x y)
+(defun interval-expt (x y &optional integer-power-p)
(case (interval-range-info x 1)
('+
;; X >= 1
(interval-expt-> x y))
('-
;; X <= 1
- (interval-expt-< x y))
+ (interval-expt-< x y integer-power-p))
(t
(destructuring-bind (left right)
(interval-split 1 x t t)
- (list (interval-expt left y)
- (interval-expt right y))))))
+ (append (interval-expt left y integer-power-p)
+ (interval-expt right y integer-power-p))))))
(defun fixup-interval-expt (bnd x-int y-int x-type y-type)
(declare (ignore x-int))
@@ -1228,12 +1394,12 @@
;; A number to some power is a number.
(specifier-type 'number)))))
-(defun merged-interval-expt (x y)
+(defun merged-interval-expt (x y &optional integer-power-p)
(let* ((x-int (numeric-type->interval x))
(y-int (numeric-type->interval y)))
(mapcar #'(lambda (type)
(fixup-interval-expt type x-int y-int x y))
- (flatten-list (interval-expt x-int y-int)))))
+ (flatten-list (interval-expt x-int y-int integer-power-p)))))
(defun expt-derive-type-aux (x y same-arg)
(declare (ignore same-arg))
@@ -1243,7 +1409,7 @@
(numeric-contagion x y))
((csubtypep y (specifier-type 'integer))
;; A real raised to an integer power is well-defined
- (merged-interval-expt x y))
+ (merged-interval-expt x y t))
(t
;; A real raised to a non-integral power is complicated....
(cond ((or (csubtypep x (specifier-type '(rational 0)))
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