diff --git a/compiler/float-tran.lisp b/compiler/float-tran.lisp index 178b979909529734b09ac37049f2d64074acd9e1..c1d5eccf82cfc11a37ca3f3a5dc9fd5d3c7203f7 100644 --- a/compiler/float-tran.lisp +++ b/compiler/float-tran.lisp @@ -5,7 +5,7 @@ ;;; Carnegie Mellon University, and has been placed in the public domain. ;;; (ext:file-comment - "$Header: /Volumes/share2/src/cmucl/cvs2git/cvsroot/src/compiler/float-tran.lisp,v 1.139 2010/04/20 17:57:46 rtoy Exp $") + "$Header: /Volumes/share2/src/cmucl/cvs2git/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)))