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|
;;;***************************************************************
;;;An ACL2 Library of Floating Point Arithmetic
;;;David M. Russinoff
;;;Advanced Micro Devices, Inc.
;;;February, 1998
;;;***************************************************************
#|
This book contains a few hacks about fl which aren't used elsewhere in support/.
|#
(in-package "ACL2")
(include-book "ground-zero")
;(include-book "basic") ;drop?
(defund fl (x)
(declare (xargs :guard (real/rationalp x)))
(floor x 1))
(local (include-book "inverted-factor"))
(local (include-book "nniq"))
(local (include-book "numerator"))
(local (include-book "denominator"))
(local (include-book "fp2"))
(local (include-book "predicate"))
(local (include-book "product"))
(local (include-book "unary-divide"))
(local (include-book "rationalp"))
(local (include-book "integerp"))
(local (include-book "fl")) ;drop?
(local (include-book "mod"))
(local (include-book "even-odd"))
(local (include-book "meta/meta-plus-equal" :dir :system))
(local (include-book "arith"))
;used anywhere?
;exported in lib/basic
(defthm fl-m-1
(implies (and (< 0 n) ;(not (equal n 0))
(integerp m)
(integerp n)
)
(= (fl (- (/ (1+ m) n)))
(1- (- (fl (/ m n))))))
:otf-flg t
:rule-classes ()
:hints (
("goal" :in-theory (disable fl-def-linear-part-2
LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE)
:use ((:instance fl-of-fraction-min-change
(p (+ 1 m)) (q n))
(:instance fl-unique (x (* M (/ N)))
(n (+ -1 (+ (/ N) (* M (/ N))))))
(:instance fl-unique (x (+ (/ N) (* M (/ N))))
(n (FL (* M (/ N)))))
))))
;remove? doesn't seem to be used anywhere or exported in lib/
;just a special case of the above...
(defthm fl-lemma
(implies (integerp m)
(= (fl (- (/ (1+ m) 2)))
(1- (- (fl (/ m 2))))))
:rule-classes ()
:hints (("goal" :use (:instance fl-m-1 (n 2)))))
|
