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; RTL - A Formal Theory of Register-Transfer Logic and Computer Arithmetic
; Copyright (C) 1995-2013 Advanced Mirco Devices, Inc.
;
; Contact:
; David Russinoff
; 1106 W 9th St., Austin, TX 78703
; http://www.russsinoff.com/
;
; This program is free software; you can redistribute it and/or modify it under
; the terms of the GNU General Public License as published by the Free Software
; Foundation; either version 2 of the License, or (at your option) any later
; version.
;
; This program is distributed in the hope that it will be useful but WITHOUT ANY
; WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
; PARTICULAR PURPOSE. See the GNU General Public License for more details.
;
; You should have received a copy of the GNU General Public License along with
; this program; see the file "gpl.txt" in this directory. If not, write to the
; Free Software Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA
; 02110-1335, USA.
;
; Author: David M. Russinoff (david@russinoff.com)
;;;***************************************************************
;;;An ACL2 Library of Floating Point Arithmetic
;;;David M. Russinoff
;;;Advanced Micro Devices, Inc.
;;;February, 1998
;;;***************************************************************
(in-package "ACL2")
;BOZO include less...
(include-book "log")
(include-book "float")
(include-book "trunc")
(include-book "land0")
(local (include-book "bits-trunc-proofs"))
(defthm bits-trunc-2
(implies (and (= n (1+ (expo x)))
(>= x 0)
(integerp k)
(> k 0)
)
(= (trunc x k)
(* (expt 2 (- n k))
(bits x (1- n) (- n k)))))
:rule-classes ())
(defthm bits-trunc-original
(implies (and (>= x (expt 2 (1- n)))
(< x (expt 2 n))
(integerp x) (> x 0)
(integerp m) (>= m n)
(integerp n) (> n k)
(integerp k) (> k 0)
)
(= (trunc x k)
(land0 x (- (expt 2 m) (expt 2 (- n k))) n)))
:rule-classes ())
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