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; Centaur Bitops Library
; Copyright (C) 2010-2011 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@centtech.com>
(in-package "BITSETS")
(include-book "std/util/define" :dir :system)
(local (include-book "ihs/logops-lemmas" :dir :system))
(local (in-theory (disable logand acl2::loghead unsigned-byte-p)))
(define bignum-extract
:parents (ttag-bitset-members)
:short "Extract a particular 32-bit slice of an integer."
((x integerp "Integer to extract from")
(slice natp "Which 32 bit slice to extract"))
:returns
(extracted natp :rule-classes :type-prescription)
:long "<p>Logically, @(call bignum-extract) is essentially:</p>
@({
(logand (ash x (* -32 slice)) (1- (expt 2 32)))
})
<p>What does this do? Imagine partitioning the integer @('x') into a list of
32-bit slices. Say that the least-significant 32 bits are the 0th slice, and
so on. The @('bignum-extract') function is just extracting the @('slice')th
slice of @('x').</p>
<p>The logical definition of @('bignum-extract') is not very efficient; when
@('x') is a bignum, the @('(ash x (* -32 slice))') term will generally require
us to create a new bignum.</p>
<p>You may <b>optionally, with a trust tag</b> load an raw Lisp replacement
which, on 64-bit CCL that takes advantage of the underlying representation of
bignums, and on other Lisps implements this function using <b>ldb</b>, which
may have or may not be more optimal.</p>"
:verify-guards nil
(mbe :logic (let ((x (ifix x))
(slice (nfix slice)))
(logand (1- (expt 2 32))
(ash x (* -32 slice))))
:exec (the (unsigned-byte 32)
(logand (the (unsigned-byte 32) (1- (expt 2 32)))
(ash x (* -32 slice)))))
///
(defthm unsigned-byte-p-of-bignum-extract
(unsigned-byte-p 32 (bignum-extract x slice)))
(make-event
`(defthm upper-bound-of-bignum-extract
(< (bignum-extract x slice) ,(expt 2 32))
:rule-classes :linear
:hints(("Goal" :use ((:instance unsigned-byte-p-of-bignum-extract))))))
(verify-guards bignum-extract))
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