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|
; Centaur Bitops Library
; Copyright (C) 2014 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: Shilpi Goel <shilpi@centtech.com>
(in-package "BITOPS")
(include-book "xdoc/top" :dir :system)
(include-book "std/basic/arith-equivs" :dir :system)
(include-book "ihs/basic-definitions" :dir :system)
(include-book "part-select")
(local (include-book "ihsext-basics"))
(local (include-book "equal-by-logbitp"))
;; (local (include-book "signed-byte-p"))
;; (local (in-theory (enable bitops::ash-1-removal)))
(local (in-theory (disable logmask)))
;; ======================================================================
(defsection bitops/part-install
:parents (bitops)
:short "This book provides a way to set a portion of an integer to
some value.")
;; ======================================================================
(defsection part-install
:parents (bitops/part-install)
:short "Set a portion of bits of an integer to some value"
:long "<p>@('part-install') is a macro that is defined in terms of
the function @('part-install-width-low'). This macro can be used to
set a portion of bits from an integer to some value.</p>
<p>Usage:</p>
@({
(part-install val x :low 8 :high 15) ;; x[15:8] = val
(part-install val x :low 8 :width 8) ;; x[15:8] = val
})
@(def part-install-width-low)
@(def part-install)
"
(local
(defthm logmask-and-ash
(implies (natp n)
(equal (+ -1 (ash 1 n))
(logmask n)))
:hints(("Goal" :in-theory (enable logmask ash-1-removal)))))
(defun-inline part-install-width-low (val x width low)
(declare (xargs :guard (and (integerp x)
(integerp val)
(natp width)
(natp low))
:guard-hints (("Goal" :in-theory
(disable
logmask ash-1-removal)))))
(mbe :logic
(let* ((x (ifix x))
(val (ifix val))
(width (nfix width))
(low (nfix low))
(val (loghead width val))
(mask (logmask width)))
(logior (logand x (lognot (ash mask low)))
(ash val low)))
:exec
(let* ((mask (1- (ash 1 width)))
(val (logand mask val)))
(logior (logand x (lognot (ash mask low)))
(ash val low)))))
;; [Shilpi]: Would be nice to have a theorem like this...
;; (defthm part-install-width-low**
;; (equal (part-install-width-low val x width low)
;; (if (zp width)
;; (ifix x)
;; (part-install-width-low
;; (logcdr val)
;; (install-bit low (logcar val) x)
;; (1- width)
;; (1+ low))))
;; :hints (("Goal" :in-theory (e/d (install-bit) (ash-1-removal)))))
(defthm natp-part-install-width-low
(implies (<= 0 x)
(natp (part-install-width-low val x width low)))
:rule-classes :type-prescription)
(defcong int-equiv equal (part-install-width-low val x width low) 1)
(defcong int-equiv equal (part-install-width-low val x width low) 2)
(defcong nat-equiv equal (part-install-width-low val x width low) 3)
(defcong nat-equiv equal (part-install-width-low val x width low) 4)
(defmacro part-install (val x &key low high width)
(cond ((and high width)
(er hard? 'part-install "Can't use :high and :width together."))
((and low high (integerp low) (integerp high))
`(part-install-width-low ,val ,x ,(+ 1 high (- low)) ,low))
((and low high)
`(part-install-width-low ,val ,x (+ 1 ,high (- ,low)) ,low))
((and low width)
`(part-install-width-low ,val ,x ,width ,low))
(t
(er hard? 'part-install
"Need either :low and :width, or :low and :high."))))
(add-macro-alias part-install part-install-width-low$inline)
(defthm unsigned-byte-p-=-n-of-part-install-width-low
(implies (and (unsigned-byte-p n x)
(<= (+ width low) n)
(natp n)
(natp low)
(natp width))
(unsigned-byte-p n (part-install-width-low val x width low)))
:hints (("Goal" :in-theory (e/d () (unsigned-byte-p)))))
(defthm unsigned-byte-p->-n-of-part-install-width-low
(implies (and (unsigned-byte-p n x)
(< n (+ width low))
(natp low)
(natp width))
(unsigned-byte-p
(+ low width)
(part-install-width-low val x width low)))
:hints (("Goal" :in-theory (e/d () (unsigned-byte-p)))))
)
;; ======================================================================
; Matt K. addition: Avoid ACL2(p) failure due to logbitp-reasoning.
(local (include-book "std/system/non-parallel-book" :dir :system))
(local (acl2::non-parallel-book))
(defsection part-select-and-part-install
:parents (bitops/part-install bitops/part-select)
:short "Interactions between @('part-select') and @('part-install')"
(defthm logbitp-of-part-select-split
(equal (logbitp n (part-select-width-low x width low))
(and (< (nfix n) (nfix width))
(logbitp (+ (nfix n) (nfix low)) x)))
:hints(("Goal" :in-theory (enable part-select-width-low))))
(defthm logbitp-of-part-install-split
(equal (logbitp n (part-install-width-low val x width low))
(if (and (< (nfix n) (+ (nfix low) (nfix width)))
(<= (nfix low) (nfix n)))
(logbitp (- (nfix n) (nfix low)) val)
(logbitp n x)))
:hints(("Goal" :in-theory (enable part-install-width-low))))
;; (local
;; (encapsulate
;; ()
;; (local (include-book "arithmetic-5/top" :dir :system))
;; (defthm loghead-b-of-lognot-ash-a-where-a->=-b
;; (implies (and (natp a)
;; (natp b)
;; (integerp x)
;; (<= b a))
;; (equal (loghead b (lognot (ash x a)))
;; (1- (ash 1 b))))
;; :hints (("Goal" :in-theory (e/d (loghead lognot) ()))))
;; ))
;; (local (include-book "arithmetic/top-with-meta" :dir :system))
;; (local
;; (defthm loghead-with-zero-or-negative-size-=-0
;; (implies (<= n 0)
;; (equal (loghead n x) 0))
;; :hints (("Goal" :in-theory (e/d (loghead**) ())))))
;; (local
;; (defthm lognot-of-logmask
;; (implies (natp width)
;; (equal (lognot (logmask width))
;; (- (ash 1 width))))
;; :hints (("Goal" :in-theory (e/d (ifix lognot expt) ())))))
;; (local
;; (defthm logcdr-minus-logcons-0-n
;; (implies (integerp n)
;; (equal (logcdr (- (logcons 0 n)))
;; (- n)))
;; :hints (("Goal" :in-theory (e/d (logcdr logcons floor) ())))))
;; (local
;; (defthm loghead-lognot-and-logmask
;; (implies (natp width)
;; (equal (loghead width (lognot (logmask width))) 0))
;; :hints (("Goal" :in-theory
;; (e/d* (ihsext-recursive-redefs ihsext-inductions)
;; (logmask ash-1-removal))))))
(defthm part-select-and-part-install-same
(equal (part-select-width-low
(part-install-width-low val x width low)
width low)
(loghead width val))
:hints ((logbitp-reasoning)))
;; (defthm logtail-a-of-logmask-b-where-a->=-b
;; (implies (and (natp a)
;; (natp b)
;; (integerp x)
;; (<= b a))
;; (equal (logtail a (logmask b))
;; 0))
;; :hints (("Goal" :in-theory (e/d* (ihsext-recursive-redefs
;; ihsext-inductions logcar logcdr)
;; (ash-1-removal)))))
(defthm part-select-and-part-install-completely-different-1
(implies (<= (+ (nfix low-i) (nfix width-i)) (nfix low-s))
(equal (part-select-width-low
(part-install-width-low val x width-i low-i)
width-s low-s)
(part-select-width-low x width-s low-s)))
:hints ((logbitp-reasoning)))
;; (local
;; (defthm loghead-b-of-shift-by-a-where-a->=-b
;; (implies (and (natp a)
;; (natp b)
;; (<= b a))
;; (equal (loghead b (ash x a))
;; 0))
;; :hints (("Goal" :in-theory (e/d () (loghead-of-ash))
;; :use ((:instance loghead-of-ash
;; (n b)
;; (x x)
;; (m a)))))))
(defthm part-select-and-part-install-completely-different-2
(implies (<= (+ (nfix low-s) (nfix width-s)) (nfix low-i))
(equal (part-select-width-low
(part-install-width-low val x width-i low-i)
width-s low-s)
(part-select-width-low x width-s low-s)))
:hints ((logbitp-reasoning)))
;; [Shilpi]: Prove theorems about over-lapping bit portions of
;; select and install?
(defthmd part-install-in-terms-of-logapp
(equal (part-install val x :width width :low low)
(logapp low x (logapp width val (logtail (+ (nfix low) (nfix width)) x))))
:hints ((logbitp-reasoning))))
;; ======================================================================
|
