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;; Copyright (C) 2017, Regents of the University of Texas
;; Written by Cuong Chau
;; License: A 3-clause BSD license. See the LICENSE file distributed with
;; ACL2.
;; Cuong Chau <ckcuong@cs.utexas.edu>
;; March 2019
(in-package "ADE")
(include-book "../merge")
(include-book "../vector-module")
(include-book "../adders/subtractor")
(include-book "../comparators/v-less")
(local (include-book "arithmetic-3/top" :dir :system))
;; ======================================================================
;; DE Module Generator of GCD-BODY1
;;
;; GCD-BODY1 performs the gcd operation in one iteration.
(defconst *gcd-body1$go-num* *merge$go-num*)
(defun gcd-body1$data-ins-len (data-size)
(declare (xargs :guard (natp data-size)))
(+ 2 (* 2 (mbe :logic (nfix data-size)
:exec data-size))))
(defun gcd-body1$ins-len (data-size)
(declare (xargs :guard (natp data-size)))
(+ (gcd-body1$data-ins-len data-size)
*gcd-body1$go-num*))
(module-generator
gcd-body1* (data-size)
(si 'gcd-body1 data-size)
(list* 'full-in 'empty-out-
(append (sis 'data-in 0 (* 2 data-size))
(sis 'go 0 *gcd-body1$go-num*)))
(list* 'act
(sis 'data-out 0 (* 2 data-size)))
()
(list
(list 'a<b?
'(a<b)
(si 'v-< data-size)
(append (rev (sis 'data-in 0 data-size))
(rev (sis 'data-in data-size data-size))))
(list 'a-b
(sis 'a-b 0 (1+ data-size))
(si 'ripple-sub data-size)
(append (sis 'data-in 0 data-size)
(sis 'data-in data-size data-size)))
(list 'out0
(sis 'data0-out 0 (* 2 data-size))
(si 'v-buf (* 2 data-size))
(append (sis 'a-b 0 data-size)
(sis 'data-in data-size data-size)))
(list 'b-a
(sis 'b-a 0 (1+ data-size))
(si 'ripple-sub data-size)
(append (sis 'data-in data-size data-size)
(sis 'data-in 0 data-size)))
(list 'out1
(sis 'data1-out 0 (* 2 data-size))
(si 'v-buf (* 2 data-size))
(append (sis 'b-a 0 data-size)
(sis 'data-in 0 data-size)))
(list 'me
(list* 'act 'act0 'act1
(sis 'data-out 0 (* 2 data-size)))
(si 'merge (* 2 data-size))
(list* 'full-in 'full-in 'empty-out- 'a<b
(append (sis 'data0-out 0 (* 2 data-size))
(sis 'data1-out 0 (* 2 data-size))
(sis 'go 0 *merge$go-num*)))))
(declare (xargs :guard (natp data-size))))
;; DE netlist generator. A generated netlist will contain an instance of
;; GCD-BODY1.
(defund gcd-body1$netlist (data-size)
(declare (xargs :guard (natp data-size)))
(cons (gcd-body1* data-size)
(union$ (merge$netlist (* 2 data-size))
(v-buf$netlist (* 2 data-size))
(v-<$netlist data-size)
(ripple-sub$netlist data-size)
:test 'equal)))
;; Recognizer for GCD-BODY1
(defund gcd-body1& (netlist data-size)
(declare (xargs :guard (and (alistp netlist)
(natp data-size))))
(b* ((subnetlist (delete-to-eq (si 'gcd-body1 data-size) netlist)))
(and (equal (assoc (si 'gcd-body1 data-size) netlist)
(gcd-body1* data-size))
(merge& subnetlist (* 2 data-size))
(v-buf& subnetlist (* 2 data-size))
(v-<& subnetlist data-size)
(ripple-sub& subnetlist data-size))))
;; Sanity check
(local
(defthmd check-gcd-body1$netlist-64
(and (net-syntax-okp (gcd-body1$netlist 64))
(net-arity-okp (gcd-body1$netlist 64))
(gcd-body1& (gcd-body1$netlist 64) 64))))
;; Extract the input and output signals for GCD-BODY1
(progn
;; Extract the input data
(defun gcd-body1$data-in (inputs data-size)
(declare (xargs :guard (and (true-listp inputs)
(natp data-size))))
(take (* 2 (mbe :logic (nfix data-size)
:exec data-size))
(nthcdr 2 inputs)))
(defthm len-gcd-body1$data-in
(equal (len (gcd-body1$data-in inputs data-size))
(* 2 (nfix data-size))))
(in-theory (disable gcd-body1$data-in))
;; Extract the "a<b" signal
(defund gcd-body1$a<b (inputs data-size)
(b* ((data-in (gcd-body1$data-in inputs data-size)))
(fv-< nil t
(rev (take data-size data-in))
(rev (nthcdr data-size data-in)))))
;; Extract the 1st input data item for the merge
(defund gcd-body1$data0-out (inputs data-size)
(b* ((data-in (gcd-body1$data-in inputs data-size)))
(v-threefix
(append (fv-adder-output t
(take data-size data-in)
(fv-not (nthcdr data-size data-in)))
(nthcdr data-size data-in)))))
(defthm len-gcd-body1$data0-out
(equal (len (gcd-body1$data0-out inputs data-size))
(* 2 (nfix data-size)))
:hints (("Goal" :in-theory (enable gcd-body1$data0-out))))
(defthm bvp-gcd-body1$data0-out
(implies (bvp (gcd-body1$data-in inputs data-size))
(bvp (gcd-body1$data0-out inputs data-size)))
:hints (("Goal" :in-theory (enable gcd-body1$data0-out))))
;; Extract the 2nd input data item for the merge
(defund gcd-body1$data1-out (inputs data-size)
(b* ((data-in (gcd-body1$data-in inputs data-size)))
(v-threefix
(append (fv-adder-output t
(nthcdr data-size data-in)
(fv-not (take data-size data-in)))
(take data-size data-in)))))
(defthm len-gcd-body1$data1-out
(equal (len (gcd-body1$data1-out inputs data-size))
(* 2 (nfix data-size)))
:hints (("Goal" :in-theory (enable gcd-body1$data1-out))))
(defthm bvp-gcd-body1$data1-out
(implies (bvp (gcd-body1$data-in inputs data-size))
(bvp (gcd-body1$data1-out inputs data-size)))
:hints (("Goal" :in-theory (enable gcd-body1$data1-out))))
;; Extract the inputs for the merge joint
(defund gcd-body1$me-inputs (inputs data-size)
(b* ((full-in (nth 0 inputs))
(empty-out- (nth 1 inputs))
(go-signals (nthcdr (gcd-body1$data-ins-len data-size) inputs))
(a<b (gcd-body1$a<b inputs data-size))
(data0-out (gcd-body1$data0-out inputs data-size))
(data1-out (gcd-body1$data1-out inputs data-size)))
(list* full-in full-in empty-out- a<b
(append data0-out data1-out go-signals))))
;; Extract the "act" signal
(defund gcd-body1$act (inputs data-size)
(merge$act (gcd-body1$me-inputs inputs data-size)
(* 2 data-size)))
(defthm gcd-body1$act-inactive
(implies (or (not (nth 0 inputs))
(equal (nth 1 inputs) t))
(not (gcd-body1$act inputs data-size)))
:hints (("Goal" :in-theory (enable gcd-body1$me-inputs
gcd-body1$act))))
;; Extract the output data
(defund gcd-body1$data-out (inputs data-size)
(fv-if (gcd-body1$a<b inputs data-size)
(gcd-body1$data1-out inputs data-size)
(gcd-body1$data0-out inputs data-size)))
(defthm len-gcd-body1$data-out
(equal (len (gcd-body1$data-out inputs data-size))
(* 2 (nfix data-size)))
:hints (("Goal" :in-theory (enable gcd-body1$data-out))))
(defthm bvp-gcd-body1$data-out
(implies (bvp (gcd-body1$data-in inputs data-size))
(bvp (gcd-body1$data-out inputs data-size)))
:hints (("Goal" :in-theory (enable gcd-body1$a<b
gcd-body1$data-out))))
)
;; The value lemma for GCD-BODY1
(encapsulate
()
(local
(defthm list-of-singleton
(implies (and (true-listp l)
(equal (len l) 1))
(equal (list (car l))
l))))
(defthm gcd-body1$value
(b* ((inputs (list* full-in empty-out-
(append data-in go-signals))))
(implies (and (posp data-size)
(gcd-body1& netlist data-size)
(true-listp data-in)
(equal (len data-in) (* 2 data-size))
(true-listp go-signals)
(equal (len go-signals) *gcd-body1$go-num*))
(equal (se (si 'gcd-body1 data-size) inputs st netlist)
(list* (gcd-body1$act inputs data-size)
(gcd-body1$data-out inputs data-size)))))
:hints (("Goal"
:do-not-induct t
:expand (:free (inputs data-size)
(se (si 'gcd-body1 data-size) inputs st netlist))
:in-theory (e/d (de-rules
fv-adder-output
gcd-body1&
gcd-body1*$destructure
gcd-body1$data-in
gcd-body1$me-inputs
gcd-body1$a<b
gcd-body1$act
gcd-body1$data-out
gcd-body1$data0-out
gcd-body1$data1-out)
(append-take-nthcdr
de-module-disabled-rules)))))
)
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