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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>
;; November 2018
(in-package "ADE")
(include-book "link-joint")
(include-book "tv-if")
(local (include-book "arithmetic-3/top" :dir :system))
;; ======================================================================
;; Construct a DE module generator for a storage-free merge joint. Prove the
;; value lemma for this module generator.
(defconst *merge$go-num* 1)
(defun merge$data-ins-len (data-size)
(declare (xargs :guard (natp data-size)))
(+ 4 (* 2 (mbe :logic (nfix data-size)
:exec data-size))))
(defun merge$ins-len (data-size)
(declare (xargs :guard (natp data-size)))
(+ (merge$data-ins-len data-size)
*merge$go-num*))
;; DE module generator of MERGE
(module-generator
merge* (data-size)
(si 'merge data-size)
(list* 'full-in0 'full-in1 'empty-out- 'select
(append (sis 'data-in0 0 data-size)
(sis 'data-in1 0 data-size)
(sis 'go 0 *merge$go-num*)))
(list* 'act 'act0 'act1
(sis 'data-out 0 data-size))
()
(list
'(g0 (select~) b-not (select))
'(g1 (ready-in0) b-and (full-in0 select~))
'(g2 (ready-in1) b-and (full-in1 select))
(list 'merge-cntl0
'(act0)
'joint-cntl
(list 'ready-in0 'empty-out- (si 'go 0)))
(list 'merge-cntl1
'(act1)
'joint-cntl
(list 'ready-in1 'empty-out- (si 'go 0)))
'(merge-cntl (act) b-or (act0 act1))
(list 'merge-op
(sis 'data-out 0 data-size)
(si 'tv-if (tree-number (make-tree data-size)))
(cons 'select
(append (sis 'data-in1 0 data-size)
(sis 'data-in0 0 data-size)))))
(declare (xargs :guard (natp data-size))))
;; DE netlist generator. A generated netlist will contain an instance of
;; MERGE.
(defund merge$netlist (data-size)
(declare (xargs :guard (natp data-size)))
(cons (merge* data-size)
(union$ (tv-if$netlist (make-tree data-size))
*joint-cntl*
:test 'equal)))
;; Recognizer for MERGE
(defund merge& (netlist data-size)
(declare (xargs :guard (and (alistp netlist)
(natp data-size))))
(b* ((subnetlist (delete-to-eq (si 'merge data-size) netlist)))
(and (equal (assoc (si 'merge data-size) netlist)
(merge* data-size))
(joint-cntl& subnetlist)
(tv-if& subnetlist (make-tree data-size)))))
;; Sanity check
(local
(defthmd check-merge$netlist-64
(and (net-syntax-okp (merge$netlist 64))
(net-arity-okp (merge$netlist 64))
(merge& (merge$netlist 64) 64))))
;; Extract the input and output signals for MERGE
(progn
;; Extract the 1st input data item
(defun merge$data-in0 (inputs data-size)
(declare (xargs :guard (and (true-listp inputs)
(natp data-size))))
(take (mbe :logic (nfix data-size)
:exec data-size)
(nthcdr 4 inputs)))
(defthm len-merge$data-in0
(equal (len (merge$data-in0 inputs data-size))
(nfix data-size)))
(in-theory (disable merge$data-in0))
;; Extract the 2nd input data item
(defun merge$data-in1 (inputs data-size)
(declare (xargs :guard (and (true-listp inputs)
(natp data-size))))
(b* ((size (mbe :logic (nfix data-size)
:exec data-size)))
(take size
(nthcdr (+ 4 size) inputs))))
(defthm len-merge$data-in1
(equal (len (merge$data-in1 inputs data-size))
(nfix data-size)))
(in-theory (disable merge$data-in1))
;; Extract the "act0" signal
(defund merge$act0 (inputs data-size)
(b* ((full-in0 (nth 0 inputs))
(empty-out- (nth 2 inputs))
(select (nth 3 inputs))
(go-signals (nthcdr (merge$data-ins-len data-size) inputs))
(go-merge (nth 0 go-signals))
(ready-in0 (f-and full-in0 (f-not select))))
(joint-act ready-in0 empty-out- go-merge)))
(defthm merge$act0-inactive
(implies (or (not (nth 0 inputs))
(equal (nth 2 inputs) t))
(not (merge$act0 inputs data-size)))
:hints (("Goal" :in-theory (enable merge$act0))))
;; Extract the "act1" signal
(defund merge$act1 (inputs data-size)
(b* ((full-in1 (nth 1 inputs))
(empty-out- (nth 2 inputs))
(select (nth 3 inputs))
(go-signals (nthcdr (merge$data-ins-len data-size) inputs))
(go-merge (nth 0 go-signals))
(ready-in1 (f-and full-in1 select)))
(joint-act ready-in1 empty-out- go-merge)))
(defthm merge$act1-inactive
(implies (or (not (nth 1 inputs))
(equal (nth 2 inputs) t))
(not (merge$act1 inputs data-size)))
:hints (("Goal" :in-theory (enable merge$act1))))
;; Extract the "act" signal
(defund merge$act (inputs data-size)
(f-or (merge$act0 inputs data-size)
(merge$act1 inputs data-size)))
(defthm merge$act-inactive
(implies (or (and (not (nth 0 inputs))
(not (nth 1 inputs)))
(equal (nth 2 inputs) t))
(not (merge$act inputs data-size)))
:hints (("Goal" :in-theory (enable merge$act))))
)
;; The value lemma for MERGE
(defthm merge$value
(b* ((inputs (list* full-in0 full-in1 empty-out- select
(append data-in0 data-in1 go-signals))))
(implies (and (posp data-size)
(merge& netlist data-size)
(true-listp data-in0)
(equal (len data-in0) data-size)
(true-listp data-in1)
(equal (len data-in1) data-size)
(true-listp go-signals)
(equal (len go-signals) *merge$go-num*))
(equal (se (si 'merge data-size) inputs st netlist)
(list* (merge$act inputs data-size)
(merge$act0 inputs data-size)
(merge$act1 inputs data-size)
(fv-if select data-in1 data-in0)))))
:hints (("Goal"
:do-not-induct t
:expand (:free (inputs data-size)
(se (si 'merge data-size) inputs st netlist))
:in-theory (e/d (de-rules
merge&
merge*$destructure
merge$act
merge$act0
merge$act1)
(de-module-disabled-rules)))))
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