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;; Copyright (C) 2018, 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>
;; January 2019
(in-package "ADE")
(include-book "adder")
(include-book "../vector-module")
(include-book "ihs/basic-definitions" :dir :system)
;; ======================================================================
;; DE Module Generator of RIPPLE-SUB
(module-generator
ripple-sub* (n)
(si 'ripple-sub n)
(append (sis 'a 0 n)
(sis 'b 0 n))
(sis 's 0 (1+ n))
()
(list
(list 'g0
(sis 'b~ 0 n)
(si 'v-not n)
(sis 'b 0 n))
'(g1 (high) vdd ())
(list 'sub
(sis 's 0 (1+ n))
(si 'ripple-add n)
(cons 'high (append (sis 'a 0 n) (sis 'b~ 0 n)))))
(declare (xargs :guard (natp n))))
;; DE netlist generator. A generated netlist will contain an instance of
;; RIPPLE-SUB.
(defund ripple-sub$netlist (n)
(declare (xargs :guard (natp n)))
(cons (ripple-sub* n)
(union$ (v-not$netlist n)
(ripple-add$netlist n)
:test 'equal)))
;; Recognizer for RIPPLE-SUB
(defund ripple-sub& (netlist n)
(declare (xargs :guard (and (alistp netlist)
(natp n))))
(b* ((subnetlist (delete-to-eq (si 'ripple-sub n) netlist)))
(and (equal (assoc (si 'ripple-sub n) netlist)
(ripple-sub* n))
(v-not& subnetlist n)
(ripple-add& subnetlist n))))
;; Sanity check
(local
(defthmd check-ripple-sub$netlist-64
(and (net-syntax-okp (ripple-sub$netlist 64))
(net-arity-okp (ripple-sub$netlist 64))
(ripple-sub& (ripple-sub$netlist 64) 64))))
;; The value lemma for RIPPLE-SUB
(defthm ripple-sub$value
(implies (and (ripple-sub& netlist n)
(natp n)
(true-listp a)
(true-listp b)
(equal n (len a))
(equal n (len b)))
(equal (se (si 'ripple-sub n) (append a b) st netlist)
(fv-adder t a (fv-not b))))
:hints (("Goal"
:expand (:free (inputs n)
(se (si 'ripple-sub n) inputs st netlist))
:in-theory (e/d* (de-rules
ripple-sub&
ripple-sub*$destructure)
(de-module-disabled-rules)))))
(encapsulate
()
(local (include-book "arithmetic-3/top" :dir :system))
(local
(defthm ripple-add-2-comp-sub-aux-1
(implies (and (posp n)
(rationalp a)
(rationalp b))
(equal (logext n
(+ a (- (expt 2 n) b)))
(logext n
(- a b))))))
(local
(set-default-hints
'((nonlinearp-default-hint stable-under-simplificationp
hist pspv))))
(local
(defthm ripple-add-2-comp-sub-aux-2
(implies (bvp x)
(equal (v-to-nat (v-not x))
(- (1- (expt 2 (len x)))
(v-to-nat x))))
:hints (("Goal" :in-theory (enable bvp v-to-nat v-not)))))
(defthm v-adder-sub-works
(implies (bv2p a b)
(equal (v-to-nat (v-adder c a (v-not b)))
(+ (if c 0 -1)
(expt 2 (len a))
(- (v-to-nat a)
(v-to-nat b))))))
(local
(defthm v-to-nat-of-repeat-nil-is-zero
(equal (v-to-nat (repeat n nil)) 0)
:hints (("Goal" :in-theory (enable v-to-nat repeat)))))
(local
(defthm v-to-nat-of-take
(implies (<= 0 n)
(equal (v-to-nat (take n l))
(- (v-to-nat l)
(* (expt 2 n) (v-to-nat (nthcdr n l))))))
:hints (("Goal" :in-theory (enable bvp v-to-nat)))))
(local
(defun nthcdr-v-adder-sub-induct (n c a b)
(if (zp n)
(list c a b)
(nthcdr-v-adder-sub-induct (1- n)
(b-or3 (b-and (car a) (not (car b)))
(b-and (car a) c)
(b-and (not (car b)) c))
(cdr a)
(cdr b)))))
(local
(defthm nthcdr-v-adder-sub-1
(implies (and (natp n)
(booleanp c)
(equal n (len a))
(equal (v-to-nat b) (v-to-nat a))
(bv2p a b))
(equal (nthcdr n (v-adder c a (v-not b)))
(list c)))
:hints (("Goal"
:in-theory (enable bvp v-adder v-not)))))
(local
(defthm nthcdr-v-adder-sub-2
(implies (and (natp n)
(booleanp c)
(equal n (len a))
(< (v-to-nat b) (v-to-nat a))
(bv2p a b))
(equal (nthcdr n (v-adder c a (v-not b)))
(list t)))
:hints (("Goal"
:induct (nthcdr-v-adder-sub-induct n c a b)
:in-theory (enable bvp v-adder v-to-nat v-not)))))
(defthm v-to-nat-of-take-of-v-adder-sub
(implies (and (natp n)
(equal n (len a))
(<= (v-to-nat b) (v-to-nat a))
(bv2p a b))
(equal (v-to-nat (v-adder-output t a (v-not b)))
(- (v-to-nat a)
(v-to-nat b))))
:hints (("Goal"
:in-theory (enable v-adder-output)
:use (:instance nthcdr-v-adder-sub-2
(c t)))))
(defthm ripple-add-2-comp-sub
(implies (and (posp n)
(equal n (len a))
(bv2p a b))
(equal (logext n (v-to-nat (v-adder t a (v-not b))))
(logext n (- (v-to-nat a) (v-to-nat b)))))
:hints (("Goal"
:in-theory (disable logext)
:use (:instance ripple-add-2-comp-sub-aux-1
(a (v-to-nat a))
(b (v-to-nat b))))))
)
(defthm ripple-sub$value-correct
(implies (and (ripple-sub& netlist n)
(posp n) ;; n must be positive.
(equal n (len a))
(bv2p a b))
(equal (logext n
(v-to-nat
(se (si 'ripple-sub n)
(append a b)
st
netlist)))
(logext n (- (v-to-nat a) (v-to-nat b)))))
:hints (("Goal" :in-theory (e/d (ripple-sub$value)
(logext
v-adder-works
v-adder-sub-works)))))
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