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Gatesplit

Vl-gatesplit-nand/nor/xnor

Split up a multi-input nand or nor gate, if necessary.

Signature
(vl-gatesplit-nand/nor/xnor x nf warnings) → (mv warnings new-decls new-gateinsts nf)
Arguments: x — NAND/NOR gate to split up (if necessary).
Guard (vl-gateinst-p x).; nf — For generating fresh names.
Guard (vl-namefactory-p nf).; warnings — Ordinary warnings accumulator.
Guard (vl-warninglist-p warnings).
Returns: warnings — Type (vl-warninglist-p warnings).; new-decls — New declarations for temporary wires.
Type (vl-vardecllist-p new-decls), given the guard.; new-gateinsts — Replacement gate instances.
Type (vl-gateinstlist-p new-gateinsts), given the guard.; nf — Type (vl-namefactory-p nf), given the guard.

From Section 7.2, nand, nor, and xnor gates have one output and many inputs. The behavior for more than 2 inputs is described as the "natural extension". We have used Verilog-XL to check that they behave as follows, at least for n = 4.

nand(o, i1, i2, ..., iN)
 -->
and(temp, i1, i2, ..., iN)
not(o, temp);

nor(o, i1, i2, ..., iN)
 -->
or(temp, i1, i2, ..., iN)
not(o, temp);

xnor(o, i1, i2, ..., iN)
 -->
xor(temp, i1, i2, ..., iN)
not(o, temp);

This is basically similar to vl-gatesplit-and/or/xor, except that we need to add a "not" gate at the end.

Definitions and Theorems

Function: vl-gatesplit-nand/nor/xnor

(defun vl-gatesplit-nand/nor/xnor (x nf warnings)
 (declare (xargs :guard (and (vl-gateinst-p x)
                             (vl-namefactory-p nf)
                             (vl-warninglist-p warnings))))
 (declare (xargs :guard (member (vl-gateinst->type x)
                                '(:vl-nand :vl-nor :vl-xnor))))
 (let ((__function__ 'vl-gatesplit-nand/nor/xnor))
  (declare (ignorable __function__))
  (b*
   ((args (list-fix (vl-gateinst->args x)))
    (nargs (length args))
    (range (vl-gateinst->range x))
    (loc (vl-gateinst->loc x))
    (origname (or (vl-gateinst->name x) "unnamed"))
    ((when range)
     (mv
      (fatal
       :type :vl-bad-gate
       :msg
       "~a0: expected all instance arrays to have been ~
                         eliminated; did you forget to run the argresolve ~
                         transform?"
       :args (list x))
      nil (list x)
      nf))
    ((when (< nargs 2))
     (mv
      (fatal
           :type :vl-bad-gate
           :msg "~a0: expected at least 2 arguments, but found ~x1."
           :args (list x nargs))
      nil (list x)
      nf))
    ((when (eql nargs 2))
     (b* (((mv warnings new-x)
           (vl-degenerate-gate-to-buf x warnings)))
       (mv warnings nil (list new-x) nf)))
    ((when (eql nargs 3))
     (mv (ok) nil (list x) nf))
    (atts (cons (cons "VL_GATESPLIT"
                      (make-vl-atom :guts (vl-string origname)))
                (vl-gateinst->atts x)))
    ((mv temp-exprs temp-decls nf)
     (vl-make-temporary-wires origname (- nargs 2)
                              nf loc))
    (all-args-out (vl-exprlist-to-plainarglist temp-exprs
                                               :dir :vl-output))
    (all-args-in (vl-exprlist-to-plainarglist temp-exprs
                                              :dir :vl-input))
    (temp-args-out (butlast all-args-out 1))
    (temp-args-in (butlast all-args-in 1))
    (main-arg-out (car (last all-args-out)))
    (main-arg-in (car (last all-args-in)))
    (o (car args))
    (i1 (cadr args))
    (i2-n (cddr args))
    (outs (append temp-args-out (list main-arg-out)))
    (lhses (cons i1 temp-args-in))
    (rhses i2-n)
    ((mv warnings gateinsts nf)
     (vl-make-gates-for-and/or/xor outs lhses rhses
                                   (case (vl-gateinst->type x)
                                         (:vl-nand :vl-and)
                                         (:vl-nor :vl-or)
                                         (:vl-xnor :vl-xor))
                                   origname loc atts nf warnings))
    ((mv final-name nf)
     (vl-namefactory-indexed-name origname nf))
    (final-gate (make-vl-gateinst :type :vl-not
                                  :name final-name
                                  :range nil
                                  :atts atts
                                  :args (list o main-arg-in)
                                  :loc loc)))
   (mv (ok)
       temp-decls
       (append gateinsts (list final-gate))
       nf))))

Theorem: vl-warninglist-p-of-vl-gatesplit-nand/nor/xnor.warnings

(defthm vl-warninglist-p-of-vl-gatesplit-nand/nor/xnor.warnings
  (b* (((mv ?warnings ?new-decls ?new-gateinsts ?nf)
        (vl-gatesplit-nand/nor/xnor x nf warnings)))
    (vl-warninglist-p warnings))
  :rule-classes :rewrite)

Theorem: vl-vardecllist-p-of-vl-gatesplit-nand/nor/xnor.new-decls

(defthm vl-vardecllist-p-of-vl-gatesplit-nand/nor/xnor.new-decls
 (implies
  (and
   (force (vl-gateinst-p x))
   (force (vl-namefactory-p nf))
   (force (vl-warninglist-p warnings))
   (force
    ((lambda (acl2::x acl2::l)
       (return-last
            'acl2::mbe1-raw
            (acl2::member-eql-exec acl2::x acl2::l)
            (return-last
                 'progn
                 (acl2::member-eql-exec$guard-check acl2::x acl2::l)
                 (member-equal acl2::x acl2::l))))
     (vl-gateinst->type$inline x)
     '(:vl-nand :vl-nor :vl-xnor))))
  (b* (((mv ?warnings ?new-decls ?new-gateinsts ?nf)
        (vl-gatesplit-nand/nor/xnor x nf warnings)))
    (vl-vardecllist-p new-decls)))
 :rule-classes :rewrite)

Theorem: vl-gateinstlist-p-of-vl-gatesplit-nand/nor/xnor.new-gateinsts

(defthm
      vl-gateinstlist-p-of-vl-gatesplit-nand/nor/xnor.new-gateinsts
 (implies
  (and
   (force (vl-gateinst-p x))
   (force (vl-namefactory-p nf))
   (force (vl-warninglist-p warnings))
   (force
    ((lambda (acl2::x acl2::l)
       (return-last
            'acl2::mbe1-raw
            (acl2::member-eql-exec acl2::x acl2::l)
            (return-last
                 'progn
                 (acl2::member-eql-exec$guard-check acl2::x acl2::l)
                 (member-equal acl2::x acl2::l))))
     (vl-gateinst->type$inline x)
     '(:vl-nand :vl-nor :vl-xnor))))
  (b* (((mv ?warnings ?new-decls ?new-gateinsts ?nf)
        (vl-gatesplit-nand/nor/xnor x nf warnings)))
    (vl-gateinstlist-p new-gateinsts)))
 :rule-classes :rewrite)

Theorem: vl-namefactory-p-of-vl-gatesplit-nand/nor/xnor.nf

(defthm vl-namefactory-p-of-vl-gatesplit-nand/nor/xnor.nf
 (implies
  (and
   (force (vl-gateinst-p x))
   (force (vl-namefactory-p nf))
   (force (vl-warninglist-p warnings))
   (force
    ((lambda (acl2::x acl2::l)
       (return-last
            'acl2::mbe1-raw
            (acl2::member-eql-exec acl2::x acl2::l)
            (return-last
                 'progn
                 (acl2::member-eql-exec$guard-check acl2::x acl2::l)
                 (member-equal acl2::x acl2::l))))
     (vl-gateinst->type$inline x)
     '(:vl-nand :vl-nor :vl-xnor))))
  (b* (((mv ?warnings ?new-decls ?new-gateinsts ?nf)
        (vl-gatesplit-nand/nor/xnor x nf warnings)))
    (vl-namefactory-p nf)))
 :rule-classes :rewrite)

Theorem: vl-gatesplit-nand/nor/xnor-mvtypes-1

(defthm vl-gatesplit-nand/nor/xnor-mvtypes-1
  (true-listp (mv-nth 1
                      (vl-gatesplit-nand/nor/xnor x nf warnings)))
  :rule-classes :type-prescription)

Theorem: vl-gatesplit-nand/nor/xnor-mvtypes-2

(defthm vl-gatesplit-nand/nor/xnor-mvtypes-2
  (true-listp (mv-nth 2
                      (vl-gatesplit-nand/nor/xnor x nf warnings)))
  :rule-classes :type-prescription)