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4vec-operations

4vec-plus

Integer addition of two 4vecs.

Signature
(4vec-plus x y) → sum
Arguments: x — Guard (4vec-p x).; y — Guard (4vec-p y).
Returns: sum — Type (4vec-p sum).

This is a fairly conservative definition in the style of the Verilog semantics: if either input has any X or Z bits anywhere, the entire result is all Xes. We return all Xes even in cases where you might think that some bits are ``obviously'' going to be driven in a certain way. For instance, when we add 4'b XX00 to 4'b ZZ01, we return all Xes even though a less conservative semantics might produce 4'b XX01.

When there are no X or Z bits anywhere, we just compute the (signed) sum of the two (signed) inputs.

Definitions and Theorems

Function: 4vec-plus

(defun 4vec-plus (x y)
  (declare (xargs :guard (and (4vec-p x) (4vec-p y))))
  (let ((__function__ '4vec-plus))
    (declare (ignorable __function__))
    (if (and (2vec-p x) (2vec-p y))
        (2vec (+ (the integer (2vec->val x))
                 (the integer (2vec->val y))))
      (4vec-x))))

Theorem: 4vec-p-of-4vec-plus

(defthm 4vec-p-of-4vec-plus
  (b* ((sum (4vec-plus x y)))
    (4vec-p sum))
  :rule-classes :rewrite)

Theorem: 4vec-plus-of-2vecx-fix-x

(defthm 4vec-plus-of-2vecx-fix-x
  (equal (4vec-plus (2vecx-fix x) y)
         (4vec-plus x y)))

Theorem: 4vec-plus-2vecx-equiv-congruence-on-x

(defthm 4vec-plus-2vecx-equiv-congruence-on-x
  (implies (2vecx-equiv x x-equiv)
           (equal (4vec-plus x y)
                  (4vec-plus x-equiv y)))
  :rule-classes :congruence)

Theorem: 4vec-plus-of-2vecx-fix-y

(defthm 4vec-plus-of-2vecx-fix-y
  (equal (4vec-plus x (2vecx-fix y))
         (4vec-plus x y)))

Theorem: 4vec-plus-2vecx-equiv-congruence-on-y

(defthm 4vec-plus-2vecx-equiv-congruence-on-y
  (implies (2vecx-equiv y y-equiv)
           (equal (4vec-plus x y)
                  (4vec-plus x y-equiv)))
  :rule-classes :congruence)