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4vec-operations

4vec-times

Integer multiplication of 4vecs.

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

This is a fairly conservative definition in the style of the Verilog semantics: if either input has any X or Z bits, the result is all X bits. Otherwise, we return the (signed) product of the two (signed) inputs.

Definitions and Theorems

Function: 4vec-times

(defun 4vec-times (x y)
  (declare (xargs :guard (and (4vec-p x) (4vec-p y))))
  (let ((__function__ '4vec-times))
    (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-times

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

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

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

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

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

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

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

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

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