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4vec-operations

4vec-minus

Integer subtraction of two 4vecs.

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

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. 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 subtract 4'b XX11 - 4'b ZZ00, we return all Xes even though a less conservative semantics might produce 4'b XX11.

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

Definitions and Theorems

Function: 4vec-minus

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

Theorem: 4vec-p-of-4vec-minus

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

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

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

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

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

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

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

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

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