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4vec-operations

4vec-uminus

Integer negation of a 4vec.

Signature
(4vec-uminus x) → -x
Arguments: x — Guard (4vec-p x).
Returns: -x — Type (4vec-p -x).

If the input has X or Z bits, the result is all X bits. Otherwise, we return the signed negation of the input.

Definitions and Theorems

Function: 4vec-uminus

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

Theorem: 4vec-p-of-4vec-uminus

(defthm 4vec-p-of-4vec-uminus
  (b* ((-x (4vec-uminus x))) (4vec-p -x))
  :rule-classes :rewrite)

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

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

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

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