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4vec-operations

4vec-offset

Negation, except Z bits become 0.

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

The closest monotonic approximation of the offset of each of the bits of the input. It differs from the actual offset in that the 4vec-offset of an X bit is X.

Definitions and Theorems

Function: 4vec-offset

(defun 4vec-offset (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec-offset))
    (declare (ignorable __function__))
    (b* (((4vec x)))
      (4vec (lognot x.lower)
            (lognot (logior x.upper x.lower))))))

Theorem: 4vec-p-of-4vec-offset

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

Theorem: 4vec-offset-bits

(defthm 4vec-offset-bits
  (equal (4vec-idx->4v n (4vec-offset x))
         (let ((in (4vec-idx->4v n x)))
           (if (eq 'z in) 'f (acl2::4v-not in)))))

Theorem: 4vec-offset-of-4vec-fix-x

(defthm 4vec-offset-of-4vec-fix-x
  (equal (4vec-offset (4vec-fix x))
         (4vec-offset x)))

Theorem: 4vec-offset-4vec-equiv-congruence-on-x

(defthm 4vec-offset-4vec-equiv-congruence-on-x
  (implies (4vec-equiv x x-equiv)
           (equal (4vec-offset x)
                  (4vec-offset x-equiv)))
  :rule-classes :congruence)