		Search-engine friendly clone of the ACL2 documentation.

4vec-operations

4vec-bitxor

Bitwise logical XOR of 4vecs.

Signature
(4vec-bitxor x y) → x^y
Arguments: x — Guard (4vec-p x).; y — Guard (4vec-p y).
Returns: x^y — Type (3vec-p! x^y).

Definitions and Theorems

Function: 4vec-bitxor

(defun 4vec-bitxor (x y)
  (declare (xargs :guard (and (4vec-p x) (4vec-p y))))
  (let ((__function__ '4vec-bitxor))
    (declare (ignorable __function__))
    (if-2vec-p (x y)
               (2vec (logxor (2vec->val x) (2vec->val y)))
               (b* (((4vec x))
                    ((4vec y))
                    (xmask (logior (logxor x.upper x.lower)
                                   (logxor y.upper y.lower))))
                 (4vec (logior xmask (logxor x.upper y.upper))
                       (logand (lognot xmask)
                               (logxor x.lower y.lower)))))))

Theorem: 3vec-p!-of-4vec-bitxor

(defthm 3vec-p!-of-4vec-bitxor
  (b* ((x^y (4vec-bitxor x y)))
    (3vec-p! x^y))
  :rule-classes :rewrite)

Theorem: 4vec-bitxor-redef

(defthm 4vec-bitxor-redef
  (equal (4vec-bitxor x y)
         (3vec-bitxor (3vec-fix x)
                      (3vec-fix y))))

Main correctness theorem: each result bit is just the ACL2::4v-xor of the corresponding input bits.

Theorem: 4vec-bitxor-bits

(defthm 4vec-bitxor-bits
  (equal (4vec-idx->4v n (4vec-bitxor x y))
         (acl2::4v-xor (4vec-idx->4v n x)
                       (4vec-idx->4v n y))))

Theorem: 4vec-bitxor-of-3vec-fix-x

(defthm 4vec-bitxor-of-3vec-fix-x
  (equal (4vec-bitxor (3vec-fix x) y)
         (4vec-bitxor x y)))

Theorem: 4vec-bitxor-3vec-equiv-congruence-on-x

(defthm 4vec-bitxor-3vec-equiv-congruence-on-x
  (implies (3vec-equiv x x-equiv)
           (equal (4vec-bitxor x y)
                  (4vec-bitxor x-equiv y)))
  :rule-classes :congruence)

Theorem: 4vec-bitxor-of-3vec-fix-y

(defthm 4vec-bitxor-of-3vec-fix-y
  (equal (4vec-bitxor x (3vec-fix y))
         (4vec-bitxor x y)))

Theorem: 4vec-bitxor-3vec-equiv-congruence-on-y

(defthm 4vec-bitxor-3vec-equiv-congruence-on-y
  (implies (3vec-equiv y y-equiv)
           (equal (4vec-bitxor x y)
                  (4vec-bitxor x y-equiv)))
  :rule-classes :congruence)