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• 3vec-operations

3vec-bitxor

Bitwise logical XOR of 3vecs.

Signature

(3vec-bitxor x y) → x^y

Arguments

x — Guard (4vec-p x).

y — Guard (4vec-p y).

Returns

x^y — Type (4vec-p x^y).

Definitions and Theorems

Function: 3vec-bitxor

(defun 3vec-bitxor (x y)
  (declare (xargs :guard (and (4vec-p x) (4vec-p y))))
  (let ((__function__ '3vec-bitxor))
    (declare (ignorable __function__))
    (if-2vec-p
         (x y)
         (2vec (logxor (2vec->val x) (2vec->val y)))
         (b* (((4vec x))
              ((4vec y))
              (xmask (logior (logand x.upper (lognot x.lower))
                             (logand y.upper (lognot y.lower)))))
           (4vec (logior xmask (logxor x.upper y.upper))
                 (logand (lognot xmask)
                         (logxor x.lower y.lower)))))))

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

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

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

(defthm 3vec-p-of-3vec-bitxor
  (b* ((?x^y (3vec-bitxor x y)))
    (implies (and (3vec-p x) (3vec-p y))
             (3vec-p x^y))))

Theorem: 3vec-bitxor-bits

(defthm 3vec-bitxor-bits
  (implies (and (3vec-p! x) (3vec-p! y))
           (equal (4vec-idx->4v n (3vec-bitxor x y))
                  (acl2::4v-xor (4vec-idx->4v n (3vec-fix x))
                                (4vec-idx->4v n (3vec-fix y))))))

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

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

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

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

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

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

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

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