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S4vecs

S4vec-bitxor

Signature
(s4vec-bitxor x y) → res
Arguments: x — Guard (s4vec-p x).; y — Guard (s4vec-p y).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-bitxor

(defun s4vec-bitxor (x y)
 (declare (xargs :guard (and (s4vec-p x) (s4vec-p y))))
 (let ((__function__ 's4vec-bitxor))
  (declare (ignorable __function__))
  (if (and (s2vec-p x) (s2vec-p y))
      (s2vec (sparseint-bitxor (s2vec->val x)
                               (s2vec->val y)))
   (b*
     (((s4vec x))
      ((s4vec y))
      (xmask (sparseint-bitor (sparseint-bitxor x.upper x.lower)
                              (sparseint-bitxor y.upper y.lower))))
    (s4vec
        (sparseint-bitor xmask
                         (sparseint-bitxor x.upper y.upper))
        (sparseint-bitandc1 xmask
                            (sparseint-bitxor x.lower y.lower)))))))

Theorem: s4vec-p-of-s4vec-bitxor

(defthm s4vec-p-of-s4vec-bitxor
  (b* ((res (s4vec-bitxor x y)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-bitxor-correct

(defthm s4vec-bitxor-correct
  (b* ((?res (s4vec-bitxor x y)))
    (equal (s4vec->4vec res)
           (4vec-bitxor (s4vec->4vec x)
                        (s4vec->4vec y)))))

Theorem: s4vec-bitxor-of-s4vec-fix-x

(defthm s4vec-bitxor-of-s4vec-fix-x
  (equal (s4vec-bitxor (s4vec-fix x) y)
         (s4vec-bitxor x y)))

Theorem: s4vec-bitxor-s4vec-equiv-congruence-on-x

(defthm s4vec-bitxor-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-bitxor x y)
                  (s4vec-bitxor x-equiv y)))
  :rule-classes :congruence)

Theorem: s4vec-bitxor-of-s4vec-fix-y

(defthm s4vec-bitxor-of-s4vec-fix-y
  (equal (s4vec-bitxor x (s4vec-fix y))
         (s4vec-bitxor x y)))

Theorem: s4vec-bitxor-s4vec-equiv-congruence-on-y

(defthm s4vec-bitxor-s4vec-equiv-congruence-on-y
  (implies (s4vec-equiv y y-equiv)
           (equal (s4vec-bitxor x y)
                  (s4vec-bitxor x y-equiv)))
  :rule-classes :congruence)