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S4vecs

S4vec-parity

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

Definitions and Theorems

Function: s4vec-parity

(defun s4vec-parity (x)
 (declare (xargs :guard (s4vec-p x)))
 (let ((__function__ 's4vec-parity))
  (declare (ignorable __function__))
  (b* (((unless (s4vec-2vec-p x)) (s4vec-x))
       (xint (s4vec->upper x))
       ((when (sparseint-< xint 0)) (s4vec-x))
       (xval (s4vec-sparseint-val (s4vec->upper x))))
   (s2vec
       (int-to-sparseint (- (fast-parity (+ 1 (integer-length xval))
                                         xval)))))))

Theorem: s4vec-p-of-s4vec-parity

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

Theorem: s4vec-parity-correct

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

Theorem: s4vec-parity-of-s4vec-fix-x

(defthm s4vec-parity-of-s4vec-fix-x
  (equal (s4vec-parity (s4vec-fix x))
         (s4vec-parity x)))

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

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