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4vec-operations

4vec-countones

Count of 1 bits in a 4vec (X-monotonic).

Signature
(4vec-countones x) → count
Arguments: x — Guard (4vec-p x).
Returns: count — Type (3vec-p! count).

Definitions and Theorems

Function: 4vec-countones

(defun 4vec-countones (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec-countones))
    (declare (ignorable __function__))
    (if (and (2vec-p x) (<= 0 (2vec->val x)))
        (b* ((x (2vec->val x)))
          (2vec (logcount x)))
      (4vec-x))))

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

(defthm 3vec-p!-of-4vec-countones
  (b* ((count (4vec-countones x)))
    (3vec-p! count))
  :rule-classes :rewrite)

Theorem: 4vec-countones-of-2vecx-fix-x

(defthm 4vec-countones-of-2vecx-fix-x
  (equal (4vec-countones (2vecx-fix x))
         (4vec-countones x)))

Theorem: 4vec-countones-2vecx-equiv-congruence-on-x

(defthm 4vec-countones-2vecx-equiv-congruence-on-x
  (implies (2vecx-equiv x x-equiv)
           (equal (4vec-countones x)
                  (4vec-countones x-equiv)))
  :rule-classes :congruence)