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4vec-operations

4vec-onehot

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

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

Definitions and Theorems

Function: 4vec-onehot

(defun 4vec-onehot (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec-onehot))
    (declare (ignorable __function__))
    (if (and (2vec-p x) (<= 0 (2vec->val x)))
        (b* ((x (2vec->val x)))
          (2vec (bool->bit (eql (logcount x) 1))))
      (4vec-x))))

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

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

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

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

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

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