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4vec-operations

4vec-clog2

Ceiling of the log2 of a, or X if any non-2-valued bits. Must be truncated to its width (nonnegative).

Signature
(4vec-clog2 a) → res
Arguments: a — Guard (4vec-p a).
Returns: res — Type (4vec-p res).

Definitions and Theorems

Function: 4vec-clog2

(defun 4vec-clog2 (a)
  (declare (xargs :guard (4vec-p a)))
  (let ((__function__ '4vec-clog2))
    (declare (ignorable __function__))
    (if (and (2vec-p a) (<= 0 (2vec->val a)))
        (2vec (integer-length (- (2vec->val a) 1)))
      (4vec-x))))

Theorem: 4vec-p-of-4vec-clog2

(defthm 4vec-p-of-4vec-clog2
  (b* ((res (4vec-clog2 a))) (4vec-p res))
  :rule-classes :rewrite)

Theorem: 4vec-clog2-of-2vecnatx-fix-a

(defthm 4vec-clog2-of-2vecnatx-fix-a
  (equal (4vec-clog2 (2vecnatx-fix a))
         (4vec-clog2 a)))

Theorem: 4vec-clog2-2vecnatx-equiv-congruence-on-a

(defthm 4vec-clog2-2vecnatx-equiv-congruence-on-a
  (implies (2vecnatx-equiv a a-equiv)
           (equal (4vec-clog2 a)
                  (4vec-clog2 a-equiv)))
  :rule-classes :congruence)