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A4vec-operations

A4vec-clog2

Symbolic version of 4vec-clog2.

Signature
(a4vec-clog2 x) → res
Arguments: x — Guard (a4vec-p x).
Returns: res — Type (a4vec-p res).

Definitions and Theorems

Function: a4vec-clog2

(defun a4vec-clog2 (x)
 (declare (xargs :guard (a4vec-p x)))
 (let ((__function__ 'a4vec-clog2))
  (declare (ignorable __function__))
  (b* (((a4vec x)))
   (a4vec-ite
      (aig-and (a2vec-p x)
               (aig-not (aig-sign-s x.upper)))
      (b* ((res (aig-integer-length-s (aig-+-ss nil '(t) x.upper))))
        (a4vec res res))
      (a4vec-x)))))

Theorem: a4vec-p-of-a4vec-clog2

(defthm a4vec-p-of-a4vec-clog2
  (b* ((res (a4vec-clog2 x)))
    (a4vec-p res))
  :rule-classes :rewrite)

Theorem: a4vec-clog2-correct

(defthm a4vec-clog2-correct
  (equal (a4vec-eval (a4vec-clog2 x) env)
         (4vec-clog2 (a4vec-eval x env))))

Theorem: a4vec-clog2-of-a4vec-fix-x

(defthm a4vec-clog2-of-a4vec-fix-x
  (equal (a4vec-clog2 (a4vec-fix x))
         (a4vec-clog2 x)))

Theorem: a4vec-clog2-a4vec-equiv-congruence-on-x

(defthm a4vec-clog2-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a4vec-clog2 x)
                  (a4vec-clog2 x-equiv)))
  :rule-classes :congruence)