		Search-engine friendly clone of the ACL2 documentation.

Sparseint

Sparseint-bitcount

Count the 1 bits in a sparseint if positive, 0 bits if negative.

Signature
(sparseint-bitcount x) → count
Arguments: x — Guard (sparseint-p x).
Returns: count — Type (natp count).

Definitions and Theorems

Function: sparseint-bitcount

(defun sparseint-bitcount (x)
  (declare (xargs :guard (sparseint-p x)))
  (let ((__function__ 'sparseint-bitcount))
    (declare (ignorable __function__))
    (sparseint$-bitcount-rec 0 (bool->bit (sparseint-< x 0))
                             (sparseint-fix x))))

Theorem: natp-of-sparseint-bitcount

(defthm natp-of-sparseint-bitcount
  (b* ((count (sparseint-bitcount x)))
    (natp count))
  :rule-classes :type-prescription)

Theorem: sparseint-bitcount-correct

(defthm sparseint-bitcount-correct
  (b* ((common-lisp::?count (sparseint-bitcount x)))
    (equal count (logcount (sparseint-val x)))))

Theorem: sparseint-bitcount-of-sparseint-fix-x

(defthm sparseint-bitcount-of-sparseint-fix-x
  (equal (sparseint-bitcount (sparseint-fix x))
         (sparseint-bitcount x)))

Theorem: sparseint-bitcount-sparseint-equiv-congruence-on-x

(defthm sparseint-bitcount-sparseint-equiv-congruence-on-x
  (implies (sparseint-equiv x x-equiv)
           (equal (sparseint-bitcount x)
                  (sparseint-bitcount x-equiv)))
  :rule-classes :congruence)