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Representation-of-integer-operations

Bitnot-uint

Bitwise complement of a value of type unsigned int [C17:6.5.3].

Definitions and Theorems

Function: bitnot-uint

(defun bitnot-uint (x)
  (declare (xargs :guard (and (uintp x))))
  (uint-from-integer-mod (lognot (integer-from-uint x))))

Theorem: uintp-of-bitnot-uint

(defthm uintp-of-bitnot-uint
  (uintp (bitnot-uint x)))

Theorem: bitnot-uint-of-uint-fix-x

(defthm bitnot-uint-of-uint-fix-x
  (equal (bitnot-uint (uint-fix x))
         (bitnot-uint x)))

Theorem: bitnot-uint-uint-equiv-congruence-on-x

(defthm bitnot-uint-uint-equiv-congruence-on-x
  (implies (uint-equiv x x-equiv)
           (equal (bitnot-uint x)
                  (bitnot-uint x-equiv)))
  :rule-classes :congruence)