		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integers

Ushort-from-integer-mod

Reduce modularly ACL2 integers to values of type unsigned short.

Signature
(ushort-from-integer-mod x) → result
Arguments: x — Guard (integerp x).
Returns: result — Type (ushortp result).

Definitions and Theorems

Function: ushort-from-integer-mod

(defun ushort-from-integer-mod (x)
  (declare (xargs :guard (integerp x)))
  (let ((__function__ 'ushort-from-integer-mod))
    (declare (ignorable __function__))
    (ushort-from-integer (mod (ifix x) (1+ (ushort-max))))))

Theorem: ushortp-of-ushort-from-integer-mod

(defthm ushortp-of-ushort-from-integer-mod
  (b* ((result (ushort-from-integer-mod x)))
    (ushortp result))
  :rule-classes :rewrite)

Theorem: ushort-from-integer-mod-of-ifix-x

(defthm ushort-from-integer-mod-of-ifix-x
  (equal (ushort-from-integer-mod (ifix x))
         (ushort-from-integer-mod x)))

Theorem: ushort-from-integer-mod-int-equiv-congruence-on-x

(defthm ushort-from-integer-mod-int-equiv-congruence-on-x
  (implies (acl2::int-equiv x x-equiv)
           (equal (ushort-from-integer-mod x)
                  (ushort-from-integer-mod x-equiv)))
  :rule-classes :congruence)