		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integers

Ulong-from-integer-mod

Reduce modularly ACL2 integers to values of type unsigned long.

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

Definitions and Theorems

Function: ulong-from-integer-mod

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

Theorem: ulongp-of-ulong-from-integer-mod

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

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

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

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

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