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Implementation-environments

Ullong-max

Maximum mathematical integer value of type unsigned long long.

Signature
(ullong-max ienv) → val
Arguments: ienv — Guard (ienvp ienv).
Returns: val — Type (natp val).

This depends on the implementation environment.

Note that the minimum unsigned signed is just 0, so there is no need to introduce a function for it.

Definitions and Theorems

Function: ullong-max

(defun ullong-max (ienv)
  (declare (xargs :guard (ienvp ienv)))
  (let ((__function__ 'ullong-max))
    (declare (ignorable __function__))
    (1- (expt 2 (* 8 (ienv->llong-bytes ienv))))))

Theorem: natp-of-ullong-max

(defthm natp-of-ullong-max
  (b* ((val (ullong-max ienv)))
    (natp val))
  :rule-classes (:rewrite :type-prescription))

Theorem: ullong-max-of-ienv-fix-ienv

(defthm ullong-max-of-ienv-fix-ienv
  (equal (ullong-max (ienv-fix ienv))
         (ullong-max ienv)))

Theorem: ullong-max-ienv-equiv-congruence-on-ienv

(defthm ullong-max-ienv-equiv-congruence-on-ienv
  (implies (ienv-equiv ienv ienv-equiv)
           (equal (ullong-max ienv)
                  (ullong-max ienv-equiv)))
  :rule-classes :congruence)