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Representation-of-integer-operations

Div-ullong-ullong

Division of a value of type unsigned long long and a value of type unsigned long long [C:6.5.5].

Definitions and Theorems

Function: div-ullong-ullong

(defun div-ullong-ullong (x y)
  (declare (xargs :guard (and (ullongp x)
                              (ullongp y)
                              (div-ullong-ullong-okp x y))))
  (ullong-from-integer-mod (truncate (integer-from-ullong x)
                                     (integer-from-ullong y))))

Theorem: ullongp-of-div-ullong-ullong

(defthm ullongp-of-div-ullong-ullong
  (ullongp (div-ullong-ullong x y)))

Theorem: div-ullong-ullong-of-ullong-fix-x

(defthm div-ullong-ullong-of-ullong-fix-x
  (equal (div-ullong-ullong (ullong-fix x) y)
         (div-ullong-ullong x y)))

Theorem: div-ullong-ullong-ullong-equiv-congruence-on-x

(defthm div-ullong-ullong-ullong-equiv-congruence-on-x
  (implies (ullong-equiv x x-equiv)
           (equal (div-ullong-ullong x y)
                  (div-ullong-ullong x-equiv y)))
  :rule-classes :congruence)

Theorem: div-ullong-ullong-of-ullong-fix-y

(defthm div-ullong-ullong-of-ullong-fix-y
  (equal (div-ullong-ullong x (ullong-fix y))
         (div-ullong-ullong x y)))

Theorem: div-ullong-ullong-ullong-equiv-congruence-on-y

(defthm div-ullong-ullong-ullong-equiv-congruence-on-y
  (implies (ullong-equiv y y-equiv)
           (equal (div-ullong-ullong x y)
                  (div-ullong-ullong x y-equiv)))
  :rule-classes :congruence)