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Representation-of-integer-operations

Rem-sint-ullong

Remainder of a value of type signed int and a value of type unsigned long long [C:6.5.5].

Definitions and Theorems

Function: rem-sint-ullong

(defun rem-sint-ullong (x y)
  (declare (xargs :guard (and (sintp x)
                              (ullongp y)
                              (rem-sint-ullong-okp x y))))
  (rem-ullong-ullong (ullong-from-sint x)
                     y))

Theorem: ullongp-of-rem-sint-ullong

(defthm ullongp-of-rem-sint-ullong
  (ullongp (rem-sint-ullong x y)))

Theorem: rem-sint-ullong-of-sint-fix-x

(defthm rem-sint-ullong-of-sint-fix-x
  (equal (rem-sint-ullong (sint-fix x) y)
         (rem-sint-ullong x y)))

Theorem: rem-sint-ullong-sint-equiv-congruence-on-x

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

Theorem: rem-sint-ullong-of-ullong-fix-y

(defthm rem-sint-ullong-of-ullong-fix-y
  (equal (rem-sint-ullong x (ullong-fix y))
         (rem-sint-ullong x y)))

Theorem: rem-sint-ullong-ullong-equiv-congruence-on-y

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