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Representation-of-integer-operations

Rem-sint-ulong

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

Definitions and Theorems

Function: rem-sint-ulong

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

Theorem: ulongp-of-rem-sint-ulong

(defthm ulongp-of-rem-sint-ulong
  (ulongp (rem-sint-ulong x y)))

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

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

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

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

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

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

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

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