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Representation-of-integer-operations

Rem-sint-sllong

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

Definitions and Theorems

Function: rem-sint-sllong

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

Theorem: sllongp-of-rem-sint-sllong

(defthm sllongp-of-rem-sint-sllong
  (sllongp (rem-sint-sllong x y)))

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

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

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

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

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

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

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

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