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Representation-of-integer-operations

Rem-sllong-sint

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

Definitions and Theorems

Function: rem-sllong-sint

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

Theorem: sllongp-of-rem-sllong-sint

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

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

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

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

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

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

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

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

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