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Representation-of-integer-operations

Rem-sllong-ulong

Remainder of a value of type signed long long and a value of type unsigned long [C17:6.5.5].

Definitions and Theorems

Function: rem-sllong-ulong

(defun rem-sllong-ulong (x y)
  (declare (xargs :guard (and (sllongp x)
                              (ulongp y)
                              (rem-sllong-ulong-okp x y))))
  (rem-ullong-ullong (ullong-from-sllong x)
                     (ullong-from-ulong y)))

Theorem: ullongp-of-rem-sllong-ulong

(defthm ullongp-of-rem-sllong-ulong
  (ullongp (rem-sllong-ulong x y)))

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

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

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

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

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

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

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

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