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Representation-of-integer-operations

Div-ulong-sllong

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

Definitions and Theorems

Function: div-ulong-sllong

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

Theorem: ullongp-of-div-ulong-sllong

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

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

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

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

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

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

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

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

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