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Representation-of-integer-operations

Rem-ullong-sshort

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

Definitions and Theorems

Function: rem-ullong-sshort

(defun rem-ullong-sshort (x y)
  (declare (xargs :guard (and (ullongp x)
                              (sshortp y)
                              (rem-ullong-sshort-okp x y))))
  (rem-ullong-ullong x (ullong-from-sshort y)))

Theorem: ullongp-of-rem-ullong-sshort

(defthm ullongp-of-rem-ullong-sshort
  (ullongp (rem-ullong-sshort x y)))

Theorem: rem-ullong-sshort-of-ullong-fix-x

(defthm rem-ullong-sshort-of-ullong-fix-x
  (equal (rem-ullong-sshort (ullong-fix x) y)
         (rem-ullong-sshort x y)))

Theorem: rem-ullong-sshort-ullong-equiv-congruence-on-x

(defthm rem-ullong-sshort-ullong-equiv-congruence-on-x
  (implies (ullong-equiv x x-equiv)
           (equal (rem-ullong-sshort x y)
                  (rem-ullong-sshort x-equiv y)))
  :rule-classes :congruence)

Theorem: rem-ullong-sshort-of-sshort-fix-y

(defthm rem-ullong-sshort-of-sshort-fix-y
  (equal (rem-ullong-sshort x (sshort-fix y))
         (rem-ullong-sshort x y)))

Theorem: rem-ullong-sshort-sshort-equiv-congruence-on-y

(defthm rem-ullong-sshort-sshort-equiv-congruence-on-y
  (implies (sshort-equiv y y-equiv)
           (equal (rem-ullong-sshort x y)
                  (rem-ullong-sshort x y-equiv)))
  :rule-classes :congruence)