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Representation-of-integer-operations

Div-sshort-ushort

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

Definitions and Theorems

Function: div-sshort-ushort

(defun div-sshort-ushort (x y)
  (declare (xargs :guard (and (sshortp x)
                              (ushortp y)
                              (div-sshort-ushort-okp x y))))
  (div-sint-sint (sint-from-sshort x)
                 (sint-from-ushort y)))

Theorem: sintp-of-div-sshort-ushort

(defthm sintp-of-div-sshort-ushort
  (sintp (div-sshort-ushort x y)))

Theorem: div-sshort-ushort-of-sshort-fix-x

(defthm div-sshort-ushort-of-sshort-fix-x
  (equal (div-sshort-ushort (sshort-fix x) y)
         (div-sshort-ushort x y)))

Theorem: div-sshort-ushort-sshort-equiv-congruence-on-x

(defthm div-sshort-ushort-sshort-equiv-congruence-on-x
  (implies (sshort-equiv x x-equiv)
           (equal (div-sshort-ushort x y)
                  (div-sshort-ushort x-equiv y)))
  :rule-classes :congruence)

Theorem: div-sshort-ushort-of-ushort-fix-y

(defthm div-sshort-ushort-of-ushort-fix-y
  (equal (div-sshort-ushort x (ushort-fix y))
         (div-sshort-ushort x y)))

Theorem: div-sshort-ushort-ushort-equiv-congruence-on-y

(defthm div-sshort-ushort-ushort-equiv-congruence-on-y
  (implies (ushort-equiv y y-equiv)
           (equal (div-sshort-ushort x y)
                  (div-sshort-ushort x y-equiv)))
  :rule-classes :congruence)