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Representation-of-integer-operations

Div-ushort-sshort

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

Definitions and Theorems

Function: div-ushort-sshort

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

Theorem: sintp-of-div-ushort-sshort

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

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

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

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

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

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

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

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

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