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Representation-of-integer-operations

Rem-uchar-sint

Remainder of a value of type unsigned char and a value of type signed int [C:6.5.5].

Definitions and Theorems

Function: rem-uchar-sint

(defun rem-uchar-sint (x y)
  (declare (xargs :guard (and (ucharp x)
                              (sintp y)
                              (rem-uchar-sint-okp x y))))
  (rem-sint-sint (sint-from-uchar x) y))

Theorem: sintp-of-rem-uchar-sint

(defthm sintp-of-rem-uchar-sint
  (sintp (rem-uchar-sint x y)))

Theorem: rem-uchar-sint-of-uchar-fix-x

(defthm rem-uchar-sint-of-uchar-fix-x
  (equal (rem-uchar-sint (uchar-fix x) y)
         (rem-uchar-sint x y)))

Theorem: rem-uchar-sint-uchar-equiv-congruence-on-x

(defthm rem-uchar-sint-uchar-equiv-congruence-on-x
  (implies (uchar-equiv x x-equiv)
           (equal (rem-uchar-sint x y)
                  (rem-uchar-sint x-equiv y)))
  :rule-classes :congruence)

Theorem: rem-uchar-sint-of-sint-fix-y

(defthm rem-uchar-sint-of-sint-fix-y
  (equal (rem-uchar-sint x (sint-fix y))
         (rem-uchar-sint x y)))

Theorem: rem-uchar-sint-sint-equiv-congruence-on-y

(defthm rem-uchar-sint-sint-equiv-congruence-on-y
  (implies (sint-equiv y y-equiv)
           (equal (rem-uchar-sint x y)
                  (rem-uchar-sint x y-equiv)))
  :rule-classes :congruence)