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Representation-of-integer-operations

Shr-sint

Right shift of a value of type signed int by an integer [C17:6.5.7].

Definitions and Theorems

Function: shr-sint

(defun shr-sint (x y)
  (declare (xargs :guard (and (sintp x)
                              (integerp y)
                              (shr-sint-okp x y))))
  (sint-from-integer (truncate (integer-from-sint x)
                               (expt 2 (ifix y)))))

Theorem: sintp-of-shr-sint

(defthm sintp-of-shr-sint
  (sintp (shr-sint x y)))

Theorem: shr-sint-of-sint-fix-x

(defthm shr-sint-of-sint-fix-x
  (equal (shr-sint (sint-fix x) y)
         (shr-sint x y)))

Theorem: shr-sint-sint-equiv-congruence-on-x

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

Theorem: shr-sint-of-ifix-y

(defthm shr-sint-of-ifix-y
  (equal (shr-sint x (ifix y))
         (shr-sint x y)))

Theorem: shr-sint-int-equiv-congruence-on-y

(defthm shr-sint-int-equiv-congruence-on-y
  (implies (acl2::int-equiv y y-equiv)
           (equal (shr-sint x y)
                  (shr-sint x y-equiv)))
  :rule-classes :congruence)