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Representation-of-integer-operations

Shr-uint

Right shift of a value of type unsigned int by an integer [C:6.5.7].

Definitions and Theorems

Function: shr-uint

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

Theorem: uintp-of-shr-uint

(defthm uintp-of-shr-uint
  (uintp (shr-uint x y)))

Theorem: shr-uint-of-uint-fix-x

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

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

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

Theorem: shr-uint-of-ifix-y

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

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

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