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Representation-of-integer-operations

Shr-ulong

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

Definitions and Theorems

Function: shr-ulong

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

Theorem: ulongp-of-shr-ulong

(defthm ulongp-of-shr-ulong
  (ulongp (shr-ulong x y)))

Theorem: shr-ulong-of-ulong-fix-x

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

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

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

Theorem: shr-ulong-of-ifix-y

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

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

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