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Representation-of-integer-operations

Shr-ulong-uint

Right shift of a value of type unsigned long and a value of type unsigned int [C:6.5.7].

Definitions and Theorems

Function: shr-ulong-uint

(defun shr-ulong-uint (x y)
  (declare (xargs :guard (and (ulongp x)
                              (uintp y)
                              (shr-ulong-uint-okp x y))))
  (shr-ulong x (integer-from-uint y)))

Theorem: ulongp-of-shr-ulong-uint

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

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

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

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

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

Theorem: shr-ulong-uint-of-uint-fix-y

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

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

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