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Representation-of-integer-operations

Shr-sllong

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

Definitions and Theorems

Function: shr-sllong

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

Theorem: sllongp-of-shr-sllong

(defthm sllongp-of-shr-sllong
  (sllongp (shr-sllong x y)))

Theorem: shr-sllong-of-sllong-fix-x

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

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

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

Theorem: shr-sllong-of-ifix-y

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

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

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