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Representation-of-integer-operations

Shl-slong

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

Definitions and Theorems

Function: shl-slong

(defun shl-slong (x y)
  (declare (xargs :guard (and (slongp x)
                              (integerp y)
                              (shl-slong-okp x y))))
  (slong-from-integer (* (integer-from-slong x)
                         (expt 2 (ifix y)))))

Theorem: slongp-of-shl-slong

(defthm slongp-of-shl-slong
  (slongp (shl-slong x y)))

Theorem: shl-slong-of-slong-fix-x

(defthm shl-slong-of-slong-fix-x
  (equal (shl-slong (slong-fix x) y)
         (shl-slong x y)))

Theorem: shl-slong-slong-equiv-congruence-on-x

(defthm shl-slong-slong-equiv-congruence-on-x
  (implies (slong-equiv x x-equiv)
           (equal (shl-slong x y)
                  (shl-slong x-equiv y)))
  :rule-classes :congruence)

Theorem: shl-slong-of-ifix-y

(defthm shl-slong-of-ifix-y
  (equal (shl-slong x (ifix y))
         (shl-slong x y)))

Theorem: shl-slong-int-equiv-congruence-on-y

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