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Representation-of-integer-operations

Shl-ulong

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

Definitions and Theorems

Function: shl-ulong

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

Theorem: ulongp-of-shl-ulong

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

Theorem: shl-ulong-of-ulong-fix-x

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

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

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

Theorem: shl-ulong-of-ifix-y

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

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

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