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Representation-of-integer-operations

Shl-ullong

Left shift of a value of type unsigned long long by an integer [C17:6.5.7].

Definitions and Theorems

Function: shl-ullong

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

Theorem: ullongp-of-shl-ullong

(defthm ullongp-of-shl-ullong
  (ullongp (shl-ullong x y)))

Theorem: shl-ullong-of-ullong-fix-x

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

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

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

Theorem: shl-ullong-of-ifix-y

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

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

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