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Representation-of-integer-operations

Shl-slong-ulong

Left shift of a value of type signed long and a value of type unsigned long [C:6.5.7].

Definitions and Theorems

Function: shl-slong-ulong

(defun shl-slong-ulong (x y)
  (declare (xargs :guard (and (slongp x)
                              (ulongp y)
                              (shl-slong-ulong-okp x y))))
  (shl-slong x (integer-from-ulong y)))

Theorem: slongp-of-shl-slong-ulong

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

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

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

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

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

Theorem: shl-slong-ulong-of-ulong-fix-y

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

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

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