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Representation-of-integer-operations

Shl-slong-sllong

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

Definitions and Theorems

Function: shl-slong-sllong

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

Theorem: slongp-of-shl-slong-sllong

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

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

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

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

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

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

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

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

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