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Representation-of-integer-operations

Shl-sint

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

Definitions and Theorems

Function: shl-sint

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

Theorem: sintp-of-shl-sint

(defthm sintp-of-shl-sint
  (sintp (shl-sint x y)))

Theorem: shl-sint-of-sint-fix-x

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

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

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

Theorem: shl-sint-of-ifix-y

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

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

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