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Representation-of-integer-operations

Shl-sllong-sshort

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

Definitions and Theorems

Function: shl-sllong-sshort

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

Theorem: sllongp-of-shl-sllong-sshort

(defthm sllongp-of-shl-sllong-sshort
  (sllongp (shl-sllong-sshort x y)))

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

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

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

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

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

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

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

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