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• Combine-functions

Combine16u

(combine16u a1 a0) merges unsigned bytes, producing the 16-bit unsigned interpretation of (a1 << 8) | a0.

Definitions and Theorems

Function: combine16u$inline

(defun combine16u$inline (a1 a0)
  (declare (type (unsigned-byte 8) a1 a0))
  (mbe :logic (logior (ash (nfix a1) 8) (nfix a0))
       :exec (the (unsigned-byte 16)
                  (logior (ash a1 8) a0))))

Theorem: combine16u-unsigned-byte

(defthm combine16u-unsigned-byte
  (implies (and (force (unsigned-byte-p 8 a1))
                (force (unsigned-byte-p 8 a0)))
           (unsigned-byte-p 16 (combine16u a1 a0))))

Theorem: combine16u-loghead-logtail

(defthm combine16u-loghead-logtail
  (implies (natp i)
           (equal (combine16u (logtail 8 i) (loghead 8 i))
                  i)))