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• Combine-functions

Combine32s

(combine32s a3 a2 a1 a0) merges unsigned bytes, producing the 32-bit signed interpretation of (a3 << 24) | (a2 << 16) | (a1 << 8) | a0.

Definitions and Theorems

Function: combine32s$inline

(defun
 combine32s$inline (a3 a2 a1 a0)
 (declare (type (unsigned-byte 8) a3 a2 a1 a0))
 (mbe
   :logic (logior (ash (fast-logext 8 (nfix a3)) 24)
                  (ash (nfix a2) 16)
                  (ash (nfix a1) 8)
                  (nfix a0))
   :exec (b* ((a3 (the (signed-byte 32)
                       (ash (the (signed-byte 8) (fast-logext 8 a3))
                            24)))
              (a2 (the (unsigned-byte 24) (ash a2 16)))
              (a1 (the (unsigned-byte 16) (ash a1 8)))
              (ans (the (unsigned-byte 16)
                        (logior (the (unsigned-byte 16) a1)
                                (the (unsigned-byte 8) a0))))
              (ans (the (unsigned-byte 24)
                        (logior (the (unsigned-byte 24) a2)
                                (the (unsigned-byte 16) ans)))))
             (the (signed-byte 32)
                  (logior (the (signed-byte 32) a3)
                          (the (signed-byte 32) ans))))))

Theorem: combine32s-signed-byte

(defthm combine32s-signed-byte
        (implies (and (force (unsigned-byte-p 8 a3))
                      (force (unsigned-byte-p 8 a2))
                      (force (unsigned-byte-p 8 a1))
                      (force (unsigned-byte-p 8 a0)))
                 (signed-byte-p 32 (combine32s a3 a2 a1 a0))))