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• Combine-functions

Combine32u

(combine32u a3 a2 a1 a0) merges unsigned bytes, producing the 32-bit unsigned interpretation of (a3 << 24) | (a2 << 16) | (a1 << 8) | a0.

Definitions and Theorems

Function: combine32u$inline

(defun combine32u$inline (a3 a2 a1 a0)
  (declare (type (unsigned-byte 8) a3 a2 a1 a0))
  (mbe :logic
       (logior (ash (nfix a3) 24)
               (ash (nfix a2) 16)
               (ash (nfix a1) 8)
               (nfix a0))
       :exec
       (b* ((a3 (the (unsigned-byte 32) (ash 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 (unsigned-byte 32)
              (logior (the (unsigned-byte 32) a3)
                      (the (unsigned-byte 24) ans))))))

Theorem: combine32u-unsigned-byte

(defthm combine32u-unsigned-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)))
           (unsigned-byte-p 32 (combine32u a3 a2 a1 a0))))

Theorem: combine32u-loghead-logtail

(defthm combine32u-loghead-logtail
  (implies (natp i)
           (equal (combine32u (logtail 24 i)
                              (loghead 8 (logtail 16 i))
                              (loghead 8 (logtail 8 i))
                              (loghead 8 i))
                  i)))