I'm not clear on why there is an attempt to use FIXED for the data
rather than an integer. The binary result is identical, but I think it
is a lot easier and clearer to say that the numbers range from
-2147483647 to +2147483647 (or -0x7fffffff to 0x7fffffff).
It seems like the following information must be sent:
1. The "normalized" value as described in most of this, though I would
prefer to describe it as a 32-bit integer rather than a fixed-point
format. The largest absolute value the device can produce is mapped to
2147483647 (thus -2147483648 cannot be produced). The "zero" value is
mapped to zero. The reason for using the normalized value is that it is
the only one a client can actually use without referring to the other
values.
2. The "range" in units. This is two numbers showing the bottom and top
end, probably in fixed format. This provides useful information to a
client even if it does not know what the units are: client can figure
out the full range in normalized space of the device: take the largest
absolute value and scale that to 214748647. Then multiply the range by
the same scale and you will have the range in normalized space. This is
necessary for a client to know if the device is at a stop.
3. The "resolution". I think this is best given as the number of steps
that cover the range, as an integer. With this information, and provided
there are less than 2^31 steps, the client can recover and distinguish
exactly the position of the device. If the resolution is less than 2^23
then the exact position can be recovered using 32-bit floats.
The units have to be chosen to be linear with the device steps, so they
may in fact be sqrt(elbows/inch) or even a more complex piece-wise function.
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