Re: This calculation is just wrong / computer can't count!

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For a 15th digit to be significant, GT's CNC would have to operate at one
atom precision on objects 100 m in size.

"Geoff" <geoff@xxxxxxxxxxxxxxx> wrote in message
news:8hovg39uevn9lf3krec13ucbek70cesn0a@xxxxxxxxxx
On Fri, 12 Oct 2007 16:42:47 +0100, "GT"
<ContactGT_remove_@xxxxxxxxxxx> wrote:


If your code were to drive a CNC machine tasked to cut objects into thirds
(assuming no waste, or equal waste from each third), then it would never
actually get it right. That is not opinion, that is fact. Each of the
thirds
would be 0.33333333333333331 of the object, so tell us Joe, which piece
would you add the extra 0.00000000000000007 ? Of course, you can't
represent
that number so who knows where is will go, but you certainly won't end up
with matching pieces.


As a CNC engineer I can tell you with certainty that all CNC
operations are INTEGER operations and not floating point. The feedback
systems are integer counters and the motors have integral encoders or
resolvers feeding converters that compute integer phase angles for
feeding into the control. The controls resolve to finite FIXED-POINT
precision of mostly 3, 4, 5 and sometimes 6 places. The fixed point
displays are only decimalized for human interpretation, in units of 1
micrometer generally and .0001 inch in the US. Such machines are
incapable of rendering numbers you described or dividing into thirds,
with one exception: rotary tables where the division would be an
integer (120/360) and the split would be perfectly lossless. Not
opinion, fact.



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