Stephen Wille Padnos wrote: > Jon Elson wrote: > > >>Jeff Epler wrote: >> >> >> >>>In emc2 there are practical limits on the precision of position values due to >>>the use of "float" as the fundamental type for "analog" values such as >>>encoder positions. For instance, the values 1.0 and 1.0 + 0.5**23 >>>(approximately 1.0000001) are both exactly representable, but no values >>>in between those two can be represented. Similarly, 2.0 and >>>2.0 + 0.5**22 (approximately 2.0000002) are both exactly representable, >>>but no values in between those two can be represented. >>> >>> http://en.wikipedia.org/wiki/Floating_Point#Implementation_in_actual_computers:_IEEE_floating-point >>> >>> >>> >> >>A very good point! It seems there would be a 25.4 X benefit >>then by using mm as the user unit instead of inches, in the case >>of these very high resolution encoders. (I think you mean + 0.5 >>* 10 ^ -23 in the above) >> > > Nope, it's 0.5 ^ 23. 0.5 is the first digit past the binary point, and > 0.5^23 is the last bit past the binary point. It seems to me that : the value 1.0 + 0.5**23 (approximately 1.0000001) would be 5, followed by 22 zeroes, followed by 1.0, assuming that you mean "**23" as x 10 to the 23rd power. This is not a number slightly larger than 1.0, unless I'm totally misunderstanding what you are trying to say above. > > >> This may really be moot in Aram's >>project as the one million count/rev encoder would provide 5 >>million counts/inch with a 5 TPI screw, and that is only about >>22 bits of resolution, assuming only a couple inches of travel. >>Even if you tried to do this with a very large machine, say 100" >>of travel, that's only 100 X 5 X 1 million = 500 million, or >>about 29 bits of resolution. >> >> > > That's just a few bits past the mantissa of a 32-bit float, which is 24 > bits. > Umm, yeah, I had been thinking this was all carried as DOUBLE floats! Definitely could be a problem with a high res encoder and a longer machine travel. > I think the 24-bit counter is still OK for an encoder that gives 1 million counts, or even 4 million counts/rev. Probably would be OK, even with +/- 8 million counts/rev, since 24 bits can represent +/- 8,388,607 integers.
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