ntpq peers formatting needs floating point for time slots.

[Achim Gratz]

Hal Murray writes:
> Looks like we are getting into the old precision vs accuracy tangle.
> Do we have a glossary with useful descriptions?
> That slot should represent the number of useful bits.

It really doesn't help that precision, accuracy and resolution have a
number of different meanings depending on the context.  It is doubly
unfortunate that NTP necessarily uses several of these contexts.

In measurement statistics, precision describes the variability of the
distribution of many repeated measurements of the same quantity and
accuracy the deviation of the location parameter on that statistic to
the "ground truth" (or more commonly to another measurement that ius
known to have higher precision and accuracy).  It is generally assumed
that the measurement process has much higher resolution than the
precision of the measurement and the measurement distribution can be
assumed to be continous.  Resolution in this context is the smallest
change in the measured quantity that will yield a discernible change of
the measured value.

In numerics and software in particular, precision and resolution are
often confused to interchangeably mean the number of digits in the
computation or presentation.  Precision should really be reserved for
the significant number of digits going into and coming out of a
computation.  Unfortunately accuracy is often used to describe the same
(how many digits can I trust).  Accuracy should really mean "how far
from the true result is the number I've got".  Accuracy can easily be
greater than the precision (e.g. if I start a calculation with a
low-precision number and have high numerical resolution and an algorithm
that doesn't amplify errors).

In the case of NTP, we have the measurements themselves, the quantized
representations of those measurements and algorithmically processed
quantities that were derived from measurements.  Asuuming that the
resolution is always large enough to not conceal otherwise available
precision, you can't get any more accurate or precise than the
measurement if you have only a single one.  Once you start having
multiple measurements, you can get both more precise (using data from
the same measurement process) as well as accurate (using data from
multiple measurement processes) than the individual measurements
themselves, provided the statistics are well-behaved and all
calculations have suitable error propagation characteristics.

Another hidden assumption is that the local clock must be stabilized
over the time-scale used for data fusing to somewhat better than that
final error since NTP uses it both as the target of the control loop and
the reference of the measurements.


Regards,
Achim.
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