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From: dennis@UTCS.UTORONTO.CA (Dennis Ferguson)
Newsgroups: comp.protocols.time.ntp
Subject: Re: What means "drift" and "compliance" ?
Message-ID: <91Feb20.212704est.18486@gpu.utcs.utoronto.ca>
Date: 21 Feb 91 02:26:56 GMT
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Lines: 65

Scott,

>>>If 4096 is the exact conversion, why the
>>>lookup table scheme in the first place? The lookup scheme is not
>>>especially linear for large values of drift, and I suspect that it may be
>>>the cause of machines with large drift values being unable to sync.
[...]
>Sorry, I thought this was reference to xntpd, where there IS something
>that I would call a "lookup table scheme" for conversion between drift and
>timestamp values. I am specifically referring to the macros TVUTOTSF and
>TSFTOTVU in include/ntp_unixclock.h which use lookups into the tables
>defined in lib/tvtots.c, lib/tstotv.c, etc. My emperical experimentation,
>the tables come out with a value averaging near 4130. If I'm looking in
>the wrong part of the code, I'd welcome pointers.

I think I know where this confusion comes from.  Xntpd does internal
time-dimensioned computations using a 64-bit fixed point format, with
the decimal point between the two 32-bit halves.  You can think of
this as working with 64-bit integer values having units of 2**(-32)
seconds.  The drift value, which is actually the error component computed
by a phase-locked loop, has dimensions of time and is computed in this
format.

Every 4 seconds the drift value is divided by 1024 and the result is
added to or subtracted from the system clock using adjtime().  (4*1024)
is where the 4096 comes from.  1024 is a scale factor which falls out
of the PLL calculations.  I think the calculation is scaled like this
so that the results don't disappear to the right of the least significant
digit of the fuzzball's internal time representation (fuzzballs use
integer milliseconds to represent time values).

So you have a time that you want to add to the system clock using
adjtime().  The time (say 0.000040 seconds, or something) is computed
in units of 2**(-32) seconds.  Adjtime(), however, wants to be told
the time in units of microseconds.  This means you have to multiply
the internal value by (10**6)/(2**32).  This is what the TSFTOTVU
macro is used for.  The tables are essentially lists of precomputed
results of this multiplication, so you can compute the microsecond
value using three table lookups and a few adds rather than actually
doing the multiply (the latter is hard to do without a 32x32=64 bit
multiply instruction).  The TVUTOTSF macro does the inverse conversion.
You can check this yourself.  For example, a struct timeval value
of 500000 usec should produce an internal format value of 0x80000000
when run through TVUTOTSF, and 250000 usec should produce 0x40000000.

It would be very interesting to know if these tables weren't linear.

As for machines with large drift values being unable to sync (or at
least, requiring you to prime the drift file with a number which is
in the ball park before they'll sync), this is limited by the capture
aperture of the PLL used (essentially, by the code which decides
when it is appropriate to slew the clock and when it is appropriate
to step it).  This is intentional.  There is a tradeoff between
the size of the frequency error you can compensate for, the speed
and stability with which you can correct phase errors, and the
quality of synchronization once everything settles down.  A wider
capture aperture would cost you either by causing clocks whose
crystals were accurate but whose time was off to take a longer time
to synchronize, or by causing larger overshoots and oscillations
when a clock was being brought into line.  As it is hard to buy
crystals which are worse than about 20 ppm off (and you'd have
to look hard to find crystals this bad), NTP's capture aperture
of about 150 ppm was probably considered plenty.

Dennis Ferguson