[LEAPSECS] Time math libraries, UTC to TAI

[Zefram]

Brooks Harris wrote:
>In the table, all the YMDhms representations are called only "Date". Those
>before 1972 are (or, I think, intended to be) Gregorian, while after 1972
>(and probably at) 1972 they are "UTC".

This is a nonsensical distinction.  UTC and the Gregorian calendar are
not in competition here.  The Gregorian calendar can be used to specify
(the coarse part of) a time on many time scales, including UTC, but also
TAI and TT.  Conversely, a UTC day can be described on many calendars,
including the Gregorian, but equally MJDN, the Julian calendar, and the
Discordian calendar.

The distinction that I think you're trying to make is a distinction
between time scales.  You're trying to contrast UTC against some class
of leapless time scales, and you would do better to describe what
you're talking about in terms of the actual time scale that has the
behaviour you want.  TAI and TT are the ones closest to the behaviour
you've previously attributed to pre-1972 NTP scalar values.  You need to
apply a fixed offset to them to get them to line up with UTC at 1972,
and the use of TAI runs into trouble for dates earlier than the start
of continuous operation of atomic clocks (mid 1955).

But in any case, you're in error in supposing that the pre-1972 NTP
dates are on some other time scale.  The NTP spec is clear that they
are all notionally UTC.  It's not real UTC, of course, because UTC
isn't defined as far back as 1900, but computing the values in the
table doesn't require an actual leap schedule.  The spec is explicit
that the leap schedule for this notional extension of UTC is unknown.
This also means that NTP is silent on whether its notional UTC includes
the real behaviour of the rubber-seconds era.

-zefram