[LEAPSECS] Time math libraries, UTC to TAI

Fri Dec 30 11:37:38 EST 2016

On 2016-12-28 04:16 PM, Steve Allen wrote:
> On Wed 2016-12-28T16:00:17 -0500, Brooks Harris hath writ:
>> I don't think so. This is POSIX so-called "1970-01-01 00:00:00 UTC"
>> not 1588/PTP. 1588/PTP epoch is 10s earlier.
> At 1970-01-01 the difference TAI - UTC(BIH) was 8.000082 SI seconds.
I trust you're calculations, and your stating it as "TAI-UTC(BIH)" makes 
it clear its not UTC(NIST) or some other UTC, and that's good. But, as 
you point out below,  ".. all of this is pedantic and moot for any 
currently operational system because it was not operational then".

The "rubber band era", the period of development of TAI and UTC from 
approximately 1960 to 1971 which led to the crucial TAI-to-UTC 
calibration point of 1972-01-01 00:00:10 (TAI) = 1972-01-01 00:00:00 
(UTC), may be seen as an interesting  but obsolete history which is now 
irrelevant to consideration of practical timekeeping.

I've been in many discussions of this issue and struggled with it 
myself. If you engage the UTC specifications starting with ITU-R Rec 460 
and attempt to understand the origins and TAI-UTC values you may first 
find -

BIPM Annual Report on Time Activities 
(http://www.bipm.org/en/bipm/tai/annual-report.html)
Table 1. Relative frequency offsets and step adjustments of UTC...
Table 2. Relationship between TAI and UTC...

Those tables list the frequency and non-integral seconds adjustments 
prior to 1972. This leads one to believe these values are relevant to 
understanding and implementing UTC. But the documentation is complex and 
unclear, leading to further research to discover or confirm your 
understanding.

There is a hole in the data of these tables; Rec 460 tells us the origin 
of TAI is "1 January 1958" but the first TAI-UTC value listed in the 
tables is in 1961 - what happened between 1958 and 1961? What does "1 
January 1958" mean; 1958-01-01 00:00:00 (TAI) or 1958-01-01 00:00:00 
(UTC)? Wait, did UTC exist in 1958? Why 1958? Eventually you might 
discover that "1 January 1958" was put in place retroactively in 1971 
(Rec 460 actually tells us so, but the history of it in the literature 
is convoluted). OK, but what is the TAI-UTC offset at 1958-01-01? Turns 
out, obscurely, zero. Hmmm. The TAI-UTC offset is exactly 10 seconds at 
TAI1972 = UTC1972. So how, exactly, should we distribute the TAI-UTC 
values across that 1958-to1972 period? And if the atomic time frequency 
itself was being changed how should we reconcile this with a system that 
has a stable frequency?

Many of us have been led down this path, and we've probably found 
Steve's excellent and extensive documentation about timescales.

In the end the only sensible thing to do is ignore these obsolete facts 
and establish a proleptic integral-second timescale. That's exactly what 
NTP does, and many POSIX-based systems. The TAI-UTC values published by 
IERS, such as 
(https://hpiers.obspm.fr/eoppc/bul/bulc/Leap_Second_History.dat), show 
no TAI-UTC values prior to TAI1972 = UTC1972.

Yet the idea that a timescale must honor these historical facts 
persists. I've come to see this whole topic of pre-1972 TAI-UTC values 
as a trap, a trip down a rabbit hole.

> The first version of IEEE 1588 was not entirely consistent with its
> text and appendix information, so it was not clear whether that time
> scale was supposed to be TAI or TAI - 10.
> The second version of IEEE 1588 clarified that the intent is TAI.
I've been involved in lengthy discussions about the PTP "epoch", and 
this has been entangled with the difficulties of defining the TAI-to-UTC 
relationship prior to 1972.

[By the way, IEEE 1588 defines "epoch" as "3.1.9 epoch: The origin of a 
timescale.". This is arguably, perhaps subtlety, not the same as the 
definition of the POSIX "the epoch", which is intentionally vague The 
term "epoch" does not appear in ISO 8601 or any IEC documents I've 
found. Caution with the term "epoch".]

1588 states "7.2.2 Epoch - The PTP epoch is 1 January 1970 00:00:00 TAI, 
which is 31 December 1969 23:59:51.999918 UTC.". (This is consistent 
with Steve's statement above - "At 1970-01-01 the difference TAI - 
UTC(BIH) was 8.000082 SI seconds."). However, this seems in conflict 
with Annex B, Table B.1 - Relationships between timescales, one entry of 
which says "NTP Seconds = PTP Seconds + 2 208 988 800 - currentUtcOffset".

It seems from long discussions that typical implementations of PTP use 
an integral second relationship between TAI and UTC, as per the 
(non-normative) Annex Table B. If date-time before 1972 UTC is treated 
as integral seconds the same way NTP and POSIX define their origins the 
PTP epoch is 1970-01-01 00:00:00 (TAI) = 1969-12-31T23:59:50 (UTC). This 
is more more consistent with NTP and the typical, or at least some, 
interpretation of POSIX "the epoch".

This is the interpretation used in the new SMPTE (Society of Motion 
Pictures and Television Engineers) ST 2059-2 and ST 2059-1 standards for 
synchronization over network systems. It is based on IEEE 1588/PTP. It 
states:

---------------
6 SMPTE Epoch and Signal Alignment
The SMPTE Epoch shall be 1970-01-01T00:00:00TAI, which is the same as 
the PTP Epoch specified in IEEE
Standard 1588-2008.

Note: The SMPTE Epoch is 63072010 seconds before 1972-01-01T00:00:00Z (UTC).
---------------

In SMPTE standards parlance the first sentence is normative, but the 
"Note" is informative. The intention of the note is to inform 
implementers that the intention for SMPTE purposes is to interpret the 
"PTP Epoch" as integral seconds before 1972-01-01T00:00:00Z (UTC). 
Unfortunately, and probably unintentionally, the text leaves some 
ambiguity because the IEEE 1588/PTP states - "... which is 31 December 
1969 23:59:51.999918 UTC" while the SMPTE "note" says, and the intention 
is it be, 1969-12-31T23:59:50 (UTC). Having been involved in these 
discussions I know the intention is the latter. The words in a standard 
matter.

One thing for sure - if we can't agree what a particular timescale's 
origin, or "epoch", means and its exact relationship to 1972-01-01 
00:00:10 (TAI) = 1972-01-01T00:00:00 (UTC) and we don't implement them 
consistently, there won't be interoperability no matter how exacting all 
the other details of the counting schemes may be.

-Brooks

> The choice of TAI - 10 would put the origin of the time scale at the
> intersection of the grey vertical line and the green horizontal line
> seen in the second plot on
> http://www.ucolick.org/~sla/leapsecs/amsci.html
> And for any system using that time scale that puts the origin at
> 1.999918 SI seconds after the (BIH average of the) radio broadcast
> time signals said it was 1970-01-01T00:00:00.
>
> But all of this is pedantic and moot for any currently operational
> system because it was not operational then.  Only a few things like
> astrometry of solar system bodies and spindown of a handful of pulsars
> have data and models with enough precision to discern this.
>
> Everything and everyone else can reasonably assert that they do not
> have to care and that every day has always had 86400 seconds of
> duration equal to what they are currently ticking.

> --
> Steve Allen<sla at ucolick.org>               WGS-84 (GPS)
> UCO/Lick Observatory--ISB 260  Natural Sciences II, Room 165  Lat  +36.99855
> 1156 High Street               Voice: +1 831 459 3046         Lng -122.06015
> Santa Cruz, CA 95064http://www.ucolick.org/~sla/    Hgt +250 m
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