# [LEAPSECS] Toasting Unix timestamp 1234567890

**Magnus Danielson**
magnus at rubidium.dyndns.org

*Sat Feb 14 16:02:44 EST 2009*

Zefram skrev:

>* Magnus Danielson wrote:
*

>>* Sorry, I think you over-interpret a poorly articulated formulation of
*

>>* mine. If you think according to "Honour the UTC definition from 1970 to
*

>>* 1972 and then the new leap-second based UTC definition from 1972 up to
*

>>* current time" then I think you should come to the same conclusion as I
*

>>* do.
*

>*
*

>* I was thinking precisely in terms of using UTC in both eras, counting
*

>* UTC seconds. Thus I count UTC's leaps of both eras.
*

>*
*

>>* Zefram skrev:
*

>>>* The current offset is about 24.107757997 s, and does not have a terminating
*

>>>* decimal representation. (This is the counting-UTC-seconds way.)
*

>>* I do not understand what that number comes from. Does not match what I
*

>>* meant at least, so you need to describe what it means.
*

>*
*

>* The 24 corresponds to the 24 positive leap seconds since 1972.
*

>* The remainder corresponds to pre-1972 leaps. In fact there is exactly
*

>* one such leap after the Unix epoch, and that is the final one at the
*

>* end of 1971 which brought UTC seconds into alignment with TAI seconds.
*

>* The duration of that leap was exactly 0.107758 TAI seconds. At the
*

>* then-prevailing rate of 1 UTC second = 1.00000003 TAI seconds, the
*

>* duration of the leap was exactly 10775800/100000003 UTC seconds, or
*

>* approximately 0.107757997 UTC seconds.
*

I gathered that eventually and it makes perfect sense. You only made a

very brief discussion over it so I did not get the right triggers. The

leap in TAI-UTC offset as measured in TAI seconds needs to be converted

into UTC seconds. However... is it the UTC seconds of the previous era

or the new era? It's a singularity so you can't use the slope of the

previous era, infact the scope of that era goes to but does not include

the UTC time of 1 Jan 1972 00:00:00, so the jump can not be included in

that era. So I think your calculation is actually wrong in this respect

and that 63072000.107758 UTC seconds is the time that has passed.

>* The number of elapsed UTC seconds from 1972-01-01T00:00:00 UTC to any
*

>* UTC midnight in 2009 is exactly 86400*(number of elapsed days) + 24 +
*

>* 10775800/100000003.
*

I am starting to disagree about the last term there.

>* It seems clear to me, but I studied it quite closely to write the Perl
*

>* module Time::UTC (which is what I've used to extract some of these
*

>* numbers). I guess it's trickier than it looks.
*

It is tricky... I think you need to explain how you interpret the

range-definitions as I interpret them a little bit different.

>>* It is a bit of a mess. Honouring the pre-1972 UTC definition for the
*

>>* pre-1972 era makes sense as it allows for a practical solution at least,
*

>>* as only integer offsets is involved.
*

>* ...
*

>>* it does not really help for the pre-1972 era where leap seconds was not
*

>>* used,
*

>*
*

>* You seem to think there were no leaps in UTC before 1972. Evidently
*

>* that's why you get confused about the fractional number of leap seconds.
*

No, I know there is leaps, but no leap seconds. There are several

fractional second leaps. I was only challangeing the wording to denote

"leap seconds" to fully disregard the shifts and ramps there is.

>>* At 1 Jan 1972 we jumped from 9,892242 to 10 s offset in one fractional
*

>>* step.
*

>*
*

>* But this is a reference to the irregular leap.
*

Yes, but you confuse my separation of leaps with leaps though the use of

the leap second mechanism in which you jump integer seconds.

>>* Before that we had a 3E-8 s/s phase ramp from 8,000082 of 1 Jan
*

>>* 1970. Neither qualify as leap seconds.
*

>*
*

>* The frequency offset isn't a leap, because it doesn't give UTC days an
*

>* irregular number of UTC seconds. But the 1971-12-31 leap, and earlier
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>* leaps that were mostly of 0.1 TAI seconds, certainly are (fractional)
*

>* leap seconds.
*

Which is also what I wanted to say. When going back to

1970-01-01T00:00:00Z and then counting from that, just disregarding leap

seconds only helps us back to what happend since 1972-01-01T00:00:00Z

since only since then the leap seconds have been used as an adjustment

mechanism. Previous to that a combination of time and frequency offsets

was used, but I do not call them leap seconds...

Also, the leap was on 1972-01-01T00:00:00, which is why it should not be

included in the 30 ppb frequency era.

>* When I first read about the rubber seconds era, I got the impression
*

>* that it was done solely by frequency offsets, with no leaps. How much
*

>* easier would our lives have been if that were the case?
*

Much.

Cheers,

Magnus

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