[LEAPSECS] Toasting Unix timestamp 1234567890

Zefram zefram at fysh.org
Sat Feb 14 15:26:10 EST 2009

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


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.

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 +

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 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


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.

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


But this is a reference to the irregular leap.

> 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
leaps that were mostly of 0.1 TAI seconds, certainly are (fractional)
leap seconds.

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?


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