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Extend back to 1961 #1
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For example, the line:
indicates that the following all represent the same instant in time:
At this instant, TAI was 4.313170 seconds ahead of Unix, and pulling ahead by 0.002592 seconds per day. By 1968-02-01 00:00:00 UTC, TAI was 6.285682 seconds ahead at 1968-02-01 00:00:06.285682. However, the next line of data
indicates that the following all represent the same instants in time:
So this means that at 1968-02-01 00:00:00 UTC, TAI suddenly jumped from 6.285682 seconds ahead to only 6.185682 seconds ahead. Since TAI is a fixture and UTC is derived from it, this in fact indicates a deliberately inserted discontinuity in UTC, from which some 0.1 TAI seconds were removed... a removed one-tenth of a leap second, as it were. And you thought there was no such thing! TAI and UTC continued to drift apart. By 1972-01-01 00:00:00 UTC, TAI was 9.892242 seconds ahead at 1972-01-01 00:00:09.892242. This leads us to beginning of the "modern era" of TAI:
Here, it is still 1972-01-01 00:00:00 UTC but it is suddenly 1972-01-01 00:00:10 TAI, thanks to the highly irregular insertion of 0.107758 "leap" TAI seconds into UTC. From this moment on,
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Done, basically. Give or take some serious thought about precision loss, and exactly how conversions behave at boundaries of leap time insertion/removal... |
As per several sources, such as this IERS listing of historic offsets between TAI and UTC and this table provided by the US Naval Observatory (ftp://maia.usno.navy.mil/ser7/tai-utc.dat), the relationship between UTC and TAI is in fact well-defined as far back as 1 January 1961. As we can (sort of) see from the table, during this earlier period from 1961 to the end of 1971, UTC seconds were very slightly shorter than TAI seconds, so the offset between the two "slid" continuously at varying rates. Both the ratio between TAI and UTC seconds and the absolute offset between TAI and UTC were adjusted manually on several discrete occasions, up until 1 January 1972 when a "final irregular jump of exactly 0.107758 TAI seconds" brought UTC to 1972-01-01 00:00:00 at the exact instant that TAI reached 1972-01-01 00:00:10, and the rest is history.
Unix time can probably be extended backwards to 1 January 1961 too, which means that in theory it should be possible to provide Unix<->TAI conversions during this earlier period.
The spectre of floating point raises its ugly head at this point...
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