[LEAPSECS] Time math libraries, UTC to TAI

[Michael.Deckers.]

    On 2016-12-31 22:39, Brooks Harris quoted a table
    from the RFC defining the NTP protocol:

>
> RFC 5905 Figure 4: Interesting Historic NTP Dates shows
>
> +-------------+------------+-----+---------------+------------------+
>    | Date        | MJD        | NTP | NTP Timestamp | Epoch            |
>    |             |            | Era | Era Offset |                  |
> +-------------+------------+-----+---------------+------------------+
>    | 1 Jan -4712 | -2,400,001 | -49 | 1,795,583,104 | 1st day Julian   |
>    | 1 Jan -1    | -679,306   | -14 | 139,775,744   | 2 BCE            |
>    | 1 Jan 0     | -678,491   | -14 | 171,311,744   | 1 BCE            |
>    | 1 Jan 1     | -678,575   | -14 | 202,939,144   | 1 CE             |
>    | 4 Oct 1582  | -100,851   | -3  | 2,873,647,488 | Last day Julian  |
>    | 15 Oct 1582 | -100,840   | -3  | 2,874,597,888 | First day        |
>    |             |            |     |               | Gregorian        |
>    | 31 Dec 1899 | 15019      | -1  | 4,294,880,896 | Last day NTP Era |
>    |             |            |     |               | -1               |
>    | 1 Jan 1900  | 15020      | 0   | 0             | First day NTP    |
>    |             |            |     |               | Era 0            |
>    | 1 Jan 1970  | 40,587     | 0   | 2,208,988,800 | First day UNIX   |
>    | 1 Jan 1972  | 41,317     | 0   | 2,272,060,800 | First day UTC    |
>    | 31 Dec 1999 | 51,543     | 0   | 3,155,587,200 | Last day 20th    |
>    |             |            |     |               | Century          |
>    | 8 Feb 2036  | 64,731     | 1   | 63,104        | First day NTP    |
>    |             |            |     |               | Era 1            |
> +-------------+------------+-----+---------------+------------------+
>
     Just to show that standards (and RFCs) must be read with caution
     because they sometimes do not mean what they say, here are a few
     inconsistencies in the table above:

     The "fffMJD" entry in the line for "Date 1 Jan 0" should be -678,941
     rather than "-678,491".

     Did you expect that the dates "1 Jan -1", "1 Jan 0", "1 Jan 1",
     "4 Oct 1582" are meant to be dates in the (proleptic) Gregorian
     calendar, while "1 Jan -4712" is meant to be a date in the
     Julian calendar?

     And of course, the "Last day Julian" should be one day before the
     "First day Gregorian" but actually is eleven days earlier.

     Michael Deckers.