[LEAPSECS] BBC radio Crowd Science

[Brooks Harris]

On 2017-01-31 01:52 PM, Warner Losh wrote:
> On Mon, Jan 30, 2017 at 2:39 PM, Tom Van Baak <tvb at leapsecond.com> wrote:
>>>> 2017-01-01T00:00:36.5 - 36 s = 2016-12-31T23:59:60.5
>>>     What kind of arithmetic is that?
>> Hi Michael,
>>
>> First, there's no problem with this, right?  (Thanks to Steve for catching typo)
>>
>> 2017-01-01T00:00:35.5 TAI = 2016-12-31T23:59:59.5 UTC
>> 2017-01-01T00:00:36.5 TAI = 2016-12-31T23:59:60.5 UTC
>> 2017-01-01T00:00:37.5 TAI = 2017-01-01T00:00:00.5 UTC
>>
>> Now, we want to use "UTC = TAI + (UTC - TAI)" notation. So which is correct:
>>
>> 2017-01-01T00:00:35.5 TAI - 36 s = 2016-12-31T23:59:59.5 UTC
>> 2017-01-01T00:00:36.5 TAI - 36 s = 2016-12-31T23:59:60.5 UTC  ??
>> 2017-01-01T00:00:37.5 TAI - 37 s = 2017-01-01T00:00:00.5 UTC
>>
>> or
>>
>> 2017-01-01T00:00:35.5 TAI - 36 s = 2016-12-31T23:59:59.5 UTC
>> 2017-01-01T00:00:36.5 TAI - 37 s = 2016-12-31T23:59:60.5 UTC  ??
>> 2017-01-01T00:00:37.5 TAI - 37 s = 2017-01-01T00:00:00.5 UTC
>>
>> Neither one is particularly clear to me. Of course in real code it all works because you special case the leap second label discontinuity and make it work. In a sense you replace normal sexagesimal arithmetic with 59-gesimal or 61-gesimal arithmetic for that one minute. But, yeah, I can see that it complicates prose and equations regarding UTC-TAI offsets.
> I think it has to be the second one because when you work through the
> math, it works out.
>
> The math simply doesn't work out for the former. 36-36 is 0, which you
> have to somehow know means 60. That's nuts, imho. However, 36-37 is
> -1. When you have an underflow, you have to borrow from the previous
> minute. That minute has 61 seconds, which when added to -1 gives 60,
> which is the correct answer.
>
> Otherwise you are in special case hell where you know there's a leap
> second so you add one more, which is solved nicely by just bumping the
> offset at the start of the leap second.
Yes, I think I understand what you mean. Your take on it does simplify 
some aspects of the math a bit, but, as I understand it, that's not what 
the specifications say. Of course, as we've been discussing, the 
specifications leave room for interpretation.

I've been in long discussions on exactly this topic, and the conclusion 
was, as I've said, TAI-UTC increments *after* the Leap Second.

We are overlapping on email responses now...

-Brooks

> Warner
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