One situation that already uses two doubles, which you may already be familiar with, is the International Astronomical Union's Standards of Fundamental Astronomy library. It uses two doubles for the date in order to be able to be able to have pico/nano second precision over thousands of years. Of course the algorithms aren't precise to that level over thousands of years, but you still need the ability to specify it to that level during the time periods they are that accurate for.
Interesting. I would have thought that fixed-point would make more sense for a time quantity. If you use a 64-bit integer to represent picoseconds, it gives you a time range of about 18 million years.
You calculated something wrong. 2^64 picoseconds is only half a year.
Once you decide you need to go over 64 bits, the exact data type is largely a matter of convenience, and I can easily see two doubles being more convenient than either a quad or a 128-bit integer. You have more than 100 bits of precision in such a scheme, and it runs pretty fast.