The End of Time

This isn't about 2012, or the Second Advent, or 2038. Well, 2038 will be very briefly mentioned.

Many computer systems consider time to be the number of seconds since an arbitrary beginning. Time is represented by the
time_t data type. Unix/Linux declares that the start of time, t = 0, to be January 1, 1970 @ 00:00:00 GMT. The specification for the Lisp lanuage uses January 1, 1900 @ 00:00:00 GMT. The CableCard specification chose January 6, 1980 @ 00:00:00 GMT. The date where time begins is known as the "epoch".

If time 0 is January 1, 1970 @ 00:00:00, when does time end? If
time_t is a signed 32-bit quantity, then the largest positive value is 0x7fffffff which corresponds to 1/19/2038 @ 3:14:07 GMT. One second later, time will "wrap" from 1/19/2038 @ 3:14:07 GMT to 12/13/1901 @ 20:45:52 GMT. This is the basis for the "year 2038" problem, not unlike the Y2K problem.

time_t is an unsigned 32-bit value, then the largest possible value is 0xffffffff which corresponds to 2/07/2106 @ 6:28:15.

On Mac OS X,
time_t can also be a signed 64-bit value. When asked "what is the date that corresponds to a time_t of 0x7fffffffffff?", there is no answer (although the time functions don't tell you there is no answer. Some of the struct tm values are silently not set). Lisp says that it should be 12/04/292277026596 15:30:07. Yes, that's over 292 billion years in the future. Approximately 20 times the current age of the universe. Lisp says it will be a Sunday.

Why can't Mac OS X handle the largest positive 64-bit
time_t value, but Lisp can? When converting from time_t to calendar form, Unix represents the year as an int (cf. tm_year in the tm struct). This imposes an upper bound on the value that can represent a year. A signed 32-bit integer has a maximum positive value of 2,147,483,647. Since mktime() and timegm() take year - 1900 as input, the largest year that can be represented is 2,147,483,647 + 1900 = 2,147,485,547. Converting 12/31/2147485547 @ 23:59:59 gives the time_t value 0xf0c2ab7c54a97f. So 0xf0c2ab7c54a97f is the largest 64-bit time_t value that can be used with a signed 32-bit tm.tm_year element. That's over 2 billion years in the future. On a Wednesday.
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