[PATCH/RFH] date: avoid "X years, 12 months" in relative dates

When relative dates are more than about a year ago, we start writing them as "Y years, M months". At the point where we calculate Y and M, we have the time delta specified as a number of days. We calculate these integers as:

  Y = days / 365
  M = (days % 365 + 15) / 30

This rounds days in the latter half of a month up to the nearest month, so that day 16 is "1 month" (or day 381 is "1 year, 1 month").

We don't round the year at all, though, meaning we can end up with "1 year, 12 months", which is silly; it should just be "2 years".

The implementation is crude but effective: we check for this silly case with a conditional and tweak the values:

  if (M == 12) {
	  Y++;
	  M = 0;
  }

It's tempting to look for a purely numerical solution, like just rounding better. But it is made difficult by the fact that our approximation of a month is "30 days", which means that a year does not actually contain 12 of our approximate months (there is a 5-day discrepancy).

So you could do:

  Y = (days + 15) / 365

which will round up the year if we are in the last 15 days. And then you would make a matching tweak for months:

  M = (days + 15) % 365 / 30;

so that they both round at exactly the same day.

But that doesn't quite work. Day 715 will be properly rounded to "2 years, 0 months", which is what we want. But days 710 through 714 remain at "1 year, 12 months", due to the 5-day discrepancy.

Another attempt would be to write it as the much more readable:

  total_months = (days + 15) / 30;
  Y = total_months / 12;
  M = total_months % 12;

But our 5-day discrepancy hits us again, and this time much worse, since the error compounds with each year. On day 3650, we should be exactly at "10 years", but the above puts us at "10 years, 2 months".

Signed-off-by: Jeff King <peff@peff.net>
---
So I thought this patch would take me about 2 minutes to write, and (as
you can probably guess from the length of the commit message), it turned
out much more complex. I'd be curious to see if anybody has a numerical
solution using integers.

With floating point, it's pretty simple:

  double one_month = 365 / 12;
  unsigned long total_months = ((double)days + (one_month / 2)) / one_month;
  unsigned long years = total_months / 12;
  unsigned long months = total_months % 12;

but I'm beginning to think it's not possible to make a simple formula with just integers. Which maybe means we should just use floating point here. Or maybe somebody can prove me to be an idiot.

 date.c          |    5 +++++
 t/t0006-date.sh |    1 +
 2 files changed, 6 insertions(+), 0 deletions(-)