Efficient algorithm for converting number of days to years (including leap years)

Question

The problem

I am writing a class for holding dates in c++, and I found the following problem:

I have a number of days N since a reference date (in

Answer 1

Obviously, the bottleneck is the year calculation. I would suggest you doing this. When you initialize the calendar, approximate the year (very rougly) by dividing the days by 365. After that, pre-form a list of all leap years before this estimation. It should be rather fast since you don't need to count all of them, just add 4 years each time. Also, while doing them, count how much of such you have. Actually, you could even count them in larger packs (i.e. there are 100 leap years every 400 years), but you will need to check for the the leap year exceptions carefully, not to skip some of them.

At the end of this, you will have the rough estimate of the year, and the amount of all leap years before it. Now you can count the precise year very easilly, without needing to iterate through anything:

leapYearCount * 366 + (lastCalculatedYear - leapYearCount) * 365