Counting the days, revisited

Many years ago I wrote about how to convert Gregorian dates to Julian Day numbers or similar counts such as rata die as used in Calendrical Calculations. This algorithm is the core of C’s mktime() function that converts a broken-down date-time into linear time_t. I recently learned from Ben Joffe that I was missing a few tricks, and my old code wasn’t as good as it could have been. Here’s a better version (using conventional not C numbering): if m > 2 { m -= 2; } else { m += 10; y -= 1; } y*365 + y/4 - y/100 + y/400 + m*979/32 + d - 336 the main idea Julian years Gregorian correction the month pattern the epoch domains and ranges leap year test length of month the main idea There’s a helpful coincidence in the Gregorian calendar. Although the month lengths aren’t obviously regular, there’s a repeating 5 month pattern that becomes easier to see when you start from March, as illustrated by the table below. This pattern resets at the end of February, midway through its third repeat,…