Adding a number of days to a calendar date

Design an algorithm that takes a date and an integer $n$ and returns the date $n$ days later, getting leap years right including the century exceptions.

Convert to a serial day count, add $n$, convert back. A year is leap if divisible by $4$, except century years, which are leap only if divisible by $400$ (so 1900 is not, 2000 is). Map the date to days since a fixed epoch (whole years, then months via a cumulative table, then days), add $n$, and invert by stepping or with a closed form; this avoids error-prone month-by-month loops and handles negative $n$ too.