number of leap days contained in a span of full days.
works with positive and negative spans.
for days < 1 year, checks whether 0-2-29 is included.
for larger spans, uses cycle decomposition symmetrical to the positive case, with century exceptions except multiples of 400

gives the number of days elapsed in a year. handles negative years/days

the number of years the given number of days fill

gives the number of days needed to reach the first day of the given month.
months are from 1-12

0 being monday

get the month and month day after the given number of days have passed starting from the beginning of the year

check if the given year is a leap year

check if the given year number corresponds to a year with 53 instead of 52 weeks according to the iso8601 standard

gives the days contained in given number of fully elapsed years

number of leap days contained in the given count of elapsed years from year 0.
result is nonnegative. for negative elapsed years, the caller subtracts this value.
leap year rule: years divisible by 4 are leap years, including year 0, except centuries not divisible by 400

maps an elapsed-year count to the corresponding calendar year label.
note: when combined with month/day offsets in negative years, the elapsed-year count may not advance monotonically with the year label