For given date in year-month-day, the day of the week can be deduced for the rule of leap years [1] and the fact that January 1, 1 is a Monday [2].
Since a year is a leap year if the year number is a multiple of 4 that is not a multiple of 100 that is not a multiple of 400. The number of leap year up to year y is given by:
def num_leap(y):
return y//4-y//100+y//400
For a common year, the numbers of days for the twelve months are:
[31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
The number of days before each month in a common year is calculated with:
p = 0
days_before_month = [
[p, p := p + m][0] for m in
[31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
]
print('[',', '.join(map(str,days_before_month)),']',sep='')
The result is:
[0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334]
Since the extra day of a leap year is added to February, the leap status of current year is only relevant when month number m<3. We can calculate the number of days from January 1, 1 as:
def day_number(y,m,d):
return (y-1)*365+num_leap(y-(m<3))+days_before_month[m-1]+d
Or, pack everything in the function:
def day_number(y,m,d):
return (y-1)*365+(lambda y:y//4-y//100+y//400)(y-(m<3))+[0,31,59,90,120,151,181,212,243,273,304,334][m-1]+d
[1] https://en.wikipedia.org/wiki/Leap_year
[2] https://en.wikipedia.org/wiki/AD_1