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>46 BC has 445 days in it for no good reason
46 BC was 445 days since that was the year the Romans transferred from a very out of sync lunar calendar to a solar calendar.
>You have to add in a leap day every 4 years if the year is past 45BC
Leap days are needed because years aren't exactly 365 days, they're closer to 365.25 days long. The alternative solution would be to add a day to each year that's a quarter of the length of the other days.
>unless the date is greater than 1582 then you have to add a leap day every 4 years unless it is divisible by 100 but not by 400
The Gregorian calendar was made since years aren't exactly 365.25 days long, they're actually 365.2425 days long. This means the Julian calendar will still go out of sync even with leap days. The Gregorian calendar fixes this by skipping leap days each century.
