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In mainframes, Julian dates are popular for that reason. YYDDD (day of year).

When is 30 days after today? 25206+30

Maybe I’m missing something but then what is 30 days after Christmas? 25389?

25389 mod 365, presumably. The very fancy mainframes probably would pick the appropriate modulus based on whether it was a leap year or not.

What happens when you want to add more than 365 days to a date, then?