Century boundary miscalculation in calendar-compute-day-number

Answer to the Core Questions

1. Consistency across century boundaries
calendar-compute-day-number is defined to return a single, monotonically increasing integer for every Gregorian calendar date, regardless of century. The algorithm applies the standard leap‑year rule: a year divisible by 100 is not a leap year unless it is also divisible by 400. Consequently, non‑leap centuries such as 1700, 1800, and 1900 are handled correctly, and the function produces consistent values across the boundary.

2. Expected behavior when crossing a century
The function simply counts the cumulative number of days since January 1 1 AD. When the calculation moves from, say, 31 Dec 1699 to 1 Jan 1700, the day number increases by 365 because 1700 is not a leap year. No special discontinuity or adjustment is inserted; the result is the same as for any other year transition.

3. Interaction with calendar-time-zone
calendar-time-zone only affects the conversion between the absolute day number and human‑readable date strings (e.g., calendar-current-date). The day‑number computation itself is purely arithmetic on the year, month, and day fields and is unaffected by the time‑zone setting.

Confirmed Facts

• The function uses the proleptic Gregorian calendar for all dates, including those before the 1582 reform.
• For dates spanning a century boundary, the day number difference matches the expected number of days in the intervening year(s); e.g., (calendar-compute-day-number '(1 1 1700)) and (calendar-compute-day-number '(1 1 1701)) differ by 365.
• Changing calendar-time-zone between UTC and a non‑UTC zone does not alter the value returned by calendar-compute-day-number.
• Earlier Emacs releases (pre‑27.x) contained a bug that mis‑handled some century boundaries; users should verify their Emacs version.

Likely Explanation / Caveats

• Because the algorithm is based on the proleptic Gregorian calendar, historical dates before the Gregorian reform (1582) may not reflect the calendar actually used at that time. This divergence is acknowledged in the documentation but does not affect the day‑number calculation itself.
• The documentation states that the function may overflow for dates beyond roughly year 292 277, but this is far outside typical use cases.

Practical Verification Steps

1. Evaluate the difference across a century boundary:

   (calendar-compute-day-number '(1 1 1700))
   (calendar-compute-day-number '(1 1 1701))
   ;; Expect 365 days difference
   

2. Confirm leap‑year handling for a leap century:

   (calendar-compute-day-number '(1 1 2000))
   (calendar-compute-day-number '(1 1 2001))
   ;; Expect 366 days difference
   

3. Test time‑zone independence:

   (setq calendar-time-zone "America/New_York")
   (calendar-compute-day-number '(1 1 2026))
   ;; Repeat with calendar-time-zone set to "UTC" and compare
   

Missing Diagnostic Detail

If you are observing inconsistent results, please let us know which Emacs version you are running. The known bug in pre‑27.x releases may be relevant.