Module:Keppel date/doc: Difference between revisions

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Converts the current (or provided) date to a Keppel date. Used by Template:Keppel date.

Algorithm

Begin with the following inputs:

year: The current year in the Gregorian calendar.
yday: The current day of the year in the Gregorian calendar.

First, define the following:

Earth leap year

$\text{year} \bmod 400 = 0$ $\text{year} \bmod 4 = 0\text{ and not }\text{year} \bmod 100 = 0$

Keppel leap year (schedule 1)

$\text{year} \bmod 4 = 2$

Keppel leap year (schedule 2)

$\text{year} \bmod 239 = 65$

earthYearLength: If it is an Earth leap year, 366; else, 365.
yearLength: Start with 389.; If it is a Keppel leap year (schedule 1), add one.; If it is a Keppel leap year (schedule 2), add one.
rolloverOffset: If it is an Earth leap year, 79; else, 78.

To calculate the result:

year

$\text{year} - 892$

If yday is less than 79, subtract one.
ydayPre

$\frac{\text{yearLength} * (\text{yday} - \text{rolloverOffset})}{\text{earthYearLength}} \bmod{\text{yearLength}}$

If yday is less than or equal to zero, then add yearLength.
lythryd

$\lceil \frac{\text{yday}}{32} \rceil$

day

$\lfloor \text{yday} - (\text{lythryd} - 1) * 32 \rfloor$

@@ Line 10: / Line 10: @@
 :The current day of the year in the Gregorian calendar.
-First, we define the following:
+First, define the following:
 ;Earth leap year
 <math mode="display">\text{year} \bmod 400 = 0</math>
@@ Line 18: / Line 18: @@
 ;Keppel leap year (schedule 2)
 <math mode="display">\text{year} \bmod 239 = 65</math>
-;<code>ydayMaxEarth</code>
+;<code>earthYearLength</code>
 :If it is an Earth leap year, 366; else, 365.
-;<code>ydayMax</code>
+;<code>yearLength</code>
 :Start with 389.
 :If it is a Keppel leap year (schedule 1), add one.
@@ Line 30: / Line 30: @@
 ;<code>year</code>
 <math mode="display">\text{year} - 892</math>
-:If <code>ydayPre</code> is less than zero, subtract one.
+:If <code>yday</code> is less than 79, subtract one.
 ;<code>ydayPre</code>
-<math mode="display">\frac{\text{ydayMax} * (\text{yday} - \text{rolloverOffset})}{\text{ydayMaxEarth}}</math>
+<math mode="display">\frac{\text{yearLength} * (\text{yday} - \text{rolloverOffset})}{\text{earthYearLength}} \bmod{\text{yearLength}}</math>
+:If <code>yday</code> is less than or equal to zero, then add <code>yearLength</code>.
-;<code>yday</code>
-<math mode="display">\text{ydayPre} \bmod{\text{ydayMaxEarth}}</math>
-:If <code>yday</code> is between zero (inclusive) and one (exclusive), then <code>yday</code> is <code>ydayMax</code>.
 ;<code>lythryd</code>
 <math mode="display">\lceil \frac{\text{yday}}{32} \rceil</math>
 ;<code>day</code>
-<math mode="display">\lfloor \text{yday} - \text{lythryd} * 32 \bmod{32} \rfloor</math>
+<math mode="display">\lfloor \text{yday} - (\text{lythryd} - 1) * 32 \rfloor</math>
 <includeonly>[[Category:Modules: tesinormed]]</includeonly>