Editing Doomsday rule (section)

==Computer formula for the anchor day of a year==
For computer use, the following formulas for the anchor day of a year are convenient.

For the Gregorian calendar:

:<math>\mbox{anchor day} =  \mbox{Tuesday} + y + \left\lfloor\frac{y}{4}\right\rfloor - \left\lfloor\frac{y}{100}\right\rfloor + \left\lfloor\frac{y}{400}\right\rfloor = \mbox{Tuesday} + 5\times (y\bmod 4) + 4\times (y\bmod 100) + 6\times (y\bmod 400)</math>
For example, the doomsday 2009 is Saturday under the Gregorian calendar (the currently accepted calendar), since

:<math>\mbox{Saturday (6)} \bmod 7 =  \mbox{Tuesday (2)} + 2009 + \left\lfloor\frac{2009}{4}\right\rfloor - \left\lfloor\frac{2009}{100}\right\rfloor + \left\lfloor\frac{2009}{400}\right\rfloor</math>

As another example, the doomsday 1946 is Thursday, since

:<math>\mbox{Thursday (4)} \bmod 7 =  \mbox{Tuesday (2)} + 1946 + \left\lfloor\frac{1946}{4}\right\rfloor - \left\lfloor\frac{1946}{100}\right\rfloor + \left\lfloor\frac{1946}{400}\right\rfloor</math>

For the Julian calendar:

:<math>\mbox{anchor day} =  \mbox{Sunday} + y + \left\lfloor\frac{y}{4}\right\rfloor = \mbox{Sunday}+ 5\times (y\bmod 4) + 3\times (y\bmod 7)</math>

The formulas apply also for the [[proleptic Gregorian calendar]] and the [[proleptic Julian calendar]]. They use the [[floor function]] and [[astronomical year numbering]] for years BC.

For comparison, see [[Julian day#Calculation|the calculation of a Julian day number]].