In a recent note, john gilmore said:
> Date: Tue, 13 Sep 2005 03:22:10 +0000
>
> There is no need to use a simplified or 'linear' leap-year correction
> calculation. For any algebraic Gregorian year value y the exact signed
> number of leap-year correction days in preceding years is easily calculated
> by the method of inclusions and exclusions. It is just
>
> C(y) = 365(y - 1)
> + (y - 1)//4
> - (y - 1)//100
> + (y - 1)//400
>
> in which '//' denotes remainder-discarding binary-integer division.
>
In fact, this returns the total number of days, not the number of
leap-year correction days.
"Algebraic" and "signed" imply the formula gives correct results
for negative years, assuming the Gregorian calendar is so extrapolated
backwards. The formula works correctly only if "//" truncates
toward negative infinity, not toward zero.
And it can be simplified to (the less referentially transparent):
C(y) = (y - 1) * 146097 // 400
-- gil
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