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  1. OMG Issue

DTV11 — incorrect formula for length of successive Gregorian years

  • Key: DTV11-86
  • Legacy Issue Number: 19197
  • Status: closed  
  • Source: yahoo.com ( Michael Deckers)
  • Summary:

    The formula given for the possible lengths
    for an integral number of successive
    Gregorian years is incorrect. It implies
    an average length of the year of 365.235 d
    while the correct value is 365.2425 d.
    For instance it is well known that any
    successive 400 Gregorian years comprise
    exactly 146 097 d, while the formula
    gives 146 094 d.
    For the record, with a little algebra,
    the number of days between Gregorian
    calendar(Y', Jan, 01) and Gregorian
    calendar(Y, Jan, 01) is easily seen
    to be
    floor( Δ¬∑365.25 )
    + floor(-3/4¬∑floor(Δ/100))
    + |Δ mod 4 > (Y - 1)mod 4|

    • Δ mod 100 > (Y - 1)mod 100

      + |Δ mod 400 > (Y - 1)mod 400|
      where Δ = Y - Y'.

  • Reported: DTV 1.0 — Tue, 28 Jan 2014 05:00 GMT
  • Disposition: Resolved — DTV 1.1
  • Disposition Summary:

    The reference is to the formula in the entry for ‘year value specifies duration value set’. The formula includes two erroneous factors of 2, and does not account for year values greater than 400 properly. The formula and the supporting concepts will be corrected.

  • Updated: Fri, 6 Mar 2015 20:58 GMT