Good news: All Excel 2007 basis 0..4 of YEARFRAC explained

["David A. Wheeler" <dwheeler@dwheeler.com>]

More good news!  We now have an algorithm for basis=4, so we
have algorithms for ALL basis values of Excel 2007's YEARFRAC.

Patrick Durusau worked out a draft set of rules for basis=4.
They didn't QUITE work with the full dataset, but I managed to
tweak them and MAKE them work. I've posted everything here:
http://www.dwheeler.com/yearfrac

A big THANKS to Patrick Durusau, who plowed through the
various datapoints to help determine what Excel's REAL algorithm was.

Basis=4 doesn't match its spec either.  A few details below.

--- David A. Wheeler


=== Details ===

Excel 2007's basis=4 _also_ does not match the spec.
The spec says that it adjusts Feb 28 and 29, but Wheeler
found that in fact it never does (!).  For example:

Excel 2007 produces:
  1999-01-05 2000-02-28 4 1.147222222
but the spec would produce:
  ((2000*360 + 2*30 + 30) - (1999*360 + 1*30 + 5))/360. = 1.1527777777777777

Excel produces:
  1999-01-05 2000-02-29 4 1.15
but the spec would produce:
  ((2000*360 + 2*30 + 30) - (1999*360 + 1*30 + 5))/360. = 1.1527777777777777


Algorithm:

def basis4(date1,date2):
  # Swap so date1 <= date2 in all cases:
  if date1 > date2:
    date1, date2 = date2, date1
  if date1 == date2:
    return 0.0
  # Change day-of-month for purposes of calculation.
  date1day, date1month, date1year = date1.day, date1.month, date1.year
  date2day, date2month, date2year = date2.day, date2.month, date2.year
  if date1day == 31: date1day = 30
  if date2day == 31: date2day = 30
  # Remarkably, do NOT change Feb. at ALL
  daydiff360 = ( (date2day + date2month * 30 + date2year * 360) -
                 (date1day + date1month * 30 + date1year * 360))
  return daydiff360 / 360.