Microsoft recently published a patch that appears to fix this
http://support.microsoft.com/kb/943075
Oddly, this patch (though already out) was not bundled with the "essential"
patches that I downloaded last week along with the trial version of Office
2007.
Values of 2^16-1-d (whether as a formula result or a constant), where d was
too small (2^-37 <= d <= 6*2^-37) to properly impact the 15-digit decimal
representation, displayed as 100000 despite still having the correct
underlying value. Values of 2^16-d displayed as 100001 despite still having
the correct underlying value. Interestingly, this seems to have been a new
intersection in Excel 2007 of two old bugs that have existed at least since
version 4, and probably since the inception of Excel.
1. There appears to have been a set of millions of valid binary numbers
(that included fractional parts) which for whatever reason were not permitted
as constant values in Excel, but were supported as the result of
calculations. The values like this that I am aware of rounded away the
trailing bits in the final three positions of a binary floating point number.
For values like 0.5 +/- d, this rounding made a perverse kind of sense as an
early attempt at the "optimization" that was introduced in 1997
http://support.microsoft.com/kb/78113
which "optimization" has led to numerous questions where a formula that by
itself appears to return zero doesn't behave like zero in a LOOKUP or IF
function or in a larger formula (because at the binary level, the result is
not and should not be zero). This rounding made less sense with numbers
like, 0.5000012207031250266453525910037569701671600341796875+/-d, where even
the "rounded" number could not be fully displayed in 15 decimal digits. This
longstanding bug appears to have been completely fixed in the original
production release of 2007, before application of the current patch.
2. There appears to have been a non-overlapping (AFAIK) set of millions of
decimal fractions that could not be displayed properly
http://support.microsoft.com/kb/161234
admits to x.848 displaying as x.8479999999 for x an integer between 2^15 and
2^16, but there are millions of other decimal fractions that were similarly
mis-displayed
http://groups.google.com/group/microsoft.public.excel.misc/msg/1b2d9f986ce8e65b
I was not previously aware of any number in this set whose incorrect display
was off by more than 1 in the 15th digit; as a result, fixing this bug has
seemed to have little or no priority with MS until now.
I believe both of these longstanding bugs to be related to the current bug
for the following reasons:
- It does not make sense that a current change to the display engine
capable of causing this current bug could have survived its testing phase
without uncovering this bug.
- If the process of displaying results (formulas as well as constants)
first went through the filter of bug 1 before being passed to the display
engine, then the 2007 patch for bug 1, would mean that display of these
impacted values had never been tested, yet the need to test their display
could easily have been overlooked.
- The patch for the current problem appears to also fully patch bug 2,
while preserving the patch for bug 1 (thank you MS for not simply restoring
bug 1).
Jerry
