Yesterday we were alerted to an issue in Excel 2007 (and Excel Services 2007) involving calculation of numbers around 65,535. The Excel team would like to provide a description of the issue and explain what we're doing about it.
BackgroundYesterday evening we were alerted to an issue in Excel 2007 (and Excel Services 2007) involving calculation of numbers around 65,535. The first example that we heard about was =77.1*850, but it became clear from our testing as well as additional reports that this was just one instance where Excel 2007 would return a value of 100,000 instead of 65,535. The majority of these additional reports were focused on multiplication (ex. =5.1*12850; =10.2*6425; =20.4*3212.5 ), but our testing showed that this really didn't have anything do to with multiplication - it manifested itself with many but not all calculations in Excel that should have resulted in 65,535 (=65535*1 and =16383.75*4 worked for instance). Further testing showed a similar phenomenon with 65,536 as well. This issue only exists in Excel 2007, not previous versions.
The ProblemThis issue was introduced when we were making changes to the Excel calculation logic in the Office 2007 time frame. Specifically, Excel incorrectly displays the result of a calculation in 12 very specific cases (outlined below). The key here is that the issue is actually not in the calculation itself (the result of the calculation stored in Excel’s memory is correct), but only in the result that is shown in the sheet. Said another way, =850*77.1 will display an incorrect value, but if you then multiply the result by 2, you will get the correct answer (i.e. if A1 contains “=850*77.1”, and A2 contains “=A1*2”, A2 will return the correct answer of 131,070).
So what, specifically, are the values that cause this display problem? Of the 9.214*10^18 different floating point numbers (floating point on wikipedia) that Excel 2007 can store, there are 6 floating point numbers (using binary representation) between 65534.99999999995 and 65535, and 6 between 65535.99999999995 and 65536 that cause this problem. You can’t actually enter these numbers into Excel directly (since Excel will round to 15 digits on entry), but any calculation returning one of those results will display this issue if the results of the calculation are displayed in a cell. All other calculation results are not affected.
The SolutionWe take calculation in Excel very seriously and we do everything we can in order to ensure that calculation is correct for all cases. We’ve come up with a fix for this issue and are in the final phases of a broad test pass in order to ensure that the fix works and doesn’t introduce any additional issues - especially any other calculation issues. This fix then needs to make its way through our official build lab and onto a download site - which we expect to happen very soon. We’ll add another post once that’s taken place with a link to the download.