from comp.arch.arithmetic on excel bug

[David G. Hough at validgh]

Sounds like a base conversion problem...

Article: 1320 of comp.arch.arithmetic
From: lindsayaazstarnet.com (Michael J. Lindsay)
Newsgroups: comp.apps.spreadsheets,comp.bugs.misc,comp.arch.arithmetic
Subject: re:math bug in Microsoft Excel
Summary: MS answer to math bug in several Excel versions
Date: 1 Oct 95 02:19:15 GMT

This is from Microsoft Web Page =  
http://www.microsoft.com/msoffice/xler0925.htm

                       "The 15 Digit Number Error
                          Question and Answers
                                 9/25/95

 I heard there is a problem with Excel changing the values of some
 specific numbers, what's the situation?
 In Microsoft Excel there is an error that will cause three specific
 sequences of fifteen digits to change their value either when entered
 as an individual entry or when derived from specific functions. This
 was brought to our attention earlier this week and we are in the
 process of creating a solution that will be available within the next
 10 days to correct the situation.
 
 Can you tell me what that means in more common terminology?
 What this means is that if you have entered one of three specific
 fifteen digit numbers or come to this number as the result of a
 formula, Microsoft Excel might have changed the value of the number.
 
 What are the chances that I have been affected?
 Although it is hard to have an exact number, we believe this will only
 affect a very small number of customers. In fact, based on our
 internal analysis the likelihood of any one of these sequence of
 digits appearing in a customer's spreadsheet is 1 in billions.
 Remember, the only way that this will affect you is if you have these
 three specific combinations of fifteen digits.
 
 If there is such a small likelihood of this occurring, why worry about
 fixing it?
 Our customers depend on Microsoft Excel to compute their numbers
 accurately and we want them to feel confident when using the product.
 Even though the probability of one of our customers having a problem
 with this is low, we can't judge the probability for each and every
 customer. So, we are trying to get all of the facts regarding this out
 so that you can determine for yourself if you need the patch. The
 solution will be available to all customers that own Microsoft Excel
 or Microsoft Office. This patch will be available at no charge
 beginning October 1, 1995 in the U.S.
 
 What are you doing to fix this?
 We have created a solution that will correct this error. We are in the
 process of testing this solution on various hardware, it will be
 available in the form of a patch which we will make available
 beginning on October 1, 1995 in the U.S.

 So, what are the numbers that cause this error?
 The specific sequences of digits are: 140737488355328, 281474976710656
 and 562949953421312. The decimal point may be in different places. In
 addition if you are dealing with calculations, the result has to be
 one of these three sequences of digits, plus or minus a number less
 than approximately = of the next decimal, times a power of 10. And
 this is only a problem when you refer to the result in certain
 functions, namely: int(), ceil(), floor(), roundup(), and if().

 Why these specific numbers?
 The common bond between these numbers is that they happen to be 2 to
 the 47th, 48th, and 49th power, respectively.
 
 Does this mean I have to check to make sure any 15 digit numbers in my
 files have not been changed by Excel?
 No. Unless you entered in one of the three specific sequence of digits
 mentioned above or have utilized one of the specific formulas
 mentioned above with very long numbers you should be fine. To double
 check, however, all you have to do once you have installed the patch
 is to open a file and press Control/Alt/F9, by doing this the patch
 will correct any numbers that were derived from functions incorrectly.
 
 How did you find out about this?
 One of our customers actually found it when they were working with a
 formula that derived the number 1.40737488355328. This customer's work
 required that he create a formula in Microsoft Excel which explicitly
 calculated 2 to the 47th and take the integer portion of it. We were
 not previously aware of this error and are grateful that it was
 brought to our attention.
 
 What versions of Microsoft Excel does this affect?
 We have found this in versions of the product dating back to Excel 3.0
 for Windows, the Macintosh and OS/2. Other versions of the product
 affected include Microsoft Excel 4.0 for Windows and the Macintosh,
 Microsoft Excel 5.0 for Windows, Windows NT and the Macintosh, and
 Microsoft Excel for Windows 95. We will make the patch available for
 no charge for any of our customers using any of these versions of
 Excel.
 
 How do I get the patch?
 Simply call Microsoft at (800) 426-9400 or (206) 635-7070 on or after
 October 1, 1995 and the patch will be sent to you at no charge. Our
 goal is to have the patch available for the Windows 3.1 and Windows 95
 versions of the product beginning on October 1, 1995 with other
 platform versions following soon thereafter."