http://www.wiredb.com/ Best selection of technology news. Mon, 12 May 2008 08:39:01 -0400 http://www.wiredb.com/1383/Explaining_the_Excel_Bug By now you've probably seen a lot of the brouhaha over a bug in the newest version of Excel, 2007. Basically, multiplying 77.1*850, which should give you 65,535, was actually displaying 100,000.Before I try to explain this, I should disclose that I did work on the Excel team, but that was thirteen years ago. I haven't been there for a long time. I don't even think I know anyone on that team any more. I'm just trying to explain the bug a little bit as a public service.The first thing you have to understand is that Excel keeps numbers, internally, in a binary format, but displays them as strings. For example, when you type 77.1, Excel stores this internally using 64 bits:0100 0000 0101 0011 0100 0110 0110 01100110 0110 0110 0110 0110 0110 0110 0110The display is showing you four characters: "7", "7", ".", and "1".Somewhere inside Excel is a function that converts binary numbers to strings for displaying. This is the code that has the bug that causes a few numbers which are extremely close to 65,535 to be formatted incorrectly as 100,000.If you use the number further along in calculations, for example, if you add 2 to the results, you'll get the right thing.=77.1*850 -> displays 100000=77.1*850+2 -> displays 65537, correctly.Just to throw people off, this bug also exists for a few numbers which are extremely close to 65,536. They display incorrectly as 100,001.=77.1*850+1 -> displays 100,001, incorrectly.This is still only a bug in the number formatting code; if you try to make a chart with that number in it, you'll get a correct chart.Now... you may have noticed that I said that this bug exists for numbers which are extremely close to 65,535, but not for 65,535 itself. Indeed if you enter 65,535 you see 65,535. But, you notice, 77.1 * 850 should be exactly 65,535, not extremely close to 65,535!Look closely at the binary representation for 77.1:0100 0000 0101 0011 0100 0110 0110 01100110 0110 0110 0110 0110 0110 0110 0110See how there's a lot of 0110 0110 0110 there at the end? That's because 0.1 has no exact representation in binary... it's a repeating binary number. It's sort of like how 1/3 has no representation in decimal. 1/3 is 0.33333333 and you have to keep writing 3's forever. If you lose patience, you get something inexact.So you can imagine how, in decimal, if you tried to do 3*1/3, and you didn't have time to write 3's forever, the result you would get would be 0.99999999, not 1, and people would get angry with you for being wrong.The same thing happens in binary with  numbers ending in 0.1: they are repeating decimals, so when you do mathematical operations on them, very small insignificant errors creep in somewhere way to the right of the decimal point. (PS: same for .2, .3, .4, .6, .7, .8, and .9, but not .5).The IEEE has a standard, IEEE 754, for how to represent floating point numbers in binary, and this is what almost everybody uses, including Excel, and they have for a really long time, and it means sometimes you get imprecise results when you add a lot of 0.1's together, but if you're rounding the numbers to a reasonable number of decimal points, you won't really care.Back to the Excel bug, which is a genuine bug, not just an artifact of this IEEE 754 stuff. Since 77.1 has no exact representation, Excel stores it as0100 0000 0101 0011 0100 0110 0110 01100110 0110 0110 0110 0110 0110 0110 0110and then when you try to multiply it by 850, you get something very close to 65,535, but not exactly 65,535, because of the fact that 77.1 wasn't stored exactly because that would take infinite memory. And this number, which is very close to 65,535, happens to be one of only 12 possible floating point numbers which trigger this bug in Excel.OK, Q&A.Q: Isn't this really, really bad?A: IMHO, no, the chance that you would see this in real life calculations is microscopic. Better worry about getting hit by a meterorite. Microsoft, of course, will be forced to tell everyone "accuracy is extremely important to us" and I'm sure they'll have a fix in a matter of days, and they'll be subjected to all kinds of well-deserved ridicule, but since I don't work there I'm free to tell you that the chance of this bug actually mattering to you as an individual is breathtakingly small.Q: Shouldn't they be testing for these kinds of things?A: I'll bet that most of the numeric testing done on the Excel team is done automatically with VBA code. Cells containing this value display as 100,000, but from VBA, they're going to look like 65,535 (since the number would be passed into the Basic runtime in binary, before the display formatting.) I'm sure there's plenty of code to test display formatting, but with a bug like this that only happens on 12 out of 18446744073709551616 possible floating point binary numbers, it's unlikely that any set of black-box tests would cover this case.Q: What caused the bug?A: I'm not sure exactly, since I don't have the code. Off the top of my head, I can't think of anything that would cause this behavior. Play around with Quanfei Wen's IEEE-754 calculator, maybe you'll find something.Q: Why not use "exact" (decimal) arithmetic?A: It's much slower than floating point arithmetic, since there's no hardware on your CPU chip to do it for you natively.Over the years, Microsoft got so much heat for floating point rounding artifacts in the Windows Calculator that they rewrote it to use an arbitrary-precision arithmetic library. Since you have to poke at Windows Calculator with a stick, it doesn't have to be as fast as Excel. That said, CPUs have gotten pretty fast. I'll bet an arbitrary-precision version of Excel would perform pretty well these days. Still, the Microsoft Excel support team has spent the last 20 years defending IEEE 754, and it's not surprising that they've started to believe in it.And let's face it -- do you really want the bright sparks who work there now, and manage to break lots of perfectly good working code -- rewriting the core calculating engine in Excel? Better keep them busy adding and removing dancing paper clips all day long.Not loving your job? Visit the Joel on Software Job Board: Great software jobs, great people. Wed, 26 Sep 2007 18:40:00 -0400 http://www.wiredb.com/1382/Microsoft_Passes_AJAX_Interoperability_Test Microsoft says, and the OpenAJAX Alliance confirms, that the company's AJAX tools passed the groups key interoperability tests. Thu, 27 Sep 2007 12:55:00 -0400 http://www.wiredb.com/1381/Google_Plugs_Google_Web_ToolKit_For_iPhone Google has plugged the Google Web ToolKit demonstrating an iPhone specific version of Google Reader. The iPhone Reader combines the Google AJAX Feed API with a user interface geared for use on the iPhone. Google’s Research Actualization Engineer Bob Vawter said that the primary take-away from this project is to say ” The Google Web Toolkit can [...] Wed, 26 Sep 2007 22:20:00 -0400 http://www.wiredb.com/1380/Googles_9th_Birthday Two weeks ago, AFP informed us that "Google, at age 10, is the official heart of the Internet. Born 10 years ago, the Google Internet search engine has grown into the electronic center of human knowledge by indexing billions of web pages as well as images, books and videos." That's true, except that Google is 9 years old. Even if Larry Page and Sergey Brin registered the google.com domain in 1997, Google was officially launched one year later."Google opened its doors in September 1998. The exact date when we celebrate our birthday has moved around over the years, depending on when people feel like having cake," says Google's help center. You can read more about it directly from Google. In the recent years, Google's birthday has been celebrated on September 27th with a doodle displayed on the homepage. Happy birthday, Google!Update: "Happy Birthday, Google!" is in Google Hot Trends. Thu, 27 Sep 2007 08:23:00 -0400 http://www.wiredb.com/1379/Google_vs._Microsoft_Dueling_DoubleClick_testimony Google and Microsoft took Capitol Hill Thursday as their rivalry spilled out during hearings on the Google's DoubleClick acquisition. Both parties have posted their prepared remarks before the Senate Subcommittee on Antitrust, Competition Policy and Consumer Rights Committee on the Judiciary. Here's a look at the backstory, Google's remarks and blog and Microsoft's testimony. So put on a little dueling banjos in the background and let's get to it. Economics and privacy: Brad Smith, Microsoft's general counsel, will argue that there are serious economic questions and consequences to consider around the Google-DoubleClick deal. His two biggest questions to ponder are: What are the economic consequences of allowing the Google to acquire its "most significant competitor," DoubleClick (all resources)? And... Thu, 27 Sep 2007 12:13:00 -0400 http://www.wiredb.com/1378/The_ASP.NET_AJAX_Control_Toolkit_Has_Been_Updated The AJAX Control Toolkit for ASP.NET 2.0 has been updated. Nothing new was added, but the bug fixes are sure to be welcome. In related news, a VS 2008 Beta 2 compatible version was also released with a couple of interesting features. And in case you did not know, they are now accepting patches. Thu, 27 Sep 2007 07:07:00 -0400 http://www.wiredb.com/1377/Open_source_vs._proprietary_software_bugs_which_get_squashed_fastest Open source actually does fix itself faster, as two studies show. Thu, 27 Sep 2007 01:19:00 -0400 http://www.wiredb.com/1376/CardSpace_requirement_for_SSL_cert_dropped In an apparent attempt to make CardSpace more accessible to the 'little guy', Microsoft has decided to drop the requirement for an SSL certificate. Thu, 27 Sep 2007 11:48:00 -0400 http://www.wiredb.com/1375/Microsoft_revamps_Live_search Filed under: Microsoft, Search Microsoft has launched an updated version of Live Search. Some of the changes will be visible in the user interface, but the company also made a bunch of changes under the hood to make the search engine more useful and reliable.Increased the site index by more than 400%Improved understanding of query intentAuto-spell correctionFaster page-loadsUses more click-stream data to improve page ranking and relevancyImproved answers to questions about specific items like weather, images, celebrities, entertainment, maps, or sports The interface is also a bit cleaner. The search box has moved to the left. The tabs for searching images, video, news have been replaced with text links (which are a bit harder to notice than tabs at first). And the fonts look a little less 1985-ish.Apparently 40 percent of the searches on Live.com involve entertainment, shopping, health, and local search, so Microsoft has focused heavily on these four areas.Read | Permalink | Email this | Comments Thu, 27 Sep 2007 05:09:00 -0400 http://www.wiredb.com/1374/AOL_IM_Security_Hole_Unplugged Researcher Aviv Raff said he has found a way to defeat the patch AOL issued to address an IM vulnerability. Wed, 26 Sep 2007 15:11:00 -0400