Dot Net Thoughts

October 20, 2007

Doubles, Decimals, and Dividing by Zero

Filed under: Misc Thoughts — dotnetthoughts @ 7:02 am
Tags: , , , , , , , ,

“.Net Exception Divide by zero” often comes up as a search criteria when this blog is hit. (I use division by zero a lot when I’m writing about errors and exception handling. It’s easy to create, and it’s easy to understand.) I couldn’t quite figure out exactly why anybody would be querying on it directly. I think I’ve figured it out, though.

Last week, I was typing up a division example for the blog. For whatever reason, I used double instead of decimal for my input parameters and return value.

   private static double Divide(double i, double j) 
      { 
         return (i / j); 
      }

When I passed in values of 5 and 0 for this method, I was expecting a divide by zero exception. Instead, my console app ran just fine and printed the word Infinity on my screen. I was totally caught off guard by this result. If you pull out an old calculus book, you’ll find that mathematicians often will say that the value of 1/x, as x approaches 0, is infinity (a standard limit), but that 1/0 is undefined. (You can’t take one object and break it into groups of zero.)

When I run the same code above using decimals, instead of doubles, I get a divide by zero exception. This is what I would expect.

With a little bit of thought and poking around, I think that there is a method behind the madness.

Doubles are floating point types. These types are specifically engineered never to throw an exception. Instead, they return values such as infinity, positive infinity, negative infinity, and not a number. Why?

I suspect that the reason has to do with precision. The double type supports numbers as small as +-5*10-324 and as large as +-1.7*10308. Its precision, however is only 15 to 16 digits. Due to the way that floating points are handled, you can’t ever be totally sure exactly what value your Double contains for very large or small numbers. For example, the following code prints out a value of 9.99988867182683E-321 in my output window when I run it:

   private static void DoublePrecision()  
   { 
       double double1 = 1 * Math.Pow((double)10, (double)-320); 
       Trace.WriteLine("double1: " + double1.ToString()); 
   }

This loss of precision means that the compiler itself can’t determine whether a value truly is zero, or if it is a really small number quite close to zero. Mathematically, 1/(10-324)2 is 1/10-648. If the first equation were plugged into .Net, the the result wouldn’t be infinity, but it would be greater than the double can deal with. The convention seems to be to return infinity for my initial divide by zero question.

Decimals, on the other hand, support numbers as small as +-1*10-28 and as large as +-7.9*1028. A decimal’s precision is 28 to 29 significant digits. Since the precision is equal to the exponential power of the range supported, the compiler knows the value it holds in the register is accurate, at least to defined precision. If it thinks it has a zero, it actually has a zero, and can safely throw a DivideByZero error if you try to use it to divide. This added precision is why Microsoft encourages decimals for financial and scientific values.

I’m making some educated guesses behind the thinking of the writers of the IEEE 754 standard, which defines floating types, but I don’t suspect I’m too far off. Let me know if you have any insights!

Good luck and code safe!

Mike

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September 22, 2007

Error Handling – Best Practices

Filed under: Best Practices — dotnetthoughts @ 6:54 am
Tags: , , , , ,

I had a question from a friend about exception handling best practices earlier this week. He’d mentioned that it’s pretty hard to find good information about the topic. I rattled back a list of fairly generic dos and don’ts that we’ve all seen with exception handling before. As I thought about it a little bit more, I came to realize that we accepted a lot of these on blind faith, so I thought I’d take a little bit closer list of some of the error handling recommendations made in the .Net Framkework Design Guidelines.

Performance

Exceptions are fairly costly operations and will generally be considerably slower than a programmatic solution.  How much slower? To find out, I wrote a quick-and-dirty test application. This application divides two values, but, instead of returning an error to the client, it returns a null when attempting to divide by zero. The project contains two implementations of the calculator object: the calculator using exceptions, and the calculator not using exceptions. The only difference between the two is the way the division by zero is handled.

In the exception version, we are defaulting the return value to null, and simply hiding the exception when it occurs.


  public decimal? Divide(decimal numerator, decimal denominator)
  {
    decimal? returnValue = null;
     try
      {
        return numerator / denominator;
      }
    catch (DivideByZeroException ex) {}
return returnValue;
  }

In the non-exception version, we are checking the denominator, and simply returning null if the denominator is equal to 0.

public decimal? Divide(decimal numerator, decimal denominator)
{
  decimal? returnValue = null;
  if (denominator != 0)
  {
     returnValue = numerator / denominator;
  }
  return returnValue;
}

While I was expecting there to be a little bit of a difference between the results, I was amazed at how big the difference was. On my machine, the object which was using exceptions ran 5000 iterations in 35 seconds. The version which explicitly checks the denominator value instead of using exception conditions ran in two milliseconds. [Note: Jon Skeet notes in the comments that this calculation is skewed, because I was running the code in the IDE at the time. He is correct. When running in the IDE, I get the 35 seconds to 2 milliseconds results. When running the compiled versions (Release or Debug), I’m seeing something on the order of 500 milliseconds to 2 milliseconds. It’s still pretty bad, but nothing on the order presented above.]

Handling Generic Exceptions

Section 7.2.2 talks about avoiding handling non-specific exceptions. For example:

catch (Exception ex) {//Handling here}

In general, this guideline is quite sound. If you are catching the general base class exception, you have no idea what has gone wrong, and shouldn’t attempt to recover from it. If an exception is thrown while writing to a file, for example, you do not know if the exception was because of an illegal file operation or due to an out-of-memory exception. It does take more time to research the appropriate exceptions that can be thrown by an object, but it can prevent a lot of pain in the long run.

The one exception I’ll often make to this rule is at the boundary of an object. If an exception has been thrown and has bubbled all the way up to the top of the stack, something truly unexpected has occurred. I’ll catch the generic exception object, log the exception to a log file, and then kill the application.

Use an Empty Throw

Section 7.2.2 also talks about using just an empty throw command when rethrowing an exception. In other words, use:

catch (Exception ex)
  {throw; }

Note that I’m not using throw ex. The primary reason for this is to maintain the stack trace. If you look at the Rethrowing Exceptions application, you’ll note that the only difference between the GoodErrorHandling and the BadErrorHandling methods is that good uses throw, and bad uses throw ex. Both methods call MyFlawedMethod which returns an InvalidOperationException. The resulting stack traces are displayed in a message box.

Examining the stack trace messages closely, you’ll notice something. The line number in the top frame of the stack points to different locations, even though the same base exception was thrown. The GoodErrorHandling frame points to the actual location of the error. When BadErrorHandling threw a new exception, however, the stack was reset and now points at the error handling in BadErrorHandling. This makes chasing down the originator of the actual error much less fun.

Code safe!
Mike

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