## Friday, April 02, 2010

### Floating point numbers and NaN

NaN expands to 'not a number'. Various floating point operations can lead to this value. IEEE-754 is the most widely used floating point computation standards. It defines 5 possible exceptions that can occur during floating point arithematic:

1) Invalid Operation: when an invalid operation is performed on a number, for example, taking square root of a negative value, taking log of 0 or a negative number, etc.
2) Division by Zero: when a number is divided by zero
3) Overflow: when the result is too large to be representable
4) Underflow: when the result is too small to be representable
5) Inexact: when the result is inexact meaning the number was rounded and caused discarding of any non-zero digits

The cases falling under invalid operation would result in a value of NaN as per the above mentioned standard. (I get -INF with gcc 3.4.4, but NaN for any negative number's logarithm). You would check for NaNs and Infinities resulting out of computations in order to determine the success and validity of the operation but that can lead to code that is cluttered with ifs and elses and can become almost un-readable. You can, however, do the checks at every logical chunk of the computation. However, NaNs and INFs can get lost mid-calculations. The standard dictates that an exceptional value NaN or INF should get propagated throughout the calculations so that the checks at the end of a computation could catch them but certain operations can lose them, for example:

1) NaN operation with INF value would result in INF, as in NaN + INF = INF.
2) INF can become 0, as in x/INF = 0

The way to catch these would be to check the sticky bits that are essentially the exception flags that are set on occurence of floating point exceptions anywhere during the calculation. But let's not get too carried away and leave it to the credibility of the programmers and users to be able to handle the various cases in the most sensible way. :-)

To conclude, here is a function that will help check if a value is a NaN or not, based on the fact that any comparison involving NaNs would result in 'false' result:

template<typename T>
bool myIsNaN(T value)
{
return value != value;
}

C99 has a function isNaN() and TR1 for C++ has included the support for this function but just in case your compiler doesn't support it. Similarly, you have isinf() that will help catch both positive and negative infinities. If you are feeling too experimental, try your own version of isinf() using numeric limits. :-)

References:

1) Trap Handlers, Sticky Bits, and Floating-point Comparisons
2) What is this NaN thing?
3) C++ Numeric limits
4) Wikipedia - IEEE 754