DesignFloatPointErrors

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In this article we demonstrate that a very elementary mathematical statement can raise big concerns for numerical applications. Richard Gomes

Reasoning

Try this simple yet tricky code:

System.out.println(0.1 + 0.1 + 0.1);

Oh well... the result is:

0.30000000000000004

What??? So... 0.1 + 0.1 + 0.1 is not 0.3 ???

Problem

This problem arises the way floating point numbers are represented in the processor and how they participate in floating point calculations.

Notice that the comparison if (x==0.3) jumped to the else branch. After the sum, the result was 0.30000000000000004 and not 0.3 as we expected. The behaviour of the if statement is correct. In fact, the error is located between the keyboard and the chair: you simply cannot do such comparison!

You have to:

• remember that floating point errors may happen;
• evaluate the epsilon associated to the operations you previously done;
• you have to consider a certain range in your comparisions

like this:

   epsilon = blah blah blah; // calculate epsilon somehow
   if ((x>=0.3-epsilon) && (x<=0.3+epsilon)) { ...

Solution

JQuantLib takes the same approach as QuantLib. It consist of calculation of epsilon after a sequence of mathematical operations which gives us the order of magnitude of the error.

RichardGomes 21:47, 27 January 2008 (UTC)