Real life example fo Floating Point error

Question

Is there any examples of a company that was burned by floating point data that caused a rounding issue? We're implementing a new system and all the monetary values are stored in floats. I think if i can show actual examples of why this has failed it'll have more weight than the theory of why the values can't be stored properly.

Answer 1

These examples are from the embedded world (Ariane 5, Patriot) but are not floating-point rounding errors stricto sensu. The Ariane 5 bug is a bug in a conversion. The Patriot bug was introduced during adaptations of the software. It involves computations in different precisions with an inherently unrepresentable constant (which happens to be the innocuous-looking 0.10).

There are two problems I foresee with binary floats for monetary values:

• decimal values as common as 0.10 cannot be represented exactly.

• If the precision is too small, what could have been a clean overflow raising an exception becomes a hard-to-track loss of precision.

Note that base-10 floating-point formats have been standardized precisely for monetary values: some currencies are worth 1/1000000 of a dollar, are never exchanged in less than thousands, and the maximum amount you may want to be able to represent is proportionally big, so a scalable representation makes sense. The intent is that the mantissa is large enough for the largest sums with the official resolution.