log in | contact | about 

Floating point arithmetic is not exact and not even deterministic. Not only results may be different across platforms and compilers, but in a non-strict (but fast) mode an outcome of the same operation may depend on the invocation context. If you use an aggressively optimizing compiler (such as Intel), it is silly to assume that same function arguments will always produce same results. The outcomes will be the same in many cases, but the results might also fluctuate by a few units in the last place (ULP). Code written with the assumption that results are always the same (i.e., assuming that floating point arithmetic is always consistent) may contain bugs that are hard to reproduce and fix.

To avoid such bugs, we may need to compare floating points numbers approximate rather than exactly. So, how do we do this? It is apparently easy to come up with a simple comparison code that works in most cases, but likely to fail in some rare cases. After some googling, I found a neat implementation of the Bruce Dawson algorithm from "Comparing Floating Point Numbers". The implementation was buried in the Google C++ Test Framework (authors Zhanyong Wan and Sean Mcafee). Thanks to Fred Richards, it was extracted and repackaged (see Fred's blog entry for a detailed description of the algorithm).

Fred's version was a bit inflexible and included only the hard coded threshold value (for numbers to to be considered the same). Thus, I had slightly modified the code to accept a threshold value as an argument of the comparing function. In addition, I made the ULP_diff function publicly available and improved the testing example. If you need a code to compare floating point numbers approximately, you can grab it from my repository.

UPDATE: I forgot to mention that Boost does have the code with similar functionality. Yet, I was looking for the code without Boost dependencies.