Is the use of machine epsilon appropriate for floating-point equality tests?

Question

_{This is a follow-up to Testing for floating-point value equality: Is there a standard name for the “precision” constant?.
There is a very similar question Double.}

Answer 1

The sad truth is: There is no appropriate epsilon for floating-point comparisons. Use another approach for floating-point equality tests if you don't want to run into serious bugs.

Approximate floating-point comparison is an amazingly tricky field, and the abs(x - y) < eps approach works only for a very limited range of values, mainly because of the absolute difference not taking into account the magnitude of the compared values, but also due to the significant digit cancellation occurring in the subtraction of two floating-point values with different exponents.

There are better approaches, using relative differences or ULPs, but they have their own shortcomings and pitfalls. Read Bruce Dawson's excellent article Comparing Floating Point Numbers, 2012 Edition for a great introduction into how tricky floating-point comparisons really are -- a must-read for anyone doing floating-point programming IMHO! I'm sure countless thousands of man-years have been spent finding out the subtle bugs due to naive floating-point comparisons.