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

Answer 1

In the past when I have had to use an epsilon value it's been very much bigger than the machine epsilon value.

Although it was for 32 bit doubles (rather than 64 bit doubles) we found that an epsilon value of 10^-6 was needed for most (if not all) calculated values in our particular application.

The value of epsilon you choose depends on the scale of your numbers. If you are dealing with the very large (10⁺¹⁰ say) then you might need a larger value of epsilon as your significant digits don't stretch very far into the fractional part (if at all). If you are dealing with the very small (10^-10 say) then obviously you need an epsilon value that's smaller than this.

You need to do some experimentation, performing your calculations and checking the differences between your output values. Only when you know the range of your potential answers will you be able to decide on a suitable value for your application.

Answer 2

How to choose a value for epsilon?

Short Answer: You take a small value which fits your applications needs.

Long Answer: Nobody can know which calculations your application does and how accurate you expect your results to be. Since rounding errors sum up machine epsilon will be almost all times far too big so you have to chose your own value. Depending on your needs, 0.01 be be sufficient, or maybe 0.00000000000001 or less will.

The question is, do you really want/need to do equality tests on floating point values? Maybe you should redesign your algorithms.