Floating point almost equal

[Porter 41]

The other day I encountered a situation where I wanted to test if two floating point values were equal. Of course, one of the first things that you are told about floating point values is that you should never test for exact equality. So I proceed to wire up:

 

Is X = Y +/- some acceptable tolerance?

 

And that worked perfectly for my use case. That is, I knew that the max. value was 1000 and the min value was 0 and the resolution (or increment) was 0.01. A tolerance of 0.001 was sufficient.

 

This got me thinking. Wouldn't it be nice to have some reusable VIs for testing if floating point values are almost equal? Unfortunately this meant taking a broader view of the problem and lead me to this interesting blog post:

 

http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/

 

I've attached VIs for the Absolute Epsilon comparison, Relative Epsilon comparison and the ULP comparison described in the blog post for double precision floating point values.

 

 

Perhaps this would be a nice addition to the somewhat barren OpenG Comparison Pallet?

 

Uploaded package to Code Repository: http://lavag.org/files/file/259-floating-point-almost-equal/

AlmostEqual_LV2013.zip

AlmostEqual_LV86.zip

Edited December 21, 2014 by Porter

[jcarmody 204]

Pertinent Idea Exchange entry - 

"Almost Equal" functions for Float comparison​s

[hooovahh 691]

Altenbach has a version, MGI has a version, and I've seen several other implementations of it.  There also exists a primitive in LabVIEW that isn't on the palette that does this, but several NI employees have said it is not stable and not to use it.

[Porter 41]

Thanks for the info.

 

MGI's solution looks somewhat like the relative epsilon solution proposed in Bruce Dawson's blog post however they use a fixed maximum relative difference of 1%. Perhaps in some cases that would be too high.

 

Altenbach's version looks identical to the AlmostEqual2sComplement() function described in another article by Bruce Dawson:

http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

 

Notice at the top of that article he states that you should not be using that method of comparison as it has a couple of major flaws. For example, comparing 2 and -2 will always return true. 

 

I have added the relative epsilon comparison to the package for completeness. This way, you can try all 3 methods if you are interested. Most of the time I really only need the absolute epsilon comparison because I know beforehand what range of values I'm comparing.

[Porter 41]

Saved to LV 8.6

[Porter 41]

Added support for SGL and EXT types. Uploaded package to Code Repository: http://lavag.org/files/file/259-floating-point-almost-equal/

[Mellroth 65]

Added support for SGL and EXT types. Uploaded package to Code Repository: http://lavag.org/files/file/259-floating-point-almost-equal/

Nice idea, but please don't use pale-yellow for addons.

The pale-yellow background color makes it easily mistaken to be a primitive in LabVIEW, and I think NI also recommends against it.

 

/J