Re: [boost] [math] RFC: comparison function objects

From: John Maddock (john_at_[hidden])
Date: 2006-04-22 05:46:50

> template <typename T>
> struct compare_absolute_error : std::binary_function<T, T, bool>
> {
>  T eps;
>  compare_absolute_error(T eps_) : eps(eps_) {}
>  bool operator()(T x, T y) const { return abs(x - y) < eps; }
> };
>
> This kind of operators occurs frequently in algorithms and are
> sometimes error-prone to write, so having a ready-made and well
> tested component
> can certainly be an advantage.
>
> Of course, we could (and should) provide a bunch of different
> comparison algorithms: absolute and relative in the first place, but
> there may be others. I believe it might be a little but useful
> addition to the math library.
>
> Main questions are:
>
> 1) Is there interest for this?

Yes, please.

> 2) What are the comparison algorithms to include?

I've already made a start, well not really a start, just a "I needed this 
functionality to move on" throw it together sort of start here: 
http://freespace.virgin.net/boost.regex/toolkit/libs/math/doc/html/math_toolkit/toolkit.html#math_toolkit.toolkit.relative_error_and_testing

Relative error in particular is a tricky one, you have to deal with:

One or both values may be zero.
One or both values may be denorms.
One or both values may be infinities.

So I guess if you wanted a really super-duper handle it all version you 
would make it policy based:

* Values below a certain threshold are regarded as zero (so all denorms are 
equivalent for example).
* Values above a threshold are regarded as effectively infinity.
* Absolute errors are used if the values are small enough.

Which of these you actually want to use in your application depend on the 
QOI of the component you're testing I guess.

Personally I treat all denorms as zeros because if the result is a denorm 
there probably isn't enough information content throughout the calculation 
that led to the denorm to get an accurate value (if you see what I mean).

Anyway, just my 2c worth, please do feel free to jump in with something 
better if you want!

John.