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

From: Alberto Ganesh Barbati (abarbati_at_[hidden])
Date: 2006-04-24 16:38:05

John Maddock ha scritto:
> 
> BTW I notice in other messages that folks have been talking about a function > object for this, but.... what use would that be for?  At present I can't see 
> anything simpler and easier to use than just a free function:
> 
> template <class T>
> T relative_error(T, T);
> 

Interesting. The other posters are talking about function objects
because I started the discussion with them. The main reasons I did that
is that function objects are more suitable to be passed as arguments to
algorithms because the compiler can inline them (more) easily. Having
free functions could be a nice addition but they shouldn't replace
function objects entirely, IMHO.

BTW, there is a subtle but important fact to consider: a function like
relative_error() is usually understood by mathematicians as a tool to
compute the error of an estimated value w.r.t. an expected value. In
particular, the two parameters have different roles and the algorithm is
asymmetric:

template <class T>
T relative_error(T value, T estimate)
{ return abs((value - estimate) / value); } // asymmetric!

(see, for example http://en.wikipedia.org/wiki/Relative_error)

However our goal is to determine whether two values are simply
near to each other. A programmer therefore could (and should) expect the
algorithm to be symmetric in the two parameters.

Of course, we could please both worlds by providing relative_error as
defined above, plus this:

template <class T>
T relative_error_symmetric(T x, T y)
{ return std::max(relative_error(x, y), relative_error(y, x)); }

and then defining the comparison function object in terms of the latter.
 What do you think?

Ganesh