[boost] Numeric constants

Subject: [boost] Numeric constants
From: John Maddock (john_at_[hidden])
Date: 2009-01-30 05:35:17

Folks, someone's just filed a feature request asking for more numeric 
constants to be added to Boost.Math (these are currently an implementation 
detail, albeit a semi-documented one: 
http://www.boost.org/doc/libs/1_37_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html), 
but we know what troubles we had agreeing on anything last time this came up 
for review!  Even so it appears to be time to fearlessly open up this 
particular can of worms again ;-)

So, it appears that there is still interest, but as you know last time we 
tried this there was no agreement on interface, some folks felt a template 
interface was essential:

template <class T> T pi();

leading to:

template <class T>
T circumference(T r)
{
   return 2 * boost::math::constants::pi<T>() * r;
}

While others were absolutely adament that they wouldn't use a syntax other 
than:

template <class T>
T circumference(T r)
{
   return 2 * pi * r;
}

Various attempts were made to solve this conundrum via expression templates 
and/or overloaded operators, but all introduced their own new issues as 
well, and IMO none were wholly satisfactory (not least due to the complexity 
introduced, a complexity that becomes all too apparent to the user if they 
do get a compiler error due to an unsupported use case).

So.... here's what I think Paul Bristow and I might be persuaded to submit:

* A library based on the existing Boost.Math code, with pi<T>() as the main 
interface / use case.
* Possibly add constants of specific precision in alternative namespaces, so 
we could have:

double circumference(double r)
{
   using namspace boost::math::double_constants;
   return 2 * pi * r;
}

And that's pretty much it: no overly complex stuff, just a really simple 
library with a few constants in it, that makes it really easy to add new 
constants when required.

Thoughts?

Regards, John.