On 11/9/05, Cromwell Enage <sponage@yahoo.com> wrote:
--- Peder Holt wrote:
I have implemented the compile-time inverse_sine and inverse_tangent (the latter only for x<=1)
Are those arcsine and arctangent metafunctions? There's an existing implementation of arctangent that should work for all real numbers.
I didn't notice. I'll check it out an look at its convergence rate.
but have a bit of a problem with arcus_cosine, which is defined as pi/2-inverse_sine.
A problem, indeed.
So far, all implementations of math metafunctions should work with both double_ and your mixed_number etc. types, but once we introduce a constant, the result type is given, unless there is some clever way of defining the constant several times for all the different input types.
Looks like we'll need a pi<> metafunction that takes in a numeric tag such as double_tag and an integral constant defining a series limit. Since your double has a fixed precision, pi<double_tag> can return a simple typedef and ignore the series limit, while the primary definition of pi<> has to return the result of the series. We're not making a "constants library" in the usual sense, so maybe we can get away with it.
If all interested parties agree with this plan, the next question is, where should we put pi<>? So far, I have two candidates:
* boost::mpl::math, since zero<> also resides there * boost::mpl::math::constants
boost::mpl::math, then probably.
Also, I have managed to squeeze more performance out of the compiler by replacing integral operations in the metafunctions with BOOST_STATIC_CONSTANT.
Yeah, I've discovered this with big_integral, too. Only backward-compatibility concerns have held me back from employing this technique elsewhere. (I don't have a Class B compiler on-hand though, so I don't know if my fears are unjustified.)
Don't think this is an issue. MSVC6.5 at least prefers BOOST_STATIC_CONSTANT, as they are much easier to handle than excessive template instantiations.
[snip code]
I think it should be possible to only use 4 arithmetic meta-operation per term, typically (a+b*x*next)/c where a,b and c are calculated using BOOST_STATIC_CONSTANT
I'll #ifdef 0 out the code to be replaced.
Ok. Regards Peder
Cromwell D. Enage
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