Re: [boost] [MPL.Math] updates for double

From: Peder Holt (peder.holt_at_[hidden])
Date: 2005-11-09 14:38:10

On 11/9/05, Cromwell Enage <sponage_at_[hidden]> wrote:
> --- Peder Holt wrote:
> > --- Cromwell Enage wrote:
> > > There's an existing implementation of arctangent
> > > that should work for all real numbers.
>
> Correction: it also only converges for |x| <= 1.
>
> > I didn't notice. I'll check it out an look at its
> > convergence rate.
>
> It's the Maclaurin series, and it's rather slow.
>

I have a series available that converges for X>1. I'll implement it
once the pi<> template is ready.

<snip>
>
> And what did I do instead?  I reimplemeted a majority
> of the advanced metafunctions by using
> Boost.Preprocessor to unroll the recursion.  (You must
> now #define the corresponding limit macro for each
> metafunction, and you have a hard limit of 255
> depending on the metafunction, but it beats exceeding
> the template instantiation depth.)  Best of all,
> euler.cpp compiles and works just fine.

Great job! I did the same for tangent, and compile times for
tangent.cpp dropped from 18 to 12 seconds.

Btw. How about making the syntax a bit clearer by dropping the
BOOST_PP_MUL etc. syntaxt? Why not just:

        typedef typename minus< \
                    int_<1> \
                  , times< \
                        divides< \
                            angle_squared \
                          , int_< \
                                (\
                                    (BOOST_MPL_LIMIT_MATH_SINE_SERIES-x)*2+1\
                                )*\
                                (\
                                    (BOOST_MPL_LIMIT_MATH_SINE_SERIES-x)*2\
                                )\
                            >\
                        > \
                      , BOOST_PP_CAT(prefix, x) \
                    > \
                >::type \

I think this is more readable, and less limited (BOOST_PP_MUL(129,2)
exceeds 256, not that it matters much, as we should never have this
long series :)

Have uploaded a version of tangent that uses the preprocessor, plus a
version of arcus_sine and an alternative arcus_tangent that does not
:) to the vault.

Regards,
Peder
>
>                               Cromwell D. Enage
>
>
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