On 11/9/05, Cromwell Enage <sponage@yahoo.com> 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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