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From: Cromwell Enage (sponage_at_[hidden])
Date: 2005-11-03 09:40:46

--- Peder Holt wrote:
> I tried implementing a power using fractions, but it
> turned out that for larger exponents its convergence
> rate was very poor. (I needed ~100 recursions for
> something like 10^20).

Yeah, that stinks.

> What we should do, is add a specialization for power
> with integral exponent. This is a very fast
> algorithm (also in respect to compile-time
> efficiency).

The current implementation calls integral_power if it
detects that exponent::tag is the same as
integral_c_tag, unsigned_big_integral_tag, or

> What we could do, is to split power(z,a) into two:
> power(z,floor(a))*power(z,a-floor(a));

Ah, a specialization for fractional exponents. We
could use integral_part for the floor function, but if
a itself is very large (>= 2^30), then
minus<a,integral_part<a> > will yield a mixed_number,
not a double. fractional_part<a> returns a rational
regardless of magnitude.

What I'll do is:
1) Create an internal metafunction in the double_::aux
namespace that does what fractional_part does now.
2) Change fractional_part so that it returns a double.
3) Implement numerator and denominator specializations
that use the metafunction in 1).

Then, with fractional_power as a template nested
within power_impl, we can return:

        integral_power<z,integral_part<a> >
      , fractional_power<z, fractional_part<a> >

                              Cromwell D. Enage

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