Re: Generalised bisection

[Ealdwulf Wuffinga <ealdwulf@googlemail.com>]

On Thu, Mar 12, 2009 at 6:45 AM, John Tapsell <johnflux@gmail.com> wrote:
> 2009/3/11 Ealdwulf Wuffinga <ealdwulf@googlemail.com>:
>> On Wed, Mar 11, 2009 at 9:35 AM, John Tapsell <johnflux@gmail.com> wrote:
>> What I use is the multiprecision floating point number class. doubles
>> don't seem to be long enough.
>
> Hmm, really really?  Sometimes this sort of thing can be fixed by just
> readjusting the formulas.  What formulas are you using that require
> more precision than doubles?

I'll have to reply to this later when I have more time. However, there
is a (rather verbose)
file in the  doc directory which describes them - in texmacs format,
but I've just uploaded
a pdf version as well. It is BayesianSearch_Debugging.pdf. The
description of this code starts in
section 2.2 (since I wrote that, I have generalised it to the DAG case
as in git).


> A little bit of math trickery helps here :-)
>
> y =  x^b
>
> log(y) = log(x^b) = b * log(x)
> e^log(y) = e^(b log(x))
>
> y = exp(b * log(x))
>
> So as long as you have 'exp' and 'log' functions, you can raise x to
> the power of b, even if b is fractional.

Sadly gmp does not have log or exp. mpfr does, but it does not have a python
interface.

Alex