Re: Generalised bisection

On Thu, Mar 12, 2009 at 6:45 AM, John Tapsell [off-list ref] wrote:

2009/3/11 Ealdwulf Wuffinga [off-list ref]:

quoted

On Wed, Mar 11, 2009 at 9:35 AM, John Tapsell [off-list ref] 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