[R] Looking for greater floating-point precision

[Martin Maechler]

>>>>> "Paul" == Paul Smith <phhs80 at gmail.com>
>>>>>     on Fri, 17 Nov 2006 12:12:52 +0000 writes:

    Paul> On 11/16/06, Prof Brian Ripley <ripley at stats.ox.ac.uk>
    Paul> wrote:
    >> > For my calculations, I am needing to use more
    >> floating-point precision > than the default one of R. Is
    >> that possible? And, if yes, how?
    >> 
    >> See package gmp (but that will be slow and cumbersome for
    >> all but simple calculations).
    >> 
    >> The real issue is that R already uses the maximum
    >> precision of the FPU for many common FPUs (but not all).
    >> Since you have forgotten to tell us anything about your
    >> environment we don't know if that applies: there may be
    >> compiler options you can use to raise the precision.
    >> 
    >> Please do study the posting guide: we are surprisingly
    >> good at mind-reading, but prefer to be told exactly what
    >> you want to do with R in what environment and why you are
    >> 'needing' something.

    Paul> Thanks, Gabor and Prof. Ripley. After some research, I
    Paul> conclude that the problem occurring to me cannot be
    Paul> removed for any finite floating-point precision. (I do
    Paul> need infinite floating-point precision.) The
    Paul> problematic operation is the successive multiplication
    Paul> of reals between 0 and 1; after a certain number of
    Paul> multiplications, significant rounding errors occur.

of course.  But that's a very well known and common problem in
several areas of applied probability and statistics.

AFAIK, in most cases the "obvious" remedy is the following:
Instead of multiplying probabilities, 
you add log-probabilities and only exp()onentiate at the end {if
needed at all}.  This also applies if your numbers in [0,1] are
not probabilities per se.

Note that R makes it particularly efficient to work with
log-probabilities, because all  d<foo>() and p<foo> functions
have a 'log' or 'log.p' argument which return log-values
already, often with much more precision and efficiency than if
you'd take the log of the probabilities yourself.

Regards,
Martin Maechler, ETH Zurich


    Paul> I did read the posting guide, but I could not
    Paul> anticipate the relevance of indicating the environment
    Paul> that I am using: Fedora Core 6 (Linux) running on a
    Paul> Pentium Dual Core and R 2.4.0.

    Paul> Paul

    Paul> ______________________________________________
    Paul> R-help at stat.math.ethz.ch mailing list
    Paul> https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do
    Paul> read the posting guide
    Paul> http://www.R-project.org/posting-guide.html and
    Paul> provide commented, minimal, self-contained,
    Paul> reproducible code.