[R] 64-bit programming
Prof Brian Ripley
ripley at stats.ox.ac.uk
Tue Sep 11 16:05:31 CEST 2001
On Tue, 11 Sep 2001 helgito at hi.is wrote:
> > Why do you think REAL*16 will give you increased accuracy? Accuracy has a
> > lot more to do with the algorithms used and their convergence criteria.
> > As R is a statistical package, numerical accuracy is almost always
> > secondary to data uncertainty.
> I tested a Solaris fotran compiler on a Sun and it allowed REAL*16 whereas
> a GNU fortran on the same machine did not. It seems to me that that the
> numerical accuracy compared to REAL*8 on an Intel-86 machine was not
> proportional. The Intel machines have a numerical stack of lenght 80 so if
> the Fortran program is well optimized you should not loose as as many digits
> as you might expect.
> REAL*8 gives about 15 digits in floating-point. It was my hope that REAL*16
> would give around 30. In my simple experiment it seemed that I only got
> about 20-25.
> Maybe the Sun or the compiler does not use a stack as the Intel-86 machines.
> I want to add several hundred thousand numbers, and their squares, which some
> are range from maybe 10^(-6) to 1 or more.
> With crude programming I fear that I am loosing important digits.
> I was wondering whether I should apply for a Sun station or wait further
Better to learn some numerical analysis. For example you could sum the
smallest first. If you want centred moments, centre first ....
There is a whole science out there of getting accurate results with low
precision (it was needed where the only fast arithmetic was a few
hexadecimal digits). That could be tricky and even needed iterative
refinement, but double precision swept all that away at least of
statistical purposes (except perhaps for people who think the normal
equations are the way to solve least-squares problems).
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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