On Mon, 18 Jul 2011, Alireza Mahani wrote:
Simon,
Thank you for elaborating on the limitations of R in handling float types. I
think I'm pretty much there with you.
As for the insufficiency of single-precision math (and hence limitations of
GPU), my personal take so far has been that double-precision becomes crucial
when some sort of error accumulation occurs. For example, in differential
equations where boundary values are integrated to arrive at interior values,
etc. On the other hand, in my personal line of work (Hierarchical Bayesian
models for quantitative marketing), we have so much inherent uncertainty and
noise at so many levels in the problem (and no significant error
accumulation sources) that single vs double precision issue is often
inconsequential for us. So I think it really depends on the field as well as
the nature of the problem.
The main reason to use only double precision in R was that on modern
CPUs double precision calculations are as fast as single-precision
ones, and with 64-bit CPUs they are a single access. So the extra
precision comes more-or-less for free. You also under-estimate the
extent to which stability of commonly used algorithms relies on double
precision. (There are stable single-precision versions, but they are
no longer commonly used. And as Simon said, in some cases stability
is ensured by using extra precision where available.)
I disagree slightly with Simon on GPUs: I am told by local experts
that the double-precision on the latest GPUs (those from the last year
or so) is perfectly usable. See the performance claims on
http://en.wikipedia.org/wiki/Nvidia_Tesla of about 50% of the SP
performance in DP.
Regards,
Alireza
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Brian D. Ripley, rip...@stats.ox.ac.uk
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