On 31 Jul, 01:24, Bill Hart <[EMAIL PROTECTED]> wrote:
> It would be interesting to see the time for Mathematica on a 32 bit
> X86 machine, since this would tell us if that is what they do.
Doh! I should have read William's timings more carefully. He gives the
times for a 32 bit machine. So I guess Mathematica doesn't use 80 bit
long doubles on a 64 bit X86 then. Still it is an option for us.
Once there is a stable version of the new code which seems to give
correct results, I'll take a closer look and see if I can spot any
obvious speed improvements. I can't promise anything. I suspect my
fundamental mistake was not realising that you still needed quite a
bit of multi-precision code for quite a few terms. In fact now that I
think about it, I don't see why I thought you could compute all the
s(h,k)'s using single limb arithmetic.
It is the multi-precision stuff that is slowing it down, no doubt.
mpfr has a 15x overhead over ordinary double precision, even at 53
bits, or so I have read. I guess there is a lot of branching to ensure
the accuracy of arithmetic. Whilst that is needed for many
applications, it probably isn't here. Sadly there don't seem to be any
decent open source alternatives for when that accuracy is not
required. I have a similar problem in some code I am currently
writing. I need precisely quad precision, so mpfr is out of the
question.
Bill.
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