On Sat, Oct 3, 2009 at 1:17 AM, rjf <fate...@gmail.com> wrote:
>
> Oh, if you are not really evaluating polynomials but just adding up a
> long list of numbers, then you can try some kind of compensating sum
> e.g.
> http://en.wikipedia.org/wiki/Kahan_summation_algorithm
>
> Though such things are perhaps unnecessary if you are happy with just
> increasing the precision of the operations (substantially. Not just a
> few bits.)
> RJF
Yes, this is just a case of evaluating a sum and there was a bug in
the addition code (which I'm entirely to blame for).
SymPy's evalf does detect cancellation and compensates by increasing
the precision, so it can evaluate expressions in ill-conditioned form
(e.g. expanded polynomials) accurately:
>>> r = 0.99999
>>> ((x-1)**10).subs(x,r)
9.99999999954490e-51
>>> ((x-1)**10).expand().subs(x,r) # catastrophic cancellation
-2.84217094304040e-14
>>> ((x-1)**10).evalf(subs={x:r})
9.99999999954490e-51
>>> ((x-1)**10).expand().evalf(subs={x:r})
9.99999999954490e-51
Fredrik
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