On 11/9/2011 10:20 AM, Raymond Toy wrote:....
....
>
> The lack of bigfloat routines for all of the special functions is a
> different problem. I know that Barton's hypergeometric code could be
> used to evaluate them, but it seems unnecessarily slow to use
> hypergeometrics to evaluate these common special functions. It would,
> however, be a reasonable workaround for this lack of coverage.
I think this is what Mathematica does for a whole bunch of stuff. I
have reported bugs in their code where this scheme gives small but
significant errors ... in particular some f(x) which mathematically
should be real for real x but returns a complex value.
You might think this would be not so bad, e.g. realpart +
epsilon*I. But if the realpart is O(epsilon), the answer is, in terms
of relative error, way off.
>
> While I recognize that people might hope for fast computing, they
> are, after all, using a computer algebra system and might be
> willing to wait for an answer that is "correct" if possible.
>
> But my proposal is more long terml thinking than a proposal to
> "fix this bug".
>
>
> Agreed.
>
> Ray