Re: Pade Approximants

"7Powers" <srivastava.vikram@xxxxxxxxx> wrote:
> I am using Payne and Hanek reduction algorithm
> to reduce my input argument between -Pi/4 and Pi/4. Am working on IEEE
> double precision format.
>
> David, upto 17 digits of accuracy is targetted. I am concerned with
> reducing the relative error.
> With Pade [11,10],maximum deviation is on the 12th digit and mean
> deviation is on the 16th digit.

Now that various other things have been clarified, I must say that I do
not understand your claim in the last sentence above. It seems to me that
the [11,10] Pade approximant of tan(x), given by you (and later Carlos)
previously in the thread, should be more than adequate for your needs.
For -Pi/4 <= x <= Pi/4, |rel. error| increases with |x|, and so the maximum
of |rel. error| occurs when |x| = Pi/4. That maximum is about 1.73*10^-24.

David
.

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