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Re: Fix Bug 83566 - cyl_bessel_j returns wrong result for x>1000 for high orders


On 01/02/2018 05:43 PM, Michele Pezzutti wrote:

On 01/02/2018 02:28 AM, Ed Smith-Rowland wrote:
I like the patch.

I have a similar one in the tr29124 branch.

Anyway, I got held up and I think it's good to have new folks looking into this.

It looks good except that you need to uglify k.

I looked at the GSL implementation, based on same reference, and their loop is cleaner. What about porting that implementation here? Possible?

My implementation is also using one more term for P than for Q, which is discouraged in GSL, according to their comments.

Ed, do you have any comment about this point?
Regarding the 2nd line, after my observations, usually term stops contributing to P, Q before k > nu/2, so actually, an offset by one is most likely without consequences.
GSL implementation is nevertheless more elegant.

Also, keep in mind that these series are asymptotic - they'll eventually blow up.

You should watch the magnitude of sequential terms and bail out of the loop if either term starts growing.

Yes, you are right. As nu increases, the multiplying '__term' gets larger, and the result will lose accuracy.
This cannot be used for large nu.
I have not been able to figure out how to detect when it starts to lose accuracy though, other than empirically. GSL has no checks on terms and uses this method only under certain conditions, on nu and x.
Otherwise, they use other methods.

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