Fortran port of the Bessels.jl library

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50

I don’t post much but yes, I was aware of the reference and the sort of discussions it came from.
This certainly cannot cause problems with backwards compatibility! that’s what I meant with the joke (sarcasm) flying over people’s head.

Thank you for the references. I will have a look at them more thoroughly. I have been using the NIST handbook frequently, yes, pretty handy and full of references.

Minimax are a quick way to get something that works, but indeed the rounding makes thing differ a lot from the ideal (exact arithmetic) polynomial. Errors of 1e-11 in the minimax turn out to be of 1e-7 when computed with e.g.single precision in fortran.
I’ve computed many and compared them to what’s available in the math libraries; often the coefficients are quite similar, but never the same.
It may seem like a good starting point, but I’m not so sure. For single precision, say a 4th order polynomial, even changing the last digit of the coefficient of x^4 makes things go from errors of 1e-8 to 1e-7 or larger. I don’t think trial and error here works, it’s too much work.
Another path is using double precision and then convert to single, though I’m trying to avoid that if possible.

51

No wonder!

Anyways, the proposal from the folks who represented the UK National Body a while ago was linked upthread which can introduce statements in Fortran such as

   default integer ( kind=selected_int_kind(r=18) )  !<-- proposed facility
   print *, range(1)
end

And a conforming processor in the future with the above program shall be required to print 18 as opposed to a likely value of 9 using your current “friendly neighborhood compiler”. If this is a joke, perhaps it should be a new theme under British humor, perhaps as 1.16 Too Practical!