perazz / fortran-bessels

Fortran port of the Bessels.jl repository

Combustion researcher, Software Developer and Consultant at WERC

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fortran-bessels's Issues

Accuracy of bessel functions for larger arguments

I was looking through the code and was curious how

fortran-bessels/src/bessels.f90

Line 100 in ee7e6f4

b = cos(ax+xn)

this line held up? I don't know how to exactly test this accuracy 😃 but I found that this simple summation is prone to some huge cancellation. Especially because the two values vary so much in magnitude.

It's much better to do something like...

s_x, c_x = sincos(x)
s_xn, c_xn = sincos(xn)
  (c_x * c_xn - s_x * s_xn)

because it essentially acts as a range reduction putting the two values at similar magnitude. Therefore, when summed they lose less precision. We are working on a slightly different approach but if Fortran has a good function to give you both sin and cos this could significantly improve the accuracy! It should only cost a few cycles but will be able to provide much better relative tolerances.

add topics

I suggest adding topics such as bessel, bessel-function, special-functions in the About section.