[R] Error in besselJ(pi/2, 1E-15)?

[Ben Bolker]

    Confirmed on

R Under development (unstable) (2025-12-22 r89219)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.3 LTS

https://github.com/r-devel/r-svn/commits/50fa23f7748e9da48a15d045b6cb23a622192725/src/nmath/bessel_j.c

  It's not surprising that this fails when nu is close to 
.Machine$double.eps (approx 1e-16, the smallest value for which 1+x != 
1, i.e. precision limit of 64-bit floats), but it looks like one would 
have to dig through the J_bessel C code 
<https://github.com/r-devel/r-svn/blob/50fa23f7748e9da48a15d045b6cb23a622192725/src/nmath/bessel_j.c#L36> 
to see exactly where the catastrophic loss of precision happens, and 
what to do about it ...

   if desired I could post this on the R bug tracker (seems appropriate).

    cheers
    Ben Bolker

On 12/28/25 11:28, Leo Mada via R-help wrote:
> Dear R-Users,
> 
> besselJ(pi/2, 0)
> # 0.4720012
> besselJ(pi/2, 1E-14)
> # 0.4720012
> besselJ(pi/2, 1E-15)
> # 4.720012e+14
> 
> There seems to be an error in besselJ(pi/2, eps), where eps is close to 0; although besselJ(pi/2, 0) is well behaved.
> 
> I am not an expert in the field - but it doesn't seem right.
> 
> Sincerely,
> 
> Leonard
> 
> 
> 	[[alternative HTML version deleted]]
> 
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-- 
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Associate chair (graduate), Mathematics & Statistics
Director, School of Computational Science and Engineering
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