Re: [Gnuplot-info] nan

[Ethan M. <eam...@gm...>]

Underflow confirmed.

The Faddeeva function is exp(-z^2) * erfc(-i*z)

Calculation of exp(-z^2) underflows to zero at about z = 27.
Gnuplot's own exp function knows to ignore the floating point
exception that is generated and just return zero.
But the implementation used by the Faddeeva function in libcerf
doesn't do this. It leaves the ERANGE error active.

I don't have an immediate fix for this in gnuplot.

The libcerf library does provide a separate function
im_w_of_x(x) that would calculate the imaginary part
without triggering an underflow, but that only helps if
the calling program already knows there will be an underflow
and calls the special case instead of the generic routine.
Gnuplot doesn't currently know to do this.

	Ethan


On Tuesday, 1 November 2022 18:02:33 PDT Ethan Merritt wrote:
> On Tuesday, 1 November 2022 14:54:01 PDT Patrick Dupre wrote:
> > Hello,
> > 
> > Setting
> > fcn(x,g,G)=-imag(1/(x+I*g)*faddeeva(x/G)
> > 
> > plot [-30:30] fcn(x,0.01,1)  
> > 
> > provides
> > nan from values less than -27.28 and more than 27.28
> > There is not reason for that
> > The value are small, but not very small
> > slightly less than
> > -0.0007586274478
> > 
> > Any idea?
> 
> Good question.  
> Something in the cerf library is setting a range error (ERANGE)
> "Math result not representable".  Possibly this is due to
> underflow of the real component, which we could ignore, but that is
> only speculation at this point.  Note the result
>   gnuplot> print faddeeva(27.)
>   {2.50797207889417e-317, 0.0209102719931009}
> which indicates that the real component has reached the smallest
> representable IEEE double float value.
> 
> I will investigate further.
> 
> 	Ethan
>