[Ecls-list] log(complex) inaccurate for some values
Raymond Toy
toy.raymond at gmail.com
Sun Apr 13 14:03:07 UTC 2008
Juan Jose Garcia-Ripoll wrote:
> The following does not imply anything. I will look into this, but I
> presume one needs special functions to handle the high precision case,
> as in CMUCL. I also wonder how many digits of accuracy this
> systematically brings in other cases.
>
>
The problem is in the calculation of log(sqrt(x^2+y^2)). If x is close
to 1 and y is small or vice versa, sqrt(x^2+y^2) is inaccurate. The
solution is to change the computation to
log(sqrt(x^2+y^2)) = 1/2*log(x^2+y^2) = 1/2*log(1+((x-1)*(x+1)+y^2)
But don't use the log function to evaluate this. Use log1p(z) =
log(1+z). Most C libraries have a log1p function already, but if not,
you can just use the series formula since z is small.
Ray
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