[Ecls-list] log(complex) inaccurate for some values

[Raymond Toy]

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