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

[Juan Jose Garcia-Ripoll]

On Mon, Apr 14, 2008 at 2:37 AM, Raymond Toy <toy.raymond at gmail.com> wrote:
>  Here's an outline for a one possible implementation of log1p.  Very likely
> not as optimized as the C version, but should work with reasonable accuracy.

Hi, looks nice. The version I found around, and which only activates
when the C library does not support log1p (Windows, probably) is one I
found googling around, and which compensates the errors in the
ordinary logarithm.

double log1p(double x)
{
        double u = 1.0 + x;
        if (u == 1) {
                return 0.0;
        } else {
                return (log(u) * x)/(u - 1.0);
        }
}

But your implementation seems more stable. The only thing that looks
expensive is the step for making "x" small. Wouldn't it suffice to use
log1p(x) = series if |x| <= 1, and log1p(x) = log1p(1/x) + log(x)
elsewhere?

Juanjo


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Facultad de Fisicas, Universidad Complutense,
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