clog

Complex natural logarithm.

SYNOPSIS:

void clog();
cmplx z, w;

clog(&z, &w);

DESCRIPTION:

Returns a complex logarithm to the base e (2.718...) of the complex argument x.

If z = x + iy, r = sqrt(x**2 + y**2),
then
       w = log(r) + i arctan(y/x).

The arctangent ranges from -PI to +PI.

ACCURACY:

                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC       -10,+10      7000       8.5e-17     1.9e-17
    IEEE      -10,+10     30000       5.0e-15     1.1e-16

Larger relative errors can be observed for z near 1 +i0. In IEEE arithmetic the peak absolute error is 5.2e-16, rms absolute error 1.0e-16.