ctan

Complex circular tangent.

SYNOPSIS:

void ctan();
cmplx z, w;

ctan(&z, &w);

DESCRIPTION:

If
     z = x + iy,

then

           sin 2x + i sinh 2y
     w = --------------------.
            cos 2x + cosh 2y

On the real axis the denominator is zero at odd multiples of PI/2. The denominator is evaluated by its Taylor series near these points.

ACCURACY:

                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC       -10,+10      5200       7.1e-17     1.6e-17
    IEEE      -10,+10     30000       7.2e-16     1.2e-16

Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.