4 double log(), f__cabs(), atan2();
5 VOID z_log(r, z) doublecomplex *r, *z;
9 extern double f__cabs(double, double);
10 void z_log(doublecomplex *r, doublecomplex *z)
13 double s, s0, t, t2, u, v;
14 double zi = z->i, zr = z->r;
18 r->r = log( f__cabs( zr, zi ) );
30 s = zr * sqrt(1 + t*t);
31 /* now s = f__cabs(zi,zr), and zr = |zr| >= |zi| = zi */
40 log(1+x) = x - x^2/2 + x^3/3 - x^4/4 + - ...
42 = x(1 - x/2 + x^2/3 -+...)
44 [sqrt(y^2 + z^2) - 1] * [sqrt(y^2 + z^2) + 1] = y^2 + z^2 - 1, so
46 sqrt(y^2 + z^2) - 1 = (y^2 + z^2 - 1) / [sqrt(y^2 + z^2) + 1]
50 t = ((zr*zr - 1.) + zi*zi) / (s + 1);