5 extern double f__cabs (double, double);
7 z_log (doublecomplex * r, doublecomplex * z)
9 double s, s0, t, t2, u, v;
10 double zi = z->i, zr = z->r;
12 r->i = atan2 (zi, zr);
14 r->r = log (f__cabs (zr, zi));
27 s = zr * sqrt (1 + t * t);
28 /* now s = f__cabs(zi,zr), and zr = |zr| >= |zi| = zi */
38 log (1 + x) = x - x ^ 2 / 2 + x ^ 3 / 3 - x ^ 4 / 4 + -...
39 = x (1 - x / 2 + x ^ 2 / 3 - +...)
40 [sqrt (y ^ 2 + z ^ 2) - 1] *[sqrt (y ^ 2 + z ^ 2) + 1] =
41 y ^ 2 + z ^ 2 - 1, so sqrt (y ^ 2 + z ^ 2) - 1 =
42 (y ^ 2 + z ^ 2 - 1) /[sqrt (y ^ 2 + z ^ 2) + 1]
44 t = ((zr * zr - 1.) + zi * zi) / (s + 1);
53 s += u / v - t * u / (v + 1);