double complex
catan(double complex z)
{
double complex w;
double a, t, x, x2, y;
x = creal (z);
y = cimag (z);
if ((x == 0.0) && (y > 1.0))
goto ovrf;
x2 = x * x;
a = 1.0 - x2 - (y * y);
if (a == 0.0)
goto ovrf;
t = 0.5 * atan2 (2.0 * x, a);
w = _redupi (t);
t = y - 1.0;
a = x2 + (t * t);
if (a == 0.0)
goto ovrf;
t = y + 1.0;
a = (x2 + (t * t))/a;
w = w + (0.25 * log (a)) * I;
return (w);
ovrf:
/*mtherr ("catan", OVERFLOW);*/
w = MAXNUM + MAXNUM * I;
return (w);
}
static double
_ctans(double complex z)
{
double f, x, x2, y, y2, rn, t;
double d;
x = fabs (2.0 * creal (z));
y = fabs (2.0 * cimag(z));
x = _redupi(x);
x = x * x;
y = y * y;
x2 = 1.0;
y2 = 1.0;
f = 1.0;
rn = 0.0;
d = 0.0;
do {
rn += 1.0;
f *= rn;
rn += 1.0;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 + x2;
t /= f;
d += t;
rn += 1.0;
f *= rn;
rn += 1.0;
f *= rn;
x2 *= x;
y2 *= y;
t = y2 - x2;
t /= f;
d += t;
}
while (fabs(t/d) > MACHEP)
;
return (d);
}
double complex catan(double complex z)
{
double complex w;
double a, t, x, x2, y;
x = creal(z);
y = cimag(z);
x2 = x * x;
a = 1.0 - x2 - (y * y);
t = 0.5 * atan2(2.0 * x, a);
w = _redupi(t);
t = y - 1.0;
a = x2 + (t * t);
t = y + 1.0;
a = (x2 + t * t)/a;
w = CMPLX(w, 0.25 * log(a));
return w;
}
