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#include "f2c.h"
#undef abs
#include "math.h"
extern double f__cabs (double, double);
void
z_log (doublecomplex * r, doublecomplex * z)
{
double s, s0, t, t2, u, v;
double zi = z->i, zr = z->r;
r->i = atan2 (zi, zr);
#ifdef Pre20000310
r->r = log (f__cabs (zr, zi));
#else
if (zi < 0)
zi = -zi;
if (zr < 0)
zr = -zr;
if (zr < zi)
{
t = zi;
zi = zr;
zr = t;
}
t = zi / zr;
s = zr * sqrt (1 + t * t);
/* now s = f__cabs(zi,zr), and zr = |zr| >= |zi| = zi */
if ((t = s - 1) < 0)
t = -t;
if (t > .01)
r->r = log (s);
else
{
#ifdef Comment
log (1 + x) = x - x ^ 2 / 2 + x ^ 3 / 3 - x ^ 4 / 4 + -...
= x (1 - x / 2 + x ^ 2 / 3 - +...)
[sqrt (y ^ 2 + z ^ 2) - 1] *[sqrt (y ^ 2 + z ^ 2) + 1] =
y ^ 2 + z ^ 2 - 1, so sqrt (y ^ 2 + z ^ 2) - 1 =
(y ^ 2 + z ^ 2 - 1) /[sqrt (y ^ 2 + z ^ 2) + 1]
#endif /*Comment */
t = ((zr * zr - 1.) + zi * zi) / (s + 1);
t2 = t * t;
s = 1. - 0.5 * t;
u = v = 1;
do
{
s0 = s;
u *= t2;
v += 2;
s += u / v - t * u / (v + 1);
}
while (s > s0);
r->r = s * t;
}
#endif
}
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