z_log.c   [plain text]

#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
}