libf2c/libF77/z_log.c

   1 #include "f2c.h"
   2
   3 #undef abs
   4 #include "math.h"
   5 extern double f__cabs (double, double);
   6 void
   7 z_log (doublecomplex * r, doublecomplex * z)
   8 {
   9   double s, s0, t, t2, u, v;
  10   double zi = z->i, zr = z->r;
  11
  12   r->i = atan2 (zi, zr);
  13 #ifdef Pre20000310
  14   r->r = log (f__cabs (zr, zi));
  15 #else
  16   if (zi < 0)
  17     zi = -zi;
  18   if (zr < 0)
  19     zr = -zr;
  20   if (zr < zi)
  21     {
  22       t = zi;
  23       zi = zr;
  24       zr = t;
  25     }
  26   t = zi / zr;
  27   s = zr * sqrt (1 + t * t);
  28   /* now s = f__cabs(zi,zr), and zr = |zr| >= |zi| = zi */
  29   if ((t = s - 1) < 0)
  30     t = -t;
  31   if (t > .01)
  32     r->r = log (s);
  33   else
  34     {
  35
  36 #ifdef Comment
  37
  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]
  43 #endif /*Comment */
  44         t = ((zr * zr - 1.) + zi * zi) / (s + 1);
  45       t2 = t * t;
  46       s = 1. - 0.5 * t;
  47       u = v = 1;
  48       do
  49         {
  50           s0 = s;
  51           u *= t2;
  52           v += 2;
  53           s += u / v - t * u / (v + 1);
  54         }
  55       while (s > s0);
  56       r->r = s * t;
  57     }
  58 #endif
  59 }