libf2c/libF77/z_log.c

   1 #include "f2c.h"
   2
   3 #ifdef KR_headers
   4 double log(), f__cabs(), atan2();
   5 VOID z_log(r, z) doublecomplex *r, *z;
   6 #else
   7 #undef abs
   8 #include "math.h"
   9 extern double f__cabs(double, double);
  10 void z_log(doublecomplex *r, doublecomplex *z)
  11 #endif
  12 {
  13         double s, s0, t, t2, u, v;
  14         double zi = z->i, zr = z->r;
  15
  16         r->i = atan2(zi, zr);
  17 #ifdef Pre20000310
  18         r->r = log( f__cabs( zr, zi ) );
  19 #else
  20         if (zi < 0)
  21                 zi = -zi;
  22         if (zr < 0)
  23                 zr = -zr;
  24         if (zr < zi) {
  25                 t = zi;
  26                 zi = zr;
  27                 zr = t;
  28                 }
  29         t = zi/zr;
  30         s = zr * sqrt(1 + t*t);
  31         /* now s = f__cabs(zi,zr), and zr = |zr| >= |zi| = zi */
  32         if ((t = s - 1) < 0)
  33                 t = -t;
  34         if (t > .01)
  35                 r->r = log(s);
  36         else {
  37
  38 #ifdef Comment
  39
  40         log(1+x) = x - x^2/2 + x^3/3 - x^4/4 + - ...
  41
  42                  = x(1 - x/2 + x^2/3 -+...)
  43
  44         [sqrt(y^2 + z^2) - 1] * [sqrt(y^2 + z^2) + 1] = y^2 + z^2 - 1, so
  45
  46         sqrt(y^2 + z^2) - 1 = (y^2 + z^2 - 1) / [sqrt(y^2 + z^2) + 1]
  47
  48 #endif /*Comment*/
  49
  50                 t = ((zr*zr - 1.) + zi*zi) / (s + 1);
  51                 t2 = t*t;
  52                 s = 1. - 0.5*t;
  53                 u = v = 1;
  54                 do {
  55                         s0 = s;
  56                         u *= t2;
  57                         v += 2;
  58                         s += u/v - t*u/(v+1);
  59                         } while(s > s0);
  60                 r->r = s*t;
  61                 }
  62 #endif
  63         }