contrib/openbsd_libm/src/s_clogf.c

   1 /*      $OpenBSD: s_clogf.c,v 1.2 2010/07/18 18:42:26 guenther Exp $    */
   2 /*
   3  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
   4  *
   5  * Permission to use, copy, modify, and distribute this software for any
   6  * purpose with or without fee is hereby granted, provided that the above
   7  * copyright notice and this permission notice appear in all copies.
   8  *
   9  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  10  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  11  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  12  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  13  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  14  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  15  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  16  */
  17
  18 /*                                                      clogf.c
  19  *
  20  *      Complex natural logarithm
  21  *
  22  *
  23  *
  24  * SYNOPSIS:
  25  *
  26  * void clogf();
  27  * cmplxf z, w;
  28  *
  29  * clogf( &z, &w );
  30  *
  31  *
  32  *
  33  * DESCRIPTION:
  34  *
  35  * Returns complex logarithm to the base e (2.718...) of
  36  * the complex argument x.
  37  *
  38  * If z = x + iy, r = sqrt( x**2 + y**2 ),
  39  * then
  40  *       w = log(r) + i arctan(y/x).
  41  *
  42  * The arctangent ranges from -PI to +PI.
  43  *
  44  *
  45  * ACCURACY:
  46  *
  47  *                      Relative error:
  48  * arithmetic   domain     # trials      peak         rms
  49  *    IEEE      -10,+10     30000       1.9e-6       6.2e-8
  50  *
  51  * Larger relative error can be observed for z near 1 +i0.
  52  * In IEEE arithmetic the peak absolute error is 3.1e-7.
  53  *
  54  */
  55
  56 #include <complex.h>
  57 #include <math.h>
  58
  59 float complex
  60 clogf(float complex z)
  61 {
  62         float complex w;
  63         float p, rr, x, y;
  64
  65         x = crealf(z);
  66         y = cimagf(z);
  67         rr = atan2f(y, x);
  68         p = cabsf(z);
  69         p = logf(p);
  70         w = p + rr * I;
  71         return (w);
  72 }