contrib/openbsd_libm/src/s_clogl.c

   1 /*      $OpenBSD: s_clogl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $    */
   2
   3 /*
   4  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
   5  *
   6  * Permission to use, copy, modify, and distribute this software for any
   7  * purpose with or without fee is hereby granted, provided that the above
   8  * copyright notice and this permission notice appear in all copies.
   9  *
  10  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  11  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  12  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  13  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  14  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  15  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  16  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  17  */
  18
  19 /*                                                      clogl.c
  20  *
  21  *      Complex natural logarithm
  22  *
  23  *
  24  *
  25  * SYNOPSIS:
  26  *
  27  * long double complex clogl();
  28  * long double complex z, w;
  29  *
  30  * w = clogl( z );
  31  *
  32  *
  33  *
  34  * DESCRIPTION:
  35  *
  36  * Returns complex logarithm to the base e (2.718...) of
  37  * the complex argument x.
  38  *
  39  * If z = x + iy, r = sqrt( x**2 + y**2 ),
  40  * then
  41  *       w = log(r) + i arctan(y/x).
  42  *
  43  * The arctangent ranges from -PI to +PI.
  44  *
  45  *
  46  * ACCURACY:
  47  *
  48  *                      Relative error:
  49  * arithmetic   domain     # trials      peak         rms
  50  *    DEC       -10,+10      7000       8.5e-17     1.9e-17
  51  *    IEEE      -10,+10     30000       5.0e-15     1.1e-16
  52  *
  53  * Larger relative error can be observed for z near 1 +i0.
  54  * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
  55  * absolute error 1.0e-16.
  56  */
  57
  58 #include <complex.h>
  59 #include <math.h>
  60
  61 long double complex
  62 clogl(long double complex z)
  63 {
  64         long double complex w;
  65         long double p, rr;
  66
  67         /*rr = sqrt(z->r * z->r  +  z->i * z->i);*/
  68         p = cabsl(z);
  69         p = logl(p);
  70         rr = atan2l(cimagl(z), creall(z));
  71         w = p + rr * I;
  72         return (w);
  73 }