compiler/stdc/math/s_cpowl.c

   1 /*      $OpenBSD: s_cpowl.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 /*                                                      cpowl
  20  *
  21  *      Complex power function
  22  *
  23  *
  24  *
  25  * SYNOPSIS:
  26  *
  27  * long double complex cpowl();
  28  * long double complex a, z, w;
  29  *
  30  * w = cpowl (a, z);
  31  *
  32  *
  33  *
  34  * DESCRIPTION:
  35  *
  36  * Raises complex A to the complex Zth power.
  37  * Definition is per AMS55 # 4.2.8,
  38  * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
  39  *
  40  * ACCURACY:
  41  *
  42  *                      Relative error:
  43  * arithmetic   domain     # trials      peak         rms
  44  *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
  45  *
  46  */
  47
  48 #include <complex.h>
  49 #include "math.h"
  50
  51 #include "math_private.h"
  52
  53 long double complex
  54 cpowl(long double complex a, long double complex z)
  55 {
  56         long double complex w;
  57         long double x, y, r, theta, absa, arga;
  58
  59         x = creall(z);
  60         y = cimagl(z);
  61         absa = cabsl(a);
  62         if (absa == 0.0L) {
  63                 return (0.0L + 0.0L * I);
  64         }
  65         arga = cargl(a);
  66         r = powl(absa, x);
  67         theta = x * arga;
  68         if (y != 0.0L) {
  69                 r = r * expl(-y * arga);
  70                 theta = theta + y * logl(absa);
  71         }
  72         w = r * cosl(theta) + (r * sinl(theta)) * I;
  73         return (w);
  74 }