lib/libm/src/s_cpow.c

   1 /*      $OpenBSD: s_cpow.c,v 1.5 2013/03/28 18:09:38 martynas 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 /*                                                      cpow
  19  *
  20  *      Complex power function
  21  *
  22  *
  23  *
  24  * SYNOPSIS:
  25  *
  26  * double complex cpow();
  27  * double complex a, z, w;
  28  *
  29  * w = cpow (a, z);
  30  *
  31  *
  32  *
  33  * DESCRIPTION:
  34  *
  35  * Raises complex A to the complex Zth power.
  36  * Definition is per AMS55 # 4.2.8,
  37  * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
  38  *
  39  * ACCURACY:
  40  *
  41  *                      Relative error:
  42  * arithmetic   domain     # trials      peak         rms
  43  *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
  44  *
  45  */
  46
  47 #include <complex.h>
  48 #include <float.h>
  49 #include <math.h>
  50
  51 double complex
  52 cpow(double complex a, double complex z)
  53 {
  54         double complex w;
  55         double x, y, r, theta, absa, arga;
  56
  57         x = creal (z);
  58         y = cimag (z);
  59         absa = cabs (a);
  60         if (absa == 0.0) {
  61                 return (0.0 + 0.0 * I);
  62         }
  63         arga = carg (a);
  64         r = pow (absa, x);
  65         theta = x * arga;
  66         if (y != 0.0) {
  67                 r = r * exp (-y * arga);
  68                 theta = theta + y * log (absa);
  69         }
  70         w = r * cos (theta) + (r * sin (theta)) * I;
  71         return (w);
  72 }
  73
  74 #if     LDBL_MANT_DIG == 53
  75 __strong_alias(cpowl, cpow);
  76 #endif  /* LDBL_MANT_DIG == 53 */