compiler/stdc/math/s_csinl.c

   1 /*      $OpenBSD: s_csinl.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 /*                                                      csinl()
  20  *
  21  *      Complex circular sine
  22  *
  23  *
  24  *
  25  * SYNOPSIS:
  26  *
  27  * long double complex csinl();
  28  * long double complex z, w;
  29  *
  30  * w = csinl( z );
  31  *
  32  *
  33  *
  34  * DESCRIPTION:
  35  *
  36  * If
  37  *     z = x + iy,
  38  *
  39  * then
  40  *
  41  *     w = sin x  cosh y  +  i cos x sinh y.
  42  *
  43  *
  44  *
  45  * ACCURACY:
  46  *
  47  *                      Relative error:
  48  * arithmetic   domain     # trials      peak         rms
  49  *    DEC       -10,+10      8400       5.3e-17     1.3e-17
  50  *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
  51  * Also tested by csin(casin(z)) = z.
  52  *
  53  */
  54
  55 #include <complex.h>
  56 #include "math.h"
  57
  58 static void
  59 cchshl(long double x, long double *c, long double *s)
  60 {
  61         long double e, ei;
  62
  63         if(fabsl(x) <= 0.5L) {
  64                 *c = coshl(x);
  65                 *s = sinhl(x);
  66         } else {
  67                 e = expl(x);
  68                 ei = 0.5L/e;
  69                 e = 0.5L * e;
  70                 *s = e - ei;
  71                 *c = e + ei;
  72         }
  73 }
  74
  75 long double complex
  76 csinl(long double complex z)
  77 {
  78         long double complex w;
  79         long double ch, sh;
  80
  81         cchshl(cimagl(z), &ch, &sh);
  82         w = sinl(creall(z)) * ch + (cosl(creall(z)) * sh) * I;
  83         return (w);
  84 }