lib/libm/src/s_csin.c

   1 /*      $OpenBSD: s_csin.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 /*                                                      csin()
  19  *
  20  *      Complex circular sine
  21  *
  22  *
  23  *
  24  * SYNOPSIS:
  25  *
  26  * double complex csin();
  27  * double complex z, w;
  28  *
  29  * w = csin (z);
  30  *
  31  *
  32  *
  33  * DESCRIPTION:
  34  *
  35  * If
  36  *     z = x + iy,
  37  *
  38  * then
  39  *
  40  *     w = sin x  cosh y  +  i cos x sinh y.
  41  *
  42  * csin(z) = -i csinh(iz).
  43  *
  44  * ACCURACY:
  45  *
  46  *                      Relative error:
  47  * arithmetic   domain     # trials      peak         rms
  48  *    DEC       -10,+10      8400       5.3e-17     1.3e-17
  49  *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
  50  * Also tested by csin(casin(z)) = z.
  51  *
  52  */
  53
  54 #include <complex.h>
  55 #include <float.h>
  56 #include <math.h>
  57
  58 /* calculate cosh and sinh */
  59
  60 static void
  61 cchsh(double x, double *c, double *s)
  62 {
  63         double e, ei;
  64
  65         if (fabs(x) <= 0.5) {
  66                 *c = cosh(x);
  67                 *s = sinh(x);
  68         }
  69         else {
  70                 e = exp(x);
  71                 ei = 0.5/e;
  72                 e = 0.5 * e;
  73                 *s = e - ei;
  74                 *c = e + ei;
  75         }
  76 }
  77
  78 double complex
  79 csin(double complex z)
  80 {
  81         double complex w;
  82         double ch, sh;
  83
  84         cchsh( cimag (z), &ch, &sh );
  85         w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I;
  86         return (w);
  87 }
  88
  89 #if     LDBL_MANT_DIG == 53
  90 __strong_alias(csinl, csin);
  91 #endif  /* LDBL_MANT_DIG == 53 */