gonzui

    1: /*      $OpenBSD: s_csin.c,v 1.2 2011/07/08 19:25:31 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: /* LINTLIBRARY */
   19: 
   20: /*                                                      csin()
   21:  *
   22:  *      Complex circular sine
   23:  *
   24:  *
   25:  *
   26:  * SYNOPSIS:
   27:  *
   28:  * double complex csin();
   29:  * double complex z, w;
   30:  *
   31:  * w = csin (z);
   32:  *
   33:  *
   34:  *
   35:  * DESCRIPTION:
   36:  *
   37:  * If
   38:  *     z = x + iy,
   39:  *
   40:  * then
   41:  *
   42:  *     w = sin x  cosh y  +  i cos x sinh y.
   43:  *
   44:  * csin(z) = -i csinh(iz).
   45:  *
   46:  * ACCURACY:
   47:  *
   48:  *                      Relative error:
   49:  * arithmetic   domain     # trials      peak         rms
   50:  *    DEC       -10,+10      8400       5.3e-17     1.3e-17
   51:  *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
   52:  * Also tested by csin(casin(z)) = z.
   53:  *
   54:  */
   55: 
   56: #include <sys/cdefs.h>
   57: #include <complex.h>
   58: #include <float.h>
   59: #include <math.h>
   60: 
   61: /* calculate cosh and sinh */
   62: 
   63: static void
   64: cchsh(double x, double *c, double *s)
   65: {
   66:         double e, ei;
   67: 
   68:         if (fabs(x) <= 0.5) {
   69:                 *c = cosh(x);
   70:                 *s = sinh(x);
   71:         }
   72:         else {
   73:                 e = exp(x);
   74:                 ei = 0.5/e;
   75:                 e = 0.5 * e;
   76:                 *s = e - ei;
   77:                 *c = e + ei;
   78:         }
   79: }
   80: 
   81: double complex
   82: csin(double complex z)
   83: {
   84:         double complex w;
   85:         double ch, sh;
   86: 
   87:         cchsh( cimag (z), &ch, &sh );
   88:         w = sin (creal(z)) * ch + (cos (creal(z)) * sh) * I;
   89:         return (w);
   90: }
   91: 
   92: #if     LDBL_MANT_DIG == 53
   93: #ifdef  lint
   94: /* PROTOLIB1 */
   95: long double complex csinl(long double complex);
   96: #else   /* lint */
   97: __weak_alias(csinl, csin);
   98: #endif  /* lint */
   99: #endif  /* LDBL_MANT_DIG == 53 */