gonzui

    1: /*      $OpenBSD: s_casin.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: /*                                                      casin()
   21:  *
   22:  *      Complex circular arc sine
   23:  *
   24:  *
   25:  *
   26:  * SYNOPSIS:
   27:  *
   28:  * double complex casin();
   29:  * double complex z, w;
   30:  *
   31:  * w = casin (z);
   32:  *
   33:  *
   34:  *
   35:  * DESCRIPTION:
   36:  *
   37:  * Inverse complex sine:
   38:  *
   39:  *                               2
   40:  * w = -i clog( iz + csqrt( 1 - z ) ).
   41:  *
   42:  * casin(z) = -i casinh(iz)
   43:  *
   44:  * ACCURACY:
   45:  *
   46:  *                      Relative error:
   47:  * arithmetic   domain     # trials      peak         rms
   48:  *    DEC       -10,+10     10100       2.1e-15     3.4e-16
   49:  *    IEEE      -10,+10     30000       2.2e-14     2.7e-15
   50:  * Larger relative error can be observed for z near zero.
   51:  * Also tested by csin(casin(z)) = z.
   52:  */
   53: 
   54: #include <sys/cdefs.h>
   55: #include <complex.h>
   56: #include <float.h>
   57: #include <math.h>
   58: 
   59: double complex
   60: casin(double complex z)
   61: {
   62:         double complex w;
   63:         static double complex ca, ct, zz, z2;
   64:         double x, y;
   65: 
   66:         x = creal (z);
   67:         y = cimag (z);
   68: 
   69:         if (y == 0.0) {
   70:                 if (fabs(x) > 1.0) {
   71:                         w = M_PI_2 + 0.0 * I;
   72:                         /*mtherr ("casin", DOMAIN);*/
   73:                 }
   74:                 else {
   75:                         w = asin (x) + 0.0 * I;
   76:                 }
   77:                 return (w);
   78:         }
   79: 
   80:         /* Power series expansion */
   81:         /*
   82:         b = cabs(z);
   83:         if( b < 0.125 ) {
   84:                 z2.r = (x - y) * (x + y);
   85:                 z2.i = 2.0 * x * y;
   86: 
   87:                 cn = 1.0;
   88:                 n = 1.0;
   89:                 ca.r = x;
   90:                 ca.i = y;
   91:                 sum.r = x;
   92:                 sum.i = y;
   93:                 do {
   94:                         ct.r = z2.r * ca.r  -  z2.i * ca.i;
   95:                         ct.i = z2.r * ca.i  +  z2.i * ca.r;
   96:                         ca.r = ct.r;
   97:                         ca.i = ct.i;
   98: 
   99:                         cn *= n;
  100:                         n += 1.0;
  101:                         cn /= n;
  102:                         n += 1.0;
  103:                         b = cn/n;
  104: 
  105:                         ct.r *= b;
  106:                         ct.i *= b;
  107:                         sum.r += ct.r;
  108:                         sum.i += ct.i;
  109:                         b = fabs(ct.r) + fabs(ct.i);
  110:                 }
  111:                 while( b > MACHEP );
  112:                 w->r = sum.r;
  113:                 w->i = sum.i;
  114:                 return;
  115:         }
  116:         */
  117: 
  118:         ca = x + y * I;
  119:         ct = ca * I;
  120:         /* sqrt( 1 - z*z) */
  121:         /* cmul( &ca, &ca, &zz ) */
  122:         /*x * x  -  y * y */
  123:         zz = (x - y) * (x + y) + (2.0 * x * y) * I;
  124: 
  125:         zz = 1.0 - creal(zz) - cimag(zz) * I;
  126:         z2 = csqrt (zz);
  127: 
  128:         zz = ct + z2;
  129:         zz = clog (zz);
  130:         /* multiply by 1/i = -i */
  131:         w = zz * (-1.0 * I);
  132:         return (w);
  133: }
  134: 
  135: #if     LDBL_MANT_DIG == 53
  136: #ifdef  lint
  137: /* PROTOLIB1 */
  138: long double complex casinl(long double complex);
  139: #else   /* lint */
  140: __weak_alias(casinl, casin);
  141: #endif  /* lint */
  142: #endif  /* LDBL_MANT_DIG == 53 */