gonzui

    1: /*      $OpenBSD: s_casinf.c,v 1.3 2011/07/20 19:28:33 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: /*                                                      casinf()
   19:  *
   20:  *      Complex circular arc sine
   21:  *
   22:  *
   23:  *
   24:  * SYNOPSIS:
   25:  *
   26:  * void casinf();
   27:  * cmplxf z, w;
   28:  *
   29:  * casinf( &z, &w );
   30:  *
   31:  *
   32:  *
   33:  * DESCRIPTION:
   34:  *
   35:  * Inverse complex sine:
   36:  *
   37:  *                               2
   38:  * w = -i clog( iz + csqrt( 1 - z ) ).
   39:  *
   40:  *
   41:  * ACCURACY:
   42:  *
   43:  *                      Relative error:
   44:  * arithmetic   domain     # trials      peak         rms
   45:  *    IEEE      -10,+10     30000       1.1e-5      1.5e-6
   46:  * Larger relative error can be observed for z near zero.
   47:  *
   48:  */
   49: 
   50: #include <complex.h>
   51: #include <math.h>
   52: 
   53: float complex
   54: casinf(float complex z)
   55: {
   56:         float complex w;
   57:         float x, y;
   58:         static float complex ca, ct, zz, z2;
   59:         /*
   60:         float cn, n;
   61:         static float a, b, s, t, u, v, y2;
   62:         static cmplxf sum;
   63:         */
   64: 
   65:         x = crealf(z);
   66:         y = cimagf(z);
   67: 
   68:         if(y == 0.0f) {
   69:                 if(fabsf(x) > 1.0f) {
   70:                         w = (float)M_PI_2 + 0.0f * I;
   71:                         /*mtherr( "casinf", DOMAIN );*/
   72:                 }
   73:                 else {
   74:                         w = asinf (x) + 0.0f * I;
   75:                 }
   76:                 return (w);
   77:         }
   78: 
   79:         /* Power series expansion */
   80:         /*
   81:         b = cabsf(z);
   82:         if(b < 0.125) {
   83:                 z2.r = (x - y) * (x + y);
   84:                 z2.i = 2.0 * x * y;
   85: 
   86:                 cn = 1.0;
   87:                 n = 1.0;
   88:                 ca.r = x;
   89:                 ca.i = y;
   90:                 sum.r = x;
   91:                 sum.i = y;
   92:                 do {
   93:                         ct.r = z2.r * ca.r  -  z2.i * ca.i;
   94:                         ct.i = z2.r * ca.i  +  z2.i * ca.r;
   95:                         ca.r = ct.r;
   96:                         ca.i = ct.i;
   97: 
   98:                         cn *= n;
   99:                         n += 1.0;
  100:                         cn /= n;
  101:                         n += 1.0;
  102:                         b = cn/n;
  103: 
  104:                         ct.r *= b;
  105:                         ct.i *= b;
  106:                         sum.r += ct.r;
  107:                         sum.i += ct.i;
  108:                         b = fabsf(ct.r) + fabsf(ct.i);
  109:                 }
  110:                 while(b > MACHEPF);
  111:                 w->r = sum.r;
  112:                 w->i = sum.i;
  113:                 return;
  114:         }
  115:         */
  116: 
  117: 
  118:         ca = x + y * I;
  119:         ct = ca * I;   /* iz */
  120:         /* sqrt( 1 - z*z) */
  121:         /* cmul( &ca, &ca, &zz ) */
  122:         /*x * x  -  y * y */
  123:         zz = (x - y) * (x + y) + (2.0f * x * y) * I;
  124:         zz = 1.0f - crealf(zz) - cimagf(zz) * I;
  125:         z2 = csqrtf (zz);
  126: 
  127:         zz = ct + z2;
  128:         zz = clogf (zz);
  129:         /* multiply by 1/i = -i */
  130:         w = zz * (-1.0f * I);
  131:         return (w);
  132: }