gonzui

    1: /*      $OpenBSD: s_ctanf.c,v 1.2 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: /*                                                      ctanf()
   19:  *
   20:  *      Complex circular tangent
   21:  *
   22:  *
   23:  *
   24:  * SYNOPSIS:
   25:  *
   26:  * void ctanf();
   27:  * cmplxf z, w;
   28:  *
   29:  * ctanf( &z, &w );
   30:  *
   31:  *
   32:  *
   33:  * DESCRIPTION:
   34:  *
   35:  * If
   36:  *     z = x + iy,
   37:  *
   38:  * then
   39:  *
   40:  *           sin 2x  +  i sinh 2y
   41:  *     w  =  --------------------.
   42:  *            cos 2x  +  cosh 2y
   43:  *
   44:  * On the real axis the denominator is zero at odd multiples
   45:  * of PI/2.  The denominator is evaluated by its Taylor
   46:  * series near these points.
   47:  *
   48:  *
   49:  * ACCURACY:
   50:  *
   51:  *                      Relative error:
   52:  * arithmetic   domain     # trials      peak         rms
   53:  *    IEEE      -10,+10     30000       3.3e-7       5.1e-8
   54:  */
   55: 
   56: #include <complex.h>
   57: #include <math.h>
   58: 
   59: #define MACHEPF 3.0e-8
   60: #define MAXNUMF 1.0e38f
   61: 
   62: static const double DP1 = 3.140625;
   63: static const double DP2 = 9.67502593994140625E-4;
   64: static const double DP3 = 1.509957990978376432E-7;
   65: 
   66: static float
   67: _redupif(float xx)
   68: {
   69:         float x, t;
   70:         long i;
   71: 
   72:         x = xx;
   73:         t = x/(float)M_PI;
   74:         if(t >= 0.0)
   75:                 t += 0.5;
   76:         else
   77:                 t -= 0.5;
   78: 
   79:         i = t; /* the multiple */
   80:         t = i;
   81:         t = ((x - t * DP1) - t * DP2) - t * DP3;
   82:         return(t);
   83: }
   84: 
   85: /*  Taylor series expansion for cosh(2y) - cos(2x)      */
   86: 
   87: static float
   88: _ctansf(float complex z)
   89: {
   90:         float f, x, x2, y, y2, rn, t, d;
   91: 
   92:         x = fabsf(2.0f * crealf(z));
   93:         y = fabsf(2.0f * cimagf(z));
   94: 
   95:         x = _redupif(x);
   96: 
   97:         x = x * x;
   98:         y = y * y;
   99:         x2 = 1.0f;
  100:         y2 = 1.0f;
  101:         f = 1.0f;
  102:         rn = 0.0f;
  103:         d = 0.0f;
  104:         do {
  105:                 rn += 1.0f;
  106:                 f *= rn;
  107:                 rn += 1.0f;
  108:                 f *= rn;
  109:                 x2 *= x;
  110:                 y2 *= y;
  111:                 t = y2 + x2;
  112:                 t /= f;
  113:                 d += t;
  114: 
  115:                 rn += 1.0f;
  116:                 f *= rn;
  117:                 rn += 1.0f;
  118:                 f *= rn;
  119:                 x2 *= x;
  120:                 y2 *= y;
  121:                 t = y2 - x2;
  122:                 t /= f;
  123:                 d += t;
  124:         }
  125:         while (fabsf(t/d) > MACHEPF)
  126:                 ;
  127:         return(d);
  128: }
  129: 
  130: float complex
  131: ctanf(float complex z)
  132: {
  133:         float complex w;
  134:         float d;
  135: 
  136:         d = cosf( 2.0f * crealf(z) ) + coshf( 2.0f * cimagf(z) );
  137: 
  138:         if(fabsf(d) < 0.25f)
  139:                 d = _ctansf(z);
  140: 
  141:         if (d == 0.0f) {
  142:                 /*mtherr( "ctanf", OVERFLOW );*/
  143:                 w = MAXNUMF + MAXNUMF * I;
  144:                 return (w);
  145:         }
  146:         w = sinf (2.0f * crealf(z)) / d + (sinhf (2.0f * cimagf(z)) / d) * I;
  147:         return (w);
  148: }