src/complex/catanf.c

   1 /* origin: OpenBSD /usr/src/lib/libm/src/s_catanf.c */
   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  *      Complex circular arc tangent
  19  *
  20  *
  21  * SYNOPSIS:
  22  *
  23  * float complex catanf();
  24  * float complex z, w;
  25  *
  26  * w = catanf( z );
  27  *
  28  *
  29  * DESCRIPTION:
  30  *
  31  * If
  32  *     z = x + iy,
  33  *
  34  * then
  35  *          1       (    2x     )
  36  * Re w  =  - arctan(-----------)  +  k PI
  37  *          2       (     2    2)
  38  *                  (1 - x  - y )
  39  *
  40  *               ( 2         2)
  41  *          1    (x  +  (y+1) )
  42  * Im w  =  - log(------------)
  43  *          4    ( 2         2)
  44  *               (x  +  (y-1) )
  45  *
  46  * Where k is an arbitrary integer.
  47  *
  48  *
  49  * ACCURACY:
  50  *
  51  *                      Relative error:
  52  * arithmetic   domain     # trials      peak         rms
  53  *    IEEE      -10,+10     30000        2.3e-6      5.2e-8
  54  */
  55
  56 #include "complex_impl.h"
  57
  58 #define MAXNUMF 1.0e38F
  59
  60 static const double DP1 = 3.140625;
  61 static const double DP2 = 9.67502593994140625E-4;
  62 static const double DP3 = 1.509957990978376432E-7;
  63
  64 static const float float_pi = M_PI;
  65
  66 static float _redupif(float xx)
  67 {
  68         float x, t;
  69         long i;
  70
  71         x = xx;
  72         t = x/float_pi;
  73         if (t >= 0.0f)
  74                 t += 0.5f;
  75         else
  76                 t -= 0.5f;
  77
  78         i = t;  /* the multiple */
  79         t = i;
  80         t = ((x - t * DP1) - t * DP2) - t * DP3;
  81         return t;
  82 }
  83
  84 float complex catanf(float complex z)
  85 {
  86         float complex w;
  87         float a, t, x, x2, y;
  88
  89         x = crealf(z);
  90         y = cimagf(z);
  91
  92         x2 = x * x;
  93         a = 1.0f - x2 - (y * y);
  94
  95         t = 0.5f * atan2f(2.0f * x, a);
  96         w = _redupif(t);
  97
  98         t = y - 1.0f;
  99         a = x2 + (t * t);
 100
 101         t = y + 1.0f;
 102         a = (x2 + (t * t))/a;
 103         w = CMPLXF(w, 0.25f * logf(a));
 104         return w;
 105 }