compiler/stdc/math/s_catanl.c

   1 /*      $OpenBSD: s_catanl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $   */
   2
   3 /*
   4  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
   5  *
   6  * Permission to use, copy, modify, and distribute this software for any
   7  * purpose with or without fee is hereby granted, provided that the above
   8  * copyright notice and this permission notice appear in all copies.
   9  *
  10  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  11  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  12  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  13  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  14  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  15  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  16  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  17  */
  18
  19 /*                                                      catanl()
  20  *
  21  *      Complex circular arc tangent
  22  *
  23  *
  24  *
  25  * SYNOPSIS:
  26  *
  27  * long double complex catanl();
  28  * long double complex z, w;
  29  *
  30  * w = catanl( z );
  31  *
  32  *
  33  *
  34  * DESCRIPTION:
  35  *
  36  * If
  37  *     z = x + iy,
  38  *
  39  * then
  40  *          1       (    2x     )
  41  * Re w  =  - arctan(-----------)  +  k PI
  42  *          2       (     2    2)
  43  *                  (1 - x  - y )
  44  *
  45  *               ( 2         2)
  46  *          1    (x  +  (y+1) )
  47  * Im w  =  - log(------------)
  48  *          4    ( 2         2)
  49  *               (x  +  (y-1) )
  50  *
  51  * Where k is an arbitrary integer.
  52  *
  53  *
  54  *
  55  * ACCURACY:
  56  *
  57  *                      Relative error:
  58  * arithmetic   domain     # trials      peak         rms
  59  *    DEC       -10,+10      5900       1.3e-16     7.8e-18
  60  *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
  61  * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
  62  * had peak relative error 1.5e-16, rms relative error
  63  * 2.9e-17.  See also clog().
  64  */
  65
  66 #include <float.h>
  67 #include <complex.h>
  68 #include "math.h"
  69
  70 static const long double PIL = 3.141592653589793238462643383279502884197169L;
  71 static const long double DP1 = 3.14159265358979323829596852490908531763125L;
  72 static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
  73 static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
  74
  75 static long double
  76 redupil(long double x)
  77 {
  78         long double t;
  79         long i;
  80
  81         t = x / PIL;
  82         if (t >= 0.0L)
  83                 t += 0.5L;
  84         else
  85                 t -= 0.5L;
  86
  87         i = t;  /* the multiple */
  88         t = i;
  89         t = ((x - t * DP1) - t * DP2) - t * DP3;
  90         return (t);
  91 }
  92
  93 long double complex
  94 catanl(long double complex z)
  95 {
  96         long double complex w;
  97         long double a, t, x, x2, y;
  98
  99         x = creall(z);
 100         y = cimagl(z);
 101
 102         if ((x == 0.0L) && (y > 1.0L))
 103                 goto ovrf;
 104
 105         x2 = x * x;
 106         a = 1.0L - x2 - (y * y);
 107         if (a == 0.0L)
 108                 goto ovrf;
 109
 110         t = atan2l(2.0L * x, a) * 0.5L;
 111         w = redupil(t);
 112
 113         t = y - 1.0L;
 114         a = x2 + (t * t);
 115         if (a == 0.0L)
 116                 goto ovrf;
 117
 118         t = y + 1.0L;
 119         a = (x2 + (t * t)) / a;
 120         w = w + (0.25L * logl(a)) * I;
 121         return (w);
 122
 123 ovrf:
 124         /*mtherr( "catanl", OVERFLOW );*/
 125         w = LDBL_MAX + LDBL_MAX * I;
 126         return (w);
 127 }