compiler/stdc/math/s_catan.c

   1 /*      $OpenBSD: s_catan.c,v 1.6 2013/07/03 04:46:36 espie 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 /*                                                      catan()
  19  *
  20  *      Complex circular arc tangent
  21  *
  22  *
  23  *
  24  * SYNOPSIS:
  25  *
  26  * double complex catan();
  27  * double complex z, w;
  28  *
  29  * w = catan (z);
  30  *
  31  *
  32  *
  33  * DESCRIPTION:
  34  *
  35  * If
  36  *     z = x + iy,
  37  *
  38  * then
  39  *          1       (    2x     )
  40  * Re w  =  - arctan(-----------)  +  k PI
  41  *          2       (     2    2)
  42  *                  (1 - x  - y )
  43  *
  44  *               ( 2         2)
  45  *          1    (x  +  (y+1) )
  46  * Im w  =  - log(------------)
  47  *          4    ( 2         2)
  48  *               (x  +  (y-1) )
  49  *
  50  * Where k is an arbitrary integer.
  51  *
  52  * catan(z) = -i catanh(iz).
  53  *
  54  * ACCURACY:
  55  *
  56  *                      Relative error:
  57  * arithmetic   domain     # trials      peak         rms
  58  *    DEC       -10,+10      5900       1.3e-16     7.8e-18
  59  *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
  60  * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
  61  * had peak relative error 1.5e-16, rms relative error
  62  * 2.9e-17.  See also clog().
  63  */
  64
  65 #include <float.h>
  66 #include <complex.h>
  67 #include "math.h"
  68
  69 #define MAXNUM 1.0e308
  70
  71 static const double DP1 = 3.14159265160560607910E0;
  72 static const double DP2 = 1.98418714791870343106E-9;
  73 static const double DP3 = 1.14423774522196636802E-17;
  74
  75 static double
  76 _redupi(double x)
  77 {
  78         double t;
  79         long i;
  80
  81         t = x/M_PI;
  82         if(t >= 0.0)
  83                 t += 0.5;
  84         else
  85                 t -= 0.5;
  86
  87         i = t;  /* the multiple */
  88         t = i;
  89         t = ((x - t * DP1) - t * DP2) - t * DP3;
  90         return (t);
  91 }
  92
  93 double complex
  94 catan(double complex z)
  95 {
  96         double complex w;
  97         double a, t, x, x2, y;
  98
  99         x = creal (z);
 100         y = cimag (z);
 101
 102         if ((x == 0.0) && (y > 1.0))
 103                 goto ovrf;
 104
 105         x2 = x * x;
 106         a = 1.0 - x2 - (y * y);
 107         if (a == 0.0)
 108                 goto ovrf;
 109
 110         t = 0.5 * atan2 (2.0 * x, a);
 111         w = _redupi (t);
 112
 113         t = y - 1.0;
 114         a = x2 + (t * t);
 115         if (a == 0.0)
 116         goto ovrf;
 117
 118         t = y + 1.0;
 119         a = (x2 + (t * t))/a;
 120         w = w + (0.25 * log (a)) * I;
 121         return (w);
 122
 123 ovrf:
 124         /*mtherr ("catan", OVERFLOW);*/
 125         w = MAXNUM + MAXNUM * I;
 126         return (w);
 127 }
 128
 129 #if     LDBL_MANT_DIG == DBL_MANT_DIG
 130 AROS_MAKE_ASM_SYM(typeof(catanl), catanl, AROS_CSYM_FROM_ASM_NAME(catanl), AROS_CSYM_FROM_ASM_NAME(catan));
 131 AROS_EXPORT_ASM_SYM(AROS_CSYM_FROM_ASM_NAME(catanl));
 132 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */