lib/libm/src/s_ctan.c

   1 /*      $OpenBSD: s_ctan.c,v 1.5 2013/03/28 18:09:38 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 /*                                                      ctan()
  19  *
  20  *      Complex circular tangent
  21  *
  22  *
  23  *
  24  * SYNOPSIS:
  25  *
  26  * double complex ctan();
  27  * double complex z, w;
  28  *
  29  * w = ctan (z);
  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  * ctan(z) = -i ctanh(iz).
  49  *
  50  * ACCURACY:
  51  *
  52  *                      Relative error:
  53  * arithmetic   domain     # trials      peak         rms
  54  *    DEC       -10,+10      5200       7.1e-17     1.6e-17
  55  *    IEEE      -10,+10     30000       7.2e-16     1.2e-16
  56  * Also tested by ctan * ccot = 1 and catan(ctan(z))  =  z.
  57  */
  58
  59 #include <complex.h>
  60 #include <float.h>
  61 #include <math.h>
  62
  63 #define MACHEP 1.1e-16
  64 #define MAXNUM 1.0e308
  65
  66 static const double DP1 = 3.14159265160560607910E0;
  67 static const double DP2 = 1.98418714791870343106E-9;
  68 static const double DP3 = 1.14423774522196636802E-17;
  69
  70 static double
  71 _redupi(double x)
  72 {
  73         double t;
  74         long i;
  75
  76         t = x/M_PI;
  77         if (t >= 0.0)
  78                 t += 0.5;
  79         else
  80                 t -= 0.5;
  81
  82         i = t;  /* the multiple */
  83         t = i;
  84         t = ((x - t * DP1) - t * DP2) - t * DP3;
  85         return (t);
  86 }
  87
  88 /*  Taylor series expansion for cosh(2y) - cos(2x)      */
  89
  90 static double
  91 _ctans(double complex z)
  92 {
  93         double f, x, x2, y, y2, rn, t;
  94         double d;
  95
  96         x = fabs (2.0 * creal (z));
  97         y = fabs (2.0 * cimag(z));
  98
  99         x = _redupi(x);
 100
 101         x = x * x;
 102         y = y * y;
 103         x2 = 1.0;
 104         y2 = 1.0;
 105         f = 1.0;
 106         rn = 0.0;
 107         d = 0.0;
 108         do {
 109                 rn += 1.0;
 110                 f *= rn;
 111                 rn += 1.0;
 112                 f *= rn;
 113                 x2 *= x;
 114                 y2 *= y;
 115                 t = y2 + x2;
 116                 t /= f;
 117                 d += t;
 118
 119                 rn += 1.0;
 120                 f *= rn;
 121                 rn += 1.0;
 122                 f *= rn;
 123                 x2 *= x;
 124                 y2 *= y;
 125                 t = y2 - x2;
 126                 t /= f;
 127                 d += t;
 128         }
 129         while (fabs(t/d) > MACHEP)
 130                 ;
 131         return (d);
 132 }
 133
 134 double complex
 135 ctan(double complex z)
 136 {
 137         double complex w;
 138         double d;
 139
 140         d = cos (2.0 * creal (z)) + cosh (2.0 * cimag (z));
 141
 142         if (fabs(d) < 0.25)
 143                 d = _ctans (z);
 144
 145         if (d == 0.0) {
 146                 /*mtherr ("ctan", OVERFLOW);*/
 147                 w = MAXNUM + MAXNUM * I;
 148                 return (w);
 149         }
 150
 151         w = sin (2.0 * creal(z)) / d + (sinh (2.0 * cimag(z)) / d) * I;
 152         return (w);
 153 }
 154
 155 #if     LDBL_MANT_DIG == 53
 156 __strong_alias(ctanl, ctan);
 157 #endif  /* LDBL_MANT_DIG == 53 */