math/s_cacosh.c

   1 /* Return arc hyperbole cosine for double value.
   2    Copyright (C) 1997, 2006, 2011 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, write to the Free
  18    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  19    02111-1307 USA.  */
  20
  21 #include <complex.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24
  25
  26 __complex__ double
  27 __cacosh (__complex__ double x)
  28 {
  29   __complex__ double res;
  30   int rcls = fpclassify (__real__ x);
  31   int icls = fpclassify (__imag__ x);
  32
  33   if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
  34     {
  35       if (icls == FP_INFINITE)
  36         {
  37           __real__ res = HUGE_VAL;
  38
  39           if (rcls == FP_NAN)
  40             __imag__ res = __nan ("");
  41           else
  42             __imag__ res = __copysign ((rcls == FP_INFINITE
  43                                         ? (__real__ x < 0.0
  44                                            ? M_PI - M_PI_4 : M_PI_4)
  45                                         : M_PI_2), __imag__ x);
  46         }
  47       else if (rcls == FP_INFINITE)
  48         {
  49           __real__ res = HUGE_VAL;
  50
  51           if (icls >= FP_ZERO)
  52             __imag__ res = __copysign (signbit (__real__ x) ? M_PI : 0.0,
  53                                        __imag__ x);
  54           else
  55             __imag__ res = __nan ("");
  56         }
  57       else
  58         {
  59           __real__ res = __nan ("");
  60           __imag__ res = __nan ("");
  61         }
  62     }
  63   else if (rcls == FP_ZERO && icls == FP_ZERO)
  64     {
  65       __real__ res = 0.0;
  66       __imag__ res = __copysign (M_PI_2, __imag__ x);
  67     }
  68   /* The factor 16 is just a guess.  */
  69   else if (16.0 * fabs (__imag__ x) < fabs (__real__ x))
  70     /* Kahan's formula which avoid cancellation through subtraction in
  71        some cases.  */
  72     res = 2.0 * __clog (__csqrt ((x + 1.0) / 2.0) + __csqrt ((x - 1.0) / 2.0));
  73   else
  74     {
  75       __complex__ double y;
  76
  77       __real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
  78       __imag__ y = 2.0 * __real__ x * __imag__ x;
  79
  80       y = __csqrt (y);
  81
  82       if (signbit (__real__ x))
  83         y = -y;
  84
  85       __real__ y += __real__ x;
  86       __imag__ y += __imag__ x;
  87
  88       res = __clog (y);
  89     }
  90
  91   return res;
  92 }
  93 weak_alias (__cacosh, cacosh)
  94 #ifdef NO_LONG_DOUBLE
  95 strong_alias (__cacosh, __cacoshl)
  96 weak_alias (__cacosh, cacoshl)
  97 #endif