math/s_cacosh.c

   1 /* Return arc hyperbole cosine for double value.
   2    Copyright (C) 1997-2013 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, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <complex.h>
  21 #include <math.h>
  22 #include <math_private.h>
  23
  24
  25 __complex__ double
  26 __cacosh (__complex__ double x)
  27 {
  28   __complex__ double res;
  29   int rcls = fpclassify (__real__ x);
  30   int icls = fpclassify (__imag__ x);
  31
  32   if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
  33     {
  34       if (icls == FP_INFINITE)
  35         {
  36           __real__ res = HUGE_VAL;
  37
  38           if (rcls == FP_NAN)
  39             __imag__ res = __nan ("");
  40           else
  41             __imag__ res = __copysign ((rcls == FP_INFINITE
  42                                         ? (__real__ x < 0.0
  43                                            ? M_PI - M_PI_4 : M_PI_4)
  44                                         : M_PI_2), __imag__ x);
  45         }
  46       else if (rcls == FP_INFINITE)
  47         {
  48           __real__ res = HUGE_VAL;
  49
  50           if (icls >= FP_ZERO)
  51             __imag__ res = __copysign (signbit (__real__ x) ? M_PI : 0.0,
  52                                        __imag__ x);
  53           else
  54             __imag__ res = __nan ("");
  55         }
  56       else
  57         {
  58           __real__ res = __nan ("");
  59           __imag__ res = __nan ("");
  60         }
  61     }
  62   else if (rcls == FP_ZERO && icls == FP_ZERO)
  63     {
  64       __real__ res = 0.0;
  65       __imag__ res = __copysign (M_PI_2, __imag__ x);
  66     }
  67   /* The factor 16 is just a guess.  */
  68   else if (16.0 * fabs (__imag__ x) < fabs (__real__ x))
  69     {
  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       if (signbit (__real__ res))
  74         __real__ res = 0.0;
  75     }
  76   else
  77     {
  78       __complex__ double y;
  79
  80       __real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
  81       __imag__ y = 2.0 * __real__ x * __imag__ x;
  82
  83       y = __csqrt (y);
  84
  85       if (signbit (__real__ x))
  86         y = -y;
  87
  88       __real__ y += __real__ x;
  89       __imag__ y += __imag__ x;
  90
  91       res = __clog (y);
  92     }
  93
  94   return res;
  95 }
  96 weak_alias (__cacosh, cacosh)
  97 #ifdef NO_LONG_DOUBLE
  98 strong_alias (__cacosh, __cacoshl)
  99 weak_alias (__cacosh, cacoshl)
 100 #endif