libquadmath/math/cacoshq.c

   1 /* Return arc hyperbole cosine for __float128 value.
   2    Copyright (C) 1997, 1998, 2006 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 "quadmath-imp.h"
  22
  23
  24 __complex128
  25 cacoshq (__complex128 x)
  26 {
  27   __complex128 res;
  28   int rcls = fpclassifyq (__real__ x);
  29   int icls = fpclassifyq (__imag__ x);
  30
  31   if (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE)
  32     {
  33       if (icls == QUADFP_INFINITE)
  34         {
  35           __real__ res = HUGE_VALQ;
  36
  37           if (rcls == QUADFP_NAN)
  38             __imag__ res = nanq ("");
  39           else
  40             __imag__ res = copysignq ((rcls == QUADFP_INFINITE
  41                                        ? (__real__ x < 0.0
  42                                           ? M_PIq - M_PI_4q : M_PI_4q)
  43                                        : M_PI_2q), __imag__ x);
  44         }
  45       else if (rcls == QUADFP_INFINITE)
  46         {
  47           __real__ res = HUGE_VALQ;
  48
  49           if (icls >= QUADFP_ZERO)
  50             __imag__ res = copysignq (signbitq (__real__ x) ? M_PIq : 0.0,
  51                                       __imag__ x);
  52           else
  53             __imag__ res = nanq ("");
  54         }
  55       else
  56         {
  57           __real__ res = nanq ("");
  58           __imag__ res = nanq ("");
  59         }
  60     }
  61   else if (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)
  62     {
  63       __real__ res = 0.0;
  64       __imag__ res = copysignq (M_PI_2q, __imag__ x);
  65     }
  66   /* The factor 16 is just a guess.  */
  67   else if (16.0Q * fabsq (__imag__ x) < fabsq (__real__ x))
  68     {
  69       /* Kahan's formula which avoid cancellation through subtraction in
  70          some cases.  */
  71       res = 2.0Q * clogq (csqrtq ((x + 1.0Q) / 2.0Q)
  72                             + csqrtq ((x - 1.0Q) / 2.0Q));
  73       if (signbitq (__real__ res))
  74         __real__ res = 0.0Q;
  75     }
  76   else
  77     {
  78       __complex128 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 = csqrtq (y);
  84
  85       if (signbitq (x))
  86         y = -y;
  87
  88       __real__ y += __real__ x;
  89       __imag__ y += __imag__ x;
  90
  91       res = clogq (y);
  92     }
  93
  94   return res;
  95 }