math/s_cacoshf.c

   1 /* Return arc hyperbole cosine for float 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
  24 #include <math_private.h>
  25
  26 __complex__ float
  27 __cacoshf (__complex__ float x)
  28 {
  29   __complex__ float 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_VALF;
  38
  39           if (rcls == FP_NAN)
  40             __imag__ res = __nanf ("");
  41           else
  42             __imag__ res = __copysignf ((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_VALF;
  50
  51           if (icls >= FP_ZERO)
  52             __imag__ res = __copysignf (signbit (__real__ x) ? M_PI : 0.0,
  53                                         __imag__ x);
  54           else
  55             __imag__ res = __nanf ("");
  56         }
  57       else
  58         {
  59           __real__ res = __nanf ("");
  60           __imag__ res = __nanf ("");
  61         }
  62     }
  63   else if (rcls == FP_ZERO && icls == FP_ZERO)
  64     {
  65       __real__ res = 0.0;
  66       __imag__ res = __copysignf (M_PI_2, __imag__ x);
  67     }
  68   /* The factor 16 is just a guess.  */
  69   else if (16.0 * fabsf (__imag__ x) < fabsf (__real__ x))
  70     /* Kahan's formula which avoid cancellation through subtraction in
  71        some cases.  */
  72     res = 2.0 * __clogf (__csqrtf ((x + 1.0) / 2.0)
  73                          + __csqrtf ((x - 1.0) / 2.0));
  74   else
  75     {
  76       __complex__ float y;
  77
  78       __real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
  79       __imag__ y = 2.0 * __real__ x * __imag__ x;
  80
  81       y = __csqrtf (y);
  82
  83       if (signbit (__real__ x))
  84         y = -y;
  85
  86       __real__ y += __real__ x;
  87       __imag__ y += __imag__ x;
  88
  89       res = __clogf (y);
  90     }
  91
  92   return res;
  93 }
  94 #ifndef __cacoshf
  95 weak_alias (__cacoshf, cacoshf)
  96 #endif