math/s_casinhf.c

   1 /* Return arc hyperbole sine for float 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 #include <float.h>
  24
  25 __complex__ float
  26 __casinhf (__complex__ float x)
  27 {
  28   __complex__ float 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 = __copysignf (HUGE_VALF, __real__ x);
  37
  38           if (rcls == FP_NAN)
  39             __imag__ res = __nanf ("");
  40           else
  41             __imag__ res = __copysignf (rcls >= FP_ZERO ? M_PI_2 : M_PI_4,
  42                                         __imag__ x);
  43         }
  44       else if (rcls <= FP_INFINITE)
  45         {
  46           __real__ res = __real__ x;
  47           if ((rcls == FP_INFINITE && icls >= FP_ZERO)
  48               || (rcls == FP_NAN && icls == FP_ZERO))
  49             __imag__ res = __copysignf (0.0, __imag__ x);
  50           else
  51             __imag__ res = __nanf ("");
  52         }
  53       else
  54         {
  55           __real__ res = __nanf ("");
  56           __imag__ res = __nanf ("");
  57         }
  58     }
  59   else if (rcls == FP_ZERO && icls == FP_ZERO)
  60     {
  61       res = x;
  62     }
  63   else
  64     {
  65       float rx, ix;
  66       __complex__ float y;
  67
  68       /* Avoid cancellation by reducing to the first quadrant.  */
  69       rx = fabsf (__real__ x);
  70       ix = fabsf (__imag__ x);
  71
  72       if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_EPSILON)
  73         {
  74           /* For large x in the first quadrant, x + csqrt (1 + x * x)
  75              is sufficiently close to 2 * x to make no significant
  76              difference to the result; avoid possible overflow from
  77              the squaring and addition.  */
  78           __real__ y = rx;
  79           __imag__ y = ix;
  80           res = __clogf (y);
  81           __real__ res += (float) M_LN2;
  82         }
  83       else
  84         {
  85           __real__ y = (rx - ix) * (rx + ix) + 1.0;
  86           __imag__ y = 2.0 * rx * ix;
  87
  88           y = __csqrtf (y);
  89
  90           __real__ y += rx;
  91           __imag__ y += ix;
  92
  93           res = __clogf (y);
  94         }
  95
  96       /* Give results the correct sign for the original argument.  */
  97       __real__ res = __copysignf (__real__ res, __real__ x);
  98       __imag__ res = __copysignf (__imag__ res, __imag__ x);
  99     }
 100
 101   return res;
 102 }
 103 #ifndef __casinhf
 104 weak_alias (__casinhf, casinhf)
 105 #endif