math/s_casinhl.c

   1 /* Return arc hyperbole sine for long 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 #include <float.h>
  24
  25 /* To avoid spurious overflows, use this definition to treat IBM long
  26    double as approximating an IEEE-style format.  */
  27 #if LDBL_MANT_DIG == 106
  28 # undef LDBL_EPSILON
  29 # define LDBL_EPSILON 0x1p-106L
  30 #endif
  31
  32 __complex__ long double
  33 __casinhl (__complex__ long double x)
  34 {
  35   __complex__ long double res;
  36   int rcls = fpclassify (__real__ x);
  37   int icls = fpclassify (__imag__ x);
  38
  39   if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
  40     {
  41       if (icls == FP_INFINITE)
  42         {
  43           __real__ res = __copysignl (HUGE_VALL, __real__ x);
  44
  45           if (rcls == FP_NAN)
  46             __imag__ res = __nanl ("");
  47           else
  48             __imag__ res = __copysignl (rcls >= FP_ZERO ? M_PI_2l : M_PI_4l,
  49                                         __imag__ x);
  50         }
  51       else if (rcls <= FP_INFINITE)
  52         {
  53           __real__ res = __real__ x;
  54           if ((rcls == FP_INFINITE && icls >= FP_ZERO)
  55               || (rcls == FP_NAN && icls == FP_ZERO))
  56             __imag__ res = __copysignl (0.0, __imag__ x);
  57           else
  58             __imag__ res = __nanl ("");
  59         }
  60       else
  61         {
  62           __real__ res = __nanl ("");
  63           __imag__ res = __nanl ("");
  64         }
  65     }
  66   else if (rcls == FP_ZERO && icls == FP_ZERO)
  67     {
  68       res = x;
  69     }
  70   else
  71     {
  72       long double rx, ix;
  73       __complex__ long double y;
  74
  75       /* Avoid cancellation by reducing to the first quadrant.  */
  76       rx = fabsl (__real__ x);
  77       ix = fabsl (__imag__ x);
  78
  79       if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_EPSILON)
  80         {
  81           /* For large x in the first quadrant, x + csqrt (1 + x * x)
  82              is sufficiently close to 2 * x to make no significant
  83              difference to the result; avoid possible overflow from
  84              the squaring and addition.  */
  85           __real__ y = rx;
  86           __imag__ y = ix;
  87           res = __clogl (y);
  88           __real__ res += M_LN2l;
  89         }
  90       else
  91         {
  92           __real__ y = (rx - ix) * (rx + ix) + 1.0;
  93           __imag__ y = 2.0 * rx * ix;
  94
  95           y = __csqrtl (y);
  96
  97           __real__ y += rx;
  98           __imag__ y += ix;
  99
 100           res = __clogl (y);
 101         }
 102
 103       /* Give results the correct sign for the original argument.  */
 104       __real__ res = __copysignl (__real__ res, __real__ x);
 105       __imag__ res = __copysignl (__imag__ res, __imag__ x);
 106     }
 107
 108   return res;
 109 }
 110 weak_alias (__casinhl, casinhl)