math/s_catanhl.c

   1 /* Return arc hyperbole tangent for long double value.
   2    Copyright (C) 1997-2014 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 __catanhl (__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 (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
  40     {
  41       if (icls == FP_INFINITE)
  42         {
  43           __real__ res = __copysignl (0.0, __real__ x);
  44           __imag__ res = __copysignl (M_PI_2l, __imag__ x);
  45         }
  46       else if (rcls == FP_INFINITE || rcls == FP_ZERO)
  47         {
  48           __real__ res = __copysignl (0.0, __real__ x);
  49           if (icls >= FP_ZERO)
  50             __imag__ res = __copysignl (M_PI_2l, __imag__ x);
  51           else
  52             __imag__ res = __nanl ("");
  53         }
  54       else
  55         {
  56           __real__ res = __nanl ("");
  57           __imag__ res = __nanl ("");
  58         }
  59     }
  60   else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  61     {
  62       res = x;
  63     }
  64   else
  65     {
  66       if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
  67           || fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
  68         {
  69           __imag__ res = __copysignl (M_PI_2l, __imag__ x);
  70           if (fabsl (__imag__ x) <= 1.0L)
  71             __real__ res = 1.0L / __real__ x;
  72           else if (fabsl (__real__ x) <= 1.0L)
  73             __real__ res = __real__ x / __imag__ x / __imag__ x;
  74           else
  75             {
  76               long double h = __ieee754_hypotl (__real__ x / 2.0L,
  77                                                 __imag__ x / 2.0L);
  78               __real__ res = __real__ x / h / h / 4.0L;
  79             }
  80         }
  81       else
  82         {
  83           if (fabsl (__real__ x) == 1.0L
  84               && fabsl (__imag__ x) < LDBL_EPSILON * LDBL_EPSILON)
  85             __real__ res = (__copysignl (0.5L, __real__ x)
  86                             * (M_LN2l - __ieee754_logl (fabsl (__imag__ x))));
  87           else
  88             {
  89               long double i2 = 0.0;
  90               if (fabsl (__imag__ x) >= LDBL_EPSILON * LDBL_EPSILON)
  91                 i2 = __imag__ x * __imag__ x;
  92
  93               long double num = 1.0L + __real__ x;
  94               num = i2 + num * num;
  95
  96               long double den = 1.0L - __real__ x;
  97               den = i2 + den * den;
  98
  99               long double f = num / den;
 100               if (f < 0.5L)
 101                 __real__ res = 0.25L * __ieee754_logl (f);
 102               else
 103                 {
 104                   num = 4.0L * __real__ x;
 105                   __real__ res = 0.25L * __log1pl (num / den);
 106                 }
 107             }
 108
 109           long double absx, absy, den;
 110
 111           absx = fabsl (__real__ x);
 112           absy = fabsl (__imag__ x);
 113           if (absx < absy)
 114             {
 115               long double t = absx;
 116               absx = absy;
 117               absy = t;
 118             }
 119
 120           if (absy < LDBL_EPSILON / 2.0L)
 121             {
 122               den = (1.0L - absx) * (1.0L + absx);
 123               if (den == -0.0L)
 124                 den = 0.0L;
 125             }
 126           else if (absx >= 1.0L)
 127             den = (1.0L - absx) * (1.0L + absx) - absy * absy;
 128           else if (absx >= 0.75L || absy >= 0.5L)
 129             den = -__x2y2m1l (absx, absy);
 130           else
 131             den = (1.0L - absx) * (1.0L + absx) - absy * absy;
 132
 133           __imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den);
 134         }
 135
 136       if (fabsl (__real__ res) < LDBL_MIN)
 137         {
 138           volatile long double force_underflow = __real__ res * __real__ res;
 139           (void) force_underflow;
 140         }
 141       if (fabsl (__imag__ res) < LDBL_MIN)
 142         {
 143           volatile long double force_underflow = __imag__ res * __imag__ res;
 144           (void) force_underflow;
 145         }
 146     }
 147
 148   return res;
 149 }
 150 weak_alias (__catanhl, catanhl)