math/s_catanh.c

   1 /* Return arc hyperbole tangent for double value.
   2    Copyright (C) 1997-2015 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__ double
  26 __catanh (__complex__ double x)
  27 {
  28   __complex__ double res;
  29   int rcls = fpclassify (__real__ x);
  30   int icls = fpclassify (__imag__ x);
  31
  32   if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
  33     {
  34       if (icls == FP_INFINITE)
  35         {
  36           __real__ res = __copysign (0.0, __real__ x);
  37           __imag__ res = __copysign (M_PI_2, __imag__ x);
  38         }
  39       else if (rcls == FP_INFINITE || rcls == FP_ZERO)
  40         {
  41           __real__ res = __copysign (0.0, __real__ x);
  42           if (icls >= FP_ZERO)
  43             __imag__ res = __copysign (M_PI_2, __imag__ x);
  44           else
  45             __imag__ res = __nan ("");
  46         }
  47       else
  48         {
  49           __real__ res = __nan ("");
  50           __imag__ res = __nan ("");
  51         }
  52     }
  53   else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  54     {
  55       res = x;
  56     }
  57   else
  58     {
  59       if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
  60           || fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
  61         {
  62           __imag__ res = __copysign (M_PI_2, __imag__ x);
  63           if (fabs (__imag__ x) <= 1.0)
  64             __real__ res = 1.0 / __real__ x;
  65           else if (fabs (__real__ x) <= 1.0)
  66             __real__ res = __real__ x / __imag__ x / __imag__ x;
  67           else
  68             {
  69               double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
  70               __real__ res = __real__ x / h / h / 4.0;
  71             }
  72         }
  73       else
  74         {
  75           if (fabs (__real__ x) == 1.0
  76               && fabs (__imag__ x) < DBL_EPSILON * DBL_EPSILON)
  77             __real__ res = (__copysign (0.5, __real__ x)
  78                             * (M_LN2 - __ieee754_log (fabs (__imag__ x))));
  79           else
  80             {
  81               double i2 = 0.0;
  82               if (fabs (__imag__ x) >= DBL_EPSILON * DBL_EPSILON)
  83                 i2 = __imag__ x * __imag__ x;
  84
  85               double num = 1.0 + __real__ x;
  86               num = i2 + num * num;
  87
  88               double den = 1.0 - __real__ x;
  89               den = i2 + den * den;
  90
  91               double f = num / den;
  92               if (f < 0.5)
  93                 __real__ res = 0.25 * __ieee754_log (f);
  94               else
  95                 {
  96                   num = 4.0 * __real__ x;
  97                   __real__ res = 0.25 * __log1p (num / den);
  98                 }
  99             }
 100
 101           double absx, absy, den;
 102
 103           absx = fabs (__real__ x);
 104           absy = fabs (__imag__ x);
 105           if (absx < absy)
 106             {
 107               double t = absx;
 108               absx = absy;
 109               absy = t;
 110             }
 111
 112           if (absy < DBL_EPSILON / 2.0)
 113             {
 114               den = (1.0 - absx) * (1.0 + absx);
 115               if (den == -0.0)
 116                 den = 0.0;
 117             }
 118           else if (absx >= 1.0)
 119             den = (1.0 - absx) * (1.0 + absx) - absy * absy;
 120           else if (absx >= 0.75 || absy >= 0.5)
 121             den = -__x2y2m1 (absx, absy);
 122           else
 123             den = (1.0 - absx) * (1.0 + absx) - absy * absy;
 124
 125           __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
 126         }
 127
 128       if (fabs (__real__ res) < DBL_MIN)
 129         {
 130           volatile double force_underflow = __real__ res * __real__ res;
 131           (void) force_underflow;
 132         }
 133       if (fabs (__imag__ res) < DBL_MIN)
 134         {
 135           volatile double force_underflow = __imag__ res * __imag__ res;
 136           (void) force_underflow;
 137         }
 138     }
 139
 140   return res;
 141 }
 142 weak_alias (__catanh, catanh)
 143 #ifdef NO_LONG_DOUBLE
 144 strong_alias (__catanh, __catanhl)
 145 weak_alias (__catanh, catanhl)
 146 #endif