math/s_catanhf.c

   1 /* Return arc hyperbole tangent for float value.
   2    Copyright (C) 1997-2016 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 __catanhf (__complex__ float x)
  27 {
  28   __complex__ float 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 = __copysignf (0.0, __real__ x);
  37           __imag__ res = __copysignf (M_PI_2, __imag__ x);
  38         }
  39       else if (rcls == FP_INFINITE || rcls == FP_ZERO)
  40         {
  41           __real__ res = __copysignf (0.0, __real__ x);
  42           if (icls >= FP_ZERO)
  43             __imag__ res = __copysignf (M_PI_2, __imag__ x);
  44           else
  45             __imag__ res = __nanf ("");
  46         }
  47       else
  48         {
  49           __real__ res = __nanf ("");
  50           __imag__ res = __nanf ("");
  51         }
  52     }
  53   else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  54     {
  55       res = x;
  56     }
  57   else
  58     {
  59       if (fabsf (__real__ x) >= 16.0f / FLT_EPSILON
  60           || fabsf (__imag__ x) >= 16.0f / FLT_EPSILON)
  61         {
  62           __imag__ res = __copysignf ((float) M_PI_2, __imag__ x);
  63           if (fabsf (__imag__ x) <= 1.0f)
  64             __real__ res = 1.0f / __real__ x;
  65           else if (fabsf (__real__ x) <= 1.0f)
  66             __real__ res = __real__ x / __imag__ x / __imag__ x;
  67           else
  68             {
  69               float h = __ieee754_hypotf (__real__ x / 2.0f,
  70                                           __imag__ x / 2.0f);
  71               __real__ res = __real__ x / h / h / 4.0f;
  72             }
  73         }
  74       else
  75         {
  76           if (fabsf (__real__ x) == 1.0f
  77               && fabsf (__imag__ x) < FLT_EPSILON * FLT_EPSILON)
  78             __real__ res = (__copysignf (0.5f, __real__ x)
  79                             * ((float) M_LN2
  80                                - __ieee754_logf (fabsf (__imag__ x))));
  81           else
  82             {
  83               float i2 = 0.0f;
  84               if (fabsf (__imag__ x) >= FLT_EPSILON * FLT_EPSILON)
  85                 i2 = __imag__ x * __imag__ x;
  86
  87               float num = 1.0f + __real__ x;
  88               num = i2 + num * num;
  89
  90               float den = 1.0f - __real__ x;
  91               den = i2 + den * den;
  92
  93               float f = num / den;
  94               if (f < 0.5f)
  95                 __real__ res = 0.25f * __ieee754_logf (f);
  96               else
  97                 {
  98                   num = 4.0f * __real__ x;
  99                   __real__ res = 0.25f * __log1pf (num / den);
 100                 }
 101             }
 102
 103           float absx, absy, den;
 104
 105           absx = fabsf (__real__ x);
 106           absy = fabsf (__imag__ x);
 107           if (absx < absy)
 108             {
 109               float t = absx;
 110               absx = absy;
 111               absy = t;
 112             }
 113
 114           if (absy < FLT_EPSILON / 2.0f)
 115             {
 116               den = (1.0f - absx) * (1.0f + absx);
 117               if (den == -0.0f)
 118                 den = 0.0f;
 119             }
 120           else if (absx >= 1.0f)
 121             den = (1.0f - absx) * (1.0f + absx) - absy * absy;
 122           else if (absx >= 0.75f || absy >= 0.5f)
 123             den = -__x2y2m1f (absx, absy);
 124           else
 125             den = (1.0f - absx) * (1.0f + absx) - absy * absy;
 126
 127           __imag__ res = 0.5f * __ieee754_atan2f (2.0f * __imag__ x, den);
 128         }
 129
 130       math_check_force_underflow_complex (res);
 131     }
 132
 133   return res;
 134 }
 135 #ifndef __catanhf
 136 weak_alias (__catanhf, catanhf)
 137 #endif