math/s_catanf.c

   1 /* Return arc tangent of complex float 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__ float
  26 __catanf (__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 (rcls == FP_INFINITE)
  35         {
  36           __real__ res = __copysignf (M_PI_2, __real__ x);
  37           __imag__ res = __copysignf (0.0, __imag__ x);
  38         }
  39       else if (icls == FP_INFINITE)
  40         {
  41           if (rcls >= FP_ZERO)
  42             __real__ res = __copysignf (M_PI_2, __real__ x);
  43           else
  44             __real__ res = __nanf ("");
  45           __imag__ res = __copysignf (0.0, __imag__ x);
  46         }
  47       else if (icls == FP_ZERO || icls == FP_INFINITE)
  48         {
  49           __real__ res = __nanf ("");
  50           __imag__ res = __copysignf (0.0, __imag__ x);
  51         }
  52       else
  53         {
  54           __real__ res = __nanf ("");
  55           __imag__ res = __nanf ("");
  56         }
  57     }
  58   else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  59     {
  60       res = x;
  61     }
  62   else
  63     {
  64       if (fabsf (__real__ x) >= 16.0f / FLT_EPSILON
  65           || fabsf (__imag__ x) >= 16.0f / FLT_EPSILON)
  66         {
  67           __real__ res = __copysignf ((float) M_PI_2, __real__ x);
  68           if (fabsf (__real__ x) <= 1.0f)
  69             __imag__ res = 1.0f / __imag__ x;
  70           else if (fabsf (__imag__ x) <= 1.0f)
  71             __imag__ res = __imag__ x / __real__ x / __real__ x;
  72           else
  73             {
  74               float h = __ieee754_hypotf (__real__ x / 2.0f,
  75                                           __imag__ x / 2.0f);
  76               __imag__ res = __imag__ x / h / h / 4.0f;
  77             }
  78         }
  79       else
  80         {
  81           float den, absx, absy;
  82
  83           absx = fabsf (__real__ x);
  84           absy = fabsf (__imag__ x);
  85           if (absx < absy)
  86             {
  87               float t = absx;
  88               absx = absy;
  89               absy = t;
  90             }
  91
  92           if (absy < FLT_EPSILON / 2.0f)
  93             {
  94               den = (1.0f - absx) * (1.0f + absx);
  95               if (den == -0.0f)
  96                 den = 0.0f;
  97             }
  98           else if (absx >= 1.0f)
  99             den = (1.0f - absx) * (1.0f + absx) - absy * absy;
 100           else if (absx >= 0.75f || absy >= 0.5f)
 101             den = -__x2y2m1f (absx, absy);
 102           else
 103             den = (1.0f - absx) * (1.0f + absx) - absy * absy;
 104
 105           __real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den);
 106
 107           if (fabsf (__imag__ x) == 1.0f
 108               && fabsf (__real__ x) < FLT_EPSILON * FLT_EPSILON)
 109             __imag__ res = (__copysignf (0.5f, __imag__ x)
 110                             * ((float) M_LN2
 111                                - __ieee754_logf (fabsf (__real__ x))));
 112           else
 113             {
 114               float r2 = 0.0f, num, f;
 115
 116               if (fabsf (__real__ x) >= FLT_EPSILON * FLT_EPSILON)
 117                 r2 = __real__ x * __real__ x;
 118
 119               num = __imag__ x + 1.0f;
 120               num = r2 + num * num;
 121
 122               den = __imag__ x - 1.0f;
 123               den = r2 + den * den;
 124
 125               f = num / den;
 126               if (f < 0.5f)
 127                 __imag__ res = 0.25f * __ieee754_logf (f);
 128               else
 129                 {
 130                   num = 4.0f * __imag__ x;
 131                   __imag__ res = 0.25f * __log1pf (num / den);
 132                 }
 133             }
 134         }
 135
 136       if (fabsf (__real__ res) < FLT_MIN)
 137         {
 138           volatile float force_underflow = __real__ res * __real__ res;
 139           (void) force_underflow;
 140         }
 141       if (fabsf (__imag__ res) < FLT_MIN)
 142         {
 143           volatile float force_underflow = __imag__ res * __imag__ res;
 144           (void) force_underflow;
 145         }
 146     }
 147
 148   return res;
 149 }
 150 #ifndef __catanf
 151 weak_alias (__catanf, catanf)
 152 #endif