math/s_catanl.c

   1 /* Return arc tangent of complex 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 __catanl (__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 (rcls == FP_INFINITE)
  42         {
  43           __real__ res = __copysignl (M_PI_2l, __real__ x);
  44           __imag__ res = __copysignl (0.0, __imag__ x);
  45         }
  46       else if (icls == FP_INFINITE)
  47         {
  48           if (rcls >= FP_ZERO)
  49             __real__ res = __copysignl (M_PI_2l, __real__ x);
  50           else
  51             __real__ res = __nanl ("");
  52           __imag__ res = __copysignl (0.0, __imag__ x);
  53         }
  54       else if (icls == FP_ZERO || icls == FP_INFINITE)
  55         {
  56           __real__ res = __nanl ("");
  57           __imag__ res = __copysignl (0.0, __imag__ x);
  58         }
  59       else
  60         {
  61           __real__ res = __nanl ("");
  62           __imag__ res = __nanl ("");
  63         }
  64     }
  65   else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  66     {
  67       res = x;
  68     }
  69   else
  70     {
  71       if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
  72           || fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
  73         {
  74           __real__ res = __copysignl (M_PI_2l, __real__ x);
  75           if (fabsl (__real__ x) <= 1.0L)
  76             __imag__ res = 1.0L / __imag__ x;
  77           else if (fabsl (__imag__ x) <= 1.0L)
  78             __imag__ res = __imag__ x / __real__ x / __real__ x;
  79           else
  80             {
  81               long double h = __ieee754_hypotl (__real__ x / 2.0L,
  82                                                 __imag__ x / 2.0L);
  83               __imag__ res = __imag__ x / h / h / 4.0L;
  84             }
  85         }
  86       else
  87         {
  88           long double den, absx, absy;
  89
  90           absx = fabsl (__real__ x);
  91           absy = fabsl (__imag__ x);
  92           if (absx < absy)
  93             {
  94               long double t = absx;
  95               absx = absy;
  96               absy = t;
  97             }
  98
  99           if (absy < LDBL_EPSILON / 2.0L)
 100             den = (1.0L - absx) * (1.0L + absx);
 101           else if (absx >= 1.0L)
 102             den = (1.0L - absx) * (1.0L + absx) - absy * absy;
 103           else if (absx >= 0.75L || absy >= 0.5L)
 104             den = -__x2y2m1l (absx, absy);
 105           else
 106             den = (1.0L - absx) * (1.0L + absx) - absy * absy;
 107
 108           __real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
 109
 110           if (fabsl (__imag__ x) == 1.0L
 111               && fabsl (__real__ x) < LDBL_EPSILON * LDBL_EPSILON)
 112             __imag__ res = (__copysignl (0.5L, __imag__ x)
 113                             * (M_LN2l - __ieee754_logl (fabsl (__real__ x))));
 114           else
 115             {
 116               long double r2 = 0.0L, num, f;
 117
 118               if (fabsl (__real__ x) >= LDBL_EPSILON * LDBL_EPSILON)
 119                 r2 = __real__ x * __real__ x;
 120
 121               num = __imag__ x + 1.0L;
 122               num = r2 + num * num;
 123
 124               den = __imag__ x - 1.0L;
 125               den = r2 + den * den;
 126
 127               f = num / den;
 128               if (f < 0.5L)
 129                 __imag__ res = 0.25L * __ieee754_logl (f);
 130               else
 131                 {
 132                   num = 4.0L * __imag__ x;
 133                   __imag__ res = 0.25L * __log1pl (num / den);
 134                 }
 135             }
 136         }
 137
 138       if (fabsl (__real__ res) < LDBL_MIN)
 139         {
 140           volatile long double force_underflow = __real__ res * __real__ res;
 141           (void) force_underflow;
 142         }
 143       if (fabsl (__imag__ res) < LDBL_MIN)
 144         {
 145           volatile long double force_underflow = __imag__ res * __imag__ res;
 146           (void) force_underflow;
 147         }
 148     }
 149
 150   return res;
 151 }
 152 weak_alias (__catanl, catanl)