libquadmath/math/clogq.c

   1 /* Compute complex natural logarithm for complex __float128.
   2    Copyright (C) 1997-2012 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 "quadmath-imp.h"
  21
  22
  23 __complex128
  24 clogq (__complex128 x)
  25 {
  26   __complex128 result;
  27   int rcls = fpclassifyq (__real__ x);
  28   int icls = fpclassifyq (__imag__ x);
  29
  30   if (__builtin_expect (rcls == QUADFP_ZERO && icls == QUADFP_ZERO, 0))
  31     {
  32       /* Real and imaginary part are 0.0.  */
  33       __imag__ result = signbitq (__real__ x) ? M_PIq : 0.0Q;
  34       __imag__ result = copysignq (__imag__ result, __imag__ x);
  35       /* Yes, the following line raises an exception.  */
  36       __real__ result = -1.0Q / fabsq (__real__ x);
  37     }
  38   else if (__builtin_expect (rcls != QUADFP_NAN && icls != QUADFP_NAN, 1))
  39     {
  40       /* Neither real nor imaginary part is NaN.  */
  41       __float128 absx = fabsq (__real__ x), absy = fabsq (__imag__ x);
  42       int scale = 0;
  43
  44       if (absx < absy)
  45         {
  46           __float128 t = absx;
  47           absx = absy;
  48           absy = t;
  49         }
  50
  51       if (absx > FLT128_MAX / 2.0)
  52         {
  53           scale = -1;
  54           absx = scalbnq (absx, scale);
  55           absy = (absy >= FLT128_MIN * 2.0Q ? scalbnq (absy, scale) : 0.0Q);
  56         }
  57       else if (absx < FLT128_MIN && absy < FLT128_MIN)
  58         {
  59           scale = FLT128_MANT_DIG;
  60           absx = scalbnq (absx, scale);
  61           absy = scalbnq (absy, scale);
  62         }
  63
  64       if (absx == 1.0Q && scale == 0)
  65         {
  66           __float128 absy2 = absy * absy;
  67           if (absy2 <= FLT128_MIN * 2.0Q)
  68             __real__ result = absy2 / 2.0Q - absy2 * absy2 / 4.0Q;
  69           else
  70             __real__ result = log1pq (absy2) / 2.0Q;
  71         }
  72       else if (absx > 1.0Q && absx < 2.0Q && absy < 1.0Q && scale == 0)
  73         {
  74           __float128 d2m1 = (absx - 1.0Q) * (absx + 1.0Q);
  75           if (absy >= FLT128_EPSILON)
  76             d2m1 += absy * absy;
  77           __real__ result = log1pq (d2m1) / 2.0Q;
  78         }
  79       else if (absx < 1.0Q
  80                && absx >= 0.75Q
  81                && absy < FLT128_EPSILON / 2.0Q
  82                && scale == 0)
  83         {
  84           __float128 d2m1 = (absx - 1.0Q) * (absx + 1.0Q);
  85           __real__ result = log1pq (d2m1) / 2.0Q;
  86         }
  87       else if (absx < 1.0 && (absx >= 0.75Q || absy >= 0.5Q) && scale == 0)
  88         {
  89           __float128 d2m1 = __quadmath_x2y2m1q (absx, absy);
  90           __real__ result = log1pq (d2m1) / 2.0Q;
  91         }
  92       else
  93         {
  94           __float128 d = hypotq (absx, absy);
  95           __real__ result = logq (d) - scale * M_LN2q;
  96         }
  97
  98       __imag__ result = atan2q (__imag__ x, __real__ x);
  99     }
 100   else
 101     {
 102       __imag__ result = nanq ("");
 103       if (rcls == QUADFP_INFINITE || icls == QUADFP_INFINITE)
 104         /* Real or imaginary part is infinite.  */
 105         __real__ result = HUGE_VALQ;
 106       else
 107         __real__ result = nanq ("");
 108     }
 109
 110   return result;
 111 }