math/s_clog.c

   1 /* Compute complex natural logarithm.
   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 <complex.h>
  21 #include <math.h>
  22 #include <math_private.h>
  23 #include <float.h>
  24
  25 __complex__ double
  26 __clog (__complex__ double x)
  27 {
  28   __complex__ double result;
  29   int rcls = fpclassify (__real__ x);
  30   int icls = fpclassify (__imag__ x);
  31
  32   if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
  33     {
  34       /* Real and imaginary part are 0.0.  */
  35       __imag__ result = signbit (__real__ x) ? M_PI : 0.0;
  36       __imag__ result = __copysign (__imag__ result, __imag__ x);
  37       /* Yes, the following line raises an exception.  */
  38       __real__ result = -1.0 / fabs (__real__ x);
  39     }
  40   else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
  41     {
  42       /* Neither real nor imaginary part is NaN.  */
  43       double absx = fabs (__real__ x), absy = fabs (__imag__ x);
  44       int scale = 0;
  45
  46       if (absx < absy)
  47         {
  48           double t = absx;
  49           absx = absy;
  50           absy = t;
  51         }
  52
  53       if (absx > DBL_MAX / 2.0)
  54         {
  55           scale = -1;
  56           absx = __scalbn (absx, scale);
  57           absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
  58         }
  59       else if (absx < DBL_MIN && absy < DBL_MIN)
  60         {
  61           scale = DBL_MANT_DIG;
  62           absx = __scalbn (absx, scale);
  63           absy = __scalbn (absy, scale);
  64         }
  65
  66       if (absx == 1.0 && scale == 0)
  67         {
  68           double absy2 = absy * absy;
  69           if (absy2 <= DBL_MIN * 2.0)
  70             {
  71 #if __FLT_EVAL_METHOD__ == 0
  72               __real__ result = absy2 / 2.0 - absy2 * absy2 / 4.0;
  73 #else
  74               volatile double force_underflow = absy2 * absy2 / 4.0;
  75               __real__ result = absy2 / 2.0 - force_underflow;
  76 #endif
  77             }
  78           else
  79             __real__ result = __log1p (absy2) / 2.0;
  80         }
  81       else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
  82         {
  83           double d2m1 = (absx - 1.0) * (absx + 1.0);
  84           if (absy >= DBL_EPSILON)
  85             d2m1 += absy * absy;
  86           __real__ result = __log1p (d2m1) / 2.0;
  87         }
  88       else if (absx < 1.0
  89                && absx >= 0.75
  90                && absy < DBL_EPSILON / 2.0
  91                && scale == 0)
  92         {
  93           double d2m1 = (absx - 1.0) * (absx + 1.0);
  94           __real__ result = __log1p (d2m1) / 2.0;
  95         }
  96       else if (absx < 1.0 && (absx >= 0.75 || absy >= 0.5) && scale == 0)
  97         {
  98           double d2m1 = __x2y2m1 (absx, absy);
  99           __real__ result = __log1p (d2m1) / 2.0;
 100         }
 101       else
 102         {
 103           double d = __ieee754_hypot (absx, absy);
 104           __real__ result = __ieee754_log (d) - scale * M_LN2;
 105         }
 106
 107       __imag__ result = __ieee754_atan2 (__imag__ x, __real__ x);
 108     }
 109   else
 110     {
 111       __imag__ result = __nan ("");
 112       if (rcls == FP_INFINITE || icls == FP_INFINITE)
 113         /* Real or imaginary part is infinite.  */
 114         __real__ result = HUGE_VAL;
 115       else
 116         __real__ result = __nan ("");
 117     }
 118
 119   return result;
 120 }
 121 weak_alias (__clog, clog)
 122 #ifdef NO_LONG_DOUBLE
 123 strong_alias (__clog, __clogl)
 124 weak_alias (__clog, clogl)
 125 #endif