math/s_clog.c

   1 /* Compute complex natural logarithm.
   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 __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 (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  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 (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
  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               double force_underflow = absy2 * absy2;
  72               __real__ result = absy2 / 2.0;
  73               math_force_eval (force_underflow);
  74             }
  75           else
  76             __real__ result = __log1p (absy2) / 2.0;
  77         }
  78       else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
  79         {
  80           double d2m1 = (absx - 1.0) * (absx + 1.0);
  81           if (absy >= DBL_EPSILON)
  82             d2m1 += absy * absy;
  83           __real__ result = __log1p (d2m1) / 2.0;
  84         }
  85       else if (absx < 1.0
  86                && absx >= 0.75
  87                && absy < DBL_EPSILON / 2.0
  88                && scale == 0)
  89         {
  90           double d2m1 = (absx - 1.0) * (absx + 1.0);
  91           __real__ result = __log1p (d2m1) / 2.0;
  92         }
  93       else if (absx < 1.0 && (absx >= 0.75 || absy >= 0.5) && scale == 0)
  94         {
  95           double d2m1 = __x2y2m1 (absx, absy);
  96           __real__ result = __log1p (d2m1) / 2.0;
  97         }
  98       else
  99         {
 100           double d = __ieee754_hypot (absx, absy);
 101           __real__ result = __ieee754_log (d) - scale * M_LN2;
 102         }
 103
 104       __imag__ result = __ieee754_atan2 (__imag__ x, __real__ x);
 105     }
 106   else
 107     {
 108       __imag__ result = __nan ("");
 109       if (rcls == FP_INFINITE || icls == FP_INFINITE)
 110         /* Real or imaginary part is infinite.  */
 111         __real__ result = HUGE_VAL;
 112       else
 113         __real__ result = __nan ("");
 114     }
 115
 116   return result;
 117 }
 118 weak_alias (__clog, clog)
 119 #ifdef NO_LONG_DOUBLE
 120 strong_alias (__clog, __clogl)
 121 weak_alias (__clog, clogl)
 122 #endif