math/s_clog10.c

   1 /* Compute complex base 10 logarithm.
   2    Copyright (C) 1997-2013 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 /* log_10 (2).  */
  26 #define M_LOG10_2 0.3010299956639811952137388947244930267682
  27
  28 __complex__ double
  29 __clog10 (__complex__ double x)
  30 {
  31   __complex__ double result;
  32   int rcls = fpclassify (__real__ x);
  33   int icls = fpclassify (__imag__ x);
  34
  35   if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
  36     {
  37       /* Real and imaginary part are 0.0.  */
  38       __imag__ result = signbit (__real__ x) ? M_PI : 0.0;
  39       __imag__ result = __copysign (__imag__ result, __imag__ x);
  40       /* Yes, the following line raises an exception.  */
  41       __real__ result = -1.0 / fabs (__real__ x);
  42     }
  43   else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
  44     {
  45       /* Neither real nor imaginary part is NaN.  */
  46       double absx = fabs (__real__ x), absy = fabs (__imag__ x);
  47       int scale = 0;
  48
  49       if (absx < absy)
  50         {
  51           double t = absx;
  52           absx = absy;
  53           absy = t;
  54         }
  55
  56       if (absx > DBL_MAX / 2.0)
  57         {
  58           scale = -1;
  59           absx = __scalbn (absx, scale);
  60           absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
  61         }
  62       else if (absx < DBL_MIN && absy < DBL_MIN)
  63         {
  64           scale = DBL_MANT_DIG;
  65           absx = __scalbn (absx, scale);
  66           absy = __scalbn (absy, scale);
  67         }
  68
  69       if (absx == 1.0 && scale == 0)
  70         {
  71           double absy2 = absy * absy;
  72           if (absy2 <= DBL_MIN * 2.0 * M_LN10)
  73             {
  74 #if __FLT_EVAL_METHOD__ == 0
  75               __real__ result = (absy2 / 2.0 - absy2 * absy2 / 4.0) * M_LOG10E;
  76 #else
  77               volatile double force_underflow = absy2 * absy2 / 4.0;
  78               __real__ result = (absy2 / 2.0 - force_underflow) * M_LOG10E;
  79 #endif
  80             }
  81           else
  82             __real__ result = __log1p (absy2) * (M_LOG10E / 2.0);
  83         }
  84       else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
  85         {
  86           double d2m1 = (absx - 1.0) * (absx + 1.0);
  87           if (absy >= DBL_EPSILON)
  88             d2m1 += absy * absy;
  89           __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
  90         }
  91       else if (absx < 1.0
  92                && absx >= 0.75
  93                && absy < DBL_EPSILON / 2.0
  94                && scale == 0)
  95         {
  96           double d2m1 = (absx - 1.0) * (absx + 1.0);
  97           __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
  98         }
  99       else if (absx < 1.0 && (absx >= 0.75 || absy >= 0.5) && scale == 0)
 100         {
 101           double d2m1 = __x2y2m1 (absx, absy);
 102           __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
 103         }
 104       else
 105         {
 106           double d = __ieee754_hypot (absx, absy);
 107           __real__ result = __ieee754_log10 (d) - scale * M_LOG10_2;
 108         }
 109
 110       __imag__ result = M_LOG10E * __ieee754_atan2 (__imag__ x, __real__ x);
 111     }
 112   else
 113     {
 114       __imag__ result = __nan ("");
 115       if (rcls == FP_INFINITE || icls == FP_INFINITE)
 116         /* Real or imaginary part is infinite.  */
 117         __real__ result = HUGE_VAL;
 118       else
 119         __real__ result = __nan ("");
 120     }
 121
 122   return result;
 123 }
 124 weak_alias (__clog10, clog10)
 125 #ifdef NO_LONG_DOUBLE
 126 strong_alias (__clog10, __clog10l)
 127 weak_alias (__clog10, clog10l)
 128 #endif