math/s_clog10l.c

   1 /* Compute complex base 10 logarithm.
   2    Copyright (C) 1997-2015 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 underflows, 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 /* log_10 (2).  */
  33 #define M_LOG10_2l 0.3010299956639811952137388947244930267682L
  34
  35 /* pi * log10 (e).  */
  36 #define M_PI_LOG10El 1.364376353841841347485783625431355770210L
  37
  38 __complex__ long double
  39 __clog10l (__complex__ long double x)
  40 {
  41   __complex__ long double result;
  42   int rcls = fpclassify (__real__ x);
  43   int icls = fpclassify (__imag__ x);
  44
  45   if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
  46     {
  47       /* Real and imaginary part are 0.0.  */
  48       __imag__ result = signbit (__real__ x) ? M_PI_LOG10El : 0.0;
  49       __imag__ result = __copysignl (__imag__ result, __imag__ x);
  50       /* Yes, the following line raises an exception.  */
  51       __real__ result = -1.0 / fabsl (__real__ x);
  52     }
  53   else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
  54     {
  55       /* Neither real nor imaginary part is NaN.  */
  56       long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x);
  57       int scale = 0;
  58
  59       if (absx < absy)
  60         {
  61           long double t = absx;
  62           absx = absy;
  63           absy = t;
  64         }
  65
  66       if (absx > LDBL_MAX / 2.0L)
  67         {
  68           scale = -1;
  69           absx = __scalbnl (absx, scale);
  70           absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L);
  71         }
  72       else if (absx < LDBL_MIN && absy < LDBL_MIN)
  73         {
  74           scale = LDBL_MANT_DIG;
  75           absx = __scalbnl (absx, scale);
  76           absy = __scalbnl (absy, scale);
  77         }
  78
  79       if (absx == 1.0L && scale == 0)
  80         {
  81           long double absy2 = absy * absy;
  82           if (absy2 <= LDBL_MIN * 2.0L * M_LN10l)
  83             {
  84               long double force_underflow = absy2 * absy2;
  85               __real__ result = absy2 * (M_LOG10El / 2.0);
  86               math_force_eval (force_underflow);
  87             }
  88           else
  89             __real__ result = __log1pl (absy2) * (M_LOG10El / 2.0L);
  90         }
  91       else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0)
  92         {
  93           long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
  94           if (absy >= LDBL_EPSILON)
  95             d2m1 += absy * absy;
  96           __real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L);
  97         }
  98       else if (absx < 1.0L
  99                && absx >= 0.75L
 100                && absy < LDBL_EPSILON / 2.0L
 101                && scale == 0)
 102         {
 103           long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
 104           __real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L);
 105         }
 106       else if (absx < 1.0L && (absx >= 0.75L || absy >= 0.5L) && scale == 0)
 107         {
 108           long double d2m1 = __x2y2m1l (absx, absy);
 109           __real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L);
 110         }
 111       else
 112         {
 113           long double d = __ieee754_hypotl (absx, absy);
 114           __real__ result = __ieee754_log10l (d) - scale * M_LOG10_2l;
 115         }
 116
 117       __imag__ result = M_LOG10El * __ieee754_atan2l (__imag__ x, __real__ x);
 118     }
 119   else
 120     {
 121       __imag__ result = __nanl ("");
 122       if (rcls == FP_INFINITE || icls == FP_INFINITE)
 123         /* Real or imaginary part is infinite.  */
 124         __real__ result = HUGE_VALL;
 125       else
 126         __real__ result = __nanl ("");
 127     }
 128
 129   return result;
 130 }
 131 weak_alias (__clog10l, clog10l)