libstdc++-v3/math/csqrt.c

   1 /* Complex square root of double value. */
   2
   3 /* Copyright (C) 1997-1999 Free Software Foundation, Inc.
   4
   5    This file is part of the GNU ISO C++ Library.  This library is free
   6    software; you can redistribute it and/or modify it under the
   7    terms of the GNU General Public License as published by the
   8    Free Software Foundation; either version 2, or (at your option)
   9    any later version.
  10
  11    This 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
  14    GNU General Public License for more details.
  15
  16    You should have received a copy of the GNU General Public License along
  17    with this library; see the file COPYING.  If not, write to the Free
  18    Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
  19    USA.
  20
  21    As a special exception, you may use this file as part of a free software
  22    library without restriction.  Specifically, if other files instantiate
  23    templates or use macros or inline functions from this file, or you compile
  24    this file and link it with other files to produce an executable, this
  25    file does not by itself cause the resulting executable to be covered by
  26    the GNU General Public License.  This exception does not however
  27    invalidate any other reasons why the executable file might be covered by
  28    the GNU General Public License.  */
  29
  30
  31 #include <math.h>
  32 #include "mathconf.h"
  33
  34
  35 __complex__ double
  36 csqrt (__complex__ double x)
  37 {
  38   __complex__ double res;
  39
  40   if (!FINITE_P (__real__ x) || !FINITE_P (__imag__ x))
  41     {
  42       if (INFINITE_P (__imag__ x))
  43         {
  44           __real__ res = HUGE_VAL;
  45           __imag__ res = __imag__ x;
  46         }
  47       else if (INFINITE_P (__real__ x))
  48         {
  49           if (__real__ x < 0.0)
  50             {
  51               __real__ res = __imag__ x != __imag__ x ? NAN : 0;
  52               __imag__ res = copysign (HUGE_VAL, __imag__ x);
  53             }
  54           else
  55             {
  56               __real__ res = __real__ x;
  57               __imag__ res = (__imag__ x != __imag__ x
  58                               ? NAN : copysign (0.0, __imag__ x));
  59             }
  60         }
  61       else
  62         {
  63           __real__ res = NAN;
  64           __imag__ res = NAN;
  65         }
  66     }
  67   else
  68     {
  69       if (__imag__ x == 0.0)
  70         {
  71           if (__real__ x < 0.0)
  72             {
  73               __real__ res = 0.0;
  74               __imag__ res = copysign (sqrt (-__real__ x), __imag__ x);
  75             }
  76           else
  77             {
  78               __real__ res = fabs (sqrt (__real__ x));
  79               __imag__ res = copysign (0.0, __imag__ x);
  80             }
  81         }
  82       else if (__real__ x == 0.0)
  83         {
  84           double r = sqrt (0.5 * fabs (__imag__ x));
  85
  86           __real__ res = copysign (r, __imag__ x);
  87           __imag__ res = r;
  88         }
  89       else
  90         {
  91           __complex__ double q;
  92           double t, r;
  93
  94           if (fabs (__imag__ x) < 2.0e-4 * fabs (__real__ x))
  95             t = 0.25 * __imag__ x * (__imag__ x / __real__ x);
  96           else
  97             t = 0.5 * (hypot (__real__ x, __imag__ x) - __real__ x);
  98
  99           r = sqrt (t);
 100
 101           __real__ q = __imag__ x / (2.0 * r);
 102           __imag__ q = r;
 103
 104           /* Heron iteration in complex arithmetic.  */
 105           res = 0.5 * (q + q / x);
 106         }
 107     }
 108
 109   return res;
 110 }