math/s_csqrt.c

   1 /* Complex square root of double value.
   2    Copyright (C) 1997, 1998, 2005, 2011 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>.
   5    Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
   6
   7    The GNU C Library is free software; you can redistribute it and/or
   8    modify it under the terms of the GNU Lesser General Public
   9    License as published by the Free Software Foundation; either
  10    version 2.1 of the License, or (at your option) any later version.
  11
  12    The GNU C Library is distributed in the hope that it will be useful,
  13    but WITHOUT ANY WARRANTY; without even the implied warranty of
  14    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15    Lesser General Public License for more details.
  16
  17    You should have received a copy of the GNU Lesser General Public
  18    License along with the GNU C Library; if not, write to the Free
  19    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  20    02111-1307 USA.  */
  21
  22 #include <complex.h>
  23 #include <math.h>
  24 #include <math_private.h>
  25
  26
  27 __complex__ double
  28 __csqrt (__complex__ double x)
  29 {
  30   __complex__ double res;
  31   int rcls = fpclassify (__real__ x);
  32   int icls = fpclassify (__imag__ x);
  33
  34   if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
  35     {
  36       if (icls == FP_INFINITE)
  37         {
  38           __real__ res = HUGE_VAL;
  39           __imag__ res = __imag__ x;
  40         }
  41       else if (rcls == FP_INFINITE)
  42         {
  43           if (__real__ x < 0.0)
  44             {
  45               __real__ res = icls == FP_NAN ? __nan ("") : 0;
  46               __imag__ res = __copysign (HUGE_VAL, __imag__ x);
  47             }
  48           else
  49             {
  50               __real__ res = __real__ x;
  51               __imag__ res = (icls == FP_NAN
  52                               ? __nan ("") : __copysign (0.0, __imag__ x));
  53             }
  54         }
  55       else
  56         {
  57           __real__ res = __nan ("");
  58           __imag__ res = __nan ("");
  59         }
  60     }
  61   else
  62     {
  63       if (__builtin_expect (icls == FP_ZERO, 0))
  64         {
  65           if (__real__ x < 0.0)
  66             {
  67               __real__ res = 0.0;
  68               __imag__ res = __copysign (__ieee754_sqrt (-__real__ x),
  69                                          __imag__ x);
  70             }
  71           else
  72             {
  73               __real__ res = fabs (__ieee754_sqrt (__real__ x));
  74               __imag__ res = __copysign (0.0, __imag__ x);
  75             }
  76         }
  77       else if (__builtin_expect (rcls == FP_ZERO, 0))
  78         {
  79           double r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
  80
  81           __real__ res = r;
  82           __imag__ res = __copysign (r, __imag__ x);
  83         }
  84       else
  85         {
  86           double d, r, s;
  87
  88           d = __ieee754_hypot (__real__ x, __imag__ x);
  89           /* Use the identity   2  Re res  Im res = Im x
  90              to avoid cancellation error in  d +/- Re x.  */
  91           if (__real__ x > 0)
  92             {
  93               r = __ieee754_sqrt (0.5 * d + 0.5 * __real__ x);
  94               s = (0.5 * __imag__ x) / r;
  95             }
  96           else
  97             {
  98               s = __ieee754_sqrt (0.5 * d - 0.5 * __real__ x);
  99               r = fabs ((0.5 * __imag__ x) / s);
 100             }
 101
 102           __real__ res = r;
 103           __imag__ res = __copysign (s, __imag__ x);
 104         }
 105     }
 106
 107   return res;
 108 }
 109 weak_alias (__csqrt, csqrt)
 110 #ifdef NO_LONG_DOUBLE
 111 strong_alias (__csqrt, __csqrtl)
 112 weak_alias (__csqrt, csqrtl)
 113 #endif