math/s_csqrt.c

   1 /* Complex square root of double value.
   2    Copyright (C) 1997-2012 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, see
  19    <http://www.gnu.org/licenses/>.  */
  20
  21 #include <complex.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24 #include <float.h>
  25
  26 __complex__ double
  27 __csqrt (__complex__ double x)
  28 {
  29   __complex__ double res;
  30   int rcls = fpclassify (__real__ x);
  31   int icls = fpclassify (__imag__ x);
  32
  33   if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
  34     {
  35       if (icls == FP_INFINITE)
  36         {
  37           __real__ res = HUGE_VAL;
  38           __imag__ res = __imag__ x;
  39         }
  40       else if (rcls == FP_INFINITE)
  41         {
  42           if (__real__ x < 0.0)
  43             {
  44               __real__ res = icls == FP_NAN ? __nan ("") : 0;
  45               __imag__ res = __copysign (HUGE_VAL, __imag__ x);
  46             }
  47           else
  48             {
  49               __real__ res = __real__ x;
  50               __imag__ res = (icls == FP_NAN
  51                               ? __nan ("") : __copysign (0.0, __imag__ x));
  52             }
  53         }
  54       else
  55         {
  56           __real__ res = __nan ("");
  57           __imag__ res = __nan ("");
  58         }
  59     }
  60   else
  61     {
  62       if (__builtin_expect (icls == FP_ZERO, 0))
  63         {
  64           if (__real__ x < 0.0)
  65             {
  66               __real__ res = 0.0;
  67               __imag__ res = __copysign (__ieee754_sqrt (-__real__ x),
  68                                          __imag__ x);
  69             }
  70           else
  71             {
  72               __real__ res = fabs (__ieee754_sqrt (__real__ x));
  73               __imag__ res = __copysign (0.0, __imag__ x);
  74             }
  75         }
  76       else if (__builtin_expect (rcls == FP_ZERO, 0))
  77         {
  78           double r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
  79
  80           __real__ res = r;
  81           __imag__ res = __copysign (r, __imag__ x);
  82         }
  83       else
  84         {
  85           double d, r, s;
  86           int scale = 0;
  87
  88           if (fabs (__real__ x) > DBL_MAX / 2.0
  89               || fabs (__imag__ x) > DBL_MAX / 2.0)
  90             {
  91               scale = 1;
  92               __real__ x = __scalbn (__real__ x, -2 * scale);
  93               __imag__ x = __scalbn (__imag__ x, -2 * scale);
  94             }
  95           else if (fabs (__real__ x) < DBL_MIN
  96                    && fabs (__imag__ x) < DBL_MIN)
  97             {
  98               scale = -(DBL_MANT_DIG / 2);
  99               __real__ x = __scalbn (__real__ x, -2 * scale);
 100               __imag__ x = __scalbn (__imag__ x, -2 * scale);
 101             }
 102
 103           d = __ieee754_hypot (__real__ x, __imag__ x);
 104           /* Use the identity   2  Re res  Im res = Im x
 105              to avoid cancellation error in  d +/- Re x.  */
 106           if (__real__ x > 0)
 107             {
 108               r = __ieee754_sqrt (0.5 * d + 0.5 * __real__ x);
 109               s = (0.5 * __imag__ x) / r;
 110             }
 111           else
 112             {
 113               s = __ieee754_sqrt (0.5 * d - 0.5 * __real__ x);
 114               r = fabs ((0.5 * __imag__ x) / s);
 115             }
 116
 117           if (scale)
 118             {
 119               r = __scalbn (r, scale);
 120               s = __scalbn (s, scale);
 121             }
 122
 123           __real__ res = r;
 124           __imag__ res = __copysign (s, __imag__ x);
 125         }
 126     }
 127
 128   return res;
 129 }
 130 weak_alias (__csqrt, csqrt)
 131 #ifdef NO_LONG_DOUBLE
 132 strong_alias (__csqrt, __csqrtl)
 133 weak_alias (__csqrt, csqrtl)
 134 #endif