math/s_csqrt.c

   1 /* Complex square root of double value.
   2    Copyright (C) 1997-2015 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 (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
  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 (__glibc_unlikely (icls == FP_ZERO))
  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 (__glibc_unlikely (rcls == FP_ZERO))
  77         {
  78           double r;
  79           if (fabs (__imag__ x) >= 2.0 * DBL_MIN)
  80             r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
  81           else
  82             r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x));
  83
  84           __real__ res = r;
  85           __imag__ res = __copysign (r, __imag__ x);
  86         }
  87       else
  88         {
  89           double d, r, s;
  90           int scale = 0;
  91
  92           if (fabs (__real__ x) > DBL_MAX / 4.0)
  93             {
  94               scale = 1;
  95               __real__ x = __scalbn (__real__ x, -2 * scale);
  96               __imag__ x = __scalbn (__imag__ x, -2 * scale);
  97             }
  98           else if (fabs (__imag__ x) > DBL_MAX / 4.0)
  99             {
 100               scale = 1;
 101               if (fabs (__real__ x) >= 4.0 * DBL_MIN)
 102                 __real__ x = __scalbn (__real__ x, -2 * scale);
 103               else
 104                 __real__ x = 0.0;
 105               __imag__ x = __scalbn (__imag__ x, -2 * scale);
 106             }
 107           else if (fabs (__real__ x) < 2.0 * DBL_MIN
 108                    && fabs (__imag__ x) < 2.0 * DBL_MIN)
 109             {
 110               scale = -((DBL_MANT_DIG + 1) / 2);
 111               __real__ x = __scalbn (__real__ x, -2 * scale);
 112               __imag__ x = __scalbn (__imag__ x, -2 * scale);
 113             }
 114
 115           d = __ieee754_hypot (__real__ x, __imag__ x);
 116           /* Use the identity   2  Re res  Im res = Im x
 117              to avoid cancellation error in  d +/- Re x.  */
 118           if (__real__ x > 0)
 119             {
 120               r = __ieee754_sqrt (0.5 * (d + __real__ x));
 121               if (scale == 1 && fabs (__imag__ x) < 1.0)
 122                 {
 123                   /* Avoid possible intermediate underflow.  */
 124                   s = __imag__ x / r;
 125                   r = __scalbn (r, scale);
 126                   scale = 0;
 127                 }
 128               else
 129                 s = 0.5 * (__imag__ x / r);
 130             }
 131           else
 132             {
 133               s = __ieee754_sqrt (0.5 * (d - __real__ x));
 134               if (scale == 1 && fabs (__imag__ x) < 1.0)
 135                 {
 136                   /* Avoid possible intermediate underflow.  */
 137                   r = fabs (__imag__ x / s);
 138                   s = __scalbn (s, scale);
 139                   scale = 0;
 140                 }
 141               else
 142                 r = fabs (0.5 * (__imag__ x / s));
 143             }
 144
 145           if (scale)
 146             {
 147               r = __scalbn (r, scale);
 148               s = __scalbn (s, scale);
 149             }
 150
 151           if (fabs (r) < DBL_MIN)
 152             {
 153               double force_underflow = r * r;
 154               math_force_eval (force_underflow);
 155             }
 156           if (fabs (s) < DBL_MIN)
 157             {
 158               double force_underflow = s * s;
 159               math_force_eval (force_underflow);
 160             }
 161
 162           __real__ res = r;
 163           __imag__ res = __copysign (s, __imag__ x);
 164         }
 165     }
 166
 167   return res;
 168 }
 169 weak_alias (__csqrt, csqrt)
 170 #ifdef NO_LONG_DOUBLE
 171 strong_alias (__csqrt, __csqrtl)
 172 weak_alias (__csqrt, csqrtl)
 173 #endif