math/s_csqrt_template.c

   1 /* Complex square root of a float type.
   2    Copyright (C) 1997-2018 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 CFLOAT
  27 M_DECL_FUNC (__csqrt) (CFLOAT x)
  28 {
  29   CFLOAT 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 = M_HUGE_VAL;
  38           __imag__ res = __imag__ x;
  39         }
  40       else if (rcls == FP_INFINITE)
  41         {
  42           if (__real__ x < 0)
  43             {
  44               __real__ res = icls == FP_NAN ? M_NAN : 0;
  45               __imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x);
  46             }
  47           else
  48             {
  49               __real__ res = __real__ x;
  50               __imag__ res = (icls == FP_NAN
  51                               ? M_NAN : M_COPYSIGN (0, __imag__ x));
  52             }
  53         }
  54       else
  55         {
  56           __real__ res = M_NAN;
  57           __imag__ res = M_NAN;
  58         }
  59     }
  60   else
  61     {
  62       if (__glibc_unlikely (icls == FP_ZERO))
  63         {
  64           if (__real__ x < 0)
  65             {
  66               __real__ res = 0;
  67               __imag__ res = M_COPYSIGN (M_SQRT (-__real__ x), __imag__ x);
  68             }
  69           else
  70             {
  71               __real__ res = M_FABS (M_SQRT (__real__ x));
  72               __imag__ res = M_COPYSIGN (0, __imag__ x);
  73             }
  74         }
  75       else if (__glibc_unlikely (rcls == FP_ZERO))
  76         {
  77           FLOAT r;
  78           if (M_FABS (__imag__ x) >= 2 * M_MIN)
  79             r = M_SQRT (M_LIT (0.5) * M_FABS (__imag__ x));
  80           else
  81             r = M_LIT (0.5) * M_SQRT (2 * M_FABS (__imag__ x));
  82
  83           __real__ res = r;
  84           __imag__ res = M_COPYSIGN (r, __imag__ x);
  85         }
  86       else
  87         {
  88           FLOAT d, r, s;
  89           int scale = 0;
  90
  91           if (M_FABS (__real__ x) > M_MAX / 4)
  92             {
  93               scale = 1;
  94               __real__ x = M_SCALBN (__real__ x, -2 * scale);
  95               __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
  96             }
  97           else if (M_FABS (__imag__ x) > M_MAX / 4)
  98             {
  99               scale = 1;
 100               if (M_FABS (__real__ x) >= 4 * M_MIN)
 101                 __real__ x = M_SCALBN (__real__ x, -2 * scale);
 102               else
 103                 __real__ x = 0;
 104               __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
 105             }
 106           else if (M_FABS (__real__ x) < 2 * M_MIN
 107                    && M_FABS (__imag__ x) < 2 * M_MIN)
 108             {
 109               scale = -((M_MANT_DIG + 1) / 2);
 110               __real__ x = M_SCALBN (__real__ x, -2 * scale);
 111               __imag__ x = M_SCALBN (__imag__ x, -2 * scale);
 112             }
 113
 114           d = M_HYPOT (__real__ x, __imag__ x);
 115           /* Use the identity   2  Re res  Im res = Im x
 116              to avoid cancellation error in  d +/- Re x.  */
 117           if (__real__ x > 0)
 118             {
 119               r = M_SQRT (M_LIT (0.5) * (d + __real__ x));
 120               if (scale == 1 && M_FABS (__imag__ x) < 1)
 121                 {
 122                   /* Avoid possible intermediate underflow.  */
 123                   s = __imag__ x / r;
 124                   r = M_SCALBN (r, scale);
 125                   scale = 0;
 126                 }
 127               else
 128                 s = M_LIT (0.5) * (__imag__ x / r);
 129             }
 130           else
 131             {
 132               s = M_SQRT (M_LIT (0.5) * (d - __real__ x));
 133               if (scale == 1 && M_FABS (__imag__ x) < 1)
 134                 {
 135                   /* Avoid possible intermediate underflow.  */
 136                   r = M_FABS (__imag__ x / s);
 137                   s = M_SCALBN (s, scale);
 138                   scale = 0;
 139                 }
 140               else
 141                 r = M_FABS (M_LIT (0.5) * (__imag__ x / s));
 142             }
 143
 144           if (scale)
 145             {
 146               r = M_SCALBN (r, scale);
 147               s = M_SCALBN (s, scale);
 148             }
 149
 150           math_check_force_underflow (r);
 151           math_check_force_underflow (s);
 152
 153           __real__ res = r;
 154           __imag__ res = M_COPYSIGN (s, __imag__ x);
 155         }
 156     }
 157
 158   return res;
 159 }
 160 declare_mgen_alias (__csqrt, csqrt)