lib/cbrt.c

   1 /* Compute cubic root of double value.
   2    Copyright (C) 1997, 2012-2019 Free Software Foundation, Inc.
   3
   4    Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
   5    Ulrich Drepper <drepper@cygnus.com>, 1997.
   6
   7    This program is free software: you can redistribute it and/or modify
   8    it under the terms of the GNU General Public License as published by
   9    the Free Software Foundation; either version 3 of the License, or
  10    (at your option) any later version.
  11
  12    This program 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
  15    GNU General Public License for more details.
  16
  17    You should have received a copy of the GNU General Public License
  18    along with this program.  If not, see <https://www.gnu.org/licenses/>.  */
  19
  20 #include <config.h>
  21
  22 /* Specification.  */
  23 #include <math.h>
  24
  25 /* MSVC with option -fp:strict refuses to compile constant initializers that
  26    contain floating-point operations.  Pacify this compiler.  */
  27 #ifdef _MSC_VER
  28 # pragma fenv_access (off)
  29 #endif
  30
  31 /* Code based on glibc/sysdeps/ieee754/dbl-64/s_cbrt.c.  */
  32
  33 #define CBRT2 1.2599210498948731648             /* 2^(1/3) */
  34 #define SQR_CBRT2 1.5874010519681994748         /* 2^(2/3) */
  35
  36 static const double factor[5] =
  37 {
  38   1.0 / SQR_CBRT2,
  39   1.0 / CBRT2,
  40   1.0,
  41   CBRT2,
  42   SQR_CBRT2
  43 };
  44
  45
  46 double
  47 cbrt (double x)
  48 {
  49   if (isfinite (x) && x != 0.0)
  50     {
  51       double xm, ym, u, t2;
  52       int xe;
  53
  54       /* Reduce X.  XM now is an range 1.0 to 0.5.  */
  55       xm = frexp (fabs (x), &xe);
  56
  57       u = (0.354895765043919860
  58            + ((1.50819193781584896
  59                + ((-2.11499494167371287
  60                    + ((2.44693122563534430
  61                        + ((-1.83469277483613086
  62                            + (0.784932344976639262 - 0.145263899385486377 * xm)
  63                              * xm)
  64                           * xm))
  65                       * xm))
  66                   * xm))
  67               * xm));
  68
  69       t2 = u * u * u;
  70
  71       ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
  72
  73       return ldexp (x > 0.0 ? ym : -ym, xe / 3);
  74     }
  75   else
  76     return x + x;
  77 }