sysdeps/ieee754/dbl-64/s_cbrt.c

   1 /* Compute cubic root of double value.
   2    Copyright (C) 1997-2014 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
   5    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 <math.h>
  22 #include <math_private.h>
  23
  24
  25 #define CBRT2 1.2599210498948731648             /* 2^(1/3) */
  26 #define SQR_CBRT2 1.5874010519681994748         /* 2^(2/3) */
  27
  28 static const double factor[5] =
  29 {
  30   1.0 / SQR_CBRT2,
  31   1.0 / CBRT2,
  32   1.0,
  33   CBRT2,
  34   SQR_CBRT2
  35 };
  36
  37
  38 double
  39 __cbrt (double x)
  40 {
  41   double xm, ym, u, t2;
  42   int xe;
  43
  44   /* Reduce X.  XM now is an range 1.0 to 0.5.  */
  45   xm = __frexp (fabs (x), &xe);
  46
  47   /* If X is not finite or is null return it (with raising exceptions
  48      if necessary.
  49      Note: *Our* version of `frexp' sets XE to zero if the argument is
  50      Inf or NaN.  This is not portable but faster.  */
  51   if (xe == 0 && fpclassify (x) <= FP_ZERO)
  52     return x + x;
  53
  54   u = (0.354895765043919860
  55        + ((1.50819193781584896
  56            + ((-2.11499494167371287
  57                + ((2.44693122563534430
  58                    + ((-1.83469277483613086
  59                        + (0.784932344976639262 - 0.145263899385486377 * xm)
  60                           * xm)
  61                       * xm))
  62                   * xm))
  63               * xm))
  64           * xm));
  65
  66   t2 = u * u * u;
  67
  68   ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
  69
  70   return __ldexp (x > 0.0 ? ym : -ym, xe / 3);
  71 }
  72 weak_alias (__cbrt, cbrt)
  73 #ifdef NO_LONG_DOUBLE
  74 strong_alias (__cbrt, __cbrtl)
  75 weak_alias (__cbrt, cbrtl)
  76 #endif