sysdeps/libm-ieee754/s_cbrt.c

   1 /* Compute cubic root of double value.
   2    Copyright (C) 1997 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 Library General Public License as
   9    published by the Free Software Foundation; either version 2 of the
  10    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    Library General Public License for more details.
  16
  17    You should have received a copy of the GNU Library General Public
  18    License along with the GNU C Library; see the file COPYING.LIB.  If not,
  19    write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
  20    Boston, MA 02111-1307, USA.  */
  21
  22 #include "math.h"
  23 #include "math_private.h"
  24
  25
  26 #define CBRT2 1.2599210498948731648             /* 2^(1/3) */
  27 #define SQR_CBRT2 1.5874010519681994748         /* 2^(2/3) */
  28
  29 static const double factor[5] =
  30 {
  31   1.0 / SQR_CBRT2,
  32   1.0 / CBRT2,
  33   1.0,
  34   CBRT2,
  35   SQR_CBRT2
  36 };
  37
  38
  39 double
  40 __cbrt (double x)
  41 {
  42   double xm, ym, u, t2;
  43   int xe;
  44
  45   /* Reduce X.  XM now is an range 1.0 to 0.5.  */
  46   xm = __frexp (fabs (x), &xe);
  47
  48   /* If X is not finite or is null return it (with raising exceptions
  49      if necessary.  */
  50   if (xe == 0)
  51     return x + x;
  52
  53  u = (0.354895765043919860
  54       + ((1.50819193781584896
  55          + ((-2.11499494167371287
  56             + ((2.44693122563534430
  57                + ((-1.83469277483613086
  58                   + (0.784932344976639262 - 0.145263899385486377 * xm) * xm)
  59                   * xm))
  60                * xm))
  61             * xm))
  62          * xm));
  63
  64   t2 = u * u * u;
  65
  66   ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
  67
  68   return __ldexp (x > 0.0 ? ym : -ym, xe / 3);
  69 }
  70 weak_alias (__cbrt, cbrt)
  71 #ifdef NO_LONG_DOUBLE
  72 strong_alias (__cbrt, __cbrtl)
  73 weak_alias (__cbrt, cbrtl)
  74 #endif