sysdeps/libm-ieee754/s_cbrtl.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 /* We don't use long double values here since U need not be computed
  30    with full precision.  */
  31 static const double factor[5] =
  32 {
  33   1.0 / SQR_CBRT2,
  34   1.0 / CBRT2,
  35   1.0,
  36   CBRT2,
  37   SQR_CBRT2
  38 };
  39
  40
  41 long double
  42 __cbrtl (long double x)
  43 {
  44   long double xm, ym, u, t2;
  45   int xe;
  46
  47   /* Reduce X.  XM now is an range 1.0 to 0.5.  */
  48   xm = __frexpl (fabs (x), &xe);
  49
  50   /* If X is not finite or is null return it (with raising exceptions
  51      if necessary.  */
  52   if (xe == 0 && (x == 0.0 || isnanl (x) || isinfl (x)))
  53     return x + x;
  54
  55   u = (0.338058687610520237
  56        + (1.67595307700780102
  57           + (-2.82414939754975962
  58              + (4.09559907378707839 +
  59                 (-4.11151425200350531
  60                  + (2.65298938441952296 +
  61                     (-0.988553671195413709
  62                      + 0.161617097923756032 * xm)
  63                     * xm)
  64                  * xm)
  65                 * xm)
  66              * xm)
  67           * xm)
  68        *xm);
  69
  70   t2 = u * u * u;
  71
  72   ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
  73
  74   return __ldexpl (x > 0.0 ? ym : -ym, xe / 3);
  75 }
  76 weak_alias (__cbrtl, cbrtl)