sysdeps/ieee754/ldbl-96/s_cbrtl.c

/* Compute cubic root of double value.
   Copyright (C) 1997 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
   Ulrich Drepper <drepper@cygnus.com>, 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

#include "math.h"
#include "math_private.h"


#define CBRT2 1.2599210498948731648		/* 2^(1/3) */
#define SQR_CBRT2 1.5874010519681994748		/* 2^(2/3) */

/* We don't use long double values here since U need not be computed
   with full precision.  */
static const double factor[5] =
{
  1.0 / SQR_CBRT2,
  1.0 / CBRT2,
  1.0,
  CBRT2,
  SQR_CBRT2
};

static const long double third = 0.3333333333333333333333333L;

long double
__cbrtl (long double x)
{
  long double xm, u;
  int xe;

  /* Reduce X.  XM now is an range 1.0 to 0.5.  */
  xm = __frexpl (fabs (x), &xe);

  /* If X is not finite or is null return it (with raising exceptions
     if necessary.
     Note: *Our* version of `frexp' sets XE to zero if the argument is
     Inf or NaN.  This is not portable but faster.  */
  if (xe == 0 && fpclassify (x) <= FP_ZERO)
    return x + x;

  u = (((-1.34661104733595206551E-1 * xm
	  + 5.46646013663955245034E-1) * xm
	 - 9.54382247715094465250E-1) * xm
	+ 1.13999833547172932737E0) * xm
       + 4.02389795645447521269E-1;

  u *= factor[2 + xe % 3];
  u = __ldexpl (x > 0.0 ? u : -u, xe / 3);

  u -= (u - (x / (u * u))) * third;
  u -= (u - (x / (u * u))) * third;
  return u;
}
weak_alias (__cbrtl, cbrtl)