/* Compute cubic root of double value.

   Copyright (C) 1997-2018 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, see

   <http://www.gnu.org/licenses/>.  */

#include <math.h>

#include <math_private.h>

#include <libm-alias-double.h>

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

#define SQR_CBRT2 1.5874010519681994748		/* 2^(2/3) */

static const double factor[5] =

{

  1.0 / SQR_CBRT2,

  1.0 / CBRT2,

  1.0,

  CBRT2,

  SQR_CBRT2

};

double

__cbrt (double x)

{

  double xm, ym, u, t2;

  int xe;

  /* Reduce X.  XM now is an range 1.0 to 0.5.  */

  xm = __frexp (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 = (0.354895765043919860

       + ((1.50819193781584896

	   + ((-2.11499494167371287

	       + ((2.44693122563534430

		   + ((-1.83469277483613086

		       + (0.784932344976639262 - 0.145263899385486377 * xm)

	                  * xm)

		      * xm))

		  * xm))

	      * xm))

	  * xm));

  t2 = u * u * u;

  ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];

  return __ldexp (x > 0.0 ? ym : -ym, xe / 3);

}

libm_alias_double (__cbrt, cbrt)