/****************************************************************************
 *
 * $Source: /usr/local/cvsroot/gccsdk/unixlib/source/math/cbrt.c,v $
 * $Date: 2002/12/22 18:22:28 $
 * $Revision: 1.3 $
 * $State: Exp $
 * $Author: admin $
 *
 ***************************************************************************/

/* @(#)s_cbrt.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_cbrt.c,v 1.8 1995/05/10 20:46:49 jtc Exp $";
#endif

#include <math.h>
#include <unixlib/math.h>
#include <unixlib/types.h>

/* cbrt(x)
 * Return cube root of x
 */
static const __uint32_t
  B1 = 715094163,		/* B1 = (682-0.03306235651)*2**20 */
  B2 = 696219795;		/* B2 = (664-0.03306235651)*2**20 */

static const double
  C = 5.42857142857142815906e-01,	/* 19/35     = 0x3FE15F15, 0xF15F15F1 */
  D = -7.05306122448979611050e-01,	/* -864/1225 = 0xBFE691DE, 0x2532C834 */
  E = 1.41428571428571436819e+00,	/* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
  F = 1.60714285714285720630e+00,	/* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
  G = 3.57142857142857150787e-01;	/* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */

double
cbrt (double x)
{
  __int32_t hx;
  double r, s, t = 0.0, w;
  __uint32_t sign;
  __uint32_t high, low;

  GET_HIGH_WORD (hx, x);
  sign = hx & 0x80000000;	/* sign= sign(x) */
  hx ^= sign;
  if (hx >= 0x7ff00000)
    return (x + x);		/* cbrt(NaN,INF) is itself */
  GET_LOW_WORD (low, x);
  if ((hx | low) == 0)
    return (x);			/* cbrt(0) is itself */

  SET_HIGH_WORD (x, hx);	/* x <- |x| */
  /* rough cbrt to 5 bits */
  if (hx < 0x00100000)		/* subnormal number */
    {
      SET_HIGH_WORD (t, 0x43500000);	/* set t= 2**54 */
      t *= x;
      GET_HIGH_WORD (high, t);
      SET_HIGH_WORD (t, high / 3 + B2);
    }
  else
    SET_HIGH_WORD (t, hx / 3 + B1);


  /* new cbrt to 23 bits, may be implemented in single precision */
  r = t * t / x;
  s = C + r * t;
  t *= G + F / (s + E + D / s);

  /* chopped to 20 bits and make it larger than cbrt(x) */
  GET_HIGH_WORD (high, t);
  INSERT_WORDS (t, high + 0x00000001, 0);


  /* one step newton iteration to 53 bits with error less than 0.667 ulps */
  s = t * t;			/* t*t is exact */
  r = x / s;
  w = t + t;
  r = (r - t) / (w + r);	/* r-s is exact */
  t = t + t * r;

  /* retore the sign bit */
  GET_HIGH_WORD (high, t);
  SET_HIGH_WORD (t, high | sign);
  return (t);
}
