/*--------------------------------------------------------------------

 *© Portions copyright (c) 2006 Nokia Corporation.  All rights reserved.

 *--------------------------------------------------------------------

*/

/* @(#)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.

 * ====================================================

 */

#ifndef __SYMBIAN32__

#ifndef lint

static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrt.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";

#endif

#endif //__SYMBIAN32__

#include <math.h>

#include "math_private.h"

/* cbrt(x)

 * Return cube root of x

 */

static const u_int32_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 */

EXPORT_C double

cbrt(double x)

{

	int32_t	hx;

	double r,s,t=0.0,w;

	u_int32_t sign;

	u_int32_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);

}