/* @(#)s_cbrt.c 1.3 95/01/18 */

/*

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

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunSoft, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice 

 * is preserved.

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

 *

 */

#include "fdlibm.h"

/* cbrt(x)

 * Return cube root of x

 */

#ifdef __STDC__

static const unsigned 

#else

static unsigned 

#endif

	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */

	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */

#ifdef __STDC__

static const double

#else

static double

#endif

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 */

#ifdef __STDC__

	double cbrt(double x) 

#else

	double cbrt(x) 

	double x;

#endif

{

	int	hx;

	double r,s,t=0.0,w;

	unsigned sign;

	hx = __HI(x);		/* high word of x */

	sign=hx&0x80000000; 		/* sign= sign(x) */

	hx  ^=sign;

	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */

	if((hx|__LO(x))==0) 

	    return(x);		/* cbrt(0) is itself */

	__HI(x) = hx;	/* x <- |x| */

    /* rough cbrt to 5 bits */

	if(hx<0x00100000) 		/* subnormal number */

	  {__HI(t)=0x43500000; 		/* set t= 2**54 */

	   t*=x; __HI(t)=__HI(t)/3+B2;

	  }

	else

	  __HI(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) */ 

	__LO(t)=0; __HI(t)+=0x00000001;

    /* 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 */

	__HI(t) |= sign;

	return(t);

}