/* @(#)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 "math.h"

/* cbrt(x)
 * Return cube root of x
 */
static const unsigned
    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) {
	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);
}