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/* @(#)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 "math_private.h"

/* cbrt(x)

 * Return cube root of x

 */

#ifdef __STDC__

static const u_int32_t

#else

static u_int32_t

#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

{

        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);

}