cbrt.c

/*
 *                               POK header
 * 
 * The following file is a part of the POK project. Any modification should
 * made according to the POK licence. You CANNOT use this file or a part of
 * this file is this part of a file for your own project
 *
 * For more information on the POK licence, please see our LICENCE FILE
 *
 * Please follow the coding guidelines described in doc/CODING_GUIDELINES
 *
 *                                      Copyright (c) 2007-2009 POK team 
 *
 * Created by julien on Fri Jan 30 14:41:34 2009 
 */

/* @(#)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.
 * ====================================================
 */

#ifdef POK_NEEDS_LIBMATH

#include <types.h>
#include <libm.h>
#include "math_private.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);
}
#endif