source: vendor/FreeBSD-msun/current/src/s_cbrtf.c

/* s_cbrtf.c -- float version of s_cbrt.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

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

#include "math.h"
#include "math_private.h"

/* cbrtf(x)
 * Return cube root of x
 */
static const unsigned
        B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
        B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */

static const float
C =  5.4285717010e-01, /* 19/35     = 0x3f0af8b0 */
D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
E =  1.4142856598e+00, /* 99/70     = 0x3fb50750 */
F =  1.6071428061e+00, /* 45/28     = 0x3fcdb6db */
G =  3.5714286566e-01; /* 5/14      = 0x3eb6db6e */

float
cbrtf(float x)
{
        float r,s,t;
        int32_t hx;
        u_int32_t sign;
        u_int32_t high;

        GET_FLOAT_WORD(hx,x);
        sign=hx&0x80000000;             /* sign= sign(x) */
        hx  ^=sign;
        if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
        if(hx==0)
            return(x);          /* cbrt(0) is itself */

        SET_FLOAT_WORD(x,hx);   /* x <- |x| */
    /* rough cbrt to 5 bits */
        if(hx<0x00800000)               /* subnormal number */
          {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
           t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
          }
        else
          SET_FLOAT_WORD(t,hx/3+B1);


    /* new cbrt to 23 bits */
        r=t*t/x;
        s=C+r*t;
        t*=G+F/(s+E+D/s);

    /* retore the sign bit */
        GET_FLOAT_WORD(high,t);
        SET_FLOAT_WORD(t,high|sign);
        return(t);
}