/* s_cbrtf.c -- float version of s_cbrt.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 * Debugged and optimized by Bruce D. Evans.
 */

/*
 * ====================================================
 * 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.
 * ====================================================
 */

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

/* cbrtf(x)
 * Return cube root of x
 */
static const unsigned
        B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
        B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */

float
cbrtf(float x)
{
        double r,T;
        float 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 */

    /* rough cbrt to 5 bits */
        if(hx<0x00800000) {             /* zero or subnormal? */
            if(hx==0)
                return(x);              /* cbrt(+-0) is itself */
            SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
            t*=x;
            GET_FLOAT_WORD(high,t);
            SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
        } else
            SET_FLOAT_WORD(t,sign|(hx/3+B1));

    /*
     * First step Halley iteration (solving t*t-x/t == 0) to 16 bits.  In
     * double precision so that its terms can be arranged for efficiency
     * without causing overflow or underflow.
     */
        T=t;
        r=T*T*T;
        T=T*((double)x+x+r)/(x+r+r);

    /*
     * Second step Halley iteration to 47 bits.  In double precision for
     * efficiency and accuracy.
     */
        r=T*T*T;
        T=T*((double)x+x+r)/(x+r+r);

    /* rounding to 24 bits is perfect in round-to-nearest mode */
        return(T);
}