source: asp3_tinet_ecnl_arm/trunk/musl-1.1.18/src/math/cbrtf.c@ 352

/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.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.
 * ====================================================
 */
/* cbrtf(x)
 * Return cube root of x
 */

#include <math.h>
#include <stdint.h>

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_t r,T;
        union {float f; uint32_t i;} u = {x};
        uint32_t hx = u.i & 0x7fffffff;

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

        /* rough cbrt to 5 bits */
        if (hx < 0x00800000) {  /* zero or subnormal? */
                if (hx == 0)
                        return x;  /* cbrt(+-0) is itself */
                u.f = x*0x1p24f;
                hx = u.i & 0x7fffffff;
                hx = hx/3 + B2;
        } else
                hx = hx/3 + B1;
        u.i &= 0x80000000;
        u.i |= hx;

        /*
         * First step Newton 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 = u.f;
        r = T*T*T;
        T = T*((double_t)x+x+r)/(x+r+r);

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

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