libm/upstream-freebsd/lib/msun/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.
 * 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 <sys/cdefs.h>
__FBSDID("$FreeBSD$");

#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 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=t;
	r=T*T*T;
	T=T*((double)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)x+x+r)/(x+r+r);

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