1/* s_cbrtf.c -- float version of s_cbrt.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 * Debugged and optimized by Bruce D. Evans.
4 */
5
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16
17#include <sys/cdefs.h>
18__FBSDID("$FreeBSD$");
19
20#include "math.h"
21#include "math_private.h"
22
23/* cbrtf(x)
24 * Return cube root of x
25 */
26static const unsigned
27	B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
28	B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
29
30float
31cbrtf(float x)
32{
33	double r,T;
34	float t;
35	int32_t hx;
36	u_int32_t sign;
37	u_int32_t high;
38
39	GET_FLOAT_WORD(hx,x);
40	sign=hx&0x80000000; 		/* sign= sign(x) */
41	hx  ^=sign;
42	if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
43
44    /* rough cbrt to 5 bits */
45	if(hx<0x00800000) { 		/* zero or subnormal? */
46	    if(hx==0)
47		return(x);		/* cbrt(+-0) is itself */
48	    SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
49	    t*=x;
50	    GET_FLOAT_WORD(high,t);
51	    SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
52	} else
53	    SET_FLOAT_WORD(t,sign|(hx/3+B1));
54
55    /*
56     * First step Newton iteration (solving t*t-x/t == 0) to 16 bits.  In
57     * double precision so that its terms can be arranged for efficiency
58     * without causing overflow or underflow.
59     */
60	T=t;
61	r=T*T*T;
62	T=T*((double)x+x+r)/(x+r+r);
63
64    /*
65     * Second step Newton iteration to 47 bits.  In double precision for
66     * efficiency and accuracy.
67     */
68	r=T*T*T;
69	T=T*((double)x+x+r)/(x+r+r);
70
71    /* rounding to 24 bits is perfect in round-to-nearest mode */
72	return(T);
73}
74