1/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 * Debugged and optimized by Bruce D. Evans.
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/* cbrtf(x)
17 * Return cube root of x
18 */
19
20#include <math.h>
21#include <stdint.h>
22
23static const unsigned
24B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
25B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
26
27float cbrtf(float x)
28{
29	double_t r,T;
30	union {float f; uint32_t i;} u = {x};
31	uint32_t hx = u.i & 0x7fffffff;
32
33	if (hx >= 0x7f800000)  /* cbrt(NaN,INF) is itself */
34		return x + x;
35
36	/* rough cbrt to 5 bits */
37	if (hx < 0x00800000) {  /* zero or subnormal? */
38		if (hx == 0)
39			return x;  /* cbrt(+-0) is itself */
40		u.f = x*0x1p24f;
41		hx = u.i & 0x7fffffff;
42		hx = hx/3 + B2;
43	} else
44		hx = hx/3 + B1;
45	u.i &= 0x80000000;
46	u.i |= hx;
47
48	/*
49	 * First step Newton iteration (solving t*t-x/t == 0) to 16 bits.  In
50	 * double precision so that its terms can be arranged for efficiency
51	 * without causing overflow or underflow.
52	 */
53	T = u.f;
54	r = T*T*T;
55	T = T*((double_t)x+x+r)/(x+r+r);
56
57	/*
58	 * Second step Newton iteration to 47 bits.  In double precision for
59	 * efficiency and accuracy.
60	 */
61	r = T*T*T;
62	T = T*((double_t)x+x+r)/(x+r+r);
63
64	/* rounding to 24 bits is perfect in round-to-nearest mode */
65	return T;
66}
67