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 "math.h"
18#include "math_private.h"
19
20/* cbrtf(x)
21 * Return cube root of x
22 */
23static const unsigned
24	B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
25	B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
26
27float
28cbrtf(float x)
29{
30	double r,T;
31	float t;
32	int32_t hx;
33	u_int32_t sign;
34	u_int32_t high;
35
36	GET_FLOAT_WORD(hx,x);
37	sign=hx&0x80000000; 		/* sign= sign(x) */
38	hx  ^=sign;
39	if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
40
41    /* rough cbrt to 5 bits */
42	if(hx<0x00800000) { 		/* zero or subnormal? */
43	    if(hx==0)
44		return(x);		/* cbrt(+-0) is itself */
45	    SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
46	    t*=x;
47	    GET_FLOAT_WORD(high,t);
48	    SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
49	} else
50	    SET_FLOAT_WORD(t,sign|(hx/3+B1));
51
52    /*
53     * First step Newton iteration (solving t*t-x/t == 0) to 16 bits.  In
54     * double precision so that its terms can be arranged for efficiency
55     * without causing overflow or underflow.
56     */
57	T=t;
58	r=T*T*T;
59	T=T*((double)x+x+r)/(x+r+r);
60
61    /*
62     * Second step Newton iteration to 47 bits.  In double precision for
63     * efficiency and accuracy.
64     */
65	r=T*T*T;
66	T=T*((double)x+x+r)/(x+r+r);
67
68    /* rounding to 24 bits is perfect in round-to-nearest mode */
69	return(T);
70}
71