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#ifndef lint
18static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrtf.c,v 1.12 2005/12/13 20:17:23 bde Exp $";
19#endif
20
21#include "math.h"
22#include "math_private.h"
23
24/* cbrtf(x)
25 * Return cube root of x
26 */
27static const unsigned
28	B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */
29	B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
30
31static const float
32C =  5.4285717010e-01, /* 19/35     = 0x3f0af8b0 */
33D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
34E =  1.4142856598e+00, /* 99/70     = 0x3fb50750 */
35F =  1.6071428061e+00, /* 45/28     = 0x3fcdb6db */
36G =  3.5714286566e-01; /* 5/14      = 0x3eb6db6e */
37
38float
39cbrtf(float x)
40{
41	float r,s,t,w;
42	int32_t hx;
43	u_int32_t sign;
44	u_int32_t high;
45
46	GET_FLOAT_WORD(hx,x);
47	sign=hx&0x80000000; 		/* sign= sign(x) */
48	hx  ^=sign;
49	if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
50	if(hx==0)
51	    return(x);		/* cbrt(0) is itself */
52
53    /* rough cbrt to 5 bits */
54	if(hx<0x00800000) { 		/* subnormal number */
55	    SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
56	    t*=x;
57	    GET_FLOAT_WORD(high,t);
58	    SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
59	} else
60	    SET_FLOAT_WORD(t,sign|(hx/3+B1));
61
62    /* new cbrt to 23 bits */
63	r=t*t/x;
64	s=C+r*t;
65	t*=G+F/(s+E+D/s);
66
67    /* chop t to 12 bits and make it larger in magnitude than cbrt(x) */
68	GET_FLOAT_WORD(high,t);
69	SET_FLOAT_WORD(t,(high&0xfffff000)+0x00001000);
70
71    /* one step Newton iteration to 24 bits with error less than 0.667 ulps */
72	s=t*t;		/* t*t is exact */
73	r=x/s;
74	w=t+t;
75	r=(r-t)/(w+r);	/* r-t is exact */
76	t=t+t*r;
77
78	return(t);
79}
80