xref: /freebsd/lib/msun/src/s_cbrtf.c (revision 1e413cf93298b5b97441a21d9a50fdcd0ee9945e)
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
18 static char rcsid[] = "$FreeBSD$";
19 #endif
20 
21 #include "math.h"
22 #include "math_private.h"
23 
24 /* cbrtf(x)
25  * Return cube root of x
26  */
27 static 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 
31 float
32 cbrtf(float x)
33 {
34 	double r,T;
35 	float t;
36 	int32_t hx;
37 	u_int32_t sign;
38 	u_int32_t high;
39 
40 	GET_FLOAT_WORD(hx,x);
41 	sign=hx&0x80000000; 		/* sign= sign(x) */
42 	hx  ^=sign;
43 	if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
44 
45     /* rough cbrt to 5 bits */
46 	if(hx<0x00800000) { 		/* zero or subnormal? */
47 	    if(hx==0)
48 		return(x);		/* cbrt(+-0) is itself */
49 	    SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
50 	    t*=x;
51 	    GET_FLOAT_WORD(high,t);
52 	    SET_FLOAT_WORD(t,sign|((high&0x7fffffff)/3+B2));
53 	} else
54 	    SET_FLOAT_WORD(t,sign|(hx/3+B1));
55 
56     /*
57      * First step Newton iteration (solving t*t-x/t == 0) to 16 bits.  In
58      * double precision so that its terms can be arranged for efficiency
59      * without causing overflow or underflow.
60      */
61 	T=t;
62 	r=T*T*T;
63 	T=T*((double)x+x+r)/(x+r+r);
64 
65     /*
66      * Second step Newton iteration to 47 bits.  In double precision for
67      * efficiency and accuracy.
68      */
69 	r=T*T*T;
70 	T=T*((double)x+x+r)/(x+r+r);
71 
72     /* rounding to 24 bits is perfect in round-to-nearest mode */
73 	return(T);
74 }
75