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 */
23 static 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
27 float
cbrtf(float x)28 cbrtf(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