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
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
cbrtf(float x)27 float 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