1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */
2 /*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
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 use core::f32;
21
22 const B1: u32 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
23 const B2: u32 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
24
25 /// Cube root (f32)
26 ///
27 /// Computes the cube root of the argument.
28 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
cbrtf(x: f32) -> f3229 pub fn cbrtf(x: f32) -> f32 {
30 let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
31
32 let mut r: f64;
33 let mut t: f64;
34 let mut ui: u32 = x.to_bits();
35 let mut hx: u32 = ui & 0x7fffffff;
36
37 if hx >= 0x7f800000 {
38 /* cbrt(NaN,INF) is itself */
39 return x + x;
40 }
41
42 /* rough cbrt to 5 bits */
43 if hx < 0x00800000 {
44 /* zero or subnormal? */
45 if hx == 0 {
46 return x; /* cbrt(+-0) is itself */
47 }
48 ui = (x * x1p24).to_bits();
49 hx = ui & 0x7fffffff;
50 hx = hx / 3 + B2;
51 } else {
52 hx = hx / 3 + B1;
53 }
54 ui &= 0x80000000;
55 ui |= hx;
56
57 /*
58 * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In
59 * double precision so that its terms can be arranged for efficiency
60 * without causing overflow or underflow.
61 */
62 t = f32::from_bits(ui) as f64;
63 r = t * t * t;
64 t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
65
66 /*
67 * Second step Newton iteration to 47 bits. In double precision for
68 * efficiency and accuracy.
69 */
70 r = t * t * t;
71 t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
72
73 /* rounding to 24 bits is perfect in round-to-nearest mode */
74 t as f32
75 }
76