libm/math/
cbrtf.rs

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
20const B1: u32 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
21const B2: u32 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */
22
23/// Cube root (f32)
24///
25/// Computes the cube root of the argument.
26#[cfg_attr(assert_no_panic, no_panic::no_panic)]
27pub fn cbrtf(x: f32) -> f32 {
28    let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
29
30    let mut r: f64;
31    let mut t: f64;
32    let mut ui: u32 = x.to_bits();
33    let mut hx: u32 = ui & 0x7fffffff;
34
35    if hx >= 0x7f800000 {
36        /* cbrt(NaN,INF) is itself */
37        return x + x;
38    }
39
40    /* rough cbrt to 5 bits */
41    if hx < 0x00800000 {
42        /* zero or subnormal? */
43        if hx == 0 {
44            return x; /* cbrt(+-0) is itself */
45        }
46        ui = (x * x1p24).to_bits();
47        hx = ui & 0x7fffffff;
48        hx = hx / 3 + B2;
49    } else {
50        hx = hx / 3 + B1;
51    }
52    ui &= 0x80000000;
53    ui |= hx;
54
55    /*
56     * First step Newton iteration (solving t*t-x/t == 0) to 16 bits.  In
57     * double precision so that its terms can be arranged for efficiency
58     * without causing overflow or underflow.
59     */
60    t = f32::from_bits(ui) as f64;
61    r = t * t * t;
62    t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
63
64    /*
65     * Second step Newton iteration to 47 bits.  In double precision for
66     * efficiency and accuracy.
67     */
68    r = t * t * t;
69    t = t * (x as f64 + x as f64 + r) / (x as f64 + r + r);
70
71    /* rounding to 24 bits is perfect in round-to-nearest mode */
72    t as f32
73}
libm/math/cbrtf.rs

libm/math/
cbrtf.rs
