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
20use core::f32;
21
22const B1: u32 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */
23const 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)]
29pub 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}
libm/math/cbrtf.rs

libm/math/
cbrtf.rs
