1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
//! Fixed-point approximation of `128 * log2(x)` used throughout the SILK signal-processing helpers.
//!
//! This module mirrors `silk_lin2log` from `silk/lin2log.c` in the reference C implementation. The
//! routine exposes a cheap logarithm that scales its input by 128, delivering results in the Q7
//! domain without resorting to floating-point math. The translation sticks closely to the C code,
//! including the implicit behaviour for zero and negative inputs.
/// Approximation of `128 * log2(x)` for 32-bit integers.
///
/// The return value lives in the Q7 domain – i.e. it is the base-2 logarithm multiplied by 128.
/// The behaviour matches the C implementation: non-positive inputs yield a result of `-128`, and
/// negative values are accepted for completeness even though the original algorithm only relies on
/// non-negative magnitudes.
#[allow(clippy::cast_possible_wrap, clippy::cast_sign_loss)]
pub fn lin2log(in_lin: i32) -> i32 {
let in_lin_u32 = in_lin as u32;
let lz = in_lin_u32.leading_zeros() as i32;
// Rotate so that the leading one sits in bit position seven, making the lower bits the
// fractional component of the logarithm in Q7 space.
let rot = 24 - lz;
let rotated = if rot >= 0 {
in_lin_u32.rotate_right(rot as u32)
} else {
in_lin_u32.rotate_left((-rot) as u32)
} as i32;
let frac_q7 = rotated & 0x7f;
let product = frac_q7 * (128 - frac_q7);
// 179/2^16 is the quadratic correction that tightens the polynomial approximation.
let correction = frac_q7 + ((i64::from(product) * 179) >> 16) as i32;
((31 - lz) * 128) + correction
}
#[cfg(test)]
mod tests {
use super::lin2log;
#[test]
fn matches_reference_values() {
let cases = [
(0, -128),
(1, 0),
(2, 128),
(3, 203),
(4, 256),
(5, 296),
(8, 384),
(16, 512),
(31, 634),
(32, 640),
(63, 765),
(64, 768),
(127, 894),
(128, 896),
(129, 897),
(1024, 1280),
(12_345, 1739),
(32_767, 1919),
(65_535, 2047),
(100_000, 2126),
(123_456_789, 3441),
(-1, 4095),
];
for (input, expected) in cases {
assert_eq!(lin2log(input), expected, "lin2log({input})");
}
}
}