1//! log base 2 approximation for a single-precision float.
2
3use super::F32;
4use core::f32::consts::LOG2_E;
5
6impl F32 {
7 /// Approximates the base 2 logarithm of the number.
8 pub fn log2(self) -> Self {
9 self.ln() * LOG2_E
10 }
11}
12
13#[cfg(test)]
14mod tests {
15 use super::F32;
16
17 pub(crate) const MAX_ERROR: f32 = 0.001;
18
19 /// log2(x) test vectors - `(input, output)`
20 pub(crate) const TEST_VECTORS: &[(f32, f32)] = &[
21 (1e-20, -66.43856),
22 (1e-19, -63.116634),
23 (1e-18, -59.794704),
24 (1e-17, -56.47278),
25 (1e-16, -53.15085),
26 (1e-15, -49.828922),
27 (1e-14, -46.506992),
28 (1e-13, -43.185066),
29 (1e-12, -39.863136),
30 (1e-11, -36.54121),
31 (1e-10, -33.21928),
32 (1e-09, -29.897352),
33 (1e-08, -26.575424),
34 (1e-07, -23.253496),
35 (1e-06, -19.931568),
36 (1e-05, -16.60964),
37 (1e-04, -13.287712),
38 (0.001, -9.965784),
39 (0.01, -6.643856),
40 (0.1, -3.321928),
41 (10.0, 3.321928),
42 (100.0, 6.643856),
43 (1000.0, 9.965784),
44 (10000.0, 13.287712),
45 (100000.0, 16.60964),
46 (1000000.0, 19.931568),
47 (10000000.0, 23.253496),
48 (100000000.0, 26.575424),
49 (1000000000.0, 29.897352),
50 (10000000000.0, 33.21928),
51 (100000000000.0, 36.54121),
52 (1000000000000.0, 39.863136),
53 (10000000000000.0, 43.185066),
54 (100000000000000.0, 46.506992),
55 (1000000000000000.0, 49.828922),
56 (1e+16, 53.15085),
57 (1e+17, 56.47278),
58 (1e+18, 59.794704),
59 (1e+19, 63.116634),
60 ];
61
62 #[test]
63 fn sanity_check() {
64 assert_eq!(F32::ONE.log2(), F32::ZERO);
65
66 for &(x, expected) in TEST_VECTORS {
67 let ln_x = F32(x).log2().0;
68 let relative_error = (ln_x - expected).abs() / expected;
69
70 assert!(
71 relative_error <= MAX_ERROR,
72 "relative_error {} too large: {} vs {}",
73 relative_error,
74 ln_x,
75 expected
76 );
77 }
78 }
79}
80