dsi_bitstream/codes/
minimal_binary.rs

1/*
2 * SPDX-FileCopyrightText: 2023 Tommaso Fontana
3 * SPDX-FileCopyrightText: 2023 Inria
4 * SPDX-FileCopyrightText: 2023 Sebastiano Vigna
5 *
6 * SPDX-License-Identifier: Apache-2.0 OR LGPL-2.1-or-later
7 */
8
9//! Minimal binary codes.
10//!
11//! A minimal binary code with upper bound *u* > 0 (AKA [truncated binary
12//! encoding](https://en.wikipedia.org/wiki/Truncated_binary_encoding)) is an
13//! optimal prefix-free code for the first *u* natural numbers with uniform
14//! distribution.
15//!
16//! There are several such codes, and the one implemented here is defined as
17//! follows: let *s* = ⌈log₂*u*⌉; then, given *x* < *u*, if *x* <
18//! 2*ˢ* − *u* then *x* is coded as the binary representation of *x*
19//! in *s* − 1 bits; otherwise, *x* is coded as the binary representation of *x*
20//! − *u* + 2*ˢ* in *s* bits.
21//!
22//! See the [codes module documentation](crate::codes) for some elaboration on
23//! the difference between the big-endian and little-endian versions of the
24//! codes.
25
26use crate::traits::*;
27
28/// Returns the length of the minimal binary code for `n` with upper bound `max`.
29#[must_use]
30#[inline(always)]
31pub fn len_minimal_binary(n: u64, max: u64) -> usize {
32    if max == 0 {
33        return 0;
34    }
35    let l = max.ilog2();
36    let limit = ((1_u64 << l) << 1).wrapping_sub(max);
37    let mut result = l as usize;
38    if n >= limit {
39        result += 1;
40    }
41    result
42}
43
44/// Trait for reading minimal binary codes.
45pub trait MinimalBinaryRead<E: Endianness>: BitRead<E> {
46    #[inline(always)]
47    fn read_minimal_binary(&mut self, max: u64) -> Result<u64, Self::Error> {
48        let l = max.ilog2();
49        let mut prefix = self.read_bits(l as _)?;
50        let limit = ((1_u64 << l) << 1).wrapping_sub(max);
51
52        Ok(if prefix < limit {
53            prefix
54        } else {
55            prefix <<= 1;
56            prefix |= self.read_bits(1)?;
57            prefix - limit
58        })
59    }
60}
61
62/// Trait for writing minimal binary codes.
63pub trait MinimalBinaryWrite<E: Endianness>: BitWrite<E> {
64    #[inline(always)]
65    fn write_minimal_binary(&mut self, n: u64, max: u64) -> Result<usize, Self::Error> {
66        let l = max.ilog2();
67        let limit = ((1_u64 << l) << 1).wrapping_sub(max);
68
69        if n < limit {
70            self.write_bits(n, l as _)?;
71            Ok(l as usize)
72        } else {
73            let to_write = n + limit;
74            self.write_bits(to_write >> 1, l as _)?;
75            self.write_bits(to_write & 1, 1)?;
76            Ok((l + 1) as usize)
77        }
78    }
79}
80
81impl<E: Endianness, B: BitRead<E>> MinimalBinaryRead<E> for B {}
82impl<E: Endianness, B: BitWrite<E>> MinimalBinaryWrite<E> for B {}
dsi_bitstream/codes/minimal_binary.rs

dsi_bitstream/codes/
minimal_binary.rs
