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/*
 * SPDX-FileCopyrightText: 2023 Tommaso Fontana
 * SPDX-FileCopyrightText: 2023 Inria
 * SPDX-FileCopyrightText: 2023 Sebastiano Vigna
 *
 * SPDX-License-Identifier: Apache-2.0 OR LGPL-2.1-or-later
 */

//! Minimal binary codes.
//!
//! A minimal binary code with upper bound `u > 0` (AKA [truncated binary
//! encoding](https://en.wikipedia.org/wiki/Truncated_binary_encoding)) is an
//! optimal prefix-free code for the first `u` natural numbers with uniform distribution.
//!
//! There are several such prefix-free codes, and the one implemented here is
//! defined as follows: if `s = ⌊log₂u⌋`, then the first `2^(s+1) - u` codewords are
//! the first binary numbers of length `s – 1`, and the remaining codewords
//! are the last `2u - 2^(s+1)` binary numbers of length `s`.

use crate::traits::*;

/// Return the length of the minimal binary code for `n` with upper bound `max`.
#[must_use]
#[inline]
pub fn len_minimal_binary(n: u64, max: u64) -> usize {
    if max == 0 {
        return 0;
    }
    let l = max.ilog2();
    let limit = (1 << (l + 1)) - max;
    let mut result = l as usize;
    if n >= limit {
        result += 1;
    }
    result
}

/// Trait for reading minimal binary codes.
pub trait MinimalBinaryRead<E: Endianness>: BitRead<E> {
    #[inline(always)]
    fn read_minimal_binary(&mut self, max: u64) -> Result<u64, Self::Error> {
        let l = max.ilog2();
        let mut prefix = self.read_bits(l as _)?;
        let limit = (1 << (l + 1)) - max;

        Ok(if prefix < limit {
            prefix
        } else {
            prefix <<= 1;
            prefix |= self.read_bits(1)?;
            prefix - limit
        })
    }
}

/// Trait for writing minimal binary codes.
pub trait MinimalBinaryWrite<E: Endianness>: BitWrite<E> {
    #[inline]
    fn write_minimal_binary(&mut self, n: u64, max: u64) -> Result<usize, Self::Error> {
        let l = max.ilog2();
        let limit = (1 << (l + 1)) - max;

        if n < limit {
            self.write_bits(n, l as _)?;
            Ok(l as usize)
        } else {
            let to_write = n + limit;
            self.write_bits(to_write >> 1, l as _)?;
            self.write_bits(to_write & 1, 1)?;
            Ok((l + 1) as usize)
        }
    }
}

impl<E: Endianness, B: BitRead<E>> MinimalBinaryRead<E> for B {}
impl<E: Endianness, B: BitWrite<E>> MinimalBinaryWrite<E> for B {}