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utils.rs
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/
utils.rs
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/// Compute the padding needed for alignement, i.e., the number so that
/// `((value + pad_align_to(value, bits) & (bits - 1) == 0`.
///
/// ```
/// use sux::utils::pad_align_to;
/// assert_eq!(7 + pad_align_to(7, 8), 8);
/// assert_eq!(8 + pad_align_to(8, 8), 8);
/// assert_eq!(9 + pad_align_to(9, 8), 16);
/// ```
pub fn pad_align_to(value: usize, bits: usize) -> usize {
value.wrapping_neg() & (bits - 1)
}
#[inline(always)]
/// Return the i-th
/// ```
/// use sux::utils::select_in_word;
///
/// assert_eq!(select_in_word(0b1, 0), 0);
/// assert_eq!(select_in_word(0b11, 1), 1);
/// assert_eq!(select_in_word(0b101, 1), 2);
/// assert_eq!(select_in_word(0x8000_0000_0000_0000, 0), 63);
/// assert_eq!(select_in_word(0x8000_0000_8000_0000, 0), 31);
/// assert_eq!(select_in_word(0x8000_0000_8000_0000, 1), 63);
/// ```
pub fn select_in_word(word: u64, rank: usize) -> usize {
debug_assert!(rank < word.count_ones() as _);
#[cfg(target_feature = "bmi2")]
{
use core::arch::x86_64::_pdep_u64;
// A Fast x86 Implementation of Select
// by Prashant Pandey, Michael A. Bender, and Rob Johnson
let mask = 1 << rank;
let one = unsafe { _pdep_u64(mask, word) };
one.trailing_zeros() as usize
}
#[cfg(not(target_feature = "bmi2"))]
{
// [1] Sebastiano Vigna. Broadword Implementation of Rank/Select
// Queries. WEA, 2008
//
// [2] Simon Gog, Matthias Petri. Optimized succinct data structures
// for massive data. Softw. Pract. Exper., 2014
//
// [3] Sebastiano Vigna. MG4J 5.2.1. http://mg4j.di.unimi.it/
//
// [4] Facebook Folly library: https://github.com/facebook/folly
//
// geq_rank_step_8.trailing_zeroes() has been replaced by
// geq_rank_step_8.count_ones() following a suggestion by
// Giuseppe Ottaviano.
const ONES_STEP_4: u64 = 0x1111111111111111;
const ONES_STEP_8: u64 = 0x0101010101010101;
const LAMBDAS_STEP_8: u64 = 0x80 * ONES_STEP_8;
let mut s = word;
s = s - ((s & (0xA * ONES_STEP_4)) >> 1);
s = (s & (0x3 * ONES_STEP_4)) + ((s >> 2) & (0x3 * ONES_STEP_4));
s = (s + (s >> 4)) & (0xF * ONES_STEP_8);
let byte_sums: u64 = s.wrapping_mul(ONES_STEP_8);
let rank_step_8: u64 = rank as u64 * ONES_STEP_8;
let geq_rank_step_8: u64 = ((rank_step_8 | LAMBDAS_STEP_8) - byte_sums) & LAMBDAS_STEP_8;
let place = (geq_rank_step_8.count_ones() * 8) as usize;
let byte_rank: u64 = rank as u64 - (((byte_sums << 8) >> place) & 0xFF_u64);
let index = ((word >> place) & 0xFF) | (byte_rank << 8);
place + SELECT_IN_BYTE[index as usize] as usize
}
}
#[inline(always)]
pub fn select_zero_in_word(word: u64, rank: usize) -> usize {
select_in_word(!word, rank)
}
#[cfg(test)]
mod test {
use crate::utils::{select_in_word, select_zero_in_word};
use rand::rngs::SmallRng;
use rand::SeedableRng;
use rand::{Rng, RngCore};
#[test]
fn test_select_in_word_sparse() {
let mut rng = SmallRng::seed_from_u64(0);
for _ in 0..100 {
let ones = rng.gen_range(1..10);
let mut word: u64 = 0;
for _ in 0..ones {
word |= 1 << rng.gen_range(0..64);
}
let mut new_word = word;
for i in 0..word.count_ones() {
assert_eq!(
select_in_word(word, i as _),
new_word.trailing_zeros() as usize,
);
new_word &= new_word - 1;
}
}
}
#[test]
fn test_select_in_word() {
let mut rng = SmallRng::seed_from_u64(0);
for _ in 0..100 {
let word = rng.next_u64();
let mut new_word = word;
for i in 0..word.count_ones() {
assert_eq!(
select_in_word(word, i as _),
new_word.trailing_zeros() as usize,
);
new_word &= new_word - 1;
}
}
}
#[test]
fn test_select_zero_in_word() {
let mut rng = SmallRng::seed_from_u64(0);
for _ in 0..100 {
let word = rng.next_u64();
let mut new_word = !word;
for i in 0..word.count_zeros() {
assert_eq!(
select_zero_in_word(word, i as _),
new_word.trailing_zeros() as usize,
);
new_word &= new_word - 1;
}
}
}
}
#[cfg(not(target_feature = "bmi2"))]
const SELECT_IN_BYTE: [u8; 2048] = [
8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
8, 8, 8, 1, 8, 2, 2, 1, 8, 3, 3, 1, 3, 2, 2, 1, 8, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1,
8, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1,
8, 6, 6, 1, 6, 2, 2, 1, 6, 3, 3, 1, 3, 2, 2, 1, 6, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1,
6, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1,
8, 7, 7, 1, 7, 2, 2, 1, 7, 3, 3, 1, 3, 2, 2, 1, 7, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1,
7, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1,
7, 6, 6, 1, 6, 2, 2, 1, 6, 3, 3, 1, 3, 2, 2, 1, 6, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1,
6, 5, 5, 1, 5, 2, 2, 1, 5, 3, 3, 1, 3, 2, 2, 1, 5, 4, 4, 1, 4, 2, 2, 1, 4, 3, 3, 1, 3, 2, 2, 1,
8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 3, 8, 3, 3, 2, 8, 8, 8, 4, 8, 4, 4, 2, 8, 4, 4, 3, 4, 3, 3, 2,
8, 8, 8, 5, 8, 5, 5, 2, 8, 5, 5, 3, 5, 3, 3, 2, 8, 5, 5, 4, 5, 4, 4, 2, 5, 4, 4, 3, 4, 3, 3, 2,
8, 8, 8, 6, 8, 6, 6, 2, 8, 6, 6, 3, 6, 3, 3, 2, 8, 6, 6, 4, 6, 4, 4, 2, 6, 4, 4, 3, 4, 3, 3, 2,
8, 6, 6, 5, 6, 5, 5, 2, 6, 5, 5, 3, 5, 3, 3, 2, 6, 5, 5, 4, 5, 4, 4, 2, 5, 4, 4, 3, 4, 3, 3, 2,
8, 8, 8, 7, 8, 7, 7, 2, 8, 7, 7, 3, 7, 3, 3, 2, 8, 7, 7, 4, 7, 4, 4, 2, 7, 4, 4, 3, 4, 3, 3, 2,
8, 7, 7, 5, 7, 5, 5, 2, 7, 5, 5, 3, 5, 3, 3, 2, 7, 5, 5, 4, 5, 4, 4, 2, 5, 4, 4, 3, 4, 3, 3, 2,
8, 7, 7, 6, 7, 6, 6, 2, 7, 6, 6, 3, 6, 3, 3, 2, 7, 6, 6, 4, 6, 4, 4, 2, 6, 4, 4, 3, 4, 3, 3, 2,
7, 6, 6, 5, 6, 5, 5, 2, 6, 5, 5, 3, 5, 3, 3, 2, 6, 5, 5, 4, 5, 4, 4, 2, 5, 4, 4, 3, 4, 3, 3, 2,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 4, 8, 4, 4, 3,
8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 5, 8, 5, 5, 3, 8, 8, 8, 5, 8, 5, 5, 4, 8, 5, 5, 4, 5, 4, 4, 3,
8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 6, 8, 6, 6, 3, 8, 8, 8, 6, 8, 6, 6, 4, 8, 6, 6, 4, 6, 4, 4, 3,
8, 8, 8, 6, 8, 6, 6, 5, 8, 6, 6, 5, 6, 5, 5, 3, 8, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3,
8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 3, 8, 8, 8, 7, 8, 7, 7, 4, 8, 7, 7, 4, 7, 4, 4, 3,
8, 8, 8, 7, 8, 7, 7, 5, 8, 7, 7, 5, 7, 5, 5, 3, 8, 7, 7, 5, 7, 5, 5, 4, 7, 5, 5, 4, 5, 4, 4, 3,
8, 8, 8, 7, 8, 7, 7, 6, 8, 7, 7, 6, 7, 6, 6, 3, 8, 7, 7, 6, 7, 6, 6, 4, 7, 6, 6, 4, 6, 4, 4, 3,
8, 7, 7, 6, 7, 6, 6, 5, 7, 6, 6, 5, 6, 5, 5, 3, 7, 6, 6, 5, 6, 5, 5, 4, 6, 5, 5, 4, 5, 4, 4, 3,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 5, 8, 8, 8, 5, 8, 5, 5, 4,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 6, 8, 6, 6, 4,
8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 6, 8, 6, 6, 5, 8, 8, 8, 6, 8, 6, 6, 5, 8, 6, 6, 5, 6, 5, 5, 4,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 4,
8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 5, 8, 8, 8, 7, 8, 7, 7, 5, 8, 7, 7, 5, 7, 5, 5, 4,
8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 6, 8, 8, 8, 7, 8, 7, 7, 6, 8, 7, 7, 6, 7, 6, 6, 4,
8, 8, 8, 7, 8, 7, 7, 6, 8, 7, 7, 6, 7, 6, 6, 5, 8, 7, 7, 6, 7, 6, 6, 5, 7, 6, 6, 5, 6, 5, 5, 4,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 6, 8, 6, 6, 5,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 5,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 6,
8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 6, 8, 8, 8, 7, 8, 7, 7, 6, 8, 7, 7, 6, 7, 6, 6, 5,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 7, 8, 7, 7, 6,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7,
];