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//! Implementation of [Compact Hilbert Indices](https://dl.acm.org/doi/10.1109/CISIS.2007.16) by
//! Chris Hamilton.
/// Right rotation of x by b bits out of n.
fn rotate_right(x: usize, b: u32, n: u32) -> usize {
let l = x & ((1 << b) - 1);
let r = x >> b;
(l << (n - b)) | r
}
/// Left rotation of x by b bits out of n.
fn rotate_left(x: usize, b: u32, n: u32) -> usize {
rotate_right(x, n - b, n)
}
/// Binary reflected Gray code.
fn gray_code(i: usize) -> usize {
i ^ (i >> 1)
}
/// e(i), the entry point for the ith sub-hypercube.
fn entry_point(i: usize) -> usize {
if i == 0 {
0
} else {
gray_code((i - 1) & !1)
}
}
/// g(i), the inter sub-hypercube direction.
fn inter_direction(i: usize) -> u32 {
// g(i) counts the trailing set bits in i
(!i).trailing_zeros()
}
/// d(i), the intra sub-hypercube direction.
fn intra_direction(i: usize) -> u32 {
if i & 1 != 0 {
inter_direction(i)
} else if i > 0 {
inter_direction(i - 1)
} else {
0
}
}
/// T transformation inverse
fn t_inverse(dims: u32, e: usize, d: u32, a: usize) -> usize {
rotate_left(a, d, dims) ^ e
}
/// GrayCodeRankInverse
fn gray_code_rank_inverse(
dims: u32,
mu: usize,
pi: usize,
r: usize,
free_bits: u32,
) -> (usize, usize) {
// The inverse rank of r
let mut i = 0;
// gray_code(i)
let mut g = 0;
let mut j = free_bits - 1;
for k in (0..dims).rev() {
if mu & (1 << k) == 0 {
g |= pi & (1 << k);
i |= (g ^ (i >> 1)) & (1 << k);
} else {
i |= ((r >> j) & 1) << k;
g |= (i ^ (i >> 1)) & (1 << k);
j = j.wrapping_sub(1);
}
}
(i, g)
}
/// ExtractMask.
fn extract_mask(bits: &[u32], i: u32) -> (usize, u32) {
// The mask
let mut mu = 0;
// popcount(mu)
let mut free_bits = 0;
let dims = bits.len();
for j in (0..dims).rev() {
mu <<= 1;
if bits[j] > i {
mu |= 1;
free_bits += 1;
}
}
(mu, free_bits)
}
/// Compute the corresponding point for a Hilbert index (CompactHilbertIndexInverse).
pub fn hilbert_point(index: usize, bits: &[u32], point: &mut [usize]) {
let dims = bits.len() as u32;
let max = *bits.iter().max().unwrap();
let sum: u32 = bits.iter().sum();
let mut e = 0;
let mut k = 0;
// Next direction; we use d instead of d + 1 everywhere
let mut d = 1;
for x in point.iter_mut() {
*x = 0;
}
for i in (0..max).rev() {
let (mut mu, free_bits) = extract_mask(bits, i);
mu = rotate_right(mu, d, dims);
let pi = rotate_right(e, d, dims) & !mu;
let r = (index >> (sum - k - free_bits)) & ((1 << free_bits) - 1);
k += free_bits;
let (w, mut l) = gray_code_rank_inverse(dims, mu, pi, r, free_bits);
l = t_inverse(dims, e, d, l);
for x in point.iter_mut() {
*x |= (l & 1) << i;
l >>= 1;
}
e = e ^ rotate_right(entry_point(w), d, dims);
d = (d + intra_direction(w) + 1) % dims;
}
}
|
