From 62e0fec044b5727efa1841138f44d9a1d9537bcf Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@tavianator.com>
Date: Sat, 2 May 2020 13:48:07 -0400
Subject: color/order: Implement color orderings

---
 src/hilbert.rs | 136 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 136 insertions(+)
 create mode 100644 src/hilbert.rs

(limited to 'src/hilbert.rs')

diff --git a/src/hilbert.rs b/src/hilbert.rs
new file mode 100644
index 0000000..c0982d4
--- /dev/null
+++ b/src/hilbert.rs
@@ -0,0 +1,136 @@
+//! 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;
+    }
+}
-- 
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