From 1ce47bfc47d1b8be0e3b608e3fa79bcd94cc9173 Mon Sep 17 00:00:00 2001
From: Christopher Haster <geky@geky.net>
Date: Sun, 31 Mar 2024 12:55:28 -0500
Subject: [PATCH] rbyd-rr: Implemented coloring during rbyd compaction

This tweaks our rbyd compaction algorithm to color the alts correctly to
represent a balanced 2-3-4 tree.

Previously, we didn't really care about coloring the compacted tree,
because we didn't really care about color when pruning unreachable
alts.

But now that we refuse to prune isolated black alts, or risk unbalancing
the underlying 2-3-4 tree, it's important we color the compacted tree
correctly. Otherwise the unreachable alts that terminate our binary nodes
will just never be pruned, unbalancing each layer of the tree by ~1.

Compaction without coloring:

  tags:                effective rby tree:
  data a   <.              .---> a
  data b   <--.        .---b-b-> b
  data c   <----.      |   .---> c
  data d   <------.    b-b-b-b-> d
  altble a <. | | |
  altble b -|-' | |
  null      |   | |    effective 2-3-4 tree:
  altble c <--.-' |      .---o  -.
  altble d -|-|---'      |   o   |
  null      | |        .-o .-o   +- h=4
  altble b -' |        | o | o   |
  altble d ---'        a b c d  -'
  null

Compaction with coloring:

  tags:                effective rby tree:
  data a   <.              .---> a
  data b   <--.        .---r-b-> b
  data c   <----.      |   .---> c
  data d   <------.    r-b-r-b-> d
  altrle a <. | | |
  altble b -|-' | |
  null      |   | |    effective 2-3-4 tree:
  altrle c <--.-' |      .---o  -.
  altble d -|-|---'    .-o .-o   +- h=2
  null      | |        a b c d  -'
  altrle b -' |
  altble d ---'
  null

Note that if the compacted tree is not full, i.e. not a power-of-two, we
need to make sure the resulting unary nodes are still colored black.
Isolated red alts are not allowed and would create even more hilarious
problems.

Fortunately there is just enough context in lfsr_rbyd_appendcompaction,
since we know exactly where each layer ends, to determine if each node
is binary or unary without needing to attempt to read unnecessary tags.

It's also worth noting the resulting unary nodes may seem like an
unnecessary side effect, but they are actually quite useful here for
preserving the underlying 2-3-4 balance! In the same way unary nodes
preserve the 2-3-4 balance during range operations, unary nodes in the
compacted tree can be consumed later to introduce new attrs without
unbalancing the tree.

Now I'm wondering, how would a rebalancing algorithm even work on a
red-black tree without unary nodes...? Did I dodge a bullet here?

Unaligned compaction with coloring:

  tags:                  effective rby tree:
  data a   <.                    .---> a
  data b   <--.              .---r-b-> b
  data c   <----.            |   .---> c
  data d   <------.      .---r-b-r-b-> d
  data e   <--------.    r-b---b---b-> e
  altrle a <. | | | |
  altble b -|-' | | |
  null      |   | | |    effective 2-3-4 tree:
  altrle c <--.-' | |          .-o  -.
  altble d -|-|---' |      .---o o   +- h=3
  null      | |     |    .-o .-o o   |
  altble e <----.---'    a b c d e  -'
  null      | | |
  altrle b <. | |
  altble d -|-' |
  null      |   |
  altble e <--.-'
  null      | |
  altrle d -' |
  altble e ---'
  null

Code changes minimal, just needed some twiddly logic in
lfsr_rbyd_appendcompaction to make this work:

           code          stack
  before: 34256           2864
  after:  34288 (+0.1%)   2864 (+0.0%)
---
 lfs.c | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/lfs.c b/lfs.c
index 6bcd0bda..53281bd4 100644
--- a/lfs.c
+++ b/lfs.c
@@ -3734,8 +3734,9 @@ static int lfsr_rbyd_appendcompaction(lfs_t *lfs, lfsr_rbyd_t *rbyd,
 
                     // ignore shrub trunks, unless we are actually compacting
                     // a shrub tree
-                    if (!lfsr_rbyd_isshrub(rbyd)
-                            && lfsr_tag_isshrub(tag__)) {
+                    if (!lfsr_tag_isalt(tag__)
+                            && lfsr_tag_isshrub(tag__)
+                            && !lfsr_rbyd_isshrub(rbyd)) {
                         trunk = off;
                         weight = 0;
                         continue;
@@ -3765,7 +3766,12 @@ static int lfsr_rbyd_appendcompaction(lfs_t *lfs, lfsr_rbyd_t *rbyd,
 
                 // connect with an altle
                 err = lfsr_rbyd_appendtag(lfs, rbyd,
-                        LFSR_TAG_ALT(LFSR_TAG_LE, LFSR_TAG_B, tag),
+                        LFSR_TAG_ALT(
+                            LFSR_TAG_LE,
+                            (i == 0 && off < layer_)
+                                ? LFSR_TAG_R
+                                : LFSR_TAG_B,
+                            tag),
                         weight,
                         rbyd->eoff - trunk);
                 if (err) {