Use fractional index to order the children of the tree

[Leeeon233]

This PR introduces the integration of the Fractional Index feature, which allows children nodes in a Tree structure to maintain order. This is particularly useful in scenarios such as ordered nested lists and ordered outline notes.

Fractional Index

We have forked the Fractional Index implementation from drifting-in-space/fractional_index and made simple extensions to fit Loro's usage requirements.

• Generate new Fractional Indexes evenly between left and right positions
• Optionally add random jitter to each generation of the Fractional Index. It can be used to avoid creating the element with the same fractional index.

Ordered Tree Node Children

With each node's creation and movement, we update a Fractional Index to represent its position. In the Tree Container, concurrent insertions or movements of new nodes at the same position will result in nodes with identical Fractional Indexes. However, we can use mechanisms like Lamport clocks as a tiebreaker. The challenge of creating or inserting nodes among those with the same Fractional Index remains.

To address this, we backtrack to the first unique Fractional Index to serve as the new right node. We then evenly distribute n new Fractional Index, assigning them to both the nodes with identical FIs and the newly created nodes.

API

import { Loro } from "loro-crdt";
let doc = new Loro();
doc.setFractionalIndexJitter(7);
let tree = doc.getTree("tree");
let root = tree.createNode();
let node = root.createNode(); // By default, append to the end of the parent node's children list
let node2 = root.createNode(0);  // Specify the child's position
node2.move(node); 
node.move(node2, 0); // Specify the child's position
node.move(); // Move to become the root node
node.moveAfter(node2);  // Move after the node
node.moveBefore(node2);  // Move before the node
node.index() // Index 0

Benchmark

group	main	rate	pr
1000 node checkout 10^3	88.0±1.52ms	3.00	263.8±3.47ms
300 deep node random checkout 10^3	751.0±4.02ms	1.85	1391.8±9.23ms
create node append/1000	199.2±0.57µs	4.62	920.9±25.80µs
create node append/10000	2.9±0.02ms	4.11	12.1±0.44ms
create node append/100000	36.3±0.19ms	7.24	262.4±3.10ms
create node append/1000000	547.3±6.89ms	21.78	11.9±0.03s
create node front/1000	200.4±1.29µs	3.89	780.5±5.02µs
create node front/10000	3.0±0.06ms	3.57	10.6±0.09ms
create node front/100000	36.8±0.68ms	6.63	244.1±2.30ms
create node front/1000000	562.9±24.39ms	18.64	10.5±0.09s
move node append/1000	870.8±47.06µs	3.03	2.6±0.53ms
move node append/10000	8.7±0.55ms	2.87	25.0±4.54ms
move node append/100000	85.9±4.05ms	3.00	257.7±14.12ms
move node append/1000000	915.3±3.72ms	9.64	8.8±0.04s
move node front/1000	876.3±50.56µs	2.95	2.6±0.52ms
move node front/10000	8.7±0.50ms	2.85	24.7±4.73ms
move node front/100000	86.9±4.55ms	2.74	237.8±3.07ms
move node front/1000000	919.5±9.55ms	9.57	8.8±0.03s
realtime tree move	625.8±141.63ms	1.00	628.2±178.52ms