Add dominance algorithm implementation

Implements "A simple, fast dominance algorithm", to find the immediate
dominators of all nodes in a graph.

- https://www.cs.tufts.edu/comp/150FP/archive/keith-cooper/dom14.pdf

This will be used for a new experimental bundler package to be added.
This adds the empty package.

Test Plan: Run `yarn test` to execute unit-tests for the implementation

Reviewers: MonicaOlejniczak

Reviewed By: MonicaOlejniczak

Pull Request: #326

packages/bundlers/bundler-experimental/.nyc.json

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+{
+  "include": ["src/**/*.ts"],
+  "watermarks": {
+    "lines": [80, 95],
+    "functions": [80, 95],
+    "branches": [80, 95],
+    "statements": [80, 95]
+  }
+}

packages/bundlers/bundler-experimental/package.json

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+{
+  "name": "@atlaspack/bundler-experimental",
+  "version": "2.12.0",
+  "license": "(MIT OR Apache-2.0)",
+  "publishConfig": {
+    "access": "public"
+  },
+  "repository": {
+    "type": "git",
+    "url": "https://github.com/atlassian-labs/atlaspack.git"
+  },
+  "main": "lib/index.js",
+  "source": "src/index.js",
+  "engines": {
+    "node": ">= 16.0.0",
+    "parcel": "^2.12.0"
+  },
+  "dependencies": {
+    "@atlaspack/core": "2.12.0",
+    "@atlaspack/diagnostic": "2.12.0",
+    "@atlaspack/feature-flags": "2.12.0",
+    "@atlaspack/graph": "3.2.0",
+    "@atlaspack/logger": "2.12.0",
+    "@atlaspack/plugin": "2.12.0",
+    "@atlaspack/rust": "2.12.0",
+    "@atlaspack/types": "2.12.0",
+    "@atlaspack/utils": "2.12.0",
+    "nullthrows": "^1.1.1"
+  },
+  "devDependencies": {
+    "@atlaspack/fs": "2.12.0"
+  }
+}

packages/bundlers/bundler-experimental/src/DominatorBundler/findAssetDominators/simpleFastDominance.js

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+// @flow strict-local
+
+import {type NodeId, Graph, ALL_EDGE_TYPES} from '@atlaspack/graph';
+
+/**
+ * Implements "A simple, fast dominance algorithm", to find the immediate
+ * dominators of all nodes in a graph.
+ *
+ * Returns a map of node IDs to their immediate dominator's node ID.
+ * This map is represented by an array where the index is the node ID and the
+ * value is its dominator.
+ *
+ * For example, given a node `3`, `dominators[3]` is the immediate dominator
+ * of node 3.
+ *
+ * - https://www.cs.tufts.edu/comp/150FP/archive/keith-cooper/dom14.pdf
+ */
+export function simpleFastDominance<T>(graph: Graph<T, number>): NodeId[] {
+  const rootNodeId = graph.rootNodeId;
+  if (rootNodeId == null) {
+    throw new Error('Graph must have a root node');
+  }
+
+  const postOrder = getGraphPostOrder(graph);
+  const reversedPostOrder = postOrder.slice().reverse();
+  const dominators = Array(graph.nodes.length).fill(null);
+
+  const postOrderIndexes = Array(graph.nodes.length).fill(null);
+  for (let i = 0; i < postOrder.length; i++) {
+    postOrderIndexes[postOrder[i]] = i;
+  }
+
+  dominators[rootNodeId] = graph.rootNodeId;
+
+  let changed = true;
+
+  while (changed) {
+    changed = false;
+
+    for (let node of reversedPostOrder) {
+      if (node === graph.rootNodeId) continue;
+
+      let newImmediateDominator = null;
+      graph.forEachNodeIdConnectedTo(
+        node,
+        (predecessor) => {
+          if (newImmediateDominator == null) {
+            newImmediateDominator = predecessor;
+          } else {
+            if (dominators[predecessor] == null) {
+              return;
+            }
+
+            newImmediateDominator = intersect(
+              postOrderIndexes,
+              dominators,
+              predecessor,
+              newImmediateDominator,
+            );
+          }
+        },
+        ALL_EDGE_TYPES,
+      );
+
+      if (dominators[node] !== newImmediateDominator) {
+        dominators[node] = newImmediateDominator;
+        changed = true;
+      }
+    }
+  }
+
+  return dominators;
+}
+
+/**
+ * Return the post-order of the graph.
+ */
+export function getGraphPostOrder<T>(
+  graph: Graph<T, number>,
+  type: number = 1,
+): NodeId[] {
+  const postOrder = [];
+  graph.traverse(
+    {
+      exit: (node) => {
+        postOrder.push(node);
+      },
+    },
+    graph.rootNodeId,
+    type,
+  );
+  return postOrder;
+}
+
+/**
+ * From "A Simple, Fast Dominance Algorithm"
+ * Keith D. Cooper, Timothy J. Harvey, and Ken Kennedy:
+ *
+ * > The intersection routine appears at the bottom of the figure.
+ * > It implements a “two-finger” algorithm – one can imagine a finger pointing
+ * > to each dominator set, each finger moving independently as the comparisons
+ * > dictate. In this case, the comparisons are on postorder numbers; for each
+ * > intersection, we start the two fingers at the ends of the two sets, and,
+ * > until the fingers point to the same postorder number, we move the finger
+ * > pointing to the smaller number back one element. Remember that nodes higher
+ * > in the dominator tree have higher postorder numbers, which is why intersect
+ * > moves the finger whose value is less than the other finger’s. When the two
+ * > fingers point at the same element, intersect returns that element. The set
+ * > resulting from the intersection begins with the returned element and chains
+ * > its way up the doms array to the entry node.
+ *
+ * `postOrder` is the post-order node list of the graph.
+ *
+ * `dominators` is the current immediate dominator state for node in the graph.
+ *
+ * This is coupled with the fact node ids are indexes into an array. It is a map
+ * of NodeId -> NodeId, where the value at index `i` is the immediate dominator
+ * of the node `i`.
+ *
+ * `predecessor` is one predecessor node id of the node we're currently
+ * computing the immediate dominator for.
+ *
+ * `newImmediateDominator` is current best immediate dominator candidate for the
+ * node we're computing the immediate dominator for.
+ *
+ * The algorithm is intersecting the dominator sets of the two predecessors and
+ * returning dominator node with the highest post-order number by walking up
+ * the dominator tree until the two sets intersect.
+ *
+ * The node with the highest post-order index is the immediate dominator, as
+ * it is the closest to the node we're computing for.
+ */
+export function intersect(
+  postOrderIndexes: number[],
+  dominators: (NodeId | null)[],
+  predecessor: NodeId,
+  newImmediateDominator: NodeId,
+): NodeId {
+  let n1: number = predecessor;
+  let n2: number = newImmediateDominator;
+  while (n1 !== n2) {
+    while (postOrderIndexes[n1] < postOrderIndexes[n2]) {
+      n1 = Number(dominators[n1]);
+    }
+    while (postOrderIndexes[n2] < postOrderIndexes[n1]) {
+      n2 = Number(dominators[n2]);
+    }
+  }
+  return n1;
+}

packages/bundlers/bundler-experimental/test/DominatorBundler/findAssetDominators/simpleFastDominance.test.js

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+// @flow strict-local
+
+import assert from 'assert';
+import {Graph} from '@atlaspack/graph';
+import {simpleFastDominance} from '../../../src/DominatorBundler/findAssetDominators/simpleFastDominance';
+
+const baseGraph = () => {
+  const inputGraph = new Graph();
+  const root = inputGraph.addNode('root');
+  inputGraph.setRootNodeId(root);
+  return {inputGraph, root};
+};
+
+describe('simpleFastDominance', () => {
+  it('it works on a linear graph', () => {
+    // digraph g {
+    //   root -> a -> b -> c -> d
+    // }
+    const {inputGraph, root} = baseGraph();
+    inputGraph.setRootNodeId(root);
+
+    const a = inputGraph.addNode('a');
+    const b = inputGraph.addNode('b');
+    const c = inputGraph.addNode('c');
+    const d = inputGraph.addNode('d');
+
+    inputGraph.addEdge(root, a);
+    inputGraph.addEdge(a, b);
+    inputGraph.addEdge(b, c);
+    inputGraph.addEdge(c, d);
+
+    const dominators = simpleFastDominance(inputGraph);
+    assert.equal(dominators[root], root);
+    assert.equal(dominators[a], root);
+    assert.equal(dominators[b], a);
+    assert.equal(dominators[c], b);
+    assert.equal(dominators[d], c);
+  });
+
+  it('it works on a tree graph', () => {
+    // digraph g {
+    //   root -> a;
+    //   root -> b;
+    //   a -> c;
+    //   a -> d;
+    //   b -> e;
+    // }
+    const {inputGraph, root} = baseGraph();
+
+    const a = inputGraph.addNode('a');
+    const b = inputGraph.addNode('b');
+    const c = inputGraph.addNode('c');
+    const d = inputGraph.addNode('d');
+    const e = inputGraph.addNode('e');
+
+    inputGraph.addEdge(root, a);
+    inputGraph.addEdge(root, b);
+    inputGraph.addEdge(a, c);
+    inputGraph.addEdge(a, d);
+    inputGraph.addEdge(b, e);
+
+    const dominators = simpleFastDominance(inputGraph);
+    assert.equal(dominators[root], root);
+    assert.equal(dominators[a], root);
+    assert.equal(dominators[b], root);
+    assert.equal(dominators[c], a);
+    assert.equal(dominators[d], a);
+    assert.equal(dominators[e], b);
+  });
+
+  it('it works on simple graph with multiple paths', () => {
+    // digraph g {
+    //   root -> a;
+    //   a -> b;
+    //   b -> c;
+    //   a -> c;
+    // }
+    const {inputGraph, root} = baseGraph();
+
+    const a = inputGraph.addNode('a');
+    const b = inputGraph.addNode('b');
+    const c = inputGraph.addNode('c');
+
+    inputGraph.addEdge(root, a);
+    inputGraph.addEdge(a, b);
+    inputGraph.addEdge(b, c);
+    inputGraph.addEdge(a, c);
+
+    const dominators = simpleFastDominance(inputGraph);
+    assert.equal(dominators[root], root);
+    assert.equal(dominators[a], root);
+    assert.equal(dominators[b], a);
+    assert.equal(dominators[c], a);
+  });
+
+  it('it works on a graph with multiple paths to nodes', () => {
+    // digraph g {
+    //   root -> a;
+    //   root -> b;
+    //   a -> c;
+    //   a -> d;
+    //   b -> d;
+    //   d -> c;
+    // }
+    const {inputGraph, root} = baseGraph();
+
+    const a = inputGraph.addNode('a');
+    const b = inputGraph.addNode('b');
+    const c = inputGraph.addNode('c');
+    const d = inputGraph.addNode('d');
+
+    inputGraph.addEdge(root, a);
+    inputGraph.addEdge(root, b);
+    inputGraph.addEdge(a, c);
+    inputGraph.addEdge(a, d);
+    inputGraph.addEdge(b, d);
+    inputGraph.addEdge(d, c);
+
+    const dominators = simpleFastDominance(inputGraph);
+    assert.equal(dominators[root], root);
+    assert.equal(dominators[a], root);
+    assert.equal(dominators[b], root);
+    assert.equal(dominators[c], root);
+    assert.equal(dominators[d], root);
+  });
+});