| 1 | /** |
| 2 | * Copyright (c) Meta Platforms, Inc. and affiliates. |
| 3 | * |
| 4 | * This source code is licensed under the MIT license found in the |
| 5 | * LICENSE file in the root directory of this source tree. |
| 6 | */ |
| 7 | |
| 8 | import prettyFormat from 'pretty-format'; |
| 9 | import {CompilerError} from '../CompilerError'; |
| 10 | import {BlockId, GeneratedSource, HIRFunction} from './HIR'; |
| 11 | import {eachTerminalSuccessor} from './visitors'; |
| 12 | |
| 13 | /* |
| 14 | * Computes the dominator tree of the given function. The returned `Dominator` stores the immediate |
| 15 | * dominator of each node in the function, which can be retrieved with `Dominator.prototype.get()`. |
| 16 | * |
| 17 | * A block X dominates block Y in the CFG if all paths to Y must flow through X. Thus the entry |
| 18 | * block dominates all other blocks. See https://en.wikipedia.org/wiki/Dominator_(graph_theory) |
| 19 | * for more. |
| 20 | */ |
| 21 | export function computeDominatorTree(fn: HIRFunction): Dominator<BlockId> { |
| 22 | const graph = buildGraph(fn); |
| 23 | const nodes = computeImmediateDominators(graph); |
| 24 | return new Dominator(graph.entry, nodes); |
| 25 | } |
| 26 | |
| 27 | /* |
| 28 | * Similar to `computeDominatorTree()` but computes the post dominators of the function. The returned |
| 29 | * `PostDominator` stores the immediate post-dominators of each node in the function. |
| 30 | * |
| 31 | * A block Y post-dominates block X in the CFG if all paths from X to the exit must flow through Y. |
| 32 | * The caller must specify whether to consider `throw` statements as exit nodes. If set to false, |
| 33 | * only return statements are considered exit nodes. |
| 34 | */ |
| 35 | export function computePostDominatorTree( |
| 36 | fn: HIRFunction, |
| 37 | options: {includeThrowsAsExitNode: boolean}, |
| 38 | ): PostDominator<BlockId> { |
| 39 | const graph = buildReverseGraph(fn, options.includeThrowsAsExitNode); |
| 40 | const nodes = computeImmediateDominators(graph); |
| 41 | |
| 42 | /* |
| 43 | * When options.includeThrowsAsExitNode is false, nodes that flow into a throws |
| 44 | * terminal and don't reach the exit node won't be in the node map. Add them |
| 45 | * with themselves as dominator to reflect that they don't flow into the exit. |
| 46 | */ |
| 47 | if (!options.includeThrowsAsExitNode) { |
| 48 | for (const [id] of fn.body.blocks) { |
| 49 | if (!nodes.has(id)) { |
| 50 | nodes.set(id, id); |
| 51 | } |
| 52 | } |
| 53 | } |
| 54 | return new PostDominator(graph.entry, nodes); |
| 55 | } |
| 56 | |
| 57 | type Node<T> = { |
| 58 | id: T; |
| 59 | index: number; |
| 60 | preds: Set<T>; |
| 61 | succs: Set<T>; |
| 62 | }; |
| 63 | type Graph<T> = { |
| 64 | entry: T; |
| 65 | nodes: Map<T, Node<T>>; |
| 66 | }; |
| 67 | |
| 68 | // A dominator tree that stores the immediate dominator for each block in function. |
| 69 | export class Dominator<T> { |
| 70 | #entry: T; |
| 71 | #nodes: Map<T, T>; |
| 72 | |
| 73 | constructor(entry: T, nodes: Map<T, T>) { |
| 74 | this.#entry = entry; |
| 75 | this.#nodes = nodes; |
| 76 | } |
| 77 | |
| 78 | // Returns the entry node |
| 79 | get entry(): T { |
| 80 | return this.#entry; |
| 81 | } |
| 82 | |
| 83 | /* |
| 84 | * Returns the immediate dominator of the block with @param id if present. Returns null |
| 85 | * if there is no immediate dominator (ie if the dominator is @param id itself). |
| 86 | */ |
| 87 | get(id: T): T | null { |
| 88 | const dominator = this.#nodes.get(id); |
| 89 | CompilerError.invariant(dominator !== undefined, { |
| 90 | reason: 'Unknown node', |
| 91 | loc: GeneratedSource, |
| 92 | }); |
| 93 | return dominator === id ? null : dominator; |
| 94 | } |
| 95 | |
| 96 | debug(): string { |
| 97 | const dominators = new Map(); |
| 98 | for (const [key, value] of this.#nodes) { |
| 99 | dominators.set(`bb${key}`, `bb${value}`); |
| 100 | } |
| 101 | return prettyFormat({ |
| 102 | entry: `bb${this.#entry}`, |
| 103 | dominators, |
| 104 | }); |
| 105 | } |
| 106 | } |
| 107 | |
| 108 | export class PostDominator<T> { |
| 109 | #exit: T; |
| 110 | #nodes: Map<T, T>; |
| 111 | |
| 112 | constructor(exit: T, nodes: Map<T, T>) { |
| 113 | this.#exit = exit; |
| 114 | this.#nodes = nodes; |
| 115 | } |
| 116 | |
| 117 | // Returns the node representing normal exit from the function, ie return terminals. |
| 118 | get exit(): T { |
| 119 | return this.#exit; |
| 120 | } |
| 121 | |
| 122 | /* |
| 123 | * Returns the immediate dominator of the block with @param id if present. Returns null |
| 124 | * if there is no immediate dominator (ie if the dominator is @param id itself). |
| 125 | */ |
| 126 | get(id: T): T | null { |
| 127 | const dominator = this.#nodes.get(id); |
| 128 | CompilerError.invariant(dominator !== undefined, { |
| 129 | reason: 'Unknown node', |
| 130 | loc: GeneratedSource, |
| 131 | }); |
| 132 | return dominator === id ? null : dominator; |
| 133 | } |
| 134 | |
| 135 | debug(): string { |
| 136 | const postDominators = new Map(); |
| 137 | for (const [key, value] of this.#nodes) { |
| 138 | postDominators.set(`bb${key}`, `bb${value}`); |
| 139 | } |
| 140 | return prettyFormat({ |
| 141 | exit: `bb${this.exit}`, |
| 142 | postDominators, |
| 143 | }); |
| 144 | } |
| 145 | } |
| 146 | |
| 147 | /* |
| 148 | * The implementation is a straightforward adaptation of https://www.cs.rice.edu/~keith/Embed/dom.pdf |
| 149 | * except that CFG nodes ordering is inverted (so the comparison functions are swapped) |
| 150 | */ |
| 151 | function computeImmediateDominators<T>(graph: Graph<T>): Map<T, T> { |
| 152 | const nodes: Map<T, T> = new Map(); |
| 153 | nodes.set(graph.entry, graph.entry); |
| 154 | let changed = true; |
| 155 | while (changed) { |
| 156 | changed = false; |
| 157 | for (const [id, node] of graph.nodes) { |
| 158 | // Skip start node |
| 159 | if (node.id === graph.entry) { |
| 160 | continue; |
| 161 | } |
| 162 | |
| 163 | // first processed predecessor |
| 164 | let newIdom: T | null = null; |
| 165 | for (const pred of node.preds) { |
| 166 | if (nodes.has(pred)) { |
| 167 | newIdom = pred; |
| 168 | break; |
| 169 | } |
| 170 | } |
| 171 | CompilerError.invariant(newIdom !== null, { |
| 172 | reason: `At least one predecessor must have been visited for block ${id}`, |
| 173 | loc: GeneratedSource, |
| 174 | }); |
| 175 | |
| 176 | for (const pred of node.preds) { |
| 177 | // For all other predecessors |
| 178 | if (pred === newIdom) { |
| 179 | continue; |
| 180 | } |
| 181 | const predDom = nodes.get(pred); |
| 182 | if (predDom !== undefined) { |
| 183 | newIdom = intersect(pred, newIdom, graph, nodes); |
| 184 | } |
| 185 | } |
| 186 | |
| 187 | if (nodes.get(id) !== newIdom) { |
| 188 | nodes.set(id, newIdom); |
| 189 | changed = true; |
| 190 | } |
| 191 | } |
| 192 | } |
| 193 | return nodes; |
| 194 | } |
| 195 | |
| 196 | function intersect<T>(a: T, b: T, graph: Graph<T>, nodes: Map<T, T>): T { |
| 197 | let block1: Node<T> = graph.nodes.get(a)!; |
| 198 | let block2: Node<T> = graph.nodes.get(b)!; |
| 199 | while (block1 !== block2) { |
| 200 | while (block1.index > block2.index) { |
| 201 | const dom = nodes.get(block1.id)!; |
| 202 | block1 = graph.nodes.get(dom)!; |
| 203 | } |
| 204 | while (block2.index > block1.index) { |
| 205 | const dom = nodes.get(block2.id)!; |
| 206 | block2 = graph.nodes.get(dom)!; |
| 207 | } |
| 208 | } |
| 209 | return block1.id; |
| 210 | } |
| 211 | |
| 212 | // Turns the HIRFunction into a simplified internal form that is shared for dominator/post-dominator computation |
| 213 | function buildGraph(fn: HIRFunction): Graph<BlockId> { |
| 214 | const graph: Graph<BlockId> = {entry: fn.body.entry, nodes: new Map()}; |
| 215 | let index = 0; |
| 216 | for (const [id, block] of fn.body.blocks) { |
| 217 | graph.nodes.set(id, { |
| 218 | id, |
| 219 | index: index++, |
| 220 | preds: block.preds, |
| 221 | succs: new Set(eachTerminalSuccessor(block.terminal)), |
| 222 | }); |
| 223 | } |
| 224 | return graph; |
| 225 | } |
| 226 | |
| 227 | /* |
| 228 | * Turns the HIRFunction into a simplified internal form that is shared for dominator/post-dominator computation, |
| 229 | * notably this version flips the graph and puts the reversed form back into RPO (such that successors are before predecessors). |
| 230 | * Note that RPO of the reversed graph isn't the same as reversed RPO of the forward graph because of loops. |
| 231 | */ |
| 232 | function buildReverseGraph( |
| 233 | fn: HIRFunction, |
| 234 | includeThrowsAsExitNode: boolean, |
| 235 | ): Graph<BlockId> { |
| 236 | const nodes: Map<BlockId, Node<BlockId>> = new Map(); |
| 237 | const exitId = fn.env.nextBlockId; |
| 238 | const exit: Node<BlockId> = { |
| 239 | id: exitId, |
| 240 | index: 0, |
| 241 | preds: new Set(), |
| 242 | succs: new Set(), |
| 243 | }; |
| 244 | nodes.set(exitId, exit); |
| 245 | |
| 246 | for (const [id, block] of fn.body.blocks) { |
| 247 | const node: Node<BlockId> = { |
| 248 | id, |
| 249 | index: 0, |
| 250 | preds: new Set(eachTerminalSuccessor(block.terminal)), |
| 251 | succs: new Set(block.preds), |
| 252 | }; |
| 253 | if (block.terminal.kind === 'return') { |
| 254 | node.preds.add(exitId); |
| 255 | exit.succs.add(id); |
| 256 | } else if (block.terminal.kind === 'throw' && includeThrowsAsExitNode) { |
| 257 | node.preds.add(exitId); |
| 258 | exit.succs.add(id); |
| 259 | } |
| 260 | nodes.set(id, node); |
| 261 | } |
| 262 | |
| 263 | // Put nodes into RPO form |
| 264 | const visited = new Set<BlockId>(); |
| 265 | const postorder: Array<BlockId> = []; |
| 266 | function visit(id: BlockId): void { |
| 267 | if (visited.has(id)) { |
| 268 | return; |
| 269 | } |
| 270 | visited.add(id); |
| 271 | const node = nodes.get(id)!; |
| 272 | for (const successor of node.succs) { |
| 273 | visit(successor); |
| 274 | } |
| 275 | postorder.push(id); |
| 276 | } |
| 277 | visit(exitId); |
| 278 | |
| 279 | const rpo: Graph<BlockId> = {entry: exitId, nodes: new Map()}; |
| 280 | let index = 0; |
| 281 | for (const id of postorder.reverse()) { |
| 282 | const node = nodes.get(id)!; |
| 283 | node.index = index++; |
| 284 | rpo.nodes.set(id, node); |
| 285 | } |
| 286 | return rpo; |
| 287 | } |