1// Copyright 2013 The Go Authors. All rights reserved. 2// Use of this source code is governed by a BSD-style 3// license that can be found in the LICENSE file. 4 5package ir 6 7// This file defines algorithms related to dominance. 8 9// Dominator tree construction ---------------------------------------- 10// 11// We use the algorithm described in Lengauer & Tarjan. 1979. A fast 12// algorithm for finding dominators in a flowgraph. 13// http://doi.acm.org/10.1145/357062.357071 14// 15// We also apply the optimizations to SLT described in Georgiadis et 16// al, Finding Dominators in Practice, JGAA 2006, 17// http://jgaa.info/accepted/2006/GeorgiadisTarjanWerneck2006.10.1.pdf 18// to avoid the need for buckets of size > 1. 19 20import ( 21 "bytes" 22 "fmt" 23 "io" 24 "math/big" 25 "os" 26 "sort" 27) 28 29// Idom returns the block that immediately dominates b: 30// its parent in the dominator tree, if any. 31// The entry node (b.Index==0) does not have a parent. 32// 33func (b *BasicBlock) Idom() *BasicBlock { return b.dom.idom } 34 35// Dominees returns the list of blocks that b immediately dominates: 36// its children in the dominator tree. 37// 38func (b *BasicBlock) Dominees() []*BasicBlock { return b.dom.children } 39 40// Dominates reports whether b dominates c. 41func (b *BasicBlock) Dominates(c *BasicBlock) bool { 42 return b.dom.pre <= c.dom.pre && c.dom.post <= b.dom.post 43} 44 45type byDomPreorder []*BasicBlock 46 47func (a byDomPreorder) Len() int { return len(a) } 48func (a byDomPreorder) Swap(i, j int) { a[i], a[j] = a[j], a[i] } 49func (a byDomPreorder) Less(i, j int) bool { return a[i].dom.pre < a[j].dom.pre } 50 51// DomPreorder returns a new slice containing the blocks of f in 52// dominator tree preorder. 53// 54func (f *Function) DomPreorder() []*BasicBlock { 55 n := len(f.Blocks) 56 order := make(byDomPreorder, n) 57 copy(order, f.Blocks) 58 sort.Sort(order) 59 return order 60} 61 62// domInfo contains a BasicBlock's dominance information. 63type domInfo struct { 64 idom *BasicBlock // immediate dominator (parent in domtree) 65 children []*BasicBlock // nodes immediately dominated by this one 66 pre, post int32 // pre- and post-order numbering within domtree 67} 68 69// buildDomTree computes the dominator tree of f using the LT algorithm. 70// Precondition: all blocks are reachable (e.g. optimizeBlocks has been run). 71// 72func buildDomTree(fn *Function) { 73 // The step numbers refer to the original LT paper; the 74 // reordering is due to Georgiadis. 75 76 // Clear any previous domInfo. 77 for _, b := range fn.Blocks { 78 b.dom = domInfo{} 79 } 80 81 idoms := make([]*BasicBlock, len(fn.Blocks)) 82 83 order := make([]*BasicBlock, 0, len(fn.Blocks)) 84 seen := fn.blockset(0) 85 var dfs func(b *BasicBlock) 86 dfs = func(b *BasicBlock) { 87 if !seen.Add(b) { 88 return 89 } 90 for _, succ := range b.Succs { 91 dfs(succ) 92 } 93 if fn.fakeExits.Has(b) { 94 dfs(fn.Exit) 95 } 96 order = append(order, b) 97 b.post = len(order) - 1 98 } 99 dfs(fn.Blocks[0]) 100 101 for i := 0; i < len(order)/2; i++ { 102 o := len(order) - i - 1 103 order[i], order[o] = order[o], order[i] 104 } 105 106 idoms[fn.Blocks[0].Index] = fn.Blocks[0] 107 changed := true 108 for changed { 109 changed = false 110 // iterate over all nodes in reverse postorder, except for the 111 // entry node 112 for _, b := range order[1:] { 113 var newIdom *BasicBlock 114 do := func(p *BasicBlock) { 115 if idoms[p.Index] == nil { 116 return 117 } 118 if newIdom == nil { 119 newIdom = p 120 } else { 121 finger1 := p 122 finger2 := newIdom 123 for finger1 != finger2 { 124 for finger1.post < finger2.post { 125 finger1 = idoms[finger1.Index] 126 } 127 for finger2.post < finger1.post { 128 finger2 = idoms[finger2.Index] 129 } 130 } 131 newIdom = finger1 132 } 133 } 134 for _, p := range b.Preds { 135 do(p) 136 } 137 if b == fn.Exit { 138 for _, p := range fn.Blocks { 139 if fn.fakeExits.Has(p) { 140 do(p) 141 } 142 } 143 } 144 145 if idoms[b.Index] != newIdom { 146 idoms[b.Index] = newIdom 147 changed = true 148 } 149 } 150 } 151 152 for i, b := range idoms { 153 fn.Blocks[i].dom.idom = b 154 if b == nil { 155 // malformed CFG 156 continue 157 } 158 if i == b.Index { 159 continue 160 } 161 b.dom.children = append(b.dom.children, fn.Blocks[i]) 162 } 163 164 numberDomTree(fn.Blocks[0], 0, 0) 165 166 // printDomTreeDot(os.Stderr, fn) // debugging 167 // printDomTreeText(os.Stderr, root, 0) // debugging 168 169 if fn.Prog.mode&SanityCheckFunctions != 0 { 170 sanityCheckDomTree(fn) 171 } 172} 173 174// buildPostDomTree is like buildDomTree, but builds the post-dominator tree instead. 175func buildPostDomTree(fn *Function) { 176 // The step numbers refer to the original LT paper; the 177 // reordering is due to Georgiadis. 178 179 // Clear any previous domInfo. 180 for _, b := range fn.Blocks { 181 b.pdom = domInfo{} 182 } 183 184 idoms := make([]*BasicBlock, len(fn.Blocks)) 185 186 order := make([]*BasicBlock, 0, len(fn.Blocks)) 187 seen := fn.blockset(0) 188 var dfs func(b *BasicBlock) 189 dfs = func(b *BasicBlock) { 190 if !seen.Add(b) { 191 return 192 } 193 for _, pred := range b.Preds { 194 dfs(pred) 195 } 196 if b == fn.Exit { 197 for _, p := range fn.Blocks { 198 if fn.fakeExits.Has(p) { 199 dfs(p) 200 } 201 } 202 } 203 order = append(order, b) 204 b.post = len(order) - 1 205 } 206 dfs(fn.Exit) 207 208 for i := 0; i < len(order)/2; i++ { 209 o := len(order) - i - 1 210 order[i], order[o] = order[o], order[i] 211 } 212 213 idoms[fn.Exit.Index] = fn.Exit 214 changed := true 215 for changed { 216 changed = false 217 // iterate over all nodes in reverse postorder, except for the 218 // exit node 219 for _, b := range order[1:] { 220 var newIdom *BasicBlock 221 do := func(p *BasicBlock) { 222 if idoms[p.Index] == nil { 223 return 224 } 225 if newIdom == nil { 226 newIdom = p 227 } else { 228 finger1 := p 229 finger2 := newIdom 230 for finger1 != finger2 { 231 for finger1.post < finger2.post { 232 finger1 = idoms[finger1.Index] 233 } 234 for finger2.post < finger1.post { 235 finger2 = idoms[finger2.Index] 236 } 237 } 238 newIdom = finger1 239 } 240 } 241 for _, p := range b.Succs { 242 do(p) 243 } 244 if fn.fakeExits.Has(b) { 245 do(fn.Exit) 246 } 247 248 if idoms[b.Index] != newIdom { 249 idoms[b.Index] = newIdom 250 changed = true 251 } 252 } 253 } 254 255 for i, b := range idoms { 256 fn.Blocks[i].pdom.idom = b 257 if b == nil { 258 // malformed CFG 259 continue 260 } 261 if i == b.Index { 262 continue 263 } 264 b.pdom.children = append(b.pdom.children, fn.Blocks[i]) 265 } 266 267 numberPostDomTree(fn.Exit, 0, 0) 268 269 // printPostDomTreeDot(os.Stderr, fn) // debugging 270 // printPostDomTreeText(os.Stderr, fn.Exit, 0) // debugging 271 272 if fn.Prog.mode&SanityCheckFunctions != 0 { // XXX 273 sanityCheckDomTree(fn) // XXX 274 } 275} 276 277// numberDomTree sets the pre- and post-order numbers of a depth-first 278// traversal of the dominator tree rooted at v. These are used to 279// answer dominance queries in constant time. 280// 281func numberDomTree(v *BasicBlock, pre, post int32) (int32, int32) { 282 v.dom.pre = pre 283 pre++ 284 for _, child := range v.dom.children { 285 pre, post = numberDomTree(child, pre, post) 286 } 287 v.dom.post = post 288 post++ 289 return pre, post 290} 291 292// numberPostDomTree sets the pre- and post-order numbers of a depth-first 293// traversal of the post-dominator tree rooted at v. These are used to 294// answer post-dominance queries in constant time. 295// 296func numberPostDomTree(v *BasicBlock, pre, post int32) (int32, int32) { 297 v.pdom.pre = pre 298 pre++ 299 for _, child := range v.pdom.children { 300 pre, post = numberPostDomTree(child, pre, post) 301 } 302 v.pdom.post = post 303 post++ 304 return pre, post 305} 306 307// Testing utilities ---------------------------------------- 308 309// sanityCheckDomTree checks the correctness of the dominator tree 310// computed by the LT algorithm by comparing against the dominance 311// relation computed by a naive Kildall-style forward dataflow 312// analysis (Algorithm 10.16 from the "Dragon" book). 313// 314func sanityCheckDomTree(f *Function) { 315 n := len(f.Blocks) 316 317 // D[i] is the set of blocks that dominate f.Blocks[i], 318 // represented as a bit-set of block indices. 319 D := make([]big.Int, n) 320 321 one := big.NewInt(1) 322 323 // all is the set of all blocks; constant. 324 var all big.Int 325 all.Set(one).Lsh(&all, uint(n)).Sub(&all, one) 326 327 // Initialization. 328 for i := range f.Blocks { 329 if i == 0 { 330 // A root is dominated only by itself. 331 D[i].SetBit(&D[0], 0, 1) 332 } else { 333 // All other blocks are (initially) dominated 334 // by every block. 335 D[i].Set(&all) 336 } 337 } 338 339 // Iteration until fixed point. 340 for changed := true; changed; { 341 changed = false 342 for i, b := range f.Blocks { 343 if i == 0 { 344 continue 345 } 346 // Compute intersection across predecessors. 347 var x big.Int 348 x.Set(&all) 349 for _, pred := range b.Preds { 350 x.And(&x, &D[pred.Index]) 351 } 352 if b == f.Exit { 353 for _, p := range f.Blocks { 354 if f.fakeExits.Has(p) { 355 x.And(&x, &D[p.Index]) 356 } 357 } 358 } 359 x.SetBit(&x, i, 1) // a block always dominates itself. 360 if D[i].Cmp(&x) != 0 { 361 D[i].Set(&x) 362 changed = true 363 } 364 } 365 } 366 367 // Check the entire relation. O(n^2). 368 ok := true 369 for i := 0; i < n; i++ { 370 for j := 0; j < n; j++ { 371 b, c := f.Blocks[i], f.Blocks[j] 372 actual := b.Dominates(c) 373 expected := D[j].Bit(i) == 1 374 if actual != expected { 375 fmt.Fprintf(os.Stderr, "dominates(%s, %s)==%t, want %t\n", b, c, actual, expected) 376 ok = false 377 } 378 } 379 } 380 381 preorder := f.DomPreorder() 382 for _, b := range f.Blocks { 383 if got := preorder[b.dom.pre]; got != b { 384 fmt.Fprintf(os.Stderr, "preorder[%d]==%s, want %s\n", b.dom.pre, got, b) 385 ok = false 386 } 387 } 388 389 if !ok { 390 panic("sanityCheckDomTree failed for " + f.String()) 391 } 392 393} 394 395// Printing functions ---------------------------------------- 396 397// printDomTree prints the dominator tree as text, using indentation. 398//lint:ignore U1000 used during debugging 399func printDomTreeText(buf *bytes.Buffer, v *BasicBlock, indent int) { 400 fmt.Fprintf(buf, "%*s%s\n", 4*indent, "", v) 401 for _, child := range v.dom.children { 402 printDomTreeText(buf, child, indent+1) 403 } 404} 405 406// printDomTreeDot prints the dominator tree of f in AT&T GraphViz 407// (.dot) format. 408//lint:ignore U1000 used during debugging 409func printDomTreeDot(buf io.Writer, f *Function) { 410 fmt.Fprintln(buf, "//", f) 411 fmt.Fprintln(buf, "digraph domtree {") 412 for i, b := range f.Blocks { 413 v := b.dom 414 fmt.Fprintf(buf, "\tn%d [label=\"%s (%d, %d)\",shape=\"rectangle\"];\n", v.pre, b, v.pre, v.post) 415 // TODO(adonovan): improve appearance of edges 416 // belonging to both dominator tree and CFG. 417 418 // Dominator tree edge. 419 if i != 0 { 420 fmt.Fprintf(buf, "\tn%d -> n%d [style=\"solid\",weight=100];\n", v.idom.dom.pre, v.pre) 421 } 422 // CFG edges. 423 for _, pred := range b.Preds { 424 fmt.Fprintf(buf, "\tn%d -> n%d [style=\"dotted\",weight=0];\n", pred.dom.pre, v.pre) 425 } 426 } 427 fmt.Fprintln(buf, "}") 428} 429 430// printDomTree prints the dominator tree as text, using indentation. 431//lint:ignore U1000 used during debugging 432func printPostDomTreeText(buf io.Writer, v *BasicBlock, indent int) { 433 fmt.Fprintf(buf, "%*s%s\n", 4*indent, "", v) 434 for _, child := range v.pdom.children { 435 printPostDomTreeText(buf, child, indent+1) 436 } 437} 438 439// printDomTreeDot prints the dominator tree of f in AT&T GraphViz 440// (.dot) format. 441//lint:ignore U1000 used during debugging 442func printPostDomTreeDot(buf io.Writer, f *Function) { 443 fmt.Fprintln(buf, "//", f) 444 fmt.Fprintln(buf, "digraph pdomtree {") 445 for _, b := range f.Blocks { 446 v := b.pdom 447 fmt.Fprintf(buf, "\tn%d [label=\"%s (%d, %d)\",shape=\"rectangle\"];\n", v.pre, b, v.pre, v.post) 448 // TODO(adonovan): improve appearance of edges 449 // belonging to both dominator tree and CFG. 450 451 // Dominator tree edge. 452 if b != f.Exit { 453 fmt.Fprintf(buf, "\tn%d -> n%d [style=\"solid\",weight=100];\n", v.idom.pdom.pre, v.pre) 454 } 455 // CFG edges. 456 for _, pred := range b.Preds { 457 fmt.Fprintf(buf, "\tn%d -> n%d [style=\"dotted\",weight=0];\n", pred.pdom.pre, v.pre) 458 } 459 } 460 fmt.Fprintln(buf, "}") 461} 462