.config/coc/extensions/coc-go-data/tools/pkg/mod/honnef.co/go/tools@v0.0.1-2020.1.5/ir/dom.go

   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
   5 package 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
  20 import (
  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 //
  33 func (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 //
  38 func (b *BasicBlock) Dominees() []*BasicBlock { return b.dom.children }
  39
  40 // Dominates reports whether b dominates c.
  41 func (b *BasicBlock) Dominates(c *BasicBlock) bool {
  42         return b.dom.pre <= c.dom.pre && c.dom.post <= b.dom.post
  43 }
  44
  45 type byDomPreorder []*BasicBlock
  46
  47 func (a byDomPreorder) Len() int           { return len(a) }
  48 func (a byDomPreorder) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
  49 func (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 //
  54 func (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.
  63 type 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 //
  72 func 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.
 175 func 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 //
 281 func 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 //
 296 func 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 //
 314 func 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
 399 func 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
 409 func 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
 432 func 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
 442 func 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 }