--- /dev/null
+// Copyright 2013 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package ir
+
+// This file defines algorithms related to dominance.
+
+// Dominator tree construction ----------------------------------------
+//
+// We use the algorithm described in Lengauer & Tarjan. 1979. A fast
+// algorithm for finding dominators in a flowgraph.
+// http://doi.acm.org/10.1145/357062.357071
+//
+// We also apply the optimizations to SLT described in Georgiadis et
+// al, Finding Dominators in Practice, JGAA 2006,
+// http://jgaa.info/accepted/2006/GeorgiadisTarjanWerneck2006.10.1.pdf
+// to avoid the need for buckets of size > 1.
+
+import (
+ "bytes"
+ "fmt"
+ "io"
+ "math/big"
+ "os"
+ "sort"
+)
+
+// Idom returns the block that immediately dominates b:
+// its parent in the dominator tree, if any.
+// The entry node (b.Index==0) does not have a parent.
+//
+func (b *BasicBlock) Idom() *BasicBlock { return b.dom.idom }
+
+// Dominees returns the list of blocks that b immediately dominates:
+// its children in the dominator tree.
+//
+func (b *BasicBlock) Dominees() []*BasicBlock { return b.dom.children }
+
+// Dominates reports whether b dominates c.
+func (b *BasicBlock) Dominates(c *BasicBlock) bool {
+ return b.dom.pre <= c.dom.pre && c.dom.post <= b.dom.post
+}
+
+type byDomPreorder []*BasicBlock
+
+func (a byDomPreorder) Len() int { return len(a) }
+func (a byDomPreorder) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
+func (a byDomPreorder) Less(i, j int) bool { return a[i].dom.pre < a[j].dom.pre }
+
+// DomPreorder returns a new slice containing the blocks of f in
+// dominator tree preorder.
+//
+func (f *Function) DomPreorder() []*BasicBlock {
+ n := len(f.Blocks)
+ order := make(byDomPreorder, n)
+ copy(order, f.Blocks)
+ sort.Sort(order)
+ return order
+}
+
+// domInfo contains a BasicBlock's dominance information.
+type domInfo struct {
+ idom *BasicBlock // immediate dominator (parent in domtree)
+ children []*BasicBlock // nodes immediately dominated by this one
+ pre, post int32 // pre- and post-order numbering within domtree
+}
+
+// buildDomTree computes the dominator tree of f using the LT algorithm.
+// Precondition: all blocks are reachable (e.g. optimizeBlocks has been run).
+//
+func buildDomTree(fn *Function) {
+ // The step numbers refer to the original LT paper; the
+ // reordering is due to Georgiadis.
+
+ // Clear any previous domInfo.
+ for _, b := range fn.Blocks {
+ b.dom = domInfo{}
+ }
+
+ idoms := make([]*BasicBlock, len(fn.Blocks))
+
+ order := make([]*BasicBlock, 0, len(fn.Blocks))
+ seen := fn.blockset(0)
+ var dfs func(b *BasicBlock)
+ dfs = func(b *BasicBlock) {
+ if !seen.Add(b) {
+ return
+ }
+ for _, succ := range b.Succs {
+ dfs(succ)
+ }
+ if fn.fakeExits.Has(b) {
+ dfs(fn.Exit)
+ }
+ order = append(order, b)
+ b.post = len(order) - 1
+ }
+ dfs(fn.Blocks[0])
+
+ for i := 0; i < len(order)/2; i++ {
+ o := len(order) - i - 1
+ order[i], order[o] = order[o], order[i]
+ }
+
+ idoms[fn.Blocks[0].Index] = fn.Blocks[0]
+ changed := true
+ for changed {
+ changed = false
+ // iterate over all nodes in reverse postorder, except for the
+ // entry node
+ for _, b := range order[1:] {
+ var newIdom *BasicBlock
+ do := func(p *BasicBlock) {
+ if idoms[p.Index] == nil {
+ return
+ }
+ if newIdom == nil {
+ newIdom = p
+ } else {
+ finger1 := p
+ finger2 := newIdom
+ for finger1 != finger2 {
+ for finger1.post < finger2.post {
+ finger1 = idoms[finger1.Index]
+ }
+ for finger2.post < finger1.post {
+ finger2 = idoms[finger2.Index]
+ }
+ }
+ newIdom = finger1
+ }
+ }
+ for _, p := range b.Preds {
+ do(p)
+ }
+ if b == fn.Exit {
+ for _, p := range fn.Blocks {
+ if fn.fakeExits.Has(p) {
+ do(p)
+ }
+ }
+ }
+
+ if idoms[b.Index] != newIdom {
+ idoms[b.Index] = newIdom
+ changed = true
+ }
+ }
+ }
+
+ for i, b := range idoms {
+ fn.Blocks[i].dom.idom = b
+ if b == nil {
+ // malformed CFG
+ continue
+ }
+ if i == b.Index {
+ continue
+ }
+ b.dom.children = append(b.dom.children, fn.Blocks[i])
+ }
+
+ numberDomTree(fn.Blocks[0], 0, 0)
+
+ // printDomTreeDot(os.Stderr, fn) // debugging
+ // printDomTreeText(os.Stderr, root, 0) // debugging
+
+ if fn.Prog.mode&SanityCheckFunctions != 0 {
+ sanityCheckDomTree(fn)
+ }
+}
+
+// buildPostDomTree is like buildDomTree, but builds the post-dominator tree instead.
+func buildPostDomTree(fn *Function) {
+ // The step numbers refer to the original LT paper; the
+ // reordering is due to Georgiadis.
+
+ // Clear any previous domInfo.
+ for _, b := range fn.Blocks {
+ b.pdom = domInfo{}
+ }
+
+ idoms := make([]*BasicBlock, len(fn.Blocks))
+
+ order := make([]*BasicBlock, 0, len(fn.Blocks))
+ seen := fn.blockset(0)
+ var dfs func(b *BasicBlock)
+ dfs = func(b *BasicBlock) {
+ if !seen.Add(b) {
+ return
+ }
+ for _, pred := range b.Preds {
+ dfs(pred)
+ }
+ if b == fn.Exit {
+ for _, p := range fn.Blocks {
+ if fn.fakeExits.Has(p) {
+ dfs(p)
+ }
+ }
+ }
+ order = append(order, b)
+ b.post = len(order) - 1
+ }
+ dfs(fn.Exit)
+
+ for i := 0; i < len(order)/2; i++ {
+ o := len(order) - i - 1
+ order[i], order[o] = order[o], order[i]
+ }
+
+ idoms[fn.Exit.Index] = fn.Exit
+ changed := true
+ for changed {
+ changed = false
+ // iterate over all nodes in reverse postorder, except for the
+ // exit node
+ for _, b := range order[1:] {
+ var newIdom *BasicBlock
+ do := func(p *BasicBlock) {
+ if idoms[p.Index] == nil {
+ return
+ }
+ if newIdom == nil {
+ newIdom = p
+ } else {
+ finger1 := p
+ finger2 := newIdom
+ for finger1 != finger2 {
+ for finger1.post < finger2.post {
+ finger1 = idoms[finger1.Index]
+ }
+ for finger2.post < finger1.post {
+ finger2 = idoms[finger2.Index]
+ }
+ }
+ newIdom = finger1
+ }
+ }
+ for _, p := range b.Succs {
+ do(p)
+ }
+ if fn.fakeExits.Has(b) {
+ do(fn.Exit)
+ }
+
+ if idoms[b.Index] != newIdom {
+ idoms[b.Index] = newIdom
+ changed = true
+ }
+ }
+ }
+
+ for i, b := range idoms {
+ fn.Blocks[i].pdom.idom = b
+ if b == nil {
+ // malformed CFG
+ continue
+ }
+ if i == b.Index {
+ continue
+ }
+ b.pdom.children = append(b.pdom.children, fn.Blocks[i])
+ }
+
+ numberPostDomTree(fn.Exit, 0, 0)
+
+ // printPostDomTreeDot(os.Stderr, fn) // debugging
+ // printPostDomTreeText(os.Stderr, fn.Exit, 0) // debugging
+
+ if fn.Prog.mode&SanityCheckFunctions != 0 { // XXX
+ sanityCheckDomTree(fn) // XXX
+ }
+}
+
+// numberDomTree sets the pre- and post-order numbers of a depth-first
+// traversal of the dominator tree rooted at v. These are used to
+// answer dominance queries in constant time.
+//
+func numberDomTree(v *BasicBlock, pre, post int32) (int32, int32) {
+ v.dom.pre = pre
+ pre++
+ for _, child := range v.dom.children {
+ pre, post = numberDomTree(child, pre, post)
+ }
+ v.dom.post = post
+ post++
+ return pre, post
+}
+
+// numberPostDomTree sets the pre- and post-order numbers of a depth-first
+// traversal of the post-dominator tree rooted at v. These are used to
+// answer post-dominance queries in constant time.
+//
+func numberPostDomTree(v *BasicBlock, pre, post int32) (int32, int32) {
+ v.pdom.pre = pre
+ pre++
+ for _, child := range v.pdom.children {
+ pre, post = numberPostDomTree(child, pre, post)
+ }
+ v.pdom.post = post
+ post++
+ return pre, post
+}
+
+// Testing utilities ----------------------------------------
+
+// sanityCheckDomTree checks the correctness of the dominator tree
+// computed by the LT algorithm by comparing against the dominance
+// relation computed by a naive Kildall-style forward dataflow
+// analysis (Algorithm 10.16 from the "Dragon" book).
+//
+func sanityCheckDomTree(f *Function) {
+ n := len(f.Blocks)
+
+ // D[i] is the set of blocks that dominate f.Blocks[i],
+ // represented as a bit-set of block indices.
+ D := make([]big.Int, n)
+
+ one := big.NewInt(1)
+
+ // all is the set of all blocks; constant.
+ var all big.Int
+ all.Set(one).Lsh(&all, uint(n)).Sub(&all, one)
+
+ // Initialization.
+ for i := range f.Blocks {
+ if i == 0 {
+ // A root is dominated only by itself.
+ D[i].SetBit(&D[0], 0, 1)
+ } else {
+ // All other blocks are (initially) dominated
+ // by every block.
+ D[i].Set(&all)
+ }
+ }
+
+ // Iteration until fixed point.
+ for changed := true; changed; {
+ changed = false
+ for i, b := range f.Blocks {
+ if i == 0 {
+ continue
+ }
+ // Compute intersection across predecessors.
+ var x big.Int
+ x.Set(&all)
+ for _, pred := range b.Preds {
+ x.And(&x, &D[pred.Index])
+ }
+ if b == f.Exit {
+ for _, p := range f.Blocks {
+ if f.fakeExits.Has(p) {
+ x.And(&x, &D[p.Index])
+ }
+ }
+ }
+ x.SetBit(&x, i, 1) // a block always dominates itself.
+ if D[i].Cmp(&x) != 0 {
+ D[i].Set(&x)
+ changed = true
+ }
+ }
+ }
+
+ // Check the entire relation. O(n^2).
+ ok := true
+ for i := 0; i < n; i++ {
+ for j := 0; j < n; j++ {
+ b, c := f.Blocks[i], f.Blocks[j]
+ actual := b.Dominates(c)
+ expected := D[j].Bit(i) == 1
+ if actual != expected {
+ fmt.Fprintf(os.Stderr, "dominates(%s, %s)==%t, want %t\n", b, c, actual, expected)
+ ok = false
+ }
+ }
+ }
+
+ preorder := f.DomPreorder()
+ for _, b := range f.Blocks {
+ if got := preorder[b.dom.pre]; got != b {
+ fmt.Fprintf(os.Stderr, "preorder[%d]==%s, want %s\n", b.dom.pre, got, b)
+ ok = false
+ }
+ }
+
+ if !ok {
+ panic("sanityCheckDomTree failed for " + f.String())
+ }
+
+}
+
+// Printing functions ----------------------------------------
+
+// printDomTree prints the dominator tree as text, using indentation.
+//lint:ignore U1000 used during debugging
+func printDomTreeText(buf *bytes.Buffer, v *BasicBlock, indent int) {
+ fmt.Fprintf(buf, "%*s%s\n", 4*indent, "", v)
+ for _, child := range v.dom.children {
+ printDomTreeText(buf, child, indent+1)
+ }
+}
+
+// printDomTreeDot prints the dominator tree of f in AT&T GraphViz
+// (.dot) format.
+//lint:ignore U1000 used during debugging
+func printDomTreeDot(buf io.Writer, f *Function) {
+ fmt.Fprintln(buf, "//", f)
+ fmt.Fprintln(buf, "digraph domtree {")
+ for i, b := range f.Blocks {
+ v := b.dom
+ fmt.Fprintf(buf, "\tn%d [label=\"%s (%d, %d)\",shape=\"rectangle\"];\n", v.pre, b, v.pre, v.post)
+ // TODO(adonovan): improve appearance of edges
+ // belonging to both dominator tree and CFG.
+
+ // Dominator tree edge.
+ if i != 0 {
+ fmt.Fprintf(buf, "\tn%d -> n%d [style=\"solid\",weight=100];\n", v.idom.dom.pre, v.pre)
+ }
+ // CFG edges.
+ for _, pred := range b.Preds {
+ fmt.Fprintf(buf, "\tn%d -> n%d [style=\"dotted\",weight=0];\n", pred.dom.pre, v.pre)
+ }
+ }
+ fmt.Fprintln(buf, "}")
+}
+
+// printDomTree prints the dominator tree as text, using indentation.
+//lint:ignore U1000 used during debugging
+func printPostDomTreeText(buf io.Writer, v *BasicBlock, indent int) {
+ fmt.Fprintf(buf, "%*s%s\n", 4*indent, "", v)
+ for _, child := range v.pdom.children {
+ printPostDomTreeText(buf, child, indent+1)
+ }
+}
+
+// printDomTreeDot prints the dominator tree of f in AT&T GraphViz
+// (.dot) format.
+//lint:ignore U1000 used during debugging
+func printPostDomTreeDot(buf io.Writer, f *Function) {
+ fmt.Fprintln(buf, "//", f)
+ fmt.Fprintln(buf, "digraph pdomtree {")
+ for _, b := range f.Blocks {
+ v := b.pdom
+ fmt.Fprintf(buf, "\tn%d [label=\"%s (%d, %d)\",shape=\"rectangle\"];\n", v.pre, b, v.pre, v.post)
+ // TODO(adonovan): improve appearance of edges
+ // belonging to both dominator tree and CFG.
+
+ // Dominator tree edge.
+ if b != f.Exit {
+ fmt.Fprintf(buf, "\tn%d -> n%d [style=\"solid\",weight=100];\n", v.idom.pdom.pre, v.pre)
+ }
+ // CFG edges.
+ for _, pred := range b.Preds {
+ fmt.Fprintf(buf, "\tn%d -> n%d [style=\"dotted\",weight=0];\n", pred.pdom.pre, v.pre)
+ }
+ }
+ fmt.Fprintln(buf, "}")
+}
projects / dotfiles / .git / blobdiff