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