462 lines
11 KiB
Go
462 lines
11 KiB
Go
|
// 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, "}")
|
||
|
|
}
|