342 lines
9.3 KiB
Go
342 lines
9.3 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 ssa
|
||
|
|
|
||
|
|
// 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"
|
||
|
|
"math/big"
|
||
|
|
"os"
|
||
|
|
"sort"
|
||
|
|
)
|
||
|
|
|
||
|
|
// Idom returns the block that immediately dominates b:
|
||
|
|
// its parent in the dominator tree, if any.
|
||
|
|
// Neither the entry node (b.Index==0) nor recover node
|
||
|
|
// (b==b.Parent().Recover()) 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, 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
|
||
|
|
}
|
||
|
|
|
||
|
|
// ltState holds the working state for Lengauer-Tarjan algorithm
|
||
|
|
// (during which domInfo.pre is repurposed for CFG DFS preorder number).
|
||
|
|
type ltState struct {
|
||
|
|
// Each slice is indexed by b.Index.
|
||
|
|
sdom []*BasicBlock // b's semidominator
|
||
|
|
parent []*BasicBlock // b's parent in DFS traversal of CFG
|
||
|
|
ancestor []*BasicBlock // b's ancestor with least sdom
|
||
|
|
}
|
||
|
|
|
||
|
|
// dfs implements the depth-first search part of the LT algorithm.
|
||
|
|
func (lt *ltState) dfs(v *BasicBlock, i int32, preorder []*BasicBlock) int32 {
|
||
|
|
preorder[i] = v
|
||
|
|
v.dom.pre = i // For now: DFS preorder of spanning tree of CFG
|
||
|
|
i++
|
||
|
|
lt.sdom[v.Index] = v
|
||
|
|
lt.link(nil, v)
|
||
|
|
for _, w := range v.Succs {
|
||
|
|
if lt.sdom[w.Index] == nil {
|
||
|
|
lt.parent[w.Index] = v
|
||
|
|
i = lt.dfs(w, i, preorder)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return i
|
||
|
|
}
|
||
|
|
|
||
|
|
// eval implements the EVAL part of the LT algorithm.
|
||
|
|
func (lt *ltState) eval(v *BasicBlock) *BasicBlock {
|
||
|
|
// TODO(adonovan): opt: do path compression per simple LT.
|
||
|
|
u := v
|
||
|
|
for ; lt.ancestor[v.Index] != nil; v = lt.ancestor[v.Index] {
|
||
|
|
if lt.sdom[v.Index].dom.pre < lt.sdom[u.Index].dom.pre {
|
||
|
|
u = v
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return u
|
||
|
|
}
|
||
|
|
|
||
|
|
// link implements the LINK part of the LT algorithm.
|
||
|
|
func (lt *ltState) link(v, w *BasicBlock) {
|
||
|
|
lt.ancestor[w.Index] = v
|
||
|
|
}
|
||
|
|
|
||
|
|
// buildDomTree computes the dominator tree of f using the LT algorithm.
|
||
|
|
// Precondition: all blocks are reachable (e.g. optimizeBlocks has been run).
|
||
|
|
//
|
||
|
|
func buildDomTree(f *Function) {
|
||
|
|
// The step numbers refer to the original LT paper; the
|
||
|
|
// reordering is due to Georgiadis.
|
||
|
|
|
||
|
|
// Clear any previous domInfo.
|
||
|
|
for _, b := range f.Blocks {
|
||
|
|
b.dom = domInfo{}
|
||
|
|
}
|
||
|
|
|
||
|
|
n := len(f.Blocks)
|
||
|
|
// Allocate space for 5 contiguous [n]*BasicBlock arrays:
|
||
|
|
// sdom, parent, ancestor, preorder, buckets.
|
||
|
|
space := make([]*BasicBlock, 5*n, 5*n)
|
||
|
|
lt := ltState{
|
||
|
|
sdom: space[0:n],
|
||
|
|
parent: space[n : 2*n],
|
||
|
|
ancestor: space[2*n : 3*n],
|
||
|
|
}
|
||
|
|
|
||
|
|
// Step 1. Number vertices by depth-first preorder.
|
||
|
|
preorder := space[3*n : 4*n]
|
||
|
|
root := f.Blocks[0]
|
||
|
|
prenum := lt.dfs(root, 0, preorder)
|
||
|
|
recover := f.Recover
|
||
|
|
if recover != nil {
|
||
|
|
lt.dfs(recover, prenum, preorder)
|
||
|
|
}
|
||
|
|
|
||
|
|
buckets := space[4*n : 5*n]
|
||
|
|
copy(buckets, preorder)
|
||
|
|
|
||
|
|
// In reverse preorder...
|
||
|
|
for i := int32(n) - 1; i > 0; i-- {
|
||
|
|
w := preorder[i]
|
||
|
|
|
||
|
|
// Step 3. Implicitly define the immediate dominator of each node.
|
||
|
|
for v := buckets[i]; v != w; v = buckets[v.dom.pre] {
|
||
|
|
u := lt.eval(v)
|
||
|
|
if lt.sdom[u.Index].dom.pre < i {
|
||
|
|
v.dom.idom = u
|
||
|
|
} else {
|
||
|
|
v.dom.idom = w
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Step 2. Compute the semidominators of all nodes.
|
||
|
|
lt.sdom[w.Index] = lt.parent[w.Index]
|
||
|
|
for _, v := range w.Preds {
|
||
|
|
u := lt.eval(v)
|
||
|
|
if lt.sdom[u.Index].dom.pre < lt.sdom[w.Index].dom.pre {
|
||
|
|
lt.sdom[w.Index] = lt.sdom[u.Index]
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
lt.link(lt.parent[w.Index], w)
|
||
|
|
|
||
|
|
if lt.parent[w.Index] == lt.sdom[w.Index] {
|
||
|
|
w.dom.idom = lt.parent[w.Index]
|
||
|
|
} else {
|
||
|
|
buckets[i] = buckets[lt.sdom[w.Index].dom.pre]
|
||
|
|
buckets[lt.sdom[w.Index].dom.pre] = w
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// The final 'Step 3' is now outside the loop.
|
||
|
|
for v := buckets[0]; v != root; v = buckets[v.dom.pre] {
|
||
|
|
v.dom.idom = root
|
||
|
|
}
|
||
|
|
|
||
|
|
// Step 4. Explicitly define the immediate dominator of each
|
||
|
|
// node, in preorder.
|
||
|
|
for _, w := range preorder[1:] {
|
||
|
|
if w == root || w == recover {
|
||
|
|
w.dom.idom = nil
|
||
|
|
} else {
|
||
|
|
if w.dom.idom != lt.sdom[w.Index] {
|
||
|
|
w.dom.idom = w.dom.idom.dom.idom
|
||
|
|
}
|
||
|
|
// Calculate Children relation as inverse of Idom.
|
||
|
|
w.dom.idom.dom.children = append(w.dom.idom.dom.children, w)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
pre, post := numberDomTree(root, 0, 0)
|
||
|
|
if recover != nil {
|
||
|
|
numberDomTree(recover, pre, post)
|
||
|
|
}
|
||
|
|
|
||
|
|
// printDomTreeDot(os.Stderr, f) // debugging
|
||
|
|
// printDomTreeText(os.Stderr, root, 0) // debugging
|
||
|
|
|
||
|
|
if f.Prog.mode&SanityCheckFunctions != 0 {
|
||
|
|
sanityCheckDomTree(f)
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// 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
|
||
|
|
}
|
||
|
|
|
||
|
|
// 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, b := range f.Blocks {
|
||
|
|
if i == 0 || b == f.Recover {
|
||
|
|
// 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 || b == f.Recover {
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
// Compute intersection across predecessors.
|
||
|
|
var x big.Int
|
||
|
|
x.Set(&all)
|
||
|
|
for _, pred := range b.Preds {
|
||
|
|
x.And(&x, &D[pred.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).
|
||
|
|
// The Recover block (if any) must be treated specially so we skip it.
|
||
|
|
ok := true
|
||
|
|
for i := 0; i < n; i++ {
|
||
|
|
for j := 0; j < n; j++ {
|
||
|
|
b, c := f.Blocks[i], f.Blocks[j]
|
||
|
|
if c == f.Recover {
|
||
|
|
continue
|
||
|
|
}
|
||
|
|
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.
|
||
|
|
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.
|
||
|
|
func printDomTreeDot(buf *bytes.Buffer, 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, "}")
|
||
|
|
}
|