go/ssa/dom.go - tools - Git at Google

 // 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, "}")
 }
	// 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, 5n, 5*n)
	lt := ltState{
	sdom: space[0:n],
	parent: space[n : 2*n],
	ancestor: space[2n : 3n],
	}

	// Step 1. Number vertices by depth-first preorder.
	preorder := space[3n : 4n]
	root := f.Blocks[0]
	prenum := lt.dfs(root, 0, preorder)
	recover := f.Recover
	if recover != nil {
	lt.dfs(recover, prenum, preorder)
	}

	buckets := space[4n : 5n]
	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", 4indent, "", 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, "}")
	}