src

dom.go (9672B)

---

 // 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"
 	"slices"
 	"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
 }
 
 // DomPreorder returns a new slice containing the blocks of f
 // in a preorder traversal of the dominator tree.
 func (f *Function) DomPreorder() []*BasicBlock {
 	slice := slices.Clone(f.Blocks)
 	sort.Slice(slice, func(i, j int) bool {
 		return slice[i].dom.pre < slice[j].dom.pre
 	})
 	return slice
 }
 
 // DomPostorder returns a new slice containing the blocks of f
 // in a postorder traversal of the dominator tree.
 // (This is not the same as a postdominance order.)
 func (f *Function) DomPostorder() []*BasicBlock {
 	slice := slices.Clone(f.Blocks)
 	sort.Slice(slice, func(i, j int) bool {
 		return slice[i].dom.post < slice[j].dom.post
 	})
 	return slice
 }
 
 // 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)
 	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 := range n {
 		for j := range n {
 			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 ----------------------------------------
 
 // printDomTreeText 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.
 // (unused; retained for debugging)
 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, "}")
 }