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Diffstat (limited to 'vendor/golang.org/x/tools/go/ssa/dom.go')
-rw-r--r-- | vendor/golang.org/x/tools/go/ssa/dom.go | 340 |
1 files changed, 340 insertions, 0 deletions
diff --git a/vendor/golang.org/x/tools/go/ssa/dom.go b/vendor/golang.org/x/tools/go/ssa/dom.go new file mode 100644 index 0000000..02c1ae8 --- /dev/null +++ b/vendor/golang.org/x/tools/go/ssa/dom.go @@ -0,0 +1,340 @@ +// 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 +} + +// DomPreorder returns a new slice containing the blocks of f +// in a preorder traversal of the dominator tree. +func (f *Function) DomPreorder() []*BasicBlock { + slice := append([]*BasicBlock(nil), 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 := append([]*BasicBlock(nil), 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 := 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 ---------------------------------------- + +// 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. +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, "}") +} |