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-// 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, "}")
-}