// Copyright 2015 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 // mark values type markKind uint8 const ( notFound markKind = 0 // block has not been discovered yet notExplored markKind = 1 // discovered and in queue, outedges not processed yet explored markKind = 2 // discovered and in queue, outedges processed done markKind = 3 // all done, in output ordering ) // This file contains code to compute the dominator tree // of a control-flow graph. // postorder computes a postorder traversal ordering for the // basic blocks in f. Unreachable blocks will not appear. func postorder(f *Func) []*Block { return postorderWithNumbering(f, []int32{}) } type blockAndIndex struct { b *Block index int // index is the number of successor edges of b that have already been explored. } // postorderWithNumbering provides a DFS postordering. // This seems to make loop-finding more robust. func postorderWithNumbering(f *Func, ponums []int32) []*Block { mark := make([]markKind, f.NumBlocks()) // result ordering var order []*Block // stack of blocks and next child to visit var s []blockAndIndex s = append(s, blockAndIndex{b: f.Entry}) mark[f.Entry.ID] = explored for len(s) > 0 { tos := len(s) - 1 x := s[tos] b := x.b i := x.index if i < len(b.Succs) { s[tos].index++ bb := b.Succs[i].Block() if mark[bb.ID] == notFound { mark[bb.ID] = explored s = append(s, blockAndIndex{b: bb}) } } else { s = s[:tos] if len(ponums) > 0 { ponums[b.ID] = int32(len(order)) } order = append(order, b) } } return order } type linkedBlocks func(*Block) []Edge const nscratchslices = 7 // experimentally, functions with 512 or fewer blocks account // for 75% of memory (size) allocation for dominator computation // in make.bash. const minscratchblocks = 512 func (cache *Cache) scratchBlocksForDom(maxBlockID int) (a, b, c, d, e, f, g []ID) { tot := maxBlockID * nscratchslices scratch := cache.domblockstore if len(scratch) < tot { // req = min(1.5*tot, nscratchslices*minscratchblocks) // 50% padding allows for graph growth in later phases. req := (tot * 3) >> 1 if req < nscratchslices*minscratchblocks { req = nscratchslices * minscratchblocks } scratch = make([]ID, req) cache.domblockstore = scratch } else { // Clear as much of scratch as we will (re)use scratch = scratch[0:tot] for i := range scratch { scratch[i] = 0 } } a = scratch[0*maxBlockID : 1*maxBlockID] b = scratch[1*maxBlockID : 2*maxBlockID] c = scratch[2*maxBlockID : 3*maxBlockID] d = scratch[3*maxBlockID : 4*maxBlockID] e = scratch[4*maxBlockID : 5*maxBlockID] f = scratch[5*maxBlockID : 6*maxBlockID] g = scratch[6*maxBlockID : 7*maxBlockID] return } func dominators(f *Func) []*Block { preds := func(b *Block) []Edge { return b.Preds } succs := func(b *Block) []Edge { return b.Succs } //TODO: benchmark and try to find criteria for swapping between // dominatorsSimple and dominatorsLT return f.dominatorsLTOrig(f.Entry, preds, succs) } // dominatorsLTOrig runs Lengauer-Tarjan to compute a dominator tree starting at // entry and using predFn/succFn to find predecessors/successors to allow // computing both dominator and post-dominator trees. func (f *Func) dominatorsLTOrig(entry *Block, predFn linkedBlocks, succFn linkedBlocks) []*Block { // Adapted directly from the original TOPLAS article's "simple" algorithm maxBlockID := entry.Func.NumBlocks() semi, vertex, label, parent, ancestor, bucketHead, bucketLink := f.Cache.scratchBlocksForDom(maxBlockID) // This version uses integers for most of the computation, // to make the work arrays smaller and pointer-free. // fromID translates from ID to *Block where that is needed. fromID := make([]*Block, maxBlockID) for _, v := range f.Blocks { fromID[v.ID] = v } idom := make([]*Block, maxBlockID) // Step 1. Carry out a depth first search of the problem graph. Number // the vertices from 1 to n as they are reached during the search. n := f.dfsOrig(entry, succFn, semi, vertex, label, parent) for i := n; i >= 2; i-- { w := vertex[i] // step2 in TOPLAS paper for _, e := range predFn(fromID[w]) { v := e.b if semi[v.ID] == 0 { // skip unreachable predecessor // not in original, but we're using existing pred instead of building one. continue } u := evalOrig(v.ID, ancestor, semi, label) if semi[u] < semi[w] { semi[w] = semi[u] } } // add w to bucket[vertex[semi[w]]] // implement bucket as a linked list implemented // in a pair of arrays. vsw := vertex[semi[w]] bucketLink[w] = bucketHead[vsw] bucketHead[vsw] = w linkOrig(parent[w], w, ancestor) // step3 in TOPLAS paper for v := bucketHead[parent[w]]; v != 0; v = bucketLink[v] { u := evalOrig(v, ancestor, semi, label) if semi[u] < semi[v] { idom[v] = fromID[u] } else { idom[v] = fromID[parent[w]] } } } // step 4 in toplas paper for i := ID(2); i <= n; i++ { w := vertex[i] if idom[w].ID != vertex[semi[w]] { idom[w] = idom[idom[w].ID] } } return idom } // dfs performs a depth first search over the blocks starting at entry block // (in arbitrary order). This is a de-recursed version of dfs from the // original Tarjan-Lengauer TOPLAS article. It's important to return the // same values for parent as the original algorithm. func (f *Func) dfsOrig(entry *Block, succFn linkedBlocks, semi, vertex, label, parent []ID) ID { n := ID(0) s := make([]*Block, 0, 256) s = append(s, entry) for len(s) > 0 { v := s[len(s)-1] s = s[:len(s)-1] // recursing on v if semi[v.ID] != 0 { continue // already visited } n++ semi[v.ID] = n vertex[n] = v.ID label[v.ID] = v.ID // ancestor[v] already zero for _, e := range succFn(v) { w := e.b // if it has a dfnum, we've already visited it if semi[w.ID] == 0 { // yes, w can be pushed multiple times. s = append(s, w) parent[w.ID] = v.ID // keep overwriting this till it is visited. } } } return n } // compressOrig is the "simple" compress function from LT paper func compressOrig(v ID, ancestor, semi, label []ID) { if ancestor[ancestor[v]] != 0 { compressOrig(ancestor[v], ancestor, semi, label) if semi[label[ancestor[v]]] < semi[label[v]] { label[v] = label[ancestor[v]] } ancestor[v] = ancestor[ancestor[v]] } } // evalOrig is the "simple" eval function from LT paper func evalOrig(v ID, ancestor, semi, label []ID) ID { if ancestor[v] == 0 { return v } compressOrig(v, ancestor, semi, label) return label[v] } func linkOrig(v, w ID, ancestor []ID) { ancestor[w] = v } // dominators computes the dominator tree for f. It returns a slice // which maps block ID to the immediate dominator of that block. // Unreachable blocks map to nil. The entry block maps to nil. func dominatorsSimple(f *Func) []*Block { // A simple algorithm for now // Cooper, Harvey, Kennedy idom := make([]*Block, f.NumBlocks()) // Compute postorder walk post := f.postorder() // Make map from block id to order index (for intersect call) postnum := make([]int, f.NumBlocks()) for i, b := range post { postnum[b.ID] = i } // Make the entry block a self-loop idom[f.Entry.ID] = f.Entry if postnum[f.Entry.ID] != len(post)-1 { f.Fatalf("entry block %v not last in postorder", f.Entry) } // Compute relaxation of idom entries for { changed := false for i := len(post) - 2; i >= 0; i-- { b := post[i] var d *Block for _, e := range b.Preds { p := e.b if idom[p.ID] == nil { continue } if d == nil { d = p continue } d = intersect(d, p, postnum, idom) } if d != idom[b.ID] { idom[b.ID] = d changed = true } } if !changed { break } } // Set idom of entry block to nil instead of itself. idom[f.Entry.ID] = nil return idom } // intersect finds the closest dominator of both b and c. // It requires a postorder numbering of all the blocks. func intersect(b, c *Block, postnum []int, idom []*Block) *Block { // TODO: This loop is O(n^2). It used to be used in nilcheck, // see BenchmarkNilCheckDeep*. for b != c { if postnum[b.ID] < postnum[c.ID] { b = idom[b.ID] } else { c = idom[c.ID] } } return b }