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Code Editor : sparsetreemap.go
// Copyright 2016 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 import "fmt" // A SparseTreeMap encodes a subset of nodes within a tree // used for sparse-ancestor queries. // // Combined with a SparseTreeHelper, this supports an Insert // to add a tree node to the set and a Find operation to locate // the nearest tree ancestor of a given node such that the // ancestor is also in the set. // // Given a set of blocks {B1, B2, B3} within the dominator tree, established // by stm.Insert()ing B1, B2, B3, etc, a query at block B // (performed with stm.Find(stm, B, adjust, helper)) // will return the member of the set that is the nearest strict // ancestor of B within the dominator tree, or nil if none exists. // The expected complexity of this operation is the log of the size // the set, given certain assumptions about sparsity (the log complexity // could be guaranteed with additional data structures whose constant- // factor overhead has not yet been justified.) // // The adjust parameter allows positioning of the insertion // and lookup points within a block -- one of // AdjustBefore, AdjustWithin, AdjustAfter, // where lookups at AdjustWithin can find insertions at // AdjustBefore in the same block, and lookups at AdjustAfter // can find insertions at either AdjustBefore or AdjustWithin // in the same block. (Note that this assumes a gappy numbering // such that exit number or exit number is separated from its // nearest neighbor by at least 3). // // The Sparse Tree lookup algorithm is described by // Paul F. Dietz. Maintaining order in a linked list. In // Proceedings of the Fourteenth Annual ACM Symposium on // Theory of Computing, pages 122–127, May 1982. // and by // Ben Wegbreit. Faster retrieval from context trees. // Communications of the ACM, 19(9):526–529, September 1976. type SparseTreeMap RBTint32 // A SparseTreeHelper contains indexing and allocation data // structures common to a collection of SparseTreeMaps, as well // as exposing some useful control-flow-related data to other // packages, such as gc. type SparseTreeHelper struct { Sdom []SparseTreeNode // indexed by block.ID Po []*Block // exported data; the blocks, in a post-order Dom []*Block // exported data; the dominator of this block. Ponums []int32 // exported data; Po[Ponums[b.ID]] == b; the index of b in Po } // NewSparseTreeHelper returns a SparseTreeHelper for use // in the gc package, for example in phi-function placement. func NewSparseTreeHelper(f *Func) *SparseTreeHelper { dom := f.Idom() ponums := make([]int32, f.NumBlocks()) po := postorderWithNumbering(f, ponums) return makeSparseTreeHelper(newSparseTree(f, dom), dom, po, ponums) } func (h *SparseTreeHelper) NewTree() *SparseTreeMap { return &SparseTreeMap{} } func makeSparseTreeHelper(sdom SparseTree, dom, po []*Block, ponums []int32) *SparseTreeHelper { helper := &SparseTreeHelper{Sdom: []SparseTreeNode(sdom), Dom: dom, Po: po, Ponums: ponums, } return helper } // A sparseTreeMapEntry contains the data stored in a binary search // data structure indexed by (dominator tree walk) entry and exit numbers. // Each entry is added twice, once keyed by entry-1/entry/entry+1 and // once keyed by exit+1/exit/exit-1. // // Within a sparse tree, the two entries added bracket all their descendant // entries within the tree; the first insertion is keyed by entry number, // which comes before all the entry and exit numbers of descendants, and // the second insertion is keyed by exit number, which comes after all the // entry and exit numbers of the descendants. type sparseTreeMapEntry struct { index *SparseTreeNode // references the entry and exit numbers for a block in the sparse tree block *Block // TODO: store this in a separate index. data interface{} sparseParent *sparseTreeMapEntry // references the nearest ancestor of this block in the sparse tree. adjust int32 // at what adjustment was this node entered into the sparse tree? The same block may be entered more than once, but at different adjustments. } // Insert creates a definition within b with data x. // adjust indicates where in the block should be inserted: // AdjustBefore means defined at a phi function (visible Within or After in the same block) // AdjustWithin means defined within the block (visible After in the same block) // AdjustAfter means after the block (visible within child blocks) func (m *SparseTreeMap) Insert(b *Block, adjust int32, x interface{}, helper *SparseTreeHelper) { rbtree := (*RBTint32)(m) blockIndex := &helper.Sdom[b.ID] if blockIndex.entry == 0 { // assert unreachable return } // sp will be the sparse parent in this sparse tree (nearest ancestor in the larger tree that is also in this sparse tree) sp := m.findEntry(b, adjust, helper) entry := &sparseTreeMapEntry{index: blockIndex, block: b, data: x, sparseParent: sp, adjust: adjust} right := blockIndex.exit - adjust _ = rbtree.Insert(right, entry) left := blockIndex.entry + adjust _ = rbtree.Insert(left, entry) // This newly inserted block may now be the sparse parent of some existing nodes (the new sparse children of this block) // Iterate over nodes bracketed by this new node to correct their parent, but not over the proper sparse descendants of those nodes. _, d := rbtree.Lub(left) // Lub (not EQ) of left is either right or a sparse child for tme := d.(*sparseTreeMapEntry); tme != entry; tme = d.(*sparseTreeMapEntry) { tme.sparseParent = entry // all descendants of tme are unchanged; // next sparse sibling (or right-bracketing sparse parent == entry) is first node after tme.index.exit - tme.adjust _, d = rbtree.Lub(tme.index.exit - tme.adjust) } } // Find returns the definition visible from block b, or nil if none can be found. // Adjust indicates where the block should be searched. // AdjustBefore searches before the phi functions of b. // AdjustWithin searches starting at the phi functions of b. // AdjustAfter searches starting at the exit from the block, including normal within-block definitions. // // Note that Finds are properly nested with Inserts: // m.Insert(b, a) followed by m.Find(b, a) will not return the result of the insert, // but m.Insert(b, AdjustBefore) followed by m.Find(b, AdjustWithin) will. // // Another way to think of this is that Find searches for inputs, Insert defines outputs. func (m *SparseTreeMap) Find(b *Block, adjust int32, helper *SparseTreeHelper) interface{} { v := m.findEntry(b, adjust, helper) if v == nil { return nil } return v.data } func (m *SparseTreeMap) findEntry(b *Block, adjust int32, helper *SparseTreeHelper) *sparseTreeMapEntry { rbtree := (*RBTint32)(m) if rbtree == nil { return nil } blockIndex := &helper.Sdom[b.ID] // The Glb (not EQ) of this probe is either the entry-indexed end of a sparse parent // or the exit-indexed end of a sparse sibling _, v := rbtree.Glb(blockIndex.entry + adjust) if v == nil { return nil } otherEntry := v.(*sparseTreeMapEntry) if otherEntry.index.exit >= blockIndex.exit { // otherEntry exit after blockIndex exit; therefore, brackets return otherEntry } // otherEntry is a sparse Sibling, and shares the same sparse parent (nearest ancestor within larger tree) sp := otherEntry.sparseParent if sp != nil { if sp.index.exit < blockIndex.exit { // no ancestor found return nil } return sp } return nil } func (m *SparseTreeMap) String() string { tree := (*RBTint32)(m) return tree.String() } func (e *sparseTreeMapEntry) String() string { if e == nil { return "nil" } return fmt.Sprintf("(index=%v, block=%v, data=%v)->%v", e.index, e.block, e.data, e.sparseParent) }
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