internal/ssa/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)
}