golang sparsetree 代码
文件路径：/src/cmd/compile/internal/ssa/sparsetree.go
/ 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
import (
"fmt"
"strings"
)
type SparseTreeNode struct {
child *Block
sibling *Block
parent *Block
/ Every block has 6 numbers associated with it:
/ entry-1, entry, entry+1, exit-1, and exit, exit+1.
/ entry and exit are conceptually the top of the block (phi functions)
/ entry+1 and exit-1 are conceptually the bottom of the block (ordinary defs)
/ entry-1 and exit+1 are conceptually "just before" the block (conditions flowing in)
/
/ This simplifies life if we wish to query information about x
/ when x is both an input to and output of a block.
entry, exit int32
}
func (s *SparseTreeNode) String() string {
return fmt.Sprintf("[%d,%d]", s.entry, s.exit)
}
func (s *SparseTreeNode) Entry() int32 {
return s.entry
}
func (s *SparseTreeNode) Exit() int32 {
return s.exit
}
const (
/ When used to lookup up definitions in a sparse tree,
/ these adjustments to a block's entry (+adjust) and
/ exit (-adjust) numbers allow a distinction to be made
/ between assignments (typically branch-dependent
/ conditionals) occurring "before" the block (e.g., as inputs
/ to the block and its phi functions), "within" the block,
/ and "after" the block.
AdjustBefore = -1 / defined before phi
AdjustWithin = 0 / defined by phi
AdjustAfter = 1 / defined within block
)
/ A SparseTree is a tree of Blocks.
/ It allows rapid ancestor queries,
/ such as whether one block dominates another.
type SparseTree []SparseTreeNode
/ newSparseTree creates a SparseTree from a block-to-parent map (array indexed by Block.ID)
func newSparseTree(f *Func, parentOf []*Block) SparseTree {
t := make(SparseTree, f.NumBlocks())
for _, b := range f.Blocks {
n := &t[b.ID]
if p := parentOf[b.ID]; p != nil {
n.parent = p
n.sibling = t[p.ID].child
t[p.ID].child = b
}
}
t.numberBlock(f.Entry, 1)
return t
}
/ newSparseOrderedTree creates a SparseTree from a block-to-parent map (array indexed by Block.ID)
/ children will appear in the reverse of their order in reverseOrder
/ in particular, if reverseOrder is a dfs-reversePostOrder, then the root-to-children
/ walk of the tree will yield a pre-order.
func newSparseOrderedTree(f *Func, parentOf, reverseOrder []*Block) SparseTree {
t := make(SparseTree, f.NumBlocks())
for _, b := range reverseOrder {
n := &t[b.ID]
if p := parentOf[b.ID]; p != nil {
n.parent = p
n.sibling = t[p.ID].child
t[p.ID].child = b
}
}
t.numberBlock(f.Entry, 1)
return t
}
/ treestructure provides a string description of the dominator
/ tree and flow structure of block b and all blocks that it
/ dominates.
func (t SparseTree) treestructure(b *Block) string {
return t.treestructure1(b, 0)
}
func (t SparseTree) treestructure1(b *Block, i int) string {
s := "\n" + strings.Repeat("\t", i) + b.String() + "->["
for i, e := range b.Succs {
if i > 0 {
s += ","
}
s += e.b.String()
}
s += "]"
if c0 := t[b.ID].child; c0 != nil {
s += "("
for c := c0; c != nil; c = t[c.ID].sibling {
if c != c0 {
s += " "
}
s += t.treestructure1(c, i+1)
}
s += ")"
}
return s
}
/ numberBlock assigns entry and exit numbers for b and b's
/ children in an in-order walk from a gappy sequence, where n
/ is the first number not yet assigned or reserved. N should
/ be larger than zero. For each entry and exit number, the
/ values one larger and smaller are reserved to indicate
/ "strictly above" and "strictly below". numberBlock returns
/ the smallest number not yet assigned or reserved (i.e., the
/ exit number of the last block visited, plus two, because
/ last.exit+1 is a reserved value.)
/
/ examples:
/
/ single node tree Root, call with n=1
/ entry=2 Root exit=5; returns 7
/
/ two node tree, Root->Child, call with n=1
/ entry=2 Root exit=11; returns 13
/ entry=5 Child exit=8
/
/ three node tree, Root->(Left, Right), call with n=1
/ entry=2 Root exit=17; returns 19
/ entry=5 Left exit=8; entry=11 Right exit=14
/
/ This is the in-order sequence of assigned and reserved numbers
/ for the last example:
/ root left left right right root
/ 1 2e 3 | 4 5e 6 | 7 8x 9 | 10 11e 12 | 13 14x 15 | 16 17x 18
func (t SparseTree) numberBlock(b *Block, n int32) int32 {
/ reserve n for entry-1, assign n+1 to entry
n++
t[b.ID].entry = n
/ reserve n+1 for entry+1, n+2 is next free number
n += 2
for c := t[b.ID].child; c != nil; c = t[c.ID].sibling {
n = t.numberBlock(c, n) / preserves n = next free number
}
/ reserve n for exit-1, assign n+1 to exit
n++
t[b.ID].exit = n
/ reserve n+1 for exit+1, n+2 is next free number, returned.
return n + 2
}
/ Sibling returns a sibling of x in the dominator tree (i.e.,
/ a node with the same immediate dominator) or nil if there
/ are no remaining siblings in the arbitrary but repeatable
/ order chosen. Because the Child-Sibling order is used
/ to assign entry and exit numbers in the treewalk, those
/ numbers are also consistent with this order (i.e.,
/ Sibling(x) has entry number larger than x's exit number).
func (t SparseTree) Sibling(x *Block) *Block {
return t[x.ID].sibling
}
/ Child returns a child of x in the dominator tree, or
/ nil if there are none. The choice of first child is
/ arbitrary but repeatable.
func (t SparseTree) Child(x *Block) *Block {
return t[x.ID].child
}
/ Parent returns the parent of x in the dominator tree, or
/ nil if x is the function's entry.
func (t SparseTree) Parent(x *Block) *Block {
return t[x.ID].parent
}
/ isAncestorEq reports whether x is an ancestor of or equal to y.
func (t SparseTree) IsAncestorEq(x, y *Block) bool {
if x == y {
return true
}
xx := &t[x.ID]
yy := &t[y.ID]
return xx.entry <= yy.entry && yy.exit <= xx.exit
}
/ isAncestor reports whether x is a strict ancestor of y.
func (t SparseTree) isAncestor(x, y *Block) bool {
if x == y {
return false
}
xx := &t[x.ID]
yy := &t[y.ID]
return xx.entry < yy.entry && yy.exit < xx.exit
}
/ domorder returns a value for dominator-oriented sorting.
/ Block domination does not provide a total ordering,
/ but domorder two has useful properties.
/ 1. If domorder(x) > domorder(y) then x does not dominate y.
/ 2. If domorder(x) < domorder(y) and domorder(y) < domorder(z) and x does not dominate y,
/ then x does not dominate z.
/
/ Property (1) means that blocks sorted by domorder always have a maximal dominant block first.
/ Property (2) allows searches for dominated blocks to exit early.
func (t SparseTree) domorder(x *Block) int32 {
/ Here is an argument that entry(x) provides the properties documented above.
/
/ Entry and exit values are assigned in a depth-first dominator tree walk.
/ For all blocks x and y, one of the following holds:
/
/ (x-dom-y) x dominates y => entry(x) < entry(y) < exit(y) < exit(x)
/ (y-dom-x) y dominates x => entry(y) < entry(x) < exit(x) < exit(y)
/ (x-then-y) neither x nor y dominates the other and x walked before y => entry(x) < exit(x) < entry(y) < exit(y)
/ (y-then-x) neither x nor y dominates the other and y walked before y => entry(y) < exit(y) < entry(x) < exit(x)
/
/ entry(x) > entry(y) eliminates case x-dom-y. This provides property (1) above.
/
/ For property (2), assume entry(x) < entry(y) and entry(y) < entry(z) and x does not dominate y.
/ entry(x) < entry(y) allows cases x-dom-y and x-then-y.
/ But by supposition, x does not dominate y. So we have x-then-y.
/
/ For contradiction, assume x dominates z.
/ Then entry(x) < entry(z) < exit(z) < exit(x).
/ But we know x-then-y, so entry(x) < exit(x) < entry(y) < exit(y).
/ Combining those, entry(x) < entry(z) < exit(z) < exit(x) < entry(y) < exit(y).
/ By supposition, entry(y) < entry(z), which allows cases y-dom-z and y-then-z.
/ y-dom-z requires entry(y) < entry(z), but we have entry(z) < entry(y).
/ y-then-z requires exit(y) < entry(z), but we have entry(z) < exit(y).
/ We have a contradiction, so x does not dominate z, as required.
return t[x.ID].entry
}