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[dev.ssa] cmd/internal/ssa: add CSE pass
Implement a simple common-subexpression elimination. It uses value numbering & a dominator tree to detect redundant computation. Change-Id: Id0ff775e439c22f4d41bdd5976176017dd2a2086 Reviewed-on: https://go-review.googlesource.com/8172 Reviewed-by: Alan Donovan <adonovan@google.com>
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@ -54,11 +54,12 @@ var passes = [...]pass{
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{"phielim", phielim},
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{"copyelim", copyelim},
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{"opt", opt},
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// cse
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{"deadcode", deadcode},
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{"generic cse", cse},
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{"generic deadcode", deadcode},
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{"fuse", fuse},
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{"lower", lower},
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// cse
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{"lowered cse", cse},
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{"lowered deadcode", deadcode},
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{"critical", critical}, // remove critical edges
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{"layout", layout}, // schedule blocks
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{"schedule", schedule}, // schedule values
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163
src/cmd/internal/ssa/cse.go
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163
src/cmd/internal/ssa/cse.go
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@ -0,0 +1,163 @@
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// Copyright 2015 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package ssa
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import (
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"sort"
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)
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// cse does common-subexpression elimination on the Function.
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// Values are just relinked, nothing is deleted. A subsequent deadcode
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// pass is required to actually remove duplicate expressions.
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func cse(f *Func) {
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// Two values are equivalent if they satisfy the following definition:
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// equivalent(v, w):
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// v.op == w.op
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// v.type == w.type
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// v.aux == w.aux
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// len(v.args) == len(w.args)
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// equivalent(v.args[i], w.args[i]) for i in 0..len(v.args)-1
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// The algorithm searches for a partition of f's values into
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// equivalence classes using the above definition.
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// It starts with a coarse partition and iteratively refines it
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// until it reaches a fixed point.
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// Make initial partition based on opcode/type/aux/nargs
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// TODO(khr): types are not canonical, so we may split unnecessarily. Fix that.
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type key struct {
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op Op
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typ Type
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aux interface{}
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nargs int
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}
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m := map[key]eqclass{}
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for _, b := range f.Blocks {
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for _, v := range b.Values {
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k := key{v.Op, v.Type, v.Aux, len(v.Args)}
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m[k] = append(m[k], v)
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}
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}
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// A partition is a set of disjoint eqclasses.
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var partition []eqclass
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for _, v := range m {
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partition = append(partition, v)
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}
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// map from value id back to eqclass id
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valueEqClass := make([]int, f.NumValues())
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for i, e := range partition {
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for _, v := range e {
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valueEqClass[v.ID] = i
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}
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}
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// Find an equivalence class where some members of the class have
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// non-equvalent arguments. Split the equivalence class appropriately.
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// Repeat until we can't find any more splits.
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for {
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changed := false
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for i, e := range partition {
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v := e[0]
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// all values in this equiv class that are not equivalent to v get moved
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// into another equiv class q.
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var q eqclass
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eqloop:
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for j := 1; j < len(e); {
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w := e[j]
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for i := 0; i < len(v.Args); i++ {
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if valueEqClass[v.Args[i].ID] != valueEqClass[w.Args[i].ID] {
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// w is not equivalent to v.
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// remove w from e
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e, e[j] = e[:len(e)-1], e[len(e)-1]
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// add w to q
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q = append(q, w)
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valueEqClass[w.ID] = len(partition)
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changed = true
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continue eqloop
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}
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}
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// v and w are equivalent. Keep w in e.
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j++
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}
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partition[i] = e
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if q != nil {
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partition = append(partition, q)
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}
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}
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if !changed {
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break
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}
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}
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// Compute dominator tree
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idom := dominators(f)
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// Compute substitutions we would like to do. We substitute v for w
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// if v and w are in the same equivalence class and v dominates w.
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rewrite := make([]*Value, f.NumValues())
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for _, e := range partition {
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sort.Sort(e) // ensure deterministic ordering
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for len(e) > 1 {
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// Find a maximal dominant element in e
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v := e[0]
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for _, w := range e[1:] {
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if dom(w.Block, v.Block, idom) {
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v = w
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}
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}
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// Replace all elements of e which v dominates
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for i := 0; i < len(e); {
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w := e[i]
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if w != v && dom(v.Block, w.Block, idom) {
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rewrite[w.ID] = v
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e, e[i] = e[:len(e)-1], e[len(e)-1]
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} else {
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i++
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}
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}
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// TODO(khr): if value is a control value, do we need to keep it block-local?
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}
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}
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// Apply substitutions
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for _, b := range f.Blocks {
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for _, v := range b.Values {
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for i, w := range v.Args {
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if x := rewrite[w.ID]; x != nil {
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v.SetArg(i, x)
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}
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}
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}
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}
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}
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// returns true if b dominates c.
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// TODO(khr): faster
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func dom(b, c *Block, idom []*Block) bool {
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// Walk up from c in the dominator tree looking for b.
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for c != nil {
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if c == b {
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return true
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}
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c = idom[c.ID]
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}
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// Reached the entry block, never saw b.
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return false
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}
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// An eqclass approximates an equivalence class. During the
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// algorithm it may represent the union of several of the
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// final equivalence classes.
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type eqclass []*Value
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// Sort an equivalence class by value ID.
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func (e eqclass) Len() int { return len(e) }
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func (e eqclass) Swap(i, j int) { e[i], e[j] = e[j], e[i] }
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func (e eqclass) Less(i, j int) bool { return e[i].ID < e[j].ID }
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121
src/cmd/internal/ssa/dom.go
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121
src/cmd/internal/ssa/dom.go
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@ -0,0 +1,121 @@
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// Copyright 2015 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package ssa
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// This file contains code to compute the dominator tree
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// of a control-flow graph.
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import "log"
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// postorder computes a postorder traversal ordering for the
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// basic blocks in f. Unreachable blocks will not appear.
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func postorder(f *Func) []*Block {
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mark := make([]byte, f.NumBlocks())
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// mark values
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const (
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notFound = 0 // block has not been discovered yet
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notExplored = 1 // discovered and in queue, outedges not processed yet
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explored = 2 // discovered and in queue, outedges processed
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done = 3 // all done, in output ordering
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)
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// result ordering
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var order []*Block
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// stack of blocks
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var s []*Block
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s = append(s, f.Entry)
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mark[f.Entry.ID] = notExplored
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for len(s) > 0 {
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b := s[len(s)-1]
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switch mark[b.ID] {
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case explored:
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// Children have all been visited. Pop & output block.
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s = s[:len(s)-1]
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mark[b.ID] = done
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order = append(order, b)
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case notExplored:
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// Children have not been visited yet. Mark as explored
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// and queue any children we haven't seen yet.
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mark[b.ID] = explored
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for _, c := range b.Succs {
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if mark[c.ID] == notFound {
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mark[c.ID] = notExplored
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s = append(s, c)
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}
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}
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default:
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log.Fatalf("bad stack state %v %d", b, mark[b.ID])
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}
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}
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return order
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}
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// dominators computes the dominator tree for f. It returns a slice
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// which maps block ID to the immediate dominator of that block.
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// Unreachable blocks map to nil. The entry block maps to nil.
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func dominators(f *Func) []*Block {
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// A simple algorithm for now
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// Cooper, Harvey, Kennedy
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idom := make([]*Block, f.NumBlocks())
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// Compute postorder walk
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post := postorder(f)
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// Make map from block id to order index (for intersect call)
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postnum := make([]int, f.NumBlocks())
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for i, b := range post {
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postnum[b.ID] = i
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}
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// Make the entry block a self-loop
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idom[f.Entry.ID] = f.Entry
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if postnum[f.Entry.ID] != len(post)-1 {
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log.Fatalf("entry block %v not last in postorder", f.Entry)
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}
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// Compute relaxation of idom entries
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for {
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changed := false
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for i := len(post) - 2; i >= 0; i-- {
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b := post[i]
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var d *Block
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for _, p := range b.Preds {
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if idom[p.ID] == nil {
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continue
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}
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if d == nil {
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d = p
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continue
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}
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d = intersect(d, p, postnum, idom)
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}
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if d != idom[b.ID] {
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idom[b.ID] = d
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changed = true
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}
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}
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if !changed {
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break
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}
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}
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// Set idom of entry block to nil instead of itself.
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idom[f.Entry.ID] = nil
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return idom
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}
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// intersect finds the closest dominator of both b and c.
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// It requires a postorder numbering of all the blocks.
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func intersect(b, c *Block, postnum []int, idom []*Block) *Block {
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for b != c {
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if postnum[b.ID] < postnum[c.ID] {
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b = idom[b.ID]
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} else {
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c = idom[c.ID]
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}
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}
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return b
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}
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@ -39,5 +39,4 @@ func lower(f *Func) {
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// TODO: others
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}
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}
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deadcode(f) // TODO: separate pass?
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}
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