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// 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 (
"cmd/compile/internal/types"
"fmt"
"sort"
)
// cse does common-subexpression elimination on the Function.
// Values are just relinked, nothing is deleted. A subsequent deadcode
// pass is required to actually remove duplicate expressions.
func cse(f *Func) {
// Two values are equivalent if they satisfy the following definition:
// equivalent(v, w):
// v.op == w.op
// v.type == w.type
// v.aux == w.aux
// v.auxint == w.auxint
// len(v.args) == len(w.args)
// v.block == w.block if v.op == OpPhi
// equivalent(v.args[i], w.args[i]) for i in 0..len(v.args)-1
// The algorithm searches for a partition of f's values into
// equivalence classes using the above definition.
// It starts with a coarse partition and iteratively refines it
// until it reaches a fixed point.
// Make initial coarse partitions by using a subset of the conditions above.
a := make([]*Value, 0, f.NumValues())
if f.auxmap == nil {
f.auxmap = auxmap{}
}
for _, b := range f.Blocks {
for _, v := range b.Values {
if v.Type.IsMemory() {
continue // memory values can never cse
}
if f.auxmap[v.Aux] == 0 {
f.auxmap[v.Aux] = int32(len(f.auxmap)) + 1
}
a = append(a, v)
}
}
partition := partitionValues(a, f.auxmap)
// map from value id back to eqclass id
valueEqClass := make([]ID, f.NumValues())
for _, b := range f.Blocks {
for _, v := range b.Values {
// Use negative equivalence class #s for unique values.
valueEqClass[v.ID] = -v.ID
}
}
var pNum ID = 1
for _, e := range partition {
if f.pass.debug > 1 && len(e) > 500 {
fmt.Printf("CSE.large partition (%d): ", len(e))
for j := 0; j < 3; j++ {
fmt.Printf("%s ", e[j].LongString())
}
fmt.Println()
}
for _, v := range e {
valueEqClass[v.ID] = pNum
}
if f.pass.debug > 2 && len(e) > 1 {
fmt.Printf("CSE.partition #%d:", pNum)
for _, v := range e {
fmt.Printf(" %s", v.String())
}
fmt.Printf("\n")
}
pNum++
}
// Split equivalence classes at points where they have
// non-equivalent arguments. Repeat until we can't find any
// more splits.
var splitPoints []int
byArgClass := new(partitionByArgClass) // reuseable partitionByArgClass to reduce allocations
for {
changed := false
// partition can grow in the loop. By not using a range loop here,
// we process new additions as they arrive, avoiding O(n^2) behavior.
for i := 0; i < len(partition); i++ {
e := partition[i]
if opcodeTable[e[0].Op].commutative {
// Order the first two args before comparison.
for _, v := range e {
if valueEqClass[v.Args[0].ID] > valueEqClass[v.Args[1].ID] {
v.Args[0], v.Args[1] = v.Args[1], v.Args[0]
}
}
}
// Sort by eq class of arguments.
byArgClass.a = e
byArgClass.eqClass = valueEqClass
sort.Sort(byArgClass)
// Find split points.
splitPoints = append(splitPoints[:0], 0)
for j := 1; j < len(e); j++ {
v, w := e[j-1], e[j]
// Note: commutative args already correctly ordered by byArgClass.
eqArgs := true
for k, a := range v.Args {
b := w.Args[k]
if valueEqClass[a.ID] != valueEqClass[b.ID] {
eqArgs = false
break
}
}
if !eqArgs {
splitPoints = append(splitPoints, j)
}
}
if len(splitPoints) == 1 {
continue // no splits, leave equivalence class alone.
}
// Move another equivalence class down in place of e.
partition[i] = partition[len(partition)-1]
partition = partition[:len(partition)-1]
i--
// Add new equivalence classes for the parts of e we found.
splitPoints = append(splitPoints, len(e))
for j := 0; j < len(splitPoints)-1; j++ {
f := e[splitPoints[j]:splitPoints[j+1]]
if len(f) == 1 {
// Don't add singletons.
valueEqClass[f[0].ID] = -f[0].ID
continue
}
for _, v := range f {
valueEqClass[v.ID] = pNum
}
pNum++
partition = append(partition, f)
}
changed = true
}
if !changed {
break
}
}
sdom := f.sdom()
// Compute substitutions we would like to do. We substitute v for w
// if v and w are in the same equivalence class and v dominates w.
rewrite := make([]*Value, f.NumValues())
byDom := new(partitionByDom) // reusable partitionByDom to reduce allocs
for _, e := range partition {
byDom.a = e
byDom.sdom = sdom
sort.Sort(byDom)
for i := 0; i < len(e)-1; i++ {
// e is sorted by domorder, so a maximal dominant element is first in the slice
v := e[i]
if v == nil {
continue
}
e[i] = nil
// Replace all elements of e which v dominates
for j := i + 1; j < len(e); j++ {
w := e[j]
if w == nil {
continue
}
if sdom.isAncestorEq(v.Block, w.Block) {
rewrite[w.ID] = v
e[j] = nil
} else {
// e is sorted by domorder, so v.Block doesn't dominate any subsequent blocks in e
break
}
}
}
}
// if we rewrite a tuple generator to a new one in a different block,
// copy its selectors to the new generator's block, so tuple generator
// and selectors stay together.
// be careful not to copy same selectors more than once (issue 16741).
copiedSelects := make(map[ID][]*Value)
for _, b := range f.Blocks {
out:
for _, v := range b.Values {
// New values are created when selectors are copied to
// a new block. We can safely ignore those new values,
// since they have already been copied (issue 17918).
if int(v.ID) >= len(rewrite) || rewrite[v.ID] != nil {
continue
}
if v.Op != OpSelect0 && v.Op != OpSelect1 {
continue
}
if !v.Args[0].Type.IsTuple() {
f.Fatalf("arg of tuple selector %s is not a tuple: %s", v.String(), v.Args[0].LongString())
}
t := rewrite[v.Args[0].ID]
if t != nil && t.Block != b {
// v.Args[0] is tuple generator, CSE'd into a different block as t, v is left behind
for _, c := range copiedSelects[t.ID] {
if v.Op == c.Op {
// an equivalent selector is already copied
rewrite[v.ID] = c
continue out
}
}
c := v.copyInto(t.Block)
rewrite[v.ID] = c
copiedSelects[t.ID] = append(copiedSelects[t.ID], c)
}
}
}
rewrites := int64(0)
// Apply substitutions
for _, b := range f.Blocks {
for _, v := range b.Values {
for i, w := range v.Args {
if x := rewrite[w.ID]; x != nil {
v.SetArg(i, x)
rewrites++
}
}
}
if v := b.Control; v != nil {
if x := rewrite[v.ID]; x != nil {
if v.Op == OpNilCheck {
// nilcheck pass will remove the nil checks and log
// them appropriately, so don't mess with them here.
continue
}
b.SetControl(x)
}
}
}
if f.pass.stats > 0 {
f.LogStat("CSE REWRITES", rewrites)
}
}
// An eqclass approximates an equivalence class. During the
// algorithm it may represent the union of several of the
// final equivalence classes.
type eqclass []*Value
// partitionValues partitions the values into equivalence classes
// based on having all the following features match:
// - opcode
// - type
// - auxint
// - aux
// - nargs
// - block # if a phi op
// - first two arg's opcodes and auxint
// - NOT first two arg's aux; that can break CSE.
// partitionValues returns a list of equivalence classes, each
// being a sorted by ID list of *Values. The eqclass slices are
// backed by the same storage as the input slice.
// Equivalence classes of size 1 are ignored.
func partitionValues(a []*Value, auxIDs auxmap) []eqclass {
sort.Sort(sortvalues{a, auxIDs})
var partition []eqclass
for len(a) > 0 {
v := a[0]
j := 1
for ; j < len(a); j++ {
w := a[j]
if cmpVal(v, w, auxIDs) != types.CMPeq {
break
}
}
if j > 1 {
partition = append(partition, a[:j])
}
a = a[j:]
}
return partition
}
func lt2Cmp(isLt bool) types.Cmp {
if isLt {
return types.CMPlt
}
return types.CMPgt
}
type auxmap map[interface{}]int32
func cmpVal(v, w *Value, auxIDs auxmap) types.Cmp {
// Try to order these comparison by cost (cheaper first)
if v.Op != w.Op {
return lt2Cmp(v.Op < w.Op)
}
if v.AuxInt != w.AuxInt {
return lt2Cmp(v.AuxInt < w.AuxInt)
}
if len(v.Args) != len(w.Args) {
return lt2Cmp(len(v.Args) < len(w.Args))
}
if v.Op == OpPhi && v.Block != w.Block {
return lt2Cmp(v.Block.ID < w.Block.ID)
}
if v.Type.IsMemory() {
// We will never be able to CSE two values
// that generate memory.
return lt2Cmp(v.ID < w.ID)
}
// OpSelect is a pseudo-op. We need to be more aggressive
// regarding CSE to keep multiple OpSelect's of the same
// argument from existing.
if v.Op != OpSelect0 && v.Op != OpSelect1 {
if tc := v.Type.Compare(w.Type); tc != types.CMPeq {
return tc
}
}
if v.Aux != w.Aux {
if v.Aux == nil {
return types.CMPlt
}
if w.Aux == nil {
return types.CMPgt
}
return lt2Cmp(auxIDs[v.Aux] < auxIDs[w.Aux])
}
return types.CMPeq
}
// Sort values to make the initial partition.
type sortvalues struct {
a []*Value // array of values
auxIDs auxmap // aux -> aux ID map
}
func (sv sortvalues) Len() int { return len(sv.a) }
func (sv sortvalues) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
func (sv sortvalues) Less(i, j int) bool {
v := sv.a[i]
w := sv.a[j]
if cmp := cmpVal(v, w, sv.auxIDs); cmp != types.CMPeq {
return cmp == types.CMPlt
}
// Sort by value ID last to keep the sort result deterministic.
return v.ID < w.ID
}
type partitionByDom struct {
a []*Value // array of values
sdom SparseTree
}
func (sv partitionByDom) Len() int { return len(sv.a) }
func (sv partitionByDom) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
func (sv partitionByDom) Less(i, j int) bool {
v := sv.a[i]
w := sv.a[j]
return sv.sdom.domorder(v.Block) < sv.sdom.domorder(w.Block)
}
type partitionByArgClass struct {
a []*Value // array of values
eqClass []ID // equivalence class IDs of values
}
func (sv partitionByArgClass) Len() int { return len(sv.a) }
func (sv partitionByArgClass) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
func (sv partitionByArgClass) Less(i, j int) bool {
v := sv.a[i]
w := sv.a[j]
for i, a := range v.Args {
b := w.Args[i]
if sv.eqClass[a.ID] < sv.eqClass[b.ID] {
return true
}
if sv.eqClass[a.ID] > sv.eqClass[b.ID] {
return false
}
}
return false
}