// 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 }