cse.go

     1  // Copyright 2015 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package ssa
     6  
     7  import (
     8  	"cmd/compile/internal/types"
     9  	"cmd/internal/src"
    10  	"fmt"
    11  	"sort"
    12  )
    13  
    14  // cse does common-subexpression elimination on the Function.
    15  // Values are just relinked, nothing is deleted. A subsequent deadcode
    16  // pass is required to actually remove duplicate expressions.
    17  func cse(f *Func) {
    18  	// Two values are equivalent if they satisfy the following definition:
    19  	// equivalent(v, w):
    20  	//   v.op == w.op
    21  	//   v.type == w.type
    22  	//   v.aux == w.aux
    23  	//   v.auxint == w.auxint
    24  	//   len(v.args) == len(w.args)
    25  	//   v.block == w.block if v.op == OpPhi
    26  	//   equivalent(v.args[i], w.args[i]) for i in 0..len(v.args)-1
    27  
    28  	// The algorithm searches for a partition of f's values into
    29  	// equivalence classes using the above definition.
    30  	// It starts with a coarse partition and iteratively refines it
    31  	// until it reaches a fixed point.
    32  
    33  	// Make initial coarse partitions by using a subset of the conditions above.
    34  	a := f.Cache.allocValueSlice(f.NumValues())
    35  	defer func() { f.Cache.freeValueSlice(a) }() // inside closure to use final value of a
    36  	a = a[:0]
    37  	if f.auxmap == nil {
    38  		f.auxmap = auxmap{}
    39  	}
    40  	for _, b := range f.Blocks {
    41  		for _, v := range b.Values {
    42  			if v.Type.IsMemory() {
    43  				continue // memory values can never cse
    44  			}
    45  			if f.auxmap[v.Aux] == 0 {
    46  				f.auxmap[v.Aux] = int32(len(f.auxmap)) + 1
    47  			}
    48  			a = append(a, v)
    49  		}
    50  	}
    51  	partition := partitionValues(a, f.auxmap)
    52  
    53  	// map from value id back to eqclass id
    54  	valueEqClass := f.Cache.allocIDSlice(f.NumValues())
    55  	defer f.Cache.freeIDSlice(valueEqClass)
    56  	for _, b := range f.Blocks {
    57  		for _, v := range b.Values {
    58  			// Use negative equivalence class #s for unique values.
    59  			valueEqClass[v.ID] = -v.ID
    60  		}
    61  	}
    62  	var pNum ID = 1
    63  	for _, e := range partition {
    64  		if f.pass.debug > 1 && len(e) > 500 {
    65  			fmt.Printf("CSE.large partition (%d): ", len(e))
    66  			for j := 0; j < 3; j++ {
    67  				fmt.Printf("%s ", e[j].LongString())
    68  			}
    69  			fmt.Println()
    70  		}
    71  
    72  		for _, v := range e {
    73  			valueEqClass[v.ID] = pNum
    74  		}
    75  		if f.pass.debug > 2 && len(e) > 1 {
    76  			fmt.Printf("CSE.partition #%d:", pNum)
    77  			for _, v := range e {
    78  				fmt.Printf(" %s", v.String())
    79  			}
    80  			fmt.Printf("\n")
    81  		}
    82  		pNum++
    83  	}
    84  
    85  	// Split equivalence classes at points where they have
    86  	// non-equivalent arguments.  Repeat until we can't find any
    87  	// more splits.
    88  	var splitPoints []int
    89  	byArgClass := new(partitionByArgClass) // reusable partitionByArgClass to reduce allocations
    90  	for {
    91  		changed := false
    92  
    93  		// partition can grow in the loop. By not using a range loop here,
    94  		// we process new additions as they arrive, avoiding O(n^2) behavior.
    95  		for i := 0; i < len(partition); i++ {
    96  			e := partition[i]
    97  
    98  			if opcodeTable[e[0].Op].commutative {
    99  				// Order the first two args before comparison.
   100  				for _, v := range e {
   101  					if valueEqClass[v.Args[0].ID] > valueEqClass[v.Args[1].ID] {
   102  						v.Args[0], v.Args[1] = v.Args[1], v.Args[0]
   103  					}
   104  				}
   105  			}
   106  
   107  			// Sort by eq class of arguments.
   108  			byArgClass.a = e
   109  			byArgClass.eqClass = valueEqClass
   110  			sort.Sort(byArgClass)
   111  
   112  			// Find split points.
   113  			splitPoints = append(splitPoints[:0], 0)
   114  			for j := 1; j < len(e); j++ {
   115  				v, w := e[j-1], e[j]
   116  				// Note: commutative args already correctly ordered by byArgClass.
   117  				eqArgs := true
   118  				for k, a := range v.Args {
   119  					b := w.Args[k]
   120  					if valueEqClass[a.ID] != valueEqClass[b.ID] {
   121  						eqArgs = false
   122  						break
   123  					}
   124  				}
   125  				if !eqArgs {
   126  					splitPoints = append(splitPoints, j)
   127  				}
   128  			}
   129  			if len(splitPoints) == 1 {
   130  				continue // no splits, leave equivalence class alone.
   131  			}
   132  
   133  			// Move another equivalence class down in place of e.
   134  			partition[i] = partition[len(partition)-1]
   135  			partition = partition[:len(partition)-1]
   136  			i--
   137  
   138  			// Add new equivalence classes for the parts of e we found.
   139  			splitPoints = append(splitPoints, len(e))
   140  			for j := 0; j < len(splitPoints)-1; j++ {
   141  				f := e[splitPoints[j]:splitPoints[j+1]]
   142  				if len(f) == 1 {
   143  					// Don't add singletons.
   144  					valueEqClass[f[0].ID] = -f[0].ID
   145  					continue
   146  				}
   147  				for _, v := range f {
   148  					valueEqClass[v.ID] = pNum
   149  				}
   150  				pNum++
   151  				partition = append(partition, f)
   152  			}
   153  			changed = true
   154  		}
   155  
   156  		if !changed {
   157  			break
   158  		}
   159  	}
   160  
   161  	sdom := f.Sdom()
   162  
   163  	// Compute substitutions we would like to do. We substitute v for w
   164  	// if v and w are in the same equivalence class and v dominates w.
   165  	rewrite := f.Cache.allocValueSlice(f.NumValues())
   166  	defer f.Cache.freeValueSlice(rewrite)
   167  	byDom := new(partitionByDom) // reusable partitionByDom to reduce allocs
   168  	for _, e := range partition {
   169  		byDom.a = e
   170  		byDom.sdom = sdom
   171  		sort.Sort(byDom)
   172  		for i := 0; i < len(e)-1; i++ {
   173  			// e is sorted by domorder, so a maximal dominant element is first in the slice
   174  			v := e[i]
   175  			if v == nil {
   176  				continue
   177  			}
   178  
   179  			e[i] = nil
   180  			// Replace all elements of e which v dominates
   181  			for j := i + 1; j < len(e); j++ {
   182  				w := e[j]
   183  				if w == nil {
   184  					continue
   185  				}
   186  				if sdom.IsAncestorEq(v.Block, w.Block) {
   187  					rewrite[w.ID] = v
   188  					e[j] = nil
   189  				} else {
   190  					// e is sorted by domorder, so v.Block doesn't dominate any subsequent blocks in e
   191  					break
   192  				}
   193  			}
   194  		}
   195  	}
   196  
   197  	rewrites := int64(0)
   198  
   199  	// Apply substitutions
   200  	for _, b := range f.Blocks {
   201  		for _, v := range b.Values {
   202  			for i, w := range v.Args {
   203  				if x := rewrite[w.ID]; x != nil {
   204  					if w.Pos.IsStmt() == src.PosIsStmt {
   205  						// about to lose a statement marker, w
   206  						// w is an input to v; if they're in the same block
   207  						// and the same line, v is a good-enough new statement boundary.
   208  						if w.Block == v.Block && w.Pos.Line() == v.Pos.Line() {
   209  							v.Pos = v.Pos.WithIsStmt()
   210  							w.Pos = w.Pos.WithNotStmt()
   211  						} // TODO and if this fails?
   212  					}
   213  					v.SetArg(i, x)
   214  					rewrites++
   215  				}
   216  			}
   217  		}
   218  		for i, v := range b.ControlValues() {
   219  			if x := rewrite[v.ID]; x != nil {
   220  				if v.Op == OpNilCheck {
   221  					// nilcheck pass will remove the nil checks and log
   222  					// them appropriately, so don't mess with them here.
   223  					continue
   224  				}
   225  				b.ReplaceControl(i, x)
   226  			}
   227  		}
   228  	}
   229  
   230  	if f.pass.stats > 0 {
   231  		f.LogStat("CSE REWRITES", rewrites)
   232  	}
   233  }
   234  
   235  // An eqclass approximates an equivalence class. During the
   236  // algorithm it may represent the union of several of the
   237  // final equivalence classes.
   238  type eqclass []*Value
   239  
   240  // partitionValues partitions the values into equivalence classes
   241  // based on having all the following features match:
   242  //   - opcode
   243  //   - type
   244  //   - auxint
   245  //   - aux
   246  //   - nargs
   247  //   - block # if a phi op
   248  //   - first two arg's opcodes and auxint
   249  //   - NOT first two arg's aux; that can break CSE.
   250  //
   251  // partitionValues returns a list of equivalence classes, each
   252  // being a sorted by ID list of *Values. The eqclass slices are
   253  // backed by the same storage as the input slice.
   254  // Equivalence classes of size 1 are ignored.
   255  func partitionValues(a []*Value, auxIDs auxmap) []eqclass {
   256  	sort.Sort(sortvalues{a, auxIDs})
   257  
   258  	var partition []eqclass
   259  	for len(a) > 0 {
   260  		v := a[0]
   261  		j := 1
   262  		for ; j < len(a); j++ {
   263  			w := a[j]
   264  			if cmpVal(v, w, auxIDs) != types.CMPeq {
   265  				break
   266  			}
   267  		}
   268  		if j > 1 {
   269  			partition = append(partition, a[:j])
   270  		}
   271  		a = a[j:]
   272  	}
   273  
   274  	return partition
   275  }
   276  func lt2Cmp(isLt bool) types.Cmp {
   277  	if isLt {
   278  		return types.CMPlt
   279  	}
   280  	return types.CMPgt
   281  }
   282  
   283  type auxmap map[Aux]int32
   284  
   285  func cmpVal(v, w *Value, auxIDs auxmap) types.Cmp {
   286  	// Try to order these comparison by cost (cheaper first)
   287  	if v.Op != w.Op {
   288  		return lt2Cmp(v.Op < w.Op)
   289  	}
   290  	if v.AuxInt != w.AuxInt {
   291  		return lt2Cmp(v.AuxInt < w.AuxInt)
   292  	}
   293  	if len(v.Args) != len(w.Args) {
   294  		return lt2Cmp(len(v.Args) < len(w.Args))
   295  	}
   296  	if v.Op == OpPhi && v.Block != w.Block {
   297  		return lt2Cmp(v.Block.ID < w.Block.ID)
   298  	}
   299  	if v.Type.IsMemory() {
   300  		// We will never be able to CSE two values
   301  		// that generate memory.
   302  		return lt2Cmp(v.ID < w.ID)
   303  	}
   304  	// OpSelect is a pseudo-op. We need to be more aggressive
   305  	// regarding CSE to keep multiple OpSelect's of the same
   306  	// argument from existing.
   307  	if v.Op != OpSelect0 && v.Op != OpSelect1 && v.Op != OpSelectN {
   308  		if tc := v.Type.Compare(w.Type); tc != types.CMPeq {
   309  			return tc
   310  		}
   311  	}
   312  
   313  	if v.Aux != w.Aux {
   314  		if v.Aux == nil {
   315  			return types.CMPlt
   316  		}
   317  		if w.Aux == nil {
   318  			return types.CMPgt
   319  		}
   320  		return lt2Cmp(auxIDs[v.Aux] < auxIDs[w.Aux])
   321  	}
   322  
   323  	return types.CMPeq
   324  }
   325  
   326  // Sort values to make the initial partition.
   327  type sortvalues struct {
   328  	a      []*Value // array of values
   329  	auxIDs auxmap   // aux -> aux ID map
   330  }
   331  
   332  func (sv sortvalues) Len() int      { return len(sv.a) }
   333  func (sv sortvalues) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
   334  func (sv sortvalues) Less(i, j int) bool {
   335  	v := sv.a[i]
   336  	w := sv.a[j]
   337  	if cmp := cmpVal(v, w, sv.auxIDs); cmp != types.CMPeq {
   338  		return cmp == types.CMPlt
   339  	}
   340  
   341  	// Sort by value ID last to keep the sort result deterministic.
   342  	return v.ID < w.ID
   343  }
   344  
   345  type partitionByDom struct {
   346  	a    []*Value // array of values
   347  	sdom SparseTree
   348  }
   349  
   350  func (sv partitionByDom) Len() int      { return len(sv.a) }
   351  func (sv partitionByDom) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
   352  func (sv partitionByDom) Less(i, j int) bool {
   353  	v := sv.a[i]
   354  	w := sv.a[j]
   355  	return sv.sdom.domorder(v.Block) < sv.sdom.domorder(w.Block)
   356  }
   357  
   358  type partitionByArgClass struct {
   359  	a       []*Value // array of values
   360  	eqClass []ID     // equivalence class IDs of values
   361  }
   362  
   363  func (sv partitionByArgClass) Len() int      { return len(sv.a) }
   364  func (sv partitionByArgClass) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
   365  func (sv partitionByArgClass) Less(i, j int) bool {
   366  	v := sv.a[i]
   367  	w := sv.a[j]
   368  	for i, a := range v.Args {
   369  		b := w.Args[i]
   370  		if sv.eqClass[a.ID] < sv.eqClass[b.ID] {
   371  			return true
   372  		}
   373  		if sv.eqClass[a.ID] > sv.eqClass[b.ID] {
   374  			return false
   375  		}
   376  	}
   377  	return false
   378  }
   379
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