# Source file src/cmd/compile/internal/ssa/cse.go

## Documentation: cmd/compile/internal/ssa

```     1  // Copyright 2015 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
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 := make([]*Value, 0, f.NumValues())
35  	if f.auxmap == nil {
36  		f.auxmap = auxmap{}
37  	}
38  	for _, b := range f.Blocks {
39  		for _, v := range b.Values {
40  			if v.Type.IsMemory() {
41  				continue // memory values can never cse
42  			}
43  			if f.auxmap[v.Aux] == 0 {
44  				f.auxmap[v.Aux] = int32(len(f.auxmap)) + 1
45  			}
46  			a = append(a, v)
47  		}
48  	}
49  	partition := partitionValues(a, f.auxmap)
50
51  	// map from value id back to eqclass id
52  	valueEqClass := make([]ID, f.NumValues())
53  	for _, b := range f.Blocks {
54  		for _, v := range b.Values {
55  			// Use negative equivalence class #s for unique values.
56  			valueEqClass[v.ID] = -v.ID
57  		}
58  	}
59  	var pNum ID = 1
60  	for _, e := range partition {
61  		if f.pass.debug > 1 && len(e) > 500 {
62  			fmt.Printf("CSE.large partition (%d): ", len(e))
63  			for j := 0; j < 3; j++ {
64  				fmt.Printf("%s ", e[j].LongString())
65  			}
66  			fmt.Println()
67  		}
68
69  		for _, v := range e {
70  			valueEqClass[v.ID] = pNum
71  		}
72  		if f.pass.debug > 2 && len(e) > 1 {
73  			fmt.Printf("CSE.partition #%d:", pNum)
74  			for _, v := range e {
75  				fmt.Printf(" %s", v.String())
76  			}
77  			fmt.Printf("\n")
78  		}
79  		pNum++
80  	}
81
82  	// Split equivalence classes at points where they have
83  	// non-equivalent arguments.  Repeat until we can't find any
84  	// more splits.
85  	var splitPoints []int
86  	byArgClass := new(partitionByArgClass) // reuseable partitionByArgClass to reduce allocations
87  	for {
88  		changed := false
89
90  		// partition can grow in the loop. By not using a range loop here,
91  		// we process new additions as they arrive, avoiding O(n^2) behavior.
92  		for i := 0; i < len(partition); i++ {
93  			e := partition[i]
94
95  			if opcodeTable[e[0].Op].commutative {
96  				// Order the first two args before comparison.
97  				for _, v := range e {
98  					if valueEqClass[v.Args[0].ID] > valueEqClass[v.Args[1].ID] {
99  						v.Args[0], v.Args[1] = v.Args[1], v.Args[0]
100  					}
101  				}
102  			}
103
104  			// Sort by eq class of arguments.
105  			byArgClass.a = e
106  			byArgClass.eqClass = valueEqClass
107  			sort.Sort(byArgClass)
108
109  			// Find split points.
110  			splitPoints = append(splitPoints[:0], 0)
111  			for j := 1; j < len(e); j++ {
112  				v, w := e[j-1], e[j]
113  				// Note: commutative args already correctly ordered by byArgClass.
114  				eqArgs := true
115  				for k, a := range v.Args {
116  					b := w.Args[k]
117  					if valueEqClass[a.ID] != valueEqClass[b.ID] {
118  						eqArgs = false
119  						break
120  					}
121  				}
122  				if !eqArgs {
123  					splitPoints = append(splitPoints, j)
124  				}
125  			}
126  			if len(splitPoints) == 1 {
127  				continue // no splits, leave equivalence class alone.
128  			}
129
130  			// Move another equivalence class down in place of e.
131  			partition[i] = partition[len(partition)-1]
132  			partition = partition[:len(partition)-1]
133  			i--
134
135  			// Add new equivalence classes for the parts of e we found.
136  			splitPoints = append(splitPoints, len(e))
137  			for j := 0; j < len(splitPoints)-1; j++ {
138  				f := e[splitPoints[j]:splitPoints[j+1]]
139  				if len(f) == 1 {
141  					valueEqClass[f[0].ID] = -f[0].ID
142  					continue
143  				}
144  				for _, v := range f {
145  					valueEqClass[v.ID] = pNum
146  				}
147  				pNum++
148  				partition = append(partition, f)
149  			}
150  			changed = true
151  		}
152
153  		if !changed {
154  			break
155  		}
156  	}
157
158  	sdom := f.sdom()
159
160  	// Compute substitutions we would like to do. We substitute v for w
161  	// if v and w are in the same equivalence class and v dominates w.
162  	rewrite := make([]*Value, f.NumValues())
163  	byDom := new(partitionByDom) // reusable partitionByDom to reduce allocs
164  	for _, e := range partition {
165  		byDom.a = e
166  		byDom.sdom = sdom
167  		sort.Sort(byDom)
168  		for i := 0; i < len(e)-1; i++ {
169  			// e is sorted by domorder, so a maximal dominant element is first in the slice
170  			v := e[i]
171  			if v == nil {
172  				continue
173  			}
174
175  			e[i] = nil
176  			// Replace all elements of e which v dominates
177  			for j := i + 1; j < len(e); j++ {
178  				w := e[j]
179  				if w == nil {
180  					continue
181  				}
182  				if sdom.isAncestorEq(v.Block, w.Block) {
183  					rewrite[w.ID] = v
184  					e[j] = nil
185  				} else {
186  					// e is sorted by domorder, so v.Block doesn't dominate any subsequent blocks in e
187  					break
188  				}
189  			}
190  		}
191  	}
192
193  	// if we rewrite a tuple generator to a new one in a different block,
194  	// copy its selectors to the new generator's block, so tuple generator
195  	// and selectors stay together.
196  	// be careful not to copy same selectors more than once (issue 16741).
197  	copiedSelects := make(map[ID][]*Value)
198  	for _, b := range f.Blocks {
199  	out:
200  		for _, v := range b.Values {
201  			// New values are created when selectors are copied to
202  			// a new block. We can safely ignore those new values,
203  			// since they have already been copied (issue 17918).
204  			if int(v.ID) >= len(rewrite) || rewrite[v.ID] != nil {
205  				continue
206  			}
207  			if v.Op != OpSelect0 && v.Op != OpSelect1 {
208  				continue
209  			}
210  			if !v.Args[0].Type.IsTuple() {
211  				f.Fatalf("arg of tuple selector %s is not a tuple: %s", v.String(), v.Args[0].LongString())
212  			}
213  			t := rewrite[v.Args[0].ID]
214  			if t != nil && t.Block != b {
215  				// v.Args[0] is tuple generator, CSE'd into a different block as t, v is left behind
216  				for _, c := range copiedSelects[t.ID] {
217  					if v.Op == c.Op {
218  						// an equivalent selector is already copied
219  						rewrite[v.ID] = c
220  						continue out
221  					}
222  				}
223  				c := v.copyInto(t.Block)
224  				rewrite[v.ID] = c
225  				copiedSelects[t.ID] = append(copiedSelects[t.ID], c)
226  			}
227  		}
228  	}
229
230  	rewrites := int64(0)
231
232  	// Apply substitutions
233  	for _, b := range f.Blocks {
234  		for _, v := range b.Values {
235  			for i, w := range v.Args {
236  				if x := rewrite[w.ID]; x != nil {
237  					if w.Pos.IsStmt() == src.PosIsStmt {
238  						// about to lose a statement marker, w
239  						// w is an input to v; if they're in the same block
240  						// and the same line, v is a good-enough new statement boundary.
241  						if w.Block == v.Block && w.Pos.Line() == v.Pos.Line() {
242  							v.Pos = v.Pos.WithIsStmt()
243  							w.Pos = w.Pos.WithNotStmt()
244  						} // TODO and if this fails?
245  					}
246  					v.SetArg(i, x)
247  					rewrites++
248  				}
249  			}
250  		}
251  		if v := b.Control; v != nil {
252  			if x := rewrite[v.ID]; x != nil {
253  				if v.Op == OpNilCheck {
254  					// nilcheck pass will remove the nil checks and log
255  					// them appropriately, so don't mess with them here.
256  					continue
257  				}
258  				b.SetControl(x)
259  			}
260  		}
261  	}
262  	if f.pass.stats > 0 {
263  		f.LogStat("CSE REWRITES", rewrites)
264  	}
265  }
266
267  // An eqclass approximates an equivalence class. During the
268  // algorithm it may represent the union of several of the
269  // final equivalence classes.
270  type eqclass []*Value
271
272  // partitionValues partitions the values into equivalence classes
273  // based on having all the following features match:
274  //  - opcode
275  //  - type
276  //  - auxint
277  //  - aux
278  //  - nargs
279  //  - block # if a phi op
280  //  - first two arg's opcodes and auxint
281  //  - NOT first two arg's aux; that can break CSE.
282  // partitionValues returns a list of equivalence classes, each
283  // being a sorted by ID list of *Values. The eqclass slices are
284  // backed by the same storage as the input slice.
285  // Equivalence classes of size 1 are ignored.
286  func partitionValues(a []*Value, auxIDs auxmap) []eqclass {
287  	sort.Sort(sortvalues{a, auxIDs})
288
289  	var partition []eqclass
290  	for len(a) > 0 {
291  		v := a[0]
292  		j := 1
293  		for ; j < len(a); j++ {
294  			w := a[j]
295  			if cmpVal(v, w, auxIDs) != types.CMPeq {
296  				break
297  			}
298  		}
299  		if j > 1 {
300  			partition = append(partition, a[:j])
301  		}
302  		a = a[j:]
303  	}
304
305  	return partition
306  }
307  func lt2Cmp(isLt bool) types.Cmp {
308  	if isLt {
309  		return types.CMPlt
310  	}
311  	return types.CMPgt
312  }
313
314  type auxmap map[interface{}]int32
315
316  func cmpVal(v, w *Value, auxIDs auxmap) types.Cmp {
317  	// Try to order these comparison by cost (cheaper first)
318  	if v.Op != w.Op {
319  		return lt2Cmp(v.Op < w.Op)
320  	}
321  	if v.AuxInt != w.AuxInt {
322  		return lt2Cmp(v.AuxInt < w.AuxInt)
323  	}
324  	if len(v.Args) != len(w.Args) {
325  		return lt2Cmp(len(v.Args) < len(w.Args))
326  	}
327  	if v.Op == OpPhi && v.Block != w.Block {
328  		return lt2Cmp(v.Block.ID < w.Block.ID)
329  	}
330  	if v.Type.IsMemory() {
331  		// We will never be able to CSE two values
332  		// that generate memory.
333  		return lt2Cmp(v.ID < w.ID)
334  	}
335  	// OpSelect is a pseudo-op. We need to be more aggressive
336  	// regarding CSE to keep multiple OpSelect's of the same
337  	// argument from existing.
338  	if v.Op != OpSelect0 && v.Op != OpSelect1 {
339  		if tc := v.Type.Compare(w.Type); tc != types.CMPeq {
340  			return tc
341  		}
342  	}
343
344  	if v.Aux != w.Aux {
345  		if v.Aux == nil {
346  			return types.CMPlt
347  		}
348  		if w.Aux == nil {
349  			return types.CMPgt
350  		}
351  		return lt2Cmp(auxIDs[v.Aux] < auxIDs[w.Aux])
352  	}
353
354  	return types.CMPeq
355  }
356
357  // Sort values to make the initial partition.
358  type sortvalues struct {
359  	a      []*Value // array of values
360  	auxIDs auxmap   // aux -> aux ID map
361  }
362
363  func (sv sortvalues) Len() int      { return len(sv.a) }
364  func (sv sortvalues) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
365  func (sv sortvalues) Less(i, j int) bool {
366  	v := sv.a[i]
367  	w := sv.a[j]
368  	if cmp := cmpVal(v, w, sv.auxIDs); cmp != types.CMPeq {
369  		return cmp == types.CMPlt
370  	}
371
372  	// Sort by value ID last to keep the sort result deterministic.
373  	return v.ID < w.ID
374  }
375
376  type partitionByDom struct {
377  	a    []*Value // array of values
378  	sdom SparseTree
379  }
380
381  func (sv partitionByDom) Len() int      { return len(sv.a) }
382  func (sv partitionByDom) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
383  func (sv partitionByDom) Less(i, j int) bool {
384  	v := sv.a[i]
385  	w := sv.a[j]
386  	return sv.sdom.domorder(v.Block) < sv.sdom.domorder(w.Block)
387  }
388
389  type partitionByArgClass struct {
390  	a       []*Value // array of values
391  	eqClass []ID     // equivalence class IDs of values
392  }
393
394  func (sv partitionByArgClass) Len() int      { return len(sv.a) }
395  func (sv partitionByArgClass) Swap(i, j int) { sv.a[i], sv.a[j] = sv.a[j], sv.a[i] }
396  func (sv partitionByArgClass) Less(i, j int) bool {
397  	v := sv.a[i]
398  	w := sv.a[j]
399  	for i, a := range v.Args {
400  		b := w.Args[i]
401  		if sv.eqClass[a.ID] < sv.eqClass[b.ID] {
402  			return true
403  		}
404  		if sv.eqClass[a.ID] > sv.eqClass[b.ID] {
405  			return false
406  		}
407  	}
408  	return false
409  }
410
```

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