Source file src/cmd/compile/internal/ssa/poset.go

Documentation: cmd/compile/internal/ssa

     1  // Copyright 2018 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  	"fmt"
     9  	"os"
    10  )
    11  
    12  // If true, check poset integrity after every mutation
    13  var debugPoset = false
    14  
    15  const uintSize = 32 << (^uint(0) >> 63) // 32 or 64
    16  
    17  // bitset is a bit array for dense indexes.
    18  type bitset []uint
    19  
    20  func newBitset(n int) bitset {
    21  	return make(bitset, (n+uintSize-1)/uintSize)
    22  }
    23  
    24  func (bs bitset) Reset() {
    25  	for i := range bs {
    26  		bs[i] = 0
    27  	}
    28  }
    29  
    30  func (bs bitset) Set(idx uint32) {
    31  	bs[idx/uintSize] |= 1 << (idx % uintSize)
    32  }
    33  
    34  func (bs bitset) Clear(idx uint32) {
    35  	bs[idx/uintSize] &^= 1 << (idx % uintSize)
    36  }
    37  
    38  func (bs bitset) Test(idx uint32) bool {
    39  	return bs[idx/uintSize]&(1<<(idx%uintSize)) != 0
    40  }
    41  
    42  type undoType uint8
    43  
    44  const (
    45  	undoInvalid     undoType = iota
    46  	undoCheckpoint           // a checkpoint to group undo passes
    47  	undoSetChl               // change back left child of undo.idx to undo.edge
    48  	undoSetChr               // change back right child of undo.idx to undo.edge
    49  	undoNonEqual             // forget that SSA value undo.ID is non-equal to undo.idx (another ID)
    50  	undoNewNode              // remove new node created for SSA value undo.ID
    51  	undoNewConstant          // remove the constant node idx from the constants map
    52  	undoAliasNode            // unalias SSA value undo.ID so that it points back to node index undo.idx
    53  	undoNewRoot              // remove node undo.idx from root list
    54  	undoChangeRoot           // remove node undo.idx from root list, and put back undo.edge.Target instead
    55  	undoMergeRoot            // remove node undo.idx from root list, and put back its children instead
    56  )
    57  
    58  // posetUndo represents an undo pass to be performed.
    59  // It's a union of fields that can be used to store information,
    60  // and typ is the discriminant, that specifies which kind
    61  // of operation must be performed. Not all fields are always used.
    62  type posetUndo struct {
    63  	typ  undoType
    64  	idx  uint32
    65  	ID   ID
    66  	edge posetEdge
    67  }
    68  
    69  const (
    70  	// Make poset handle constants as unsigned numbers.
    71  	posetFlagUnsigned = 1 << iota
    72  )
    73  
    74  // A poset edge. The zero value is the null/empty edge.
    75  // Packs target node index (31 bits) and strict flag (1 bit).
    76  type posetEdge uint32
    77  
    78  func newedge(t uint32, strict bool) posetEdge {
    79  	s := uint32(0)
    80  	if strict {
    81  		s = 1
    82  	}
    83  	return posetEdge(t<<1 | s)
    84  }
    85  func (e posetEdge) Target() uint32 { return uint32(e) >> 1 }
    86  func (e posetEdge) Strict() bool   { return uint32(e)&1 != 0 }
    87  func (e posetEdge) String() string {
    88  	s := fmt.Sprint(e.Target())
    89  	if e.Strict() {
    90  		s += "*"
    91  	}
    92  	return s
    93  }
    94  
    95  // posetNode is a node of a DAG within the poset.
    96  type posetNode struct {
    97  	l, r posetEdge
    98  }
    99  
   100  // poset is a union-find data structure that can represent a partially ordered set
   101  // of SSA values. Given a binary relation that creates a partial order (eg: '<'),
   102  // clients can record relations between SSA values using SetOrder, and later
   103  // check relations (in the transitive closure) with Ordered. For instance,
   104  // if SetOrder is called to record that A<B and B<C, Ordered will later confirm
   105  // that A<C.
   106  //
   107  // It is possible to record equality relations between SSA values with SetEqual and check
   108  // equality with Equal. Equality propagates into the transitive closure for the partial
   109  // order so that if we know that A<B<C and later learn that A==D, Ordered will return
   110  // true for D<C.
   111  //
   112  // It is also possible to record inequality relations between nodes with SetNonEqual;
   113  // non-equality relations are not transitive, but they can still be useful: for instance
   114  // if we know that A<=B and later we learn that A!=B, we can deduce that A<B.
   115  // NonEqual can be used to check whether it is known that the nodes are different, either
   116  // because SetNonEqual was called before, or because we know that they are strictly ordered.
   117  //
   118  // poset will refuse to record new relations that contradict existing relations:
   119  // for instance if A<B<C, calling SetOrder for C<A will fail returning false; also
   120  // calling SetEqual for C==A will fail.
   121  //
   122  // poset is implemented as a forest of DAGs; in each DAG, if there is a path (directed)
   123  // from node A to B, it means that A<B (or A<=B). Equality is represented by mapping
   124  // two SSA values to the same DAG node; when a new equality relation is recorded
   125  // between two existing nodes, the nodes are merged, adjusting incoming and outgoing edges.
   126  //
   127  // Constants are specially treated. When a constant is added to the poset, it is
   128  // immediately linked to other constants already present; so for instance if the
   129  // poset knows that x<=3, and then x is tested against 5, 5 is first added and linked
   130  // 3 (using 3<5), so that the poset knows that x<=3<5; at that point, it is able
   131  // to answer x<5 correctly. This means that all constants are always within the same
   132  // DAG; as an implementation detail, we enfoce that the DAG containtining the constants
   133  // is always the first in the forest.
   134  //
   135  // poset is designed to be memory efficient and do little allocations during normal usage.
   136  // Most internal data structures are pre-allocated and flat, so for instance adding a
   137  // new relation does not cause any allocation. For performance reasons,
   138  // each node has only up to two outgoing edges (like a binary tree), so intermediate
   139  // "extra" nodes are required to represent more than two relations. For instance,
   140  // to record that A<I, A<J, A<K (with no known relation between I,J,K), we create the
   141  // following DAG:
   142  //
   143  //	  A
   144  //	 / \
   145  //	I  extra
   146  //	    /  \
   147  //	   J    K
   148  type poset struct {
   149  	lastidx   uint32            // last generated dense index
   150  	flags     uint8             // internal flags
   151  	values    map[ID]uint32     // map SSA values to dense indexes
   152  	constants map[int64]uint32  // record SSA constants together with their value
   153  	nodes     []posetNode       // nodes (in all DAGs)
   154  	roots     []uint32          // list of root nodes (forest)
   155  	noneq     map[uint32]bitset // non-equal relations
   156  	undo      []posetUndo       // undo chain
   157  }
   158  
   159  func newPoset() *poset {
   160  	return &poset{
   161  		values:    make(map[ID]uint32),
   162  		constants: make(map[int64]uint32, 8),
   163  		nodes:     make([]posetNode, 1, 16),
   164  		roots:     make([]uint32, 0, 4),
   165  		noneq:     make(map[uint32]bitset),
   166  		undo:      make([]posetUndo, 0, 4),
   167  	}
   168  }
   169  
   170  func (po *poset) SetUnsigned(uns bool) {
   171  	if uns {
   172  		po.flags |= posetFlagUnsigned
   173  	} else {
   174  		po.flags &^= posetFlagUnsigned
   175  	}
   176  }
   177  
   178  // Handle children
   179  func (po *poset) setchl(i uint32, l posetEdge) { po.nodes[i].l = l }
   180  func (po *poset) setchr(i uint32, r posetEdge) { po.nodes[i].r = r }
   181  func (po *poset) chl(i uint32) uint32          { return po.nodes[i].l.Target() }
   182  func (po *poset) chr(i uint32) uint32          { return po.nodes[i].r.Target() }
   183  func (po *poset) children(i uint32) (posetEdge, posetEdge) {
   184  	return po.nodes[i].l, po.nodes[i].r
   185  }
   186  
   187  // upush records a new undo step. It can be used for simple
   188  // undo passes that record up to one index and one edge.
   189  func (po *poset) upush(typ undoType, p uint32, e posetEdge) {
   190  	po.undo = append(po.undo, posetUndo{typ: typ, idx: p, edge: e})
   191  }
   192  
   193  // upushnew pushes an undo pass for a new node
   194  func (po *poset) upushnew(id ID, idx uint32) {
   195  	po.undo = append(po.undo, posetUndo{typ: undoNewNode, ID: id, idx: idx})
   196  }
   197  
   198  // upushneq pushes a new undo pass for a nonequal relation
   199  func (po *poset) upushneq(idx1 uint32, idx2 uint32) {
   200  	po.undo = append(po.undo, posetUndo{typ: undoNonEqual, ID: ID(idx1), idx: idx2})
   201  }
   202  
   203  // upushalias pushes a new undo pass for aliasing two nodes
   204  func (po *poset) upushalias(id ID, i2 uint32) {
   205  	po.undo = append(po.undo, posetUndo{typ: undoAliasNode, ID: id, idx: i2})
   206  }
   207  
   208  // upushconst pushes a new undo pass for a new constant
   209  func (po *poset) upushconst(idx uint32, old uint32) {
   210  	po.undo = append(po.undo, posetUndo{typ: undoNewConstant, idx: idx, ID: ID(old)})
   211  }
   212  
   213  // addchild adds i2 as direct child of i1.
   214  func (po *poset) addchild(i1, i2 uint32, strict bool) {
   215  	i1l, i1r := po.children(i1)
   216  	e2 := newedge(i2, strict)
   217  
   218  	if i1l == 0 {
   219  		po.setchl(i1, e2)
   220  		po.upush(undoSetChl, i1, 0)
   221  	} else if i1r == 0 {
   222  		po.setchr(i1, e2)
   223  		po.upush(undoSetChr, i1, 0)
   224  	} else {
   225  		// If n1 already has two children, add an intermediate extra
   226  		// node to record the relation correctly (without relating
   227  		// n2 to other existing nodes). Use a non-deterministic value
   228  		// to decide whether to append on the left or the right, to avoid
   229  		// creating degenerated chains.
   230  		//
   231  		//      n1
   232  		//     /  \
   233  		//   i1l  extra
   234  		//        /   \
   235  		//      i1r   n2
   236  		//
   237  		extra := po.newnode(nil)
   238  		if (i1^i2)&1 != 0 { // non-deterministic
   239  			po.setchl(extra, i1r)
   240  			po.setchr(extra, e2)
   241  			po.setchr(i1, newedge(extra, false))
   242  			po.upush(undoSetChr, i1, i1r)
   243  		} else {
   244  			po.setchl(extra, i1l)
   245  			po.setchr(extra, e2)
   246  			po.setchl(i1, newedge(extra, false))
   247  			po.upush(undoSetChl, i1, i1l)
   248  		}
   249  	}
   250  }
   251  
   252  // newnode allocates a new node bound to SSA value n.
   253  // If n is nil, this is an extra node (= only used internally).
   254  func (po *poset) newnode(n *Value) uint32 {
   255  	i := po.lastidx + 1
   256  	po.lastidx++
   257  	po.nodes = append(po.nodes, posetNode{})
   258  	if n != nil {
   259  		if po.values[n.ID] != 0 {
   260  			panic("newnode for Value already inserted")
   261  		}
   262  		po.values[n.ID] = i
   263  		po.upushnew(n.ID, i)
   264  	} else {
   265  		po.upushnew(0, i)
   266  	}
   267  	return i
   268  }
   269  
   270  // lookup searches for a SSA value into the forest of DAGS, and return its node.
   271  // Constants are materialized on the fly during lookup.
   272  func (po *poset) lookup(n *Value) (uint32, bool) {
   273  	i, f := po.values[n.ID]
   274  	if !f && n.isGenericIntConst() {
   275  		po.newconst(n)
   276  		i, f = po.values[n.ID]
   277  	}
   278  	return i, f
   279  }
   280  
   281  // newconst creates a node for a constant. It links it to other constants, so
   282  // that n<=5 is detected true when n<=3 is known to be true.
   283  // TODO: this is O(N), fix it.
   284  func (po *poset) newconst(n *Value) {
   285  	if !n.isGenericIntConst() {
   286  		panic("newconst on non-constant")
   287  	}
   288  
   289  	// If the same constant is already present in the poset through a different
   290  	// Value, just alias to it without allocating a new node.
   291  	val := n.AuxInt
   292  	if po.flags&posetFlagUnsigned != 0 {
   293  		val = int64(n.AuxUnsigned())
   294  	}
   295  	if c, found := po.constants[val]; found {
   296  		po.values[n.ID] = c
   297  		po.upushalias(n.ID, 0)
   298  		return
   299  	}
   300  
   301  	// Create the new node for this constant
   302  	i := po.newnode(n)
   303  
   304  	// If this is the first constant, put it as a new root, as
   305  	// we can't record an existing connection so we don't have
   306  	// a specific DAG to add it to. Notice that we want all
   307  	// constants to be in root #0, so make sure the new root
   308  	// goes there.
   309  	if len(po.constants) == 0 {
   310  		idx := len(po.roots)
   311  		po.roots = append(po.roots, i)
   312  		po.roots[0], po.roots[idx] = po.roots[idx], po.roots[0]
   313  		po.upush(undoNewRoot, i, 0)
   314  		po.constants[val] = i
   315  		po.upushconst(i, 0)
   316  		return
   317  	}
   318  
   319  	// Find the lower and upper bound among existing constants. That is,
   320  	// find the higher constant that is lower than the one that we're adding,
   321  	// and the lower constant that is higher.
   322  	// The loop is duplicated to handle signed and unsigned comparison,
   323  	// depending on how the poset was configured.
   324  	var lowerptr, higherptr uint32
   325  
   326  	if po.flags&posetFlagUnsigned != 0 {
   327  		var lower, higher uint64
   328  		val1 := n.AuxUnsigned()
   329  		for val2, ptr := range po.constants {
   330  			val2 := uint64(val2)
   331  			if val1 == val2 {
   332  				panic("unreachable")
   333  			}
   334  			if val2 < val1 && (lowerptr == 0 || val2 > lower) {
   335  				lower = val2
   336  				lowerptr = ptr
   337  			} else if val2 > val1 && (higherptr == 0 || val2 < higher) {
   338  				higher = val2
   339  				higherptr = ptr
   340  			}
   341  		}
   342  	} else {
   343  		var lower, higher int64
   344  		val1 := n.AuxInt
   345  		for val2, ptr := range po.constants {
   346  			if val1 == val2 {
   347  				panic("unreachable")
   348  			}
   349  			if val2 < val1 && (lowerptr == 0 || val2 > lower) {
   350  				lower = val2
   351  				lowerptr = ptr
   352  			} else if val2 > val1 && (higherptr == 0 || val2 < higher) {
   353  				higher = val2
   354  				higherptr = ptr
   355  			}
   356  		}
   357  	}
   358  
   359  	if lowerptr == 0 && higherptr == 0 {
   360  		// This should not happen, as at least one
   361  		// other constant must exist if we get here.
   362  		panic("no constant found")
   363  	}
   364  
   365  	// Create the new node and connect it to the bounds, so that
   366  	// lower < n < higher. We could have found both bounds or only one
   367  	// of them, depending on what other constants are present in the poset.
   368  	// Notice that we always link constants together, so they
   369  	// are always part of the same DAG.
   370  	switch {
   371  	case lowerptr != 0 && higherptr != 0:
   372  		// Both bounds are present, record lower < n < higher.
   373  		po.addchild(lowerptr, i, true)
   374  		po.addchild(i, higherptr, true)
   375  
   376  	case lowerptr != 0:
   377  		// Lower bound only, record lower < n.
   378  		po.addchild(lowerptr, i, true)
   379  
   380  	case higherptr != 0:
   381  		// Higher bound only. To record n < higher, we need
   382  		// an extra root:
   383  		//
   384  		//        extra
   385  		//        /   \
   386  		//      root   \
   387  		//       /      n
   388  		//     ....    /
   389  		//       \    /
   390  		//       higher
   391  		//
   392  		i2 := higherptr
   393  		r2 := po.findroot(i2)
   394  		if r2 != po.roots[0] { // all constants should be in root #0
   395  			panic("constant not in root #0")
   396  		}
   397  		extra := po.newnode(nil)
   398  		po.changeroot(r2, extra)
   399  		po.upush(undoChangeRoot, extra, newedge(r2, false))
   400  		po.addchild(extra, r2, false)
   401  		po.addchild(extra, i, false)
   402  		po.addchild(i, i2, true)
   403  	}
   404  
   405  	po.constants[val] = i
   406  	po.upushconst(i, 0)
   407  }
   408  
   409  // aliasnewnode records that a single node n2 (not in the poset yet) is an alias
   410  // of the master node n1.
   411  func (po *poset) aliasnewnode(n1, n2 *Value) {
   412  	i1, i2 := po.values[n1.ID], po.values[n2.ID]
   413  	if i1 == 0 || i2 != 0 {
   414  		panic("aliasnewnode invalid arguments")
   415  	}
   416  
   417  	po.values[n2.ID] = i1
   418  	po.upushalias(n2.ID, 0)
   419  }
   420  
   421  // aliasnodes records that all the nodes i2s are aliases of a single master node n1.
   422  // aliasnodes takes care of rearranging the DAG, changing references of parent/children
   423  // of nodes in i2s, so that they point to n1 instead.
   424  // Complexity is O(n) (with n being the total number of nodes in the poset, not just
   425  // the number of nodes being aliased).
   426  func (po *poset) aliasnodes(n1 *Value, i2s bitset) {
   427  	i1 := po.values[n1.ID]
   428  	if i1 == 0 {
   429  		panic("aliasnode for non-existing node")
   430  	}
   431  	if i2s.Test(i1) {
   432  		panic("aliasnode i2s contains n1 node")
   433  	}
   434  
   435  	// Go through all the nodes to adjust parent/chidlren of nodes in i2s
   436  	for idx, n := range po.nodes {
   437  		// Do not touch i1 itself, otherwise we can create useless self-loops
   438  		if uint32(idx) == i1 {
   439  			continue
   440  		}
   441  		l, r := n.l, n.r
   442  
   443  		// Rename all references to i2s into i1
   444  		if i2s.Test(l.Target()) {
   445  			po.setchl(uint32(idx), newedge(i1, l.Strict()))
   446  			po.upush(undoSetChl, uint32(idx), l)
   447  		}
   448  		if i2s.Test(r.Target()) {
   449  			po.setchr(uint32(idx), newedge(i1, r.Strict()))
   450  			po.upush(undoSetChr, uint32(idx), r)
   451  		}
   452  
   453  		// Connect all children of i2s to i1 (unless those children
   454  		// are in i2s as well, in which case it would be useless)
   455  		if i2s.Test(uint32(idx)) {
   456  			if l != 0 && !i2s.Test(l.Target()) {
   457  				po.addchild(i1, l.Target(), l.Strict())
   458  			}
   459  			if r != 0 && !i2s.Test(r.Target()) {
   460  				po.addchild(i1, r.Target(), r.Strict())
   461  			}
   462  			po.setchl(uint32(idx), 0)
   463  			po.setchr(uint32(idx), 0)
   464  			po.upush(undoSetChl, uint32(idx), l)
   465  			po.upush(undoSetChr, uint32(idx), r)
   466  		}
   467  	}
   468  
   469  	// Reassign all existing IDs that point to i2 to i1.
   470  	// This includes n2.ID.
   471  	for k, v := range po.values {
   472  		if i2s.Test(v) {
   473  			po.values[k] = i1
   474  			po.upushalias(k, v)
   475  		}
   476  	}
   477  
   478  	// If one of the aliased nodes is a constant, then make sure
   479  	// po.constants is updated to point to the master node.
   480  	for val, idx := range po.constants {
   481  		if i2s.Test(idx) {
   482  			po.constants[val] = i1
   483  			po.upushconst(i1, idx)
   484  		}
   485  	}
   486  }
   487  
   488  func (po *poset) isroot(r uint32) bool {
   489  	for i := range po.roots {
   490  		if po.roots[i] == r {
   491  			return true
   492  		}
   493  	}
   494  	return false
   495  }
   496  
   497  func (po *poset) changeroot(oldr, newr uint32) {
   498  	for i := range po.roots {
   499  		if po.roots[i] == oldr {
   500  			po.roots[i] = newr
   501  			return
   502  		}
   503  	}
   504  	panic("changeroot on non-root")
   505  }
   506  
   507  func (po *poset) removeroot(r uint32) {
   508  	for i := range po.roots {
   509  		if po.roots[i] == r {
   510  			po.roots = append(po.roots[:i], po.roots[i+1:]...)
   511  			return
   512  		}
   513  	}
   514  	panic("removeroot on non-root")
   515  }
   516  
   517  // dfs performs a depth-first search within the DAG whose root is r.
   518  // f is the visit function called for each node; if it returns true,
   519  // the search is aborted and true is returned. The root node is
   520  // visited too.
   521  // If strict, ignore edges across a path until at least one
   522  // strict edge is found. For instance, for a chain A<=B<=C<D<=E<F,
   523  // a strict walk visits D,E,F.
   524  // If the visit ends, false is returned.
   525  func (po *poset) dfs(r uint32, strict bool, f func(i uint32) bool) bool {
   526  	closed := newBitset(int(po.lastidx + 1))
   527  	open := make([]uint32, 1, 64)
   528  	open[0] = r
   529  
   530  	if strict {
   531  		// Do a first DFS; walk all paths and stop when we find a strict
   532  		// edge, building a "next" list of nodes reachable through strict
   533  		// edges. This will be the bootstrap open list for the real DFS.
   534  		next := make([]uint32, 0, 64)
   535  
   536  		for len(open) > 0 {
   537  			i := open[len(open)-1]
   538  			open = open[:len(open)-1]
   539  
   540  			// Don't visit the same node twice. Notice that all nodes
   541  			// across non-strict paths are still visited at least once, so
   542  			// a non-strict path can never obscure a strict path to the
   543  			// same node.
   544  			if !closed.Test(i) {
   545  				closed.Set(i)
   546  
   547  				l, r := po.children(i)
   548  				if l != 0 {
   549  					if l.Strict() {
   550  						next = append(next, l.Target())
   551  					} else {
   552  						open = append(open, l.Target())
   553  					}
   554  				}
   555  				if r != 0 {
   556  					if r.Strict() {
   557  						next = append(next, r.Target())
   558  					} else {
   559  						open = append(open, r.Target())
   560  					}
   561  				}
   562  			}
   563  		}
   564  		open = next
   565  		closed.Reset()
   566  	}
   567  
   568  	for len(open) > 0 {
   569  		i := open[len(open)-1]
   570  		open = open[:len(open)-1]
   571  
   572  		if !closed.Test(i) {
   573  			if f(i) {
   574  				return true
   575  			}
   576  			closed.Set(i)
   577  			l, r := po.children(i)
   578  			if l != 0 {
   579  				open = append(open, l.Target())
   580  			}
   581  			if r != 0 {
   582  				open = append(open, r.Target())
   583  			}
   584  		}
   585  	}
   586  	return false
   587  }
   588  
   589  // Returns true if there is a path from i1 to i2.
   590  // If strict ==  true: if the function returns true, then i1 <  i2.
   591  // If strict == false: if the function returns true, then i1 <= i2.
   592  // If the function returns false, no relation is known.
   593  func (po *poset) reaches(i1, i2 uint32, strict bool) bool {
   594  	return po.dfs(i1, strict, func(n uint32) bool {
   595  		return n == i2
   596  	})
   597  }
   598  
   599  // findroot finds i's root, that is which DAG contains i.
   600  // Returns the root; if i is itself a root, it is returned.
   601  // Panic if i is not in any DAG.
   602  func (po *poset) findroot(i uint32) uint32 {
   603  	// TODO(rasky): if needed, a way to speed up this search is
   604  	// storing a bitset for each root using it as a mini bloom filter
   605  	// of nodes present under that root.
   606  	for _, r := range po.roots {
   607  		if po.reaches(r, i, false) {
   608  			return r
   609  		}
   610  	}
   611  	panic("findroot didn't find any root")
   612  }
   613  
   614  // mergeroot merges two DAGs into one DAG by creating a new extra root
   615  func (po *poset) mergeroot(r1, r2 uint32) uint32 {
   616  	// Root #0 is special as it contains all constants. Since mergeroot
   617  	// discards r2 as root and keeps r1, make sure that r2 is not root #0,
   618  	// otherwise constants would move to a different root.
   619  	if r2 == po.roots[0] {
   620  		r1, r2 = r2, r1
   621  	}
   622  	r := po.newnode(nil)
   623  	po.setchl(r, newedge(r1, false))
   624  	po.setchr(r, newedge(r2, false))
   625  	po.changeroot(r1, r)
   626  	po.removeroot(r2)
   627  	po.upush(undoMergeRoot, r, 0)
   628  	return r
   629  }
   630  
   631  // collapsepath marks n1 and n2 as equal and collapses as equal all
   632  // nodes across all paths between n1 and n2. If a strict edge is
   633  // found, the function does not modify the DAG and returns false.
   634  // Complexity is O(n).
   635  func (po *poset) collapsepath(n1, n2 *Value) bool {
   636  	i1, i2 := po.values[n1.ID], po.values[n2.ID]
   637  	if po.reaches(i1, i2, true) {
   638  		return false
   639  	}
   640  
   641  	// Find all the paths from i1 to i2
   642  	paths := po.findpaths(i1, i2)
   643  	// Mark all nodes in all the paths as aliases of n1
   644  	// (excluding n1 itself)
   645  	paths.Clear(i1)
   646  	po.aliasnodes(n1, paths)
   647  	return true
   648  }
   649  
   650  // findpaths is a recursive function that calculates all paths from cur to dst
   651  // and return them as a bitset (the index of a node is set in the bitset if
   652  // that node is on at least one path from cur to dst).
   653  // We do a DFS from cur (stopping going deep any time we reach dst, if ever),
   654  // and mark as part of the paths any node that has a children which is already
   655  // part of the path (or is dst itself).
   656  func (po *poset) findpaths(cur, dst uint32) bitset {
   657  	seen := newBitset(int(po.lastidx + 1))
   658  	path := newBitset(int(po.lastidx + 1))
   659  	path.Set(dst)
   660  	po.findpaths1(cur, dst, seen, path)
   661  	return path
   662  }
   663  
   664  func (po *poset) findpaths1(cur, dst uint32, seen bitset, path bitset) {
   665  	if cur == dst {
   666  		return
   667  	}
   668  	seen.Set(cur)
   669  	l, r := po.chl(cur), po.chr(cur)
   670  	if !seen.Test(l) {
   671  		po.findpaths1(l, dst, seen, path)
   672  	}
   673  	if !seen.Test(r) {
   674  		po.findpaths1(r, dst, seen, path)
   675  	}
   676  	if path.Test(l) || path.Test(r) {
   677  		path.Set(cur)
   678  	}
   679  }
   680  
   681  // Check whether it is recorded that i1!=i2
   682  func (po *poset) isnoneq(i1, i2 uint32) bool {
   683  	if i1 == i2 {
   684  		return false
   685  	}
   686  	if i1 < i2 {
   687  		i1, i2 = i2, i1
   688  	}
   689  
   690  	// Check if we recorded a non-equal relation before
   691  	if bs, ok := po.noneq[i1]; ok && bs.Test(i2) {
   692  		return true
   693  	}
   694  	return false
   695  }
   696  
   697  // Record that i1!=i2
   698  func (po *poset) setnoneq(n1, n2 *Value) {
   699  	i1, f1 := po.lookup(n1)
   700  	i2, f2 := po.lookup(n2)
   701  
   702  	// If any of the nodes do not exist in the poset, allocate them. Since
   703  	// we don't know any relation (in the partial order) about them, they must
   704  	// become independent roots.
   705  	if !f1 {
   706  		i1 = po.newnode(n1)
   707  		po.roots = append(po.roots, i1)
   708  		po.upush(undoNewRoot, i1, 0)
   709  	}
   710  	if !f2 {
   711  		i2 = po.newnode(n2)
   712  		po.roots = append(po.roots, i2)
   713  		po.upush(undoNewRoot, i2, 0)
   714  	}
   715  
   716  	if i1 == i2 {
   717  		panic("setnoneq on same node")
   718  	}
   719  	if i1 < i2 {
   720  		i1, i2 = i2, i1
   721  	}
   722  	bs := po.noneq[i1]
   723  	if bs == nil {
   724  		// Given that we record non-equality relations using the
   725  		// higher index as a key, the bitsize will never change size.
   726  		// TODO(rasky): if memory is a problem, consider allocating
   727  		// a small bitset and lazily grow it when higher indices arrive.
   728  		bs = newBitset(int(i1))
   729  		po.noneq[i1] = bs
   730  	} else if bs.Test(i2) {
   731  		// Already recorded
   732  		return
   733  	}
   734  	bs.Set(i2)
   735  	po.upushneq(i1, i2)
   736  }
   737  
   738  // CheckIntegrity verifies internal integrity of a poset. It is intended
   739  // for debugging purposes.
   740  func (po *poset) CheckIntegrity() {
   741  	// Record which index is a constant
   742  	constants := newBitset(int(po.lastidx + 1))
   743  	for _, c := range po.constants {
   744  		constants.Set(c)
   745  	}
   746  
   747  	// Verify that each node appears in a single DAG, and that
   748  	// all constants are within the first DAG
   749  	seen := newBitset(int(po.lastidx + 1))
   750  	for ridx, r := range po.roots {
   751  		if r == 0 {
   752  			panic("empty root")
   753  		}
   754  
   755  		po.dfs(r, false, func(i uint32) bool {
   756  			if seen.Test(i) {
   757  				panic("duplicate node")
   758  			}
   759  			seen.Set(i)
   760  			if constants.Test(i) {
   761  				if ridx != 0 {
   762  					panic("constants not in the first DAG")
   763  				}
   764  			}
   765  			return false
   766  		})
   767  	}
   768  
   769  	// Verify that values contain the minimum set
   770  	for id, idx := range po.values {
   771  		if !seen.Test(idx) {
   772  			panic(fmt.Errorf("spurious value [%d]=%d", id, idx))
   773  		}
   774  	}
   775  
   776  	// Verify that only existing nodes have non-zero children
   777  	for i, n := range po.nodes {
   778  		if n.l|n.r != 0 {
   779  			if !seen.Test(uint32(i)) {
   780  				panic(fmt.Errorf("children of unknown node %d->%v", i, n))
   781  			}
   782  			if n.l.Target() == uint32(i) || n.r.Target() == uint32(i) {
   783  				panic(fmt.Errorf("self-loop on node %d", i))
   784  			}
   785  		}
   786  	}
   787  }
   788  
   789  // CheckEmpty checks that a poset is completely empty.
   790  // It can be used for debugging purposes, as a poset is supposed to
   791  // be empty after it's fully rolled back through Undo.
   792  func (po *poset) CheckEmpty() error {
   793  	if len(po.nodes) != 1 {
   794  		return fmt.Errorf("non-empty nodes list: %v", po.nodes)
   795  	}
   796  	if len(po.values) != 0 {
   797  		return fmt.Errorf("non-empty value map: %v", po.values)
   798  	}
   799  	if len(po.roots) != 0 {
   800  		return fmt.Errorf("non-empty root list: %v", po.roots)
   801  	}
   802  	if len(po.constants) != 0 {
   803  		return fmt.Errorf("non-empty constants: %v", po.constants)
   804  	}
   805  	if len(po.undo) != 0 {
   806  		return fmt.Errorf("non-empty undo list: %v", po.undo)
   807  	}
   808  	if po.lastidx != 0 {
   809  		return fmt.Errorf("lastidx index is not zero: %v", po.lastidx)
   810  	}
   811  	for _, bs := range po.noneq {
   812  		for _, x := range bs {
   813  			if x != 0 {
   814  				return fmt.Errorf("non-empty noneq map")
   815  			}
   816  		}
   817  	}
   818  	return nil
   819  }
   820  
   821  // DotDump dumps the poset in graphviz format to file fn, with the specified title.
   822  func (po *poset) DotDump(fn string, title string) error {
   823  	f, err := os.Create(fn)
   824  	if err != nil {
   825  		return err
   826  	}
   827  	defer f.Close()
   828  
   829  	// Create reverse index mapping (taking aliases into account)
   830  	names := make(map[uint32]string)
   831  	for id, i := range po.values {
   832  		s := names[i]
   833  		if s == "" {
   834  			s = fmt.Sprintf("v%d", id)
   835  		} else {
   836  			s += fmt.Sprintf(", v%d", id)
   837  		}
   838  		names[i] = s
   839  	}
   840  
   841  	// Create reverse constant mapping
   842  	consts := make(map[uint32]int64)
   843  	for val, idx := range po.constants {
   844  		consts[idx] = val
   845  	}
   846  
   847  	fmt.Fprintf(f, "digraph poset {\n")
   848  	fmt.Fprintf(f, "\tedge [ fontsize=10 ]\n")
   849  	for ridx, r := range po.roots {
   850  		fmt.Fprintf(f, "\tsubgraph root%d {\n", ridx)
   851  		po.dfs(r, false, func(i uint32) bool {
   852  			if val, ok := consts[i]; ok {
   853  				// Constant
   854  				var vals string
   855  				if po.flags&posetFlagUnsigned != 0 {
   856  					vals = fmt.Sprint(uint64(val))
   857  				} else {
   858  					vals = fmt.Sprint(int64(val))
   859  				}
   860  				fmt.Fprintf(f, "\t\tnode%d [shape=box style=filled fillcolor=cadetblue1 label=<%s <font point-size=\"6\">%s [%d]</font>>]\n",
   861  					i, vals, names[i], i)
   862  			} else {
   863  				// Normal SSA value
   864  				fmt.Fprintf(f, "\t\tnode%d [label=<%s <font point-size=\"6\">[%d]</font>>]\n", i, names[i], i)
   865  			}
   866  			chl, chr := po.children(i)
   867  			for _, ch := range []posetEdge{chl, chr} {
   868  				if ch != 0 {
   869  					if ch.Strict() {
   870  						fmt.Fprintf(f, "\t\tnode%d -> node%d [label=\" <\" color=\"red\"]\n", i, ch.Target())
   871  					} else {
   872  						fmt.Fprintf(f, "\t\tnode%d -> node%d [label=\" <=\" color=\"green\"]\n", i, ch.Target())
   873  					}
   874  				}
   875  			}
   876  			return false
   877  		})
   878  		fmt.Fprintf(f, "\t}\n")
   879  	}
   880  	fmt.Fprintf(f, "\tlabelloc=\"t\"\n")
   881  	fmt.Fprintf(f, "\tlabeldistance=\"3.0\"\n")
   882  	fmt.Fprintf(f, "\tlabel=%q\n", title)
   883  	fmt.Fprintf(f, "}\n")
   884  	return nil
   885  }
   886  
   887  // Ordered reports whether n1<n2. It returns false either when it is
   888  // certain that n1<n2 is false, or if there is not enough information
   889  // to tell.
   890  // Complexity is O(n).
   891  func (po *poset) Ordered(n1, n2 *Value) bool {
   892  	if debugPoset {
   893  		defer po.CheckIntegrity()
   894  	}
   895  	if n1.ID == n2.ID {
   896  		panic("should not call Ordered with n1==n2")
   897  	}
   898  
   899  	i1, f1 := po.lookup(n1)
   900  	i2, f2 := po.lookup(n2)
   901  	if !f1 || !f2 {
   902  		return false
   903  	}
   904  
   905  	return i1 != i2 && po.reaches(i1, i2, true)
   906  }
   907  
   908  // OrderedOrEqual reports whether n1<=n2. It returns false either when it is
   909  // certain that n1<=n2 is false, or if there is not enough information
   910  // to tell.
   911  // Complexity is O(n).
   912  func (po *poset) OrderedOrEqual(n1, n2 *Value) bool {
   913  	if debugPoset {
   914  		defer po.CheckIntegrity()
   915  	}
   916  	if n1.ID == n2.ID {
   917  		panic("should not call Ordered with n1==n2")
   918  	}
   919  
   920  	i1, f1 := po.lookup(n1)
   921  	i2, f2 := po.lookup(n2)
   922  	if !f1 || !f2 {
   923  		return false
   924  	}
   925  
   926  	return i1 == i2 || po.reaches(i1, i2, false)
   927  }
   928  
   929  // Equal reports whether n1==n2. It returns false either when it is
   930  // certain that n1==n2 is false, or if there is not enough information
   931  // to tell.
   932  // Complexity is O(1).
   933  func (po *poset) Equal(n1, n2 *Value) bool {
   934  	if debugPoset {
   935  		defer po.CheckIntegrity()
   936  	}
   937  	if n1.ID == n2.ID {
   938  		panic("should not call Equal with n1==n2")
   939  	}
   940  
   941  	i1, f1 := po.lookup(n1)
   942  	i2, f2 := po.lookup(n2)
   943  	return f1 && f2 && i1 == i2
   944  }
   945  
   946  // NonEqual reports whether n1!=n2. It returns false either when it is
   947  // certain that n1!=n2 is false, or if there is not enough information
   948  // to tell.
   949  // Complexity is O(n) (because it internally calls Ordered to see if we
   950  // can infer n1!=n2 from n1<n2 or n2<n1).
   951  func (po *poset) NonEqual(n1, n2 *Value) bool {
   952  	if debugPoset {
   953  		defer po.CheckIntegrity()
   954  	}
   955  	if n1.ID == n2.ID {
   956  		panic("should not call NonEqual with n1==n2")
   957  	}
   958  
   959  	// If we never saw the nodes before, we don't
   960  	// have a recorded non-equality.
   961  	i1, f1 := po.lookup(n1)
   962  	i2, f2 := po.lookup(n2)
   963  	if !f1 || !f2 {
   964  		return false
   965  	}
   966  
   967  	// Check if we recorded inequality
   968  	if po.isnoneq(i1, i2) {
   969  		return true
   970  	}
   971  
   972  	// Check if n1<n2 or n2<n1, in which case we can infer that n1!=n2
   973  	if po.Ordered(n1, n2) || po.Ordered(n2, n1) {
   974  		return true
   975  	}
   976  
   977  	return false
   978  }
   979  
   980  // setOrder records that n1<n2 or n1<=n2 (depending on strict). Returns false
   981  // if this is a contradiction.
   982  // Implements SetOrder() and SetOrderOrEqual()
   983  func (po *poset) setOrder(n1, n2 *Value, strict bool) bool {
   984  	i1, f1 := po.lookup(n1)
   985  	i2, f2 := po.lookup(n2)
   986  
   987  	switch {
   988  	case !f1 && !f2:
   989  		// Neither n1 nor n2 are in the poset, so they are not related
   990  		// in any way to existing nodes.
   991  		// Create a new DAG to record the relation.
   992  		i1, i2 = po.newnode(n1), po.newnode(n2)
   993  		po.roots = append(po.roots, i1)
   994  		po.upush(undoNewRoot, i1, 0)
   995  		po.addchild(i1, i2, strict)
   996  
   997  	case f1 && !f2:
   998  		// n1 is in one of the DAGs, while n2 is not. Add n2 as children
   999  		// of n1.
  1000  		i2 = po.newnode(n2)
  1001  		po.addchild(i1, i2, strict)
  1002  
  1003  	case !f1 && f2:
  1004  		// n1 is not in any DAG but n2 is. If n2 is a root, we can put
  1005  		// n1 in its place as a root; otherwise, we need to create a new
  1006  		// extra root to record the relation.
  1007  		i1 = po.newnode(n1)
  1008  
  1009  		if po.isroot(i2) {
  1010  			po.changeroot(i2, i1)
  1011  			po.upush(undoChangeRoot, i1, newedge(i2, strict))
  1012  			po.addchild(i1, i2, strict)
  1013  			return true
  1014  		}
  1015  
  1016  		// Search for i2's root; this requires a O(n) search on all
  1017  		// DAGs
  1018  		r := po.findroot(i2)
  1019  
  1020  		// Re-parent as follows:
  1021  		//
  1022  		//                  extra
  1023  		//     r            /   \
  1024  		//      \   ===>   r    i1
  1025  		//      i2          \   /
  1026  		//                    i2
  1027  		//
  1028  		extra := po.newnode(nil)
  1029  		po.changeroot(r, extra)
  1030  		po.upush(undoChangeRoot, extra, newedge(r, false))
  1031  		po.addchild(extra, r, false)
  1032  		po.addchild(extra, i1, false)
  1033  		po.addchild(i1, i2, strict)
  1034  
  1035  	case f1 && f2:
  1036  		// If the nodes are aliased, fail only if we're setting a strict order
  1037  		// (that is, we cannot set n1<n2 if n1==n2).
  1038  		if i1 == i2 {
  1039  			return !strict
  1040  		}
  1041  
  1042  		// If we are trying to record n1<=n2 but we learned that n1!=n2,
  1043  		// record n1<n2, as it provides more information.
  1044  		if !strict && po.isnoneq(i1, i2) {
  1045  			strict = true
  1046  		}
  1047  
  1048  		// Both n1 and n2 are in the poset. This is the complex part of the algorithm
  1049  		// as we need to find many different cases and DAG shapes.
  1050  
  1051  		// Check if n1 somehow reaches n2
  1052  		if po.reaches(i1, i2, false) {
  1053  			// This is the table of all cases we need to handle:
  1054  			//
  1055  			//      DAG          New      Action
  1056  			//      ---------------------------------------------------
  1057  			// #1:  N1<=X<=N2 |  N1<=N2 | do nothing
  1058  			// #2:  N1<=X<=N2 |  N1<N2  | add strict edge (N1<N2)
  1059  			// #3:  N1<X<N2   |  N1<=N2 | do nothing (we already know more)
  1060  			// #4:  N1<X<N2   |  N1<N2  | do nothing
  1061  
  1062  			// Check if we're in case #2
  1063  			if strict && !po.reaches(i1, i2, true) {
  1064  				po.addchild(i1, i2, true)
  1065  				return true
  1066  			}
  1067  
  1068  			// Case #1, #3, or #4: nothing to do
  1069  			return true
  1070  		}
  1071  
  1072  		// Check if n2 somehow reaches n1
  1073  		if po.reaches(i2, i1, false) {
  1074  			// This is the table of all cases we need to handle:
  1075  			//
  1076  			//      DAG           New      Action
  1077  			//      ---------------------------------------------------
  1078  			// #5:  N2<=X<=N1  |  N1<=N2 | collapse path (learn that N1=X=N2)
  1079  			// #6:  N2<=X<=N1  |  N1<N2  | contradiction
  1080  			// #7:  N2<X<N1    |  N1<=N2 | contradiction in the path
  1081  			// #8:  N2<X<N1    |  N1<N2  | contradiction
  1082  
  1083  			if strict {
  1084  				// Cases #6 and #8: contradiction
  1085  				return false
  1086  			}
  1087  
  1088  			// We're in case #5 or #7. Try to collapse path, and that will
  1089  			// fail if it realizes that we are in case #7.
  1090  			return po.collapsepath(n2, n1)
  1091  		}
  1092  
  1093  		// We don't know of any existing relation between n1 and n2. They could
  1094  		// be part of the same DAG or not.
  1095  		// Find their roots to check whether they are in the same DAG.
  1096  		r1, r2 := po.findroot(i1), po.findroot(i2)
  1097  		if r1 != r2 {
  1098  			// We need to merge the two DAGs to record a relation between the nodes
  1099  			po.mergeroot(r1, r2)
  1100  		}
  1101  
  1102  		// Connect n1 and n2
  1103  		po.addchild(i1, i2, strict)
  1104  	}
  1105  
  1106  	return true
  1107  }
  1108  
  1109  // SetOrder records that n1<n2. Returns false if this is a contradiction
  1110  // Complexity is O(1) if n2 was never seen before, or O(n) otherwise.
  1111  func (po *poset) SetOrder(n1, n2 *Value) bool {
  1112  	if debugPoset {
  1113  		defer po.CheckIntegrity()
  1114  	}
  1115  	if n1.ID == n2.ID {
  1116  		panic("should not call SetOrder with n1==n2")
  1117  	}
  1118  	return po.setOrder(n1, n2, true)
  1119  }
  1120  
  1121  // SetOrderOrEqual records that n1<=n2. Returns false if this is a contradiction
  1122  // Complexity is O(1) if n2 was never seen before, or O(n) otherwise.
  1123  func (po *poset) SetOrderOrEqual(n1, n2 *Value) bool {
  1124  	if debugPoset {
  1125  		defer po.CheckIntegrity()
  1126  	}
  1127  	if n1.ID == n2.ID {
  1128  		panic("should not call SetOrder with n1==n2")
  1129  	}
  1130  	return po.setOrder(n1, n2, false)
  1131  }
  1132  
  1133  // SetEqual records that n1==n2. Returns false if this is a contradiction
  1134  // (that is, if it is already recorded that n1<n2 or n2<n1).
  1135  // Complexity is O(1) if n2 was never seen before, or O(n) otherwise.
  1136  func (po *poset) SetEqual(n1, n2 *Value) bool {
  1137  	if debugPoset {
  1138  		defer po.CheckIntegrity()
  1139  	}
  1140  	if n1.ID == n2.ID {
  1141  		panic("should not call Add with n1==n2")
  1142  	}
  1143  
  1144  	i1, f1 := po.lookup(n1)
  1145  	i2, f2 := po.lookup(n2)
  1146  
  1147  	switch {
  1148  	case !f1 && !f2:
  1149  		i1 = po.newnode(n1)
  1150  		po.roots = append(po.roots, i1)
  1151  		po.upush(undoNewRoot, i1, 0)
  1152  		po.aliasnewnode(n1, n2)
  1153  	case f1 && !f2:
  1154  		po.aliasnewnode(n1, n2)
  1155  	case !f1 && f2:
  1156  		po.aliasnewnode(n2, n1)
  1157  	case f1 && f2:
  1158  		if i1 == i2 {
  1159  			// Already aliased, ignore
  1160  			return true
  1161  		}
  1162  
  1163  		// If we recorded that n1!=n2, this is a contradiction.
  1164  		if po.isnoneq(i1, i2) {
  1165  			return false
  1166  		}
  1167  
  1168  		// If we already knew that n1<=n2, we can collapse the path to
  1169  		// record n1==n2 (and vice versa).
  1170  		if po.reaches(i1, i2, false) {
  1171  			return po.collapsepath(n1, n2)
  1172  		}
  1173  		if po.reaches(i2, i1, false) {
  1174  			return po.collapsepath(n2, n1)
  1175  		}
  1176  
  1177  		r1 := po.findroot(i1)
  1178  		r2 := po.findroot(i2)
  1179  		if r1 != r2 {
  1180  			// Merge the two DAGs so we can record relations between the nodes
  1181  			po.mergeroot(r1, r2)
  1182  		}
  1183  
  1184  		// Set n2 as alias of n1. This will also update all the references
  1185  		// to n2 to become references to n1
  1186  		i2s := newBitset(int(po.lastidx) + 1)
  1187  		i2s.Set(i2)
  1188  		po.aliasnodes(n1, i2s)
  1189  	}
  1190  	return true
  1191  }
  1192  
  1193  // SetNonEqual records that n1!=n2. Returns false if this is a contradiction
  1194  // (that is, if it is already recorded that n1==n2).
  1195  // Complexity is O(n).
  1196  func (po *poset) SetNonEqual(n1, n2 *Value) bool {
  1197  	if debugPoset {
  1198  		defer po.CheckIntegrity()
  1199  	}
  1200  	if n1.ID == n2.ID {
  1201  		panic("should not call SetNonEqual with n1==n2")
  1202  	}
  1203  
  1204  	// Check whether the nodes are already in the poset
  1205  	i1, f1 := po.lookup(n1)
  1206  	i2, f2 := po.lookup(n2)
  1207  
  1208  	// If either node wasn't present, we just record the new relation
  1209  	// and exit.
  1210  	if !f1 || !f2 {
  1211  		po.setnoneq(n1, n2)
  1212  		return true
  1213  	}
  1214  
  1215  	// See if we already know this, in which case there's nothing to do.
  1216  	if po.isnoneq(i1, i2) {
  1217  		return true
  1218  	}
  1219  
  1220  	// Check if we're contradicting an existing equality relation
  1221  	if po.Equal(n1, n2) {
  1222  		return false
  1223  	}
  1224  
  1225  	// Record non-equality
  1226  	po.setnoneq(n1, n2)
  1227  
  1228  	// If we know that i1<=i2 but not i1<i2, learn that as we
  1229  	// now know that they are not equal. Do the same for i2<=i1.
  1230  	// Do this check only if both nodes were already in the DAG,
  1231  	// otherwise there cannot be an existing relation.
  1232  	if po.reaches(i1, i2, false) && !po.reaches(i1, i2, true) {
  1233  		po.addchild(i1, i2, true)
  1234  	}
  1235  	if po.reaches(i2, i1, false) && !po.reaches(i2, i1, true) {
  1236  		po.addchild(i2, i1, true)
  1237  	}
  1238  
  1239  	return true
  1240  }
  1241  
  1242  // Checkpoint saves the current state of the DAG so that it's possible
  1243  // to later undo this state.
  1244  // Complexity is O(1).
  1245  func (po *poset) Checkpoint() {
  1246  	po.undo = append(po.undo, posetUndo{typ: undoCheckpoint})
  1247  }
  1248  
  1249  // Undo restores the state of the poset to the previous checkpoint.
  1250  // Complexity depends on the type of operations that were performed
  1251  // since the last checkpoint; each Set* operation creates an undo
  1252  // pass which Undo has to revert with a worst-case complexity of O(n).
  1253  func (po *poset) Undo() {
  1254  	if len(po.undo) == 0 {
  1255  		panic("empty undo stack")
  1256  	}
  1257  	if debugPoset {
  1258  		defer po.CheckIntegrity()
  1259  	}
  1260  
  1261  	for len(po.undo) > 0 {
  1262  		pass := po.undo[len(po.undo)-1]
  1263  		po.undo = po.undo[:len(po.undo)-1]
  1264  
  1265  		switch pass.typ {
  1266  		case undoCheckpoint:
  1267  			return
  1268  
  1269  		case undoSetChl:
  1270  			po.setchl(pass.idx, pass.edge)
  1271  
  1272  		case undoSetChr:
  1273  			po.setchr(pass.idx, pass.edge)
  1274  
  1275  		case undoNonEqual:
  1276  			po.noneq[uint32(pass.ID)].Clear(pass.idx)
  1277  
  1278  		case undoNewNode:
  1279  			if pass.idx != po.lastidx {
  1280  				panic("invalid newnode index")
  1281  			}
  1282  			if pass.ID != 0 {
  1283  				if po.values[pass.ID] != pass.idx {
  1284  					panic("invalid newnode undo pass")
  1285  				}
  1286  				delete(po.values, pass.ID)
  1287  			}
  1288  			po.setchl(pass.idx, 0)
  1289  			po.setchr(pass.idx, 0)
  1290  			po.nodes = po.nodes[:pass.idx]
  1291  			po.lastidx--
  1292  
  1293  		case undoNewConstant:
  1294  			// FIXME: remove this O(n) loop
  1295  			var val int64
  1296  			var i uint32
  1297  			for val, i = range po.constants {
  1298  				if i == pass.idx {
  1299  					break
  1300  				}
  1301  			}
  1302  			if i != pass.idx {
  1303  				panic("constant not found in undo pass")
  1304  			}
  1305  			if pass.ID == 0 {
  1306  				delete(po.constants, val)
  1307  			} else {
  1308  				// Restore previous index as constant node
  1309  				// (also restoring the invariant on correct bounds)
  1310  				oldidx := uint32(pass.ID)
  1311  				po.constants[val] = oldidx
  1312  			}
  1313  
  1314  		case undoAliasNode:
  1315  			ID, prev := pass.ID, pass.idx
  1316  			cur := po.values[ID]
  1317  			if prev == 0 {
  1318  				// Born as an alias, die as an alias
  1319  				delete(po.values, ID)
  1320  			} else {
  1321  				if cur == prev {
  1322  					panic("invalid aliasnode undo pass")
  1323  				}
  1324  				// Give it back previous value
  1325  				po.values[ID] = prev
  1326  			}
  1327  
  1328  		case undoNewRoot:
  1329  			i := pass.idx
  1330  			l, r := po.children(i)
  1331  			if l|r != 0 {
  1332  				panic("non-empty root in undo newroot")
  1333  			}
  1334  			po.removeroot(i)
  1335  
  1336  		case undoChangeRoot:
  1337  			i := pass.idx
  1338  			l, r := po.children(i)
  1339  			if l|r != 0 {
  1340  				panic("non-empty root in undo changeroot")
  1341  			}
  1342  			po.changeroot(i, pass.edge.Target())
  1343  
  1344  		case undoMergeRoot:
  1345  			i := pass.idx
  1346  			l, r := po.children(i)
  1347  			po.changeroot(i, l.Target())
  1348  			po.roots = append(po.roots, r.Target())
  1349  
  1350  		default:
  1351  			panic(pass.typ)
  1352  		}
  1353  	}
  1354  
  1355  	if debugPoset && po.CheckEmpty() != nil {
  1356  		panic("poset not empty at the end of undo")
  1357  	}
  1358  }
  1359  

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