Adding upstream version 1.16.10.upstream/1.16.10upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1359 insertions, 0 deletions

diff --git a/src/cmd/compile/internal/ssa/poset.go b/src/cmd/compile/internal/ssa/poset.go
new file mode 100644
index 0000000..f5a2b3a
--- /dev/null
+++ b/src/cmd/compile/internal/ssa/poset.go
@@ -0,0 +1,1359 @@
+// Copyright 2018 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 (
+	"fmt"
+	"os"
+)
+
+// If true, check poset integrity after every mutation
+var debugPoset = false
+
+const uintSize = 32 << (^uint(0) >> 32 & 1) // 32 or 64
+
+// bitset is a bit array for dense indexes.
+type bitset []uint
+
+func newBitset(n int) bitset {
+	return make(bitset, (n+uintSize-1)/uintSize)
+}
+
+func (bs bitset) Reset() {
+	for i := range bs {
+		bs[i] = 0
+	}
+}
+
+func (bs bitset) Set(idx uint32) {
+	bs[idx/uintSize] |= 1 << (idx % uintSize)
+}
+
+func (bs bitset) Clear(idx uint32) {
+	bs[idx/uintSize] &^= 1 << (idx % uintSize)
+}
+
+func (bs bitset) Test(idx uint32) bool {
+	return bs[idx/uintSize]&(1<<(idx%uintSize)) != 0
+}
+
+type undoType uint8
+
+const (
+	undoInvalid     undoType = iota
+	undoCheckpoint           // a checkpoint to group undo passes
+	undoSetChl               // change back left child of undo.idx to undo.edge
+	undoSetChr               // change back right child of undo.idx to undo.edge
+	undoNonEqual             // forget that SSA value undo.ID is non-equal to undo.idx (another ID)
+	undoNewNode              // remove new node created for SSA value undo.ID
+	undoNewConstant          // remove the constant node idx from the constants map
+	undoAliasNode            // unalias SSA value undo.ID so that it points back to node index undo.idx
+	undoNewRoot              // remove node undo.idx from root list
+	undoChangeRoot           // remove node undo.idx from root list, and put back undo.edge.Target instead
+	undoMergeRoot            // remove node undo.idx from root list, and put back its children instead
+)
+
+// posetUndo represents an undo pass to be performed.
+// It's an union of fields that can be used to store information,
+// and typ is the discriminant, that specifies which kind
+// of operation must be performed. Not all fields are always used.
+type posetUndo struct {
+	typ  undoType
+	idx  uint32
+	ID   ID
+	edge posetEdge
+}
+
+const (
+	// Make poset handle constants as unsigned numbers.
+	posetFlagUnsigned = 1 << iota
+)
+
+// A poset edge. The zero value is the null/empty edge.
+// Packs target node index (31 bits) and strict flag (1 bit).
+type posetEdge uint32
+
+func newedge(t uint32, strict bool) posetEdge {
+	s := uint32(0)
+	if strict {
+		s = 1
+	}
+	return posetEdge(t<<1 | s)
+}
+func (e posetEdge) Target() uint32 { return uint32(e) >> 1 }
+func (e posetEdge) Strict() bool   { return uint32(e)&1 != 0 }
+func (e posetEdge) String() string {
+	s := fmt.Sprint(e.Target())
+	if e.Strict() {
+		s += "*"
+	}
+	return s
+}
+
+// posetNode is a node of a DAG within the poset.
+type posetNode struct {
+	l, r posetEdge
+}
+
+// poset is a union-find data structure that can represent a partially ordered set
+// of SSA values. Given a binary relation that creates a partial order (eg: '<'),
+// clients can record relations between SSA values using SetOrder, and later
+// check relations (in the transitive closure) with Ordered. For instance,
+// if SetOrder is called to record that A<B and B<C, Ordered will later confirm
+// that A<C.
+//
+// It is possible to record equality relations between SSA values with SetEqual and check
+// equality with Equal. Equality propagates into the transitive closure for the partial
+// order so that if we know that A<B<C and later learn that A==D, Ordered will return
+// true for D<C.
+//
+// It is also possible to record inequality relations between nodes with SetNonEqual;
+// non-equality relations are not transitive, but they can still be useful: for instance
+// if we know that A<=B and later we learn that A!=B, we can deduce that A<B.
+// NonEqual can be used to check whether it is known that the nodes are different, either
+// because SetNonEqual was called before, or because we know that they are strictly ordered.
+//
+// poset will refuse to record new relations that contradict existing relations:
+// for instance if A<B<C, calling SetOrder for C<A will fail returning false; also
+// calling SetEqual for C==A will fail.
+//
+// poset is implemented as a forest of DAGs; in each DAG, if there is a path (directed)
+// from node A to B, it means that A<B (or A<=B). Equality is represented by mapping
+// two SSA values to the same DAG node; when a new equality relation is recorded
+// between two existing nodes,the nodes are merged, adjusting incoming and outgoing edges.
+//
+// Constants are specially treated. When a constant is added to the poset, it is
+// immediately linked to other constants already present; so for instance if the
+// poset knows that x<=3, and then x is tested against 5, 5 is first added and linked
+// 3 (using 3<5), so that the poset knows that x<=3<5; at that point, it is able
+// to answer x<5 correctly. This means that all constants are always within the same
+// DAG; as an implementation detail, we enfoce that the DAG containtining the constants
+// is always the first in the forest.
+//
+// poset is designed to be memory efficient and do little allocations during normal usage.
+// Most internal data structures are pre-allocated and flat, so for instance adding a
+// new relation does not cause any allocation. For performance reasons,
+// each node has only up to two outgoing edges (like a binary tree), so intermediate
+// "dummy" nodes are required to represent more than two relations. For instance,
+// to record that A<I, A<J, A<K (with no known relation between I,J,K), we create the
+// following DAG:
+//
+//         A
+//        / \
+//       I  dummy
+//           /  \
+//          J    K
+//
+type poset struct {
+	lastidx   uint32            // last generated dense index
+	flags     uint8             // internal flags
+	values    map[ID]uint32     // map SSA values to dense indexes
+	constants map[int64]uint32  // record SSA constants together with their value
+	nodes     []posetNode       // nodes (in all DAGs)
+	roots     []uint32          // list of root nodes (forest)
+	noneq     map[uint32]bitset // non-equal relations
+	undo      []posetUndo       // undo chain
+}
+
+func newPoset() *poset {
+	return &poset{
+		values:    make(map[ID]uint32),
+		constants: make(map[int64]uint32, 8),
+		nodes:     make([]posetNode, 1, 16),
+		roots:     make([]uint32, 0, 4),
+		noneq:     make(map[uint32]bitset),
+		undo:      make([]posetUndo, 0, 4),
+	}
+}
+
+func (po *poset) SetUnsigned(uns bool) {
+	if uns {
+		po.flags |= posetFlagUnsigned
+	} else {
+		po.flags &^= posetFlagUnsigned
+	}
+}
+
+// Handle children
+func (po *poset) setchl(i uint32, l posetEdge) { po.nodes[i].l = l }
+func (po *poset) setchr(i uint32, r posetEdge) { po.nodes[i].r = r }
+func (po *poset) chl(i uint32) uint32          { return po.nodes[i].l.Target() }
+func (po *poset) chr(i uint32) uint32          { return po.nodes[i].r.Target() }
+func (po *poset) children(i uint32) (posetEdge, posetEdge) {
+	return po.nodes[i].l, po.nodes[i].r
+}
+
+// upush records a new undo step. It can be used for simple
+// undo passes that record up to one index and one edge.
+func (po *poset) upush(typ undoType, p uint32, e posetEdge) {
+	po.undo = append(po.undo, posetUndo{typ: typ, idx: p, edge: e})
+}
+
+// upushnew pushes an undo pass for a new node
+func (po *poset) upushnew(id ID, idx uint32) {
+	po.undo = append(po.undo, posetUndo{typ: undoNewNode, ID: id, idx: idx})
+}
+
+// upushneq pushes a new undo pass for a nonequal relation
+func (po *poset) upushneq(idx1 uint32, idx2 uint32) {
+	po.undo = append(po.undo, posetUndo{typ: undoNonEqual, ID: ID(idx1), idx: idx2})
+}
+
+// upushalias pushes a new undo pass for aliasing two nodes
+func (po *poset) upushalias(id ID, i2 uint32) {
+	po.undo = append(po.undo, posetUndo{typ: undoAliasNode, ID: id, idx: i2})
+}
+
+// upushconst pushes a new undo pass for a new constant
+func (po *poset) upushconst(idx uint32, old uint32) {
+	po.undo = append(po.undo, posetUndo{typ: undoNewConstant, idx: idx, ID: ID(old)})
+}
+
+// addchild adds i2 as direct child of i1.
+func (po *poset) addchild(i1, i2 uint32, strict bool) {
+	i1l, i1r := po.children(i1)
+	e2 := newedge(i2, strict)
+
+	if i1l == 0 {
+		po.setchl(i1, e2)
+		po.upush(undoSetChl, i1, 0)
+	} else if i1r == 0 {
+		po.setchr(i1, e2)
+		po.upush(undoSetChr, i1, 0)
+	} else {
+		// If n1 already has two children, add an intermediate dummy
+		// node to record the relation correctly (without relating
+		// n2 to other existing nodes). Use a non-deterministic value
+		// to decide whether to append on the left or the right, to avoid
+		// creating degenerated chains.
+		//
+		//      n1
+		//     /  \
+		//   i1l  dummy
+		//        /   \
+		//      i1r   n2
+		//
+		dummy := po.newnode(nil)
+		if (i1^i2)&1 != 0 { // non-deterministic
+			po.setchl(dummy, i1r)
+			po.setchr(dummy, e2)
+			po.setchr(i1, newedge(dummy, false))
+			po.upush(undoSetChr, i1, i1r)
+		} else {
+			po.setchl(dummy, i1l)
+			po.setchr(dummy, e2)
+			po.setchl(i1, newedge(dummy, false))
+			po.upush(undoSetChl, i1, i1l)
+		}
+	}
+}
+
+// newnode allocates a new node bound to SSA value n.
+// If n is nil, this is a dummy node (= only used internally).
+func (po *poset) newnode(n *Value) uint32 {
+	i := po.lastidx + 1
+	po.lastidx++
+	po.nodes = append(po.nodes, posetNode{})
+	if n != nil {
+		if po.values[n.ID] != 0 {
+			panic("newnode for Value already inserted")
+		}
+		po.values[n.ID] = i
+		po.upushnew(n.ID, i)
+	} else {
+		po.upushnew(0, i)
+	}
+	return i
+}
+
+// lookup searches for a SSA value into the forest of DAGS, and return its node.
+// Constants are materialized on the fly during lookup.
+func (po *poset) lookup(n *Value) (uint32, bool) {
+	i, f := po.values[n.ID]
+	if !f && n.isGenericIntConst() {
+		po.newconst(n)
+		i, f = po.values[n.ID]
+	}
+	return i, f
+}
+
+// newconst creates a node for a constant. It links it to other constants, so
+// that n<=5 is detected true when n<=3 is known to be true.
+// TODO: this is O(N), fix it.
+func (po *poset) newconst(n *Value) {
+	if !n.isGenericIntConst() {
+		panic("newconst on non-constant")
+	}
+
+	// If the same constant is already present in the poset through a different
+	// Value, just alias to it without allocating a new node.
+	val := n.AuxInt
+	if po.flags&posetFlagUnsigned != 0 {
+		val = int64(n.AuxUnsigned())
+	}
+	if c, found := po.constants[val]; found {
+		po.values[n.ID] = c
+		po.upushalias(n.ID, 0)
+		return
+	}
+
+	// Create the new node for this constant
+	i := po.newnode(n)
+
+	// If this is the first constant, put it as a new root, as
+	// we can't record an existing connection so we don't have
+	// a specific DAG to add it to. Notice that we want all
+	// constants to be in root #0, so make sure the new root
+	// goes there.
+	if len(po.constants) == 0 {
+		idx := len(po.roots)
+		po.roots = append(po.roots, i)
+		po.roots[0], po.roots[idx] = po.roots[idx], po.roots[0]
+		po.upush(undoNewRoot, i, 0)
+		po.constants[val] = i
+		po.upushconst(i, 0)
+		return
+	}
+
+	// Find the lower and upper bound among existing constants. That is,
+	// find the higher constant that is lower than the one that we're adding,
+	// and the lower constant that is higher.
+	// The loop is duplicated to handle signed and unsigned comparison,
+	// depending on how the poset was configured.
+	var lowerptr, higherptr uint32
+
+	if po.flags&posetFlagUnsigned != 0 {
+		var lower, higher uint64
+		val1 := n.AuxUnsigned()
+		for val2, ptr := range po.constants {
+			val2 := uint64(val2)
+			if val1 == val2 {
+				panic("unreachable")
+			}
+			if val2 < val1 && (lowerptr == 0 || val2 > lower) {
+				lower = val2
+				lowerptr = ptr
+			} else if val2 > val1 && (higherptr == 0 || val2 < higher) {
+				higher = val2
+				higherptr = ptr
+			}
+		}
+	} else {
+		var lower, higher int64
+		val1 := n.AuxInt
+		for val2, ptr := range po.constants {
+			if val1 == val2 {
+				panic("unreachable")
+			}
+			if val2 < val1 && (lowerptr == 0 || val2 > lower) {
+				lower = val2
+				lowerptr = ptr
+			} else if val2 > val1 && (higherptr == 0 || val2 < higher) {
+				higher = val2
+				higherptr = ptr
+			}
+		}
+	}
+
+	if lowerptr == 0 && higherptr == 0 {
+		// This should not happen, as at least one
+		// other constant must exist if we get here.
+		panic("no constant found")
+	}
+
+	// Create the new node and connect it to the bounds, so that
+	// lower < n < higher. We could have found both bounds or only one
+	// of them, depending on what other constants are present in the poset.
+	// Notice that we always link constants together, so they
+	// are always part of the same DAG.
+	switch {
+	case lowerptr != 0 && higherptr != 0:
+		// Both bounds are present, record lower < n < higher.
+		po.addchild(lowerptr, i, true)
+		po.addchild(i, higherptr, true)
+
+	case lowerptr != 0:
+		// Lower bound only, record lower < n.
+		po.addchild(lowerptr, i, true)
+
+	case higherptr != 0:
+		// Higher bound only. To record n < higher, we need
+		// a dummy root:
+		//
+		//        dummy
+		//        /   \
+		//      root   \
+		//       /      n
+		//     ....    /
+		//       \    /
+		//       higher
+		//
+		i2 := higherptr
+		r2 := po.findroot(i2)
+		if r2 != po.roots[0] { // all constants should be in root #0
+			panic("constant not in root #0")
+		}
+		dummy := po.newnode(nil)
+		po.changeroot(r2, dummy)
+		po.upush(undoChangeRoot, dummy, newedge(r2, false))
+		po.addchild(dummy, r2, false)
+		po.addchild(dummy, i, false)
+		po.addchild(i, i2, true)
+	}
+
+	po.constants[val] = i
+	po.upushconst(i, 0)
+}
+
+// aliasnewnode records that a single node n2 (not in the poset yet) is an alias
+// of the master node n1.
+func (po *poset) aliasnewnode(n1, n2 *Value) {
+	i1, i2 := po.values[n1.ID], po.values[n2.ID]
+	if i1 == 0 || i2 != 0 {
+		panic("aliasnewnode invalid arguments")
+	}
+
+	po.values[n2.ID] = i1
+	po.upushalias(n2.ID, 0)
+}
+
+// aliasnodes records that all the nodes i2s are aliases of a single master node n1.
+// aliasnodes takes care of rearranging the DAG, changing references of parent/children
+// of nodes in i2s, so that they point to n1 instead.
+// Complexity is O(n) (with n being the total number of nodes in the poset, not just
+// the number of nodes being aliased).
+func (po *poset) aliasnodes(n1 *Value, i2s bitset) {
+	i1 := po.values[n1.ID]
+	if i1 == 0 {
+		panic("aliasnode for non-existing node")
+	}
+	if i2s.Test(i1) {
+		panic("aliasnode i2s contains n1 node")
+	}
+
+	// Go through all the nodes to adjust parent/chidlren of nodes in i2s
+	for idx, n := range po.nodes {
+		// Do not touch i1 itself, otherwise we can create useless self-loops
+		if uint32(idx) == i1 {
+			continue
+		}
+		l, r := n.l, n.r
+
+		// Rename all references to i2s into i1
+		if i2s.Test(l.Target()) {
+			po.setchl(uint32(idx), newedge(i1, l.Strict()))
+			po.upush(undoSetChl, uint32(idx), l)
+		}
+		if i2s.Test(r.Target()) {
+			po.setchr(uint32(idx), newedge(i1, r.Strict()))
+			po.upush(undoSetChr, uint32(idx), r)
+		}
+
+		// Connect all chidren of i2s to i1 (unless those children
+		// are in i2s as well, in which case it would be useless)
+		if i2s.Test(uint32(idx)) {
+			if l != 0 && !i2s.Test(l.Target()) {
+				po.addchild(i1, l.Target(), l.Strict())
+			}
+			if r != 0 && !i2s.Test(r.Target()) {
+				po.addchild(i1, r.Target(), r.Strict())
+			}
+			po.setchl(uint32(idx), 0)
+			po.setchr(uint32(idx), 0)
+			po.upush(undoSetChl, uint32(idx), l)
+			po.upush(undoSetChr, uint32(idx), r)
+		}
+	}
+
+	// Reassign all existing IDs that point to i2 to i1.
+	// This includes n2.ID.
+	for k, v := range po.values {
+		if i2s.Test(v) {
+			po.values[k] = i1
+			po.upushalias(k, v)
+		}
+	}
+
+	// If one of the aliased nodes is a constant, then make sure
+	// po.constants is updated to point to the master node.
+	for val, idx := range po.constants {
+		if i2s.Test(idx) {
+			po.constants[val] = i1
+			po.upushconst(i1, idx)
+		}
+	}
+}
+
+func (po *poset) isroot(r uint32) bool {
+	for i := range po.roots {
+		if po.roots[i] == r {
+			return true
+		}
+	}
+	return false
+}
+
+func (po *poset) changeroot(oldr, newr uint32) {
+	for i := range po.roots {
+		if po.roots[i] == oldr {
+			po.roots[i] = newr
+			return
+		}
+	}
+	panic("changeroot on non-root")
+}
+
+func (po *poset) removeroot(r uint32) {
+	for i := range po.roots {
+		if po.roots[i] == r {
+			po.roots = append(po.roots[:i], po.roots[i+1:]...)
+			return
+		}
+	}
+	panic("removeroot on non-root")
+}
+
+// dfs performs a depth-first search within the DAG whose root is r.
+// f is the visit function called for each node; if it returns true,
+// the search is aborted and true is returned. The root node is
+// visited too.
+// If strict, ignore edges across a path until at least one
+// strict edge is found. For instance, for a chain A<=B<=C<D<=E<F,
+// a strict walk visits D,E,F.
+// If the visit ends, false is returned.
+func (po *poset) dfs(r uint32, strict bool, f func(i uint32) bool) bool {
+	closed := newBitset(int(po.lastidx + 1))
+	open := make([]uint32, 1, 64)
+	open[0] = r
+
+	if strict {
+		// Do a first DFS; walk all paths and stop when we find a strict
+		// edge, building a "next" list of nodes reachable through strict
+		// edges. This will be the bootstrap open list for the real DFS.
+		next := make([]uint32, 0, 64)
+
+		for len(open) > 0 {
+			i := open[len(open)-1]
+			open = open[:len(open)-1]
+
+			// Don't visit the same node twice. Notice that all nodes
+			// across non-strict paths are still visited at least once, so
+			// a non-strict path can never obscure a strict path to the
+			// same node.
+			if !closed.Test(i) {
+				closed.Set(i)
+
+				l, r := po.children(i)
+				if l != 0 {
+					if l.Strict() {
+						next = append(next, l.Target())
+					} else {
+						open = append(open, l.Target())
+					}
+				}
+				if r != 0 {
+					if r.Strict() {
+						next = append(next, r.Target())
+					} else {
+						open = append(open, r.Target())
+					}
+				}
+			}
+		}
+		open = next
+		closed.Reset()
+	}
+
+	for len(open) > 0 {
+		i := open[len(open)-1]
+		open = open[:len(open)-1]
+
+		if !closed.Test(i) {
+			if f(i) {
+				return true
+			}
+			closed.Set(i)
+			l, r := po.children(i)
+			if l != 0 {
+				open = append(open, l.Target())
+			}
+			if r != 0 {
+				open = append(open, r.Target())
+			}
+		}
+	}
+	return false
+}
+
+// Returns true if there is a path from i1 to i2.
+// If strict ==  true: if the function returns true, then i1 <  i2.
+// If strict == false: if the function returns true, then i1 <= i2.
+// If the function returns false, no relation is known.
+func (po *poset) reaches(i1, i2 uint32, strict bool) bool {
+	return po.dfs(i1, strict, func(n uint32) bool {
+		return n == i2
+	})
+}
+
+// findroot finds i's root, that is which DAG contains i.
+// Returns the root; if i is itself a root, it is returned.
+// Panic if i is not in any DAG.
+func (po *poset) findroot(i uint32) uint32 {
+	// TODO(rasky): if needed, a way to speed up this search is
+	// storing a bitset for each root using it as a mini bloom filter
+	// of nodes present under that root.
+	for _, r := range po.roots {
+		if po.reaches(r, i, false) {
+			return r
+		}
+	}
+	panic("findroot didn't find any root")
+}
+
+// mergeroot merges two DAGs into one DAG by creating a new dummy root
+func (po *poset) mergeroot(r1, r2 uint32) uint32 {
+	// Root #0 is special as it contains all constants. Since mergeroot
+	// discards r2 as root and keeps r1, make sure that r2 is not root #0,
+	// otherwise constants would move to a different root.
+	if r2 == po.roots[0] {
+		r1, r2 = r2, r1
+	}
+	r := po.newnode(nil)
+	po.setchl(r, newedge(r1, false))
+	po.setchr(r, newedge(r2, false))
+	po.changeroot(r1, r)
+	po.removeroot(r2)
+	po.upush(undoMergeRoot, r, 0)
+	return r
+}
+
+// collapsepath marks n1 and n2 as equal and collapses as equal all
+// nodes across all paths between n1 and n2. If a strict edge is
+// found, the function does not modify the DAG and returns false.
+// Complexity is O(n).
+func (po *poset) collapsepath(n1, n2 *Value) bool {
+	i1, i2 := po.values[n1.ID], po.values[n2.ID]
+	if po.reaches(i1, i2, true) {
+		return false
+	}
+
+	// Find all the paths from i1 to i2
+	paths := po.findpaths(i1, i2)
+	// Mark all nodes in all the paths as aliases of n1
+	// (excluding n1 itself)
+	paths.Clear(i1)
+	po.aliasnodes(n1, paths)
+	return true
+}
+
+// findpaths is a recursive function that calculates all paths from cur to dst
+// and return them as a bitset (the index of a node is set in the bitset if
+// that node is on at least one path from cur to dst).
+// We do a DFS from cur (stopping going deep any time we reach dst, if ever),
+// and mark as part of the paths any node that has a children which is already
+// part of the path (or is dst itself).
+func (po *poset) findpaths(cur, dst uint32) bitset {
+	seen := newBitset(int(po.lastidx + 1))
+	path := newBitset(int(po.lastidx + 1))
+	path.Set(dst)
+	po.findpaths1(cur, dst, seen, path)
+	return path
+}
+
+func (po *poset) findpaths1(cur, dst uint32, seen bitset, path bitset) {
+	if cur == dst {
+		return
+	}
+	seen.Set(cur)
+	l, r := po.chl(cur), po.chr(cur)
+	if !seen.Test(l) {
+		po.findpaths1(l, dst, seen, path)
+	}
+	if !seen.Test(r) {
+		po.findpaths1(r, dst, seen, path)
+	}
+	if path.Test(l) || path.Test(r) {
+		path.Set(cur)
+	}
+}
+
+// Check whether it is recorded that i1!=i2
+func (po *poset) isnoneq(i1, i2 uint32) bool {
+	if i1 == i2 {
+		return false
+	}
+	if i1 < i2 {
+		i1, i2 = i2, i1
+	}
+
+	// Check if we recorded a non-equal relation before
+	if bs, ok := po.noneq[i1]; ok && bs.Test(i2) {
+		return true
+	}
+	return false
+}
+
+// Record that i1!=i2
+func (po *poset) setnoneq(n1, n2 *Value) {
+	i1, f1 := po.lookup(n1)
+	i2, f2 := po.lookup(n2)
+
+	// If any of the nodes do not exist in the poset, allocate them. Since
+	// we don't know any relation (in the partial order) about them, they must
+	// become independent roots.
+	if !f1 {
+		i1 = po.newnode(n1)
+		po.roots = append(po.roots, i1)
+		po.upush(undoNewRoot, i1, 0)
+	}
+	if !f2 {
+		i2 = po.newnode(n2)
+		po.roots = append(po.roots, i2)
+		po.upush(undoNewRoot, i2, 0)
+	}
+
+	if i1 == i2 {
+		panic("setnoneq on same node")
+	}
+	if i1 < i2 {
+		i1, i2 = i2, i1
+	}
+	bs := po.noneq[i1]
+	if bs == nil {
+		// Given that we record non-equality relations using the
+		// higher index as a key, the bitsize will never change size.
+		// TODO(rasky): if memory is a problem, consider allocating
+		// a small bitset and lazily grow it when higher indices arrive.
+		bs = newBitset(int(i1))
+		po.noneq[i1] = bs
+	} else if bs.Test(i2) {
+		// Already recorded
+		return
+	}
+	bs.Set(i2)
+	po.upushneq(i1, i2)
+}
+
+// CheckIntegrity verifies internal integrity of a poset. It is intended
+// for debugging purposes.
+func (po *poset) CheckIntegrity() {
+	// Record which index is a constant
+	constants := newBitset(int(po.lastidx + 1))
+	for _, c := range po.constants {
+		constants.Set(c)
+	}
+
+	// Verify that each node appears in a single DAG, and that
+	// all constants are within the first DAG
+	seen := newBitset(int(po.lastidx + 1))
+	for ridx, r := range po.roots {
+		if r == 0 {
+			panic("empty root")
+		}
+
+		po.dfs(r, false, func(i uint32) bool {
+			if seen.Test(i) {
+				panic("duplicate node")
+			}
+			seen.Set(i)
+			if constants.Test(i) {
+				if ridx != 0 {
+					panic("constants not in the first DAG")
+				}
+			}
+			return false
+		})
+	}
+
+	// Verify that values contain the minimum set
+	for id, idx := range po.values {
+		if !seen.Test(idx) {
+			panic(fmt.Errorf("spurious value [%d]=%d", id, idx))
+		}
+	}
+
+	// Verify that only existing nodes have non-zero children
+	for i, n := range po.nodes {
+		if n.l|n.r != 0 {
+			if !seen.Test(uint32(i)) {
+				panic(fmt.Errorf("children of unknown node %d->%v", i, n))
+			}
+			if n.l.Target() == uint32(i) || n.r.Target() == uint32(i) {
+				panic(fmt.Errorf("self-loop on node %d", i))
+			}
+		}
+	}
+}
+
+// CheckEmpty checks that a poset is completely empty.
+// It can be used for debugging purposes, as a poset is supposed to
+// be empty after it's fully rolled back through Undo.
+func (po *poset) CheckEmpty() error {
+	if len(po.nodes) != 1 {
+		return fmt.Errorf("non-empty nodes list: %v", po.nodes)
+	}
+	if len(po.values) != 0 {
+		return fmt.Errorf("non-empty value map: %v", po.values)
+	}
+	if len(po.roots) != 0 {
+		return fmt.Errorf("non-empty root list: %v", po.roots)
+	}
+	if len(po.constants) != 0 {
+		return fmt.Errorf("non-empty constants: %v", po.constants)
+	}
+	if len(po.undo) != 0 {
+		return fmt.Errorf("non-empty undo list: %v", po.undo)
+	}
+	if po.lastidx != 0 {
+		return fmt.Errorf("lastidx index is not zero: %v", po.lastidx)
+	}
+	for _, bs := range po.noneq {
+		for _, x := range bs {
+			if x != 0 {
+				return fmt.Errorf("non-empty noneq map")
+			}
+		}
+	}
+	return nil
+}
+
+// DotDump dumps the poset in graphviz format to file fn, with the specified title.
+func (po *poset) DotDump(fn string, title string) error {
+	f, err := os.Create(fn)
+	if err != nil {
+		return err
+	}
+	defer f.Close()
+
+	// Create reverse index mapping (taking aliases into account)
+	names := make(map[uint32]string)
+	for id, i := range po.values {
+		s := names[i]
+		if s == "" {
+			s = fmt.Sprintf("v%d", id)
+		} else {
+			s += fmt.Sprintf(", v%d", id)
+		}
+		names[i] = s
+	}
+
+	// Create reverse constant mapping
+	consts := make(map[uint32]int64)
+	for val, idx := range po.constants {
+		consts[idx] = val
+	}
+
+	fmt.Fprintf(f, "digraph poset {\n")
+	fmt.Fprintf(f, "\tedge [ fontsize=10 ]\n")
+	for ridx, r := range po.roots {
+		fmt.Fprintf(f, "\tsubgraph root%d {\n", ridx)
+		po.dfs(r, false, func(i uint32) bool {
+			if val, ok := consts[i]; ok {
+				// Constant
+				var vals string
+				if po.flags&posetFlagUnsigned != 0 {
+					vals = fmt.Sprint(uint64(val))
+				} else {
+					vals = fmt.Sprint(int64(val))
+				}
+				fmt.Fprintf(f, "\t\tnode%d [shape=box style=filled fillcolor=cadetblue1 label=<%s <font point-size=\"6\">%s [%d]</font>>]\n",
+					i, vals, names[i], i)
+			} else {
+				// Normal SSA value
+				fmt.Fprintf(f, "\t\tnode%d [label=<%s <font point-size=\"6\">[%d]</font>>]\n", i, names[i], i)
+			}
+			chl, chr := po.children(i)
+			for _, ch := range []posetEdge{chl, chr} {
+				if ch != 0 {
+					if ch.Strict() {
+						fmt.Fprintf(f, "\t\tnode%d -> node%d [label=\" <\" color=\"red\"]\n", i, ch.Target())
+					} else {
+						fmt.Fprintf(f, "\t\tnode%d -> node%d [label=\" <=\" color=\"green\"]\n", i, ch.Target())
+					}
+				}
+			}
+			return false
+		})
+		fmt.Fprintf(f, "\t}\n")
+	}
+	fmt.Fprintf(f, "\tlabelloc=\"t\"\n")
+	fmt.Fprintf(f, "\tlabeldistance=\"3.0\"\n")
+	fmt.Fprintf(f, "\tlabel=%q\n", title)
+	fmt.Fprintf(f, "}\n")
+	return nil
+}
+
+// Ordered reports whether n1<n2. It returns false either when it is
+// certain that n1<n2 is false, or if there is not enough information
+// to tell.
+// Complexity is O(n).
+func (po *poset) Ordered(n1, n2 *Value) bool {
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+	if n1.ID == n2.ID {
+		panic("should not call Ordered with n1==n2")
+	}
+
+	i1, f1 := po.lookup(n1)
+	i2, f2 := po.lookup(n2)
+	if !f1 || !f2 {
+		return false
+	}
+
+	return i1 != i2 && po.reaches(i1, i2, true)
+}
+
+// Ordered reports whether n1<=n2. It returns false either when it is
+// certain that n1<=n2 is false, or if there is not enough information
+// to tell.
+// Complexity is O(n).
+func (po *poset) OrderedOrEqual(n1, n2 *Value) bool {
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+	if n1.ID == n2.ID {
+		panic("should not call Ordered with n1==n2")
+	}
+
+	i1, f1 := po.lookup(n1)
+	i2, f2 := po.lookup(n2)
+	if !f1 || !f2 {
+		return false
+	}
+
+	return i1 == i2 || po.reaches(i1, i2, false)
+}
+
+// Equal reports whether n1==n2. It returns false either when it is
+// certain that n1==n2 is false, or if there is not enough information
+// to tell.
+// Complexity is O(1).
+func (po *poset) Equal(n1, n2 *Value) bool {
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+	if n1.ID == n2.ID {
+		panic("should not call Equal with n1==n2")
+	}
+
+	i1, f1 := po.lookup(n1)
+	i2, f2 := po.lookup(n2)
+	return f1 && f2 && i1 == i2
+}
+
+// NonEqual reports whether n1!=n2. It returns false either when it is
+// certain that n1!=n2 is false, or if there is not enough information
+// to tell.
+// Complexity is O(n) (because it internally calls Ordered to see if we
+// can infer n1!=n2 from n1<n2 or n2<n1).
+func (po *poset) NonEqual(n1, n2 *Value) bool {
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+	if n1.ID == n2.ID {
+		panic("should not call NonEqual with n1==n2")
+	}
+
+	// If we never saw the nodes before, we don't
+	// have a recorded non-equality.
+	i1, f1 := po.lookup(n1)
+	i2, f2 := po.lookup(n2)
+	if !f1 || !f2 {
+		return false
+	}
+
+	// Check if we recored inequality
+	if po.isnoneq(i1, i2) {
+		return true
+	}
+
+	// Check if n1<n2 or n2<n1, in which case we can infer that n1!=n2
+	if po.Ordered(n1, n2) || po.Ordered(n2, n1) {
+		return true
+	}
+
+	return false
+}
+
+// setOrder records that n1<n2 or n1<=n2 (depending on strict). Returns false
+// if this is a contradiction.
+// Implements SetOrder() and SetOrderOrEqual()
+func (po *poset) setOrder(n1, n2 *Value, strict bool) bool {
+	i1, f1 := po.lookup(n1)
+	i2, f2 := po.lookup(n2)
+
+	switch {
+	case !f1 && !f2:
+		// Neither n1 nor n2 are in the poset, so they are not related
+		// in any way to existing nodes.
+		// Create a new DAG to record the relation.
+		i1, i2 = po.newnode(n1), po.newnode(n2)
+		po.roots = append(po.roots, i1)
+		po.upush(undoNewRoot, i1, 0)
+		po.addchild(i1, i2, strict)
+
+	case f1 && !f2:
+		// n1 is in one of the DAGs, while n2 is not. Add n2 as children
+		// of n1.
+		i2 = po.newnode(n2)
+		po.addchild(i1, i2, strict)
+
+	case !f1 && f2:
+		// n1 is not in any DAG but n2 is. If n2 is a root, we can put
+		// n1 in its place as a root; otherwise, we need to create a new
+		// dummy root to record the relation.
+		i1 = po.newnode(n1)
+
+		if po.isroot(i2) {
+			po.changeroot(i2, i1)
+			po.upush(undoChangeRoot, i1, newedge(i2, strict))
+			po.addchild(i1, i2, strict)
+			return true
+		}
+
+		// Search for i2's root; this requires a O(n) search on all
+		// DAGs
+		r := po.findroot(i2)
+
+		// Re-parent as follows:
+		//
+		//                  dummy
+		//     r            /   \
+		//      \   ===>   r    i1
+		//      i2          \   /
+		//                    i2
+		//
+		dummy := po.newnode(nil)
+		po.changeroot(r, dummy)
+		po.upush(undoChangeRoot, dummy, newedge(r, false))
+		po.addchild(dummy, r, false)
+		po.addchild(dummy, i1, false)
+		po.addchild(i1, i2, strict)
+
+	case f1 && f2:
+		// If the nodes are aliased, fail only if we're setting a strict order
+		// (that is, we cannot set n1<n2 if n1==n2).
+		if i1 == i2 {
+			return !strict
+		}
+
+		// If we are trying to record n1<=n2 but we learned that n1!=n2,
+		// record n1<n2, as it provides more information.
+		if !strict && po.isnoneq(i1, i2) {
+			strict = true
+		}
+
+		// Both n1 and n2 are in the poset. This is the complex part of the algorithm
+		// as we need to find many different cases and DAG shapes.
+
+		// Check if n1 somehow reaches n2
+		if po.reaches(i1, i2, false) {
+			// This is the table of all cases we need to handle:
+			//
+			//      DAG          New      Action
+			//      ---------------------------------------------------
+			// #1:  N1<=X<=N2 |  N1<=N2 | do nothing
+			// #2:  N1<=X<=N2 |  N1<N2  | add strict edge (N1<N2)
+			// #3:  N1<X<N2   |  N1<=N2 | do nothing (we already know more)
+			// #4:  N1<X<N2   |  N1<N2  | do nothing
+
+			// Check if we're in case #2
+			if strict && !po.reaches(i1, i2, true) {
+				po.addchild(i1, i2, true)
+				return true
+			}
+
+			// Case #1, #3 o #4: nothing to do
+			return true
+		}
+
+		// Check if n2 somehow reaches n1
+		if po.reaches(i2, i1, false) {
+			// This is the table of all cases we need to handle:
+			//
+			//      DAG           New      Action
+			//      ---------------------------------------------------
+			// #5:  N2<=X<=N1  |  N1<=N2 | collapse path (learn that N1=X=N2)
+			// #6:  N2<=X<=N1  |  N1<N2  | contradiction
+			// #7:  N2<X<N1    |  N1<=N2 | contradiction in the path
+			// #8:  N2<X<N1    |  N1<N2  | contradiction
+
+			if strict {
+				// Cases #6 and #8: contradiction
+				return false
+			}
+
+			// We're in case #5 or #7. Try to collapse path, and that will
+			// fail if it realizes that we are in case #7.
+			return po.collapsepath(n2, n1)
+		}
+
+		// We don't know of any existing relation between n1 and n2. They could
+		// be part of the same DAG or not.
+		// Find their roots to check whether they are in the same DAG.
+		r1, r2 := po.findroot(i1), po.findroot(i2)
+		if r1 != r2 {
+			// We need to merge the two DAGs to record a relation between the nodes
+			po.mergeroot(r1, r2)
+		}
+
+		// Connect n1 and n2
+		po.addchild(i1, i2, strict)
+	}
+
+	return true
+}
+
+// SetOrder records that n1<n2. Returns false if this is a contradiction
+// Complexity is O(1) if n2 was never seen before, or O(n) otherwise.
+func (po *poset) SetOrder(n1, n2 *Value) bool {
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+	if n1.ID == n2.ID {
+		panic("should not call SetOrder with n1==n2")
+	}
+	return po.setOrder(n1, n2, true)
+}
+
+// SetOrderOrEqual records that n1<=n2. Returns false if this is a contradiction
+// Complexity is O(1) if n2 was never seen before, or O(n) otherwise.
+func (po *poset) SetOrderOrEqual(n1, n2 *Value) bool {
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+	if n1.ID == n2.ID {
+		panic("should not call SetOrder with n1==n2")
+	}
+	return po.setOrder(n1, n2, false)
+}
+
+// SetEqual records that n1==n2. Returns false if this is a contradiction
+// (that is, if it is already recorded that n1<n2 or n2<n1).
+// Complexity is O(1) if n2 was never seen before, or O(n) otherwise.
+func (po *poset) SetEqual(n1, n2 *Value) bool {
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+	if n1.ID == n2.ID {
+		panic("should not call Add with n1==n2")
+	}
+
+	i1, f1 := po.lookup(n1)
+	i2, f2 := po.lookup(n2)
+
+	switch {
+	case !f1 && !f2:
+		i1 = po.newnode(n1)
+		po.roots = append(po.roots, i1)
+		po.upush(undoNewRoot, i1, 0)
+		po.aliasnewnode(n1, n2)
+	case f1 && !f2:
+		po.aliasnewnode(n1, n2)
+	case !f1 && f2:
+		po.aliasnewnode(n2, n1)
+	case f1 && f2:
+		if i1 == i2 {
+			// Already aliased, ignore
+			return true
+		}
+
+		// If we recorded that n1!=n2, this is a contradiction.
+		if po.isnoneq(i1, i2) {
+			return false
+		}
+
+		// If we already knew that n1<=n2, we can collapse the path to
+		// record n1==n2 (and viceversa).
+		if po.reaches(i1, i2, false) {
+			return po.collapsepath(n1, n2)
+		}
+		if po.reaches(i2, i1, false) {
+			return po.collapsepath(n2, n1)
+		}
+
+		r1 := po.findroot(i1)
+		r2 := po.findroot(i2)
+		if r1 != r2 {
+			// Merge the two DAGs so we can record relations between the nodes
+			po.mergeroot(r1, r2)
+		}
+
+		// Set n2 as alias of n1. This will also update all the references
+		// to n2 to become references to n1
+		i2s := newBitset(int(po.lastidx) + 1)
+		i2s.Set(i2)
+		po.aliasnodes(n1, i2s)
+	}
+	return true
+}
+
+// SetNonEqual records that n1!=n2. Returns false if this is a contradiction
+// (that is, if it is already recorded that n1==n2).
+// Complexity is O(n).
+func (po *poset) SetNonEqual(n1, n2 *Value) bool {
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+	if n1.ID == n2.ID {
+		panic("should not call SetNonEqual with n1==n2")
+	}
+
+	// Check whether the nodes are already in the poset
+	i1, f1 := po.lookup(n1)
+	i2, f2 := po.lookup(n2)
+
+	// If either node wasn't present, we just record the new relation
+	// and exit.
+	if !f1 || !f2 {
+		po.setnoneq(n1, n2)
+		return true
+	}
+
+	// See if we already know this, in which case there's nothing to do.
+	if po.isnoneq(i1, i2) {
+		return true
+	}
+
+	// Check if we're contradicting an existing equality relation
+	if po.Equal(n1, n2) {
+		return false
+	}
+
+	// Record non-equality
+	po.setnoneq(n1, n2)
+
+	// If we know that i1<=i2 but not i1<i2, learn that as we
+	// now know that they are not equal. Do the same for i2<=i1.
+	// Do this check only if both nodes were already in the DAG,
+	// otherwise there cannot be an existing relation.
+	if po.reaches(i1, i2, false) && !po.reaches(i1, i2, true) {
+		po.addchild(i1, i2, true)
+	}
+	if po.reaches(i2, i1, false) && !po.reaches(i2, i1, true) {
+		po.addchild(i2, i1, true)
+	}
+
+	return true
+}
+
+// Checkpoint saves the current state of the DAG so that it's possible
+// to later undo this state.
+// Complexity is O(1).
+func (po *poset) Checkpoint() {
+	po.undo = append(po.undo, posetUndo{typ: undoCheckpoint})
+}
+
+// Undo restores the state of the poset to the previous checkpoint.
+// Complexity depends on the type of operations that were performed
+// since the last checkpoint; each Set* operation creates an undo
+// pass which Undo has to revert with a worst-case complexity of O(n).
+func (po *poset) Undo() {
+	if len(po.undo) == 0 {
+		panic("empty undo stack")
+	}
+	if debugPoset {
+		defer po.CheckIntegrity()
+	}
+
+	for len(po.undo) > 0 {
+		pass := po.undo[len(po.undo)-1]
+		po.undo = po.undo[:len(po.undo)-1]
+
+		switch pass.typ {
+		case undoCheckpoint:
+			return
+
+		case undoSetChl:
+			po.setchl(pass.idx, pass.edge)
+
+		case undoSetChr:
+			po.setchr(pass.idx, pass.edge)
+
+		case undoNonEqual:
+			po.noneq[uint32(pass.ID)].Clear(pass.idx)
+
+		case undoNewNode:
+			if pass.idx != po.lastidx {
+				panic("invalid newnode index")
+			}
+			if pass.ID != 0 {
+				if po.values[pass.ID] != pass.idx {
+					panic("invalid newnode undo pass")
+				}
+				delete(po.values, pass.ID)
+			}
+			po.setchl(pass.idx, 0)
+			po.setchr(pass.idx, 0)
+			po.nodes = po.nodes[:pass.idx]
+			po.lastidx--
+
+		case undoNewConstant:
+			// FIXME: remove this O(n) loop
+			var val int64
+			var i uint32
+			for val, i = range po.constants {
+				if i == pass.idx {
+					break
+				}
+			}
+			if i != pass.idx {
+				panic("constant not found in undo pass")
+			}
+			if pass.ID == 0 {
+				delete(po.constants, val)
+			} else {
+				// Restore previous index as constant node
+				// (also restoring the invariant on correct bounds)
+				oldidx := uint32(pass.ID)
+				po.constants[val] = oldidx
+			}
+
+		case undoAliasNode:
+			ID, prev := pass.ID, pass.idx
+			cur := po.values[ID]
+			if prev == 0 {
+				// Born as an alias, die as an alias
+				delete(po.values, ID)
+			} else {
+				if cur == prev {
+					panic("invalid aliasnode undo pass")
+				}
+				// Give it back previous value
+				po.values[ID] = prev
+			}
+
+		case undoNewRoot:
+			i := pass.idx
+			l, r := po.children(i)
+			if l|r != 0 {
+				panic("non-empty root in undo newroot")
+			}
+			po.removeroot(i)
+
+		case undoChangeRoot:
+			i := pass.idx
+			l, r := po.children(i)
+			if l|r != 0 {
+				panic("non-empty root in undo changeroot")
+			}
+			po.changeroot(i, pass.edge.Target())
+
+		case undoMergeRoot:
+			i := pass.idx
+			l, r := po.children(i)
+			po.changeroot(i, l.Target())
+			po.roots = append(po.roots, r.Target())
+
+		default:
+			panic(pass.typ)
+		}
+	}
+
+	if debugPoset && po.CheckEmpty() != nil {
+		panic("poset not empty at the end of undo")
+	}
+}