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Diffstat (limited to 'src/cmd/compile/internal/ssa/poset.go')
| -rw-r--r-- | src/cmd/compile/internal/ssa/poset.go | 1359 |
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..ee884ca --- /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) >> 63) // 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 +// "extra" 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 extra +// / \ +// 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 extra + // 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 extra + // / \ + // i1r n2 + // + extra := po.newnode(nil) + if (i1^i2)&1 != 0 { // non-deterministic + po.setchl(extra, i1r) + po.setchr(extra, e2) + po.setchr(i1, newedge(extra, false)) + po.upush(undoSetChr, i1, i1r) + } else { + po.setchl(extra, i1l) + po.setchr(extra, e2) + po.setchl(i1, newedge(extra, false)) + po.upush(undoSetChl, i1, i1l) + } + } +} + +// newnode allocates a new node bound to SSA value n. +// If n is nil, this is an extra 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 + // an extra root: + // + // extra + // / \ + // 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") + } + extra := po.newnode(nil) + po.changeroot(r2, extra) + po.upush(undoChangeRoot, extra, newedge(r2, false)) + po.addchild(extra, r2, false) + po.addchild(extra, 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 extra 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) +} + +// OrderedOrEqual 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 + // extra 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: + // + // extra + // r / \ + // \ ===> r i1 + // i2 \ / + // i2 + // + extra := po.newnode(nil) + po.changeroot(r, extra) + po.upush(undoChangeRoot, extra, newedge(r, false)) + po.addchild(extra, r, false) + po.addchild(extra, 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") + } +} |