| // 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 |
| // "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) |
| } |
| |
| // 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 |
| // 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") |
| } |
| } |