1 use crate::frozen::Frozen;
2 use crate::fx::{FxHashSet, FxIndexSet};
3 use rustc_index::bit_set::BitMatrix;
12 #[derive(Clone, Debug)]
13 pub struct TransitiveRelationBuilder<T> {
14 // List of elements. This is used to map from a T to a usize.
15 elements: FxIndexSet<T>,
17 // List of base edges in the graph. Require to compute transitive
19 edges: FxHashSet<Edge>,
23 pub struct TransitiveRelation<T> {
24 // Frozen transitive relation elements and edges.
25 builder: Frozen<TransitiveRelationBuilder<T>>,
27 // Cached transitive closure derived from the edges.
28 closure: Frozen<BitMatrix<usize, usize>>,
31 impl<T> Deref for TransitiveRelation<T> {
32 type Target = Frozen<TransitiveRelationBuilder<T>>;
34 fn deref(&self) -> &Self::Target {
39 impl<T: Clone> Clone for TransitiveRelation<T> {
40 fn clone(&self) -> Self {
42 builder: Frozen::freeze(self.builder.deref().clone()),
43 closure: Frozen::freeze(self.closure.deref().clone()),
48 // HACK(eddyb) manual impl avoids `Default` bound on `T`.
49 impl<T: Eq + Hash> Default for TransitiveRelationBuilder<T> {
50 fn default() -> Self {
51 TransitiveRelationBuilder { elements: Default::default(), edges: Default::default() }
55 #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Debug, Hash)]
58 #[derive(Clone, PartialEq, Eq, Debug, Hash)]
64 impl<T: Eq + Hash + Copy> TransitiveRelationBuilder<T> {
65 pub fn is_empty(&self) -> bool {
69 pub fn elements(&self) -> impl Iterator<Item = &T> {
73 fn index(&self, a: T) -> Option<Index> {
74 self.elements.get_index_of(&a).map(Index)
77 fn add_index(&mut self, a: T) -> Index {
78 let (index, _added) = self.elements.insert_full(a);
82 /// Applies the (partial) function to each edge and returns a new
83 /// relation builder. If `f` returns `None` for any end-point,
85 pub fn maybe_map<F, U>(&self, mut f: F) -> Option<TransitiveRelationBuilder<U>>
87 F: FnMut(T) -> Option<U>,
88 U: Clone + Debug + Eq + Hash + Copy,
90 let mut result = TransitiveRelationBuilder::default();
91 for edge in &self.edges {
92 result.add(f(self.elements[edge.source.0])?, f(self.elements[edge.target.0])?);
97 /// Indicate that `a < b` (where `<` is this relation)
98 pub fn add(&mut self, a: T, b: T) {
99 let a = self.add_index(a);
100 let b = self.add_index(b);
101 let edge = Edge { source: a, target: b };
102 self.edges.insert(edge);
105 /// Compute the transitive closure derived from the edges, and converted to
106 /// the final result. After this, all elements will be immutable to maintain
107 /// the correctness of the result.
108 pub fn freeze(self) -> TransitiveRelation<T> {
109 let mut matrix = BitMatrix::new(self.elements.len(), self.elements.len());
110 let mut changed = true;
113 for edge in &self.edges {
114 // add an edge from S -> T
115 changed |= matrix.insert(edge.source.0, edge.target.0);
117 // add all outgoing edges from T into S
118 changed |= matrix.union_rows(edge.target.0, edge.source.0);
121 TransitiveRelation { builder: Frozen::freeze(self), closure: Frozen::freeze(matrix) }
125 impl<T: Eq + Hash + Copy> TransitiveRelation<T> {
126 /// Applies the (partial) function to each edge and returns a new
127 /// relation including transitive closures.
128 pub fn maybe_map<F, U>(&self, f: F) -> Option<TransitiveRelation<U>>
130 F: FnMut(T) -> Option<U>,
131 U: Clone + Debug + Eq + Hash + Copy,
133 Some(self.builder.maybe_map(f)?.freeze())
136 /// Checks whether `a < target` (transitively)
137 pub fn contains(&self, a: T, b: T) -> bool {
138 match (self.index(a), self.index(b)) {
139 (Some(a), Some(b)) => self.with_closure(|closure| closure.contains(a.0, b.0)),
140 (None, _) | (_, None) => false,
144 /// Thinking of `x R y` as an edge `x -> y` in a graph, this
145 /// returns all things reachable from `a`.
147 /// Really this probably ought to be `impl Iterator<Item = &T>`, but
148 /// I'm too lazy to make that work, and -- given the caching
149 /// strategy -- it'd be a touch tricky anyhow.
150 pub fn reachable_from(&self, a: T) -> Vec<T> {
151 match self.index(a) {
153 self.with_closure(|closure| closure.iter(a.0).map(|i| self.elements[i]).collect())
159 /// Picks what I am referring to as the "postdominating"
160 /// upper-bound for `a` and `b`. This is usually the least upper
161 /// bound, but in cases where there is no single least upper
162 /// bound, it is the "mutual immediate postdominator", if you
163 /// imagine a graph where `a < b` means `a -> b`.
165 /// This function is needed because region inference currently
166 /// requires that we produce a single "UB", and there is no best
167 /// choice for the LUB. Rather than pick arbitrarily, I pick a
168 /// less good, but predictable choice. This should help ensure
169 /// that region inference yields predictable results (though it
170 /// itself is not fully sufficient).
172 /// Examples are probably clearer than any prose I could write
173 /// (there are corresponding tests below, btw). In each case,
174 /// the query is `postdom_upper_bound(a, b)`:
177 /// // Returns Some(x), which is also LUB.
183 /// // Returns `Some(x)`, which is not LUB (there is none)
184 /// // diagonal edges run left-to-right.
190 /// // Returns `None`.
194 pub fn postdom_upper_bound(&self, a: T, b: T) -> Option<T> {
195 let mubs = self.minimal_upper_bounds(a, b);
196 self.mutual_immediate_postdominator(mubs)
199 /// Viewing the relation as a graph, computes the "mutual
200 /// immediate postdominator" of a set of points (if one
201 /// exists). See `postdom_upper_bound` for details.
202 pub fn mutual_immediate_postdominator(&self, mut mubs: Vec<T>) -> Option<T> {
206 1 => return Some(mubs[0]),
208 let m = mubs.pop().unwrap();
209 let n = mubs.pop().unwrap();
210 mubs.extend(self.minimal_upper_bounds(n, m));
216 /// Returns the set of bounds `X` such that:
218 /// - `a < X` and `b < X`
219 /// - there is no `Y != X` such that `a < Y` and `Y < X`
220 /// - except for the case where `X < a` (i.e., a strongly connected
221 /// component in the graph). In that case, the smallest
222 /// representative of the SCC is returned (as determined by the
223 /// internal indices).
225 /// Note that this set can, in principle, have any size.
226 pub fn minimal_upper_bounds(&self, a: T, b: T) -> Vec<T> {
227 let (Some(mut a), Some(mut b)) = (self.index(a), self.index(b)) else {
231 // in some cases, there are some arbitrary choices to be made;
232 // it doesn't really matter what we pick, as long as we pick
233 // the same thing consistently when queried, so ensure that
234 // (a, b) are in a consistent relative order
236 mem::swap(&mut a, &mut b);
239 let lub_indices = self.with_closure(|closure| {
240 // Easy case is when either a < b or b < a:
241 if closure.contains(a.0, b.0) {
244 if closure.contains(b.0, a.0) {
248 // Otherwise, the tricky part is that there may be some c
249 // where a < c and b < c. In fact, there may be many such
250 // values. So here is what we do:
252 // 1. Find the vector `[X | a < X && b < X]` of all values
253 // `X` where `a < X` and `b < X`. In terms of the
254 // graph, this means all values reachable from both `a`
255 // and `b`. Note that this vector is also a set, but we
256 // use the term vector because the order matters
257 // to the steps below.
258 // - This vector contains upper bounds, but they are
259 // not minimal upper bounds. So you may have e.g.
260 // `[x, y, tcx, z]` where `x < tcx` and `y < tcx` and
261 // `z < x` and `z < y`:
263 // z --+---> x ----+----> tcx
268 // In this case, we really want to return just `[z]`.
269 // The following steps below achieve this by gradually
270 // reducing the list.
271 // 2. Pare down the vector using `pare_down`. This will
272 // remove elements from the vector that can be reached
273 // by an earlier element.
274 // - In the example above, this would convert `[x, y,
275 // tcx, z]` to `[x, y, z]`. Note that `x` and `y` are
276 // still in the vector; this is because while `z < x`
277 // (and `z < y`) holds, `z` comes after them in the
279 // 3. Reverse the vector and repeat the pare down process.
280 // - In the example above, we would reverse to
281 // `[z, y, x]` and then pare down to `[z]`.
282 // 4. Reverse once more just so that we yield a vector in
283 // increasing order of index. Not necessary, but why not.
285 // I believe this algorithm yields a minimal set. The
286 // argument is that, after step 2, we know that no element
287 // can reach its successors (in the vector, not the graph).
288 // After step 3, we know that no element can reach any of
289 // its predecessors (because of step 2) nor successors
290 // (because we just called `pare_down`)
292 // This same algorithm is used in `parents` below.
294 let mut candidates = closure.intersect_rows(a.0, b.0); // (1)
295 pare_down(&mut candidates, closure); // (2)
296 candidates.reverse(); // (3a)
297 pare_down(&mut candidates, closure); // (3b)
304 .map(|i| self.elements[i])
308 /// Given an element A, returns the maximal set {B} of elements B
313 /// - for each i, j: `B[i]` R `B[j]` does not hold
315 /// The intuition is that this moves "one step up" through a lattice
316 /// (where the relation is encoding the `<=` relation for the lattice).
317 /// So e.g., if the relation is `->` and we have
325 /// then `parents(a)` returns `[b, c]`. The `postdom_parent` function
326 /// would further reduce this to just `f`.
327 pub fn parents(&self, a: T) -> Vec<T> {
328 let Some(a) = self.index(a) else {
332 // Steal the algorithm for `minimal_upper_bounds` above, but
333 // with a slight tweak. In the case where `a R a`, we remove
334 // that from the set of candidates.
335 let ancestors = self.with_closure(|closure| {
336 let mut ancestors = closure.intersect_rows(a.0, a.0);
338 // Remove anything that can reach `a`. If this is a
339 // reflexive relation, this will include `a` itself.
340 ancestors.retain(|&e| !closure.contains(e, a.0));
342 pare_down(&mut ancestors, closure); // (2)
343 ancestors.reverse(); // (3a)
344 pare_down(&mut ancestors, closure); // (3b)
351 .map(|i| self.elements[i])
355 fn with_closure<OP, R>(&self, op: OP) -> R
357 OP: FnOnce(&BitMatrix<usize, usize>) -> R,
362 /// Lists all the base edges in the graph: the initial _non-transitive_ set of element
363 /// relations, which will be later used as the basis for the transitive closure computation.
364 pub fn base_edges(&self) -> impl Iterator<Item = (T, T)> + '_ {
367 .map(move |edge| (self.elements[edge.source.0], self.elements[edge.target.0]))
371 /// Pare down is used as a step in the LUB computation. It edits the
372 /// candidates array in place by removing any element j for which
373 /// there exists an earlier element i<j such that i -> j. That is,
374 /// after you run `pare_down`, you know that for all elements that
375 /// remain in candidates, they cannot reach any of the elements that
378 /// Examples follow. Assume that a -> b -> c and x -> y -> z.
380 /// - Input: `[a, b, x]`. Output: `[a, x]`.
381 /// - Input: `[b, a, x]`. Output: `[b, a, x]`.
382 /// - Input: `[a, x, b, y]`. Output: `[a, x]`.
383 fn pare_down(candidates: &mut Vec<usize>, closure: &BitMatrix<usize, usize>) {
385 while let Some(&candidate_i) = candidates.get(i) {
390 while let Some(&candidate_j) = candidates.get(j) {
391 if closure.contains(candidate_i, candidate_j) {
392 // If `i` can reach `j`, then we can remove `j`. So just
393 // mark it as dead and move on; subsequent indices will be
394 // shifted into its place.
397 candidates[j - dead] = candidate_j;
401 candidates.truncate(j - dead);