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mark 2020-08-27 22:58:48 -05:00 • committed by Vadim Petrochenkov
parent db534b3ac2
commit 9e5f7d5631
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compiler/rustc_data_structures/src/transitive_relation.rs Normal file
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use crate::fx::FxIndexSet;
use crate::sync::Lock;
use rustc_index::bit_set::BitMatrix;
use std::fmt::Debug;
use std::hash::Hash;
use std::mem;
#[cfg(test)]
mod tests;
#[derive(Clone, Debug)]
pub struct TransitiveRelation<T: Eq + Hash> {
// List of elements. This is used to map from a T to a usize.
elements: FxIndexSet<T>,
// List of base edges in the graph. Require to compute transitive
// closure.
edges: Vec<Edge>,
// This is a cached transitive closure derived from the edges.
// Currently, we build it lazilly and just throw out any existing
// copy whenever a new edge is added. (The Lock is to permit
// the lazy computation.) This is kind of silly, except for the
// fact its size is tied to `self.elements.len()`, so I wanted to
// wait before building it up to avoid reallocating as new edges
// are added with new elements. Perhaps better would be to ask the
// user for a batch of edges to minimize this effect, but I
// already wrote the code this way. :P -nmatsakis
closure: Lock<Option<BitMatrix<usize, usize>>>,
}
// HACK(eddyb) manual impl avoids `Default` bound on `T`.
impl<T: Eq + Hash> Default for TransitiveRelation<T> {
fn default() -> Self {
TransitiveRelation {
elements: Default::default(),
edges: Default::default(),
closure: Default::default(),
}
}
}
#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Debug)]
struct Index(usize);
#[derive(Clone, PartialEq, Eq, Debug)]
struct Edge {
source: Index,
target: Index,
}
impl<T: Clone + Debug + Eq + Hash> TransitiveRelation<T> {
pub fn is_empty(&self) -> bool {
self.edges.is_empty()
}
pub fn elements(&self) -> impl Iterator<Item = &T> {
self.elements.iter()
}
fn index(&self, a: &T) -> Option<Index> {
self.elements.get_index_of(a).map(Index)
}
fn add_index(&mut self, a: T) -> Index {
let (index, added) = self.elements.insert_full(a);
if added {
// if we changed the dimensions, clear the cache
*self.closure.get_mut() = None;
}
Index(index)
}
/// Applies the (partial) function to each edge and returns a new
/// relation. If `f` returns `None` for any end-point, returns
/// `None`.
pub fn maybe_map<F, U>(&self, mut f: F) -> Option<TransitiveRelation<U>>
where
F: FnMut(&T) -> Option<U>,
U: Clone + Debug + Eq + Hash + Clone,
{
let mut result = TransitiveRelation::default();
for edge in &self.edges {
result.add(f(&self.elements[edge.source.0])?, f(&self.elements[edge.target.0])?);
}
Some(result)
}
/// Indicate that `a < b` (where `<` is this relation)
pub fn add(&mut self, a: T, b: T) {
let a = self.add_index(a);
let b = self.add_index(b);
let edge = Edge { source: a, target: b };
if !self.edges.contains(&edge) {
self.edges.push(edge);
// added an edge, clear the cache
*self.closure.get_mut() = None;
}
}
/// Checks whether `a < target` (transitively)
pub fn contains(&self, a: &T, b: &T) -> bool {
match (self.index(a), self.index(b)) {
(Some(a), Some(b)) => self.with_closure(|closure| closure.contains(a.0, b.0)),
(None, _) | (_, None) => false,
}
}
/// Thinking of `x R y` as an edge `x -> y` in a graph, this
/// returns all things reachable from `a`.
///
/// Really this probably ought to be `impl Iterator<Item = &T>`, but
/// I'm too lazy to make that work, and -- given the caching
/// strategy -- it'd be a touch tricky anyhow.
pub fn reachable_from(&self, a: &T) -> Vec<&T> {
match self.index(a) {
Some(a) => {
self.with_closure(|closure| closure.iter(a.0).map(|i| &self.elements[i]).collect())
}
None => vec![],
}
}
/// Picks what I am referring to as the "postdominating"
/// upper-bound for `a` and `b`. This is usually the least upper
/// bound, but in cases where there is no single least upper
/// bound, it is the "mutual immediate postdominator", if you
/// imagine a graph where `a < b` means `a -> b`.
///
/// This function is needed because region inference currently
/// requires that we produce a single "UB", and there is no best
/// choice for the LUB. Rather than pick arbitrarily, I pick a
/// less good, but predictable choice. This should help ensure
/// that region inference yields predictable results (though it
/// itself is not fully sufficient).
///
/// Examples are probably clearer than any prose I could write
/// (there are corresponding tests below, btw). In each case,
/// the query is `postdom_upper_bound(a, b)`:
///
/// ```text
/// // Returns Some(x), which is also LUB.
/// a -> a1 -> x
/// ^
/// |
/// b -> b1 ---+
///
/// // Returns `Some(x)`, which is not LUB (there is none)
/// // diagonal edges run left-to-right.
/// a -> a1 -> x
/// \/ ^
/// /\ |
/// b -> b1 ---+
///
/// // Returns `None`.
/// a -> a1
/// b -> b1
/// ```
pub fn postdom_upper_bound(&self, a: &T, b: &T) -> Option<&T> {
let mubs = self.minimal_upper_bounds(a, b);
self.mutual_immediate_postdominator(mubs)
}
/// Viewing the relation as a graph, computes the "mutual
/// immediate postdominator" of a set of points (if one
/// exists). See `postdom_upper_bound` for details.
pub fn mutual_immediate_postdominator<'a>(&'a self, mut mubs: Vec<&'a T>) -> Option<&'a T> {
loop {
match mubs.len() {
0 => return None,
1 => return Some(mubs[0]),
_ => {
let m = mubs.pop().unwrap();
let n = mubs.pop().unwrap();
mubs.extend(self.minimal_upper_bounds(n, m));
}
}
}
}
/// Returns the set of bounds `X` such that:
///
/// - `a < X` and `b < X`
/// - there is no `Y != X` such that `a < Y` and `Y < X`
/// - except for the case where `X < a` (i.e., a strongly connected
/// component in the graph). In that case, the smallest
/// representative of the SCC is returned (as determined by the
/// internal indices).
///
/// Note that this set can, in principle, have any size.
pub fn minimal_upper_bounds(&self, a: &T, b: &T) -> Vec<&T> {
let (mut a, mut b) = match (self.index(a), self.index(b)) {
(Some(a), Some(b)) => (a, b),
(None, _) | (_, None) => {
return vec![];
}
};
// in some cases, there are some arbitrary choices to be made;
// it doesn't really matter what we pick, as long as we pick
// the same thing consistently when queried, so ensure that
// (a, b) are in a consistent relative order
if a > b {
mem::swap(&mut a, &mut b);
}
let lub_indices = self.with_closure(|closure| {
// Easy case is when either a < b or b < a:
if closure.contains(a.0, b.0) {
return vec![b.0];
}
if closure.contains(b.0, a.0) {
return vec![a.0];
}
// Otherwise, the tricky part is that there may be some c
// where a < c and b < c. In fact, there may be many such
// values. So here is what we do:
//
// 1. Find the vector `[X | a < X && b < X]` of all values
// `X` where `a < X` and `b < X`. In terms of the
// graph, this means all values reachable from both `a`
// and `b`. Note that this vector is also a set, but we
// use the term vector because the order matters
// to the steps below.
// - This vector contains upper bounds, but they are
// not minimal upper bounds. So you may have e.g.
// `[x, y, tcx, z]` where `x < tcx` and `y < tcx` and
// `z < x` and `z < y`:
//
// z --+---> x ----+----> tcx
// | |
// | |
// +---> y ----+
//
// In this case, we really want to return just `[z]`.
// The following steps below achieve this by gradually
// reducing the list.
// 2. Pare down the vector using `pare_down`. This will
// remove elements from the vector that can be reached
// by an earlier element.
// - In the example above, this would convert `[x, y,
// tcx, z]` to `[x, y, z]`. Note that `x` and `y` are
// still in the vector; this is because while `z < x`
// (and `z < y`) holds, `z` comes after them in the
// vector.
// 3. Reverse the vector and repeat the pare down process.
// - In the example above, we would reverse to
// `[z, y, x]` and then pare down to `[z]`.
// 4. Reverse once more just so that we yield a vector in
// increasing order of index. Not necessary, but why not.
//
// I believe this algorithm yields a minimal set. The
// argument is that, after step 2, we know that no element
// can reach its successors (in the vector, not the graph).
// After step 3, we know that no element can reach any of
// its predecesssors (because of step 2) nor successors
// (because we just called `pare_down`)
//
// This same algorithm is used in `parents` below.
let mut candidates = closure.intersect_rows(a.0, b.0); // (1)
pare_down(&mut candidates, closure); // (2)
candidates.reverse(); // (3a)
pare_down(&mut candidates, closure); // (3b)
candidates
});
lub_indices
.into_iter()
.rev() // (4)
.map(|i| &self.elements[i])
.collect()
}
/// Given an element A, returns the maximal set {B} of elements B
/// such that
///
/// - A != B
/// - A R B is true
/// - for each i, j: `B[i]` R `B[j]` does not hold
///
/// The intuition is that this moves "one step up" through a lattice
/// (where the relation is encoding the `<=` relation for the lattice).
/// So e.g., if the relation is `->` and we have
///
/// ```
/// a -> b -> d -> f
/// | ^
/// +--> c -> e ---+
/// ```
///
/// then `parents(a)` returns `[b, c]`. The `postdom_parent` function
/// would further reduce this to just `f`.
pub fn parents(&self, a: &T) -> Vec<&T> {
let a = match self.index(a) {
Some(a) => a,
None => return vec![],
};
// Steal the algorithm for `minimal_upper_bounds` above, but
// with a slight tweak. In the case where `a R a`, we remove
// that from the set of candidates.
let ancestors = self.with_closure(|closure| {
let mut ancestors = closure.intersect_rows(a.0, a.0);
// Remove anything that can reach `a`. If this is a
// reflexive relation, this will include `a` itself.
ancestors.retain(|&e| !closure.contains(e, a.0));
pare_down(&mut ancestors, closure); // (2)
ancestors.reverse(); // (3a)
pare_down(&mut ancestors, closure); // (3b)
ancestors
});
ancestors
.into_iter()
.rev() // (4)
.map(|i| &self.elements[i])
.collect()
}
/// A "best" parent in some sense. See `parents` and
/// `postdom_upper_bound` for more details.
pub fn postdom_parent(&self, a: &T) -> Option<&T> {
self.mutual_immediate_postdominator(self.parents(a))
}
fn with_closure<OP, R>(&self, op: OP) -> R
where
OP: FnOnce(&BitMatrix<usize, usize>) -> R,
{
let mut closure_cell = self.closure.borrow_mut();
let mut closure = closure_cell.take();
if closure.is_none() {
closure = Some(self.compute_closure());
}
let result = op(closure.as_ref().unwrap());
*closure_cell = closure;
result
}
fn compute_closure(&self) -> BitMatrix<usize, usize> {
let mut matrix = BitMatrix::new(self.elements.len(), self.elements.len());
let mut changed = true;
while changed {
changed = false;
for edge in &self.edges {
// add an edge from S -> T
changed |= matrix.insert(edge.source.0, edge.target.0);
// add all outgoing edges from T into S
changed |= matrix.union_rows(edge.target.0, edge.source.0);
}
}
matrix
}
/// Lists all the base edges in the graph: the initial _non-transitive_ set of element
/// relations, which will be later used as the basis for the transitive closure computation.
pub fn base_edges(&self) -> impl Iterator<Item = (&T, &T)> {
self.edges
.iter()
.map(move |edge| (&self.elements[edge.source.0], &self.elements[edge.target.0]))
}
}
/// Pare down is used as a step in the LUB computation. It edits the
/// candidates array in place by removing any element j for which
/// there exists an earlier element i<j such that i -> j. That is,
/// after you run `pare_down`, you know that for all elements that
/// remain in candidates, they cannot reach any of the elements that
/// come after them.
///
/// Examples follow. Assume that a -> b -> c and x -> y -> z.
///
/// - Input: `[a, b, x]`. Output: `[a, x]`.
/// - Input: `[b, a, x]`. Output: `[b, a, x]`.
/// - Input: `[a, x, b, y]`. Output: `[a, x]`.
fn pare_down(candidates: &mut Vec<usize>, closure: &BitMatrix<usize, usize>) {
let mut i = 0;
while let Some(&candidate_i) = candidates.get(i) {
i += 1;
let mut j = i;
let mut dead = 0;
while let Some(&candidate_j) = candidates.get(j) {
if closure.contains(candidate_i, candidate_j) {
// If `i` can reach `j`, then we can remove `j`. So just
// mark it as dead and move on; subsequent indices will be
// shifted into its place.
dead += 1;
} else {
candidates[j - dead] = candidate_j;
}
j += 1;
}
candidates.truncate(j - dead);
}
}