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