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//! Compute dominators of a control-flow graph.
//!
//! # The Dominance Relation
//!
//! In a directed graph with a root node **R**, a node **A** is said to *dominate* a
//! node **B** iff every path from **R** to **B** contains **A**.
//!
//! The node **A** is said to *strictly dominate* the node **B** iff **A** dominates
//! **B** and **A ≠ B**.
//!
//! The node **A** is said to be the *immediate dominator* of a node **B** iff it
//! strictly dominates **B** and there does not exist any node **C** where **A**
//! dominates **C** and **C** dominates **B**.
use std::cmp::Ordering;
use std::collections::{hash_map::Iter, HashMap, HashSet};
use std::hash::Hash;
use crate::visit::{DfsPostOrder, GraphBase, IntoNeighbors, Visitable, Walker};
/// The dominance relation for some graph and root.
#[derive(Debug, Clone)]
pub struct Dominators<N>
where
N: Copy + Eq + Hash,
{
root: N,
dominators: HashMap<N, N>,
}
impl<N> Dominators<N>
where
N: Copy + Eq + Hash,
{
/// Get the root node used to construct these dominance relations.
pub fn root(&self) -> N {
self.root
}
/// Get the immediate dominator of the given node.
///
/// Returns `None` for any node that is not reachable from the root, and for
/// the root itself.
pub fn immediate_dominator(&self, node: N) -> Option<N> {
if node == self.root {
None
} else {
self.dominators.get(&node).cloned()
}
}
/// Iterate over the given node's strict dominators.
///
/// If the given node is not reachable from the root, then `None` is
/// returned.
pub fn strict_dominators(&self, node: N) -> Option<DominatorsIter<N>> {
if self.dominators.contains_key(&node) {
Some(DominatorsIter {
dominators: self,
node: self.immediate_dominator(node),
})
} else {
None
}
}
/// Iterate over all of the given node's dominators (including the given
/// node itself).
///
/// If the given node is not reachable from the root, then `None` is
/// returned.
pub fn dominators(&self, node: N) -> Option<DominatorsIter<N>> {
if self.dominators.contains_key(&node) {
Some(DominatorsIter {
dominators: self,
node: Some(node),
})
} else {
None
}
}
/// Iterate over all nodes immediately dominated by the given node (not
/// including the given node itself).
pub fn immediately_dominated_by(&self, node: N) -> DominatedByIter<N> {
DominatedByIter {
iter: self.dominators.iter(),
node,
}
}
}
/// Iterator for a node's dominators.
#[derive(Debug, Clone)]
pub struct DominatorsIter<'a, N>
where
N: 'a + Copy + Eq + Hash,
{
dominators: &'a Dominators<N>,
node: Option<N>,
}
impl<'a, N> Iterator for DominatorsIter<'a, N>
where
N: 'a + Copy + Eq + Hash,
{
type Item = N;
fn next(&mut self) -> Option<Self::Item> {
let next = self.node.take();
if let Some(next) = next {
self.node = self.dominators.immediate_dominator(next);
}
next
}
}
/// Iterator for nodes dominated by a given node.
#[derive(Debug, Clone)]
pub struct DominatedByIter<'a, N>
where
N: 'a + Copy + Eq + Hash,
{
iter: Iter<'a, N, N>,
node: N,
}
impl<'a, N> Iterator for DominatedByIter<'a, N>
where
N: 'a + Copy + Eq + Hash,
{
type Item = N;
fn next(&mut self) -> Option<Self::Item> {
for next in self.iter.by_ref() {
if next.1 == &self.node {
return Some(*next.0);
}
}
None
}
fn size_hint(&self) -> (usize, Option<usize>) {
let (_, upper) = self.iter.size_hint();
(0, upper)
}
}
/// The undefined dominator sentinel, for when we have not yet discovered a
/// node's dominator.
const UNDEFINED: usize = ::std::usize::MAX;
/// This is an implementation of the engineered ["Simple, Fast Dominance
/// Algorithm"][0] discovered by Cooper et al.
///
/// This algorithm is **O(|V|²)**, and therefore has slower theoretical running time
/// than the Lengauer-Tarjan algorithm (which is **O(|E| log |V|)**. However,
/// Cooper et al found it to be faster in practice on control flow graphs of up
/// to ~30,000 vertices.
///
/// [0]: http://www.hipersoft.rice.edu/grads/publications/dom14.pdf
pub fn simple_fast<G>(graph: G, root: G::NodeId) -> Dominators<G::NodeId>
where
G: IntoNeighbors + Visitable,
<G as GraphBase>::NodeId: Eq + Hash,
{
let (post_order, predecessor_sets) = simple_fast_post_order(graph, root);
let length = post_order.len();
debug_assert!(length > 0);
debug_assert!(post_order.last() == Some(&root));
// From here on out we use indices into `post_order` instead of actual
// `NodeId`s wherever possible. This greatly improves the performance of
// this implementation, but we have to pay a little bit of upfront cost to
// convert our data structures to play along first.
// Maps a node to its index into `post_order`.
let node_to_post_order_idx: HashMap<_, _> = post_order
.iter()
.enumerate()
.map(|(idx, &node)| (node, idx))
.collect();
// Maps a node's `post_order` index to its set of predecessors's indices
// into `post_order` (as a vec).
let idx_to_predecessor_vec =
predecessor_sets_to_idx_vecs(&post_order, &node_to_post_order_idx, predecessor_sets);
let mut dominators = vec![UNDEFINED; length];
dominators[length - 1] = length - 1;
let mut changed = true;
while changed {
changed = false;
// Iterate in reverse post order, skipping the root.
for idx in (0..length - 1).rev() {
debug_assert!(post_order[idx] != root);
// Take the intersection of every predecessor's dominator set; that
// is the current best guess at the immediate dominator for this
// node.
let new_idom_idx = {
let mut predecessors = idx_to_predecessor_vec[idx]
.iter()
.filter(|&&p| dominators[p] != UNDEFINED);
let new_idom_idx = predecessors.next().expect(
"Because the root is initialized to dominate itself, and is the \
first node in every path, there must exist a predecessor to this \
node that also has a dominator",
);
predecessors.fold(*new_idom_idx, |new_idom_idx, &predecessor_idx| {
intersect(&dominators, new_idom_idx, predecessor_idx)
})
};
debug_assert!(new_idom_idx < length);
if new_idom_idx != dominators[idx] {
dominators[idx] = new_idom_idx;
changed = true;
}
}
}
// All done! Translate the indices back into proper `G::NodeId`s.
debug_assert!(!dominators.iter().any(|&dom| dom == UNDEFINED));
Dominators {
root,
dominators: dominators
.into_iter()
.enumerate()
.map(|(idx, dom_idx)| (post_order[idx], post_order[dom_idx]))
.collect(),
}
}
fn intersect(dominators: &[usize], mut finger1: usize, mut finger2: usize) -> usize {
loop {
match finger1.cmp(&finger2) {
Ordering::Less => finger1 = dominators[finger1],
Ordering::Greater => finger2 = dominators[finger2],
Ordering::Equal => return finger1,
}
}
}
fn predecessor_sets_to_idx_vecs<N>(
post_order: &[N],
node_to_post_order_idx: &HashMap<N, usize>,
mut predecessor_sets: HashMap<N, HashSet<N>>,
) -> Vec<Vec<usize>>
where
N: Copy + Eq + Hash,
{
post_order
.iter()
.map(|node| {
predecessor_sets
.remove(node)
.map(|predecessors| {
predecessors
.into_iter()
.map(|p| *node_to_post_order_idx.get(&p).unwrap())
.collect()
})
.unwrap_or_default()
})
.collect()
}
type PredecessorSets<NodeId> = HashMap<NodeId, HashSet<NodeId>>;
fn simple_fast_post_order<G>(
graph: G,
root: G::NodeId,
) -> (Vec<G::NodeId>, PredecessorSets<G::NodeId>)
where
G: IntoNeighbors + Visitable,
<G as GraphBase>::NodeId: Eq + Hash,
{
let mut post_order = vec![];
let mut predecessor_sets = HashMap::new();
for node in DfsPostOrder::new(graph, root).iter(graph) {
post_order.push(node);
for successor in graph.neighbors(node) {
predecessor_sets
.entry(successor)
.or_insert_with(HashSet::new)
.insert(node);
}
}
(post_order, predecessor_sets)
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_iter_dominators() {
let doms: Dominators<u32> = Dominators {
root: 0,
dominators: [(2, 1), (1, 0), (0, 0)].iter().cloned().collect(),
};
let all_doms: Vec<_> = doms.dominators(2).unwrap().collect();
assert_eq!(vec![2, 1, 0], all_doms);
assert_eq!(None::<()>, doms.dominators(99).map(|_| unreachable!()));
let strict_doms: Vec<_> = doms.strict_dominators(2).unwrap().collect();
assert_eq!(vec![1, 0], strict_doms);
assert_eq!(
None::<()>,
doms.strict_dominators(99).map(|_| unreachable!())
);
let dom_by: Vec<_> = doms.immediately_dominated_by(1).collect();
assert_eq!(vec![2], dom_by);
assert_eq!(None, doms.immediately_dominated_by(99).next());
}
}