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256 changes: 256 additions & 0 deletions src/ir/analysis.rs
Original file line number Diff line number Diff line change
@@ -0,0 +1,256 @@
//! Fix-point analyses on the IR using the monotone framework.
use std::fmt;

/// An analysis in the monotone framework.
///
/// Implementors of this trait must maintain the following two invariants:
///
/// 1. The concrete data must be a member of a finite-height lattice.
/// 2. The concrete `constrain` method must be monotone: that is,
/// if `x <= y`, then `constrain(x) <= constrain(y)`.
///
/// If these invariants do not hold, iteration to a fix-point might never
/// complete.
///
/// For a simple example analysis, see the `ReachableFrom` type in the `tests`
/// module below.
pub trait MonotoneFramework: Sized + fmt::Debug {
/// The type of node in our dependency graph.
///
/// This is just generic (and not `ItemId`) so that we can easily unit test
/// without constructing real `Item`s and their `ItemId`s.
type Node: Copy;

/// Any extra data that is needed during computation.
///
/// Again, this is just generic (and not `&BindgenContext`) so that we can
/// easily unit test without constructing real `BindgenContext`s full of
/// real `Item`s and real `ItemId`s.
type Extra: Sized;

/// The final output of this analysis. Once we have reached a fix-point, we
/// convert `self` into this type, and return it as the final result of the
/// analysis.
type Output: From<Self> + fmt::Debug;

/// Construct a new instance of this analysis.
fn new(extra: Self::Extra) -> Self;

/// Get the initial set of nodes from which to start the analysis. Unless
/// you are sure of some domain-specific knowledge, this should be the
/// complete set of nodes.
fn initial_worklist(&self) -> Vec<Self::Node>;

/// Update the analysis for the given node.
///
/// If this results in changing our internal state (ie, we discovered that
/// we have not reached a fix-point and iteration should continue), return
/// `true`. Otherwise, return `false`. When `constrain` returns false for
/// all nodes in the set, we have reached a fix-point and the analysis is
/// complete.
fn constrain(&mut self, node: Self::Node) -> bool;

/// For each node `d` that depends on the given `node`'s current answer when
/// running `constrain(d)`, call `f(d)`. This informs us which new nodes to
/// queue up in the worklist when `constrain(node)` reports updated
/// information.
fn each_depending_on<F>(&self, node: Self::Node, f: F)
where F: FnMut(Self::Node);
}

/// Run an analysis in the monotone framework.
pub fn analyze<Analysis>(extra: Analysis::Extra) -> Analysis::Output
where Analysis: MonotoneFramework,
{
let mut analysis = Analysis::new(extra);
let mut worklist = analysis.initial_worklist();

while let Some(node) = worklist.pop() {
if analysis.constrain(node) {
analysis.each_depending_on(node, |needs_work| {
worklist.push(needs_work);
});
}
}

analysis.into()
}

#[cfg(test)]
mod tests {
use super::*;
use std::collections::{HashMap, HashSet};

// Here we find the set of nodes that are reachable from any given
// node. This is a lattice mapping nodes to subsets of all nodes. Our join
// function is set union.
//
// This is our test graph:
//
// +---+ +---+
// | | | |
// | 1 | .----| 2 |
// | | | | |
// +---+ | +---+
// | | ^
// | | |
// | +---+ '------'
// '----->| |
// | 3 |
// .------| |------.
// | +---+ |
// | ^ |
// v | v
// +---+ | +---+ +---+
// | | | | | | |
// | 4 | | | 5 |--->| 6 |
// | | | | | | |
// +---+ | +---+ +---+
// | | | |
// | | | v
// | +---+ | +---+
// | | | | | |
// '----->| 7 |<-----' | 8 |
// | | | |
// +---+ +---+
//
// And here is the mapping from a node to the set of nodes that are
// reachable from it within the test graph:
//
// 1: {3,4,5,6,7,8}
// 2: {2}
// 3: {3,4,5,6,7,8}
// 4: {3,4,5,6,7,8}
// 5: {3,4,5,6,7,8}
// 6: {8}
// 7: {3,4,5,6,7,8}
// 8: {}

#[derive(Clone, Copy, Debug, Hash, PartialEq, Eq)]
struct Node(usize);

#[derive(Clone, Debug, Default, PartialEq, Eq)]
struct Graph(HashMap<Node, Vec<Node>>);

impl Graph {
fn make_test_graph() -> Graph {
let mut g = Graph::default();
g.0.insert(Node(1), vec![Node(3)]);
g.0.insert(Node(2), vec![Node(2)]);
g.0.insert(Node(3), vec![Node(4), Node(5)]);
g.0.insert(Node(4), vec![Node(7)]);
g.0.insert(Node(5), vec![Node(6), Node(7)]);
g.0.insert(Node(6), vec![Node(8)]);
g.0.insert(Node(7), vec![Node(3)]);
g.0.insert(Node(8), vec![]);
g
}

fn reverse(&self) -> Graph {
let mut reversed = Graph::default();
for (node, edges) in self.0.iter() {
reversed.0.entry(*node).or_insert(vec![]);
for referent in edges.iter() {
reversed.0.entry(*referent).or_insert(vec![]).push(*node);
}
}
reversed
}
}

#[derive(Clone, Debug, PartialEq, Eq)]
struct ReachableFrom<'a> {
reachable: HashMap<Node, HashSet<Node>>,
graph: &'a Graph,
reversed: Graph,
}

impl<'a> MonotoneFramework for ReachableFrom<'a> {
type Node = Node;
type Extra = &'a Graph;
type Output = HashMap<Node, HashSet<Node>>;

fn new(graph: &'a Graph) -> ReachableFrom {
let reversed = graph.reverse();
ReachableFrom {
reachable: Default::default(),
graph: graph,
reversed: reversed,
}
}

fn initial_worklist(&self) -> Vec<Node> {
self.graph.0.keys().cloned().collect()
}

fn constrain(&mut self, node: Node) -> bool {
// The set of nodes reachable from a node `x` is
//
// reachable(x) = s_0 U s_1 U ... U reachable(s_0) U reachable(s_1) U ...
//
// where there exist edges from `x` to each of `s_0, s_1, ...`.
//
// Yes, what follows is a **terribly** inefficient set union
// implementation. Don't copy this code outside of this test!

let original_size =
self.reachable.entry(node).or_insert(HashSet::new()).len();

for sub_node in self.graph.0[&node].iter() {
self.reachable.get_mut(&node).unwrap().insert(*sub_node);

let sub_reachable = self.reachable
.entry(*sub_node)
.or_insert(HashSet::new())
.clone();

for transitive in sub_reachable {
self.reachable.get_mut(&node).unwrap().insert(transitive);
}
}

let new_size = self.reachable[&node].len();
original_size != new_size
}

fn each_depending_on<F>(&self, node: Node, mut f: F)
where F: FnMut(Node),
{
for dep in self.reversed.0[&node].iter() {
f(*dep);
}
}
}

impl<'a> From<ReachableFrom<'a>> for HashMap<Node, HashSet<Node>> {
fn from(reachable: ReachableFrom<'a>) -> Self {
reachable.reachable
}
}

#[test]
fn monotone() {
let g = Graph::make_test_graph();
let reachable = analyze::<ReachableFrom>(&g);
println!("reachable = {:#?}", reachable);

fn nodes<A>(nodes: A) -> HashSet<Node>
where A: AsRef<[usize]>,
{
nodes.as_ref().iter().cloned().map(Node).collect()
}

let mut expected = HashMap::new();
expected.insert(Node(1), nodes([3, 4, 5, 6, 7, 8]));
expected.insert(Node(2), nodes([2]));
expected.insert(Node(3), nodes([3, 4, 5, 6, 7, 8]));
expected.insert(Node(4), nodes([3, 4, 5, 6, 7, 8]));
expected.insert(Node(5), nodes([3, 4, 5, 6, 7, 8]));
expected.insert(Node(6), nodes([8]));
expected.insert(Node(7), nodes([3, 4, 5, 6, 7, 8]));
expected.insert(Node(8), nodes([]));
println!("expected = {:#?}", expected);

assert_eq!(reachable, expected);
}
}
3 changes: 2 additions & 1 deletion src/ir/context.rs
Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,8 @@ use super::int::IntKind;
use super::item::{IsOpaque, Item, ItemAncestors, ItemCanonicalPath, ItemSet};
use super::item_kind::ItemKind;
use super::module::{Module, ModuleKind};
use super::named::{UsedTemplateParameters, analyze};
use super::named::UsedTemplateParameters;
use super::analysis::analyze;
use super::template::{TemplateInstantiation, TemplateParameters};
use super::traversal::{self, Edge, ItemTraversal};
use super::ty::{FloatKind, Type, TypeKind};
Expand Down
1 change: 1 addition & 0 deletions src/ir/mod.rs
Original file line number Diff line number Diff line change
Expand Up @@ -4,6 +4,7 @@
//! the IR.

pub mod annotations;
pub mod analysis;
pub mod comp;
pub mod context;
pub mod derive;
Expand Down
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