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+//! Fix-point analyses on the IR using the "monotone framework".
+//!
+//! A lattice is a set with a partial ordering between elements, where there is
+//! a single least upper bound and a single greatest least bound for every
+//! subset. We are dealing with finite lattices, which means that it has a
+//! finite number of elements, and it follows that there exists a single top and
+//! a single bottom member of the lattice. For example, the power set of a
+//! finite set forms a finite lattice where partial ordering is defined by set
+//! inclusion, that is `a <= b` if `a` is a subset of `b`. Here is the finite
+//! lattice constructed from the set {0,1,2}:
+//!
+//! ```text
+//! .----- Top = {0,1,2} -----.
+//! / | \
+//! / | \
+//! / | \
+//! {0,1} -------. {0,2} .--------- {1,2}
+//! | \ / \ / |
+//! | / \ |
+//! | / \ / \ |
+//! {0} --------' {1} `---------- {2}
+//! \ | /
+//! \ | /
+//! \ | /
+//! `------ Bottom = {} ------'
+//! ```
+//!
+//! A monotone function `f` is a function where if `x <= y`, then it holds that
+//! `f(x) <= f(y)`. It should be clear that running a monotone function to a
+//! fix-point on a finite lattice will always terminate: `f` can only "move"
+//! along the lattice in a single direction, and therefore can only either find
+//! a fix-point in the middle of the lattice or continue to the top or bottom
+//! depending if it is ascending or descending the lattice respectively.
+//!
+//! For a deeper introduction to the general form of this kind of analysis, see
+//! [Static Program Analysis by Anders Møller and Michael I. Schwartzbach][spa].
+//!
+//! [spa]: https://cs.au.dk/~amoeller/spa/spa.pdf
+
+// Re-export individual analyses.
+mod template_params;
+pub(crate) use self::template_params::UsedTemplateParameters;
+mod derive;
+pub use self::derive::DeriveTrait;
+pub(crate) use self::derive::{as_cannot_derive_set, CannotDerive};
+mod has_vtable;
+pub(crate) use self::has_vtable::{
+ HasVtable, HasVtableAnalysis, HasVtableResult,
+};
+mod has_destructor;
+pub(crate) use self::has_destructor::HasDestructorAnalysis;
+mod has_type_param_in_array;
+pub(crate) use self::has_type_param_in_array::HasTypeParameterInArray;
+mod has_float;
+pub(crate) use self::has_float::HasFloat;
+mod sizedness;
+pub(crate) use self::sizedness::{
+ Sizedness, SizednessAnalysis, SizednessResult,
+};
+
+use crate::ir::context::{BindgenContext, ItemId};
+
+use crate::ir::traversal::{EdgeKind, Trace};
+use crate::HashMap;
+use std::fmt;
+use std::ops;
+
+/// 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(crate) 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
+ /// `ConstrainResult::Changed`. Otherwise, return `ConstrainResult::Same`.
+ /// When `constrain` returns `ConstrainResult::Same` for all nodes in the
+ /// set, we have reached a fix-point and the analysis is complete.
+ fn constrain(&mut self, node: Self::Node) -> ConstrainResult;
+
+ /// 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);
+}
+
+/// Whether an analysis's `constrain` function modified the incremental results
+/// or not.
+#[derive(Debug, Copy, Clone, PartialEq, Eq)]
+pub(crate) enum ConstrainResult {
+ /// The incremental results were updated, and the fix-point computation
+ /// should continue.
+ Changed,
+
+ /// The incremental results were not updated.
+ Same,
+}
+
+impl Default for ConstrainResult {
+ fn default() -> Self {
+ ConstrainResult::Same
+ }
+}
+
+impl ops::BitOr for ConstrainResult {
+ type Output = Self;
+
+ fn bitor(self, rhs: ConstrainResult) -> Self::Output {
+ if self == ConstrainResult::Changed || rhs == ConstrainResult::Changed {
+ ConstrainResult::Changed
+ } else {
+ ConstrainResult::Same
+ }
+ }
+}
+
+impl ops::BitOrAssign for ConstrainResult {
+ fn bitor_assign(&mut self, rhs: ConstrainResult) {
+ *self = *self | rhs;
+ }
+}
+
+/// Run an analysis in the monotone framework.
+pub(crate) 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 let ConstrainResult::Changed = analysis.constrain(node) {
+ analysis.each_depending_on(node, |needs_work| {
+ worklist.push(needs_work);
+ });
+ }
+ }
+
+ analysis.into()
+}
+
+/// Generate the dependency map for analysis
+pub(crate) fn generate_dependencies<F>(
+ ctx: &BindgenContext,
+ consider_edge: F,
+) -> HashMap<ItemId, Vec<ItemId>>
+where
+ F: Fn(EdgeKind) -> bool,
+{
+ let mut dependencies = HashMap::default();
+
+ for &item in ctx.allowlisted_items() {
+ dependencies.entry(item).or_insert_with(Vec::new);
+
+ {
+ // We reverse our natural IR graph edges to find dependencies
+ // between nodes.
+ item.trace(
+ ctx,
+ &mut |sub_item: ItemId, edge_kind| {
+ if ctx.allowlisted_items().contains(&sub_item) &&
+ consider_edge(edge_kind)
+ {
+ dependencies
+ .entry(sub_item)
+ .or_insert_with(Vec::new)
+ .push(item);
+ }
+ },
+ &(),
+ );
+ }
+ }
+ dependencies
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+ use crate::{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_with(Vec::new);
+ for referent in edges.iter() {
+ reversed
+ .0
+ .entry(*referent)
+ .or_insert_with(Vec::new)
+ .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,
+ reversed,
+ }
+ }
+
+ fn initial_worklist(&self) -> Vec<Node> {
+ self.graph.0.keys().cloned().collect()
+ }
+
+ fn constrain(&mut self, node: Node) -> ConstrainResult {
+ // 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_default().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_default().clone();
+
+ for transitive in sub_reachable {
+ self.reachable.get_mut(&node).unwrap().insert(transitive);
+ }
+ }
+
+ let new_size = self.reachable[&node].len();
+ if original_size != new_size {
+ ConstrainResult::Changed
+ } else {
+ ConstrainResult::Same
+ }
+ }
+
+ 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::default();
+ 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);
+ }
+}