| //! 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 use self::template_params::UsedTemplateParameters; |
| mod derive; |
| pub use self::derive::{as_cannot_derive_set, CannotDerive, DeriveTrait}; |
| mod has_vtable; |
| pub use self::has_vtable::{HasVtable, HasVtableAnalysis, HasVtableResult}; |
| mod has_destructor; |
| pub use self::has_destructor::HasDestructorAnalysis; |
| mod has_type_param_in_array; |
| pub use self::has_type_param_in_array::HasTypeParameterInArray; |
| mod has_float; |
| pub use self::has_float::HasFloat; |
| mod sizedness; |
| pub 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 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 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 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 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(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) -> 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_insert(HashSet::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_insert(HashSet::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); |
| } |
| } |