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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].
//!
// 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);
}
}