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<h1 id="dataflow-analysis"><a class="header" href="#dataflow-analysis">Dataflow Analysis</a></h1>
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<ul>
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<li><a href="#defining-a-dataflow-analysis">Defining a Dataflow Analysis</a>
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<ul>
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<li><a href="#transfer-functions-and-effects">Transfer Functions and Effects</a></li>
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<li><a href="#before-effects">"Before" Effects</a></li>
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<li><a href="#convergence">Convergence</a></li>
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</ul>
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</li>
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<li><a href="#a-brief-example">A Brief Example</a></li>
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<li><a href="#inspecting-the-results-of-a-dataflow-analysis">Inspecting the Results of a Dataflow Analysis</a>
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<ul>
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<li><a href="#graphviz-diagrams">Graphviz Diagrams</a></li>
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</ul>
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</li>
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</ul>
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<p>If you work on the MIR, you will frequently come across various flavors of
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<a href="https://en.wikipedia.org/wiki/Data-flow_analysis#Basic_principles">dataflow analysis</a>. <code>rustc</code> uses dataflow to find uninitialized
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variables, determine what variables are live across a generator <code>yield</code>
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statement, and compute which <code>Place</code>s are borrowed at a given point in the
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control-flow graph. Dataflow analysis is a fundamental concept in modern
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compilers, and knowledge of the subject will be helpful to prospective
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contributors.</p>
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<p>However, this documentation is not a general introduction to dataflow analysis.
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It is merely a description of the framework used to define these analyses in
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<code>rustc</code>. It assumes that the reader is familiar with the core ideas as well as
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some basic terminology, such as "transfer function", "fixpoint" and "lattice".
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If you're unfamiliar with these terms, or if you want a quick refresher,
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<a href="https://cs.au.dk/~amoeller/spa/"><em>Static Program Analysis</em></a> by Anders Møller and Michael I. Schwartzbach is an
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excellent, freely available textbook. For those who prefer audiovisual
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learning, we previously recommended a series of short lectures
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by the Goethe University Frankfurt on YouTube, but it has since been deleted.
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See <a href="https://github.com/rust-lang/rustc-dev-guide/pull/1295">this PR</a> for the context and <a href="https://github.com/rust-lang/rustc-dev-guide/pull/1295#issuecomment-1118131294">this comment</a>
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for the alternative lectures.</p>
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<h2 id="defining-a-dataflow-analysis"><a class="header" href="#defining-a-dataflow-analysis">Defining a Dataflow Analysis</a></h2>
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<p>A dataflow analysis is defined by the <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/trait.Analysis.html"><code>Analysis</code></a> trait. In addition to the
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type of the dataflow state, this trait defines the initial value of that state
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at entry to each block, as well as the direction of the analysis, either
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forward or backward. The domain of your dataflow analysis must be a <a href="https://en.wikipedia.org/wiki/Lattice_(order)">lattice</a>
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(strictly speaking a join-semilattice) with a well-behaved <code>join</code> operator. See
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documentation for the <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/lattice/index.html"><code>lattice</code></a> module, as well as the <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/lattice/trait.JoinSemiLattice.html"><code>JoinSemiLattice</code></a>
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trait, for more information.</p>
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<h3 id="transfer-functions-and-effects"><a class="header" href="#transfer-functions-and-effects">Transfer Functions and Effects</a></h3>
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<p>The dataflow framework in <code>rustc</code> allows each statement (and terminator) inside
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a basic block to define its own transfer function. For brevity, these
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individual transfer functions are known as "effects". Each effect is applied
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successively in dataflow order, and together they define the transfer function
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for the entire basic block. It's also possible to define an effect for
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particular outgoing edges of some terminators (e.g.
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<a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/trait.Analysis.html#tymethod.apply_call_return_effect"><code>apply_call_return_effect</code></a> for the <code>success</code> edge of a <code>Call</code>
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terminator). Collectively, these are referred to as "per-edge effects".</p>
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<h3 id="before-effects"><a class="header" href="#before-effects">"Before" Effects</a></h3>
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<p>Observant readers of the documentation may notice that there are actually <em>two</em>
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possible effects for each statement and terminator, the "before" effect and the
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unprefixed (or "primary") effect. The "before" effects are applied immediately
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before the unprefixed effect <strong>regardless of the direction of the analysis</strong>.
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In other words, a backward analysis will apply the "before" effect and then the
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"primary" effect when computing the transfer function for a basic block, just
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like a forward analysis.</p>
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<p>The vast majority of analyses should use only the unprefixed effects: Having
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multiple effects for each statement makes it difficult for consumers to know
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where they should be looking. However, the "before" variants can be useful in
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some scenarios, such as when the effect of the right-hand side of an assignment
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statement must be considered separately from the left-hand side.</p>
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<h3 id="convergence"><a class="header" href="#convergence">Convergence</a></h3>
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<p>Your analysis must converge to "fixpoint", otherwise it will run forever.
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Converging to fixpoint is just another way of saying "reaching equilibrium".
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In order to reach equilibrium, your analysis must obey some laws. One of the
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laws it must obey is that the bottom value<sup class="footnote-reference" id="fr-bottom-purpose-1"><a href="#footnote-bottom-purpose">1</a></sup> joined with some
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other value equals the second value. Or, as an equation:</p>
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<blockquote>
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<p><em>bottom</em> join <em>x</em> = <em>x</em></p>
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</blockquote>
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<p>Another law is that your analysis must have a "top value" such that</p>
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<blockquote>
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<p><em>top</em> join <em>x</em> = <em>top</em></p>
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</blockquote>
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<p>Having a top value ensures that your semilattice has a finite height, and the
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law state above ensures that once the dataflow state reaches top, it will no
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longer change (the fixpoint will be top).</p>
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<h2 id="a-brief-example"><a class="header" href="#a-brief-example">A Brief Example</a></h2>
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<p>This section provides a brief example of a simple data-flow analysis at a high
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level. It doesn't explain everything you need to know, but hopefully it will
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make the rest of this page clearer.</p>
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<p>Let's say we want to do a simple analysis to find if <code>mem::transmute</code> may have
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been called by a certain point in the program. Our analysis domain will just
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be a <code>bool</code> that records whether <code>transmute</code> has been called so far. The bottom
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value will be <code>false</code>, since by default <code>transmute</code> has not been called. The top
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value will be <code>true</code>, since our analysis is done as soon as we determine that
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<code>transmute</code> has been called. Our join operator will just be the boolean OR (<code>||</code>)
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operator. We use OR and not AND because of this case:</p>
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<pre><pre class="playground"><code class="language-rust"><span class="boring">#![allow(unused)]
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</span><span class="boring">fn main() {
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</span><span class="boring">unsafe fn example(some_cond: bool) {
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</span>let x = if some_cond {
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std::mem::transmute::<i32, u32>(0_i32) // transmute was called!
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} else {
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1_u32 // transmute was not called
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};
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// Has transmute been called by this point? We conservatively approximate that
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// as yes, and that is why we use the OR operator.
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println!("x: {}", x);
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<span class="boring">}
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</span><span class="boring">}</span></code></pre></pre>
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<h2 id="inspecting-the-results-of-a-dataflow-analysis"><a class="header" href="#inspecting-the-results-of-a-dataflow-analysis">Inspecting the Results of a Dataflow Analysis</a></h2>
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<p>Once you have constructed an analysis, you must call <code>iterate_to_fixpoint</code>
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which will return a <code>Results</code>, which contains the dataflow state at fixpoint
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upon entry of each block. Once you have a <code>Results</code>, you can inspect the
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dataflow state at fixpoint at any point in the CFG. If you only need the state
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at a few locations (e.g., each <code>Drop</code> terminator) use a <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/struct.ResultsCursor.html"><code>ResultsCursor</code></a>. If
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you need the state at <em>every</em> location, a <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/trait.ResultsVisitor.html"><code>ResultsVisitor</code></a> will be more
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efficient.</p>
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<pre><code class="language-text"> Analysis
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| iterate_to_fixpoint()
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Results
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/ \
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into_results_cursor(…) / \ visit_with(…)
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/ \
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ResultsCursor ResultsVisitor
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</code></pre>
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<p>For example, the following code uses a <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/trait.ResultsVisitor.html"><code>ResultsVisitor</code></a>...</p>
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<pre><code class="language-rust ignore">// Assuming `MyVisitor` implements `ResultsVisitor<FlowState = MyAnalysis::Domain>`...
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let mut my_visitor = MyVisitor::new();
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// inspect the fixpoint state for every location within every block in RPO.
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let results = MyAnalysis::new()
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.iterate_to_fixpoint(tcx, body, None);
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results.visit_with(body, &mut my_visitor);`</code></pre>
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<p>whereas this code uses <a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/struct.ResultsCursor.html"><code>ResultsCursor</code></a>:</p>
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<pre><code class="language-rust ignore">let mut results = MyAnalysis::new()
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.iterate_to_fixpoint(tcx, body, None);
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.into_results_cursor(body);
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// Inspect the fixpoint state immediately before each `Drop` terminator.
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for (bb, block) in body.basic_blocks().iter_enumerated() {
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if let TerminatorKind::Drop { .. } = block.terminator().kind {
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results.seek_before_primary_effect(body.terminator_loc(bb));
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let state = results.get();
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println!("state before drop: {:#?}", state);
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}
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}</code></pre>
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<h3 id="graphviz-diagrams"><a class="header" href="#graphviz-diagrams">Graphviz Diagrams</a></h3>
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<p>When the results of a dataflow analysis are not what you expect, it often helps
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to visualize them. This can be done with the <code>-Z dump-mir</code> flags described in
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<a href="./debugging.html">Debugging MIR</a>. Start with <code>-Z dump-mir=F -Z dump-mir-dataflow</code>, where <code>F</code> is
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either "all" or the name of the MIR body you are interested in.</p>
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<p>These <code>.dot</code> files will be saved in your <code>mir_dump</code> directory and will have the
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<a href="https://doc.rust-lang.org/nightly/nightly-rustc/rustc_mir_dataflow/trait.Analysis.html#associatedconstant.NAME"><code>NAME</code></a> of the analysis (e.g. <code>maybe_inits</code>) as part of their filename. Each
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visualization will display the full dataflow state at entry and exit of each
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block, as well as any changes that occur in each statement and terminator. See
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the example below:</p>
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<p><img src="../img/dataflow-graphviz-example.png" alt="A graphviz diagram for a dataflow analysis" /></p>
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<hr>
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<ol class="footnote-definition"><li id="footnote-bottom-purpose">
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<p>The bottom value's primary purpose is as the initial dataflow
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state. Each basic block's entry state is initialized to bottom before the
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analysis starts. <a href="#fr-bottom-purpose-1">↩</a></p>
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</li>
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</ol>
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