Next: Debugging the Analyzer, Up: Static Analyzer [Contents][Index]

### 27.1 Analyzer Internals

#### 27.1.1 Overview

At a high-level, we’re doing coverage-guided symbolic execution of the user’s code.

The analyzer implementation works on the gimple-SSA representation. (I chose this in the hopes of making it easy to work with LTO to do whole-program analysis).

The implementation is read-only: it doesn’t attempt to change anything, just emit warnings.

The gimple representation can be seen using `-fdump-ipa-analyzer`.

> Tip: If the analyzer ICEs before this is written out, one workaround is to use `--param=analyzer-bb-explosion-factor=0` to force the analyzer to bail out after analyzing the first basic block.

First, we build a `supergraph` which combines the callgraph and all of the CFGs into a single directed graph, with both interprocedural and intraprocedural edges. The nodes and edges in the supergraph are called “supernodes” and “superedges”, and often referred to in code as `snodes` and `sedges`. Basic blocks in the CFGs are split at interprocedural calls, so there can be more than one supernode per basic block. Most statements will be in just one supernode, but a call statement can appear in two supernodes: at the end of one for the call, and again at the start of another for the return.

The supergraph can be seen using `-fdump-analyzer-supergraph`.

We then build an `analysis_plan` which walks the callgraph to determine which calls might be suitable for being summarized (rather than fully explored) and thus in what order to explore the functions.

Next is the heart of the analyzer: we use a worklist to explore state within the supergraph, building an "exploded graph". Nodes in the exploded graph correspond to <point, state> pairs, as in "Precise Interprocedural Dataflow Analysis via Graph Reachability" (Thomas Reps, Susan Horwitz and Mooly Sagiv) - but note that we’re not using the algorithm described in that paper, just the “exploded graph” terminology.

We reuse nodes for <point, state> pairs we’ve already seen, and avoid tracking state too closely, so that (hopefully) we rapidly converge on a final exploded graph, and terminate the analysis. We also bail out if the number of exploded <end-of-basic-block, state> nodes gets larger than a particular multiple of the total number of basic blocks (to ensure termination in the face of pathological state-explosion cases, or bugs). We also stop exploring a point once we hit a limit of states for that point.

We can identify problems directly when processing a <point, state> instance. For example, if we’re finding the successors of

       <point: before-stmt: "free (ptr);",
        state: {"ptr": freed}>

then we can detect a double-free of "ptr". We can then emit a path to reach the problem by finding the simplest route through the graph.

Program points in the analysis are much more fine-grained than in the CFG and supergraph, with points (and thus potentially exploded nodes) for various events, including before individual statements. By default the exploded graph merges multiple consecutive statements in a supernode into one exploded edge to minimize the size of the exploded graph. This can be suppressed via `-fanalyzer-fine-grained`. The fine-grained approach seems to make things simpler and more debuggable that other approaches I tried, in that each point is responsible for one thing.

Program points in the analysis also have a "call string" identifying the stack of callsites below them, so that paths in the exploded graph correspond to interprocedurally valid paths: we always return to the correct call site, propagating state information accordingly. We avoid infinite recursion by stopping the analysis if a callsite appears more than `analyzer-max-recursion-depth` in a callstring (defaulting to 2).

#### 27.1.2 Graphs

Nodes and edges in the exploded graph are called “exploded nodes” and “exploded edges” and often referred to in the code as `enodes` and `eedges` (especially when distinguishing them from the `snodes` and `sedges` in the supergraph).

Each graph numbers its nodes, giving unique identifiers - supernodes are referred to throughout dumps in the form ‘`SN': index`’ and exploded nodes in the form ‘`EN: index`’ (e.g. ‘`SN: 2`’ and ‘`EN:29`’).

The supergraph can be seen using `-fdump-analyzer-supergraph-graph`.

The exploded graph can be seen using `-fdump-analyzer-exploded-graph` and other dump options. Exploded nodes are color-coded in the .dot output based on state-machine states to make it easier to see state changes at a glance.

#### 27.1.3 State Tracking

There’s a tension between:

- precision of analysis in the straight-line case, vs
- exponential blow-up in the face of control flow.

For example, in general, given this CFG:

          A
         / \
        B   C
         \ /
          D
         / \
        E   F
         \ /
          G

we want to avoid differences in state-tracking in B and C from leading to blow-up. If we don’t prevent state blowup, we end up with exponential growth of the exploded graph like this:

               1:A
              /   \
             /     \
            /       \
          2:B       3:C
           |         |
          4:D       5:D        (2 exploded nodes for D)
         /   \     /   \
       6:E   7:F 8:E   9:F
        |     |   |     |
       10:G 11:G 12:G  13:G    (4 exploded nodes for G)

Similar issues arise with loops.

To prevent this, we follow various approaches:

1. state pruning: which tries to discard state that won’t be relevant later on withing the function. This can be disabled via `-fno-analyzer-state-purge`.
2. state merging. We can try to find the commonality between two program_state instances to make a third, simpler program_state. We have two strategies here:
   1. the worklist keeps new nodes for the same program_point together, and tries to merge them before processing, and thus before they have successors. Hence, in the above, the two nodes for D (4 and 5) reach the front of the worklist together, and we create a node for D with the merger of the incoming states.
   2. try merging with the state of existing enodes for the program_point (which may have already been explored). There will be duplication, but only one set of duplication; subsequent duplicates are more likely to hit the cache. In particular, (hopefully) all merger chains are finite, and so we guarantee termination. This is intended to help with loops: we ought to explore the first iteration, and then have a "subsequent iterations" exploration, which uses a state merged from that of the first, to be more abstract.

   We avoid merging pairs of states that have state-machine differences, as these are the kinds of differences that are likely to be most interesting. So, for example, given:

             if (condition)
               ptr = malloc (size);
             else
               ptr = local_buf;

             .... do things with 'ptr'

             if (condition)
               free (ptr);

             ...etc

   then we end up with an exploded graph that looks like this:

                          if (condition)
                            / T      \ F
                   ---------          ----------
                  /                             \
             ptr = malloc (size)             ptr = local_buf
                 |                               |
             copy of                         copy of
               "do things with 'ptr'"          "do things with 'ptr'"
             with ptr: heap-allocated        with ptr: stack-allocated
                 |                               |
             if (condition)                  if (condition)
                 | known to be T                 | known to be F
             free (ptr);                         |
                  \                             /
                   -----------------------------
                                | ('ptr' is pruned, so states can be merged)
                               etc

   where some duplication has occurred, but only for the places where the the different paths are worth exploringly separately.

   Merging can be disabled via `-fno-analyzer-state-merge`.

#### 27.1.4 Region Model

Part of the state stored at a `exploded_node` is a `region_model`. This is an implementation of the region-based ternary model described in "A Memory Model for Static Analysis of C Programs" (Zhongxing Xu, Ted Kremenek, and Jian Zhang).

A `region_model` encapsulates a representation of the state of memory, with a `store` recording a binding between `region` instances, to `svalue` instances. The bindings are organized into clusters, where regions accessible via well-defined pointer arithmetic are in the same cluster. The representation is graph-like because values can be pointers to regions. It also stores a constraint_manager, capturing relationships between the values.

Because each node in the `exploded_graph` has a `region_model`, and each of the latter is graph-like, the `exploded_graph` is in some ways a graph of graphs.

Here’s an example of printing a `program_state`, showing the `region_model` within it, along with state for the `malloc` state machine.

    (gdb) call debug (*this)
    rmodel:
    stack depth: 1
      frame (index 0): frame: ‘test’@1
    clusters within frame: ‘test’@1
      cluster for: ptr_3: &HEAP_ALLOCATED_REGION(12)
    m_called_unknown_fn: FALSE
    constraint_manager:
      equiv classes:
      constraints:
    malloc:
      0x2e89590: &HEAP_ALLOCATED_REGION(12): unchecked ('ptr_3')

This is the state at the point of returning from `calls_malloc` back to `test` in the following:

    void *
    calls_malloc (void)
    {
      void *result = malloc (1024);
      return result;
    }

    void test (void)
    {
      void *ptr = calls_malloc ();
      /* etc.  */
    }

Within the store, there is the cluster for `ptr_3` within the frame for `test`, where the whole cluster is bound to a pointer value, pointing at `HEAP_ALLOCATED_REGION(12)`. Additionally, this pointer has the `unchecked` state for the `malloc` state machine indicating it hasn’t yet been checked against NULL since the allocation call.

#### 27.1.5 Analyzer Paths

We need to explain to the user what the problem is, and to persuade them that there really is a problem. Hence having a `diagnostic_path` isn’t just an incidental detail of the analyzer; it’s required.

Paths ought to be:

- interprocedurally-valid
- feasible

Without state-merging, all paths in the exploded graph are feasible (in terms of constraints being satisfied). With state-merging, paths in the exploded graph can be infeasible.

We collate warnings and only emit them for the simplest path e.g. for a bug in a utility function, with lots of routes to calling it, we only emit the simplest path (which could be intraprocedural, if it can be reproduced without a caller).

We thus want to find the shortest feasible path through the exploded graph from the origin to the exploded node at which the diagnostic was saved. Unfortunately, if we simply find the shortest such path and check if it’s feasible we might falsely reject the diagnostic, as there might be a longer path that is feasible. Examples include the cases where the diagnostic requires us to go at least once around a loop for a later condition to be satisfied, or where for a later condition to be satisfied we need to enter a suite of code that the simpler path skips.

We attempt to find the shortest feasible path to each diagnostic by first constructing a “trimmed graph” from the exploded graph, containing only those nodes and edges from which there are paths to the target node, and using Dijkstra’s algorithm to order the trimmed nodes by minimal distance to the target.

We then use a worklist to iteratively build a “feasible graph” (actually a tree), capturing the pertinent state along each path, in which every path to a “feasible node” is feasible by construction, restricting ourselves to the trimmed graph to ensure we stay on target, and ordering the worklist so that the first feasible path we find to the target node is the shortest possible path. Hence we start by trying the shortest possible path, but if that fails, we explore progressively longer paths, eventually trying iterations through loops. The exploration is captured in the feasible_graph, which can be dumped as a .dot file via `-fdump-analyzer-feasibility` to visualize the exploration. The indices of the feasible nodes show the order in which they were created. We effectively explore the tree of feasible paths in order of shortest path until we either find a feasible path to the target node, or hit a limit and give up.

This is something of a brute-force approach, but the trimmed graph hopefully keeps the complexity manageable.

This algorithm can be disabled (for debugging purposes) via `-fno-analyzer-feasibility`, which simply uses the shortest path, and notes if it is infeasible.

The above gives us a shortest feasible `exploded_path` through the `exploded_graph` (a list of `exploded_edge *`). We use this `exploded_path` to build a `diagnostic_path` (a list of events for the diagnostic subsystem) - specifically a `checker_path`.

Having built the `checker_path`, we prune it to try to eliminate events that aren’t relevant, to minimize how much the user has to read.

After pruning, we notify each event in the path of its ID and record the IDs of interesting events, allowing for events to refer to other events in their descriptions. The `pending_diagnostic` class has various vfuncs to support emitting more precise descriptions, so that e.g.

- a deref-of-unchecked-malloc diagnostic might use:

        returning possibly-NULL pointer to 'make_obj' from 'allocator'

  for a `return_event` to make it clearer how the unchecked value moves from callee back to caller

- a double-free diagnostic might use:

        second 'free' here; first 'free' was at (3)

  and a use-after-free might use

        use after 'free' here; memory was freed at (2)

At this point we can emit the diagnostic.

#### 27.1.6 Limitations

- Only for C so far
- The implementation of call summaries is currently very simplistic.
- Lack of function pointer analysis
- The constraint-handling code assumes reflexivity in some places (that values are equal to themselves), which is not the case for NaN. As a simple workaround, constraints on floating-point values are currently ignored.
- There are various other limitations in the region model (grep for TODO/xfail in the testsuite).
- The constraint_manager’s implementation of transitivity is currently too expensive to enable by default and so must be manually enabled via `-fanalyzer-transitivity`).
- The checkers are currently hardcoded and don’t allow for user extensibility (e.g. adding allocate/release pairs).
- Although the analyzer’s test suite has a proof-of-concept test case for LTO, LTO support hasn’t had extensive testing. There are various lang-specific things in the analyzer that assume C rather than LTO. For example, SSA names are printed to the user in “raw” form, rather than printing the underlying variable name.

Next: Debugging the Analyzer, Up: Static Analyzer [Contents][Index]