Pointer analysis

For the following example program, a points-to analysis would compute that the points-to set of p is {x, y}.

int x;
int y;
int* p = unknown() ? &x : &y;

As a form of static analysis, fully precise pointer analysis can be shown to be undecidable.[1] Most approaches are sound, but range widely in performance and precision. Many design decisions impact both the precision and performance of an analysis; often (but not always) lower precision yields higher performance. These choices include:[2][3]

• Field sensitivity (also known as structure sensitivity): An analysis can either treat each field of a struct or object separately, or merge them.
• Array sensitivity: An array-sensitive pointer analysis models each index in an array separately. Other choices include modelling just the first entry separately and the rest together, or merging all array entries.
• Context sensitivity or polyvariance: Pointer analyses may qualify points-to information with a summary of the control flow leading to each program point.
• Flow sensitivity: An analysis can model the impact of intraprocedural control flow on points-to facts.
• Heap modeling: Run-time allocations may be abstracted by:
  • their allocation sites (the statement or instruction that performs the allocation, e.g., a call to malloc or an object constructor),
  • a more complex model based on a shape analysis,
  • the type of the allocation, or
  • one single allocation (this is called heap-insensitivity).
• Heap cloning: Heap- and context-sensitive analyses may further qualify each allocation site by a summary of the control flow leading to the instruction or statement performing the allocation.
• Subset constraints or equality constraints: When propagating points-to facts, different program statements may induce different constraints on a variable's points-to sets. Equality constraints (like those used in Steensgaard's algorithm) can be tracked with a union-find data structure, leading to high performance at the expense of the precision of a subset-constraint based analysis (e.g., Andersen's algorithm).

Pointer analysis algorithms are used to convert collected raw pointer usages (assignments of one pointer to another or assigning a pointer to point to another one) to a useful graph of what each pointer can point to.[4]

Steensgaard's algorithm and Andersen's algorithm are common context-insensitive, flow-insensitive algorithms for pointer analysis. They are often used in compilers, and have implementations in the LLVM codebase.

Many approaches to flow-insensitive pointer analysis can be understood as forms of abstract interpretation, where heap allocations are abstracted by their allocation site (i.e., a program location).[5]

Flow-insensitive pointer analyses often abstract possible runtime allocations by their allocation site. At runtime, this program creates three separate heap allocations. A flow-insensitive pointer analysis would treat these as a single abstract memory location, leading to a loss of precision.

Many flow-insensitive algorithms are specified in Datalog, including those in the Soot analysis framework for Java.[6]

Context-sensitive, flow-sensitive algorithms achieve higher precision, generally at the cost of some performance, by analyzing each procedure several times, once per context.[7] Most analyses use a "context-string" approach, where contexts consist of a list of entries (common choices of context entry include call sites, allocation sites, and types).[8] To ensure termination (and more generally, scalability), such analyses generally use a k-limiting approach, where the context has a fixed maximum size, and the least recently added elements are removed as needed.[9] Three common variants of context-sensitive, flow-insensitive analysis are:[10]

• Call-site sensitivity
• Object sensitivity
• Type sensitivity

int *id(int* x) {
  return x;
}
int main() {
  int y;
  int z;
  int *y2 = id(&y); // call-site 1
  int *z2 = id(&z); // call-site 2
  return 0;
}

• Zyrianov, Vlas; Newman, Christian D.; Guarnera, Drew T.; Collard, Michael L.; Maletic, Jonathan I. (2019). "srcPtr: A Framework for Implementing Static Pointer Analysis Approaches" (PDF). ICPC '19: Proceedings of the 27th IEEE International Conference on Program Comprehension. Montreal, Canada: IEEE.
• Smaragdakis, Yannis; Balatsouras, George (2015). "Pointer Analysis" (PDF). Foundations and Trends in Programming Languages. 2 (1): 1–69. doi:10.1561/2500000014. Retrieved May 30, 2019.
• Li, Yue; Tan/, Tian; Møller, Anders; Smaragdakis, Yannis (2020-05-18). "A Principled Approach to Selective Context Sensitivity for Pointer Analysis". ACM Transactions on Programming Languages and Systems. 42 (2): 10:1–10:40. doi:10.1145/3381915. ISSN 0164-0925. S2CID 214812357.
• Michael Hind (2001). "Pointer analysis: haven't we solved this problem yet?" (PDF). PASTE '01: Proceedings of the 2001 ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering. ACM. pp. 54–61. ISBN 1-58113-413-4.
• Steensgaard, Bjarne (1996). "Points-to analysis in almost linear time" (PDF). POPL '96: Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages. New York, NY, USA: ACM. pp. 32–41. doi:10.1145/237721.237727. ISBN 0-89791-769-3.
• Andersen, Lars Ole (1994). Program Analysis and Specialization for the C Programming Language (PDF) (PhD thesis).