Section: Research Program

Expressivity and Scalability of Static Analyses

The design and implementation of efficient compilers becomes more difficult each day, as they need to bridge the gap between complex languages and complex architectures. Application developers use languages that bring them close to the problem that they need to solve which explains the importance of high-level programming languages. However, high-level programming languages tend to become more distant from the hardware which they are meant to command.

In this research direction, we propose to design expressive and scalable static analyses for compilers. This topic is closely linked to Sections 3.1 and 3.3 since the design of an efficient intermediate representation is made while regarding the analyses it enables. The intermediate representation should be expressive enough to embed maximal information; however if the representation is too complex the design of scalable analyses will be harder.

The analyses we plan to design in this activity will of course be mainly driven by the HPC dataflow optimizations we mentioned in the preceding sections; however we will also target other kinds of analyses applicable to more general purpose programs. We will thus consider two main directions:

• Extend the applicability of the polyhedral model, in order to deal with HPC applications that do not fit totally in this category. More specifically, we plan to work on more complex control and also on complex data structures, like sparse matrices, which are heavily used in HPC.

• Design of specialized static analyses for memory diagnostic and optimization inside general purpose compilers.

For both activities, we plan to cross fertilize ideas coming from the abstract interpretation community as well as language design, dataflow semantics, and WCET estimation techniques.

Correct by construction analyses. The design of well-defined semantics for the chosen programming language and intermediate representation will allow us to show the correctness of our analyses. The precise study of the semantics of Section 3.1 will allow us to adapt the analysis to the characteristics of the language, and prove that such an adaptation is well founded. This approach will be applicable both on the source language and on the intermediate representation.

Such wellfoundedness criteria relatively to the language semantics will first be used to design our analyses, and then to study which extensions of the languages can be envisioned and analyzed safely, and which extensions (if any) are difficult to analyze and should be avoided. Here the correct identification of a core language for our formal studies (see Section 3.1) will play a crucial role as the core language should feature all the characteristics that might make the analysis difficult or incorrect.

Scalable abstract domains. We already have experience in designing low-cost semi relational abstract domains for pointers [44], [42], as well as tailoring static analyses for specialized applications in compilation [30], [50], Synchronous Dataflow scheduling [49], and extending the polyhedral model to irregular applications [15]. We also have experience in the design of various static verification techniques adapted to different programming paradigms.

Expected impact

The impact of this work is the significantly widened applicability of various tools/compilers related to parallelization: allow optimizations for a larger class of programs, and allow low-cost analysis that scale to very large programs.

We target both analysis for optimization and analysis to detect, or prove the absence of bugs.

Scientific Program

Short-term and ongoing activities.

Together with Paul Iannetta and Lionel Morel (INSA/CEA LETI), we are currently working on the semantic rephrasing of the polyhedral model  [34]. The objective is to clearly redefine the key notions of the polyhedral model on general flowchart programs operating on arrays, lists and trees. We reformulate the algorithms that are performed to compute dependencies in a more semantic fashion, i.e. considering the program semantics instead of syntactical criteria. The next step is to express classical scheduling and code generation activities in this framework, in order to overcome the classical syntactic restrictions of the polyhedral model.

Medium-term activities.

In medium term, we want to extend the polyhedral model for more general data-structures like lists and sparse matrices. For that purpose, we need to find polyhedral (or other shapes) abstractions for non-array data-structures; the main difficulty is to deal with non-linearity and/or partial information (namely, over-approximations of the data layout, or over-approximation of the program behavior). This activity will rely on a formalization of the optimization activities (dependency computation, scheduling, compilation) in a more general Abstract-Interpretation based framework in order to make the approximations explicit.

At the same time, we plan to continue to work on scaling static analyses for general purpose programs, in the spirit of Maroua Maalej's PhD  [41], whose contribution is a sequence of memory analyses inside production compilers. We already began a collaboration with Sylvain Collange (PACAP team of IRISA Laboratory) on the design of static analyses to optimize copies from the global memory of a GPU to the block kernels (to increase locality). In particular, we have the objective to design specialized analyses but with an explicit notion of cost/precision compromise, in the spirit of the paper  [36] that tries to formalize the cost/precision compromise of interprocedural analyses with respect to a “context sensitivity parameter”.

Long-term activities.

In a longer-term vision, the work on scalable static analyses, whether or not directed from the dataflow activities, will be pursued in the direction of large general-purpose programs.

An ambitious challenge is to find a generic way of adapting existing (relational) abstract domains within the Single Static Information  [20] framework so as to improve their scalability. With this framework, we would be able to design static analyses, in the spirit of the seminal paper  [25] which gave a theoretical scheme for classical abstract interpretation analyses.

We also plan to work on the interface between the analyses and their optimization clients inside production compilers.