Section: New Results

Automatic Distribution of Synchronous Programs

Participants : Gwenaël Delaval [contact person] , Alain Girault, Gregor Goessler, Xavier Nicollin, Gideon Smeding.

Modular distribution

Synchronous programming languages describe functionally centralized systems, where every value, input, output, or function is always directly available for every operation. However, most embedded systems are nowadays composed of several computing resources. The aim of this work is to provide a language-oriented solution to describe functionally distributed reactive systems. This research is conducted within the Inria large scale action Synchronics and is a joint work with Marc Pouzet (ENS, Parkas team from Rocquencourt) and Xavier Nicollin (Grenoble INP, Verimag lab).

We are working on type systems to formalize, in a uniform way, both the clock calculus and the location calculus of a synchronous data-flow programming language (the Heptagon language, inspired from Lucid Synchrone [38] ). On one hand, the clock calculus infers the clock of each variable in the program and checks the clock consistency: e.g., a time-homogeneous function, like + , should be applied to variables with identical clocks. On the other hand, the location calculus infers the spatial distribution of computations and checks the spatial consistency: e.g., a centralized operator, like + , should be applied to variables located at the same location. Compared to the PhD of Gwenaël Delaval [48] , [49] , the goal is to achieve modular distribution. By modular, we mean that we want to compile each function of the program into a single function capable of running on any computing location. We make use of our uniform type system to express the computing locations as first-class abstract types, exactly like clocks, which allows us to compile a typed variable (typed by both the clock and the location calculi) into if ... then ... else ... structures, whose conditions will be valuations of the clock and location variables.

We currently work on an example of software-defined radio. We have shown on this example how to use a modified clock calculus to describe the localisation of values as clocks, and the architecture as clocks (for the computing resources) and their relations (for communication links).

Distribution of synchronous programs under real-time constraints

With the objective to distribute synchronous data-flow programs (e.g., Lustre ) over GALS architectures, such that the difference between the original and synchronous systems satisfy given bounds, we have developed a quantitative clock calculus to (1) describe timing properties of the architecture's clock domain, and (2) describe the acceptable difference between the original and distributed programs. The clock calculus is inspired by the network calculus [67] , with the difference that clocks are described only with respect to one-another, not with respect to real-time.

As a first result, we have applied our clock calculus to analyze the properties of periodic synchronous data-flow programs executed on a network of processors. Because our clock calculus is relational, it can model and preserve correlated variations of streams. In particular, the common case of a data-flow system that splits a stream for separate treatment, and joins them afterwards, this analysis yields more precise result than comparable methods [24] .

We have been able to use the clock calculus as an abstract domain to perform abstract interpretation of synchronous boolean data-flow programs and their distribution on synchronous nodes that communicate asynchronously by sampling shared memory. The analysis discovers the relative clock drift of all clocks of the distributed system as well as bounds on the distance from the original program.

In case the guaranteed maximal distance is too large, we provide methods to synthesize bounds on the relative drift of the architecture's clocks that ensure an acceptable distance. Given the synthesized bounds, we use the known clock drifts and program behavior to synthesize light weight protocols.