Section: New Results

Specifying multi-clock Lustre programs

Participants : Timothy Bourke, Guillaume Iooss, Baptiste Pauget, Marc Pouzet.

It is sometimes desirable to compile a single synchronous language program into multiple tasks for execution by a real-time operating system. We have been investigating this question from three different perspectives.

Harmonic clocks

We studied the extension of a synchronous language with periodic harmonic clocks based on the work of Mandel et al. [31], [37], [32], [35], [36] on n-synchrony and the extension proposed by Forget et al. [33]

Mandel et al. considered a language with periodic clocks expressed as ultimately periodic binary sequences. The decision procedures (equality, inclusion, precedence) for such an expressive language can be very costly. It is thus sometimes useful to apply an envelope-based abstraction, that is, one where sets of clocks are represented by a rational slope and an interval. Forget considered simpler “harmonic” clocks. His decision procedures conincide with those for the envelope-based abstraction but without any loss of information. During his M2 ineternship, B. Pauget continued this line of work by extending the input language of the Vélus Lustre compiler with harmonic clocks. This work was the starting point for the proposal of a new intermediate language for a synchronous compiler that is capable of exploiting clock information to apply agressive optimizations and generate parallel code.

New Intermediate Language MObc (Multi Object Code)

This intermediate language is reminiscent of the intermediate Obc language used in the Vélus and Heptagon compiler, but with some important differences and new features. MObc permits a synchronous function to be represented as a set of named state variables and possibly nested blocks with a partial ordering which express the way blocks can and must be called. In comparison, Obc represents a synchronous function as a set of state variables and a transition function that is itself written in a sequential language. Each block comprises a set of equations in Single Static Assignment (SSA) form, that is, exactly one equation per variable, so as to simplify the implementation of a number of classic optimizations (for example, constant propagation, inlining, common sub-expression elimination, code specialisation). Then, every block is translated into a step function (e.g., a C function). This intermediate language has been designed to facilitate the generation of code for a real-time OS and a multi-core target. This work exploits two older results: the article of Caspi et al. [30] that introduces an object representation for synchronous nodes and a “scheduling policy” that specifies how their methods may be called, and; the work of Pouzet et al. [38] on the calculation of input/output relations to merge calculations. We are preparing and article on this subject.

Clocking constraints, communication latencies, and constraint solving

In this approach, the top-level node of a Lustre program is distinguished from inner nodes. It may contain special annotations to specify the triggering and other details of node instances from which separate “tasks” are to be generated. Special operators are introduced to describe the buffering between top-level instances. Notably, different forms of the fby and current operators are provided. Some of the operators are under-specified and a constraint solver is used to determine their exact meaning, that is, whether the signal is delayed by zero, one, or more cycles of the receiving clock, which depends on the scheduling of the source and destination nodes. Scheduling is formalized as a constraint solving problem based on latency constraints between some pairs of input/outputs that are specified by the designer. G. Iooss has been prototyping these ideas in the academic Heptagon compiler.

This work is funded by a direct industrial contract with Airbus. In collaboration (this year) with Michel Angot Vincent Bregeon Jean Souyris (Airbus, R&D) and Matthieu Boitrel (Airbus BE).