LACS: A Language for Affine Communication Structures

We propose a language which provides a uniied notation for specifying parallel assignment, communication and reduction operations in massively parallel programs. It is designed around a Parallel Assignment Statement (PAS), and Atomic Communication Events (ACE's), and can be used to describe most common communication libraries like 1-to-1 transfer, broadcast, personalized communication, reduce, scans, etc., as APL-style one-liners. LACS uses convex polyhedra and aane transformations, and hence, tools from linear algebra can be used for compile time analysis. We can automatically detect when a PAS in LACS is well formed, has write connicts, etc. We can also detect the presence of communication activities like scatters, reduces, scans, and their generalizations. R esum e : On propose un langage qui donne une notation uniforme pour sp eciier des aaectations parall eles et des op erations de communication et de r eduction dans les programmes massivement parall eles. Il est construit autour d'une instruction d'aaectation parall ele (PAS), et d' ev enements atomiques de communication (ACE). En LACS, on peut exprimer la majorit e les op erations de communication les plus fr equentes en une seule ligne (comme en APL) : `1-to-1 transfer', diiusion, `personalized communication', r eduction, `scans', etc. LACS utilise des poly edres conv exes et des transformations aanes, et il est donc possible d'utiliser les outils de l'alg ebre lin eaire pour l'analyse statique. On peut d etecter automatiquement quand une PAS est bien form ee, a des connits d' ecritures, etc. On peut aussi d etecter automatiquement la pr esence d'activit es de communication comme des`scatters', r eduction, `scans' et leur g eneralizationes. Consider the problem of specifying communication activity in massively parallel programs (data parallel, nested loop and/or single assignment). Our principal data structure is the multidimensional array, so we have data variables such as X, Y etc. To access them, we have index variables such as i, j, etc. A data variable may be accessed only by constructing an appropriate index expression|an aane combination (i.e., linear combinations plus a constant) of index variables. An Atomic Communication Event (ACE) is speciied with a source, a destination, and a transfer operator, =>. We can have multiple destinations (broadcast), and/or multiple sources (reduction). All this is a single ACE. We specify collections of simultaneous ACE's as a Parallel Assignment Statement (PAS). The only way to specify \collections" (both for multiple sources and destinations, and for the ACE's that make up …