Reliable scalable symbolic computation: The design of SymGridPar2

Abstract

Symbolic computation is an important area of both Mathematics and Computer Science, with many large computations that would benefit from parallel execution. Symbolic computations are, however, challenging to parallelise as they have complex data and control structures, and both dynamic and highly irregular parallelism. The SymGridPar framework (SGP) has been developed to address these challenges on small-scale parallel architectures. However the multicore revolution means that the number of cores and the number of failures are growing exponentially, and that the communication topology is becoming increasingly complex. Hence an improved parallel symbolic computation framework is required.This paper presents the design and initial evaluation of SymGridPar2 (SGP2), a successor to SymGridPar that is designed to provide scalability onto 10 5 cores, and hence also provide fault tolerance. We present the SGP2 design goals, principles and architecture. We describe how scalability is achieved using layering and by allowing the programmer to control task placement. We outline how fault tolerance is provided by supervising remote computations, and outline higher-level fault tolerance abstractions.We describe the SGP2 implementation status and development plans. We report the scalability and efficiency, including weak scaling to about 32,000 cores, and investigate the overheads of tolerating faults for simple symbolic computations.

High-Performance Computer Algebra: A Hecke Algebra Case Study

“…In related and ongoing work we report good performance results for small algebraic kernels on far larger HPC configurations, e. g. weak scaling of the sumEuler kernel (summing up Euler's ϕ function over large intervals) on up to 32K HECToR cores [20]. Core failures are predicted to rise along with the number of cores.…”

“…Hence the sequential GAP 4.6 instances are coordinated over the network by a distributed middleware, the SymGridPar2 (SGP2) framework [20]. The middleware occupies one core per multicore node and controls (via a RPC-like protocol) independent GAP 4.6 instances running on the remaining cores ( Figure 1).…”

“…This combination of characteristics means that symbolic computations are not well suited to conventional HPC paradigms with their emphasis on iteration over floating point arrays, and has motivated the development of scalable domain-specific scheduling and management frameworks like SymGrid-Par [16] and SymGridPar2 (SGP2) [20].…”

HPC‐GAP: engineering a 21st‐century high‐performance computer algebra system

“…Many basic SGP2 skeletons, for instance parGAPCalls, rely on HdpH work stealing, typically without imposing constraints on work stealing distances; we refer to [4] for examples of SGP2 skeletons that make use of radii for bounding work stealing. On-demand random task placement performs well with irregular parallelism.…”

“…SGP2 offers a number of skeletons implementing such a two-level task distribution, for example, the parMap2Level and parMap2LevelRelaxed skeletons used in Section 5.3, and detailed in [4].…”