Generic access to symbolic computing services

Symbolic computation is one of the computational domains that requires large computational resources. Computer Algebra Systems (CAS), the main tools used for symbolic computations, are mainly designed to be used as software tools installed on standalone machines that do not provide the required resources for solving large symbolic computation problems. In order to support symbolic computations an infrastructure built upon massively distributed computational environments must be developed. Building an infrastructure for symbolic computations requires a thorough analysis of the most important requirements raised by the symbolic computation world and must be built based on the most suitable architectural styles and technologies. The architecture that we propose is composed of several main components: the Computer Algebra System (CAS) Server that exposes the functionality implemented by one or more supporting CASs through generic interfaces of Grid Services; the Architecture for Grid Symbolic Services Orchestration (AGSSO) Server that allows seamless composition of CAS Server capabilities; and client side libraries to assist the users in describing workflows for symbolic computations directly within the CAS environment. We have also designed and developed a framework for automatic data management of mathematical content that relies on OpenMath encoding. To support the validation and fine tuning of the system we have developed a simulation platform that mimics the environment on which the architecture is deployed

High-Performance Computer Algebra: A Hecke Algebra Case Study

We describe the first ever parallelisation of an algebraic computation at modern HPC scale. Our case study poses challenges typical of the domain: it is a multi-phase application with dynamic task creation and irregular parallelism over complex control and data structures. Our starting point is a sequential algorithm for finding invariant bilinear forms in the representation theory of Hecke algebras, implemented in the GAP computational group theory system. After optimising the sequential code we develop a parallel algorithm that exploits the new skeleton-based SGP2 framework to parallelise the three most computationally-intensive phases. To this end we develop a new domain-specific skeleton, parBufferTryReduce. We report good parallel performance both on a commodity cluster and on a national HPC, delivering speedups up to 548 over the optimised sequential implementation on 1024 cores

Transparent fault tolerance for scalable functional computation

Reliability is set to become a major concern on emergent large-scale architectures. While there are many parallel languages, and indeed many parallel functional languages, very few address reliability. The notable exception is the widely emulated Erlang distributed actor model that provides explicit supervision and recovery of actors with isolated state. We investigate scalable transparent fault tolerant functional computation with automatic supervision and recovery of tasks. We do so by developing HdpH-RS, a variant of the Haskell distributed parallel Haskell (HdpH) DSL with Reliable Scheduling. Extending the distributed work stealing protocol of HdpH for task supervision and recovery is challenging. To eliminate elusive concurrency bugs, we validate the HdpH-RS work stealing protocol using the SPIN model checker. HdpH-RS differs from the actor model in that its principal entities are tasks, i.e. independent stateless computations, rather than isolated stateful actors. Thanks to statelessness, fault recovery can be performed automatically and entirely hidden in the HdpH-RS runtime system. Statelessness is also key for proving a crucial property of the semantics of HdpH-RS: fault recovery does not change the result of the program, akin to deterministic parallelism. HdpH-RS provides a simple distributed fork/join-style programming model, with minimal exposure of fault tolerance at the language level, and a library of higher level abstractions such as algorithmic skeletons. In fact, the HdpH-RS DSL is exactly the same as the HdpH DSL, hence users can opt in or out of fault tolerant execution without any refactoring. Computations in HdpH-RS are always as reliable as the root node, no matter how many nodes and cores are actually used. We benchmark HdpH-RS on conventional clusters and an HPC platform: all benchmarks survive Chaos Monkey random fault injection; the system scales well e.g. up to 1,400 cores on the HPC; reliability and recovery overheads are consistently low even at scale

Reliable massively parallel symbolic computing : fault tolerance for a distributed Haskell

As the number of cores in manycore systems grows exponentially, the number of failures is also predicted to grow exponentially. Hence massively parallel computations must be able to tolerate faults. Moreover new approaches to language design and system architecture are needed to address the resilience of massively parallel heterogeneous architectures. Symbolic computation has underpinned key advances in Mathematics and Computer Science, for example in number theory, cryptography, and coding theory. Computer algebra software systems facilitate symbolic mathematics. Developing these at scale has its own distinctive set of challenges, as symbolic algorithms tend to employ complex irregular data and control structures. SymGridParII is a middleware for parallel symbolic computing on massively parallel High Performance Computing platforms. A key element of SymGridParII is a domain specific language (DSL) called Haskell Distributed Parallel Haskell (HdpH). It is explicitly designed for scalable distributed-memory parallelism, and employs work stealing to load balance dynamically generated irregular task sizes. To investigate providing scalable fault tolerant symbolic computation we design, implement and evaluate a reliable version of HdpH, HdpH-RS. Its reliable scheduler detects and handles faults, using task replication as a key recovery strategy. The scheduler supports load balancing with a fault tolerant work stealing protocol. The reliable scheduler is invoked with two fault tolerance primitives for implicit and explicit work placement, and 10 fault tolerant parallel skeletons that encapsulate common parallel programming patterns. The user is oblivious to many failures, they are instead handled by the scheduler. An operational semantics describes small-step reductions on states. A simple abstract machine for scheduling transitions and task evaluation is presented. It defines the semantics of supervised futures, and the transition rules for recovering tasks in the presence of failure. The transition rules are demonstrated with a fault-free execution, and three executions that recover from faults. The fault tolerant work stealing has been abstracted in to a Promela model. The SPIN model checker is used to exhaustively search the intersection of states in this automaton to validate a key resiliency property of the protocol. It asserts that an initially empty supervised future on the supervisor node will eventually be full in the presence of all possible combinations of failures. The performance of HdpH-RS is measured using five benchmarks. Supervised scheduling achieves a speedup of 757 with explicit task placement and 340 with lazy work stealing when executing Summatory Liouville up to 1400 cores of a HPC architecture. Moreover, supervision overheads are consistently low scaling up to 1400 cores. Low recovery overheads are observed in the presence of frequent failure when lazy on-demand work stealing is used. A Chaos Monkey mechanism has been developed for stress testing resiliency with random failure combinations. All unit tests pass in the presence of random failure, terminating with the expected results