Hierarchical Parallelisation of Functional Renormalisation Group Calculations -- hp-fRG

The functional renormalisation group (fRG) has evolved into a versatile tool in condensed matter theory for studying important aspects of correlated electron systems. Practical applications of the method often involve a high numerical effort, motivating the question in how far High Performance Computing (HPC) can leverage the approach. In this work we report on a multi-level parallelisation of the underlying computational machinery and show that this can speed up the code by several orders of magnitude. This in turn can extend the applicability of the method to otherwise inaccessible cases. We exploit three levels of parallelisation: Distributed computing by means of Message Passing (MPI), shared-memory computing using OpenMP, and vectorisation by means of SIMD units (single-instruction-multiple-data). Results are provided for two distinct High Performance Computing (HPC) platforms, namely the IBM-based BlueGene/Q system JUQUEEN and an Intel Sandy-Bridge-based development cluster. We discuss how certain issues and obstacles were overcome in the course of adapting the code. Most importantly, we conclude that this vast improvement can actually be accomplished by introducing only moderate changes to the code, such that this strategy may serve as a guideline for other researcher to likewise improve the efficiency of their codes

Using ACL2 to Verify Loop Pipelining in Behavioral Synthesis

Behavioral synthesis involves compiling an Electronic System-Level (ESL) design into its Register-Transfer Level (RTL) implementation. Loop pipelining is one of the most critical and complex transformations employed in behavioral synthesis. Certifying the loop pipelining algorithm is challenging because there is a huge semantic gap between the input sequential design and the output pipelined implementation making it infeasible to verify their equivalence with automated sequential equivalence checking techniques. We discuss our ongoing effort using ACL2 to certify loop pipelining transformation. The completion of the proof is work in progress. However, some of the insights developed so far may already be of value to the ACL2 community. In particular, we discuss the key invariant we formalized, which is very different from that used in most pipeline proofs. We discuss the needs for this invariant, its formalization in ACL2, and our envisioned proof using the invariant. We also discuss some trade-offs, challenges, and insights developed in course of the project.Comment: In Proceedings ACL2 2014, arXiv:1406.123

A Test Suite for High-Performance Parallel Java

The Java programming language has a number of features that make it attractive for writing high-quality, portable parallel programs. A pure object formulation, strong typing and the exception model make programs easier to create, debug, and maintain. The elegant threading provides a simple route to parallelism on shared-memory machines. Anticipating great improvements in numerical performance, this paper presents a suite of simple programs that indicate how a pure Java Navier-Stokes solver might perform. The suite includes a parallel Euler solver. We present results from a 32-processor Hewlett-Packard machine and a 4-processor Sun server. While speedup is excellent on both machines, indicating a high-quality thread scheduler, the single-processor performance needs much improvement

A Fast Compiler for NetKAT

High-level programming languages play a key role in a growing number of networking platforms, streamlining application development and enabling precise formal reasoning about network behavior. Unfortunately, current compilers only handle "local" programs that specify behavior in terms of hop-by-hop forwarding behavior, or modest extensions such as simple paths. To encode richer "global" behaviors, programmers must add extra state -- something that is tricky to get right and makes programs harder to write and maintain. Making matters worse, existing compilers can take tens of minutes to generate the forwarding state for the network, even on relatively small inputs. This forces programmers to waste time working around performance issues or even revert to using hardware-level APIs. This paper presents a new compiler for the NetKAT language that handles rich features including regular paths and virtual networks, and yet is several orders of magnitude faster than previous compilers. The compiler uses symbolic automata to calculate the extra state needed to implement "global" programs, and an intermediate representation based on binary decision diagrams to dramatically improve performance. We describe the design and implementation of three essential compiler stages: from virtual programs (which specify behavior in terms of virtual topologies) to global programs (which specify network-wide behavior in terms of physical topologies), from global programs to local programs (which specify behavior in terms of single-switch behavior), and from local programs to hardware-level forwarding tables. We present results from experiments on real-world benchmarks that quantify performance in terms of compilation time and forwarding table size