Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR

Full quantum mechanical analysis of atomic three-grating Mach-Zehnder interferometry

Atomic three-grating Mach-Zehnder interferometry constitutes an important tool to probe fundamental aspects of the quantum theory. There is, however, a remarkable gap in the literature between the oversimplified models and robust numerical simulations considered to describe the corresponding experiments. Consequently, the former usually lead to paradoxical scenarios, such as the wave-particle dual behavior of atoms, while the latter make difficult the data analysis in simple terms. Here these issues are tackled by means of a simple grating working model consisting of evenly-spaced Gaussian slits. As is shown, this model suffices to explore and explain such experiments both analytically and numerically, giving a good account of the full atomic journey inside the interferometer, and hence contributing to make less mystic the physics involved. More specifically, it provides a clear and unambiguous picture of the wavefront splitting that takes place inside the interferometer, illustrating how the momentum along each emerging diffraction order is well defined even though the wave function itself still displays a rather complex shape. To this end, the local transverse momentum is also introduced in this context as a reliable analytical tool. The splitting, apart from being a key issue to understand atomic Mach-Zehnder interferometry, also demonstrates at a fundamental level how wave and particle aspects are always present in the experiment, without incurring in any contradiction or interpretive paradox. On the other hand, at a practical level, the generality and versatility of the model and methodology presented, makes them suitable to attack analogous problems in a simple manner after a convenient tuning.Comment: 17 pages, 6 figures (remarkably improved version

Parallelization of dynamic programming recurrences in computational biology

The rapid growth of biosequence databases over the last decade has led to a performance bottleneck in the applications analyzing them. In particular, over the last five years DNA sequencing capacity of next-generation sequencers has been doubling every six months as costs have plummeted. The data produced by these sequencers is overwhelming traditional compute systems. We believe that in the future compute performance, not sequencing, will become the bottleneck in advancing genome science. In this work, we investigate novel computing platforms to accelerate dynamic programming algorithms, which are popular in bioinformatics workloads. We study algorithm-specific hardware architectures that exploit fine-grained parallelism in dynamic programming kernels using field-programmable gate arrays: FPGAs). We advocate a high-level synthesis approach, using the recurrence equation abstraction to represent dynamic programming and polyhedral analysis to exploit parallelism. We suggest a novel technique within the polyhedral model to optimize for throughput by pipelining independent computations on an array. This design technique improves on the state of the art, which builds latency-optimal arrays. We also suggest a method to dynamically switch between a family of designs using FPGA reconfiguration to achieve a significant performance boost. We have used polyhedral methods to parallelize the Nussinov RNA folding algorithm to build a family of accelerators that can trade resources for parallelism and are between 15-130x faster than a modern dual core CPU implementation. A Zuker RNA folding accelerator we built on a single workstation with four Xilinx Virtex 4 FPGAs outperforms 198 3 GHz Intel Core 2 Duo processors. Furthermore, our design running on a single FPGA is an order of magnitude faster than competing implementations on similar-generation FPGAs and graphics processors. Our work is a step toward the goal of automated synthesis of hardware accelerators for dynamic programming algorithms

Clustered VLIW architecture based on queue register files

Institute for Computing Systems ArchitectureInstruction-level parallelism (ILP) is a set of hardware and software techniques that allow parallel execution of machine operations. Superscalar architectures rely most heavily upon hardware schemes to identify parallelism among operations. Although successful in terms of performance, the hardware complexity involved might limit the scalability of this model. VLIW architectures use a different approach to exploit ILP. In this case all data dependence analyses and scheduling of operations are performed at compile time, resulting in a simpler hardware organization. This allows the inclusion of a larger number of functional units (FUs) into a single chip. IN spite of this relative simplification, the scalability of VLIW architectures can be constrained by the size and number of ports of the register file. VLIW machines often use software pipelining techniques to improve the execution of loop structures, which can increase the register pressure. Furthermore, the access time of a register file can be compromised by the number of ports, causing a negative impact on the machine cycle time. For these reasons we understand that the benefits of having parallel FUs, which have motivated the investigation of alternative machine designs. This thesis presents a scalar VLIW architecture comprising clusters of FUs and private register files. Register files organised as queue structures are used as a mechanism for inter-cluster communication, allowing the enforcement of fixed latency in the process. This scheme presents better possibilities in terms of scalability as the size of the individual register files is not determined by the total number of FUs, suggesting that the silicon area may grow only linearly with respect to the total number of FUs. However, the effectiveness of such an organization depends on the efficiency of the code partitioning strategy. We have developed an algorithm for a clustered VLIW architecture integrating both software pipelining and code partitioning in a a single procedure. Experimental results show it may allow performance levels close to an unclustered machine without communication restraints. Finally, we have developed silicon area and cycle time models to quantify the scalability of performance and cost for this class of architecture

Coarse-grained reconfigurable array architectures

Coarse-Grained Reconfigurable Array (CGRA) architectures accelerate the same inner loops that benefit from the high ILP support in VLIW architectures. By executing non-loop code on other cores, however, CGRAs can focus on such loops to execute them more efficiently. This chapter discusses the basic principles of CGRAs, and the wide range of design options available to a CGRA designer, covering a large number of existing CGRA designs. The impact of different options on flexibility, performance, and power-efficiency is discussed, as well as the need for compiler support. The ADRES CGRA design template is studied in more detail as a use case to illustrate the need for design space exploration, for compiler support and for the manual fine-tuning of source code