Runtime-assisted optimizations in the on-chip memory hierarchy

Following Moore's Law, the number of transistors on chip has been increasing exponentially, which has led to the increasing complexity of modern processors. As a result, the efficient programming of such systems has become more difficult. Many programming models have been developed to answer this issue. Of particular interest are task-based programming models that employ simple annotations to define parallel work in an application. The information available at the level of the runtime systems associated with these programming models offers great potential for improving hardware design. Moreover, due to technological limitations, Moore's Law is predicted to eventually come to an end, so novel paradigms are necessary to maintain the current performance improvement trends. The main goal of this thesis is to exploit the knowledge about a parallel application available at the runtime system level to improve the design of the on-chip memory hierarchy. The coupling of the runtime system and the microprocessor enables a better hardware design without hurting the programmability. The first contribution is a set of insertion policies for shared last-level caches that exploit information about tasks and task data dependencies. The intuition behind this proposal revolves around the observation that parallel threads exhibit different memory access patterns. Even within the same thread, accesses to different variables often follow distinct patterns. The proposed policies insert cache lines into different logical positions depending on the dependency type and task type to which the corresponding memory request belongs. The second proposal optimizes the execution of reductions, defined as a programming pattern that combines input data to form the resulting reduction variable. This is achieved with a runtime-assisted technique for performing reductions in the processor's cache hierarchy. The proposal's goal is to be a universally applicable solution regardless of the reduction variable type, size and access pattern. On the software level, the programming model is extended to let a programmer specify the reduction variables for tasks, as well as the desired cache level where a certain reduction will be performed. The source-to-source compiler and the runtime system are extended to translate and forward this information to the underlying hardware. On the hardware level, private and shared caches are equipped with functional units and the accompanying logic to perform reductions at the cache level. This design avoids unnecessary data movements to the core and back as the data is operated at the place where it resides. The third contribution is a runtime-assisted prioritization scheme for memory requests inside the on-chip memory hierarchy. The proposal is based on the notion of a critical path in the context of parallel codes and a known fact that accelerating critical tasks reduces the execution time of the whole application. In the context of this work, task criticality is observed at a level of a task type as it enables simple annotation by the programmer. The acceleration of critical tasks is achieved by the prioritization of corresponding memory requests in the microprocessor.Siguiendo la ley de Moore, el número de transistores en los chips ha crecido exponencialmente, lo que ha comportado una mayor complejidad en los procesadores modernos y, como resultado, de la dificultad de la programación eficiente de estos sistemas. Se han desarrollado muchos modelos de programación para resolver este problema; un ejemplo particular son los modelos de programación basados en tareas, que emplean anotaciones sencillas para definir los Trabajos paralelos de una aplicación. La información de que disponen los sistemas en tiempo de ejecución (runtime systems) asociada con estos modelos de programación ofrece un enorme potencial para la mejora del diseño del hardware. Por otro lado, las limitaciones tecnológicas hacen que la ley de Moore pueda dejar de cumplirse próximamente, por lo que se necesitan paradigmas nuevos para mantener las tendencias actuales de mejora de rendimiento. El objetivo principal de esta tesis es aprovechar el conocimiento de las aplicaciones paral·leles de que dispone el runtime system para mejorar el diseño de la jerarquía de memoria del chip. El acoplamiento del runtime system junto con el microprocesador permite realizar mejores diseños hardware sin afectar Negativamente en la programabilidad de dichos sistemas. La primera contribución de esta tesis consiste en un conjunto de políticas de inserción para las memorias caché compartidas de último nivel que aprovecha la información de las tareas y las dependencias de datos entre estas. La intuición tras esta propuesta se basa en la observación de que los hilos de ejecución paralelos muestran distintos patrones de acceso a memoria e, incluso dentro del mismo hilo, los accesos a diferentes variables a menudo siguen patrones distintos. Las políticas que se proponen insertan líneas de caché en posiciones lógicas diferentes en función de los tipos de dependencia y tarea a los que corresponde la petición de memoria. La segunda propuesta optimiza la ejecución de las reducciones, que se definen como un patrón de programación que combina datos de entrada para conseguir la variable de reducción como resultado. Esto se consigue mediante una técnica asistida por el runtime system para la realización de reducciones en la jerarquía de la caché del procesador, con el objetivo de ser una solución aplicable de forma universal sin depender del tipo de la variable de la reducción, su tamaño o el patrón de acceso. A nivel de software, el modelo de programación se extiende para que el programador especifique las variables de reducción de las tareas, así como el nivel de caché escogido para que se realice una determinada reducción. El compilador fuente a Fuente (compilador source-to-source) y el runtime ssytem se modifican para que traduzcan y pasen esta información al hardware subyacente, evitando así movimientos de datos innecesarios hacia y desde el núcleo del procesador, al realizarse la operación donde se encuentran los datos de la misma. La tercera contribución proporciona un esquema de priorización asistido por el runtime system para peticiones de memoria dentro de la jerarquía de memoria del chip. La propuesta se basa en la noción de camino crítico en el contexto de los códigos paralelos y en el hecho conocido de que acelerar tareas críticas reduce el tiempo de ejecución de la aplicación completa. En el contexto de este trabajo, la criticidad de las tareas se considera a nivel del tipo de tarea ya que permite que el programador las indique mediante anotaciones sencillas. La aceleración de las tareas críticas se consigue priorizando las correspondientes peticiones de memoria en el microprocesador.Seguint la llei de Moore, el nombre de transistors que contenen els xips ha patit un creixement exponencial, fet que ha provocat un augment de la complexitat dels processadors moderns i, per tant, de la dificultat de la programació eficient d’aquests sistemes. Per intentar solucionar-ho, s’han desenvolupat diversos models de programació; un exemple particular en són els models basats en tasques, que fan servir anotacions senzilles per definir treballs paral·lels dins d’una aplicació. La informació que hi ha al nivell dels sistemes en temps d’execució (runtime systems) associada amb aquests models de programació ofereix un gran potencial a l’hora de millorar el disseny del maquinari. D’altra banda, les limitacions tecnològiques fan que la llei de Moore pugui deixar de complir-se properament, per la qual cosa calen nous paradigmes per mantenir les tendències actuals en la millora de rendiment. L’objectiu principal d’aquesta tesi és aprofitar els coneixements que el runtime System té d’una aplicació paral·lela per millorar el disseny de la jerarquia de memòria dins el xip. L’acoblament del runtime system i el microprocessador permet millorar el disseny del maquinari sense malmetre la programabilitat d’aquests sistemes. La primera contribució d’aquesta tesi consisteix en un conjunt de polítiques d’inserció a les memòries cau (cache memories) compartides d’últim nivell que aprofita informació sobre tasques i les dependències de dades entre aquestes. La intuïció que hi ha al darrere d’aquesta proposta es basa en el fet que els fils d’execució paral·lels mostren diferents patrons d’accés a la memòria; fins i tot dins el mateix fil, els accessos a variables diferents sovint segueixen patrons diferents. Les polítiques que s’hi proposen insereixen línies de la memòria cau a diferents ubicacions lògiques en funció dels tipus de dependència i de tasca als quals correspon la petició de memòria. La segona proposta optimitza l’execució de les reduccions, que es defineixen com un patró de programació que combina dades d’entrada per aconseguir la variable de reducció com a resultat. Això s’aconsegueix mitjançant una tècnica assistida pel runtime system per dur a terme reduccions en la jerarquia de la memòria cau del processador, amb l’objectiu que la proposta sigui aplicable de manera universal, sense dependre del tipus de la variable a la qual es realitza la reducció, la seva mida o el patró d’accés. A nivell de programari, es realitza una extensió del model de programació per facilitar que el programador especifiqui les variables de les reduccions que usaran les tasques, així com el nivell de memòria cau desitjat on s’hauria de realitzar una certa reducció. El compilador font a font (compilador source-to-source) i el runtime system s’amplien per traduir i passar aquesta informació al maquinari subjacent. A nivell de maquinari, les memòries cau privades i compartides s’equipen amb unitats funcionals i la lògica corresponent per poder dur a terme les reduccions a la pròpia memòria cau, evitant així moviments de dades innecessaris entre el nucli del processador i la jerarquia de memòria. La tercera contribució proporciona un esquema de priorització assistit pel runtime System per peticions de memòria dins de la jerarquia de memòria del xip. La proposta es basa en la noció de camí crític en el context dels codis paral·lels i en el fet conegut que l’acceleració de les tasques que formen part del camí crític redueix el temps d’execució de l’aplicació sencera. En el context d’aquest treball, la criticitat de les tasques s’observa al nivell del seu tipus ja que permet que el programador les indiqui mitjançant anotacions senzilles. L’acceleració de les tasques crítiques s’aconsegueix prioritzant les corresponents peticions de memòria dins el microprocessador

Microarchitectural techniques to reduce energy consumption in the memory hierarchy

This thesis states that dynamic profiling of the memory reference stream can improve energy and performance in the memory hierarchy. The research presented in this theses provides multiple instances of using lightweight hardware structures to profile the memory reference stream. The objective of this research is to develop microarchitectural techniques to reduce energy consumption at different levels of the memory hierarchy. Several simple and implementable techniques were developed as a part of this research. One of the techniques identifies and eliminates redundant refresh operations in DRAM and reduces DRAM refresh power. Another, reduces leakage energy in L2 and higher level caches for multiprocessor systems. The emphasis of this research has been to develop several techniques of obtaining energy savings in caches using a simple hardware structure called the counting Bloom filter (CBF). CBFs have been used to predict L2 cache misses and obtain energy savings by not accessing the L2 cache on a predicted miss. A simple extension of this technique allows CBFs to do way-estimation of set associative caches to reduce energy in cache lookups. Another technique using CBFs track addresses in a Virtual Cache and reduce false synonym lookups. Finally this thesis presents a technique to reduce dynamic power consumption in level one caches using significance compression. The significant energy and performance improvements demonstrated by the techniques presented in this thesis suggest that this work will be of great value for designing memory hierarchies of future computing platforms.Ph.D.Committee Chair: Lee, Hsien-Hsin S.; Committee Member: Cahtterjee,Abhijit; Committee Member: Mukhopadhyay, Saibal; Committee Member: Pande, Santosh; Committee Member: Yalamanchili, Sudhaka

Dependable Computing on Inexact Hardware through Anomaly Detection.

Reliability of transistors is on the decline as transistors continue to shrink in size. Aggressive voltage scaling is making the problem even worse. Scaled-down transistors are more susceptible to transient faults as well as permanent in-field hardware failures. In order to continue to reap the benefits of technology scaling, it has become imperative to tackle the challenges risen due to the decreasing reliability of devices for the mainstream commodity market. Along with the worsening reliability, achieving energy efficiency and performance improvement by scaling is increasingly providing diminishing marginal returns. More than any other time in history, the semiconductor industry faces the crossroad of unreliability and the need to improve energy efficiency. These challenges of technology scaling can be tackled by categorizing the target applications in the following two categories: traditional applications that have relatively strict correctness requirement on outputs and emerging class of soft applications, from various domains such as multimedia, machine learning, and computer vision, that are inherently inaccuracy tolerant to a certain degree. Traditional applications can be protected against hardware failures by low-cost detection and protection methods while soft applications can trade off quality of outputs to achieve better performance or energy efficiency. For traditional applications, I propose an efficient, software-only application analysis and transformation solution to detect data and control flow transient faults. The intelligence of the data flow solution lies in the use of dynamic application information such as control flow, memory and value profiling. The control flow protection technique achieves its efficiency by simplifying signature calculations in each basic block and by performing checking at a coarse-grain level. For soft applications, I develop a quality control technique. The quality control technique employs continuous, light-weight checkers to ensure that the approximation is controlled and application output is acceptable. Overall, I show that the use of low-cost checkers to produce dependable results on commodity systems---constructed from inexact hardware components---is efficient and practical.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113341/1/dskhudia_1.pd

Decompose and Conquer: Addressing Evasive Errors in Systems on Chip

Modern computer chips comprise many components, including microprocessor cores, memory modules, on-chip networks, and accelerators. Such system-on-chip (SoC) designs are deployed in a variety of computing devices: from internet-of-things, to smartphones, to personal computers, to data centers. In this dissertation, we discuss evasive errors in SoC designs and how these errors can be addressed efficiently. In particular, we focus on two types of errors: design bugs and permanent faults. Design bugs originate from the limited amount of time allowed for design verification and validation. Thus, they are often found in functional features that are rarely activated. Complete functional verification, which can eliminate design bugs, is extremely time-consuming, thus impractical in modern complex SoC designs. Permanent faults are caused by failures of fragile transistors in nano-scale semiconductor manufacturing processes. Indeed, weak transistors may wear out unexpectedly within the lifespan of the design. Hardware structures that reduce the occurrence of permanent faults incur significant silicon area or performance overheads, thus they are infeasible for most cost-sensitive SoC designs. To tackle and overcome these evasive errors efficiently, we propose to leverage the principle of decomposition to lower the complexity of the software analysis or the hardware structures involved. To this end, we present several decomposition techniques, specific to major SoC components. We first focus on microprocessor cores, by presenting a lightweight bug-masking analysis that decomposes a program into individual instructions to identify if a design bug would be masked by the program's execution. We then move to memory subsystems: there, we offer an efficient memory consistency testing framework to detect buggy memory-ordering behaviors, which decomposes the memory-ordering graph into small components based on incremental differences. We also propose a microarchitectural patching solution for memory subsystem bugs, which augments each core node with a small distributed programmable logic, instead of including a global patching module. In the context of on-chip networks, we propose two routing reconfiguration algorithms that bypass faulty network resources. The first computes short-term routes in a distributed fashion, localized to the fault region. The second decomposes application-aware routing computation into simple routing rules so to quickly find deadlock-free, application-optimized routes in a fault-ridden network. Finally, we consider general accelerator modules in SoC designs. When a system includes many accelerators, there are a variety of interactions among them that must be verified to catch buggy interactions. To this end, we decompose such inter-module communication into basic interaction elements, which can be reassembled into new, interesting tests. Overall, we show that the decomposition of complex software algorithms and hardware structures can significantly reduce overheads: up to three orders of magnitude in the bug-masking analysis and the application-aware routing, approximately 50 times in the routing reconfiguration latency, and 5 times on average in the memory-ordering graph checking. These overhead reductions come with losses in error coverage: 23% undetected bug-masking incidents, 39% non-patchable memory bugs, and occasionally we overlook rare patterns of multiple faults. In this dissertation, we discuss the ideas and their trade-offs, and present future research directions.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147637/1/doowon_1.pd

Operating System Support for Redundant Multithreading

Failing hardware is a fact and trends in microprocessor design indicate that the fraction of hardware suffering from permanent and transient faults will continue to increase in future chip generations. Researchers proposed various solutions to this issue with different downsides: Specialized hardware components make hardware more expensive in production and consume additional energy at runtime. Fault-tolerant algorithms and libraries enforce specific programming models on the developer. Compiler-based fault tolerance requires the source code for all applications to be available for recompilation. In this thesis I present ASTEROID, an operating system architecture that integrates applications with different reliability needs. ASTEROID is built on top of the L4/Fiasco.OC microkernel and extends the system with Romain, an operating system service that transparently replicates user applications. Romain supports single- and multi-threaded applications without requiring access to the application's source code. Romain replicates applications and their resources completely and thereby does not rely on hardware extensions, such as ECC-protected memory. In my thesis I describe how to efficiently implement replication as a form of redundant multithreading in software. I develop mechanisms to manage replica resources and to make multi-threaded programs behave deterministically for replication. I furthermore present an approach to handle applications that use shared-memory channels with other programs. My evaluation shows that Romain provides 100% error detection and more than 99.6% error correction for single-bit flips in memory and general-purpose registers. At the same time, Romain's execution time overhead is below 14% for single-threaded applications running in triple-modular redundant mode. The last part of my thesis acknowledges that software-implemented fault tolerance methods often rely on the correct functioning of a certain set of hardware and software components, the Reliable Computing Base (RCB). I introduce the concept of the RCB and discuss what constitutes the RCB of the ASTEROID system and other fault tolerance mechanisms. Thereafter I show three case studies that evaluate approaches to protecting RCB components and thereby aim to achieve a software stack that is fully protected against hardware errors

Dependable Embedded Systems

This Open Access book introduces readers to many new techniques for enhancing and optimizing reliability in embedded systems, which have emerged particularly within the last five years. This book introduces the most prominent reliability concerns from today’s points of view and roughly recapitulates the progress in the community so far. Unlike other books that focus on a single abstraction level such circuit level or system level alone, the focus of this book is to deal with the different reliability challenges across different levels starting from the physical level all the way to the system level (cross-layer approaches). The book aims at demonstrating how new hardware/software co-design solution can be proposed to ef-fectively mitigate reliability degradation such as transistor aging, processor variation, temperature effects, soft errors, etc. Provides readers with latest insights into novel, cross-layer methods and models with respect to dependability of embedded systems; Describes cross-layer approaches that can leverage reliability through techniques that are pro-actively designed with respect to techniques at other layers; Explains run-time adaptation and concepts/means of self-organization, in order to achieve error resiliency in complex, future many core systems

Simulation Native des Systèmes Multiprocesseurs sur Puce à l'aide de la Virtualisation Assistée par le Matériel

L'intégration de plusieurs processeurs hétérogènes en un seul système sur puce (SoC) est une tendance claire dans les systèmes embarqués. La conception et la vérification de ces systèmes nécessitent des plateformes rapides de simulation, et faciles à construire. Parmi les approches de simulation de logiciels, la simulation native est un bon candidat grâce à l'exécution native de logiciel embarqué sur la machine hôte, ce qui permet des simulations à haute vitesse, sans nécessiter le développement de simulateurs d'instructions. Toutefois, les techniques de simulation natives existantes exécutent le logiciel de simulation dans l'espace de mémoire partagée entre le matériel modélisé et le système d'exploitation hôte. Il en résulte de nombreux problèmes, par exemple les conflits l'espace d'adressage et les chevauchements de mémoire ainsi que l'utilisation des adresses de la machine hôte plutôt des celles des plates-formes matérielles cibles. Cela rend pratiquement impossible la simulation native du code existant fonctionnant sur la plate-forme cible. Pour surmonter ces problèmes, nous proposons l'ajout d'une couche transparente de traduction de l'espace adressage pour séparer l'espace d'adresse cible de celui du simulateur de hôte. Nous exploitons la technologie de virtualisation assistée par matériel (HAV pour Hardware-Assisted Virtualization) à cet effet. Cette technologie est maintenant disponibles sur plupart de processeurs grande public à usage général. Les expériences montrent que cette solution ne dégrade pas la vitesse de simulation native, tout en gardant la possibilité de réaliser l'évaluation des performances du logiciel simulé. La solution proposée est évolutive et flexible et nous fournit les preuves nécessaires pour appuyer nos revendications avec des solutions de simulation multiprocesseurs et hybrides. Nous abordons également la simulation d'exécutables cross- compilés pour les processeurs VLIW (Very Long Instruction Word) en utilisant une technique de traduction binaire statique (SBT) pour généré le code natif. Ainsi il n'est pas nécessaire de faire de traduction à la volée ou d'interprétation des instructions. Cette approche est intéressante dans les situations où le code source n'est pas disponible ou que la plate-forme cible n'est pas supporté par les compilateurs reciblable, ce qui est généralement le cas pour les processeurs VLIW. Les simulateurs générés s'exécutent au-dessus de notre plate-forme basée sur le HAV et modélisent les processeurs de la série C6x de Texas Instruments (TI). Les résultats de simulation des binaires pour VLIW montrent une accélération de deux ordres de grandeur par rapport aux simulateurs précis au cycle près.Integration of multiple heterogeneous processors into a single System-on-Chip (SoC) is a clear trend in embedded systems. Designing and verifying these systems require high-speed and easy-to-build simulation platforms. Among the software simulation approaches, native simulation is a good candidate since the embedded software is executed natively on the host machine, resulting in high speed simulations and without requiring instruction set simulator development effort. However, existing native simulation techniques execute the simulated software in memory space shared between the modeled hardware and the host operating system. This results in many problems, including address space conflicts and overlaps as well as the use of host machine addresses instead of the target hardware platform ones. This makes it practically impossible to natively simulate legacy code running on the target platform. To overcome these issues, we propose the addition of a transparent address space translation layer to separate the target address space from that of the host simulator. We exploit the Hardware-Assisted Virtualization (HAV) technology for this purpose, which is now readily available on almost all general purpose processors. Experiments show that this solution does not degrade the native simulation speed, while keeping the ability to accomplish software performance evaluation. The proposed solution is scalable as well as flexible and we provide necessary evidence to support our claims with multiprocessor and hybrid simulation solutions. We also address the simulation of cross-compiled Very Long Instruction Word (VLIW) executables, using a Static Binary Translation (SBT) technique to generated native code that does not require run-time translation or interpretation support. This approach is interesting in situations where either the source code is not available or the target platform is not supported by any retargetable compilation framework, which is usually the case for VLIW processors. The generated simulators execute on top of our HAV based platform and model the Texas Instruments (TI) C6x series processors. Simulation results for VLIW binaries show a speed-up of around two orders of magnitude compared to the cycle accurate simulators.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Software instruction caching

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 185-193).As microprocessor complexities and costs skyrocket, designers are looking for ways to simplify their designs to reduce costs, improve energy efficiency, or squeeze more computational elements on each chip. This is particularly true for the embedded domain where cost and energy consumption are paramount. Software instruction caches have the potential to provide the required performance while using simpler, more efficient hardware. A software cache consists of a simple array memory (such as a scratchpad) and a software system that is capable of automatically managing that memory as a cache. Software caches have several advantages over traditional hardware caches. Without complex cache-management logic, the processor hardware is cheaper and easier to design, verify and manufacture. The reduced access energy of simple memories can result in a net energy savings if management overhead is kept low. Software caches can also be customized to each individual program's needs, improving performance or eliminating unpredictable timing for real-time embedded applications. The greatest challenge for a software cache is providing good performance using general-purpose instructions for cache management rather than specially-designed hardware. This thesis designs and implements a working system (Flexicache) on an actual embedded processor and uses it to investigate the strengths and weaknesses of software instruction caches. Although both data and instruction caches can be implemented in software, very different techniques are used to optimize performance; this work focuses exclusively on software instruction caches. The Flexicache system consists of two software components: a static off-line preprocessor to add caching to an application and a dynamic runtime system to manage memory during execution. Key interfaces and optimizations are identified and characterized. The system is evaluated in detail from the standpoints of both performance and energy consumption. The results indicate that software instruction caches can perform comparably to hardware caches in embedded processors. On most benchmarks, the overhead relative to a hardware cache is less than 12% and can be as low as 2.4%. At the same time, the software cache uses up to 6% less energy. This is achieved using a simple, directly-addressed memory and without requiring any complex, specialized hardware structures.by Jason Eric Miller.Ph.D

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