Doctor of Philosophy

dissertationEmerging trends such as growing architectural diversity and increased emphasis on energy and power efficiency motivate the need for code that adapts to its execution context (input dataset and target architecture). Unfortunately, writing such code remains difficult, and is typically attempted only by a small group of motivated expert programmers who are highly knowledgeable about the relationship between software and its hardware mapping. In this dissertation, we introduce novel abstractions and techniques based on automatic performance tuning that enable both experts and nonexperts (application developers) to produce adaptive code. We present two new frameworks for adaptive programming: Nitro and Surge. Nitro enables expert programmers to specify code variants, or alternative implementations of the same computation, together with meta-information for selecting among them. It then utilizes supervised classification to select an optimal code variant at runtime based on characteristics of the execution context. Surge, on the other hand, provides a high-level nested data-parallel programming interface for application developers to specify computations. It then employs a two-level mechanism to automatically generate code variants and then tunes them using Nitro. The resulting code performs on par with or better than handcrafted reference implementations on both CPUs and GPUs. In addition to abstractions for expressing code variants, this dissertation also presents novel strategies for adaptively tuning them. First, we introduce a technique for dynamically selecting an optimal code variant at runtime based on characteristics of the input dataset. On five high-performance GPU applications, variants tuned using this strategy achieve over 93% of the performance of variants selected through exhaustive search. Next, we present a novel approach based on multitask learning to develop a code variant selection model on a target architecture from training on different source architectures. We evaluate this approach on a set of six benchmark applications and a collection of six NVIDIA GPUs from three distinct architecture generations. Finally, we implement support for combined code variant and frequency selection based on multiple objectives, including power and energy efficiency. Using this strategy, we construct a GPU sorting implementation that provides improved energy and power efficiency with less than a proportional drop in sorting throughput

Toatie : functional hardware description with dependent types

Describing correct circuits remains a tall order, despite four decades of evolution in Hardware Description Languages (HDLs). Many enticing circuit architectures require recursive structures or complex compile-time computation — two patterns that prove difficult to capture in traditional HDLs. In a signal processing context, the Fast FIR Algorithm (FFA) structure for efficient parallel filtering proves to be naturally recursive, and most Multiple Constant Multiplication (MCM) blocks decompose multiplications into graphs of simple shifts and adds using demanding compile time computation. Generalised versions of both remain mostly in academic folklore. The implementations which do exist are often ad hoc circuit generators, written in software languages. These pose challenges for verification and are resistant to composition. Embedded functional HDLs, that represent circuits as data, allow for these descriptions at the cost of forcing the designer to work at the gate-level. A promising alternative is to use a stand-alone compiler, representing circuits as plain functions, exemplified by the CλaSH HDL. This, however, raises new challenges in capturing a circuit’s staging — which expressions in the single language should be reduced during compile-time elaboration, and which should remain in the circuit’s run-time? To better reflect the physical separation between circuit phases, this work proposes a new functional HDL (representing circuits as functions) with first-class staging constructs. Orthogonal to this, there are also long-standing challenges in the verification of parameterised circuit families. Industry surveys have consistently reported that only a slim minority of FPGA projects reach production without non-trivial bugs. While a healthy growth in the adoption of automatic formal methods is also reported, the majority of testing remains dynamic — presenting difficulties for testing entire circuit families at once. This research offers an alternative verification methodology via the combination of dependent types and automatic synthesis of user-defined data types. Given precise enough types for synthesisable data, this environment can be used to develop circuit families with full functional verification in a correct-by-construction fashion. This approach allows for verification of entire circuit families (not just one concrete member) and side-steps the state-space explosion of model checking methods. Beyond the existing work, this research offers synthesis of combinatorial circuits — not just a software model of their behaviour. This additional step requires careful consideration of staging, erasure & irrelevance, deriving bit representations of user-defined data types, and a new synthesis scheme. This thesis contributes steps towards HDLs with sufficient expressivity for awkward, combinatorial signal processing structures, allowing for a correct-by-construction approach, and a prototype compiler for netlist synthesis.Describing correct circuits remains a tall order, despite four decades of evolution in Hardware Description Languages (HDLs). Many enticing circuit architectures require recursive structures or complex compile-time computation — two patterns that prove difficult to capture in traditional HDLs. In a signal processing context, the Fast FIR Algorithm (FFA) structure for efficient parallel filtering proves to be naturally recursive, and most Multiple Constant Multiplication (MCM) blocks decompose multiplications into graphs of simple shifts and adds using demanding compile time computation. Generalised versions of both remain mostly in academic folklore. The implementations which do exist are often ad hoc circuit generators, written in software languages. These pose challenges for verification and are resistant to composition. Embedded functional HDLs, that represent circuits as data, allow for these descriptions at the cost of forcing the designer to work at the gate-level. A promising alternative is to use a stand-alone compiler, representing circuits as plain functions, exemplified by the CλaSH HDL. This, however, raises new challenges in capturing a circuit’s staging — which expressions in the single language should be reduced during compile-time elaboration, and which should remain in the circuit’s run-time? To better reflect the physical separation between circuit phases, this work proposes a new functional HDL (representing circuits as functions) with first-class staging constructs. Orthogonal to this, there are also long-standing challenges in the verification of parameterised circuit families. Industry surveys have consistently reported that only a slim minority of FPGA projects reach production without non-trivial bugs. While a healthy growth in the adoption of automatic formal methods is also reported, the majority of testing remains dynamic — presenting difficulties for testing entire circuit families at once. This research offers an alternative verification methodology via the combination of dependent types and automatic synthesis of user-defined data types. Given precise enough types for synthesisable data, this environment can be used to develop circuit families with full functional verification in a correct-by-construction fashion. This approach allows for verification of entire circuit families (not just one concrete member) and side-steps the state-space explosion of model checking methods. Beyond the existing work, this research offers synthesis of combinatorial circuits — not just a software model of their behaviour. This additional step requires careful consideration of staging, erasure & irrelevance, deriving bit representations of user-defined data types, and a new synthesis scheme. This thesis contributes steps towards HDLs with sufficient expressivity for awkward, combinatorial signal processing structures, allowing for a correct-by-construction approach, and a prototype compiler for netlist synthesis

Power and Energy Aware Heterogeneous Computing Platform

During the last decade, wireless technologies have experienced significant development, most notably in the form of mobile cellular radio evolution from GSM to UMTS/HSPA and thereon to Long-Term Evolution (LTE) for increasing the capacity and speed of wireless data networks. Considering the real-time constraints of the new wireless standards and their demands for parallel processing, reconfigurable architectures and in particular, multicore platforms are part of the most successful platforms due to providing high computational parallelism and throughput. In addition to that, by moving toward Internet-of-Things (IoT), the number of wireless sensors and IP-based high throughput network routers is growing at a rapid pace. Despite all the progression in IoT, due to power and energy consumption, a single chip platform for providing multiple communication standards and a large processing bandwidth is still missing.The strong demand for performing different sets of operations by the embedded systems and increasing the computational performance has led to the use of heterogeneous multicore architectures with the help of accelerators for computationally-intensive data-parallel tasks acting as coprocessors. Currently, highly heterogeneous systems are the most power-area efficient solution for performing complex signal processing systems. Additionally, the importance of IoT has increased significantly the need for heterogeneous and reconfigurable platforms.On the other hand, subsequent to the breakdown of the Dennardian scaling and due to the enormous heat dissipation, the performance of a single chip was obstructed by the utilization wall since all cores cannot be clocked at their maximum operating frequency. Therefore, a thermal melt-down might be happened as a result of high instantaneous power dissipation. In this context, a large fraction of the chip, which is switched-off (Dark) or operated at a very low frequency (Dim) is called Dark Silicon. The Dark Silicon issue is a constraint for the performance of computers, especially when the up-coming IoT scenario will demand a very high performance level with high energy efficiency. Among the suggested solution to combat the problem of Dark-Silicon, the use of application-specific accelerators and in particular Coarse-Grained Reconfigurable Arrays (CGRAs) are the main motivation of this thesis work.This thesis deals with design and implementation of Software Defined Radio (SDR) as well as High Efficiency Video Coding (HEVC) application-specific accelerators for computationally intensive kernels and data-parallel tasks. One of the most important data transmission schemes in SDR due to its ability of providing high data rates is Orthogonal Frequency Division Multiplexing (OFDM). This research work focuses on the evaluation of Heterogeneous Accelerator-Rich Platform (HARP) by implementing OFDM receiver blocks as designs for proof-of-concept. The HARP template allows the designer to instantiate a heterogeneous reconfigurable platform with a very large amount of custom-tailored computational resources while delivering a high performance in terms of many high-level metrics. The availability of this platform lays an excellent foundation to investigate techniques and methods to replace the Dark or Dim part of chip with high-performance silicon dissipating very low power and energy. Furthermore, this research work is also addressing the power and energy issues of the embedded computing systems by tailoring the HARP for self-aware and energy-aware computing models. In this context, the instantaneous power dissipation and therefore the heat dissipation of HARP are mitigated on FPGA/ASIC by using Dynamic Voltage and Frequency Scaling (DVFS) to minimize the dark/dim part of the chip. Upgraded HARP for self-aware and energy-aware computing can be utilized as an energy-efficient general-purpose transceiver platform that is cognitive to many radio standards and can provide high throughput while consuming as little energy as possible. The evaluation of HARP has shown promising results, which makes it a suitable platform for avoiding Dark Silicon in embedded computing platforms and also for diverse needs of IoT communications.In this thesis, the author designed the blocks of OFDM receiver by crafting templatebased CGRA devices and then attached them to HARP’s Network-on-Chip (NoC) nodes. The performance of application-specific accelerators generated from templatebased CGRAs, the performance of the entire platform subsequent to integrating the CGRA nodes on HARP and the NoC traffic are recorded in terms of several highlevel performance metrics. In evaluating HARP on FPGA prototype, it delivers a performance of 0.012 GOPS/mW. Because of the scalability and regularity in HARP, the author considered its value as architectural constant. In addition to showing the gain and the benefits of maximizing the number of reconfigurable processing resources on a platform in comparison to the scaled performance of several state-of-the-art platforms, HARP’s architectural constant ensures application-independent figure of merit. HARP is further evaluated by implementing various sizes of Discrete Cosine transform (DCT) and Discrete Sine Transform (DST) dedicated for HEVC standard, which showed its ability to sustain Full HD 1080p format at 30 fps on FPGA. The author also integrated self-aware computing model in HARP to mitigate the power dissipation of an OFDM receiver. In the case of FPGA implementation, the total power dissipation of the platform showed 16.8% reduction due to employing the Feedback Control System (FCS) technique with Dynamic Frequency Scaling (DFS). Furthermore, by moving to ASIC technology and scaling both frequency and voltage simultaneously, significant dynamic power reduction (up to 82.98%) was achieved, which proved the DFS/DVFS techniques as one step forward to mitigate the Dark Silicon issue

Architectural explorations for streaming accelerators with customized memory layouts

El concepto básico de la arquitectura mono-nucleo en los procesadores de propósito general se ajusta bien a un modelo de programación secuencial. La integración de multiples núcleos en un solo chip ha permitido a los procesadores correr partes del programa en paralelo. Sin embargo, la explotación del enorme paralelismo disponible en muchas aplicaciones de alto rendimiento y de los datos correspondientes es difícil de conseguir usando unicamente multicores de propósito general. La aparición de aceleradores tipo streaming y de los correspondientes modelos de programación han mejorado esta situación proporcionando arquitecturas orientadas al proceso de flujos de datos. La idea básica detrás del diseño de estas arquitecturas responde a la necesidad de procesar conjuntos enormes de datos. Estos dispositivos de alto rendimiento orientados a flujos permiten el procesamiento rapido de datos mediante el uso eficiente de computación paralela y comunicación entre procesos. Los aceleradores streaming orientados a flujos, igual que en otros procesadores, consisten en diversos componentes micro-arquitectonicos como por ejemplo las estructuras de memoria, las unidades de computo, las unidades de control, los canales de Entrada/Salida y controles de Entrada/Salida, etc. Sin embargo, los requisitos del flujo de datos agregan algunas características especiales e imponen otras restricciones que afectan al rendimiento. Estos dispositivos, por lo general, ofrecen un gran número de recursos computacionales, pero obligan a reorganizar los conjuntos de datos en paralelo, maximizando la independiencia para alimentar los recursos de computación en forma de flujos. La disposición de datos en conjuntos independientes de flujos paralelos no es una tarea sencilla. Es posible que se tenga que cambiar la estructura de un algoritmo en su conjunto o, incluso, puede requerir la reescritura del algoritmo desde cero. Sin embargo, todos estos esfuerzos para la reordenación de los patrones de las aplicaciones de acceso a datos puede que no sean muy útiles para lograr un rendimiento óptimo. Esto es debido a las posibles limitaciones microarquitectonicas de la plataforma de destino para los mecanismos hardware de prefetch, el tamaño y la granularidad del almacenamiento local, y la flexibilidad para disponer de forma serial los datos en el interior del almacenamiento local. Las limitaciones de una plataforma de streaming de proposito general para el prefetching de datos, almacenamiento y demas procedimientos para organizar y mantener los datos en forma de flujos paralelos e independientes podría ser eliminado empleando técnicas a nivel micro-arquitectonico. Esto incluye el uso de memorias personalizadas especificamente para las aplicaciones en el front-end de una arquitectura streaming. El objetivo de esta tesis es presentar exploraciones arquitectónicas de los aceleradores streaming con diseños de memoria personalizados. En general, la tesis cubre tres aspectos principales de tales aceleradores. Estos aspectos se pueden clasificar como: i) Diseño de aceleradores de aplicaciones específicas con diseños de memoria personalizados, ii) diseño de aceleradores con memorias personalizadas basados en plantillas, y iii) exploraciones del espacio de diseño para dispositivos orientados a flujos con las memorias estándar y personalizadas. Esta tesis concluye con la propuesta conceptual de una Blacksmith Streaming Architecture (BSArc). El modelo de computación Blacksmith permite la adopción a nivel de hardware de un front-end de aplicación específico utilizando una GPU como back-end. Esto permite maximizar la explotación de la localidad de datos y el paralelismo a nivel de datos de una aplicación mientras que proporciona un flujo mayor de datos al back-end. Consideramos que el diseño de estos procesadores con memorias especializadas debe ser proporcionado por expertos del dominio de aplicación en la forma de plantillas.The basic concept behind the architecture of a general purpose CPU core conforms well to a serial programming model. The integration of more cores on a single chip helped CPUs in running parts of a program in parallel. However, the utilization of huge parallelism available from many high performance applications and the corresponding data is hard to achieve from these general purpose multi-cores. Streaming accelerators and the corresponding programing models improve upon this situation by providing throughput oriented architectures. The basic idea behind the design of these architectures matches the everyday increasing requirements of processing huge data sets. These high-performance throughput oriented devices help in high performance processing of data by using efficient parallel computations and streaming based communications. The throughput oriented streaming accelerators ¿ similar to the other processors ¿ consist of numerous types of micro-architectural components including the memory structures, compute units, control units, I/O channels and I/O controls etc. However, the throughput requirements add some special features and impose other restrictions for the performance purposes. These devices, normally, offer a large number of compute resources but restrict the applications to arrange parallel and maximally independent data sets to feed the compute resources in the form of streams. The arrangement of data into independent sets of parallel streams is not an easy and simple task. It may need to change the structure of an algorithm as a whole or even it can require to write a new algorithm from scratch for the target application. However, all these efforts for the re-arrangement of application data access patterns may still not be very helpful to achieve the optimal performance. This is because of the possible micro-architectural constraints of the target platform for the hardware pre-fetching mechanisms, the size and the granularity of the local storage and the flexibility in data marshaling inside the local storage. The constraints of a general purpose streaming platform on the data pre-fetching, storing and maneuvering to arrange and maintain it in the form of parallel and independent streams could be removed by employing micro-architectural level design approaches. This includes the usage of application specific customized memories in the front-end of a streaming architecture. The focus of this thesis is to present architectural explorations for the streaming accelerators using customized memory layouts. In general the thesis covers three main aspects of such streaming accelerators in this research. These aspects can be categorized as : i) Design of Application Specific Accelerators with Customized Memory Layout ii) Template Based Design Support for Customized Memory Accelerators and iii) Design Space Explorations for Throughput Oriented Devices with Standard and Customized Memories. This thesis concludes with a conceptual proposal on a Blacksmith Streaming Architecture (BSArc). The Blacksmith Computing allow the hardware-level adoption of an application specific front-end with a GPU like streaming back-end. This gives an opportunity to exploit maximum possible data locality and the data level parallelism from an application while providing a throughput natured powerful back-end. We consider that the design of these specialized memory layouts for the front-end of the device are provided by the application domain experts in the form of templates. These templates are adjustable according to a device and the problem size at the device's configuration time. The physical availability of such an architecture may still take time. However, simulation framework helps in architectural explorations to give insight into the proposal and predicts potential performance benefits for such an architecture.Postprint (published version

Architectural explorations for streaming accelerators with customized memory layouts

El concepto básico de la arquitectura mono-nucleo en los procesadores de propósito general se ajusta bien a un modelo de programación secuencial. La integración de multiples núcleos en un solo chip ha permitido a los procesadores correr partes del programa en paralelo. Sin embargo, la explotación del enorme paralelismo disponible en muchas aplicaciones de alto rendimiento y de los datos correspondientes es difícil de conseguir usando unicamente multicores de propósito general. La aparición de aceleradores tipo streaming y de los correspondientes modelos de programación han mejorado esta situación proporcionando arquitecturas orientadas al proceso de flujos de datos. La idea básica detrás del diseño de estas arquitecturas responde a la necesidad de procesar conjuntos enormes de datos. Estos dispositivos de alto rendimiento orientados a flujos permiten el procesamiento rapido de datos mediante el uso eficiente de computación paralela y comunicación entre procesos. Los aceleradores streaming orientados a flujos, igual que en otros procesadores, consisten en diversos componentes micro-arquitectonicos como por ejemplo las estructuras de memoria, las unidades de computo, las unidades de control, los canales de Entrada/Salida y controles de Entrada/Salida, etc. Sin embargo, los requisitos del flujo de datos agregan algunas características especiales e imponen otras restricciones que afectan al rendimiento. Estos dispositivos, por lo general, ofrecen un gran número de recursos computacionales, pero obligan a reorganizar los conjuntos de datos en paralelo, maximizando la independiencia para alimentar los recursos de computación en forma de flujos. La disposición de datos en conjuntos independientes de flujos paralelos no es una tarea sencilla. Es posible que se tenga que cambiar la estructura de un algoritmo en su conjunto o, incluso, puede requerir la reescritura del algoritmo desde cero. Sin embargo, todos estos esfuerzos para la reordenación de los patrones de las aplicaciones de acceso a datos puede que no sean muy útiles para lograr un rendimiento óptimo. Esto es debido a las posibles limitaciones microarquitectonicas de la plataforma de destino para los mecanismos hardware de prefetch, el tamaño y la granularidad del almacenamiento local, y la flexibilidad para disponer de forma serial los datos en el interior del almacenamiento local. Las limitaciones de una plataforma de streaming de proposito general para el prefetching de datos, almacenamiento y demas procedimientos para organizar y mantener los datos en forma de flujos paralelos e independientes podría ser eliminado empleando técnicas a nivel micro-arquitectonico. Esto incluye el uso de memorias personalizadas especificamente para las aplicaciones en el front-end de una arquitectura streaming. El objetivo de esta tesis es presentar exploraciones arquitectónicas de los aceleradores streaming con diseños de memoria personalizados. En general, la tesis cubre tres aspectos principales de tales aceleradores. Estos aspectos se pueden clasificar como: i) Diseño de aceleradores de aplicaciones específicas con diseños de memoria personalizados, ii) diseño de aceleradores con memorias personalizadas basados en plantillas, y iii) exploraciones del espacio de diseño para dispositivos orientados a flujos con las memorias estándar y personalizadas. Esta tesis concluye con la propuesta conceptual de una Blacksmith Streaming Architecture (BSArc). El modelo de computación Blacksmith permite la adopción a nivel de hardware de un front-end de aplicación específico utilizando una GPU como back-end. Esto permite maximizar la explotación de la localidad de datos y el paralelismo a nivel de datos de una aplicación mientras que proporciona un flujo mayor de datos al back-end. Consideramos que el diseño de estos procesadores con memorias especializadas debe ser proporcionado por expertos del dominio de aplicación en la forma de plantillas.The basic concept behind the architecture of a general purpose CPU core conforms well to a serial programming model. The integration of more cores on a single chip helped CPUs in running parts of a program in parallel. However, the utilization of huge parallelism available from many high performance applications and the corresponding data is hard to achieve from these general purpose multi-cores. Streaming accelerators and the corresponding programing models improve upon this situation by providing throughput oriented architectures. The basic idea behind the design of these architectures matches the everyday increasing requirements of processing huge data sets. These high-performance throughput oriented devices help in high performance processing of data by using efficient parallel computations and streaming based communications. The throughput oriented streaming accelerators ¿ similar to the other processors ¿ consist of numerous types of micro-architectural components including the memory structures, compute units, control units, I/O channels and I/O controls etc. However, the throughput requirements add some special features and impose other restrictions for the performance purposes. These devices, normally, offer a large number of compute resources but restrict the applications to arrange parallel and maximally independent data sets to feed the compute resources in the form of streams. The arrangement of data into independent sets of parallel streams is not an easy and simple task. It may need to change the structure of an algorithm as a whole or even it can require to write a new algorithm from scratch for the target application. However, all these efforts for the re-arrangement of application data access patterns may still not be very helpful to achieve the optimal performance. This is because of the possible micro-architectural constraints of the target platform for the hardware pre-fetching mechanisms, the size and the granularity of the local storage and the flexibility in data marshaling inside the local storage. The constraints of a general purpose streaming platform on the data pre-fetching, storing and maneuvering to arrange and maintain it in the form of parallel and independent streams could be removed by employing micro-architectural level design approaches. This includes the usage of application specific customized memories in the front-end of a streaming architecture. The focus of this thesis is to present architectural explorations for the streaming accelerators using customized memory layouts. In general the thesis covers three main aspects of such streaming accelerators in this research. These aspects can be categorized as : i) Design of Application Specific Accelerators with Customized Memory Layout ii) Template Based Design Support for Customized Memory Accelerators and iii) Design Space Explorations for Throughput Oriented Devices with Standard and Customized Memories. This thesis concludes with a conceptual proposal on a Blacksmith Streaming Architecture (BSArc). The Blacksmith Computing allow the hardware-level adoption of an application specific front-end with a GPU like streaming back-end. This gives an opportunity to exploit maximum possible data locality and the data level parallelism from an application while providing a throughput natured powerful back-end. We consider that the design of these specialized memory layouts for the front-end of the device are provided by the application domain experts in the form of templates. These templates are adjustable according to a device and the problem size at the device's configuration time. The physical availability of such an architecture may still take time. However, simulation framework helps in architectural explorations to give insight into the proposal and predicts potential performance benefits for such an architecture

A language and a system for program optimization

Hardware complexity has increased over time, and as architectures evolve and new ones are adopted, programs must often be altered by numerous optimizations to attain maximum computing power on each target environment. As a result, the code becomes unrecognizable over time, hard to maintain, and challenging to modify. Furthermore, as the code evolves, it is hard to keep the optimizations up to date. The need to develop and maintain separate versions of the application for each target platform is an immense undertaking, especially for the large and long-lived applications commonly found in the high-performance computing (HPC) community. This dissertation presents Locus, a new system, and a language for optimizing complex, long-lived applications for different platforms. We describe the requirements that we believe are necessary for making automatic performance tuning widely adopted. We present the design and implementation of a system that fulfills these requirements. It includes a domain-specific language that can represent complex collections of transformations, an interface to integrate external modules, and a database to manage platform-specific efficient code. The database allows the system’s users to access optimized code without having to install the code generation toolset. The Locus language allows the definition of a search space combined with the programming of optimization sequences separated from the application’s reference code. After all, we present an approach for performance portability. Our thesis is that we can ameliorate the difficulty of optimizing applications using a methodology based on optimization programming and automated empirical search. Our system automatically selects, generates, and executes candidate implementations to find the one with the best performance. We present examples to illustrate the power and simplicity of the language. The experimental evaluation shows that exploring the space of candidate implementations typically leads to better performing codes than those produced by conventional compiler optimizations that are based solely on heuristics. Locus was able to generate a matrix-matrix multiplication code that outperformed the IBM XLC internal hand-optimized version by 2× on the Power 9 processors. On Intel E5, Locus generates code with performance comparable to Intel MKL’s. We also improve performance relative to the reference implementation of up to 4× on stencil computations. Locus ability to integrate complex search spaces with optimization sequences can result in very complicated optimization programs. Locus compiler applies optimizations to remove from the optimization sequences unnecessary search statements making the exploration for faster implementations more accessible. We optimize matrix transpose, matrix-matrix multiplication, fast Fourier transform, symmetric eigenproblem, and sparse matrix-vector multiplication through divide and conquer. We implement three strategies using the Locus language to create search spaces to find the best shapes of the base case and the best ways of subdividing the problem. The search space representation for the divide-and-conquer strategy uses a combination of recursion and OR blocks. The Locus compiler automatically expands the recursion and ensures that the search space is correctly represented. The results showed that the empirical search was important to improve performance by generating faster base cases and finding the best splitting. We also use Locus to optimize large, complex applications. We match the performance of hand-optimized kernels of the Kripke transport code for different input data layouts. The Plascom2 multi-physics application is optimized to find the best way to use a multi-core CPU and GPU. The use of Tangram, Hydra, and OpenMP provided an interesting search space that improved performance by approximately 4.3× on ZAXPY and ZXDOTY kernels. Lastly, in a similar fashion to how a compiler works, we applied a search space representing a collection of optimization sequences to 856 loops extracted from 16 benchmarks that resulted in good performance improvements