Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

PyCUDA and PyOpenCL: A Scripting-Based Approach to GPU Run-Time Code Generation

High-performance computing has recently seen a surge of interest in heterogeneous systems, with an emphasis on modern Graphics Processing Units (GPUs). These devices offer tremendous potential for performance and efficiency in important large-scale applications of computational science. However, exploiting this potential can be challenging, as one must adapt to the specialized and rapidly evolving computing environment currently exhibited by GPUs. One way of addressing this challenge is to embrace better techniques and develop tools tailored to their needs. This article presents one simple technique, GPU run-time code generation (RTCG), along with PyCUDA and PyOpenCL, two open-source toolkits that support this technique. In introducing PyCUDA and PyOpenCL, this article proposes the combination of a dynamic, high-level scripting language with the massive performance of a GPU as a compelling two-tiered computing platform, potentially offering significant performance and productivity advantages over conventional single-tier, static systems. The concept of RTCG is simple and easily implemented using existing, robust infrastructure. Nonetheless it is powerful enough to support (and encourage) the creation of custom application-specific tools by its users. The premise of the paper is illustrated by a wide range of examples where the technique has been applied with considerable success.Comment: Submitted to Parallel Computing, Elsevie

Implicit transactional memory in kilo-instruction multiprocessors

Although they have been the main server technology for many years, multiprocessors are undergoing a renaissance due to multi-core chips and the attractive scalability properties of combining a number of such multi-core chips into a system. The widespread use of multiprocessor systems will make performance losses due to consistency models and synchronization styles of popular programming models even more evident than they already are. Known architectural approaches to combat these losses are generally too complex, too specialized, or not transparent to software. In this article, we introduce implicit transactional memory as a generalized architectural concept to remove unnecessary performance losses caused by consistency models and synchronization styles. We show how the concept of implicit transactions can be implemented with low complexity by leveraging the multi-checkpoint mechanism of the Kilo-Instruction Processor. By relying on a general speculation substrate, this method supports even the strictest consistency model – sequential consistency – potentially as effectively as weaker models and it allows multiple threads to speculatively execute critical sections, beyond barriers and event synchronizations.Postprint (published version

Compile-time support for thread-level speculation

Una de las principales preocupaciones de las ciencias de la computación es el estudio de las capacidades paralelas tanto de programas como de los procesadores que los ejecutan. Existen varias razones que hacen muy deseable el desarrollo de técnicas que paralelicen automáticamente el código. Entre ellas se encuentran el inmenso número de programas secuenciales existentes ya escritos, la complejidad de los lenguajes de programación paralelos, y los conocimientos que se requieren para paralelizar un código. Sin embargo, los actuales mecanismos de paralelización automática implementados en los compiladores comerciales no son capaces de paralelizar la mayoría de los bucles en un código [1], debido a la dependencias de datos que existen entre ellos [2]. Por lo tanto, se hace necesaria la búsqueda de nuevas técnicas, como la paralelización especulativa [3-5], que saquen beneficio de las potenciales capacidades paralelas del hardware y arquitecturas multiprocesador actuales. Sin embargo, ésta y otras técnicas requieren la intervención manual de programadores experimentados. Antes de ofrecer soluciones alternativas, se han evaluado las capacidades de paralelización de los compiladores comerciales, exponiendo las limitaciones de los mecanismos de paralelización automática que implementan. El estudio revela que estos mecanismos de paralelización automática sólo alcanzan un 19% de speedup en promedio para los benchmarks del SPEC CPU2006 [6], siendo este un resultado significativamente inferior al obtenido por técnicas de paralelización especulativa [7]. Sin embargo, la paralelización especulativa requiere una extensa modificación manual del código por parte de programadores. Esta Tesis aborda este problema definiendo una nueva cláusula OpenMP [8], llamada ¿speculative¿, que permite señalar qué variables pueden llevar a una violación de dependencia. Además, esta Tesis también propone un sistema en tiempo de compilación que, usando la información sobre los accesos a las variables que proporcionan las cláusulas OpenMP, añade automáticamente todo el código necesario para gestionar la ejecución especulativa de un programa. Esto libera al programador de modificar el código manualmente, evitando posibles errores y una tediosa tarea. El código generado por nuestro sistema enlaza con la librería de ejecución especulativamente paralela desarrollada por Estebanez, García-Yagüez, Llanos y Gonzalez-Escribano [9,10].Departamento de Informática (Arquitectura y Tecnología de Computadores, Ciencias de la Computación e Inteligencia Artificial, Lenguajes y Sistemas Informáticos

Elixir: synthesis of parallel irregular algorithms

Algorithms in new application areas like machine learning and data analytics usually operate on unstructured sparse graphs. Writing efficient parallel code to implement these algorithms is very challenging for a number of reasons. First, there may be many algorithms to solve a problem and each algorithm may have many implementations. Second, synchronization, which is necessary for correct parallel execution, introduces potential problems such as data-races and deadlocks. These issues interact in subtle ways, making the best solution dependent both on the parallel platform and on properties of the input graph. Consequently, implementing and selecting the best parallel solution can be a daunting task for non-experts, since we have few performance models for predicting the performance of parallel sparse graph programs on parallel hardware. This dissertation presents a synthesis methodology and a system, Elixir, that addresses these problems by (i) allowing programmers to specify solutions at a high level of abstraction, and (ii) generating many parallel implementations automatically and using search to find the best one. An Elixir specification consists of a set of operators capturing the main algorithm logic and a schedule specifying how to efficiently apply the operators. Elixir employs sophisticated automated reasoning to merge these two components, and uses techniques based on automated planning to insert synchronization and synthesize efficient parallel code. Experimental evaluation of our approach demonstrates that the performance of the Elixir generated code is competitive to, and can even outperform, hand-optimized code written by expert programmers for many interesting graph benchmarks.Computer Science