Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.

Learn how to accelerate C++ programs using data parallelism. This open access book enables C++ programmers to be at the forefront of this exciting and important new development that is helping to push computing to new levels. It is full of practical advice, detailed explanations, and code examples to illustrate key topics. Data parallelism in C++ enables access to parallel resources in a modern heterogeneous system, freeing you from being locked into any particular computing device. Now a single C++ application can use any combination of devices—including GPUs, CPUs, FPGAs and AI ASICs—that are suitable to the problems at hand. This book begins by introducing data parallelism and foundational topics for effective use of the SYCL standard from the Khronos Group and Data Parallel C++ (DPC++), the open source compiler used in this book. Later chapters cover advanced topics including error handling, hardware-specific programming, communication and synchronization, and memory model considerations. Data Parallel C++ provides you with everything needed to use SYCL for programming heterogeneous systems. What You'll Learn Accelerate C++ programs using data-parallel programming Target multiple device types (e.g. CPU, GPU, FPGA) Use SYCL and SYCL compilers Connect with computing’s heterogeneous future via Intel’s oneAPI initiative Who This Book Is For Those new data-parallel programming and computer programmers interested in data-parallel programming using C++.

ScaLAPACK is an acronym for Scalable Linear Algebra Package or Scalable LAPACK. It is a library of high-performance linear algebra routines for distributed memory message-passing MIMD computers and networks of workstations supporting parallel virtual machine (PVM) and/or message passing interface (MPI). It is a continuation of the LAPACK project, which designed and produced analogous software for workstations, vector supercomputers, and shared memory parallel computers. Both libraries contain routines for solving systems of linear equations, least squares problems, and eigenvalue problems. The goals of both projects are efficiency, scalability, reliability, portability, flexibility, and ease of use.

The CUDA Handbook begins where CUDA by Example (Addison-Wesley, 2011) leaves off, discussing CUDA hardware and software in greater detail and covering both CUDA 5.0 and Kepler. Every CUDA developer, from the casual to the most sophisticated, will find something here of interest and immediate usefulness. Newer CUDA developers will see how the hardware processes commands and how the driver checks progress; more experienced CUDA developers will appreciate the expert coverage of topics such as the driver API and context migration, as well as the guidance on how best to structure CPU/GPU data interchange and synchronization. The accompanying open source code–more than 25,000 lines of it, freely available at www.cudahandbook.com–is specifically intended to be reused and repurposed by developers. Designed to be both a comprehensive reference and a practical cookbook, the text is divided into the following three parts: Part I, Overview, gives high-level descriptions of the hardware and software that make CUDA possible. Part II, Details, provides thorough descriptions of every aspect of CUDA, including Memory Streams and events Models of execution, including the dynamic parallelism feature, new with CUDA 5.0 and SM 3.5 The streaming multiprocessors, including descriptions of all features through SM 3.5 Programming multiple GPUs Texturing The source code accompanying Part II is presented as reusable microbenchmarks and microdemos, designed to expose specific hardware characteristics or highlight specific use cases. Part III, Select Applications, details specific families of CUDA applications and key parallel algorithms, including Streaming workloads Reduction Parallel prefix sum (Scan) N-body Image Processing These algorithms cover the full range of potential CUDA applications.

Annotation SC17: The International Conference for High Performance Computing, Networking, Storage and Analysis Nov 12, 2017-Nov 17, 2017 Denver, USA. You can view more information about this proceeding and all of ACM�s other published conference proceedings from the ACM Digital Library: http://www.acm.org/dl.