Gather-scatter
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Gather-scatter
Gather/scatter is a type of memory addressing that at once collects (gathers) from, or stores (scatters) data to, multiple, arbitrary indices. Examples of its use include sparse linear algebra operations, sorting algorithms, fast Fourier transforms, and some computational graph theory problems. It is the vector equivalent of register indirect addressing, with gather involving indexed reads, and scatter, indexed writes. Vector processors (and some SIMD units in CPUs) have hardware support for gather and scatter operations. Definitions Gather A sparsely populated vector y holding N non-empty elements can be represented by two densely populated vectors of length N; x containing the non-empty elements of y, and idx giving the index in y where x's element is located. The gather of y into x, denoted x \leftarrow y, _x, assigns x(i)=y(idx(i)) with idx having already been calculated. Assuming no pointer aliasing between x[], y[],idx[], a C (programming language), C implementation is ...
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AVX2
Advanced Vector Extensions (AVX) are extensions to the x86 instruction set architecture for microprocessors from Intel and Advanced Micro Devices (AMD). They were proposed by Intel in March 2008 and first supported by Intel with the Sandy Bridge processor shipping in Q1 2011 and later by AMD with the Bulldozer processor shipping in Q3 2011. AVX provides new features, new instructions and a new coding scheme. AVX2 (also known as Haswell New Instructions) expands most integer commands to 256 bits and introduces new instructions. They were first supported by Intel with the Haswell processor, which shipped in 2013. AVX-512 expands AVX to 512-bit support using a new EVEX prefix encoding proposed by Intel in July 2013 and first supported by Intel with the Knights Landing co-processor, which shipped in 2016. In conventional processors, AVX-512 was introduced with Skylake server and HEDT processors in 2017. Advanced Vector Extensions AVX uses sixteen YMM registers to perform a sin ...
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Vector Processor
In computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called ''vectors''. This is in contrast to scalar processors, whose instructions operate on single data items only, and in contrast to some of those same scalar processors having additional single instruction, multiple data (SIMD) or SWAR Arithmetic Units. Vector processors can greatly improve performance on certain workloads, notably numerical simulation and similar tasks. Vector processing techniques also operate in video-game console hardware and in graphics accelerators. Vector machines appeared in the early 1970s and dominated supercomputer design through the 1970s into the 1990s, notably the various Cray platforms. The rapid fall in the price-to-performance ratio of conventional microprocessor designs led to a decline in vector supercom ...
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Memory Access Pattern
In computing, a memory access pattern or IO access pattern is the pattern with which a system or program reads and writes memory on secondary storage. These patterns differ in the level of locality of reference and drastically affect cache performance, and also have implications for the approach to parallelism and distribution of workload in shared memory systems. Further, cache coherency issues can affect multiprocessor performance, which means that certain memory access patterns place a ceiling on parallelism (which manycore approaches seek to break). Computer memory is usually described as "random access", but traversals by software will still exhibit patterns that can be exploited for efficiency. Various tools exist to help system designers and programmers understand, analyse and improve the memory access pattern, including VTune and Vectorization Advisor, including tools to address GPU memory access patterns Memory access patterns also have implications for security, which ...
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Vector Processing
In computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called ''vectors''. This is in contrast to scalar processors, whose instructions operate on single data items only, and in contrast to some of those same scalar processors having additional single instruction, multiple data (SIMD) or SWAR Arithmetic Units. Vector processors can greatly improve performance on certain workloads, notably numerical simulation and similar tasks. Vector processing techniques also operate in video-game console hardware and in graphics accelerators. Vector machines appeared in the early 1970s and dominated supercomputer design through the 1970s into the 1990s, notably the various Cray platforms. The rapid fall in the price-to-performance ratio of conventional microprocessor designs led to a decline in vector supercomput ...
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Fast Fourier Transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O\left(N^2\right), which arises if one simply applies the definition of DFT, to O(N \log N), where N is the data size. The difference in speed can be enormous, especially for long data sets where ''N'' may be in the thousands or millions. In the presence of round-off error, many FFT algorithm ...
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Scalable Vector Extension
AArch64 or ARM64 is the 64-bit extension of the ARM architecture family. It was first introduced with the Armv8-A architecture. Arm releases a new extension every year. ARMv8.x and ARMv9.x extensions and features Announced in October 2011, ARMv8-A represents a fundamental change to the ARM architecture. It adds an optional 64-bit architecture, named "AArch64", and the associated new "A64" instruction set. AArch64 provides user-space compatibility with the existing 32-bit architecture ("AArch32" / ARMv7-A), and instruction set ("A32"). The 16-32bit Thumb instruction set is referred to as "T32" and has no 64-bit counterpart. ARMv8-A allows 32-bit applications to be executed in a 64-bit OS, and a 32-bit OS to be under the control of a 64-bit hypervisor. ARM announced their Cortex-A53 and Cortex-A57 cores on 30 October 2012. Apple was the first to release an ARMv8-A compatible core (Cyclone) in a consumer product (iPhone 5S). AppliedMicro, using an FPGA, was the first to demo ARMv8 ...
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Parallel Computing
Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: bit-level, instruction-level, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling.S.V. Adve ''et al.'' (November 2008)"Parallel Computing Research at Illinois: The UPCRC Agenda" (PDF). Parallel@Illinois, University of Illinois at Urbana-Champaign. "The main techniques for these performance benefits—increased clock frequency and smarter but increasingly complex architectures—are now hitting the so-called power wall. The computer industry has accepted that future performance increases must largely come from increasing the number of processors (or cores) on a die, rather than m ...
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Sparse Matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The ...
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Compute Kernel
In computing, a compute kernel is a routine compiled for high throughput accelerators (such as graphics processing units (GPUs), digital signal processors (DSPs) or field-programmable gate arrays (FPGAs)), separate from but used by a main program (typically running on a central processing unit). They are sometimes called compute shaders, sharing execution units with vertex shaders and pixel shaders on GPUs, but are not limited to execution on one class of device, or graphics APIs. Description Compute kernels roughly correspond to inner loops when implementing algorithms in traditional languages (except there is no implied sequential operation), or to code passed to internal iterators. They may be specified by a separate programming language such as "OpenCL C" (managed by the OpenCL API), as "compute shaders" written in a shading language (managed by a graphics API such as OpenGL), or embedded directly in application code written in a high level language, as in the case of ...
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Vectorization (other)
Vectorization may refer to: Computing * Array programming, a style of computer programming where operations are applied to whole arrays instead of individual elements * Automatic vectorization, a compiler optimization that transforms loops to vector operations * Image tracing, the creation of vector from raster graphics * Word embedding, mapping words to vectors, in natural language processing Other uses * Vectorization (mathematics) In mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a column vector. Specifically, the vectorization of a matrix ''A'', denoted vec(''A''), is t ..., a linear transformation which converts a matrix into a column vector * Drug vectorization, to (intra)cellular targeting See also * Vector (other) * Vector graphics (other) {{disambiguation ...
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SIMD
Single instruction, multiple data (SIMD) is a type of parallel processing in Flynn's taxonomy. SIMD can be internal (part of the hardware design) and it can be directly accessible through an instruction set architecture (ISA), but it should not be confused with an ISA. SIMD describes computers with multiple processing elements that perform the same operation on multiple data points simultaneously. Such machines exploit data level parallelism, but not concurrency: there are simultaneous (parallel) computations, but each unit performs the exact same instruction at any given moment (just with different data). SIMD is particularly applicable to common tasks such as adjusting the contrast in a digital image or adjusting the volume of digital audio. Most modern CPU designs include SIMD instructions to improve the performance of multimedia use. SIMD has three different subcategories in Flynn's 1972 Taxonomy, one of which is SIMT. SIMT should not be confused with software thr ...
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Prefetch
Prefetching in computer science is a technique for speeding up fetch operations by beginning a fetch operation whose result is expected to be needed soon. Usually this is before it is ''known'' to be needed, so there is a risk of wasting time by prefetching data that will not be used. The technique can be applied in several circumstances: * Cache prefetching, a speedup technique used by computer processors where instructions or data are fetched before they are needed * Prefetch input queue (PIQ), in computer architecture, pre-loading machine code from memory * Link prefetching, a web mechanism for prefetching links * Prefetcher technology in modern releases of Microsoft Windows * Cache control instruction#Prefetch, prefetch instructions, for example provided by ** PREFETCH, an X86 instruction listings, X86 instruction in computing * Prefetch buffer, a feature of DDR SDRAM memory * Paging#Anticipatory paging, Swap prefetch, in computer operating systems, anticipatory paging See al ...
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