General-purpose computing on graphics processing units (GPGPU, GPGP or less often GP²U) is the means of using a graphics processing unit (GPU), which typically handles computation only for computer graphics, to perform computation in applications traditionally handled by the central processing unit (CPU).^[1][2][3] Any GPU providing a functionally complete set of operations performed on arbitrary bits can compute any computable value. Additionally, the use of multiple graphics cards in one computer, or large numbers of graphics chips, further parallelizes the already parallel nature of graphics processing.^[4]

Programmability[link]

In principle, any boolean function can be built-up from a functionally complete set of logic operators. An early example of general purpose computing with a GPU involved performing additions by using an early stream processor called a blitter to invoke a special sequence of logical operations on bit vectors.^[5] Such methods are seldom used today as modern GPUs now include support for more advanced mathematical operations including addition, multiplication, and often certain transcendental functions.

The programmability of the pipelines have trended^{[clarification needed]} according to Microsoft’s DirectX specification,^{[citation needed]} with DirectX 8 introducing Shader Model 1.1, DirectX 8.1 Pixel Shader Models 1.2, 1.3 and 1.4, and DirectX 9 defining Shader Model 2.x and 3.0. Each shader model increased the programming model flexibilities and capabilities, ensuring the conforming hardware follows suit. The DirectX 10 specification introduces Shader Model 4.0 which unifies the programming specification for vertex, geometry (“Geometry Shaders” are new to DirectX 10) and fragment processing allowing for a better fit for unified shader hardware, thus providing one computational pool of programmable resource.^[vague]

Data types[link]

Pre-DirectX 9 graphics cards only supported paletted or integer color types. Various formats are available, each containing a red element, a green element, and a blue element.^{[citation needed]} Sometimes an additional alpha value is added, to be used for transparency. Common formats are:

• 8 bits per pixel – Sometimes palette mode, where each value is an index in a table with the real color value specified in one of the other formats. Sometimes two bits for red, three bits for green, and three bits for blue.
• 16 bits per pixel – Usually allocated as five bits for red, six bits for green, and five bits for blue.
• 24 bits per pixel – eight bits for each of red, green, and blue
• 32 bits per pixel – eight bits for each of red, green, blue, and alpha

For early fixed-function or limited programmability graphics (i.e. up to and including DirectX 8.1-compliant GPUs) this was sufficient because this is also the representation used in displays. This representation does have certain limitations, however. Given sufficient graphics processing power even graphics programmers would like to use better formats, such as floating point data formats, to obtain effects such as high dynamic range imaging. Many GPGPU applications require floating point accuracy, which came with graphics cards conforming to the DirectX 9 specification.

DirectX 9 Shader Model 2.x suggested the support of two precision types: full and partial precision. Full precision support could either be FP32 or FP24 (floating point 32- or 24-bit per component) or greater, while partial precision was FP16. ATI’s R300 series of GPUs supported FP24 precision only in the programmable fragment pipeline (although FP32 was supported in the vertex processors) while Nvidia’s NV30 series supported both FP16 and FP32; other vendors such as S3 Graphics and XGI supported a mixture of formats up to FP24.

Shader Model 3.0 altered the specification, increasing full precision requirements to a minimum of FP32 support in the fragment pipeline. ATI’s Shader Model 3.0 compliant R5xx generation (Radeon X1000 series) supports just FP32 throughout the pipeline while Nvidia’s NV4x and G7x series continued to support both FP32 full precision and FP16 partial precisions. Although not stipulated by Shader Model 3.0, both ATI and Nvidia’s Shader Model 3.0 GPUs introduced support for blendable FP16 render targets, more easily facilitating the support for High Dynamic Range Rendering.^{[citation needed]}

The implementations of floating point on Nvidia GPUs are mostly IEEE compliant; however, this is not true across all vendors.^[6] This has implications for correctness which are considered important to some scientific applications. While 64-bit floating point values (double precision float) are commonly available on CPUs, these are not universally supported on GPUs; some GPU architectures sacrifice IEEE compliance while others lack double-precision altogether. There have been efforts to emulate double-precision floating point values on GPUs; however, the speed tradeoff negates any benefit to offloading the computation onto the GPU in the first place.^[7]

Most operations on the GPU operate in a vectorized fashion: one operation can be performed on up to four values at once. For instance, if one color <R1, G1, B1> is to be modulated by another color <R2, G2, B2>, the GPU can produce the resulting color <R1*R2, G1*G2, B1*B2> in one operation. This functionality is useful in graphics because almost every basic data type is a vector (either 2-, 3-, or 4-dimensional). Examples include vertices, colors, normal vectors, and texture coordinates. Many other applications can put this to good use, and because of their higher performance, vector instructions (SIMD) have long been available on CPUs.

In 2002, James Fung et al developed OpenVIDIA at University of Toronto, and demonstrated this work, which was later published in 2003, 2004, and 2005,^[8] in conjunction with a collaboration between University of Toronto and nVIDIA. In November 2006 Nvidia launched CUDA, an SDK and API that allows using the C programming language to code algorithms for execution on Geforce 8 series GPUs. OpenCL, an open standard defined by the Khronos Group^[9] provides a cross-platform GPGPU platform that additionally supports data parallel compute on CPUs. OpenCL is actively supported on Intel, AMD, Nvidia and ARM platforms. GPGPU compared, for example, to traditional floating point accelerators such as the 64-bit CSX700 boards from ClearSpeed that are used in today's supercomputers, current top-end GPUs from AMD and Nvidia emphasize single-precision (32-bit) computation; double-precision (64-bit) computation executes more slowly.^{[citation needed]}

GPGPU programming concepts[link]

GPUs are designed specifically for graphics and thus are very restrictive in operations and programming. Because of their nature, GPUs are only effective for problems that can be solved using stream processing and the hardware can only be used in certain ways.

Stream processing[link]

GPUs can only process independent vertices and fragments, but can process many of them in parallel. This is especially effective when the programmer wants to process many vertices or fragments in the same way. In this sense, GPUs are stream processors – processors that can operate in parallel by running one kernel on many records in a stream at once.

A stream is simply a set of records that require similar computation. Streams provide data parallelism. Kernels are the functions that are applied to each element in the stream. In the GPUs, vertices and fragments are the elements in streams and vertex and fragment shaders are the kernels to be run on them. Since GPUs process elements independently there is no way to have shared or static data. For each element we can only read from the input, perform operations on it, and write to the output. It is permissible to have multiple inputs and multiple outputs, but never a piece of memory that is both readable and writable.^[vague]

Arithmetic intensity is defined as the number of operations performed per word of memory transferred. It is important for GPGPU applications to have high arithmetic intensity else the memory access latency will limit computational speedup.^[10]

Ideal GPGPU applications have large data sets, high parallelism, and minimal dependency between data elements.

GPU programming concepts[link]

Computational resources[link]

There are a variety of computational resources available on the GPU:

• Programmable processors – Vertex, primitive, and fragment pipelines allow programmer to perform kernel on streams of data
• Rasterizer – creates fragments and interpolates per-vertex constants such as texture coordinates and color
• Texture Unit – read only memory interface
• Framebuffer – write only memory interface

In fact, the programmer can substitute a write only texture for output instead of the framebuffer. This is accomplished either through Render to Texture (RTT), Render-To-Backbuffer-Copy-To-Texture (RTBCTT), or the more recent stream-out.

Textures as stream[link]

The most common form for a stream to take in GPGPU is a 2D grid because this fits naturally with the rendering model built into GPUs. Many computations naturally map into grids: matrix algebra, image processing, physically based simulation, and so on.

Since textures are used as memory, texture lookups are then used as memory reads. Certain operations can be done automatically by the GPU because of this.

Kernels[link]

Kernels can be thought of as the body of loops. For example, if the programmer were operating on a grid on the CPU they might have code that looked like this:

<source lang=C>

// Input and output grids have 10000 x 10000 or 100 million elements.

void transform_10k_by_10k_grid(float in[10000][10000], float *out[10000][10000]) {

 for(int x = 0; x < 10000; x++)
 {
   for(int y = 0; y < 10000; y++)
   {
     // The next line is executed 100 million times
     *out[x][y] = do_some_hard_work(in[x][y]);
   }
 }

}

</source>

On the GPU, the programmer only specifies the body of the loop as the kernel and what data to loop over by invoking geometry processing.

Flow control[link]

In sequential code it is possible to control the flow of the program using if-then-else statements and various forms of loops. Such flow control structures have only recently been added to GPUs.^[11] Conditional writes could be accomplished using a properly crafted series of arithmetic/bit operations, but looping and conditional branching were not possible.

Recent GPUs allow branching, but usually with a performance penalty. Branching should generally be avoided in inner loops, whether in CPU or GPU code, and various methods, such as static branch resolution, pre-computation, predication, loop splitting,^[12] and Z-cull^[13] can be used to achieve branching when hardware support does not exist.

GPU methods[link]

Map[link]

The map operation simply applies the given function (the kernel) to every element in the stream. A simple example is multiplying each value in the stream by a constant (increasing the brightness of an image). The map operation is simple to implement on the GPU. The programmer generates a fragment for each pixel on screen and applies a fragment program to each one. The result stream of the same size is stored in the output buffer.

Reduce[link]

Some computations require calculating a smaller stream (possibly a stream of only 1 element) from a larger stream. This is called a reduction of the stream. Generally a reduction can be accomplished in multiple steps. The results from the prior step are used as the input for the current step and the range over which the operation is applied is reduced until only one stream element remains.

Stream filtering[link]

Stream filtering is essentially a non-uniform reduction. Filtering involves removing items from the stream based on some criteria.

Scatter[link]

The scatter operation is most naturally defined on the vertex processor. The vertex processor is able to adjust the position of the vertex, which allows the programmer to control where information is deposited on the grid. Other extensions are also possible, such as controlling how large an area the vertex affects.

The fragment processor cannot perform a direct scatter operation because the location of each fragment on the grid is fixed at the time of the fragment's creation and cannot be altered by the programmer. However, a logical scatter operation may sometimes be recast or implemented with an additional gather step. A scatter implementation would first emit both an output value and an output address. An immediately following gather operation uses address comparisons to see whether the output value maps to the current output slot.

Gather[link]

The fragment processor is able to read textures in a random access fashion, so it can gather information from any grid cell, or multiple grid cells, as desired.^[vague]

Sort[link]

The sort operation transforms an unordered set of elements into an ordered set of elements. The most common implementation on GPUs is using sorting networks.^[13]

Search[link]

The search operation allows the programmer to find a particular element within the stream, or possibly find neighbors of a specified element. The GPU is not used to speed up the search for an individual element, but instead is used to run multiple searches in parallel.^{[citation needed]}

Data structures[link]

A variety of data structures can be represented on the GPU:

• Dense arrays
• Sparse arrays – static or dynamic
• Adaptive structures

Applications[link]

The following are some of the areas where GPUs have been used for general purpose computing:

• MATLAB acceleration using the Parallel Computing Toolbox and MATLAB Distributed Computing Server,^[14] as well as 3rd party packages like Jacket.
• k-nearest neighbor algorithm^[15]
• Computer clusters or a variation of a parallel computing (utilizing GPU cluster technology) for highly calculation-intensive tasks:
  • High-performance computing clusters (HPC clusters) (often termed supercomputers)
    • including cluster technologies like Message Passing Interface, and single-system image (SSI), distributed computing, and Beowulf
  • Grid computing (a form of distributed computing) (networking many heterogeneous computers to create a virtual computer architecture)
  • Load-balancing clusters (sometimes termed a server farm)
• Physical based simulation and physics engines (usually based on Newtonian physics models)
  • Conway's Game of Life, cloth simulation, incompressible fluid flow by solution of Navier-Stokes equations
• Statistical physics
  • Ising model
• Lattice gauge theory
• Segmentation – 2D and 3D
• Level-set methods
• CT reconstruction
• Fast Fourier transform
• Tone mapping
• Audio signal processing
  • Audio and Sound Effects Processing, to use a GPU for DSP (digital signal processing)
  • Analog signal processing
  • Speech processing
• Digital image processing
• Video Processing^[16]
  • Hardware accelerated video decoding and post-processing
    • Motion compensation (mo comp)
    • Inverse discrete cosine transform (iDCT)
    • Variable-length decoding (VLD)
    • Inverse quantization (IQ)
    • In-loop deblocking
    • Bitstream processing (CAVLC/CABAC) using special purpose hardware for this task because this is a serial task not suitable for regular GPGPU computation
    • Deinterlacing
      • Spatial-temporal de-interlacing
    • Noise reduction
    • Edge enhancement
    • Color correction
  • Hardware accelerated video encoding and pre-processing
• Global illumination – ray tracing, photon mapping, radiosity among others, subsurface scattering
• Geometric computing – constructive solid geometry, distance fields, collision detection, transparency computation, shadow generation
• Scientific computing
  • Monte Carlo simulation of light propagation^[17]
  • Weather forecasting
  • Climate research
  • Molecular modeling on GPU
  • Quantum mechanical physics
  • Astrophysics^[18]
• Bioinformatics^[19][20]
• Computational finance
• Medical imaging
• Computer vision
• Digital signal processing / signal processing
• Control engineering
• Neural networks
• Database operations^[21]
• Lattice Boltzmann methods
• Cryptography and cryptanalysis
  • Implementation of MD6
  • Implementation of AES^[22][23]
  • Implementation of DES
  • Implementation of RSA^[24]
  • Implementation of ECC
  • Password cracking^[25][26]
• Electronic Design Automation^[27][28][29]
• Antivirus software^[30][31]
• Intrusion Detection^[32][33]
• Bitcoin peer-to-peer currency relies on a distributed computing network for performing SHA256 calculations where GPGPUs have become the dominant mode of calculation

See also[link]

• OpenMP
• OpenHMPP^[34]
• Graphics processing unit
  • Comparison of ATI graphics processing units
  • Comparison of Nvidia graphics processing units
  • Graphics pipeline
  • Graphics card
• Stream processing
• Mark Harris founder of GPGPU.org, coined term "GPGPU"
• Physics engine is a computer program that simulates Newtonian physics, on CPU, GPU or physics processing unit (PPU)
  • Physics processing unit (PPU)
• Havok Physics, FX, commercial physics engine middleware SDK for computer and video games
• PhysX SDK, commercial realtime physics engine middleware SDK developed by AGEIA
  • AGEIA also designed a dedicated physics processing unit expansion card designed to accelerate the PhysX SDK
• GPU programming libraries/layers:
  • Close to Metal, now called Stream, AMD/ATI's GPGPU technology for ATI Radeon-based GPUs
  • Compute Unified Device Architecture (CUDA), Nvidia's GPGPU technology for their GeForce-, Quadro- and Tesla-based GPUs
  • Lib Sh, a GPGPU library for C++
  • BrookGPU is the Stanford University Graphics group's compiler and runtime implementation of the Brook stream programming language
  • Open Computing Language (OpenCL) cross-platform GPGPU language for GPUs (AMD/ATI/Nvidia) and general purpose CPUs
    Apple's GPU utilization introduced in Mac OS X v10.6 ‘Snow Leopard’
  • C++ AMP C++ Accelerated Massive Parallelism accelerates execution of C++ code by taking advantage of data-parallel hardware such as a graphics processing unit (GPU) on a discrete graphics card.
  • DirectCompute Microsoft's GPU computing API - Initially released with the DirectX 11 API
  • Renderscript Google's GPU computing and rendering API for Android
• Audio processing unit (DSP can also be done via GPU with GPGPU technology)
• List of emerging technologies
• Larrabee (microarchitecture)

References[link]

External links[link]

• openhmpp.org - New Open Standard for Many-Core
• OCLTools Open Source OpenCL Compiler and Linker
• GPGPU.org - General-Purpose Computation Using Graphics Hardware
• GPGPU Wiki
• SIGGRAPH 2005 GPGPU Course Notes
• IEEE VIS 2005 GPGPU Course Notes
• NVIDIA Developer Zone
• AMD GPU Tools
• CPU vs. GPGPU
• What is GPU Computing?
• Tech Report article: "ATI stakes claims on physics, GPGPU ground" by Scott Wasson
• GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model - porting a standard model to GPU hardware
• GPGPU Computing @ Duke Statistical Science
• GPGPU Programming in F# using the Microsoft Research Accelerator system.
• GPGPU Review, Tobias Preis, European Physical Journal Special Topics 194, 87-119 (2011)

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