GPGPU

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General-Purpose Computing on Graphics Processing Units (GPGPU, also referred to as GPGP and to a lesser extent GP^2) is a recent trend in computer science that uses the Graphics Processing Unit to perform the computations rather than the CPU. The addition of programmable stages and higher precision arithmetic to the GPU rendering pipeline have allowed software developers to use the GPU for non graphics related applications. Because of the extremely parallel nature of the graphics pipeline the GPU is especially useful for programs that can be cast as stream processing problems.

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[edit] GPU Improvements

For many years GPU functionality was very limited. In fact, for many years the GPU was only used to accelerate certain parts of the graphics pipeline. Some improvements were needed before GPGPU became feasible.

[edit] Programmability

Programmable vertex and fragment shaders were added to the graphics pipeline to enable game programmers to generate even more realistic effects. Vertex shaders allow the programmer to alter per-vertex attributes, such as position, color, texture coordinates, and normal vector. Fragment shaders are used to calculate the color of a fragment, or per-pixel. Programmable fragment shaders allow the programmer to substitute, for example, a lighting model other than those provided by default by the graphics card, typically simple Gouraud shading. Shaders have enabled graphics programmers to create lens effects, displacement mapping, and depth of field.

The programmability of the pipelines have trended according the Microsoft’s DirectX specification, with DirectX8 introducing Shader Model 1.1, DirectX8.1 Pixel Shader Models 1.2, 1.3 and 1.4, and DirectX9 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 DirectX10 specification unifies the programming specification for vertex, geometry (“Geometry Shaders” are new to DirectX10) and fragment processing allowing for a better fit for unified shader hardware, thus providing a single pool of computational pool of programmable resource.

[edit] Data types

Pre DirectX9 graphics cards only supported paletted or integral color types. Various formats are available, each containing a red element, a green element, and a blue element. Sometimes an additional alpha value is added, to be used for transparency. Common formats are:

  • 8 bits per pixel - Palette mode, where each value is an index into a table with the real color value specified in one of the other formats. Possibly 2 bits for red, 3 bits for green, and 3 bits for blue.
  • 16 bits per pixel - Usually allocated as 5 bits for red, 6 bits for green, and 5 bits for blue.
  • 24 bits per pixel - 8 bits for each of red, green, and blue
  • 32 bits per pixel - 8 bits for each of red, green, blue, and alpha

For early fixed function or limited programmability graphics (i.e. up to and including DirectX8.1 compliant GPU's) 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, in order to obtain effects such as high dynamic range imaging. Many GPGPU applications require floating point accuracy, which came with graphics cards conforming to the DirectX9 specification.

DirectX9 Shader Model 2.x suggested the support of two precision types: full and partial precision. Full precision support could either be and FP24 (floating point 24-bit per component) or greater, while partial precision was FP16. ATI’s R300 series of GPU’s 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 GPU’s introduced support for blendable FP16 render targets, easier facilitating the support for High Dynamic Range Rendering.

The implementations of floating point on GPUs are generally not IEEE compliant, and generally do not match across vendors. 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 currently available on GPUs. Some applications require at least double precision floating point values and thus cannot currently be ported to GPUs. There have been efforts to emulate double precision floating point values on GPUs[1].

Most operations on the GPU operate in a vectorized fashion: a single 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 a single operation. This functionality is useful in graphics because almost everything 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 this vector instructions (SIMD) have already been added to CPUs.

[edit] GPGPU programming concepts

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

[edit] Stream processing

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 a single 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 with recent improvements in graphics cards, multiple outputs, but never a piece of memory that is both readable and writable.

Arithmetic intensity is defined as the operations performed per word of memory transferred. It is important for GPGPU applications to have high arithmetic intensity or memory access latency will limit computation speed.

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

[edit] GPU programming concepts

[edit] Computational resources

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

  • Programmable processors - Vertex and fragment pipelines allow programmer to perform kernel on streams of data
  • Rasterizer - creates fragments and interpolates per-vertex constants such as texure 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), Copy-To-Texture(CTT), or the more recent framebuffer_objects. This texture is write only, but once the operation is complete it can then be switched for use as input.

[edit] Textures as stream

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.

A common way to perform operations on a grid is to draw a screen sized quad, which creates a fragment for each pixel. A fragment program is run on each fragment and the resulting pixel is stored into the framebuffer for display. If the algorithm involves multiple steps, Render-To-Texture (RTT) or Copy-To-Texture (CTT) can be used to store the result to a texture, which can then be read as input for the next step.

Since textures are used as memory, texture coordinates are then used as memory addresses. Certain operations can be done automatically by the GPU because of this. For example, it is common to specify texture coordinates (i.e. input addresses) for the corners of a full screen quad and have the GPU do the work of calculating the appropriate input address for each fragment generated. This data is then provided to the programmer at no additional cost.

[edit] Kernels

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

/* Pseudocode */

x = 1000
y = 1000

make array x by y

for each "x" { // Loop this block 1000 times
  for each "y" { // Loop this block 1000 times
    do_some_hard_work(x, y) // This is done 1000x1000 times (1 000 000)
  }
}

On the GPU, the programmer only specifies the body of the loop as the kernel and what data to loop over by drawing geometry. For example, if the programmer wanted to run the kernel over the entire grid, he would draw a full screen quad to create fragments over each grid cell (i.e. over each pixel).

[edit] Flow control

In regular programs 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. Conditional writes could be accomplished using a series of simpler instructions, 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 techniques, such as static branch resolution, pre-computation, and Z-cull[2] can be used to achieve branching when hardware support does not exist.

[edit] GPU techniques

[edit] Map

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.

[edit] Reduce

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 previous step are used as the input for the current step and the range over which the operation is applied is halved each step until only one stream element remains. For two dimensional problems the output size is halved in both directions, resulting in one quarter the number of elements as in the previous step.

[edit] Stream filtering

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

[edit] Scatter

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.

[edit] Gather

The gather operation is only possible on the fragment processor. 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. The vertex processor cannot perform the gather operation because it cannot access the data from other vertices in the stream. Recent graphics cards allow for the vertex processor to read texture data, but this is not truly a gather operation since the gather is not operating on the vertex stream itself.

[edit] Sort

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[3].

[edit] Search

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.

[edit] Data structures

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

  • Dense Arrays
  • Sparse Arrays - static or dynamic
  • Adaptive Structures

[edit] Applications

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

[edit] References

  1. ↑ Double precision on GPUs (Proceedings of ASIM 2005): Dominik Goddeke, Robert Strzodka, and Stefan Turek. Accelerating Double Precision (FEM) Simulations with (GPUs). Proceedings of ASIM 2005 - 18th Symposium on Simulation Technique, 2005.
  2. ↑ Survey paper (to appear in Computer Graphics Forum 2007; revision of Eurographics STAR, August 2005): John D. Owens, David Luebke, Naga Govindaraju, Mark Harris, Jens Krüger, Aaron E. Lefohn, and Tim Purcell. "A Survey of General-Purpose Computation on Graphics Hardware. Computer Graphics Forum, volume 26, 2007. To appear.

[edit] See also

[edit] External links

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