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Replacing each dot product with a unique scalar gives
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and these equations can be expressed as the single matrix equation
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This matrix equation relates the scalar components of a in the n basis with those in the e basis . Each matrix element cjk is the direction cosine relating nj to ek. The term direction cosine refers to the cosine of the angle between two unit vectors, which is also equal to their dot product. Therefore,
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By referring collectively to e1, e2, e3 as the e basis and to n1, n2, n3 as the n basis, the matrix containing all the cjk is known as the "transformation matrix from e to n", or the "rotation matrix from e to n" , or the "direction cosine matrix from e to n" . The properties of a rotation matrix are such that its inverse is equal to its transpose. This means that the "rotation matrix from e to n" is the transpose of "rotation matrix from n to e".
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The properties of a direction cosine matrix, C are:
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The advantage of this method is that a direction cosine matrix can usually be obtained independently by using Euler angles or a quaternion to relate the two vector bases, so the basis conversions can be performed directly, without having to work out all the dot products described above.
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By applying several matrix multiplications in succession, any vector can be expressed in any basis so long as the set of direction cosines is known relating the successive bases.
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With the exception of the cross and triple products, the above formulae generalise to two dimensions and higher dimensions. For example, addition generalises to two dimensions as
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The cross product does not readily generalise to other dimensions, though the closely related exterior product does, whose result is a bivector. In two dimensions this is simply a pseudoscalar
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A seven-dimensional cross product is similar to the cross product in that its result is a vector orthogonal to the two arguments; there is however no natural way of selecting one of the possible such products.
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Vectors have many uses in physics and other sciences.
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In abstract vector spaces, the length of the arrow depends on a dimensionless scale. If it represents, for example, a force, the "scale" is of physical dimension length/force. Thus there is typically consistency in scale among quantities of the same dimension, but otherwise scale ratios may vary; for example, if "1 newton" and "5 m" are both represented with an arrow of 2 cm, the scales are 1 m:50 N and 1:250 respectively. Equal length of vectors of different dimension has no particular significance unless there is some proportionality constant inherent in the system that the diagram represents. Also length of a unit vector has no coordinate-system-invariant significance.
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Often in areas of physics and mathematics, a vector evolves in time, meaning that it depends on a time parameter t. For instance, if r represents the position vector of a particle, then r gives a parametric representation of the trajectory of the particle. Vector-valued functions can be differentiated and integrated by differentiating or integrating the components of the vector, and many of the familiar rules from calculus continue to hold for the derivative and integral of vector-valued functions.
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The position of a point x = in three-dimensional space can be represented as a position vector whose base point is the origin
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4,115
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Given two points x = , y = their displacement is a vector
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The velocity v of a point or particle is a vector, its length gives the speed. For constant velocity the position at time t will be
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Acceleration a of a point is vector which is the time derivative of velocity. Its dimensions are length/time2.
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Force is a vector with dimensions of mass×length/time2 and Newton's second law is the scalar multiplication
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Work is the dot product of force and displacement
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In the language of differential geometry, the requirement that the components of a vector transform according to the same matrix of the coordinate transition is equivalent to defining a contravariant vector to be a tensor of contravariant rank one. Alternatively, a contravariant vector is defined to be a tangent vector, and the rules for transforming a contravariant vector follow from the chain rule.
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Some vectors transform like contravariant vectors, except that when they are reflected through a mirror, they flip and gain a minus sign. A transformation that switches right-handedness to left-handedness and vice versa like a mirror does is said to change the orientation of space. A vector which gains a minus sign when the orientation of space changes is called a pseudovector or an axial vector. Ordinary vectors are sometimes called true vectors or polar vectors to distinguish them from pseudovectors. Pseudovectors occur most frequently as the cross product of two ordinary vectors.
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One example of a pseudovector is angular velocity. Driving in a car, and looking forward, each of the wheels has an angular velocity vector pointing to the left. If the world is reflected in a mirror which switches the left and right side of the car, the reflection of this angular velocity vector points to the right, but the actual angular velocity vector of the wheel still points to the left, corresponding to the minus sign. Other examples of pseudovectors include magnetic field, torque, or more generally any cross product of two vectors.
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This distinction between vectors and pseudovectors is often ignored, but it becomes important in studying symmetry properties. See parity .
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MIMD architectures may be used in a number of application areas such as computer-aided design/computer-aided manufacturing, simulation, modeling, and as communication switches. MIMD machines can be of either shared memory or distributed memory categories. These classifications are based on how MIMD processors access memory. Shared memory machines may be of the bus-based, extended, or hierarchical type. Distributed memory machines may have hypercube or mesh interconnection schemes.
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An example of MIMD system is Intel Xeon Phi, descended from Larrabee microarchitecture. These processors have multiple processing cores that can execute different instructions on different data.
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Most parallel computers, as of 2013, are MIMD systems.
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In shared memory model the processors are all connected to a "globally available" memory, via either software or hardware means. The operating system usually maintains its memory coherence.
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From a programmer's point of view, this memory model is better understood than the distributed memory model. Another advantage is that memory coherence is managed by the operating system and not the written program. Two known disadvantages are: scalability beyond thirty-two processors is difficult, and the shared memory model is less flexible than the distributed memory model.
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There are many examples of shared memory : UMA , COMA .
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MIMD machines with shared memory have processors which share a common, central memory. In the simplest form, all processors are attached to a bus which connects them to memory. This means that every machine with shared memory shares a specific CM, common bus system for all the clients.
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For example, if we consider a bus with clients A, B, C connected on one side and P, Q, R connected on the opposite side,
any one of the clients will communicate with the other by means of the bus interface between them.
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MIMD machines with hierarchical shared memory use a hierarchy of buses to give processors access to each other's memory. Processors on different boards may communicate through inter-nodal buses. Buses support communication between boards. With this type of architecture, the machine may support over nine thousand processors.
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In distributed memory MIMD machines, each processor has its own individual memory location. Each processor has no direct knowledge about other processor's memory. For data to be shared, it must be passed from one processor to another as a message. Since there is no shared memory, contention is not as great a problem with these machines. It is not economically feasible to connect a large number of processors directly to each other. A way to avoid this multitude of direct connections is to connect each processor to just a few others. This type of design can be inefficient because of the added time required to pass a message from one processor to another along the message path. The amount of time required for processors to perform simple message routing can be substantial. Systems were designed to reduce this time loss and hypercube and mesh are among two of the popular interconnection schemes.
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Examples of distributed memory include MPP , COW and NUMA . The former is complex and expensive: Many super-computers coupled by broad-band networks. Examples include hypercube and mesh interconnections. COW is the "home-made" version for a fraction of the price.
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In an MIMD distributed memory machine with a hypercube system interconnection network containing four processors, a processor and a memory module are placed at each vertex of a square. The diameter of the system is the minimum number of steps it takes for one processor to send a message to the processor that is the farthest away. So, for example, the diameter of a 2-cube is 2. In a hypercube system with eight processors and each processor and memory module being placed in the vertex of a cube, the diameter is 3. In general, a system that contains 2^N processors with each processor directly connected to N other processors, the diameter of the system is N. One disadvantage of a hypercube system is that it must be configured in powers of two, so a machine must be built that could potentially have many more processors than is really needed for the application.
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In an MIMD distributed memory machine with a mesh interconnection network, processors are placed in a two-dimensional grid. Each processor is connected to its four immediate neighbors. Wrap around connections may be provided at the edges of the mesh. One advantage of the mesh interconnection network over the hypercube is that the mesh system need not be configured in powers of two. A disadvantage is that the diameter of the mesh network is greater than the hypercube for systems with more than four processors.
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Such machines exploit data level parallelism, but not concurrency: there are simultaneous computations, but each unit performs the exact same instruction at any given moment . 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 threads or hardware threads, both of which are task time-sharing . SIMT is true simultaneous parallel hardware-level execution.
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Modern graphics processing units are often wide SIMD implementations, capable of branches, loads, and stores on 128 or 256 bits at a time.
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The first use of SIMD instructions was in the ILLIAC IV, which was completed in 1966.
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SIMD was the basis for vector supercomputers of the early 1970s such as the CDC Star-100 and the Texas Instruments ASC, which could operate on a "vector" of data with a single instruction. Vector processing was especially popularized by Cray in the 1970s and 1980s. Vector processing architectures are now considered separate from SIMD computers: Duncan's Taxonomy includes them where Flynn's Taxonomy does not, due to Flynn's work pre-dating the Cray-1 .
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The first era of modern SIMD computers was characterized by massively parallel processing-style supercomputers such as the Thinking Machines CM-1 and CM-2. These computers had many limited-functionality processors that would work in parallel. For example, each of 65,536 single-bit processors in a Thinking Machines CM-2 would execute the same instruction at the same time, allowing, for instance, to logically combine 65,536 pairs of bits at a time, using a hypercube-connected network or processor-dedicated RAM to find its operands. Supercomputing moved away from the SIMD approach when inexpensive scalar MIMD approaches based on commodity processors such as the Intel i860 XP became more powerful, and interest in SIMD waned.
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The current era of SIMD processors grew out of the desktop-computer market rather than the supercomputer market. As desktop processors became powerful enough to support real-time gaming and audio/video processing during the 1990s, demand grew for this particular type of computing power, and microprocessor vendors turned to SIMD to meet the demand. Hewlett-Packard introduced MAX instructions into PA-RISC 1.1 desktops in 1994 to accelerate MPEG decoding. Sun Microsystems introduced SIMD integer instructions in its "VIS" instruction set extensions in 1995, in its UltraSPARC I microprocessor. MIPS followed suit with their similar MDMX system.
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The first widely deployed desktop SIMD was with Intel's MMX extensions to the x86 architecture in 1996. This sparked the introduction of the much more powerful AltiVec system in the Motorola PowerPC and IBM's POWER systems. Intel responded in 1999 by introducing the all-new SSE system. Since then, there have been several extensions to the SIMD instruction sets for both architectures. Advanced vector extensions AVX, AVX2 and AVX-512 are developed by Intel. AMD supports AVX, AVX2, and AVX-512 in their current products.
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All of these developments have been oriented toward support for real-time graphics, and are therefore oriented toward processing in two, three, or four dimensions, usually with vector lengths of between two and sixteen words, depending on data type and architecture. When new SIMD architectures need to be distinguished from older ones, the newer architectures are then considered "short-vector" architectures, as earlier SIMD and vector supercomputers had vector lengths from 64 to 64,000. A modern supercomputer is almost always a cluster of MIMD computers, each of which implements SIMD instructions.
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An application that may take advantage of SIMD is one where the same value is being added to a large number of data points, a common operation in many multimedia applications. One example would be changing the brightness of an image. Each pixel of an image consists of three values for the brightness of the red , green and blue portions of the color. To change the brightness, the R, G and B values are read from memory, a value is added to them, and the resulting values are written back out to memory. Audio DSPs would likewise, for volume control, multiply both Left and Right channels simultaneously.
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With a SIMD processor there are two improvements to this process. For one the data is understood to be in blocks, and a number of values can be loaded all at once. Instead of a series of instructions saying "retrieve this pixel, now retrieve the next pixel", a SIMD processor will have a single instruction that effectively says "retrieve n pixels" . For a variety of reasons, this can take much less time than retrieving each pixel individually, as with a traditional CPU design.
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Another advantage is that the instruction operates on all loaded data in a single operation. In other words, if the SIMD system works by loading up eight data points at once, the add operation being applied to the data will happen to all eight values at the same time. This parallelism is separate from the parallelism provided by a superscalar processor; the eight values are processed in parallel even on a non-superscalar processor, and a superscalar processor may be able to perform multiple SIMD operations in parallel.
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To remedy problems 1 and 5, RISC-V's vector extension uses an alternative approach: instead of exposing the sub-register-level details to the programmer, the instruction set abstracts them out as a few "vector registers" that use the same interfaces across all CPUs with this instruction set. The hardware handles all alignment issues and "strip-mining" of loops. Machines with different vector sizes would be able to run the same code. LLVM calls this vector type "vscale".
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An order of magnitude increase in code size is not uncommon, when compared to equivalent scalar or equivalent vector code, and an order of magnitude or greater effectiveness is achievable with Vector ISAs.
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ARM's Scalable Vector Extension takes another approach, known in Flynn's Taxonomy as "Associative Processing", more commonly known today as "Predicated" SIMD. This approach is not as compact as Vector processing but is still far better than non-predicated SIMD. Detailed comparative examples are given in the Vector processing page.
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Small-scale SIMD became popular on general-purpose CPUs in the early 1990s and continued through 1997 and later with Motion Video Instructions for Alpha. SIMD instructions can be found, to one degree or another, on most CPUs, including IBM's AltiVec and SPE for PowerPC, HP's PA-RISC Multimedia Acceleration eXtensions , Intel's MMX and iwMMXt, SSE, SSE2, SSE3 SSSE3 and SSE4.x, AMD's 3DNow!, ARC's ARC Video subsystem, SPARC's VIS and VIS2, Sun's MAJC, ARM's Neon technology, MIPS' MDMX and MIPS-3D. The IBM, Sony, Toshiba co-developed Cell Processor's SPU's instruction set is heavily SIMD based. Philips, now NXP, developed several SIMD processors named Xetal. The Xetal has 320 16-bit processor elements especially designed for vision tasks.
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Intel's AVX-512 SIMD instructions process 512 bits of data at once.
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SIMD instructions are widely used to process 3D graphics, although modern graphics cards with embedded SIMD have largely taken over this task from the CPU. Some systems also include permute functions that re-pack elements inside vectors, making them particularly useful for data processing and compression. They are also used in cryptography. The trend of general-purpose computing on GPUs may lead to wider use of SIMD in the future.
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Adoption of SIMD systems in personal computer software was at first slow, due to a number of problems. One was that many of the early SIMD instruction sets tended to slow overall performance of the system due to the re-use of existing floating point registers. Other systems, like MMX and 3DNow!, offered support for data types that were not interesting to a wide audience and had expensive context switching instructions to switch between using the FPU and MMX registers. Compilers also often lacked support, requiring programmers to resort to assembly language coding.
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SIMD on x86 had a slow start. The introduction of 3DNow! by AMD and SSE by Intel confused matters somewhat, but today the system seems to have settled down and newer compilers should result in more SIMD-enabled software. Intel and AMD now both provide optimized math libraries that use SIMD instructions, and open source alternatives like libSIMD, SIMDx86 and SLEEF have started to appear .
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Apple Computer had somewhat more success, even though they entered the SIMD market later than the rest. AltiVec offered a rich system and can be programmed using increasingly sophisticated compilers from Motorola, IBM and GNU, therefore assembly language programming is rarely needed. Additionally, many of the systems that would benefit from SIMD were supplied by Apple itself, for example iTunes and QuickTime. However, in 2006, Apple computers moved to Intel x86 processors. Apple's APIs and development tools were modified to support SSE2 and SSE3 as well as AltiVec. Apple was the dominant purchaser of PowerPC chips from IBM and Freescale Semiconductor. Even though Apple has stopped using PowerPC processors in their products, further development of AltiVec is continued in several PowerPC and Power ISA designs from Freescale and IBM.
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SIMD within a register, or SWAR, is a range of techniques and tricks used for performing SIMD in general-purpose registers on hardware that does not provide any direct support for SIMD instructions. This can be used to exploit parallelism in certain algorithms even on hardware that does not support SIMD directly.
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It is common for publishers of the SIMD instruction sets to make their own C/C++ language extensions with intrinsic functions or special datatypes guaranteeing the generation of vector code. Intel, AltiVec, and ARM NEON provide extensions widely adopted by the compilers targeting their CPUs.
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The GNU C Compiler takes the extensions a step further by abstracting them into a universal interface that can be used on any platform by providing a way of defining SIMD datatypes. The LLVM Clang compiler also implements the feature, with an analogous interface defined in the IR. Rust's packed_simd crate uses this interface, and so does Swift 2.0+.
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C++ has an experimental interface std::experimental::simd that works similarly to the GCC extension. LLVM's libcxx seems to implement it. For GCC and libstdc++, a wrapper library that builds on top of the GCC extension is available.
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Microsoft added SIMD to .NET in RyuJIT. The System.Numerics.Vector package, available on NuGet, implements SIMD datatypes. Java also has a new proposed API for SIMD instructions available in OpenJDK 17 in an incubator module. It also has a safe fallback mechanism on unsupported CPUs to simple loops.
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Instead of providing an SIMD datatype, compilers can also be hinted to auto-vectorize some loops, potentially taking some assertions about the lack of data dependency. This is not as flexible as manipulating SIMD variables directly, but is easier to use. OpenMP 4.0+ has a #pragma omp simd hint. This OpenMP interface has replaced a wide set of nonstandard extensions, including Cilk's #pragma simd, GCC's #pragma GCC ivdep, and many more.
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Consumer software is typically expected to work on a range of CPUs covering multiple generations, which could limit the programmer's ability to use new SIMD instructions to improve the computational performance of a program. The solution is to include multiple versions of the same code that uses either older or newer SIMD technologies, and pick one that best fits the user's CPU at run-time . There are two main camps of solutions:
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FMV, manually coded in assembly language, is quite commonly used in a number of performance-critical libraries such as glibc and libjpeg-turbo. Intel C++ Compiler, GNU Compiler Collection since GCC 6, and Clang since clang 7 allow for a simplified approach, with the compiler taking care of function duplication and selection. GCC and clang requires explicit target_clones labels in the code to "clone" functions, while ICC does so automatically . The Rust programming language also supports FMV. The setup is similar to GCC and Clang in that the code defines what instruction sets to compile for, but cloning is manually done via inlining.
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As using FMV requires code modification on GCC and Clang, vendors more commonly use library multi-versioning: this is easier to achieve as only compiler switches need to be changed. Glibc supports LMV and this functionality is adopted by the Intel-backed Clear Linux project.
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In 2013 John McCutchan announced that he had created a high-performance interface to SIMD instruction sets for the Dart programming language, bringing the benefits of SIMD to web programs for the first time. The interface consists of two types:
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Instances of these types are immutable and in optimized code are mapped directly to SIMD registers. Operations expressed in Dart typically are compiled into a single instruction without any overhead. This is similar to C and C++ intrinsics. Benchmarks for 4×4 matrix multiplication, 3D vertex transformation, and Mandelbrot set visualization show near 400% speedup compared to scalar code written in Dart.
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McCutchan's work on Dart, now called SIMD.js, has been adopted by ECMAScript and Intel announced at IDF 2013 that they are implementing McCutchan's specification for both V8 and SpiderMonkey. However, by 2017, SIMD.js has been taken out of the ECMAScript standard queue in favor of pursuing a similar interface in WebAssembly. As of August 2020, the WebAssembly interface remains unfinished, but its portable 128-bit SIMD feature has already seen some use in many engines.
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Emscripten, Mozilla's C/C++-to-JavaScript compiler, with extensions can enable compilation of C++ programs that make use of SIMD intrinsics or GCC-style vector code to the SIMD API of JavaScript, resulting in equivalent speedups compared to scalar code. It also supports the WebAssembly 128-bit SIMD proposal.
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It has generally proven difficult to find sustainable commercial applications for SIMD-only processors.
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One that has had some measure of success is the GAPP, which was developed by Lockheed Martin and taken to the commercial sector by their spin-off Teranex. The GAPP's recent incarnations have become a powerful tool in real-time video processing applications like conversion between various video standards and frame rates , deinterlacing, image noise reduction, adaptive video compression, and image enhancement.
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A more ubiquitous application for SIMD is found in video games: nearly every modern video game console since 1998 has incorporated a SIMD processor somewhere in its architecture. The PlayStation 2 was unusual in that one of its vector-float units could function as an autonomous DSP executing its own instruction stream, or as a coprocessor driven by ordinary CPU instructions. 3D graphics applications tend to lend themselves well to SIMD processing as they rely heavily on operations with 4-dimensional vectors. Microsoft's Direct3D 9.0 now chooses at runtime processor-specific implementations of its own math operations, including the use of SIMD-capable instructions.
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A later processor that used vector processing is the Cell Processor used in the Playstation 3, which was developed by IBM in cooperation with Toshiba and Sony. It uses a number of SIMD processors and is geared towards the huge datasets required by 3D and video processing applications. It differs from traditional ISAs by being SIMD from the ground up with no separate scalar registers.
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Ziilabs produced an SIMD type processor for use on mobile devices, such as media players and mobile phones.
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Larger scale commercial SIMD processors are available from ClearSpeed Technology, Ltd. and Stream Processors, Inc. ClearSpeed's CSX600 has 96 cores each with two double-precision floating point units while the CSX700 has 192. Stream Processors is headed by computer architect Bill Dally. Their Storm-1 processor contains 80 SIMD cores controlled by a MIPS CPU.
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Arcade system boards have used specialized graphics circuits since the 1970s. In early video game hardware, RAM for frame buffers was expensive, so video chips composited data together as the display was being scanned out on the monitor.
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A specialized barrel shifter circuit helped the CPU animate the framebuffer graphics for various 1970s arcade video games from Midway and Taito, such as Gun Fight , Sea Wolf , and Space Invaders . The Namco Galaxian arcade system in 1979 used specialized graphics hardware that supported RGB color, multi-colored sprites, and tilemap backgrounds. The Galaxian hardware was widely used during the golden age of arcade video games, by game companies such as Namco, Centuri, Gremlin, Irem, Konami, Midway, Nichibutsu, Sega, and Taito.
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The Atari 2600 in 1977 used a video shifter called the Television Interface Adaptor. Atari 8-bit computers had ANTIC, a video processor which interpreted instructions describing a "display list"—the way the scan lines map to specific bitmapped or character modes and where the memory is stored . 6502 machine code subroutines could be triggered on scan lines by setting a bit on a display list instruction. ANTIC also supported smooth vertical and horizontal scrolling independent of the CPU.
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The NEC µPD7220 was the first implementation of a personal computer graphics display processor as a single large-scale integration integrated circuit chip. This enabled the design of low-cost, high-performance video graphics cards such as those from Number Nine Visual Technology. It became the best-known GPU until the mid-1980s. It was the first fully integrated VLSI metal–oxide–semiconductor graphics display processor for PCs, supported up to 1024×1024 resolution, and laid the foundations for the emerging PC graphics market. It was used in a number of graphics cards and was licensed for clones such as the Intel 82720, the first of Intel's graphics processing units. The Williams Electronics arcade games Robotron 2084, Joust, Sinistar, and Bubbles, all released in 1982, contain custom blitter chips for operating on 16-color bitmaps.
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In 1984, Hitachi released ARTC HD63484, the first major CMOS graphics processor for personal computers. The ARTC could display up to 4K resolution when in monochrome mode. It was used in a number of graphics cards and terminals during the late 1980s. In 1985, the Amiga was released with a custom graphics chip including a blitter for bitmap manipulation, line drawing, and area fill. It also included a coprocessor with its own simple instruction set, that was capable of manipulating graphics hardware registers in sync with the video beam , or driving the blitter. In 1986, Texas Instruments released the TMS34010, the first fully programmable graphics processor. It could run general-purpose code, but it had a graphics-oriented instruction set. During 1990–1992, this chip became the basis of the Texas Instruments Graphics Architecture Windows accelerator cards.
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In 1987, the IBM 8514 graphics system was released. It was one of the first video cards for IBM PC compatibles to implement fixed-function 2D primitives in electronic hardware. Sharp's X68000, released in 1987, used a custom graphics chipset with a 65,536 color palette and hardware support for sprites, scrolling, and multiple playfields. It served as a development machine for Capcom's CP System arcade board. Fujitsu's FM Towns computer, released in 1989, had support for a 16,777,216 color palette. In 1988, the first dedicated polygonal 3D graphics boards were introduced in arcades with the Namco System 21 and Taito Air System.
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IBM introduced its proprietary Video Graphics Array display standard in 1987, with a maximum resolution of 640×480 pixels. In November 1988, NEC Home Electronics announced its creation of the Video Electronics Standards Association to develop and promote a Super VGA computer display standard as a successor to VGA. Super VGA enabled graphics display resolutions up to 800×600 pixels, a 36% increase.
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In 1991, S3 Graphics introduced the S3 86C911, which its designers named after the Porsche 911 as an indication of the performance increase it promised. The 86C911 spawned a variety of imitators: by 1995, all major PC graphics chip makers had added 2D acceleration support to their chips. Fixed-function Windows accelerators surpassed expensive general-purpose graphics coprocessors in Windows performance, and such coprocessors faded from the PC market.
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Throughout the 1990s, 2D GUI acceleration evolved. As manufacturing capabilities improved, so did the level of integration of graphics chips. Additional application programming interfaces arrived for a variety of tasks, such as Microsoft's WinG graphics library for Windows 3.x, and their later DirectDraw interface for hardware acceleration of 2D games in Windows 95 and later.
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In the early- and mid-1990s, real-time 3D graphics became increasingly common in arcade, computer, and console games, which led to increasing public demand for hardware-accelerated 3D graphics. Early examples of mass-market 3D graphics hardware can be found in arcade system boards such as the Sega Model 1, Namco System 22, and Sega Model 2, and the fifth-generation video game consoles such as the Saturn, PlayStation, and Nintendo 64. Arcade systems such as the Sega Model 2 and SGI Onyx-based Namco Magic Edge Hornet Simulator in 1993 were capable of hardware T&L years before appearing in consumer graphics cards. Another early example is the Super FX chip, a RISC-based on-cartridge graphics chip used in some SNES games, notably Doom and Star Fox. Some systems used DSPs to accelerate transformations. Fujitsu, which worked on the Sega Model 2 arcade system, began working on integrating T&L into a single LSI solution for use in home computers in 1995; the Fujitsu Pinolite, the first 3D geometry processor for personal computers, released in 1997. The first hardware T&L GPU on home video game consoles was the Nintendo 64's Reality Coprocessor, released in 1996. In 1997, Mitsubishi released the 3Dpro/2MP, a GPU capable of transformation and lighting, for workstations and Windows NT desktops; ATi used it for its FireGL 4000 graphics card, released in 1997.
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The term "GPU" was coined by Sony in reference to the 32-bit Sony GPU in the PlayStation video game console, released in 1994.
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In the PC world, notable failed attempts for low-cost 3D graphics chips included the S3 ViRGE, ATI Rage, and Matrox Mystique. These chips were essentially previous-generation 2D accelerators with 3D features bolted on. Many were pin-compatible with the earlier-generation chips for ease of implementation and minimal cost. Initially, 3D graphics were possible only with discrete boards dedicated to accelerating 3D functions acceleration entirely) such as the PowerVR and the 3dfx Voodoo. However, as manufacturing technology continued to progress, video, 2D GUI acceleration, and 3D functionality were all integrated into one chip. Rendition's Verite chipsets were among the first to do this well. In 1997, Rendition collaborated with Hercules and Fujitsu on a "Thriller Conspiracy" project which combined a Fujitsu FXG-1 Pinolite geometry processor with a Vérité V2200 core to create a graphics card with a full T&L engine years before Nvidia's GeForce 256; This card, designed to reduce the load placed upon the system's CPU, never made it to market. NVIDIA RIVA 128 was one of the first consumer-facing GPU integrated 3D processing unit and 2D processing unit on a chip.
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OpenGL appeared in the early '90s as a professional graphics API, but originally suffered from performance issues which allowed the Glide API to become a dominant force on the PC in the late '90s. These issues were quickly overcome and the Glide API fell by the wayside. Software implementations of OpenGL were common during this time, although the influence of OpenGL eventually led to widespread hardware support. DirectX became popular among Windows game developers during the late '90s. Unlike OpenGL, Microsoft insisted on providing strict one-to-one support of hardware. The approach made DirectX less popular as a standalone graphics API initially, since many GPUs provided their own specific features, which existing OpenGL applications were already able to benefit from, leaving DirectX often one generation behind.
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Microsoft began to work more closely with hardware developers and started to target the releases of DirectX to coincide with those of the supporting graphics hardware. Direct3D 5.0 was the first version of the API to gain widespread adoption in the gaming market, and it competed directly with more-hardware-specific, often proprietary, graphics libraries, while OpenGL maintained a strong following. Direct3D 7.0 introduced support for hardware-accelerated transform and lighting for Direct3D; OpenGL had this capability from its inception. 3D accelerator cards moved beyond being simple rasterizers to add another significant hardware stage to the 3D rendering pipeline. The Nvidia GeForce 256 was the first consumer-level card with hardware-accelerated T&L; professional 3D cards already had this capability. Hardware transform and lighting—existing features of OpenGL—came to consumer-level hardware in the '90s and set the precedent for later pixel shader and vertex shader units which were far more flexible and programmable.
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Nvidia was first to produce a chip capable of programmable shading: the GeForce 3. Each pixel could now be processed by a short program that could include additional image textures as inputs, and each geometric vertex could likewise be processed by a short program before it was projected onto the screen. Used in the Xbox console, this chip competed with the one in the PlayStation 2, which used a custom vector unit for hardware accelerated vertex processing . The earliest incarnations of shader execution engines used in Xbox were not general purpose and could not execute arbitrary pixel code. Vertices and pixels were processed by different units which had their own resources, with pixel shaders having tighter constraints . Pixel shading engines were actually more akin to a highly customizable function block and did not really "run" a program. Many of these disparities between vertex and pixel shading were not addressed until the Unified Shader Model.
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In October 2002, with the introduction of the ATI Radeon 9700 , the world's first Direct3D 9.0 accelerator, pixel and vertex shaders could implement looping and lengthy floating point math, and were quickly becoming as flexible as CPUs, yet orders of magnitude faster for image-array operations. Pixel shading is often used for bump mapping, which adds texture to make an object look shiny, dull, rough, or even round or extruded.
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With the introduction of the Nvidia GeForce 8 series and new generic stream processing units, GPUs became more generalized computing devices. Parallel GPUs are making computational inroads against the CPU, and a subfield of research, dubbed GPU computing or GPGPU for general purpose computing on GPU, has found applications in fields as diverse as machine learning, oil exploration, scientific image processing, linear algebra, statistics, 3D reconstruction, and stock options pricing. GPGPU was the precursor to what is now called a compute shader and actually abused the hardware to a degree by treating the data passed to algorithms as texture maps and executing algorithms by drawing a triangle or quad with an appropriate pixel shader. This entails some overheads since units like the scan converter are involved where they are not needed .
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Nvidia's CUDA platform, first introduced in 2007, was the earliest widely adopted programming model for GPU computing. OpenCL is an open standard defined by the Khronos Group that allows for the development of code for both GPUs and CPUs with an emphasis on portability. OpenCL solutions are supported by Intel, AMD, Nvidia, and ARM, and according to a report in 2011 by Evans Data, OpenCL had become the second most popular HPC tool.
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In 2010, Nvidia partnered with Audi to power their cars' dashboards, using the Tegra GPU to provide increased functionality to cars' navigation and entertainment systems. Advances in GPU technology in cars helped advance self-driving technology. AMD's Radeon HD 6000 series cards were released in 2010, and in 2011 AMD released its 6000M Series discrete GPUs for mobile devices. The Kepler line of graphics cards by Nvidia were released in 2012 and were used in the Nvidia's 600 and 700 series cards. A feature in this GPU microarchitecture included GPU boost, a technology that adjusts the clock-speed of a video card to increase or decrease it according to its power draw. The Kepler microarchitecture was manufactured on the 28 nm process.
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The PS4 and Xbox One were released in 2013; they both use GPUs based on AMD's Radeon HD 7850 and 7790. Nvidia's Kepler line of GPUs was followed by the Maxwell line, manufactured on the same process. Nvidia's 28 nm chips were manufactured by TSMC in Taiwan using the 28 nm process. Compared to the 40 nm technology from the past, this manufacturing process allowed a 20 percent boost in performance while drawing less power. Virtual reality headsets have high system requirements; manufacturers recommended the GTX 970 and the R9 290X or better at the time of their release. Cards based on the Pascal microarchitecture were released in 2016. The GeForce 10 series of cards are of this generation of graphics cards. They are made using the 16 nm manufacturing process which improves upon previous microarchitectures. Nvidia released one non-consumer card under the new Volta architecture, the Titan V. Changes from the Titan XP, Pascal's high-end card, include an increase in the number of CUDA cores, the addition of tensor cores, and HBM2. Tensor cores are designed for deep learning, while high-bandwidth memory is on-die, stacked, lower-clocked memory that offers an extremely wide memory bus. To emphasize that the Titan V is not a gaming card, Nvidia removed the "GeForce GTX" suffix it adds to consumer gaming cards.
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In 2018, Nvidia launched the RTX 20 series GPUs that added ray-tracing cores to GPUs, improving their performance on lighting effects. Polaris 11 and Polaris 10 GPUs from AMD are fabricated by a 14 nm process. Their release resulted in a substantial increase in the performance per watt of AMD video cards. AMD also released the Vega GPU series for the high end market as a competitor to Nvidia's high end Pascal cards, also featuring HBM2 like the Titan V.
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In 2019, AMD released the successor to their Graphics Core Next microarchitecture/instruction set. Dubbed RDNA, the first product featuring it was the Radeon RX 5000 series of video cards.
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The company announced that the successor to the RDNA microarchitecture would be incremental . AMD unveiled the Radeon RX 6000 series, its RDNA 2 graphics cards with support for hardware-accelerated ray tracing. The product series, launched in late 2020, consisted of the RX 6800, RX 6800 XT, and RX 6900 XT. The RX 6700 XT, which is based on Navi 22, was launched in early 2021.
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The PlayStation 5 and Xbox Series X and Series S were released in 2020; they both use GPUs based on the RDNA 2 microarchitecture with incremental improvements and different GPU configurations in each system's implementation.
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Intel first entered the GPU market in the late 1990s, but produced lackluster 3D accelerators compared to the competition at the time. Rather than attempting to compete with the high-end manufacturers Nvidia and ATI/AMD, they began integrating Intel Graphics Technology GPUs into motherboard chipsets, beginning with the Intel 810 for the Pentium III, and later into CPUs. They began with the Intel Atom 'Pineview' laptop processor in 2009, continuing in 2010 with desktop processors in the first generation of the Intel Core line and with contemporary Pentiums and Celerons. This resulted in a large nominal market share, as the majority of computers with an Intel CPU also featured this embedded graphics processor. These generally lagged behind discrete processors in performance. Intel re-entered the discrete GPU market in 2022 with its Arc series, which competed with the then-current GeForce 30 series and Radeon 6000 series cards at competitive prices.
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