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Power Law Of Cache Misses
A power law is a mathematical relationship between two quantities in which one is directly proportional to some power of the other. The power law for cache misses was first established by C. K. Chow in his 1974 paper, supported by experimental data on hit ratios for stack processing by Richard Mattson in 1971. The power law of cache misses can be used to narrow down the cache sizes to practical ranges, given a tolerable miss rate, as one of the early steps while designing the cache hierarchy for a uniprocessor system. The power law for cache misses can be stated as : M = M_0 C^ where ''M'' is the miss rate for a cache of size ''C'' and ''M''0 is the miss rate of a baseline cache. The exponent ''α'' is workload-specific and typically ranges from 0.3 to 0.7. Caveats The power law can only give an estimate of the miss rate only up to a certain value of cache size. A large enough cache eliminates capacity misses and increasing the cache size further will not reduce the miss rate a ...
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Stack (abstract Data Type)
In computer science, a stack is an abstract data type that serves as a collection of elements, with two main operations: * Push, which adds an element to the collection, and * Pop, which removes the most recently added element that was not yet removed. Additionally, a peek operation can, without modifying the stack, return the value of the last element added. Calling this structure a ''stack'' is by analogy to a set of physical items stacked one atop another, such as a stack of plates. The order in which an element added to or removed from a stack is described as last in, first out, referred to by the acronym LIFO. As with a stack of physical objects, this structure makes it easy to take an item off the top of the stack, but accessing a datum deeper in the stack may require taking off multiple other items first. Considered as a linear data structure, or more abstractly a sequential collection, the push and pop operations occur only at one end of the structure, referred to ...
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Richard Mattson
Richard Lewis Mattson (born May 29, 1935) is an American computer scientist known for his pioneering work on using memory trace data to simulate the performance of the memory hierarchy. He developed the stack distance profile, and used it to model page misses in virtual memory systems as a function of the amount of real memory available. The same methods have been applied as well more recently for modeling the behavior of CPU caches at lower levels of the memory hierarchy, and of web caches for internet content. Mattson was born in Greeley, Colorado. He graduated from the University of California, Berkeley in 1957, with honors in electrical engineering. He became a student of Bernard Widrow at Stanford University, where he completed his doctorate in 1962. His dissertation was ''The Analysis and Synthesis of Adaptive Systems Which Use Networks of Threshold Elements''. He then became a faculty member at Stanford himself, before moving to IBM Research in 1965. While at Stanford, he s ...
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CPU Cache
A CPU cache is a hardware cache used by the central processing unit (CPU) of a computer to reduce the average cost (time or energy) to access data from the main memory. A cache is a smaller, faster memory, located closer to a processor core, which stores copies of the data from frequently used main memory locations. Most CPUs have a hierarchy of multiple cache levels (L1, L2, often L3, and rarely even L4), with different instruction-specific and data-specific caches at level 1. The cache memory is typically implemented with static random-access memory (SRAM), in modern CPUs by far the largest part of them by chip area, but SRAM is not always used for all levels (of I- or D-cache), or even any level, sometimes some latter or all levels are implemented with eDRAM. Other types of caches exist (that are not counted towards the "cache size" of the most important caches mentioned above), such as the translation lookaside buffer (TLB) which is part of the memory management unit (MMU) w ...
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Cache Hierarchy
Cache hierarchy, or multi-level caches, refers to a memory architecture that uses a hierarchy of memory stores based on varying access speeds to cache data. Highly requested data is cached in high-speed access memory stores, allowing swifter access by central processing unit (CPU) cores. Cache hierarchy is a form and part of memory hierarchy and can be considered a form of tiered storage. This design was intended to allow CPU cores to process faster despite the memory latency of main memory access. Accessing main memory can act as a bottleneck for CPU core performance as the CPU waits for data, while making all of main memory high-speed may be prohibitively expensive. High-speed caches are a compromise allowing high-speed access to the data most-used by the CPU, permitting a faster CPU clock. Background In the history of computer and electronic chip development, there was a period when increases in CPU speed outpaced the improvements in memory access speed. The gap between the ...
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Uniprocessor System
A uniprocessor system is defined as a computer system that has a single central processing unit that is used to execute computer tasks. As more and more modern software is able to make use of multiprocessing architectures, such as SMP and MPP, the term ''uniprocessor'' is therefore used to distinguish the class of computers where all processing tasks share a single CPU. Most desktop computer A desktop computer (often abbreviated desktop) is a personal computer designed for regular use at a single location on or near a desk due to its size and power requirements. The most common configuration has a case that houses the power supply ...s are shipped with multiprocessing architectures since the 2010s. As such, this kind of system uses a type of architecture that is based on a single computing unit. All operations (additions, multiplications, etc.) are thus done sequentially on the unit. Further reading Parallel computing {{Compu-hardware-stub ...
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Cache (computing)
In computing, a cache ( ) is a hardware or software component that stores data so that future requests for that data can be served faster; the data stored in a cache might be the result of an earlier computation or a copy of data stored elsewhere. A ''cache hit'' occurs when the requested data can be found in a cache, while a ''cache miss'' occurs when it cannot. Cache hits are served by reading data from the cache, which is faster than recomputing a result or reading from a slower data store; thus, the more requests that can be served from the cache, the faster the system performs. To be cost-effective and to enable efficient use of data, caches must be relatively small. Nevertheless, caches have proven themselves in many areas of computing, because typical computer applications access data with a high degree of locality of reference. Such access patterns exhibit temporal locality, where data is requested that has been recently requested already, and spatial locality, where d ...
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Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_. The exponent is usually shown as a superscript to the right of the base. In that case, is called "''b'' raised to the ''n''th power", "''b'' (raised) to the power of ''n''", "the ''n''th power of ''b''", "''b'' to the ''n''th power", or most briefly as "''b'' to the ''n''th". Starting from the basic fact stated above that, for any positive integer n, b^n is n occurrences of b all multiplied by each other, several other properties of exponentiation directly follow. In particular: \begin b^ & = \underbrace_ \\[1ex] & = \underbrace_ \times \underbrace_ \\[1ex] & = b^n \times b^m \end In other words, when multiplying a base raised to ...
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Working Memory
Working memory is a cognitive system with a limited capacity that can hold information temporarily. It is important for reasoning and the guidance of decision-making and behavior. Working memory is often used synonymously with short-term memory, but some theorists consider the two forms of memory distinct, assuming that working memory allows for the manipulation of stored information, whereas short-term memory only refers to the short-term storage of information. Working memory is a theoretical concept central to cognitive psychology, neuropsychology, and neuroscience. History The term "working memory" was coined by Miller, Galanter, and Pribram, and was used in the 1960s in the context of theories that likened the mind to a computer. In 1968, Atkinson and Shiffrin used the term to describe their "short-term store". What we now call working memory was formerly referred to variously as a "short-term store" or short-term memory, primary memory, immediate memory, operant memo ...
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Cache Placement Policies
A CPU cache is a memory which holds the recently utilized data by the processor. A block of memory cannot necessarily be placed randomly in the cache and may be restricted to a single cache line or a set of cache lines by the cache placement policy. In other words, the cache placement policy determines where a particular memory block can be placed when it goes into the cache. There are three different policies available for placement of a memory block in the cache: direct-mapped, fully associative, and set-associative. Originally this space of cache organizations was described using the term "congruence mapping". Direct-mapped cache In a direct-mapped cache structure, the cache is organized into multiple sets with a single cache line per set. Based on the address of the memory block, it can only occupy a single cache line. The cache can be framed as a column matrix. To place a block in the cache * The set is determined by the index bits derived from the address of the mem ...
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Cache Hierarchy
Cache hierarchy, or multi-level caches, refers to a memory architecture that uses a hierarchy of memory stores based on varying access speeds to cache data. Highly requested data is cached in high-speed access memory stores, allowing swifter access by central processing unit (CPU) cores. Cache hierarchy is a form and part of memory hierarchy and can be considered a form of tiered storage. This design was intended to allow CPU cores to process faster despite the memory latency of main memory access. Accessing main memory can act as a bottleneck for CPU core performance as the CPU waits for data, while making all of main memory high-speed may be prohibitively expensive. High-speed caches are a compromise allowing high-speed access to the data most-used by the CPU, permitting a faster CPU clock. Background In the history of computer and electronic chip development, there was a period when increases in CPU speed outpaced the improvements in memory access speed. The gap between the ...
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Cache Performance Measurement And Metric
A CPU cache is a piece of hardware that reduces access time to data in memory by keeping some part of the frequently used data of the main memory in a 'cache' of smaller and faster memory. The performance of a computer system depends on the performance of all individual units—which include execution units like integer, branch and floating point, I/O units, bus, caches and memory systems. The gap between processor speed and main memory speed has grown exponentially. Until 2001–05, CPU speed, as measured by clock frequency, grew annually by 55%, whereas memory speed only grew by 7%. This problem is known as the memory wall. The motivation for a cache and its hierarchy is to bridge this speed gap and overcome the memory wall. The critical component in most high-performance computers is the cache. Since the cache exists to bridge the speed gap, its performance measurement and metrics are important in designing and choosing various parameters like cache size, associativity, replacem ...
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Cache (computing)
In computing, a cache ( ) is a hardware or software component that stores data so that future requests for that data can be served faster; the data stored in a cache might be the result of an earlier computation or a copy of data stored elsewhere. A ''cache hit'' occurs when the requested data can be found in a cache, while a ''cache miss'' occurs when it cannot. Cache hits are served by reading data from the cache, which is faster than recomputing a result or reading from a slower data store; thus, the more requests that can be served from the cache, the faster the system performs. To be cost-effective and to enable efficient use of data, caches must be relatively small. Nevertheless, caches have proven themselves in many areas of computing, because typical computer applications access data with a high degree of locality of reference. Such access patterns exhibit temporal locality, where data is requested that has been recently requested already, and spatial locality, where d ...
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