Loop Dependence Analysis
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Loop Dependence Analysis
In computer science, loop dependence analysis is a process which can be used to find dependencies within iterations of a loop with the goal of determining different relationships between statements. These dependent relationships are tied to the order in which different statements access memory locations. Using the analysis of these relationships, execution of the loop can be organized to allow multiple processors to work on different portions of the loop in parallel. This is known as parallel processing. In general, loops can consume a lot of processing time when executed as serial code. Through parallel processing, it is possible to reduce the total execution time of a program through sharing the processing load among multiple processors. The process of organizing statements to allow multiple processors to work on different portions of a loop is often referred to as parallelization. In order to see how we can exploit parallelization, we have to first analyze the dependencies wi ...
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Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ...
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Thomas Seiller
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Idaho * Thomas, Illinois * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts and entertainment * ''Thomas'' (Burton novel), a 1969 nove ...
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Automatic Parallelization
Automatic parallelization, also auto parallelization, or autoparallelization refers to converting sequential code into multi-threaded and/or vectorized code in order to use multiple processors simultaneously in a shared-memory multiprocessor ( SMP) machine. Fully automatic parallelization of sequential programs is a challenge because it requires complex program analysis and the best approach may depend upon parameter values that are not known at compilation time. The programming control structures on which autoparallelization places the most focus are loops, because, in general, most of the execution time of a program takes place inside some form of loop. There are two main approaches to parallelization of loops: pipelined multi-threading and cyclic multi-threading. For example, consider a loop that on each iteration applies a hundred operations, and runs for a thousand iterations. This can be thought of as a grid of 100 columns by 1000 rows, a total of 100,000 operations. Cyc ...
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Loop Skewing
The polyhedral model (also called the polytope method) is a mathematical framework for programs that perform large numbers of operations -- too large to be explicitly enumerated -- thereby requiring a ''compact'' representation. Nested loop programs are the typical, but not the only example, and the most common use of the model is for loop nest optimization in program optimization. The polyhedral method treats each loop iteration within nested loops as lattice points inside mathematical objects called polytope, polyhedra, performs affine transformations or more general non-affine transformations such as Loop tiling, tiling on the polytopes, and then converts the transformed polytopes into equivalent, but optimized (depending on targeted optimization goal), loop nests through polyhedra scanning. Simple example Consider the following example written in C (programming language), C: const int n = 100; int i, j; int a[n][n] = ; for (i = 1; i < n; i++) for (i = 0; i < n; i++)
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Loop Interchange
Loop or LOOP may refer to: Brands and enterprises * Loop (mobile), a Bulgarian virtual network operator and co-founder of Loop Live * Loop, clothing, a company founded by Carlos Vasquez in the 1990s and worn by Digable Planets * Loop Mobile, an Indian mobile phone operator * Loop Internet, an internet service provider in Pennsylvania, United States * Loop, a reusable container program announced in 2019 by TerraCycle Geography * Loop, Germany, a municipality in Schleswig-Holstein * Loop (Texarkana), a roadway loop around Texarkana, Arkansas, United States * Loop, Blair County, Pennsylvania, United States * Loop, Indiana County, Pennsylvania, United States * Loop, West Virginia, United States * Loop 101, a semi-beltway of the Phoenix Metropolitan Area * Loop 202, a semi-beltway of the Phoenix Metropolitan Area * Loop 303, a semi-beltway of the Phoenix Metropolitan Area * Chicago Loop, the downtown neighborhood of Chicago bounded by the elevated railway The Loop ** L ...
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Loop Fusion
Loop fission (or loop distribution) is a compiler optimization in which a loop is broken into multiple loops over the same index range with each taking only a part of the original loop's body. The goal is to break down a large loop body into smaller ones to achieve better utilization of locality of reference. This optimization is most efficient in multi-core processors that can split a task into multiple tasks for each processor. Conversely, loop fusion (or loop jamming) is a compiler optimization and loop transformation which replaces multiple loops with a single one. Loop fusion does not always improve run-time speed. On some architectures, two loops may actually perform better than one loop because, for example, there is increased data locality within each loop. One of the main benefits of loop fusion is that it allows temporary allocations to be avoided, which can lead to huge performance gains in numerical computing languages such as Julia when doing elementwise operations ...
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Loop Splitting
Loop splitting is a compiler optimization An optimizing compiler is a compiler designed to generate code that is optimized in aspects such as minimizing program execution time, memory usage, storage size, and power consumption. Optimization is generally implemented as a sequence of op ... technique. It attempts to simplify a loop or eliminate dependencies by breaking it into multiple loops which have the same bodies but iterate over different contiguous portions of the index range. Loop peeling Loop peeling is a special case of loop splitting which splits any problematic first (or last) few iterations from the loop and performs them outside of the loop body. Suppose a loop was written like this: int p = 10; for (int i=0; i<10; ++i) Notice that p = 10 only for the first iteration, and for all other iterations, p = i - 1. A compiler can take advantage of this by
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Loop Transformation
In compiler theory, loop optimization is the process of increasing execution speed and reducing the overheads associated with loops. It plays an important role in improving cache performance and making effective use of parallel processing capabilities. Most execution time of a scientific program is spent on loops; as such, many compiler optimization techniques have been developed to make them faster. Representation of computation and transformations Since instructions inside loops can be executed repeatedly, it is frequently not possible to give a bound on the number of instruction executions that will be impacted by a loop optimization. This presents challenges when reasoning about the correctness and benefits of a loop optimization, specifically the representations of the computation being optimized and the optimization(s) being performed.In the book Reasoning About Program Transformations', Jean-Francois Collard discusses in depth the general question of representing exec ...
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Loop-level Parallelism
Loop-level parallelism is a form of parallelism in software programming that is concerned with extracting parallel tasks from loops. The opportunity for loop-level parallelism often arises in computing programs where data is stored in random access data structures. Where a sequential program will iterate over the data structure and operate on indices one at a time, a program exploiting loop-level parallelism will use multiple threads or processes which operate on some or all of the indices at the same time. Such parallelism provides a speedup to overall execution time of the program, typically in line with Amdahl's law. Description For simple loops, where each iteration is independent of the others, loop-level parallelism can be embarrassingly parallel, as parallelizing only requires assigning a process to handle each iteration. However, many algorithms are designed to run sequentially, and fail when parallel processes race due to dependence within the code. Sequential algori ...
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DOPIPE
DOPIPE parallelism is a method to perform loop-level parallelism by pipelining the statements in a loop. Pipelined parallelism may exist at different levels of abstraction like loops, functions and algorithmic stages. The extent of parallelism depends upon the programmers' ability to make best use of this concept. It also depends upon factors like identifying and separating the independent tasks and executing them parallelly. Background The main purpose of employing loop-level parallelism is to search and split sequential tasks of a program and convert them into parallel tasks without any prior information about the algorithm. Parts of data that are recurring and consume significant amount of execution time are good candidates for loop-level parallelism. Some common applications of loop-level parallelism are found in mathematical analysis that uses multiple-dimension matrices which are iterated in nested loops. There are different kind of parallelization techniques which are us ...
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Alias Analysis
Alias analysis is a technique in compiler theory, used to determine if a storage location may be accessed in more than one way. Two pointers are said to be aliased if they point to the same location. Alias analysis techniques are usually classified by flow-sensitivity and context-sensitivity. They may determine may-alias or must-alias information. The term alias analysis is often used interchangeably with points-to analysis, a specific case. Alias analysers intend to make and compute useful information for understanding aliasing in programs. Overview In general, alias analysis determines whether or not separate memory references point to the same area of memory. This allows the compiler to determine what variables in the program will be affected by a statement. For example, consider the following section of code that accesses members of structures: p.foo = 1; q.foo = 2; i = p.foo + 3; There are three possible alias cases here: #The variables p and q cannot alias (i.e., t ...
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Banerjee Test
In compiler theory In computing, a compiler is a computer program that Translator (computing), translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primaril ..., the Banerjee test is a dependence test. The Banerjee test assumes that all loop indices are independent, however in reality, this is often not true. The Banerjee test is a conservative test. That is, it will not break a dependence that does not exist. This means that the only thing the test can guarantee is the absence of a dependence. General form For a loop of the form: for(i=0; i j ~~ \textrm ~~ f \left ( i \right ) = g \left ( j \right ) \! For a loop of the form: for(i=0; i A true dependence exists between statement ''s1'' and statement ''s2'' if and only if : \exists i, j \in \left
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