Cognitive philology

Cognitive philology is the science that studies written and oral texts as the product of human mental processes. Studies in cognitive philology compare documentary evidence emerging from textual investigations with results of experimental research, especially in the fields of cognitive and ecological psychology, neurosciences and artificial intelligence. "The point is not the text, but the mind that made it". Cognitive Philology aims to foster communication between literary, textual, philological disciplines on the one hand and researches across the whole range of the cognitive, evolutionary, ecological and human sciences on the other. Cognitive philology: investigates transmission of oral and written text, and categorization processes which lead to classification of knowledge, mostly relying on the information theory; studies how narratives emerge in so called natural conversation and selective process which lead to the rise of literary standards for storytelling, mostly relying on embodied semantics; explores the evolutive and evolutionary role played by rhythm and metre in human ontogenetic and phylogenetic development and the pertinence of the semantic association during processing of cognitive maps; Provides the scientific ground for multimedia critical editions of literary texts. Among the founding thinkers and noteworthy scholars devoted to such investigations are: Alan Richardson: Studies Theory of Mind in early-modern and contemporary literature. Anatole Pierre Fuksas Benoît de Cornulier David Herman: Professor of English at North Carolina State University and an adjunct professor of linguistics at Duke University. He is the author of "Universal Grammar and Narrative Form" and the editor of "Narratologies: New Perspectives on Narrative Analysis". Domenico Fiormonte François Recanati Gilles Fauconnier, a professor in Cognitive science at the University of California, San Diego. He was one of the founders of cognitive linguistics in the 1970s through his work on pragmatic scales and mental spaces. His research explores the areas of conceptual integration and compressions of conceptual mappings in terms of the emergent structure in language. Julián Santano Moreno Luca Nobile Manfred Jahn in Germany Mark Turner Paolo Canettieri

Augment (app)

Augment is an augmented reality SaaS platform that allows users to visualize their products in 3D in real environment and in real-time through tablets or smartphones. The software can be used for retail, e-commerce, architecture, and other purposes. Augment created a mobile app of the same name, used to visualize 3D models in augmented reality and a web application called Augment Manager for 3D content management. The company is based in Paris, France, and was founded in October 2011 by Jean-François Chianetta, Cyril Champier, and Mickaël Jordan. In March 2016, Augment announced €3 million in its series-A round from Salesforce Ventures, which bringing the total funding since launch to $4.7 million. Augment lets businesses and 3D professionals visualize projects in their actual size and environment, on iPhone, iPad, and Android, using the power of augmented reality. Users can print the Augment tracker or create their own tracker to place the 3D models in space and at scale in real time. Common uses of the technology include product presentations, interactive print campaigns and e-Commerce product visualization. Augment has just released its augmented reality SDK solutions for retail and augmented commerce. The SDK solutions, available for both native mobile app and web integrations, allow companies to embed augmented reality product visualization in their existing eCommerce platforms. == Technology == Augment uses the following 3D technologies: Vuforia Augmented Reality SDK OpenGL == Customer cases == Companies such as Coca-Cola, Siemens, Nokia, Nestle, and Boeing are using Augment's solutions. == History == Augment was first created by Jean-François Chianetta in October 2011. Chianetta later teamed up with Cyril Champier and Mickaël Jordan for further development. The co-founding team was among the 12 startups of Season 3 of French accelerator Le Camping. The team raised one million euros (US$1,300,000) in April 2013 and moved its office to Paris. In March 2016, Augment raised US$3M Series A funding from Salesforce and other investors. In 2013, Augment's first service, Boost Business Catalog, was made available to help businesses catalogue and display their product models. Customers can rotate the images in 3D and view augmented content before deciding what to buy. == Awards == "Best Innovation" at Ecommerce Mag Trophy 2013

Reservoir sampling

Reservoir sampling is a family of randomized algorithms for choosing a simple random sample, without replacement, of k items from a population of unknown size n in a single pass over the items. The size of the population n is not known to the algorithm and is typically too large for all n items to fit into main memory. The population is revealed to the algorithm over time, and the algorithm cannot look back at previous items. At any point, the current state of the algorithm must permit extraction of a simple random sample without replacement of size k over the part of the population seen so far. == Motivation == Suppose we see a sequence of items, one at a time. We want to keep 10 items in memory, and we want them to be selected at random from the sequence. If we know the total number of items n and can access the items arbitrarily, then the solution is easy: select 10 distinct indices i between 1 and n with equal probability, and keep the i-th elements. The problem is that we do not always know the exact n in advance. == Simple: Algorithm R == A simple and popular but slow algorithm, Algorithm R, was created by Jeffrey Vitter. Initialize an array R {\displaystyle R} indexed from 1 {\displaystyle 1} to k {\displaystyle k} , containing the first k items of the input x 1 , . . . , x k {\displaystyle x_{1},...,x_{k}} . This is the reservoir. For each new input x i {\displaystyle x_{i}} , generate a random number j uniformly in { 1 , . . . , i } {\displaystyle \{1,...,i\}} . If j ∈ { 1 , . . . , k } {\displaystyle j\in \{1,...,k\}} , then set R [ j ] := x i . {\displaystyle R[j]:=x_{i}.} Otherwise, discard x i {\displaystyle x_{i}} . Return R {\displaystyle R} after all inputs are processed. This algorithm works by induction on i ≥ k {\displaystyle i\geq k} . While conceptually simple and easy to understand, this algorithm needs to generate a random number for each item of the input, including the items that are discarded. The algorithm's asymptotic running time is thus O ( n ) {\displaystyle O(n)} . Generating this amount of randomness and the linear run time causes the algorithm to be unnecessarily slow if the input population is large. This is Algorithm R, implemented as follows: == Optimal: Algorithm L == If we generate n {\displaystyle n} random numbers u 1 , . . . , u n ∼ U [ 0 , 1 ] {\displaystyle u_{1},...,u_{n}\sim U[0,1]} independently, then the indices of the smallest k {\displaystyle k} of them is a uniform sample of the k {\displaystyle k} -subsets of { 1 , . . . , n } {\displaystyle \{1,...,n\}} . The process can be done without knowing n {\displaystyle n} : Keep the smallest k {\displaystyle k} of u 1 , . . . , u i {\displaystyle u_{1},...,u_{i}} that has been seen so far, as well as w i {\displaystyle w_{i}} , the index of the largest among them. For each new u i + 1 {\displaystyle u_{i+1}} , compare it with u w i {\displaystyle u_{w_{i}}} . If u i + 1 < u w i {\displaystyle u_{i+1}

Source criticism

Source criticism (or information evaluation) is the process of evaluating an information source, i.e.: a document, a person, a speech, a fingerprint, a photo, an observation, or anything used in order to obtain knowledge. In relation to a given purpose, a given information source may be more or less valid, reliable or relevant. Broadly, "source criticism" is the interdisciplinary study of how information sources are evaluated for given tasks. == Meaning == Problems in translation: The Danish word kildekritik, like the Norwegian word kildekritikk and the Swedish word källkritik, derived from the German Quellenkritik and is closely associated with the German historian Leopold von Ranke (1795–1886). Historian Wolfgang Hardtwig wrote: His [Ranke's] first work Geschichte der romanischen und germanischen Völker von 1494–1514 (History of the Latin and Teutonic Nations from 1494 to 1514) (1824) was a great success. It already showed some of the basic characteristics of his conception of Europe, and was of historiographical importance particularly because Ranke made an exemplary critical analysis of his sources in a separate volume, Zur Kritik neuerer Geschichtsschreiber (On the Critical Methods of Recent Historians). In this work he raised the method of textual criticism used in the late eighteenth century, particularly in classical philology to the standard method of scientific historical writing. (Hardtwig, 2001, p. 12739) Historical theorist Chris Lorenz wrote: The larger part of the nineteenth and twentieth centuries would be dominated by the research-oriented conception of historical method of the so-called Historical School in Germany, led by historians as Leopold Ranke and Berthold Niebuhr. Their conception of history, long been regarded as the beginning of modern, 'scientific' history, harked back to the 'narrow' conception of historical method, limiting the methodical character of history to source criticism. (Lorenz, 2001) In the early 21st century, source criticism is a growing field in, among other fields, library and information science. In this context source criticism is studied from a broader perspective than just, for example, history, classical philology, or biblical studies (but there, too, it has more recently received new attention). == Principles == The following principles are from two Scandinavian textbooks on source criticism, written by the historians Olden-Jørgensen (1998) and Thurén (1997): Human sources may be relics (e.g. a fingerprint) or narratives (e.g. a statement or a letter). Relics are more credible sources than narratives. A given source may be forged or corrupted; strong indications of the originality of the source increases its reliability. The closer a source is to the event which it purports to describe, the more one can trust it to give an accurate description of what really happened A primary source is more reliable than a secondary source, which in turn is more reliable than a tertiary source and so on. If a number of independent sources contain the same message, the credibility of the message is strongly increased. The tendency of a source is its motivation for providing some kind of bias. Tendencies should be minimized or supplemented with opposite motivations. If it can be demonstrated that the witness (or source) has no direct interest in creating bias, the credibility of the message is increased. Two other principles are: Knowledge of source criticism cannot substitute for subject knowledge: "Because each source teaches you more and more about your subject, you will be able to judge with ever-increasing precision the usefulness and value of any prospective source. In other words, the more you know about the subject, the more precisely you can identify what you must still find out". (Bazerman, 1995, p. 304). The reliability of a given source is relative to the questions put to it. "The empirical case study showed that most people find it difficult to assess questions of cognitive authority and media credibility in a general sense, for example, by comparing the overall credibility of newspapers and the Internet. Thus these assessments tend to be situationally sensitive. Newspapers, television and the Internet were frequently used as sources of orienting information, but their credibility varied depending on the actual topic at hand" (Savolainen, 2007). The following questions are often good ones to ask about any source according to the American Library Association (1994) and Engeldinger (1988): How was the source located? What type of source is it? Who is the author and what are the qualifications of the author in regard to the topic that is discussed? When was the information published? In which country was it published? What is the reputation of the publisher? Does the source show a particular cultural or political bias? For literary sources complementing criteria are: Does the source contain a bibliography? Has the material been reviewed by a group of peers, or has it been edited? How does the article/book compare with similar articles/books? == Levels of generality == Some principles of source criticism are universal, other principles are specific for certain kinds of information sources. There is today no consensus about the similarities and differences between source criticism in the natural science and humanities. Logical positivism claimed that all fields of knowledge were based on the same principles. Much of the criticism of logical positivism claimed that positivism is the basis of the sciences, whereas hermeneutics is the basis of the humanities. This was, for example, the position of Jürgen Habermas. A newer position, in accordance with, among others, Hans-Georg Gadamer and Thomas Kuhn, understands both science and humanities as determined by researchers' preunderstanding and paradigms. Hermeneutics is thus a universal theory. The difference is, however, that the sources of the humanities are themselves products of human interests and preunderstanding, whereas the sources of the natural sciences are not. Humanities are thus "doubly hermeneutic". Natural scientists, however, are also using human products (such as scientific papers) which are products of preunderstanding (and can lead to, for example, academic fraud). == Contributing fields == === Epistemology === Epistemological theories are the basic theories about how knowledge is obtained and are thus the most general theories about how to evaluate information sources. Empiricism evaluates sources by considering the observations (or sensations) on which they are based. Sources without basis in experience are not seen as valid. Rationalism provides low priority to sources based on observations. In order to be meaningful, observations must be explained by clear ideas or concepts. It is the logical structure and the well definedness that is in focus in evaluating information sources from the rationalist point of view. Historicism evaluates information sources on the basis of their reflection of their sociocultural context and their theoretical development. Pragmatism evaluate sources on the basis of how their values and usefulness to accomplish certain outcomes. Pragmatism is skeptical about claimed neutral information sources. The evaluation of knowledge or information sources cannot be more certain than is the construction of knowledge. If one accepts the principle of fallibilism then one also has to accept that source criticism can never 100% verify knowledge claims. As discussed in the next section, source criticism is intimately linked to scientific methods. The presence of fallacies of argument in sources is another kind of philosophical criterion for evaluating sources. Fallacies are presented by Walton (1998). Among the fallacies are the ad hominem fallacy (the use of personal attack to try to undermine or refute a person's argument) and the straw man fallacy (when one arguer misrepresents another's position to make it appear less plausible than it really is, in order more easily to criticize or refute it.) === Research methodology === Research methods are methods used to produce scholarly knowledge. The methods that are relevant for producing knowledge are also relevant for evaluating knowledge. An example of a book that turns methodology upside-down and uses it to evaluate produced knowledge is Katzer; Cook & Crouch (1998). === Science studies === Studies of quality evaluation processes such as peer review, book reviews and of the normative criteria used in evaluation of scientific and scholarly research. Another field is the study of scientific misconduct. Harris (1979) provides a case study of how a famous experiment in psychology, Little Albert, has been distorted throughout the history of psychology, starting with the author (Watson) himself, general textbook authors, behavior therapists, and a prominent learning theorist. Harris proposes possible causes for these distortions and analyzes the Albert study as an ex

Hybrid algorithm

A hybrid algorithm is an algorithm that combines two or more other algorithms that solve the same problem, either choosing one based on some characteristic of the data, or switching between them over the course of the algorithm. This is generally done to combine desired features of each, so that the overall algorithm is better than the individual components. "Hybrid algorithm" does not refer to simply combining multiple algorithms to solve a different problem – many algorithms can be considered as combinations of simpler pieces – but only to combining algorithms that solve the same problem, but differ in other characteristics, notably performance. == Examples == In computer science, hybrid algorithms are very common in optimized real-world implementations of recursive algorithms, particularly implementations of divide-and-conquer or decrease-and-conquer algorithms, where the size of the data decreases as one moves deeper in the recursion. In this case, one algorithm is used for the overall approach (on large data), but deep in the recursion, it switches to a different algorithm, which is more efficient on small data. A common example is in sorting algorithms, where the insertion sort, which is inefficient on large data, but very efficient on small data (say, five to ten elements), is used as the final step, after primarily applying another algorithm, such as merge sort or quicksort. Merge sort and quicksort are asymptotically optimal on large data, but the overhead becomes significant if applying them to small data, hence the use of a different algorithm at the end of the recursion. A highly optimized hybrid sorting algorithm is Timsort, which combines merge sort, insertion sort, together with additional logic (including binary search) in the merging logic. A general procedure for a simple hybrid recursive algorithm is short-circuiting the base case, also known as arm's-length recursion. In this case whether the next step will result in the base case is checked before the function call, avoiding an unnecessary function call. For example, in a tree, rather than recursing to a child node and then checking if it is null, checking null before recursing. This is useful for efficiency when the algorithm usually encounters the base case many times, as in many tree algorithms, but is otherwise considered poor style, particularly in academia, due to the added complexity. Another example of hybrid algorithms for performance reasons are introsort and introselect, which combine one algorithm for fast average performance, falling back on another algorithm to ensure (asymptotically) optimal worst-case performance. Introsort begins with a quicksort, but switches to a heap sort if quicksort is not progressing well; analogously introselect begins with quickselect, but switches to median of medians if quickselect is not progressing well. Centralized distributed algorithms can often be considered as hybrid algorithms, consisting of an individual algorithm (run on each distributed processor), and a combining algorithm (run on a centralized distributor) – these correspond respectively to running the entire algorithm on one processor, or running the entire computation on the distributor, combining trivial results (a one-element data set from each processor). A basic example of these algorithms are distribution sorts, particularly used for external sorting, which divide the data into separate subsets, sort the subsets, and then combine the subsets into totally sorted data; examples include bucket sort and flashsort. However, in general distributed algorithms need not be hybrid algorithms, as individual algorithms or combining or communication algorithms may be solving different problems. For example, in models such as MapReduce, the Map and Reduce step solve different problems, and are combined to solve a different, third problem.

Machine vision

Machine vision is the technology and methods used to provide imaging-based automatic inspection and analysis for such applications as automatic inspection, process control, and robot guidance, usually in industry. Machine vision refers to many technologies, software and hardware products, integrated systems, actions, methods and expertise. Machine vision as a systems engineering discipline can be considered distinct from computer vision, a form of computer science. It attempts to integrate existing technologies in new ways and apply them to solve real world problems. The term is the prevalent one for these functions in industrial automation environments but is also used for these functions in other environment vehicle guidance. The overall machine vision process includes planning the details of the requirements and project, and then creating a solution. During run-time, the process starts with imaging, followed by automated analysis of the image and extraction of the required information. == Definition == Definitions of the term "Machine vision" vary, but all include the technology and methods used to extract information from an image on an automated basis, as opposed to image processing, where the output is another image. The information extracted can be a simple good-part/bad-part signal, or more a complex set of data such as the identity, position and orientation of each object in an image. The information can be used for such applications as automatic inspection and robot and process guidance in industry, for security monitoring and vehicle guidance. This field encompasses a large number of technologies, software and hardware products, integrated systems, actions, methods and expertise. Machine vision is practically the only term used for these functions in industrial automation applications; the term is less universal for these functions in other environments such as security and vehicle guidance. Machine vision as a systems engineering discipline can be considered distinct from computer vision, a form of basic computer science; machine vision attempts to integrate existing technologies in new ways and apply them to solve real world problems in a way that meets the requirements of industrial automation and similar application areas. The term is also used in a broader sense by trade shows and trade groups such as the Automated Imaging Association and the European Machine Vision Association. This broader definition also encompasses products and applications most often associated with image processing. The primary uses for machine vision are automatic inspection and industrial robot/process guidance. In more recent times the terms computer vision and machine vision have converged to a greater degree. See glossary of machine vision. == Imaging based automatic inspection and sorting == The primary uses for machine vision are imaging-based automatic inspection and sorting and robot guidance.; in this section the former is abbreviated as "automatic inspection". The overall process includes planning the details of the requirements and project, and then creating a solution. This section describes the technical process that occurs during the operation of the solution. === Methods and sequence of operation === The first step in the automatic inspection sequence of operation is acquisition of an image, typically using cameras, lenses, and lighting that has been designed to provide the differentiation required by subsequent processing. MV software packages and programs developed in them then employ various digital image processing techniques to extract the required information, and often make decisions (such as pass/fail) based on the extracted information. === Equipment === The components of an automatic inspection system usually include lighting, a camera or other imager, a processor, software, and output devices. === Imaging === The imaging device (e.g. camera) can either be separate from the main image processing unit or combined with it in which case the combination is generally called a smart camera or smart sensor. Inclusion of the full processing function into the same enclosure as the camera is often referred to as embedded processing. When separated, the connection may be made to specialized intermediate hardware, a custom processing appliance, or a frame grabber within a computer using either an analog or standardized digital interface (Camera Link, CoaXPress). MV implementations also use digital cameras capable of direct connections (without a framegrabber) to a computer via FireWire, USB or Gigabit Ethernet interfaces. While conventional (2D visible light) imaging is most commonly used in MV, alternatives include multispectral imaging, hyperspectral imaging, imaging various infrared bands, line scan imaging, 3D imaging of surfaces and X-ray imaging. Key differentiations within MV 2D visible light imaging are monochromatic vs. color, frame rate, resolution, and whether or not the imaging process is simultaneous over the entire image, making it suitable for moving processes. Though the vast majority of machine vision applications are solved using two-dimensional imaging, machine vision applications utilizing 3D imaging are a growing niche within the industry. The most commonly used method for 3D imaging is scanning based triangulation which utilizes motion of the product or image during the imaging process. A laser is projected onto the surfaces of an object. In machine vision this is accomplished with a scanning motion, either by moving the workpiece, or by moving the camera & laser imaging system. The line is viewed by a camera from a different angle; the deviation of the line represents shape variations. Lines from multiple scans are assembled into a depth map or point cloud. Stereoscopic vision is used in special cases involving unique features present in both views of a pair of cameras. Other 3D methods used for machine vision are time of flight and grid based. One method is grid array based systems using pseudorandom structured light system as employed by the Microsoft Kinect system circa 2012. === Image processing === After an image is acquired, it is processed. Central processing functions are generally done by a CPU, a GPU, a FPGA or a combination of these. Deep learning training and inference impose higher processing performance requirements. Multiple stages of processing are generally used in a sequence that ends up as a desired result. A typical sequence might start with tools such as filters which modify the image, followed by extraction of objects, then extraction (e.g. measurements, reading of codes) of data from those objects, followed by communicating that data, or comparing it against target values to create and communicate "pass/fail" results. Machine vision image processing methods include; Stitching/Registration: Combining of adjacent 2D or 3D images. Filtering (e.g. morphological filtering) Thresholding: Thresholding starts with setting or determining a gray value that will be useful for the following steps. The value is then used to separate portions of the image, and sometimes to transform each portion of the image to simply black and white based on whether it is below or above that grayscale value. Pixel counting: counts the number of light or dark pixels Segmentation: Partitioning a digital image into multiple segments to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Edge detection: finding object edges Color Analysis: Identify parts, products and items using color, assess quality from color, and isolate features using color. Blob detection and extraction: inspecting an image for discrete blobs of connected pixels (e.g. a black hole in a grey object) as image landmarks. Neural network / deep learning / machine learning processing: weighted and self-training multi-variable decision making Circa 2019 there is a large expansion of this, using deep learning and machine learning to significantly expand machine vision capabilities. The most common result of such processing is classification. Examples of classification are object identification,"pass fail" classification of identified objects and OCR. Pattern recognition including template matching. Finding, matching, and/or counting specific patterns. This may include location of an object that may be rotated, partially hidden by another object, or varying in size. Barcode, Data Matrix and "2D barcode" reading Optical character recognition: automated reading of text such as serial numbers Gauging/Metrology: measurement of object dimensions (e.g. in pixels, inches or millimeters) Comparison against target values to determine a "pass or fail" or "go/no go" result. For example, with code or bar code verification, the read value is compared to the stored target value. For gauging, a measurement is compared against the proper value and tolerances. For verification of alpha-numberic codes, the

XOR swap algorithm

In computer programming, the exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two variables without using the temporary variable which is normally required. The algorithm is primarily a novelty and a way of demonstrating properties of the exclusive or operation. It is sometimes discussed as a program optimization, but there are almost no cases where swapping via exclusive or provides benefit over the standard, obvious technique. == The algorithm == Conventional swapping requires the use of a temporary storage variable. Using the XOR swap algorithm, however, no temporary storage is needed. The algorithm is as follows: Since XOR is a commutative operation, either X XOR Y or Y XOR X can be used interchangeably in any of the foregoing three lines. Note that on some architectures the first operand of the XOR instruction specifies the target location at which the result of the operation is stored, preventing this interchangeability. The algorithm typically corresponds to three machine-code instructions, represented by corresponding pseudocode and assembly instructions in the three rows of the following table: In the above System/370 assembly code sample, R1 and R2 are distinct registers, and each XR operation leaves its result in the register named in the first argument. Using x86 assembly, values X and Y are in registers eax and ebx (respectively), and xor places the result of the operation in the first register (Note: x86 supports XCHG instruction so using triple XOR do not make sense on this architecture). In RISC-V assembly, value X and Y are in registers x10 and x11, and xor places the result of the operation in the first operand. However, in the pseudocode or high-level language version or implementation, the algorithm fails if x and y use the same storage location, since the value stored in that location will be zeroed out by the first XOR instruction, and then remain zero; it will not be "swapped with itself". This is not the same as if x and y have the same values. The trouble only comes when x and y use the same storage location, in which case their values must already be equal. That is, if x and y use the same storage location, then the line: sets x to zero (because x = y so X XOR Y is zero) and sets y to zero (since it uses the same storage location), causing x and y to lose their original values. == Proof of correctness == The binary operation XOR over bit strings of length N {\displaystyle N} exhibits the following properties (where ⊕ {\displaystyle \oplus } denotes XOR): L1. Commutativity: A ⊕ B = B ⊕ A {\displaystyle A\oplus B=B\oplus A} L2. Associativity: ( A ⊕ B ) ⊕ C = A ⊕ ( B ⊕ C ) {\displaystyle (A\oplus B)\oplus C=A\oplus (B\oplus C)} L3. Identity exists: there is a bit string, 0, (of length N) such that A ⊕ 0 = A {\displaystyle A\oplus 0=A} for any A {\displaystyle A} L4. Each element is its own inverse: for each A {\displaystyle A} , A ⊕ A = 0 {\displaystyle A\oplus A=0} . Suppose that we have two distinct registers R1 and R2 as in the table below, with initial values A and B respectively. We perform the operations below in sequence, and reduce our results using the properties listed above. === Linear algebra interpretation === As XOR can be interpreted as binary addition and a pair of bits can be interpreted as a vector in a two-dimensional vector space over the field with two elements, the steps in the algorithm can be interpreted as multiplication by 2×2 matrices over the field with two elements. For simplicity, assume initially that x and y are each single bits, not bit vectors. For example, the step: which also has the implicit: corresponds to the matrix ( 1 1 0 1 ) {\displaystyle \left({\begin{smallmatrix}1&1\\0&1\end{smallmatrix}}\right)} as ( 1 1 0 1 ) ( x y ) = ( x + y y ) . {\displaystyle {\begin{pmatrix}1&1\\0&1\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}={\begin{pmatrix}x+y\\y\end{pmatrix}}.} The sequence of operations is then expressed as: ( 1 1 0 1 ) ( 1 0 1 1 ) ( 1 1 0 1 ) = ( 0 1 1 0 ) {\displaystyle {\begin{pmatrix}1&1\\0&1\end{pmatrix}}{\begin{pmatrix}1&0\\1&1\end{pmatrix}}{\begin{pmatrix}1&1\\0&1\end{pmatrix}}={\begin{pmatrix}0&1\\1&0\end{pmatrix}}} (working with binary values, so 1 + 1 = 0 {\displaystyle 1+1=0} ), which expresses the elementary matrix of switching two rows (or columns) in terms of the transvections (shears) of adding one element to the other. To generalize to where X and Y are not single bits, but instead bit vectors of length n, these 2×2 matrices are replaced by 2n×2n block matrices such as ( I n I n 0 I n ) . {\displaystyle \left({\begin{smallmatrix}I_{n}&I_{n}\\0&I_{n}\end{smallmatrix}}\right).} These matrices are operating on values, not on variables (with storage locations), hence this interpretation abstracts away from issues of storage location and the problem of both variables sharing the same storage location. == Code example == A C function that implements the XOR swap algorithm: The code first checks if the addresses are distinct and uses a guard clause to exit the function early if they are equal. Without that check, if they were equal, the algorithm would fold to a triple x ^= x resulting in zero. == Reasons for avoidance in practice == On modern CPU architectures, the XOR technique can be slower than using a temporary variable to do swapping. At least on recent x86 CPUs, both by AMD and Intel, moving between registers regularly incurs zero latency. (This is called MOV-elimination.) Even if there is not any architectural register available to use, the XCHG instruction will be at least as fast as the three XORs taken together. Another reason is that modern CPUs strive to execute instructions in parallel via instruction pipelines. In the XOR technique, the inputs to each operation depend on the results of the previous operation, so they must be executed in strictly sequential order, negating any benefits of instruction-level parallelism. === Aliasing === The XOR swap is also complicated in practice by aliasing. If an attempt is made to XOR-swap the contents of some location with itself, the result is that the location is zeroed out and its value lost. Therefore, XOR swapping must not be used blindly in a high-level language if aliasing is possible. This issue does not apply if the technique is used in assembly to swap the contents of two registers. Similar problems occur with call by name, as in Jensen's Device, where swapping i and A[i] via a temporary variable yields incorrect results due to the arguments being related: swapping via temp = i; i = A[i]; A[i] = temp changes the value for i in the second statement, which then results in the incorrect i value for A[i] in the third statement. == Variations == The underlying principle of the XOR swap algorithm can be applied to any operation meeting criteria L1 through L4 above. Replacing XOR by addition and subtraction gives various slightly different, but largely equivalent, formulations. For example: Unlike the XOR swap, this variation requires that the underlying processor or programming language uses a method such as modular arithmetic or bignums to guarantee that the computation of X + Y cannot cause an error due to integer overflow. Therefore, it is seen even more rarely in practice than the XOR swap. However, the implementation of AddSwap above in the C programming language always works even in case of integer overflow, since, according to the C standard, addition and subtraction of unsigned integers follow the rules of modular arithmetic, i. e. are done in the cyclic group Z / 2 s Z {\displaystyle \mathbb {Z} /2^{s}\mathbb {Z} } where s {\displaystyle s} is the number of bits of unsigned int. Indeed, the correctness of the algorithm follows from the fact that the formulas ( x + y ) − y = x {\displaystyle (x+y)-y=x} and ( x + y ) − ( ( x + y ) − y ) = y {\displaystyle (x+y)-((x+y)-y)=y} hold in any abelian group. This generalizes the proof for the XOR swap algorithm: XOR is both the addition and subtraction in the abelian group ( Z / 2 Z ) s {\displaystyle (\mathbb {Z} /2\mathbb {Z} )^{s}} (which is the direct sum of s copies of Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } ). This doesn't hold when dealing with the signed int type (the default for int). Signed integer overflow is an undefined behavior in C and thus modular arithmetic is not guaranteed by the standard, which may lead to incorrect results. The sequence of operations in AddSwap can be expressed via matrix multiplication as: ( 1 − 1 0 1 ) ( 1 0 1 − 1 ) ( 1 1 0 1 ) = ( 0 1 1 0 ) {\displaystyle {\begin{pmatrix}1&-1\\0&1\end{pmatrix}}{\begin{pmatrix}1&0\\1&-1\end{pmatrix}}{\begin{pmatrix}1&1\\0&1\end{pmatrix}}={\begin{pmatrix}0&1\\1&0\end{pmatrix}}} == Application to register allocation == On architectures lacking a dedicated swap instruction, because it avoids the extra temporary register, the XOR swap algorithm is required for optimal register allocatio