how is Multiply and At. Long. Last. ASAP connected?
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Multiply (ASAP Rocky song) "Multiply" is a song recorded by American rapper ASAP Rocky, which was made available for online streaming on October 3, 2014. Four days later, it was released as a digital single by RCA Records. The song features Juicy J and was produced by Curtis Heron. A music video for the track was co-directed by ASAP Rocky and Shomi Patwary. The single serves as a promotional single for Rocky's third studio album "At. Long. Last. ASAP"
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At. Long. Last. ASAP At. Long. Last. ASAP (stylized as AT.LONG.LAST.A$AP) is the second studio album by American rapper ASAP Rocky . It was released on May 26, 2015, by A$AP Worldwide, Polo Grounds Music, and RCA Records. The record serves as a sequel from Rocky's previous studio effort "Long. Live. ASAP" (2013). In 2013, the recording sessions first took place, during a release of "Long. Live. A$AP". The album's executive production was provided by Danger Mouse, mentor ASAP Yams and Rocky himself, featuring production by Rocky and Danger Mouse, as well as a variety of several high-profile producers, including co-executive producers Hector Delgado and Juicy J, Jim Jonsin, FNZ, Frans Mernick, Kanye West, Thelonious Martin and Mark Ronson, among others.
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History of logarithms The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer. The Napierian logarithms were published first in 1614. Henry Briggs introduced common (base 10) logarithms, which were easier to use. Tables of logarithms were published in many forms over four centuries. The idea of logarithms was also used to construct the slide rule, which became ubiquitous in science and engineering until the 1970s. A breakthrough generating the natural logarithm was the result of a search for an expression of area against a rectangular hyperbola, and required the assimilation of a new function into standard mathematics.
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Floating-point unit A floating-point unit (FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating point numbers. Typical operations are addition, subtraction, multiplication, division, square root, and bitshifting. Some systems (particularly older, microcode-based architectures) can also perform various transcendental functions such as exponential or trigonometric calculations, though in most modern processors these are done with software library routines.
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Window operator In modal logic, the window operator formula_1 is a modal operator with the following semantic definition:
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Fetch-and-add In computer science, the fetch-and-add CPU instruction (FAA) atomically increments the contents of a memory location by a specified value.
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The Compendious Book on Calculation by Completion and Balancing The Compendious Book on Calculation by Completion and Balancing
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Event loop In computer science, the event loop, message dispatcher, message loop, message pump, or run loop is a programming construct that waits for and dispatches events or messages in a program. It works by making a request to some internal or external "event provider" (that generally blocks the request until an event has arrived), and then it calls the relevant event handler ("dispatches the event"). The event-loop may be used in conjunction with a reactor, if the event provider follows the file interface, which can be selected or 'polled' (the Unix system call, not actual polling). The event loop almost always operates asynchronously with the message originator.
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Asynchronous cellular automaton Cellular automata, as with other multi-agent system models, usually treat time as discrete and state updates as occurring synchronously. The state of every cell in the model is updated together, before any of the new states influence other cells. In contrast, an asynchronous cellular automaton is able to update individual cells independently, in such a way that the new state of a cell affects the calculation of states in neighbouring cells.
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Asynchronous method invocation In multithreaded computer programming, asynchronous method invocation (AMI), also known as asynchronous method calls or the asynchronous pattern is a design pattern in which the call site is not blocked while waiting for the called code to finish. Instead, the calling thread is notified when the reply arrives. Polling for a reply is an undesired option.
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Time To First Byte Time To First Byte (TTFB) is a measurement used as an indication of the responsiveness of a webserver or other network resource.
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Multiplicative inverse In mathematics, a multiplicative inverse or reciprocal for a number "x", denoted by 1/"x" or "x", is a number which when multiplied by "x" yields the multiplicative identity, 1. The multiplicative inverse of a fraction "a"/"b" is "b"/"a". For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function "f"("x") that maps "x" to 1/"x", is one of the simplest examples of a function which is its own inverse (an involution).
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Asynchronous method dispatch Asynchronous method dispatch (AMD) is a data communication method used when there is a need for the server side to handle a large number of long lasting client requests. Using synchronous method dispatch (SMD), this scenario may turn the server into an unavailable busy state resulting in a connection failure response caused by a network connection request timeout.
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Additive map In algebra an additive map, Z-linear map or additive function is a function that preserves the addition operation:
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Iterated function In mathematics, an iterated function is a function "X → X" (that is, a function from some set X to itself) which is obtained by composing another function "f" : "X → X" with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial number, the result of applying a given function is fed again in the function as input, and this process is repeated.
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0.999... In mathematics, 0.999... (also written 0.9 , among other ways), denotes the repeating decimal consisting of infinitely many 9 after the decimal point (and one 0 before it). This repeating decimal represents the smallest number no less than all decimal numbers 0.9, 0.99, 0.999, etc. This number can be shown to equal 1. In other words, "0.999..." and "1" represent the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs. The technique used depends on target audience, background assumptions, historical context, and preferred development of the real numbers, the system within which 0.999... is commonly defined. (In other systems, 0.999... can have the same meaning, a different definition, or be undefined.)
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Time complexity In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the length of the string representing the input. The time complexity of an algorithm is commonly expressed using big O notation, which excludes coefficients and lower order terms. When expressed this way, the time complexity is said to be described "asymptotically", i.e., as the input size goes to infinity. For example, if the time required by an algorithm on all inputs of size "n" is at most 5"n" + 3"n" for any "n" (bigger than some "n"), the asymptotic time complexity is O("n").
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MultiLisp MultiLisp was a functional programming language and dialect of Scheme, extended with constructs for parallel execution and shared memory. These extensions involve side effects, rendering MultiLisp non-deterministic. In addition to its parallel-programming extensions, MultiLisp also had some unusual garbage collection and task scheduling algorithms. Like Scheme, MultiLisp was oriented toward symbolic computation. Unlike some parallel programming languages, MultiLisp incorporated constructs for causing side effects and for explicitly introducing parallelism.
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Sequence transformation In mathematics, a sequence transformation is an operator acting on a given space of sequences (a sequence space). Sequence transformations include linear mappings such as convolution with another sequence, and resummation of a sequence and, more generally, are commonly used for series acceleration, that is, for improving the rate of convergence of a slowly convergent sequence or series. Sequence transformations are also commonly used to compute the antilimit of a divergent series numerically, and are used in conjunction with extrapolation methods.
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Infinite regress An infinite regress in a series of propositions arises if the truth of proposition "P" requires the support of proposition "P", the truth of proposition "P" requires the support of proposition "P", ... , the truth of proposition "P" requires the support of proposition "P", ad infinitum.
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Polynomial long division In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones. Sometimes using a shorthand version called synthetic division is faster, with less writing and fewer calculations.
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Addition-chain exponentiation In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by positive integer powers that requires a minimal number of multiplications. This corresponds to the sequence A003313 on the Online Encyclopedia of Integer Sequences. It works by creating the shortest addition chain that generates the desired exponent. Each exponentiation in the chain can be evaluated by multiplying two of the earlier exponentiation results. More generally, "addition-chain exponentiation" may also refer to exponentiation by non-minimal addition chains constructed by a variety of algorithms (since a shortest addition chain is very difficult to find).