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<p><b>New page</b></p><div>[[File:Abramowitz&Stegun.page97.agr.jpg|Abramowitz&Stegun.page97.agr|thumb]] '''Lookup table'''<br />
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A '''lookup table''' is an array or matrix used to map input values to corresponding output values, often to expedite the process of computation. Lookup tables are widely used in various fields such as [[computer science]], [[mathematics]], [[cryptography]], and [[digital signal processing]].<br />
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==Overview==<br />
Lookup tables are designed to replace runtime computation with a simpler array indexing operation. This can significantly speed up the process, especially in scenarios where the same computation is performed repeatedly. The basic idea is to precompute the results of a function and store them in a table, which can then be accessed using the input values as indices.<br />
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==Applications==<br />
===Computer Science===<br />
In [[computer science]], lookup tables are commonly used in [[hash tables]], [[database indexing]], and [[data compression]] algorithms. They are also used in [[graphics processing]] to accelerate the rendering of images and in [[networking]] for routing and address resolution.<br />
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===Mathematics===<br />
In [[mathematics]], lookup tables can be used to store precomputed values of functions such as [[trigonometric functions]], [[logarithms]], and [[factorials]]. This is particularly useful in numerical methods and [[scientific computing]].<br />
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===Cryptography===<br />
In [[cryptography]], lookup tables are used in the implementation of [[block ciphers]] and [[hash functions]]. For example, the [[S-box]] in the [[Advanced Encryption Standard]] (AES) is a type of lookup table.<br />
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===Digital Signal Processing===<br />
In [[digital signal processing]], lookup tables are used to implement [[finite impulse response]] (FIR) filters and other signal processing algorithms. They help in reducing the computational complexity and improving the efficiency of real-time signal processing systems.<br />
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==Advantages==<br />
* **Speed**: Lookup tables can significantly reduce the time complexity of certain operations by replacing complex computations with simple array indexing.<br />
* **Simplicity**: They simplify the implementation of algorithms by precomputing and storing results.<br />
* **Consistency**: Lookup tables provide consistent and repeatable results, which is crucial in applications like cryptography and digital signal processing.<br />
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==Disadvantages==<br />
* **Memory Usage**: Lookup tables can consume a significant amount of memory, especially if the table is large or if the input space is vast.<br />
* **Initialization Time**: The time required to precompute and initialize the lookup table can be substantial.<br />
* **Scalability**: Lookup tables may not scale well with increasing input size or dimensionality.<br />
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==Related Pages==<br />
* [[Hash table]]<br />
* [[Database indexing]]<br />
* [[Data compression]]<br />
* [[Graphics processing]]<br />
* [[Network routing]]<br />
* [[Trigonometric functions]]<br />
* [[Logarithms]]<br />
* [[Factorials]]<br />
* [[Block cipher]]<br />
* [[Hash function]]<br />
* [[Finite impulse response]]<br />
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==See Also==<br />
* [[Array data structure]]<br />
* [[Matrix (mathematics)]]<br />
* [[Precomputation]]<br />
* [[Algorithm optimization]]<br />
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[[Category:Computer science]]<br />
[[Category:Mathematics]]<br />
[[Category:Cryptography]]<br />
[[Category:Digital signal processing]]<br />
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