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In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are potentially limited only by the available memory of the host system.
In mathematics, the extended real number system [a] is obtained from the real number system by adding two elements denoted + and [b] that are respectively greater and lower than every real number. This allows for treating the potential infinities of infinitely increasing sequences and infinitely decreasing series as actual infinities .
The projectively extended real line can be visualized as the real number line wrapped around a circle (by some form of stereographic projection) with an additional point at infinity. In real analysis , the projectively extended real line (also called the one-point compactification of the real line ), is the extension of the set of the real ...
The aleph numbers differ from the infinity commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the ...
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Some numbers may have several possible floating-point representations. For instance, if b = 10, and p = 7, then −12.345 can be represented by −12345×10 −3, −123450×10 −4, and −1234500×10 −5. However, for most operations, such as arithmetic operations, the result (value) does not depend on the representation of the inputs.
Saturation arithmetic is a version of arithmetic in which all operations, such as addition and multiplication, are limited to a fixed range between a minimum and maximum value. If the result of an operation is greater than the maximum, it is set (" clamped ") to the maximum; if it is below the minimum, it is clamped to the minimum.