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Truncation of positive real numbers can be done using the floor function. Given a number x ∈ R + {\displaystyle x\in \mathbb {R} _{+}} to be truncated and n ∈ N 0 {\displaystyle n\in \mathbb {N} _{0}} , the number of elements to be kept behind the decimal point, the truncated value of x is
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
Rounding should preserve symmetries that already exist between the domain and range. With finite precision (or a discrete domain), this translates to removing bias. A rounding method should have utility in computer science or human arithmetic where finite precision is used, and speed is a consideration.
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Programming languages are used for controlling the behavior of a machine (often a computer). Like natural languages, programming languages follow rules for syntax and semantics. There are thousands of programming languages [1] and new ones are created every year.
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
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