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When computing mathematical functions such as square roots, logarithms, and sines [3] the predecessor of numpy, numeric, was originally created by jim hugunin with contributions from several other developers There are two prevailing definitions, denoted here as rounding machine epsilon or the formal definition and interval machine epsilon or mainstream definition

In the mainstream definition, machine epsilon is independent of rounding method, and is defined simply as the difference between 1 and the next larger floating point number. In both technical and informal language, a round number is often interpreted to stand for a value or values near to the nominal value expressed. [3] rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them

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Arithmetic right shifts for negative numbers are equivalent to division using rounding towards 0 in ones' complement representation of signed numbers as was used by some historic computers, but this is no longer in general use. In mathematics and digital signal processing, quantization is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements Rounding and truncation are typical examples of quantization processes. If the number falls midway, it is rounded to the nearest value above (for positive numbers) or below (for negative numbers).

[1] so, 590 is rounder than 592, but 590 is less round than 600

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