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I'm trying to develop a architecture hardware to make a implementation of an algorithm that can be descompose in terms of sums, multiplications, subtractions and exponential functions. I'm trying to modelling $\exp(-x)$ through Taylor series. The domain of my function is bounded between $0$ and $1500$, but I want to use a particular Taylor approximation whose domain is bounded between $0$ and $0.5$.

Is there any way to get an approximation using the my tailor series whose domain is bounded between $0$ and $0.5$ to modelling the function whose domain is bounded between $0$ and $1500$?

The function I want to model for bounded domain is $\exp(-x)$. Thank you for your help.

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    The computation of the exponential is a well studied problem, I would imagine, and I very much doubt it is done in practice using Taylor series, which tend to be *really* bad approximations for anything but proving theorems. Have you looked at standard implementations (like the one in the GMP library)?2013-02-23

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You can certainly find the Taylor series of exp(-x) around 0.25. Wolfram Alpha gives an answer. Then you can plug large numbers into it if you want. It just won't be at all accurate. But I don't think I am understanding what you mean by your boldface question.

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    About my boldface question: I mean that if I can use a T.series expression of a function whose domain is bounded between 0 and 0.5 to get an approximation for a function bounded between 0 and 1500. The problem with using the Taylor series approximations is that only are true for a narrow margin around the point of evaluation.2011-02-04
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    How to get a Taylor approximation to a much larger margin than unity, than ten units or even a hundred? .I think TS could be a solution for a margin of 10 units at most, but not for 100 units or more.2011-02-04
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    You can use other series than Taylor, for example a Chebyshev one, which minimizes the error over a domain. It still will need many terms over a wide range. Another approach is to accurately calculate exp(x) over a small range and use the properties of exponents to extend it. And for exp(-x), if x gets very large, you can just return 0.2011-02-04