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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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