Some systems (particularly older, microcode-based architectures) can also perform various transcendental functions such as exponential or trigonometric calculations, though in most modern processors these are done with software library routines.
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A class of functions, which are 'similar to the exponential function' was given the name 'E-functions' by Siegel.
In the 1990s, Alex Wilkie showed that one has the same result if instead of adding every analytic function, one just adds the exponential function to R to get the ordered real field with exponentiation, Rexp, a result known as Wilkie's theorem.