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README.md
benchmark_template.cpp
fastexp.cpp
fastexp.h
ieee.h
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README.md

fastexp

fastexp is a small C++ template library that implements fast, vectorizable approximations of the exponential function.

Warning

The functions provided here are approximations with limited validity. Thus always check if they suit your usecase before using them.

Moreover, these implementation contain no safeguards against overflows so it is up to the user to ensure the arguments are in the right range.

Approximations

A formal description of the two approximations available can be found here.

Truncated Product

This approximation expresses the exponential as an infinite product which is evaluated up to a certain threshold. The computation of the product is implemented using exponentiation by squaring.

The plot below gives the error for different degrees of the approximation of different argument ranges. This approximation should work well when:

  • The argument x is small and/or positive
  • An approximation that is limited from above by the true exponential is desired

img

IEEE Manipulation

This approximation was proposed by Schraudolph and refined by Malossi et al. and exploits the definition of the IEE 754 floating point format to approximate the exponential. The plot below displays the relative errors obtained using the approximation. This approximation should work well if

  • The absolute value of the argument x is larger than 1

img

Performance

So far, I was only able to run the benchmark on an Intel Core i7-2640M CPU (2.80GHz). The plots below show compute times for different approximations compared to the standard library implementations. The benchmark scenario is the computation of the exponential function to an array containing 100 million elements.

Single Precision

img

Double Precision

img

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