the following technical report has undergone extensive revision since it
was first announced here. Among other things, the EXP macro itself has
been modified (faster still), and its mean, maximum, and RMS relative
approximation error are now derived analytically.
With best regards,
--
Dr. Nicol N. Schraudolph Tel: +41-91-970-3877
IDSIA Fax: +41-91-911-9839
Corso Elvezia 36
CH-6900 Lugano http://www.idsia.ch/~nic/
Switzerland
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Technical Report IDSIA-07-98:
A Fast, Compact Approximation of the Exponential Function
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Nicol N. Schraudolph
Neural network simulations often spend a large proportion of their time
computing exponential functions. Since the exponentiation routines of
typical math libraries are rather slow, their replacement with a fast
approximation can greatly reduce the overall computation time. This
note describes how exponentiation can be approximated by manipulating
the components of a standard (IEEE-754) floating-point representation.
This models the exponential function as well as a lookup table with
linear interpolation, but is significantly faster and more compact.
ftp://ftp.idsia.ch/pub/nic/exp.ps.gz (10 pages, 145 kB compressed)