Calculating Mathematically Complex Functions Issue 87

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Thanks to their flexibility and performance,
FPGAs have found
their way into a number of industrial,
science, military and other
applications that require the calculation
of complex mathematical problems
or transfer functions. It is not uncommon to
see tight accuracy and calculation latency
times in the more critical applications.
When using an FPGA to implement mathematical
functions, engineers normally
choose fixed-point mathematics (see Xcell
Journal issue 80, “The Basics of FPGA
Mathematics,” http://issuu.com/xcelljournal/
docs/xcell80/44?e=2232228/2002872).
Also, there are many algorithms, such as
CORDIC, that you can use to calculate transcendental
functions (see Xcell Journal issue
79, “How to Use the CORDIC Algorithm
in Your FPGA,” http://www.xilinx.com/
publications/archives/xcel l/Xcell79.pdf).
However, when confronting functions that
are very mathematically complex, there are
more efficient ways of dealing with them than
by implementing the exact demanding function
within the FPGA. To understand these
alternative approaches—especially one of
them, polynomial approximation—let us first
define the problem.

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