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Old 05-03-2006, 06:25 AM
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Default Table-lookup CORDIC


Table-lookup implementation of CORDIC


The idea of unification of CORDIC and table-lookup is the follo-
wing: taking leftmost m bits of the argument X ( for example for fu-
nction sin X ) and using them as a input address of ROM with the
capacity
2**m words we can skip the first m iterations and begin from (m+1)-th
iteration taking the table values as the initial values of iterative
variables.
The total number of iterations in that case is (n-m) , where n - word
length.
Correspondingly the number of table constants (arctan, ln) de-
creased on m.
We considered and verified that approach for trigonometric, hyperbolic,

and exp, log, and sqrt functions.

That approach can be completed by stopping of iterations on n/2-th
iteration, suggested by T.C.Chen in 1972, and consequent linear inter-
polation. In such case , unifiing that with table-lookup approach
the total number of iteration is (n/2-m).

If for example n=24, m=8 we should execute only 4 iterations.

All the detailes of the implementation of this approach you
can find in:

1. Analyse of the table lookup and table-algorithmic methods of the
elementary functions evaluation. V.Baykov, V.Smolov , Published in
The Journal "Electronic modeling" (Engineering Simulation) 1980, N1,
p.22-27
This journals are translated into English in the USA, since 1981
http://www.rql.kiev.ua/electr_model/.

2. The book: Special-purpose processors:iterative algorithms
and structures" pages: 134-143 (Vladimir Baykov, Vladimir Smolov),
Moscow, 1985
(this book in 1988-1995 was sent to many American and European
scientists who are working in the Computer Arithmetic area)
http://baykov.de/Cordic1985.htm

3. and in the Usenet group comp.arch. arithmetic at 16 Juini 1995
in:
http://groups.google.com/groups?hl=r...r=&sa=N&tab=wg

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