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:
- 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 formatting link
- 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) formatting link
- and in the Usenet group comp.arch. arithmetic at 16 Juini 1995 in: formatting link