α-CORDIC: An adaptive CORDIC algorithm

Abstract

In this work we briefly review the basic CORDIC algorithm and its drawbacks. Next, we propose an adaptive CORDIC algorithm (a-CORDIC) which removes all the CORDIC drawbacks: (a) the number of iterations is reduced, (b) full machine accuracy is assured, (c) the scale-factor problem is eliminated, (d) the operating range is unlimited, (e) computation noise is reduced, and (f) ability to utilize the fast multiply/accumulate instructions now prevalent in digital signal processing (DSP) chips is added. The new algorithm uses a better strategy for choosing the step size in each iteration, but requires a parallel multiplier and extra look-up tables. This condition is easily satisfied in most new microprocessor chips. Simulation results, assuming 32-bit floating-point data format, are presented which clearly show the advantages of the proposed algorithm.Dans ce travail nous rappelons brievement les bases de 1'algorithme CORDIC ainsi que ses ctesavantages. Par la suite nous proposons un algorithme CORDIC adaptatif (a-CORDIC) qui 61imine tous les d6savantages de 1'algorithme CORDIC original: (a) le nombre d'itdrations est r6duit, (b) la precision maximale de la machine est assured, (c) le probleme du facteur d'gchelle est 61imin6, (d) la plage de travail devient illimitee, (e) le bruit relief au processus de calcul est r6duit et (f) 1'utilisation des instructions de multiplications/accumulations rapides disponibles dans les circuits int6gr6s DSP devient possible.

Parallel Computers

“…Defi nition 1. 5 An output edge in a DG is one that starts from a node but does not terminate on any other node. It represents one of the algorithm outputs.…”

“…The author developed a parallel CORDIC algorithm (high -performance coordinate rotation digital computer [HCORDIC]) that is faster than the bit -serial CORDIC but relies on the fact that modern ALUs contain a multiplier [5,6] . Thus the presence of a parallel multiplier speeds up not only the multiplication operation but the evaluation of many elementary functions.…”

“…The X confi guration is the default confi guration where the SE allows simultaneous data fl ow in the vertical and horizontal directions without interference. If CP (3,5) was in the X confi guration, then In the T confi guration, the CP allows data fl ow in the horizontal direction and interrupts data fl ow in the vertical direction. Data fl owing vertically at the output are a copy of the horizontal data.…”

“…Data fl owing vertically at the output are a copy of the horizontal data. For example, if CP (3,5) was in the T confi guration, then data fl owing horizontally originate at input 3. Data fl owing downward at the output are a copy of the horizontal data coming from row 3.…”

“…Table 6.1 summarizes some of the OpenMP pragma directives Listing 6. 5 The following code fragment shows how #omp comp parallel compiler directive is sued to fork additional threads to execute the tasks specifi ed by the affected code section : // The code between brackets will run in parallel statement 1; statement 2; statement 3; Ӈ }…”