Expanding the Range of Convergence of the CORDIC Algorithm

The limitations on the numerical values of the functional arguments that are passed to the CORDIC computational units are discussed, with a special emphasis on the binary, fixed-point hardware implementation. Research in the area of expanding the allowed ranges of the input variables for which accurate output values can be obtained is presented. The methods proposed to expand the range of convergence for the CORDIC algorithm do not necessitate any unwidely overhead calculation, thus making this work amenable to a hardware implementation. The number of extra iterations introduced in the modified CORDIC algorithms is significantly less than the number of extra iterations discussed elsewhere. This reduction in the number of extra iterations will lead to a faster hardware implementation. Examples demonstrate the usefulness of the methods in realistic situations. >

[1]  Xiaobo Sharon Hu,et al.  The application of bit-serial CORDIC computational units to the design of inverse kinematics processors , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[2]  Jean-Michel Muller,et al.  Discrete Basis and Computation of Elementary Functions , 1985, IEEE Transactions on Computers.

[3]  Yu Hen Hu,et al.  Doubly pipelined Cordic array for digital signal processing algorithms , 1987 .

[4]  Sin Hitotumatu.  Complex arithmetic through CORDIC , 1975 .

[5]  Jing Li,et al.  Bit-serial CORDIC circuits for use in a VLSI silicon compiler , 1989, IEEE International Symposium on Circuits and Systems,.

[6]  Jack E. Volder.  The CORDIC Trigonometric Computing Technique , 1959, IRE Trans. Electron. Comput..

[7]  J.-M. Delosme,et al.  VLSI implementation of rotations in pseudo-Euclidean spaces , 1983, ICASSP.

[8]  Michael Andrews,et al.  A pipelined computer architecture for unified elementary function evaluation , 1978 .

[9]  J. S. Walther,et al.  A unified algorithm for elementary functions , 1899, AFIPS '71 (Spring).

[10]  Haviland,et al.  A Cordic Arithmetic Processor Chip , 1980, IEEE Transactions on Computers.

[11]  Dan H. Daggett,et al.  Decimal-Binary Conversions in CORDIC , 1959, IRE Trans. Electron. Comput..