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CORDIC-Based Computation of ArcCos

Abstract

CORDIC-based algorithms to compute cos\(\cos ^{ - 1} (t),\sin ^{ - 1} (t)\) and \(\sqrt {1 - t^2 }\) are proposed. The implementation requires a standard CORDIC module plus a module to compute the direction of rotation, this being the same hardware required for the extended CORDIC vectoring, recently proposed by the authors [T. Lang and E. Antelo, IEEE Transactions on Computers, vol. 47, no. 7, 1998, pp. 736–749.]. Although these functions can be obtained as a special case of this extended vectoring, the specific algorithm we propose here presents two significant improvements: (1) it uses the same datapath width as the standard CORDIC, even when t has 2n bits (to achieve a granularity of 2−n for the whole range). In contrast, the extended vectoring unit requires about 2n bits. (2) no repetitions of iterations are needed (the extended vectoring needs some repetitions). The proposed algorithm is compatible with the extended vectoring and, in contrast with previous implementations, the number of iterations and the delay of each iteration are the same as for the conventional CORDIC algorithm.

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References

  1. C. Krieger and B.J. Hosticka, “Inverse Kinematics Computations with Modified CORDIC Iterations,” IEE Proc. Comput. Digit. Tech., vol. 143, no.1, 1996, pp. 87–92.

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  2. T. Lang and E. Antelo, “CORDICVectoring with Arbitrary Target Value,” IEEE Transactions on Computers, vol. 47, no.7, 1998, pp. 736–749.

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  3. C. Mazenc, X. Merrheim, and J.M. Muller, “Computing Functions cos-1 and sin-1 Using CORDIC,” IEEE Transactions on Computers, vol. 42, no.1, 1993, pp. 118–122.

    Article  Google Scholar 

  4. V. Baykov, “Problems of Elementary Functions Evaluation Based on Digit by Digit (CORDIC) Technique,” Ph.D. Thesis, Leningrad State University of Electrical Engineering, 1972 (a comment of the author about the approach used in his thesis to compute the ArcSin function is available in http://devil.ece.utexas.edu/tutorial/double.html).

  5. Y.H. Hu, “The Quantization Effects of the CORDIC Algorithm,” IEEE Transactions on Signal Processing, April 1992, pp. 834–844.

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Lang, T., Antelo, E. CORDIC-Based Computation of ArcCos. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 25, 19–38 (2000). https://doi.org/10.1023/A:1008121502359

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  • DOI: https://doi.org/10.1023/A:1008121502359

Keywords

  • Truncation Error
  • Previous Implementation
  • Ideal Algorithm
  • CORDIC Algorithm
  • Extended Vector