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Efficient Numerical Function Generators Using LUT Cascades for High-Speed Computation

This paper presents an innovative architecture and synthesis method for high-speed computation of fixed-point numerical functions, utilizing lookup table (LUT) cascades. It addresses the performance bottleneck in compute-bound applications by employing piecewise linear approximation based on non-uniform segmentation. The study outlines various architectures for numerical function generators (NFGs), provides design examples, and evaluates performance across different configurations. The proposed method ensures fast generation of NFGs with high precision, proving valuable for a wide range of computing applications.

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Efficient Numerical Function Generators Using LUT Cascades for High-Speed Computation

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  1. Numerical Function GeneratorsUsing LUT Cascades Presenter：Pin-Chong Chen Advisor ： Tsung-Chu Huang 2010/05/31

  2. References • Sasao, T.; Nagayama, S.; Butler, J.T.;” Numerical Function Generators Using LUT Cascades” Computers, IEEE Transactions on Volume: 56 , Issue: 6 Digital Object Identifier: 10.1109/TC.2007.1033 Publication Year: 2007

  3. Outline • Introduction • Piecewise linear approximation based on non-uniform segmentation • Architecture for NFGS • Example design • Evaluation and Results • Conclusions

  4. Introduction • The evaluation of functions is often the performance bottleneck of many compute-bound applications. • This paper proposes an architecture and a synthesis method for high-speed computation of fixed-point numerical functions. • This architecture is based on the lookup table (LUT) cascade.

  5. Synthesis system

  6. Uniform and non-uniform segmentations

  7. Nonuniform segmentation algorithm

  8. Example 1

  9. Architectures

  10. Example Design

  11. Evaluation(1)

  12. Evaluation(2)

  13. Evaluation(3)

  14. Conclusions • This paper proposed an architecture and a synthesis method for programmable NFGs for various distribution. • This method is useful to generate fast NFGs for a wide range of functions in up to 24-bit precision.

  15. Thanks for your attention.

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