Pipelined Range Reduction Based Truncated Multiplier

ZHU Baozhou; LEI Yuanwu; PENG Yuanxi

doi:10.1049/cje.2019.07.003

Volume 28 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Electronics > 2019 > 28(6): 1158-1164

ZHU Baozhou, LEI Yuanwu, PENG Yuanxi, “Pipelined Range Reduction Based Truncated Multiplier,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1158-1164, 2019, doi: 10.1049/cje.2019.07.003

Citation:

ZHU Baozhou, LEI Yuanwu, PENG Yuanxi, “Pipelined Range Reduction Based Truncated Multiplier,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1158-1164, 2019, doi: 10.1049/cje.2019.07.003

ZHU Baozhou, LEI Yuanwu, PENG Yuanxi, “Pipelined Range Reduction Based Truncated Multiplier,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1158-1164, 2019, doi: 10.1049/cje.2019.07.003

Citation:

ZHU Baozhou, LEI Yuanwu, PENG Yuanxi, “Pipelined Range Reduction Based Truncated Multiplier,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1158-1164, 2019, doi: 10.1049/cje.2019.07.003

PDF( 1412 KB)

Pipelined Range Reduction Based Truncated Multiplier

doi: 10.1049/cje.2019.07.003

College of Computer, National University of Defense and Technology, Changsha 410073, China

Funds: This work is supported by the National Natural Science Foundations of China (No.61402499, No.61672526).

More Information

Corresponding author: PENG Yuanxi (corresponding author) was born in 1966.He received the B.S.degree in computer science in 1988 from Sichuan University in China and the M.S.and Ph.D.degrees in computer science from NUDT in China in 1998 and 2001,respectively.He was a visiting professor in Department of Electronic and Computer Engineering,University of Toronto,Canada during 2010-2011.He has been a professor of Computer School in NUDT since 2011.His research interests are in the areas of high performance computing,multi-and manycore architectures,on-chip networks,cache coherence protocols and architectural support for parallel programming.(Email:pyx@nudt.edu.cn)
Received Date: 2017-03-23
Rev Recd Date: 2018-05-31
Publish Date: 2019-11-10

Abstract

Abstract

Range reduction is the initial and essential stage of function computation, but its pipelined implementation has the drawbacks of large cost and terrible accuracy. We proposed low cost and accurate pipelined range reduction, which adopts truncated multiplier with optimized bit-width to reduce the cost of pipelined implementation and achieve the accuracy within 1 unit in the last place (ulp). TCORDIC algorithm is a widely used algorithm to compute floating-point sine/cosine function, and we implemented the combination of TCORDIC and our range reduction algorithms, verifying the goal of accuracy within 1 ulp.
- Pipelined range reduction,
- Truncated multiplier,
- Low cost,
- Floating-point

FullText(HTML)

References(19)

References

M. Dukhan and R. Vuduc, "Methods for high-throughput computation of elementary functions", International Conference on Parallel Processing and Applied Mathematics, pp.86-95, 2013.

J. M. Muller, "Elementary functions:Algorithms and implementation", Numerical Algorithms, Vol.16, No.3-4, pp.381-382, 1982.

P. Kulaga, P. Sapiecha and K. Sxp, "Approximation algorithm for the argument reduction problem", in Computer Recognition Systems, Springer, Berlin, Heidelberg, pp.243-248.2005.

C. Kormanyos, "Algorithm 910:A portable c++multiple precision system for special-function calculations", ACM Transactions on Mathematical Software, Vol.37, No.4, pp.1-27, 2011.

H. D. L. Saintgenies, D. Defour and G. Revy, "Range reduction based on pythagorean triples for trigonometric function evaluation", in 2015 IEEE 26th International Conference on Application-specific Systems, Architectures and Processors (ASAP), IEEE, pp.74-81.2015.

F. J. Jaime, J. Villalba, J. Hormigo, et al., "Pipelined range reduction for floating point numbers", in IEEE International Conference on Application-specific Systems, Architecture and Processors, pp.145-152, 2006.

X. Qian, H. Zhang, J. Yang, et al., "Circuit implementation of floating point range reduction for trigonometric functions", International Symposium on Circuits and Systems, pp.3010-3013, 2007.

C. L. Spencer, Y. X. Zou and B. L. Sumner, "Method and apparatus for additive range reduction", Patent, 9563402, U.S., 2017-02-07.

W. J. Cody and W. M. Waite, "Software manual for the elementary functions", SIAM Review, Vol.24, No.1, pp.91-93, 1982.

R. C. Li, S. Boldo and M. Daumas, "Theorems on efficient argument reductions", Proceedings of 2003 IEEE Symposium on Computer Arithmetic, pp.129-136, 2003.

S. Boldo, M. Daumas and R. C. Li, "Formally verified argument reduction with a fused multiply-add", IEEE Transactions on Computers, Vol.58, No.8, pp.1139-1145, 2008.

K. C. Ng, "Argument reduction for huge arguments:Good to the last bit", Technical Report, USA, 1992.

B. Cui, W. Zheng and S. Feng, "New range reduction algorithm using 64-bit integer computation", IEEE International Conference on Computer Science and Information Technology, pp.595-599, 2010.

N. Brisebarre, D. Defour, P. Kornerup, et al., "A new rangereduction algorithm", IEEE Transactions on Computers, Vol.54, No.3, pp.331-339, 2005.

J. Villalba, T. Lang and M. A. Gonzalez, "Doubleresidue modular range reduction for floating-point hard-ware implementations", IEEE Transactions on Computers, Vol.55, No.3, pp.254-267, 2006.

F. J. Jaime, J. Villalba, J. Hormigo, et al., "Pipelined architecture for additive range reduction", Journal of Signal Processing Systems, Vol.53, No.1, pp.103-112, 2008.

F. J. Jaime, J. Hormigo, J. Villalba, et al., "Pipelined architecture for accurate floating point range reduction", Proc. 7th Conf. Real Numbers Comput., pp.59-68, 2006.

F. J. Jaime, M. A. Nchez, J. Hormigo, et al., "Highspeed algorithms and architectures for range reduction computation", IEEE Transactions on Very Large Scale Integration Systems, Vol.19, No.3, pp.512-516, 2011.

Zhu. Baozhou, Lei. Yuanwu, Peng. Yuanxi, et al., "Low latency and low error floating-point sine/cosine function based TCORDIC algorithm", IEEE Transactions on Circuits and Systems I:Regular Papers, Vol.64, No.4, pp.1-14, 2016.

Relative Articles

Supplements(0)

Cited By

Proportional views