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Journal of Information Science and Engineering, Vol. 23 No. 5, pp. 1579-1596 (September 2007)

Performance-Improved Computation of Very Large Word-Length LNS Addition/Subtraction Using Signed-Digit Arithmetic*

Chichyang Chen and Rui-Lin Chen
Department of Information Engineering and Computer Science
Feng Chia University
Taichung, 407 Taiwan

Pipelined computation of very large word-length logarithmic number system (LNS) addition/subtraction requires a lot of hardware and long pipeline latency. This paper proposes a base-e exponential algorithm to simplify the exponential computation and to replace half of the pipeline stages by multiplication-and-accumulate operations. By using this approach, the circuit area and the pipeline latency of the previously proposed 64-bit basic LNS addition/subtraction unit can be reduced by 42.4% and 39.22%, respectively. Based on the base-e exponential algorithm approach, we also develop signed- digit (SD) exponential, SD discretization, and SD on-line logarithmic algorithms to further increase the throughput and to reduce the pipeline latency of the LNS computation. From our synthesis results, the throughput of the 64-bit LNS unit can be increased by 61.9% and the pipeline latency can be reduced by 55.0%, without increasing the hardware cost of the basic LNS unit. The circuit area of the 64-bit hardware-reduced LNS unit is estimated to be only 6.89 times the circuit area of a comparable 64-bit floating-point unit. We conclude that the proposed approaches have significantly improved the performance of the previously proposed LNS unit and have made a significant progress towards the implementation of very large word-length LNS arithmetic.

Keywords: logarithmic number system, base-e exponential algorithm, on-line logarithmic algorithm, signed-digit arithmetic, pipeline architecture

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Received June 17, 2005; revised September 16 & October 18, 2005 & March 3, 2006; accepted April 25, 2006.
Communicated by Liang-Gee Chen.
*This work was supported by the National Science Council of Taiwan, R.O.C. under contract No. NSC 91- 2213-E-035-017.