A hybrid number system processor with geometric and complex arithmetic capabilities

Lai, Feipei; Wu, Cheng-Shing

doi:10.1109/12.83639

Cited by 31 publications

(14 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By using the analysis method in [8], we can derive that the maximum value of the error ε 2 is |ε 2 | max = 2…”

Section: Error Analysis Of the Base-e Exponential Algorithmmentioning

confidence: 99%

“…In [8], in order to enhance the precision in computing the Ψ 2 function, an algorithm for detecting the number l 1 of the leading-one bits in 2 −v F was devised. This detection can be used to predict the number of the leading-zero bits in (1 − 2 log (1 2 2 ) log (2 (1 2 2 )) ,…”

Section: Design Of the Basic Lns Addition/subtraction Unitmentioning

confidence: 99%

“…By using our hardware-reduced LNS approach, a 64-bit LNS unit can be designed to have a circuit area equal to 6.89 times the circuit area of a comparable 64-bit FLP unit with addition, subtraction, multiplication, and division operations. The pipelined computational approach proposed in [8] is the first one that tackled on the design of 64-bit LNS addition/subtraction unit and has made a theoretical advancement in the development of very large word-length LNS arithmetic. On the other hand, the approaches proposed in this paper have made a significant progress on the practical implementation of very large word-length LNS arithmetic.…”

mentioning

confidence: 99%

“…With this approach, the size of the lookup tables is only a third-order polynomial function of the word length of the LNS operands and the cost of the other circuits is only proportional to the square of the word length. For convenience, the LNS unit designed in [8] is referred to as the basic LNS unit hereafter. Although the size of the lookup tables used in the basic LNS unit is very small, the cost of the other circuits remains large.…”

mentioning

confidence: 99%

“…However, we can expect that the size of the coefficient tables used in these computational methods will increase exponentially. In [8], the values of the Φ r 0 and Ψ r 0 functions are computed by three overlapped pipelined algorithms: exponential, discretization, and digit on-line logarithmic algorithms. With this approach, the size of the lookup tables is only a third-order polynomial function of the word length of the LNS operands and the cost of the other circuits is only proportional to the square of the word length.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Performance-improved computation of very large word-length LNS addition/subtraction using signed-digit arithmetic

Chen

Proceedings IEEE International Conference on Application-Specific Systems, Architectures, and Processors. ASAP 2003

View full text Add to dashboard Cite

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.

show abstract

“…By using the analysis method in [8], we can derive that the maximum value of the error ε 2 is |ε 2 | max = 2…”

Section: Error Analysis Of the Base-e Exponential Algorithmmentioning

confidence: 99%

Section: Design Of the Basic Lns Addition/subtraction Unitmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%