A novel pipelined method is proposed to compute the addition/subtraction in very large word-length logarithmic number system (LNS) arithmetic. Digit-parallel additive-normalization and digit on-line multiplicative-normalization methods are adopted to compute the exponential and logarithmic functions, respectively, in LNS addition/subtraction. These two methods can both be implemented in a pipelined and regular architecture. The size of the required lookup tables is now proportional to a third-order polynomial function, instead of an exponential function, of the word length. The total size of the tables in a 32-bit LNS unit is estimated to be less than 53.5 kbits and the total size of the table's in a 64-bit LNS unit will be less than 471 kbits. Furthermore, the hardware cost of the other circuits in the proposed LNS unit is only proportional to the square of the word length. This study also develops a simple leading-zero-bits prediction technique that can significantly enhance the precision in LNS addition/subtraction computation. When compared to floating-point arithmetic design, our approach still suffers from large hardware cost and pipeline latency. However, the proposed approach has provided a theoretical advancement in the development of very large word-length LNS arithmetic.

Logarithmic number system (LNS) has the advantages of regular data flow high speed, and high precision. However, the development of LNS arithmetic is hindered by the large size of the lookup tables used in LNS addition/subtraction, since the size is exponentially proportional to the word length of the operands. To overcome this large-table problem, LNS addition/subtraction is proposed to be computed in a pipelined manner. The computation includes an exponential stage and a logarithmic stage. The exponential stage is implemented by using digit-parallel additive normalization and the logarithmic stage is implemented by using digit on-line multiplicative normalization. It has been computed that the size of the lookup tables used in a 33-bit LNS unit is about 0.543 Mbits, which is very small. The hardware cost of the other circuits in this LNS unit is only linearly proportional to the word length of the operands. We conclude that the proposed method makes large word-length LNS arithmetic possible.