Journal of the ACM (JACM)
FOCUS microcomputer number system
Communications of the ACM
A 20 Bit Logarithmic Number System Processor
IEEE Transactions on Computers
Probabilistic error analysis of floating point and crd arithmetics
Probabilistic error analysis of floating point and crd arithmetics
Applying Aeatures of IEEE 754 to Sign/Logarithm Arithmetic
IEEE Transactions on Computers - Special issue on computer arithmetic
IEEE Transactions on Computers - Special issue on computer arithmetic
Interleaved Memory Function Interpolators with Application to an Accurate LNS Arithmetic Unit
IEEE Transactions on Computers
Arithmetic Co-Transformations in the Real and Complex Logarithmic Number Systems
IEEE Transactions on Computers
ARVLSI '99 Proceedings of the 20th Anniversary Conference on Advanced Research in VLSI
Design of a versatile and cost-effective hybrid floating-point/LNS arithmetic processor
Proceedings of the 17th ACM Great Lakes symposium on VLSI
EURASIP Journal on Applied Signal Processing
Improving 2D-log-number-system representations by use of an optimal base
EURASIP Journal on Advances in Signal Processing
| Hi-index | 14.99 |
A number system that offers advantages in some situations over conventional floating point and sign/logarithmic number systems is described. Redundant logarithmic arithmetic, like conventional logarithmic arithmetic, relies on table lookups to make the arithmetic unit simpler than an equivalent floating point unit. The cost of 32 bit subtraction in a redundant logarithmic number system is lower than previously published logarithmic subtraction methods. The total memory requirement for a 29-bit redundant logarithmic unit is 16 K words compared to 22 K words by the best previously published conventional sign logarithm unit, assuming similar addition techniques are employed. A redundant logarithmic number system can be implemented with online arithmetic, which would be impractical for a conventional sign logarithm number system. The disadvantages of redundant arithmetic are typical of redundant number systems. First, the redundancy doubles the storage requirements for data values. Second, the representation can become ill-conditioned, especially as a result of iterated multiplications. Third, division and square root operations are more difficult to implement in redundant logarithmic arithmetic.