IEEE Transactions on Computers
Redundant Logarithmic Arithmetic
IEEE Transactions on Computers
Initializing RAM-based logarithmic processors
Journal of VLSI Signal Processing Systems - Special issue: 1990 Workshop on VLSI signal processing
Applying Aeatures of IEEE 754 to Sign/Logarithm Arithmetic
IEEE Transactions on Computers - Special issue on computer arithmetic
A 20 Bit Logarithmic Number System Processor
IEEE Transactions on Computers
Interleaved Memory Function Interpolators with Application to an Accurate LNS Arithmetic Unit
IEEE Transactions on Computers
Semi-Logarithmic Number Systems
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Arithmetic on the European Logarithmic Microprocessor
IEEE Transactions on Computers - Special issue on computer arithmetic
Fast Fourier Transforms Using the Complex Logarithmic Number System
Journal of VLSI Signal Processing Systems
A Tool for Unbiased Comparison between Logarithmic and Floating-point Arithmetic
Journal of VLSI Signal Processing Systems
A Novel Cotransformation for LNS Subtraction
Journal of Signal Processing Systems
Hi-index | 14.98 |
The real logarithmic number system, which represents a value with a sign bit and a quantized logarithm, can be generalized to create the complex logarithmic number system, which replaces the sign bit with a quantized angle in a log/polar coordinate system. Although multiplication and related operations are easy in both real and complex systems, addition and subtraction are hard, especially when interpolation is used to implement the system. Both real and complex logarithmic arithmetic benefit from the use of co-transformation, which converts an addition or subtraction from a region where interpolation is expensive to a region where it is easier. Two co-transformations that accomplish this goal are introduced. The first is an approximation based on real analysis of the subtraction logarithm. The second is based on simple algebra that applies for both real and complex values and that works for both addition and subtraction.