The logarithmic number system has been proposed as an alternative to floating-point arithmetic. Multiplication, division and square-root operations are accomplished with inexpensive fixed-point methods, but addition and subtraction are considerably more challenging. Recent work has demonstrated that these operations too can be done with similar speed and accuracy to their FP equivalents, but the necessary circuitry is complex. In particular, it is dominated by the need for large ROM tables for the storage and interpolation of non-linear functions. We describe a new co-transformation procedure that eliminates much of the ROM space and allows the easy synthesis of the remainder in logic, and we then evaluate several interpolation methods that might benefit from it. Synthesised 32-bit implementations are compared with floating-point units, and show substantial reductions in delay, with equivalent accuracy and area.

The logarithmic number system has been proposed as an alternative to floating-point arithmetic. Multiplication, division and square-root operations are accomplished with fixed-point methods, but addition and subtraction are considerably more challenging. Recent work has demonstrated that these operations too can be done with similar speed and accuracy to their FP equivalents, but the necessary circuitry is complex. In particular, it is dominated by the need for large ROM tables for the storage of non-linear functions. This paper describes two algorithms, a new co-transformation procedure and an improvement to an existing interpolation method, that reduce these tables to an extent that allows their easy synthesis in logic. An implementation shows substantial reductions in area and delay from the previous best 32-bit realisation, with equivalent accuracy.