Section: New Results

Application-specific number systems

Participant : Sylvain Collange.

This research is done in collaboration with Mark G. Arnold, XLNS Research, USA.

Reconfigurable FPGA platforms let designers build efficient application-specific circuits, when the performance or energy efficiency of general-purpose CPUs is insufficient, and the production volume is not enough to offset the very high cost of building a dedicated integrated circuit (ASIC). One way to take advantage of the flexibility offered by FPGAs is to tailor arithmetic operators for the application. In particular, the Logarithmic Number System (LNS) is suitable for embedded applications dealing with low-precision, high-dynamic range numbers.

Like floating-point, LNS can represent numbers from a wide dynamic range with constant relative accuracy. However, while standard floating-point offer so-called subnormal numbers to represent numbers close to zero with constant absolute accuracy, LNS numbers abruptly overflow to zero, resulting in a gap in representable numbers close to zero that can impact the accuracy of numerical algorithms.

We proposed a generalization of LNS that incorporate features analogous to subnormal floating-point [18] , [28] . The Denormal LNS (DLNS) system we introduce defines a class of hybrid number systems that offer quasi-constant absolute accuracy close to zero and quasi-constant relative accuracy on larger numbers. These systems can be configured to range from pure LNS (constant relative accuracy) to fixed-point (constant absolute accuracy across the whole range).