Efficient floating-point logarithm unit for FPGAs

As FPGAs become larger, new fabrics, in particular DSPs, allow for a wider range of applications, specifically floating-point intensive codes, to be efficiently executed. The logarithm is a widely used function in many scientific applications. We present the design of an efficient and sufficiently accurate Logarithm Approximation Unit (LAU) that uses a Look-Up Table (LUT) based approximation, in reconfigurable logic. The LAU has been verified through post place and route simulations, tested on actual FPGA, and is freely available for download. An important property of the LAU architecture is, that it only requires 2% of overall hardware resources on a medium-size FPGA (Xilinx V5SX95T) and thereby allows for easy integration with more complex architectures. Under single precision (SP) the LAU is 11 and 1.6 times faster than the GNU and Intel Math Kernel Library (MKL) implementations and up to 1.44 times faster than the FloPoCo reconfigurable logarithm unit, while occupying slightly less resources. Under double precision (DP) the LAU is 18 and 2.5 times faster than the GNU and Intel MKL implementations and up to 1.66 times faster than the FloPoCo logarithm while occupying significantly less resources. The LUT-based approximation is sufficiently accurate for our target application and provides a flexible mechanism to adapt the LAU to specific accuracy requirements.