Area efficient floating-point adder and multiplier with IEEE-754 compatible semantics

In this paper we describe an open source floating-point adder and multiplier implemented using a 36-bit custom number format based on radix-16 and optimized for the 7-series FPGAs from Xilinx. Although this number format is not identical to the single-precision IEEE-754 format, the floatingpoint operators are designed in such a way that the numerical results for a given operation will be identical to the result from an IEEE-754 compliant operator with support for round-to-nearest even, NaNs and Infs, and subnormal numbers. The drawback of this number format is that the rounding step is more involved than in a regular, radix-2 based operator. On the other hand, the use of a high radix means that the area cost associated with normalization and denormalization can be reduced, leading to a net area advantage for the custom number format, under the assumption that support for subnormal numbers is required. The area of the floating-point adder in a Kintex-7 FPGA is 261 slice LUTs and the area of the floating-point multiplier is 235 slice LUTs and 2 DSP48E blocks. The adder can operate at 319 MHz and the multiplier can operate at a frequency of 305 MHz.