On Approximate 8-bit Floating-Point Operations Using Integer Operations

TL;DR

This paper explores efficient approximate 8-bit floating-point operations implemented with integer arithmetic, demonstrating faithful and correct rounding methods, and showcasing hardware benefits especially on FPGA platforms.

Contribution

It introduces methods for faithful and correct rounding of 8-bit floating-point operations using integer operations, with hardware implementation insights.

Findings

Faithful rounding achievable for two-bit mantissa formats.

Correct rounding results obtained with simple integer-based methods.

Significant resource savings on FPGA implementations.

Abstract

In this work, approximate eight-bit floating-point operations performed using simple integer operations is discussed. For two-bit mantissa formats, faithful rounding can always be obtained for the considered operations. For all operations, correctly rounded results can be obtained for different rounding modes, either directly or by adding a conditional carry in. For three-bit mantissa formats, faithful rounding can be sometimes be obtained directly, while for other operations a conditional carry in must be added. Correctly rounded results can be obtained for most operations and rounding modes using slightly more complicated expressions for the carry in. Hardware implementation results for multiplication using both standard cell and FPGA technology are presented illustrating the potential benefit of integer computation. Especially for FPGA, significant resource savings are obtained.