Measuring Improvement When Using HUB Formats to Implement Floating-Point Systems Under Round-to-Nearest

Abstract

Abstract-This paper analyzes the benefits of using HUB formats to implement floating-point arithmetic under round-tonearest mode from a quantitative point of view. Using HUB formats to represent numbers allows the removal of the rounding logic of arithmetic units, including sticky-bit computation. This is shown for floating-point adders, multipliers, and converters. Experimental analysis demonstrates that HUB formats and the corresponding arithmetic units maintain the same accuracy as conventional ones. On the other hand, the implementation of these units, based on basic architectures, shows that HUB formats simultaneously improve area, speed, and power consumption. Specifically, based on data obtained from the synthesis, a HUB single-precision adder is about 14% faster but consumes 38% less area and 26% less power than the conventional adder. Similarly, a HUB single-precision multiplier is 17% faster, uses 22% less area, and consumes slightly less power than conventional multiplier. At the same speed, the adder and multiplier achieve area and power reductions of up to 50% and 40%, respectively.

Floating Point Square Root under HUB Format

“…Thus, the unbiased rounding is achieved by truncation and forcing the LSB of the representative form to zero, that is the bit M ′ [m−2] = 0, as proved in [5]. Thus, this unbiased round to nearest is not so different from the IEEE 745 tie to even, since it is like a tie to even of the representative form.…”

“…In some applications, this causes annoying statistical anomalies. To avoid this problem in those applications, an unbiased round to nearest is achieved in [5] for HUB without carry propagation. The tie condition takes place when the bits beyond bit…”

“…The efficiency of using HUB for fixed-point representation has been showed in [3] and [4] and for floating-point in [5], [6] and [7] (HUB format is not valid for pure integer numbers). In [6] a half-precision floating-point HUB unit is used for high dynamic range image and video systems (based on additions and multiplications).…”

“…In [5] the authors carry out an analysis of using HUB format for floating point adders, multipliers and converters from a quantitative point of view. Experimental studies demonstrate that HUB format keeps the same accuracy as conventional format for the aforementioned units, simultaneously improving area, speed and power consumption (14% speed-up, 38% less area and 26% less power for single precision floating point adder, 17% speed-up, 22% less area and slightly less power for the floating point multiplier).…”

Unbiased Rounding for HUB Floating-Point Addition

“…In [11], the authors analyze the benefits of using HUB format for FP adders, multipliers, and converters. Experimental analysis demonstrate that HUB format maintains the same accuracy as the conventional format for the aforementioned units, simultaneously improving area, speed, and power consumption (14% speed-up, 38% less area and 26% less power for single precision FP adder, 17% speed-up, 22% less area and slightly less power for the FP multiplier).…”