Hardware Design of a Binary Integer Decimal-based IEEE P754 Rounding Unit

Abstract

Because of the growing importance of decimal floating-point (DFP) arithmetic, specifications for it were recently added to the draft revision of the IEEE 754 Standard (IEEE P754). In this paper, we present a hardware design for a rounding unit for 64-bit DFP numbers (decimal64) that use the IEEE P754 binary encoding of DFP numbers, which is widely known as the Binary Integer Decimal (BID) encoding. We summarize the technique used for rounding, present the theory and design of the BID rounding unit, and evaluate its critical path delay, latency, and area for combinational and pipelined designs. Over 86% of the rounding unit's area is due to a 55-bit by 54-bit binary multiplier, which can be shared with a double-precision binary floating-point multiplier. To our knowledge, this is the first hardware design for rounding IEEE P754 BID-encoded DFP numbers.

Hardware design of a Binary Integer Decimal-based floating-point adder

“…The same hardware used in Case 2 can also improve the latency of Case 1, when Z Ic < 10 16 and A exp ≠ B exp . Since rounding is not needed when Z Ic < 10 16 , the result may come directly from the Add/Subtract and Absolute Value Unit, bypassing the rounder.…”

“…We use a rounder that has been enhanced from the BID rounder design presented in [16]. The design presented in [16] only performs rounding up to 16 decimal digits and cannot be used to implement our algorithm. There are two major enhancements to this design.…”

“…Our BID adder differs from previous DFP adder designs, which operate on DPD-encoded numbers [14,15]. It uses a novel hardware component for decimal digit counting and leverages an enhanced version of a previously published BID rounding unit [16]. Furthermore, operations are performed with variable latency to optimize common cases.…”

Decimal Floating Point Number System

“…Rounding of BID encoded numbers poses a similar challenge [28,29]. DPD is easier to add and round but requires "decimal" not binary adders.…”