Multi-input Addition Research Articles

Improved Synthesis of Compressor Trees in High-Level Synthesis for Modern FPGAs

In this paper, an approach to synthesize compressor trees in high-level synthesis is proposed. We target the modern field-programmable gate arrays, which integrate carry chains and support fast ternary adders. Two main improvements are achieved in our approach: 1) based on the proposed modified bitmask analysis, we perform bit-level numerical optimizations to shrink the scale of generated compressor trees and achieve a better area-delay performance; 2) by estimating the arrival time of each multi-input addition operand, we combine the use of generalized parallel counters and ternary adders in compressor trees to further reduce the area while maintaining a similar delay performance. A series of experiments shows that our approach reduces the area significantly while maintaining similar delay performance, as compared to the existing approaches.

Improving FPGA Performance for Carry-Save Arithmetic

The selective use of carry-save arithmetic, where appropriate, can accelerate a variety of arithmetic-dominated circuits. Carry-save arithmetic occurs naturally in a variety of DSP applications, and further opportunities to exploit it can be exposed through systematic data flow transformations that can be applied by a hardware compiler. Field-programmable gate arrays (FPGAs), however, are not particularly well suited to carry-save arithmetic. To address this concern, we introduce the ?field programmable counter array? (FPCA), an accelerator for carry-save arithmetic intended for integration into an FPGA as an alternative to DSP blocks. In addition to multiplication and multiply accumulation, the FPCA can accelerate more general carry-save operations, such as multi-input addition (e.g., add k > 2 integers) and multipliers that have been fused with other adders. Our experiments show that the FPCA accelerates a wider variety of applications than DSP blocks and improves performance, area utilization, and energy consumption compared with soft FPGA logic.

An FPGA Logic Cell and Carry Chain Configurable as a 6:2 or 7:2 Compressor

To improve FPGA performance for arithmetic circuits that are dominated by multi-input addition operations, an FPGA logic block is proposed that can be configured as a 6:2 or 7:2 compressor. Compressors have been used successfully in the past to realize parallel multipliers in VLSI technology; however, the peculiar structure of FPGA logic blocks, coupled with the high cost of the routing network relative to ASIC technology, renders compressors ineffective when mapped onto the general logic of an FPGA. On the other hand, current FPGA logic cells have already been enhanced with carry chains to improve arithmetic functionality, for example, to realize fast ternary carry-propagate addition. The contribution of this article is a new FPGA logic cell that is specialized to help realize efficient compressor trees on FPGAs. The new FPGA logic cell has two variants that can respectively be configured as a 6:2 or a 7:2 compressor using additional carry chains that, coupled with lookup tables, provide the necessary functionality. Experiments show that the use of these modified logic cells significantly reduces the delay of compressor trees synthesized on FPGAs compared to state-of-the-art synthesis techniques, with a moderate increase in area and power consumption.

Field Programmable Compressor Trees

Multi-input addition occurs in a variety of arithmetically intensive signal processing applications. The DSP blocks embedded in high-performance FPGAs perform fixed bitwidth parallel multiplication and Multiply-ACcumulate (MAC) operations. In theory, the compressor trees contained within the multipliers could implement multi-input addition; however, they are not exposed to the programmer. To improve FPGA performance for these applications, this article introduces the Field Programmable Compressor Tree (FPCT) as an alternative to the DSP blocks. By providing just a compressor tree, the FPCT can perform multi-input addition along with parallel multiplication and MAC in conjunction with a small amount of FPGA general logic. Furthermore, the user can configure the FPCT to precisely match the bitwidths of the operands being summed. Although an FPCT cannot beat the performance of a well-designed ASIC compressor tree of fixed bitwidth, for example, 9×9 and 18×18-bit multipliers/MACs in DSP blocks, its configurable bitwidth and ability to perform multi-input addition is ideal for reconfigurable devices that are used across a variety of applications.