Compressor Tree Synthesis Research Articles

Area Optimized Synthesis of Compressor Trees on Xilinx FPGAs Using Generalized Parallel Counters

Early compressor trees based on carry-save adders and single-column parallel counters show good performance in ASIC design, but do not adapt well to modern field-programmable gate arrays (FPGAs). Recently, compressor trees built from generalized parallel counters (GPCs) were synthesized on FPGAs to address this issue. Despite the improved timing performance of GPC-based compressor trees, area reduction is not as significant as delay, and can be further optimized. In this paper, we propose improved GPC mappings as well as new approaches for GPC cascading and binding for Xilinx FPGAs. With these improvements, we develop an integer linear programming (ILP) method for FPGA synthesis of GPC-based compressor trees that supports cascading and binding between GPCs. Experimental results show that the single-cycle compressor trees produced by the proposed ILP can reduce the average area by 42.40% compared with those generated by existing heuristic method, but are 13.16% slower; the pipelined compressor trees produced by the proposed ILP can reduce the average area by 33.43% at the cost of an average 14.35% decrease in maximum clock frequency compared with those obtained by existing heuristic method.

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.

Advanced Compressor Tree Synthesis for FPGAs

This work presents novel methods for the optimization of compressor trees for FPGAs as required in many arithmetic computations. As demonstrated in recent work, important key elements for the design of efficient but fast compressor trees are target-optimized 4:2 compressors as well as generalized parallel counters (GPCs). However, the optimization of a compressor tree for minimal resources using both compressors and GPCs has not been addressed so far. As this combined optimization is a non-trivial task, three methods are proposed to find best solutions for a given problem size: 1) a heuristic that obtains compressor trees with typically less resources and fewer stages than state-of-the-art heuristics, 2) an integer linear programming (ILP)-based methodology that finds optimal compressor trees using the fewest stages possible, 3) a combined approach that partially solves the problem heuristically to reduce the search space for the ILP-based method. In all methods, the cost for pipeline registers can be included. Synthesis experiments show that the proposed methods provide pipelined compressor trees with about 40 percent less LUTs compared to trees of 2-input adders at the cost of being about 12 ...20 percent slower.

An Exact Approach for GPC-Based Compressor Tree Synthesis

An Exact Approach for GPC-Based Compressor Tree Synthesis

Compressor tree synthesis on commercial high-performance FPGAs

Compressor trees are a class of circuits that generalizes multioperand addition and the partial product reduction trees of parallel multipliers using carry-save arithmetic. Compressor trees naturally occur in many DSP applications, such as FIR filters, and, in the more general case, their use can be maximized through the application of high-level transformations to arithmetically intensive data flow graphs. Due to the presence of carry-chains, it has long been thought that trees of 2- or 3-input carry-propagate adders are more efficient than compressor trees for FPGA synthesis; however, this is not the case. This article presents a heuristic for FPGA synthesis of compressor trees that outperforms adder trees and exploits carry-chains when possible. The experimental results show that, on average, the use of compressor trees can reduce critical path delay by 33% and 45% respectively, compared to adder trees synthesized on the Xilinx Virtex-5 and Altera Stratix III FPGAs.