This paper presents a fast and scalable algorithm for buffer and splitter insertion in AQFP circuits. The method maps each wire to a homeomorphic graph, constructs an additional-delay-free multi-ary forest, and merges it into an optimal tree under delay and fanout constraints. The formulation guarantees per-wire optimality in terms of maximum additional delay, total additional delay, and internal node count. A circuit-level refinement further reduces redundant insertion by identifying and adjusting critical wires. On standard AQFP benchmarks, the proposed approach achieves 2.72×, 525.70×, and 1.33× speedups over [1], [2], and [3], respectively, while maintaining comparable insertion counts and logic depths.

Sparse linear solvers play a crucial role in transistor-level circuit simulation, especially for large-scale post-layout circuit simulation when considering complex parasitic effects. As semiconductor technology advances rapidly, the increasing sizes of circuits result in sparse linear solvers that require extended execution times and additional memory resources. Consequently, high-performance sparse linear solvers emerge as pivotal tools to facilitate rapid circuit simulation and verification. However, circuit matrices frequently exhibit high sparsity and non-uniform distributions of nonzero elements, compounding the challenge of achieving efficient acceleration. Recently, the flourishing developments in machine learning technology and the continuous enhancement of hardware capabilities have presented new opportunities for accelerating sparse linear solvers. This paper provides a perspective review of these technological advancements, while also highlighting the challenges and future opportunities in this evolving landscape.

Adiabatic quantum-flux-parametron (AQFP) logic, known for its energy efficiency, has emerged as a prominent superconductor-based logic family, surpassing traditional rapid single flux quantum (RSFQ) logic. In AQFP circuits, each cell operates on AC power, serving as both a power supply and clock signal to drive data flow across clock phases. However, signal attenuation with increasing wirelength may result in more potential data errors. To address this, rows of buffers are inserted as repeaters to ensure data synchronization and avoid wirelength violations. However, these inserted buffer rows in the AQFP placement significantly amplifies power consumption and circuit delay. To address these challenges, in this paper, we propose an innovative and analytical method for the placement of AQFP. The proposed method aims at minimizing the need for additional buffers. The framework incorporates two key features: (1) entanglement entropy for topology initialization and (2) projection for placement and buffering. These features offer advantages such as avoiding intensive computations, including fix-order Lagrangian optimization in large-scale scenarios, while significantly reducing the required number of buffer rows. The experimental results validate the efficiency of the proposed framework, demonstrating an average reduction of 81% in the required number of buffers and acceleration of 1.88x in the processing time compared with the state-of-the-art method.

The relentless pursuit of energy-efficient electronic devices necessitates advanced methodologies for low-power design verification, with a particular focus on mitigating power supply noise. The challenges posed by shrinking voltage margins in low-power designs lead to a significant demand for rapid and accurate power supply noise simulation and verification techniques. Too large supply noise inevitably results in the raise of supply level, thereby hurting the lower power design target. Spectral methods have demonstrated as a great alternative to produce a sparse sub-matrix with spectral-similarity property as the preconditioner to efficiently reduce the iteration number and solve the linear system for supply noise verification. However, existing methods either suffer from high computational complexity or rely on approximations to reduce computational time. Therefore, a novel approach is needed to efficiently generate high-quality preconditioners. In this paper, we propose a two-stage spectral-aware algorithm to address these challenges. Our approach has three main highlights. Firstly, by introducing spectral-aware weights, we can better assess the priority of edges and construct high-quality spanning trees with the minimum relative condition number. Secondly, by leveraging eigenvalue transformation strategies, we can quickly and accurately recover off-tree edges that are spectrally critical, avoiding time-consuming iterative computations. Thirdly, we proposed a fast computation method to further decrease the computational complexity of the effective resistance. Compared with two SOTA methods, GRASS and feGRASS, our approach demonstrates higher accuracy and efficiency in preconditioner generation (37.3x and 2.13x speedup, respectively) as well as significant improvements in accelerating the linear solver for power supply noise analysis in power grid simulation and other Laplacian graphs (5.16x and 1.70x speedup, respectively).

Sparse matrix-vector multiplication ($S$pMV) is pivotal in many scientific computing and engineering applications. Considering the memory-intensive nature and irregular data access patterns inherent in SpMV, its acceleration is typically bounded by the limited bandwidth. Multiple memory channels of the emerging high bandwidth memory (HBM) provide exceptional bandwidth, offering a great opportunity to boost the performance of SpMV. However, ensuring high bandwidth utilization with low memory access conflicts is still non-trivial. In this paper, we present Cuper, a high-performance SpMV accelerator on HBM-equipped FPGAs. Through customizing the dataflow to be HBM-compatible with the proposed sparse storage format, the bandwidth utilization can be sufficiently enhanced. Furthermore, a two-step reordering algorithm and perceptual decoder-centric hardware architecture are designed to greatly mitigate read-after-write (RAW) conflicts, enhance the vector reusability and on-chip memory utilization. The evaluation of 12 large matrices shows that Cuper's geomean throughput outperforms the four latest SpMV accelerators HiSparse, GraphLily, Sextans, and Serpens, by 3.28×, 1.99×, 1.75×, and 1.44×, respectively. Furthermore, the geomean bandwidth efficiency shows 3.28×, 2.20×, 2.82×, and 1.31x improvements, while the geomean energy efficiency has 3.59×, 2.08×, 2.21×, and 1.44× optimizations, respectively. Cuper also demonstrates 2.51× throughput and 7.97× energy efficiency of improvement over the K80 GPU on 2,757 SuiteSparse matrices.

Solving sparse linear systems dominates the simulation time for nonlinear integrated circuits. Developing an effective preconditioner is crucial for accelerating the iterative solver when dealing with large-scale circuit matrices, yet this remains a challenging task. In this paper, we introduce an efficient sparsification-based preconditioner method that significantly reduces the number of iterations needed in iterative solvers. Our method transforms nonlinear components into symmetric Laplacian matrices, enabling the inclusion of both nonlinear and linear elements in the sparsification process. We then intersect the generated sparsifier with the original Modified Nodal Analysis (MNA) matrix to further reduce the sparsity, thereby decreasing preconditioner factorization time. Furthermore, we enhance the parallelization of the spectral sparsification strategy by integrating block RMQ and point exclusivity algorithms, which substantially speeds up preprocessing. Experiment results demonstrate acceleration of 2.50x, 13.46x, 2.18x on average in serial, 3.72x, 24.23x, 3.86x on average in parallel, and memory reduction of 21.3%, 21.7%, 88.0% on average when solving nonlinear circuit matrices compared to the state-of-the-art solver GPSCP, feGRASS, and direct solver KLU, respectively.